Finite Group Databasebeta

← C2×#20286996 #28260975

Subgroups — C2×#20286996 #28260975

Order 13568.

2082 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×#16811341C211yesmaximal, characteristic
2C2×#16811286C211yesmaximal, characteristic
3#20286996C2116yesmaximal, direct product factor
4C2×#16810972C211yesmaximal, characteristic, complemented
5C2×#16810966C211yesmaximal, characteristic, complemented
6C2×#16810907C211yesmaximal, characteristic, complemented
7C2×#16810882C211yesmaximal, characteristic, complemented
8C2×#16810879C211yesmaximal, characteristic, complemented
9C2×#16810832C211yesmaximal, characteristic, complemented
10C2×#16810781C211yesmaximal, characteristic, complemented
11C2×#16810780C211yesmaximal, characteristic, complemented
12C2×#16810717C211yesmaximal, characteristic, complemented
13C2×#16810698C211yesmaximal, characteristic
14C2×#16810631C211yesmaximal, characteristic, complemented
15C2×#16810630C211yesmaximal, characteristic, complemented
16C2×C53×#485C211yesmaximal, characteristic, complemented
17C23×Dic106C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×Dic212C2211yescharacteristic
20C22×Dic212C2211yescharacteristic
21C22×#11719925C2211yescharacteristic
22C22×#11719917C2211yescharacteristic
23C22×#11719912C2211yescharacteristic
24#16811341—24no—
25#16811341C2218yes—
26#16811286—24no—
27#16811286C2218yes—
28C2×#13133216—21no—
29C2×#13133216C2211yescharacteristic
30C2×#13133215C2211yescharacteristic
31C2×#13133211—21no—
32C2×#13133210—21no—
33C2×#13133203—21no—
34C2×#13133197C2211yescharacteristic
35C2×#13133197C2211yescharacteristic
36C2×#13133196C2211yescharacteristic
37C2×#13133195—21no—
38C2×#13133194—21no—
39C2×C4×Dic106—21no—
40C2×#13133182C2211yescharacteristic
41C2×#13133182C2211yescharacteristic
42C2×C4×C22⋊D53C2211yescharacteristic
43C2×#13133177—21no—
44C2×#13133175C2211yescharacteristic
45#16810972C2218yescomplemented
46#16810966C2218yescomplemented
47#16810907C2218yescomplemented
48#16810882C2218yescomplemented
49#16810879C2218yescomplemented
50#16810832C2218yescomplemented
51#16810781C2218yescomplemented
52#16810780C2218yescomplemented
53#16810717C2218yescomplemented
54#16810698C2218yes—
55C2×#13133148C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57#16810631C2218yescomplemented
58#16810630C2218yescomplemented
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63C2×#13133140C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66C2×#13133140C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C8×Dic53C2211yescharacteristic
69C2×C22⋊Q8×C53C2211yescharacteristic
70C2×#117×C53C2211yescharacteristic
71C53×#485C2218yescomplemented
72C2×#107×C53C2211yescharacteristic
73C2×#106×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×Dic106—24no—
78C22×Dic106—22no—
79C22×Dic106—21no—
80C22×Dic106—21no—
81C22×Dic106—21no—
82C22×Dic106—42no—
83C22×Dic106C2311yescharacteristic
