Finite Group Databasebeta

← C2×#20286765 #28260697

Subgroups — C2×#20286765 #28260697

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×#16811311C211yesmaximal, characteristic
2C2×#16811288C211yesmaximal, characteristic
3#20286765C2116yesmaximal, direct product factor
4C2×#16810962C211yesmaximal, characteristic, complemented
5C2×#16810952C211yesmaximal, characteristic, complemented
6C2×#16810927C211yesmaximal, characteristic, complemented
7C2×#16810880C211yesmaximal, characteristic, complemented
8C2×#16810863C211yesmaximal, characteristic, complemented
9C2×#16810830C211yesmaximal, characteristic, complemented
10C2×#16810780C211yesmaximal, characteristic, complemented
11C2×#16810780C211yesmaximal, characteristic, complemented
12C2×#16810731C211yesmaximal, characteristic, complemented
13C2×#16810696C211yesmaximal, characteristic
14C2×#16810630C211yesmaximal, characteristic, complemented
15C2×#103×D53C211yesmaximal, characteristic, complemented
16C2×C53×#491C211yesmaximal, characteristic, complemented
17C22×Q8×D53C2211yescharacteristic
18C22×Q8×D53C2211yescharacteristic
19C22×Dic212C2211yescharacteristic
20C22×#11719925C2211yescharacteristic
21C22×#11719925C2211yescharacteristic
22C22×#11719912C2211yescharacteristic
23C22×C8×D53C2211yescharacteristic
24#16811311—24no—
25#16811311C2218yes—
26#16811288—24no—
27#16811288C2218yes—
28C2×#13133216—21no—
29C2×#13133212—21no—
30C2×#13133208—21no—
31C2×#13133202—21no—
32C2×#13133197C2211yescharacteristic
33C2×#13133197C2211yescharacteristic
34C2×#13133195—21no—
35C2×#13133195—21no—
36C2×#13133193C2211yescharacteristic
37C2×#13133193C2211yescharacteristic
38C2×C4×Dic106C2211yescharacteristic
39C2×C4×Dic106C2211yescharacteristic
40C2×C4×D212C2211yescharacteristic
41C2×#13133179—21no—
42C2×#13133175—21no—
43C2×#13133175C2211yescharacteristic
44C2×C4⋊C4×D53C2211yescharacteristic
45#16810962C2218yescomplemented
46#16810952C2218yescomplemented
47#16810927C2218yescomplemented
48#16810880C2218yescomplemented
49#16810863C2218yescomplemented
50#16810830C2218yescomplemented
51#16810780C2218yescomplemented
52#16810780C2218yescomplemented
53#16810731C2218yescomplemented
54#16810696C2218yes—
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×C4⋊#88322C2211yescharacteristic
59#16810630C2218yescomplemented
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133141C2211yescharacteristic
63C2×#13133141C2211yescharacteristic
64C2×#13133140C2211yescharacteristic
65C2×#13133140C2211yescharacteristic
66#103×D53C2218yescomplemented
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
69C2×C4⋊Q8×C53C2211yescharacteristic
70C2×#125×C53C2211yescharacteristic
71C53×#491C2218yescomplemented
72C2×#103×C53C2211yescharacteristic
73C2×#103×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106—21no—
79C22×Dic106C2311yescharacteristic
80C22×Dic106C2311yescharacteristic
81C2×Q8×D53—22no—
82C2×Q8×D53—22no—
83C2×Q8×D53—24no—
84C2×Q8×D53—24no—
85C2×Q8×D53—42no—
86C2×Q8×D53—42no—
87C2×Q8×D53C2314yes—
88C2×Q8×D53C2314yes—
89C22×D212D411yescharacteristic
90C22×C4×D53—21no—
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C22×C4×D53C2311yescharacteristic
