Finite Group Databasebeta

← C2×#21436264 #29465308

Subgroups — C2×#21436264 #29465308

Order 15104.

2158 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838105C211yesmaximal, characteristic
2C2×Q8×D236C211yesmaximal, characteristic, complemented
3#21436264C2116yesmaximal, direct product factor
4C2×#16837772C211yesmaximal, characteristic, complemented
5C2×#16837739C211yesmaximal, characteristic, complemented
6C2×#16837746C211yesmaximal, characteristic, complemented
7C2×#16837649C211yesmaximal, characteristic, complemented
8C2×#16837632C211yesmaximal, characteristic, complemented
9C2×#16837608C211yesmaximal, characteristic, complemented
10C2×#16837542C211yesmaximal, characteristic, complemented
11C2×#16837542C211yesmaximal, characteristic, complemented
12C2×#16837500C211yesmaximal, characteristic, complemented
13C2×#16837472C211yesmaximal, characteristic, complemented
14C2×#16837409C211yesmaximal, characteristic, complemented
15C2×#103×D59C211yesmaximal, characteristic, complemented
16C2×C59×#479C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×Q8×D59C2211yescharacteristic
19C22×#11745660C2211yescharacteristic
20C22×#11745660C2211yescharacteristic
21C22×#11745671C2211yescharacteristic
22C22×#11745659C2211yescharacteristic
23C22×C8×D59C2211yescharacteristic
24#16838105—24no—
25#16838105C2218yes—
26Q8×D236—24no—
27Q8×D236C2218yescomplemented
28C2×#14273727—21no—
29C2×#14273727C2211yescharacteristic
30C2×#14273722—21no—
31C2×#14273712—21no—
32C2×#14273707—21no—
33C2×#14273707—21no—
34C2×#14273707C2211yescharacteristic
35C2×#14273707C2211yescharacteristic
36C2×#14273702—21no—
37C2×#14273702C2211yescharacteristic
38C2×#14273702C2211yescharacteristic
39C2×C4×D236—21no—
40C2×C4×D236C2211yescharacteristic
41C2×C4×D236C2211yescharacteristic
42C2×#14273689—21no—
43C2×#14273685C2211yescharacteristic
44C2×C4⋊C4×D59C2211yescharacteristic
45#16837772C2218yescomplemented
46#16837746C2218yescomplemented
47#16837739C2218yescomplemented
48#16837649C2218yescomplemented
49#16837632C2218yescomplemented
50#16837608C2218yescomplemented
51#16837542C2218yescomplemented
52#16837542C2218yescomplemented
53#16837500C2218yescomplemented
54#16837472C2218yescomplemented
55C2×#14273660C2211yescharacteristic
56#16837409C2218yescomplemented
57C2×#14273652C2211yescharacteristic
58C2×#14273652C2211yescharacteristic
59C2×#14273651C2211yescharacteristic
60C2×#14273650C2211yescharacteristic
61C2×#14273650C2211yescharacteristic
62C2×#14273650C2211yescharacteristic
63C2×#14273650C2211yescharacteristic
64#103×D59C2218yescomplemented
65C2×#14273647C2211yescharacteristic
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
81C2×Q8×D59—22no—
82C2×Q8×D59—22no—
83C2×Q8×D59—24no—
84C2×Q8×D59—24no—
85C2×Q8×D59—42no—
86C2×Q8×D59—42no—
87C2×Q8×D59C2314yes—
88C2×Q8×D59C2314yes—
89C22×D236—21no—
90C22×D236—21no—
