Finite Group Databasebeta

← C2×#21437702 #29495771

Subgroups — C2×#21437702 #29495771

Order 15104.

8722 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21437702C2132yesmaximal, direct product factor
2C2×#16838134C211yesmaximal, characteristic, complemented
3C2×#16838110C211yesmaximal, characteristic, complemented
4C2×#16838108C211yesmaximal, characteristic, complemented
5C2×#16838105C211yesmaximal, characteristic, complemented
6C2×#16838104C211yesmaximal, characteristic, complemented
7C2×#16838103C212yesmaximal, complemented
8C2×#16838077C212yesmaximal, complemented
9C2×#16838075C212yesmaximal, complemented
10C2×#16838045C211yesmaximal, characteristic, complemented
11C2×#16838044C212yesmaximal, complemented
12C2×#16838043C211yesmaximal, characteristic, complemented
13C2×#16838036C211yesmaximal, characteristic, complemented
14C2×#16837949C211yesmaximal, characteristic, complemented
15C2×#16837939C211yesmaximal, characteristic, complemented
16C2×#16837930C212yesmaximal, complemented
17C2×#16837914C212yesmaximal, complemented
18C2×#16837911C212yesmaximal, complemented
19C2×C4×#11745689C211yesmaximal, characteristic, complemented
20C2×C4×#11745685C211yesmaximal, characteristic, complemented
21C22×C4×D236C211yesmaximal, characteristic, complemented
22C2×C4×D4×D59C212yesmaximal, complemented
23C2×C4×D4×D59C211yesmaximal, characteristic, complemented
24C2×C59×#529C211yesmaximal, characteristic, complemented
25C22×#11745689C2211yescharacteristic
26C22×#11745685C2211yescharacteristic
27C22×#11745685C2212yescomplemented
28C23×D236C2211yescharacteristic
29C22×D4×D59C2212yes—
30C22×D4×D59C2211yescharacteristic
31C23×C4×D59C2212yescomplemented
32C23×C4×D59C2212yescomplemented
33#16838134C22116yescomplemented
34#16838110C22116yescomplemented
35#16838108C22116yescomplemented
36#16838105C22116yescomplemented
37#16838104C22116yescomplemented
38#16838103C22132yescomplemented
39#16838077C22132yescomplemented
40#16838075C22132yescomplemented
41#16838045C22116yescomplemented
42#16838044C22132yescomplemented
43#16838043C22116yescomplemented
44#16838036C22116yescomplemented
45#16837949C22116yescomplemented
46C2×#14273726C2211yescharacteristic, complemented
47C2×#14273723C2211yescharacteristic
48#16837939C22116yescomplemented
49#16837930C22132yescomplemented
50C2×#14273722C2212yescomplemented
51C2×#14273722C2212yescomplemented
52C2×#14273720C2212yescomplemented
53C2×#14273718C2211yescharacteristic, complemented
54C2×#14273717C2212yescomplemented
55C2×#14273716C2211yescharacteristic, complemented
56C2×#14273713C2212yescomplemented
57C2×#14273713C2212yescomplemented
58#16837914C22132yescomplemented
59#16837911C22132yescomplemented
60C2×#14273712C2212yescomplemented
61C2×#14273712C2212yescomplemented
62C2×#14273712C2212yescomplemented
63C2×#14273711C2212yescomplemented
64C2×#14273711C2212yescomplemented
65C2×#14273709C2212yescomplemented
66C2×#14273709C2212yescomplemented
67C2×#14273707C2212yescomplemented
68C2×#14273707C2212yescomplemented
69C2×#14273705C2212yescomplemented
70C2×#14273705C2212yescomplemented
71C2×#14273704C2212yescomplemented
72C2×#14273703C2211yescharacteristic, complemented
73C2×#14273702C2211yescharacteristic
74C2×#14273702C2212yescomplemented
75C2×#14273702C2211yescharacteristic, complemented
76C2×#14273702C2212yescomplemented
77C2×#14273700C2212yes—
78C2×#14273700C2212yescomplemented
79C2×#14273700C2212yescomplemented
80C2×#14273699C2212yescomplemented
81C2×#14273698C2211yescharacteristic, complemented
82C2×#14273697C2212yes—
83C2×#14273697C2212yescomplemented
84C2×#14273697C2212yescomplemented
85C2×#14273695C2212yes—
86C4×#11745689C22116yescomplemented
87C4×#11745685C22116yescomplemented
88C2×Q8×Dic59C2211yescharacteristic, complemented
89C2×C4×Dic118C2211yescharacteristic, complemented
90C2×C4×Dic118C2211yescharacteristic, complemented
91C2×C4×D236C2211yescharacteristic
92C2×C4×D236C2211yescharacteristic
93C2×C4×D236C2212yescomplemented
94C2×C4×D236C2212yescomplemented
95C2×C4×D236C2212yescomplemented
96C2×C4×D236C2211yescharacteristic, complemented
97C2×C4×D236C2211yescharacteristic, complemented
98C2×C4×D236C2211yescharacteristic, complemented
99C2×C4×D236C2211yescharacteristic, complemented
100C2×C4×D236C2212yescomplemented
101C2×C4×D236C22116yescomplemented
102C2×D4×Dic59C2212yescomplemented
103C2×D4×Dic59C2211yescharacteristic, complemented
104C2×#14273689C2211yescharacteristic
105C2×#14273689C2211yescharacteristic
106C2×#14273689C2212yescomplemented
107C2×#14273689C2212yescomplemented
108C2×C4×C22⋊D59C2211yescharacteristic
109C2×C4×C22⋊D59C2211yescharacteristic
110C2×C4×C22⋊D59C2212yescomplemented
111C2×C4×C22⋊D59C2212yescomplemented
112C2×C4×C22⋊D59C2211yescharacteristic, complemented
113C2×C4×C22⋊D59C2211yescharacteristic, complemented
114C2×(C22⋊D59)⋊C4C2212yes—
115C2×(C22⋊D59)⋊C4C2212yescomplemented
116C2×(C22⋊D59)⋊C4C2212yescomplemented
117C4×D4×D59C22132yescomplemented
118C4×D4×D59C22116yescomplemented
119C2×#14273686C2211yescharacteristic, complemented
120C2×#14273685C2212yescomplemented
