Finite Group Databasebeta

← C2×#21437830 #29497035

Subgroups — C2×#21437830 #29497035

Order 15104.

8006 conjugacy classes of subgroups.

The subgroup lattice has 1384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437830C2132yesmaximal, direct product factor
2C2×#16838115C211yesmaximal, characteristic, complemented
3C2×#16838102C211yesmaximal, characteristic, complemented
4C2×#16838099C211yesmaximal, characteristic, complemented
5C2×#16838098C211yesmaximal, characteristic, complemented
6C2×#16838096C211yesmaximal, characteristic, complemented
7C2×#16838082C212yesmaximal, complemented
8C2×#16838076C212yesmaximal, complemented
9C2×#16838055C211yesmaximal, characteristic, complemented
10C2×#16838052C211yesmaximal, characteristic, complemented
11C2×#16838045C212yesmaximal, complemented
12C2×#16838041C212yesmaximal, complemented
13C2×#16838029C211yesmaximal, characteristic, complemented
14C2×#16838016C212yesmaximal, complemented
15C2×#16838002C212yesmaximal, complemented
16C2×#16837968C211yesmaximal, characteristic, complemented
17C2×#16837951C212yesmaximal, complemented
18C2×#16837930C212yesmaximal, complemented
19C2×#16837911C211yesmaximal, characteristic, complemented
20C2×#121×D59C211yesmaximal, characteristic, complemented
21C2×#16837882C211yesmaximal, characteristic, complemented
22C2×#16837874C211yesmaximal, characteristic, complemented
23C2×#117×D59C211yesmaximal, characteristic, complemented
24C2×C59×#555C211yesmaximal, characteristic, complemented
25C22×#11745689C2212yescomplemented
26C22×#11745685C2211yescharacteristic
27C22×#11745687C2212yescomplemented
28C22×D4×D59C2211yescharacteristic
29C22×D4×D59C2212yes—
30C23×C4×D59C2211yescharacteristic
31#16838115C22116yescomplemented
32#16838102C22116yescomplemented
33#16838099C22116yescomplemented
34#16838098C22116yescomplemented
35#16838096C22116yescomplemented
36#16838082C22132yescomplemented
37#16838076C22132yescomplemented
38#16838055C22116yescomplemented
39#16838052C22116yescomplemented
40#16838045C22132yescomplemented
41#16838041C22132yescomplemented
42#16838029C22116yescomplemented
43#16838016C22132yescomplemented
44#16838002C22132yescomplemented
45#16837968C22116yescomplemented
46#16837951C22132yescomplemented
47C2×#14273726C2211yescharacteristic, complemented
48C2×#14273725C2212yescomplemented
49C2×#14273723C2212yescomplemented
50#16837930C22132yescomplemented
51C2×#14273722C2212yescomplemented
52C2×#14273721C2212yescomplemented
53C2×#14273720C2212yescomplemented
54C2×#14273720C2212yescomplemented
55C2×#14273719C2211yescharacteristic, complemented
56C2×#14273718C2211yescharacteristic, complemented
57C2×#14273717C2212yescomplemented
58C2×#14273715C2212yescomplemented
59C2×#14273713C2212yescomplemented
60C2×#14273713C2212yescomplemented
61#16837911C22116yescomplemented
62C2×#14273712C2211yescharacteristic
63C2×#14273712C2212yescomplemented
64C2×#14273712C2212yescomplemented
65C2×#14273710C2212yescomplemented
66C2×#14273709C2211yescharacteristic
67C2×#14273709C2212yescomplemented
68C2×#14273709C2212yescomplemented
69C2×#14273709C2212yescomplemented
70C2×#14273708C2212yescomplemented
71C2×#14273708C2212yescomplemented
72C2×#14273705C2212yes—
73C2×#14273705C2211yescharacteristic, complemented
74C2×#14273704C2211yescharacteristic, complemented
75C2×#14273704C2212yescomplemented
76C2×#14273703C2212yes—
77C2×#14273703C2212yescomplemented
78C2×#14273702C2211yescharacteristic
79C2×#14273702C2211yescharacteristic, complemented
80C2×#14273701C2211yescharacteristic
81C2×#14273701C2211yescharacteristic, complemented
82C2×#14273700C2212yes—
83C2×#14273700C2212yescomplemented
84C2×#14273700C2212yescomplemented
85C2×#14273700C2212yescomplemented
86C2×#14273700C2211yescharacteristic, complemented
87C2×#14273699C2212yes—
88C2×#14273699C2211yescharacteristic, complemented
89C2×#14273699C2212yescomplemented
90C2×#14273698C2211yescharacteristic
91C2×#14273698C2212yescomplemented
92C2×#14273698C2211yescharacteristic, complemented
93#121×D59C22116yescomplemented
94C2×#14273697C2211yescharacteristic
95C2×#14273697C2212yes—
96C2×#14273695C2211yescharacteristic
97C2×#14273695C2212yes—
98#16837882C22116yescomplemented
99#16837874C22116yescomplemented
100C2×C4×Dic118C2212yescomplemented
101C2×C4×D236C2212yes—
102C2×C4×D236C2211yescharacteristic, complemented
103C2×C4×D236C2212yescomplemented
104C2×C4×D236C2211yescharacteristic, complemented
105C2×D4×Dic59C2211yescharacteristic, complemented
106C2×#14273689C2211yescharacteristic, complemented
107C2×C4×C22⋊D59C2212yescomplemented
108C2×C4×C22⋊D59C2212yescomplemented
109C2×C4×C22⋊D59C2211yescharacteristic, complemented
110C2×C4×C22⋊D59C2211yescharacteristic, complemented
111C2×(C22⋊D59)⋊C4C2212yes—
112C2×(C22⋊D59)⋊C4C2212yescomplemented
113C2×(C22⋊D59)⋊C4C2212yescomplemented
114C2×(C22⋊D59)⋊C4C2212yescomplemented
115C2×(C22⋊D59)⋊C4C2212yescomplemented
116C2×#14273686C2211yescharacteristic, complemented