91C22×D236D411yescharacteristic
92C22×D236C2311yescharacteristic
93C22×C4×D59—21no—
94C22×C4×D59—21no—
95C22×C4×D59—21no—
96C22×C4×D59—21no—
97C22×C4×D59C2311yescharacteristic
98C22×C4×D59C2311yescharacteristic
99C2×#11745660—42no—
100C2×#11745660—42no—
101C2×#11745660C2314yes—
102C2×#11745660C2314yes—
103C2×#11745671—24no—
104C2×#11745671C2314yes—
105C2×#11745659—42no—
106C2×#11745659C2314yes—
107C22×C59⋊C8C2311yescharacteristic
108C22×C59⋊C8C2311yescharacteristic
109C2×C8×D59—42no—
110C2×C8×D59C2314yes—
111#14273727—22no—
112#14273727—28no—
113#14273727C2314yes—
114#14273722—28no—
115#14273712—28no—
116#14273707—22no—
117#14273707—22no—
118#14273707—28no—
119#14273707—28no—
120#14273707C2314yes—
121#14273707C2314yes—
122#14273702—28no—
123#14273702—22no—
124#14273702—22no—
125#14273702C2314yes—
126#14273702C2314yes—
127C4×D236—28no—
128C4×D236—22no—
129C4×D236D414yes—
130C4×D236C2314yes—
131C4×D236C2314yes—
132#14273689—28no—
133#14273685—22no—
134#14273685C2314yes—
135C2×C4⋊Dic59—21no—
136C2×C4⋊Dic59—21no—
137C2×C4⋊Dic59—21no—
138C2×C4⋊Dic59—21no—
139C2×C4⋊Dic59D411yescharacteristic
140C2×C4⋊Dic59C2311yescharacteristic
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)⋊C4—21no—
150C2×(C2×D59)⋊C4D411yescharacteristic
151C2×(C2×D59)⋊C4D411yescharacteristic
152C2×C4×Dic59—21no—
153#14273660C2314yes—
154#14273652C2314yes—
155#14273652C2314yes—
156#14273651C2314yes—
157#14273650C2314yes—
158#14273650C2314yes—
159#14273650C2314yes—
160#14273650C2314yes—
161#14273647C2314yes—
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×D59—21no—
186C23×D59C2×D411yescharacteristic
187C23×D59C2×D411yescharacteristic
188C2×Q8×C59—21no—
189C2×Q8×C59—22no—
190C2×Q8×C59#4114yes—
191C2×Q8×C59C2412yes—
192C22×C4×C59—21no—
193C22×C4×C59—21no—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59C2×D411yescharacteristic
197C22×C4×C59C2×D411yescharacteristic
198C22×C4×C59C2411yescharacteristic
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×D236—22no—
212C2×D236—22no—
213C2×D236—24no—
214C2×D236—21no—
215C2×D236—24no—
216C2×D236—44no—
217C2×D236—82no—
218C2×D236C2×D414yes—
219C2×D236C2412yes—
220C2×C4×D59—22no—
221C2×C4×D59—22no—
222C2×C4×D59—22no—
223C2×C4×D59—22no—
224C2×C4×D59—24no—
225C2×C4×D59—24no—
226C2×C4×D59—24no—
227C2×C4×D59—24no—
228C2×C4×D59—44no—
229C2×C4×D59—44no—
230C2×C4×D59—82no—
231C2×C4×D59—82no—
232C2×C4×D59C2×D412yes—
233C2×C4×D59C2×D412yes—
234C2×C4×D59C2412yes—
235C2×C4×D59C2412yes—
236C2×Dic118—22no—
237C2×Dic118—22no—
238C2×Dic118—22no—
239C2×Dic118—22no—
240C2×Dic118—21no—
241C2×Dic118—21no—
242C2×Dic118—24no—
243C2×Dic118—24no—
244C2×Dic118—44no—
245C2×Dic118—44no—
246C2×Dic118C2412yes—
247C2×Dic118C2412yes—
248C2×C8×C59—22no—
249C2×C8×C59—22no—
250C2×C8×C59C2412yes—
251C2×C8×C59C2412yes—
252C4⋊C4×C59—24no—
253C4⋊C4×C59—24no—
254C4⋊C4×C59—24no—
