Finite Group Databasebeta

← #28292913

Subgroups — #28292913

Order 13568.

6636 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289391C218yesmaximal, complemented
2#20289343C214yesmaximal, complemented
3#20289271C214yesmaximal, complemented
4#20289221C212yesmaximal, complemented
5#20289142C212yesmaximal, complemented
6#20288964C211yesmaximal, characteristic, complemented
7#20288954C211yesmaximal, characteristic, complemented
8#20288942C212yesmaximal, complemented
9#20288704C214yesmaximal, complemented
10#20288693C214yesmaximal, complemented
11#20288676C214yesmaximal, complemented
12#20288659C214yesmaximal, complemented
13#20288641C218yesmaximal, complemented
14#20288637C212yesmaximal, complemented
15#20288611C212yesmaximal, complemented
16#20288427C214yesmaximal, complemented
17#20288407C214yesmaximal, complemented
18C2×#16811157C212yesmaximal, complemented
19C53×#3444C211yesmaximal, characteristic, complemented
20#16811376C2214yescomplemented
21#16811372C2214yescomplemented
22#16811372C2218yescomplemented
23#16811370C2218yescomplemented
24#16811363C2214yes—
25#16811360C2214yescomplemented
26#16811358C2214yescomplemented
27#16811356C2218yescomplemented
28#16811351C2214yescomplemented
29#16811346C2214yescomplemented
30#16811345C2218yescomplemented
31#16811340C2218yescomplemented
32#16811336C2218yescomplemented
33#16811335C2214yescomplemented
34#16811333C2214yescomplemented
35#16811330C2214yescomplemented
36#16811327C2218yescomplemented
37#16811324C2218yescomplemented
38#16811323C2218yescomplemented
39#16811322C2218yescomplemented
40#16811322C2218yescomplemented
41#16811319C2214yes—
42#16811319C2214yescomplemented
43#16811316C2218yescomplemented
44#16811314C2218yescomplemented
45#16811313C2214yescomplemented
46#16811313C2214yescomplemented
47#16811312C2218yescomplemented
48#16811309C2218yescomplemented
49#16811306C2218yescomplemented
50#16811306C2218yescomplemented
51#16811305C2218yescomplemented
52#16811304C2214yescomplemented
53#16811303C2214yescomplemented
54#16811302C2218yescomplemented
55#16811302C2218yescomplemented
56#16811300C2218yescomplemented
57#16811298C2218yescomplemented
58#16811297C2218yescomplemented
59#16811297C2218yescomplemented
60D4×Dic106C2214yescomplemented
61#16811282C2214yescomplemented
62#16811282C2214yescomplemented
63#16811277C2214yescomplemented
64#16811272C2218yescomplemented
65#16811269C2214yescomplemented
66#16811269C2214yescomplemented
67#16811262C2218yescomplemented
68#16811261C2218yescomplemented
69#16811260C2218yescomplemented
70D4×D212C2214yes—
71#16811255C2214yes—
72#16811252C2214yescomplemented
73#16811248C2214yescomplemented
74#16811245C2218yescomplemented
75#16811244C2214yescomplemented
76#16811244C2214yescomplemented
77#16811243C2218yescomplemented
78#16811237C2218yescomplemented
79#16811235C2212yescomplemented
80#16811235C2212yescomplemented
81#16811232C2218yescomplemented
82#16811231C2218yescomplemented
83#16811228C2212yes—
84#16811228C2212yescomplemented
85#16811223C2218yescomplemented
86#16811222C2214yescomplemented
87#16811221C2218yescomplemented
88#16811219C2218yescomplemented
89#16811218C2214yescomplemented
90#16811215C2218yescomplemented
91#16811215C2218yescomplemented
92#16811213C2214yes—
93#16811210C2214yescomplemented
94#16811207C2218yescomplemented
95#16811206C2218yescomplemented
96#16811206C2218yescomplemented
97#16811205C2218yescomplemented
98#16811201C2214yescomplemented
99#16811200C2214yescomplemented
100#16811194C2212yescomplemented
101#16811187C2212yes—
102#16811181C2214yes—
103#16811180C2212yescomplemented
104#16811173C2212yescomplemented
105#16811157C2214yescomplemented
106#16811157C2214yescomplemented
107#16811157C2214yescomplemented
108#16811157C2214yescomplemented
109#16811157C2214yescomplemented
110#16811157C2214yescomplemented
111#16811157C2214yescomplemented
112#16811157C2214yescomplemented
113#16811157C2214yescomplemented
114#16811157C2214yescomplemented
115#16811150C2218yescomplemented
116#16811150C2218yescomplemented
117C2×#13133211C2214yescomplemented
118C2×#13133209C2212yescomplemented
119C2×#13133209C2212yescomplemented
120C2×#13133205C2212yescomplemented
121C2×#13133205C2212yescomplemented