117C2×#14273685C2211yescharacteristic
118C2×#14273685C2211yescharacteristic
119C2×#14273685C2211yescharacteristic, complemented
120C2×#14273684C2211yescharacteristic
121C2×#14273684C2212yes—
122C2×#14273684C2212yescomplemented
123C2×#14273683C2212yescomplemented
124#117×D59C22116yescomplemented
125C22×C4⋊Dic59C2211yescharacteristic, complemented
126C2×C4⋊C4×D59C2211yescharacteristic
127C2×C4⋊C4×D59C2211yescharacteristic, complemented
128C2×C4⋊C4×D59C2211yescharacteristic, complemented
129C2×C4⋊C4×D59C2211yescharacteristic, complemented
130C22×(C2×D59)⋊C4C2212yes—
131C2×C22⋊C4×D59C2212yes—
132C2×C22⋊C4×D59C2212yes—
133C2×C22⋊C4×D59C2212yes—
134C2×C42×D59C2212yescomplemented
135C59×#555C22116yescomplemented
136C2×C4⋊Q8×C59C2211yescharacteristic, complemented
137C2×#124×C59C2212yescomplemented
138C2×#124×C59C2212yescomplemented
139C2×#121×C59C2211yescharacteristic
140C2×#121×C59C2212yescomplemented
141C2×#121×C59C2211yescharacteristic, complemented
142C2×C4×D4×C59C2211yescharacteristic, complemented
143C2×C4×D4×C59C2211yescharacteristic, complemented
144C2×#117×C59C2211yescharacteristic, complemented
145C2×#117×C59C2211yescharacteristic, complemented
146C2×#117×C59C2212yescomplemented
147C24×D59C2311yescharacteristic
148C24×D59C2312yes—
149C2×#11745689—48no—
150C2×#11745689C23116yescomplemented
151C2×#11745685—28no—
152C2×#11745685C2318yes—
153C2×#11745687—48no—
154C2×#11745687C23116yescomplemented
155C22×Dic118C2311yescharacteristic
156C22×Dic118C2312yes—
157C22×D236C2311yescharacteristic
158C22×D236C2311yescharacteristic
159C22×D236C2312yes—
160C22×D236C2311yescharacteristic
161C22×D236C2312yes—
162C22×C22⋊D59C2312yes—
163C22×C22⋊D59C2312yes—
164C22×C22⋊D59C2311yescharacteristic
165C22×C22⋊D59C2311yescharacteristic
166C22×C22⋊D59C2311yescharacteristic
167C22×C22⋊D59C2311yescharacteristic
168C22×C22⋊D59C2312yes—
169C22×C22⋊D59C2312yes—
170C22×C22⋊D59C2312yes—
171C2×D4×D59—28no—
172C2×D4×D59—48no—
173C2×D4×D59C2318yes—
174C2×D4×D59C23116yes—
175C23×Dic59C2311yescharacteristic
176C23×Dic59C2312yes—
177C23×Dic59C2312yes—
178C22×C4×D59—28no—
179C22×C4×D59C2318yes—
180C22×C4×D59C2311yescharacteristic
181C22×C4×D59C2311yescharacteristic
182C22×C4×D59C2311yescharacteristic
183C22×C4×D59C2311yescharacteristic
184C22×C4×D59C2312yes—
185C22×C4×D59C2312yes—
186C22×C4×D59C2312yes—
187C22×C4×D59C2312yes—
188C22×C4×D59C2312yes—
189C22×C4×D59C2312yes—
190C22×C4×D59C2311yescharacteristic
191#14273726C2318yescomplemented
192#14273725C23116yescomplemented
193#14273723C23116yescomplemented
194#14273722C23116yescomplemented
195#14273721C23116yescomplemented
196#14273720C23116yescomplemented
197#14273720C23116yescomplemented
198#14273719C2318yescomplemented
199#14273718C2318yescomplemented
200#14273717C23116yescomplemented
201#14273715C23116yescomplemented
202#14273713C23116yescomplemented
203#14273713C23116yescomplemented
204#14273712C2318yes—
205#14273712C23116yescomplemented
206#14273712C23116yescomplemented
207#14273710C23116yescomplemented
208#14273709C2318yes—
209#14273709C23116yescomplemented
210#14273709C23116yescomplemented
211#14273709C23116yescomplemented
212#14273708C23116yescomplemented
213#14273708C23116yescomplemented
214#14273705C23116yes—
215#14273705C2318yescomplemented
216#14273704C2318yescomplemented
217#14273704C23116yescomplemented
218#14273703C23116yes—
219#14273703C23116yescomplemented
220#14273702C2318yes—
221#14273702C2318yescomplemented
222#14273701C2318yes—
223#14273701C2318yescomplemented
224#14273700C23116yes—
225#14273700C2318yescomplemented
226#14273700C23116yescomplemented
227#14273700C23116yescomplemented
228#14273700C23116yescomplemented
229#14273699C23116yes—
230#14273699C2318yescomplemented
231#14273699C23116yescomplemented
232#14273698C2318yes—
233#14273698C2318yescomplemented
234#14273698C23116yescomplemented
235#14273697C2318yes—
236#14273697C23116yes—
237#14273695C2318yes—
238#14273695C23116yes—
239C4×Dic118C23116yescomplemented
240C4×D236C23116yes—
241C4×D236C2318yescomplemented
242C4×D236C23116yescomplemented
243C4×D236C2318yescomplemented
244D4×Dic59C2318yescomplemented
245#14273689C2318yescomplemented
246C4×C22⋊D59C2318yescomplemented
247C4×C22⋊D59C2318yescomplemented
248C4×C22⋊D59C23116yescomplemented
249C4×C22⋊D59C23116yescomplemented
250(C22⋊D59)⋊C4C23116yes—
251(C22⋊D59)⋊C4C23116yescomplemented
252(C22⋊D59)⋊C4C23116yescomplemented
253(C22⋊D59)⋊C4C23116yescomplemented
254(C22⋊D59)⋊C4C23116yescomplemented
255#14273686C2318yescomplemented
256#14273685C2318yes—
257#14273685C2318yes—
258#14273685C2318yescomplemented
259#14273684C2318yes—
260#14273684C23116yes—
261#14273684C23116yescomplemented
262#14273683C23116yescomplemented
263C2×C4⋊Dic59C2311yescharacteristic
264C2×C4⋊Dic59C2311yescharacteristic
265C2×C4⋊Dic59C2312yes—
266C2×C4⋊Dic59C2311yescharacteristic
267C2×C4⋊Dic59C2312yes—
268C2×C4⋊Dic59C2311yescharacteristic
269C2×C4⋊Dic59C2318yescomplemented
270C2×Dic59⋊C4C2312yes—
271C2×Dic59⋊C4C2312yes—