84C22×Dic106C2311yescharacteristic
85C22×Dic106C2314yes—
86C22×Dic106C2311yescharacteristic
87C2×Q8×D53—22no—
88C2×Q8×D53—24no—
89C2×Q8×D53—42no—
90C2×Q8×D53C2314yes—
91C22×C22⋊D53D411yescharacteristic
92C23×Dic53—21no—
93C22×C4×D53—21no—
94C22×C4×D53C2311yescharacteristic
95C2×Dic212—24no—
96C2×Dic212—42no—
97C2×Dic212C2314yes—
98C2×Dic212C2314yes—
99C2×#11719925—42no—
100C2×#11719925C2314yes—
101C2×#11719917—42no—
102C2×#11719917C2314yes—
103C2×#11719912—42no—
104C2×#11719912C2314yes—
105C22×#88322C2311yescharacteristic
106C22×#88322C2311yescharacteristic
107#13133216—28no—
108#13133216—22no—
109#13133216C2314yes—
110#13133215—22no—
111#13133215C2314yes—
112#13133211—28no—
113#13133210—28no—
114#13133203—28no—
115#13133197—22no—
116#13133197—22no—
117#13133197C2314yes—
118#13133197C2314yes—
119#13133196—22no—
120#13133196C2314yes—
121#13133195—28no—
122#13133194—28no—
123C4×Dic106—28no—
124#13133182—22no—
125#13133182—22no—
126#13133182C2314yes—
127#13133182C2314yes—
128C4×C22⋊D53D414yes—
129C4×C22⋊D53C2314yes—
130#13133177—28no—
131#13133175—22no—
132#13133175C2314yes—
133C2×C4⋊Dic53—21no—
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53C2311yescharacteristic
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919—21no—
141C2×#11719919—21no—
142C2×#11719919D411yescharacteristic
143C2×C22⋊Dic53—21no—
144C2×C22⋊Dic53D411yescharacteristic
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921D411yescharacteristic
149C2×C4×Dic53—21no—
150C2×C4×Dic53—21no—
151C2×C4×Dic53—21no—
152C2×C4×Dic53C2311yescharacteristic
153#13133148C2314yes—
154#13133146C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133141C2314yes—
158#13133140C2314yes—
159#13133140C2314yes—
160#13133140C2314yes—
161#13133140C2314yes—
162#13133140C2314yes—
163#13133129C2314yes—
164C8×Dic53C2314yes—
165C22×Q8×C53C2311yescharacteristic
166C23×C4×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C22⋊Q8×C53—22no—
170C22⋊Q8×C53C2314yes—
171#117×C53—22no—
172#117×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C4⋊C4×C53C2311yescharacteristic
177C2×C22⋊C4×C53—21no—
178C2×C22⋊C4×C53—21no—
179C2×C42×C53—21no—
180#107×C53C2314yes—
181#106×C53C2314yes—
182#103×C53C2314yes—
183#103×C53C2314yes—
184C22⋊C8×C53C2314yes—
185C24×C53C2×D411yescharacteristic
186C23×D53C2×D411yescharacteristic
187C2×Q8×C53—21no—
188C2×Q8×C53—22no—
189C2×Q8×C53—22no—
190C2×Q8×C53C2412yes—
191C22×C4×C53—22no—
192C22×C4×C53—22no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D412yes—
199C22×C4×C53C2412yes—
200C22×C4×C53C2411yescharacteristic
201C2×C22⋊D53—24no—
202C2×C22⋊D53C2×D414yes—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—24no—
208C22×Dic53—44no—
209C22×Dic53C2×D411yescharacteristic
210C22×Dic53C2×D411yescharacteristic
211C22×Dic53C2×D411yescharacteristic
212Q8×D53—28no—
213Q8×D53—44no—
214Q8×D53—48no—
215C2×C4×D53—22no—
216C2×C4×D53—22no—
