Finite Group Databasebeta

← C2×#20284977 #28252407

Subgroups — C2×#20284977 #28252407

Order 13568.

2134 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811244C211yesmaximal, characteristic, complemented
2#20284977C2116yesmaximal, direct product factor
3C2×#16810958C211yesmaximal, characteristic, complemented
4C2×#16810936C211yesmaximal, characteristic, complemented
5C2×#16810918C211yesmaximal, characteristic, complemented
6C2×#16810903C211yesmaximal, characteristic, complemented
7C2×#16810845C211yesmaximal, characteristic, complemented
8C2×#16810838C211yesmaximal, characteristic, complemented
9C2×#16810785C211yesmaximal, characteristic, complemented
10C2×#16810768C211yesmaximal, characteristic
11C2×#16810723C211yesmaximal, characteristic, complemented
12C2×#16810721C211yesmaximal, characteristic, complemented
13C2×C4×#11719925C211yesmaximal, characteristic, complemented
14C2×C4×#11719922C211yesmaximal, characteristic, complemented
15C2×#16810684C211yesmaximal, characteristic, complemented
16C2×C53×#520C211yesmaximal, characteristic, complemented
17C22×#11719925C2211yescharacteristic
18C22×#11719923C2211yescharacteristic
19C22×#11719924C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21#16811244—24no—
22#16811244C2218yescomplemented
23C2×#13133217C2211yescharacteristic
24C2×#13133212—21no—
25C2×#13133205C2211yescharacteristic
26C2×#13133203—21no—
27C2×#13133199—21no—
28C2×#13133196C2211yescharacteristic
29C2×#13133195—21no—
30C2×#13133191C2211yescharacteristic
31C2×C4×Dic106C2211yescharacteristic
32C2×C4×D212C2211yescharacteristic
33#16810958C2218yescomplemented
34#16810936C2218yescomplemented
35#16810918C2218yescomplemented
36#16810903C2218yescomplemented
37#16810845C2218yescomplemented
38#16810838C2218yescomplemented
39#16810785C2218yescomplemented
40#16810768C2218yes—
41#16810723C2218yescomplemented
42#16810721C2218yescomplemented
43C4×#11719925C2218yescomplemented
44C4×#11719922C2218yescomplemented
45#16810684C2218yescomplemented
46C2×#13133150C2211yescharacteristic
47C2×#13133150C2211yescharacteristic
48C2×#13133150C2211yescharacteristic
49C2×#13133150C2211yescharacteristic
50C2×C4⋊#88322C2211yescharacteristic
51C2×C4⋊#88322C2211yescharacteristic
52C2×#13133141C2211yescharacteristic
53C2×#13133141C2211yescharacteristic
54C2×#13133140C2211yescharacteristic
55C2×#13133140C2211yescharacteristic
56C2×#13133138C2211yescharacteristic
57C2×#13133138C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59C2×#13133137C2211yescharacteristic
60C2×C22⋊#88322C2211yescharacteristic
61C2×C22⋊#88322C2211yescharacteristic
62C2×#13133128C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C22×#41×C53C2211yescharacteristic
65C53×#520—24no—
66C53×#520C2218yescomplemented
67C2×C4×Q8×C53C2211yescharacteristic
68C2×C4×Q8×C53C2211yescharacteristic
69C2×C4×D4×C53—21no—
70C2×C4×D4×C53—21no—
71C2×C4×D4×C53C2211yescharacteristic
72C2×C4×D4×C53C2211yescharacteristic
73C2×#117×C53—21no—
74C2×#117×C53C2211yescharacteristic
