Finite Group Databasebeta

← #28293019

Subgroups — #28293019

Order 13568.

7148 conjugacy classes of subgroups.

The subgroup lattice has 1352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289287C214yesmaximal, complemented
2#20289253C214yesmaximal, complemented
3#20289180C214yesmaximal, complemented
4#20289129C212yesmaximal, complemented
5#20289113C212yesmaximal, complemented
6#20289104C214yesmaximal, complemented
7#20288937C214yesmaximal, complemented
8#20288792C214yesmaximal, complemented
9#20288764C214yesmaximal, complemented
10#20288622C212yesmaximal, complemented
11#20288616C214yesmaximal, complemented
12#20288589C212yesmaximal, complemented
13#20288577C212yesmaximal, complemented
14#20288567C212yesmaximal, complemented
15#20288531C212yesmaximal, complemented
16#20288518C212yesmaximal, complemented
17#20288495C212yesmaximal, complemented
18#20288481C212yesmaximal, complemented
19#20288444C214yesmaximal, complemented
20#20288395C214yesmaximal, complemented
21#20288011C211yesmaximal, characteristic, complemented
22C2×#16811180C211yesmaximal, characteristic, complemented
23C2×C53×#532C211yesmaximal, characteristic, complemented
24C2×#13133264C2214yescomplemented
25#16811373C2218yescomplemented
26#16811368C22116yescomplemented
27#16811367C2218yescomplemented
28#16811359C2214yescomplemented
29#16811359C2214yescomplemented
30#16811356C2218yescomplemented
31#16811353C2214yescomplemented
32#16811348C2214yescomplemented
33#16811343C2214yescomplemented
34#16811343C2214yescomplemented
35#16811342C2218yescomplemented
36#16811338C2214yescomplemented
37#16811337C2218yescomplemented
38#16811334C2214yescomplemented
39#16811332C2218yescomplemented
40#16811332C2218yescomplemented
41#16811330C2214yescomplemented
42#16811330C2214yescomplemented
43#16811328C2218yes—
44#16811325C2218yescomplemented
45#16811323C2218yescomplemented
46#16811320C2218yescomplemented
47#16811313C2218yescomplemented
48#16811299C22116yes—
49#16811294C2214yescomplemented
50#16811293C2214yescomplemented
51#16811293C2214yescomplemented
52D4×Dic106C2214yescomplemented
53D4×Dic106C2214yescomplemented
54D4×Dic106C2214yescomplemented
55#16811288C2214yescomplemented
56Q8×C22⋊D53C2218yes—
57#16811282C2218yescomplemented
58#16811281C2218yescomplemented
59#16811280C2218yescomplemented
60#16811279C2218yescomplemented
61#16811278C2214yescomplemented
62#16811278C2214yescomplemented
63#16811277C2214yescomplemented
64#16811273C2218yescomplemented
65#16811273C2218yescomplemented
66#16811272C22116yescomplemented
67#16811272C2218yescomplemented
68#16811267C2218yes—
69#16811267C2218yes—
70#16811267C22116yes—
71#16811254C2214yes—
72#16811250C2218yescomplemented
73#16811249C2218yes—
74#16811242C2218yescomplemented
75#16811240C2218yescomplemented
76#16811240C2218yescomplemented
77#16811238C2218yescomplemented
78#16811237C22116yescomplemented
79#16811227C2218yescomplemented
80#16811226C2218yescomplemented
81#16811218C2218yescomplemented
82#16811215C22116yescomplemented
83#16811211C2218yes—
84#16811202C2218yescomplemented
85#16811201C2218yescomplemented
86#16811201C2214yescomplemented
87#16811200C2218yescomplemented
88#16811194C2214yescomplemented
89#16811194C2218yescomplemented
90#16811193C2218yescomplemented
91#16811190C2214yes—
92#16811180C2212yes—
93#16811180C2212yes—
94#16811180C2212yes—
95#16811180C2212yes—
96#16811180C2211yescharacteristic
97#16811180C2212yescomplemented
98#16811180C2212yescomplemented
99#16811180C2212yescomplemented
100#16811180C2212yescomplemented
101#16811180C2211yescharacteristic, complemented
102#16811180C2211yescharacteristic, complemented
103#16811178C2214yescomplemented
104#16811173C2211yescharacteristic
105#16811173C2211yescharacteristic, complemented
106#16811173C2211yescharacteristic, complemented
107#16811171C2214yescomplemented
108#16811171C2214yescomplemented
109#16811168C2218yescomplemented
110C2×#13133217C2211yescharacteristic, complemented
111C2×#13133217C2211yescharacteristic, complemented
112C4⋊Q8×D53C2214yescomplemented
113#16811157C2212yes—
114#16811157C2212yes—
115#16811157C2212yescomplemented
116#16811157C2212yescomplemented
117#16811157C2212yescomplemented
118#16811157C2212yescomplemented
119#16811154C2218yescomplemented
