Finite Group Databasebeta

← C2×#20288792 #28292295

Subgroups — C2×#20288792 #28292295

Order 13568.

7758 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288792C2132yesmaximal, direct product factor
2C2×#16811359C211yesmaximal, characteristic, complemented
3C2×#16811356C212yesmaximal, complemented
4C2×#16811353C211yesmaximal, characteristic, complemented
5C2×#16811334C211yesmaximal, characteristic, complemented
6C2×#16811332C212yesmaximal, complemented
7C2×#16811293C211yesmaximal, characteristic, complemented
8C2×#16811279C212yesmaximal, complemented
9C2×#16811273C212yesmaximal, complemented
10C2×#16811272C214yesmaximal, complemented
11C2×#16811238C212yesmaximal, complemented
12C2×#16811237C214yesmaximal, complemented
13C2×#16811168C212yesmaximal, complemented
14C2×#16811157C211yesmaximal, characteristic, complemented
15C2×#16811154C212yesmaximal, complemented
16C2×#16811102C212yesmaximal, complemented
17C22×C4×Dic106C211yesmaximal, characteristic, complemented
18C2×C53×#532C211yesmaximal, characteristic, complemented
19C22×#11719947C2212yes—
20C22×#11719947C2214yes—
21C23×Dic106C2211yescharacteristic
22#16811359C22116yescomplemented
23#16811356C22132yescomplemented
24#16811353C22116yescomplemented
25#16811334C22116yescomplemented
26#16811332C22132yescomplemented
27#16811293C22116yescomplemented
28#16811279C22132yescomplemented
29#16811273C22132yescomplemented
30#16811272C22164yescomplemented
31#16811238C22132yescomplemented
32#16811237C22164yescomplemented
33#16811168C22132yescomplemented
34C2×#13133216C2212yes—
35C2×#13133216C2212yes—
36C2×#13133215C2214yes—
37C2×#13133213C2212yes—
38#16811157C22116yescomplemented
39#16811154C22132yescomplemented
40C2×#13133211C2212yes—
41C2×#13133210C2214yes—
42C2×#13133209C2211yescharacteristic
43C2×#13133208C2212yes—
44C2×#13133205C2211yescharacteristic
45C2×#13133204C2212yes—
46C2×#13133204C2212yes—
47C2×#13133203C2214yes—
48C2×#13133203C2214yes—
49C2×#13133200C2214yes—
50C2×#13133200C2212yes—
51C2×#13133199C2214yes—
52C2×#13133198C2214yes—
53C2×#13133198C2214yes—
54C2×#13133197C2212yes—
55C2×#13133196C2214yes—
56C2×#13133196C2211yescharacteristic
57C2×#13133194C2214yes—
58C2×#13133194C2214yes—
59C2×#13133193C2214yes—
60C2×#13133191C2211yescharacteristic
61C2×#13133189C2214yes—
62C2×#13133189C2214yes—
63C2×#13133188C2212yes—
64#16811102C22132yescomplemented
65C2×C4×Dic106C2211yescharacteristic
66C2×C4×Dic106C2211yescharacteristic
67C2×C4×Dic106C2212yes—
68C2×C4×Dic106C2211yescharacteristic
69C2×C4×Dic106C2212yes—
70C2×C4×Dic106C2211yescharacteristic
71C2×C4×Dic106C2211yescharacteristic
72C2×C4×Dic106C22116yescomplemented
73C2×#13133182C2212yes—
74C2×#13133182C2212yes—