75C22×C4⋊C4×C53—21no—
76C22×C4⋊C4×C53C2211yescharacteristic
77C22×Dic106—21no—
78C22×Dic106C2311yescharacteristic
79C22×D212C2311yescharacteristic
80C22×C22⋊D53—21no—
81C22×C4×D53—21no—
82C2×#11719925—24no—
83C2×#11719925C2314yes—
84C2×#11719923—24no—
85C2×#11719923C2314yes—
86C2×#11719924—24no—
87C2×#11719924C2314yes—
88C2×#11719922—24no—
89C2×#11719922C2314yes—
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94#13133217—22no—
95#13133217C2314yes—
96#13133212—28no—
97#13133205—22no—
98#13133205C2314yes—
99#13133203—28no—
100#13133199—28no—
101#13133196—22no—
102#13133196C2314yes—
103#13133195—28no—
104#13133191—22no—
105#13133191C2314yes—
106C4×Dic106—22no—
107C4×Dic106C2314yes—
108C4×D212—22no—
109C4×D212C2314yes—
110C2×C4⋊Dic53—21no—
111C2×C4⋊Dic53C2311yescharacteristic
112C2×C4⋊Dic53C2311yescharacteristic
113C2×#11719919—21no—
114C2×#11719919—21no—
115C2×C22⋊Dic53—21no—
116C2×#11719921—21no—
117C2×#11719921—21no—
118C2×#11719921—21no—
119C2×#11719921—21no—
120C2×C4×Dic53—21no—
121#13133150C2314yes—
122#13133150C2314yes—
123#13133150C2314yes—
124#13133150C2314yes—
125C4⋊#88322C2314yes—
126C4⋊#88322C2314yes—
127#13133141C2314yes—
128#13133141C2314yes—
129#13133140C2314yes—
130#13133140C2314yes—
131#13133138C2314yes—
132#13133138C2314yes—
133#13133137C2314yes—
134#13133137C2314yes—
135C22⋊#88322C2314yes—
136C22⋊#88322C2314yes—
137#13133128C2314yes—
138C4×#88322C2314yes—
139C2×#41×C53—24no—
140C2×#41×C53—24no—
141C2×#41×C53—22no—
142C2×#41×C53C2314yes—
143C22×Q8×C53C2311yescharacteristic
144C22×D4×C53—21no—
145C22×D4×C53C2311yescharacteristic
146C23×C4×C53—21no—
147C23×C4×C53—21no—
148C23×C4×C53—21no—
149C23×C4×C53—21no—
150C23×C4×C53C2311yescharacteristic
151C4×Q8×C53—22no—
152C4×Q8×C53—22no—
153C4×Q8×C53C2314yes—
154C4×Q8×C53C2314yes—
155C4×D4×C53—28no—
156C4×D4×C53—28no—
157C4×D4×C53—22no—
158C4×D4×C53—22no—
159C4×D4×C53C2314yes—
160C4×D4×C53C2314yes—
161#117×C53—28no—
162#117×C53D414yes—
163#117×C53C2314yes—
164C2×C4⋊C4×C53—28no—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53—22no—
169C2×C4⋊C4×C53D411yescharacteristic
170C2×C4⋊C4×C53D411yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C4⋊C4×C53C2311yescharacteristic
173C2×C4⋊C4×C53C2314yes—
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53D411yescharacteristic
177C2×C22⋊C4×C53D411yescharacteristic
178C2×C42×C53—21no—
179C2×C42×C53—21no—
180C2×C42×C53C2311yescharacteristic
181C2×C42×C53C2311yescharacteristic
182C24×C53—21no—
183C24×C53C2×D411yescharacteristic
184C23×D53—21no—
185#41×C53—216no—
186#41×C53—28no—
187#41×C53—28no—
188C2×Q8×C53—21no—
189C2×Q8×C53—22no—
190C2×Q8×C53#4114yes—
191C2×Q8×C53C2412yes—
192C2×D4×C53—28no—
193C2×D4×C53—24no—
194C2×D4×C53—21no—
195C2×D4×C53—22no—
196C2×D4×C53#4114yes—
197C2×D4×C53C2412yes—
198C22×C4×C53—28no—
199C22×C4×C53—21no—
200C22×C4×C53—24no—
201C22×C4×C53—22no—
202C22×C4×C53—22no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—24no—
206C22×C4×C53—24no—
