Finite Group Databasebeta

← C2×#21436144 #29465292

Subgroups — C2×#21436144 #29465292

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×#16838090C211yesmaximal, characteristic
2C2×Q8×D236C211yesmaximal, characteristic
3#21436144C2116yesmaximal, direct product factor
4C2×#16837772C211yesmaximal, characteristic, complemented
5C2×#16837745C211yesmaximal, characteristic, complemented
6C2×#16837734C211yesmaximal, characteristic, complemented
7C2×#16837661C211yesmaximal, characteristic, complemented
8C2×#16837644C211yesmaximal, characteristic, complemented
9C2×#16837613C211yesmaximal, characteristic, complemented
10C2×#16837559C211yesmaximal, characteristic, complemented
11C2×#16837559C211yesmaximal, characteristic, complemented
12C2×#16837507C211yesmaximal, characteristic, complemented
13C2×#16837472C211yesmaximal, characteristic
14C2×#16837409C211yesmaximal, characteristic, complemented
15C2×#103×D59C211yesmaximal, characteristic, complemented
16C2×C59×#479C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×Q8×D59C2211yescharacteristic
19C22×Dic236C2211yescharacteristic
20C22×Dic236C2211yescharacteristic
21C22×#11745672C2211yescharacteristic
22C22×#11745659C2211yescharacteristic
23C22×C8×D59C2211yescharacteristic
24#16838090—24no—
25#16838090C2218yes—
26Q8×D236—24no—
27Q8×D236C2218yes—
28C2×#14273727—21no—
29C2×#14273727C2211yescharacteristic
30C2×#14273722—21no—
31C2×#14273718—21no—
32C2×#14273712—21no—
33C2×#14273707—21no—
34C2×#14273707—21no—
35C2×#14273707C2211yescharacteristic
36C2×#14273707C2211yescharacteristic
37C2×#14273707C2211yescharacteristic
38C2×#14273707C2211yescharacteristic
39C2×C4×Dic118C2211yescharacteristic
40C2×C4×D236—21no—
41C2×C4×D236C2211yescharacteristic
42C2×#14273685—21no—
43C2×#14273685C2211yescharacteristic
44C2×C4⋊C4×D59C2211yescharacteristic
45#16837772C2218yescomplemented
46#16837745C2218yescomplemented
47#16837734C2218yescomplemented
48#16837661C2218yescomplemented
49#16837644C2218yescomplemented
50#16837613C2218yescomplemented
51#16837559C2218yescomplemented
52#16837559C2218yescomplemented
53#16837507C2218yescomplemented
54#16837472C2218yes—
55C2×#14273658C2211yescharacteristic
56#16837409C2218yescomplemented
57C2×#14273652C2211yescharacteristic
58C2×#14273652C2211yescharacteristic
59C2×#14273651C2211yescharacteristic
60C2×#14273650C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65#103×D59C2218yescomplemented
66C2×(C2×D59)⋊C8C2211yescharacteristic
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273638C2211yescharacteristic
69C2×#125×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C59×#479C2218yescomplemented
72C2×#107×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×C4⋊C8×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#103×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118—21no—
79C22×Dic118C2311yescharacteristic