217C2×C4×D53—24no—
218C2×C4×D53—44no—
219C2×C4×D53C2×D412yes—
220C2×C4×D53C2412yes—
221C2×Dic106—21no—
222C2×Dic106—22no—
223C2×Dic106—22no—
224C2×Dic106—22no—
225C2×Dic106—22no—
226C2×Dic106—22no—
227C2×Dic106—28no—
228C2×Dic106—21no—
229C2×Dic106—24no—
230C2×Dic106—21no—
231C2×Dic106—24no—
232C2×Dic106—24no—
233C2×Dic106—44no—
234C2×Dic106—48no—
235C2×Dic106—44no—
236C2×Dic106—44no—
237C2×Dic106—44no—
238C2×Dic106#4114yes—
239C2×Dic106C2412yes—
240C2×Dic106C2412yes—
241C2×Dic106C2412yes—
242C2×C8×C53—22no—
243C2×C8×C53—22no—
244C2×C8×C53C2412yes—
245C2×C8×C53C2412yes—
246C4⋊C4×C53—24no—
247C4⋊C4×C53—21no—
248C4⋊C4×C53—21no—
249C4⋊C4×C53—21no—
250C4⋊C4×C53C2412yes—
251C4⋊C4×C53C2412yes—
252C4⋊C4×C53C2412yes—
253C22⋊C4×C53—24no—
254C22⋊C4×C53—24no—
255C42×C53—24no—
256C22⋊Dic53—24no—
257C22⋊Dic53C2×D414yes—
258#11719925—44no—
259#11719921—24no—
260#11719921—24no—
261#11719921—24no—
262#11719921C2×D414yes—
263C4⋊Dic53—21no—
264C4⋊Dic53—24no—
265C4⋊Dic53—24no—
266C4⋊Dic53C2412yes—
267#11719919—24no—
268#11719919—24no—
269#11719919—24no—
270#11719919—24no—
271#11719919—24no—
272#11719919—24no—
273#11719919C2×D414yes—
274C4×Dic53—24no—
275C4×Dic53—24no—
276C4×Dic53—24no—
277C4×Dic53C2×D412yes—
278C4×Dic53C2412yes—
279#11719917—44no—
280C2×#88322—22no—
281C2×#88322—22no—
282C2×#88322C2412yes—
283C2×#88322C2412yes—
284Dic212—28no—
285Dic212—44no—
286#11719912—44no—
287C23×C53—22no—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53C22×D412yes—
291C23×C53C22×D411yescharacteristic
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—22no—
295C22×D53C22×D412yes—
296Q8×C53—22no—
297Q8×C53—22no—
298Q8×C53—42no—
299C2×C4×C53—22no—
300C2×C4×C53—24no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—42no—
308C2×C4×C53—42no—
309C2×C4×C53—42no—
310C2×C4×C53—42no—
311C2×C4×C53C22×D412yes—
312C2×C4×C53C22×D411yescharacteristic
313C2×C4×C53C2×#4112yes—
314C2×C4×C53H(5,𝔽2)12yes—
315C2×C4×C53C2511yescharacteristic
316C22⋊D53—28no—
317C2×Dic53—24no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—48no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53#13714yes—
329C2×Dic53C22×D412yes—
330C2×Dic53C22×D412yes—
331C2×Dic53C22×D412yes—
332C4×D53—24no—
333C4×D53—22no—
334C4×D53—22no—
335C4×D53—48no—
336Dic106—24no—
337Dic106—22no—
338Dic106—22no—
339Dic106—22no—
340Dic106—22no—
341Dic106—22no—
342Dic106—48no—
343Dic106—48no—
344Dic106—42no—
345Dic106—42no—
346Dic106—48no—
347Dic106C2×#4114yes—
348C8×C53—22no—
349C8×C53—22no—
350#88322—22no—
351#88322—22no—
352C2×#3328—531nomaximal, Sylow
353C22×C53—22no—
354C22×C53—22no—
355C22×C53—22no—
356C22×C53—44no—
357C22×C53#54612yes—
358C22×C53C2×#13712yes—
359C22×C53#57812yes—
360C22×C53C23×D411yescharacteristic
361C2×D53—22no—
362C2×D53—22no—
363C2×D53—22no—
364C2×D53—44no—
365C4×C53—22no—
366C4×C53—42no—
367C4×C53—42no—
368C4×C53—42no—
369C4×C53—42no—
370C4×C53#54612yes—
371C4×C53C22×#4111yescharacteristic