120C2×#13133209C2212yescomplemented
121#16811134C2212yes—
122#16811134C2212yes—
123#16811134C2212yes—
124#16811134C2218yes—
125C2×#13133196C2212yes—
126C2×#13133196C2212yes—
127C2×#13133196C2218yes—
128#16811106C2214yescomplemented
129#16811104C2214yes—
130#16811102C2218yescomplemented
131#16811098C2214yes—
132C4×#11719945C2212yes—
133C4×#11719945C2212yescomplemented
134C4×#11719945C2212yescomplemented
135C2×C4×Dic106C2212yescomplemented
136C2×C4×Dic106C2212yescomplemented
137C2×#13133176C2212yes—
138C22×#41×C53C2212yes—
139C53×#532C2212yes—
140C53×#532C2212yes—
141C53×#532C2212yes—
142C53×#532C2212yes—
143C53×#532C2212yes—
144C53×#532C2212yes—
145C53×#532C2212yes—
146C53×#532C2212yes—
147C2×C4⋊Q8×C53C2211yescharacteristic
148C2×#127×C53C2211yescharacteristic
149C2×#124×C53C2212yes—
150C2×#121×C53C2212yes—
151C2×#121×C53C2212yes—
152C2×C4×D4×C53C2212yes—
153C2×C4×D4×C53C2212yes—
154C22×C42×C53C2211yescharacteristic
155#13133264—416no—
156C2×#11719945C2312yes—
157C2×#11719945C2312yes—
158C2×#11719945C2318yes—
159C2×#11719945C2312yes—
160C2×#11719947C23116yes—
161C2×#11719947C2318yes—
162C2×#11719947C2318yes—
163C22×Dic106C2312yes—
164C22×Dic106C2312yes—
165C22×Dic106C2318yes—
166C2×Q8×D53C2318yes—
167#13133217C2312yes—
168#13133217C2312yes—
169#13133217C2312yes—
170#13133217C2311yescharacteristic
171#13133217C2311yescharacteristic
172#13133217C2312yes—
173#13133217C2311yescharacteristic
174#13133217C2312yes—
175#13133217C2312yes—
176#13133217C2312yes—
177#13133217C2312yes—
178#13133216C2318yes—
179#13133216C2318yes—
180#13133216C2318yes—
181#13133215C2318yes—
182#13133215C23116yes—
183#13133214C2311yescharacteristic
184#13133213C2318yes—
185#13133211C2314yes—
186#13133211C2314yes—
187#13133210C23116yes—
188#13133210C23116yes—
189#13133210C23116yes—
190#13133209C2312yes—
191#13133209C2314yes—
192#13133209C2312yes—
193#13133209C2314yes—
194#13133209C2312yes—
195#13133209C2314yes—
196#13133209C2314yes—
197#13133208C2318yes—
198#13133208C2318yes—
199#13133207C23116yes—
200#13133205C2312yes—
201#13133205C2312yes—
202#13133205C2312yes—
203#13133204C2318yes—
204#13133204C23116yes—
205#13133204C2318yes—
206#13133204C2318yes—
207#13133203C23116yes—
208#13133203C23116yes—
209#13133201C23116yes—
210#13133200C2314yes—
211#13133200C23116yes—
212#13133200C2314yes—
213#13133200C2314yes—
214#13133199C23116yes—
215#13133199C23116yes—
216#13133198C23116yes—
217#13133198C23116yes—
218#13133198C23116yes—
219#13133198C23116yes—
220#13133197C2318yes—
221#13133196C2314yes—
222#13133196C2314yes—
223#13133196C23116yes—
224#13133196C2314yes—
225#13133196C23116yes—
226#13133196C2318yes—
227#13133196C2318yes—
228#13133196C2318yes—
229#13133196C2314yes—
230#13133196C2312yes—
231#13133196C2314yes—
232#13133196C2314yes—
233#13133196C2314yes—
234#13133196C2314yes—
235#13133196C2312yes—
236#13133196C2312yes—
237#13133196C2312yes—
238#13133196C2312yes—
239#13133196C2312yes—
240#13133195C23116yes—
241#13133194C23116yes—
242#13133194C23116yes—
243#13133194C23116yes—
244#13133194C23116yes—
245#13133194C23116yes—
246#13133193C2318yes—
247#13133193C23116yes—
248#13133191C2318yes—
249#13133191C2312yes—
250#13133191C2312yes—
251#13133191C2312yes—
252#13133191C2312yes—
253#13133191C2312yes—
254#13133191C2312yes—
255#13133190C23116yes—
256#13133189C23116yes—
257#13133189C23116yes—
258#13133189C23116yes—
259#13133189C23116yes—
260#13133188C2318yes—
261#13133188C2318yes—
262#13133188C23116yes—
263#13133188C2318yes—
264#13133188C2318yes—
265#13133186C2314yes—
266#13133186C23116yes—
267Q8×Dic53C2318yes—
268C4×Dic106C2314yes—
269C4×Dic106C2314yes—
270C4×Dic106C2314yes—
271C4×Dic106C2312yes—
272C4×Dic106C2312yes—
273C4×Dic106C2314yes—
274C4×Dic106C2314yes—
275C4×Dic106C2312yes—
276C4×Dic106C2314yes—
277C4×Dic106C2312yes—
278C4×Dic106C2314yes—
279C4×Dic106C2314yes—
280C4×Dic106C2312yes—
281C4×Dic106C2312yes—
282#13133182C2318yes—
283#13133182C2318yes—
284C4×D212C2312yes—
285C4×D212C2312yes—
286C4×D212C2312yes—
287C4×D212C2312yes—
288C4×D212C2312yes—
289C4×D212C2312yes—
290D4×Dic53C23116yes—
291D4×Dic53C2318yes—
292D4×Dic53C2318yes—
293D4×Dic53C2318yes—
294D4×Dic53C2318yes—
295D4×Dic53C2318yes—
296D4×Dic53C2318yes—
297#13133179C2318yes—
298C4×C22⋊D53C2314yes—
299C4×C22⋊D53C2314yes—