94C22×C4×D53C2311yescharacteristic
95C2×Dic212—24no—
96C2×Dic212C2314yes—
97C2×#11719925—42no—
98C2×#11719925—42no—
99C2×#11719925C2314yes—
100C2×#11719925C2314yes—
101C2×#11719912—42no—
102C2×#11719912C2314yes—
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105C2×C8×D53—42no—
106C2×C8×D53C2314yes—
107#13133216—28no—
108#13133212—28no—
109#13133208—28no—
110#13133202—28no—
111#13133197—22no—
112#13133197—22no—
113#13133197C2314yes—
114#13133197C2314yes—
115#13133195—28no—
116#13133195—28no—
117#13133193—22no—
118#13133193—22no—
119#13133193C2314yes—
120#13133193C2314yes—
121C4×Dic106—22no—
122C4×Dic106—22no—
123C4×Dic106C2314yes—
124C4×Dic106C2314yes—
125C4×D212D414yes—
126C4×D212C2314yes—
127#13133179—28no—
128#13133175—28no—
129#13133175—22no—
130#13133175C2314yes—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53—21no—
133C2×C4⋊Dic53D411yescharacteristic
134C2×C4⋊Dic53C2311yescharacteristic
135C2×C4⋊Dic53C2311yescharacteristic
136C2×#11719919—21no—
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919—21no—
141C4⋊C4×D53—22no—
142C4⋊C4×D53C2314yes—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921D411yescharacteristic
149C2×#11719921D411yescharacteristic
150C2×C4×Dic53—21no—
151C2×C4×Dic53—21no—
152C2×C4×Dic53—21no—
153#13133150C2314yes—
154#13133149C2314yes—
155#13133148C2314yes—
156C4⋊#88322C2314yes—
157#13133142C2314yes—
158#13133142C2314yes—
159#13133141C2314yes—
160#13133141C2314yes—
161#13133140C2314yes—
162#13133140C2314yes—
163#13133129C2314yes—
164#13133129C2314yes—
165C22×Q8×C53C2311yescharacteristic
166C22×Q8×C53C2311yescharacteristic
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C4⋊Q8×C53—22no—
170C4⋊Q8×C53C2314yes—
171#125×C53—22no—
172#125×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53—21no—
175C2×C4⋊C4×C53—21no—
176C2×C4⋊C4×C53—21no—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C42×C53C2311yescharacteristic
180#103×C53C2314yes—
181#103×C53C2314yes—
182#103×C53C2314yes—
183#103×C53C2314yes—
184#97×C53C2314yes—
185C23×D53C2×D411yescharacteristic
186C23×D53C2×D411yescharacteristic
187C2×Q8×C53—21no—
188C2×Q8×C53—21no—
189C2×Q8×C53—22no—
190C2×Q8×C53—22no—
191C2×Q8×C53—22no—
192C2×Q8×C53—22no—
193C2×Q8×C53C2412yes—
194C2×Q8×C53C2412yes—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53C2×D411yescharacteristic
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2411yescharacteristic
202C22×Dic53—21no—
203C22×Dic53—21no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53C2×D411yescharacteristic
207C22×Dic53C2×D411yescharacteristic
208Q8×D53—28no—
209Q8×D53—28no—
210Q8×D53—44no—
211Q8×D53—44no—
212Q8×D53—48no—
213Q8×D53—48no—
214C2×D212—24no—
215C2×D212C2×D414yes—
216C2×C4×D53—22no—
217C2×C4×D53—22no—
218C2×C4×D53—22no—
219C2×C4×D53—22no—
220C2×C4×D53—24no—
221C2×C4×D53—24no—
222C2×C4×D53—24no—
223C2×C4×D53—44no—
224C2×C4×D53—44no—
225C2×C4×D53—44no—
226C2×C4×D53C2×D412yes—
227C2×C4×D53C2×D412yes—
228C2×C4×D53C2412yes—
229C2×C4×D53C2412yes—
230C2×Dic106—21no—
231C2×Dic106—22no—
232C2×Dic106—22no—
233C2×Dic106—22no—
234C2×Dic106—21no—
235C2×Dic106—24no—
236C2×Dic106—24no—
237C2×Dic106—44no—
238C2×Dic106—44no—