372C4×C53C2×H(5,𝔽2)11yescharacteristic
373Dic53—24no—
374Dic53—22no—
375Dic53—22no—
376Dic53—42no—
377Dic53—42no—
378Dic53—42no—
379Dic53C2×#13714yes—
380C2×#556—531no—
381C2×D4×Q8—531no—
382#3328—5316no—
383C2×#487—531no—
384C2×#485—531no—
385C2×#485D5311yescharacteristic, complemented
386C2×#475—531no—
387C2×#470—531no—
388C2×#470—531no—
389C2×#462—531no—
390C2×#451—531no—
391C2×#451—531no—
392C2×C4×Q16—531no—
393C2×#436—531no—
394C2×#419—531no—
395C2×#419—531no—
396C2×C53—42no—
397C2×C53#332814yescomplemented
398C2×C53C2×#54611yescharacteristic
399C2×C53C22×#13711yescharacteristic
400C2×C53C2×#57811yescharacteristic
401D53—42no—
402C23×Q8—531no—
403C23×Q8—531no—
404C22×Q16—531no—
405C22×Q16—531no—
406C22×Q16—531no—
407C22×M16—531no—
408C22×M16—531no—
409#556—538no—
410#556—1064no—
411D4×Q8—538no—
412D4×Q8—1064no—
413C2×C4⋊Q8—531no—
414C2×C4⋊Q8—531no—
415C2×C4⋊Q8—1061no—
416C2×#126—1061no—
417C2×#126—1061no—
418C2×#124—1061no—
419C2×C22⋊Q8—531no—
420C2×C22⋊Q8—531no—
421C2×C22⋊Q8—531no—
422C2×C22⋊Q8—1061no—
423C2×C22⋊Q8—1061no—
424C2×C22⋊Q8C2×D5311yescharacteristic
425C2×C4×Q8—531no—
426C2×C4×Q8—531no—
427C2×C4×Q8—1061no—
428C2×C4×D4—531no—
429C2×C4×D4—1061no—
430C2×#117—531no—
431C2×#117C2×D5311yescharacteristic
432#487—538no—
433#485—538no—
434#485C2×D5318yescomplemented
435#475—538no—
436#470—538no—
437#470—538no—
438#462—538no—
439#451—538no—
440#451—538no—
441C4×Q16—538no—
442#436—538no—
443C2×#107C2×D5311yescharacteristic
444C2×#106—531no—
445C2×#106C2×D5311yescharacteristic
446C2×C4⋊C8—531no—
447#419—538no—
448#419—538no—
449C2×#103—531no—
450C2×#103—531no—
451C2×#103—531no—
452C2×#103—531no—
453C2×#103—531no—
454C2×#103—531no—
455C2×#103—531no—
456C2×#103—531no—
457C2×#103C2×D5311yescharacteristic
458C2×#103C2×D5311yescharacteristic
459C2×C22⋊C8—531no—
460C2×C22⋊C8C2×D5311yescharacteristic
461C2×C4×C8—531no—
462C53C2×#332811yescharacteristic, complemented, Sylow
463C22×Q8—534no—
464C22×Q8—531no—
465C22×Q8—531no—
466C22×Q8—531no—
467C22×Q8—534no—
468C22×Q8—1061no—
469C22×Q8—1061no—
470C22×Q8—1064no—
471C22×Q8—1062no—
472C22×Q8—1061no—
473C22×Q8—1062no—
474C22×Q8—1064no—
475C22×Q8—2122no—
476C22×Q8—2122no—
477C22×Q8C22×D5311yescharacteristic
478C22×D4—531no—
479C23×C4—531no—
480C23×C4—1061no—
481C23×C4—1061no—
482C23×C4C22×D5311yescharacteristic
483C2×Q16—534no—
484C2×Q16—534no—
485C2×Q16—534no—
486C2×Q16—1064no—
487C2×Q16—2122no—
488C2×Q16—2122no—
489C2×M16—534no—
490C2×M16—534no—
491C2×M16—2122no—
492C2×M16—2122no—
493C22×C8—531no—
494C22×C8—531no—
495C22×C8C22×D5311yescharacteristic
496C22×C8C22×D5311yescharacteristic
497C4⋊Q8—534no—
498C4⋊Q8—534no—
499C4⋊Q8—1062no—
500C4⋊Q8—1062no—
501C4⋊Q8—1068no—
502#126—1068no—
503#126—1068no—
504#124—1068no—
505C22⋊Q8—22no—
506C22⋊Q8—534no—
507C22⋊Q8—534no—
508C22⋊Q8—534no—
509C22⋊Q8—1068no—
510C22⋊Q8—1068no—
511C22⋊Q8—1062no—
512C22⋊Q8—1062no—