122#16811131C2218yescomplemented
123C2×#13133200C2214yescomplemented
124#123×D53C2218yescomplemented
125C2×#13133196C2212yescomplemented
126C2×#13133191C2212yes—
127#16811103C2214yescomplemented
128#16811102C2218yescomplemented
129#16811100C2212yescomplemented
130#16811097C2212yescomplemented
131#16811095C2218yescomplemented
132C2×C4×Dic106C2212yescomplemented
133C2×C4×D212C2212yescomplemented
134C2×C4×C22⋊D53C2214yescomplemented
135C2×#13133174C2214yescomplemented
136C53×#533C2212yescomplemented
137C53×#533C2211yescharacteristic, complemented
138C53×#532C2211yescharacteristic, complemented
139C53×#532C2212yescomplemented
140C53×#529C2214yescomplemented
141C53×#529C2214yescomplemented
142C53×#529C2212yescomplemented
143C53×#529C2212yescomplemented
144C53×#525C2211yescharacteristic
145C53×#525C2214yescomplemented
146C53×#525C2211yescharacteristic, complemented
147C4×#41×C53C2211yescharacteristic, complemented
148C4×#41×C53C2211yescharacteristic, complemented
149C4×#41×C53C2214yescomplemented
150C22×C42×C53C2211yescharacteristic, complemented
151C2×#11719945C2314yes—
152C2×#11719947C2318yes—
153C22×Dic106C2312yes—
154C22×Dic106C2312yes—
155C22×D212C2312yes—
156C22×D212C2312yes—
157C22×C22⋊D53C2314yes—
158C2×D4×D53C2318yes—
159C22×C4×D53C2314yes—
160#13133217C2314yes—
161#13133217C2312yes—
162#13133216C2318yes—
163#13133215C2318yes—
164#13133215C2314yes—
165#13133214C2312yes—
166#13133213C2314yes—
167#13133212C2318yes—
168#13133212C2318yes—
169#13133212C2318yes—
170#13133212C2318yes—
171#13133212C2318yes—
172#13133212C2318yes—
173#13133211C2318yes—
174#13133211C2318yes—
175#13133211C2318yes—
176#13133211C2318yes—
177#13133211C2318yes—
178#13133211C2318yes—
179#13133210C2318yes—
180#13133210C2318yes—
181#13133210C2318yes—
182#13133210C2318yes—
183#13133209C2314yes—
184#13133209C2318yes—
185#13133209C2312yes—
186#13133209C2314yes—
187#13133209C2312yes—
188#13133209C2314yes—
189#13133209C2314yes—
190#13133208C2318yes—
191#13133207C2318yes—
192#13133207C2318yes—
193#13133207C2318yes—
194#13133207C2318yes—
195#13133207C2318yes—
196#13133207C2318yes—
197#13133206C2318yes—
198#13133206C2314yes—
199#13133205C2314yes—
200#13133205C2314yes—
201#13133205C2314yes—
202#13133205C2318yes—
203#13133205C2314yes—
204#13133205C2314yes—
205#13133204C2314yes—
206#13133203C2318yes—
207#13133203C2318yes—
208#13133203C2318yes—
209#13133203C2318yes—
210#13133202C2318yes—
211#13133202C2318yes—
212#13133202C2318yes—
213#13133202C2318yes—
214#13133202C2318yes—
215#13133202C2318yes—
216#13133201C2318yes—
217#13133201C2318yes—
218#13133200C2318yes—
219#13133200C2318yes—
220#13133200C2318yes—
221#13133200C2318yes—
222#13133200C2318yes—
223#13133200C2318yes—
224#13133199C2318yes—
225#13133199C2318yes—
226#13133199C2318yes—
227#13133199C2318yes—
228#13133198C2318yes—
229#13133198C2318yes—
230#13133198C2314yes—
231#13133198C2314yes—
232#13133197C2318yes—
233#13133196C2314yes—
234#13133196C2314yes—
235#13133196C2318yes—
236#13133196C2314yes—
237#13133196C2314yes—
238#13133196C2314yes—
239#13133196C2314yes—
240#13133195C2318yes—
241#13133195C2318yes—
242#13133195C2318yes—
243#13133195C2318yes—
244#13133195C2318yes—
245#13133195C2318yes—
246#13133194C2318yes—
247#13133194C2318yes—
248#13133194C2318yes—
249#13133194C2318yes—
250#13133193C2318yes—
251#13133193C2318yes—
252#13133193C2318yes—
253#13133192C2318yes—
254#13133191C2314yes—
255#13133191C2314yes—
256#13133191C2314yes—
257#13133191C2318yes—
258#13133191C2314yes—
259#13133191C2314yes—
260#13133191C2314yes—
261#13133190C2318yes—
262#13133190C2318yes—
263#13133190C2318yes—
264#13133190C2318yes—
265#13133189C2318yes—
266#13133189C2318yes—
267#13133189C2318yes—
268#13133189C2318yes—
269#13133189C2318yes—
270#13133189C2318yes—
271#13133188C2318yes—
272#13133187C2318yes—
273#13133187C2318yes—
274#13133185C2318yes—
275#13133185C2318yes—
276#13133185C2314yes—
277#13133185C2314yes—
278C4×Dic106C2314yes—
279C4×Dic106C2314yes—
280C4×Dic106C2314yes—
281C4×Dic106C2318yes—
282C4×Dic106C2314yes—
283C4×Dic106C2314yes—
284C4×Dic106C2314yes—
285#13133182C2318yes—
286#13133182C2318yes—
287C4×D212C2314yes—
288C4×D212C2314yes—
289C4×D212C2318yes—
