Finite Group Databasebeta

← C2×#21436152 #29465300

Subgroups — C2×#21436152 #29465300

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×#16838093C211yesmaximal, characteristic
2C2×Q8×D236C211yesmaximal, characteristic
3#21436152C2116yesmaximal, direct product factor
4C2×#16837771C211yesmaximal, characteristic, complemented
5C2×#16837746C211yesmaximal, characteristic, complemented
6C2×#16837734C211yesmaximal, characteristic, complemented
7C2×#16837709C211yesmaximal, characteristic, complemented
8C2×#16837659C211yesmaximal, characteristic, complemented
9C2×#16837642C211yesmaximal, characteristic, complemented
10C2×#16837612C211yesmaximal, characteristic, complemented
11C2×#16837556C211yesmaximal, characteristic, complemented
12C2×#16837556C211yesmaximal, characteristic, complemented
13C2×#16837475C211yesmaximal, characteristic
14C2×#16837409C211yesmaximal, characteristic, complemented
15C2×#103×D59C211yesmaximal, characteristic, complemented
16C2×C59×#441C211yesmaximal, characteristic, complemented
17C22×Q8×D59C2211yescharacteristic
18C22×Q8×D59C2211yescharacteristic
19C22×#11745672C2211yescharacteristic
20C22×#11745672C2211yescharacteristic
21C22×#11745659C2211yescharacteristic
22C22×C8×D59C2211yescharacteristic
23#16838093—24no—
24#16838093C2218yes—
25Q8×D236—24no—
26Q8×D236C2218yes—
27C2×#14273727—21no—
28C2×#14273727C2211yescharacteristic
29C2×#14273721—21no—
30C2×#14273719C2211yescharacteristic
31C2×#14273717—21no—
32C2×#14273712—21no—
33C2×#14273707—21no—
34C2×#14273707—21no—
35C2×#14273707C2211yescharacteristic
36C2×#14273707C2211yescharacteristic
37C2×#14273703C2211yescharacteristic
38C2×#14273703C2211yescharacteristic
39C2×C4×D236—21no—
40C2×C4×D236C2211yescharacteristic
41C2×#14273685C2211yescharacteristic
42C2×#14273684—21no—
43C2×C4⋊C4×D59C2211yescharacteristic
44#16837771C2218yescomplemented
45#16837746C2218yescomplemented
46#16837734C2218yescomplemented
47#16837709C2218yescomplemented
48#16837659C2218yescomplemented
49#16837642C2218yescomplemented
50#16837612C2218yescomplemented
51#16837556C2218yescomplemented
52#16837556C2218yescomplemented
53#16837475C2218yes—
54C2×#14273660C2211yescharacteristic
55C2×#14273658C2211yescharacteristic
56C2×C4⋊(C59⋊C8)C2211yescharacteristic
57#16837409C2218yescomplemented
58C2×#14273652C2211yescharacteristic
59C2×#14273652C2211yescharacteristic
60C2×#14273652C2211yescharacteristic
61C2×#14273652C2211yescharacteristic
62C2×#14273651C2211yescharacteristic
63C2×#14273651C2211yescharacteristic
64C2×#14273650C2211yescharacteristic
65C2×#14273650C2211yescharacteristic
66#103×D59C2218yescomplemented
67C2×(C2×D59)⋊C8C2211yescharacteristic
68C2×(C2×D59)⋊C8C2211yescharacteristic
69C22×Q16×C59C2211yescharacteristic
70C2×C4×Q8×C59C2211yescharacteristic
71C2×C4×Q8×C59C2211yescharacteristic
72C59×#441C2218yescomplemented
73C2×#106×C59C2211yescharacteristic
74C2×#103×C59C2211yescharacteristic
75C2×#103×C59C2211yescharacteristic
76C2×#97×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×D236D411yescharacteristic
90C22×C4×D59—21no—
91C22×C4×D59—21no—
92C22×C4×D59—21no—
93C22×C4×D59C2311yescharacteristic
94C22×C4×D59C2311yescharacteristic
95C2×#11745672—42no—
96C2×#11745672—42no—
97C2×#11745672C2314yes—
98C2×#11745672C2314yes—
