Finite Group Databasebeta

← C2×#21432938 #29452797

Subgroups — C2×#21432938 #29452797

Order 15104.

2730 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273759C211yesmaximal, characteristic
2C2×#16837884C211yesmaximal, characteristic
3C2×#16837878C211yesmaximal, characteristic, complemented
4#21432938C2116yesmaximal, direct product factor
5C2×#16837506C211yesmaximal, characteristic, complemented
6C2×#16837505C211yesmaximal, characteristic, complemented
7C2×#16837504C211yesmaximal, characteristic, complemented
8C2×Q16×Dic59C211yesmaximal, characteristic, complemented
9C2×C4×#11745672C211yesmaximal, characteristic, complemented
10C2×C4×#11745671C211yesmaximal, characteristic, complemented
11C2×#16837489C211yesmaximal, characteristic, complemented
12C2×#16837441C211yesmaximal, characteristic, complemented
13C2×#16837397C211yesmaximal, characteristic
14C2×#103×D59C211yesmaximal, characteristic, complemented
15C2×#16837359C211yesmaximal, characteristic, complemented
16C2×C59×#441C211yesmaximal, characteristic, complemented
17C22×#11745689C2211yescharacteristic
18C22×Q8×D59C2211yescharacteristic
19C2×#14273759C4116yescomplemented
20C2×#14273759C2218yes—
21C22×#11745672C2211yescharacteristic
22C22×#11745660C2211yescharacteristic
23C22×#11745671C2211yescharacteristic
24C22×#11745659C2211yescharacteristic
25C22×C8×D59C2211yescharacteristic
26#16837884—24no—
27#16837884C2218yes—
28#16837878—24no—
29#16837878C2218yescomplemented
30C2×Q8×Dic59C2211yescharacteristic
31C2×Q8×Dic59C2211yescharacteristic
32C2×C4×Dic118—21no—
33C2×C4×Dic118C2211yescharacteristic
34C2×#14273692—21no—
35C2×#14273692C2211yescharacteristic
36C2×C4×D236—21no—
37C2×C4×D236C2211yescharacteristic
38C2×#14273689—21no—
39C2×#14273689C2211yescharacteristic
40C2×#14273685—21no—
41C2×#14273685C2211yescharacteristic
42C2×#14273684—21no—
43C2×#14273684—21no—
44C2×#14273684C2211yescharacteristic
45C2×C4⋊C4×D59—21no—
46C2×C4⋊C4×D59C2211yescharacteristic
47#16837506C2218yescomplemented
48#16837505C2218yescomplemented
49#16837504C2218yescomplemented
50Q16×Dic59C2218yescomplemented
51C4×#11745672C2218yescomplemented
52C4×#11745671C2218yescomplemented
53#16837489C2218yescomplemented
54#16837441C2218yescomplemented
55C2×#14273661C2211yescharacteristic
56C2×#14273660C2211yescharacteristic
57C2×#14273658C2211yescharacteristic
58#16837397C2218yes—
59C2×#14273652C2211yescharacteristic
60C2×#14273651C2211yescharacteristic
61C2×#14273651C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63#103×D59C2218yescomplemented
64C2×#14273649C2211yescharacteristic
65C2×#14273647C2211yescharacteristic
66#16837359C2218yescomplemented
67C2×#14273637C2211yescharacteristic