300C4×C22⋊D53C23116yes—
301C4×C22⋊D53C2314yes—
302C4×C22⋊D53C23116yes—
303C4×C22⋊D53C2314yes—
304C4×C22⋊D53C2314yes—
305C4×C22⋊D53C2314yes—
306#13133177C23116yes—
307#13133176C2314yes—
308#13133176C2318yes—
309#13133176C2314yes—
310#13133176C2314yes—
311#13133176C2314yes—
312#13133176C2312yes—
313#13133176C2312yes—
314#13133176C2312yes—
315#13133175C2318yes—
316#13133174C2314yes—
317#13133174C2314yes—
318#13133174C2314yes—
319#13133173C23116yes—
320C2×C4⋊Dic53C2312yes—
321C2×C4⋊Dic53C2312yes—
322C2×C4⋊Dic53C2318yes—
323C2×C4⋊Dic53C2312yes—
324C2×C4⋊Dic53C2312yes—
325C2×#11719919C2314yes—
326C2×#11719919C23116yes—
327C2×#11719919C2314yes—
328C4⋊C4×D53C2318yes—
329C4⋊C4×D53C2318yes—
330C2×C22⋊Dic53C2314yes—
331C2×C22⋊Dic53C23116yes—
332C2×C4×Dic53C2314yes—
333C42×D53C2314yes—
334C2×#41×C53—48no—
335C2×#41×C53C2314yes—
336C2×#41×C53C2314yes—
337C2×#41×C53C2314yes—
338C2×#41×C53C2314yes—
339C22×Q8×C53C2312yes—
340C22×D4×C53C2312yes—
341C22×D4×C53C2312yes—
342C22×D4×C53C2314yes—
343C22×D4×C53C2312yes—
344C23×C4×C53C2311yescharacteristic
345C23×C4×C53C2311yescharacteristic
346C23×C4×C53C2311yescharacteristic
347C23×C4×C53C2314yes—
348C4⋊Q8×C53C2312yes—
349C4⋊Q8×C53C2312yes—
350C4⋊Q8×C53C2312yes—
351C4⋊Q8×C53C2312yes—
352#127×C53C2312yes—
353#127×C53C2312yes—
354#127×C53C2312yes—
355#127×C53C2312yes—
356#124×C53C2314yes—
357#124×C53C2314yes—
358#124×C53C2314yes—
359#124×C53C2314yes—
360#121×C53C2314yes—
361#121×C53C2314yes—
362#121×C53C2314yes—
363#121×C53C2314yes—
364#121×C53C2314yes—
365#121×C53C2314yes—
366#121×C53C2314yes—
367#121×C53C2314yes—
368C4×D4×C53C2314yes—
369C4×D4×C53C2314yes—
370C4×D4×C53C2314yes—
371C4×D4×C53C2314yes—
372C4×D4×C53C2314yes—
373C4×D4×C53C2314yes—
374C4×D4×C53C2314yes—
375C4×D4×C53C2314yes—
376C2×C4⋊C4×C53C2312yes—
377C2×C4⋊C4×C53C2312yes—
378C2×C22⋊C4×C53C2314yes—
379C2×C22⋊C4×C53C2314yes—
380C2×C42×C53C2311yescharacteristic
381C2×C42×C53C2311yescharacteristic
382C2×C42×C53C2311yescharacteristic
383C2×C42×C53C2311yescharacteristic
384C2×C42×C53C2311yescharacteristic
385C2×C42×C53C2311yescharacteristic
386C2×C42×C53C2311yescharacteristic
387C2×C42×C53C2311yescharacteristic
388C2×C42×C53C2311yescharacteristic
389C2×C42×C53C2311yescharacteristic
390C2×C42×C53C2311yescharacteristic
391C2×C42×C53C2311yescharacteristic
392C24×C53C2411yescharacteristic
393C24×C53C2414yes—
394#41×C53—216no—
395#41×C53—48no—
396#41×C53—48no—
397#41×C53—48no—
398C2×Q8×C53—44no—
399C2×Q8×C53C2414yes—
400C2×Q8×C53C2414yes—
401C2×D4×C53—28no—
402C2×D4×C53—44no—
403C2×D4×C53—44no—
404C2×D4×C53—48no—
405C2×D4×C53C2414yes—
406C2×D4×C53C2414yes—
407C2×D4×C53C2414yes—
408C2×D4×C53C2418yes—
409C2×D4×C53C2414yes—
410C2×D4×C53C2414yes—
411C2×D4×C53C2418yes—
412C2×D4×C53C2414yes—
413C22×C4×C53—24no—
414C22×C4×C53—24no—
415C22×C4×C53—42no—
416C22×C4×C53—48no—
417C22×C4×C53C2411yescharacteristic
418C22×C4×C53C2411yescharacteristic
419C22×C4×C53C2411yescharacteristic
420C22×C4×C53C2411yescharacteristic
421C22×C4×C53C2411yescharacteristic
422C22×C4×C53C2411yescharacteristic
423C22×C4×C53C2411yescharacteristic
424C22×C4×C53C2411yescharacteristic
425C22×C4×C53C2411yescharacteristic
426C22×C4×C53C2411yescharacteristic
427C22×C4×C53C2411yescharacteristic
428C22×C4×C53C2411yescharacteristic
429C22×C4×C53C2411yescharacteristic
430C22×C4×C53C2418yes—
431C22×C4×C53C2411yescharacteristic
432C22×C4×C53C2411yescharacteristic
433C22×C4×C53C2411yescharacteristic
434C22×C4×C53C2414yes—
435C22×C4×C53C2418yes—
436C22×C4×C53C2411yescharacteristic
437C22×C4×C53C2411yescharacteristic
438C2×C22⋊D53C2414yes—
439C2×C22⋊D53C2414yes—
440C2×C22⋊D53C24116yes—
441C2×C22⋊D53C2414yes—
442C2×C22⋊D53C24116yes—
443C22×Dic53C2414yes—
444C22×Dic53C2414yes—
445C22×Dic53C24116yes—
446C22×Dic53C24116yes—
447Q8×D53—416no—
448#11719947—416no—
449#11719947—416no—
450#11719947—432no—
451#11719945—28no—
452#11719945—28no—
453#11719945—416no—
454#11719945—44no—
455C2×D212C2412yes—
456C2×D212C2412yes—
457C2×D212C2412yes—
458C2×C4×D53C2414yes—
459C2×C4×D53C2414yes—
460C2×C4×D53C2414yes—
461C2×C4×D53C24116yes—
462C2×Dic106—28no—
463C2×Dic106—44no—
464C2×Dic106—416no—
465C2×Dic106C2412yes—
466C2×Dic106C2414yes—
467C2×Dic106C2412yes—
468C2×Dic106C2414yes—
469C2×Dic106C2414yes—
470C2×Dic106C2412yes—
