Finite Group Databasebeta

← C2×#21436145 #29465293

Subgroups — C2×#21436145 #29465293

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×#16838087C211yesmaximal, characteristic
2C2×#16838065C211yesmaximal, characteristic
3#21436145C2116yesmaximal, direct product factor
4C2×#16837769C211yesmaximal, characteristic, complemented
5C2×#16837746C211yesmaximal, characteristic, complemented
6C2×#16837712C211yesmaximal, characteristic, complemented
7C2×#16837661C211yesmaximal, characteristic, complemented
8C2×#16837641C211yesmaximal, characteristic, complemented
9C2×#16837611C211yesmaximal, characteristic, complemented
10C2×#16837560C211yesmaximal, characteristic, complemented
11C2×#16837559C211yesmaximal, characteristic, complemented
12C2×#16837508C211yesmaximal, characteristic, complemented
13C2×#16837470C211yesmaximal, characteristic
14C2×#16837409C211yesmaximal, characteristic, complemented
15C22×#14273650C211yesmaximal, characteristic, complemented
16C2×C59×#483C211yesmaximal, characteristic, complemented
17C23×Dic118C2211yescharacteristic
18C22×Q8×D59C2211yescharacteristic
19C22×Dic236C2211yescharacteristic
20C22×Dic236C2211yescharacteristic
21C22×#11745672C2211yescharacteristic
22C22×#11745659C2211yescharacteristic
23C23×C59⋊C8C2211yescharacteristic
24#16838087—24no—
25#16838087C2218yes—
26#16838065—24no—
27#16838065C2218yes—
28C2×#14273726—21no—
29C2×#14273725C2211yescharacteristic
30C2×#14273722—21no—
31C2×#14273718C2211yescharacteristic
32C2×#14273717—21no—
33C2×#14273710—21no—
34C2×#14273707C2211yescharacteristic
35C2×#14273707C2211yescharacteristic
36C2×#14273706C2211yescharacteristic
37C2×#14273705—21no—
38C2×#14273704—21no—
39C2×#14273692C2211yescharacteristic
40C2×#14273692C2211yescharacteristic
41C2×C4×C22⋊D59C2211yescharacteristic
42C2×(C22⋊D59)⋊C4—21no—
43C2×#14273686—21no—
44C2×#14273685C2211yescharacteristic
45#16837769C2218yescomplemented
46#16837746C2218yescomplemented
47#16837712C2218yescomplemented
48#16837661C2218yescomplemented
49#16837641C2218yescomplemented
50#16837611C2218yescomplemented
51#16837560C2218yescomplemented
52#16837559C2218yescomplemented
53#16837508C2218yescomplemented
54#16837470C2218yes—
55C2×#14273660C2211yescharacteristic
56C2×Dic59⋊C8C2211yescharacteristic
57#16837409C2218yescomplemented
58C2×#14273652C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65C2×#14273650C2211yescharacteristic
66C2×#14273650C2218yescomplemented
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×#14273637C2211yescharacteristic
69C2×C22⋊Q8×C59C2211yescharacteristic
70C22×C4⋊C4×C59C2211yescharacteristic
71C59×#483C2218yescomplemented
72C2×#106×C59C2211yescharacteristic
73C2×#106×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×C22⋊C8×C59C2211yescharacteristic
77C22×Dic118—24no—
78C22×Dic118—21no—
79C22×Dic118—22no—
80C22×Dic118—21no—
81C22×Dic118—42no—
82C22×Dic118C2311yescharacteristic
83C22×Dic118C2311yescharacteristic
84C22×Dic118C2314yes—
85C22×Dic118C2311yescharacteristic
86C2×Q8×D59—22no—
87C2×Q8×D59—24no—
88C2×Q8×D59—42no—
89C2×Q8×D59C2314yes—
90C22×C22⋊D59D411yescharacteristic
91C23×Dic59—21no—
92C22×C4×D59—21no—
93C22×C4×D59C2311yescharacteristic
94C2×Dic236—24no—
95C2×Dic236—42no—
96C2×Dic236C2314yes—
