Finite Group Databasebeta

← C2×#21436141 #29465289

Subgroups — C2×#21436141 #29465289

Order 15104.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic118C211yesmaximal, characteristic
2#21436141C2116yesmaximal, direct product factor
3C2×#16837772C211yesmaximal, characteristic, complemented
4C2×#16837743C211yesmaximal, characteristic, complemented
5C2×#16837732C211yesmaximal, characteristic, complemented
6C2×#16837706C211yesmaximal, characteristic, complemented
7C2×#16837658C211yesmaximal, characteristic, complemented
8C2×#16837641C211yesmaximal, characteristic, complemented
9C2×#16837612C211yesmaximal, characteristic, complemented
10C2×#16837557C211yesmaximal, characteristic, complemented
11C2×#16837557C211yesmaximal, characteristic, complemented
12C2×#16837507C211yesmaximal, characteristic, complemented
13C2×#16837474C211yesmaximal, characteristic
14C2×#16837410C211yesmaximal, characteristic, complemented
15C22×#14273650C211yesmaximal, characteristic, complemented
16C2×C59×#552C211yesmaximal, characteristic
17C23×Dic118C2211yescharacteristic
18C23×Dic118C2211yescharacteristic
19C22×#11745672C2211yescharacteristic
20C22×#11745672C2211yescharacteristic
21C22×#11745672C2211yescharacteristic
22C22×#11745664C2211yescharacteristic
23C23×C59⋊C8C2211yescharacteristic
24D4×Dic118—24no—
25D4×Dic118C2218yes—
26C2×#14273727C2211yescharacteristic
27C2×#14273726—21no—
28C2×#14273706C2211yescharacteristic
29C2×#14273706C2211yescharacteristic
30C2×#14273704—21no—
31C2×#14273704—21no—
32C2×C4×Dic118C2211yescharacteristic
33C2×D4×Dic59—21no—
34#16837772C2218yescomplemented
35#16837743C2218yescomplemented
36#16837732C2218yescomplemented
37#16837706C2218yescomplemented
38#16837658C2218yescomplemented
39#16837641C2218yescomplemented
40#16837612C2218yescomplemented
41#16837557C2218yescomplemented
42#16837557C2218yescomplemented
43#16837507C2218yescomplemented
44#16837474C2218yes—
45C2×#14273660C2211yescharacteristic
46C2×#14273658C2211yescharacteristic
47C2×#14273658C2211yescharacteristic
48C2×C4⋊(C59⋊C8)C2211yescharacteristic
49#16837410C2218yescomplemented
50C2×#14273651C2211yescharacteristic
51C2×#14273650C2211yescharacteristic
52C2×#14273650C2211yescharacteristic
53C2×#14273650C2211yescharacteristic
54C2×#14273650C2211yescharacteristic
55C2×#14273650C2211yescharacteristic
56C2×#14273650C2211yescharacteristic
57C2×#14273650C2211yescharacteristic
58C2×#14273650C2211yescharacteristic
59C2×#14273650C2211yescharacteristic
60C2×#14273650C2218yescomplemented
61C2×C22⋊(C59⋊C8)C2211yescharacteristic
62C2×C22⋊(C59⋊C8)C2211yescharacteristic
63C2×#14273638C2211yescharacteristic
64C59×#552—24no—
65C59×#552C2218yes—
66C2×#126×C59—21no—
67C2×#125×C59—21no—
68C2×#125×C59C2211yescharacteristic
69C2×#123×C59—21no—
70C2×C22⋊Q8×C59C2211yescharacteristic
71C2×C22⋊Q8×C59C2211yescharacteristic
72C2×C4×Q8×C59C2211yescharacteristic
73C2×C4×D4×C59C2211yescharacteristic
74C2×#117×C59—21no—
75C2×#117×C59C2211yescharacteristic