471C2×Dic106C2414yes—
472C2×Dic106C24116yes—
473C4⋊C4×C53C2414yes—
474C4⋊C4×C53C2414yes—
475C4⋊C4×C53C2414yes—
476C4⋊C4×C53C2414yes—
477C22⋊C4×C53C2418yes—
478C22⋊C4×C53C2418yes—
479C22⋊C4×C53C2418yes—
480C22⋊C4×C53C2418yes—
481C42×C53C2411yescharacteristic
482C42×C53C2411yescharacteristic
483C42×C53C2411yescharacteristic
484C42×C53C2411yescharacteristic
485C42×C53C2411yescharacteristic
486C42×C53C2411yescharacteristic
487C42×C53C2411yescharacteristic
488C42×C53C2411yescharacteristic
489C42×C53C2411yescharacteristic
490C42×C53C2411yescharacteristic
491C42×C53C2411yescharacteristic
492C42×C53C2411yescharacteristic
493C42×C53C2411yescharacteristic
494C42×C53C2411yescharacteristic
495C42×C53C2411yescharacteristic
496C42×C53C2411yescharacteristic
497C22⋊Dic53C2414yes—
498C22⋊Dic53C2418yes—
499C22⋊Dic53C2418yes—
500C22⋊Dic53C24116yes—
501C22⋊Dic53C24116yes—
502C22⋊Dic53C24116yes—
503C22⋊Dic53C2414yes—
504C22⋊Dic53C2414yes—
505C22⋊Dic53C24116yes—
506#11719921C2414yes—
507#11719921C2414yes—
508#11719921C2414yes—
509#11719921C2414yes—
510#11719921C2414yes—
511#11719921C2414yes—
512#11719921C24116yes—
513C4⋊Dic53C2414yes—
514C4⋊Dic53C2414yes—
515C4⋊Dic53C2412yes—
516C4⋊Dic53C2414yes—
517C4⋊Dic53C2414yes—
518C4⋊Dic53C2414yes—
519C4⋊Dic53C2414yes—
520C4⋊Dic53C2414yes—
521C4⋊Dic53C24116yes—
522C4⋊Dic53C2414yes—
523C4⋊Dic53C2412yes—
524C4⋊Dic53C2412yes—
525C4⋊Dic53C2412yes—
526C4⋊Dic53C2412yes—
527C4⋊Dic53C2412yes—
528#11719919C24116yes—
529#11719919C24116yes—
530#11719919C2414yes—
531#11719919C2418yes—
532#11719919C24116yes—
533#11719919C2418yes—
534#11719919C2418yes—
535#11719919C2418yes—
536#11719919C2414yes—
537#11719919C2414yes—
538#11719919C2414yes—
539#11719919C2414yes—
540#11719919C2414yes—
541C4×Dic53C2414yes—
542C4×Dic53C2414yes—
543C4×Dic53C2414yes—
544C4×Dic53C2418yes—
545C4×Dic53C2418yes—
546C4×Dic53C24116yes—
547C23×C53—22no—
548C23×C53—22no—
549C23×C53—28no—
550C23×C53—41no—
551C23×C53—44no—
552C23×C53—44no—
553C23×C53C2518yes—
554C23×C53C2511yescharacteristic
555C23×C53C2511yescharacteristic
556C23×C53C2511yescharacteristic
557C22×D53C2514yes—
558Q8×C53—28no—
559Q8×C53—44no—
560D4×C53—216no—
561D4×C53—28no—
562D4×C53—28no—
563D4×C53—28no—
564D4×C53—28no—
565D4×C53—44no—
566D4×C53—48no—
567D4×C53—44no—
568C2×C4×C53—22no—
569C2×C4×C53—22no—
570C2×C4×C53—216no—
571C2×C4×C53—22no—
572C2×C4×C53—22no—
573C2×C4×C53—22no—
574C2×C4×C53—22no—
575C2×C4×C53—22no—
576C2×C4×C53—22no—
577C2×C4×C53—22no—
578C2×C4×C53—22no—
579C2×C4×C53—22no—
580C2×C4×C53—22no—
581C2×C4×C53—22no—
582C2×C4×C53—41no—
583C2×C4×C53—41no—
584C2×C4×C53—41no—
585C2×C4×C53—44no—
586C2×C4×C53—48no—
587C2×C4×C53H(5,𝔽2)14yes—
588C2×C4×C532−1+414yescomplemented
589C2×C4×C53C2511yescharacteristic
590C2×C4×C53C2518yes—
591C2×C4×C53C2511yescharacteristic
592C2×C4×C53C2511yescharacteristic
593C2×C4×C53C2511yescharacteristic
594C2×C4×C53C2511yescharacteristic
595C2×C4×C53C2511yescharacteristic
596C2×C4×C53C2511yescharacteristic
597C2×C4×C53C2511yescharacteristic
598C2×C4×C53C2511yescharacteristic
599C2×C4×C53C2511yescharacteristic
600C2×C4×C53C2511yescharacteristic
601C2×C4×C53C2511yescharacteristic
602C22⋊D53—28no—
603C22⋊D53—28no—
604C22⋊D53—416no—
605C22⋊D53—44no—
606C22⋊D53—416no—
607C2×Dic53—28no—
608C2×Dic53—416no—
609C2×Dic53—44no—
610C2×Dic53—416no—
611C2×Dic53C2514yes—
612C2×Dic53C2518yes—
613C2×Dic53C2518yes—
614C2×Dic53C2514yes—
615C2×Dic53C2514yes—
616D212—24no—
617D212—24no—
618D212—42no—
619C4×D53—28no—
620C4×D53—28no—
621C4×D53—28no—
622C4×D53—416no—
623Dic106—28no—
624Dic106—28no—
625Dic106—24no—
626Dic106—24no—
627Dic106—28no—
628Dic106—44no—
629Dic106—416no—
630Dic106—42no—
631#62835—531nomaximal, Sylow
632C22×C53—21no—
633C22×C53—21no—
634C22×C53—21no—
635C22×C53—21no—
636C22×C53—28no—
637C22×C53—21no—
638C22×C53—21no—
639C22×C53—28no—
640C22×C53—28no—
641C22×C53—21no—
642C22×C53—44no—
643C22×C53—88no—
644C22×C53C2×H(5,𝔽2)12yes—
645C22×C53C2×2−1+412yes—
646C22×C53C2611yescharacteristic
647C2×D53—24no—
648C2×D53—24no—
649C2×D53—24no—
650C4×C53—28no—
651C4×C53—21no—
652C4×C53—21no—
653C4×C53—21no—
654C4×C53—21no—
655C4×C53—21no—
656C4×C53—21no—
657C4×C53—21no—
658C4×C53C2×H(5,𝔽2)12yes—
659C4×C53C2×H(5,𝔽2)12yes—
660C4×C53C2×2−1+412yes—
661C4×C53C2×2−1+412yes—
