Finite Group Databasebeta

← C2×#21434783 #29458577

Subgroups — C2×#21434783 #29458577

Order 15104.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16838017C211yesmaximal, characteristic, complemented
2C2×#16838003C211yesmaximal, characteristic, complemented
3#21434783C2116yesmaximal, direct product factor
4C2×#16837810C211yesmaximal, characteristic, complemented
5C2×#16837790C211yesmaximal, characteristic, complemented
6C2×#16837755C211yesmaximal, characteristic, complemented
7C2×#16837747C211yesmaximal, characteristic, complemented
8C2×#16837652C211yesmaximal, characteristic, complemented
9C2×#16837649C211yesmaximal, characteristic, complemented
10C2×#16837637C211yesmaximal, characteristic, complemented
11C2×#16837630C211yesmaximal, characteristic, complemented
12C2×#16837512C211yesmaximal, characteristic, complemented
13C2×#16837502C211yesmaximal, characteristic, complemented
14C2×C4×#11745660C211yesmaximal, characteristic, complemented
15C2×#16837356C211yesmaximal, characteristic, complemented
16C2×C4×D8×C59C211yesmaximal, characteristic, complemented
17C22×#11745660C2211yescharacteristic
18C22×#11745670C2211yescharacteristic
19C22×#11745669C2211yescharacteristic
20C22×#11745659C2211yescharacteristic
21C22×C8×D59C2211yescharacteristic
22#16838017—24no—
23#16838017C2218yescomplemented
24#16838003—24no—
25#16838003C2218yescomplemented
26C2×#14273726C2211yescharacteristic
27C2×#14273723C2211yescharacteristic
28C2×#14273720—21no—
29C2×#14273718C2211yescharacteristic
30C2×#14273714C2211yescharacteristic
31C2×#14273713—21no—
32C2×#14273710—21no—
33C2×#14273710—21no—
34C2×#14273709—21no—
35C2×#14273707C2211yescharacteristic
36C2×#14273706—21no—
37C2×#14273702C2211yescharacteristic
38C2×#14273701—21no—
39C2×#14273700—21no—
40C2×#14273698C2211yescharacteristic
41C2×#14273698C2211yescharacteristic
42C2×C4×Dic118C2211yescharacteristic
43C2×C4×D236C2211yescharacteristic
44C2×#14273684C2211yescharacteristic
45#16837810C2218yescomplemented
46#16837790C2218yescomplemented
47#16837755C2218yescomplemented
48#16837747C2218yescomplemented
49#16837652C2218yescomplemented
50#16837649C2218yescomplemented
51#16837637C2218yescomplemented
52#16837630C2218yescomplemented
53#16837512C2218yescomplemented
54#16837502C2218yescomplemented
55C4×#11745660C2218yescomplemented
56C2×#14273660C2211yescharacteristic
57C2×#14273659C2211yescharacteristic
58C2×#14273658C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273650C2211yescharacteristic
61C2×#14273649C2211yescharacteristic
62C2×#14273648C2211yescharacteristic
63C2×#14273648C2211yescharacteristic
64C2×#14273647C2211yescharacteristic
65#16837356C2218yescomplemented
66C2×#14273638C2211yescharacteristic
67C2×#14273637C2211yescharacteristic
68C2×C8×Dic59C2211yescharacteristic
69C22×D8×C59C2211yescharacteristic
70C2×C4×D4×C59C2211yescharacteristic
71C2×C4×D4×C59C2211yescharacteristic
72C4×D8×C59C2218yescomplemented
73C2×#107×C59C2211yescharacteristic
74C2×#102×C59C2211yescharacteristic
75C2×#102×C59C2211yescharacteristic