76C22×C4⋊C4×C59C2211yescharacteristic
77C22×Dic118—24no—
78C22×Dic118—24no—
79C22×Dic118—21no—
80C22×Dic118—21no—
81C22×Dic118—22no—
82C22×Dic118—22no—
83C22×Dic118—42no—
84C22×Dic118—42no—
85C22×Dic118C2311yescharacteristic
86C22×Dic118C2311yescharacteristic
87C22×Dic118C2314yes—
88C22×Dic118C2314yes—
89C22×Dic118C2311yescharacteristic
90C23×Dic59—21no—
91C23×Dic59—21no—
92C2×#11745672—24no—
93C2×#11745672—42no—
94C2×#11745672—42no—
95C2×#11745672C2314yes—
96C2×#11745672C2314yes—
97C2×#11745672C2314yes—
98C2×#11745664—42no—
99C2×#11745664C2314yes—
100C22×C59⋊C8—42no—
101C22×C59⋊C8C2311yescharacteristic
102C22×C59⋊C8C2311yescharacteristic
103C22×C59⋊C8C2311yescharacteristic
104C22×C59⋊C8C2311yescharacteristic
105C22×C59⋊C8C2314yes—
106#14273727—22no—
107#14273727C2314yes—
108#14273726—28no—
109#14273706—22no—
110#14273706—22no—
111#14273706C2314yes—
112#14273706C2314yes—
113#14273704—28no—
114#14273704—28no—
115C4×Dic118—22no—
116C4×Dic118C2314yes—
117D4×Dic59—28no—
118C2×C4⋊Dic59—21no—
119C2×C4⋊Dic59—21no—
120C2×C4⋊Dic59C2311yescharacteristic
121C2×Dic59⋊C4—21no—
122C2×Dic59⋊C4—21no—
123C2×Dic59⋊C4—21no—
124C2×C22⋊Dic59—21no—
125C2×C22⋊Dic59—21no—
126C2×C4×Dic59—21no—
127#14273660C2314yes—
128#14273658C2314yes—
129#14273658C2314yes—
130C4⋊(C59⋊C8)C2314yes—
131#14273651C2314yes—
132#14273650C2314yes—
133#14273650C2314yes—
134#14273650C2314yes—
135#14273650C2314yes—
136#14273650C2314yes—
137#14273650C2314yes—
138#14273650C2314yes—
139#14273650C2314yes—
140#14273650C2314yes—
141C22⋊(C59⋊C8)C2314yes—
142C22⋊(C59⋊C8)C2314yes—
143#14273638C2314yes—
144C22×Q8×C59C2311yescharacteristic
145C22×D4×C59D411yescharacteristic
146C23×C4×C59—21no—
147C23×C4×C59C2311yescharacteristic
148C23×C4×C59C2311yescharacteristic
149#126×C59—28no—
150#125×C59—28no—
151#125×C59—22no—
152#125×C59C2314yes—
153#123×C59—28no—
154C22⋊Q8×C59—22no—
155C22⋊Q8×C59—22no—
156C22⋊Q8×C59C2314yes—
157C22⋊Q8×C59C2314yes—
158C4×Q8×C59—22no—
159C4×Q8×C59C2314yes—
160C4×D4×C59D414yes—
161C4×D4×C59C2314yes—
162#117×C59—22no—
163#117×C59—28no—
164#117×C59C2314yes—
165C2×C4⋊C4×C59—21no—
166C2×C4⋊C4×C59—22no—
167C2×C4⋊C4×C59—21no—
168C2×C4⋊C4×C59—21no—
169C2×C4⋊C4×C59—21no—
170C2×C4⋊C4×C59—21no—
171C2×C4⋊C4×C59—21no—
172C2×C4⋊C4×C59D411yescharacteristic
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C4⋊C4×C59C2311yescharacteristic
176C2×C4⋊C4×C59C2314yes—
177C2×C22⋊C4×C59—21no—
178C2×C22⋊C4×C59—21no—
179C2×C22⋊C4×C59—21no—
180C2×C22⋊C4×C59D411yescharacteristic
181C2×C22⋊C4×C59D411yescharacteristic
182C2×C42×C59—21no—
183C2×C42×C59—21no—
184C2×C42×C59C2311yescharacteristic
185C24×C59C2×D411yescharacteristic
186C24×C59C2×D411yescharacteristic
187C2×Q8×C59—21no—
188C2×Q8×C59—22no—
189C2×Q8×C59—22no—
190C2×Q8×C59C2412yes—
191C2×D4×C59—24no—
192C2×D4×C59C2×D414yes—
193C22×C4×C59—22no—
194C22×C4×C59—22no—
195C22×C4×C59—22no—
196C22×C4×C59—22no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—24no—