662C4×C53#58512yes—
663Dic53—28no—
664Dic53—24no—
665Dic53—24no—
666Dic53—28no—
667Dic53—24no—
668#3561—534no—
669#3559—534no—
670#3554—534no—
671#3550—532no—
672#3548—532no—
673#3547—534no—
674#3536—534no—
675#3522—534no—
676#3520—534no—
677#3511—534no—
678#3511—532no—
679#3508—532no—
680#3507—532no—
681#3506—532no—
682#3503—532no—
683#3501—532no—
684#3499—532no—
685#3497—532no—
686#3494—534no—
687#3489—534no—
688#3444—531no—
689C2×#533—531no—
690C2×#532D5311yescharacteristic, complemented
691C2×C53—22no—
692C2×C53—22no—
693C2×C53—41no—
694C2×C53—48no—
695C2×C53C22×H(5,𝔽2)11yescharacteristic
696C2×C53C22×2−1+411yescharacteristic
697C2×C53C2×#58511yescharacteristic
698D53—44no—
699C2×2−1+4—534no—
700C22×#41C2×D5312yes—
701#563—538no—
702#562—538no—
703#562—5316no—
704#559—534no—
705#559—534no—
706#559—538no—
707Q82—534no—
708#557—534no—
709#556—538no—
710#556—534no—
711#556—534no—
712#555—538no—
713#555—534no—
714#554—534no—
715#554—534no—
716#554—534no—
717#554—538no—
718#554—538no—
719#554—538no—
720#553—538no—
721#553—538no—
722#553—538no—
723#552—538no—
724#551—5316no—
725#550—534no—
726#550—534no—
727#550—534no—
728D4×Q8—538no—
729D4×Q8—534no—
730D4×Q8—534no—
731D4×Q8—534no—
732D4×Q8—534no—
733#548—538no—
734#548—538no—
735#548—538no—
736#548—538no—
737#547—538no—
738#547—5316no—
739#547—538no—
740#547—538no—
741#547—534no—
742#547—534no—
743#547—534no—
744#546—5316no—
745#546—538no—
746#546—538no—
747#544—538no—
748#544—534no—
749#543—538no—
750#542—538no—
751#542—5316no—
752#542—538no—
753#542—538no—
754#542—538no—
755#540—538no—
756#540—538no—
757#539—538no—
758#539—5316no—
759#538—538no—
760#537—534no—
761#537—538no—
762#537—538no—
763#537—538no—
764#536—534no—
765#536—538no—
766#536—538no—
767#535—534no—
768#533—534no—
769#533—532no—
770#533—532no—
771#533—532no—
772#533—532no—
773#533—532no—
774#533—532no—
775#533—532no—
776#533—532no—
777#533—531no—
778#533—531no—
779#533—531no—
780#532—534no—
781#532—534no—
782#532—538no—
783#532—531no—
784#532—531no—
785#532—531no—
786#532C2×D5312yes—
787#532C2×D5312yes—
788#532C2×D5312yes—
789#532C2×D5312yes—
790#532C2×D5312yes—
791#532C2×D5312yes—
792#532C2×D5312yes—
793#532C2×D5312yes—
794C2×C4⋊Q8—534no—
795C2×C4⋊Q8—531no—
796C2×C4⋊Q8—531no—
797C2×C4⋊Q8C2×D5311yescharacteristic
798C2×#127C2×D5311yescharacteristic
799#529—538no—
800#529—532no—
801#529—532no—
802#529—532no—
803#529—532no—
804#529—532no—
805#529—532no—
806C2×#125—532no—
807C2×#124C2×D5312yes—
808#525—532no—
809#525—532no—
810#525—532no—
811#525—538no—
812C2×C22⋊Q8—532no—
813C2×C22⋊Q8—532no—
814C2×C22⋊Q8—538no—
815C2×#121C2×D5312yes—
816C2×#121C2×D5312yes—
817#520—534no—
818#520—538no—
819#520—534no—
820#518—534no—
821C4×#41—532no—
822C4×#41—532no—
823C4×#41—532no—
824C2×C4×Q8—532no—
825C2×C4×Q8—532no—
826C2×C4×D4C2×D5312yes—
827C2×C4×D4C2×D5312yes—
828C2×#117—532no—
829C22×C42C2×D5311yescharacteristic
830C53#6283511yescharacteristic, complemented, Sylow
8312−1+4—21216no—
832C2×#41—48no—
833C2×#41—538no—
834C2×#41—538no—
835C2×#41—5316no—
836C2×#41—532no—
837C2×#41—532no—
838C2×#41—532no—
839C2×#41—538no—
840C2×#41C22×D5314yes—
841C2×#41C22×D5314yes—
842C2×#41C22×D5314yes—
843C2×#41C22×D5314yes—
844C22×Q8—538no—
845C22×Q8—532no—
846C22×Q8—532no—
847C22×Q8—538no—
848C22×Q8C22×D5312yes—
849C22×D4C22×D5312yes—
850C22×D4C22×D5312yes—
851C22×D4C22×D5314yes—
852C22×D4C22×D5312yes—
853C23×C4C22×D5311yescharacteristic
854C23×C4C22×D5311yescharacteristic
855C23×C4C22×D5314yes—
856C23×C4C22×D5311yescharacteristic
857C4⋊Q8—538no—
858C4⋊Q8—5316no—
859C4⋊Q8—538no—
860C4⋊Q8—538no—
861C4⋊Q8—538no—
862C4⋊Q8—532no—
863C4⋊Q8—532no—
864C4⋊Q8—532no—
865C4⋊Q8—532no—
866C4⋊Q8—532no—
867C4⋊Q8—532no—
868C4⋊Q8—532no—
869C4⋊Q8—532no—
870C4⋊Q8—531no—
871C4⋊Q8—531no—
872C4⋊Q8—531no—
873C4⋊Q8C22×D5312yes—
874C4⋊Q8C22×D5312yes—
875C4⋊Q8C22×D5312yes—
876C4⋊Q8C22×D5312yes—
877#127—538no—
878#127—531no—
879#127C22×D5312yes—
880#127C22×D5312yes—
881#127C22×D5312yes—
882#127C22×D5312yes—
883#126—5316no—
884#126—5316no—
885#126—5316no—
886#126—534no—
887#126—534no—
888#125—538no—
889#125—538no—
890#125—5316no—
891#125—534no—
892#125—534no—
893#125—534no—
894#125—534no—
895#125—532no—
896#125—532no—
897#125—532no—
898#124—538no—
899#124—538no—