80C22×Dic118C2311yescharacteristic
81C22×Dic118C2311yescharacteristic
82C2×Q8×D59—22no—
83C2×Q8×D59—22no—
84C2×Q8×D59—24no—
85C2×Q8×D59—24no—
86C2×Q8×D59—42no—
87C2×Q8×D59—42no—
88C2×Q8×D59C2314yes—
89C2×Q8×D59C2314yes—
90C22×D236D411yescharacteristic
91C22×C4×D59—21no—
92C22×C4×D59—21no—
93C22×C4×D59—21no—
94C22×C4×D59C2311yescharacteristic
95C22×C4×D59C2311yescharacteristic
96C2×Dic236—42no—
97C2×Dic236—42no—
98C2×Dic236C2314yes—
99C2×Dic236C2314yes—
100C2×#11745672—24no—
101C2×#11745672C2314yes—
102C2×#11745659—42no—
103C2×#11745659C2314yes—
104C22×C59⋊C8C2311yescharacteristic
105C22×C59⋊C8C2311yescharacteristic
106C2×C8×D59—42no—
107C2×C8×D59C2314yes—
108#14273727—22no—
109#14273727—28no—
110#14273727C2314yes—
111#14273722—28no—
112#14273718—28no—
113#14273712—28no—
114#14273707—22no—
115#14273707—22no—
116#14273707—22no—
117#14273707—22no—
118#14273707—28no—
119#14273707—28no—
120#14273707C2314yes—
121#14273707C2314yes—
122#14273707C2314yes—
123#14273707C2314yes—
124C4×Dic118—22no—
125C4×Dic118C2314yes—
126C4×D236—28no—
127C4×D236D414yes—
128C4×D236C2314yes—
129#14273685—22no—
130#14273685—28no—
131#14273685C2314yes—
132C2×C4⋊Dic59—21no—
133C2×C4⋊Dic59—21no—
134C2×C4⋊Dic59—21no—
135C2×C4⋊Dic59—21no—
136C2×C4⋊Dic59—21no—
137C2×C4⋊Dic59—21no—
138C2×C4⋊Dic59D411yescharacteristic
139C2×C4⋊Dic59C2311yescharacteristic
140C2×Dic59⋊C4—21no—
141C2×Dic59⋊C4—21no—
142C4⋊C4×D59—22no—
143C4⋊C4×D59C2314yes—
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4—21no—
149C2×(C2×D59)⋊C4D411yescharacteristic
150C2×(C2×D59)⋊C4D411yescharacteristic
151C2×C4×Dic59—21no—
152C2×C4×Dic59—21no—
153#14273658C2314yes—
154#14273652C2314yes—
155#14273652C2314yes—
156#14273651C2314yes—
157#14273650C2314yes—
158#14273650C2314yes—
159#14273650C2314yes—
160#14273650C2314yes—
161#14273650C2314yes—
162(C2×D59)⋊C8C2314yes—
163(C2×D59)⋊C8C2314yes—
164#14273638C2314yes—
165C22×Q8×C59C2311yescharacteristic
166C22×C8×C59C2311yescharacteristic
167C22×C8×C59C2311yescharacteristic
168#125×C59—22no—
169#125×C59C2314yes—
170C4×Q8×C59—22no—
171C4×Q8×C59C2314yes—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59—21no—
174C2×C4⋊C4×C59—21no—
175C2×C4⋊C4×C59C2311yescharacteristic
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C42×C59—21no—
179C2×C42×C59C2311yescharacteristic
180#107×C59C2314yes—
181#106×C59C2314yes—
182C4⋊C8×C59C2314yes—
183#103×C59C2314yes—
184#103×C59C2314yes—
185C23×D59C2×D411yescharacteristic
186C23×D59C2×D411yescharacteristic
187C2×Q8×C59—21no—
188C2×Q8×C59—22no—
189C2×Q8×C59#4114yes—
190C2×Q8×C59C2412yes—
191C22×C4×C59—21no—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59C2×D411yescharacteristic
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2411yescharacteristic
198C22×Dic59—21no—
199C22×Dic59—21no—
200C22×Dic59—21no—
201C22×Dic59—21no—
202C22×Dic59C2×D411yescharacteristic
203C22×Dic59C2×D411yescharacteristic