75C2×C4×D212C2211yescharacteristic
76C2×D4×Dic53C2212yes—
77C2×D4×Dic53C2212yes—
78C2×D4×Dic53C2214yes—
79C2×D4×Dic53C2212yes—
80C2×#13133179C2212yes—
81C2×C4×C22⋊D53C2214yes—
82C2×C4×C22⋊D53C2212yes—
83C2×#13133177C2214yes—
84C2×#13133174C2212yes—
85C2×#13133173C2214yes—
86C22×C4⋊Dic53C2211yescharacteristic
87C22×#11719919C2212yes—
88C22×#11719919C2214yes—
89C2×C4⋊C4×D53C2212yes—
90C22×C4×Dic53C2212yes—
91C22×#41×C53C2212yes—
92C53×#532C22116yescomplemented
93C2×C4⋊Q8×C53C2211yescharacteristic
94C2×#127×C53C2211yescharacteristic
95C2×#124×C53C2212yes—
96C2×#121×C53C2212yes—
97C2×#121×C53C2212yes—
98C2×C4×D4×C53C2212yes—
99C2×C4×D4×C53C2212yes—
100C22×C42×C53C2211yescharacteristic
101C2×#11719947—216no—
102C2×#11719947—416no—
103C2×#11719947C23116yes—
104C2×#11719947C23132yes—
105C22×Dic106—28no—
106C22×Dic106C2318yes—
107C22×Dic106C2311yescharacteristic
108C22×Dic106C2312yes—
109C22×Dic106C2311yescharacteristic
110C22×Dic106C2314yes—
111C22×Dic106C2311yescharacteristic
112C22×D212C2311yescharacteristic
113C22×C22⋊D53C2314yes—
114C22×C22⋊D53C2312yes—
115C22×C22⋊D53C2314yes—
116C23×Dic53C2312yes—
117C23×Dic53C2312yes—
118C23×Dic53C2314yes—
119C23×Dic53C2314yes—
120C22×C4×D53C2312yes—
121C22×C4×D53C2314yes—
122#13133216C23116yes—
123#13133216C23116yes—
124#13133215C23132yes—
125#13133213C23116yes—
126#13133211C23116yes—
127#13133210C23132yes—
128#13133209C2318yes—
129#13133208C23116yes—
130#13133205C2318yes—
131#13133204C23116yes—
132#13133204C23116yes—
133#13133203C23132yes—
134#13133203C23132yes—
135#13133200C23116yes—
136#13133200C23132yes—
137#13133199C23132yes—
138#13133198C23132yes—
139#13133198C23132yes—
140#13133197C23116yes—
141#13133196C23132yes—
142#13133196C2318yes—
143#13133194C23132yes—
144#13133194C23132yes—
145#13133193C23132yes—
146#13133191C2318yes—
147#13133189C23132yes—
148#13133189C23132yes—
149#13133188C23116yes—
150C4×Dic106C2318yes—
151C4×Dic106C23116yes—
152C4×Dic106C2318yes—
153C4×Dic106C2318yes—
154C4×Dic106C23116yes—
155C4×Dic106C2318yes—
156C4×Dic106C2318yes—
157#13133182C23116yes—
158#13133182C23116yes—
159C4×D212C2318yes—
160D4×Dic53C23132yes—
161D4×Dic53C23116yes—
162D4×Dic53C23116yes—
163D4×Dic53C23116yes—
164#13133179C23116yes—
165C4×C22⋊D53C23132yes—
166C4×C22⋊D53C23116yes—
167#13133177C23132yes—
168#13133174C23116yes—
169#13133173C23132yes—
170C2×C4⋊Dic53C2318yes—
171C2×C4⋊Dic53C2311yescharacteristic
172C2×C4⋊Dic53C2311yescharacteristic
173C2×C4⋊Dic53C2312yes—
174C2×C4⋊Dic53C2311yescharacteristic
175C2×C4⋊Dic53C2311yescharacteristic
176C2×C4⋊Dic53C2314yes—
177C2×#11719919C23116yes—
178C2×#11719919C23132yes—
179C2×#11719919C2314yes—
180C2×#11719919C2312yes—
181C2×#11719919C2312yes—