239C2×Dic106#4114yes—
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—24no—
248C4⋊C4×C53—24no—
249C4⋊C4×C53—24no—
250C4⋊C4×C53—21no—
251C4⋊C4×C53—21no—
252C4⋊C4×C53C2412yes—
253C4⋊C4×C53C2412yes—
254C42×C53C2×D412yes—
255C42×C53C2412yes—
256#11719925—44no—
257#11719925—44no—
258#11719921—24no—
259#11719921—24no—
260#11719921—24no—
261#11719921—24no—
262#11719921—24no—
263#11719921C2×D414yes—
264#11719921C2×D414yes—
265C4⋊Dic53—21no—
266C4⋊Dic53—21no—
267C4⋊Dic53—24no—
268C4⋊Dic53—24no—
269C4⋊Dic53C2×D414yes—
270C4⋊Dic53C2412yes—
271C4⋊Dic53C2412yes—
272#11719919—24no—
273#11719919—24no—
274#11719919—24no—
275#11719919—24no—
276#11719919—24no—
277C4×Dic53—24no—
278C4×Dic53—24no—
279C4×Dic53—24no—
280C2×#88322—22no—
281C2×#88322—22no—
282C2×#88322C2412yes—
283C2×#88322C2412yes—
284Dic212—28no—
285#11719912—44no—
286C8×D53—44no—
287C23×C53C22×D411yescharacteristic
288C22×D53—22no—
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—22no—
293C22×D53#13714yes—
294C22×D53C22×D412yes—
295C22×D53C22×D412yes—
296Q8×C53—22no—
297Q8×C53—22no—
298Q8×C53—22no—
299Q8×C53—22no—
300Q8×C53—42no—
301Q8×C53—42no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—42no—
309C2×C4×C53—42no—
310C2×C4×C53—42no—
311C2×C4×C53—42no—
312C2×C4×C53C22×D412yes—
313C2×C4×C53C22×D412yes—
314C2×C4×C53C22×D411yescharacteristic
315C2×C4×C53C2×#4112yes—
316C2×C4×C53H(5,𝔽2)12yes—
317C2×C4×C53C2511yescharacteristic
318C2×Dic53—24no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—42no—
326C2×Dic53—42no—
327C2×Dic53—42no—
328C2×Dic53C22×D412yes—
329C2×Dic53C22×D412yes—
330D212—28no—
331C4×D53—24no—
332C4×D53—24no—
333C4×D53—22no—
334C4×D53—22no—
335C4×D53—22no—
336C4×D53—22no—
337C4×D53—48no—
338C4×D53—48no—
339C4×D53—48no—
340Dic106—24no—
341Dic106—22no—
342Dic106—22no—
343Dic106—22no—
344Dic106—48no—
345Dic106—48no—
346Dic106—42no—
347Dic106C2×#4114yes—
348C8×C53—22no—
349C8×C53—22no—
350#88322—22no—
351#88322—22no—
352C2×#3312—531nomaximal, Sylow
353C22×C53#54612yes—
354C22×C53C2×#13712yes—
355C22×C53#57812yes—
356C22×C53C23×D411yescharacteristic
357C2×D53—22no—
358C2×D53—28no—
359C2×D53—22no—
360C2×D53—22no—
361C2×D53—22no—
362C2×D53—22no—
363C2×D53—44no—
364C2×D53C2×#13714yes—
365C4×C53—22no—
366C4×C53—22no—
367C4×C53—42no—
368C4×C53—42no—
369C4×C53—42no—
370C4×C53—42no—
371C4×C53#54612yes—
372C4×C53C22×#4111yescharacteristic
373C4×C53C2×H(5,𝔽2)11yescharacteristic
374Dic53—24no—
375Dic53—22no—
376Dic53—22no—
377Dic53—42no—
378Dic53—42no—
379Dic53—42no—
380C2×#552—531no—
381C2×D4×Q8—531no—
382#3312—5316no—
383C2×#491D5311yescharacteristic, complemented
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×#435—531no—
394C2×#419—531no—
395C22×#103—531no—
396C2×C53#331214yescomplemented
397C2×C53C2×#54611yescharacteristic
398C2×C53C22×#13711yescharacteristic
399C2×C53C2×#57811yescharacteristic
400D53—24no—
401D53—42no—
402C23×Q8—531no—
403C23×Q8—531no—
404C22×Q16—531no—
405C22×Q16—531no—
406C22×Q16—531no—
407C22×M16—531no—
408C23×C8—531no—
409#552—538no—
410#552—1064no—
411D4×Q8—538no—
412D4×Q8—1064no—
413C2×C4⋊Q8—1061no—
414C2×C4⋊Q8C2×D5311yescharacteristic
415C2×#126—1061no—
416C2×#125—1061no—