202C22×C4×C59—44no—
203C22×C4×C59C2×D411yescharacteristic
204C22×C4×C59C2×D411yescharacteristic
205C22×C4×C59C2×D411yescharacteristic
206C22×C4×C59C2×D411yescharacteristic
207C22×C4×C59C2×D412yes—
208C22×C4×C59C2×D412yes—
209C22×C4×C59C2412yes—
210C22×C4×C59C2412yes—
211C22×C4×C59C2411yescharacteristic
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59—21no—
215C22×Dic59—21no—
216C22×Dic59—24no—
217C22×Dic59—24no—
218C22×Dic59—44no—
219C22×Dic59—44no—
220C2×Dic118—21no—
221C2×Dic118—22no—
222C2×Dic118—22no—
223C2×Dic118—22no—
224C2×Dic118—22no—
225C2×Dic118—22no—
226C2×Dic118—28no—
227C2×Dic118—28no—
228C2×Dic118—24no—
229C2×Dic118—24no—
230C2×Dic118—21no—
231C2×Dic118—21no—
232C2×Dic118—44no—
233C2×Dic118—44no—
234C2×Dic118—48no—
235C2×Dic118—48no—
236C2×Dic118—44no—
237C2×Dic118—44no—
238C2×Dic118#4114yes—
239C2×Dic118C2412yes—
240C2×Dic118C2412yes—
241C2×Dic118C2412yes—
242C4⋊C4×C59—21no—
243C4⋊C4×C59—21no—
244C4⋊C4×C59—24no—
245C4⋊C4×C59—24no—
246C4⋊C4×C59—24no—
247C4⋊C4×C59—24no—
248C4⋊C4×C59—24no—
249C4⋊C4×C59—24no—
250C4⋊C4×C59—21no—
251C4⋊C4×C59C2×D414yes—
252C4⋊C4×C59C2412yes—
253C4⋊C4×C59C2412yes—
254C4⋊C4×C59C2412yes—
255C22⋊C4×C59—24no—
256C22⋊C4×C59—24no—
257C22⋊C4×C59—24no—
258C22⋊C4×C59C2×D414yes—
259C22⋊C4×C59C2×D414yes—
260C42×C59—24no—
261C42×C59—24no—
262C42×C59C2×D412yes—
263C42×C59C2412yes—
264C22⋊Dic59—24no—
265C22⋊Dic59—24no—
266#11745672—28no—
267#11745672—44no—
268#11745672—44no—
269C4⋊Dic59—24no—
270C4⋊Dic59—24no—
271C4⋊Dic59—21no—
272C4⋊Dic59C2412yes—
273Dic59⋊C4—24no—
274Dic59⋊C4—24no—
275Dic59⋊C4—24no—
276C4×Dic59—24no—
277#11745664—44no—
278C2×C59⋊C8—22no—
279C2×C59⋊C8—22no—
280C2×C59⋊C8—22no—
281C2×C59⋊C8—22no—
282C2×C59⋊C8—44no—
283C2×C59⋊C8C2412yes—
284C2×C59⋊C8C2412yes—
285C2×C59⋊C8C2412yes—
286C2×C59⋊C8C2412yes—
287C23×C59—22no—
288C23×C59—22no—
289C23×C59—22no—
290C23×C59—22no—
291C23×C59—22no—
292C23×C59#13714yes—
293C23×C59C22×D412yes—
294C23×C59C22×D412yes—
295C23×C59C22×D411yescharacteristic
296Q8×C59—22no—
297Q8×C59—22no—
298Q8×C59—42no—
299D4×C59—28no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—24no—
305C2×C4×C59—24no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—22no—
310C2×C4×C59—22no—
311C2×C4×C59—22no—
312C2×C4×C59—22no—
313C2×C4×C59—22no—
314C2×C4×C59—42no—
315C2×C4×C59—48no—
316C2×C4×C59—42no—
317C2×C4×C59—42no—
318C2×C4×C59—42no—
319C2×C4×C59C22×D412yes—
320C2×C4×C59C22×D412yes—
321C2×C4×C59C22×D412yes—
322C2×C4×C59C22×D412yes—
323C2×C4×C59C22×D411yescharacteristic
324C2×C4×C59C2×#4112yes—
325C2×C4×C59H(5,𝔽2)12yes—
326C2×C4×C59C2511yescharacteristic
327C2×Dic59—24no—
328C2×Dic59—22no—
329C2×Dic59—22no—
330C2×Dic59—22no—
331C2×Dic59—22no—
332C2×Dic59—48no—
333C2×Dic59—48no—
334C2×Dic59—42no—
335C2×Dic59—42no—
336C2×Dic59—42no—
337Dic118—24no—
338Dic118—22no—
339Dic118—22no—
340Dic118—22no—
341Dic118—22no—
342Dic118—22no—
343Dic118—48no—
344Dic118—48no—
345Dic118—42no—
346Dic118—42no—
347Dic118C2×#4114yes—
348C59⋊C8—22no—
