Finite Group Databasebeta

← C2×#21436192 #29465343

Subgroups — C2×#21436192 #29465343

Order 15104.

2126 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838092C211yesmaximal, characteristic, complemented
2#21436192C2116yesmaximal, direct product factor
3C2×#16837770C211yesmaximal, characteristic, complemented
4C2×#16837735C211yesmaximal, characteristic, complemented
5C2×#16837740C211yesmaximal, characteristic, complemented
6C2×#16837702C211yesmaximal, characteristic, complemented
7C2×#16837658C211yesmaximal, characteristic, complemented
8C2×#16837641C211yesmaximal, characteristic, complemented
9C2×#16837609C211yesmaximal, characteristic, complemented
10C2×#16837564C211yesmaximal, characteristic, complemented
11C2×#16837564C211yesmaximal, characteristic, complemented
12C2×#16837502C211yesmaximal, characteristic, complemented
13C2×#16837474C211yesmaximal, characteristic, complemented
14C2×#16837403C211yesmaximal, characteristic, complemented
15C2×#16837398C211yesmaximal, characteristic, complemented
16C2×C59×#547C211yesmaximal, characteristic
17C22×#11745672C2211yescharacteristic
18C22×#11745672C2211yescharacteristic
19C22×#11745670C2211yescharacteristic
20C22×#11745664C2211yescharacteristic
21C23×C59⋊C8C2211yescharacteristic
22#16838092—24no—
23#16838092C2218yescomplemented
24C2×#14273720—21no—
25C2×#14273719C2211yescharacteristic
26C2×#14273717—21no—
27C2×#14273708—21no—
28C2×#14273706C2211yescharacteristic
29C2×#14273706C2211yescharacteristic
30C2×C4×Dic118C2211yescharacteristic
31C2×#14273686C2211yescharacteristic
32C2×#14273683—21no—
33C22×C4⋊Dic59C2211yescharacteristic
34#16837770C2218yescomplemented
35#16837740C2218yescomplemented
36#16837735C2218yescomplemented
37#16837702C2218yescomplemented
38#16837658C2218yescomplemented
39#16837641C2218yescomplemented
40#16837609C2218yescomplemented
41#16837564C2218yescomplemented
42#16837564C2218yescomplemented
43#16837502C2218yescomplemented
44#16837474C2218yescomplemented
45C2×#14273660C2211yescharacteristic
46C2×#14273660C2211yescharacteristic
47C2×#14273658C2211yescharacteristic
48C2×C4⋊(C59⋊C8)C2211yescharacteristic
49#16837403C2218yescomplemented
50#16837398C2218yescomplemented
51C2×#14273651C2211yescharacteristic
52C2×#14273651C2211yescharacteristic
53C2×#14273651C2211yescharacteristic
54C2×#14273651C2211yescharacteristic
55C2×#14273651C2211yescharacteristic
56C2×#14273651C2211yescharacteristic
57C2×#14273650C2211yescharacteristic
58C2×#14273648C2211yescharacteristic
59C2×#14273648C2211yescharacteristic
60C2×#14273648C2211yescharacteristic
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×C22⋊(C59⋊C8)C2211yescharacteristic