204Q8×D59—28no—
205Q8×D59—28no—
206Q8×D59—44no—
207Q8×D59—44no—
208Q8×D59—48no—
209Q8×D59—48no—
210C2×D236—24no—
211C2×D236C2×D414yes—
212C2×C4×D59—22no—
213C2×C4×D59—22no—
214C2×C4×D59—22no—
215C2×C4×D59—22no—
216C2×C4×D59—24no—
217C2×C4×D59—24no—
218C2×C4×D59—24no—
219C2×C4×D59—44no—
220C2×C4×D59—44no—
221C2×C4×D59—44no—
222C2×C4×D59C2×D412yes—
223C2×C4×D59C2×D412yes—
224C2×C4×D59C2412yes—
225C2×C4×D59C2412yes—
226C2×Dic118—22no—
227C2×Dic118—22no—
228C2×Dic118—22no—
229C2×Dic118—22no—
230C2×Dic118—22no—
231C2×Dic118—22no—
232C2×Dic118—21no—
233C2×Dic118—21no—
234C2×Dic118—21no—
235C2×Dic118—24no—
236C2×Dic118—24no—
237C2×Dic118—44no—
238C2×Dic118—44no—
239C2×Dic118C2412yes—
240C2×Dic118C2412yes—
241C2×Dic118C2412yes—
242C2×C8×C59—22no—
243C2×C8×C59—22no—
244C2×C8×C59C2412yes—
245C2×C8×C59C2412yes—
246C4⋊C4×C59—24no—
247C4⋊C4×C59—24no—
248C4⋊C4×C59—24no—
249C4⋊C4×C59—21no—
250C4⋊C4×C59—21no—
251C4⋊C4×C59—21no—
252C4⋊C4×C59C2412yes—
253C4⋊C4×C59C2412yes—
254C4⋊C4×C59C2412yes—
255C42×C59—24no—
256C42×C59C2×D412yes—
257C42×C59C2412yes—
258#11745672—28no—
259(C2×D59)⋊C4—24no—
260(C2×D59)⋊C4—24no—
261(C2×D59)⋊C4—24no—
262(C2×D59)⋊C4—24no—
263(C2×D59)⋊C4—24no—
264(C2×D59)⋊C4C2×D414yes—
265(C2×D59)⋊C4C2×D414yes—
266C4⋊Dic59—21no—
267C4⋊Dic59—24no—
268C4⋊Dic59—24no—
269C4⋊Dic59—24no—
270C4⋊Dic59—24no—
271C4⋊Dic59—24no—
272C4⋊Dic59—24no—
273C4⋊Dic59C2×D414yes—
274C4⋊Dic59C2412yes—
275Dic59⋊C4—24no—
276Dic59⋊C4—24no—
277C4×Dic59—24no—
278C4×Dic59—24no—
279C2×C59⋊C8—22no—
280C2×C59⋊C8—22no—
281C2×C59⋊C8C2412yes—
282C2×C59⋊C8C2412yes—
283Dic236—44no—
284Dic236—44no—
285#11745659—44no—
286C8×D59—44no—
287C23×C59C22×D411yescharacteristic
288C22×D59—22no—
289C22×D59—22no—
290C22×D59—22no—
291C22×D59—22no—
292C22×D59—22no—
293C22×D59#13714yes—
294C22×D59C22×D412yes—
295C22×D59C22×D412yes—
296Q8×C59—24no—
297Q8×C59—22no—
298Q8×C59C2×#4114yes—
299C2×C4×C59—24no—
300C2×C4×C59—22no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—42no—
307C2×C4×C59—42no—
308C2×C4×C59—42no—
309C2×C4×C59C22×D412yes—
310C2×C4×C59C22×D412yes—
311C2×C4×C59C22×D411yescharacteristic
312C2×C4×C59C2×#4112yes—
313C2×C4×C59H(5,𝔽2)12yes—
314C2×C4×C59C2511yescharacteristic
315C2×Dic59—22no—
316C2×Dic59—22no—
317C2×Dic59—22no—
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—42no—
322C2×Dic59—42no—
323C2×Dic59—42no—
324C2×Dic59—42no—
325C2×Dic59C22×D412yes—
326C2×Dic59C22×D412yes—
327D236—28no—
328C4×D59—24no—
329C4×D59—24no—
330C4×D59—22no—
331C4×D59—22no—
332C4×D59—22no—
333C4×D59—22no—
334C4×D59—48no—
335C4×D59—48no—
336C4×D59—48no—
337Dic118—22no—
338Dic118—22no—
339Dic118—22no—
340Dic118—22no—
341Dic118—22no—
342Dic118—22no—
343Dic118—48no—
344Dic118—48no—
345Dic118—42no—
346Dic118—42no—
347Dic118—42no—
348C8×C59—22no—
349C8×C59—22no—
350C59⋊C8—22no—
351C59⋊C8—22no—
352C2×#3312—591nomaximal, Sylow
