Finite Group Databasebeta

← #28292989

Subgroups — #28292989

Order 13568.

7900 conjugacy classes of subgroups.

The subgroup lattice has 1660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289235C214yesmaximal, complemented
2#20289224C214yesmaximal, complemented
3#20289118C212yesmaximal, complemented
4#20289109C212yesmaximal, complemented
5#20289082C214yesmaximal, complemented
6#20289074C214yesmaximal, complemented
7#20288953C212yesmaximal, complemented
8#20288948C212yesmaximal, complemented
9#20288745C214yesmaximal, complemented
10#20288737C214yesmaximal, complemented
11#20288627C212yesmaximal, complemented
12#20288616C212yesmaximal, complemented
13#20288591C211yesmaximal, characteristic, complemented
14#20288584C212yesmaximal, complemented
15#20288563C214yesmaximal, complemented
16#20288491C212yesmaximal, complemented
17#20288488C212yesmaximal, complemented
18#20288475C214yesmaximal, complemented
19#20288383C214yesmaximal, complemented
20#20288378C214yesmaximal, complemented
21#20288008C211yesmaximal, characteristic, complemented
22#532×D53C212yesmaximal, complemented
23C53×#3508C211yesmaximal, characteristic, complemented
24C2×#13133263C2214yescomplemented
25C2×#13133262C2214yescomplemented
26C2×#41×D53C2214yescomplemented
27#16811370C2218yescomplemented
28#16811366C2214yescomplemented
29#16811365C2214yescomplemented
30#16811362C2214yescomplemented
31#16811361C2218yescomplemented
32#16811360C2214yescomplemented
33#16811358C2214yescomplemented
34#16811356C2214yescomplemented
35#16811355C2214yescomplemented
36#16811345C2214yescomplemented
37#16811342C2214yescomplemented
38#16811337C2214yescomplemented
39#16811336C2214yescomplemented
40#16811335C2214yescomplemented
41#16811332C2214yescomplemented
42#16811329C2214yescomplemented
43#16811326C2214yescomplemented
44#16811323C2214yescomplemented
45#16811322C2218yescomplemented
46#16811320C2214yescomplemented
47#16811318C2218yescomplemented
48#16811317C2214yescomplemented
49#16811294C2214yescomplemented
50#16811294C2214yescomplemented
51#16811294C2214yescomplemented
52#16811293C2214yescomplemented
53#16811293C2214yescomplemented
54#16811292C2214yescomplemented
55#16811291C2214yescomplemented
56#16811285C2214yescomplemented
57#16811283C2214yescomplemented
58#16811281C2214yescomplemented
59#16811280C2214yescomplemented
60#16811275C2214yescomplemented
61#16811272C2214yescomplemented
62#16811271C2218yescomplemented
63#16811270C2214yescomplemented
64#16811270C2218yescomplemented
65#16811269C2214yescomplemented
66#16811269C2214yescomplemented
67#16811269C2218yescomplemented
68#16811268C2214yescomplemented
69#16811266C2214yescomplemented
70#16811265C2218yescomplemented
71#16811263C2218yescomplemented
72#16811263C2218yescomplemented
73#16811262C2218yescomplemented
74#16811261C2214yescomplemented
75D4×D212C2214yescomplemented
76D4×D212C2214yescomplemented
77#16811258C2214yescomplemented
78#16811258C2214yescomplemented
79#16811258C2214yescomplemented
80#16811257C2214yescomplemented