76C2×C4×C8×C59C2211yescharacteristic
77C22×Dic118—21no—
78C22×Dic118C2311yescharacteristic
79C22×D236—21no—
80C22×D236C2311yescharacteristic
81C22×C22⋊D59—21no—
82C22×C22⋊D59—21no—
83C22×C22⋊D59—21no—
84C22×C22⋊D59—21no—
85C22×C4×D59—21no—
86C22×C4×D59C2311yescharacteristic
87C2×#11745660—24no—
88C2×#11745660C2314yes—
89C2×#11745670—24no—
90C2×#11745670C2314yes—
91C2×#11745669—24no—
92C2×#11745669C2314yes—
93C2×#11745659—24no—
94C2×#11745659C2314yes—
95C22×C59⋊C8C2311yescharacteristic
96C22×C59⋊C8C2311yescharacteristic
97C2×C8×D59—24no—
98C2×C8×D59C2314yes—
99#14273726—22no—
100#14273726C2314yes—
101#14273723—22no—
102#14273723C2314yes—
103#14273720—28no—
104#14273718—22no—
105#14273718C2314yes—
106#14273714—22no—
107#14273714C2314yes—
108#14273713—28no—
109#14273710—28no—
110#14273710—28no—
111#14273709—28no—
112#14273707—22no—
113#14273707C2314yes—
114#14273706—28no—
115#14273702—22no—
116#14273702C2314yes—
117#14273701—28no—
118#14273700—28no—
119#14273698—22no—
120#14273698—22no—
121#14273698C2314yes—
122#14273698C2314yes—
123C4×Dic118—22no—
124C4×Dic118C2314yes—
125C4×D236—22no—
126C4×D236C2314yes—
127#14273684D414yes—
128#14273684C2314yes—
129C2×C4⋊Dic59—21no—
130C2×C4⋊Dic59—21no—
131C2×C4⋊Dic59C2311yescharacteristic
132C2×C4⋊Dic59C2311yescharacteristic
133C2×Dic59⋊C4—21no—
134C2×Dic59⋊C4—21no—
135C2×Dic59⋊C4—21no—
136C2×Dic59⋊C4D411yescharacteristic
137C2×Dic59⋊C4D411yescharacteristic
138C2×C22⋊Dic59—21no—
139C2×C22⋊Dic59—21no—
140C2×C22⋊Dic59—21no—
141C2×C22⋊Dic59—21no—
142C2×(C2×D59)⋊C4—21no—
143C2×(C2×D59)⋊C4—21no—
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4D411yescharacteristic
146C2×(C2×D59)⋊C4D411yescharacteristic
147C2×C4×Dic59—21no—
148C2×C4×Dic59C2311yescharacteristic
149#14273660C2314yes—
150#14273659C2314yes—
151#14273658C2314yes—
152#14273652C2314yes—
153#14273650C2314yes—
154#14273649C2314yes—
155#14273648C2314yes—
156#14273648C2314yes—
157#14273647C2314yes—
158#14273638C2314yes—
159#14273637C2314yes—
160C8×Dic59C2314yes—
161C22×D4×C59C2311yescharacteristic
162C22×D4×C59C2311yescharacteristic
163C23×C4×C59—21no—
164C23×C4×C59—21no—
165C2×D8×C59—24no—
166C2×D8×C59C2314yes—
167C22×C8×C59C2311yescharacteristic
168C22×C8×C59C2311yescharacteristic
169C4×D4×C59—22no—
170C4×D4×C59—22no—
171C4×D4×C59C2314yes—
172C4×D4×C59C2314yes—
173C2×C4⋊C4×C59C2311yescharacteristic
174C2×C4⋊C4×C59C2311yescharacteristic
175C2×C22⋊C4×C59—21no—
176C2×C22⋊C4×C59—21no—
177C2×C42×C59C2311yescharacteristic
178#107×C59C2314yes—
179#102×C59C2314yes—
180#102×C59C2314yes—
181C4×C8×C59C2314yes—
182C24×C59—21no—
183C24×C59—21no—
184C23×D59—21no—
185C23×D59C2×D411yescharacteristic
186C2×D4×C59—21no—
187C2×D4×C59—21no—
188C2×D4×C59—22no—
189C2×D4×C59—22no—
190C2×D4×C59—22no—
191C2×D4×C59—22no—
192C2×D4×C59C2412yes—
193C2×D4×C59C2412yes—
194C22×C4×C59—21no—
195C22×C4×C59—21no—
196C22×C4×C59—24no—
197C22×C4×C59—24no—
198C22×C4×C59—82no—
199C22×C4×C59—82no—
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2×D411yescharacteristic
202C22×C4×C59C2411yescharacteristic