290C4×D212C2314yes—
291C4×D212C2314yes—
292C4×D212C2314yes—
293C4×D212C2314yes—
294D4×Dic53C2318yes—
295D4×Dic53C2318yes—
296#13133179C2318yes—
297#13133179C2318yes—
298C4×C22⋊D53C2318yes—
299C4×C22⋊D53C2318yes—
300C4×C22⋊D53C2318yes—
301C4×C22⋊D53C2318yes—
302C4×C22⋊D53C2318yes—
303C4×C22⋊D53C2318yes—
304#13133177C2318yes—
305#13133177C2318yes—
306#13133177C2318yes—
307#13133177C2318yes—
308#13133177C2318yes—
309#13133177C2318yes—
310#13133176C2312yes—
311#13133176C2312yes—
312#13133175C2318yes—
313#13133175C2318yes—
314#13133174C2318yes—
315#13133174C2318yes—
316#13133174C2318yes—
317#13133174C2318yes—
318#13133174C2318yes—
319#13133174C2318yes—
320#13133173C2318yes—
321#13133173C2318yes—
322#13133173C2318yes—
323C2×C4⋊Dic53C2312yes—
324C2×C4⋊Dic53C2314yes—
325C2×C4⋊Dic53C2312yes—
326C2×#11719919C2314yes—
327C2×#11719919C2318yes—
328C2×#11719919C2314yes—
329C2×#11719919C2314yes—
330C2×#11719919C2314yes—
331C4⋊C4×D53C2318yes—
332C4⋊C4×D53C2318yes—
333C2×C22⋊Dic53C2314yes—
334C2×#11719921C2314yes—
335C2×#11719921C2318yes—
336C2×#11719921C2314yes—
337C2×#11719921C2314yes—
338C2×#11719921C2314yes—
339C22⋊C4×D53C2318yes—
340C22⋊C4×D53C2318yes—
341C22⋊C4×D53C2318yes—
342C2×C4×Dic53C2314yes—
343C2×#41×C53C2314yes—
344C2×#41×C53C2311yescharacteristic
345C2×#41×C53C2311yescharacteristic
346C23×C4×C53C2311yescharacteristic
347C23×C4×C53C2312yes—
348C4⋊Q8×C53C2311yescharacteristic
349C4⋊Q8×C53C2312yes—
350#127×C53C2311yescharacteristic
351#126×C53C2314yes—
352#126×C53C2314yes—
353#125×C53C2312yes—
354#125×C53C2314yes—
355#124×C53C2311yescharacteristic
356#124×C53C2311yescharacteristic
357#124×C53C2314yes—
358#123×C53C2312yes—
359#123×C53C2312yes—
360#123×C53C2314yes—
361#123×C53C2314yes—
362C22⋊Q8×C53C2314yes—
363C22⋊Q8×C53C2312yes—
364C22⋊Q8×C53C2314yes—
365C22⋊Q8×C53C2312yes—
366#121×C53C2312yes—
367#121×C53C2314yes—
368#121×C53C2312yes—
369#121×C53C2314yes—
370#120×C53C2312yes—
371#120×C53C2312yes—
372C4×Q8×C53C2312yes—
373C4×Q8×C53C2314yes—
374C4×Q8×C53C2312yes—
375C4×Q8×C53C2314yes—
376C4×D4×C53C2314yes—
377C4×D4×C53C2314yes—
378C4×D4×C53C2314yes—
379C4×D4×C53C2312yes—
380C4×D4×C53C2314yes—
381C4×D4×C53C2314yes—
382C4×D4×C53C2314yes—
383C4×D4×C53C2314yes—
384C4×D4×C53C2312yes—
385C4×D4×C53C2314yes—
386#117×C53C2314yes—
387#117×C53C2314yes—
388#117×C53C2311yescharacteristic
389#117×C53C2311yescharacteristic
390#117×C53C2314yes—
391#117×C53C2312yes—
392#117×C53C2312yes—
393C2×C42×C53C2312yes—
394C2×C42×C53C2311yescharacteristic
395C2×C42×C53C2312yes—
396C2×C42×C53C2312yes—
397C2×C42×C53C2312yes—
398C2×C42×C53C2312yes—
399C2×C42×C53C2311yescharacteristic
400C2×C42×C53C2312yes—
401C2×C42×C53C2312yes—
402C24×C53C2411yescharacteristic
403C23×D53C2414yes—
404C23×D53C2414yes—
405#41×C53—42no—
406#41×C53—42no—
407#41×C53—48no—
408C2×Q8×C53C2411yescharacteristic
409C2×Q8×C53C2414yes—
410C2×Q8×C53C2411yescharacteristic
411C2×D4×C53C2414yes—
412C2×D4×C53C2414yes—
413C2×D4×C53C2412yes—
414C2×D4×C53C2412yes—
415C2×D4×C53C2411yescharacteristic
416C2×D4×C53C2414yes—
417C2×D4×C53C2411yescharacteristic
418C22×C4×C53—42no—
419C22×C4×C53—44no—
420C22×C4×C53C2412yes—
421C22×C4×C53C2411yescharacteristic
422C22×C4×C53C2412yes—
423C22×C4×C53C2412yes—
424C22×C4×C53C2412yes—
425C22×C4×C53C2412yes—
426C22×C4×C53C2412yes—
427C22×C4×C53C2412yes—
428C22×C4×C53C2412yes—
429C22×C4×C53C2412yes—
430C22×C4×C53C2412yes—
431C22×C4×C53C2411yescharacteristic
432C22×C4×C53C2414yes—
433C22×C4×C53C2414yes—
434C2×C22⋊D53—48no—
435C2×C22⋊D53C2418yes—
436C2×C22⋊D53C2418yes—
437C2×C22⋊D53C2418yes—
438C2×C22⋊D53C2418yes—
439C2×C22⋊D53C2418yes—
440C22×Dic53C2414yes—
441C22×Dic53C2414yes—
442C22×Dic53C2414yes—
443C22×Dic53C2414yes—
444C22×Dic53C2418yes—
445#11719947—416no—
446D4×D53—416no—
447#11719945—48no—
448C2×D212—44no—
449C2×D212—44no—
450C2×D212C2414yes—
451C2×D212C2414yes—
452C2×D212C2418yes—
453C2×D212C2414yes—
454C2×C4×D53—48no—
455C2×C4×D53C2418yes—
456C2×C4×D53C2418yes—
457C2×C4×D53C2418yes—
458C2×C4×D53C2418yes—
459C2×C4×D53C2418yes—
460C2×Dic106—44no—
461C2×Dic106—44no—
462C2×Dic106C2414yes—
463C2×Dic106C2414yes—
464C2×Dic106C2418yes—
465C2×Dic106C2414yes—
466C4⋊C4×C53C2412yes—