63C2×#14273638C2211yescharacteristic
64C22×#41×C59C2211yescharacteristic
65C22×#41×C59C2211yescharacteristic
66C59×#547—24no—
67C59×#547C2218yes—
68C2×C4⋊Q8×C59C2211yescharacteristic
69C2×#123×C59—21no—
70C2×#123×C59—21no—
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×C22⋊Q8×C59C2211yescharacteristic
73C2×#121×C59—21no—
74C2×C4×D4×C59C2211yescharacteristic
75C2×C4×D4×C59C2211yescharacteristic
76C22×C4⋊C4×C59—21no—
77C22×Dic118C2311yescharacteristic
78C23×Dic59—21no—
79C2×#11745672—42no—
80C2×#11745672—42no—
81C2×#11745672C2314yes—
82C2×#11745672C2314yes—
83C2×#11745670—24no—
84C2×#11745670C2314yes—
85C2×#11745664—42no—
86C2×#11745664C2314yes—
87C22×C59⋊C8—42no—
88C22×C59⋊C8C2311yescharacteristic
89C22×C59⋊C8C2311yescharacteristic
90C22×C59⋊C8C2311yescharacteristic
91C22×C59⋊C8C2311yescharacteristic
92C22×C59⋊C8C2314yes—
93#14273720—28no—
94#14273719—22no—
95#14273719C2314yes—
96#14273717—28no—
97#14273708—28no—
98#14273706—22no—
99#14273706—22no—
100#14273706C2314yes—
101#14273706C2314yes—
102C4×Dic118—22no—
103C4×Dic118C2314yes—
104#14273686—22no—
105#14273686C2314yes—
106#14273683—28no—
107C2×C4⋊Dic59—21no—
108C2×C4⋊Dic59—22no—
109C2×C4⋊Dic59C2311yescharacteristic
110C2×C4⋊Dic59C2311yescharacteristic
111C2×C4⋊Dic59C2311yescharacteristic
112C2×C4⋊Dic59C2314yes—
113C2×Dic59⋊C4—21no—
114C2×Dic59⋊C4—21no—
115C2×Dic59⋊C4—21no—
116C2×Dic59⋊C4—21no—
117C2×Dic59⋊C4—21no—
118C2×C22⋊Dic59—21no—
119C2×C22⋊Dic59—21no—
120C2×C22⋊Dic59—21no—
121C2×C4×Dic59—21no—
122C2×C4×Dic59—21no—
123#14273660C2314yes—
124#14273660C2314yes—
125#14273658C2314yes—
126C4⋊(C59⋊C8)C2314yes—
127#14273651C2314yes—
128#14273651C2314yes—
129#14273651C2314yes—
130#14273651C2314yes—
131#14273651C2314yes—
132#14273651C2314yes—
133#14273650C2314yes—
134#14273648C2314yes—
135#14273648C2314yes—
136#14273648C2314yes—
137C22⋊(C59⋊C8)C2314yes—
138C22⋊(C59⋊C8)C2314yes—
139#14273638C2314yes—
140C2×#41×C59—22no—
141C2×#41×C59—22no—
142C2×#41×C59—24no—
143C2×#41×C59—24no—
144C2×#41×C59—42no—
145C2×#41×C59—42no—
146C2×#41×C59C2314yes—
147C2×#41×C59C2314yes—
148C22×Q8×C59C2311yescharacteristic
149C22×Q8×C59C2311yescharacteristic
150C22×D4×C59—21no—
151C22×D4×C59—21no—
152C22×D4×C59D411yescharacteristic
153C22×D4×C59C2311yescharacteristic
154C23×C4×C59—21no—
155C23×C4×C59—21no—
156C23×C4×C59—21no—
157C23×C4×C59C2311yescharacteristic
158C23×C4×C59C2311yescharacteristic
159C4⋊Q8×C59—22no—
160C4⋊Q8×C59C2314yes—
161#123×C59—28no—
162#123×C59—28no—
163C22⋊Q8×C59—22no—
164C22⋊Q8×C59—22no—
165C22⋊Q8×C59C2314yes—
166C22⋊Q8×C59C2314yes—
167#121×C59—28no—
168C4×D4×C59—22no—
169C4×D4×C59D414yes—