900#124—538no—
901#124—5316no—
902#124—5316no—
903#124—5316no—
904#124—532no—
905#124—532no—
906#124—532no—
907#124C22×D5314yes—
908#124C22×D5314yes—
909#124C22×D5314yes—
910#124C22×D5314yes—
911#123—5316no—
912#123—5316no—
913#123—5316no—
914#123—5316no—
915#123—534no—
916#123—534no—
917#123—534no—
918#123—5316no—
919#123—5316no—
920#123—5316no—
921#123—5316no—
922C22⋊Q8—538no—
923C22⋊Q8—5316no—
924C22⋊Q8—532no—
925C22⋊Q8—534no—
926C22⋊Q8—534no—
927C22⋊Q8—534no—
928C22⋊Q8—534no—
929C22⋊Q8—534no—
930C22⋊Q8—534no—
931C22⋊Q8—534no—
932C22⋊Q8—534no—
933C22⋊Q8—538no—
934C22⋊Q8—538no—
935C22⋊Q8—5316no—
936C22⋊Q8—5316no—
937C22⋊Q8—532no—
938C22⋊Q8—532no—
939C22⋊Q8—532no—
940C22⋊Q8—532no—
941C22⋊Q8—532no—
942C22⋊Q8—538no—
943C22⋊Q8—538no—
944C22⋊Q8—5316no—
945C22⋊Q8—5316no—
946C22⋊Q8—5316no—
947C22⋊Q8—5316no—
948C22⋊Q8—5316no—
949C22⋊Q8—5316no—
950#121—538no—
951#121—538no—
952#121—5316no—
953#121—538no—
954#121—538no—
955#121—5316no—
956#121—5316no—
957#121—5316no—
958#121—5316no—
959#121—532no—
960#121—532no—
961#121—532no—
962#121—532no—
963#121—532no—
964#121—532no—
965#121—538no—
966#121—5316no—
967#121C22×D5314yes—
968#121C22×D5314yes—
969#121C22×D5314yes—
970#121C22×D5314yes—
971#121C22×D5314yes—
972#121C22×D5314yes—
973#121C22×D5314yes—
974#121C22×D5314yes—
975#120—534no—
976#120—5316no—
977C4×Q8—538no—
978C4×Q8—538no—
979C4×Q8—538no—
980C4×Q8—534no—
981C4×Q8—534no—
982C4×Q8—534no—
983C4×Q8—534no—
984C4×Q8—534no—
985C4×Q8—534no—
986C4×Q8—534no—
987C4×Q8—534no—
988C4×Q8—532no—
989C4×Q8—532no—
990C4×Q8—532no—
991C4×Q8—532no—
992C4×Q8—532no—
993C4×Q8—532no—
994C4×D4—538no—
995C4×D4—538no—
996C4×D4—538no—
997C4×D4—538no—
998C4×D4—5316no—
999C4×D4—538no—
1000C4×D4—538no—
1001C4×D4—534no—
1002C4×D4—534no—
1003C4×D4—534no—
1004C4×D4—534no—
1005C4×D4—534no—
1006C4×D4—534no—
1007C4×D4—5316no—
1008C4×D4—5316no—
1009C4×D4—538no—
1010C4×D4—5316no—
1011C4×D4—532no—
1012C4×D4—532no—
1013C4×D4—532no—
1014C4×D4—532no—
1015C4×D4—532no—
1016C4×D4—532no—
1017C4×D4C22×D5314yes—
1018C4×D4C22×D5314yes—
1019C4×D4C22×D5314yes—
1020C4×D4C22×D5314yes—
1021C4×D4C22×D5314yes—
1022C4×D4C22×D5314yes—
1023C4×D4C22×D5314yes—
1024C4×D4C22×D5314yes—
1025#117—534no—
1026#117—534no—
1027#117—534no—
1028#117—534no—
1029#117—532no—
1030#117—532no—
1031#117—532no—
1032#117—538no—
1033#117—538no—
1034#117—5316no—
1035#117—534no—
1036#117—534no—
1037#117—534no—
1038C2×C4⋊C4—532no—
1039C2×C4⋊C4—532no—
1040C2×C4⋊C4—532no—
1041C2×C4⋊C4—534no—
1042C2×C4⋊C4—534no—
1043C2×C4⋊C4—532no—
1044C2×C4⋊C4—538no—
1045C2×C4⋊C4—5316no—
1046C2×C4⋊C4—538no—
1047C2×C4⋊C4—538no—
1048C2×C4⋊C4C22×D5312yes—
1049C2×C4⋊C4C22×D5312yes—
1050C2×C22⋊C4—534no—
1051C2×C22⋊C4—5316no—
1052C2×C22⋊C4C22×D5314yes—
1053C2×C22⋊C4C22×D5314yes—
1054C2×C42—534no—
1055C2×C42—534no—
1056C2×C42C22×D5311yescharacteristic
1057C2×C42C22×D5311yescharacteristic
1058C2×C42C22×D5311yescharacteristic
1059C2×C42C22×D5311yescharacteristic
1060C2×C42C22×D5311yescharacteristic
1061C2×C42C22×D5311yescharacteristic
1062C2×C42C22×D5311yescharacteristic
1063C2×C42C22×D5311yescharacteristic
1064C2×C42C22×D5311yescharacteristic
1065C2×C42C22×D5311yescharacteristic
1066C2×C42C22×D5311yescharacteristic
1067C2×C42C22×D5311yescharacteristic
1068C24C23×D5311yescharacteristic
1069C24C23×D5314yes—
1070#41—216no—
1071#41—48no—
1072#41—48no—
1073#41—48no—
1074#41—1068no—
1075#41—1068no—
1076#41—2124no—
1077#41—21216no—
1078#41—21232no—
1079#41—21216no—
1080#41—21216no—
1081C2×Q8—44no—
1082C2×Q8—532no—
1083C2×Q8—534no—
1084C2×Q8—532no—
1085C2×Q8—534no—
1086C2×Q8—534no—
1087C2×Q8—532no—
1088C2×Q8—534no—
1089C2×Q8—5316no—
1090C2×Q8—1068no—
1091C2×Q8—2124no—
1092C2×Q8—21216no—
1093C2×Q8—21216no—
1094C2×Q8C23×D5314yes—
1095C2×Q8C23×D5314yes—
1096C2×D4—28no—
1097C2×D4—44no—
1098C2×D4—44no—
1099C2×D4—48no—
1100C2×D4—534no—
1101C2×D4—534no—
1102C2×D4—534no—
1103C2×D4—5316no—
1104C2×D4—5316no—
1105C2×D4—532no—
1106C2×D4—532no—
1107C2×D4—532no—
1108C2×D4C23×D5314yes—
1109C2×D4C23×D5314yes—
1110C2×D4C23×D5314yes—
1111C2×D4C23×D5318yes—
1112C2×D4C23×D5314yes—
1113C2×D4C23×D5314yes—
1114C2×D4C23×D5318yes—
1115C2×D4C23×D5314yes—
1116C22×C4—24no—
1117C22×C4—24no—
1118C22×C4—42no—
1119C22×C4—48no—
1120C22×C4—534no—
1121C22×C4—534no—
1122C22×C4—5316no—