467C4⋊C4×C53C2414yes—
468C4⋊C4×C53C2414yes—
469C4⋊C4×C53C2412yes—
470C4⋊C4×C53C2414yes—
471C4⋊C4×C53C2414yes—
472C4⋊C4×C53C2414yes—
473C4⋊C4×C53C2414yes—
474C4⋊C4×C53C2414yes—
475C4⋊C4×C53C2414yes—
476C22⋊C4×C53C2414yes—
477C22⋊C4×C53C2414yes—
478C22⋊C4×C53C2412yes—
479C22⋊C4×C53C2412yes—
480C22⋊C4×C53C2414yes—
481C22⋊C4×C53C2414yes—
482C22⋊C4×C53C2414yes—
483C22⋊C4×C53C2414yes—
484C22⋊C4×C53C2414yes—
485C22⋊C4×C53C2414yes—
486C42×C53C2411yescharacteristic
487C42×C53C2412yes—
488C42×C53C2411yescharacteristic
489C42×C53C2412yes—
490C42×C53C2412yes—
491C42×C53C2412yes—
492C42×C53C2411yescharacteristic
493C42×C53C2412yes—
494C42×C53C2412yes—
495C42×C53C2411yescharacteristic
496C42×C53C2414yes—
497C42×C53C2414yes—
498C42×C53C2412yes—
499C42×C53C2412yes—
500C22⋊Dic53C2414yes—
501C22⋊Dic53C2418yes—
502C22⋊Dic53C2418yes—
503C22⋊Dic53C2418yes—
504C22⋊Dic53C2414yes—
505C22⋊Dic53C2418yes—
506#11719921C2418yes—
507#11719921C2418yes—
508#11719921C2418yes—
509#11719921C2418yes—
510#11719921C2418yes—
511#11719921C2418yes—
512#11719921C2418yes—
513#11719921C2418yes—
514#11719921C2418yes—
515#11719921C2418yes—
516#11719921C2418yes—
517#11719921C2418yes—
518#11719921C2418yes—
519#11719921C2418yes—
520C4⋊Dic53C2418yes—
521C4⋊Dic53C2418yes—
522C4⋊Dic53C2414yes—
523C4⋊Dic53C2414yes—
524C4⋊Dic53C2414yes—
525C4⋊Dic53C2414yes—
526C4⋊Dic53C2418yes—
527#11719919C2418yes—
528#11719919C2418yes—
529#11719919C2418yes—
530#11719919C2418yes—
531#11719919C2418yes—
532#11719919C2418yes—
533#11719919C2418yes—
534#11719919C2418yes—
535#11719919C2418yes—
536#11719919C2418yes—
537#11719919C2418yes—
538#11719919C2418yes—
539#11719919C2418yes—
540#11719919C2418yes—
541C4×Dic53C2418yes—
542C4×Dic53C2418yes—
543C4×Dic53C2414yes—
544C4×Dic53C2414yes—
545C4×Dic53C2418yes—
546C4×Dic53C2418yes—
547C23×C53—24no—
548C23×C53—41no—
549C23×C53C2512yes—
550C23×C53C2512yes—
551C23×C53C2511yescharacteristic
552C23×C53C2512yes—
553C22×D53—28no—
554C22×D53—44no—
555C22×D53—44no—
556C22×D53—44no—
557C22×D53—48no—
558C22×D53C2518yes—
559Q8×C53—44no—
560Q8×C53—41no—
561Q8×C53—41no—
562D4×C53—28no—
563D4×C53—28no—
564D4×C53—42no—
565D4×C53—42no—
566D4×C53—44no—
567D4×C53—41no—
568D4×C53—41no—
569C2×C4×C53—24no—
570C2×C4×C53—24no—
571C2×C4×C53—24no—
572C2×C4×C53—24no—
573C2×C4×C53—24no—
574C2×C4×C53—22no—
575C2×C4×C53—41no—
576C2×C4×C53—42no—
577C2×C4×C53—42no—
578C2×C4×C53—42no—
579C2×C4×C53—42no—
580C2×C4×C53—42no—
581C2×C4×C53—44no—
582C2×C4×C53—44no—
583C2×C4×C53C2514yes—
584C2×C4×C53C2512yes—
585C2×C4×C53C2512yes—
586C2×C4×C53C2512yes—
587C2×C4×C53C2512yes—
588C2×C4×C53C2512yes—
589C2×C4×C53C2514yes—
590C2×C4×C53C2512yes—
591C2×C4×C53C2512yes—
592C2×C4×C53C2511yescharacteristic
593C2×C4×C53C2511yescharacteristic
594C22⋊D53—216no—
595C22⋊D53—48no—
596C22⋊D53—48no—
597C22⋊D53—48no—
598C22⋊D53—48no—
599C2×Dic53—28no—
600C2×Dic53—44no—
601C2×Dic53—44no—
602C2×Dic53—48no—
603C2×Dic53—44no—
604C2×Dic53C2518yes—
605C2×Dic53C2518yes—
606C2×Dic53C2518yes—
607D212—28no—
608D212—44no—
609D212—44no—
610D212—48no—
611C4×D53—48no—
612C4×D53—48no—
613C4×D53—48no—
614C4×D53—48no—
615C4×D53—48no—
616Dic106—28no—
617Dic106—44no—
618Dic106—44no—
619Dic106—48no—
620#62829—531nomaximal, Sylow
621C22×C53—22no—
622C22×C53—22no—
623C22×C53—24no—
624C22×C53—22no—
625C22×C53—22no—
626C22×C53—22no—
627C22×C53—24no—
628C22×C53—21no—
629C22×C53—44no—
630C22×C53#58514yes—
631C22×C53C2611yescharacteristic
632C2×D53—28no—
633C2×D53—28no—
634C2×D53—28no—
635C2×D53—88no—
636C2×D53—164no—
637C4×C53—24no—
638C4×C53—22no—
639C4×C53—22no—
640C4×C53—22no—
641C4×C53—22no—
642C4×C53—22no—
643C4×C53—24no—
644C4×C53—22no—
645C4×C53—22no—
646C4×C53—21no—
647C4×C53#58512yes—
648Dic53—28no—
649Dic53—28no—
650Dic53—28no—
651#3566—538no—
652#3564—534no—
653#3560—534no—
654#3557—532no—
655#3551—532no—
656#3538—531no—
657#3537—531no—
658#3536—532no—
659#3516—534no—
660#3515—534no—
661#3514—534no—
662#3513—534no—
663#3513—538no—
664#3512—532no—
665#3510—532no—
666#3493—534no—
667#3491—534no—
668#3444D5311yescharacteristic, complemented
669C2×#529—532no—
670C2×C53—24no—
671C2×C53—42no—
672C2×C53—42no—
673C2×C53—41no—
674C2×C53C2×#58512yes—
675C2×C53C2×#58511yescharacteristic