121C2×#14273685C2211yescharacteristic, complemented
122C2×#14273684C2211yescharacteristic, complemented
123C2×#14273684C2211yescharacteristic, complemented
124C2×#14273684C2212yescomplemented
125C22×C4⋊Dic59C2211yescharacteristic, complemented
126C2×C4⋊C4×D59C2212yescomplemented
127C2×C4⋊C4×D59C2211yescharacteristic, complemented
128C22×(C2×D59)⋊C4C2212yescomplemented
129C2×C22⋊C4×D59C2212yescomplemented
130C2×C22⋊C4×D59C2212yescomplemented
131C2×C22⋊C4×D59C2212yescomplemented
132C2×C42×D59C2211yescharacteristic, complemented
133C2×C42×D59C2212yescomplemented
134C2×C42×D59C2211yescharacteristic, complemented
135C59×#529C22116yescomplemented
136C2×#126×C59C2212yescomplemented
137C2×#125×C59C2211yescharacteristic, complemented
138C2×#124×C59C2211yescharacteristic, complemented
139C2×#123×C59C2212yescomplemented
140C2×C22⋊Q8×C59C2211yescharacteristic, complemented
141C2×#121×C59C2211yescharacteristic
142C2×C4×Q8×C59C2211yescharacteristic, complemented
143C2×C4×D4×C59C2212yescomplemented
144C2×C4×D4×C59C2211yescharacteristic, complemented
145C2×#117×C59C2212yescomplemented
146C22×C42×C59C2211yescharacteristic, complemented
147C24×D59C2312yes—
148C24×D59C2312yes—
149C2×#11745689—28no—
150C2×#11745689C2318yes—
151C2×#11745685—28no—
152C2×#11745685—48no—
153C2×#11745685C2318yes—
154C2×#11745685C23116yescomplemented
155C22×Dic118C2311yescharacteristic
156C22×Dic118C2312yes—
157C22×D236—28no—
158C22×D236C2312yes—
159C22×D236C2312yes—
160C22×D236C2312yes—
161C22×D236C2311yescharacteristic
162C22×D236C2311yescharacteristic
163C22×D236C2318yes—
164C22×D236C2312yes—
165C22×D236C2311yescharacteristic
166C22×C22⋊D59C2311yescharacteristic
167C22×C22⋊D59C2312yes—
168C22×C22⋊D59C2312yes—
169C22×C22⋊D59C2312yes—
170C22×C22⋊D59C2312yes—
171C22×C22⋊D59C2311yescharacteristic
172C2×D4×D59—216no—
173C2×D4×D59—28no—
174C2×D4×D59C23116yes—
175C2×D4×D59C2318yes—
176C23×Dic59C2312yes—
177C23×Dic59C2312yes—
178C22×C4×D59—48no—
179C22×C4×D59—48no—
180C22×C4×D59C2311yescharacteristic
181C22×C4×D59C2312yes—
182C22×C4×D59C2311yescharacteristic
183C22×C4×D59C2311yescharacteristic
184C22×C4×D59C2312yes—
185C22×C4×D59C2311yescharacteristic
186C22×C4×D59C2311yescharacteristic
187C22×C4×D59C2312yes—
188C22×C4×D59C2312yes—
189C22×C4×D59C2311yescharacteristic
190C22×C4×D59C2312yes—
191C22×C4×D59C2312yes—
192C22×C4×D59C2312yes—
193C22×C4×D59C2312yes—
194C22×C4×D59C23116yescomplemented
195C22×C4×D59C23116yescomplemented
196#14273726C2318yescomplemented
197#14273723C2318yes—
198#14273722C23116yescomplemented
199#14273722C23116yescomplemented
200#14273720C23116yescomplemented
201#14273718C2318yescomplemented
202#14273717C23116yescomplemented
203#14273716C2318yescomplemented
204#14273713C23116yescomplemented
205#14273713C23116yescomplemented
206#14273712C23116yescomplemented
207#14273712C23116yescomplemented
208#14273712C23116yescomplemented
209#14273711C23116yescomplemented
210#14273711C23116yescomplemented
211#14273709C23116yescomplemented
212#14273709C23116yescomplemented
213#14273707C23116yescomplemented
214#14273707C23116yescomplemented
215#14273705C23116yescomplemented
216#14273705C23116yescomplemented
217#14273704C23116yescomplemented
218#14273703C2318yescomplemented
219#14273702C2318yes—
220#14273702C23116yescomplemented
221#14273702C23116yescomplemented
222#14273702C2318yescomplemented
223#14273700C23116yes—
224#14273700C23116yescomplemented
225#14273700C23116yescomplemented
226#14273699C23116yescomplemented
227#14273698C2318yescomplemented
228#14273697C23116yes—
229#14273697C23116yescomplemented
230#14273697C23116yescomplemented
231#14273695C23116yes—
232Q8×Dic59C2318yescomplemented
233C4×Dic118C2318yescomplemented
234C4×Dic118C2318yescomplemented
235C4×D236C2318yes—
236C4×D236C2318yes—
237C4×D236C23116yescomplemented
238C4×D236C2318yescomplemented
239C4×D236C23116yescomplemented
240C4×D236C23116yescomplemented
241C4×D236C2318yescomplemented
242C4×D236C2318yescomplemented
243C4×D236C23116yescomplemented
244C4×D236C2318yescomplemented
245D4×Dic59C23116yescomplemented
246D4×Dic59C2318yescomplemented
247#14273689C2318yes—
248#14273689C2318yes—
249#14273689C23116yescomplemented
250#14273689C23116yescomplemented
251C4×C22⋊D59C2318yes—
252C4×C22⋊D59C2318yes—
253C4×C22⋊D59C2318yescomplemented
254C4×C22⋊D59C23116yescomplemented
255C4×C22⋊D59C23116yescomplemented
256C4×C22⋊D59C2318yescomplemented
257(C22⋊D59)⋊C4C23116yes—
258(C22⋊D59)⋊C4C23116yescomplemented
259(C22⋊D59)⋊C4C23116yescomplemented
260#14273686C2318yescomplemented
261#14273685C23116yescomplemented
262#14273685C2318yescomplemented
263#14273684C23116yescomplemented
264#14273684C2318yescomplemented
265#14273684C2318yescomplemented
266C2×C4⋊Dic59C2311yescharacteristic
267C2×C4⋊Dic59C2312yes—
268C2×C4⋊Dic59C2311yescharacteristic
269C2×C4⋊Dic59C2312yes—
270C2×C4⋊Dic59C2312yes—
271C2×C4⋊Dic59C2311yescharacteristic
272C2×C4⋊Dic59C2311yescharacteristic
273C2×C4⋊Dic59C2318yescomplemented
274C2×Dic59⋊C4C2312yes—
275C2×Dic59⋊C4C2311yescharacteristic
276C2×Dic59⋊C4C2312yes—
277C2×Dic59⋊C4C2312yes—
278C2×Dic59⋊C4C2312yes—