417C2×#125C2×D5311yescharacteristic
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—531no—
428C2×C4×D4—1061no—
429C2×#117—531no—
430C2×#117—1061no—
431C22×C4⋊C4—531no—
432#491C2×D5318yescomplemented
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#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—531no—
453C2×#103—531no—
454C2×#103—538no—
455C2×#103C2×D5311yescharacteristic
456C2×#103C2×D5311yescharacteristic
457C2×#103C2×D5311yescharacteristic
458C2×#103C2×D5311yescharacteristic
459C2×C22⋊C8—531no—
460C2×C22⋊C8—531no—
461C2×#97C2×D5311yescharacteristic
462C53C2×#331211yescharacteristic, complemented, Sylow
463C22×Q8—534no—
464C22×Q8—534no—
465C22×Q8—531no—
466C22×Q8—531no—
467C22×Q8—1061no—
468C22×Q8—1061no—
469C22×Q8—1062no—
470C22×Q8—1062no—
471C22×Q8—1064no—
472C22×Q8—1064no—
473C22×Q8—2122no—
474C22×Q8—2122no—
475C22×Q8C22×D5311yescharacteristic
476C22×Q8C22×D5311yescharacteristic
477C22×D4—531no—
478C23×C4—531no—
479C23×C4—531no—
480C23×C4—1061no—
481C23×C4—1061no—
482C23×C4—1061no—
483C2×Q16—534no—
484C2×Q16—534no—
485C2×Q16—534no—
486C2×Q16—1064no—
487C2×Q16—2122no—
488C2×Q16—2122no—
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—22no—
498C4⋊Q8—1068no—
499C4⋊Q8C22×D5314yes—
500#126—1068no—
501#125—22no—
502#125—1068no—
503#125C22×D5314yes—
504#123—1068no—
505C22⋊Q8—534no—
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⋊Q8—1062no—
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—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—531no—
530C2×C4⋊C4—531no—
531C2×C4⋊C4—531no—
532C2×C4⋊C4—534no—
533C2×C4⋊C4—1062no—
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⋊C4C22×D5311yescharacteristic
542C2×C4⋊C4C22×D5311yescharacteristic
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×C22⋊C4—1061no—
550C2×C42—1061no—
551C2×C42—1061no—
552C2×C42—1061no—
553C2×C42C22×D5311yescharacteristic
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#103C22×D5314yes—
565#103C22×D5314yes—
566#103C22×D5314yes—
567#103C22×D5314yes—
568C22⋊C8—534no—
569C22⋊C8—534no—
570#97C22×D5314yes—
571C24—531no—
572C24—531no—
573C2×Q8—21no—
574C2×Q8—21no—
575C2×Q8—22no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—534no—
580C2×Q8—532no—
581C2×Q8—532no—
582C2×Q8—1064no—
583C2×Q8—1064no—
584C2×Q8—1061no—
585C2×Q8—1061no—
586C2×Q8—1062no—
587C2×Q8—1068no—
588C2×Q8—1068no—
589C2×Q8—1062no—
590C2×Q8—1062no—
591C2×Q8—2124no—
592C2×Q8—2124no—
593C2×Q8—2124no—
594C2×Q8—2124no—
595C2×Q8—2128no—
596C2×Q8—2128no—
597C2×Q8C23×D5312yes—
598C2×Q8C23×D5312yes—
599C2×D4—534no—
600C2×D4—1064no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—531no—
606C22×C4—531no—
607C22×C4—532no—
608C22×C4—532no—
609C22×C4—532no—
610C22×C4—532no—
611C22×C4—1064no—
612C22×C4—1064no—
613C22×C4—1064no—
614C22×C4—1061no—
615C22×C4—1062no—
616C22×C4—1062no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—1061no—
620C22×C4—1061no—
621C22×C4—1061no—
622C22×C4—2124no—
623C22×C4—2124no—
624C22×C4—2124no—
625C22×C4D4×D5311yescharacteristic
626C22×C4D4×D5311yescharacteristic
627C22×C4C23×D5311yescharacteristic
628Q16—1068no—
629Q16—2124no—