349C59⋊C8—22no—
350C59⋊C8—22no—
351C59⋊C8—22no—
352C2×#3312—591nomaximal, Sylow
353C22×C59—22no—
354C22×C59—28no—
355C22×C59—22no—
356C22×C59—22no—
357C22×C59—22no—
358C22×C59—22no—
359C22×C59—44no—
360C22×C59#54612yes—
361C22×C59C2×#13714yes—
362C22×C59C2×#13712yes—
363C22×C59#57812yes—
364C22×C59C23×D411yescharacteristic
365C4×C59—22no—
366C4×C59—22no—
367C4×C59—22no—
368C4×C59—22no—
369C4×C59—42no—
370C4×C59—42no—
371C4×C59—42no—
372C4×C59—42no—
373C4×C59#54612yes—
374C4×C59C22×#4111yescharacteristic
375C4×C59C2×H(5,𝔽2)11yescharacteristic
376Dic59—24no—
377Dic59—42no—
378Dic59—42no—
379Dic59—42no—
380C2×#552D5911yescharacteristic
381C2×D4×Q8—591no—
382#3312—5916no—
383C2×#491—591no—
384C2×#485—591no—
385C2×#483—591no—
386C2×#479—591no—
387C2×#470—591no—
388C2×#467—591no—
389C2×#462—591no—
390C2×#451—591no—
391C2×#451—591no—
392C2×#441—591no—
393C2×#435—591no—
394C2×#419—591no—
395C22×#103—591no—
396C2×C59—24no—
397C2×C59—42no—
398C2×C59#331214yescomplemented
399C2×C59C2×#54611yescharacteristic
400C2×C59C22×#13711yescharacteristic
401C2×C59C2×#57811yescharacteristic
402C23×Q8—591no—
403C23×Q8—591no—
404C22×Q16—591no—
405C22×Q16—591no—
406C22×Q16—591no—
407C22×M16—591no—
408C23×C8—591no—
409#552—24no—
410#552C2×D5918yes—
411D4×Q8—598no—
412D4×Q8—1184no—
413C2×C4⋊Q8—591no—
414C2×C4⋊Q8—1181no—
415C2×#126—21no—
416C2×#125—21no—
417C2×#125C2×D5911yescharacteristic
418C2×#123—21no—
419C2×C22⋊Q8—591no—
420C2×C22⋊Q8—591no—
421C2×C22⋊Q8—1181no—
422C2×C22⋊Q8—1181no—
423C2×C22⋊Q8C2×D5911yescharacteristic
424C2×C22⋊Q8C2×D5911yescharacteristic
425C2×C4×Q8—591no—
426C2×C4×Q8C2×D5911yescharacteristic
427C2×C4×D4—1181no—
428C2×C4×D4C2×D5911yescharacteristic
429C2×#117—21no—
430C2×#117C2×D5911yescharacteristic
431C22×C4⋊C4C2×D5911yescharacteristic
432#491—598no—
433#485—598no—
434#483—598no—
435#479—598no—
436#470—598no—
437#467—598no—
438#462—598no—
439#451—598no—
440#451—598no—
441#441—598no—
442#435—598no—
443C2×#107—591no—
444C2×#106—591no—
445C2×#106—591no—
446C2×C4⋊C8—591no—
447#419—598no—
448C2×#103—591no—
449C2×#103—591no—
450C2×#103—591no—
451C2×#103—591no—
452C2×#103—591no—
453C2×#103—591no—
454C2×#103—591no—
455C2×#103—591no—
456C2×#103—591no—
457C2×#103—591no—
458C2×#103—598no—
459C2×C22⋊C8—591no—
460C2×C22⋊C8—591no—
461C2×#97—591no—
462C59C2×#331211yescharacteristic, complemented, Sylow
463C22×Q8—591no—
464C22×Q8—591no—
465C22×Q8—591no—
466C22×Q8—594no—
467C22×Q8—594no—
468C22×Q8—1184no—
469C22×Q8—1184no—
470C22×Q8—1181no—
471C22×Q8—1181no—
472C22×Q8—1182no—
473C22×Q8—1182no—
474C22×Q8—2362no—
475C22×Q8—2362no—
476C22×Q8C22×D5911yescharacteristic
477C22×D4C22⋊D5911yescharacteristic
478C23×C4—21no—
479C23×C4—1181no—
480C23×C4—1181no—
481C23×C4C22×D5911yescharacteristic
482C23×C4C22×D5911yescharacteristic
483C2×Q16—594no—
484C2×Q16—594no—
485C2×Q16—594no—
486C2×Q16—1184no—
487C2×Q16—2362no—
488C2×Q16—2362no—
489C2×M16—594no—
490C2×M16—2362no—
491C22×C8—591no—
492C22×C8—591no—