207C22×C4×C53—24no—
208C22×C4×C53—82no—
209C22×C4×C53—82no—
210C22×C4×C53—82no—
211C22×C4×C53C2×D411yescharacteristic
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D411yescharacteristic
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D412yes—
217C22×C4×C53C2412yes—
218C22×C4×C53C2411yescharacteristic
219C2×C22⋊D53—24no—
220C2×C22⋊D53—82no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C2×D212—22no—
225C2×D212—22no—
226C2×D212—21no—
227C2×D212C2412yes—
228C2×C4×D53—24no—
229C2×C4×D53—82no—
230C2×Dic106—22no—
231C2×Dic106—22no—
232C2×Dic106—21no—
233C2×Dic106—24no—
234C2×Dic106—82no—
235C2×Dic106C2412yes—
236C4⋊C4×C53—24no—
237C4⋊C4×C53—24no—
238C4⋊C4×C53—24no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53C2×D414yes—
242C4⋊C4×C53C2×D414yes—
243C4⋊C4×C53C2412yes—
244C4⋊C4×C53C2412yes—
245C22⋊C4×C53—24no—
246C22⋊C4×C53—24no—
247C22⋊C4×C53C2×D414yes—
248C22⋊C4×C53C2×D414yes—
249C42×C53—24no—
250C42×C53—24no—
251C42×C53C2×D412yes—
252C42×C53C2×D412yes—
253C42×C53C2412yes—
254C42×C53C2412yes—
255C22⋊Dic53—24no—
256#11719925—28no—
257#11719924—28no—
258#11719923—28no—
259#11719922—28no—
260#11719921—24no—
261#11719921—24no—
262#11719921—24no—
263#11719921—24no—
264C4⋊Dic53—24no—
265C4⋊Dic53—21no—
266C4⋊Dic53—21no—
267C4⋊Dic53C2412yes—
268C4⋊Dic53C2412yes—
269#11719919—24no—
270#11719919—24no—
271C4×Dic53—24no—
272C2×#88322—22no—
273C2×#88322—22no—
274C2×#88322—22no—
275C2×#88322—22no—
276C2×#88322C2412yes—
277C2×#88322C2412yes—
278C2×#88322C2412yes—
279C2×#88322C2412yes—
280C23×C53—22no—
281C23×C53—24no—
282C23×C53—22no—
283C23×C53—22no—
284C23×C53—22no—
285C23×C53—42no—
286C23×C53—42no—
287C23×C53C22×D412yes—
288C23×C53C22×D411yescharacteristic
289C22×D53—22no—
290C22×D53—42no—
291C22×D53—42no—
292C22×D53—42no—
293Q8×C53—24no—
294Q8×C53—22no—
295Q8×C53C2×#4114yes—
296D4×C53—216no—
297D4×C53—24no—
298D4×C53—22no—
299D4×C53C2×#4114yes—
300C2×C4×C53—216no—
301C2×C4×C53—22no—
302C2×C4×C53—24no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—24no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—84no—
316C2×C4×C53—84no—
317C2×C4×C53—84no—
318C2×C4×C53C22×D412yes—
319C2×C4×C53C22×D412yes—
320C2×C4×C53C22×D412yes—
321C2×C4×C53C22×D412yes—
322C2×C4×C53C22×D412yes—
323C2×C4×C53C22×D411yescharacteristic
324C2×C4×C53C2×#4112yes—
325C2×C4×C53C2×#4112yes—
326C2×C4×C53C2511yescharacteristic
327C22⋊D53—84no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334D212—22no—
335D212—22no—
336D212—42no—
337C4×D53—84no—
338Dic106—22no—
339Dic106—22no—
340Dic106—42no—
341Dic106—84no—
342#88322—22no—
343#88322—22no—
344#88322—22no—
345#88322—22no—
346C2×#3124—531nomaximal, Sylow
347C22×C53—22no—
348C22×C53—24no—
349C22×C53—22no—
350C22×C53—22no—
351C22×C53—44no—
352C22×C53—48no—
353C22×C53—42no—
354C22×C53—42no—
355C22×C53#52512yes—
356C22×C53#57612yes—
357C22×C53#57812yes—
358C22×C53C23×D411yescharacteristic
359C2×D53—42no—
360C2×D53—42no—
361C2×D53—42no—
362C2×D53—84no—
363C4×C53—22no—
364C4×C53—24no—