279C2×Dic59⋊C4C2311yescharacteristic
280C2×Dic59⋊C4C2311yescharacteristic
281C2×Dic59⋊C4C2311yescharacteristic
282C4⋊C4×D59C23116yescomplemented
283C4⋊C4×D59C2318yescomplemented
284C2×C22⋊Dic59C2312yes—
285C2×C22⋊Dic59C2312yes—
286C2×C22⋊Dic59C2311yescharacteristic
287C2×C22⋊Dic59C2311yescharacteristic
288C2×(C2×D59)⋊C4C2311yescharacteristic
289C2×(C2×D59)⋊C4C2312yes—
290C2×(C2×D59)⋊C4C2312yes—
291C2×(C2×D59)⋊C4C2312yes—
292C2×(C2×D59)⋊C4C2312yes—
293C2×(C2×D59)⋊C4C2312yes—
294C2×(C2×D59)⋊C4C2312yes—
295C2×(C2×D59)⋊C4C2312yes—
296C2×(C2×D59)⋊C4C2311yescharacteristic
297C2×(C2×D59)⋊C4C2312yes—
298C2×(C2×D59)⋊C4C2311yescharacteristic
299C2×(C2×D59)⋊C4C2312yes—
300C2×(C2×D59)⋊C4C2312yes—
301C2×(C2×D59)⋊C4C2312yes—
302C2×(C2×D59)⋊C4C2311yescharacteristic
303C2×(C2×D59)⋊C4C2312yes—
304C2×(C2×D59)⋊C4C23116yescomplemented
305C22⋊C4×D59C23116yescomplemented
306C22⋊C4×D59C23116yescomplemented
307C22⋊C4×D59C23116yescomplemented
308C2×C4×Dic59C2311yescharacteristic
309C2×C4×Dic59C2312yes—
310C2×C4×Dic59C2311yescharacteristic
311C2×C4×Dic59C2312yes—
312C2×C4×Dic59C2311yescharacteristic
313C2×C4×Dic59C2311yescharacteristic
314C2×C4×Dic59C2311yescharacteristic
315C2×C4×Dic59C2311yescharacteristic
316C42×D59C23116yescomplemented
317C42×D59C2318yescomplemented
318C42×D59C2318yescomplemented
319C22×Q8×C59C2311yescharacteristic
320C22×D4×C59C2311yescharacteristic
321C22×D4×C59C2312yes—
322C23×C4×C59C2311yescharacteristic
323C23×C4×C59C2312yes—
324C23×C4×C59C2311yescharacteristic
325C23×C4×C59C2311yescharacteristic
326#126×C59C23116yescomplemented
327#125×C59C2318yescomplemented
328#124×C59C2318yescomplemented
329#123×C59C23116yescomplemented
330C22⋊Q8×C59C2318yescomplemented
331#121×C59C2318yes—
332C4×Q8×C59C2318yescomplemented
333C4×D4×C59C23116yescomplemented
334C4×D4×C59C2318yescomplemented
335#117×C59C23116yescomplemented
336C2×C4⋊C4×C59C2311yescharacteristic
337C2×C4⋊C4×C59C2312yes—
338C2×C4⋊C4×C59C2312yes—
339C2×C4⋊C4×C59C2311yescharacteristic
340C2×C4⋊C4×C59C2312yes—
341C2×C4⋊C4×C59C2312yes—
342C2×C22⋊C4×C59C2312yes—
343C2×C22⋊C4×C59C2312yes—
344C2×C22⋊C4×C59C2312yes—
345C2×C22⋊C4×C59C2312yes—
346C2×C22⋊C4×C59C2312yes—
347C2×C42×C59C2311yescharacteristic
348C2×C42×C59C2311yescharacteristic
349C2×C42×C59C2311yescharacteristic
350C2×C42×C59C2311yescharacteristic
351C2×C42×C59C2312yes—
352C2×C42×C59C2318yescomplemented
353C24×C59C2412yes—
354C24×C59C2411yescharacteristic
355C23×D59—28no—
356C23×D59—28no—
357C23×D59—28no—
358C23×D59—28no—
359C23×D59—44no—
360C23×D59—44no—
361C23×D59C2412yes—
362C23×D59C2411yescharacteristic
363C23×D59C2418yes—
364C23×D59C2418yes—
365C23×D59C2411yescharacteristic
366C23×D59C2412yes—
367C2×Q8×C59—24no—
368C2×Q8×C59C2414yes—
369C2×D4×C59—28no—
370C2×D4×C59—24no—
371C2×D4×C59C2418yes—
372C2×D4×C59C2414yes—
373C22×C4×C59—24no—
374C22×C4×C59—24no—
375C22×C4×C59—24no—
376C22×C4×C59—28no—
377C22×C4×C59C2411yescharacteristic
378C22×C4×C59C2411yescharacteristic
379C22×C4×C59C2411yescharacteristic
380C22×C4×C59C2411yescharacteristic
381C22×C4×C59C2412yes—
382C22×C4×C59C2412yes—
383C22×C4×C59C2414yes—
384C22×C4×C59C2414yes—
385C22×C4×C59C2414yes—
386C22×C4×C59C2412yes—
387C22×C4×C59C2418yes—
388C22×C4×C59C2411yescharacteristic
389C22×C4×C59C2411yescharacteristic
390C2×C22⋊D59—24no—
391C2×C22⋊D59—28no—
392C2×C22⋊D59—28no—
393C2×C22⋊D59—44no—
394C2×C22⋊D59—44no—
395C2×C22⋊D59#4118yescomplemented
396C2×C22⋊D59C2418yes—
397C2×C22⋊D59C2418yes—
398C2×C22⋊D59C2414yes—
399C2×C22⋊D59C2418yes—
400C2×C22⋊D59C2418yes—
401C2×C22⋊D59C2414yes—
402C22×Dic59—44no—
403C22×Dic59—44no—
404C22×Dic59C2411yescharacteristic
405C22×Dic59C2411yescharacteristic
406C22×Dic59C2411yescharacteristic
407C22×Dic59C2412yes—
408C22×Dic59C2411yescharacteristic
409C22×Dic59C2411yescharacteristic
410C22×Dic59C2412yes—
411C22×Dic59C2418yes—
412C22×Dic59C2418yes—
413C22×Dic59C2411yescharacteristic
414#11745689—232no—
415D4×D59—264no—
416D4×D59—232no—
417#11745685—232no—
418#11745685—432no—
419C2×D236—28no—
420C2×D236—28no—
421C2×D236—24no—
422C2×D236—28no—
423C2×D236—24no—
424C2×D236—232no—
425C2×D236—44no—
426C2×D236#4118yescomplemented
427C2×D236C2418yes—
428C2×D236C2418yes—
429C2×D236C2418yes—
430C2×D236C2414yes—
431C2×D236C2414yes—
432C2×D236C2418yes—
433C2×D236C2414yes—
434C2×C4×D59—24no—
435C2×C4×D59—28no—
436C2×C4×D59—24no—
437C2×C4×D59—24no—
438C2×C4×D59—24no—
439C2×C4×D59—28no—
440C2×C4×D59—28no—
441C2×C4×D59—24no—
442C2×C4×D59—28no—
443C2×C4×D59—24no—
444C2×C4×D59—432no—
445C2×C4×D59—432no—
446C2×C4×D59—44no—
447C2×C4×D59—44no—
448C2×C4×D59—44no—
449C2×C4×D59—44no—
450C2×C4×D59C2414yes—
451C2×C4×D59C2418yes—
452C2×C4×D59C2414yes—
453C2×C4×D59C2418yes—
454C2×C4×D59C2414yes—
455C2×C4×D59C2414yes—
456C2×C4×D59C2414yes—
457C2×C4×D59C2418yes—
458C2×C4×D59C2414yes—
459C2×C4×D59C2418yes—
460C2×C4×D59C2418yes—
461C2×C4×D59C2418yes—
462C2×C4×D59C2418yes—
463C2×C4×D59C2418yes—
464C2×Dic118—24no—
465C2×Dic118—44no—
466C2×Dic118C2414yes—
467C2×Dic118C2418yes—
468C4⋊C4×C59C2418yes—
469C4⋊C4×C59C2418yes—
470C4⋊C4×C59C2414yes—
471C4⋊C4×C59C2418yes—