676D53—48no—
677#563—534no—
678#563—538no—
679#563—534no—
680#562—538no—
681#560—534no—
682#560—534no—
683#559—534no—
684#559—538no—
685#557—534no—
686#556—538no—
687#556—538no—
688#556—534no—
689#555—534no—
690#555—538no—
691#554—538no—
692#554—534no—
693#554—534no—
694#553—538no—
695#553—538no—
696#553—534no—
697#553—534no—
698#553—538no—
699#553—538no—
700#553—538no—
701#552—538no—
702#552—538no—
703#552—538no—
704#552—534no—
705#552—534no—
706#552—538no—
707#552—538no—
708#552—538no—
709#551—538no—
710#551—534no—
711#551—538no—
712#551—534no—
713#551—538no—
714#551—538no—
715#551—538no—
716#551—538no—
717D4×Q8—534no—
718#548—534no—
719#548—534no—
720#547—538no—
721#547—534no—
722#546—538no—
723#546—538no—
724#546—538no—
725#546—534no—
726#546—534no—
727D42—534no—
728D42—534no—
729#544—534no—
730#543—534no—
731#542—538no—
732#542—538no—
733#542—538no—
734#542—534no—
735#542—534no—
736#541—538no—
737#541—538no—
738#541—532no—
739#541—532no—
740#540—538no—
741#540—532no—
742#540—532no—
743#539—538no—
744#539—534no—
745#539—538no—
746#539—534no—
747#539—538no—
748#539—538no—
749#538—538no—
750#538—534no—
751#538—534no—
752#538—538no—
753#538—538no—
754#538—538no—
755#537—534no—
756#537—534no—
757#536—532no—
758#535—532no—
759#534—534no—
760#533—532no—
761#533C2×D5311yescharacteristic, complemented
762#533C2×D5312yescomplemented
763#532—532no—
764#532C2×D5311yescharacteristic, complemented
765#532C2×D5312yescomplemented
766#529—538no—
767#529—538no—
768#529—534no—
769#529—534no—
770#529—534no—
771#529—534no—
772#529—534no—
773#529—534no—
774#529—534no—
775#529—534no—
776#529—534no—
777#529—534no—
778#529C2×D5312yescomplemented
779#529C2×D5312yescomplemented
780#529C2×D5314yescomplemented
781#529C2×D5314yescomplemented
782C2×#126—534no—
783C2×#125—532no—
784C2×#125—532no—
785C2×#124—532no—
786C2×#124—532no—
787#525—538no—
788#525C2×D5311yescharacteristic
789#525C2×D5314yescomplemented
790#525C2×D5311yescharacteristic, complemented
791C2×#123—534no—
792C2×#123—538no—
793C2×C22⋊Q8—532no—
794C2×#121—532no—
795#520—538no—
796#520—534no—
797#519—532no—
798#518—538no—
799#518—532no—
800C4×#41C2×D5311yescharacteristic, complemented
801C4×#41C2×D5311yescharacteristic, complemented
802C4×#41C2×D5314yescomplemented
803C2×C4×Q8—532no—
804C2×C4×D4—534no—
805C2×C4×D4—532no—
806C2×#117—534no—
807C22×C42C2×D5311yescharacteristic, complemented
808C53#6282911yescharacteristic, complemented, Sylow
809C2×#41—538no—
810C2×#41—534no—
811C2×#41C22×D5311yescharacteristic
812C2×#41C22×D5311yescharacteristic
813C2×#41C22×D5314yes—
814C22×Q8—532no—
815C22×Q8—532no—
816C22×D4—534no—
817C22×D4—538no—
818C22×D4—532no—
819C22×D4—532no—
820C23×C4—534no—
821C23×C4C22×D5312yes—
822C23×C4C22×D5311yescharacteristic
823C4⋊Q8—534no—
824C4⋊Q8—538no—
825C4⋊Q8—538no—
826C4⋊Q8—532no—
827C4⋊Q8—534no—
828C4⋊Q8C22×D5312yes—
829C4⋊Q8C22×D5311yescharacteristic
830#127—534no—
831#127—532no—
832#127C22×D5311yescharacteristic
833#126—538no—
834#126—538no—
835#126—538no—
836#126—538no—
837#126—538no—
838#126—538no—
839#126—538no—
840#126—538no—
841#126—538no—
842#126—538no—
843#126—538no—
844#126—538no—
845#126—538no—
846#126—538no—
847#126—538no—
848#126—538no—
849#126C22×D5314yes—
850#126C22×D5314yes—
851#125—538no—
852#125—538no—
853#125—538no—
854#125—538no—
855#125—538no—
856#125—538no—
857#125—538no—
858#125—534no—
859#125—534no—
860#125—534no—
861#125—534no—
862#125—538no—
863#125—532no—
864#125—532no—
865#125C22×D5314yes—
866#125C22×D5312yes—
867#124—534no—
868#124—538no—
869#124—534no—
870#124—538no—
871#124—538no—
872#124—538no—
873#124—538no—
874#124—534no—
875#124—534no—
876#124—534no—
877#124—534no—
878#124—538no—
879#124—534no—
880#124C22×D5314yes—
881#124C22×D5311yescharacteristic
882#124C22×D5311yescharacteristic
883#123—538no—
884#123—534no—
885#123—534no—
886#123—538no—
887#123—538no—
888#123—538no—
889#123—538no—
890#123—538no—
891#123—538no—
892#123—538no—
893#123—538no—
894#123—538no—
895#123—538no—
896#123—538no—
897#123—538no—
898#123—538no—
899#123—538no—
900#123—538no—
901#123—538no—
902#123—538no—
903#123—538no—
904#123—538no—
905#123C22×D5314yes—
906#123C22×D5314yes—
