Finite Group Databasebeta

← #28293048

Subgroups — #28293048

Order 13568.

6428 conjugacy classes of subgroups.

The subgroup lattice has 1688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289314C214yesmaximal, complemented
2#20289311C214yesmaximal, complemented
3#20289207C212yesmaximal, complemented
4#20289204C212yesmaximal, complemented
5#20289199C212yesmaximal, complemented
6#20289195C214yesmaximal, complemented
7#20289121C212yesmaximal, complemented
8#20288957C214yesmaximal, complemented
9#20288808C214yesmaximal, complemented
10#20288803C214yesmaximal, complemented
11#20288598C212yesmaximal, complemented
12#20288598C214yesmaximal, complemented
13#20288596C212yesmaximal, complemented
14#20288582C211yesmaximal, characteristic, complemented
15#20288581C212yesmaximal, complemented
16#20288580C211yesmaximal, characteristic, complemented
17#20288533C212yesmaximal, complemented
18#20288530C212yesmaximal, complemented
19#20288524C212yesmaximal, complemented
20#20288520C211yesmaximal, characteristic, complemented
21#20288470C212yesmaximal, complemented
22#20288462C214yesmaximal, complemented
23#20288457C212yesmaximal, complemented
24#20288012C211yesmaximal, characteristic
25C2×#16811177C211yesmaximal, characteristic, complemented
26#533×D53C211yesmaximal, characteristic, complemented
27C53×#3502C211yesmaximal, characteristic, complemented
28C53⋊#564C2218yescomplemented
29#16811377C2218yes—
30#16811372C2218yes—
31#16811372C2218yescomplemented
32#16811358C2212yescomplemented
33#16811358C2212yescomplemented
34Q8×Dic106C2212yescomplemented
35#16811353C2212yescomplemented
36#16811353C2214yescomplemented
37#16811352C2212yescomplemented
38#16811351C2214yescomplemented
39#16811351C2212yescomplemented
40#16811351C2212yescomplemented
41#16811351C2214yescomplemented
42#16811351C2214yescomplemented
43#16811350C2214yescomplemented
44#16811350C2214yescomplemented
45#16811349C2214yescomplemented
46#16811349C2214yescomplemented
47#16811348C2212yescomplemented
48#16811348C2218yescomplemented
49#16811348C2214yescomplemented
50#16811348C2214yescomplemented
51#16811347C2214yes—
52#16811347C2214yescomplemented
53#16811347C2212yescomplemented
54#16811346C2214yes—
55#16811346C2214yescomplemented
56#16811346C2212yescomplemented
57#16811345C2218yes—
58#16811345C2214yescomplemented
59#16811345C2214yescomplemented
60#16811345C2214yescomplemented
61#16811345C2214yescomplemented
62#16811345C2214yescomplemented
63#16811334C2214yes—
64#16811334C2212yescomplemented
65#16811333C2214yes—
66#16811333C2212yescomplemented
67#16811329C2214yescomplemented
68#16811327C2218yes—
69#16811315C2218yes—
70#16811314C2218yes—
71#16811314C2214yes—
72#16811314C2214yes—
73#16811314C2214yescomplemented
74#16811311C2214yes—
75#16811311C2214yes—
76#16811311C2214yescomplemented
77#16811306C2218yes—
78#16811306C2218yes—
79#16811306C2218yes—
80#16811305C2218yes—
81#16811305C2218yes—
82#16811305C2218yes—
83#16811305C2218yescomplemented
84#16811300C2218yes—
85#16811297C2218yes—
86#16811288C2218yes—
87#16811288C2214yescomplemented
88#16811288C2214yescomplemented
89#16811286C2218yes—
90#16811253C2214yescomplemented
91#16811252C2214yes—
92#16811251C2212yes—
93#16811250C2214yes—
94#16811250C2218yes—
95#16811250C2214yescomplemented
96#16811250C2218yescomplemented
97#16811247C2214yes—
98#16811247C2214yes—
99#16811245C2214yes—
100#16811245C2214yes—
101#16811236C2214yes—
102#16811234C2214yes—
103#16811234C2218yescomplemented
104#16811232C2218yes—
105#16811232C2218yescomplemented
106#16811232C2218yescomplemented
107#16811232C2218yescomplemented
108#16811232C2218yescomplemented
109#16811231C2214yes—
110#16811231C2214yes—
111#16811231C2218yescomplemented
112#16811231C2214yescomplemented
113#16811231C2214yescomplemented
114#16811222C2214yes—
115#16811221C2218yes—
116#16811220C2214yes—
117#16811199C2212yes—
118#16811198C2214yes—
119#16811198C2218yes—
120#16811197C2212yes—
121#16811180C2211yescharacteristic
122#16811179C2212yes—
123#16811179C2214yescomplemented
124#16811178C2211yescharacteristic
125#16811178C2211yescharacteristic
126#16811178C2211yescharacteristic
127#16811178C2211yescharacteristic
128#16811178C2214yes—
129#16811177C2212yes—
130#16811177C2212yes—
131#16811177C2212yes—
132#16811177C2212yes—
133#16811177C2212yes—
134#16811177C2212yes—
135#16811177C2212yes—
136#16811177C2212yes—
137#16811177C2212yes—
138#16811177C2212yes—
139#16811177C2214yes—
140#16811177C2214yescomplemented
141#16811177C2214yescomplemented
142#16811176C2212yes—
143#16811175C2212yes—
144#16811175C2212yes—
145#16811175C2214yes—
146#16811174C2211yescharacteristic
147#16811174C2211yescharacteristic
148#16811173C2211yescharacteristic
149C2×#13133216C2211yescharacteristic
150C2×#13133215C2211yescharacteristic
151C4⋊Q8×D53C2211yescharacteristic
152C4⋊Q8×D53C2211yescharacteristic
153C4⋊Q8×D53C2214yescomplemented
154#16811160C2212yes—
155#16811160C2212yes—
156#16811160C2214yes—
