Finite Group Databasebeta

← C2×#20286768 #28260700

Subgroups — C2×#20286768 #28260700

Order 13568.

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×#16811313C211yesmaximal, characteristic
2C2×D4×Dic106C211yesmaximal, characteristic
3#20286768C2116yesmaximal, direct product factor
4C2×#16810992C211yesmaximal, characteristic, complemented
5C2×#16810965C211yesmaximal, characteristic, complemented
6C2×#16810954C211yesmaximal, characteristic, complemented
7C2×#16810931C211yesmaximal, characteristic, complemented
8C2×#16810881C211yesmaximal, characteristic, complemented
9C2×#16810864C211yesmaximal, characteristic, complemented
10C2×#16810834C211yesmaximal, characteristic, complemented
11C2×#16810781C211yesmaximal, characteristic, complemented
12C2×#16810781C211yesmaximal, characteristic, complemented
13C2×#16810731C211yesmaximal, characteristic, complemented
14C2×#16810633C211yesmaximal, characteristic, complemented
15C22×#13133142C211yesmaximal, characteristic, complemented
16C2×C53×#435C211yesmaximal, characteristic
17C23×Dic106C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C22×Dic212C2211yescharacteristic
20C22×Dic212C2211yescharacteristic
21C22×Dic212C2211yescharacteristic
22#16811313—24no—
23#16811313C2218yes—
24D4×Dic106—24no—
25D4×Dic106C2218yes—
26C2×#13133217C2211yescharacteristic
27C2×#13133216—21no—
28C2×#13133210—21no—
29C2×#13133209C2211yescharacteristic
30C2×#13133207—21no—
31C2×#13133198—21no—
32C2×#13133196C2211yescharacteristic
33C2×#13133196C2211yescharacteristic
34C2×#13133196C2211yescharacteristic
35C2×#13133196C2211yescharacteristic
36C2×#13133194—21no—
37C2×#13133194—21no—
38C2×C4×Dic106C2211yescharacteristic
39C2×C4×Dic106C2211yescharacteristic
40C2×D4×Dic53—21no—
41C2×#13133176C2211yescharacteristic
42C2×#13133173—21no—
43C22×C4⋊Dic53C2211yescharacteristic
44#16810992C2218yescomplemented
45#16810965C2218yescomplemented
46#16810954C2218yescomplemented
47#16810931C2218yescomplemented
48#16810881C2218yescomplemented
49#16810864C2218yescomplemented
50#16810834C2218yescomplemented
51#16810781C2218yescomplemented
52#16810781C2218yescomplemented
53#16810731C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133149C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57#16810633C2218yescomplemented
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133142C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2211yescharacteristic
65C2×#13133142C2211yescharacteristic
66C2×#13133142C2211yescharacteristic
67C2×#13133142C2211yescharacteristic
68C2×#13133142C2218yescomplemented
69C22×M16×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#435C2218yes—
73C2×C4⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic
75C2×C22⋊C8×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106—24no—
78C22×Dic106—24no—
79C22×Dic106—22no—
80C22×Dic106—22no—
81C22×Dic106—21no—