272C2×Dic59⋊C4C2311yescharacteristic
273C2×Dic59⋊C4C2312yes—
274C2×Dic59⋊C4C2312yes—
275C2×Dic59⋊C4C2311yescharacteristic
276C2×Dic59⋊C4C2312yes—
277C2×Dic59⋊C4C2312yes—
278C2×Dic59⋊C4C2312yes—
279C2×Dic59⋊C4C2311yescharacteristic
280C2×Dic59⋊C4C2311yescharacteristic
281C2×Dic59⋊C4C2312yes—
282C4⋊C4×D59C2318yes—
283C4⋊C4×D59C2318yescomplemented
284C4⋊C4×D59C2318yescomplemented
285C4⋊C4×D59C2318yescomplemented
286C2×C22⋊Dic59C2312yes—
287C2×C22⋊Dic59C2312yes—
288C2×C22⋊Dic59C2312yes—
289C2×C22⋊Dic59C2312yes—
290C2×C22⋊Dic59C2311yescharacteristic
291C2×C22⋊Dic59C2311yescharacteristic
292C2×(C2×D59)⋊C4C2312yes—
293C2×(C2×D59)⋊C4C2311yescharacteristic
294C2×(C2×D59)⋊C4C2312yes—
295C2×(C2×D59)⋊C4C2311yescharacteristic
296C2×(C2×D59)⋊C4C2312yes—
297C2×(C2×D59)⋊C4C2311yescharacteristic
298C2×(C2×D59)⋊C4C2312yes—
299C2×(C2×D59)⋊C4C2312yes—
300C2×(C2×D59)⋊C4C2312yes—
301C2×(C2×D59)⋊C4C2311yescharacteristic
302C2×(C2×D59)⋊C4C2312yes—
303C2×(C2×D59)⋊C4C2312yes—
304C2×(C2×D59)⋊C4C2311yescharacteristic
305C2×(C2×D59)⋊C4C2311yescharacteristic
306C2×(C2×D59)⋊C4C23116yes—
307C2×(C2×D59)⋊C4C2312yes—
308C22⋊C4×D59C23116yes—
309C22⋊C4×D59C23116yes—
310C22⋊C4×D59C23116yes—
311C2×C4×Dic59C2312yes—
312C2×C4×Dic59C2312yes—
313C2×C4×Dic59C2311yescharacteristic
314C2×C4×Dic59C2312yes—
315C2×C4×Dic59C2312yes—
316C42×D59C23116yescomplemented
317C22×Q8×C59C2312yes—
318C22×D4×C59C2311yescharacteristic
319C22×D4×C59C2312yes—
320C22×D4×C59C2311yescharacteristic
321C22×D4×C59C2312yes—
322C23×C4×C59C2311yescharacteristic
323C23×C4×C59C2311yescharacteristic
324C23×C4×C59C2312yes—
325C4⋊Q8×C59C2318yescomplemented
326#124×C59C23116yescomplemented
327#124×C59C23116yescomplemented
328#121×C59C2318yes—
329#121×C59C2318yescomplemented
330#121×C59C23116yescomplemented
331C4×D4×C59C2318yescomplemented
332C4×D4×C59C2318yescomplemented
333#117×C59C23116yescomplemented
334#117×C59C2318yescomplemented
335#117×C59C2318yescomplemented
336C2×C4⋊C4×C59C2311yescharacteristic
337C2×C4⋊C4×C59C2311yescharacteristic
338C2×C4⋊C4×C59C2312yes—
339C2×C4⋊C4×C59C2311yescharacteristic
340C2×C4⋊C4×C59C2311yescharacteristic
341C2×C22⋊C4×C59C2311yescharacteristic
342C2×C22⋊C4×C59C2312yes—
343C2×C22⋊C4×C59C2312yes—
344C2×C22⋊C4×C59C2311yescharacteristic
345C2×C22⋊C4×C59C2312yes—
346C2×C22⋊C4×C59C2312yes—
347C2×C22⋊C4×C59C2312yes—
348C2×C42×C59C2312yes—
349C2×C42×C59C2311yescharacteristic
350C2×C42×C59C2312yes—
351C24×C59C2411yescharacteristic
352C24×C59C2412yes—
353C24×C59C2411yescharacteristic
354C23×D59—24no—
355C23×D59—24no—
356C23×D59—28no—
357C23×D59—42no—
358C23×D59—44no—
359C23×D59—44no—
360C23×D59C2412yes—
361C23×D59C2411yescharacteristic
362C23×D59C2414yes—
363C23×D59C2411yescharacteristic
364C23×D59C2411yescharacteristic
365C23×D59C2418yes—
366C2×Q8×C59—44no—
367C2×Q8×C59C2418yes—
368C2×D4×C59—24no—
369C2×D4×C59—42no—
370C2×D4×C59—44no—
371C2×D4×C59—44no—
372C2×D4×C59C2414yes—
373C2×D4×C59C2414yes—
374C2×D4×C59C2418yes—
375C2×D4×C59C2418yes—
376C22×C4×C59—24no—
377C22×C4×C59—24no—
378C22×C4×C59—44no—
379C22×C4×C59C2411yescharacteristic
380C22×C4×C59C2412yes—
381C22×C4×C59C2411yescharacteristic
382C22×C4×C59C2411yescharacteristic
383C22×C4×C59C2412yes—
384C22×C4×C59C2412yes—
385C22×C4×C59C2411yescharacteristic
386C22×C4×C59C2414yes—
387C22×C4×C59C2414yes—
388C22×C4×C59C2418yes—
389C22×C4×C59C2411yescharacteristic
390C2×C22⋊D59—24no—
391C2×C22⋊D59—28no—
392C2×C22⋊D59—24no—
393C2×C22⋊D59—28no—
394C2×C22⋊D59—24no—
395C2×C22⋊D59—44no—
396C2×C22⋊D59—42no—
397C2×C22⋊D59—44no—
398C2×C22⋊D59—44no—
399C2×C22⋊D59C2414yes—
400C2×C22⋊D59C2414yes—
401C2×C22⋊D59C2418yes—
402C2×C22⋊D59C2414yes—
403C2×C22⋊D59C2418yes—
404C2×C22⋊D59C2418yes—
405C2×C22⋊D59C2418yes—
406C2×C22⋊D59C2414yes—
407C2×C22⋊D59C2418yes—
408C22×Dic59—24no—
409C22×Dic59—44no—
410C22×Dic59—44no—
411C22×Dic59C2411yescharacteristic
412C22×Dic59C2412yes—
413C22×Dic59C2412yes—
414C22×Dic59C2411yescharacteristic
415C22×Dic59C2411yescharacteristic
416C22×Dic59C2412yes—
417C22×Dic59C2411yescharacteristic
418C22×Dic59C2414yes—
419C22×Dic59C2418yes—
420C22×Dic59C2418yes—
421C22×Dic59C2411yescharacteristic
422#11745689—432no—
423#11745687—432no—
424D4×D59—232no—
425D4×D59—432no—
426#11745685—232no—
427C2×D236—24no—
428C2×D236—28no—
429C2×D236—24no—
430C2×D236—24no—
431C2×D236—44no—
432C2×D236C2414yes—
433C2×D236C2414yes—
434C2×D236C2414yes—
435C2×D236C2418yes—
436C2×D236C2418yes—
437C2×C4×D59—24no—
438C2×C4×D59—28no—
439C2×C4×D59—24no—
440C2×C4×D59—24no—
441C2×C4×D59—24no—
442C2×C4×D59—232no—
443C2×C4×D59—44no—
444C2×C4×D59—44no—
445C2×C4×D59—44no—
446C2×C4×D59—44no—
447C2×C4×D59—44no—
448C2×C4×D59#4118yescomplemented
449C2×C4×D59C2414yes—
450C2×C4×D59C2418yes—
451C2×C4×D59C2414yes—
452C2×C4×D59C2414yes—
453C2×C4×D59C2414yes—
454C2×C4×D59C2418yes—
455C2×C4×D59C2418yes—
456C2×C4×D59C2418yes—
457C2×C4×D59C2418yes—
458C2×C4×D59C2418yes—
459C2×C4×D59C2414yes—
460C2×Dic118—24no—
461C2×Dic118—44no—
462C2×Dic118C2414yes—
