Finite Group Databasebeta

← C2×#21437882 #29497154

Subgroups — C2×#21437882 #29497154

Order 15104.

11534 conjugacy classes of subgroups.

The subgroup lattice has 1528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273774C211yesmaximal, characteristic, complemented
2C22×#14273772C211yesmaximal, characteristic, complemented
3#21437882C2132yesmaximal, direct product factor
4C2×#16838062C211yesmaximal, characteristic, complemented
5C2×#16838061C211yesmaximal, characteristic, complemented
6C2×#16838060C211yesmaximal, characteristic, complemented
7C2×#16838058C211yesmaximal, characteristic, complemented
8C2×#16838047C211yesmaximal, characteristic, complemented
9C2×#16838046C211yesmaximal, characteristic, complemented
10C2×#16838044C212yesmaximal, complemented
11C2×#16838042C212yesmaximal, complemented
12C2×#16838041C212yesmaximal, complemented
13C2×#16838040C211yesmaximal, characteristic, complemented
14C2×#16838039C212yesmaximal, complemented
15C2×#16837975C211yesmaximal, characteristic, complemented
16C2×#16837974C212yesmaximal, complemented
17C2×#16837968C211yesmaximal, characteristic, complemented
18C2×#16837967C212yesmaximal, complemented
19C2×#16837949C211yesmaximal, characteristic, complemented
20C2×#16837947C212yesmaximal, complemented
21C22×#14273713C212yesmaximal, complemented
22C2×#124×D59C211yesmaximal, characteristic, complemented
23C2×C4×#11745687C211yesmaximal, characteristic, complemented
24C2×C59×#546C211yesmaximal, characteristic, complemented
25C2×#14273774—216no—
26C2×#14273774C22116yescomplemented
27C2×#14273772—216no—
28C2×#14273772C22116yescomplemented
29C22×#11745685C2211yescharacteristic
30C22×#11745685C2211yescharacteristic
31C22×#11745685C2212yescomplemented
32C22×#11745685C2211yescharacteristic, complemented
33C22×#11745687C2211yescharacteristic
34C22×#11745687C2212yes—
35C22×#11745687C2211yescharacteristic
36C22×#11745687C2212yescomplemented
37C22×#11745687C2211yescharacteristic, complemented
38C22×#11745687C2212yescomplemented
39C23×Dic118C2211yescharacteristic, complemented
40C23×Dic118C2212yescomplemented
41C22×Q8×D59C2211yescharacteristic, complemented
42C22×Q8×D59C2211yescharacteristic, complemented
43C23×C22⋊D59C2212yes—
44C23×C22⋊D59C2212yes—
45C22×D4×D59C2211yescharacteristic
46C22×D4×D59C2212yes—
47C22×D4×D59C2211yescharacteristic
48#16838062C22116yescomplemented
49#16838061C22116yescomplemented
50#16838060C22116yescomplemented
51#16838058C22116yescomplemented
52#16838047C22116yescomplemented
53#16838046C22116yescomplemented
54#16838044C22132yescomplemented
55#16838042C22132yescomplemented
56#16838041C22132yescomplemented
57#16838040C22116yescomplemented
58#16838039C22132yescomplemented
59#16837975C22116yescomplemented
60#16837974C22132yescomplemented
61#16837968C22116yescomplemented
62#16837967C22132yescomplemented
63#16837949C22116yescomplemented
64#16837947C22132yescomplemented
65C2×#14273726C2212yescomplemented
66C2×#14273726C2211yescharacteristic, complemented
67C2×#14273723C2212yescomplemented
68C2×#14273723C2211yescharacteristic, complemented
69C2×#14273716C2211yescharacteristic, complemented
70C2×#14273715C2211yescharacteristic, complemented
71C2×#14273714C2211yescharacteristic, complemented
72C2×#14273713C2212yescomplemented
73C2×#14273713C2212yescomplemented
74C2×#14273713C2212yescomplemented
75C2×#14273713C2212yescomplemented
76C2×#14273713C2212yescomplemented
77C2×#14273713C2212yescomplemented
78C2×#14273713C2211yescharacteristic, complemented
79C2×#14273713C2212yescomplemented
80C2×#14273713C2212yescomplemented
81C2×#14273713C2211yescharacteristic, complemented
82C2×#14273713C22132yescomplemented
83#124×D59C22116yescomplemented
84C2×#14273712C2212yescomplemented
85C2×#14273711C2212yescomplemented
86C2×#14273710C2212yescomplemented
87C2×#14273709C2212yescomplemented
88C2×#14273708C2212yescomplemented
89C2×#14273707C2211yescharacteristic, complemented
90C2×#14273706C2211yescharacteristic, complemented
91C2×#14273705C2212yescomplemented
92C2×#14273705C2212yescomplemented
93C2×#14273704C2212yescomplemented
94C2×#14273704C2212yescomplemented
95C2×#14273703C2211yescharacteristic, complemented
96C2×#14273702C2211yescharacteristic, complemented
97C2×#14273702C2211yescharacteristic, complemented
98C2×#14273701C2211yescharacteristic, complemented
99C2×#14273701C2212yescomplemented
100C2×#14273700C2211yescharacteristic, complemented
101C2×#14273700C2211yescharacteristic, complemented
102C2×#14273700C2212yescomplemented
103C2×#14273700C2212yescomplemented
104C2×#14273699C2212yescomplemented
105C2×#14273699C2212yescomplemented
106C2×#14273699C2212yescomplemented
107C2×#14273699C2212yescomplemented
108C2×#14273698C2211yescharacteristic, complemented
109C2×#14273698C2211yescharacteristic, complemented
110C2×#14273697C2212yescomplemented
111C2×#14273697C2212yescomplemented
112C2×#14273696C2212yescomplemented
113C2×#14273695C2212yescomplemented
114C2×#14273695C2212yescomplemented
115C4×#11745687C22116yescomplemented
116C2×C4×Dic118C2211yescharacteristic, complemented
117C2×#14273692C2211yescharacteristic, complemented
118C2×C4×D236C2211yescharacteristic, complemented
119C2×D4×Dic59C2211yescharacteristic, complemented
120C2×D4×Dic59C2212yescomplemented
121C2×#14273689C2212yescomplemented
122C2×C4×C22⋊D59C2212yescomplemented
123C2×C4×C22⋊D59C2211yescharacteristic, complemented
124C2×C4×C22⋊D59C2211yescharacteristic, complemented
125C2×(C22⋊D59)⋊C4C2212yescomplemented
126C2×(C22⋊D59)⋊C4C2212yescomplemented