82C22×Dic106—21no—
83C22×Dic106—42no—
84C22×Dic106—42no—
85C22×Dic106C2311yescharacteristic
86C22×Dic106C2311yescharacteristic
87C22×Dic106C2311yescharacteristic
88C22×Dic106C2314yes—
89C22×Dic106C2314yes—
90C22×Dic106C2311yescharacteristic
91C23×Dic53—21no—
92C23×Dic53—21no—
93C23×Dic53—21no—
94C2×Dic212—24no—
95C2×Dic212—42no—
96C2×Dic212—42no—
97C2×Dic212C2314yes—
98C2×Dic212C2314yes—
99C2×Dic212C2314yes—
100#13133217—22no—
101#13133217C2314yes—
102#13133216—28no—
103#13133210—28no—
104#13133209—22no—
105#13133209C2314yes—
106#13133207—28no—
107#13133198—28no—
108#13133196—22no—
109#13133196—22no—
110#13133196—22no—
111#13133196—22no—
112#13133196C2314yes—
113#13133196C2314yes—
114#13133196C2314yes—
115#13133196C2314yes—
116#13133194—28no—
117#13133194—28no—
118C4×Dic106—22no—
119C4×Dic106—22no—
120C4×Dic106C2314yes—
121C4×Dic106C2314yes—
122D4×Dic53—28no—
123#13133176—22no—
124#13133176C2314yes—
125#13133173—28no—
126C2×C4⋊Dic53—22no—
127C2×C4⋊Dic53—21no—
128C2×C4⋊Dic53—21no—
129C2×C4⋊Dic53—21no—
130C2×C4⋊Dic53C2314yes—
131C2×C4⋊Dic53C2311yescharacteristic
132C2×C4⋊Dic53C2311yescharacteristic
133C2×C4⋊Dic53C2311yescharacteristic
134C2×C4⋊Dic53C2311yescharacteristic
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919—21no—
141C2×#11719919—21no—
142C2×#11719919—21no—
143C2×C22⋊Dic53—21no—
144C2×C22⋊Dic53—21no—
145C2×C22⋊Dic53—21no—
146C2×C22⋊Dic53—21no—
147C2×C22⋊Dic53—21no—
148C2×C4×Dic53—21no—
149C2×C4×Dic53—21no—
150C2×C4×Dic53—21no—
151#13133151C2314yes—
152#13133149C2314yes—
153#13133149C2314yes—
154#13133142C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133142C2314yes—
158#13133142C2314yes—
159#13133142C2314yes—
160#13133142C2314yes—
161#13133142C2314yes—
162#13133142C2314yes—
163#13133142C2314yes—
164C22×D4×C53D411yescharacteristic
165C23×C4×C53C2311yescharacteristic
166C23×C4×C53C2311yescharacteristic
167C2×M16×C53—42no—
168C2×M16×C53C2314yes—
169C22×C8×C53—42no—
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2311yescharacteristic
174C22×C8×C53C2314yes—
175C4×D4×C53D414yes—
176C4×D4×C53C2314yes—
177C2×C4⋊C4×C53D411yescharacteristic
178C2×C22⋊C4×C53D411yescharacteristic
179C2×C22⋊C4×C53D411yescharacteristic
180C2×C42×C53C2311yescharacteristic
181C4⋊C8×C53C2314yes—
182C22⋊C8×C53C2314yes—
183C22⋊C8×C53C2314yes—
184#97×C53C2314yes—
185C24×C53C2×D411yescharacteristic
186C24×C53C2×D411yescharacteristic
187C2×D4×C53—24no—
188C2×D4×C53C2×D414yes—
189C22×C4×C53—22no—
190C22×C4×C53—22no—
191C22×C4×C53—22no—
192C22×C4×C53—22no—
193C22×C4×C53C2×D411yescharacteristic
194C22×C4×C53C2×D411yescharacteristic
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D412yes—
198C22×C4×C53C2×D412yes—
199C22×C4×C53C2412yes—
200C22×C4×C53C2412yes—
201C22×C4×C53C2411yescharacteristic
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—24no—
211C22×Dic53—24no—
212C22×Dic53—24no—