463C2×Dic118C2418yes—
464C4⋊C4×C59C2414yes—
465C4⋊C4×C59C2414yes—
466C4⋊C4×C59C2414yes—
467C4⋊C4×C59C2414yes—
468C4⋊C4×C59C2418yes—
469C22⋊C4×C59C2418yes—
470C22⋊C4×C59C2418yes—
471C22⋊C4×C59C2418yes—
472C22⋊C4×C59C2418yes—
473C22⋊C4×C59C2418yes—
474C22⋊C4×C59C2414yes—
475C22⋊C4×C59C2414yes—
476C42×C59C2418yes—
477C42×C59C2418yes—
478C42×C59C2414yes—
479C22⋊Dic59C2418yes—
480C22⋊Dic59C2418yes—
481C22⋊Dic59C2418yes—
482C22⋊Dic59C2418yes—
483C22⋊Dic59C2414yes—
484C22⋊Dic59C2414yes—
485(C2×D59)⋊C4C2418yes—
486(C2×D59)⋊C4C2414yes—
487(C2×D59)⋊C4C2418yes—
488(C2×D59)⋊C4C2418yes—
489(C2×D59)⋊C4C2418yes—
490(C2×D59)⋊C4C2414yes—
491(C2×D59)⋊C4C2418yes—
492(C2×D59)⋊C4C2418yes—
493(C2×D59)⋊C4C2418yes—
494(C2×D59)⋊C4C2418yes—
495(C2×D59)⋊C4C2414yes—
496(C2×D59)⋊C4C2414yes—
497(C2×D59)⋊C4C2414yes—
498(C2×D59)⋊C4C2418yes—
499(C2×D59)⋊C4C2414yes—
500C4⋊Dic59C2414yes—
501C4⋊Dic59C2414yes—
502C4⋊Dic59C2414yes—
503C4⋊Dic59C2418yes—
504C4⋊Dic59C2418yes—
505C4⋊Dic59C2414yes—
506Dic59⋊C4C2418yes—
507Dic59⋊C4C2418yes—
508Dic59⋊C4C2418yes—
509Dic59⋊C4C2418yes—
510Dic59⋊C4C2414yes—
511Dic59⋊C4C2414yes—
512Dic59⋊C4C2414yes—
513Dic59⋊C4C2418yes—
514Dic59⋊C4C2418yes—
515Dic59⋊C4C2418yes—
516Dic59⋊C4C2418yes—
517Dic59⋊C4C2414yes—
518C4×Dic59C2418yes—
519C4×Dic59C2418yes—
520C4×Dic59C2418yes—
521C4×Dic59C2414yes—
522C4×Dic59C2418yes—
523C23×C59—22no—
524C23×C59—22no—
525C23×C59—24no—
526C23×C59—22no—
527C23×C59—24no—
528C23×C59—22no—
529C23×C59—22no—
530C23×C59—24no—
531C23×C59—22no—
532C23×C59C2512yes—
533C23×C59C2514yes—
534C23×C59C2512yes—
535C23×C59C2511yescharacteristic
536C22×D59—22no—
537C22×D59—22no—
538C22×D59—22no—
539C22×D59—22no—
540C22×D59—22no—
541C22×D59—24no—
542C22×D59—22no—
543C22×D59—24no—
544C22×D59—24no—
545C22×D59—22no—
546C22×D59—28no—
547C22×D59—28no—
548C22×D59—216no—
549C22×D59—44no—
550C22×D59—416no—
551C22×D59—48no—
552C22×D59—48no—
553C22×D59—816no—
554C22×D59C2×#4114yes—
555C22×D59H(5,𝔽2)14yes—
556C22×D59C2514yes—
557C22×D59C2512yes—
558C22×D59C2512yes—
559C22×D59C2512yes—
560Q8×C59—48no—
561D4×C59—28no—
562D4×C59—48no—
563D4×C59—48no—
564D4×C59—44no—
565C2×C4×C59—22no—
566C2×C4×C59—22no—
567C2×C4×C59—24no—
568C2×C4×C59—24no—
569C2×C4×C59—22no—
570C2×C4×C59—24no—
571C2×C4×C59—22no—
572C2×C4×C59—28no—
573C2×C4×C59—28no—
574C2×C4×C59—48no—
575C2×C4×C59C2×#4114yes—
576C2×C4×C59C2512yes—
577C2×C4×C59C2514yes—
578C2×C4×C59C2514yes—
579C2×C4×C59C2512yes—
580C2×C4×C59C2514yes—
581C2×C4×C59C2512yes—
582C2×C4×C59C2512yes—
583C2×C4×C59C2512yes—
584C22⋊D59—28no—
585C22⋊D59—216no—
586C22⋊D59—28no—
587C22⋊D59—28no—
588C22⋊D59—216no—
589C22⋊D59—48no—
590C22⋊D59—44no—
591C22⋊D59—48no—
592C22⋊D59—48no—
593C2×Dic59—22no—
594C2×Dic59—22no—
595C2×Dic59—22no—
596C2×Dic59—24no—
597C2×Dic59—24no—
598C2×Dic59—22no—
599C2×Dic59—24no—
600C2×Dic59—28no—
601C2×Dic59—48no—
602C2×Dic59—48no—
603C2×Dic59C2×#4114yes—
604C2×Dic59C2514yes—
605C2×Dic59C2512yes—
606C2×Dic59C2514yes—
607C2×Dic59C2512yes—
608C2×Dic59C2514yes—
609C2×Dic59C2512yes—
610C2×Dic59C2512yes—
611C2×Dic59C2512yes—
612D236—28no—
613D236—216no—
614D236—28no—
615D236—28no—
616D236—48no—
617C4×D59—28no—
618C4×D59—216no—
619C4×D59—28no—
620C4×D59—28no—
621C4×D59—28no—
622C4×D59—48no—
623C4×D59—48no—
624C4×D59—48no—
625C4×D59—48no—
626C4×D59—48no—
627C4×D59C2×#41116yescomplemented
628Dic118—28no—
629Dic118—48no—
630C2×#3494—591nomaximal, Sylow
631C22×C59—22no—
632C22×C59—22no—
633C22×C59—24no—
634C22×C59—22no—
635C22×C59—24no—
636C22×C59—22no—
637C22×C59—22no—
638C22×C59—24no—
639C22×C59—22no—
640C22×C59—44no—
641C22×C59—48no—
642C22×C59—44no—
643C22×C59C22×#4112yes—
644C22×C59C2×H(5,𝔽2)12yes—
645C22×C59#58512yes—
646C22×C59C2611yescharacteristic
647C2×D59—22no—
648C2×D59—22no—
649C2×D59—22no—
650C2×D59—22no—
651C2×D59—28no—
652C2×D59—28no—
653C2×D59—22no—
654C2×D59—24no—
655C2×D59—22no—
656C2×D59—24no—
657C2×D59—24no—
658C2×D59—22no—
659C2×D59—416no—
660C2×D59—44no—
661C2×D59—48no—
662C2×D59—816no—
663C2×D59C22×#4114yes—
664C2×D59C2×H(5,𝔽2)14yes—
665C4×C59—22no—
666C4×C59—22no—
667C4×C59—24no—
668C4×C59—24no—
669C4×C59—22no—
670C4×C59—24no—
671C4×C59—22no—
672C4×C59C22×#4114yes—
673Dic59—22no—
674Dic59—22no—
675Dic59—22no—
676Dic59—24no—
677Dic59—24no—
678Dic59—22no—
679Dic59—24no—
680Dic59C22×#4114yes—
681#3494—5932no—
682C2×#555—591no—
683C2×#555D5911yescharacteristic, complemented
684C2×#553—591no—
685C2×#553—591no—
686C2×#553—591no—
687C2×#553—591no—
688C2×#551—592no—
689C2×#551—592no—
690C2×#547—591no—
691C2×#547—591no—
692C2×#546—592no—
693C2×#546—592no—
694C2×#544—591no—
695C2×#542—592no—
696C2×#540—592no—
697C2×#535—591no—
698C2×#532—592no—
699C2×#529—592no—
700C2×#525—591no—
701C22×#121—591no—
702C2×#520—591no—
703C2×#518—591no—
704C22×#117—591no—
705C2×C59—42no—
706C2×C59—44no—
707C2×C59—42no—
708C2×C59#349414yescomplemented
709C2×C59C23×#4111yescharacteristic
710C2×C59C22×H(5,𝔽2)11yescharacteristic
711C2×C59C2×#58511yescharacteristic
712D59—24no—
713D59—24no—