97C2×Dic236C2314yes—
98C2×#11745672—42no—
99C2×#11745672C2314yes—
100C2×#11745659—42no—
101C2×#11745659C2314yes—
102C22×C59⋊C8—42no—
103C22×C59⋊C8C2311yescharacteristic
104C22×C59⋊C8C2311yescharacteristic
105C22×C59⋊C8C2314yes—
106#14273726—28no—
107#14273725—22no—
108#14273725C2314yes—
109#14273722—28no—
110#14273718—22no—
111#14273718C2314yes—
112#14273717—28no—
113#14273710—28no—
114#14273707—22no—
115#14273707—22no—
116#14273707C2314yes—
117#14273707C2314yes—
118#14273706—22no—
119#14273706C2314yes—
120#14273705—28no—
121#14273704—28no—
122#14273692—22no—
123#14273692—22no—
124#14273692C2314yes—
125#14273692C2314yes—
126C4×C22⋊D59D414yes—
127C4×C22⋊D59C2314yes—
128(C22⋊D59)⋊C4—28no—
129#14273686—28no—
130#14273685—22no—
131#14273685C2314yes—
132C2×C4⋊Dic59—21no—
133C2×C4⋊Dic59—21no—
134C2×C4⋊Dic59—21no—
135C2×C4⋊Dic59C2311yescharacteristic
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4—21no—
140C2×Dic59⋊C4—21no—
141C2×Dic59⋊C4—21no—
142C2×Dic59⋊C4D411yescharacteristic
143C2×C22⋊Dic59—21no—
144C2×C22⋊Dic59D411yescharacteristic
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4D411yescharacteristic
149C2×C4×Dic59—21no—
150C2×C4×Dic59—21no—
151C2×C4×Dic59—21no—
152C2×C4×Dic59C2311yescharacteristic
153#14273660C2314yes—
154Dic59⋊C8C2314yes—
155#14273652C2314yes—
156#14273652C2314yes—
157#14273651C2314yes—
158#14273650C2314yes—
159#14273650C2314yes—
160#14273650C2314yes—
161#14273650C2314yes—
162#14273650C2314yes—
163(C2×D59)⋊C8C2314yes—
164#14273637C2314yes—
165C22×Q8×C59C2311yescharacteristic
166C23×C4×C59—21no—
167C23×C4×C59C2311yescharacteristic
168C22×C8×C59C2311yescharacteristic
169C22×C8×C59C2311yescharacteristic
170C22⋊Q8×C59—22no—
171C22⋊Q8×C59C2314yes—
172C2×C4⋊C4×C59—21no—
173C2×C4⋊C4×C59—21no—
174C2×C4⋊C4×C59—22no—
175C2×C4⋊C4×C59C2311yescharacteristic
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C4⋊C4×C59C2314yes—
179C2×C22⋊C4×C59—21no—
180#106×C59C2314yes—
181#106×C59C2314yes—
182#103×C59C2314yes—
183#103×C59C2314yes—
184C22⋊C8×C59C2314yes—
185C24×C59C2×D411yescharacteristic
186C23×D59C2×D411yescharacteristic
187C2×Q8×C59—21no—
188C2×Q8×C59—22no—
189C2×Q8×C59—22no—
190C2×Q8×C59C2412yes—
191C22×C4×C59—22no—
192C22×C4×C59—22no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—24no—
198C22×C4×C59—44no—
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D412yes—
201C22×C4×C59C2412yes—
202C22×C4×C59C2411yescharacteristic
203C2×C22⋊D59—24no—
204C2×C22⋊D59C2×D414yes—
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59—21no—
209C22×Dic59—24no—
210C22×Dic59—44no—
211C22×Dic59C2×D411yescharacteristic
212C22×Dic59C2×D411yescharacteristic
213C22×Dic59C2×D411yescharacteristic
214Q8×D59—28no—
215Q8×D59—44no—
216Q8×D59—48no—
217C2×C4×D59—22no—
218C2×C4×D59—22no—
219C2×C4×D59—24no—
220C2×C4×D59—44no—
221C2×C4×D59C2×D412yes—
222C2×C4×D59C2412yes—
223C2×Dic118—21no—
224C2×Dic118—22no—
225C2×Dic118—22no—
226C2×Dic118—22no—
227C2×Dic118—22no—
228C2×Dic118—22no—
229C2×Dic118—28no—
230C2×Dic118—21no—
231C2×Dic118—24no—
232C2×Dic118—21no—
233C2×Dic118—24no—
234C2×Dic118—44no—
235C2×Dic118—48no—
236C2×Dic118—44no—
237C2×Dic118—44no—
238C2×Dic118#4114yes—
239C2×Dic118C2412yes—
240C2×Dic118C2412yes—
241C2×Dic118C2412yes—