203C2×C22⋊D59—24no—
204C2×C22⋊D59—24no—
205C2×C22⋊D59—24no—
206C2×C22⋊D59—24no—
207C2×C22⋊D59—82no—
208C2×C22⋊D59—82no—
209C2×C22⋊D59—82no—
210C2×C22⋊D59—82no—
211C22×Dic59—21no—
212C22×Dic59—21no—
213C22×Dic59—21no—
214C22×Dic59C2×D411yescharacteristic
215C22×Dic59C2×D411yescharacteristic
216C22×Dic59C2×D411yescharacteristic
217C2×D236—22no—
218C2×D236—22no—
219C2×D236—21no—
220C2×D236—24no—
221C2×D236—82no—
222C2×D236C2412yes—
223C2×C4×D59—22no—
224C2×C4×D59—22no—
225C2×C4×D59—24no—
226C2×C4×D59—82no—
227C2×C4×D59C2×D412yes—
228C2×C4×D59C2412yes—
229C2×Dic118—22no—
230C2×Dic118—22no—
231C2×Dic118—21no—
232C2×Dic118—24no—
233C2×Dic118—82no—
234C2×Dic118C2412yes—
235D8×C59—28no—
236C2×C8×C59—22no—
237C2×C8×C59#4114yes—
238C2×C8×C59C2412yes—
239C2×C8×C59C2412yes—
240C4⋊C4×C59—21no—
241C4⋊C4×C59—21no—
242C4⋊C4×C59C2412yes—
243C4⋊C4×C59C2412yes—
244C22⋊C4×C59—24no—
245C22⋊C4×C59—24no—
246C42×C59C2×D412yes—
247C42×C59C2412yes—
248C22⋊Dic59—24no—
249C22⋊Dic59—24no—
250C22⋊Dic59—24no—
251C22⋊Dic59—24no—
252#11745670—28no—
253#11745669—28no—
254(C2×D59)⋊C4—24no—
255(C2×D59)⋊C4—24no—
256(C2×D59)⋊C4—24no—
257(C2×D59)⋊C4C2×D414yes—
258(C2×D59)⋊C4C2×D414yes—
259C4⋊Dic59—21no—
260C4⋊Dic59—21no—
261C4⋊Dic59—24no—
262C4⋊Dic59—24no—
263C4⋊Dic59C2412yes—
264C4⋊Dic59C2412yes—
265Dic59⋊C4—24no—
266Dic59⋊C4—24no—
267Dic59⋊C4—24no—
268Dic59⋊C4C2×D414yes—
269Dic59⋊C4C2×D414yes—
270C4×Dic59—24no—
271C4×Dic59C2×D412yes—
272C4×Dic59C2412yes—
273C2×C59⋊C8—22no—
274C2×C59⋊C8#4114yes—
275C2×C59⋊C8C2412yes—
276C2×C59⋊C8C2412yes—
277#11745660—28no—
278#11745659—28no—
279C8×D59—28no—
280C23×C59—22no—
281C23×C59—22no—
282C23×C59—42no—
283C23×C59—42no—
284C23×C59—42no—
285C23×C59—42no—
286C23×C59—42no—
287C23×C59—42no—
288C23×C59C22×D411yescharacteristic
289C22×D59—22no—
290C22×D59—22no—
291C22×D59—22no—
292C22×D59—22no—
293C22×D59—42no—
294C22×D59—42no—
295C22×D59—42no—
296C22×D59C22×D412yes—
297D4×C59—22no—
298D4×C59—22no—
299D4×C59—22no—
300D4×C59—22no—
301D4×C59—42no—
302D4×C59—42no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—42no—
308C2×C4×C59—42no—
309C2×C4×C59—84no—
310C2×C4×C59—84no—
311C2×C4×C59C22×D412yes—
312C2×C4×C59C22×D412yes—
313C2×C4×C59C22×D411yescharacteristic
314C2×C4×C59C2×#4112yes—
315C2×C4×C59C2×#4112yes—
316C2×C4×C59C2511yescharacteristic
317C22⋊D59—84no—
318C22⋊D59—84no—
319C22⋊D59—84no—
320C22⋊D59—84no—
321C2×Dic59—22no—
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—
332C2×Dic59C22×D412yes—
333D236—22no—
334D236—22no—
335D236—42no—
336D236—84no—
337C4×D59—24no—
338C4×D59—22no—
339C4×D59—22no—
340C4×D59—84no—
341Dic118—22no—
342Dic118—22no—
343Dic118—42no—
344Dic118—84no—
345C8×C59—22no—
346C8×C59C2×#4114yes—
347C59⋊C8—22no—
348C59⋊C8C2×#4114yes—
349C2×#3179—591nomaximal, Sylow
350C22×C59—42no—
351C22×C59—42no—
352C22×C59—42no—
353C22×C59—42no—
354C22×C59—42no—
355C22×C59—42no—
356C22×C59—84no—
357C22×C59—84no—
358C22×C59#53212yes—
359C22×C59#57612yes—
360C22×C59#57712yes—
361C22×C59C23×D411yescharacteristic
362C2×D59—22no—