513C22⋊Q8—1062no—
514C22⋊Q8C22×D5314yes—
515C4×Q8—534no—
516C4×Q8—534no—
517C4×Q8—1068no—
518C4×Q8—1062no—
519C4×Q8—1062no—
520C4×D4—534no—
521C4×D4—534no—
522C4×D4—1068no—
523#117—22no—
524#117—534no—
525#117—1062no—
526#117C22×D5314yes—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—531no—
529C2×C4⋊C4—531no—
530C2×C4⋊C4—1061no—
531C2×C4⋊C4—1061no—
532C2×C4⋊C4—1061no—
533C2×C4⋊C4—1061no—
534C2×C4⋊C4—1061no—
535C2×C4⋊C4—1061no—
536C2×C4⋊C4—1061no—
537C2×C4⋊C4—1061no—
538C2×C4⋊C4C22×D5311yescharacteristic
539C2×C4⋊C4C22×D5311yescharacteristic
540C2×C4⋊C4C22×D5311yescharacteristic
541C2×C22⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C22⋊C4—531no—
544C2×C22⋊C4—531no—
545C2×C22⋊C4—1061no—
546C2×C22⋊C4—1061no—
547C2×C22⋊C4—1061no—
548C2×C22⋊C4—1061no—
549C2×C42—21no—
550C2×C42—531no—
551C2×C42—1061no—
552C2×C42—1061no—
553C2×C42—1061no—
554#107C22×D5314yes—
555#106—534no—
556#106C22×D5314yes—
557C4⋊C8—534no—
558#103—534no—
559#103—534no—
560#103—534no—
561#103—534no—
562#103—534no—
563#103—534no—
564#103—534no—
565#103—534no—
566#103C22×D5314yes—
567#103C22×D5314yes—
568C22⋊C8—534no—
569C22⋊C8C22×D5314yes—
570C4×C8—534no—
571C24—531no—
572C24D4×D5311yescharacteristic
573C2×Q8—21no—
574C2×Q8—22no—
575C2×Q8—22no—
576C2×Q8—534no—
577C2×Q8—532no—
578C2×Q8—532no—
579C2×Q8—532no—
580C2×Q8—1064no—
581C2×Q8—1064no—
582C2×Q8—1068no—
583C2×Q8—1061no—
584C2×Q8—1061no—
585C2×Q8—1064no—
586C2×Q8—1061no—
587C2×Q8—1062no—
588C2×Q8—1068no—
589C2×Q8—1062no—
590C2×Q8—1062no—
591C2×Q8—1062no—
592C2×Q8—1062no—
593C2×Q8—2124no—
594C2×Q8—2124no—
595C2×Q8—2128no—
596C2×Q8—2124no—
597C2×Q8—2124no—
598C2×Q8—2124no—
599C2×Q8—2128no—
600C2×Q8C23×D5312yes—
601C2×D4—534no—
602C2×D4—1064no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—531no—
610C22×C4—531no—
611C22×C4—531no—
612C22×C4—532no—
613C22×C4—532no—
614C22×C4—1064no—
615C22×C4—1061no—
616C22×C4—1062no—
617C22×C4—1062no—
618C22×C4—1064no—
619C22×C4—1061no—
620C22×C4—1061no—
621C22×C4—1061no—
622C22×C4—2124no—
623C22×C4—2124no—
624C22×C4D4×D5312yes—
625C22×C4D4×D5311yescharacteristic
626C22×C4C23×D5312yes—
627C22×C4C23×D5311yescharacteristic
628Q16—1068no—
629Q16—2124no—
630Q16—2124no—
631M16—2124no—
632M16—2124no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—532no—
636C2×C8—532no—
637C2×C8—1062no—
638C2×C8—1062no—
639C2×C8C23×D5312yes—
640C2×C8C23×D5312yes—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—534no—
646C4⋊C4—532no—
647C4⋊C4—1064no—
648C4⋊C4—1064no—
649C4⋊C4—1064no—
650C4⋊C4—1064no—
651C4⋊C4—1064no—
652C4⋊C4—1064no—
653C4⋊C4—1064no—
654C4⋊C4—1061no—
655C4⋊C4—1064no—
656C4⋊C4C23×D5312yes—
657C4⋊C4C23×D5312yes—
658C4⋊C4C23×D5312yes—
659C22⋊C4—24no—
660C22⋊C4—24no—
661C22⋊C4—534no—
662C22⋊C4—534no—
663C22⋊C4—1064no—
664C22⋊C4—1064no—
665C22⋊C4—1064no—
666C22⋊C4—1064no—
667C42—24no—
668C42—532no—
669C42—532no—
670C42—1064no—
671C42—1064no—