182C2×#11719919C2314yes—
183C2×#11719919C2312yes—
184C2×#11719919C2312yes—
185C2×#11719919C2312yes—
186C2×#11719919C2312yes—
187C2×#11719919C2312yes—
188C2×#11719919C2314yes—
189C2×#11719919C2312yes—
190C4⋊C4×D53C23116yes—
191C2×C22⋊Dic53C2314yes—
192C2×C22⋊Dic53C2312yes—
193C2×C22⋊Dic53C2314yes—
194C2×C22⋊Dic53C2314yes—
195C2×C22⋊Dic53C2314yes—
196C2×#11719921C2312yes—
197C2×#11719921C2312yes—
198C2×#11719921C2312yes—
199C2×#11719921C2314yes—
200C2×#11719921C2312yes—
201C2×C4×Dic53C2312yes—
202C2×C4×Dic53C2312yes—
203C2×C4×Dic53C2312yes—
204C2×C4×Dic53C2312yes—
205C2×C4×Dic53C23116yes—
206C2×C4×Dic53C2314yes—
207C2×C4×Dic53C2312yes—
208C2×#41×C53—48no—
209C2×#41×C53C23116yes—
210C22×Q8×C53C2312yes—
211C22×D4×C53C2312yes—
212C22×D4×C53C2312yes—
213C22×D4×C53C2314yes—
214C22×D4×C53C2312yes—
215C23×C4×C53C2311yescharacteristic
216C23×C4×C53C2311yescharacteristic
217C23×C4×C53C2311yescharacteristic
218C23×C4×C53C2314yes—
219C4⋊Q8×C53C2318yes—
220#127×C53C2318yes—
221#124×C53C23116yes—
222#121×C53C23116yes—
223#121×C53C23116yes—
224C4×D4×C53C23116yes—
225C4×D4×C53C23116yes—
226C2×C4⋊C4×C53C2312yes—
227C2×C4⋊C4×C53C2312yes—
228C2×C22⋊C4×C53C2314yes—
229C2×C22⋊C4×C53C2314yes—
230C2×C42×C53C2311yescharacteristic
231C2×C42×C53C2311yescharacteristic
232C2×C42×C53C2311yescharacteristic
233C2×C42×C53C2311yescharacteristic
234C2×C42×C53C2318yes—
235C24×C53C2414yes—
236C24×C53C2411yescharacteristic
237C23×D53C2412yes—
238#41×C53—432no—
239C2×Q8×C53—44no—
240C2×Q8×C53C2418yes—
241C2×D4×C53—216no—
242C2×D4×C53—28no—
243C2×D4×C53—28no—
244C2×D4×C53—44no—
245C2×D4×C53C2418yes—
246C2×D4×C53C2418yes—
247C2×D4×C53C24116yes—
248C2×D4×C53C2418yes—
249C22×C4×C53—24no—
250C22×C4×C53—24no—
251C22×C4×C53—24no—
252C22×C4×C53—48no—
253C22×C4×C53C2411yescharacteristic
254C22×C4×C53C2411yescharacteristic
255C22×C4×C53C2414yes—
256C22×C4×C53C2414yes—
257C22×C4×C53C2411yescharacteristic
258C22×C4×C53C2411yescharacteristic
259C22×C4×C53C2414yes—
260C22×C4×C53C2414yes—
261C22×C4×C53C24116yes—
262C22×C4×C53C2411yescharacteristic
263C22×C4×C53C2411yescharacteristic
264C2×C22⋊D53—28no—
265C2×C22⋊D53—216no—
266C2×C22⋊D53—48no—
267C2×C22⋊D53C24116yes—
268C2×C22⋊D53C2418yes—
269C2×C22⋊D53C24116yes—
270C22×Dic53—28no—
271C22×Dic53—28no—
272C22×Dic53—216no—
273C22×Dic53—48no—
274C22×Dic53C2412yes—
275C22×Dic53C2412yes—
276C22×Dic53C2412yes—
277C22×Dic53C2412yes—
278C22×Dic53C2418yes—
279C22×Dic53C2418yes—
280C22×Dic53C2412yes—
281C22×Dic53C2412yes—
282C22×Dic53C24116yes—
283C22×Dic53C24116yes—
284C22×Dic53C2412yes—
285#11719947—264no—
286#11719947—464no—
287C2×D212—24no—
288C2×D212C2414yes—
289C2×C4×D53—28no—
290C2×C4×D53—48no—
291C2×C4×D53C2418yes—