157#16811159C2212yes—
158#16811159C2212yes—
159#16811159C2214yes—
160#16811158C2212yes—
161#16811158C2212yes—
162#16811158C2214yes—
163#16811157C2214yes—
164C2×#13133207C2212yes—
165#125×D53C2212yes—
166#16811136C2212yes—
167#16811136C2212yes—
168#16811135C2212yes—
169C2×#13133197C2211yescharacteristic
170C2×#13133195C2212yes—
171C2×#13133193C2211yescharacteristic
172C22⋊Q8×D53C2212yes—
173C22⋊Q8×D53C2212yes—
174#16811105C2214yes—
175#16811104C2212yes—
176#16811103C2212yes—
177#16811100C2212yes—
178#16811099C2214yes—
179#16811099C2218yescomplemented
180C4×#11719949C2212yes—
181C4×#11719949C2212yes—
182#16811091C2212yes—
183C2×C4×Dic106C2211yescharacteristic
184C2×C4×Dic106C2212yes—
185C4×Q8×D53C2212yes—
186C4×Q8×D53C2212yes—
187C2×#13133174C2212yes—
188#117×D53C2212yes—
189C2×C42×D53C2211yescharacteristic
190Q82×C53C2212yescomplemented
191Q82×C53C2212yescomplemented
192C53×#557C2214yescomplemented
193C53×#557C2214yescomplemented
194C53×#557C2212yescomplemented
195C53×#557C2212yescomplemented
196C53×#544C2212yes—
197C53×#544C2214yes—
198C53×#533C2211yescharacteristic
199C53×#533C2211yescharacteristic
200C53×#533C2214yes—
201C53×#519C2212yes—
202C2×C4×Q8×C53C2211yescharacteristic
203C2×#11719949C2312yes—
204C2×#11719949C2312yes—
205C2×#11719945C2312yes—
206C22×Dic106C2311yescharacteristic
207C22×Dic106C2312yes—
208C2×Q8×D53C2312yes—
209C2×Q8×D53C2318yes—
210C2×Q8×D53C2312yes—
211C22×C4×D53C2311yescharacteristic
212C22×C4×D53C2311yescharacteristic
213C22×C4×D53C2311yescharacteristic
214#13133217C2314yes—
215#13133217C2311yescharacteristic
216#13133217C2311yescharacteristic
217#13133217C2314yes—
218#13133217C2311yescharacteristic
219#13133216C2318yes—
220#13133216C2318yes—
221#13133216C2318yes—
222#13133216C2312yes—
223#13133216C2312yes—
224#13133216C2314yes—
225#13133216C2314yes—
226#13133216C2312yes—
227#13133216C2312yes—
228#13133216C2312yes—
229#13133216C2312yes—
230#13133216C2312yes—
231#13133216C2312yes—
232#13133215C2318yes—
233#13133215C2318yes—
234#13133215C2312yes—
235#13133215C2312yes—
236#13133215C2312yes—
237#13133215C2314yes—
238#13133215C2314yes—
239#13133215C2318yes—
240#13133215C2312yes—
241#13133215C2312yes—
242#13133215C2312yes—
243#13133214C2311yescharacteristic
244#13133212C2318yes—
245#13133212C2318yes—
246#13133212C2318yes—
247#13133212C2318yes—
248#13133212C2318yes—
249#13133212C2318yes—
250#13133212C2318yes—
251#13133212C2318yes—
252#13133212C2318yes—
253#13133212C2318yes—
254#13133212C2318yes—
255#13133212C2314yes—
256#13133212C2314yes—
257#13133211C2318yes—
258#13133211C2318yes—
259#13133211C2318yes—
260#13133211C2318yes—
261#13133211C2318yes—
262#13133209C2318yes—
263#13133209C2318yes—
264#13133209C2318yes—
265#13133209C2314yes—
266#13133209C2312yes—
267#13133209C2314yes—
268#13133208C2318yes—
269#13133208C2318yes—
270#13133208C2318yes—
271#13133208C2318yes—
272#13133208C2314yes—
273#13133208C2314yes—
274#13133208C2312yes—
275#13133208C2312yes—
276#13133208C2312yes—
277#13133208C2312yes—
278#13133207C2318yes—
279#13133207C2318yes—
280#13133207C2318yes—
281#13133207C2318yes—
282#13133207C2318yes—
283#13133207C2318yes—
284#13133207C2314yes—
285#13133207C2318yes—
286#13133207C2318yes—
287#13133207C2318yes—
288#13133207C2318yes—
289#13133207C2318yes—
290#13133207C2318yes—
291#13133207C2314yes—
292#13133207C2314yes—
293#13133207C2314yes—
294#13133207C2314yes—
295#13133207C2314yes—
296#13133206C2318yes—
297#13133206C2314yes—
298#13133206C2312yes—
299#13133206C2314yes—
300#13133206C2312yes—
301#13133205C2318yes—
302#13133205C2312yes—
303#13133205C2314yes—
304#13133205C2314yes—
305#13133202C2318yes—
306#13133202C2318yes—
307#13133202C2318yes—
308#13133202C2318yes—
309#13133202C2314yes—
310#13133202C2318yes—
311#13133202C2318yes—
312#13133202C2314yes—
313#13133201C2318yes—
314#13133201C2314yes—
315#13133200C2318yes—
316#13133197C2318yes—
317#13133197C2314yes—
318#13133197C2312yes—
319#13133197C2312yes—
320#13133197C2314yes—
321#13133197C2312yes—
322#13133197C2312yes—
323#13133197C2312yes—
324#13133197C2312yes—
325#13133197C2312yes—
326#13133197C2312yes—
327#13133196C2312yes—
328#13133196C2312yes—
329#13133195C2318yes—
330#13133195C2318yes—
331#13133195C2314yes—
332#13133195C2318yes—
333#13133195C2318yes—
334#13133195C2318yes—
335#13133195C2318yes—
336#13133195C2318yes—
337#13133195C2314yes—
338#13133195C2318yes—
339#13133195C2318yes—
340#13133195C2314yes—
341#13133195C2314yes—
342#13133195C2314yes—
343#13133195C2314yes—
344#13133194C2314yes—
345#13133194C2318yes—
346#13133194C2314yes—
347#13133193C2318yes—
348#13133193C2318yes—
349#13133193C2318yes—
350#13133193C2318yes—
351#13133193C2314yes—
352#13133193C2312yes—
353#13133193C2312yes—
354#13133193C2314yes—
355#13133193C2312yes—
356#13133193C2312yes—
357#13133193C2312yes—
358#13133193C2312yes—
359#13133193C2312yes—
360#13133193C2312yes—
361#13133192C2312yes—
362#13133192C2312yes—
363#13133192C2312yes—