242C2×C8×C59—22no—
243C2×C8×C59—22no—
244C2×C8×C59C2412yes—
245C2×C8×C59C2412yes—
246C4⋊C4×C59—21no—
247C4⋊C4×C59—21no—
248C4⋊C4×C59—24no—
249C4⋊C4×C59—24no—
250C4⋊C4×C59—21no—
251C4⋊C4×C59C2412yes—
252C4⋊C4×C59C2412yes—
253C4⋊C4×C59C2412yes—
254C22⋊C4×C59—24no—
255C22⋊Dic59—24no—
256C22⋊Dic59C2×D414yes—
257#11745672—44no—
258(C2×D59)⋊C4—24no—
259(C2×D59)⋊C4—24no—
260(C2×D59)⋊C4—24no—
261(C2×D59)⋊C4C2×D414yes—
262C4⋊Dic59—21no—
263C4⋊Dic59—24no—
264C4⋊Dic59—24no—
265C4⋊Dic59—24no—
266C4⋊Dic59C2412yes—
267Dic59⋊C4—24no—
268Dic59⋊C4—24no—
269Dic59⋊C4—24no—
270Dic59⋊C4—24no—
271Dic59⋊C4—24no—
272Dic59⋊C4—24no—
273Dic59⋊C4C2×D414yes—
274C4×Dic59—24no—
275C4×Dic59—24no—
276C4×Dic59—24no—
277C4×Dic59C2×D412yes—
278C4×Dic59C2412yes—
279C2×C59⋊C8—22no—
280C2×C59⋊C8—22no—
281C2×C59⋊C8—44no—
282C2×C59⋊C8C2412yes—
283C2×C59⋊C8C2412yes—
284Dic236—28no—
285Dic236—44no—
286#11745659—44no—
287C23×C59—22no—
288C23×C59—22no—
289C23×C59#13714yes—
290C23×C59C22×D412yes—
291C23×C59C22×D411yescharacteristic
292C22×D59—22no—
293C22×D59—22no—
294C22×D59—22no—
295C22×D59C22×D412yes—
296Q8×C59—22no—
297Q8×C59—22no—
298Q8×C59—42no—
299C2×C4×C59—22no—
300C2×C4×C59—24no—
301C2×C4×C59—22no—
302C2×C4×C59—22no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—42no—
308C2×C4×C59—48no—
309C2×C4×C59—42no—
310C2×C4×C59—42no—
311C2×C4×C59—42no—
312C2×C4×C59C22×D412yes—
313C2×C4×C59C22×D411yescharacteristic
314C2×C4×C59C2×#4112yes—
315C2×C4×C59H(5,𝔽2)12yes—
316C2×C4×C59C2511yescharacteristic
317C22⋊D59—28no—
318C2×Dic59—24no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—48no—
327C2×Dic59—42no—
328C2×Dic59—42no—
329C2×Dic59—42no—
330C2×Dic59C22×D412yes—
331C2×Dic59C22×D412yes—
332C2×Dic59C22×D412yes—
333C4×D59—24no—
334C4×D59—22no—
335C4×D59—22no—
336C4×D59—48no—
337Dic118—24no—
338Dic118—22no—
339Dic118—22no—
340Dic118—22no—
341Dic118—22no—
342Dic118—22no—
343Dic118—48no—
344Dic118—48no—
345Dic118—42no—
346Dic118—42no—
347Dic118C2×#4114yes—
348C8×C59—22no—
349C8×C59—22no—
350C59⋊C8—22no—
351C59⋊C8—22no—
352C2×#3312—591nomaximal, Sylow
353C22×C59—22no—
354C22×C59—28no—
355C22×C59—22no—
356C22×C59#54612yes—
357C22×C59C2×#13714yes—
358C22×C59C2×#13712yes—
359C22×C59#57812yes—
360C22×C59C23×D411yescharacteristic
361C2×D59—22no—
362C2×D59—22no—
363C2×D59—22no—
364C2×D59—44no—
365C4×C59—22no—
366C4×C59—42no—
367C4×C59—42no—
368C4×C59—42no—
369C4×C59—42no—
370C4×C59#54612yes—
371C4×C59C22×#4111yescharacteristic
372C4×C59C2×H(5,𝔽2)11yescharacteristic
373Dic59—24no—
374Dic59—22no—
375Dic59—22no—
376Dic59—22no—
377Dic59—42no—
378Dic59—42no—
379Dic59—42no—
380C2×#552—591no—
381C2×D4×Q8—591no—
382#3312—5916no—
383C2×#491—591no—
384C2×#485—591no—
385C2×#483D5911yescharacteristic, complemented
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#331214yescomplemented
398C2×C59C2×#54611yescharacteristic
399C2×C59C22×#13711yescharacteristic
400C2×C59C2×#57811yescharacteristic
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—591no—
417C2×#125—1181no—
418C2×#123—1181no—
419C2×C22⋊Q8—591no—
420C2×C22⋊Q8—591no—
421C2×C22⋊Q8—591no—
422C2×C22⋊Q8—1181no—
423C2×C22⋊Q8—1181no—
424C2×C22⋊Q8C2×D5911yescharacteristic
425C2×C4×Q8—591no—
426C2×C4×Q8—591no—
427C2×C4×D4—591no—