363C2×D59—22no—
364C2×D59—22no—
365C2×D59—44no—
366C2×D59—42no—
367C2×D59—42no—
368C2×D59—42no—
369C2×D59—84no—
370C4×C59—22no—
371C4×C59—22no—
372C4×C59—42no—
373C4×C59—42no—
374C4×C59#53212yes—
375C4×C59C22×#4111yescharacteristic
376C4×C59C22×#4111yescharacteristic
377Dic59—22no—
378Dic59—22no—
379Dic59—22no—
380Dic59—42no—
381Dic59—42no—
382Dic59—42no—
383C2×#542—591no—
384C2×#540—591no—
385#3179—5916no—
386C2×#501—591no—
387C2×#496—591no—
388C2×#488—591no—
389C2×#486—591no—
390C2×#469—591no—
391C2×#468—591no—
392C2×#466—591no—
393C2×#465—591no—
394C2×#442—591no—
395C2×#440—591no—
396C2×C4×SD16—591no—
397C2×C4×D8D5911yescharacteristic, complemented
398C2×#405—591no—
399C2×C59—82no—
400C2×C59—82no—
401C2×C59#317914yescomplemented
402C2×C59C2×#53211yescharacteristic
403C2×C59C2×#57611yescharacteristic
404C2×C59C2×#57711yescharacteristic
405D59—42no—
406D59—82no—
407C22×SD16—591no—
408C22×SD16—591no—
409C22×D8—591no—
410C22×D8C2×D5911yescharacteristic
411C22×M16—591no—
412C23×C8—591no—
413#542—598no—
414#542—1184no—
415#540—598no—
416#540—1184no—
417C2×C4⋊Q8—591no—
418C2×#127—591no—
419C2×#126—1181no—
420C2×#125—591no—
421C2×#124—591no—
422C2×#124—1181no—
423C2×#123—1181no—
424C2×#123—1181no—
425C2×#123—1181no—
426C2×C22⋊Q8—591no—
427C2×C22⋊Q8—1181no—
428C2×#121—591no—
429C2×#121—591no—
430C2×#121—591no—
431C2×#121—1181no—
432C2×#121—1181no—
433C2×C4×Q8—591no—
434C2×C4×D4—591no—
435C2×C4×D4C2×D5911yescharacteristic
436C2×C4×D4C2×D5911yescharacteristic
437C2×#117—591no—
438#501—598no—
439#496—598no—
440#488—598no—
441#486—598no—
442#469—598no—
443#468—598no—
444#466—598no—
445#465—598no—
446#442—598no—
447#440—598no—
448C4×SD16—598no—
449C4×D8C2×D5918yescomplemented
450C2×#107—591no—
451C2×#107C2×D5911yescharacteristic
452C2×#106—591no—
453C2×#106—591no—
454C2×#103—591no—
455C2×#103—591no—
456C2×#102—591no—
457C2×#102—591no—
458C2×#102—591no—
459C2×#102—591no—
460C2×#102C2×D5911yescharacteristic
461C2×#102C2×D5911yescharacteristic
462#405—598no—
463C2×#97—591no—
464C2×#97—591no—
465C2×C4×C8—591no—
466C2×C4×C8C2×D5911yescharacteristic
467C59C2×#317911yescharacteristic, complemented, Sylow
468C22×Q8—591no—
469C22×Q8—1181no—
470C22×D4—591no—
471C22×D4—1181no—
472C22×D4—1181no—
473C22×D4—1181no—
474C22×D4—1181no—
475C22×D4—1181no—
476C22×D4C22×D5911yescharacteristic
477C22×D4C22×D5911yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—591no—
481C23×C4—1181no—
482C2×SD16—594no—
483C2×SD16—594no—
484C2×SD16—1184no—
485C2×SD16—1184no—
486C2×D8—24no—
487C2×D8—594no—
488C2×D8—1184no—
489C2×D8C22×D5914yes—
490C2×M16—594no—
491C2×M16—1184no—
492C22×C8—591no—
493C22×C8—591no—
494C22×C8—594no—
495C22×C8—1184no—
496C22×C8C22×D5911yescharacteristic
497C22×C8C22×D5911yescharacteristic
498C4⋊Q8—594no—
499C4⋊Q8—1182no—
500#127—594no—
501#127—1182no—
502#126—1188no—
503#125—594no—
504#125—1182no—
505#124—594no—
506#124—1182no—
507#124—1188no—
508#123—1188no—
509#123—1188no—
510#123—1188no—
511C22⋊Q8—594no—
512C22⋊Q8—1182no—
513C22⋊Q8—1188no—
514#121—594no—