81#16811257C2214yescomplemented
82#16811257C2218yescomplemented
83#16811257C2214yescomplemented
84#16811257C2214yescomplemented
85D4×C22⋊D53C2214yescomplemented
86D4×C22⋊D53C2214yescomplemented
87D4×C22⋊D53C2214yescomplemented
88D4×C22⋊D53C2214yescomplemented
89#16811255C2214yescomplemented
90#16811255C2214yescomplemented
91#16811246C2214yescomplemented
92#16811245C2214yescomplemented
93#16811240C2214yescomplemented
94#16811238C2214yescomplemented
95#16811228C2212yescomplemented
96#16811228C2212yescomplemented
97#16811226C2214yescomplemented
98#16811224C2214yescomplemented
99#16811211C2218yescomplemented
100#16811209C2218yescomplemented
101#16811209C2218yescomplemented
102#16811207C2218yescomplemented
103#16811206C2218yescomplemented
104#16811205C2218yescomplemented
105#16811203C2214yescomplemented
106#16811202C2218yescomplemented
107#16811202C2214yescomplemented
108#16811200C2218yescomplemented
109#16811191C2214yescomplemented
110#16811191C2214yescomplemented
111#16811190C2214yescomplemented
112#16811189C2214yescomplemented
113#16811188C2218yescomplemented
114#16811187C2214yescomplemented
115#16811187C2212yescomplemented
116#16811186C2218yescomplemented
117#16811186C2214yescomplemented
118#16811186C2214yescomplemented
119#16811184C2218yescomplemented
120#16811183C2218yescomplemented
121#16811180C2211yescharacteristic, complemented
122#16811178C2212yescomplemented
123#16811177C2212yescomplemented
124#16811176C2211yescharacteristic, complemented
125#16811174C2212yescomplemented
126#16811174C2212yescomplemented
127#16811173C2212yescomplemented
128#16811173C2212yescomplemented
129#16811172C2214yescomplemented
130#16811171C2212yescomplemented
131#16811171C2212yescomplemented
132#16811170C2212yescomplemented
133#16811170C2214yescomplemented
134#16811170C2214yescomplemented
135#16811169C2211yescharacteristic, complemented
136#16811169C2214yescomplemented
137#16811168C2214yescomplemented
138#16811168C2214yescomplemented
139C4⋊Q8×D53C2212yescomplemented
140C2×#13133214C2211yescharacteristic, complemented
141#127×D53C2212yescomplemented
142#127×D53C2212yescomplemented
143#16811160C2212yescomplemented
144#16811155C2212yescomplemented
145#16811153C2212yescomplemented
146#16811153C2212yescomplemented
147#16811151C2212yescomplemented
148#16811151C2212yescomplemented
149#124×D53C2214yescomplemented
150#16811135C2211yescharacteristic, complemented
151#16811132C2212yescomplemented
152#16811132C2212yescomplemented
153#16811132C2218yescomplemented
154#16811131C2218yescomplemented
155#16811130C2211yescharacteristic, complemented
156C2×#13133190C2218yescomplemented
157#121×D53C2214yescomplemented
158#121×D53C2218yescomplemented
159#121×D53C2214yescomplemented
160#16811105C2214yescomplemented
161#16811102C2214yescomplemented
162#16811097C2212yescomplemented
163#16811095C2214yescomplemented
164C4×#11719945C2211yescharacteristic, complemented
165C4×#11719945C2212yescomplemented
166C4×#11719945C2212yescomplemented
167C4×D4×D53C2214yescomplemented