493C22×C8—591no—
494C22×C8—591no—
495C22×C8—594no—
496C22×C8—2362no—
497C4⋊Q8—594no—
498C4⋊Q8—1188no—
499C4⋊Q8—1182no—
500#126—28no—
501#125—28no—
502#125—22no—
503#125C22×D5914yes—
504#123—28no—
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—594no—
508C22⋊Q8—594no—
509C22⋊Q8—1182no—
510C22⋊Q8—1182no—
511C22⋊Q8—1188no—
512C22⋊Q8—1188no—
513C22⋊Q8C22×D5914yes—
514C22⋊Q8C22×D5914yes—
515C4×Q8—22no—
516C4×Q8—594no—
517C4×Q8—1182no—
518C4×Q8C22×D5914yes—
519C4×D4—1188no—
520C4×D4C22⋊D5914yes—
521C4×D4C22×D5914yes—
522#117—22no—
523#117—28no—
524#117C22×D5914yes—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—591no—
533C2×C4⋊C4—1181no—
534C2×C4⋊C4—1181no—
535C2×C4⋊C4—1181no—
536C2×C4⋊C4—1181no—
537C2×C4⋊C4—1181no—
538C2×C4⋊C4C22⋊D5911yescharacteristic
539C2×C4⋊C4C22×D5911yescharacteristic
540C2×C4⋊C4C22×D5911yescharacteristic
541C2×C4⋊C4C22×D5914yes—
542C2×C4⋊C4C22×D5911yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—1181no—
547C2×C22⋊C4—1181no—
548C2×C22⋊C4C22⋊D5911yescharacteristic
549C2×C22⋊C4C22⋊D5911yescharacteristic
550C2×C42—21no—
551C2×C42—21no—
552C2×C42—1181no—
553C2×C42C22×D5911yescharacteristic
554#107—594no—
555#106—594no—
556#106—594no—
557C4⋊C8—594no—
558#103—594no—
559#103—594no—
560#103—594no—
561#103—594no—
562#103—594no—
563#103—594no—
564#103—594no—
565#103—594no—
566#103—594no—
567#103—594no—
568C22⋊C8—594no—
569C22⋊C8—594no—
570#97—594no—
571C24C2×C22⋊D5911yescharacteristic
572C24C2×C22⋊D5911yescharacteristic
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—594no—
577C2×Q8—592no—
578C2×Q8—592no—
579C2×Q8—592no—
580C2×Q8—1188no—
581C2×Q8—1188no—
582C2×Q8—1181no—
583C2×Q8—1184no—
584C2×Q8—1184no—
585C2×Q8—1181no—
586C2×Q8—1181no—
587C2×Q8—1182no—
588C2×Q8—1182no—
589C2×Q8—1182no—
590C2×Q8—1182no—
591C2×Q8—1182no—
592C2×Q8—2364no—
593C2×Q8—2364no—
594C2×Q8—2364no—
595C2×Q8—2364no—
596C2×Q8—2368no—
597C2×Q8—2368no—
598C2×Q8C23×D5912yes—
599C2×D4—24no—
600C2×D4C2×C22⋊D5914yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—44no—
611C22×C4—1181no—
612C22×C4—1184no—
613C22×C4—1184no—
614C22×C4—1181no—
615C22×C4—1181no—
616C22×C4—1181no—
617C22×C4—2364no—
618C22×C4—2364no—
619C22×C4C2×C22⋊D5912yes—
620C22×C4C2×C22⋊D5912yes—
621C22×C4C2×C22⋊D5911yescharacteristic
622C22×C4C2×C22⋊D5911yescharacteristic
623C22×C4C2×C22⋊D5911yescharacteristic
624C22×C4C2×C22⋊D5911yescharacteristic
625C22×C4C23×D5912yes—
626C22×C4C23×D5912yes—
627C22×C4C23×D5911yescharacteristic
628Q16—1188no—
629Q16—2364no—
630Q16—2364no—
631M16—2364no—
632C2×C8—592no—
633C2×C8—592no—
634C2×C8—592no—
635C2×C8—592no—
636C2×C8—1182no—
637C2×C8—1182no—
638C2×C8—1182no—
639C2×C8—1182no—
640C2×C8—2364no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—24no—
649C4⋊C4—21no—
650C4⋊C4—592no—
651C4⋊C4—1181no—
652C4⋊C4—1184no—
653C4⋊C4—1184no—
654C4⋊C4—1184no—
655C4⋊C4—1184no—
656C4⋊C4—1184no—
657C4⋊C4C2×C22⋊D5914yes—
658C4⋊C4C23×D5912yes—
659C4⋊C4C23×D5912yes—