428C2×C4×D4—1181no—
429C2×#117—591no—
430C2×#117—1181no—
431C22×C4⋊C4C2×D5911yescharacteristic
432#491—598no—
433#485—598no—
434#483C2×D5918yescomplemented
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×#106C2×D5911yescharacteristic
445C2×#106C2×D5911yescharacteristic
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—598no—
457C2×#103C2×D5911yescharacteristic
458C2×#103C2×D5911yescharacteristic
459C2×C22⋊C8—591no—
460C2×C22⋊C8C2×D5911yescharacteristic
461C2×#97—591no—
462C59C2×#331211yescharacteristic, complemented, Sylow
463C22×Q8—594no—
464C22×Q8—591no—
465C22×Q8—591no—
466C22×Q8—591no—
467C22×Q8—594no—
468C22×Q8—1181no—
469C22×Q8—1184no—
470C22×Q8—1182no—
471C22×Q8—1181no—
472C22×Q8—1182no—
473C22×Q8—1184no—
474C22×Q8—2362no—
475C22×Q8—2362no—
476C22×Q8C22×D5911yescharacteristic
477C22×D4—591no—
478C23×C4—21no—
479C23×C4—591no—
480C23×C4—1181no—
481C23×C4—1181no—
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—594no—
494C22×C8—2362no—
495C22×C8C22×D5911yescharacteristic
496C22×C8C22×D5911yescharacteristic
497C4⋊Q8—594no—
498C4⋊Q8—1182no—
499C4⋊Q8—1188no—
500#126—1188no—
501#125—594no—
502#125—1182no—
503#125—1188no—
504#123—1188no—
505C22⋊Q8—22no—
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⋊Q8C22×D5914yes—
515C4×Q8—594no—
516C4×Q8—594no—
517C4×Q8—1182no—
518C4×Q8—1182no—
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—22no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—591no—
529C2×C4⋊C4—591no—
530C2×C4⋊C4—1181no—
531C2×C4⋊C4—1181no—
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⋊C4C22×D5911yescharacteristic
540C2×C4⋊C4C22×D5911yescharacteristic
541C2×C4⋊C4C22×D5914yes—
542C2×C4⋊C4C22×D5911yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—591no—
545C2×C22⋊C4—591no—
546C2×C22⋊C4—1181no—
547C2×C22⋊C4—1181no—
548C2×C22⋊C4—1181no—
549C2×C22⋊C4—1181no—
550C2×C42—591no—
551C2×C42—1181no—
552C2×C42—1181no—
553C2×C42—1181no—
554#107—594no—
555#106C22×D5914yes—
556#106C22×D5914yes—
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#103C22×D5914yes—
567#103C22×D5914yes—
568C22⋊C8—594no—
569C22⋊C8C22×D5914yes—
570#97—594no—
571C24—591no—
572C24D4×D5911yescharacteristic
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—594no—
577C2×Q8—592no—
578C2×Q8—592no—
579C2×Q8—592no—
580C2×Q8—1184no—
581C2×Q8—1188no—
582C2×Q8—1181no—
583C2×Q8—1181no—
584C2×Q8—1184no—
585C2×Q8—1181no—
586C2×Q8—1182no—
587C2×Q8—1188no—
588C2×Q8—1182no—
589C2×Q8—1182no—
590C2×Q8—1182no—
591C2×Q8—1182no—
592C2×Q8—2364no—
593C2×Q8—2364no—
594C2×Q8—2368no—
595C2×Q8—2364no—
596C2×Q8—2364no—
597C2×Q8—2368no—
598C2×Q8C23×D5912yes—
599C2×D4—594no—
600C2×D4—1184no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—24no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—44no—
609C22×C4—591no—
610C22×C4—591no—
611C22×C4—591no—
612C22×C4—592no—
613C22×C4—592no—
614C22×C4—1184no—
615C22×C4—1181no—
616C22×C4—1182no—
617C22×C4—1182no—
618C22×C4—1184no—
619C22×C4—1181no—
620C22×C4—1181no—
621C22×C4—1181no—
622C22×C4—2364no—
623C22×C4—2364no—
624C22×C4D4×D5912yes—
625C22×C4D4×D5911yescharacteristic
626C22×C4C23×D5912yes—
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—21no—
642C4⋊C4—21no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—594no—