68C2×C4×C59⋊C8C2211yescharacteristic
69C2×C8×Dic59C2211yescharacteristic
70C22×Q16×C59C2211yescharacteristic
71C2×C4×Q8×C59C2211yescharacteristic
72C2×C4×Q8×C59C2211yescharacteristic
73C59×#441C2218yescomplemented
74C2×#106×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#103×C59C2211yescharacteristic
77C2×#97×C59C2211yescharacteristic
78C2×#11745689—22no—
79C2×#11745689—24no—
80C2×#11745689C2×C418yes—
81C2×#11745689C2314yes—
82C22×Dic118—21no—
83C22×Dic118C2311yescharacteristic
84C2×Q8×D59—22no—
85C2×Q8×D59—24no—
86C2×Q8×D59C2×C418yescomplemented
87C2×Q8×D59C2314yes—
88C22×D236—21no—
89C22×D236C2311yescharacteristic
90C22×C4×D59—21no—
91C22×C4×D59—21no—
92C22×C4×D59—21no—
93C22×C4×D59—21no—
94C22×C4×D59—21no—
95C22×C4×D59C2311yescharacteristic
96#14273759C2×C4164yescomplemented
97C2×#11745672C2×C418yescomplemented
98C2×#11745672C2314yes—
99C2×#11745660C2×C418yescomplemented
100C2×#11745660C2314yes—
101C2×#11745671C2×C418yescomplemented
102C2×#11745671C2314yes—
103C2×#11745659C2×C418yescomplemented
104C2×#11745659C2314yes—
105C22×C59⋊C8C2311yescharacteristic
106C22×C59⋊C8C2311yescharacteristic
107C2×C8×D59—24no—
108C2×C8×D59C2314yes—
109Q8×Dic59—22no—
110Q8×Dic59—22no—
111Q8×Dic59C2314yes—
112Q8×Dic59C2314yes—
113C4×Dic118—22no—
114C4×Dic118—28no—
115C4×Dic118C2314yes—
116#14273692—28no—
117#14273692—22no—
118#14273692C2314yes—
119C4×D236—22no—
120C4×D236—28no—
121C4×D236C2314yes—
122#14273689—28no—
123#14273689—22no—
124#14273689C2314yes—
125#14273685—22no—
126#14273685—28no—
127#14273685C2314yes—
128#14273684—28no—
129#14273684—28no—
130#14273684D414yes—
131#14273684C2314yes—
132C2×C4⋊Dic59—21no—
133C2×C4⋊Dic59—21no—
134C2×C4⋊Dic59C2311yescharacteristic
135C2×C4⋊Dic59C2311yescharacteristic
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4D411yescharacteristic
140C2×Dic59⋊C4D411yescharacteristic
141C4⋊C4×D59—22no—
142C4⋊C4×D59—28no—
143C4⋊C4×D59C2314yes—
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4D411yescharacteristic
148C2×(C2×D59)⋊C4D411yescharacteristic
149C2×C4×Dic59—21no—
150C2×C4×Dic59—21no—
151C2×C4×Dic59—21no—
152C2×C4×Dic59—21no—
153C2×C4×Dic59—21no—
154C2×C4×Dic59C2311yescharacteristic
155#14273661C2314yes—
156#14273660C2314yes—
157#14273658C2314yes—
158#14273652C2314yes—
159#14273651C2314yes—
160#14273651C2314yes—
161#14273650C2314yes—
162#14273649C2314yes—
163#14273647C2314yes—
164#14273637C2314yes—
165C4×C59⋊C8C2314yes—
166C8×Dic59C2314yes—
167C22×Q8×C59C2311yescharacteristic
168C22×Q8×C59C2311yescharacteristic
169C2×Q16×C59C2×C418yescomplemented
170C2×Q16×C59C2314yes—
171C22×C8×C59C2311yescharacteristic
172C22×C8×C59C2311yescharacteristic
173C4×Q8×C59—22no—
174C4×Q8×C59—22no—
175C4×Q8×C59C2314yes—
