Finite Group Databasebeta

← C2×#20286770 #28260702

Subgroups — C2×#20286770 #28260702

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×#16811315C211yesmaximal, characteristic
2C2×Q8×C22⋊D53C211yesmaximal, characteristic
3#20286770C2116yesmaximal, direct product factor
4C2×#16810990C211yesmaximal, characteristic, complemented
5C2×#16810962C211yesmaximal, characteristic, complemented
6C2×#16810954C211yesmaximal, characteristic, complemented
7C2×#16810928C211yesmaximal, characteristic, complemented
8C2×#16810878C211yesmaximal, characteristic, complemented
9C2×#16810862C211yesmaximal, characteristic, complemented
10C2×#16810831C211yesmaximal, characteristic, complemented
11C2×#16810777C211yesmaximal, characteristic, complemented
12C2×#16810730C211yesmaximal, characteristic, complemented
13C2×#16810691C211yesmaximal, characteristic
14C2×#16810630C211yesmaximal, characteristic, complemented
15C22×#13133141C211yesmaximal, characteristic, complemented
16C2×C53×#451C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×#11719925C2211yescharacteristic
19C22×#11719912C2211yescharacteristic
20C23×#88322C2211yescharacteristic
21#16811315—24no—
22#16811315C2218yes—
23Q8×C22⋊D53—24no—
24Q8×C22⋊D53C2218yes—
25C2×#13133215—21no—
26C2×#13133215C2211yescharacteristic
27C2×#13133212—21no—
28C2×#13133208—21no—
29C2×#13133208C2211yescharacteristic
30C2×#13133201—21no—
31C2×#13133196—21no—
32C2×#13133196C2211yescharacteristic
33C2×#13133193—21no—
34C2×#13133193C2211yescharacteristic
35C2×#13133193C2211yescharacteristic
36C2×Q8×Dic53C2211yescharacteristic
37C2×Q8×Dic53C2211yescharacteristic
38C2×C4×C22⋊D53—21no—
39C2×C4×C22⋊D53C2211yescharacteristic
40C2×#13133175C2211yescharacteristic
41C2×#13133173—21no—
42C22×C4⋊Dic53C2211yescharacteristic
43#16810990C2218yescomplemented
44#16810962C2218yescomplemented
45#16810954C2218yescomplemented
46#16810928C2218yescomplemented
47#16810878C2218yescomplemented
48#16810862C2218yescomplemented
49#16810831C2218yescomplemented
50#16810777C2218yescomplemented
51#16810730C2218yescomplemented
52#16810691C2218yes—
53C2×#13133150C2211yescharacteristic
54C2×#13133149C2211yescharacteristic
55C2×#13133149C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57#16810630C2218yescomplemented
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133141C2211yescharacteristic
65C2×#13133141C2218yescomplemented
66C2×#13133140C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C23×Q8×C53C2211yescharacteristic
70C22×Q16×C53C2211yescharacteristic
71C22×Q16×C53C2211yescharacteristic
72C2×C22⋊Q8×C53C2211yescharacteristic
73C53×#451C2218yescomplemented
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C2×Q8×D53—22no—
80C2×Q8×D53—24no—
81C2×Q8×D53—42no—
82C2×Q8×D53C2314yes—
83C22×C22⋊D53D411yescharacteristic
84C23×Dic53—21no—
85C22×C4×D53—21no—
86C22×C4×D53C2311yescharacteristic
87C2×#11719925—42no—
88C2×#11719925C2314yes—
89C2×#11719912—42no—
90C2×#11719912C2314yes—
91C22×#88322—42no—
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94C22×#88322C2314yes—
95#13133215—28no—
96#13133215—22no—
97#13133215C2314yes—
98#13133212—28no—
99#13133208—28no—
100#13133208—22no—
101#13133208C2314yes—
102#13133201—28no—
103#13133196—28no—