170C4×D4×C59C2314yes—
171C4×D4×C59C2314yes—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59—21no—
174C2×C4⋊C4×C59—21no—
175C2×C4⋊C4×C59—21no—
176C2×C4⋊C4×C59—28no—
177C2×C4⋊C4×C59D411yescharacteristic
178C2×C4⋊C4×C59C2311yescharacteristic
179C2×C22⋊C4×C59—21no—
180C2×C22⋊C4×C59—21no—
181C2×C22⋊C4×C59—21no—
182C2×C22⋊C4×C59D411yescharacteristic
183C2×C22⋊C4×C59D411yescharacteristic
184C2×C42×C59C2311yescharacteristic
185C24×C59—21no—
186C24×C59C2×D411yescharacteristic
187C24×C59C2×D411yescharacteristic
188#41×C59—28no—
189#41×C59—28no—
190#41×C59—44no—
191#41×C59—44no—
192#41×C59—48no—
193#41×C59—48no—
194C2×Q8×C59—21no—
195C2×Q8×C59—21no—
196C2×Q8×C59—22no—
197C2×Q8×C59—22no—
198C2×Q8×C59—22no—
199C2×Q8×C59—22no—
200C2×Q8×C59C2412yes—
201C2×Q8×C59C2412yes—
202C2×D4×C59—24no—
203C2×D4×C59—24no—
204C2×D4×C59—21no—
205C2×D4×C59—22no—
206C2×D4×C59—42no—
207C2×D4×C59—44no—
208C2×D4×C59—44no—
209C2×D4×C59C2×D414yes—
210C2×D4×C59#4114yes—
211C2×D4×C59C2412yes—
212C22×C4×C59—22no—
213C22×C4×C59—22no—
214C22×C4×C59—22no—
215C22×C4×C59—22no—
216C22×C4×C59—21no—
217C22×C4×C59—21no—
218C22×C4×C59—21no—
219C22×C4×C59—24no—
220C22×C4×C59—24no—
221C22×C4×C59—24no—
222C22×C4×C59—44no—
223C22×C4×C59—44no—
224C22×C4×C59—44no—
225C22×C4×C59C2×D411yescharacteristic
226C22×C4×C59C2×D411yescharacteristic
227C22×C4×C59C2×D411yescharacteristic
228C22×C4×C59C2×D411yescharacteristic
229C22×C4×C59C2×D412yes—
230C22×C4×C59C2×D412yes—
231C22×C4×C59C2412yes—
232C22×C4×C59C2412yes—
233C22×C4×C59C2411yescharacteristic
234C22×Dic59—21no—
235C22×Dic59—21no—
236C22×Dic59—21no—
237C22×Dic59—21no—
238C22×Dic59—24no—
239C22×Dic59—44no—
240C2×Dic118—22no—
241C2×Dic118—22no—
242C2×Dic118—21no—
243C2×Dic118C2412yes—
244C4⋊C4×C59—24no—
245C4⋊C4×C59—24no—
246C4⋊C4×C59—24no—
247C4⋊C4×C59—24no—
248C4⋊C4×C59—21no—
249C4⋊C4×C59C2×D414yes—
250C4⋊C4×C59C2412yes—
251C22⋊C4×C59—24no—
252C22⋊C4×C59—24no—
253C22⋊C4×C59—24no—
254C22⋊C4×C59C2×D414yes—
255C22⋊C4×C59C2×D414yes—
256C42×C59C2×D412yes—
257C42×C59C2412yes—
258C22⋊Dic59—24no—
259C22⋊Dic59—24no—
260C22⋊Dic59—24no—
261#11745672—44no—
262#11745672—44no—
263#11745670—28no—
264C4⋊Dic59—21no—
265C4⋊Dic59—21no—
266C4⋊Dic59—24no—
267C4⋊Dic59—21no—
268C4⋊Dic59C2412yes—
269C4⋊Dic59C2412yes—
270C4⋊Dic59C2412yes—
271Dic59⋊C4—24no—
272Dic59⋊C4—24no—
273Dic59⋊C4—24no—
274Dic59⋊C4—24no—
275Dic59⋊C4—24no—
276C4×Dic59—24no—
277C4×Dic59—24no—
278#11745664—44no—
279C2×C59⋊C8—22no—
280C2×C59⋊C8—22no—
281C2×C59⋊C8—22no—
282C2×C59⋊C8—22no—
283C2×C59⋊C8—44no—
284C2×C59⋊C8C2412yes—
285C2×C59⋊C8C2412yes—
286C2×C59⋊C8C2412yes—
287C2×C59⋊C8C2412yes—
288C23×C59—22no—
289C23×C59—22no—