364#13133192C2312yes—
365#13133191C2312yes—
366#13133191C2312yes—
367#13133187C2314yes—
368Q8×Dic53C2318yes—
369Q8×Dic53C2312yes—
370Q8×Dic53C2312yes—
371Q8×Dic53C2314yes—
372Q8×Dic53C2314yes—
373Q8×Dic53C2312yes—
374Q8×Dic53C2312yes—
375C4×Dic106C2318yes—
376C4×Dic106C2314yes—
377C4×Dic106C2314yes—
378C4×Dic106C2318yes—
379C4×Dic106C2318yes—
380C4×Dic106C2314yes—
381C4×Dic106C2314yes—
382C4×Dic106C2312yes—
383C4×Dic106C2314yes—
384C4×Dic106C2312yes—
385C4×Dic106C2312yes—
386C4×Dic106C2312yes—
387C4×Dic106C2314yes—
388C4×Dic106C2312yes—
389C4×Dic106C2312yes—
390C4×Dic106C2314yes—
391C4×Dic106C2314yes—
392C4×Dic106C2314yes—
393C4×Dic106C2314yes—
394#13133182C2318yes—
395#13133182C2318yes—
396#13133182C2318yes—
397#13133182C2314yes—
398#13133182C2312yes—
399#13133182C2314yes—
400#13133182C2312yes—
401#13133182C2314yes—
402#13133182C2314yes—
403#13133182C2314yes—
404#13133182C2314yes—
405#13133182C2312yes—
406#13133182C2312yes—
407C4×D212C2318yes—
408C4×D212C2314yes—
409C4×D212C2314yes—
410C4×D212C2314yes—
411C4×D212C2314yes—
412C4×D212C2312yes—
413C4×D212C2312yes—
414#13133179C2314yes—
415#13133179C2318yes—
416#13133179C2312yes—
417#13133179C2312yes—
418#13133179C2314yes—
419#13133179C2314yes—
420#13133179C2314yes—
421#13133179C2312yes—
422#13133179C2312yes—
423C4×C22⋊D53C2318yes—
424#13133177C2314yes—
425#13133177C2318yes—
426#13133177C2314yes—
427#13133176C2312yes—
428#13133175C2318yes—
429#13133175C2318yes—
430#13133175C2318yes—
431#13133175C2312yes—
432#13133175C2314yes—
433#13133175C2314yes—
434#13133175C2312yes—
435#13133175C2312yes—
436#13133175C2314yes—
437#13133175C2312yes—
438#13133175C2314yes—
439#13133174C2318yes—
440#13133174C2314yes—
441#13133174C2318yes—
442#13133174C2314yes—
443#13133174C2318yes—
444#13133174C2318yes—
445#13133174C2318yes—
446#13133174C2314yes—
447#13133174C2314yes—
448#13133174C2314yes—
449#13133174C2314yes—
450#13133173C2318yes—
451#13133173C2314yes—
452C2×C4⋊Dic53C2312yes—
453C2×C4⋊Dic53C2311yescharacteristic
454C2×#11719919C2312yes—
455C2×#11719919C2312yes—
456C2×#11719919C2312yes—
457C2×#11719919C2312yes—
458C2×#11719919C2312yes—
459C4⋊C4×D53C2312yes—
460C4⋊C4×D53C2314yes—
461C4⋊C4×D53C2318yes—
462C4⋊C4×D53C2312yes—
463C4⋊C4×D53C2314yes—
464C4⋊C4×D53C2314yes—
465C4⋊C4×D53C2312yes—
466C4⋊C4×D53C2312yes—
467C4⋊C4×D53C2314yes—
468C2×#11719921C2312yes—
469C2×#11719921C2312yes—
470C22⋊C4×D53C2314yes—
471C2×C4×Dic53C2311yescharacteristic
472C2×C4×Dic53C2311yescharacteristic
473C2×C4×Dic53C2311yescharacteristic
474C2×C4×Dic53C2312yes—
475C42×D53C2311yescharacteristic
476C42×D53C2311yescharacteristic
477C42×D53C2311yescharacteristic
478C42×D53C2311yescharacteristic
479C42×D53C2311yescharacteristic
480C42×D53C2311yescharacteristic
481C42×D53C2311yescharacteristic
482C42×D53C2311yescharacteristic
483C42×D53C2314yes—
484C42×D53C2314yes—
485C22×Q8×C53C2311yescharacteristic
486C4⋊Q8×C53C2318yes—
487C4⋊Q8×C53C2314yes—
488C4⋊Q8×C53C2314yes—
489C4⋊Q8×C53C2311yescharacteristic
490C4⋊Q8×C53C2311yescharacteristic
491C4⋊Q8×C53C2314yes—
492C4⋊Q8×C53C2311yescharacteristic
493C4⋊Q8×C53C2311yescharacteristic
494C4⋊Q8×C53C2314yes—
495C4⋊Q8×C53C2318yes—
496#125×C53C2318yes—
497#125×C53C2318yes—
498#125×C53C2318yes—
499#125×C53C2314yes—
500#125×C53C2312yes—
501#125×C53C2312yes—
502#125×C53C2314yes—
503C22⋊Q8×C53C2318yes—
504C22⋊Q8×C53C2312yes—
505C22⋊Q8×C53C2312yes—
506C22⋊Q8×C53C2312yes—
507C22⋊Q8×C53C2312yes—
508C4×Q8×C53C2312yes—
509C4×Q8×C53C2312yes—
510C4×Q8×C53C2312yes—
511C4×Q8×C53C2312yes—
512C4×Q8×C53C2314yes—
513C4×Q8×C53C2314yes—
514C4×Q8×C53C2314yes—
515C4×Q8×C53C2314yes—
516C4×Q8×C53C2318yes—
517C4×Q8×C53C2312yes—
518C4×Q8×C53C2312yes—
519C4×Q8×C53C2312yes—
520C4×Q8×C53C2314yes—
521C4×Q8×C53C2314yes—
522C4×Q8×C53C2312yes—
523#117×C53C2318yes—
524#117×C53C2312yes—
525#117×C53C2312yes—
526C2×C4⋊C4×C53C2311yescharacteristic
527C2×C4⋊C4×C53C2312yes—
528C2×C42×C53C2311yescharacteristic
529C2×C42×C53C2312yes—
530C23×D53C2411yescharacteristic
531C2×Q8×C53—24no—
532C2×Q8×C53C2412yes—
533C2×Q8×C53C2412yes—
534C2×Q8×C53C2412yes—
535C2×Q8×C53C2412yes—
536C2×Q8×C53C2412yes—
537C2×Q8×C53C2418yes—
538C2×Q8×C53C2412yes—
539C22×C4×C53C2411yescharacteristic
540C22×C4×C53C2412yes—
541C22×C4×C53C2411yescharacteristic
542C22×C4×C53C2412yes—
543C22×C4×C53C2411yescharacteristic
544C2×C22⋊D53C2414yes—
545C22×Dic53C2411yescharacteristic
546C22×Dic53C2411yescharacteristic
547C22×Dic53C2411yescharacteristic
548C22×Dic53C2412yes—
549C22×Dic53C2412yes—
550#11719949—28no—
551#11719949—44no—
552Q8×D53—28no—
553Q8×D53—416no—
554Q8×D53—44no—
555#11719945—28no—
556C2×D212C2412yes—
557C2×D212C2414yes—
558C2×D212C2412yes—
559C2×D212C2414yes—
560C2×D212C2412yes—
561C2×C4×D53—24no—
562C2×C4×D53—24no—
563C2×C4×D53—42no—
564C2×C4×D53C2411yescharacteristic
565C2×C4×D53C2411yescharacteristic
566C2×C4×D53C2411yescharacteristic
567C2×C4×D53C2411yescharacteristic
568C2×C4×D53C2411yescharacteristic