365C4×C53—22no—
366C4×C53—22no—
367C4×C53—22no—
368C4×C53—22no—
369C4×C53—42no—
370C4×C53—42no—
371C4×C53#52512yes—
372C4×C53C22×#4111yescharacteristic
373C4×C53C22×#4111yescharacteristic
374Dic53—42no—
375Dic53—42no—
376Dic53—42no—
377C2×#542—531no—
378C2×#520D5311yescharacteristic, complemented
379#3124—5316no—
380C2×#484—531no—
381C2×#480—531no—
382C2×#477—531no—
383C2×#474—531no—
384C2×#464—531no—
385C2×#463—531no—
386C2×#452—531no—
387C2×#449—531no—
388C2×#440—531no—
389C2×#440—531no—
390C2×C4×Q16—531no—
391C2×C4×D8—531no—
392C2×#433—531no—
393C2×C53—42no—
394C2×C53—44no—
395C2×C53#312414yescomplemented
396C2×C53C2×#52511yescharacteristic
397C2×C53C2×#57611yescharacteristic
398C2×C53C2×#57811yescharacteristic
399D53—82no—
400C22×#41C2×D5311yescharacteristic
401C22×Q16—531no—
402C22×SD16—531no—
403C22×SD16—531no—
404C22×D8—531no—
405#542—538no—
406#542—1064no—
407C2×C4⋊Q8—531no—
408C2×#126—1061no—
409C2×#124—531no—
410C2×#124—1061no—
411C2×#123—1061no—
412C2×C22⋊Q8—531no—
413C2×C22⋊Q8—1061no—
414C2×#121—531no—
415#520—24no—
416#520C2×D5318yescomplemented
417C2×C4×Q8—531no—
418C2×C4×Q8C2×D5311yescharacteristic
419C2×C4×Q8C2×D5311yescharacteristic
420C2×C4×D4—21no—
421C2×C4×D4—21no—
422C2×C4×D4—531no—
423C2×C4×D4C2×D5311yescharacteristic
424C2×C4×D4C2×D5311yescharacteristic
425C2×#117—21no—
426C2×#117C2×D5311yescharacteristic
427C22×C4⋊C4—21no—
428C22×C4⋊C4C2×D5311yescharacteristic
429#484—538no—
430#480—538no—
431#477—538no—
432#474—538no—
433#464—538no—
434#463—538no—
435#452—538no—
436#449—538no—
437#440—538no—
438#440—538no—
439C4×Q16—538no—
440C4×D8—538no—
441#433—538no—
442C2×#107—531no—
443C2×#107—531no—
444C2×#107—531no—
445C2×#107—531no—
446C2×C4⋊C8—531no—
447C2×C4⋊C8—531no—
448C2×#103—531no—
449C2×#103—531no—
450C2×#103—531no—
451C2×#103—531no—
452C2×#102—531no—
453C2×#102—531no—
454C2×#102—531no—
455C2×#102—531no—
456C2×C22⋊C8—531no—
457C2×C22⋊C8—531no—
458C2×#97—531no—
459C2×C4×C8—531no—
460C53C2×#312411yescharacteristic, complemented, Sylow
461C2×#41—24no—
462C2×#41—24no—
463C2×#41—22no—
464C2×#41C22×D5314yes—
465C22×Q8—531no—
466C22×Q8—1061no—
467C22×Q8C22×D5311yescharacteristic
468C22×D4—21no—
469C22×D4—531no—
470C22×D4—1061no—
471C22×D4C22×D5311yescharacteristic
472C23×C4—21no—
473C23×C4—21no—
474C23×C4—21no—
475C23×C4—21no—
476C23×C4—1061no—
477C23×C4C22×D5311yescharacteristic
478C2×Q16—534no—
479C2×Q16—1064no—
480C2×SD16—534no—
481C2×SD16—534no—
482C2×SD16—1064no—
483C2×SD16—1064no—
484C2×D8—534no—
485C2×D8—1064no—
486C22×C8—531no—
487C22×C8—531no—
488C22×C8—531no—
489C22×C8—531no—
490C4⋊Q8—534no—
491C4⋊Q8—1062no—
492#126—1068no—
493#124—534no—
494#124—1068no—
495#124—1062no—
496#123—1068no—
497C22⋊Q8—534no—
498C22⋊Q8—1062no—
499C22⋊Q8—1068no—
500#121—534no—
501#121—1062no—
502C4×Q8—22no—
503C4×Q8—22no—
504C4×Q8—534no—
505C4×Q8—1062no—
506C4×Q8C22×D5314yes—
507C4×Q8C22×D5314yes—
508C4×D4—28no—
509C4×D4—28no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—534no—