99C2×#11745659—42no—
100C2×#11745659C2314yes—
101C22×C59⋊C8C2311yescharacteristic
102C22×C59⋊C8C2311yescharacteristic
103C2×C8×D59—42no—
104C2×C8×D59C2314yes—
105#14273727—22no—
106#14273727—28no—
107#14273727C2314yes—
108#14273721—28no—
109#14273719—22no—
110#14273719C2314yes—
111#14273717—28no—
112#14273712—28no—
113#14273707—22no—
114#14273707—22no—
115#14273707—28no—
116#14273707—28no—
117#14273707C2314yes—
118#14273707C2314yes—
119#14273703—22no—
120#14273703—22no—
121#14273703C2314yes—
122#14273703C2314yes—
123C4×D236—28no—
124C4×D236D414yes—
125C4×D236C2314yes—
126#14273685—22no—
127#14273685C2314yes—
128#14273684—28no—
129C2×C4⋊Dic59—21no—
130C2×C4⋊Dic59—21no—
131C2×C4⋊Dic59—21no—
132C2×C4⋊Dic59—21no—
133C2×C4⋊Dic59D411yescharacteristic
134C2×C4⋊Dic59C2311yescharacteristic
135C2×C4⋊Dic59C2311yescharacteristic
136C2×Dic59⋊C4—21no—
137C2×Dic59⋊C4—21no—
138C2×Dic59⋊C4—21no—
139C2×Dic59⋊C4—21no—
140C2×Dic59⋊C4—21no—
141C4⋊C4×D59—22no—
142C4⋊C4×D59C2314yes—
143C2×(C2×D59)⋊C4—21no—
144C2×(C2×D59)⋊C4—21no—
145C2×(C2×D59)⋊C4—21no—
146C2×(C2×D59)⋊C4—21no—
147C2×(C2×D59)⋊C4—21no—
148C2×(C2×D59)⋊C4D411yescharacteristic
149C2×(C2×D59)⋊C4D411yescharacteristic
150C2×C4×Dic59—21no—
151#14273660C2314yes—
152#14273658C2314yes—
153C4⋊(C59⋊C8)C2314yes—
154#14273652C2314yes—
155#14273652C2314yes—
156#14273652C2314yes—
157#14273652C2314yes—
158#14273651C2314yes—
159#14273651C2314yes—
160#14273650C2314yes—
161#14273650C2314yes—
162(C2×D59)⋊C8C2314yes—
163(C2×D59)⋊C8C2314yes—
164C22×Q8×C59C2311yescharacteristic
165C22×Q8×C59C2311yescharacteristic
166C2×Q16×C59—24no—
167C2×Q16×C59C2314yes—
168C22×C8×C59C2311yescharacteristic
169C22×C8×C59C2311yescharacteristic
170C4×Q8×C59—22no—
171C4×Q8×C59—22no—
172C4×Q8×C59C2314yes—
173C4×Q8×C59C2314yes—
174C2×C4⋊C4×C59—21no—
175C2×C4⋊C4×C59—21no—
176C2×C4⋊C4×C59C2311yescharacteristic
177C2×C4⋊C4×C59C2311yescharacteristic
178C2×C42×C59—21no—
179C2×C42×C59—21no—
180C2×C42×C59C2311yescharacteristic
181#106×C59C2314yes—
182#103×C59C2314yes—
183#103×C59C2314yes—
184#97×C59C2314yes—
185C23×D59C2×D411yescharacteristic
186C23×D59C2×D411yescharacteristic
187C2×Q8×C59—21no—
188C2×Q8×C59—21no—
189C2×Q8×C59—22no—
190C2×Q8×C59—22no—
191C2×Q8×C59—22no—
192C2×Q8×C59#4114yes—
193C2×Q8×C59C2412yes—
194C2×Q8×C59C2412yes—
195C22×C4×C59—21no—
196C22×C4×C59—21no—
197C22×C4×C59—21no—
198C22×C4×C59—21no—
199C22×C4×C59C2×D411yescharacteristic
200C22×C4×C59C2×D411yescharacteristic
201C22×C4×C59C2411yescharacteristic
202C22×Dic59—21no—
203C22×Dic59—21no—
204C22×Dic59—21no—
205C22×Dic59—21no—
206C22×Dic59C2×D411yescharacteristic
207C22×Dic59C2×D411yescharacteristic
208Q8×D59—28no—
209Q8×D59—28no—
210Q8×D59—44no—
211Q8×D59—44no—
212Q8×D59—48no—
213Q8×D59—48no—
214C2×D236—24no—
215C2×D236C2×D414yes—
216C2×C4×D59—22no—
217C2×C4×D59—22no—
218C2×C4×D59—22no—
219C2×C4×D59—22no—
220C2×C4×D59—24no—
221C2×C4×D59—24no—
222C2×C4×D59—24no—
223C2×C4×D59—44no—
224C2×C4×D59—44no—
225C2×C4×D59—44no—
226C2×C4×D59C2×D412yes—
227C2×C4×D59C2×D412yes—
228C2×C4×D59C2412yes—
229C2×C4×D59C2412yes—
230C2×Dic118—22no—
231C2×Dic118—22no—
232C2×Dic118—22no—
233C2×Dic118—22no—
234C2×Dic118—21no—
235C2×Dic118—21no—
236C2×Dic118—24no—
237C2×Dic118—24no—
238C2×Dic118—44no—
239C2×Dic118—44no—