569C2×C4×D53C2411yescharacteristic
570C2×C4×D53C2411yescharacteristic
571C2×C4×D53C2411yescharacteristic
572C2×C4×D53C2411yescharacteristic
573C2×C4×D53C2414yes—
574C2×C4×D53C2414yes—
575C2×C4×D53C2414yes—
576C2×C4×D53C2414yes—
577C2×C4×D53C2411yescharacteristic
578C2×C4×D53C2411yescharacteristic
579C2×C4×D53C2414yes—
580C2×C4×D53C2418yes—
581C2×C4×D53C2418yes—
582C2×C4×D53C2411yescharacteristic
583C2×Dic106—24no—
584C2×Dic106—44no—
585C2×Dic106C2412yes—
586C2×Dic106C2412yes—
587C2×Dic106C2414yes—
588C2×Dic106C2412yes—
589C2×Dic106C2414yes—
590C2×Dic106C2414yes—
591C2×Dic106C2412yes—
592C2×Dic106C2418yes—
593C2×Dic106C2412yes—
594C2×Dic106C2414yes—
595C4⋊C4×C53C2412yes—
596C4⋊C4×C53C2412yes—
597C4⋊C4×C53C2414yes—
598C4⋊C4×C53C2414yes—
599C4⋊C4×C53C2412yes—
600C4⋊C4×C53C2412yes—
601C4⋊C4×C53C2418yes—
602C4⋊C4×C53C2412yes—
603C4⋊C4×C53C2412yes—
604C4⋊C4×C53C2418yes—
605C4⋊C4×C53C2414yes—
606C4⋊C4×C53C2414yes—
607C4⋊C4×C53C2412yes—
608C4⋊C4×C53C2412yes—
609C4⋊C4×C53C2412yes—
610C4⋊C4×C53C2412yes—
611C4⋊C4×C53C2418yes—
612C4⋊C4×C53C2418yes—
613C4⋊C4×C53C2414yes—
614C4⋊C4×C53C2414yes—
615C4⋊C4×C53C2418yes—
616C22⋊C4×C53C2414yes—
617C22⋊C4×C53C2414yes—
618C42×C53C2411yescharacteristic
619C42×C53C2411yescharacteristic
620C42×C53C2414yes—
621C42×C53C2411yescharacteristic
622C42×C53C2411yescharacteristic
623C42×C53C2414yes—
624C42×C53C2414yes—
625C42×C53C2414yes—
626C42×C53C2418yes—
627C42×C53C2418yes—
628C22⋊Dic53C2414yes—
629#11719921C2414yes—
630#11719921C2414yes—
631#11719921C2414yes—
632#11719921C2414yes—
633#11719921C2414yes—
634#11719921C2414yes—
635#11719921C2418yes—
636#11719921C2414yes—
637#11719921C2414yes—
638#11719921C2414yes—
639#11719921C2418yes—
640#11719921C2414yes—
641#11719921C2414yes—
642#11719921C2418yes—
643#11719921C2418yes—
644#11719921C2418yes—
645#11719921C2418yes—
646#11719921C2414yes—
647#11719921C2414yes—
648#11719921C2414yes—
649C4⋊Dic53C2412yes—
650C4⋊Dic53C2412yes—
651C4⋊Dic53C2412yes—
652C4⋊Dic53C2412yes—
653C4⋊Dic53C2418yes—
654C4⋊Dic53C2414yes—
655C4⋊Dic53C2412yes—
656C4⋊Dic53C2414yes—
657C4⋊Dic53C2414yes—
658C4⋊Dic53C2412yes—
659C4⋊Dic53C2414yes—
660C4⋊Dic53C2412yes—
661C4⋊Dic53C2414yes—
662C4⋊Dic53C2412yes—
663C4⋊Dic53C2414yes—
664C4⋊Dic53C2418yes—
665C4⋊Dic53C2418yes—
666#11719919C2414yes—
667#11719919C2414yes—
668#11719919C2414yes—
669#11719919C2414yes—
670#11719919C2414yes—
671#11719919C2414yes—
672#11719919C2418yes—
673#11719919C2418yes—
674#11719919C2414yes—
675#11719919C2414yes—
676#11719919C2414yes—
677#11719919C2414yes—
678#11719919C2414yes—
679#11719919C2414yes—
680#11719919C2414yes—
681#11719919C2414yes—
682#11719919C2414yes—
683#11719919C2414yes—
684#11719919C2414yes—
685#11719919C2414yes—
686#11719919C2418yes—
687#11719919C2418yes—
688#11719919C2414yes—
689#11719919C2414yes—
690#11719919C2418yes—
691#11719919C2418yes—
692#11719919C2418yes—
693#11719919C2418yes—
694C4×Dic53C2411yescharacteristic
695C4×Dic53C2411yescharacteristic
696C4×Dic53C2411yescharacteristic
697C4×Dic53C2411yescharacteristic
698C4×Dic53C2411yescharacteristic
699C4×Dic53C2411yescharacteristic
700C4×Dic53C2411yescharacteristic
701C4×Dic53C2411yescharacteristic
702C4×Dic53C2411yescharacteristic
703C4×Dic53C2411yescharacteristic
704C4×Dic53C2411yescharacteristic
705C4×Dic53C2411yescharacteristic
706C4×Dic53C2414yes—
707C4×Dic53C2414yes—
708C4×Dic53C2414yes—
709C4×Dic53C2414yes—
710C4×Dic53C2414yes—
711C4×Dic53C2414yes—
712C4×Dic53C2414yes—
713C4×Dic53C2418yes—
714C4×Dic53C2418yes—
715C4×Dic53C2418yes—
716C4×Dic53C2418yes—
717C23×C53C2511yescharacteristic
718C22×D53—22no—
719C22×D53—22no—
720C22×D53—41no—
721C22×D53C2514yes—
722C22×D53C2511yescharacteristic
723C22×D53C2511yescharacteristic
724Q8×C53—24no—
725Q8×C53—24no—
726Q8×C53—24no—
727Q8×C53—24no—
728Q8×C53—48no—
729Q8×C53—42no—
730Q8×C53—42no—
731C2×C4×C53—24no—
732C2×C4×C53—22no—
733C2×C4×C53—42no—
734C2×C4×C53—41no—
735C2×C4×C532−1+414yes—
736C2×C4×C53C2514yes—
737C2×C4×C53C2511yescharacteristic
738C2×C4×C53C2514yes—
739C2×C4×C53C2514yes—
740C2×C4×C53C2514yes—
741C2×C4×C53C2511yescharacteristic
742C2×C4×C53C2511yescharacteristic
743C2×C4×C53C2514yes—
744C2×C4×C53C2514yes—
745C2×C4×C53C2511yescharacteristic
746C2×C4×C53C2511yescharacteristic
747C2×C4×C53C2511yescharacteristic
748C22⋊D53—28no—
749C2×Dic53—24no—
750C2×Dic53—22no—
751C2×Dic53—22no—
752C2×Dic53—22no—
753C2×Dic53—42no—
754C2×Dic53C2514yes—
755C2×Dic53C2514yes—
756C2×Dic53C2511yescharacteristic
757C2×Dic53C2514yes—
758C2×Dic53C2514yes—
759C2×Dic53C2514yes—
760C2×Dic53C2511yescharacteristic
761C2×Dic53C2511yescharacteristic
762C2×Dic53C2511yescharacteristic
763C2×Dic53C2511yescharacteristic
764C2×Dic53C2511yescharacteristic
765D212—28no—
766D212—24no—
767D212—24no—
768D212—44no—
769D212—42no—
770C4×D53—22no—
771C4×D53—28no—
772C4×D53—22no—
773C4×D53—22no—
774C4×D53—22no—
775C4×D53—22no—
776C4×D53—22no—
777C4×D53—28no—
778C4×D53—22no—
779C4×D53—28no—
780C4×D53—22no—