127C2×(C22⋊D59)⋊C4C2212yescomplemented
128C2×#14273685C2211yescharacteristic, complemented
129C2×#14273683C2212yescomplemented
130C22×C22⋊Dic59C2212yescomplemented
131C22×(C2×D59)⋊C4C2212yescomplemented
132C22×(C2×D59)⋊C4C2212yescomplemented
133C2×C22⋊C4×D59C2212yescomplemented
134C2×C22⋊C4×D59C2212yescomplemented
135C22×C4×Dic59C2212yescomplemented
136C2×C42×D59C2211yescharacteristic, complemented
137C22×#41×C59C2211yescharacteristic, complemented
138C23×D4×C59C2211yescharacteristic
139C59×#546C22116yescomplemented
140C2×#124×C59C2211yescharacteristic, complemented
141C2×#123×C59C2212yescomplemented
142C2×C22⋊Q8×C59C2211yescharacteristic, complemented
143C2×#121×C59C2212yescomplemented
144C2×#121×C59C2211yescharacteristic, complemented
145C2×#120×C59C2212yescomplemented
146C2×C4×D4×C59C2211yescharacteristic, complemented
147C2×C4×D4×C59C2211yescharacteristic, complemented
148C22×C22⋊C4×C59C2212yescomplemented
149C24×D59C2312yes—
150C24×D59C2312yes—
151#14273774—2128no—
152#14273772—2128no—
153C2×#11745685—216no—
154C2×#11745685—28no—
155C2×#11745685—28no—
156C2×#11745685—28no—
157C2×#11745685C2318yes—
158C2×#11745685C2318yes—
159C2×#11745685C2318yescomplemented
160C2×#11745685C23116yescomplemented
161C2×#11745687—28no—
162C2×#11745687—216no—
163C2×#11745687—216no—
164C2×#11745687—216no—
165C2×#11745687—28no—
166C2×#11745687D4116yescomplemented
167C2×#11745687C23116yes—
168C2×#11745687C2318yes—
169C2×#11745687C2318yes—
170C2×#11745687C23116yescomplemented
171C2×#11745687C23116yescomplemented
172C2×#11745687C2318yescomplemented
173C22×Dic118—216no—
174C22×Dic118—28no—
175C22×Dic118C2312yes—
176C22×Dic118C2312yes—
177C22×Dic118C2311yescharacteristic
178C22×Dic118C2312yes—
179C22×Dic118C2311yescharacteristic
180C22×Dic118C2311yescharacteristic
181C22×Dic118C2311yescharacteristic
182C22×Dic118C23116yescomplemented
183C22×Dic118C2318yescomplemented
184C2×Q8×D59—28no—
185C2×Q8×D59—28no—
186C2×Q8×D59C2318yescomplemented
187C2×Q8×D59C2318yescomplemented
188C22×D236C2311yescharacteristic
189C22×D236C2311yescharacteristic
190C22×D236C2311yescharacteristic
191C22×D236C2311yescharacteristic
192C22×D236C2312yes—
193C22×C22⋊D59—216no—
194C22×C22⋊D59—216no—
195C22×C22⋊D59C2312yes—
196C22×C22⋊D59C2311yescharacteristic
197C22×C22⋊D59C2311yescharacteristic
198C22×C22⋊D59C2312yes—
199C22×C22⋊D59C2312yes—
200C22×C22⋊D59C2312yes—
201C22×C22⋊D59C2312yes—
202C22×C22⋊D59C2311yescharacteristic
203C22×C22⋊D59C23116yes—
204C22×C22⋊D59C2311yescharacteristic
205C22×C22⋊D59C23116yes—
206C22×C22⋊D59C2311yescharacteristic
207C22×C22⋊D59C2312yes—
208C22×C22⋊D59C2311yescharacteristic
209C22×C22⋊D59C2312yes—
210C22×C22⋊D59C2312yes—
211C2×D4×D59—28no—
212C2×D4×D59—216no—
213C2×D4×D59—28no—
214C2×D4×D59C2318yes—
215C2×D4×D59C2318yes—
216C2×D4×D59C23116yes—
217C23×Dic59C2312yes—
218C23×Dic59C2312yes—
219C23×Dic59C2312yes—
220C23×Dic59C2312yes—
221C23×Dic59C2312yes—
222C22×C4×D59C2311yescharacteristic
223C22×C4×D59C2312yes—
224C22×C4×D59C2311yescharacteristic
225C22×C4×D59C2312yes—
226C22×C4×D59C2312yes—
227C22×C4×D59C2311yescharacteristic
228C22×C4×D59C2311yescharacteristic
229C22×C4×D59C2311yescharacteristic
230#14273726C23116yescomplemented
231#14273726C2318yescomplemented
232#14273723C23116yescomplemented
233#14273723C2318yescomplemented
234#14273716C2318yescomplemented
235#14273715C2318yescomplemented
236#14273714C2318yescomplemented
237#14273713C23116yescomplemented
238#14273713C23116yescomplemented
239#14273713C2318yescomplemented
240#14273713C23116yescomplemented
241#14273713C23116yescomplemented
242#14273713C23116yescomplemented
243#14273713C23116yescomplemented
244#14273713C23116yescomplemented
245#14273713C23116yescomplemented
246#14273713C2318yescomplemented
247#14273712C23116yescomplemented
248#14273711C23116yescomplemented
249#14273710C23116yescomplemented
250#14273709C23116yescomplemented
251#14273708C23116yescomplemented
252#14273707C2318yescomplemented
253#14273706C2318yescomplemented
254#14273705C23116yescomplemented
255#14273705C23116yescomplemented
256#14273704C23116yescomplemented
257#14273704C23116yescomplemented
258#14273703C2318yescomplemented
259#14273702C2318yescomplemented
260#14273702C2318yescomplemented
261#14273701C23116yescomplemented
262#14273701C2318yescomplemented
263#14273700C2318yescomplemented
264#14273700C2318yescomplemented
265#14273700C23116yescomplemented
266#14273700C23116yescomplemented
267#14273699C23116yescomplemented
268#14273699C23116yescomplemented
269#14273699C23116yescomplemented
270#14273699C23116yescomplemented
271#14273698C2318yescomplemented
272#14273698C2318yescomplemented
273#14273697C23116yescomplemented
274#14273697C23116yescomplemented
275#14273696C23116yescomplemented
276#14273695C23116yescomplemented
277#14273695C23116yescomplemented
278C4×Dic118C2318yescomplemented
279#14273692C2318yescomplemented
280C4×D236C2318yescomplemented
281D4×Dic59C23116yescomplemented
282D4×Dic59C2318yescomplemented
283#14273689C23116yescomplemented
284C4×C22⋊D59C2318yescomplemented
285C4×C22⋊D59C2318yescomplemented
286C4×C22⋊D59C23116yescomplemented
287(C22⋊D59)⋊C4C23116yescomplemented
288(C22⋊D59)⋊C4C23116yescomplemented
289(C22⋊D59)⋊C4C23116yescomplemented
290#14273685C2318yescomplemented
291#14273683C23116yescomplemented
292C2×C4⋊Dic59C2311yescharacteristic
293C2×C4⋊Dic59C2311yescharacteristic
294C2×C4⋊Dic59C2312yes—
295C2×Dic59⋊C4C2312yes—
296C2×Dic59⋊C4C2312yes—
297C2×Dic59⋊C4C2312yes—
298C2×Dic59⋊C4C2312yes—