255C4⋊C4×C59—21no—
256C4⋊C4×C59—21no—
257C4⋊C4×C59—21no—
258C4⋊C4×C59C2412yes—
259C4⋊C4×C59C2412yes—
260C4⋊C4×C59C2412yes—
261C42×C59—24no—
262C42×C59C2×D412yes—
263C42×C59C2412yes—
264#11745671—28no—
265(C2×D59)⋊C4—24no—
266(C2×D59)⋊C4—24no—
267(C2×D59)⋊C4—24no—
268(C2×D59)⋊C4—24no—
269(C2×D59)⋊C4—24no—
270(C2×D59)⋊C4—24no—
271(C2×D59)⋊C4C2×D414yes—
272(C2×D59)⋊C4C2×D414yes—
273C4⋊Dic59—21no—
274C4⋊Dic59—24no—
275C4⋊Dic59—24no—
276C4⋊Dic59—24no—
277C4⋊Dic59—24no—
278C4⋊Dic59C2×D414yes—
279C4⋊Dic59C2412yes—
280Dic59⋊C4—24no—
281C4×Dic59—24no—
282C2×C59⋊C8—22no—
283C2×C59⋊C8—22no—
284C2×C59⋊C8C2412yes—
285C2×C59⋊C8C2412yes—
286#11745660—44no—
287#11745660—44no—
288#11745659—44no—
289C8×D59—44no—
290C23×C59C22×D411yescharacteristic
291C22×D59—22no—
292C22×D59—22no—
293C22×D59—22no—
294C22×D59—22no—
295C22×D59—22no—
296C22×D59—22no—
297C22×D59—42no—
298C22×D59—42no—
299C22×D59—42no—
300C22×D59#13714yes—
301C22×D59C22×D412yes—
302C22×D59C22×D412yes—
303Q8×C59—24no—
304Q8×C59—22no—
305Q8×C59C2×#4114yes—
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×C59—42no—
316C2×C4×C59C22×D412yes—
317C2×C4×C59C22×D412yes—
318C2×C4×C59C22×D411yescharacteristic
319C2×C4×C59C2×#4112yes—
320C2×C4×C59H(5,𝔽2)12yes—
321C2×C4×C59C2511yescharacteristic
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—22no—
325C2×Dic59—22no—
326C2×Dic59—22no—
327C2×Dic59—42no—
328C2×Dic59—42no—
329C2×Dic59—42no—
330C2×Dic59C22×D412yes—
331C2×Dic59C22×D412yes—
332D236—28no—
333D236—22no—
334D236—22no—
335D236—48no—
336D236—42no—
337D236—84no—
338C4×D59—24no—
339C4×D59—24no—
340C4×D59—22no—
341C4×D59—22no—
342C4×D59—22no—
343C4×D59—22no—
344C4×D59—48no—
345C4×D59—48no—
346C4×D59—84no—
347C4×D59—84no—
348Dic118—22no—
349Dic118—22no—
350Dic118—22no—
351Dic118—22no—
352Dic118—48no—
353Dic118—48no—
354Dic118—42no—
355Dic118—42no—
356C8×C59—22no—
357C8×C59—22no—
358C59⋊C8—22no—
359C59⋊C8—22no—
360C2×#3320—591nomaximal, Sylow
361C22×C59#54612yes—
362C22×C59C2×#13712yes—
363C22×C59#57712yes—
364C22×C59C23×D411yescharacteristic
365C2×D59—22no—
366C2×D59—28no—
367C2×D59—22no—
368C2×D59—22no—
369C2×D59—22no—
370C2×D59—22no—
371C2×D59—44no—
372C2×D59—42no—
373C2×D59—42no—
374C2×D59—42no—
375C2×D59—84no—
376C2×D59C2×#13714yes—
377C4×C59—24no—
378C4×C59—22no—
379C4×C59—22no—
380C4×C59—42no—
381C4×C59—42no—
382C4×C59—42no—
383C4×C59#54612yes—
384C4×C59C22×#4111yescharacteristic
385C4×C59C2×H(5,𝔽2)11yescharacteristic
386Dic59—22no—
387Dic59—22no—
388Dic59—42no—
389Dic59—42no—
390Dic59—42no—
391C2×#553—591no—
392C2×D4×Q8—591no—
393#3320—5916no—
394C2×#491—591no—
395C2×#484—591no—
396C2×#485—591no—
397C2×#479D5911yescharacteristic, complemented
398C2×#468—591no—
399C2×#465—591no—
400C2×#461—591no—
401C2×#448—591no—
402C2×#448—591no—
403C2×#440—591no—
404C2×#435—591no—
405C2×#419—591no—
406C22×#103—591no—