213C22×Dic53—44no—
214C22×Dic53—44no—
215C22×Dic53—44no—
216C2×Dic106—21no—
217C2×Dic106—22no—
218C2×Dic106—22no—
219C2×Dic106—22no—
220C2×Dic106—22no—
221C2×Dic106—22no—
222C2×Dic106—22no—
223C2×Dic106—22no—
224C2×Dic106—28no—
225C2×Dic106—28no—
226C2×Dic106—21no—
227C2×Dic106—24no—
228C2×Dic106—24no—
229C2×Dic106—21no—
230C2×Dic106—21no—
231C2×Dic106—44no—
232C2×Dic106—44no—
233C2×Dic106—48no—
234C2×Dic106—48no—
235C2×Dic106—44no—
236C2×Dic106—44no—
237C2×Dic106#4114yes—
238C2×Dic106C2412yes—
239C2×Dic106C2412yes—
240C2×Dic106C2412yes—
241C2×Dic106C2412yes—
242M16×C53—44no—
243C2×C8×C53—22no—
244C2×C8×C53—22no—
245C2×C8×C53—22no—
246C2×C8×C53—22no—
247C2×C8×C53—44no—
248C2×C8×C53C2412yes—
249C2×C8×C53C2412yes—
250C2×C8×C53C2412yes—
251C2×C8×C53C2412yes—
252C4⋊C4×C53C2×D414yes—
253C22⋊C4×C53C2×D414yes—
254C22⋊C4×C53C2×D414yes—
255C42×C53C2×D412yes—
256C42×C53C2412yes—
257C22⋊Dic53—24no—
258C22⋊Dic53—24no—
259C22⋊Dic53—24no—
260C22⋊Dic53—24no—
261C22⋊Dic53—24no—
262C4⋊Dic53—21no—
263C4⋊Dic53—21no—
264C4⋊Dic53—24no—
265C4⋊Dic53—24no—
266C4⋊Dic53—24no—
267C4⋊Dic53—21no—
268C4⋊Dic53—21no—
269C4⋊Dic53C2412yes—
270C4⋊Dic53C2412yes—
271C4⋊Dic53C2412yes—
272C4⋊Dic53C2412yes—
273#11719919—24no—
274#11719919—24no—
275#11719919—24no—
276#11719919—24no—
277#11719919—24no—
278#11719919—24no—
279#11719919—24no—
280#11719919—24no—
281C4×Dic53—24no—
282C4×Dic53—24no—
283C4×Dic53—24no—
284Dic212—28no—
285Dic212—44no—
286Dic212—44no—
287C23×C53—22no—
288C23×C53—22no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53#13714yes—
293C23×C53C22×D412yes—
294C23×C53C22×D412yes—
295C23×C53C22×D411yescharacteristic
296D4×C53—28no—
297C2×C4×C53—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—24no—
302C2×C4×C53—24no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53C22×D412yes—
308C2×C4×C53C22×D412yes—
309C2×C4×C53C22×D412yes—
310C2×C4×C53C22×D412yes—
311C2×C4×C53C22×D411yescharacteristic
312C2×C4×C53C2×#4112yes—
313C2×C4×C53H(5,𝔽2)12yes—
314C2×C4×C53C2511yescharacteristic
315C2×Dic53—24no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—48no—
325C2×Dic53—48no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53—42no—
329C2×Dic53—48no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334Dic106—24no—
335Dic106—22no—
336Dic106—22no—
337Dic106—22no—
338Dic106—22no—
339Dic106—22no—
340Dic106—22no—
341Dic106—22no—
342Dic106—48no—
343Dic106—48no—
344Dic106—42no—
345Dic106—42no—
346Dic106—42no—
347Dic106C2×#4114yes—
348C8×C53—22no—
349C8×C53—22no—
350C8×C53—22no—
351C8×C53—22no—
352C2×#3312—531nomaximal, Sylow
353C22×C53—22no—
354C22×C53—28no—
355C22×C53—22no—
356C22×C53—22no—
357C22×C53—22no—
358C22×C53—22no—
359C22×C53—44no—
360C22×C53#54612yes—
361C22×C53C2×#13714yes—
362C22×C53C2×#13712yes—
363C22×C53#57812yes—
364C22×C53C23×D411yescharacteristic
365C4×C53—22no—
366C4×C53—22no—
367C4×C53—22no—