781C4×D53—22no—
782C4×D53—28no—
783C4×D53—41no—
784C4×D53—41no—
785C4×D53—48no—
786C4×D53—44no—
787C4×D53—48no—
788C4×D532−1+414yes—
789Dic106—24no—
790Dic106—24no—
791Dic106—24no—
792Dic106—24no—
793Dic106—28no—
794Dic106—28no—
795Dic106—28no—
796Dic106—44no—
797Dic106—42no—
798Dic106—48no—
799#62837—531nomaximal, Sylow
800C22×C53—21no—
801C22×C53—21no—
802C22×C53C2×2−1+412yes—
803C22×C53C2611yescharacteristic
804C2×D53—21no—
805C2×D53—21no—
806C2×D53—21no—
807C2×D53—21no—
808C2×D53—24no—
809C2×D53—24no—
810C2×D53—24no—
811C2×D53—21no—
812C2×D53—44no—
813C2×D53C2×2−1+412yes—
814C4×C53—24no—
815C4×C53—21no—
816C4×C53—24no—
817C4×C53—24no—
818C4×C53—24no—
819C4×C53—24no—
820C4×C53—21no—
821C4×C53—24no—
822C4×C53—21no—
823C4×C53C2×2−1+412yes—
824C4×C53C2×2−1+412yes—
825C4×C53C2×2−1+412yes—
826Dic53—24no—
827Dic53—24no—
828Dic53—24no—
829Dic53—21no—
830Dic53—21no—
831Dic53—21no—
832Dic53—24no—
833Dic53—24no—
834Dic53—21no—
835Dic53C2×2−1+412yes—
836Dic53#58512yes—
837#3563—534no—
838#3563—534no—
839#3556—532no—
840#3555—532no—
841#3555—534no—
842#3555—532no—
843#3550—532no—
844#3538—534no—
845#3523—534no—
846#3523—534no—
847#3509—532no—
848#3509—534no—
849#3509—532no—
850#3507—532no—
851#3507—531no—
852#3507—531no—
853#3503—532no—
854#3503—532no—
855#3502—532no—
856#3502—531no—
857#3502D5311yescharacteristic, complemented
858#3495—532no—
859#3495—534no—
860#3495—532no—
861#3444—531no—
862C2×#533—531no—
863C2×#533—531no—
864C2×C53—22no—
865C2×C53C22×2−1+411yescharacteristic
866C2×C53C22×2−1+411yescharacteristic
867C2×C53C2×#58511yescharacteristic
868D53—22no—
869D53—44no—
870D53—41no—
871#564—538no—
872#563—538no—
873#563—538no—
874#563—538no—
875#559—532no—
876#559—532no—
877Q82—532no—
878Q82—534no—
879Q82—532no—
880Q82C2×D5312yescomplemented
881Q82C2×D5312yescomplemented
882#557—532no—
883#557—538no—
884#557—534no—
885#557—534no—
886#557—534no—
887#557—534no—
888#557—534no—
889#557—534no—
890#557—532no—
891#557—534no—
892#557—532no—
893#557—534no—
894#557—534no—
895#557—532no—
896#557C2×D5312yescomplemented
897#557C2×D5312yescomplemented
898#557C2×D5314yescomplemented
899#557C2×D5314yescomplemented
900#556—534no—
901#556—532no—
902#556—534no—
903#556—538no—
904#556—534no—
905#556—534no—
906#556—534no—
907#556—534no—
908#556—534no—
909#556—534no—
910#556—532no—
911#556—534no—
912#554—534no—
913#554—532no—
914#554—534no—
915#554—538no—
916#554—534no—
917#554—532no—
918#552—538no—
919#552—538no—
920#552—538no—
921#552—538no—
922#552—534no—
923#552—534no—
924#552—534no—
925#552—538no—
926#552—534no—
927#552—534no—
928#552—538no—
929#552—534no—
930#552—538no—
931#552—538no—
932#552—538no—
933#551—538no—
934#551—538no—
935D4×Q8—538no—
936D4×Q8—534no—
937D4×Q8—534no—
938D4×Q8—538no—
939#544—534no—
940#544—538no—
941#544—538no—
942#544—534no—
943#544—534no—
944#544—534no—
945#544—532no—
946#544C2×D5312yes—
947#544C2×D5314yes—
948#542—534no—
949#542—534no—
950#542—534no—
951#542—534no—
952#541—534no—
953#541—538no—
954#541—534no—
955#541—538no—
956#541—538no—
957#541—538no—
958#541—538no—
959#541—538no—
960#541—534no—
961#541—534no—
962#541—534no—
963#541—534no—
964#541—538no—
965#539—538no—
966#539—534no—
967#539—534no—
968#536—532no—
969#536—534no—
970#536—538no—
971#536—532no—
972#533—531no—
973#533—531no—
974#533—531no—
975#533—531no—
976#533—534no—
977#533—532no—
978#533—534no—
979#533—532no—
980#533—532no—
981#533—534no—
982#533—532no—
983#533—532no—
984#533—532no—
985#533—532no—
986#533—532no—
987#533—532no—
988#533—532no—
989#533—532no—
990#533—532no—
991#533—532no—
992#533—534no—
993#533—534no—
994#533—534no—
995#533—532no—
996#533—531no—
997#533C2×D5311yescharacteristic
998#533C2×D5311yescharacteristic
999#533C2×D5314yes—
1000#532—531no—
1001#532—531no—
1002#532—531no—
1003C2×C4⋊Q8—531no—
1004C2×C4⋊Q8—531no—
1005C2×C4⋊Q8—531no—
1006C2×C4⋊Q8—534no—
1007C2×C4⋊Q8—531no—
1008#529—532no—
1009#529—532no—
1010#529—534no—
1011#529—532no—
1012#529—532no—
1013#529—534no—
1014#529—532no—
1015#529—532no—
1016#529—534no—
1017#529—534no—
1018C2×#125—532no—
1019C2×#125—532no—
1020#525—532no—
1021#525—532no—
1022#525—532no—
1023C2×C22⋊Q8—531no—
1024C2×C22⋊Q8—532no—
1025C2×C22⋊Q8—532no—
1026C2×C22⋊Q8—532no—
1027C2×C22⋊Q8—531no—
1028#520—534no—
1029#520—532no—
1030#520—532no—
1031#519—534no—
1032#519—538no—
1033#519—532no—
1034#519C2×D5312yes—
1035C4×#41—532no—
1036C4×#41—532no—
1037C4×#41—532no—
1038C2×C4×Q8—532no—
1039C2×C4×Q8—532no—
1040C2×C4×Q8—531no—
1041C2×C4×Q8—532no—
1042C2×C4×Q8C2×D5311yescharacteristic
1043C2×#117—532no—
1044C2×#117—532no—
1045C22×C42—531no—
1046C53#6283711yescharacteristic, complemented, Sylow
1047C2×#41—532no—
1048C2×#41—532no—
1049C2×#41—532no—
1050C22×Q8—532no—
1051C22×Q8—532no—
1052C22×Q8—538no—
1053C22×Q8—531no—
1054C22×Q8—532no—
1055C22×Q8C22×D5311yescharacteristic
1056C23×C4—531no—
1057C23×C4—531no—
1058C23×C4—531no—
1059C4⋊Q8—532no—
1060C4⋊Q8—532no—
1061C4⋊Q8—532no—