299C2×Dic59⋊C4C2311yescharacteristic
300C2×Dic59⋊C4C2311yescharacteristic
301C2×C22⋊Dic59C2312yes—
302C2×C22⋊Dic59C2312yes—
303C2×C22⋊Dic59C2312yes—
304C2×C22⋊Dic59C2311yescharacteristic
305C2×C22⋊Dic59C2312yes—
306C2×C22⋊Dic59C2311yescharacteristic
307C2×C22⋊Dic59C2312yes—
308C2×C22⋊Dic59C23116yescomplemented
309C2×(C2×D59)⋊C4C2312yes—
310C2×(C2×D59)⋊C4C2312yes—
311C2×(C2×D59)⋊C4C2312yes—
312C2×(C2×D59)⋊C4C2312yes—
313C2×(C2×D59)⋊C4C2311yescharacteristic
314C2×(C2×D59)⋊C4C2312yes—
315C2×(C2×D59)⋊C4C2311yescharacteristic
316C2×(C2×D59)⋊C4C2312yes—
317C2×(C2×D59)⋊C4C2312yes—
318C2×(C2×D59)⋊C4C2311yescharacteristic
319C2×(C2×D59)⋊C4C2312yes—
320C2×(C2×D59)⋊C4C2312yes—
321C2×(C2×D59)⋊C4C2311yescharacteristic
322C2×(C2×D59)⋊C4C23116yescomplemented
323C2×(C2×D59)⋊C4C23116yescomplemented
324C22⋊C4×D59C23116yescomplemented
325C22⋊C4×D59C23116yescomplemented
326C2×C4×Dic59C2311yescharacteristic
327C2×C4×Dic59C2311yescharacteristic
328C2×C4×Dic59C2312yes—
329C2×C4×Dic59C2312yes—
330C2×C4×Dic59C2312yes—
331C2×C4×Dic59C2311yescharacteristic
332C2×C4×Dic59C23116yescomplemented
333C42×D59C2318yescomplemented
334C25×C59C2312yes—
335C2×#41×C59—28no—
336C2×#41×C59C2318yescomplemented
337C22×Q8×C59C2311yescharacteristic
338C22×D4×C59—28no—
339C22×D4×C59C2311yescharacteristic
340C22×D4×C59C2312yes—
341C22×D4×C59C2312yes—
342C22×D4×C59C2318yes—
343C22×D4×C59C2311yescharacteristic
344C22×D4×C59C2312yes—
345C22×D4×C59C2311yescharacteristic
346C23×C4×C59C2311yescharacteristic
347C23×C4×C59C2311yescharacteristic
348C23×C4×C59C2312yes—
349C23×C4×C59C2312yes—
350#124×C59C2318yescomplemented
351#123×C59C23116yescomplemented
352C22⋊Q8×C59C2318yescomplemented
353#121×C59C23116yescomplemented
354#121×C59C2318yescomplemented
355#120×C59C23116yescomplemented
356C4×D4×C59C2318yescomplemented
357C4×D4×C59C2318yescomplemented
358C2×C4⋊C4×C59C2311yescharacteristic
359C2×C4⋊C4×C59C2311yescharacteristic
360C2×C4⋊C4×C59C2312yes—
361C2×C22⋊C4×C59C2312yes—
362C2×C22⋊C4×C59C2312yes—
363C2×C22⋊C4×C59C2312yes—
364C2×C22⋊C4×C59C2312yes—
365C2×C22⋊C4×C59C2311yescharacteristic
366C2×C22⋊C4×C59C2311yescharacteristic
367C2×C22⋊C4×C59C2312yes—
368C2×C22⋊C4×C59C23116yescomplemented
369C2×C42×C59C2311yescharacteristic
370C24×C59—28no—
371C24×C59—44no—
372C24×C59—44no—
373C24×C59C2411yescharacteristic
374C24×C59C2412yes—
375C24×C59C2411yescharacteristic
376C24×C59C2412yes—
377C24×C59C2418yes—
378C23×D59—28no—
379C23×D59—28no—
380C23×D59—44no—
381C23×D59—44no—
382C23×D59—44no—
383C23×D59—44no—
384C23×D59C2412yes—
385C23×D59C2411yescharacteristic
386C23×D59C2411yescharacteristic
387C23×D59C2411yescharacteristic
388C23×D59C2418yes—
389C23×D59C2418yes—
390#41×C59—232no—
391C2×Q8×C59—24no—
392C2×Q8×C59C2414yes—
393C2×D4×C59—28no—
394C2×D4×C59—28no—
395C2×D4×C59—232no—
396C2×D4×C59—24no—
397C2×D4×C59—42no—
398C2×D4×C59—44no—
399C2×D4×C59C2×D418yes—
400C2×D4×C59C2418yes—
401C2×D4×C59C2418yes—
402C2×D4×C59C2414yes—
403C2×D4×C59C2414yes—
404C2×D4×C59C2418yes—
405C2×D4×C59C2414yes—
406C22×C4×C59—28no—
407C22×C4×C59—24no—
408C22×C4×C59—24no—
409C22×C4×C59—44no—
410C22×C4×C59C2411yescharacteristic
411C22×C4×C59C2411yescharacteristic
412C22×C4×C59C2412yes—
413C22×C4×C59C2411yescharacteristic
414C22×C4×C59C2412yes—
415C22×C4×C59C2411yescharacteristic
416C22×C4×C59C2418yes—
417C22×C4×C59C2414yes—
418C22×C4×C59C2414yes—
419C22×C4×C59C2418yes—
420C22×C4×C59C2411yescharacteristic
421C2×C22⋊D59—28no—
422C2×C22⋊D59—28no—
423C2×C22⋊D59—24no—
424C2×C22⋊D59—24no—
425C2×C22⋊D59—264no—
426C2×C22⋊D59—28no—
427C2×C22⋊D59—28no—
428C2×C22⋊D59—24no—
429C2×C22⋊D59—28no—
430C2×C22⋊D59—264no—
431C2×C22⋊D59—24no—
432C2×C22⋊D59—42no—
433C2×C22⋊D59—42no—
434C2×C22⋊D59—44no—
435C2×C22⋊D59—44no—
436C2×C22⋊D59C2×D4116yes—
437C2×C22⋊D59C2414yes—
438C2×C22⋊D59C2418yes—
439C2×C22⋊D59C2414yes—
440C2×C22⋊D59C2418yes—
441C2×C22⋊D59C2418yes—
442C2×C22⋊D59C2418yes—
443C2×C22⋊D59C2418yes—
444C2×C22⋊D59C2414yes—
445C2×C22⋊D59C2414yes—
446C2×C22⋊D59C2418yes—
447C2×C22⋊D59C2418yes—
448C2×C22⋊D59C2414yes—
449C2×C22⋊D59C2414yes—
450C2×C22⋊D59C2418yes—
451C22×Dic59—28no—
452C22×Dic59—28no—
453C22×Dic59—28no—
454C22×Dic59—44no—
455C22×Dic59C2×D4116yes—
456C22×Dic59C2411yescharacteristic
457C22×Dic59C2412yes—
458C22×Dic59C2411yescharacteristic
459C22×Dic59C2412yes—
460C22×Dic59C2411yescharacteristic
461C22×Dic59C2411yescharacteristic
462C22×Dic59C2418yes—
463C22×Dic59C2418yes—
464C22×Dic59C2418yes—
465C22×Dic59C2418yes—
466C22×Dic59C2411yescharacteristic
467C22×Dic59C2412yes—
468C22×Dic59C2418yes—
469Q8×D59—232no—
470Q8×D59—232no—
471#11745687—232no—
472#11745687—264no—
473#11745687—264no—
474#11745687—264no—
475#11745687—232no—
476#11745687C2×D4164yescomplemented
477D4×D59—232no—
478D4×D59—264no—
479D4×D59—232no—
480#11745685—264no—
481#11745685—232no—
482#11745685—232no—
483#11745685—232no—
484C2×D236—24no—
485C2×D236—24no—
486C2×D236—24no—
487C2×D236—42no—
488C2×D236—44no—
489C2×D236C2414yes—
490C2×D236C2414yes—
491C2×D236C2414yes—
492C2×D236C2418yes—
493C2×D236C2414yes—
494C2×C4×D59—28no—
495C2×C4×D59—24no—
496C2×C4×D59—24no—
497C2×C4×D59—28no—
498C2×C4×D59—28no—
499C2×C4×D59—42no—
500C2×C4×D59—42no—
501C2×C4×D59C2×D418yes—
502C2×C4×D59C2418yes—
503C2×C4×D59C2418yes—
504C2×C4×D59C2418yes—
505C2×C4×D59C2414yes—
506C2×C4×D59C2414yes—
507C2×C4×D59C2414yes—
508C2×C4×D59C2414yes—
509C2×C4×D59C2414yes—
510C2×Dic118—24no—
511C2×Dic118—28no—
512C2×Dic118—28no—
513C2×Dic118—24no—
514C2×Dic118—28no—
515C2×Dic118—264no—
516C2×Dic118—24no—
517C2×Dic118—232no—