176C4×Q8×C59C2314yes—
177C2×C4⋊C4×C59—21no—
178C2×C4⋊C4×C59—21no—
179C2×C4⋊C4×C59C2311yescharacteristic
180C2×C4⋊C4×C59C2311yescharacteristic
181C2×C42×C59—21no—
182C2×C42×C59—21no—
183C2×C42×C59C2311yescharacteristic
184#106×C59C2314yes—
185#103×C59C2314yes—
186#103×C59C2314yes—
187#97×C59C2314yes—
188C23×D59—21no—
189C23×D59C2×D411yescharacteristic
190C2×Q8×C59—21no—
191C2×Q8×C59—21no—
192C2×Q8×C59—22no—
193C2×Q8×C59—22no—
194C2×Q8×C59C22×C414yes—
195C2×Q8×C59C22×C414yes—
196C2×Q8×C59C2412yes—
197C2×Q8×C59C2412yes—
198C22×C4×C59—21no—
199C22×C4×C59—21no—
200C22×C4×C59—21no—
201C22×C4×C59—21no—
202C22×C4×C59C2×D411yescharacteristic
203C22×C4×C59C2×D411yescharacteristic
204C22×C4×C59C2411yescharacteristic
205C22×Dic59—21no—
206C22×Dic59—21no—
207C22×Dic59—21no—
208C22×Dic59C2×D411yescharacteristic
209C22×Dic59C2×D411yescharacteristic
210C22×Dic59C2×D411yescharacteristic
211#11745689—216no—
212#11745689—28no—
213#11745689C22×C4116yes—
214Q8×D59—216no—
215Q8×D59—28no—
216Q8×D59C22×C4116yescomplemented
217C2×D236—28no—
218C2×D236—24no—
219C2×D236—21no—
220C2×D236—22no—
221C2×D236C22×C414yes—
222C2×D236C2412yes—
223C2×C4×D59—28no—
224C2×C4×D59—24no—
225C2×C4×D59—28no—
226C2×C4×D59—24no—
227C2×C4×D59—24no—
228C2×C4×D59—24no—
229C2×C4×D59—24no—
230C2×C4×D59—82no—
231C2×C4×D59—82no—
232C2×C4×D59—82no—
233C2×C4×D59C22×C414yes—
234C2×C4×D59C2×D412yes—
235C2×C4×D59#4114yes—
236C2×C4×D59C2412yes—
237C2×Dic118—21no—
238C2×Dic118—22no—
239C2×Dic118—28no—
240C2×Dic118—24no—
241C2×Dic118C22×C414yes—
242C2×Dic118C2412yes—
243Q16×C59C22×C4116yescomplemented
244C2×C8×C59—22no—
245C2×C8×C59C22×C414yes—
246C2×C8×C59C2412yes—
247C2×C8×C59C2412yes—
248C4⋊C4×C59—24no—
249C4⋊C4×C59—24no—
250C4⋊C4×C59—21no—
251C4⋊C4×C59—21no—
252C4⋊C4×C59C2412yes—
253C4⋊C4×C59C2412yes—
254C42×C59—24no—
255C42×C59—24no—
256C42×C59C2×D412yes—
257C42×C59C2412yes—
258#11745672C22×C4116yescomplemented
259#11745671C22×C4116yescomplemented
260(C2×D59)⋊C4—24no—
261(C2×D59)⋊C4—24no—
262(C2×D59)⋊C4—24no—
263(C2×D59)⋊C4C2×D414yes—
264(C2×D59)⋊C4C2×D414yes—
265C4⋊Dic59—21no—
266C4⋊Dic59—21no—
267C4⋊Dic59—24no—
268C4⋊Dic59—24no—
269C4⋊Dic59C2412yes—
270C4⋊Dic59C2412yes—
271Dic59⋊C4—24no—
272Dic59⋊C4—24no—
273Dic59⋊C4—24no—
274Dic59⋊C4C2×D414yes—
275Dic59⋊C4C2×D414yes—
276C4×Dic59—24no—
277C4×Dic59—24no—
278C4×Dic59—24no—
279C4×Dic59—24no—
280C4×Dic59—24no—
281C4×Dic59C2×D412yes—
282C4×Dic59C2412yes—
283C2×C59⋊C8—22no—
284C2×C59⋊C8C22×C414yes—
285C2×C59⋊C8C2412yes—
286C2×C59⋊C8C2412yes—
287#11745660C22×C4116yescomplemented
288#11745659C22×C4116yescomplemented
289C8×D59—28no—
290C23×C59C22×D411yescharacteristic
291C22×D59—22no—
292C22×D59—22no—
293C22×D59—24no—
294C22×D59—22no—