353C22×C59#54612yes—
354C22×C59C2×#13712yes—
355C22×C59#57812yes—
356C22×C59C23×D411yescharacteristic
357C2×D59—22no—
358C2×D59—28no—
359C2×D59—22no—
360C2×D59—22no—
361C2×D59—22no—
362C2×D59—22no—
363C2×D59—44no—
364C2×D59C2×#13714yes—
365C4×C59—24no—
366C4×C59—22no—
367C4×C59—22no—
368C4×C59—42no—
369C4×C59—42no—
370C4×C59—42no—
371C4×C59#54612yes—
372C4×C59C22×#4111yescharacteristic
373C4×C59C2×H(5,𝔽2)11yescharacteristic
374Dic59—22no—
375Dic59—22no—
376Dic59—42no—
377Dic59—42no—
378Dic59—42no—
379Dic59—42no—
380C2×#552—591no—
381C2×D4×Q8—591no—
382#3312—5916no—
383C2×#491—591no—
384C2×#485—591no—
385C2×#483—591no—
386C2×#479D5911yescharacteristic, complemented
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#331214yescomplemented
397C2×C59C2×#54611yescharacteristic
398C2×C59C22×#13711yescharacteristic
399C2×C59C2×#57811yescharacteristic
400D59—24no—
401D59—42no—
402C23×Q8—591no—
403C23×Q8—591no—
404C22×Q16—591no—
405C22×Q16—591no—
406C22×Q16—591no—
407C22×M16—591no—
408C23×C8—591no—
409#552—598no—
410#552—1184no—
411D4×Q8—598no—
412D4×Q8—1184no—
413C2×C4⋊Q8—591no—
414C2×C4⋊Q8—1181no—
415C2×#126—1181no—
416C2×#125—1181no—
417C2×#125C2×D5911yescharacteristic
418C2×#123—1181no—
419C2×C22⋊Q8—591no—
420C2×C22⋊Q8—591no—
421C2×C22⋊Q8—591no—
422C2×C22⋊Q8—591no—
423C2×C22⋊Q8—1181no—
424C2×C22⋊Q8—1181no—
425C2×C4×Q8—591no—
426C2×C4×Q8C2×D5911yescharacteristic
427C2×C4×D4—591no—
428C2×C4×D4—1181no—
429C2×#117—591no—
430C2×#117—1181no—
431C22×C4⋊C4—591no—
432#491—598no—
433#485—598no—
434#483—598no—
435#479C2×D5918yescomplemented
436#470—598no—
437#467—598no—
438#462—598no—
439#451—598no—
440#451—598no—
441#441—598no—
442#435—598no—
443C2×#107C2×D5911yescharacteristic
444C2×#106—591no—
445C2×#106C2×D5911yescharacteristic
446C2×C4⋊C8C2×D5911yescharacteristic
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—598no—
457C2×#103C2×D5911yescharacteristic
458C2×#103C2×D5911yescharacteristic
459C2×C22⋊C8—591no—
460C2×C22⋊C8—591no—
461C2×#97—591no—
462C59C2×#331211yescharacteristic, complemented, Sylow
463C22×Q8—594no—
464C22×Q8—594no—
465C22×Q8—591no—
466C22×Q8—591no—
467C22×Q8—591no—
468C22×Q8—1181no—
469C22×Q8—1181no—
470C22×Q8—1182no—
471C22×Q8—1182no—
472C22×Q8—1184no—
473C22×Q8—1184no—
474C22×Q8—2362no—
475C22×Q8—2362no—
476C22×Q8C22×D5911yescharacteristic
477C22×D4—591no—
478C23×C4—591no—
479C23×C4—591no—
480C23×C4—1181no—
481C23×C4—1181no—
482C23×C4—1181no—
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—594no—
494C22×C8—2362no—
495C22×C8C22×D5911yescharacteristic
496C22×C8C22×D5911yescharacteristic
497C4⋊Q8—594no—
498C4⋊Q8—1188no—
499C4⋊Q8—1182no—
500#126—1188no—
501#125—22no—
502#125—1188no—
503#125C22×D5914yes—
504#123—1188no—
505C22⋊Q8—594no—
506C22⋊Q8—594no—
507C22⋊Q8—594no—
508C22⋊Q8—594no—
509C22⋊Q8—1188no—
510C22⋊Q8—1188no—
511C22⋊Q8—1182no—
512C22⋊Q8—1182no—
513C22⋊Q8—1182no—
514C22⋊Q8—1182no—