1062C4⋊Q8—532no—
1063C4⋊Q8—532no—
1064C4⋊Q8—532no—
1065C4⋊Q8—538no—
1066C4⋊Q8—534no—
1067C4⋊Q8—534no—
1068C4⋊Q8—538no—
1069C4⋊Q8—538no—
1070C4⋊Q8—532no—
1071C4⋊Q8—532no—
1072C4⋊Q8—532no—
1073C4⋊Q8—532no—
1074C4⋊Q8—532no—
1075C4⋊Q8—532no—
1076C4⋊Q8—532no—
1077C4⋊Q8—532no—
1078C4⋊Q8—538no—
1079C4⋊Q8—534no—
1080C4⋊Q8—534no—
1081C4⋊Q8—538no—
1082C4⋊Q8—538no—
1083C4⋊Q8—531no—
1084C4⋊Q8—531no—
1085C4⋊Q8—534no—
1086C4⋊Q8—531no—
1087C4⋊Q8—534no—
1088C4⋊Q8C22×D5311yescharacteristic
1089C4⋊Q8C22×D5311yescharacteristic
1090C4⋊Q8C22×D5314yes—
1091C4⋊Q8C22×D5311yescharacteristic
1092C4⋊Q8C22×D5311yescharacteristic
1093C4⋊Q8C22×D5314yes—
1094C4⋊Q8C22×D5314yes—
1095C4⋊Q8C22×D5314yes—
1096C4⋊Q8C22×D5318yes—
1097C4⋊Q8C22×D5318yes—
1098#127—531no—
1099#126—534no—
1100#126—534no—
1101#126—538no—
1102#126—538no—
1103#126—538no—
1104#126—538no—
1105#126—538no—
1106#126—538no—
1107#126—538no—
1108#126—538no—
1109#126—538no—
1110#126—538no—
1111#126—538no—
1112#126—538no—
1113#126—538no—
1114#126—538no—
1115#126—538no—
1116#126—538no—
1117#125—534no—
1118#125—534no—
1119#125—534no—
1120#125—532no—
1121#125—532no—
1122#125—534no—
1123#125—534no—
1124#125—534no—
1125#125—532no—
1126#125—532no—
1127#125—534no—
1128#125—534no—
1129#125—538no—
1130#125—538no—
1131#125—538no—
1132#125—538no—
1133#125—538no—
1134#125—538no—
1135#125—538no—
1136#125—538no—
1137#125—538no—
1138#125—538no—
1139#125—538no—
1140#125—538no—
1141#125—538no—
1142#125—538no—
1143#125—538no—
1144#125—538no—
1145#125—532no—
1146#125—534no—
1147#125—534no—
1148#125—538no—
1149#125—538no—
1150#125—538no—
1151#125C22×D5312yes—
1152#125C22×D5312yes—
1153#125C22×D5314yes—
1154#125C22×D5314yes—
1155#125C22×D5318yes—
1156#125C22×D5318yes—
1157#125C22×D5318yes—
1158#124—532no—
1159#124—532no—
1160#124—534no—
1161#124—534no—
1162#124—538no—
1163#124—532no—
1164#124—534no—
1165#124—534no—
1166#124—538no—
1167#123—538no—
1168#123—534no—
1169#123—534no—
1170#123—538no—
1171#123—538no—
1172#123—538no—
1173#123—538no—
1174#123—538no—
1175#123—538no—
1176#123—534no—
1177#123—538no—
1178C22⋊Q8—532no—
1179C22⋊Q8—532no—
1180C22⋊Q8—532no—
1181C22⋊Q8—532no—
1182C22⋊Q8—532no—
1183C22⋊Q8—532no—
1184C22⋊Q8—532no—
1185C22⋊Q8—532no—
1186C22⋊Q8—534no—
1187C22⋊Q8—534no—
1188C22⋊Q8—538no—
1189C22⋊Q8—538no—
1190C22⋊Q8—538no—
1191C22⋊Q8—538no—
1192C22⋊Q8—532no—
1193C22⋊Q8—532no—
1194C22⋊Q8—532no—
1195C22⋊Q8—534no—
1196C22⋊Q8—534no—
1197C22⋊Q8—534no—
1198C22⋊Q8—532no—
1199C22⋊Q8—532no—
1200C22⋊Q8—534no—
1201C22⋊Q8—532no—
1202C22⋊Q8—534no—
1203C22⋊Q8—532no—
1204C22⋊Q8—534no—
1205C22⋊Q8—532no—
1206C22⋊Q8—532no—
1207C22⋊Q8—532no—
1208C22⋊Q8—538no—
1209C22⋊Q8—538no—
1210C22⋊Q8—538no—
1211C22⋊Q8—534no—
1212C22⋊Q8—538no—
1213C22⋊Q8—534no—
1214C22⋊Q8—538no—
1215C22⋊Q8—538no—
1216C22⋊Q8—538no—
1217C22⋊Q8—538no—
1218C22⋊Q8—538no—
1219C22⋊Q8—538no—
1220C22⋊Q8—534no—
1221C22⋊Q8—534no—
1222C22⋊Q8—538no—
1223C22⋊Q8C22×D5312yes—
1224C22⋊Q8C22×D5312yes—
1225C22⋊Q8C22×D5312yes—
1226C22⋊Q8C22×D5312yes—
1227C22⋊Q8C22×D5318yes—
1228#121—532no—
1229#121—532no—
1230#121—532no—
1231#121—532no—
1232#121—532no—
1233#121—532no—
1234#120—534no—
1235C4×Q8—532no—
1236C4×Q8—532no—
1237C4×Q8—532no—
1238C4×Q8—532no—
1239C4×Q8—534no—
1240C4×Q8—538no—
1241C4×Q8—534no—
1242C4×Q8—534no—
1243C4×Q8—532no—
1244C4×Q8—534no—
1245C4×Q8—532no—
1246C4×Q8—532no—
1247C4×Q8—532no—
1248C4×Q8—534no—
1249C4×Q8—538no—
1250C4×Q8—538no—
1251C4×Q8—538no—
1252C4×Q8—534no—
1253C4×Q8—534no—
1254C4×Q8—534no—
1255C4×Q8—534no—
1256C4×Q8—534no—
1257C4×Q8—534no—
1258C4×Q8—534no—
1259C4×Q8—532no—
1260C4×Q8—534no—
1261C4×Q8—532no—
1262C4×Q8—534no—
1263C4×Q8—532no—
1264C4×Q8—532no—
1265C4×Q8—532no—
1266C4×Q8—532no—
1267C4×Q8—534no—
1268C4×Q8—538no—
1269C4×Q8—534no—
1270C4×Q8—538no—
1271C4×Q8—538no—
1272C4×Q8—534no—
1273C4×Q8—534no—
1274C4×Q8C22×D5312yes—
1275C4×Q8C22×D5312yes—
1276C4×Q8C22×D5312yes—
1277C4×Q8C22×D5312yes—
1278C4×Q8C22×D5312yes—
1279C4×Q8C22×D5312yes—
1280C4×Q8C22×D5312yes—
1281C4×Q8C22×D5312yes—
1282C4×Q8C22×D5318yes—
1283C4×Q8C22×D5314yes—
1284C4×Q8C22×D5314yes—
1285C4×Q8C22×D5314yes—
1286C4×Q8C22×D5314yes—
1287C4×Q8C22×D5314yes—
1288C4×Q8C22×D5314yes—
1289C4×D4—538no—
1290C4×D4—534no—
1291C4×D4—534no—
1292C4×D4—532no—
1293C4×D4—532no—
1294C4×D4—532no—
1295C4×D4—532no—
1296C4×D4—538no—
1297C4×D4—534no—
1298C4×D4—534no—
1299C4×D4—534no—
1300C4×D4—534no—
1301C4×D4—538no—
1302C4×D4—534no—
1303C4×D4—534no—
1304C4×D4—532no—
1305C4×D4—532no—
1306C4×D4—538no—
1307C4×D4—534no—
1308C4×D4—534no—
1309#117—532no—
1310#117—532no—
1311#117—532no—
1312#117—532no—
1313#117—534no—
1314#117—532no—
1315#117—534no—
1316#117—538no—
1317#117—538no—
1318#117—538no—
1319#117—534no—
1320#117—534no—
1321#117—534no—
1322#117—538no—
1323#117—534no—
1324#117—534no—
1325#117—534no—
1326#117—534no—
1327#117—534no—
1328#117—534no—
1329#117—538no—
1330#117—538no—
1331#117—538no—
1332#117—538no—
1333#117—538no—
1334#117C22×D5312yes—
1335#117C22×D5312yes—