472C4⋊C4×C59C2414yes—
473C4⋊C4×C59C2418yes—
474C22⋊C4×C59C2418yes—
475C22⋊C4×C59C2418yes—
476C22⋊C4×C59C2418yes—
477C22⋊C4×C59C2418yes—
478C22⋊C4×C59C2418yes—
479C42×C59C2414yes—
480C42×C59C2414yes—
481C42×C59C2414yes—
482C42×C59C2414yes—
483C42×C59C2418yes—
484C22⋊Dic59C2414yes—
485C22⋊Dic59C2418yes—
486C22⋊Dic59C2418yes—
487C22⋊Dic59C2414yes—
488(C2×D59)⋊C4C2414yes—
489(C2×D59)⋊C4C2418yes—
490(C2×D59)⋊C4C2418yes—
491(C2×D59)⋊C4C2418yes—
492(C2×D59)⋊C4C2418yes—
493(C2×D59)⋊C4C2418yes—
494(C2×D59)⋊C4C2418yes—
495(C2×D59)⋊C4C2418yes—
496(C2×D59)⋊C4C2418yes—
497(C2×D59)⋊C4C2414yes—
498(C2×D59)⋊C4C2414yes—
499(C2×D59)⋊C4C2414yes—
500(C2×D59)⋊C4C2418yes—
501(C2×D59)⋊C4C2418yes—
502(C2×D59)⋊C4C2418yes—
503(C2×D59)⋊C4C2418yes—
504C4⋊Dic59C2414yes—
505C4⋊Dic59C2418yes—
506C4⋊Dic59C2414yes—
507C4⋊Dic59C2418yes—
508C4⋊Dic59C2418yes—
509C4⋊Dic59C2414yes—
510C4⋊Dic59C2414yes—
511Dic59⋊C4C2414yes—
512Dic59⋊C4C2418yes—
513Dic59⋊C4C2418yes—
514Dic59⋊C4C2414yes—
515Dic59⋊C4C2414yes—
516Dic59⋊C4C2414yes—
517Dic59⋊C4C2418yes—
518Dic59⋊C4C2418yes—
519C4×Dic59C2414yes—
520C4×Dic59C2414yes—
521C4×Dic59C2414yes—
522C4×Dic59C2414yes—
523C4×Dic59C2418yes—
524C4×Dic59C2418yes—
525C4×Dic59C2414yes—
526C4×Dic59C2414yes—
527C23×C59—22no—
528C23×C59—22no—
529C23×C59—24no—
530C23×C59—24no—
531C23×C59—24no—
532C23×C59C2×#4114yes—
533C23×C59C2514yes—
534C23×C59C2512yes—
535C23×C59C2511yescharacteristic
536C22×D59—22no—
537C22×D59—24no—
538C22×D59—22no—
539C22×D59—24no—
540C22×D59—22no—
541C22×D59—22no—
542C22×D59—24no—
543C22×D59—24no—
544C22×D59—216no—
545C22×D59—24no—
546C22×D59—22no—
547C22×D59—216no—
548C22×D59—216no—
549C22×D59—216no—
550C22×D59—48no—
551C22×D59—48no—
552C22×D59—432no—
553C22×D59—432no—
554C22×D59C2×#4114yes—
555C22×D59C2×#4118yes—
556C22×D59C2514yes—
557C22×D59C2512yes—
558C22×D59C2512yes—
559C22×D59C2514yes—
560Q8×C59—28no—
561D4×C59—216no—
562D4×C59—28no—
563C2×C4×C59—22no—
564C2×C4×C59—22no—
565C2×C4×C59—24no—
566C2×C4×C59—24no—
567C2×C4×C59—22no—
568C2×C4×C59—28no—
569C2×C4×C59—24no—
570C2×C4×C59—22no—
571C2×C4×C59—28no—
572C2×C4×C59—28no—
573C2×C4×C59—216no—
574C2×C4×C59C2×#4114yes—
575C2×C4×C59H(5,𝔽2)14yes—
576C2×C4×C59C2512yes—
577C2×C4×C59C2514yes—
578C2×C4×C59C2514yes—
579C2×C4×C59C2512yes—
580C2×C4×C59C2512yes—
581C2×C4×C59C2514yes—
582C2×C4×C59C2512yes—
583C2×C4×C59C2512yes—
584C2×C4×C59C2512yes—
585C22⋊D59—28no—
586C22⋊D59—216no—
587C22⋊D59—216no—
588C22⋊D59—48no—
589C22⋊D59—48no—
590C22⋊D59C2×#41116yescomplemented
591C2×Dic59—22no—
592C2×Dic59—22no—
593C2×Dic59—22no—
594C2×Dic59—22no—
595C2×Dic59—24no—
596C2×Dic59—22no—
597C2×Dic59—24no—
598C2×Dic59—48no—
599C2×Dic59—48no—
600C2×Dic59C2×#4114yes—
601C2×Dic59C2512yes—
602C2×Dic59C2512yes—
603C2×Dic59C2512yes—
604C2×Dic59C2512yes—
605C2×Dic59C2512yes—
606C2×Dic59C2514yes—
607C2×Dic59C2514yes—
608C2×Dic59C2512yes—
609D236—216no—
610D236—28no—
611D236—216no—
612D236—216no—
613D236—28no—
614D236—48no—
615D236C2×#41116yescomplemented
616C4×D59—28no—
617C4×D59—216no—
618C4×D59—28no—
619C4×D59—28no—
620C4×D59—28no—
621C4×D59—216no—
622C4×D59—216no—
623C4×D59—28no—
624C4×D59—28no—
625C4×D59—216no—
626C4×D59—48no—
627C4×D59—48no—
628C4×D59—48no—
629C4×D59—48no—
630Dic118—28no—
631Dic118—48no—
632C2×#3481—591nomaximal, Sylow
633C22×C59—22no—
634C22×C59—22no—
635C22×C59—28no—
636C22×C59—24no—
637C22×C59—24no—
638C22×C59—24no—
639C22×C59—48no—
640C22×C59C22×#4114yes—
641C22×C59C22×#4112yes—
642C22×C59C22×#4112yes—
643C22×C59C2×H(5,𝔽2)12yes—
644C22×C59C2611yescharacteristic
645C2×D59—22no—
646C2×D59—24no—
647C2×D59—22no—
648C2×D59—24no—
649C2×D59—28no—
650C2×D59—216no—
651C2×D59—22no—
652C2×D59—22no—
653C2×D59—24no—
654C2×D59—24no—
655C2×D59—24no—
656C2×D59—22no—
657C2×D59—432no—
658C2×D59—432no—
659C2×D59—44no—
660C2×D59—48no—
661C2×D59C22×#4114yes—
662C2×D59C22×#4118yes—
663C4×C59—22no—
664C4×C59—22no—
665C4×C59—24no—
666C4×C59—24no—
667C4×C59—22no—
668C4×C59—24no—
669C4×C59—22no—
670C4×C59C22×#4114yes—
671C4×C59C2×H(5,𝔽2)14yes—
672Dic59—22no—
673Dic59—22no—
674Dic59—22no—
675Dic59—22no—
676Dic59—24no—
677Dic59—22no—
678Dic59—24no—
679Dic59C22×#4114yes—
680#3481—5932no—
681C2×#559—591no—
682C2×#554—591no—
683C2×#554—591no—
684C2×#553—592no—
685C2×#553—591no—
686C2×#553—591no—
687C2×#551—592no—
688C2×#551—592no—
689C2×#546—591no—
690C2×#546—592no—
691C2×#546—591no—
692C2×D42—591no—
693C2×#532—591no—
694C2×#529—591no—
695C2×#529—592no—
696C2×#529D5911yescharacteristic, complemented
697C2×#525—592no—
698C2×#525—592no—
699C2×C4×#41—591no—
700C2×C4×#41—591no—
701C22×C4×D4—591no—
702C22×C4×D4—592no—
703C22×C4×D4—591no—
704C2×C59—24no—
705C2×C59—44no—
706C2×C59#348114yescomplemented
707C2×C59C23×#4111yescharacteristic
708C2×C59C23×#4111yescharacteristic
709C2×C59C22×H(5,𝔽2)11yescharacteristic
710D59—24no—
711D59—28no—
712D59—42no—
713D59—44no—
714C22×#41—591no—
715C22×#41—591no—
716C22×#41—592no—
717C23×D4—592no—
718C23×D4—591no—
719C23×D4—591no—
720C24×C4—592no—
721C24×C4—592no—
722#559—5916no—
723#554—5916no—
724#554—5916no—
725#553—5932no—
726#553—5916no—
727#553—5916no—
728#551—5932no—