515C4×Q8—22no—
516C4×Q8—594no—
517C4×Q8—1182no—
518C4×Q8C22×D5914yes—
519C4×D4—594no—
520C4×D4—594no—
521C4×D4—1188no—
522#117—594no—
523#117—1188no—
524#117—1182no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—591no—
529C2×C4⋊C4—591no—
530C2×C4⋊C4—594no—
531C2×C4⋊C4—1182no—
532C2×C4⋊C4—1181no—
533C2×C4⋊C4—1181no—
534C2×C4⋊C4—1181no—
535C2×C4⋊C4—1181no—
536C2×C4⋊C4—1181no—
537C2×C4⋊C4—1181no—
538C2×C4⋊C4—1181no—
539C2×C4⋊C4—1181no—
540C2×C4⋊C4C22×D5911yescharacteristic
541C2×C4⋊C4C22×D5911yescharacteristic
542C2×C4⋊C4C22×D5911yescharacteristic
543C2×C22⋊C4—591no—
544C2×C22⋊C4—591no—
545C2×C22⋊C4—1181no—
546C2×C22⋊C4—1181no—
547C2×C22⋊C4—1181no—
548C2×C22⋊C4—1181no—
549C2×C22⋊C4—1181no—
550C2×C42—21no—
551C2×C42—1181no—
552C2×C42—1181no—
553C2×C42C22×D5911yescharacteristic
554#107C22×D5914yes—
555#106—594no—
556#106C22×D5914yes—
557C4⋊C8C22×D5914yes—
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#103C22×D5914yes—
567#103C22×D5914yes—
568C22⋊C8—594no—
569C22⋊C8—594no—
570#97—594no—
571C24—591no—
572C24—591no—
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—592no—
576C2×Q8—592no—
577C2×Q8—592no—
578C2×Q8—1184no—
579C2×Q8—1184no—
580C2×Q8—1181no—
581C2×Q8—1181no—
582C2×Q8—1181no—
583C2×Q8—1188no—
584C2×Q8—1188no—
585C2×Q8—1182no—
586C2×Q8—1182no—
587C2×Q8—1182no—
588C2×Q8—1182no—
589C2×Q8—1182no—
590C2×Q8—1182no—
591C2×Q8—2364no—
592C2×Q8—2364no—
593C2×Q8—2364no—
594C2×Q8—2364no—
595C2×Q8—2368no—
596C2×Q8—2368no—
597C2×Q8#1174568914yes—
598C2×Q8C23×D5912yes—
599C2×D4—594no—
600C2×D4—1184no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—591no—
606C22×C4—591no—
607C22×C4—592no—
608C22×C4—592no—
609C22×C4—592no—
610C22×C4—592no—
611C22×C4—1184no—
612C22×C4—1184no—
613C22×C4—1184no—
614C22×C4—1182no—
615C22×C4—1182no—
616C22×C4—1182no—
617C22×C4—1182no—
618C22×C4—1181no—
619C22×C4—1181no—
620C22×C4—1181no—
621C22×C4—1181no—
622C22×C4—2364no—
623C22×C4—2364no—
624C22×C4—2364no—
625C22×C4D4×D5911yescharacteristic
626C22×C4D4×D5911yescharacteristic
627C22×C4C23×D5911yescharacteristic
628Q16—1188no—
629Q16—2364no—
630Q16—2364no—
631M16—2364no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—592no—
635C2×C8—592no—
636C2×C8—1182no—
637C2×C8—1182no—
638C2×C8—2364no—
639C2×C8C23×D5912yes—
640C2×C8C23×D5912yes—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—594no—
648C4⋊C4—592no—
649C4⋊C4—1184no—
650C4⋊C4—1184no—
651C4⋊C4—1184no—
652C4⋊C4—1184no—
653C4⋊C4—1184no—
654C4⋊C4—1181no—
655C4⋊C4—1184no—
656C4⋊C4—1184no—
657C4⋊C4—1184no—
658C4⋊C4C23×D5912yes—
659C4⋊C4C23×D5912yes—
660C4⋊C4C23×D5912yes—
661C22⋊C4—594no—
662C22⋊C4—594no—
663C22⋊C4—1184no—
664C22⋊C4—1184no—
665C22⋊C4—1184no—
666C22⋊C4—1184no—
667C22⋊C4—1184no—
668C42—24no—
669C42—1184no—
670C42—1184no—
671C42D4×D5912yes—
672C42C23×D5912yes—
673C23—594no—
674C23—592no—
675C23—592no—
676C23—1182no—
677C23—1182no—