714D59—42no—
715D59—44no—
716C22×#41—592no—
717C22×#41—592no—
718C22×#41—591no—
719C23×D4—591no—
720C23×D4—592no—
721C24×C4—591no—
722#555—5916no—
723#555C2×D59116yescomplemented
724#553—5916no—
725#553—5916no—
726#553—5916no—
727#553—5916no—
728#551—5932no—
729#551—5932no—
730#547—5916no—
731#547—5916no—
732#546—5932no—
733#546—5932no—
734#544—5916no—
735#542—5932no—
736#540—5932no—
737#535—5916no—
738#532—5932no—
739C2×C4⋊Q8—592no—
740C2×C4⋊Q8—591no—
741C2×C4⋊Q8C2×D5911yescharacteristic, complemented
742C2×#127—592no—
743#529—5932no—
744C2×#126—592no—
745C2×#126—592no—
746C2×#126—592no—
747C2×#126—592no—
748C2×#125—592no—
749C2×#125—591no—
750C2×#125—591no—
751C2×#124—592no—
752C2×#124—592no—
753C2×#124—592no—
754C2×#124C2×D5912yescomplemented
755C2×#124C2×D5912yescomplemented
756#525—5916no—
757C2×#123—592no—
758C2×#123—592no—
759C2×#123—592no—
760C2×#123—591no—
761C2×#123—592no—
762C2×#123—592no—
763C2×#123—591no—
764C2×#123—592no—
765C2×#123—592no—
766C2×#123—592no—
767C2×C22⋊Q8—592no—
768C2×C22⋊Q8—592no—
769C2×C22⋊Q8—592no—
770C2×C22⋊Q8—591no—
771C2×C22⋊Q8—591no—
772C2×C22⋊Q8—592no—
773C2×#121—591no—
774C2×#121—591no—
775C2×#121—592no—
776C2×#121—592no—
777C2×#121—591no—
778C2×#121—592no—
779C2×#121—591no—
780C2×#121—591no—
781C2×#121—5916no—
782C2×#121—591no—
783C2×#121—591no—
784C2×#121—592no—
785C2×#121—591no—
786C2×#121—592no—
787C2×#121—592no—
788C2×#121—592no—
789C2×#121C2×D5911yescharacteristic
790C2×#121C2×D5911yescharacteristic, complemented
791C2×#121C2×D5912yescomplemented
792C2×#120—591no—
793C2×#120—592no—
794C2×#120—591no—
795C2×#120—592no—
796#520—5916no—
797#518—5916no—
798C2×C4×Q8—592no—
799C2×C4×D4—591no—
800C2×C4×D4—592no—
801C2×C4×D4—591no—
802C2×C4×D4—591no—
803C2×C4×D4—592no—
804C2×C4×D4—591no—
805C2×C4×D4—592no—
806C2×C4×D4—592no—
807C2×C4×D4—592no—
808C2×C4×D4—592no—
809C2×C4×D4—592no—
810C2×C4×D4—591no—
811C2×C4×D4—592no—
812C2×C4×D4—591no—
813C2×C4×D4—592no—
814C2×C4×D4C2×D5911yescharacteristic, complemented
815C2×C4×D4C2×D5911yescharacteristic, complemented
816C2×#117—591no—
817C2×#117—5916no—
818C2×#117—591no—
819C2×#117—591no—
820C2×#117—591no—
821C2×#117—592no—
822C2×#117—592no—
823C2×#117—591no—
824C2×#117—592no—
825C2×#117C2×D5911yescharacteristic, complemented
826C2×#117C2×D5911yescharacteristic, complemented
827C2×#117C2×D5912yescomplemented
828C22×C4⋊C4—591no—
829C22×C4⋊C4—591no—
830C22×C4⋊C4—591no—
831C22×C4⋊C4—591no—
832C22×C4⋊C4—591no—
833C22×C22⋊C4—592no—
834C22×C22⋊C4—592no—
835C22×C22⋊C4—592no—
836C22×C22⋊C4—592no—
837C22×C42—592no—
838C59C2×#349411yescharacteristic, complemented, Sylow
839C25—591no—
840C25—592no—
841C2×#41—5916no—
842C2×#41—5916no—
843C2×#41—598no—
844C2×#41—1188no—
845C2×#41—2368no—
846C2×#41—2368no—
847C22×Q8—591no—
848C22×Q8—592no—
849C22×Q8C22×D5912yes—
850C22×D4—591no—
851C22×D4—592no—
852C22×D4—591no—
853C22×D4—591no—
854C22×D4—592no—
855C22×D4—591no—
856C22×D4—592no—
857C22×D4—592no—
858C22×D4—592no—
859C22×D4—598no—
860C22×D4—5916no—
861C22×D4—591no—
862C22×D4—591no—
863C22×D4—591no—
864C22×D4—592no—
865C22×D4—592no—
866C22×D4—1188no—
867C22×D4—2368no—
868C22×D4C22×D5911yescharacteristic
869C22×D4C22×D5911yescharacteristic
870C22×D4C22×D5912yes—
871C22×D4C22×D5912yes—
872C23×C4—591no—
873C23×C4—591no—
874C23×C4—592no—
875C23×C4—592no—
876C23×C4—591no—
877C23×C4—592no—
878C23×C4—591no—
879C23×C4—591no—
880C23×C4—598no—
881C23×C4—591no—
882C23×C4—592no—
883C23×C4—592no—
884C23×C4—592no—
885C23×C4—592no—
886C23×C4—592no—
887C23×C4—1188no—
888C23×C4C22×D5911yescharacteristic
889C23×C4C22×D5911yescharacteristic
890C23×C4C22×D5912yes—
891C4⋊Q8—5916no—
892C4⋊Q8—598no—
893C4⋊Q8C22×D5918yescomplemented
894#127—5916no—
895#126—5916no—
896#126—5916no—
897#126—5916no—
898#126—5916no—
899#125—5916no—
900#125—598no—
901#125—598no—
902#124—5916no—
903#124—5916no—
904#124—5916no—
905#124C22×D59116yescomplemented
906#124C22×D59116yescomplemented
907#123—5916no—
908#123—5916no—
909#123—5916no—
910#123—598no—
911#123—5916no—
912#123—5916no—
913#123—598no—
914#123—5916no—
915#123—5916no—
916#123—5916no—
917C22⋊Q8—5916no—
918C22⋊Q8—5916no—
919C22⋊Q8—598no—
920C22⋊Q8—5916no—
921C22⋊Q8—598no—
922C22⋊Q8—5916no—
923#121—5916no—
924#121—598no—
925#121—598no—
926#121—598no—
927#121—5916no—
928#121—5916no—
929#121—598no—
930#121—598no—
931#121—598no—
932#121—598no—
933#121—5916no—
934#121—598no—
935#121—5916no—
936#121—5916no—
937#121—5916no—
938#121C22×D5918yes—
939#121C22×D5918yescomplemented
940#121C22×D59116yescomplemented
941#120—598no—
942#120—5916no—
943#120—598no—
944#120—5916no—
945C4×Q8—5916no—
946C4×D4—598no—
947C4×D4—5916no—
948C4×D4—598no—
949C4×D4—598no—
950C4×D4—5916no—
951C4×D4—598no—
952C4×D4—5916no—
953C4×D4—5916no—
954C4×D4—5916no—
955C4×D4—5916no—
956C4×D4—5916no—
957C4×D4—598no—
958C4×D4—5916no—
959C4×D4—598no—
960C4×D4—5916no—
961C4×D4C22×D5918yescomplemented
962C4×D4C22×D5918yescomplemented
963#117—598no—
964#117—598no—
965#117—598no—