292C2×C4×D53C24116yes—
293C2×Dic106—24no—
294C2×Dic106—24no—
295C2×Dic106—28no—
296C2×Dic106—232no—
297C2×Dic106—48no—
298C2×Dic106#4118yescomplemented
299C2×Dic106C2414yes—
300C2×Dic106C2418yes—
301C2×Dic106C2414yes—
302C2×Dic106C24116yes—
303C2×Dic106C2414yes—
304C4⋊C4×C53C2418yes—
305C4⋊C4×C53C2418yes—
306C22⋊C4×C53C24116yes—
307C22⋊C4×C53C24116yes—
308C42×C53C2414yes—
309C42×C53C2414yes—
310C42×C53C2414yes—
311C42×C53C2414yes—
312C22⋊Dic53C24116yes—
313C22⋊Dic53C2418yes—
314C22⋊Dic53C24116yes—
315C22⋊Dic53C24116yes—
316C22⋊Dic53C24116yes—
317#11719921C2418yes—
318#11719921C2418yes—
319#11719921C2418yes—
320#11719921C24116yes—
321#11719921C2418yes—
322C4⋊Dic53C2414yes—
323C4⋊Dic53C2414yes—
324C4⋊Dic53C2418yes—
325C4⋊Dic53C2414yes—
326C4⋊Dic53C2414yes—
327C4⋊Dic53C24116yes—
328#11719919C24116yes—
329#11719919C2418yes—
330#11719919C2418yes—
331#11719919C24116yes—
332#11719919C2418yes—
333#11719919C2418yes—
334#11719919C2418yes—
335#11719919C2418yes—
336#11719919C2418yes—
337#11719919C24116yes—
338#11719919C2418yes—
339C4×Dic53C2418yes—
340C4×Dic53C2418yes—
341C4×Dic53C2418yes—
342C4×Dic53C2418yes—
343C4×Dic53C24116yes—
344C4×Dic53C2418yes—
345C23×C53—22no—
346C23×C53—22no—
347C23×C53—28no—
348C23×C53—28no—
349C23×C53—28no—
350C23×C53H(5,𝔽2)14yes—
351C23×C53C2518yes—
352C23×C53C2512yes—
353C23×C53C2511yescharacteristic
354C22×D53—24no—
355C22×D53—24no—
356C22×D53—24no—
357C22×D53C2514yes—
358Q8×C53—48no—
359D4×C53—232no—
360D4×C53—216no—
361D4×C53—216no—
362D4×C53—48no—
363C2×C4×C53—22no—
364C2×C4×C53—28no—
365C2×C4×C53—22no—
366C2×C4×C53—22no—
367C2×C4×C53—28no—
368C2×C4×C53—22no—
369C2×C4×C53—28no—
370C2×C4×C53—28no—
371C2×C4×C53—416no—
372C2×C4×C53C2×#4114yes—
373C2×C4×C532−1+414yes—
374C2×C4×C53C2512yes—
375C2×C4×C53C2518yes—
376C2×C4×C53C2512yes—
377C2×C4×C53C2512yes—
378C2×C4×C53C2512yes—
379C2×C4×C53C2512yes—
380C2×C4×C53C2512yes—
381C22⋊D53—216no—
382C22⋊D53—232no—
383C22⋊D53—416no—
384C2×Dic53—24no—
385C2×Dic53—24no—
386C2×Dic53—24no—
387C2×Dic53—24no—
388C2×Dic53—24no—
389C2×Dic53—216no—
390C2×Dic53—24no—
391C2×Dic53—216no—
392C2×Dic53—232no—
393C2×Dic53—416no—
394C2×Dic53C2×#4118yes—
395C2×Dic53C2514yes—
396C2×Dic53C2514yes—
397C2×Dic53C2514yes—
398C2×Dic53C2514yes—
399C2×Dic53C2514yes—
400C2×Dic53C2514yes—
401C2×Dic53C2514yes—
402D212—28no—
403C4×D53—216no—
404C4×D53—416no—
405Dic106—28no—
406Dic106—28no—
407Dic106—216no—
408Dic106—416no—
409Dic106C2×#41116yescomplemented
410C2×#3522—531nomaximal, Sylow
411C22×C53—22no—
412C22×C53—22no—
413C22×C53—28no—
414C22×C53—28no—
415C22×C53—28no—
416C22×C53—28no—
417C22×C53—416no—
418C22×C53C22×#4112yes—
419C22×C53C2×H(5,𝔽2)14yes—
420C22×C53C2×H(5,𝔽2)12yes—