240C2×Dic118C2412yes—
241C2×Dic118C2412yes—
242Q16×C59—28no—
243C2×C8×C59—22no—
244C2×C8×C59—22no—
245C2×C8×C59C2412yes—
246C2×C8×C59C2412yes—
247C4⋊C4×C59—24no—
248C4⋊C4×C59—24no—
249C4⋊C4×C59—21no—
250C4⋊C4×C59—21no—
251C4⋊C4×C59C2412yes—
252C4⋊C4×C59C2412yes—
253C42×C59—24no—
254C42×C59—24no—
255C42×C59C2×D412yes—
256C42×C59C2412yes—
257#11745672—44no—
258#11745672—44no—
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—21no—
270C4⋊Dic59—24no—
271C4⋊Dic59—24no—
272C4⋊Dic59C2×D414yes—
273C4⋊Dic59C2412yes—
274C4⋊Dic59C2412yes—
275Dic59⋊C4—24no—
276Dic59⋊C4—24no—
277Dic59⋊C4—24no—
278Dic59⋊C4—24no—
279Dic59⋊C4—24no—
280C4×Dic59—24no—
281C2×C59⋊C8—22no—
282C2×C59⋊C8—22no—
283C2×C59⋊C8C2412yes—
284C2×C59⋊C8C2412yes—
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×C59—22no—
299Q8×C59—22no—
300Q8×C59—42no—
301Q8×C59C2×#4114yes—
302C2×C4×C59—24no—
303C2×C4×C59—22no—
304C2×C4×C59—22no—
305C2×C4×C59—22no—
306C2×C4×C59—22no—
307C2×C4×C59—22no—
308C2×C4×C59—22no—
309C2×C4×C59—42no—
310C2×C4×C59—42no—
311C2×C4×C59—42no—
312C2×C4×C59C22×D412yes—
313C2×C4×C59C22×D412yes—
314C2×C4×C59C22×D411yescharacteristic
315C2×C4×C59C2×#4112yes—
316C2×C4×C59H(5,𝔽2)12yes—
317C2×C4×C59C2511yescharacteristic
318C2×Dic59—22no—
319C2×Dic59—22no—
320C2×Dic59—22no—
321C2×Dic59—22no—
322C2×Dic59—22no—
323C2×Dic59—22no—
324C2×Dic59—42no—
325C2×Dic59—42no—
326C2×Dic59—42no—
327C2×Dic59—42no—
328C2×Dic59C22×D412yes—
329C2×Dic59C22×D412yes—
330D236—28no—
331C4×D59—24no—
332C4×D59—24no—
333C4×D59—22no—
334C4×D59—22no—
335C4×D59—22no—
336C4×D59—22no—
337C4×D59—48no—
338C4×D59—48no—
339C4×D59—48no—
340Dic118—22no—
341Dic118—22no—
342Dic118—22no—
343Dic118—22no—
344Dic118—48no—
345Dic118—48no—
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×#479—591no—
387C2×#470—591no—
388C2×#467—591no—
389C2×#462—591no—
390C2×#451—591no—
391C2×#451—591no—
392C2×#441D5911yescharacteristic, complemented
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×Q16C2×D5911yescharacteristic
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—591no—
423C2×C22⋊Q8—1181no—
424C2×C22⋊Q8—1181no—
425C2×C4×Q8C2×D5911yescharacteristic
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#479—598no—
436#470—598no—
437#467—598no—
438#462—598no—
439#451—598no—
440#451—598no—
441#441C2×D5918yescomplemented
442#435—598no—
443C2×#107—591no—
444C2×#106—591no—
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⋊C8—591no—
461C2×#97C2×D5911yescharacteristic
462C59C2×#331211yescharacteristic, complemented, Sylow
463C22×Q8—594no—
464C22×Q8—594no—
465C22×Q8—591no—
466C22×Q8—591no—
467C22×Q8—1181no—
468C22×Q8—1181no—
469C22×Q8—1182no—
470C22×Q8—1182no—
471C22×Q8—1184no—
472C22×Q8—1184no—
473C22×Q8—2362no—
474C22×Q8—2362no—
475C22×Q8C22×D5911yescharacteristic
476C22×Q8C22×D5911yescharacteristic
477C22×D4—591no—
478C23×C4—591no—
479C23×C4—591no—
480C23×C4—1181no—
481C23×C4—1181no—
482C23×C4—1181no—
483C2×Q16—24no—
484C2×Q16—594no—
485C2×Q16—594no—
486C2×Q16—2362no—
487C2×Q16—2362no—
488C2×Q16C22×D5914yes—
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—594no—
502#125—1188no—
503#125—1182no—
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—22no—
517C4×Q8C22×D5914yes—
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—591no—