104#13133196—22no—
105#13133196C2314yes—
106#13133193—28no—
107#13133193—22no—
108#13133193—22no—
109#13133193C2314yes—
110#13133193C2314yes—
111Q8×Dic53—22no—
112Q8×Dic53—22no—
113Q8×Dic53C2314yes—
114Q8×Dic53C2314yes—
115C4×C22⋊D53—28no—
116C4×C22⋊D53D414yes—
117C4×C22⋊D53C2314yes—
118#13133175—22no—
119#13133175C2314yes—
120#13133173—28no—
121C2×C4⋊Dic53—22no—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53—21no—
125C2×C4⋊Dic53—21no—
126C2×C4⋊Dic53C2314yes—
127C2×C4⋊Dic53C2311yescharacteristic
128C2×C4⋊Dic53C2311yescharacteristic
129C2×C4⋊Dic53C2311yescharacteristic
130C2×#11719919—21no—
131C2×#11719919—21no—
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919D411yescharacteristic
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53D411yescharacteristic
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921D411yescharacteristic
143C2×C4×Dic53—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53C2311yescharacteristic
147#13133150C2314yes—
148#13133149C2314yes—
149#13133149C2314yes—
150#13133146C2314yes—
151#13133142C2314yes—
152#13133142C2314yes—
153#13133141C2314yes—
154#13133141C2314yes—
155#13133141C2314yes—
156#13133141C2314yes—
157#13133141C2314yes—
158#13133140C2314yes—
159#13133129C2314yes—
160#13133127C2314yes—
161C22×Q8×C53—22no—
162C22×Q8×C53—21no—
163C22×Q8×C53—24no—
164C22×Q8×C53—42no—
165C22×Q8×C53C2311yescharacteristic
166C22×Q8×C53C2311yescharacteristic
167C22×Q8×C53C2314yes—
168C22×Q8×C53C2311yescharacteristic
169C23×C4×C53—21no—
170C23×C4×C53C2311yescharacteristic
171C2×Q16×C53—24no—
172C2×Q16×C53—42no—
173C2×Q16×C53C2314yes—
174C2×Q16×C53C2314yes—
175C22×C8×C53C2311yescharacteristic
176C22×C8×C53C2311yescharacteristic
177C22⋊Q8×C53—22no—
178C22⋊Q8×C53C2314yes—
179C2×C4⋊C4×C53—21no—
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C22⋊C4×C53—21no—
182#103×C53C2314yes—
183#103×C53C2314yes—
184C22⋊C8×C53C2314yes—
185C24×C53C2×D411yescharacteristic
186C23×D53C2×D411yescharacteristic
187C2×Q8×C53—21no—
188C2×Q8×C53—21no—
189C2×Q8×C53—24no—
190C2×Q8×C53—21no—
191C2×Q8×C53—22no—
192C2×Q8×C53—28no—
193C2×Q8×C53—22no—
194C2×Q8×C53—22no—
195C2×Q8×C53—22no—
196C2×Q8×C53—22no—
197C2×Q8×C53—44no—
198C2×Q8×C53—44no—
199C2×Q8×C53—48no—
200C2×Q8×C53#4114yes—
201C2×Q8×C53C2412yes—
202C2×Q8×C53C2412yes—
203C2×Q8×C53C2412yes—
204C22×C4×C53—21no—
205C22×C4×C53—22no—
206C22×C4×C53—22no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53—24no—
211C22×C4×C53—44no—
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D412yes—
214C22×C4×C53C2412yes—
215C22×C4×C53C2411yescharacteristic
216C2×C22⋊D53—24no—
217C2×C22⋊D53C2×D414yes—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—24no—
223C22×Dic53—44no—
224C22×Dic53C2×D411yescharacteristic
225C22×Dic53C2×D411yescharacteristic
226C22×Dic53C2×D411yescharacteristic
227Q8×D53—28no—
228Q8×D53—44no—
229Q8×D53—48no—
230C2×C4×D53—22no—
231C2×C4×D53—22no—
232C2×C4×D53—24no—
233C2×C4×D53—44no—
234C2×C4×D53C2×D412yes—
235C2×C4×D53C2412yes—
236C2×Dic106—22no—
237C2×Dic106—22no—
238C2×Dic106—21no—
239C2×Dic106—24no—
240C2×Dic106—44no—
241C2×Dic106C2412yes—
242Q16×C53—28no—
243Q16×C53—44no—
244C2×C8×C53—22no—
245C2×C8×C53—22no—
246C2×C8×C53C2412yes—
247C2×C8×C53C2412yes—