907#123C22×D5312yes—
908#123C22×D5312yes—
909C22⋊Q8—538no—
910C22⋊Q8—538no—
911C22⋊Q8—538no—
912C22⋊Q8—534no—
913C22⋊Q8—534no—
914C22⋊Q8—534no—
915C22⋊Q8—534no—
916C22⋊Q8—534no—
917C22⋊Q8—534no—
918C22⋊Q8—538no—
919C22⋊Q8—538no—
920C22⋊Q8—538no—
921C22⋊Q8—538no—
922C22⋊Q8—538no—
923C22⋊Q8—538no—
924C22⋊Q8—538no—
925C22⋊Q8—538no—
926C22⋊Q8—538no—
927C22⋊Q8—538no—
928C22⋊Q8—538no—
929C22⋊Q8—538no—
930C22⋊Q8C22×D5312yes—
931C22⋊Q8C22×D5314yes—
932C22⋊Q8C22×D5312yes—
933C22⋊Q8C22×D5314yes—
934#121—538no—
935#121—538no—
936#121—538no—
937#121—538no—
938#121—538no—
939#121—538no—
940#121—538no—
941#121—534no—
942#121—534no—
943#121—534no—
944#121—534no—
945#121—534no—
946#121—534no—
947#121—538no—
948#121—538no—
949#121—538no—
950#121—538no—
951#121—538no—
952#121—538no—
953#121C22×D5312yes—
954#121C22×D5312yes—
955#121C22×D5314yes—
956#121C22×D5314yes—
957#120—538no—
958#120—534no—
959#120—534no—
960#120—538no—
961#120—538no—
962#120—538no—
963#120C22×D5312yes—
964#120C22×D5312yes—
965C4×Q8—538no—
966C4×Q8—538no—
967C4×Q8—534no—
968C4×Q8—534no—
969C4×Q8—534no—
970C4×Q8—534no—
971C4×Q8—534no—
972C4×Q8—534no—
973C4×Q8—538no—
974C4×Q8C22×D5314yes—
975C4×Q8C22×D5312yes—
976C4×Q8C22×D5314yes—
977C4×Q8C22×D5312yes—
978C4×D4—538no—
979C4×D4—538no—
980C4×D4—538no—
981C4×D4—538no—
982C4×D4—538no—
983C4×D4—538no—
984C4×D4—538no—
985C4×D4—538no—
986C4×D4—538no—
987C4×D4—538no—
988C4×D4—538no—
989C4×D4—538no—
990C4×D4—538no—
991C4×D4—538no—
992C4×D4—538no—
993C4×D4—538no—
994C4×D4—534no—
995C4×D4—534no—
996C4×D4—534no—
997C4×D4—534no—
998C4×D4—534no—
999C4×D4—538no—
1000C4×D4—534no—
1001C4×D4C22×D5314yes—
1002C4×D4C22×D5314yes—
1003C4×D4C22×D5314yes—
1004C4×D4C22×D5314yes—
1005C4×D4C22×D5314yes—
1006C4×D4C22×D5314yes—
1007C4×D4C22×D5314yes—
1008C4×D4C22×D5314yes—
1009C4×D4C22×D5312yes—
1010C4×D4C22×D5312yes—
1011#117—532no—
1012#117—532no—
1013#117—538no—
1014#117—538no—
1015#117—538no—
1016#117—538no—
1017#117—538no—
1018#117—538no—
1019#117—538no—
1020#117—538no—
1021#117—538no—
1022#117—538no—
1023#117—538no—
1024#117C22×D5312yes—
1025#117C22×D5312yes—
1026#117C22×D5311yescharacteristic
1027#117C22×D5311yescharacteristic
1028#117C22×D5314yes—
1029#117C22×D5314yes—
1030#117C22×D5314yes—
1031C2×C4⋊C4—534no—
1032C2×C4⋊C4—534no—
1033C2×C4⋊C4—532no—
1034C2×C4⋊C4—534no—
1035C2×C4⋊C4—532no—
1036C2×C4⋊C4—534no—
1037C2×C4⋊C4—534no—
1038C2×C4⋊C4—538no—
1039C2×C4⋊C4—538no—
1040C2×C4⋊C4—538no—
1041C2×C22⋊C4—534no—
1042C2×C22⋊C4—534no—
1043C2×C22⋊C4—534no—
1044C2×C22⋊C4—534no—
1045C2×C22⋊C4—534no—
1046C2×C22⋊C4—538no—
1047C2×C22⋊C4—538no—
1048C2×C22⋊C4—538no—
1049C2×C22⋊C4—538no—
1050C2×C42—534no—
1051C2×C42C22×D5312yes—
1052C2×C42C22×D5312yes—
1053C2×C42C22×D5312yes—
1054C2×C42C22×D5312yes—
1055C2×C42C22×D5312yes—
1056C2×C42C22×D5311yescharacteristic
1057C2×C42C22×D5312yes—
1058C2×C42C22×D5312yes—
1059C2×C42C22×D5311yescharacteristic
1060C24—534no—
1061C24—534no—
1062C24C23×D5311yescharacteristic
1063#41—42no—
1064#41—42no—
1065#41—48no—
1066#41—2128no—
1067#41—21216no—
1068C2×Q8—534no—
1069C2×Q8—538no—
1070C2×Q8—534no—
1071C2×Q8—534no—
1072C2×Q8—2124no—
1073C2×Q8—2124no—
1074C2×Q8C23×D5311yescharacteristic
1075C2×Q8C23×D5314yes—
1076C2×Q8C23×D5311yescharacteristic
1077C2×D4—538no—
1078C2×D4—538no—
1079C2×D4—538no—
1080C2×D4—538no—
1081C2×D4—538no—
1082C2×D4—534no—
1083C2×D4—534no—
1084C2×D4—538no—
1085C2×D4—534no—
1086C2×D4—2124no—
1087C2×D4—2124no—
1088C2×D4—21216no—
1089C2×D4—2128no—
1090C2×D4C23×D5314yes—
1091C2×D4C23×D5314yes—
1092C2×D4C23×D5311yescharacteristic
1093C2×D4C23×D5312yes—
1094C2×D4C23×D5314yes—
1095C2×D4C23×D5312yes—
1096C2×D4C23×D5311yescharacteristic
1097C22×C4—42no—
1098C22×C4—44no—
1099C22×C4—534no—
1100C22×C4—534no—
1101C22×C4—534no—
1102C22×C4—534no—
1103C22×C4—538no—
1104C22×C4—538no—
1105C22×C4—538no—
1106C22×C4—538no—
1107C22×C4—538no—
1108C22×C4—538no—
1109C22×C4—2128no—
1110C22×C4C23×D5312yes—
1111C22×C4C23×D5312yes—
1112C22×C4C23×D5312yes—
1113C22×C4C23×D5311yescharacteristic
1114C22×C4C23×D5312yes—
1115C22×C4C23×D5312yes—
1116C22×C4C23×D5312yes—
1117C22×C4C23×D5312yes—
1118C22×C4C23×D5312yes—
1119C22×C4C23×D5312yes—
1120C22×C4C23×D5312yes—