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⋊C4—1181no—
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—21no—
552C2×C42—1181no—
553C2×C42C22×D5911yescharacteristic
554#107—594no—
555#106—594no—
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⋊C8—594no—
570#97C22×D5914yes—
571C24—591no—
572C24—591no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—592no—
579C2×Q8—592no—
580C2×Q8—1184no—
581C2×Q8—1184no—
582C2×Q8—1181no—
583C2×Q8—1181no—
584C2×Q8—1188no—
585C2×Q8—1188no—
586C2×Q8—1182no—
587C2×Q8—1182no—
588C2×Q8—1182no—
589C2×Q8—1182no—
590C2×Q8—2364no—
591C2×Q8—2364no—
592C2×Q8—2364no—
593C2×Q8—2364no—
594C2×Q8—2368no—
595C2×Q8—2368no—
596C2×Q8#1174568514yes—
597C2×Q8C23×D5912yes—
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—28no—
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—21no—
644C4⋊C4—21no—
645C4⋊C4—594no—
646C4⋊C4—592no—
647C4⋊C4—592no—
648C4⋊C4—1184no—
649C4⋊C4—1184no—
650C4⋊C4—1184no—
651C4⋊C4—1184no—
652C4⋊C4—1184no—
653C4⋊C4—1181no—
654C4⋊C4—1181no—
655C4⋊C4—1184no—
656C4⋊C4—1184no—
657C4⋊C4—1184no—
658C4⋊C4—1184no—
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—24no—
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—22no—
685Q8—22no—
686Q8—42no—
687Q8—1182no—
688Q8—1182no—
689Q8—1182no—
690Q8—1182no—
691Q8—2368no—
692Q8—2368no—
693Q8—2362no—
694Q8—2362no—
695Q8C2×#1174568514yes—
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×#1174568512yes—
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#1683804812yes—
747C22#137×D5912yes—
748C22#1683821812yes—
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#1683804812yes—
763C4C22×#1174568511yescharacteristic
764C4C2×#1427377311yescharacteristic
765C2—1184no—
766C2—2362no—
767C2#2143615214yesdirect product factor
768C2C2×#1683804811yescharacteristic
769C2C2×#137×D5911yescharacteristic
770C2C2×#1683821811yescharacteristic
subgroupG/H
centerC23C2×D4×D59
commutator, cosocleC2×C4×C59C25
FrattiniC2×C4C24×D59
FittingC2×C59×#441C2
socleC23×C59C22×D4
prime radicalC22×D236D4
hypercenterC2×#441D59
hypocenterC59C2×#3312
LCSG ▷ C2×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. #21436152C2direct (N × H)
4. C2×#16837771C2semidirect
5. C2×#16837746C2semidirect
6. C2×#16837734C2semidirect
7. C2×#16837709C2semidirect
8. C2×#16837659C2semidirect
9. C2×#16837642C2semidirect
10. C2×#16837612C2semidirect
11. C2×#16837556C2semidirect
12. C2×#16837556C2semidirect
14. C2×#16837409C2semidirect
15. C2×#103×D59C2semidirect
16. C2×C59×#441C2semidirect
44. #16837771C22semidirect
45. #16837746C22semidirect
46. #16837734C22semidirect
47. #16837709C22semidirect
48. #16837659C22semidirect
49. #16837642C22semidirect
50. #16837612C22semidirect
51. #16837556C22semidirect
52. #16837556C22semidirect
57. #16837409C22semidirect
66. #103×D59C22semidirect
72. C59×#441C22semidirect
392. C2×#441D59semidirect
396. C2×C59#3312semidirect
441. #441C2×D59semidirect
462. C59C2×#3312semidirect
767. C2#21436152direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168380932
C2×Q8×D2362
#214361522
C2×#168377712
C2×#168377462
C2×#168377342
C2×#168377092
C2×#168376592
C2×#168376422
C2×#168376122
C2×#168375562
C2×#168374752
C2×#168374092
C2×#103×D592
C2×C59×#4412
C2×#331259