248C4⋊C4×C53—24no—
249C4⋊C4×C53—21no—
250C4⋊C4×C53C2412yes—
251C22⋊C4×C53—24no—
252C22⋊Dic53—24no—
253C22⋊Dic53C2×D414yes—
254#11719925—44no—
255#11719921—24no—
256#11719921—24no—
257#11719921—24no—
258#11719921C2×D414yes—
259C4⋊Dic53—21no—
260C4⋊Dic53—21no—
261C4⋊Dic53—24no—
262C4⋊Dic53—21no—
263C4⋊Dic53—24no—
264C4⋊Dic53—24no—
265C4⋊Dic53—24no—
266C4⋊Dic53C2412yes—
267C4⋊Dic53C2412yes—
268C4⋊Dic53C2412yes—
269#11719919—24no—
270#11719919—24no—
271#11719919—24no—
272#11719919—24no—
273#11719919—24no—
274#11719919—24no—
275#11719919C2×D414yes—
276C4×Dic53—24no—
277C4×Dic53—24no—
278C4×Dic53—24no—
279C4×Dic53C2×D412yes—
280C4×Dic53C2412yes—
281C2×#88322—22no—
282C2×#88322—22no—
283C2×#88322—44no—
284C2×#88322C2412yes—
285C2×#88322C2412yes—
286#11719912—44no—
287C23×C53—22no—
288C23×C53—22no—
289C23×C53#13714yes—
290C23×C53C22×D412yes—
291C23×C53C22×D411yescharacteristic
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—22no—
295C22×D53C22×D412yes—
296Q8×C53—24no—
297Q8×C53—22no—
298Q8×C53—22no—
299Q8×C53—22no—
300Q8×C53—22no—
301Q8×C53—22no—
302Q8×C53—48no—
303Q8×C53—42no—
304Q8×C53—42no—
305Q8×C53C2×#4114yes—
306C2×C4×C53—24no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—24no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—48no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53—42no—
319C2×C4×C53C22×D412yes—
320C2×C4×C53C22×D411yescharacteristic
321C2×C4×C53C2×#4112yes—
322C2×C4×C53H(5,𝔽2)12yes—
323C2×C4×C53C2511yescharacteristic
324C22⋊D53—28no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—42no—
333C2×Dic53—48no—
334C2×Dic53—42no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53C22×D412yes—
338C2×Dic53C22×D412yes—
339C2×Dic53C22×D412yes—
340C4×D53—24no—
341C4×D53—22no—
342C4×D53—22no—
343C4×D53—48no—
344Dic106—22no—
345Dic106—22no—
346Dic106—48no—
347Dic106—42no—
348C8×C53—22no—
349C8×C53—22no—
350#88322—22no—
351#88322—22no—
352C2×#3312—531nomaximal, Sylow
353C22×C53—22no—
354C22×C53—28no—
355C22×C53—22no—
356C22×C53#54612yes—
357C22×C53C2×#13714yes—
358C22×C53C2×#13712yes—
359C22×C53#57812yes—
360C22×C53C23×D411yescharacteristic
361C2×D53—22no—
362C2×D53—22no—
363C2×D53—22no—
364C2×D53—44no—
365C4×C53—24no—
366C4×C53—22no—
367C4×C53—42no—
368C4×C53—42no—
369C4×C53—42no—
370C4×C53#54612yes—
371C4×C53C22×#4111yescharacteristic
372C4×C53C2×H(5,𝔽2)11yescharacteristic
373Dic53—22no—
374Dic53—22no—
375Dic53—22no—
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×#451D5311yescharacteristic, complemented
392C2×#441—531no—
393C2×#435—531no—
394C2×#419—531no—
395C22×#103—531no—
396C2×C53—24no—
397C2×C53#331214yescomplemented
398C2×C53C2×#54611yescharacteristic
399C2×C53C22×#13711yescharacteristic
400C2×C53C2×#57811yescharacteristic
401D53—42no—
402C23×Q8—531no—
403C23×Q8C2×D5311yescharacteristic
404C22×Q16—531no—
405C22×Q16C2×D5311yescharacteristic
406C22×Q16C2×D5311yescharacteristic
407C22×M16—531no—
408C23×C8—531no—
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—1061no—
423C2×C22⋊Q8—1061no—
424C2×C22⋊Q8C2×D5311yescharacteristic
425C2×C4×Q8—531no—
426C2×C4×Q8—531no—
427C2×C4×D4—531no—
428C2×C4×D4—1061no—
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#451C2×D5318yescomplemented
441#441—538no—