1121C22×C4C23×D5311yescharacteristic
1122C22×C4C23×D5314yes—
1123C22×C4C23×D5314yes—
1124C4⋊C4—538no—
1125C4⋊C4—538no—
1126C4⋊C4—534no—
1127C4⋊C4—538no—
1128C4⋊C4—534no—
1129C4⋊C4—538no—
1130C4⋊C4—538no—
1131C4⋊C4—538no—
1132C4⋊C4—538no—
1133C4⋊C4—538no—
1134C4⋊C4—538no—
1135C4⋊C4—534no—
1136C4⋊C4—538no—
1137C4⋊C4—538no—
1138C4⋊C4—538no—
1139C4⋊C4—534no—
1140C4⋊C4—538no—
1141C4⋊C4—538no—
1142C4⋊C4—538no—
1143C4⋊C4—538no—
1144C4⋊C4—538no—
1145C4⋊C4C23×D5314yes—
1146C4⋊C4C23×D5314yes—
1147C4⋊C4C23×D5314yes—
1148C4⋊C4C23×D5314yes—
1149C4⋊C4C23×D5314yes—
1150C4⋊C4C23×D5312yes—
1151C4⋊C4C23×D5314yes—
1152C4⋊C4C23×D5314yes—
1153C4⋊C4C23×D5312yes—
1154C4⋊C4C23×D5314yes—
1155C22⋊C4—538no—
1156C22⋊C4—534no—
1157C22⋊C4—538no—
1158C22⋊C4—538no—
1159C22⋊C4—534no—
1160C22⋊C4—538no—
1161C22⋊C4—538no—
1162C22⋊C4—538no—
1163C22⋊C4—538no—
1164C22⋊C4—538no—
1165C22⋊C4—538no—
1166C22⋊C4—538no—
1167C22⋊C4—538no—
1168C22⋊C4—538no—
1169C22⋊C4—538no—
1170C22⋊C4—538no—
1171C22⋊C4—538no—
1172C22⋊C4—538no—
1173C22⋊C4—538no—
1174C22⋊C4—538no—
1175C22⋊C4C23×D5314yes—
1176C22⋊C4C23×D5314yes—
1177C22⋊C4C23×D5314yes—
1178C22⋊C4C23×D5314yes—
1179C22⋊C4C23×D5314yes—
1180C22⋊C4C23×D5314yes—
1181C22⋊C4C23×D5314yes—
1182C22⋊C4C23×D5312yes—
1183C22⋊C4C23×D5312yes—
1184C22⋊C4C23×D5314yes—
1185C42—538no—
1186C42—538no—
1187C42—538no—
1188C42—534no—
1189C42—538no—
1190C42—534no—
1191C42C23×D5311yescharacteristic
1192C42C23×D5311yescharacteristic
1193C42C23×D5312yes—
1194C42C23×D5312yes—
1195C42C23×D5312yes—
1196C42C23×D5311yescharacteristic
1197C42C23×D5312yes—
1198C42C23×D5312yes—
1199C42C23×D5312yes—
1200C42C23×D5311yescharacteristic
1201C42C23×D5314yes—
1202C42C23×D5314yes—
1203C42C23×D5312yes—
1204C42C23×D5312yes—
1205C23—24no—
1206C23—41no—
1207C23—538no—
1208C23—1068no—
1209C23—2124no—
1210C23—2128no—
1211C23—2124no—
1212C23—2124no—
1213C23C24×D5312yes—
1214C23C24×D5311yescharacteristic
1215C23C24×D5312yes—
1216C23C24×D5312yes—
1217Q8—41no—
1218Q8—41no—
1219Q8—44no—
1220Q8—1068no—
1221Q8—2124no—
1222Q8—2124no—
1223Q8—2128no—
1224D4—28no—
1225D4—28no—
1226D4—41no—
1227D4—41no—
1228D4—44no—
1229D4—42no—
1230D4—42no—
1231D4—10616no—
1232D4—1068no—
1233D4—2124no—
1234D4—2124no—
1235D4—2128no—
1236D4—2128no—
1237D4—2128no—
1238D4—2128no—
1239D4—2128no—
1240C2×C4—24no—
1241C2×C4—24no—
1242C2×C4—24no—
1243C2×C4—22no—
1244C2×C4—24no—
1245C2×C4—24no—
1246C2×C4—42no—
1247C2×C4—42no—
1248C2×C4—42no—
1249C2×C4—42no—
1250C2×C4—42no—
1251C2×C4—41no—
1252C2×C4—44no—
1253C2×C4—44no—
1254C2×C4—538no—
1255C2×C4—538no—
1256C2×C4—538no—
1257C2×C4—1068no—
1258C2×C4—2128no—
1259C2×C4—2128no—
1260C2×C4—2128no—
1261C2×C4—2128no—
1262C2×C4—2128no—
1263C2×C4—2124no—
1264C2×C4—2124no—
1265C2×C4—2124no—
1266C2×C4—2128no—
1267C2×C4C24×D5312yes—
1268C2×C4C24×D5312yes—
1269C2×C4C24×D5312yes—
1270C2×C4C24×D5314yes—
1271C2×C4C24×D5314yes—
1272C2×C4C24×D5312yes—
1273C2×C4C24×D5311yescharacteristic
1274C2×C4C24×D5312yes—
1275C2×C4C24×D5312yes—
1276C2×C4C24×D5312yes—
1277C2×C4C24×D5311yescharacteristic
1278C22—22no—
1279C22—22no—
1280C22—21no—
1281C22—22no—
1282C22—22no—
1283C22—22no—
1284C22—24no—
1285C22—24no—
1286C22—44no—
1287C22—8484no—
1288C22—1068no—
1289C22—1068no—
1290C22—1068no—
1291C22—4248no—
1292C22#1681145914yes—
1293C22C25×D5311yescharacteristic
1294C4—22no—
1295C4—22no—
1296C4—22no—
1297C4—22no—
1298C4—21no—
1299C4—22no—
1300C4—22no—
1301C4—22no—
1302C4—24no—
1303C4—24no—
1304C4—1068no—
1305C4—1068no—
1306C4—1068no—
1307C4#1681145912yes—
1308C2—24no—
1309C2—41no—
1310C2—42no—
1311C2—42no—
1312C2—2128no—
1313C2C2×#1681145912yes—
1314C2C2×#1681145911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3444C2
hypercenter#3444D53
hypocenterC53#62829
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #20289391C2semidirect
2. #20289343C2semidirect
3. #20289271C2semidirect
4. #20289221C2semidirect
5. #20289142C2semidirect
6. #20288964C2semidirect
7. #20288954C2semidirect
8. #20288942C2semidirect
9. #20288704C2semidirect
10. #20288693C2semidirect
11. #20288676C2semidirect
12. #20288659C2semidirect
13. #20288641C2semidirect
14. #20288637C2semidirect
15. #20288611C2semidirect
16. #20288427C2semidirect
17. #20288407C2semidirect