421C22×C53C2×2−1+412yes—
422C22×C53C2611yescharacteristic
423C2×D53—24no—
424C2×D53—24no—
425C2×D53—24no—
426C2×D53—48no—
427C4×C53—22no—
428C4×C53—28no—
429C4×C53—22no—
430C4×C53—22no—
431C4×C53—22no—
432C4×C53C22×#4114yes—
433C4×C53C2×2−1+414yes—
434Dic53—24no—
435Dic53—24no—
436Dic53—24no—
437Dic53—24no—
438Dic53—24no—
439Dic53—24no—
440Dic53C22×#4118yes—
441#3522—5332no—
442C2×#559—531no—
443C2×#559—532no—
444C2×Q82—531no—
445C2×#554—531no—
446C2×#554—532no—
447C2×#550—531no—
448C2×#548—532no—
449C2×#547—534no—
450C2×#547—532no—
451C2×#542—534no—
452C2×#542—532no—
453C2×#532—532no—
454C2×#532D5311yescharacteristic, complemented
455C2×#529—531no—
456C2×#529—532no—
457C2×#520—532no—
458C22×C4×Q8—531no—
459C2×C53—24no—
460C2×C53—48no—
461C2×C53#352214yescomplemented
462C2×C53C23×#4111yescharacteristic
463C2×C53C22×H(5,𝔽2)11yescharacteristic
464C2×C53C22×2−1+411yescharacteristic
465D53—44no—
466C22×#41—532no—
467C22×#41—534no—
468C22×#41C2×D5312yes—
469C23×Q8—531no—
470#559—5316no—
471#559—5332no—
472Q82—5316no—
473#554—5316no—
474#554—5332no—
475#550—5316no—
476#548—5332no—
477#547—5364no—
478#547—5332no—
479#542—5364no—
480#542—5332no—
481#532—5332no—
482#532C2×D53116yescomplemented
483C2×C4⋊Q8—534no—
484C2×C4⋊Q8—532no—
485C2×C4⋊Q8—532no—
486C2×C4⋊Q8C2×D5311yescharacteristic
487C2×#127—532no—
488C2×#127C2×D5311yescharacteristic
489#529—5332no—
490#529—5316no—
491C2×#126—534no—
492C2×#126—532no—
493C2×#125—532no—
494C2×#125—531no—
495C2×#124—532no—
496C2×#124—532no—
497C2×#124—534no—
498C2×#124—534no—
499C2×#124—531no—
500C2×#124C2×D5312yes—
501C2×#123—534no—
502C2×#123—534no—
503C2×#123—532no—
504C2×#123—534no—
505C2×#123—534no—
506C2×C22⋊Q8—534no—
507C2×C22⋊Q8—531no—
508C2×C22⋊Q8—534no—
509C2×C22⋊Q8—532no—
510C2×C22⋊Q8—534no—
511C2×C22⋊Q8—534no—
512C2×#121—532no—
513C2×#121—534no—
514C2×#121—534no—
515C2×#121—531no—
516C2×#121C2×D5312yes—
517C2×#121C2×D5312yes—
518#520—5332no—
519C2×C4×Q8—532no—
520C2×C4×Q8—532no—
521C2×C4×Q8—531no—
522C2×C4×Q8—532no—
523C2×C4×Q8—531no—
524C2×C4×Q8—531no—
525C2×C4×Q8—531no—
526C2×C4×Q8—532no—
527C2×C4×Q8—531no—
528C2×C4×Q8—5316no—
529C2×C4×D4—532no—
530C2×C4×D4—534no—
531C2×C4×D4—532no—
532C2×C4×D4—532no—
533C2×C4×D4—534no—
534C2×C4×D4—532no—
535C2×C4×D4—532no—
536C2×C4×D4—534no—
537C2×C4×D4—531no—
538C2×C4×D4C2×D5312yes—
539C2×C4×D4C2×D5312yes—
540C2×#117—534no—
541C2×#117—532no—
542C22×C4⋊C4—532no—
543C22×C4⋊C4—534no—
544C22×C4⋊C4—531no—
545C22×C4⋊C4—532no—
546C22×C42—532no—
547C22×C42C2×D5311yescharacteristic
548C53C2×#352211yescharacteristic, complemented, Sylow
549C2×#41—48no—
550C2×#41—5316no—
551C2×#41—5332no—
552C2×#41—10616no—
553C2×#41—21216no—