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—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—21no—
646C4⋊C4—21no—
647C4⋊C4—534no—
648C4⋊C4—532no—
649C4⋊C4—532no—
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—1064no—
659C4⋊C4C23×D5312yes—
660C4⋊C4C23×D5312yes—
661C22⋊C4—534no—
662C22⋊C4—534no—
663C22⋊C4—1064no—
664C22⋊C4—1064no—
665C22⋊C4—1064no—
666C22⋊C4—1064no—
667C22⋊C4—1064no—
668C42—1064no—
669C42—1064no—
670C42—1064no—
671C42D4×D5312yes—
672C42C23×D5312yes—
673C23—534no—
674C23—532no—
675C23—532no—
676C23—1062no—
677C23—1062no—
678C23—1062no—
679C23—1062no—
680C23—1062no—
681C23C2×D4×D5311yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—42no—
687Q8—42no—
688Q8—534no—
689Q8—1064no—
690Q8—1062no—
691Q8—1062no—
692Q8—1062no—
693Q8—2128no—
694Q8—2128no—
695Q8—2122no—
696D4—1068no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—532no—
708C2×C4—532no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—1064no—
712C2×C4—1062no—
713C2×C4—1064no—
714C2×C4—1064no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—1062no—
718C2×C4—1062no—
719C2×C4—1062no—
720C2×C4—1062no—
721C2×C4—1062no—
722C2×C4—2128no—
723C2×C4—2128no—
724C2×C4—2128no—
725C2×C4—2122no—
726C2×C4—2122no—
727C2×C4—2122no—
728C2×C4C2×D4×D5312yes—
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—534no—
739C22—1068no—
740C22—1062no—
741C22—1062no—
742C22—1062no—
743C22—1062no—
744C22—1062no—
745C22—2124no—
746C22#1681126612yes—
747C22#137×D5312yes—
748C22#1681143912yes—
749C22C22×D4×D5311yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—1062no—
757C4—1062no—
758C4—1064no—
759C4—2122no—
760C4—2122no—
761C4—2122no—
762C4#1681126612yes—
763C4C2×#41×D5311yescharacteristic
764C4C2×#1313326311yescharacteristic
765C2—1064no—
766C2—2122no—
767C2#2028676514yesdirect product factor
768C2C2×#1681126611yescharacteristic
769C2C2×#137×D5311yescharacteristic
770C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#491C2
socleC23×C53C22×D4
prime radicalC22×D212D4
hypercenterC2×#491D53
hypocenterC53C2×#3312
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
3. #20286765C2direct (N × H)
4. C2×#16810962C2semidirect
5. C2×#16810952C2semidirect
6. C2×#16810927C2semidirect
7. C2×#16810880C2semidirect
8. C2×#16810863C2semidirect
9. C2×#16810830C2semidirect
10. C2×#16810780C2semidirect
11. C2×#16810780C2semidirect
12. C2×#16810731C2semidirect
14. C2×#16810630C2semidirect
15. C2×#103×D53C2semidirect
16. C2×C53×#491C2semidirect
45. #16810962C22semidirect
46. #16810952C22semidirect
47. #16810927C22semidirect
48. #16810880C22semidirect
49. #16810863C22semidirect
50. #16810830C22semidirect
51. #16810780C22semidirect
52. #16810780C22semidirect
53. #16810731C22semidirect
59. #16810630C22semidirect
66. #103×D53C22semidirect
71. C53×#491C22semidirect
383. C2×#491D53semidirect
396. C2×C53#3312semidirect
432. #491C2×D53semidirect
462. C53C2×#3312semidirect
767. C2#20286765direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113112
C2×#168112882
#202867652
C2×#168109622
C2×#168109522
C2×#168109272
C2×#168108802
C2×#168108632
C2×#168108302
C2×#168107802
C2×#168107312
C2×#168106962
C2×#168106302
C2×#103×D532
C2×C53×#4912
C2×#331253