442#435—538no—
443C2×#107—531no—
444C2×#106—531no—
445C2×#106—531no—
446C2×C4⋊C8—531no—
447#419—538no—
448C2×#103—531no—
449C2×#103—531no—
450C2×#103—531no—
451C2×#103—531no—
452C2×#103—538no—
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×#97—531no—
462C53C2×#331211yescharacteristic, complemented, Sylow
463C22×Q8—21no—
464C22×Q8—22no—
465C22×Q8—24no—
466C22×Q8—42no—
467C22×Q8—534no—
468C22×Q8—531no—
469C22×Q8—1061no—
470C22×Q8—1062no—
471C22×Q8—1064no—
472C22×Q8—2122no—
473C22×Q8C22×D5311yescharacteristic
474C22×Q8C22×D5311yescharacteristic
475C22×Q8C22×D5314yes—
476C22×Q8C22×D5311yescharacteristic
477C22×D4—531no—
478C23×C4—21no—
479C23×C4—531no—
480C23×C4—1061no—
481C23×C4—1061no—
482C23×C4C22×D5311yescharacteristic
483C2×Q16—24no—
484C2×Q16—42no—
485C2×Q16—534no—
486C2×Q16—2122no—
487C2×Q16C22×D5314yes—
488C2×Q16C22×D5314yes—
489C2×M16—534no—
490C2×M16—2122no—
491C22×C8—531no—
492C22×C8—531no—
493C22×C8—534no—
494C22×C8—2122no—
495C22×C8C22×D5311yescharacteristic
496C22×C8C22×D5311yescharacteristic
497C4⋊Q8—534no—
498C4⋊Q8—1062no—
499C4⋊Q8—1068no—
500#126—1068no—
501#125—534no—
502#125—1062no—
503#125—1068no—
504#123—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—1062no—
518C4×Q8—1062no—
519C4×D4—534no—
520C4×D4—534no—
521C4×D4—1068no—
522#117—534no—
523#117—1068no—
524#117—1062no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—531no—
527C2×C4⋊C4—531no—
528C2×C4⋊C4—531no—
529C2×C4⋊C4—534no—
530C2×C4⋊C4—531no—
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⋊C4—1061no—
539C2×C4⋊C4—1061no—
540C2×C4⋊C4—1062no—
541C2×C4⋊C4—1061no—
542C2×C4⋊C4C22×D5311yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—531no—
545C2×C22⋊C4—531no—
546C2×C22⋊C4—1061no—
547C2×C22⋊C4—1061no—
548C2×C22⋊C4—1061no—
549C2×C22⋊C4—1061no—
550C2×C42—531no—
551C2×C42—1061no—
552C2×C42—1061no—
553C2×C42—1061no—
554#107—534no—
555#106—534no—
556#106—534no—
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—
570#97—534no—
571C24—531no—
572C24D4×D5311yescharacteristic
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—24no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—28no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—44no—
584C2×Q8—44no—
585C2×Q8—48no—
586C2×Q8—532no—
587C2×Q8—1064no—
588C2×Q8—1061no—
589C2×Q8—1068no—
590C2×Q8—1062no—
591C2×Q8—1062no—
592C2×Q8—2124no—
593C2×Q8—2124no—
594C2×Q8—2128no—
595C2×Q8#1171994714yes—
596C2×Q8C23×D5312yes—
597C2×Q8C23×D5312yes—
598C2×Q8C23×D5312yes—
599C2×D4—534no—
600C2×D4—1064no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—24no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—44no—
609C22×C4—531no—
610C22×C4—531no—
611C22×C4—531no—
612C22×C4—532no—
613C22×C4—532no—
614C22×C4—1064no—
615C22×C4—1062no—
616C22×C4—1062no—
617C22×C4—1064no—
618C22×C4—1061no—
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—28no—
629Q16—44no—
630Q16—2124no—
631M16—2124no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—532no—
635C2×C8—532no—
636C2×C8—1062no—
637C2×C8—1062no—
638C2×C8—2124no—
639C2×C8C23×D5312yes—
640C2×C8C23×D5312yes—
641C4⋊C4—24no—
642C4⋊C4—21no—
643C4⋊C4—534no—
644C4⋊C4—532no—
645C4⋊C4—532no—
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—1064no—