518C2×Dic118C2×D418yes—
519C2×Dic118C2418yes—
520C2×Dic118C2418yes—
521C2×Dic118C2414yes—
522C2×Dic118C2418yes—
523C2×Dic118C2414yes—
524C2×Dic118C2414yes—
525C2×Dic118C2414yes—
526C4⋊C4×C59C2414yes—
527C4⋊C4×C59C2414yes—
528C4⋊C4×C59C2418yes—
529C22⋊C4×C59C2414yes—
530C22⋊C4×C59C2418yes—
531C22⋊C4×C59C2418yes—
532C22⋊C4×C59C2418yes—
533C22⋊C4×C59C2418yes—
534C22⋊C4×C59C2414yes—
535C22⋊C4×C59C2418yes—
536C42×C59C2414yes—
537C22⋊Dic59C2418yes—
538C22⋊Dic59C2418yes—
539C22⋊Dic59C2414yes—
540C22⋊Dic59C2418yes—
541C22⋊Dic59C2418yes—
542C22⋊Dic59C2418yes—
543C22⋊Dic59C2414yes—
544(C2×D59)⋊C4C2418yes—
545(C2×D59)⋊C4C2418yes—
546(C2×D59)⋊C4C2418yes—
547(C2×D59)⋊C4C2418yes—
548(C2×D59)⋊C4C2414yes—
549(C2×D59)⋊C4C2414yes—
550(C2×D59)⋊C4C2418yes—
551(C2×D59)⋊C4C2418yes—
552(C2×D59)⋊C4C2418yes—
553(C2×D59)⋊C4C2418yes—
554(C2×D59)⋊C4C2418yes—
555(C2×D59)⋊C4C2414yes—
556(C2×D59)⋊C4C2414yes—
557C4⋊Dic59C2414yes—
558C4⋊Dic59C2418yes—
559C4⋊Dic59C2414yes—
560Dic59⋊C4C2418yes—
561Dic59⋊C4C2418yes—
562Dic59⋊C4C2418yes—
563Dic59⋊C4C2418yes—
564Dic59⋊C4C2414yes—
565Dic59⋊C4C2414yes—
566C4×Dic59C2414yes—
567C4×Dic59C2414yes—
568C4×Dic59C2414yes—
569C4×Dic59C2418yes—
570C4×Dic59C2418yes—
571C4×Dic59C2418yes—
572C23×C59—24no—
573C23×C59—24no—
574C23×C59—22no—
575C23×C59—24no—
576C23×C59—22no—
577C23×C59—22no—
578C23×C59—22no—
579C23×C59—24no—
580C23×C59—22no—
581C23×C59—24no—
582C23×C59—22no—
583C23×C59—216no—
584C23×C59—48no—
585C23×C59—48no—
586C23×C59—816no—
587C23×C59C22×D418yes—
588C23×C59C2514yes—
589C23×C59C2512yes—
590C23×C59C2512yes—
591C23×C59C2514yes—
592C23×C59C2511yescharacteristic
593C22×D59—22no—
594C22×D59—22no—
595C22×D59—22no—
596C22×D59—22no—
597C22×D59—24no—
598C22×D59—22no—
599C22×D59—22no—
600C22×D59—24no—
601C22×D59—22no—
602C22×D59—22no—
603C22×D59—24no—
604C22×D59—216no—
605C22×D59—216no—
606C22×D59—48no—
607C22×D59—48no—
608C22×D59—48no—
609C22×D59—48no—
610C22×D59—816no—
611C22×D59—816no—
612C22×D59C22×D414yes—
613C22×D59C2514yes—
614C22×D59C2512yes—
615C22×D59C2512yes—
616C22×D59C2512yes—
617Q8×C59—28no—
618D4×C59—216no—
619D4×C59—216no—
620D4×C59—28no—
621D4×C59—44no—
622D4×C59—48no—
623D4×C59C22×D4116yes—
624C2×C4×C59—22no—
625C2×C4×C59—24no—
626C2×C4×C59—216no—
627C2×C4×C59—22no—
628C2×C4×C59—22no—
629C2×C4×C59—22no—
630C2×C4×C59—24no—
631C2×C4×C59—28no—
632C2×C4×C59—28no—
633C2×C4×C59—48no—
634C2×C4×C59C22×D414yes—
635C2×C4×C59C2512yes—
636C2×C4×C59C2514yes—
637C2×C4×C59C2512yes—
638C2×C4×C59C2512yes—
639C2×C4×C59C2512yes—
640C2×C4×C59C2514yes—
641C2×C4×C59C2512yes—
642C22⋊D59—216no—
643C22⋊D59—216no—
644C22⋊D59—28no—
645C22⋊D59—28no—
646C22⋊D59—28no—
647C22⋊D59—28no—
648C22⋊D59—216no—
649C22⋊D59—216no—
650C22⋊D59—216no—
651C22⋊D59—44no—
652C22⋊D59—44no—
653C22⋊D59—48no—
654C22⋊D59—48no—
655C22⋊D59C22×D4132yes—
656C2×Dic59—24no—
657C2×Dic59—22no—
658C2×Dic59—216no—
659C2×Dic59—22no—
660C2×Dic59—22no—
661C2×Dic59—22no—
662C2×Dic59—24no—
663C2×Dic59—216no—
664C2×Dic59—216no—
665C2×Dic59—48no—
666C2×Dic59C22×D414yes—
667C2×Dic59C22×D418yes—
668C2×Dic59C22×D4132yes—
669C2×Dic59C2512yes—
670C2×Dic59C2512yes—
671C2×Dic59C2514yes—
672C2×Dic59C2512yes—
673C2×Dic59C2514yes—
674C2×Dic59C2512yes—
675C2×Dic59C2512yes—
676C2×Dic59C2514yes—
677D236—28no—
678D236—28no—
679D236—28no—
680D236—44no—
681D236—48no—
682C4×D59—216no—
683C4×D59—28no—
684C4×D59—28no—
685C4×D59—216no—
686C4×D59—216no—
687C4×D59—44no—
688C4×D59—44no—
689C4×D59C22×D4116yes—
690Dic118—28no—
691Dic118—28no—
692Dic118—216no—
693Dic118—216no—
694Dic118—216no—
695Dic118—28no—
696Dic118C22×D4116yes—
697C2×#3500—591nomaximal, Sylow
698C22×C59—24no—
699C22×C59—24no—
700C22×C59—216no—
701C22×C59—22no—
702C22×C59—24no—
703C22×C59—22no—
704C22×C59—22no—
705C22×C59—22no—
706C22×C59—24no—
707C22×C59—22no—
708C22×C59—24no—
709C22×C59—22no—
710C22×C59—48no—
711C22×C59—44no—
712C22×C59—44no—
713C22×C59—816no—
714C22×C59C23×D418yes—
715C22×C59C23×D412yes—
716C22×C59#58512yes—
717C22×C59#58512yes—
718C22×C59C2611yescharacteristic
719C2×D59—22no—
720C2×D59—22no—
721C2×D59—28no—
722C2×D59—22no—
723C2×D59—22no—
724C2×D59—24no—
725C2×D59—22no—
726C2×D59—22no—
727C2×D59—24no—
728C2×D59—22no—
729C2×D59—22no—
730C2×D59—24no—
731C2×D59—44no—
732C2×D59—48no—
733C2×D59—44no—
734C2×D59—816no—
735C2×D59—816no—
736C2×D59C23×D414yes—
737C4×C59—22no—
738C4×C59—24no—
739C4×C59—22no—
740C4×C59—22no—
741C4×C59—22no—
742C4×C59—24no—
743C4×C59C23×D414yes—
744Dic59—24no—
745Dic59—22no—
746Dic59—22no—
747Dic59—22no—
748Dic59—22no—
749Dic59—24no—
750Dic59C23×D414yes—
751Dic59C23×D418yes—
752C22×2−1+4—591no—
753C22×H(5,𝔽2)—591no—
754#3500—5932no—
755C2×#548—591no—
756C2×#548—591no—
757C2×#548—591no—
758C2×#548—591no—
759C2×#546—591no—
760C2×#546—591no—
761C2×#546—592no—
762C2×#546—592no—
763C2×#546—592no—
764C2×#546—591no—
765C2×#546—592no—
766C2×#546D5911yescharacteristic, complemented
767C2×#536—592no—
768C2×#536—591no—
769C2×#535—591no—
770C2×#535—592no—
771C2×#532—592no—
772C2×#532—591no—
773C22×#124—591no—
774C22×#124—592no—
775C2×C4×#41—591no—
776C2×C59—28no—
777C2×C59—44no—
778C2×C59—42no—
779C2×C59—42no—
780C2×C59#350014yescomplemented
781C2×C59C24×D411yescharacteristic
782C2×C59C2×#58511yescharacteristic
783C2×C59C2×#58511yescharacteristic
784D59—24no—
785D59—42no—
786D59—44no—
787D59—42no—
788C2×2−1+4—5916no—
789C2×2−1+4—11816no—
790C2×H(5,𝔽2)—5916no—
791C2×H(5,𝔽2)—11816no—
792C22×#41—591no—
793C22×#41—592no—
794C22×#41—591no—
795C22×#41—592no—
796C22×#41—591no—
797C22×#41—592no—
798C22×#41—591no—
799C22×#41—591no—