1123C22×C4—5316no—
1124C22×C4—534no—
1125C22×C4—534no—
1126C22×C4—534no—
1127C22×C4—5316no—
1128C22×C4C23×D5311yescharacteristic
1129C22×C4C23×D5311yescharacteristic
1130C22×C4C23×D5311yescharacteristic
1131C22×C4C23×D5311yescharacteristic
1132C22×C4C23×D5311yescharacteristic
1133C22×C4C23×D5311yescharacteristic
1134C22×C4C23×D5311yescharacteristic
1135C22×C4C23×D5311yescharacteristic
1136C22×C4C23×D5311yescharacteristic
1137C22×C4C23×D5311yescharacteristic
1138C22×C4C23×D5311yescharacteristic
1139C22×C4C23×D5311yescharacteristic
1140C22×C4C23×D5311yescharacteristic
1141C22×C4C23×D5318yes—
1142C22×C4C23×D5311yescharacteristic
1143C22×C4C23×D5311yescharacteristic
1144C22×C4C23×D5311yescharacteristic
1145C22×C4C23×D5314yes—
1146C22×C4C23×D5318yes—
1147C22×C4C23×D5311yescharacteristic
1148C22×C4C23×D5311yescharacteristic
1149C4⋊C4—532no—
1150C4⋊C4—534no—
1151C4⋊C4—534no—
1152C4⋊C4—534no—
1153C4⋊C4—534no—
1154C4⋊C4—538no—
1155C4⋊C4—5316no—
1156C4⋊C4—534no—
1157C4⋊C4—534no—
1158C4⋊C4—534no—
1159C4⋊C4—534no—
1160C4⋊C4—5316no—
1161C4⋊C4—5316no—
1162C4⋊C4—5316no—
1163C4⋊C4—538no—
1164C4⋊C4—538no—
1165C4⋊C4—538no—
1166C4⋊C4—534no—
1167C4⋊C4—532no—
1168C4⋊C4—534no—
1169C4⋊C4—532no—
1170C4⋊C4—532no—
1171C4⋊C4—532no—
1172C4⋊C4—532no—
1173C4⋊C4—534no—
1174C4⋊C4—534no—
1175C4⋊C4—534no—
1176C4⋊C4—534no—
1177C4⋊C4C23×D5314yes—
1178C4⋊C4C23×D5314yes—
1179C4⋊C4C23×D5314yes—
1180C4⋊C4C23×D5314yes—
1181C22⋊C4—534no—
1182C22⋊C4—538no—
1183C22⋊C4—538no—
1184C22⋊C4—5316no—
1185C22⋊C4—5316no—
1186C22⋊C4—534no—
1187C22⋊C4—5316no—
1188C22⋊C4—5316no—
1189C22⋊C4—534no—
1190C22⋊C4—534no—
1191C22⋊C4—534no—
1192C22⋊C4—534no—
1193C22⋊C4—534no—
1194C22⋊C4—5316no—
1195C22⋊C4—534no—
1196C22⋊C4—534no—
1197C22⋊C4C23×D5318yes—
1198C22⋊C4C23×D5318yes—
1199C22⋊C4C23×D5318yes—
1200C22⋊C4C23×D5318yes—
1201C42—538no—
1202C42—534no—
1203C42—534no—
1204C42—534no—
1205C42—538no—
1206C42—5316no—
1207C42C23×D5311yescharacteristic
1208C42C23×D5311yescharacteristic
1209C42C23×D5311yescharacteristic
1210C42C23×D5311yescharacteristic
1211C42C23×D5311yescharacteristic
1212C42C23×D5311yescharacteristic
1213C42C23×D5311yescharacteristic
1214C42C23×D5311yescharacteristic
1215C42C23×D5311yescharacteristic
1216C42C23×D5311yescharacteristic
1217C42C23×D5311yescharacteristic
1218C42C23×D5311yescharacteristic
1219C42C23×D5311yescharacteristic
1220C42C23×D5311yescharacteristic
1221C42C23×D5311yescharacteristic
1222C42C23×D5311yescharacteristic
1223C23—22no—
1224C23—22no—
1225C23—28no—
1226C23—41no—
1227C23—44no—
1228C23—44no—
1229C23—534no—
1230C23C24×D5311yescharacteristic
1231C23C24×D5318yes—
1232C23C24×D5311yescharacteristic
1233C23C24×D5311yescharacteristic
1234Q8—28no—
1235Q8—44no—
1236Q8—1068no—
1237Q8—1068no—
1238Q8—1064no—
1239Q8—1064no—
1240Q8—1068no—
1241Q8—2124no—
1242Q8—21216no—
1243Q8—2122no—
1244D4—216no—
1245D4—28no—
1246D4—28no—
1247D4—28no—
1248D4—28no—
1249D4—44no—
1250D4—44no—
1251D4—48no—
1252D4—1068no—
1253D4—1068no—
1254D4—1064no—
1255D4—1064no—
1256D4—2122no—
1257D4—2124no—
1258D4—21216no—
1259D4—21216no—
1260C2×C4—22no—
1261C2×C4—22no—
1262C2×C4—22no—
1263C2×C4—22no—
1264C2×C4—22no—
1265C2×C4—22no—
1266C2×C4—216no—
1267C2×C4—22no—
1268C2×C4—22no—
1269C2×C4—22no—
1270C2×C4—22no—
1271C2×C4—22no—
1272C2×C4—22no—
1273C2×C4—22no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—44no—
1278C2×C4—48no—
1279C2×C4—534no—
1280C2×C4—538no—
1281C2×C4—534no—
1282C2×C4—534no—
1283C2×C4—538no—
1284C2×C4—1068no—
1285C2×C4—1068no—
1286C2×C4—1068no—
1287C2×C4—1068no—
1288C2×C4—21216no—
1289C2×C4—2124no—
1290C2×C4—21216no—
1291C2×C4—21216no—
1292C2×C4#1313326214yes—
1293C2×C4#1313326414yescomplemented
1294C2×C4C24×D5311yescharacteristic
1295C2×C4C24×D5318yes—
1296C2×C4C24×D5311yescharacteristic
1297C2×C4C24×D5311yescharacteristic
1298C2×C4C24×D5311yescharacteristic
1299C2×C4C24×D5311yescharacteristic
1300C2×C4C24×D5311yescharacteristic
1301C2×C4C24×D5311yescharacteristic
1302C2×C4C24×D5311yescharacteristic
1303C2×C4C24×D5311yescharacteristic
1304C2×C4C24×D5311yescharacteristic
1305C2×C4C24×D5311yescharacteristic
1306C2×C4C24×D5311yescharacteristic
1307C22—21no—
1308C22—21no—
1309C22—21no—
1310C22—21no—
1311C22—21no—
1312C22—28no—
1313C22—21no—
1314C22—28no—
1315C22—21no—