554C2×#41C22×D53116yes—
555C22×Q8—531no—
556C22×Q8—531no—
557C22×Q8—532no—
558C22×Q8—531no—
559C22×Q8—538no—
560C22×Q8—534no—
561C22×Q8—1068no—
562C22×Q8C22×D5312yes—
563C22×D4—534no—
564C22×D4—532no—
565C22×D4—534no—
566C22×D4—531no—
567C22×D4C22×D5312yes—
568C22×D4C22×D5312yes—
569C22×D4C22×D5314yes—
570C22×D4C22×D5312yes—
571C23×C4—532no—
572C23×C4—534no—
573C23×C4—532no—
574C23×C4—534no—
575C23×C4—532no—
576C23×C4—534no—
577C23×C4C22×D5311yescharacteristic
578C23×C4C22×D5311yescharacteristic
579C23×C4C22×D5311yescharacteristic
580C23×C4C22×D5314yes—
581C4⋊Q8—5332no—
582C4⋊Q8—5316no—
583C4⋊Q8—5316no—
584C4⋊Q8C22×D5318yes—
585#127—5316no—
586#127C22×D5318yes—
587#126—5332no—
588#126—5316no—
589#125—5316no—
590#125—538no—
591#124—5316no—
592#124—5316no—
593#124—5332no—
594#124—5332no—
595#124—538no—
596#124C22×D53116yes—
597#123—5332no—
598#123—5332no—
599#123—5316no—
600#123—5332no—
601#123—5332no—
602C22⋊Q8—5332no—
603C22⋊Q8—538no—
604C22⋊Q8—5332no—
605C22⋊Q8—5316no—
606C22⋊Q8—5332no—
607C22⋊Q8—5332no—
608#121—5332no—
609#121—5316no—
610#121—5332no—
611#121—538no—
612#121C22×D53116yes—
613#121C22×D53116yes—
614C4×Q8—5316no—
615C4×Q8—5316no—
616C4×Q8—538no—
617C4×Q8—5316no—
618C4×Q8—538no—
619C4×Q8—538no—
620C4×Q8—538no—
621C4×Q8—5316no—
622C4×Q8—538no—
623C4×D4—5316no—
624C4×D4—5332no—
625C4×D4—5316no—
626C4×D4—5316no—
627C4×D4—5332no—
628C4×D4—5316no—
629C4×D4—5316no—
630C4×D4—5332no—
631C4×D4—538no—
632C4×D4C22×D53116yes—
633C4×D4C22×D53116yes—
634#117—5332no—
635#117—5316no—
636C2×C4⋊C4—532no—
637C2×C4⋊C4—531no—
638C2×C4⋊C4—534no—
639C2×C4⋊C4—532no—
640C2×C4⋊C4—534no—
641C2×C4⋊C4—532no—
642C2×C4⋊C4—531no—
643C2×C4⋊C4—532no—
644C2×C4⋊C4—532no—
645C2×C4⋊C4—532no—
646C2×C4⋊C4—5316no—
647C2×C4⋊C4—538no—
648C2×C4⋊C4—5332no—
649C2×C4⋊C4—532no—
650C2×C4⋊C4—531no—
651C2×C4⋊C4—531no—
652C2×C4⋊C4—532no—
653C2×C4⋊C4—534no—
654C2×C4⋊C4—534no—
655C2×C4⋊C4—532no—
656C2×C4⋊C4—5316no—
657C2×C4⋊C4C22×D5312yes—
658C2×C4⋊C4C22×D5312yes—
659C2×C22⋊C4—534no—
660C2×C22⋊C4—532no—
661C2×C22⋊C4—534no—
662C2×C22⋊C4—534no—
663C2×C22⋊C4—534no—
664C2×C22⋊C4—532no—
665C2×C22⋊C4—532no—
666C2×C22⋊C4—532no—
667C2×C22⋊C4—534no—
668C2×C22⋊C4—532no—
669C2×C22⋊C4C22×D5314yes—
670C2×C22⋊C4C22×D5314yes—
671C2×C42—532no—
672C2×C42—534no—
673C2×C42—532no—
674C2×C42—532no—
675C2×C42—532no—
676C2×C42—532no—
677C2×C42—5316no—
678C2×C42C22×D5311yescharacteristic
679C2×C42C22×D5311yescharacteristic
680C2×C42C22×D5311yescharacteristic
681C2×C42C22×D5311yescharacteristic
682C2×C42C22×D5318yes—
683C24—532no—
684C24C23×D5314yes—
685C24C23×D5311yescharacteristic
686#41—432no—
687#41—10664no—
688#41—21264no—
689C2×Q8—44no—
690C2×Q8—538no—
691C2×Q8—534no—
692C2×Q8—534no—