800C22×#41—591no—
801C22×#41—592no—
802C22×#41C2×D5911yescharacteristic, complemented
803C23×Q8—591no—
804C23×Q8—591no—
805C23×Q8—592no—
806C23×Q8—591no—
807C23×D4—592no—
808C23×D4—592no—
809C23×D4—591no—
810C23×D4—592no—
811C23×D4—591no—
812C23×D4C2×D5911yescharacteristic
813#548—5916no—
814#548—5916no—
815#548—5916no—
816#548—5916no—
817#546—5916no—
818#546—5916no—
819#546—5932no—
820#546—5932no—
821#546—5932no—
822#546—5916no—
823#546—5932no—
824#546C2×D59116yescomplemented
825#536—5932no—
826#536—5916no—
827#535—5916no—
828#535—5932no—
829#532—5932no—
830#532—5916no—
831C2×C4⋊Q8—592no—
832C2×C4⋊Q8—591no—
833C2×#127—592no—
834C2×#127—591no—
835C2×#124—591no—
836C2×#124—591no—
837C2×#124—5916no—
838C2×#124—592no—
839C2×#124—591no—
840C2×#124—592no—
841C2×#124—592no—
842C2×#124—592no—
843C2×#124—592no—
844C2×#124—592no—
845C2×#124—592no—
846C2×#124—592no—
847C2×#124—591no—
848C2×#124—5932no—
849C2×#124—591no—
850C2×#124C2×D5911yescharacteristic, complemented
851C2×#123—592no—
852C2×#123—592no—
853C2×#123—592no—
854C2×#123—592no—
855C2×#123—592no—
856C2×#123C2×D5912yescomplemented
857C2×C22⋊Q8—591no—
858C2×C22⋊Q8—591no—
859C2×C22⋊Q8—592no—
860C2×C22⋊Q8—592no—
861C2×C22⋊Q8—591no—
862C2×C22⋊Q8—592no—
863C2×C22⋊Q8—592no—
864C2×C22⋊Q8C2×D5911yescharacteristic, complemented
865C2×#121—591no—
866C2×#121—591no—
867C2×#121—592no—
868C2×#121—592no—
869C2×#121—592no—
870C2×#121—592no—
871C2×#121—592no—
872C2×#121—591no—
873C2×#121—591no—
874C2×#121—591no—
875C2×#121—591no—
876C2×#121—591no—
877C2×#121—592no—
878C2×#121—592no—
879C2×#121C2×D5912yescomplemented
880C2×#121C2×D5911yescharacteristic, complemented
881C2×#120—592no—
882C2×#120—592no—
883C2×#120—592no—
884C2×#120—592no—
885C2×#120—592no—
886C2×#120C2×D5912yescomplemented
887C4×#41—5916no—
888C2×C4×Q8—591no—
889C2×C4×Q8—591no—
890C2×C4×D4—591no—
891C2×C4×D4—592no—
892C2×C4×D4—592no—
893C2×C4×D4—591no—
894C2×C4×D4—591no—
895C2×C4×D4—592no—
896C2×C4×D4—592no—
897C2×C4×D4—592no—
898C2×C4×D4—592no—
899C2×C4×D4—591no—
900C2×C4×D4C2×D5911yescharacteristic, complemented
901C2×C4×D4C2×D5911yescharacteristic, complemented
902C2×#117—591no—
903C2×#117—592no—
904C22×C22⋊C4—592no—
905C22×C22⋊C4—592no—
906C22×C22⋊C4—592no—
907C22×C22⋊C4—592no—
908C22×C22⋊C4—592no—
909C22×C22⋊C4C2×D5912yescomplemented
910C22×C42—592no—
911C22×C42—591no—
912C59C2×#350011yescharacteristic, complemented, Sylow
913C25—592no—
914C25—592no—
915C25C22×D5912yes—
9162−1+4—118128no—
917H(5,𝔽2)—118128no—
918C2×#41—28no—
919C2×#41—5916no—
920C2×#41—598no—
921C2×#41—5916no—
922C2×#41—5916no—
923C2×#41—598no—
924C2×#41—5916no—
925C2×#41—598no—
926C2×#41—598no—
927C2×#41—598no—
928C2×#41—5916no—
929C2×#41—598no—
930C2×#41—1188no—
931C2×#41—1188no—
932C2×#41—11816no—
933C2×#41—1188no—
934C2×#41—11816no—
935C2×#41—11816no—
936C2×#41—11816no—
937C2×#41—1188no—
938C2×#41—1188no—
939C2×#41C22×D5918yescomplemented
940C22×Q8—598no—
941C22×Q8—598no—
942C22×Q8—591no—
943C22×Q8—592no—
944C22×Q8—592no—
945C22×Q8—591no—
946C22×Q8—592no—
947C22×Q8—591no—
948C22×Q8—5916no—
949C22×Q8—591no—
950C22×Q8—598no—
951C22×Q8—11816no—
952C22×Q8—1188no—
953C22×Q8—1188no—
954C22×Q8—1188no—
955C22×Q8C22×D5911yescharacteristic
956C22×D4—28no—
957C22×D4—592no—
958C22×D4—591no—
959C22×D4—592no—
960C22×D4—591no—
961C22×D4—592no—
962C22×D4—592no—
963C22×D4—592no—
964C22×D4—592no—
965C22×D4—591no—
966C22×D4—5916no—
967C22×D4—591no—
968C22×D4—5916no—
969C22×D4—591no—
970C22×D4—592no—
971C22×D4—592no—
972C22×D4—591no—
973C22×D4—598no—
974C22×D4—5916no—
975C22×D4—598no—
976C22×D4—591no—
977C22×D4—591no—
978C22×D4—591no—
979C22×D4—592no—
980C22×D4—591no—
981C22×D4—1188no—
982C22×D4—11816no—
983C22×D4—11816no—
984C22×D4—11816no—
985C22×D4—1188no—
986C22×D4C22×D5912yes—
987C22×D4C22×D5912yes—
988C22×D4C22×D5911yescharacteristic
989C22×D4C22×D5918yes—
990C22×D4C22×D5912yes—
991C22×D4C22×D5911yescharacteristic
992C22×D4C22×D5911yescharacteristic
993C23×C4—592no—
994C23×C4—591no—
995C23×C4—592no—
996C23×C4—592no—
997C23×C4—592no—
998C23×C4—592no—
999C23×C4—592no—
1000C23×C4—592no—
1001C23×C4—591no—
1002C23×C4—592no—
1003C23×C4—591no—
1004C23×C4—591no—
1005C23×C4—591no—
1006C23×C4C22×D5912yes—
1007C23×C4C22×D5911yescharacteristic
1008C23×C4C22×D5911yescharacteristic
1009C23×C4C22×D5912yes—
1010C4⋊Q8—5916no—
1011C4⋊Q8—598no—
1012#127—5916no—
1013#127—598no—
1014#124—598no—
1015#124—598no—
1016#124—5916no—
1017#124—598no—
1018#124—5916no—
1019#124—5916no—
1020#124—5916no—
1021#124—5916no—
1022#124—5916no—
1023#124—5916no—
1024#124—5916no—
1025#124—598no—
1026#124—598no—
1027#124C22×D5918yescomplemented
1028#123—5916no—
1029#123—5916no—
1030#123—5916no—
1031#123—5916no—
1032#123—5916no—
1033#123C22×D59116yescomplemented
1034C22⋊Q8—598no—
1035C22⋊Q8—598no—
1036C22⋊Q8—5916no—
1037C22⋊Q8—5916no—
1038C22⋊Q8—598no—
1039C22⋊Q8—5916no—
1040C22⋊Q8—5916no—
1041C22⋊Q8C22×D5918yescomplemented
1042#121—598no—
1043#121—5916no—
1044#121—5916no—
1045#121—598no—
1046#121—5916no—
1047#121—5916no—
1048#121—5916no—
1049#121—598no—
1050#121—598no—
1051#121—598no—
1052#121—598no—
1053#121—598no—
1054#121—5916no—
1055#121—5916no—
1056#121C22×D59116yescomplemented
1057#121C22×D5918yescomplemented
1058#120—5916no—
1059#120—5916no—
1060#120—5916no—
1061#120—5916no—
1062#120—5916no—
1063#120C22×D59116yescomplemented
1064C4×Q8—598no—
1065C4×Q8—598no—
1066C4×D4—598no—
1067C4×D4—5916no—
1068C4×D4—5916no—
1069C4×D4—598no—
1070C4×D4—598no—
1071C4×D4—5916no—
1072C4×D4—5916no—
1073C4×D4—5916no—