647C4⋊C4—592no—
648C4⋊C4—1184no—
649C4⋊C4—1184no—
650C4⋊C4—1184no—
651C4⋊C4—1184no—
652C4⋊C4—1184no—
653C4⋊C4—1184no—
654C4⋊C4—1184no—
655C4⋊C4—1184no—
656C4⋊C4—1181no—
657C4⋊C4—1184no—
658C4⋊C4C23×D5912yes—
659C4⋊C4C23×D5912yes—
660C4⋊C4C23×D5912yes—
661C22⋊C4—24no—
662C22⋊C4—594no—
663C22⋊C4—594no—
664C22⋊C4—1184no—
665C22⋊C4—1184no—
666C22⋊C4—1184no—
667C22⋊C4—1184no—
668C42—592no—
669C42—592no—
670C42—1184no—
671C42—1184no—
672C42—1184no—
673C23—22no—
674C23—22no—
675C23—592no—
676C23—1182no—
677C23—1182no—
678C23—1182no—
679C23#1427375614yes—
680C23C2×D4×D5912yes—
681C23C2×D4×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—1188no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—48no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—592no—
711C2×C4—592no—
712C2×C4—592no—
713C2×C4—1182no—
714C2×C4—1182no—
715C2×C4—1182no—
716C2×C4—1182no—
717C2×C4—1184no—
718C2×C4—1182no—
719C2×C4—1182no—
720C2×C4—1184no—
721C2×C4—1182no—
722C2×C4—1182no—
723C2×C4—1182no—
724C2×C4—2368no—
725C2×C4—2368no—
726C2×C4—2362no—
727C2×C4—2362no—
728C2×C4—2362no—
729C2×C4C2×D4×D5912yes—
730C2×C4C2×D4×D5911yescharacteristic
731C2×C4#41×D5912yes—
732C2×C4#1427377312yes—
733C2×C4C24×D5911yescharacteristic
734C8—22no—
735C8—22no—
736C8—1182no—
737C8—1182no—
738C22—22no—
739C22—22no—
740C22—28no—
741C22—1182no—
742C22—1182no—
743C22—1182no—
744C22—2364no—
745C22#1683804412yes—
746C22C2×#1427375614yes—
747C22C2×#1427375612yes—
748C22#1683821812yes—
749C22C22×D4×D5911yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—1182no—
756C4—1184no—
757C4—1182no—
758C4—1182no—
759C4—2362no—
760C4—2362no—
761C4—2362no—
762C4#1683804412yes—
763C4C2×#41×D5911yescharacteristic
764C4C2×#1427377311yescharacteristic
765C2—24no—
766C2—2362no—
767C2#2143614514yesdirect product factor
768C2C2×#1683804411yescharacteristic
769C2C22×#1427375611yescharacteristic
770C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#483C2
socleC23×C59C22×D4
prime radicalC22×C22⋊D59D4
hypercenterC2×#483D59
hypocenterC59C2×#3312
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
3. #21436145C2direct (N × H)
4. C2×#16837769C2semidirect
5. C2×#16837746C2semidirect
6. C2×#16837712C2semidirect
7. C2×#16837661C2semidirect
8. C2×#16837641C2semidirect
9. C2×#16837611C2semidirect
10. C2×#16837560C2semidirect
11. C2×#16837559C2semidirect
12. C2×#16837508C2semidirect
14. C2×#16837409C2semidirect
15. C22×#14273650C2semidirect
16. C2×C59×#483C2semidirect
45. #16837769C22semidirect
46. #16837746C22semidirect
47. #16837712C22semidirect
48. #16837661C22semidirect
49. #16837641C22semidirect
50. #16837611C22semidirect
51. #16837560C22semidirect
52. #16837559C22semidirect
53. #16837508C22semidirect
57. #16837409C22semidirect
66. C2×#14273650C22semidirect
71. C59×#483C22semidirect
385. C2×#483D59semidirect
397. C2×C59#3312semidirect
434. #483C2×D59semidirect
462. C59C2×#3312semidirect
767. C2#21436145direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380872
C2×#168380652
#214361452
C2×#168377692
C2×#168377462
C2×#168377122
C2×#168376612
C2×#168376412
C2×#168376112
C2×#168375602
C2×#168375592
C2×#168375082
C2×#168374702
C2×#168374092
C22×#142736502
C2×C59×#4832
C2×#331259