693C2×Q8—538no—
694C2×Q8—534no—
695C2×Q8—5316no—
696C2×Q8—1068no—
697C2×Q8—10632no—
698C2×Q8—1064no—
699C2×Q8—1064no—
700C2×Q8—2128no—
701C2×Q8C23×D5318yes—
702C2×D4—216no—
703C2×D4—28no—
704C2×D4—28no—
705C2×D4—44no—
706C2×D4—5316no—
707C2×D4—538no—
708C2×D4—5316no—
709C2×D4—534no—
710C2×D4—10616no—
711C2×D4—1068no—
712C2×D4—1064no—
713C2×D4—2128no—
714C2×D4C23×D5318yes—
715C2×D4C23×D5318yes—
716C2×D4C23×D53116yes—
717C2×D4C23×D5318yes—
718C22×C4—24no—
719C22×C4—24no—
720C22×C4—24no—
721C22×C4—48no—
722C22×C4—532no—
723C22×C4—538no—
724C22×C4—538no—
725C22×C4—5316no—
726C22×C4—532no—
727C22×C4—532no—
728C22×C4—532no—
729C22×C4—532no—
730C22×C4—532no—
731C22×C4—532no—
732C22×C4—5316no—
733C22×C4—538no—
734C22×C4—5316no—
735C22×C4—1068no—
736C22×C4—10616no—
737C22×C4—1068no—
738C22×C4—1068no—
739C22×C4—2128no—
740C22×C4—2128no—
741C22×C4C23×D5314yes—
742C22×C4C23×D5314yes—
743C22×C4C23×D5314yes—
744C22×C4C23×D5311yescharacteristic
745C22×C4C23×D5314yes—
746C22×C4C23×D5311yescharacteristic
747C22×C4C23×D5311yescharacteristic
748C22×C4C23×D5311yescharacteristic
749C22×C4C23×D53116yes—
750C22×C4C23×D5311yescharacteristic
751C22×C4C23×D5311yescharacteristic
752C4⋊C4—538no—
753C4⋊C4—534no—
754C4⋊C4—5316no—
755C4⋊C4—538no—
756C4⋊C4—5316no—
757C4⋊C4—538no—
758C4⋊C4—534no—
759C4⋊C4—538no—
760C4⋊C4—538no—
761C4⋊C4—538no—
762C4⋊C4—538no—
763C4⋊C4—534no—
764C4⋊C4—534no—
765C4⋊C4—538no—
766C4⋊C4—5316no—
767C4⋊C4—5316no—
768C4⋊C4—538no—
769C4⋊C4C23×D5318yes—
770C4⋊C4C23×D5318yes—
771C22⋊C4—5316no—
772C22⋊C4—538no—
773C22⋊C4—5316no—
774C22⋊C4—5316no—
775C22⋊C4—5316no—
776C22⋊C4—538no—
777C22⋊C4—538no—
778C22⋊C4—538no—
779C22⋊C4—5316no—
780C22⋊C4—538no—
781C22⋊C4C23×D53116yes—
782C22⋊C4C23×D53116yes—
783C42—538no—
784C42—538no—
785C42—538no—
786C42—538no—
787C42—5316no—
788C42—538no—
789C42C23×D5314yes—
790C42C23×D5314yes—
791C42C23×D5314yes—
792C42C23×D5314yes—
793C23—22no—
794C23—22no—
795C23—28no—
796C23—28no—
797C23—28no—
798C23—534no—
799C23—1064no—
800C23—1064no—
801C23—1064no—
802C23#1313326214yes—
803C23C24×D5318yes—
804C23C24×D5312yes—
805C23C24×D5311yescharacteristic
806Q8—48no—
807Q8—5316no—
808Q8—10616no—
809Q8—1068no—
810Q8—1068no—
811Q8—21216no—
812D4—232no—
813D4—216no—
814D4—216no—
815D4—48no—
816D4—10632no—
817D4—10616no—
818D4—1068no—
819D4—21216no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—28no—
824C2×C4—28no—
825C2×C4—22no—
826C2×C4—28no—
827C2×C4—28no—
828C2×C4—416no—
829C2×C4—538no—
830C2×C4—534no—
831C2×C4—534no—
832C2×C4—534no—
833C2×C4—534no—
834C2×C4—534no—
835C2×C4—534no—
836C2×C4—534no—
837C2×C4—10616no—
838C2×C4—10632no—
839C2×C4—1064no—
840C2×C4—1064no—
841C2×C4—1064no—
842C2×C4—1064no—