368C4×C53—22no—
369C4×C53#54612yes—
370C4×C53C22×#4111yescharacteristic
371C4×C53C2×H(5,𝔽2)11yescharacteristic
372Dic53—24no—
373Dic53—42no—
374Dic53—42no—
375Dic53—42no—
376Dic53—42no—
377Dic53—42no—
378Dic53—42no—
379Dic53—42no—
380C2×#552—531no—
381C2×D4×Q8—531no—
382#3312—5316no—
383C2×#491—531no—
384C2×#485—531no—
385C2×#483—531no—
386C2×#479—531no—
387C2×#470—531no—
388C2×#467—531no—
389C2×#462—531no—
390C2×#451—531no—
391C2×#451—531no—
392C2×#441—531no—
393C2×#435D5311yescharacteristic
394C2×#419—531no—
395C22×#103—531no—
396C2×C53—24no—
397C2×C53—42no—
398C2×C53#331214yescomplemented
399C2×C53C2×#54611yescharacteristic
400C2×C53C22×#13711yescharacteristic
401C2×C53C2×#57811yescharacteristic
402C23×Q8—531no—
403C23×Q8—531no—
404C22×Q16—531no—
405C22×Q16—531no—
406C22×Q16—531no—
407C22×M16C2×D5311yescharacteristic
408C23×C8C2×D5311yescharacteristic
409#552—538no—
410#552—1064no—
411D4×Q8—538no—
412D4×Q8—1064no—
413C2×C4⋊Q8—531no—
414C2×C4⋊Q8—1061no—
415C2×#126—1061no—
416C2×#125—531no—
417C2×#125—1061no—
418C2×#123—1061no—
419C2×C22⋊Q8—531no—
420C2×C22⋊Q8—531no—
421C2×C22⋊Q8—531no—
422C2×C22⋊Q8—531no—
423C2×C22⋊Q8—1061no—
424C2×C22⋊Q8—1061no—
425C2×C4×Q8—531no—
426C2×C4×Q8—531no—
427C2×C4×D4—1061no—
428C2×C4×D4C2×D5311yescharacteristic
429C2×#117—531no—
430C2×#117—1061no—
431C22×C4⋊C4—531no—
432#491—538no—
433#485—538no—
434#483—538no—
435#479—538no—
436#470—538no—
437#467—538no—
438#462—538no—
439#451—538no—
440#451—538no—
441#441—538no—
442#435C2×D5318yes—
443C2×#107—531no—
444C2×#106—531no—
445C2×#106—531no—
446C2×C4⋊C8C2×D5311yescharacteristic
447#419—538no—
448C2×#103—531no—
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×#103—538no—
458C2×#103—531no—
459C2×C22⋊C8C2×D5311yescharacteristic
460C2×C22⋊C8C2×D5311yescharacteristic
461C2×#97C2×D5311yescharacteristic
462C53C2×#331211yescharacteristic, complemented, Sylow
463C22×Q8—531no—
464C22×Q8—531no—
465C22×Q8—531no—
466C22×Q8—531no—
467C22×Q8—534no—
468C22×Q8—534no—
469C22×Q8—1064no—
470C22×Q8—1064no—
471C22×Q8—1061no—
472C22×Q8—1061no—
473C22×Q8—1062no—
474C22×Q8—1062no—
475C22×Q8—2122no—
476C22×Q8—2122no—
477C22×D4D21211yescharacteristic
478C23×C4—1061no—
479C23×C4—1061no—
480C23×C4—1061no—
481C23×C4C22×D5311yescharacteristic
482C23×C4C22×D5311yescharacteristic
483C2×Q16—534no—
484C2×Q16—534no—
485C2×Q16—534no—
486C2×Q16—1064no—
487C2×Q16—2122no—
488C2×Q16—2122no—
489C2×M16—42no—
490C2×M16C22×D5314yes—
491C22×C8—42no—
492C22×C8C22×D5311yescharacteristic
493C22×C8C22×D5311yescharacteristic
494C22×C8C22×D5311yescharacteristic
495C22×C8C22×D5311yescharacteristic
496C22×C8C22×D5314yes—
497C4⋊Q8—534no—
498C4⋊Q8—1068no—
499C4⋊Q8—1062no—
500#126—1068no—
501#125—534no—
502#125—1068no—
503#125—1062no—
504#123—1068no—
505C22⋊Q8—534no—
506C22⋊Q8—534no—
507C22⋊Q8—534no—
508C22⋊Q8—534no—
509C22⋊Q8—1062no—
510C22⋊Q8—1062no—