678C23—1182no—
679C23—1182no—
680C23—1182no—
681C23C2×D4×D5911yescharacteristic
682Q8—22no—
683Q8—24no—
684Q8—1182no—
685Q8—1182no—
686Q8—1182no—
687Q8—1182no—
688Q8—1182no—
689Q8—1182no—
690Q8—2368no—
691Q8—2368no—
692Q8—2362no—
693Q8—2362no—
694Q8—2362no—
695Q8C2×#1174568914yes—
696D4—1188no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—592no—
708C2×C4—592no—
709C2×C4—1182no—
710C2×C4—1182no—
711C2×C4—1182no—
712C2×C4—1182no—
713C2×C4—1182no—
714C2×C4—1182no—
715C2×C4—1184no—
716C2×C4—1184no—
717C2×C4—1182no—
718C2×C4—1182no—
719C2×C4—1182no—
720C2×C4—1182no—
721C2×C4—2368no—
722C2×C4—2368no—
723C2×C4—2368no—
724C2×C4—2362no—
725C2×C4—2362no—
726C2×C4—2362no—
727C2×C4—2362no—
728C2×C4C2×D4×D5912yes—
729C2×C4C2×D4×D5912yes—
730C2×C4C2×D4×D5911yescharacteristic
731C2×C4C2×#1174568912yes—
732C2×C4#1427377312yes—
733C2×C4C24×D5911yescharacteristic
734C8—22no—
735C8—22no—
736C8—1182no—
737C8—1182no—
738C22—594no—
739C22—1182no—
740C22—1182no—
741C22—1188no—
742C22—1182no—
743C22—1182no—
744C22—1182no—
745C22—2364no—
746C22#1683804312yes—
747C22#137×D5912yes—
748C22#1683821612yes—
749C22C22×D4×D5911yescharacteristic
750C4—24no—
751C4—22no—
752C4—22no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—1182no—
757C4—1182no—
758C4—2362no—
759C4—2362no—
760C4—2362no—
761C4—2362no—
762C4#1683804312yes—
763C4C22×#1174568911yescharacteristic
764C4C2×#1427377311yescharacteristic
765C2—1184no—
766C2—2362no—
767C2#2143614414yesdirect product factor
768C2C2×#1683804311yescharacteristic
769C2C2×#137×D5911yescharacteristic
770C2C2×#1683821611yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#479C2
socleC23×C59C22×D4
prime radicalC22×D236D4
hypercenterC2×#479D59
hypocenterC59C2×#3312
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
3. #21436144C2direct (N × H)
4. C2×#16837772C2semidirect
5. C2×#16837745C2semidirect
6. C2×#16837734C2semidirect
7. C2×#16837661C2semidirect
8. C2×#16837644C2semidirect
9. C2×#16837613C2semidirect
10. C2×#16837559C2semidirect
11. C2×#16837559C2semidirect
12. C2×#16837507C2semidirect
14. C2×#16837409C2semidirect
15. C2×#103×D59C2semidirect
16. C2×C59×#479C2semidirect
45. #16837772C22semidirect
46. #16837745C22semidirect
47. #16837734C22semidirect
48. #16837661C22semidirect
49. #16837644C22semidirect
50. #16837613C22semidirect
51. #16837559C22semidirect
52. #16837559C22semidirect
53. #16837507C22semidirect
56. #16837409C22semidirect
65. #103×D59C22semidirect
71. C59×#479C22semidirect
386. C2×#479D59semidirect
396. C2×C59#3312semidirect
435. #479C2×D59semidirect
462. C59C2×#3312semidirect
767. C2#21436144direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380902
C2×Q8×D2362
#214361442
C2×#168377722
C2×#168377452
C2×#168377342
C2×#168376612
C2×#168376442
C2×#168376132
C2×#168375592
C2×#168375072
C2×#168374722
C2×#168374092
C2×#103×D592
C2×C59×#4792
C2×#331259