966#117—598no—
967#117—5916no—
968#117—5916no—
969#117—598no—
970#117—5916no—
971#117C22×D5918yescomplemented
972#117C22×D5918yescomplemented
973#117C22×D59116yescomplemented
974C2×C4⋊C4—591no—
975C2×C4⋊C4—591no—
976C2×C4⋊C4—591no—
977C2×C4⋊C4—592no—
978C2×C4⋊C4—592no—
979C2×C4⋊C4—592no—
980C2×C4⋊C4—592no—
981C2×C4⋊C4—592no—
982C2×C4⋊C4—598no—
983C2×C4⋊C4—591no—
984C2×C4⋊C4—591no—
985C2×C4⋊C4—591no—
986C2×C4⋊C4—592no—
987C2×C4⋊C4—592no—
988C2×C4⋊C4—592no—
989C2×C4⋊C4—592no—
990C2×C4⋊C4—592no—
991C2×C4⋊C4—591no—
992C2×C4⋊C4—591no—
993C2×C4⋊C4—598no—
994C2×C4⋊C4—598no—
995C2×C4⋊C4—598no—
996C2×C4⋊C4—598no—
997C2×C4⋊C4C22×D5911yescharacteristic
998C2×C4⋊C4C22×D5911yescharacteristic
999C2×C4⋊C4C22×D5911yescharacteristic
1000C2×C4⋊C4C22×D5911yescharacteristic
1001C2×C4⋊C4C22×D5912yes—
1002C2×C22⋊C4—592no—
1003C2×C22⋊C4—592no—
1004C2×C22⋊C4—592no—
1005C2×C22⋊C4—592no—
1006C2×C22⋊C4—591no—
1007C2×C22⋊C4—591no—
1008C2×C22⋊C4—592no—
1009C2×C22⋊C4—591no—
1010C2×C22⋊C4—591no—
1011C2×C22⋊C4—592no—
1012C2×C22⋊C4—592no—
1013C2×C22⋊C4—592no—
1014C2×C22⋊C4—592no—
1015C2×C22⋊C4—5916no—
1016C2×C22⋊C4—592no—
1017C2×C22⋊C4—592no—
1018C2×C22⋊C4—592no—
1019C2×C22⋊C4—591no—
1020C2×C22⋊C4—591no—
1021C2×C22⋊C4—591no—
1022C2×C22⋊C4—592no—
1023C2×C22⋊C4—591no—
1024C2×C22⋊C4—5916no—
1025C2×C22⋊C4—5916no—
1026C2×C22⋊C4—5916no—
1027C2×C22⋊C4C22×D5912yes—
1028C2×C22⋊C4C22×D5912yes—
1029C2×C22⋊C4C22×D5912yes—
1030C2×C22⋊C4C22×D5912yes—
1031C2×C22⋊C4C22×D5912yes—
1032C2×C22⋊C4C22×D5911yescharacteristic
1033C2×C22⋊C4C22×D5911yescharacteristic
1034C2×C42—592no—
1035C2×C42—592no—
1036C2×C42—592no—
1037C2×C42—592no—
1038C2×C42—591no—
1039C2×C42—5916no—
1040C2×C42C22×D5912yes—
1041C2×C42C22×D5911yescharacteristic
1042C2×C42C22×D5912yes—
1043C24—591no—
1044C24—591no—
1045C24—592no—
1046C24—591no—
1047C24—594no—
1048C24—598no—
1049C24—1188no—
1050C24—1184no—
1051C24—1184no—
1052C24—2364no—
1053C24—2364no—
1054C24—2362no—
1055C24C23×D5911yescharacteristic
1056C24C23×D5912yes—
1057C24C23×D5911yescharacteristic
1058#41—11832no—
1059#41—23632no—
1060#41—23632no—
1061C2×Q8—44no—
1062C2×Q8—594no—
1063C2×Q8—598no—
1064C2×Q8—1184no—
1065C2×Q8—2364no—
1066C2×Q8C23×D5918yes—
1067C2×D4—24no—
1068C2×D4—44no—
1069C2×D4—44no—
1070C2×D4—42no—
1071C2×D4—594no—
1072C2×D4—598no—
1073C2×D4—594no—
1074C2×D4—594no—
1075C2×D4—598no—
1076C2×D4—594no—
1077C2×D4—598no—
1078C2×D4—598no—
1079C2×D4—598no—
1080C2×D4—594no—
1081C2×D4—594no—
1082C2×D4—594no—
1083C2×D4—598no—
1084C2×D4—598no—
1085C2×D4—1188no—
1086C2×D4—1184no—
1087C2×D4—1184no—
1088C2×D4—11832no—
1089C2×D4—1188no—
1090C2×D4—1184no—
1091C2×D4—1188no—
1092C2×D4—1184no—
1093C2×D4—1184no—
1094C2×D4—1184no—
1095C2×D4—2364no—
1096C2×D4—2364no—
1097C2×D4—2362no—
1098C2×D4—2364no—
1099C2×D4—2364no—
1100C2×D4—23632no—
1101C2×D4C23×D5914yes—
1102C2×D4C23×D5914yes—
1103C2×D4C23×D5918yes—
1104C2×D4C23×D5918yes—
1105C22×C4—24no—
1106C22×C4—24no—
1107C22×C4—44no—
1108C22×C4—591no—
1109C22×C4—598no—
1110C22×C4—594no—
1111C22×C4—594no—
1112C22×C4—591no—
1113C22×C4—592no—
1114C22×C4—592no—
1115C22×C4—591no—
1116C22×C4—591no—
1117C22×C4—592no—
1118C22×C4—591no—
1119C22×C4—598no—
1120C22×C4—598no—
1121C22×C4—594no—
1122C22×C4—598no—
1123C22×C4—594no—
1124C22×C4—594no—
1125C22×C4—594no—
1126C22×C4—598no—
1127C22×C4—598no—
1128C22×C4—598no—
1129C22×C4—598no—
1130C22×C4—598no—
1131C22×C4—1184no—
1132C22×C4—11832no—
1133C22×C4—1184no—
1134C22×C4—1188no—
1135C22×C4—1184no—
1136C22×C4—1184no—
1137C22×C4—1184no—
1138C22×C4—2364no—
1139C22×C4—2364no—
1140C22×C4—2364no—
1141C22×C4—2364no—
1142C22×C4—2364no—
1143C22×C4—2364no—
1144C22×C4—2364no—
1145C22×C4C23×D5914yes—
1146C22×C4C23×D5914yes—
1147C22×C4C23×D5911yescharacteristic
1148C22×C4C23×D5912yes—
1149C22×C4C23×D5912yes—
1150C22×C4C23×D5911yescharacteristic
1151C22×C4C23×D5911yescharacteristic
1152C22×C4C23×D5911yescharacteristic
1153C22×C4C23×D5912yes—
1154C22×C4C23×D5918yes—
1155C22×C4C23×D5911yescharacteristic
1156C4⋊C4—594no—
1157C4⋊C4—594no—
1158C4⋊C4—594no—
1159C4⋊C4—598no—
1160C4⋊C4—598no—
1161C4⋊C4—598no—
1162C4⋊C4—598no—
1163C4⋊C4—598no—
1164C4⋊C4—594no—
1165C4⋊C4—594no—
1166C4⋊C4—594no—
1167C4⋊C4—598no—
1168C4⋊C4—598no—
1169C4⋊C4—598no—
1170C4⋊C4—598no—
1171C4⋊C4—598no—
1172C4⋊C4—594no—
1173C4⋊C4—594no—
1174C4⋊C4C23×D5914yes—
1175C4⋊C4C23×D5914yes—
1176C4⋊C4C23×D5914yes—
1177C4⋊C4C23×D5914yes—
1178C4⋊C4C23×D5918yes—
1179C22⋊C4—598no—
1180C22⋊C4—598no—
1181C22⋊C4—598no—
1182C22⋊C4—598no—
1183C22⋊C4—594no—
1184C22⋊C4—594no—
1185C22⋊C4—598no—
1186C22⋊C4—594no—
1187C22⋊C4—594no—
1188C22⋊C4—598no—
1189C22⋊C4—598no—
1190C22⋊C4—598no—
1191C22⋊C4—598no—
1192C22⋊C4—598no—
1193C22⋊C4—598no—
1194C22⋊C4—598no—
1195C22⋊C4—594no—
1196C22⋊C4—594no—
1197C22⋊C4—594no—
1198C22⋊C4—598no—
1199C22⋊C4—594no—
1200C22⋊C4C23×D5918yes—
1201C22⋊C4C23×D5918yes—
1202C22⋊C4C23×D5918yes—
1203C22⋊C4C23×D5918yes—
1204C22⋊C4C23×D5918yes—
1205C22⋊C4C23×D5914yes—
1206C22⋊C4C23×D5914yes—
1207C42—598no—