660C4⋊C4C23×D5912yes—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—1184no—
665C22⋊C4—1184no—
666C22⋊C4C2×C22⋊D5914yes—
667C22⋊C4C2×C22⋊D5914yes—
668C42—24no—
669C42—24no—
670C42—1184no—
671C42C2×C22⋊D5912yes—
672C42C23×D5912yes—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23#1427375714yes—
679C23C22×C22⋊D5912yes—
680C23C22×C22⋊D5912yes—
681C23C22×C22⋊D5911yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—42no—
685Q8—594no—
686Q8—1182no—
687Q8—1184no—
688Q8—1182no—
689Q8—1182no—
690Q8—1182no—
691Q8—1182no—
692Q8—2368no—
693Q8—2368no—
694Q8—2362no—
695Q8—2362no—
696D4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—48no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—1182no—
717C2×C4—1184no—
718C2×C4—1182no—
719C2×C4—1182no—
720C2×C4—1182no—
721C2×C4—2368no—
722C2×C4—2368no—
723C2×C4—2362no—
724C2×C4—2362no—
725C2×C4—2362no—
726C2×C4C22×C22⋊D5912yes—
727C2×C4C22×C22⋊D5912yes—
728C2×C4C22×C22⋊D5912yes—
729C2×C4C22×C22⋊D5912yes—
730C2×C4C22×C22⋊D5911yescharacteristic
731C2×C4#41×D5912yes—
732C2×C4#1427377312yes—
733C2×C4C24×D5911yescharacteristic
734C8—1182no—
735C8—1182no—
736C8—1182no—
737C8—1182no—
738C22—22no—
739C22—22no—
740C22—28no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—44no—
745C22#1683804012yes—
746C22C2×#1427375714yes—
747C22C2×#1427375712yes—
748C22#1683821712yes—
749C22C23×C22⋊D5911yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—1184no—
759C4—2362no—
760C4—2362no—
761C4—2362no—
762C4#1683804012yes—
763C4C2×#41×D5911yescharacteristic
764C4C2×#1427377311yescharacteristic
765C2—24no—
766C2—42no—
767C2#2143614114yesdirect product factor
768C2C2×#1683804011yescharacteristic
769C2C22×#1427375711yescharacteristic
770C2C2×#1683821711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#552C2
socleC23×C59C22×D4
prime radicalC22×D4×C59D4
hypercenterC2×#552D59
hypocenterC59C2×#3312
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #21436141C2direct (N × H)
3. C2×#16837772C2semidirect
4. C2×#16837743C2semidirect
5. C2×#16837732C2semidirect
6. C2×#16837706C2semidirect
7. C2×#16837658C2semidirect
8. C2×#16837641C2semidirect
9. C2×#16837612C2semidirect
10. C2×#16837557C2semidirect
11. C2×#16837557C2semidirect
12. C2×#16837507C2semidirect
14. C2×#16837410C2semidirect
15. C22×#14273650C2semidirect
34. #16837772C22semidirect
35. #16837743C22semidirect
36. #16837732C22semidirect
37. #16837706C22semidirect
38. #16837658C22semidirect
39. #16837641C22semidirect
40. #16837612C22semidirect
41. #16837557C22semidirect
42. #16837557C22semidirect
43. #16837507C22semidirect
49. #16837410C22semidirect
60. C2×#14273650C22semidirect
398. C2×C59#3312semidirect
462. C59C2×#3312semidirect
767. C2#21436141direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Dic1182
#214361412
C2×#168377722
C2×#168377432
C2×#168377322
C2×#168377062
C2×#168376582
C2×#168376412
C2×#168376122
C2×#168375572
C2×#168375072
C2×#168374742
C2×#168374102
C22×#142736502
C2×C59×#5522
C2×#331259