655C4⋊C4—1061no—
656C4⋊C4—1061no—
657C4⋊C4—1064no—
658C4⋊C4—1061no—
659C4⋊C4—1064no—
660C4⋊C4C23×D5312yes—
661C22⋊C4—24no—
662C22⋊C4—534no—
663C22⋊C4—534no—
664C22⋊C4—1064no—
665C22⋊C4—1064no—
666C22⋊C4—1064no—
667C22⋊C4—1064no—
668C42—532no—
669C42—532no—
670C42—1064no—
671C42—1064no—
672C42—1064no—
673C23—22no—
674C23—22no—
675C23—532no—
676C23—1062no—
677C23—1062no—
678C23—1062no—
679C23#1313324914yes—
680C23C2×D4×D5312yes—
681C23C2×D4×D5311yescharacteristic
682Q8—22no—
683Q8—24no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—22no—
688Q8—48no—
689Q8—42no—
690Q8—42no—
691Q8—1062no—
692Q8—1062no—
693Q8—2128no—
694Q8—2122no—
695Q8C2×#1171994714yes—
696D4—1068no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—48no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—532no—
711C2×C4—532no—
712C2×C4—532no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—1062no—
718C2×C4—1064no—
719C2×C4—1062no—
720C2×C4—1062no—
721C2×C4—1062no—
722C2×C4—1062no—
723C2×C4—2128no—
724C2×C4—2128no—
725C2×C4—2122no—
726C2×C4—2122no—
727C2×C4—2122no—
728C2×C4—2122no—
729C2×C4C2×D4×D5312yes—
730C2×C4C2×D4×D5311yescharacteristic
731C2×C4C2×#1171994712yes—
732C2×C4#1313326212yes—
733C2×C4C24×D5311yescharacteristic
734C8—22no—
735C8—22no—
736C8—1062no—
737C8—1062no—
738C22—28no—
739C22—22no—
740C22—22no—
741C22—1062no—
742C22—1062no—
743C22—1062no—
744C22—2124no—
745C22#1681126012yes—
746C22C2×#1313324914yes—
747C22C2×#1313324912yes—
748C22#1681143912yes—
749C22C22×D4×D5311yescharacteristic
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—1062no—
756C4—1062no—
757C4—1062no—
758C4—2122no—
759C4—2122no—
760C4—2122no—
761C4—2122no—
762C4#1681126012yes—
763C4C22×#1171994711yescharacteristic
764C4C2×#1313326211yescharacteristic
765C2—24no—
766C2—2122no—
767C2#2028677014yesdirect product factor
768C2C2×#1681126011yescharacteristic
769C2C22×#1313324911yescharacteristic
770C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#451C2
socleC23×C53C22×D4
prime radicalC22×C22⋊D53D4
hypercenterC2×#451D53
hypocenterC53C2×#3312
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. #20286770C2direct (N × H)
4. C2×#16810990C2semidirect
5. C2×#16810962C2semidirect
6. C2×#16810954C2semidirect
7. C2×#16810928C2semidirect
8. C2×#16810878C2semidirect
9. C2×#16810862C2semidirect
10. C2×#16810831C2semidirect
11. C2×#16810777C2semidirect
12. C2×#16810730C2semidirect
14. C2×#16810630C2semidirect
15. C22×#13133141C2semidirect
16. C2×C53×#451C2semidirect
43. #16810990C22semidirect
44. #16810962C22semidirect
45. #16810954C22semidirect
46. #16810928C22semidirect
47. #16810878C22semidirect
48. #16810862C22semidirect
49. #16810831C22semidirect
50. #16810777C22semidirect
51. #16810730C22semidirect
57. #16810630C22semidirect
65. C2×#13133141C22semidirect
73. C53×#451C22semidirect
391. C2×#451D53semidirect
397. C2×C53#3312semidirect
440. #451C2×D53semidirect
462. C53C2×#3312semidirect
767. C2#20286770direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113152
C2×Q8×C22⋊D532
#202867702
C2×#168109902
C2×#168109622
C2×#168109542
C2×#168109282
C2×#168108782
C2×#168108622
C2×#168108312
C2×#168107772
C2×#168107302
C2×#168106912
C2×#168106302
C22×#131331412
C2×C53×#4512
C2×#331253