168C4×D4×D53C2214yescomplemented
169C2×C42×D53C2211yescharacteristic, complemented
170C53×#559C2214yescomplemented
171C53×#550C2214yescomplemented
172C53×#546C2214yescomplemented
173C53×#546C2214yescomplemented
174C53×#540C2212yescomplemented
175C53×#540C2212yescomplemented
176C53×#535C2212yescomplemented
177C53×#533C2211yescharacteristic, complemented
178C53×#532C2212yescomplemented
179C53×#532C2212yescomplemented
180C2×#127×C53C2211yescharacteristic, complemented
181C53×#518C2212yescomplemented
182C4×#41×C53C2211yescharacteristic, complemented
183#13133263—416no—
184#13133262—416no—
185C2×#11719949C2314yes—
186C2×#11719949C2314yes—
187C2×#11719945C2312yes—
188C2×#11719945C2312yes—
189C2×#11719945C2318yes—
190C2×#11719945C2314yes—
191C2×#11719945C2314yes—
192C2×#11719945C2318yes—
193C2×#11719945C2311yescharacteristic
194C2×#11719947C2314yes—
195C2×#11719947C2314yes—
196C2×#11719947C2318yes—
197C2×#11719947C2318yes—
198#41×D53—416no—
199C2×Q8×D53C2314yes—
200C22×D212C2314yes—
201C22×D212C2318yes—
202C22×D212C2312yes—
203C22×C22⋊D53C2318yes—
204C22×C22⋊D53C2318yes—
205C2×D4×D53C2314yes—
206C2×D4×D53C2318yes—
207C2×D4×D53C2314yes—
208C2×D4×D53C2314yes—
209C2×D4×D53C2318yes—
210C2×D4×D53C2314yes—
211C2×D4×D53C2314yes—
212C2×D4×D53C2318yes—
213C2×D4×D53C2318yes—
214C2×D4×D53C2314yes—
215C22×C4×D53C2312yes—
216C22×C4×D53C2311yescharacteristic
217C22×C4×D53C2318yes—
218#13133217C2312yes—
219#13133216C2312yes—
220#13133216C2314yes—
221#13133216C2314yes—
222#13133215C2314yes—
223#13133215C2311yescharacteristic
224#13133214C2314yes—
225#13133214C2312yes—
226#13133214C2312yes—
227#13133213C2318yes—
228#13133213C2314yes—
229#13133213C2314yes—
230#13133213C2314yes—
231#13133213C2314yes—
232#13133213C2314yes—
233#13133213C2314yes—
234#13133213C2314yes—
235#13133213C2311yescharacteristic
236#13133212C2318yes—
237#13133212C2312yes—
238#13133212C2312yes—
239#13133211C2318yes—
240#13133210C2318yes—
241#13133210C2318yes—
242#13133210C2312yes—
243#13133210C2312yes—
244#13133209C2312yes—
245#13133208C2314yes—
246#13133208C2312yes—
247#13133207C2312yes—
248#13133207C2312yes—
249#13133206C2314yes—
250#13133206C2314yes—
251#13133206C2311yescharacteristic
252#13133206C2314yes—
253#13133205C2314yes—
254#13133205C2318yes—
255#13133205C2314yes—
256#13133204C2318yes—
257#13133204C2314yes—
258#13133204C2311yescharacteristic
259#13133204C2314yes—
260#13133203C2318yes—
261#13133203C2318yes—
262#13133203C2318yes—
263#13133203C2318yes—
264#13133203C2318yes—
265#13133203C2312yes—
266#13133203C2312yes—
267#13133202C2312yes—
268#13133202C2312yes—
269#13133202C2318yes—
270#13133202C2318yes—
271#13133202C2318yes—
272#13133201C2318yes—
273#13133201C2312yes—
274#13133200C2318yes—
275#13133200C2318yes—
276#13133199C2318yes—
277#13133199C2312yes—
278#13133199C2318yes—
279#13133199C2318yes—
280#13133199C2312yes—
281#13133198C2318yes—
282#13133198C2311yescharacteristic
283#13133198C2311yescharacteristic
284#13133197C2314yes—
285#13133197C2318yes—