295C22×D59—42no—
296C22×D59—42no—
297C22×D59C4×D414yes—
298C22×D59C22×D412yes—
299Q8×C59—24no—
300Q8×C59—24no—
301Q8×C59—22no—
302Q8×C59—22no—
303Q8×C59C23×C414yes—
304Q8×C59C23×C414yes—
305C2×C4×C59—24no—
306C2×C4×C59—24no—
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—42no—
314C2×C4×C59—42no—
315C2×C4×C59C23×C412yes—
316C2×C4×C59C22×D412yes—
317C2×C4×C59C22×D412yes—
318C2×C4×C59C22×D411yescharacteristic
319C2×C4×C59C2×#4112yes—
320C2×C4×C59C2511yescharacteristic
321C2×Dic59—24no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—42no—
328C2×Dic59—42no—
329C2×Dic59C4×D414yes—
330C2×Dic59C22×D412yes—
331C2×Dic59C22×D412yes—
332C2×Dic59C22×D412yes—
333D236—216no—
334D236—24no—
335D236—22no—
336D236C23×C414yes—
337C4×D59—216no—
338C4×D59—216no—
339C4×D59—84no—
340C4×D59—84no—
341C4×D59—84no—
342C4×D59C4×D418yes—
343C4×D59C23×C414yes—
344C4×D59C2×#4114yes—
345Dic118—24no—
346Dic118—22no—
347Dic118—216no—
348Dic118C23×C414yes—
349C8×C59—22no—
350C8×C59C23×C414yes—
351C59⋊C8—22no—
352C59⋊C8C23×C414yes—
353C2×#2947—591nomaximal, Sylow
354C22×C59C2×C4×D412yes—
355C22×C59#57712yes—
356C22×C59#57812yes—
357C22×C59C23×D411yescharacteristic
358C2×D59—28no—
359C2×D59—22no—
360C2×D59—22no—
361C2×D59—24no—
362C2×D59—48no—
363C2×D59—42no—
364C2×D59—42no—
365C2×D59C2×C4×D414yes—
366C4×C59—24no—
367C4×C59—24no—
368C4×C59—22no—
369C4×C59—22no—
370C4×C59—42no—
371C4×C59—42no—
372C4×C59C2×C4×D412yes—
373C4×C59C24×C411yescharacteristic
374C4×C59C22×#4111yescharacteristic
375Dic59—24no—
376Dic59—22no—
377Dic59—22no—
378Dic59—42no—
379Dic59—42no—
380Dic59C2×C4×D414yes—
381C22×#137—591no—
382C2×#520—591no—
383C2×#519—591no—
384#2947—5916no—
385C2×#441—591no—
386C2×#441D5911yescharacteristic, complemented
387C2×#440—591no—
388C2×#440—591no—
389C2×C4×Q16—591no—
390C2×C4×Q16—591no—
391C2×C4×SD16—591no—
392C2×C4×SD16—591no—
393C2×#428—591no—
394C2×#416—591no—
395C22×#103—591no—
396C2×#405—591no—
397C2×C59#294714yescomplemented
398C2×C59C22×C4×D411yescharacteristic
399C2×C59C2×#57711yescharacteristic
400C2×C59C2×#57811yescharacteristic
401D59—24no—
402D59—44no—
403C22×#41—591no—
404C23×Q8—591no—
405C2×#137—5916no—
406C2×#137—598no—
407C22×Q16—591no—
408C22×Q16C2×D5911yescharacteristic
409C22×SD16—591no—
410C22×SD16—591no—
411C22×M16—591no—
412C23×C8—591no—
413#520—598no—
414#520—1184no—
415#519—598no—
416#519—1184no—
417C2×C4×Q8—591no—
418C2×C4×Q8—591no—
419C2×C4×Q8—591no—
420C2×C4×Q8—591no—
421C2×C4×Q8—1181no—
422C2×C4×Q8—1181no—
423C2×C4×Q8C2×D5911yescharacteristic
424C2×C4×Q8C2×D5911yescharacteristic
425C2×C4×D4—591no—
426C2×C4×D4—591no—
427C2×C4×D4—1181no—
428C2×C4×D4—1181no—
429C2×#117—591no—
430C2×#117—591no—
431C2×#117—1181no—