843C2×C4—10616no—
844C2×C4—1064no—
845C2×C4—1064no—
846C2×C4—10616no—
847C2×C4—21216no—
848C2×C4—21216no—
849C2×C4#41×D5314yes—
850C2×C4#1313326414yes—
851C2×C4C24×D5312yes—
852C2×C4C24×D5318yes—
853C2×C4C24×D5312yes—
854C2×C4C24×D5312yes—
855C2×C4C24×D5312yes—
856C2×C4C24×D5312yes—
857C2×C4C24×D5312yes—
858C22—28no—
859C22—22no—
860C22—22no—
861C22—28no—
862C22—28no—
863C22—28no—
864C22—416no—
865C22—1064no—
866C22—1064no—
867C22—1064no—
868C22—2128no—
869C22C2×#41×D5312yes—
870C22C2×#1313326214yes—
871C22C2×#1313326212yes—
872C22C2×#1313326412yes—
873C22C25×D5311yescharacteristic
874C4—22no—
875C4—22no—
876C4—22no—
877C4—28no—
878C4—22no—
879C4—538no—
880C4—1064no—
881C4—1064no—
882C4—1064no—
883C4—1064no—
884C4—1064no—
885C4—1064no—
886C4C2×#41×D5314yes—
887C4C2×#1313326414yes—
888C2—24no—
889C2—48no—
890C2—2124no—
891C2#2028879214yesdirect product factor
892C2C22×#41×D5311yescharacteristic
893C2C22×#1313326211yescharacteristic
894C2C22×#1313326411yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#532C2
socleC23×C53C25
hypercenterC2×#532D53
hypocenterC53C2×#3522
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #20288792C2direct (N × H)
2. C2×#16811359C2semidirect
3. C2×#16811356C2semidirect
4. C2×#16811353C2semidirect
5. C2×#16811334C2semidirect
6. C2×#16811332C2semidirect
7. C2×#16811293C2semidirect
8. C2×#16811279C2semidirect
9. C2×#16811273C2semidirect
10. C2×#16811272C2semidirect
11. C2×#16811238C2semidirect
12. C2×#16811237C2semidirect
13. C2×#16811168C2semidirect
14. C2×#16811157C2semidirect
15. C2×#16811154C2semidirect
16. C2×#16811102C2semidirect
17. C22×C4×Dic106C2semidirect
18. C2×C53×#532C2semidirect
22. #16811359C22semidirect
23. #16811356C22semidirect
24. #16811353C22semidirect
25. #16811334C22semidirect
26. #16811332C22semidirect
27. #16811293C22semidirect
28. #16811279C22semidirect
29. #16811273C22semidirect
30. #16811272C22semidirect
31. #16811238C22semidirect
32. #16811237C22semidirect
33. #16811168C22semidirect
38. #16811157C22semidirect
39. #16811154C22semidirect
64. #16811102C22semidirect
72. C2×C4×Dic106C22semidirect
92. C53×#532C22semidirect
298. C2×Dic106#41semidirect
409. Dic106C2×#41semidirect
454. C2×#532D53semidirect
461. C2×C53#3522semidirect
482. #532C2×D53semidirect
548. C53C2×#3522semidirect
891. C2#20288792direct (N × H)

Maximal subgroups

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

subgroupindex
#202887922
C2×#168113592
C2×#168113562
C2×#168113532
C2×#168113342
C2×#168113322
C2×#168112932
C2×#168112792
C2×#168112732
C2×#168112722
C2×#168112382
C2×#168112372
C2×#168111682
C2×#168111572
C2×#168111542
C2×#168111022
C22×C4×Dic1062
C2×C53×#5322
C2×#352253