290C23×C59—24no—
291C23×C59—22no—
292C23×C59—22no—
293C23×C59—22no—
294C23×C59—22no—
295C23×C59—22no—
296C23×C59—42no—
297C23×C59—42no—
298C23×C59C22×D412yes—
299C23×C59C22×D412yes—
300C23×C59C22×D411yescharacteristic
301Q8×C59—22no—
302Q8×C59—22no—
303Q8×C59—22no—
304Q8×C59—22no—
305Q8×C59—42no—
306Q8×C59—42no—
307D4×C59—24no—
308D4×C59—22no—
309D4×C59—44no—
310D4×C59—48no—
311D4×C59—48no—
312D4×C59C2×#4114yes—
313C2×C4×C59—22no—
314C2×C4×C59—22no—
315C2×C4×C59—22no—
316C2×C4×C59—22no—
317C2×C4×C59—24no—
318C2×C4×C59—24no—
319C2×C4×C59—22no—
320C2×C4×C59—22no—
321C2×C4×C59—22no—
322C2×C4×C59—22no—
323C2×C4×C59—22no—
324C2×C4×C59—22no—
325C2×C4×C59—22no—
326C2×C4×C59—48no—
327C2×C4×C59—48no—
328C2×C4×C59—48no—
329C2×C4×C59—42no—
330C2×C4×C59—42no—
331C2×C4×C59—42no—
332C2×C4×C59C22×D412yes—
333C2×C4×C59C22×D412yes—
334C2×C4×C59C22×D412yes—
335C2×C4×C59C22×D412yes—
336C2×C4×C59C22×D411yescharacteristic
337C2×C4×C59C2×#4112yes—
338C2×C4×C59H(5,𝔽2)12yes—
339C2×C4×C59C2511yescharacteristic
340C2×Dic59—22no—
341C2×Dic59—22no—
342C2×Dic59—22no—
343C2×Dic59—22no—
344C2×Dic59—48no—
345C2×Dic59—42no—
346C2×Dic59—42no—
347C2×Dic59—42no—
348C2×Dic59—42no—
349Dic118—22no—
350Dic118—22no—
351Dic118—42no—
352C59⋊C8—22no—
353C59⋊C8—22no—
354C59⋊C8—22no—
355C59⋊C8—22no—
356C2×#3315—591nomaximal, Sylow
357C22×C59—22no—
358C22×C59—22no—
359C22×C59—24no—
360C22×C59—22no—
361C22×C59—22no—
362C22×C59—22no—
363C22×C59—22no—
364C22×C59—44no—
365C22×C59—44no—
366C22×C59—48no—
367C22×C59—42no—
368C22×C59—42no—
369C22×C59#54612yes—
370C22×C59#57512yes—
371C22×C59#57812yes—
372C22×C59C23×D411yescharacteristic
373C4×C59—22no—
374C4×C59—22no—
375C4×C59—22no—
376C4×C59—22no—
377C4×C59—42no—
378C4×C59—42no—
379C4×C59—42no—
380C4×C59#54612yes—
381C4×C59C22×#4111yescharacteristic
382C4×C59C2×H(5,𝔽2)11yescharacteristic
383Dic59—42no—
384Dic59—42no—
385Dic59—42no—
386Dic59—42no—
387C2×#552—591no—
388C2×#547D5911yescharacteristic
389#3315—5916no—
390C2×#491—591no—
391C2×#484—591no—
392C2×#485—591no—
393C2×#478—591no—
394C2×#470—591no—
395C2×#467—591no—
396C2×#462—591no—
397C2×#452—591no—
398C2×#452—591no—
399C2×#440—591no—
400C2×#435—591no—
401C2×#417—591no—
402C2×#416—591no—
403C2×C59—42no—
404C2×C59—42no—
405C2×C59—44no—
406C2×C59#331514yescomplemented
407C2×C59C2×#54611yescharacteristic
408C2×C59C2×#57511yescharacteristic
409C2×C59C2×#57811yescharacteristic
410C22×#41C2×D5911yescharacteristic
411C22×#41C2×D5911yescharacteristic
412C22×Q16—591no—
413C22×Q16—591no—
414C22×SD16—591no—
415C22×M16—591no—
416C23×C8—591no—
417#552—598no—
418#552—1184no—
419#547—24no—
420#547C2×D5918yes—