432C2×#117—1181no—
433C2×#117—1181no—
434C22×C4⋊C4—591no—
435C22×C4⋊C4—1181no—
436#441—598no—
437#441C2×D5918yescomplemented
438#440—598no—
439#440—598no—
440C4×Q16—598no—
441C4×Q16—598no—
442C4×SD16—598no—
443C4×SD16—598no—
444#428—598no—
445C2×#107—591no—
446C2×#107—591no—
447C2×#106—591no—
448C2×#106C2×D5911yescharacteristic
449#416—598no—
450C2×#103—591no—
451C2×#103—591no—
452C2×#103—591no—
453C2×#103—591no—
454C2×#103—598no—
455C2×#103C2×D5911yescharacteristic
456C2×#103C2×D5911yescharacteristic
457C2×#102—591no—
458C2×#102—591no—
459#405—598no—
460C2×#97—591no—
461C2×#97C2×D5911yescharacteristic
462C2×C4×C8—591no—
463C2×C4×C8—591no—
464C59C2×#294711yescharacteristic, complemented, Sylow
465C2×#41—598no—
466C2×#41—594no—
467C2×#41—1182no—
468C2×#41—1184no—
469C22×Q8—598no—
470C22×Q8—594no—
471C22×Q8—591no—
472C22×Q8—1181no—
473C22×Q8—1182no—
474C22×Q8—1184no—
475C22×Q8C22×D5911yescharacteristic
476C22×Q8C22×D5911yescharacteristic
477C22×D4—591no—
478C22×D4—1181no—
479C23×C4—591no—
480C23×C4—1181no—
481C23×C4—1181no—
482C23×C4—1181no—
483C23×C4—1181no—
484C23×C4—1181no—
485#137—5964no—
486C2×Q16—598no—
487C2×Q16—594no—
488C2×Q16C4×D5918yescomplemented
489C2×Q16C22×D5914yes—
490C2×SD16—598no—
491C2×SD16—594no—
492C2×SD16—598no—
493C2×SD16—594no—
494C2×M16—598no—
495C2×M16—594no—
496C22×C8—591no—
497C22×C8—591no—
498C22×C8—594no—
499C22×C8—1184no—
500C22×C8C22×D5911yescharacteristic
501C22×C8C22×D5911yescharacteristic
502C4×Q8—22no—
503C4×Q8—22no—
504C4×Q8—594no—
505C4×Q8—594no—
506C4×Q8—594no—
507C4×Q8—594no—
508C4×Q8—1188no—
509C4×Q8—1182no—
510C4×Q8—1182no—
511C4×Q8—1182no—
512C4×Q8—1188no—
513C4×Q8—1182no—
514C4×Q8C22×D5914yes—
515C4×Q8C22×D5914yes—
516C4×D4—594no—
517C4×D4—594no—
518C4×D4—1188no—
519C4×D4—1182no—
520C4×D4—1188no—
521C4×D4—1182no—
522#117—594no—
523#117—594no—
524#117—594no—
525#117—1188no—
526#117—1188no—
527#117—1188no—
528#117—1182no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—591no—
532C2×C4⋊C4—591no—
533C2×C4⋊C4—591no—
534C2×C4⋊C4—591no—
535C2×C4⋊C4—594no—
536C2×C4⋊C4—1188no—
537C2×C4⋊C4—1182no—
538C2×C4⋊C4—1181no—
539C2×C4⋊C4—1181no—
540C2×C4⋊C4—1181no—
541C2×C4⋊C4—1181no—
542C2×C4⋊C4—1181no—
543C2×C4⋊C4C22×D5911yescharacteristic
544C2×C4⋊C4C22×D5911yescharacteristic
545C2×C22⋊C4—591no—
546C2×C22⋊C4—591no—
547C2×C22⋊C4—1181no—
548C2×C22⋊C4—1181no—
549C2×C22⋊C4—1181no—
550C2×C42—21no—
551C2×C42—21no—
552C2×C42—591no—
553C2×C42—1181no—
554C2×C42—1181no—
555C2×C42—1181no—
556C2×C42—1181no—
557C2×C42—1181no—
558C2×C42C22×D5911yescharacteristic
559#107—594no—
560#107—594no—
561#106—594no—
562#106C22×D5914yes—
563#103—594no—
564#103—594no—
565#103—594no—
566#103—594no—
567#103C22×D5914yes—