1316C22—28no—
1317C22—44no—
1318C22—88no—
1319C22—1064no—
1320C22—1064no—
1321C22—1064no—
1322C22C2×#1313326212yes—
1323C22C2×#1313326412yes—
1324C22C25×D5311yescharacteristic
1325C4—21no—
1326C4—21no—
1327C4—28no—
1328C4—21no—
1329C4—21no—
1330C4—21no—
1331C4—21no—
1332C4—21no—
1333C4—1064no—
1334C4—1068no—
1335C4—1064no—
1336C4—1064no—
1337C4—1068no—
1338C4C2×#1313326212yes—
1339C4C2×#1313326212yes—
1340C4C2×#1313326412yes—
1341C4C2×#1313326412yes—
1342C4#1681145912yes—
1343C2—22no—
1344C2—22no—
1345C2—41no—
1346C2—48no—
1347C2—2124no—
1348C2C22×#1313326211yescharacteristic
1349C2C22×#1313326411yescharacteristic
1350C2C2×#1681145911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC2×C53×#532C2
hypercenterC2×#532D53
hypocenterC53#62835
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #20289287C2semidirect
2. #20289253C2semidirect
3. #20289180C2semidirect
4. #20289129C2semidirect
5. #20289113C2semidirect
6. #20289104C2semidirect
7. #20288937C2semidirect
8. #20288792C2semidirect
9. #20288764C2semidirect
10. #20288622C2semidirect
11. #20288616C2semidirect
12. #20288589C2semidirect
13. #20288577C2semidirect
14. #20288567C2semidirect
15. #20288531C2semidirect
16. #20288518C2semidirect
17. #20288495C2semidirect
18. #20288481C2semidirect
19. #20288444C2semidirect
20. #20288395C2semidirect
21. #20288011C2semidirect
22. C2×#16811180C2semidirect
23. C2×C53×#532C2semidirect
24. C2×#13133264C22semidirect
25. #16811373C22semidirect
26. #16811368C22semidirect
27. #16811367C22semidirect
28. #16811359C22semidirect
29. #16811359C22semidirect
30. #16811356C22semidirect
31. #16811353C22semidirect
32. #16811348C22semidirect
33. #16811343C22semidirect
34. #16811343C22semidirect
35. #16811342C22semidirect
36. #16811338C22semidirect
37. #16811337C22semidirect
38. #16811334C22semidirect
39. #16811332C22semidirect
40. #16811332C22semidirect
41. #16811330C22semidirect
42. #16811330C22semidirect
44. #16811325C22semidirect
45. #16811323C22semidirect
46. #16811320C22semidirect
47. #16811313C22semidirect
49. #16811294C22semidirect
50. #16811293C22semidirect
51. #16811293C22semidirect
52. D4×Dic106C22semidirect
53. D4×Dic106C22semidirect
54. D4×Dic106C22semidirect
55. #16811288C22semidirect
57. #16811282C22semidirect
58. #16811281C22semidirect
59. #16811280C22semidirect
60. #16811279C22semidirect
61. #16811278C22semidirect
62. #16811278C22semidirect
63. #16811277C22semidirect
64. #16811273C22semidirect
65. #16811273C22semidirect
66. #16811272C22semidirect
67. #16811272C22semidirect
72. #16811250C22semidirect
74. #16811242C22semidirect
75. #16811240C22semidirect
76. #16811240C22semidirect
77. #16811238C22semidirect
78. #16811237C22semidirect
79. #16811227C22semidirect
80. #16811226C22semidirect
81. #16811218C22semidirect
82. #16811215C22semidirect
84. #16811202C22semidirect
85. #16811201C22semidirect
86. #16811201C22semidirect
87. #16811200C22semidirect
88. #16811194C22semidirect
89. #16811194C22semidirect
90. #16811193C22semidirect
97. #16811180C22semidirect
98. #16811180C22semidirect
99. #16811180C22semidirect
100. #16811180C22semidirect
101. #16811180C22semidirect
102. #16811180C22semidirect
103. #16811178C22semidirect
105. #16811173C22semidirect
106. #16811173C22semidirect
107. #16811171C22semidirect
108. #16811171C22semidirect
109. #16811168C22semidirect
110. C2×#13133217C22semidirect
111. C2×#13133217C22semidirect
112. C4⋊Q8×D53C22semidirect
115. #16811157C22semidirect
116. #16811157C22semidirect
117. #16811157C22semidirect
118. #16811157C22semidirect
119. #16811154C22semidirect
120. C2×#13133209C22semidirect
128. #16811106C22semidirect
130. #16811102C22semidirect
133. C4×#11719945C22semidirect
134. C4×#11719945C22semidirect
135. C2×C4×Dic106C22semidirect
136. C2×C4×Dic106C22semidirect
588. C2×C4×C532−1+4semidirect
690. C2×#532D53semidirect
830. C53#62835semidirect
1293. C2×C4#13133264semidirect

Maximal subgroups

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

subgroupindex
#202892872
#202892532
#202891802
#202891292
#202891132
#202891042
#202889372
#202887922
#202887642
#202886222
#202886162
#202885892
#202885772
#202885672
#202885312
#202885182
#202884952
#202884812
#202884442
#202883952
#202880112
C2×#168111802
C2×C53×#5322
#6283553