407C2×C59#332014yescomplemented
408C2×C59C2×#54611yescharacteristic
409C2×C59C22×#13711yescharacteristic
410C2×C59C2×#57711yescharacteristic
411D59—24no—
412D59—42no—
413D59—82no—
414C23×Q8—591no—
415C23×Q8—591no—
416C22×SD16—591no—
417C22×SD16—591no—
418C22×SD16—591no—
419C22×M16—591no—
420C23×C8—591no—
421#553—598no—
422#553—1184no—
423D4×Q8—598no—
424D4×Q8—1184no—
425C2×C4⋊Q8—591no—
426C2×C4⋊Q8—1181no—
427C2×#126—1181no—
428C2×#125C2×D5911yescharacteristic
429C2×#123—1181no—
430C2×C22⋊Q8—591no—
431C2×C22⋊Q8—591no—
432C2×C22⋊Q8—1181no—
433C2×C22⋊Q8—1181no—
434C2×#121—591no—
435C2×#121—591no—
436C2×#121—1181no—
437C2×C4×Q8C2×D5911yescharacteristic
438C2×C4×D4—591no—
439C2×C4×D4—591no—
440C2×C4×D4—1181no—
441C2×C4×D4—1181no—
442C2×#117—591no—
443C22×C4⋊C4—591no—
444#491—598no—
445#485—598no—
446#484—598no—
447#479C2×D5918yescomplemented
448#468—598no—
449#465—598no—
450#461—598no—
451#448—598no—
452#448—598no—
453#440—598no—
454#435—598no—
455C2×#107—591no—
456C2×#107C2×D5911yescharacteristic
457C2×#106C2×D5911yescharacteristic
458C2×C4⋊C8C2×D5911yescharacteristic
459#419—598no—
460C2×#103—591no—
461C2×#103—591no—
462C2×#103—591no—
463C2×#103—591no—
464C2×#103—591no—
465C2×#103—591no—
466C2×#103—591no—
467C2×#103—598no—
468C2×#103C2×D5911yescharacteristic
469C2×#103C2×D5911yescharacteristic
470C2×#102—591no—
471C2×C22⋊C8—591no—
472C2×C22⋊C8—591no—
473C2×#97—591no—
474C59C2×#332011yescharacteristic, complemented, Sylow
475C22×Q8—594no—
476C22×Q8—594no—
477C22×Q8—591no—
478C22×Q8—591no—
479C22×Q8—1181no—
480C22×Q8—1181no—
481C22×Q8—1182no—
482C22×Q8—1182no—
483C22×Q8—1184no—
484C22×Q8—1184no—
485C22×Q8—2362no—
486C22×Q8—2362no—
487C22×Q8C22×D5911yescharacteristic
488C22×D4—591no—
489C22×D4—591no—
490C22×D4—1181no—
491C22×D4—1181no—
492C23×C4—591no—
493C23×C4—591no—
494C23×C4—1181no—
495C23×C4—1181no—
496C23×C4—1181no—
497C23×C4—1181no—
498C2×SD16—594no—
499C2×SD16—594no—
500C2×SD16—594no—
501C2×SD16—1184no—
502C2×SD16—2362no—
503C2×SD16—2362no—
504C2×M16—594no—
505C2×M16—2362no—
506C22×C8—591no—
507C22×C8—591no—
508C22×C8—594no—
509C22×C8—2362no—
510C22×C8C22×D5911yescharacteristic
511C22×C8C22×D5911yescharacteristic
512C4⋊Q8—594no—
513C4⋊Q8—1188no—
514C4⋊Q8—1182no—
515#126—1188no—
516#125—22no—
517#125C22×D5914yes—
518#123—1188no—
519C22⋊Q8—594no—
520C22⋊Q8—594no—
521C22⋊Q8—1188no—
522C22⋊Q8—1188no—
523C22⋊Q8—1182no—
524C22⋊Q8—1182no—
525#121—594no—
526#121—594no—
527#121—1182no—
528#121—1182no—
529#121—1188no—
530C4×Q8—22no—
531C4×Q8C22×D5914yes—
532C4×D4—594no—
533C4×D4—594no—
534C4×D4—594no—
535C4×D4—1188no—
536C4×D4—1188no—
537C4×D4—1182no—
538#117—594no—
539#117—1182no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—591no—
544C2×C4⋊C4—591no—
545C2×C4⋊C4—594no—
546C2×C4⋊C4—1182no—
547C2×C4⋊C4—1181no—
548C2×C4⋊C4—1181no—
549C2×C4⋊C4—1181no—
550C2×C4⋊C4—1181no—