1336#117C22×D5318yes—
1337C2×C4⋊C4—532no—
1338C2×C4⋊C4—532no—
1339C2×C4⋊C4—531no—
1340C2×C4⋊C4—532no—
1341C2×C4⋊C4—532no—
1342C2×C4⋊C4—532no—
1343C2×C4⋊C4—532no—
1344C2×C4⋊C4—532no—
1345C2×C4⋊C4—532no—
1346C2×C4⋊C4—532no—
1347C2×C4⋊C4—534no—
1348C2×C4⋊C4—534no—
1349C2×C4⋊C4—532no—
1350C2×C4⋊C4—538no—
1351C2×C4⋊C4—534no—
1352C2×C4⋊C4—534no—
1353C2×C4⋊C4C22×D5311yescharacteristic
1354C2×C4⋊C4C22×D5312yes—
1355C2×C22⋊C4—532no—
1356C2×C22⋊C4—532no—
1357C2×C22⋊C4—534no—
1358C2×C42—532no—
1359C2×C42—531no—
1360C2×C42—531no—
1361C2×C42—531no—
1362C2×C42—534no—
1363C2×C42—531no—
1364C2×C42—531no—
1365C2×C42—534no—
1366C2×C42—531no—
1367C2×C42—531no—
1368C2×C42—531no—
1369C2×C42—531no—
1370C2×C42—531no—
1371C2×C42—531no—
1372C2×C42C22×D5312yes—
1373C2×C42C22×D5311yescharacteristic
1374C24—531no—
1375#41—1068no—
1376#41—1068no—
1377#41—2124no—
1378C2×Q8—24no—
1379C2×Q8—534no—
1380C2×Q8—532no—
1381C2×Q8—532no—
1382C2×Q8—532no—
1383C2×Q8—532no—
1384C2×Q8—534no—
1385C2×Q8—534no—
1386C2×Q8—532no—
1387C2×Q8—534no—
1388C2×Q8—538no—
1389C2×Q8—1068no—
1390C2×Q8—1064no—
1391C2×Q8—2124no—
1392C2×Q8—2124no—
1393C2×Q8—21216no—
1394C2×Q8C23×D5312yes—
1395C2×Q8C23×D5312yes—
1396C2×Q8C23×D5312yes—
1397C2×Q8C23×D5312yes—
1398C2×Q8C23×D5312yes—
1399C2×Q8C23×D5318yes—
1400C2×Q8C23×D5312yes—
1401C2×D4—534no—
1402C2×D4—534no—
1403C2×D4—532no—
1404C2×D4—532no—
1405C2×D4—534no—
1406C2×D4—532no—
1407C22×C4—531no—
1408C22×C4—531no—
1409C22×C4—531no—
1410C22×C4—531no—
1411C22×C4—532no—
1412C22×C4—532no—
1413C22×C4—531no—
1414C22×C4—531no—
1415C22×C4—531no—
1416C22×C4—531no—
1417C22×C4—531no—
1418C22×C4—531no—
1419C22×C4—531no—
1420C22×C4—531no—
1421C22×C4—531no—
1422C22×C4—534no—
1423C22×C4—534no—
1424C22×C4—534no—
1425C22×C4—534no—
1426C22×C4—531no—
1427C22×C4—531no—
1428C22×C4—534no—
1429C22×C4—538no—
1430C22×C4—538no—
1431C22×C4—1064no—
1432C22×C4—1064no—
1433C22×C4—2122no—
1434C22×C4C23×D5311yescharacteristic
1435C22×C4C23×D5312yes—
1436C22×C4C23×D5311yescharacteristic
1437C22×C4C23×D5312yes—
1438C22×C4C23×D5311yescharacteristic
1439C4⋊C4—534no—
1440C4⋊C4—534no—
1441C4⋊C4—532no—
1442C4⋊C4—532no—
1443C4⋊C4—534no—
1444C4⋊C4—532no—
1445C4⋊C4—534no—
1446C4⋊C4—534no—
1447C4⋊C4—534no—
1448C4⋊C4—534no—
1449C4⋊C4—534no—
1450C4⋊C4—534no—
1451C4⋊C4—534no—
1452C4⋊C4—534no—
1453C4⋊C4—534no—
1454C4⋊C4—532no—
1455C4⋊C4—532no—
1456C4⋊C4—538no—
1457C4⋊C4—538no—
1458C4⋊C4—538no—
1459C4⋊C4—534no—
1460C4⋊C4—534no—
1461C4⋊C4—534no—
1462C4⋊C4—534no—
1463C4⋊C4—534no—
1464C4⋊C4—534no—
1465C4⋊C4—534no—
1466C4⋊C4—534no—
1467C4⋊C4—534no—
1468C4⋊C4—534no—
1469C4⋊C4—532no—
1470C4⋊C4—532no—
1471C4⋊C4—534no—
1472C4⋊C4—532no—
1473C4⋊C4—534no—
1474C4⋊C4—534no—
1475C4⋊C4—534no—
1476C4⋊C4—538no—
1477C4⋊C4—538no—
1478C4⋊C4—538no—
1479C4⋊C4—538no—
1480C4⋊C4—538no—
1481C4⋊C4—538no—
1482C4⋊C4—538no—
1483C4⋊C4—538no—
1484C4⋊C4C23×D5312yes—
1485C4⋊C4C23×D5312yes—
1486C4⋊C4C23×D5312yes—
1487C4⋊C4C23×D5314yes—
1488C4⋊C4C23×D5312yes—
1489C4⋊C4C23×D5318yes—
1490C4⋊C4C23×D5314yes—
1491C4⋊C4C23×D5312yes—
1492C4⋊C4C23×D5312yes—
1493C4⋊C4C23×D5314yes—
1494C4⋊C4C23×D5314yes—
1495C4⋊C4C23×D5312yes—
1496C4⋊C4C23×D5314yes—
1497C4⋊C4C23×D5312yes—
1498C4⋊C4C23×D5314yes—
1499C4⋊C4C23×D5318yes—
1500C4⋊C4C23×D5318yes—
1501C4⋊C4C23×D5312yes—
1502C4⋊C4C23×D5312yes—
1503C4⋊C4C23×D5318yes—
1504C4⋊C4C23×D5318yes—
1505C22⋊C4—534no—
1506C22⋊C4—534no—
1507C22⋊C4—534no—
1508C22⋊C4—534no—
1509C22⋊C4—534no—
1510C22⋊C4—534no—
1511C22⋊C4—534no—
1512C22⋊C4—534no—
1513C22⋊C4—534no—
1514C22⋊C4—534no—
1515C22⋊C4—538no—
1516C22⋊C4—538no—
1517C22⋊C4—534no—
1518C22⋊C4—534no—
1519C22⋊C4—534no—
1520C22⋊C4—534no—
1521C22⋊C4—534no—
1522C22⋊C4—538no—
1523C22⋊C4—538no—
1524C22⋊C4—538no—
1525C22⋊C4—538no—
1526C22⋊C4C23×D5314yes—
1527C22⋊C4C23×D5314yes—
1528C42—531no—
1529C42—531no—
1530C42—531no—
1531C42—531no—
1532C42—531no—
1533C42—531no—
1534C42—531no—
1535C42—531no—
1536C42—531no—
1537C42—531no—
1538C42—531no—
1539C42—531no—
1540C42—534no—
1541C42—534no—
1542C42—534no—
1543C42—534no—
1544C42—534no—
1545C42—534no—
1546C42—534no—
1547C42—538no—
1548C42—538no—
1549C42—538no—
1550C42—538no—
1551C42C23×D5311yescharacteristic
1552C42C23×D5311yescharacteristic
1553C42C23×D5311yescharacteristic
1554C42C23×D5311yescharacteristic
1555C42C23×D5314yes—
1556C42C23×D5314yes—
1557C42C23×D5314yes—
1558C42C23×D5314yes—
1559C42C23×D5318yes—
1560C42C23×D5318yes—
1561C23—531no—
1562C23—531no—
1563C23—534no—
1564C23—1062no—
1565C23—1062no—
1566C23—2121no—
1567C23C24×D5311yescharacteristic
1568Q8—24no—
1569Q8—24no—
1570Q8—24no—
1571Q8—24no—
1572Q8—42no—
1573Q8—48no—
1574Q8—42no—
1575Q8—1068no—
1576Q8—1068no—
1577Q8—1068no—
1578Q8—1064no—
1579Q8—1064no—
1580Q8—1064no—
1581Q8—1064no—
1582Q8—2122no—
1583Q8—2124no—
1584Q8—2128no—
1585D4—1068no—
1586D4—1068no—
1587D4—1064no—
1588D4—1064no—
1589D4—2122no—
1590D4—2124no—
1591C2×C4—24no—
1592C2×C4—22no—
1593C2×C4—41no—
1594C2×C4—42no—
1595C2×C4—531no—
1596C2×C4—531no—