511C22⋊Q8—1062no—
512C22⋊Q8—1062no—
513C22⋊Q8—1068no—
514C22⋊Q8—1068no—
515C4×Q8—534no—
516C4×Q8—534no—
517C4×Q8—1062no—
518C4×Q8—1062no—
519C4×D4—1068no—
520C4×D4D21214yes—
521C4×D4C22×D5314yes—
522#117—534no—
523#117—1062no—
524#117—1068no—
525C2×C4⋊C4—531no—
526C2×C4⋊C4—531no—
527C2×C4⋊C4—534no—
528C2×C4⋊C4—531no—
529C2×C4⋊C4—531no—
530C2×C4⋊C4—1061no—
531C2×C4⋊C4—1062no—
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⋊C4—1061no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1061no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4D21211yescharacteristic
543C2×C22⋊C4—1061no—
544C2×C22⋊C4—1061no—
545C2×C22⋊C4—1061no—
546C2×C22⋊C4—1061no—
547C2×C22⋊C4—1061no—
548C2×C22⋊C4D21211yescharacteristic
549C2×C22⋊C4D21211yescharacteristic
550C2×C42—1061no—
551C2×C42—1061no—
552C2×C42—1061no—
553C2×C42C22×D5311yescharacteristic
554#107—534no—
555#106—534no—
556#106—534no—
557C4⋊C8C22×D5314yes—
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#103—534no—
567#103—534no—
568C22⋊C8C22×D5314yes—
569C22⋊C8C22×D5314yes—
570#97C22×D5314yes—
571C24C2×D21211yescharacteristic
572C24C2×D21211yescharacteristic
573C2×Q8—534no—
574C2×Q8—532no—
575C2×Q8—532no—
576C2×Q8—532no—
577C2×Q8—532no—
578C2×Q8—1068no—
579C2×Q8—1068no—
580C2×Q8—1061no—
581C2×Q8—1061no—
582C2×Q8—1064no—
583C2×Q8—1064no—
584C2×Q8—1061no—
585C2×Q8—1061no—
586C2×Q8—1062no—
587C2×Q8—1062no—
588C2×Q8—1062no—
589C2×Q8—1062no—
590C2×Q8—1062no—
591C2×Q8—1062no—
592C2×Q8—1062no—
593C2×Q8—2124no—
594C2×Q8—2124no—
595C2×Q8—2124no—
596C2×Q8—2124no—
597C2×Q8—2128no—
598C2×Q8—2128no—
599C2×D4—24no—
600C2×D4C2×D21214yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—1061no—
606C22×C4—1064no—
607C22×C4—1064no—
608C22×C4—1064no—
609C22×C4—1061no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—1061no—
613C22×C4—1061no—
614C22×C4—1061no—
615C22×C4—1061no—
616C22×C4—2124no—
617C22×C4—2124no—
618C22×C4—2124no—
619C22×C4C2×D21212yes—
620C22×C4C2×D21212yes—
621C22×C4C2×D21211yescharacteristic
622C22×C4C2×D21211yescharacteristic
623C22×C4C2×D21211yescharacteristic
624C22×C4C2×D21211yescharacteristic
625C22×C4C23×D5312yes—
626C22×C4C23×D5312yes—
627C22×C4C23×D5311yescharacteristic
628Q16—1068no—
629Q16—2124no—
630Q16—2124no—
631M16—44no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—22no—
635C2×C8—22no—
636C2×C8—44no—
637C2×C8C23×D5312yes—
638C2×C8C23×D5312yes—
639C2×C8C23×D5312yes—
640C2×C8C23×D5312yes—
641C4⋊C4—532no—
642C4⋊C4—532no—
643C4⋊C4—532no—
644C4⋊C4—532no—
645C4⋊C4—1061no—
646C4⋊C4—1061no—
647C4⋊C4—1064no—
648C4⋊C4—1061no—
649C4⋊C4—1061no—
650C4⋊C4—1064no—
651C4⋊C4—1064no—
652C4⋊C4—1064no—
653C4⋊C4—1064no—
654C4⋊C4—1064no—
655C4⋊C4—1064no—
656C4⋊C4—1064no—
657C4⋊C4—1064no—
658C4⋊C4—1064no—
659C4⋊C4—1064no—
660C4⋊C4C2×D21214yes—
661C22⋊C4—1064no—
662C22⋊C4—1064no—
663C22⋊C4—1064no—
664C22⋊C4—1064no—
665C22⋊C4—1064no—