1208C42—598no—
1209C42—598no—
1210C42—598no—
1211C42—594no—
1212C42C23×D5918yes—
1213C42C23×D5914yes—
1214C42C23×D5918yes—
1215C23—22no—
1216C23—22no—
1217C23—24no—
1218C23—22no—
1219C23—24no—
1220C23—22no—
1221C23—24no—
1222C23—22no—
1223C23—22no—
1224C23—594no—
1225C23—594no—
1226C23—592no—
1227C23—592no—
1228C23—594no—
1229C23—592no—
1230C23—11816no—
1231C23—1188no—
1232C23—1188no—
1233C23—1182no—
1234C23—1182no—
1235C23—1182no—
1236C23—1182no—
1237C23—1182no—
1238C23—1184no—
1239C23—1182no—
1240C23—1184no—
1241C23—1184no—
1242C23—1182no—
1243C23—47216no—
1244C23—2368no—
1245C23—2368no—
1246C23—2364no—
1247C23—23616no—
1248C23C24×D5912yes—
1249C23C24×D5914yes—
1250C23C24×D5912yes—
1251C23C24×D5911yescharacteristic
1252Q8—48no—
1253Q8—1188no—
1254Q8—2368no—
1255D4—28no—
1256D4—48no—
1257D4—44no—
1258D4—48no—
1259D4—11816no—
1260D4—1188no—
1261D4—1188no—
1262D4—11816no—
1263D4—1188no—
1264D4—11816no—
1265D4—1188no—
1266D4—1188no—
1267D4—1188no—
1268D4—2368no—
1269D4—2364no—
1270D4—2368no—
1271D4—2368no—
1272D4—2368no—
1273C2×C4—22no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—24no—
1277C2×C4—22no—
1278C2×C4—22no—
1279C2×C4—24no—
1280C2×C4—28no—
1281C2×C4—28no—
1282C2×C4—48no—
1283C2×C4—594no—
1284C2×C4—592no—
1285C2×C4—5916no—
1286C2×C4—592no—
1287C2×C4—594no—
1288C2×C4—594no—
1289C2×C4—592no—
1290C2×C4—592no—
1291C2×C4—594no—
1292C2×C4—592no—
1293C2×C4—1188no—
1294C2×C4—1188no—
1295C2×C4—11816no—
1296C2×C4—1188no—
1297C2×C4—1182no—
1298C2×C4—1182no—
1299C2×C4—1184no—
1300C2×C4—1184no—
1301C2×C4—1182no—
1302C2×C4—1182no—
1303C2×C4—1184no—
1304C2×C4—1188no—
1305C2×C4—1188no—
1306C2×C4—2368no—
1307C2×C4—2368no—
1308C2×C4—2368no—
1309C2×C4—2368no—
1310C2×C4—2368no—
1311C2×C4—2368no—
1312C2×C4—2368no—
1313C2×C4#41×D5914yes—
1314C2×C4C24×D5912yes—
1315C2×C4C24×D5914yes—
1316C2×C4C24×D5914yes—
1317C2×C4C24×D5912yes—
1318C2×C4C24×D5912yes—
1319C2×C4C24×D5912yes—
1320C2×C4C24×D5914yes—
1321C2×C4C24×D5912yes—
1322C22—22no—
1323C22—22no—
1324C22—24no—
1325C22—22no—
1326C22—24no—
1327C22—22no—
1328C22—24no—
1329C22—22no—
1330C22—22no—
1331C22—48no—
1332C22—44no—
1333C22—44no—
1334C22—594no—
1335C22—594no—
1336C22—1188no—
1337C22—1188no—
1338C22—1182no—
1339C22—1182no—
1340C22—1182no—
1341C22—1182no—
1342C22—1182no—
1343C22—1184no—
1344C22—1182no—
1345C22—1184no—
1346C22—1184no—
1347C22—1182no—
1348C22—47216no—
1349C22—23616no—
1350C22—2368no—
1351C22—2364no—
1352C22C2×#41×D5912yes—
1353C22H(5,𝔽2)×D5912yes—
1354C22#1683823812yes—
1355C22C25×D5911yescharacteristic
1356C4—22no—
1357C4—22no—
1358C4—24no—
1359C4—24no—
1360C4—22no—
1361C4—22no—
1362C4—24no—
1363C4—594no—
1364C4—1182no—
1365C4—1182no—
1366C4—1184no—
1367C4—1184no—
1368C4—1182no—
1369C4—1182no—
1370C4—1184no—
1371C4C2×#41×D5914yes—
1372C2—44no—
1373C2—42no—
1374C2—42no—
1375C2—1184no—
1376C2—1184no—
1377C2—2364no—
1378C2—2362no—
1379C2#2143783014yesdirect product factor
1380C2C22×#41×D5911yescharacteristic
1381C2C2×H(5,𝔽2)×D5911yescharacteristic
1382C2C2×#1683823811yescharacteristic
subgroupG/H
centerC23C24×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#555C2
socleC23×C59C25
hypercenterC2×#555D59
hypocenterC59C2×#3494
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. #21437830C2direct (N × H)
2. C2×#16838115C2semidirect
3. C2×#16838102C2semidirect
4. C2×#16838099C2semidirect
5. C2×#16838098C2semidirect
6. C2×#16838096C2semidirect
7. C2×#16838082C2semidirect
8. C2×#16838076C2semidirect
9. C2×#16838055C2semidirect
10. C2×#16838052C2semidirect
11. C2×#16838045C2semidirect
12. C2×#16838041C2semidirect
13. C2×#16838029C2semidirect
14. C2×#16838016C2semidirect
15. C2×#16838002C2semidirect
16. C2×#16837968C2semidirect
17. C2×#16837951C2semidirect
18. C2×#16837930C2semidirect
19. C2×#16837911C2semidirect
20. C2×#121×D59C2semidirect
21. C2×#16837882C2semidirect
22. C2×#16837874C2semidirect
23. C2×#117×D59C2semidirect
24. C2×C59×#555C2semidirect
25. C22×#11745689C22semidirect
27. C22×#11745687C22semidirect
31. #16838115C22semidirect
32. #16838102C22semidirect
33. #16838099C22semidirect
34. #16838098C22semidirect
35. #16838096C22semidirect
36. #16838082C22semidirect
37. #16838076C22semidirect
38. #16838055C22semidirect
39. #16838052C22semidirect
40. #16838045C22semidirect
41. #16838041C22semidirect
42. #16838029C22semidirect
43. #16838016C22semidirect
44. #16838002C22semidirect
45. #16837968C22semidirect
46. #16837951C22semidirect
47. C2×#14273726C22semidirect
48. C2×#14273725C22semidirect
49. C2×#14273723C22semidirect
50. #16837930C22semidirect
51. C2×#14273722C22semidirect
52. C2×#14273721C22semidirect
53. C2×#14273720C22semidirect
54. C2×#14273720C22semidirect
55. C2×#14273719C22semidirect
56. C2×#14273718C22semidirect
57. C2×#14273717C22semidirect
58. C2×#14273715C22semidirect
59. C2×#14273713C22semidirect
60. C2×#14273713C22semidirect
61. #16837911C22semidirect
63. C2×#14273712C22semidirect
64. C2×#14273712C22semidirect
65. C2×#14273710C22semidirect