1074C4×D4—5916no—
1075C4×D4—598no—
1076C4×D4C22×D5918yescomplemented
1077C4×D4C22×D5918yescomplemented
1078#117—598no—
1079#117—5916no—
1080C2×C4⋊C4—592no—
1081C2×C4⋊C4—592no—
1082C2×C4⋊C4—591no—
1083C2×C4⋊C4—591no—
1084C2×C4⋊C4—592no—
1085C2×C4⋊C4—592no—
1086C2×C4⋊C4—591no—
1087C2×C4⋊C4—592no—
1088C2×C4⋊C4—591no—
1089C2×C4⋊C4C22×D5911yescharacteristic
1090C2×C4⋊C4C22×D5912yes—
1091C2×C4⋊C4C22×D5911yescharacteristic
1092C2×C22⋊C4—592no—
1093C2×C22⋊C4—591no—
1094C2×C22⋊C4—592no—
1095C2×C22⋊C4—592no—
1096C2×C22⋊C4—592no—
1097C2×C22⋊C4—5916no—
1098C2×C22⋊C4—592no—
1099C2×C22⋊C4—591no—
1100C2×C22⋊C4—592no—
1101C2×C22⋊C4—591no—
1102C2×C22⋊C4—591no—
1103C2×C22⋊C4—592no—
1104C2×C22⋊C4—592no—
1105C2×C22⋊C4—592no—
1106C2×C22⋊C4—592no—
1107C2×C22⋊C4—592no—
1108C2×C22⋊C4—592no—
1109C2×C22⋊C4—592no—
1110C2×C22⋊C4—5916no—
1111C2×C22⋊C4—5916no—
1112C2×C22⋊C4—592no—
1113C2×C22⋊C4—591no—
1114C2×C22⋊C4—591no—
1115C2×C22⋊C4—5916no—
1116C2×C22⋊C4—5916no—
1117C2×C22⋊C4C22×D5912yes—
1118C2×C22⋊C4C22×D5912yes—
1119C2×C22⋊C4C22×D5911yescharacteristic
1120C2×C22⋊C4C22×D5912yes—
1121C2×C22⋊C4C22×D5912yes—
1122C2×C22⋊C4C22×D5912yes—
1123C2×C22⋊C4C22×D5911yescharacteristic
1124C2×C22⋊C4C22×D59116yescomplemented
1125C2×C42—592no—
1126C2×C42—591no—
1127C2×C42—592no—
1128C2×C42—592no—
1129C2×C42—591no—
1130C2×C42—5916no—
1131C2×C42—591no—
1132C2×C42—598no—
1133C2×C42C22×D5911yescharacteristic
1134C24—28no—
1135C24—44no—
1136C24—44no—
1137C24—591no—
1138C24—592no—
1139C24—591no—
1140C24—591no—
1141C24—598no—
1142C24—598no—
1143C24—1188no—
1144C24—1188no—
1145C24—2364no—
1146C24—2364no—
1147C24—2364no—
1148C24—2364no—
1149C24C23×D5912yes—
1150C24C23×D5911yescharacteristic
1151C24C23×D5911yescharacteristic
1152C24C23×D5912yes—
1153C24C23×D5918yes—
1154#41—232no—
1155#41—5964no—
1156#41—11832no—
1157#41—11832no—
1158#41—11864no—
1159#41—11832no—
1160#41—11864no—
1161#41—11864no—
1162#41—11864no—
1163#41—11832no—
1164#41—11832no—
1165C2×Q8—24no—
1166C2×Q8—598no—
1167C2×Q8—594no—
1168C2×Q8—598no—
1169C2×Q8—598no—
1170C2×Q8—594no—
1171C2×Q8—598no—
1172C2×Q8—594no—
1173C2×Q8—594no—
1174C2×Q8—1184no—
1175C2×Q8—1188no—
1176C2×Q8—1188no—
1177C2×Q8—1188no—
1178C2×Q8—11864no—
1179C2×Q8—1184no—
1180C2×Q8—11832no—
1181C2×Q8—11832no—
1182C2×Q8—11832no—
1183C2×Q8—1184no—
1184C2×Q8C23×D5914yes—
1185C2×D4—28no—
1186C2×D4—28no—
1187C2×D4—232no—
1188C2×D4—24no—
1189C2×D4—44no—
1190C2×D4—42no—
1191C2×D4—5916no—
1192C2×D4—598no—
1193C2×D4—594no—
1194C2×D4—598no—
1195C2×D4—594no—
1196C2×D4—598no—
1197C2×D4—598no—
1198C2×D4—598no—
1199C2×D4—598no—
1200C2×D4—594no—
1201C2×D4—594no—
1202C2×D4—594no—
1203C2×D4—598no—
1204C2×D4—598no—
1205C2×D4—594no—
1206C2×D4—594no—
1207C2×D4—594no—
1208C2×D4—594no—
1209C2×D4—598no—
1210C2×D4—594no—
1211C2×D4—1184no—
1212C2×D4—1184no—
1213C2×D4—11832no—
1214C2×D4—1184no—
1215C2×D4—1188no—
1216C2×D4—1188no—
1217C2×D4—1188no—
1218C2×D4—11864no—
1219C2×D4—1184no—
1220C2×D4—11864no—
1221C2×D4—11864no—
1222C2×D4—1184no—
1223C2×D4—1184no—
1224C2×D4—1188no—
1225C2×D4—1188no—
1226C2×D4—11832no—
1227C2×D4—1184no—
1228C2×D4—2364no—
1229C2×D4—2362no—
1230C2×D4—2362no—
1231C2×D4—2362no—
1232C2×D4—2364no—
1233C2×D4—2364no—
1234C2×D4D4×D5918yes—
1235C2×D4C23×D5918yes—
1236C2×D4C23×D5918yes—
1237C2×D4C23×D5914yes—
1238C2×D4C23×D5918yes—
1239C2×D4C23×D5914yes—
1240C2×D4C23×D5914yes—
1241C22×C4—28no—
1242C22×C4—24no—
1243C22×C4—24no—
1244C22×C4—44no—
1245C22×C4—5916no—
1246C22×C4—598no—
1247C22×C4—591no—
1248C22×C4—592no—
1249C22×C4—598no—
1250C22×C4—594no—
1251C22×C4—598no—
1252C22×C4—598no—
1253C22×C4—598no—
1254C22×C4—591no—
1255C22×C4—591no—
1256C22×C4—592no—
1257C22×C4—591no—
1258C22×C4—592no—
1259C22×C4—591no—
1260C22×C4—598no—
1261C22×C4—598no—
1262C22×C4—598no—
1263C22×C4—594no—
1264C22×C4—598no—
1265C22×C4—594no—
1266C22×C4—594no—
1267C22×C4—594no—
1268C22×C4—1188no—
1269C22×C4—1188no—
1270C22×C4—1188no—
1271C22×C4—1188no—
1272C22×C4—1188no—
1273C22×C4—1188no—
1274C22×C4—1184no—
1275C22×C4—1184no—
1276C22×C4—2362no—
1277C22×C4—2362no—
1278C22×C4—2364no—
1279C22×C4C23×D5918yes—
1280C22×C4C23×D5914yes—
1281C22×C4C23×D5914yes—
1282C22×C4C23×D5911yescharacteristic
1283C22×C4C23×D5912yes—
1284C22×C4C23×D5911yescharacteristic
1285C22×C4C23×D5912yes—
1286C22×C4C23×D5911yescharacteristic
1287C22×C4C23×D5911yescharacteristic
1288C22×C4C23×D5918yes—
1289C22×C4C23×D5911yescharacteristic
1290C4⋊C4—598no—
1291C4⋊C4—598no—
1292C4⋊C4—594no—
1293C4⋊C4—594no—
1294C4⋊C4—598no—
1295C4⋊C4—598no—
1296C4⋊C4—594no—
1297C4⋊C4—598no—
1298C4⋊C4—594no—
1299C4⋊C4C23×D5914yes—
1300C4⋊C4C23×D5918yes—
1301C4⋊C4C23×D5914yes—
1302C22⋊C4—598no—
1303C22⋊C4—594no—
1304C22⋊C4—598no—
1305C22⋊C4—598no—
1306C22⋊C4—598no—
1307C22⋊C4—598no—
1308C22⋊C4—594no—
1309C22⋊C4—598no—
1310C22⋊C4—594no—
1311C22⋊C4—594no—
1312C22⋊C4—598no—
1313C22⋊C4—598no—
1314C22⋊C4—598no—
1315C22⋊C4—598no—
1316C22⋊C4—598no—
1317C22⋊C4—598no—
1318C22⋊C4—598no—
1319C22⋊C4—598no—
1320C22⋊C4—594no—
1321C22⋊C4—594no—
1322C22⋊C4C23×D5918yes—
1323C22⋊C4C23×D5918yes—
1324C22⋊C4C23×D5914yes—
1325C22⋊C4C23×D5918yes—
1326C22⋊C4C23×D5918yes—
1327C22⋊C4C23×D5918yes—
1328C22⋊C4C23×D5914yes—
1329C42—594no—
1330C42—598no—
1331C42—594no—
1332C42—598no—
1333C42—598no—
1334C42—594no—
1335C42C23×D5914yes—
1336C23—24no—
1337C23—24no—
1338C23—22no—
1339C23—22no—
1340C23—24no—
1341C23—22no—
1342C23—24no—
1343C23—22no—
1344C23—22no—
1345C23—22no—
1346C23—24no—
1347C23—216no—
1348C23—48no—
1349C23—48no—
1350C23—816no—
1351C23—594no—
1352C23—592no—
1353C23—594no—