421C2×C4⋊Q8C2×D5911yescharacteristic
422C2×#126—1181no—
423C2×#125—591no—
424C2×#125—1181no—
425C2×#123—21no—
426C2×#123—21no—
427C2×#123—1181no—
428C2×C22⋊Q8—591no—
429C2×C22⋊Q8—591no—
430C2×C22⋊Q8C2×D5911yescharacteristic
431C2×C22⋊Q8C2×D5911yescharacteristic
432C2×#121—21no—
433C2×C4×Q8—591no—
434C2×C4×D4C2×D5911yescharacteristic
435C2×C4×D4C2×D5911yescharacteristic
436C2×#117—591no—
437C2×#117—1181no—
438C22×C4⋊C4—21no—
439C22×C4⋊C4—591no—
440#491—598no—
441#485—598no—
442#484—598no—
443#478—598no—
444#470—598no—
445#467—598no—
446#462—598no—
447#452—598no—
448#452—598no—
449#440—598no—
450#435—598no—
451C2×#107—591no—
452C2×#107—591no—
453C2×#106—591no—
454C2×C4⋊C8—591no—
455#417—598no—
456#416—598no—
457C2×#103—591no—
458C2×#103—591no—
459C2×#103—591no—
460C2×#103—591no—
461C2×#103—591no—
462C2×#103—591no—
463C2×#103—591no—
464C2×#102—591no—
465C2×#102—591no—
466C2×#102—591no—
467C2×C22⋊C8—591no—
468C2×C22⋊C8—591no—
469C2×#97—591no—
470C59C2×#331511yescharacteristic, complemented, Sylow
471C2×#41—22no—
472C2×#41—22no—
473C2×#41—24no—
474C2×#41—24no—
475C2×#41—42no—
476C2×#41—42no—
477C2×#41C22×D5914yes—
478C2×#41C22×D5914yes—
479C22×Q8—591no—
480C22×Q8C22×D5911yescharacteristic
481C22×Q8C22×D5911yescharacteristic
482C22×D4—21no—
483C22×D4—21no—
484C22×D4C22⋊D5911yescharacteristic
485C22×D4C22×D5911yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—21no—
489C23×C4—1181no—
490C23×C4C22×D5911yescharacteristic
491C23×C4C22×D5911yescharacteristic
492C2×Q16—594no—
493C2×Q16—594no—
494C2×Q16—2362no—
495C2×Q16—2362no—
496C2×SD16—594no—
497C2×SD16—1184no—
498C2×M16—594no—
499C2×M16—2362no—
500C22×C8—591no—
501C22×C8—591no—
502C22×C8—591no—
503C22×C8—591no—
504C22×C8—594no—
505C22×C8—2362no—
506C4⋊Q8—22no—
507C4⋊Q8C22×D5914yes—
508#126—1188no—
509#125—594no—
510#125—1188no—
511#125—1182no—
512#123—28no—
513#123—28no—
514#123—1188no—
515C22⋊Q8—22no—
516C22⋊Q8—22no—
517C22⋊Q8—594no—
518C22⋊Q8—594no—
519C22⋊Q8—1182no—
520C22⋊Q8—1182no—
521C22⋊Q8C22×D5914yes—
522C22⋊Q8C22×D5914yes—
523#121—28no—
524C4×Q8—594no—
525C4×Q8—1182no—
526C4×D4—22no—
527C4×D4C22⋊D5914yes—
528C4×D4C22×D5914yes—
529C4×D4C22×D5914yes—
530#117—594no—
531#117—1182no—
532#117—1188no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—28no—
538C2×C4⋊C4—591no—
539C2×C4⋊C4—591no—
540C2×C4⋊C4—594no—
541C2×C4⋊C4—591no—
542C2×C4⋊C4—1181no—
543C2×C4⋊C4—1182no—
544C2×C4⋊C4—1181no—
545C2×C4⋊C4—1181no—
546C2×C4⋊C4—1181no—
547C2×C4⋊C4—1181no—
548C2×C4⋊C4—1181no—
549C2×C4⋊C4C22⋊D5911yescharacteristic
550C2×C4⋊C4C22×D5911yescharacteristic
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—1181no—
555C2×C22⋊C4—1181no—