729#551—5932no—
730#546—5916no—
731#546—5932no—
732#546—5916no—
733D42—5916no—
734#532—5916no—
735C2×C4⋊Q8—591no—
736C2×#127—591no—
737#529—5916no—
738#529—5932no—
739#529C2×D59116yescomplemented
740C2×#126—592no—
741C2×#126—592no—
742C2×#126—592no—
743C2×#126C2×D5912yescomplemented
744C2×#125—592no—
745C2×#125—591no—
746C2×#125C2×D5911yescharacteristic, complemented
747C2×#124—591no—
748C2×#124—592no—
749C2×#124—592no—
750C2×#124C2×D5911yescharacteristic, complemented
751#525—5932no—
752#525—5932no—
753C2×#123—592no—
754C2×#123—592no—
755C2×#123—592no—
756C2×#123—592no—
757C2×#123—592no—
758C2×#123—592no—
759C2×#123—592no—
760C2×#123C2×D5912yescomplemented
761C2×C22⋊Q8—591no—
762C2×C22⋊Q8—592no—
763C2×C22⋊Q8—592no—
764C2×C22⋊Q8—592no—
765C2×C22⋊Q8—592no—
766C2×C22⋊Q8—592no—
767C2×C22⋊Q8C2×D5911yescharacteristic, complemented
768C2×#121—591no—
769C2×#121—592no—
770C2×#121—591no—
771C2×#121—592no—
772C2×#121—592no—
773C2×#121—591no—
774C2×#121—592no—
775C2×#121—592no—
776C2×#121—592no—
777C2×#121C2×D5911yescharacteristic
778C2×#120—592no—
779C2×#120—592no—
780C2×#120—592no—
781C2×#120—592no—
782C4×#41—5916no—
783C4×#41—5916no—
784C2×C4×Q8—591no—
785C2×C4×Q8—591no—
786C2×C4×Q8—591no—
787C2×C4×Q8C2×D5911yescharacteristic, complemented
788C2×C4×D4—592no—
789C2×C4×D4—591no—
790C2×C4×D4—591no—
791C2×C4×D4—592no—
792C2×C4×D4—592no—
793C2×C4×D4—591no—
794C2×C4×D4—591no—
795C2×C4×D4—591no—
796C2×C4×D4—5932no—
797C2×C4×D4—5916no—
798C2×C4×D4—591no—
799C2×C4×D4—592no—
800C2×C4×D4—591no—
801C2×C4×D4—592no—
802C2×C4×D4—592no—
803C2×C4×D4—592no—
804C2×C4×D4—592no—
805C2×C4×D4—591no—
806C2×C4×D4—592no—
807C2×C4×D4—592no—
808C2×C4×D4—591no—
809C2×C4×D4—591no—
810C2×C4×D4—592no—
811C2×C4×D4—591no—
812C2×C4×D4—592no—
813C2×C4×D4—591no—
814C2×C4×D4—591no—
815C2×C4×D4—5916no—
816C2×C4×D4C2×D5912yescomplemented
817C2×C4×D4C2×D5911yescharacteristic, complemented
818C2×#117—591no—
819C2×#117—592no—
820C2×#117—591no—
821C2×#117—591no—
822C2×#117—591no—
823C2×#117—592no—
824C2×#117C2×D5912yescomplemented
825C22×C4⋊C4—591no—
826C22×C4⋊C4—592no—
827C22×C4⋊C4—591no—
828C22×C22⋊C4—592no—
829C22×C22⋊C4—592no—
830C22×C22⋊C4—592no—
831C22×C22⋊C4—592no—
832C22×C42—591no—
833C22×C42—592no—
834C22×C42—591no—
835C22×C42C2×D5911yescharacteristic, complemented
836C59C2×#348111yescharacteristic, complemented, Sylow
837C25—592no—
838C25—592no—
839C2×#41—598no—
840C2×#41—598no—
841C2×#41—5916no—
842C2×#41—1188no—
843C2×#41—1188no—
844C2×#41—2368no—
845C22×Q8—591no—
846C22×Q8—592no—
847C22×Q8C22×D5911yescharacteristic
848C22×D4—591no—
849C22×D4—591no—
850C22×D4—592no—
851C22×D4—592no—
852C22×D4—592no—
853C22×D4—592no—
854C22×D4—5916no—
855C22×D4—598no—
856C22×D4—591no—
857C22×D4—592no—
858C22×D4—591no—
859C22×D4—592no—
860C22×D4—592no—
861C22×D4—591no—
862C22×D4—598no—
863C22×D4—592no—
864C22×D4—1188no—
865C22×D4—11816no—
866C22×D4—1188no—
867C22×D4C22×D5912yes—
868C22×D4C22×D5911yescharacteristic
869C23×C4—592no—
870C23×C4—592no—
871C23×C4—592no—
872C23×C4—591no—
873C23×C4—592no—
874C23×C4—591no—
875C23×C4—591no—
876C23×C4—591no—
877C23×C4—592no—
878C23×C4—591no—
879C23×C4—592no—
880C23×C4—591no—
881C23×C4—592no—
882C23×C4—592no—
883C23×C4—592no—
884C23×C4—592no—
885C23×C4—5916no—
886C23×C4—5916no—
887C23×C4—2368no—
888C23×C4—2368no—
889C23×C4C22×D5911yescharacteristic
890C23×C4C22×D5911yescharacteristic
891C23×C4C22×D5912yes—
892C23×C4C22×D5911yescharacteristic
893C4⋊Q8—598no—
894#127—598no—
895#126—5916no—
896#126—5916no—
897#126—5916no—
898#126C22×D59116yescomplemented
899#125—5916no—
900#125—598no—
901#125C22×D5918yescomplemented
902#124—598no—
903#124—5916no—
904#124—5916no—
905#124C22×D5918yescomplemented
906#123—5916no—
907#123—5916no—
908#123—5916no—
909#123—5916no—
910#123—5916no—
911#123—5916no—
912#123—5916no—
913#123C22×D59116yescomplemented
914C22⋊Q8—598no—
915C22⋊Q8—5916no—
916C22⋊Q8—5916no—
917C22⋊Q8—5916no—
918C22⋊Q8—5916no—
919C22⋊Q8—5916no—
920C22⋊Q8C22×D5918yescomplemented
921#121—5916no—
922#121—598no—
923#121—5916no—
924#121—5916no—
925#121—598no—
926#121—598no—
927#121—5916no—
928#121—5916no—
929#121—5916no—
930#121C22×D5918yes—
931#120—5916no—
932#120—5916no—
933#120—5916no—
934#120—5916no—
935C4×Q8—598no—
936C4×Q8—598no—
937C4×Q8—598no—
938C4×Q8C22×D5918yescomplemented
939C4×D4—5916no—
940C4×D4—598no—
941C4×D4—598no—
942C4×D4—5916no—
943C4×D4—5916no—
944C4×D4—598no—
945C4×D4—598no—
946C4×D4—598no—
947C4×D4—598no—
948C4×D4—5916no—
949C4×D4—598no—
950C4×D4—5916no—
951C4×D4—5916no—
952C4×D4—5916no—
953C4×D4—5916no—
954C4×D4—598no—
955C4×D4—5916no—
956C4×D4—5916no—
957C4×D4—598no—
958C4×D4—598no—
959C4×D4—5916no—
960C4×D4—598no—
961C4×D4—5916no—
962C4×D4—598no—
963C4×D4—598no—
964C4×D4C22×D59116yescomplemented
965C4×D4C22×D5918yescomplemented
966#117—598no—
967#117—5916no—
968#117—598no—
969#117—598no—
970#117—598no—
971#117—5916no—
972#117C22×D59116yescomplemented
973C2×C4⋊C4—591no—
974C2×C4⋊C4—591no—
975C2×C4⋊C4—592no—
976C2×C4⋊C4—591no—
977C2×C4⋊C4—592no—
978C2×C4⋊C4—592no—
979C2×C4⋊C4—592no—
980C2×C4⋊C4—598no—
981C2×C4⋊C4—591no—