551C2×C4⋊C4—1181no—
552C2×C4⋊C4C22×D5911yescharacteristic
553C2×C4⋊C4C22×D5911yescharacteristic
554C2×C4⋊C4C22×D5911yescharacteristic
555C2×C22⋊C4—591no—
556C2×C22⋊C4—591no—
557C2×C22⋊C4—1181no—
558C2×C22⋊C4—1181no—
559C2×C22⋊C4—1181no—
560C2×C22⋊C4—1181no—
561C2×C22⋊C4—1181no—
562C2×C22⋊C4—1181no—
563C2×C42—21no—
564C2×C42—1181no—
565C2×C42C22×D5911yescharacteristic
566#107—594no—
567#107C22×D5914yes—
568#106C22×D5914yes—
569C4⋊C8C22×D5914yes—
570#103—594no—
571#103—594no—
572#103—594no—
573#103—594no—
574#103—594no—
575#103—594no—
576#103—594no—
577#103C22×D5914yes—
578#103C22×D5914yes—
579#102—594no—
580C22⋊C8—594no—
581C22⋊C8—594no—
582#97—594no—
583C24—591no—
584C24—591no—
585C24—1181no—
586C2×Q8—21no—
587C2×Q8—22no—
588C2×Q8—592no—
589C2×Q8—592no—
590C2×Q8—1184no—
591C2×Q8—1184no—
592C2×Q8—1181no—
593C2×Q8—1181no—
594C2×Q8—1188no—
595C2×Q8—1188no—
596C2×Q8—1182no—
597C2×Q8—1182no—
598C2×Q8—1182no—
599C2×Q8—1182no—
600C2×Q8—2364no—
601C2×Q8—2364no—
602C2×Q8—2364no—
603C2×Q8—2364no—
604C2×Q8—2368no—
605C2×Q8—2368no—
606C2×Q8#1174568914yes—
607C2×Q8C23×D5912yes—
608C2×D4—594no—
609C2×D4—592no—
610C2×D4—1184no—
611C2×D4—1184no—
612C2×D4—1184no—
613C2×D4—1181no—
614C2×D4—1182no—
615C2×D4—1182no—
616C2×D4—4722no—
617C2×D4—2364no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—591no—
623C22×C4—591no—
624C22×C4—592no—
625C22×C4—592no—
626C22×C4—592no—
627C22×C4—592no—
628C22×C4—1184no—
629C22×C4—1184no—
630C22×C4—1184no—
631C22×C4—1182no—
632C22×C4—1182no—
633C22×C4—1182no—
634C22×C4—1182no—
635C22×C4—1181no—
636C22×C4—1181no—
637C22×C4—1181no—
638C22×C4—1184no—
639C22×C4—4722no—
640C22×C4—4722no—
641C22×C4—2364no—
642C22×C4—2364no—
643C22×C4D4×D5911yescharacteristic
644C22×C4D4×D5911yescharacteristic
645C22×C4C23×D5911yescharacteristic
646SD16—1188no—
647SD16—2364no—
648SD16—2364no—
649M16—2364no—
650C2×C8—22no—
651C2×C8—22no—
652C2×C8—592no—
653C2×C8—592no—
654C2×C8—1182no—
655C2×C8—1182no—
656C2×C8—2364no—
657C2×C8C23×D5912yes—
658C2×C8C23×D5912yes—
659C4⋊C4—24no—
660C4⋊C4—24no—
661C4⋊C4—24no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—594no—
666C4⋊C4—592no—
667C4⋊C4—1184no—
668C4⋊C4—1184no—
669C4⋊C4—1184no—
670C4⋊C4—1181no—
671C4⋊C4—1184no—
672C4⋊C4—1184no—
673C4⋊C4C23×D5912yes—
674C4⋊C4C23×D5912yes—
675C4⋊C4C23×D5912yes—
676C22⋊C4—594no—
677C22⋊C4—594no—
678C22⋊C4—1184no—
679C22⋊C4—1184no—
680C22⋊C4—1184no—
681C22⋊C4—1184no—
682C22⋊C4—1184no—
683C22⋊C4—1184no—
684C42—24no—
685C42—1184no—
686C42D4×D5912yes—
687C42C23×D5912yes—
688C23—594no—
689C23—592no—
690C23—592no—
691C23—1182no—
692C23—1182no—
693C23—1182no—
694C23—1182no—
695C23—1182no—
696C23—1182no—
697C23—2362no—
698C23—2362no—
699C23—2362no—
700C23C2×D4×D5911yescharacteristic
701Q8—22no—
702Q8—24no—
703Q8—1182no—
704Q8—1182no—
705Q8—1182no—
706Q8—1182no—
707Q8—2368no—
708Q8—2368no—
709Q8—2362no—