515#121—594no—
516#121—594no—
517#121—1188no—
518#121—1188no—
519#121—1182no—
520#121—1182no—
521#121—1182no—
522C4×Q8—594no—
523C4×Q8—1182no—
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—594no—
527C4×D4—1182no—
528C4×D4C22×D5914yes—
529C4×D4C22×D5914yes—
530#117—594no—
531#117—594no—
532C2×C4⋊C4—591no—
533C2×C4⋊C4—591no—
534C2×C4⋊C4—591no—
535C2×C4⋊C4—591no—
536C2×C4⋊C4—1181no—
537C2×C4⋊C4—1181no—
538C2×C4⋊C4—1181no—
539C2×C4⋊C4—1181no—
540C2×C4⋊C4—1181no—
541C2×C4⋊C4C22×D5911yescharacteristic
542C2×C4⋊C4C22×D5911yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—591no—
546C2×C22⋊C4—591no—
547C2×C22⋊C4—1181no—
548C2×C22⋊C4—1181no—
549C2×C22⋊C4—1181no—
550C2×C22⋊C4—1181no—
551C2×C22⋊C4—1181no—
552C2×C22⋊C4—1181no—
553C2×C22⋊C4—1181no—
554C2×C42—591no—
555C2×C42—1181no—
556C2×C42C22×D5911yescharacteristic
557#107—594no—
558#107C22×D5914yes—
559#106—594no—
560#106—594no—
561#103—594no—
562#103—594no—
563#102—594no—
564#102—594no—
565#102—594no—
566#102—594no—
567#102C22×D5914yes—
568#102C22×D5914yes—
569#97—594no—
570#97—594no—
571C4×C8—594no—
572C4×C8C22×D5914yes—
573C24—21no—
574C24—21no—
575C24—591no—
576C24—1181no—
577C2×Q8—592no—
578C2×Q8—1184no—
579C2×Q8—1181no—
580C2×Q8—1182no—
581C2×Q8—1182no—
582C2×Q8—4722no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—22no—
588C2×D4—22no—
589C2×D4—592no—
590C2×D4—1184no—
591C2×D4—1184no—
592C2×D4—1184no—
593C2×D4—1184no—
594C2×D4—1184no—
595C2×D4—1181no—
596C2×D4—1182no—
597C2×D4—1182no—
598C2×D4—4722no—
599C2×D4—4722no—
600C2×D4—4722no—
601C2×D4—4722no—
602C2×D4—4722no—
603C2×D4C23×D5912yes—
604C2×D4C23×D5912yes—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—24no—
608C22×C4—24no—
609C22×C4—82no—
610C22×C4—82no—
611C22×C4—591no—
612C22×C4—591no—
613C22×C4—591no—
614C22×C4—592no—
615C22×C4—592no—
616C22×C4—1182no—
617C22×C4—1182no—
618C22×C4—1181no—
619C22×C4—1181no—
620C22×C4—1181no—
621C22×C4—1184no—
622C22×C4—4722no—
623C22×C4D4×D5911yescharacteristic
624C22×C4D4×D5911yescharacteristic
625C22×C4C23×D5911yescharacteristic
626SD16—1188no—
627SD16—1188no—
628D8—28no—
629D8—1188no—
630M16—1188no—
631C2×C8—22no—
632C2×C8—594no—
633C2×C8—592no—
634C2×C8—592no—
635C2×C8—1188no—
636C2×C8—1182no—
637C2×C8#1174568514yes—
638C2×C8C23×D5912yes—
639C2×C8C23×D5912yes—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—594no—
643C4⋊C4—594no—
644C4⋊C4—592no—
645C4⋊C4—592no—
646C4⋊C4—1184no—
647C4⋊C4—1184no—
648C4⋊C4—1184no—
649C4⋊C4—1184no—
650C4⋊C4—1181no—
651C4⋊C4—1181no—
652C4⋊C4—1184no—
653C4⋊C4C23×D5912yes—
654C4⋊C4C23×D5912yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—594no—
658C22⋊C4—594no—
659C22⋊C4—1184no—
660C22⋊C4—1184no—
661C22⋊C4—1184no—
662C22⋊C4—1184no—
663C22⋊C4—1184no—
664C22⋊C4—1184no—
665C22⋊C4—1184no—
666C42—592no—
667C42—592no—
668C42—1184no—
669C42D4×D5912yes—
670C42C23×D5912yes—
671C23—22no—
672C23—22no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—592no—
680C23—1182no—
681C23—1182no—
682C23—1182no—
683C23—1182no—
684C23—2362no—
685C23—2362no—
686C23—2362no—