556C2×C22⋊C4—1181no—
557C2×C22⋊C4C22⋊D5911yescharacteristic
558C2×C22⋊C4C22⋊D5911yescharacteristic
559C2×C42—1181no—
560C2×C42—1181no—
561C2×C42C22×D5911yescharacteristic
562#107—594no—
563#107—594no—
564#106—594no—
565C4⋊C8—594no—
566#103—594no—
567#103—594no—
568#103—594no—
569#103—594no—
570#103—594no—
571#103—594no—
572#103—594no—
573#102—594no—
574#102—594no—
575#102—594no—
576C22⋊C8—594no—
577C22⋊C8—594no—
578#97—594no—
579C24—21no—
580C24C2×C22⋊D5911yescharacteristic
581C24C2×C22⋊D5911yescharacteristic
582#41—28no—
583#41—28no—
584#41—44no—
585#41—44no—
586#41—48no—
587#41—48no—
588C2×Q8—21no—
589C2×Q8—21no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—22no—
593C2×Q8—22no—
594C2×Q8—592no—
595C2×Q8—1181no—
596C2×Q8—1182no—
597C2×Q8—1182no—
598C2×Q8C23×D5912yes—
599C2×Q8C23×D5912yes—
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—42no—
605C2×D4—44no—
606C2×D4—44no—
607C2×D4#1174568714yes—
608C2×D4C2×C22⋊D5914yes—
609C2×D4C23×D5912yes—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—24no—
618C22×C4—24no—
619C22×C4—24no—
620C22×C4—44no—
621C22×C4—44no—
622C22×C4—44no—
623C22×C4—1184no—
624C22×C4—1181no—
625C22×C4—1181no—
626C22×C4—1181no—
627C22×C4—1181no—
628C22×C4—2364no—
629C22×C4C2×C22⋊D5912yes—
630C22×C4C2×C22⋊D5912yes—
631C22×C4C2×C22⋊D5911yescharacteristic
632C22×C4C2×C22⋊D5911yescharacteristic
633C22×C4C2×C22⋊D5911yescharacteristic
634C22×C4C2×C22⋊D5911yescharacteristic
635C22×C4C23×D5912yes—
636C22×C4C23×D5912yes—
637C22×C4C23×D5911yescharacteristic
638Q16—2364no—
639Q16—2364no—
640SD16—1188no—
641M16—2364no—
642C2×C8—592no—
643C2×C8—592no—
644C2×C8—592no—
645C2×C8—592no—
646C2×C8—1182no—
647C2×C8—1182no—
648C2×C8—1182no—
649C2×C8—1182no—
650C2×C8—2364no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—24no—
654C4⋊C4—24no—
655C4⋊C4—21no—
656C4⋊C4—592no—
657C4⋊C4—592no—
658C4⋊C4—592no—
659C4⋊C4—1181no—
660C4⋊C4—1181no—
661C4⋊C4—1184no—
662C4⋊C4—1181no—
663C4⋊C4—1184no—
664C4⋊C4—1184no—
665C4⋊C4—1184no—
666C4⋊C4—1184no—
667C4⋊C4—1184no—
668C4⋊C4C2×C22⋊D5914yes—
669C4⋊C4C23×D5912yes—
670C22⋊C4—24no—
671C22⋊C4—24no—
672C22⋊C4—24no—
673C22⋊C4—1184no—
674C22⋊C4—1184no—
675C22⋊C4—1184no—
676C22⋊C4C2×C22⋊D5914yes—
677C22⋊C4C2×C22⋊D5914yes—
678C42—1184no—
679C42—1184no—
680C42C2×C22⋊D5912yes—
681C42C23×D5912yes—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—24no—
690C23—42no—
691C23—42no—
692C23C22×C22⋊D5912yes—
693C23C22×C22⋊D5912yes—
694C23C22×C22⋊D5911yescharacteristic
695Q8—22no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—42no—
700Q8—42no—
701Q8—1182no—
702Q8—1182no—
703Q8—2362no—
704D4—22no—
705D4—24no—
706D4—44no—