1354C23—592no—
1355C23—592no—
1356C23—11816no—
1357C23—1182no—
1358C23—1182no—
1359C23—11816no—
1360C23—1182no—
1361C23—1184no—
1362C23—1182no—
1363C23—1182no—
1364C23—1184no—
1365C23—1182no—
1366C23—1182no—
1367C23—1182no—
1368C23—1184no—
1369C23—47216no—
1370C23—47216no—
1371C23—2368no—
1372C23—2368no—
1373C23—2368no—
1374C23—2368no—
1375C23C2×D4×D5918yes—
1376C23C24×D5914yes—
1377C23C24×D5912yes—
1378C23C24×D5912yes—
1379C23C24×D5914yes—
1380C23C24×D5911yescharacteristic
1381Q8—28no—
1382Q8—5916no—
1383Q8—1188no—
1384Q8—11816no—
1385Q8—11816no—
1386Q8—11816no—
1387Q8—1188no—
1388Q8—1188no—
1389D4—216no—
1390D4—216no—
1391D4—28no—
1392D4—48no—
1393D4—44no—
1394D4—5932no—
1395D4—1188no—
1396D4—1188no—
1397D4—1188no—
1398D4—11816no—
1399D4—11816no—
1400D4—11816no—
1401D4—1188no—
1402D4—1188no—
1403D4—1188no—
1404D4—11816no—
1405D4—11816no—
1406D4—1188no—
1407D4—2368no—
1408D4—2364no—
1409D4—2364no—
1410D4—2364no—
1411D4—2368no—
1412D4—2368no—
1413D4C2×D4×D59116yes—
1414C2×C4—22no—
1415C2×C4—22no—
1416C2×C4—24no—
1417C2×C4—216no—
1418C2×C4—22no—
1419C2×C4—24no—
1420C2×C4—22no—
1421C2×C4—28no—
1422C2×C4—28no—
1423C2×C4—48no—
1424C2×C4—594no—
1425C2×C4—598no—
1426C2×C4—5932no—
1427C2×C4—592no—
1428C2×C4—594no—
1429C2×C4—5916no—
1430C2×C4—592no—
1431C2×C4—592no—
1432C2×C4—594no—
1433C2×C4—592no—
1434C2×C4—594no—
1435C2×C4—592no—
1436C2×C4—11816no—
1437C2×C4—11816no—
1438C2×C4—11816no—
1439C2×C4—11816no—
1440C2×C4—11816no—
1441C2×C4—1182no—
1442C2×C4—1184no—
1443C2×C4—1182no—
1444C2×C4—11816no—
1445C2×C4—1182no—
1446C2×C4—1182no—
1447C2×C4—1184no—
1448C2×C4—1188no—
1449C2×C4—1188no—
1450C2×C4—2364no—
1451C2×C4—2364no—
1452C2×C4—2368no—
1453C2×C4C2×D4×D5914yes—
1454C2×C4C24×D5912yes—
1455C2×C4C24×D5914yes—
1456C2×C4C24×D5912yes—
1457C2×C4C24×D5914yes—
1458C2×C4C24×D5912yes—
1459C2×C4C24×D5912yes—
1460C2×C4C24×D5912yes—
1461C22—24no—
1462C22—24no—
1463C22—216no—
1464C22—22no—
1465C22—22no—
1466C22—24no—
1467C22—22no—
1468C22—24no—
1469C22—22no—
1470C22—22no—
1471C22—22no—
1472C22—24no—
1473C22—44no—
1474C22—48no—
1475C22—44no—
1476C22—816no—
1477C22—594no—
1478C22—1182no—
1479C22—1182no—
1480C22—1188no—
1481C22—1182no—
1482C22—1184no—
1483C22—1182no—
1484C22—1182no—
1485C22—1184no—
1486C22—1182no—
1487C22—1182no—
1488C22—1182no—
1489C22—1184no—
1490C22—47216no—
1491C22—47216no—
1492C22—2364no—
1493C22—2368no—
1494C22—2364no—
1495C22C22×D4×D5918yes—
1496C22C22×D4×D5912yes—
1497C22#1683823712yes—
1498C22#1683823812yes—
1499C22C25×D5911yescharacteristic
1500C4—22no—
1501C4—22no—
1502C4—24no—
1503C4—22no—
1504C4—24no—
1505C4—22no—
1506C4—594no—
1507C4—598no—
1508C4—1182no—
1509C4—1184no—
1510C4—1182no—
1511C4—1182no—
1512C4—1182no—
1513C4—1184no—
1514C4C22×D4×D5914yes—
1515C2—28no—
1516C2—42no—
1517C2—44no—
1518C2—42no—
1519C2—1184no—
1520C2—2362no—
1521C2—2364no—
1522C2—2362no—
1523C2#2143788214yesdirect product factor
1524C2C23×D4×D5911yescharacteristic
1525C2C2×#1683823711yescharacteristic
1526C2C2×#1683823811yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#546C2
socleC23×C59C25
hypercenterC2×#546D59
hypocenterC59C2×#3500
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#546

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#14273774C2semidirect
2. C22×#14273772C2semidirect
3. #21437882C2direct (N × H)
4. C2×#16838062C2semidirect
5. C2×#16838061C2semidirect
6. C2×#16838060C2semidirect
7. C2×#16838058C2semidirect
8. C2×#16838047C2semidirect
9. C2×#16838046C2semidirect
10. C2×#16838044C2semidirect
11. C2×#16838042C2semidirect
12. C2×#16838041C2semidirect
13. C2×#16838040C2semidirect
14. C2×#16838039C2semidirect
15. C2×#16837975C2semidirect
16. C2×#16837974C2semidirect
17. C2×#16837968C2semidirect
18. C2×#16837967C2semidirect
19. C2×#16837949C2semidirect
20. C2×#16837947C2semidirect
21. C22×#14273713C2semidirect
22. C2×#124×D59C2semidirect
23. C2×C4×#11745687C2semidirect
24. C2×C59×#546C2semidirect
26. C2×#14273774C22semidirect
28. C2×#14273772C22semidirect
31. C22×#11745685C22semidirect
32. C22×#11745685C22semidirect
36. C22×#11745687C22semidirect
37. C22×#11745687C22semidirect
38. C22×#11745687C22semidirect
39. C23×Dic118C22semidirect
40. C23×Dic118C22semidirect
41. C22×Q8×D59C22semidirect
42. C22×Q8×D59C22semidirect
48. #16838062C22semidirect
49. #16838061C22semidirect
50. #16838060C22semidirect
51. #16838058C22semidirect
52. #16838047C22semidirect
53. #16838046C22semidirect
54. #16838044C22semidirect
55. #16838042C22semidirect
56. #16838041C22semidirect
57. #16838040C22semidirect
58. #16838039C22semidirect
59. #16837975C22semidirect
60. #16837974C22semidirect
61. #16837968C22semidirect
62. #16837967C22semidirect
63. #16837949C22semidirect
64. #16837947C22semidirect
65. C2×#14273726C22semidirect
66. C2×#14273726C22semidirect
67. C2×#14273723C22semidirect
68. C2×#14273723C22semidirect
69. C2×#14273716C22semidirect
70. C2×#14273715C22semidirect
71. C2×#14273714C22semidirect
72. C2×#14273713C22semidirect
73. C2×#14273713C22semidirect
74. C2×#14273713C22semidirect
75. C2×#14273713C22semidirect
76. C2×#14273713C22semidirect
77. C2×#14273713C22semidirect
78. C2×#14273713C22semidirect
79. C2×#14273713C22semidirect
80. C2×#14273713C22semidirect
81. C2×#14273713C22semidirect
82. C2×#14273713C22semidirect
83. #124×D59C22semidirect
84. C2×#14273712C22semidirect
85. C2×#14273711C22semidirect
86. C2×#14273710C22semidirect
87. C2×#14273709C22semidirect
88. C2×#14273708C22semidirect
89. C2×#14273707C22semidirect
90. C2×#14273706C22semidirect