982C2×C4⋊C4—591no—
983C2×C4⋊C4—592no—
984C2×C4⋊C4—591no—
985C2×C4⋊C4—591no—
986C2×C4⋊C4—591no—
987C2×C4⋊C4—592no—
988C2×C4⋊C4—592no—
989C2×C4⋊C4—5916no—
990C2×C4⋊C4—598no—
991C2×C4⋊C4C22×D5911yescharacteristic
992C2×C4⋊C4C22×D5912yes—
993C2×C4⋊C4C22×D5911yescharacteristic
994C2×C4⋊C4C22×D5912yes—
995C2×C4⋊C4C22×D5912yes—
996C2×C4⋊C4C22×D5912yes—
997C2×C22⋊C4—591no—
998C2×C22⋊C4—592no—
999C2×C22⋊C4—592no—
1000C2×C22⋊C4—591no—
1001C2×C22⋊C4—591no—
1002C2×C22⋊C4—592no—
1003C2×C22⋊C4—592no—
1004C2×C22⋊C4—592no—
1005C2×C22⋊C4—592no—
1006C2×C22⋊C4—592no—
1007C2×C22⋊C4—592no—
1008C2×C22⋊C4—592no—
1009C2×C22⋊C4—592no—
1010C2×C22⋊C4—5916no—
1011C2×C22⋊C4—592no—
1012C2×C22⋊C4—591no—
1013C2×C22⋊C4—591no—
1014C2×C22⋊C4—592no—
1015C2×C22⋊C4—591no—
1016C2×C22⋊C4—592no—
1017C2×C22⋊C4—592no—
1018C2×C22⋊C4—5916no—
1019C2×C22⋊C4—5916no—
1020C2×C22⋊C4—5916no—
1021C2×C22⋊C4C22×D5912yes—
1022C2×C22⋊C4C22×D5912yes—
1023C2×C22⋊C4C22×D5912yes—
1024C2×C22⋊C4C22×D5912yes—
1025C2×C22⋊C4C22×D5912yes—
1026C2×C42—591no—
1027C2×C42—592no—
1028C2×C42—591no—
1029C2×C42—592no—
1030C2×C42—591no—
1031C2×C42—591no—
1032C2×C42—591no—
1033C2×C42—591no—
1034C2×C42—5916no—
1035C2×C42—598no—
1036C2×C42—598no—
1037C2×C42C22×D5911yescharacteristic
1038C2×C42C22×D5911yescharacteristic
1039C2×C42C22×D5912yes—
1040C2×C42C22×D5911yescharacteristic
1041C2×C42C22×D5911yescharacteristic
1042C2×C42C22×D5918yescomplemented
1043C24—591no—
1044C24—592no—
1045C24—592no—
1046C24—591no—
1047C24—598no—
1048C24—598no—
1049C24—1188no—
1050C24—1188no—
1051C24—1188no—
1052C24—1188no—
1053C24—2364no—
1054C24—2364no—
1055C24C23×D5912yes—
1056C24C23×D5911yescharacteristic
1057#41—11832no—
1058#41—11832no—
1059#41—23632no—
1060C2×Q8—24no—
1061C2×Q8—594no—
1062C2×Q8—598no—
1063C2×Q8—1184no—
1064C2×Q8—2364no—
1065C2×Q8C23×D5914yes—
1066C2×D4—28no—
1067C2×D4—24no—
1068C2×D4—598no—
1069C2×D4—594no—
1070C2×D4—594no—
1071C2×D4—598no—
1072C2×D4—598no—
1073C2×D4—598no—
1074C2×D4—598no—
1075C2×D4—598no—
1076C2×D4—594no—
1077C2×D4—598no—
1078C2×D4—594no—
1079C2×D4—598no—
1080C2×D4—598no—
1081C2×D4—594no—
1082C2×D4—598no—
1083C2×D4—11832no—
1084C2×D4—1188no—
1085C2×D4—1188no—
1086C2×D4—1184no—
1087C2×D4—1188no—
1088C2×D4—1188no—
1089C2×D4—11864no—
1090C2×D4—11832no—
1091C2×D4—1188no—
1092C2×D4—1184no—
1093C2×D4—1184no—
1094C2×D4—2364no—
1095C2×D4—2364no—
1096C2×D4—2364no—
1097C2×D4C23×D5918yes—
1098C2×D4C23×D5914yes—
1099C22×C4—24no—
1100C22×C4—24no—
1101C22×C4—24no—
1102C22×C4—28no—
1103C22×C4—591no—
1104C22×C4—591no—
1105C22×C4—591no—
1106C22×C4—591no—
1107C22×C4—591no—
1108C22×C4—592no—
1109C22×C4—591no—
1110C22×C4—592no—
1111C22×C4—598no—
1112C22×C4—598no—
1113C22×C4—598no—
1114C22×C4—594no—
1115C22×C4—598no—
1116C22×C4—594no—
1117C22×C4—594no—
1118C22×C4—594no—
1119C22×C4—594no—
1120C22×C4—598no—
1121C22×C4—594no—
1122C22×C4—598no—
1123C22×C4—598no—
1124C22×C4—598no—
1125C22×C4—598no—
1126C22×C4—598no—
1127C22×C4—1188no—
1128C22×C4—1184no—
1129C22×C4—1184no—
1130C22×C4—1188no—
1131C22×C4—1184no—
1132C22×C4—1184no—
1133C22×C4—1184no—
1134C22×C4—1188no—
1135C22×C4—1188no—
1136C22×C4—1184no—
1137C22×C4—23632no—
1138C22×C4—23632no—
1139C22×C4—2364no—
1140C22×C4—2364no—
1141C22×C4—2364no—
1142C22×C4—2364no—
1143C22×C4—2364no—
1144C22×C4—2364no—
1145C22×C4C23×D5911yescharacteristic
1146C22×C4C23×D5912yes—
1147C22×C4C23×D5912yes—
1148C22×C4C23×D5911yescharacteristic
1149C22×C4C23×D5911yescharacteristic
1150C22×C4C23×D5911yescharacteristic
1151C22×C4C23×D5914yes—
1152C22×C4C23×D5914yes—
1153C22×C4C23×D5914yes—
1154C22×C4C23×D5912yes—
1155C22×C4C23×D5918yes—
1156C22×C4C23×D5911yescharacteristic
1157C22×C4C23×D5911yescharacteristic
1158C4⋊C4—594no—
1159C4⋊C4—594no—
1160C4⋊C4—598no—
1161C4⋊C4—594no—
1162C4⋊C4—598no—
1163C4⋊C4—598no—
1164C4⋊C4—598no—
1165C4⋊C4—594no—
1166C4⋊C4—594no—
1167C4⋊C4—598no—
1168C4⋊C4—594no—
1169C4⋊C4—594no—
1170C4⋊C4—594no—
1171C4⋊C4—598no—
1172C4⋊C4—598no—
1173C4⋊C4C23×D5914yes—
1174C4⋊C4C23×D5918yes—
1175C4⋊C4C23×D5914yes—
1176C4⋊C4C23×D5918yes—
1177C4⋊C4C23×D5918yes—
1178C4⋊C4C23×D5918yes—
1179C22⋊C4—594no—
1180C22⋊C4—598no—
1181C22⋊C4—598no—
1182C22⋊C4—594no—
1183C22⋊C4—594no—
1184C22⋊C4—598no—
1185C22⋊C4—598no—
1186C22⋊C4—598no—
1187C22⋊C4—598no—
1188C22⋊C4—598no—
1189C22⋊C4—598no—
1190C22⋊C4—598no—
1191C22⋊C4—598no—
1192C22⋊C4—598no—
1193C22⋊C4—594no—
1194C22⋊C4—594no—
1195C22⋊C4—598no—
1196C22⋊C4—594no—
1197C22⋊C4—598no—
1198C22⋊C4—598no—
1199C22⋊C4C23×D5918yes—
1200C22⋊C4C23×D5918yes—
1201C22⋊C4C23×D5918yes—
1202C22⋊C4C23×D5918yes—
1203C22⋊C4C23×D5918yes—
1204C42—594no—
1205C42—594no—
1206C42—594no—
1207C42—598no—
1208C42—594no—
1209C42—598no—
1210C42—594no—
1211C42—594no—
1212C42C23×D5914yes—
1213C42C23×D5918yes—
1214C42C23×D5914yes—
1215C42C23×D5914yes—
1216C42C23×D5914yes—
1217C23—22no—
1218C23—22no—
1219C23—24no—
1220C23—24no—
1221C23—24no—
1222C23—594no—
1223C23—598no—
1224C23—592no—
1225C23—594no—
1226C23—594no—
1227C23—592no—
1228C23—11816no—
1229C23—11816no—
1230C23—11816no—
1231C23—1184no—
1232C23—1182no—
1233C23—1184no—
1234C23—1182no—
1235C23—1182no—
1236C23—1182no—