707D4—48no—
708D4—48no—
709D4C2×#1174568714yes—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—48no—
724C2×C4—48no—
725C2×C4—48no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—1182no—
730C2×C4—1182no—
731C2×C4—1182no—
732C2×C4—1182no—
733C2×C4—2368no—
734C2×C4—2362no—
735C2×C4—2362no—
736C2×C4—2362no—
737C2×C4—2362no—
738C2×C4C22×C22⋊D5912yes—
739C2×C4C22×C22⋊D5912yes—
740C2×C4C22×C22⋊D5912yes—
741C2×C4C22×C22⋊D5912yes—
742C2×C4C22×C22⋊D5911yescharacteristic
743C2×C4C2×#1174568712yes—
744C2×C4#1427377212yes—
745C2×C4C24×D5911yescharacteristic
746C8—1182no—
747C8—1182no—
748C8—1182no—
749C8—1182no—
750C22—22no—
751C22—22no—
752C22—24no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—44no—
758C22—44no—
759C22—48no—
760C22—42no—
761C22—42no—
762C22#1683804612yes—
763C22#1683820012yes—
764C22#1683821712yes—
765C22C23×C22⋊D5911yescharacteristic
766C4—22no—
767C4—22no—
768C4—22no—
769C4—22no—
770C4—42no—
771C4—42no—
772C4—42no—
773C4—2362no—
774C4—2362no—
775C4—2362no—
776C4—2362no—
777C4#1683804612yes—
778C4C22×#1174568711yescharacteristic
779C4C2×#1427377211yescharacteristic
780C2—42no—
781C2—42no—
782C2—44no—
783C2#2143619214yesdirect product factor
784C2C2×#1683804611yescharacteristic
785C2C2×#1683820011yescharacteristic
786C2C2×#1683821711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
Fitting, prime radicalC2×C59×#547C2
socleC23×C59C22×D4
hypercenterC2×#547D59
hypocenterC59C2×#3315
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#16838092C2semidirect
2. #21436192C2direct (N × H)
3. C2×#16837770C2semidirect
4. C2×#16837735C2semidirect
5. C2×#16837740C2semidirect
6. C2×#16837702C2semidirect
7. C2×#16837658C2semidirect
8. C2×#16837641C2semidirect
9. C2×#16837609C2semidirect
10. C2×#16837564C2semidirect
11. C2×#16837564C2semidirect
12. C2×#16837502C2semidirect
13. C2×#16837474C2semidirect
14. C2×#16837403C2semidirect
15. C2×#16837398C2semidirect
23. #16838092C22semidirect
34. #16837770C22semidirect
35. #16837740C22semidirect
36. #16837735C22semidirect
37. #16837702C22semidirect
38. #16837658C22semidirect
39. #16837641C22semidirect
40. #16837609C22semidirect
41. #16837564C22semidirect
42. #16837564C22semidirect
43. #16837502C22semidirect
44. #16837474C22semidirect
49. #16837403C22semidirect
50. #16837398C22semidirect
406. C2×C59#3315semidirect
470. C59C2×#3315semidirect
783. C2#21436192direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380922
#214361922
C2×#168377702
C2×#168377352
C2×#168377402
C2×#168377022
C2×#168376582
C2×#168376412
C2×#168376092
C2×#168375642
C2×#168375022
C2×#168374742
C2×#168374032
C2×#168373982
C2×C59×#5472
C2×#331559