568#103C22×D5914yes—
569#102—594no—
570#102—594no—
571#97—594no—
572#97C22×D5914yes—
573C4×C8—594no—
574C4×C8—594no—
575C24—591no—
576C24—1181no—
577#41—5916no—
578#41—1188no—
579#41—11816no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—5916no—
585C2×Q8—594no—
586C2×Q8—592no—
587C2×Q8—1184no—
588C2×Q8—1188no—
589C2×Q8—1188no—
590C2×Q8—11816no—
591C2×Q8—1181no—
592C2×Q8—1182no—
593C2×Q8C2×C4×D5914yes—
594C2×Q8C2×C4×D5914yes—
595C2×Q8C23×D5912yes—
596C2×Q8C23×D5912yes—
597C2×D4—594no—
598C2×D4—592no—
599C2×D4—1184no—
600C2×D4—1188no—
601C2×D4—1181no—
602C2×D4—1182no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—591no—
608C22×C4—594no—
609C22×C4—592no—
610C22×C4—594no—
611C22×C4—592no—
612C22×C4—591no—
613C22×C4—591no—
614C22×C4—1184no—
615C22×C4—1188no—
616C22×C4—1184no—
617C22×C4—1184no—
618C22×C4—1188no—
619C22×C4—1184no—
620C22×C4—1181no—
621C22×C4—1181no—
622C22×C4—1181no—
623C22×C4—1184no—
624C22×C4—4722no—
625C22×C4—4722no—
626C22×C4—4722no—
627C22×C4D4×D5911yescharacteristic
628C22×C4D4×D5911yescharacteristic
629C22×C4C23×D5911yescharacteristic
630Q16—5916no—
631Q16C2×C4×D59116yescomplemented
632SD16—5916no—
633SD16—5916no—
634M16—5916no—
635C2×C8—22no—
636C2×C8—594no—
637C2×C8—592no—
638C2×C8—592no—
639C2×C8—1188no—
640C2×C8—1182no—
641C2×C8C2×C4×D5914yes—
642C2×C8C23×D5912yes—
643C2×C8C23×D5912yes—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—21no—
648C4⋊C4—594no—
649C4⋊C4—594no—
650C4⋊C4—592no—
651C4⋊C4—592no—
652C4⋊C4—1184no—
653C4⋊C4—1184no—
654C4⋊C4—1184no—
655C4⋊C4—1184no—
656C4⋊C4—1181no—
657C4⋊C4—1181no—
658C4⋊C4—1184no—
659C4⋊C4C23×D5912yes—
660C4⋊C4C23×D5912yes—
661C22⋊C4—594no—
662C22⋊C4—594no—
663C22⋊C4—1184no—
664C22⋊C4—1184no—
665C22⋊C4—1184no—
666C42—24no—
667C42—24no—
668C42—592no—
669C42—592no—
670C42—1184no—
671C42—1184no—
672C42—1184no—
673C42—1184no—
674C42—1184no—
675C42D4×D5912yes—
676C42C23×D5912yes—
677C23—592no—
678C23—594no—
679C23—1182no—
680C23—1182no—
681C23—1182no—
682C23—1184no—
683C23—2362no—
684C23—2362no—
685C23C2×D4×D5911yescharacteristic
686Q8—22no—
687Q8—22no—
688Q8—24no—
689Q8—24no—
690Q8—594no—
691Q8—11816no—
692Q8—1182no—
693Q8—1184no—
694Q8C22×C4×D5914yes—
695Q8C22×C4×D5914yes—
696D4—594no—
697D4—11816no—
698D4—1182no—
699D4—1184no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—592no—
711C2×C4—594no—
712C2×C4—594no—
713C2×C4—594no—
714C2×C4—598no—
715C2×C4—592no—
716C2×C4—592no—
717C2×C4—11816no—
718C2×C4—11816no—
719C2×C4—1182no—
720C2×C4—1182no—
721C2×C4—1182no—
722C2×C4—1184no—
723C2×C4—1182no—
724C2×C4—1182no—
725C2×C4—4724no—
726C2×C4—4724no—
727C2×C4—4724no—
728C2×C4—2362no—
729C2×C4—2362no—
730C2×C4C22×C4×D5912yes—
731C2×C4C2×D4×D5912yes—