672C42—1064no—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—532no—
677C23—1062no—
678C23—1062no—
679C23—1062no—
680C23C2×D4×D5312yes—
681C23C2×D4×D5311yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—42no—
685Q8—534no—
686Q8—1064no—
687Q8—1062no—
688Q8—1062no—
689Q8—1062no—
690Q8—1062no—
691Q8—1062no—
692Q8—2128no—
693Q8—2128no—
694Q8—2128no—
695Q8—2122no—
696Q8—2122no—
697D4—1068no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—534no—
711C2×C4—532no—
712C2×C4—532no—
713C2×C4—532no—
714C2×C4—1062no—
715C2×C4—1064no—
716C2×C4—1062no—
717C2×C4—1062no—
718C2×C4—1064no—
719C2×C4—1062no—
720C2×C4—1062no—
721C2×C4—1062no—
722C2×C4—1062no—
723C2×C4—1062no—
724C2×C4—2128no—
725C2×C4—2128no—
726C2×C4—2122no—
727C2×C4—2122no—
728C2×C4—2122no—
729C2×C4C2×D4×D5312yes—
730C2×C4C2×D4×D5311yescharacteristic
731C2×C4#41×D5312yes—
732C2×C4#1313326312yes—
733C2×C4C24×D5311yescharacteristic
734C8—22no—
735C8—22no—
736C8—1062no—
737C8—1062no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—44no—
742C22—1062no—
743C22—1062no—
744C22—1062no—
745C22—2124no—
746C22#1681126512yes—
747C22#137×D5312yes—
748C22#1681143712yes—
749C22C22×D4×D5311yescharacteristic
750C4—22no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—534no—
756C4—1062no—
757C4—1064no—
758C4—1062no—
759C4—2122no—
760C4—2122no—
761C4—2122no—
762C4#1681126512yes—
763C4C2×#41×D5311yescharacteristic
764C4C2×#1313326311yescharacteristic
765C2—42no—
766C2—2122no—
767C2#2028699614yesdirect product factor
768C2C2×#1681126511yescharacteristic
769C2C2×#137×D5311yescharacteristic
770C2C2×#1681143711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#485C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
hypercenterC2×#485D53
hypocenterC53C2×#3328
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
3. #20286996C2direct (N × H)
4. C2×#16810972C2semidirect
5. C2×#16810966C2semidirect
6. C2×#16810907C2semidirect
7. C2×#16810882C2semidirect
8. C2×#16810879C2semidirect
9. C2×#16810832C2semidirect
10. C2×#16810781C2semidirect
11. C2×#16810780C2semidirect
12. C2×#16810717C2semidirect
14. C2×#16810631C2semidirect
15. C2×#16810630C2semidirect
16. C2×C53×#485C2semidirect
45. #16810972C22semidirect
46. #16810966C22semidirect
47. #16810907C22semidirect
48. #16810882C22semidirect
49. #16810879C22semidirect
50. #16810832C22semidirect
51. #16810781C22semidirect
52. #16810780C22semidirect
53. #16810717C22semidirect
57. #16810631C22semidirect
58. #16810630C22semidirect
71. C53×#485C22semidirect
385. C2×#485D53semidirect
397. C2×C53#3328semidirect
434. #485C2×D53semidirect
462. C53C2×#3328semidirect
767. C2#20286996direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113412
C2×#168112862
#202869962
C2×#168109722
C2×#168109662
C2×#168109072
C2×#168108822
C2×#168108792
C2×#168108322
C2×#168107812
C2×#168107802
C2×#168107172
C2×#168106982
C2×#168106312
C2×#168106302
C2×C53×#4852
C2×#332853