513C4×D4—1062no—
514C4×D4C22×D5314yes—
515C4×D4C22×D5314yes—
516#117—28no—
517#117C22⋊D5314yes—
518#117C22×D5314yes—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—22no—
523C2×C4⋊C4—28no—
524C2×C4⋊C4—531no—
525C2×C4⋊C4—531no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4—1061no—
529C2×C4⋊C4C22⋊D5311yescharacteristic
530C2×C4⋊C4C22⋊D5311yescharacteristic
531C2×C4⋊C4C22×D5311yescharacteristic
532C2×C4⋊C4C22×D5311yescharacteristic
533C2×C4⋊C4C22×D5314yes—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—1061no—
537C2×C22⋊C4—1061no—
538C2×C22⋊C4—1061no—
539C2×C22⋊C4—1061no—
540C2×C22⋊C4—1061no—
541C2×C22⋊C4C22⋊D5311yescharacteristic
542C2×C22⋊C4C22⋊D5311yescharacteristic
543C2×C42—21no—
544C2×C42—21no—
545C2×C42—1061no—
546C2×C42C22×D5311yescharacteristic
547C2×C42C22×D5311yescharacteristic
548#107—534no—
549#107—534no—
550#107—534no—
551#107—534no—
552C4⋊C8—534no—
553C4⋊C8—534no—
554#103—534no—
555#103—534no—
556#103—534no—
557#103—534no—
558#102—534no—
559#102—534no—
560#102—534no—
561#102—534no—
562C22⋊C8—534no—
563C22⋊C8—534no—
564#97—534no—
565C4×C8—534no—
566C24—21no—
567C24—1061no—
568C24C2×C22⋊D5311yescharacteristic
569#41—216no—
570#41—28no—
571#41—28no—
572C2×Q8—21no—
573C2×Q8—22no—
574C2×Q8—532no—
575C2×Q8—1064no—
576C2×Q8—1061no—
577C2×Q8—1062no—
578C2×Q8—1062no—
579C2×Q8—4242no—
580C2×Q8#1171994514yes—
581C2×Q8C23×D5312yes—
582C2×D4—28no—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—532no—
587C2×D4—1064no—
588C2×D4—1061no—
589C2×D4—1062no—
590C2×D4—1062no—
591C2×D4—4242no—
592C2×D4#1171994514yes—
593C2×D4C23×D5312yes—
594C22×C4—28no—
595C22×C4—21no—
596C22×C4—24no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—82no—
605C22×C4—82no—
606C22×C4—82no—
607C22×C4—1061no—
608C22×C4—1061no—
609C22×C4—1061no—
610C22×C4—1064no—
611C22×C4—4242no—
612C22×C4C2×C22⋊D5312yes—
613C22×C4C2×C22⋊D5311yescharacteristic
614C22×C4C2×C22⋊D5311yescharacteristic
615C22×C4C2×C22⋊D5311yescharacteristic
616C22×C4C2×C22⋊D5311yescharacteristic
617C22×C4C2×C22⋊D5311yescharacteristic
618C22×C4C23×D5312yes—
619C22×C4C23×D5311yescharacteristic
620Q16—1068no—
621SD16—1068no—
622SD16—1068no—
623D8—1068no—
624C2×C8—532no—
625C2×C8—532no—
626C2×C8—532no—
627C2×C8—532no—
628C2×C8—1062no—
629C2×C8—1062no—
630C2×C8—1062no—
631C2×C8—1062no—
632C4⋊C4—24no—
633C4⋊C4—24no—
634C4⋊C4—24no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—532no—
638C4⋊C4—532no—
639C4⋊C4—1061no—
640C4⋊C4—1061no—
641C4⋊C4—1064no—
642C4⋊C4—1064no—
643C4⋊C4—1064no—
644C4⋊C4C2×C22⋊D5314yes—
645C4⋊C4C2×C22⋊D5314yes—
646C4⋊C4C23×D5312yes—
647C4⋊C4C23×D5312yes—
648C22⋊C4—24no—
649C22⋊C4—24no—
650C22⋊C4—1064no—
651C22⋊C4—1064no—
652C22⋊C4—1064no—
653C22⋊C4—1064no—
654C22⋊C4—1064no—
655C22⋊C4C2×C22⋊D5314yes—
656C22⋊C4C2×C22⋊D5314yes—
657C42—24no—
658C42—24no—
659C42—1064no—
660C42C2×C22⋊D5312yes—
661C42C2×C22⋊D5312yes—
662C42C23×D5312yes—
663C42C23×D5312yes—
664C23—22no—
665C23—24no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—42no—