710Q8—2362no—
711Q8C2×#1174568914yes—
712D4—1188no—
713D4—1182no—
714D4—1182no—
715D4—4724no—
716D4—2368no—
717D4—2362no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—592no—
729C2×C4—592no—
730C2×C4—1182no—
731C2×C4—1182no—
732C2×C4—1182no—
733C2×C4—1182no—
734C2×C4—1182no—
735C2×C4—1182no—
736C2×C4—1184no—
737C2×C4—1184no—
738C2×C4—1182no—
739C2×C4—1182no—
740C2×C4—1182no—
741C2×C4—4724no—
742C2×C4—4724no—
743C2×C4—2368no—
744C2×C4—2368no—
745C2×C4—2362no—
746C2×C4—2362no—
747C2×C4—2362no—
748C2×C4C2×D4×D5912yes—
749C2×C4C2×D4×D5912yes—
750C2×C4C2×D4×D5911yescharacteristic
751C2×C4C2×#1174568912yes—
752C2×C4#1427377312yes—
753C2×C4C24×D5911yescharacteristic
754C8—22no—
755C8—22no—
756C8—1182no—
757C8—1182no—
758C22—594no—
759C22—1182no—
760C22—1188no—
761C22—1182no—
762C22—1182no—
763C22—1182no—
764C22—1182no—
765C22—4724no—
766C22—2362no—
767C22—2362no—
768C22—2362no—
769C22—2364no—
770C22#1683804312yes—
771C22#137×D5912yes—
772C22#1683820912yes—
773C22C22×D4×D5911yescharacteristic
774C4—24no—
775C4—22no—
776C4—22no—
777C4—42no—
778C4—42no—
779C4—42no—
780C4—1182no—
781C4—1182no—
782C4—2362no—
783C4—2362no—
784C4—2362no—
785C4#1683804312yes—
786C4C22×#1174568911yescharacteristic
787C4C2×#1427377311yescharacteristic
788C2—1184no—
789C2—4722no—
790C2—2362no—
791C2#2143626414yesdirect product factor
792C2C2×#1683804311yescharacteristic
793C2C2×#137×D5911yescharacteristic
794C2C2×#1683820911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#479C2
socleC23×C59C22×D4
prime radicalC2×#16838105C2
hypercenterC2×#479D59
hypocenterC59C2×#3320
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
2. C2×Q8×D236C2semidirect
3. #21436264C2direct (N × H)
4. C2×#16837772C2semidirect
5. C2×#16837739C2semidirect
6. C2×#16837746C2semidirect
7. C2×#16837649C2semidirect
8. C2×#16837632C2semidirect
9. C2×#16837608C2semidirect
10. C2×#16837542C2semidirect
11. C2×#16837542C2semidirect
12. C2×#16837500C2semidirect
13. C2×#16837472C2semidirect
14. C2×#16837409C2semidirect
15. C2×#103×D59C2semidirect
16. C2×C59×#479C2semidirect
27. Q8×D236C22semidirect
45. #16837772C22semidirect
46. #16837746C22semidirect
47. #16837739C22semidirect
48. #16837649C22semidirect
49. #16837632C22semidirect
50. #16837608C22semidirect
51. #16837542C22semidirect
52. #16837542C22semidirect
53. #16837500C22semidirect
54. #16837472C22semidirect
56. #16837409C22semidirect
64. #103×D59C22semidirect
71. C59×#479C22semidirect
397. C2×#479D59semidirect
407. C2×C59#3320semidirect
447. #479C2×D59semidirect
474. C59C2×#3320semidirect
791. C2#21436264direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168381052
C2×Q8×D2362
#214362642
C2×#168377722
C2×#168377392
C2×#168377462
C2×#168376492
C2×#168376322
C2×#168376082
C2×#168375422
C2×#168375002
C2×#168374722
C2×#168374092
C2×#103×D592
C2×C59×#4792
C2×#332059