18. C2×#16811157C2semidirect
19. C53×#3444C2semidirect
20. #16811376C22semidirect
21. #16811372C22semidirect
22. #16811372C22semidirect
23. #16811370C22semidirect
25. #16811360C22semidirect
26. #16811358C22semidirect
27. #16811356C22semidirect
28. #16811351C22semidirect
29. #16811346C22semidirect
30. #16811345C22semidirect
31. #16811340C22semidirect
32. #16811336C22semidirect
33. #16811335C22semidirect
34. #16811333C22semidirect
35. #16811330C22semidirect
36. #16811327C22semidirect
37. #16811324C22semidirect
38. #16811323C22semidirect
39. #16811322C22semidirect
40. #16811322C22semidirect
42. #16811319C22semidirect
43. #16811316C22semidirect
44. #16811314C22semidirect
45. #16811313C22semidirect
46. #16811313C22semidirect
47. #16811312C22semidirect
48. #16811309C22semidirect
49. #16811306C22semidirect
50. #16811306C22semidirect
51. #16811305C22semidirect
52. #16811304C22semidirect
53. #16811303C22semidirect
54. #16811302C22semidirect
55. #16811302C22semidirect
56. #16811300C22semidirect
57. #16811298C22semidirect
58. #16811297C22semidirect
59. #16811297C22semidirect
60. D4×Dic106C22semidirect
61. #16811282C22semidirect
62. #16811282C22semidirect
63. #16811277C22semidirect
64. #16811272C22semidirect
65. #16811269C22semidirect
66. #16811269C22semidirect
67. #16811262C22semidirect
68. #16811261C22semidirect
69. #16811260C22semidirect
72. #16811252C22semidirect
73. #16811248C22semidirect
74. #16811245C22semidirect
75. #16811244C22semidirect
76. #16811244C22semidirect
77. #16811243C22semidirect
78. #16811237C22semidirect
79. #16811235C22semidirect
80. #16811235C22semidirect
81. #16811232C22semidirect
82. #16811231C22semidirect
84. #16811228C22semidirect
85. #16811223C22semidirect
86. #16811222C22semidirect
87. #16811221C22semidirect
88. #16811219C22semidirect
89. #16811218C22semidirect
90. #16811215C22semidirect
91. #16811215C22semidirect
93. #16811210C22semidirect
94. #16811207C22semidirect
95. #16811206C22semidirect
96. #16811206C22semidirect
97. #16811205C22semidirect
98. #16811201C22semidirect
99. #16811200C22semidirect
100. #16811194C22semidirect
103. #16811180C22semidirect
104. #16811173C22semidirect
105. #16811157C22semidirect
106. #16811157C22semidirect
107. #16811157C22semidirect
108. #16811157C22semidirect
109. #16811157C22semidirect
110. #16811157C22semidirect
111. #16811157C22semidirect
112. #16811157C22semidirect
113. #16811157C22semidirect
114. #16811157C22semidirect
115. #16811150C22semidirect
116. #16811150C22semidirect
117. C2×#13133211C22semidirect
118. C2×#13133209C22semidirect
119. C2×#13133209C22semidirect
120. C2×#13133205C22semidirect
121. C2×#13133205C22semidirect
122. #16811131C22semidirect
123. C2×#13133200C22semidirect
124. #123×D53C22semidirect
125. C2×#13133196C22semidirect
127. #16811103C22semidirect
128. #16811102C22semidirect
129. #16811100C22semidirect
130. #16811097C22semidirect
131. #16811095C22semidirect
132. C2×C4×Dic106C22semidirect
133. C2×C4×D212C22semidirect
134. C2×C4×C22⋊D53C22semidirect
135. C2×#13133174C22semidirect
136. C53×#533C22semidirect
137. C53×#533C22semidirect
138. C53×#532C22semidirect
139. C53×#532C22semidirect
140. C53×#529C22semidirect
141. C53×#529C22semidirect
142. C53×#529C22semidirect
143. C53×#529C22semidirect
145. C53×#525C22semidirect
146. C53×#525C22semidirect
147. C4×#41×C53C22semidirect
148. C4×#41×C53C22semidirect
149. C4×#41×C53C22semidirect
150. C22×C42×C53C22semidirect
668. #3444D53semidirect
761. #533C2×D53semidirect
762. #533C2×D53semidirect
764. #532C2×D53semidirect
765. #532C2×D53semidirect
778. #529C2×D53semidirect
779. #529C2×D53semidirect
780. #529C2×D53semidirect
781. #529C2×D53semidirect
789. #525C2×D53semidirect
790. #525C2×D53semidirect
800. C4×#41C2×D53semidirect
801. C4×#41C2×D53semidirect
802. C4×#41C2×D53semidirect
807. C22×C42C2×D53semidirect
808. C53#62829semidirect

Maximal subgroups

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

subgroupindex
#202893912
#202893432
#202892712
#202892212
#202891422
#202889642
#202889542
#202889422
#202887042
#202886932
#202886762
#202886592
#202886412
#202886372
#202886112
#202884272
#202884072
C2×#168111572
C53×#34442
#6282953