666C22⋊C4C2×D21214yes—
667C22⋊C4C2×D21214yes—
668C42—1064no—
669C42—1064no—
670C42—1064no—
671C42C2×D21212yes—
672C42C23×D5312yes—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23#1313325014yes—
679C23C22×D21212yes—
680C23C22×D21212yes—
681C23C22×D21211yescharacteristic
682Q8—534no—
683Q8—1064no—
684Q8—1062no—
685Q8—1062no—
686Q8—1062no—
687Q8—1062no—
688Q8—1062no—
689Q8—1062no—
690Q8—1062no—
691Q8—2128no—
692Q8—2128no—
693Q8—2122no—
694Q8—2122no—
695Q8—2122no—
696D4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—1064no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—2128no—
717C2×C4—2128no—
718C2×C4—2122no—
719C2×C4—2122no—
720C2×C4—2122no—
721C2×C4—2128no—
722C2×C4—2122no—
723C2×C4—2122no—
724C2×C4—2122no—
725C2×C4—2122no—
726C2×C4C22×D21212yes—
727C2×C4C22×D21212yes—
728C2×C4C22×D21212yes—
729C2×C4C22×D21212yes—
730C2×C4C22×D21211yescharacteristic
731C2×C4#41×D5312yes—
732C2×C4#1313326212yes—
733C2×C4C24×D5311yescharacteristic
734C8—22no—
735C8—22no—
736C8—22no—
737C8—22no—
738C22—28no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—44no—
745C22#1681126812yes—
746C22C2×#1313325014yes—
747C22C2×#1313325012yes—
748C22#1681144012yes—
749C22C23×D21211yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—1064no—
755C4—2122no—
756C4—2122no—
757C4—2122no—
758C4—2122no—
759C4—2122no—
760C4—2122no—
761C4—2122no—
762C4#1681126812yes—
763C4C2×#41×D5311yescharacteristic
764C4C2×#1313326211yescharacteristic
765C2—24no—
766C2—42no—
767C2#2028676814yesdirect product factor
768C2C2×#1681126811yescharacteristic
769C2C22×#1313325011yescharacteristic
770C2C2×#1681144011yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#435C2
socleC23×C53C22×D4
prime radicalC22×D4×C53D4
hypercenterC2×#435D53
hypocenterC53C2×#3312
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #20286768C2direct (N × H)
4. C2×#16810992C2semidirect
5. C2×#16810965C2semidirect
6. C2×#16810954C2semidirect
7. C2×#16810931C2semidirect
8. C2×#16810881C2semidirect
9. C2×#16810864C2semidirect
10. C2×#16810834C2semidirect
11. C2×#16810781C2semidirect
12. C2×#16810781C2semidirect
13. C2×#16810731C2semidirect
14. C2×#16810633C2semidirect
15. C22×#13133142C2semidirect
44. #16810992C22semidirect
45. #16810965C22semidirect
46. #16810954C22semidirect
47. #16810931C22semidirect
48. #16810881C22semidirect
49. #16810864C22semidirect
50. #16810834C22semidirect
51. #16810781C22semidirect
52. #16810781C22semidirect
53. #16810731C22semidirect
57. #16810633C22semidirect
68. C2×#13133142C22semidirect
398. C2×C53#3312semidirect
462. C53C2×#3312semidirect
767. C2#20286768direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113132
C2×D4×Dic1062
#202867682
C2×#168109922
C2×#168109652
C2×#168109542
C2×#168109312
C2×#168108812
C2×#168108642
C2×#168108342
C2×#168107812
C2×#168107312
C2×#168106332
C22×#131331422
C2×C53×#4352
C2×#331253