1237C23—11816no—
1238C23—1184no—
1239C23—1184no—
1240C23—1184no—
1241C23—1182no—
1242C23—2368no—
1243C23—2368no—
1244C23—23632no—
1245C23—23632no—
1246C23#41×D5914yes—
1247C23C24×D5914yes—
1248C23C24×D5912yes—
1249C23C24×D5911yescharacteristic
1250Q8—28no—
1251Q8—1188no—
1252Q8—2368no—
1253D4—216no—
1254D4—28no—
1255D4—5916no—
1256D4—5916no—
1257D4—11816no—
1258D4—11816no—
1259D4—1188no—
1260D4—11816no—
1261D4—11816no—
1262D4—11816no—
1263D4—1188no—
1264D4—1188no—
1265D4—2368no—
1266D4—2368no—
1267D4—2368no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—28no—
1272C2×C4—24no—
1273C2×C4—24no—
1274C2×C4—22no—
1275C2×C4—24no—
1276C2×C4—28no—
1277C2×C4—28no—
1278C2×C4—216no—
1279C2×C4—594no—
1280C2×C4—592no—
1281C2×C4—592no—
1282C2×C4—592no—
1283C2×C4—592no—
1284C2×C4—592no—
1285C2×C4—594no—
1286C2×C4—592no—
1287C2×C4—594no—
1288C2×C4—11816no—
1289C2×C4—1188no—
1290C2×C4—1188no—
1291C2×C4—11816no—
1292C2×C4—1182no—
1293C2×C4—1182no—
1294C2×C4—1182no—
1295C2×C4—1182no—
1296C2×C4—1184no—
1297C2×C4—1184no—
1298C2×C4—1182no—
1299C2×C4—1188no—
1300C2×C4—1188no—
1301C2×C4—1188no—
1302C2×C4—11816no—
1303C2×C4—11816no—
1304C2×C4—1188no—
1305C2×C4—2368no—
1306C2×C4—2368no—
1307C2×C4—2368no—
1308C2×C4—2368no—
1309C2×C4—2368no—
1310C2×C4—2368no—
1311C2×C4#41×D5914yes—
1312C2×C4#1427377314yes—
1313C2×C4C24×D5912yes—
1314C2×C4C24×D5914yes—
1315C2×C4C24×D5914yes—
1316C2×C4C24×D5912yes—
1317C2×C4C24×D5912yes—
1318C2×C4C24×D5912yes—
1319C2×C4C24×D5914yes—
1320C2×C4C24×D5912yes—
1321C2×C4C24×D5912yes—
1322C22—28no—
1323C22—22no—
1324C22—22no—
1325C22—24no—
1326C22—24no—
1327C22—24no—
1328C22—48no—
1329C22—594no—
1330C22—598no—
1331C22—11816no—
1332C22—1188no—
1333C22—1184no—
1334C22—1182no—
1335C22—1184no—
1336C22—1182no—
1337C22—1182no—
1338C22—1182no—
1339C22—1184no—
1340C22—1184no—
1341C22—1184no—
1342C22—1182no—
1343C22—23632no—
1344C22—23632no—
1345C22—2368no—
1346C22—2364no—
1347C22C2×#41×D5914yes—
1348C22C2×#41×D5912yes—
1349C22C2×#41×D5912yes—
1350C22C2×#1427377312yes—
1351C22C25×D5911yescharacteristic
1352C4—22no—
1353C4—22no—
1354C4—22no—
1355C4—24no—
1356C4—24no—
1357C4—22no—
1358C4—24no—
1359C4—594no—
1360C4—1182no—
1361C4—1182no—
1362C4—1182no—
1363C4—1182no—
1364C4—1184no—
1365C4—1184no—
1366C4—1182no—
1367C4C2×#41×D5914yes—
1368C4C2×#1427377314yes—
1369C2—24no—
1370C2—44no—
1371C2—1188no—
1372C2—1184no—
1373C2—2364no—
1374C2—2362no—
1375C2#2143770214yesdirect product factor
1376C2C22×#41×D5911yescharacteristic
1377C2C22×#41×D5911yescharacteristic
1378C2C22×#1427377311yescharacteristic
subgroupG/H
centerC22×C4C23×D59
commutator, cosocleC22×C59C26
FrattiniC22C25×D59
FittingC2×C59×#529C2
socleC23×C59C25
hypercenterC2×#529D59
hypocenterC59C2×#3481
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #21437702C2direct (N × H)
2. C2×#16838134C2semidirect
3. C2×#16838110C2semidirect
4. C2×#16838108C2semidirect
5. C2×#16838105C2semidirect
6. C2×#16838104C2semidirect
7. C2×#16838103C2semidirect
8. C2×#16838077C2semidirect
9. C2×#16838075C2semidirect
10. C2×#16838045C2semidirect
11. C2×#16838044C2semidirect
12. C2×#16838043C2semidirect
13. C2×#16838036C2semidirect
14. C2×#16837949C2semidirect
15. C2×#16837939C2semidirect
16. C2×#16837930C2semidirect
17. C2×#16837914C2semidirect
18. C2×#16837911C2semidirect
19. C2×C4×#11745689C2semidirect
20. C2×C4×#11745685C2semidirect
21. C22×C4×D236C2semidirect
22. C2×C4×D4×D59C2semidirect
23. C2×C4×D4×D59C2semidirect
24. C2×C59×#529C2semidirect
27. C22×#11745685C22semidirect
31. C23×C4×D59C22semidirect
32. C23×C4×D59C22semidirect
33. #16838134C22semidirect
34. #16838110C22semidirect
35. #16838108C22semidirect
36. #16838105C22semidirect
37. #16838104C22semidirect
38. #16838103C22semidirect
39. #16838077C22semidirect
40. #16838075C22semidirect
41. #16838045C22semidirect
42. #16838044C22semidirect
43. #16838043C22semidirect
44. #16838036C22semidirect
45. #16837949C22semidirect
46. C2×#14273726C22semidirect
48. #16837939C22semidirect
49. #16837930C22semidirect
50. C2×#14273722C22semidirect
51. C2×#14273722C22semidirect
52. C2×#14273720C22semidirect
53. C2×#14273718C22semidirect
54. C2×#14273717C22semidirect
55. C2×#14273716C22semidirect
56. C2×#14273713C22semidirect
57. C2×#14273713C22semidirect
58. #16837914C22semidirect
59. #16837911C22semidirect
60. C2×#14273712C22semidirect
61. C2×#14273712C22semidirect
62. C2×#14273712C22semidirect
63. C2×#14273711C22semidirect
64. C2×#14273711C22semidirect
65. C2×#14273709C22semidirect
66. C2×#14273709C22semidirect
67. C2×#14273707C22semidirect
68. C2×#14273707C22semidirect
69. C2×#14273705C22semidirect
70. C2×#14273705C22semidirect
71. C2×#14273704C22semidirect
72. C2×#14273703C22semidirect
74. C2×#14273702C22semidirect
75. C2×#14273702C22semidirect
76. C2×#14273702C22semidirect
78. C2×#14273700C22semidirect
79. C2×#14273700C22semidirect
80. C2×#14273699C22semidirect
81. C2×#14273698C22semidirect
83. C2×#14273697C22semidirect
84. C2×#14273697C22semidirect
86. C4×#11745689C22semidirect
87. C4×#11745685C22semidirect
88. C2×Q8×Dic59C22semidirect