67. C2×#14273709C22semidirect
68. C2×#14273709C22semidirect
69. C2×#14273709C22semidirect
70. C2×#14273708C22semidirect
71. C2×#14273708C22semidirect
73. C2×#14273705C22semidirect
74. C2×#14273704C22semidirect
75. C2×#14273704C22semidirect
77. C2×#14273703C22semidirect
79. C2×#14273702C22semidirect
81. C2×#14273701C22semidirect
83. C2×#14273700C22semidirect
84. C2×#14273700C22semidirect
85. C2×#14273700C22semidirect
86. C2×#14273700C22semidirect
88. C2×#14273699C22semidirect
89. C2×#14273699C22semidirect
91. C2×#14273698C22semidirect
92. C2×#14273698C22semidirect
93. #121×D59C22semidirect
98. #16837882C22semidirect
99. #16837874C22semidirect
100. C2×C4×Dic118C22semidirect
102. C2×C4×D236C22semidirect
103. C2×C4×D236C22semidirect
104. C2×C4×D236C22semidirect
105. C2×D4×Dic59C22semidirect
106. C2×#14273689C22semidirect
107. C2×C4×C22⋊D59C22semidirect
108. C2×C4×C22⋊D59C22semidirect
109. C2×C4×C22⋊D59C22semidirect
110. C2×C4×C22⋊D59C22semidirect
112. C2×(C22⋊D59)⋊C4C22semidirect
113. C2×(C22⋊D59)⋊C4C22semidirect
114. C2×(C22⋊D59)⋊C4C22semidirect
115. C2×(C22⋊D59)⋊C4C22semidirect
116. C2×#14273686C22semidirect
119. C2×#14273685C22semidirect
122. C2×#14273684C22semidirect
123. C2×#14273683C22semidirect
124. #117×D59C22semidirect
125. C22×C4⋊Dic59C22semidirect
127. C2×C4⋊C4×D59C22semidirect
128. C2×C4⋊C4×D59C22semidirect
129. C2×C4⋊C4×D59C22semidirect
134. C2×C42×D59C22semidirect
135. C59×#555C22semidirect
136. C2×C4⋊Q8×C59C22semidirect
137. C2×#124×C59C22semidirect
138. C2×#124×C59C22semidirect
140. C2×#121×C59C22semidirect
141. C2×#121×C59C22semidirect
142. C2×C4×D4×C59C22semidirect
143. C2×C4×D4×C59C22semidirect
144. C2×#117×C59C22semidirect
145. C2×#117×C59C22semidirect
146. C2×#117×C59C22semidirect
150. C2×#11745689C23semidirect
154. C2×#11745687C23semidirect
191. #14273726C23semidirect
192. #14273725C23semidirect
193. #14273723C23semidirect
194. #14273722C23semidirect
195. #14273721C23semidirect
196. #14273720C23semidirect
197. #14273720C23semidirect
198. #14273719C23semidirect
199. #14273718C23semidirect
200. #14273717C23semidirect
201. #14273715C23semidirect
202. #14273713C23semidirect
203. #14273713C23semidirect
205. #14273712C23semidirect
206. #14273712C23semidirect
207. #14273710C23semidirect
209. #14273709C23semidirect
210. #14273709C23semidirect
211. #14273709C23semidirect
212. #14273708C23semidirect
213. #14273708C23semidirect
215. #14273705C23semidirect
216. #14273704C23semidirect
217. #14273704C23semidirect
219. #14273703C23semidirect
221. #14273702C23semidirect
223. #14273701C23semidirect
225. #14273700C23semidirect
226. #14273700C23semidirect
227. #14273700C23semidirect
228. #14273700C23semidirect
230. #14273699C23semidirect
231. #14273699C23semidirect
233. #14273698C23semidirect
234. #14273698C23semidirect
239. C4×Dic118C23semidirect
241. C4×D236C23semidirect
242. C4×D236C23semidirect
243. C4×D236C23semidirect
244. D4×Dic59C23semidirect
245. #14273689C23semidirect
246. C4×C22⋊D59C23semidirect
247. C4×C22⋊D59C23semidirect
248. C4×C22⋊D59C23semidirect
249. C4×C22⋊D59C23semidirect
251. (C22⋊D59)⋊C4C23semidirect
252. (C22⋊D59)⋊C4C23semidirect
253. (C22⋊D59)⋊C4C23semidirect
254. (C22⋊D59)⋊C4C23semidirect
255. #14273686C23semidirect
258. #14273685C23semidirect
261. #14273684C23semidirect
262. #14273683C23semidirect
269. C2×C4⋊Dic59C23semidirect
283. C4⋊C4×D59C23semidirect
284. C4⋊C4×D59C23semidirect
285. C4⋊C4×D59C23semidirect
316. C42×D59C23semidirect
325. C4⋊Q8×C59C23semidirect
326. #124×C59C23semidirect
327. #124×C59C23semidirect
329. #121×C59C23semidirect
330. #121×C59C23semidirect
331. C4×D4×C59C23semidirect
332. C4×D4×C59C23semidirect
333. #117×C59C23semidirect
334. #117×C59C23semidirect
335. #117×C59C23semidirect
448. C2×C4×D59#41semidirect
627. C4×D59C2×#41semidirect
683. C2×#555D59semidirect
708. C2×C59#3494semidirect
723. #555C2×D59semidirect
741. C2×C4⋊Q8C2×D59semidirect
754. C2×#124C2×D59semidirect
755. C2×#124C2×D59semidirect
790. C2×#121C2×D59semidirect
791. C2×#121C2×D59semidirect
814. C2×C4×D4C2×D59semidirect
815. C2×C4×D4C2×D59semidirect
825. C2×#117C2×D59semidirect
826. C2×#117C2×D59semidirect
827. C2×#117C2×D59semidirect
838. C59C2×#3494semidirect
893. C4⋊Q8C22×D59semidirect
905. #124C22×D59semidirect
906. #124C22×D59semidirect
939. #121C22×D59semidirect
940. #121C22×D59semidirect
961. C4×D4C22×D59semidirect
962. C4×D4C22×D59semidirect
971. #117C22×D59semidirect
972. #117C22×D59semidirect
973. #117C22×D59semidirect
1379. C2#21437830direct (N × H)

Maximal subgroups

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

subgroupindex
#214378302
C2×#168381152
C2×#168381022
C2×#168380992
C2×#168380982
C2×#168380962
C2×#168380822
C2×#168380762
C2×#168380552
C2×#168380522
C2×#168380452
C2×#168380412
C2×#168380292
C2×#168380162
C2×#168380022
C2×#168379682
C2×#168379512
C2×#168379302
C2×#168379112
C2×#121×D592
C2×#168378822
C2×#168378742
C2×#117×D592
C2×C59×#5552
C2×#349459