91. C2×#14273705C22semidirect
92. C2×#14273705C22semidirect
93. C2×#14273704C22semidirect
94. C2×#14273704C22semidirect
95. C2×#14273703C22semidirect
96. C2×#14273702C22semidirect
97. C2×#14273702C22semidirect
98. C2×#14273701C22semidirect
99. C2×#14273701C22semidirect
100. C2×#14273700C22semidirect
101. C2×#14273700C22semidirect
102. C2×#14273700C22semidirect
103. C2×#14273700C22semidirect
104. C2×#14273699C22semidirect
105. C2×#14273699C22semidirect
106. C2×#14273699C22semidirect
107. C2×#14273699C22semidirect
108. C2×#14273698C22semidirect
109. C2×#14273698C22semidirect
110. C2×#14273697C22semidirect
111. C2×#14273697C22semidirect
112. C2×#14273696C22semidirect
113. C2×#14273695C22semidirect
114. C2×#14273695C22semidirect
115. C4×#11745687C22semidirect
116. C2×C4×Dic118C22semidirect
117. C2×#14273692C22semidirect
118. C2×C4×D236C22semidirect
119. C2×D4×Dic59C22semidirect
120. C2×D4×Dic59C22semidirect
121. C2×#14273689C22semidirect
122. C2×C4×C22⋊D59C22semidirect
123. C2×C4×C22⋊D59C22semidirect
124. C2×C4×C22⋊D59C22semidirect
125. C2×(C22⋊D59)⋊C4C22semidirect
126. C2×(C22⋊D59)⋊C4C22semidirect
127. C2×(C22⋊D59)⋊C4C22semidirect
128. C2×#14273685C22semidirect
129. C2×#14273683C22semidirect
130. C22×C22⋊Dic59C22semidirect
131. C22×(C2×D59)⋊C4C22semidirect
132. C22×(C2×D59)⋊C4C22semidirect
133. C2×C22⋊C4×D59C22semidirect
134. C2×C22⋊C4×D59C22semidirect
135. C22×C4×Dic59C22semidirect
136. C2×C42×D59C22semidirect
137. C22×#41×C59C22semidirect
139. C59×#546C22semidirect
140. C2×#124×C59C22semidirect
141. C2×#123×C59C22semidirect
142. C2×C22⋊Q8×C59C22semidirect
143. C2×#121×C59C22semidirect
144. C2×#121×C59C22semidirect
145. C2×#120×C59C22semidirect
146. C2×C4×D4×C59C22semidirect
147. C2×C4×D4×C59C22semidirect
148. C22×C22⋊C4×C59C22semidirect
159. C2×#11745685C23semidirect
160. C2×#11745685C23semidirect
166. C2×#11745687D4semidirect
170. C2×#11745687C23semidirect
171. C2×#11745687C23semidirect
172. C2×#11745687C23semidirect
182. C22×Dic118C23semidirect
183. C22×Dic118C23semidirect
186. C2×Q8×D59C23semidirect
187. C2×Q8×D59C23semidirect
230. #14273726C23semidirect
231. #14273726C23semidirect
232. #14273723C23semidirect
233. #14273723C23semidirect
234. #14273716C23semidirect
235. #14273715C23semidirect
236. #14273714C23semidirect
237. #14273713C23semidirect
238. #14273713C23semidirect
239. #14273713C23semidirect
240. #14273713C23semidirect
241. #14273713C23semidirect
242. #14273713C23semidirect
243. #14273713C23semidirect
244. #14273713C23semidirect
245. #14273713C23semidirect
246. #14273713C23semidirect
247. #14273712C23semidirect
248. #14273711C23semidirect
249. #14273710C23semidirect
250. #14273709C23semidirect
251. #14273708C23semidirect
252. #14273707C23semidirect
253. #14273706C23semidirect
254. #14273705C23semidirect
255. #14273705C23semidirect
256. #14273704C23semidirect
257. #14273704C23semidirect
258. #14273703C23semidirect
259. #14273702C23semidirect
260. #14273702C23semidirect
261. #14273701C23semidirect
262. #14273701C23semidirect
263. #14273700C23semidirect
264. #14273700C23semidirect
265. #14273700C23semidirect
266. #14273700C23semidirect
267. #14273699C23semidirect
268. #14273699C23semidirect
269. #14273699C23semidirect
270. #14273699C23semidirect
271. #14273698C23semidirect
272. #14273698C23semidirect
273. #14273697C23semidirect
274. #14273697C23semidirect
275. #14273696C23semidirect
276. #14273695C23semidirect
277. #14273695C23semidirect
278. C4×Dic118C23semidirect
279. #14273692C23semidirect
280. C4×D236C23semidirect
281. D4×Dic59C23semidirect
282. D4×Dic59C23semidirect
283. #14273689C23semidirect
284. C4×C22⋊D59C23semidirect
285. C4×C22⋊D59C23semidirect
286. C4×C22⋊D59C23semidirect
287. (C22⋊D59)⋊C4C23semidirect
288. (C22⋊D59)⋊C4C23semidirect
289. (C22⋊D59)⋊C4C23semidirect
290. #14273685C23semidirect
291. #14273683C23semidirect
308. C2×C22⋊Dic59C23semidirect
322. C2×(C2×D59)⋊C4C23semidirect
323. C2×(C2×D59)⋊C4C23semidirect
324. C22⋊C4×D59C23semidirect
325. C22⋊C4×D59C23semidirect
332. C2×C4×Dic59C23semidirect
333. C42×D59C23semidirect
336. C2×#41×C59C23semidirect
350. #124×C59C23semidirect
351. #123×C59C23semidirect
352. C22⋊Q8×C59C23semidirect
353. #121×C59C23semidirect
354. #121×C59C23semidirect
355. #120×C59C23semidirect
356. C4×D4×C59C23semidirect
357. C4×D4×C59C23semidirect
368. C2×C22⋊C4×C59C23semidirect
476. #11745687C2×D4semidirect
766. C2×#546D59semidirect
780. C2×C59#3500semidirect
802. C22×#41C2×D59semidirect
824. #546C2×D59semidirect
850. C2×#124C2×D59semidirect
856. C2×#123C2×D59semidirect
864. C2×C22⋊Q8C2×D59semidirect
879. C2×#121C2×D59semidirect
880. C2×#121C2×D59semidirect
886. C2×#120C2×D59semidirect
900. C2×C4×D4C2×D59semidirect
901. C2×C4×D4C2×D59semidirect
909. C22×C22⋊C4C2×D59semidirect
912. C59C2×#3500semidirect
939. C2×#41C22×D59semidirect
1027. #124C22×D59semidirect
1033. #123C22×D59semidirect
1041. C22⋊Q8C22×D59semidirect
1056. #121C22×D59semidirect
1057. #121C22×D59semidirect
1063. #120C22×D59semidirect
1076. C4×D4C22×D59semidirect
1077. C4×D4C22×D59semidirect
1124. C2×C22⋊C4C22×D59semidirect
1523. C2#21437882direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#142737742
C22×#142737722
#214378822
C2×#168380622
C2×#168380612
C2×#168380602
C2×#168380582
C2×#168380472
C2×#168380462
C2×#168380442
C2×#168380422
C2×#168380412
C2×#168380402
C2×#168380392
C2×#168379752
C2×#168379742
C2×#168379682
C2×#168379672
C2×#168379492
C2×#168379472
C22×#142737132
C2×#124×D592
C2×C4×#117456872
C2×C59×#5462
C2×#350059