687C23C2×D4×D5911yescharacteristic
688Q8—1182no—
689Q8—1182no—
690Q8—4724no—
691Q8—2362no—
692D4—22no—
693D4—22no—
694D4—22no—
695D4—22no—
696D4—42no—
697D4—42no—
698D4—1182no—
699D4—1182no—
700D4—4724no—
701D4—4724no—
702D4—4724no—
703D4—4724no—
704D4—4724no—
705D4—2362no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—84no—
713C2×C4—84no—
714C2×C4—592no—
715C2×C4—592no—
716C2×C4—592no—
717C2×C4—1182no—
718C2×C4—1182no—
719C2×C4—1182no—
720C2×C4—1184no—
721C2×C4—1182no—
722C2×C4—1182no—
723C2×C4—1182no—
724C2×C4—1182no—
725C2×C4—1182no—
726C2×C4—4724no—
727C2×C4—2362no—
728C2×C4—2362no—
729C2×C4—2362no—
730C2×C4C2×D4×D5912yes—
731C2×C4C2×D4×D5912yes—
732C2×C4C2×D4×D5911yescharacteristic
733C2×C4#41×D5912yes—
734C2×C4C2×#1174568512yes—
735C2×C4C24×D5911yescharacteristic
736C8—22no—
737C8—594no—
738C8—1182no—
739C8C2×#1174568514yes—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—84no—
747C22—84no—
748C22—1182no—
749C22—1182no—
750C22—1182no—
751C22—4724no—
752C22—2362no—
753C22—2362no—
754C22—2362no—
755C22—2364no—
756C22#1683794912yes—
757C22#1683820312yes—
758C22#1683820912yes—
759C22C22×D4×D5911yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—1182no—
765C4—1182no—
766C4—1182no—
767C4—2362no—
768C4—2362no—
769C4—2362no—
770C4#1683794912yes—
771C4C2×#41×D5911yescharacteristic
772C4C22×#1174568511yescharacteristic
773C2—82no—
774C2—82no—
775C2—4722no—
776C2—2362no—
777C2#2143478314yesdirect product factor
778C2C2×#1683794911yescharacteristic
779C2C2×#1683820311yescharacteristic
780C2C2×#1683820911yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C4×D8×C59C2
socleC23×C59C22×D4
hypercenterC2×C4×D8D59
hypocenterC59C2×#3179
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. C2×#16838017C2semidirect
2. C2×#16838003C2semidirect
3. #21434783C2direct (N × H)
4. C2×#16837810C2semidirect
5. C2×#16837790C2semidirect
6. C2×#16837755C2semidirect
7. C2×#16837747C2semidirect
8. C2×#16837652C2semidirect
9. C2×#16837649C2semidirect
10. C2×#16837637C2semidirect
11. C2×#16837630C2semidirect
12. C2×#16837512C2semidirect
13. C2×#16837502C2semidirect
14. C2×C4×#11745660C2semidirect
15. C2×#16837356C2semidirect
16. C2×C4×D8×C59C2semidirect
23. #16838017C22semidirect
25. #16838003C22semidirect
45. #16837810C22semidirect
46. #16837790C22semidirect
47. #16837755C22semidirect
48. #16837747C22semidirect
49. #16837652C22semidirect
50. #16837649C22semidirect
51. #16837637C22semidirect
52. #16837630C22semidirect
53. #16837512C22semidirect
54. #16837502C22semidirect
55. C4×#11745660C22semidirect
65. #16837356C22semidirect
72. C4×D8×C59C22semidirect
397. C2×C4×D8D59semidirect
401. C2×C59#3179semidirect
449. C4×D8C2×D59semidirect
467. C59C2×#3179semidirect
777. C2#21434783direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380172
C2×#168380032
#214347832
C2×#168378102
C2×#168377902
C2×#168377552
C2×#168377472
C2×#168376522
C2×#168376492
C2×#168376372
C2×#168376302
C2×#168375122
C2×#168375022
C2×C4×#117456602
C2×#168373562
C2×C4×D8×C592
C2×#317959