670C23—42no—
671C23—1062no—
672C23—2122no—
673C23—2122no—
674C23—2122no—
675C23C22×C22⋊D5312yes—
676C23C22×C22⋊D5311yescharacteristic
677Q8—24no—
678Q8—22no—
679Q8—1062no—
680Q8—1062no—
681Q8—4244no—
682Q8—2122no—
683Q8C2×#1171994514yes—
684D4—216no—
685D4—24no—
686D4—22no—
687D4—1062no—
688D4—1062no—
689D4—4244no—
690D4—2122no—
691D4C2×#1171994514yes—
692C2×C4—216no—
693C2×C4—22no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—84no—
708C2×C4—84no—
709C2×C4—84no—
710C2×C4—1062no—
711C2×C4—1062no—
712C2×C4—1062no—
713C2×C4—4244no—
714C2×C4—2122no—
715C2×C4—2122no—
716C2×C4—2122no—
717C2×C4C22×C22⋊D5312yes—
718C2×C4C22×C22⋊D5312yes—
719C2×C4C22×C22⋊D5312yes—
720C2×C4C22×C22⋊D5312yes—
721C2×C4C22×C22⋊D5312yes—
722C2×C4C22×C22⋊D5311yescharacteristic
723C2×C4C2×#1171994512yes—
724C2×C4C2×#1171994512yes—
725C2×C4C24×D5311yescharacteristic
726C8—1062no—
727C8—1062no—
728C8—1062no—
729C8—1062no—
730C22—22no—
731C22—22no—
732C22—22no—
733C22—24no—
734C22—44no—
735C22—48no—
736C22—42no—
737C22—42no—
738C22—4244no—
739C22—2122no—
740C22—2122no—
741C22—2122no—
742C22#1681113412yes—
743C22#1681142612yes—
744C22#1681143812yes—
745C22C23×C22⋊D5311yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—2122no—
755C4—2122no—
756C4—2122no—
757C4#1681113412yes—
758C4C22×#1171994511yescharacteristic
759C4C22×#1171994511yescharacteristic
760C2—42no—
761C2—44no—
762C2—4242no—
763C2#2028497714yesdirect product factor
764C2C2×#1681113411yescharacteristic
765C2C2×#1681142611yescharacteristic
766C2C2×#1681143811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#520C2
socleC23×C53C22×D4
prime radicalC2×#16810768C2
hypercenterC2×#520D53
hypocenterC53C2×#3124
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. C2×#16811244C2semidirect
2. #20284977C2direct (N × H)
3. C2×#16810958C2semidirect
4. C2×#16810936C2semidirect
5. C2×#16810918C2semidirect
6. C2×#16810903C2semidirect
7. C2×#16810845C2semidirect
8. C2×#16810838C2semidirect
9. C2×#16810785C2semidirect
11. C2×#16810723C2semidirect
12. C2×#16810721C2semidirect
13. C2×C4×#11719925C2semidirect
14. C2×C4×#11719922C2semidirect
15. C2×#16810684C2semidirect
16. C2×C53×#520C2semidirect
22. #16811244C22semidirect
33. #16810958C22semidirect
34. #16810936C22semidirect
35. #16810918C22semidirect
36. #16810903C22semidirect
37. #16810845C22semidirect
38. #16810838C22semidirect
39. #16810785C22semidirect
41. #16810723C22semidirect
42. #16810721C22semidirect
43. C4×#11719925C22semidirect
44. C4×#11719922C22semidirect
45. #16810684C22semidirect
66. C53×#520C22semidirect
378. C2×#520D53semidirect
395. C2×C53#3124semidirect
416. #520C2×D53semidirect
460. C53C2×#3124semidirect
763. C2#20284977direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112442
#202849772
C2×#168109582
C2×#168109362
C2×#168109182
C2×#168109032
C2×#168108452
C2×#168108382
C2×#168107852
C2×#168107682
C2×#168107232
C2×#168107212
C2×C4×#117199252
C2×C4×#117199222
C2×#168106842
C2×C53×#5202
C2×#312453