732C2×C4C2×D4×D5912yes—
733C2×C4C2×D4×D5911yescharacteristic
734C2×C4#41×D5912yes—
735C2×C4C24×D5911yescharacteristic
736C8—22no—
737C8—594no—
738C8—1182no—
739C8C22×C4×D5914yes—
740C22—594no—
741C22—1188no—
742C22—1182no—
743C22—1182no—
744C22—1184no—
745C22—2368no—
746C22—2362no—
747C22—2362no—
748C22C4×D4×D5912yes—
749C22#1683821112yes—
750C22#1683821812yes—
751C22C22×D4×D5911yescharacteristic
752C4—24no—
753C4—24no—
754C4—22no—
755C4—22no—
756C4—42no—
757C4—42no—
758C4—594no—
759C4—1184no—
760C4—1182no—
761C4—1182no—
762C4—2362no—
763C4—2362no—
764C4C4×D4×D5912yes—
765C4C23×C4×D5911yescharacteristic
766C4C2×#41×D5911yescharacteristic
767C2—1184no—
768C2—2364no—
769C2#2143293814yesdirect product factor
770C2C2×C4×D4×D5911yescharacteristic
771C2C2×#1683821111yescharacteristic
772C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutatorC4×C59C24×C4
FrattiniC2×C4C24×D59
FittingC2×C59×#441C2
socleC23×C59C22×D4
prime radicalC22×#11745689C22
cosocleC2×C4×C59C25
hypercenterC2×#441D59
hypocenterC59C2×#2947
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. C2×#16837878C2semidirect
4. #21432938C2direct (N × H)
5. C2×#16837506C2semidirect
6. C2×#16837505C2semidirect
7. C2×#16837504C2semidirect
8. C2×Q16×Dic59C2semidirect
9. C2×C4×#11745672C2semidirect
10. C2×C4×#11745671C2semidirect
11. C2×#16837489C2semidirect
12. C2×#16837441C2semidirect
14. C2×#103×D59C2semidirect
15. C2×#16837359C2semidirect
16. C2×C59×#441C2semidirect
19. C2×#14273759C4semidirect
29. #16837878C22semidirect
47. #16837506C22semidirect
48. #16837505C22semidirect
49. #16837504C22semidirect
50. Q16×Dic59C22semidirect
51. C4×#11745672C22semidirect
52. C4×#11745671C22semidirect
53. #16837489C22semidirect
54. #16837441C22semidirect
63. #103×D59C22semidirect
66. #16837359C22semidirect
73. C59×#441C22semidirect
86. C2×Q8×D59C2×C4semidirect
96. #14273759C2×C4semidirect
97. C2×#11745672C2×C4semidirect
99. C2×#11745660C2×C4semidirect
101. C2×#11745671C2×C4semidirect
103. C2×#11745659C2×C4semidirect
169. C2×Q16×C59C2×C4semidirect
216. Q8×D59C22×C4semidirect
243. Q16×C59C22×C4semidirect
258. #11745672C22×C4semidirect
259. #11745671C22×C4semidirect
287. #11745660C22×C4semidirect
288. #11745659C22×C4semidirect
386. C2×#441D59semidirect
397. C2×C59#2947semidirect
437. #441C2×D59semidirect
464. C59C2×#2947semidirect
488. C2×Q16C4×D59semidirect
631. Q16C2×C4×D59semidirect
769. C2#21432938direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737592
C2×#168378842
C2×#168378782
#214329382
C2×#168375062
C2×#168375052
C2×#168375042
C2×Q16×Dic592
C2×C4×#117456722
C2×C4×#117456712
C2×#168374892
C2×#168374412
C2×#168373972
C2×#103×D592
C2×#168373592
C2×C59×#4412
C2×#294759