1597C2×C4—534no—
1598C2×C4—531no—
1599C2×C4—534no—
1600C2×C4—534no—
1601C2×C4—534no—
1602C2×C4—531no—
1603C2×C4—531no—
1604C2×C4—531no—
1605C2×C4—534no—
1606C2×C4—534no—
1607C2×C4—1062no—
1608C2×C4—1062no—
1609C2×C4—1062no—
1610C2×C4—1068no—
1611C2×C4—1068no—
1612C2×C4—1062no—
1613C2×C4—1068no—
1614C2×C4—1062no—
1615C2×C4—1062no—
1616C2×C4—1062no—
1617C2×C4—1064no—
1618C2×C4—1062no—
1619C2×C4—1062no—
1620C2×C4—1062no—
1621C2×C4—1062no—
1622C2×C4—1062no—
1623C2×C4—1068no—
1624C2×C4—2121no—
1625C2×C4—2121no—
1626C2×C4—2128no—
1627C2×C4—2124no—
1628C2×C4—2128no—
1629C2×C4—2122no—
1630C2×C4#1313326514yes—
1631C2×C4C24×D5311yescharacteristic
1632C2×C4C24×D5314yes—
1633C2×C4C24×D5314yes—
1634C2×C4C24×D5314yes—
1635C2×C4C24×D5311yescharacteristic
1636C2×C4C24×D5314yes—
1637C2×C4C24×D5311yescharacteristic
1638C2×C4C24×D5314yes—
1639C2×C4C24×D5314yes—
1640C2×C4C24×D5311yescharacteristic
1641C2×C4C24×D5311yescharacteristic
1642C2×C4C24×D5311yescharacteristic
1643C22—21no—
1644C22—21no—
1645C22—532no—
1646C22—1061no—
1647C22—1061no—
1648C22—1061no—
1649C22—1064no—
1650C22—1061no—
1651C22—1064no—
1652C22—1064no—
1653C22—1061no—
1654C22—2124no—
1655C22C2×#1313326512yes—
1656C22C25×D5311yescharacteristic
1657C4—21no—
1658C4—24no—
1659C4—24no—
1660C4—24no—
1661C4—21no—
1662C4—21no—
1663C4—24no—
1664C4—24no—
1665C4—24no—
1666C4—532no—
1667C4—532no—
1668C4—1061no—
1669C4—1064no—
1670C4—1061no—
1671C4—1061no—
1672C4—1064no—
1673C4—1064no—
1674C4—1061no—
1675C4—1064no—
1676C4—1064no—
1677C42−1+4×D5312yes—
1678C4C2×#1313326512yes—
1679C4C2×#1313326512yes—
1680C2—22no—
1681C2—1062no—
1682C2—2121no—
1683C2—2124no—
1684C2C2×2−1+4×D5311yescharacteristic
1685C2C22×#1313326511yescharacteristic
1686C2#585×D5311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3502C2
prime radical#20288012C2
hypercenter#3502D53
hypocenterC53#62837
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3502

Complements

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

NH ≅ G/Ntype
1. #20289314C2semidirect
2. #20289311C2semidirect
3. #20289207C2semidirect
4. #20289204C2semidirect
5. #20289199C2semidirect
6. #20289195C2semidirect
7. #20289121C2semidirect
8. #20288957C2semidirect
9. #20288808C2semidirect
10. #20288803C2semidirect
11. #20288598C2semidirect
12. #20288598C2semidirect
13. #20288596C2semidirect
14. #20288582C2semidirect
15. #20288581C2semidirect
16. #20288580C2semidirect
17. #20288533C2semidirect
18. #20288530C2semidirect
19. #20288524C2semidirect
20. #20288520C2semidirect
21. #20288470C2semidirect
22. #20288462C2semidirect
23. #20288457C2semidirect
25. C2×#16811177C2semidirect
26. #533×D53C2semidirect
27. C53×#3502C2semidirect
28. C53⋊#564C22semidirect
31. #16811372C22semidirect
32. #16811358C22semidirect
33. #16811358C22semidirect
34. Q8×Dic106C22semidirect
35. #16811353C22semidirect
36. #16811353C22semidirect
37. #16811352C22semidirect
38. #16811351C22semidirect
39. #16811351C22semidirect
40. #16811351C22semidirect
41. #16811351C22semidirect
42. #16811351C22semidirect
43. #16811350C22semidirect
44. #16811350C22semidirect
45. #16811349C22semidirect
46. #16811349C22semidirect
47. #16811348C22semidirect
48. #16811348C22semidirect
49. #16811348C22semidirect
50. #16811348C22semidirect
52. #16811347C22semidirect
53. #16811347C22semidirect
55. #16811346C22semidirect
56. #16811346C22semidirect
58. #16811345C22semidirect
59. #16811345C22semidirect
60. #16811345C22semidirect
61. #16811345C22semidirect
62. #16811345C22semidirect
64. #16811334C22semidirect
66. #16811333C22semidirect
67. #16811329C22semidirect
73. #16811314C22semidirect
76. #16811311C22semidirect
83. #16811305C22semidirect
87. #16811288C22semidirect
88. #16811288C22semidirect
90. #16811253C22semidirect
95. #16811250C22semidirect
96. #16811250C22semidirect
103. #16811234C22semidirect
105. #16811232C22semidirect
106. #16811232C22semidirect
107. #16811232C22semidirect
108. #16811232C22semidirect
111. #16811231C22semidirect
112. #16811231C22semidirect
113. #16811231C22semidirect
123. #16811179C22semidirect
140. #16811177C22semidirect
141. #16811177C22semidirect
153. C4⋊Q8×D53C22semidirect
179. #16811099C22semidirect
190. Q82×C53C22semidirect
191. Q82×C53C22semidirect
192. C53×#557C22semidirect
193. C53×#557C22semidirect
194. C53×#557C22semidirect
195. C53×#557C22semidirect
857. #3502D53semidirect
880. Q82C2×D53semidirect
881. Q82C2×D53semidirect
896. #557C2×D53semidirect
897. #557C2×D53semidirect
898. #557C2×D53semidirect
899. #557C2×D53semidirect
1046. C53#62837semidirect

Maximal subgroups

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

subgroupindex
#202893142
#202893112
#202892072
#202892042
#202891992
#202891952
#202891212
#202889572
#202888082
#202888032
#202885982
#202885962
#202885822
#202885812
#202885802
#202885332
#202885302
#202885242
#202885202
#202884702
#202884622
#202884572
#202880122
C2×#168111772
#533×D532
C53×#35022
#6283753