89. C2×C4×Dic118C22semidirect
90. C2×C4×Dic118C22semidirect
93. C2×C4×D236C22semidirect
94. C2×C4×D236C22semidirect
95. C2×C4×D236C22semidirect
96. C2×C4×D236C22semidirect
97. C2×C4×D236C22semidirect
98. C2×C4×D236C22semidirect
99. C2×C4×D236C22semidirect
100. C2×C4×D236C22semidirect
101. C2×C4×D236C22semidirect
102. C2×D4×Dic59C22semidirect
103. C2×D4×Dic59C22semidirect
106. C2×#14273689C22semidirect
107. C2×#14273689C22semidirect
110. C2×C4×C22⋊D59C22semidirect
111. C2×C4×C22⋊D59C22semidirect
112. C2×C4×C22⋊D59C22semidirect
113. C2×C4×C22⋊D59C22semidirect
115. C2×(C22⋊D59)⋊C4C22semidirect
116. C2×(C22⋊D59)⋊C4C22semidirect
117. C4×D4×D59C22semidirect
118. C4×D4×D59C22semidirect
119. C2×#14273686C22semidirect
120. C2×#14273685C22semidirect
121. C2×#14273685C22semidirect
122. C2×#14273684C22semidirect
123. C2×#14273684C22semidirect
124. C2×#14273684C22semidirect
125. C22×C4⋊Dic59C22semidirect
126. C2×C4⋊C4×D59C22semidirect
127. C2×C4⋊C4×D59C22semidirect
128. C22×(C2×D59)⋊C4C22semidirect
129. C2×C22⋊C4×D59C22semidirect
130. C2×C22⋊C4×D59C22semidirect
131. C2×C22⋊C4×D59C22semidirect
132. C2×C42×D59C22semidirect
133. C2×C42×D59C22semidirect
134. C2×C42×D59C22semidirect
135. C59×#529C22semidirect
136. C2×#126×C59C22semidirect
137. C2×#125×C59C22semidirect
138. C2×#124×C59C22semidirect
139. C2×#123×C59C22semidirect
140. C2×C22⋊Q8×C59C22semidirect
142. C2×C4×Q8×C59C22semidirect
143. C2×C4×D4×C59C22semidirect
144. C2×C4×D4×C59C22semidirect
145. C2×#117×C59C22semidirect
146. C22×C42×C59C22semidirect
154. C2×#11745685C23semidirect
194. C22×C4×D59C23semidirect
195. C22×C4×D59C23semidirect
196. #14273726C23semidirect
198. #14273722C23semidirect
199. #14273722C23semidirect
200. #14273720C23semidirect
201. #14273718C23semidirect
202. #14273717C23semidirect
203. #14273716C23semidirect
204. #14273713C23semidirect
205. #14273713C23semidirect
206. #14273712C23semidirect
207. #14273712C23semidirect
208. #14273712C23semidirect
209. #14273711C23semidirect
210. #14273711C23semidirect
211. #14273709C23semidirect
212. #14273709C23semidirect
213. #14273707C23semidirect
214. #14273707C23semidirect
215. #14273705C23semidirect
216. #14273705C23semidirect
217. #14273704C23semidirect
218. #14273703C23semidirect
220. #14273702C23semidirect
221. #14273702C23semidirect
222. #14273702C23semidirect
224. #14273700C23semidirect
225. #14273700C23semidirect
226. #14273699C23semidirect
227. #14273698C23semidirect
229. #14273697C23semidirect
230. #14273697C23semidirect
232. Q8×Dic59C23semidirect
233. C4×Dic118C23semidirect
234. C4×Dic118C23semidirect
237. C4×D236C23semidirect
238. C4×D236C23semidirect
239. C4×D236C23semidirect
240. C4×D236C23semidirect
241. C4×D236C23semidirect
242. C4×D236C23semidirect
243. C4×D236C23semidirect
244. C4×D236C23semidirect
245. D4×Dic59C23semidirect
246. D4×Dic59C23semidirect
249. #14273689C23semidirect
250. #14273689C23semidirect
253. C4×C22⋊D59C23semidirect
254. C4×C22⋊D59C23semidirect
255. C4×C22⋊D59C23semidirect
256. C4×C22⋊D59C23semidirect
258. (C22⋊D59)⋊C4C23semidirect
259. (C22⋊D59)⋊C4C23semidirect
260. #14273686C23semidirect
261. #14273685C23semidirect
262. #14273685C23semidirect
263. #14273684C23semidirect
264. #14273684C23semidirect
265. #14273684C23semidirect
273. C2×C4⋊Dic59C23semidirect
282. C4⋊C4×D59C23semidirect
283. C4⋊C4×D59C23semidirect
304. C2×(C2×D59)⋊C4C23semidirect
305. C22⋊C4×D59C23semidirect
306. C22⋊C4×D59C23semidirect
307. C22⋊C4×D59C23semidirect
316. C42×D59C23semidirect
317. C42×D59C23semidirect
318. C42×D59C23semidirect
326. #126×C59C23semidirect
327. #125×C59C23semidirect
328. #124×C59C23semidirect
329. #123×C59C23semidirect
330. C22⋊Q8×C59C23semidirect
332. C4×Q8×C59C23semidirect
333. C4×D4×C59C23semidirect
334. C4×D4×C59C23semidirect
335. #117×C59C23semidirect
352. C2×C42×C59C23semidirect
395. C2×C22⋊D59#41semidirect
426. C2×D236#41semidirect
590. C22⋊D59C2×#41semidirect
615. D236C2×#41semidirect
696. C2×#529D59semidirect
706. C2×C59#3481semidirect
739. #529C2×D59semidirect
743. C2×#126C2×D59semidirect
746. C2×#125C2×D59semidirect
750. C2×#124C2×D59semidirect
760. C2×#123C2×D59semidirect
767. C2×C22⋊Q8C2×D59semidirect
787. C2×C4×Q8C2×D59semidirect
816. C2×C4×D4C2×D59semidirect
817. C2×C4×D4C2×D59semidirect
824. C2×#117C2×D59semidirect
835. C22×C42C2×D59semidirect
836. C59C2×#3481semidirect
898. #126C22×D59semidirect
901. #125C22×D59semidirect
905. #124C22×D59semidirect
913. #123C22×D59semidirect
920. C22⋊Q8C22×D59semidirect
938. C4×Q8C22×D59semidirect
964. C4×D4C22×D59semidirect
965. C4×D4C22×D59semidirect
972. #117C22×D59semidirect
1042. C2×C42C22×D59semidirect
1375. C2#21437702direct (N × H)

Maximal subgroups

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

subgroupindex
#214377022
C2×#168381342
C2×#168381102
C2×#168381082
C2×#168381052
C2×#168381042
C2×#168381032
C2×#168380772
C2×#168380752
C2×#168380452
C2×#168380442
C2×#168380432
C2×#168380362
C2×#168379492
C2×#168379392
C2×#168379302
C2×#168379142
C2×#168379112
C2×C4×#117456892
C2×C4×#117456852
C22×C4×D2362
C2×C4×D4×D592
C2×C59×#5292
C2×#348159