286#13133197C2312yes—
287#13133196C2314yes—
288#13133196C2318yes—
289#13133195C2318yes—
290#13133195C2318yes—
291#13133195C2312yes—
292#13133195C2312yes—
293#13133194C2318yes—
294#13133194C2318yes—
295#13133194C2312yes—
296#13133194C2312yes—
297#13133193C2314yes—
298#13133193C2312yes—
299#13133192C2318yes—
300#13133192C2314yes—
301#13133192C2314yes—
302#13133192C2314yes—
303#13133192C2314yes—
304#13133192C2312yes—
305#13133191C2318yes—
306#13133191C2314yes—
307#13133191C2314yes—
308#13133191C2318yes—
309#13133191C2318yes—
310#13133191C2314yes—
311#13133191C2314yes—
312#13133190C2318yes—
313#13133190C2318yes—
314#13133190C2318yes—
315#13133190C2318yes—
316#13133190C2318yes—
317#13133190C2318yes—
318#13133190C2318yes—
319#13133190C2318yes—
320#13133190C2318yes—
321#13133190C2318yes—
322#13133190C2312yes—
323#13133190C2318yes—
324#13133190C2318yes—
325#13133190C2312yes—
326#13133189C2318yes—
327#13133189C2318yes—
328#13133189C2318yes—
329#13133189C2318yes—
330#13133189C2318yes—
331#13133189C2318yes—
332#13133189C2318yes—
333#13133189C2318yes—
334#13133189C2312yes—
335#13133189C2312yes—
336#13133188C2314yes—
337#13133188C2318yes—
338#13133188C2318yes—
339#13133188C2318yes—
340#13133188C2314yes—
341#13133188C2318yes—
342#13133188C2314yes—
343#13133188C2314yes—
344#13133188C2312yes—
345#13133187C2318yes—
346#13133187C2318yes—
347#13133187C2318yes—
348#13133187C2318yes—
349#13133187C2312yes—
350#13133187C2318yes—
351#13133186C2318yes—
352#13133186C2318yes—
353#13133185C2314yes—
354#13133185C2314yes—
355#13133185C2318yes—
356#13133185C2318yes—
357#13133185C2318yes—
358#13133185C2318yes—
359#13133185C2318yes—
360#13133185C2318yes—
361#13133185C2318yes—
362#13133185C2311yescharacteristic
363#13133185C2311yescharacteristic
364Q8×Dic53C2314yes—
365C4×Dic106C2314yes—
366C4×Dic106C2312yes—
367C4×Dic106C2312yes—
368C4×Dic106C2312yes—
369C4×Dic106C2312yes—
370C4×Dic106C2312yes—
371#13133182C2314yes—
372C4×D212C2312yes—
373C4×D212C2314yes—
374C4×D212C2318yes—
375C4×D212C2314yes—
376C4×D212C2312yes—
377C4×D212C2312yes—
378C4×D212C2314yes—
379C4×D212C2312yes—
380C4×D212C2312yes—
381C4×D212C2314yes—
382D4×Dic53C2314yes—
383D4×Dic53C2314yes—
384D4×Dic53C2314yes—
385D4×Dic53C2314yes—
386#13133179C2318yes—
387#13133179C2318yes—
388#13133179C2314yes—
389#13133179C2314yes—
390#13133179C2314yes—
391#13133179C2314yes—
392C4×C22⋊D53C2312yes—
393C4×C22⋊D53C2318yes—
394C4×C22⋊D53C2312yes—
395C4×C22⋊D53C2312yes—
396C4×C22⋊D53C2312yes—
397C4×C22⋊D53C2318yes—
398C4×C22⋊D53C2312yes—
399C4×C22⋊D53C2312yes—
400C4×C22⋊D53C2312yes—
401C4×C22⋊D53C2318yes—
402C4×C22⋊D53C2312yes—
403C4×C22⋊D53C2318yes—
404C4×C22⋊D53C2312yes—
405C4×C22⋊D53C2312yes—
406#13133177C2318yes—
407#13133177C2318yes—
408#13133177C2318yes—
409#13133177C2318yes—
410#13133176C2312yes—
411#13133176C2311yescharacteristic
412#13133176C2312yes—
413#13133176C2312yes—
414#13133175C2314yes—
415#13133174C2318yes—
416#13133174C2312yes—
417#13133174C2312yes—
418#13133174C2312yes—
419#13133174C2312yes—
420#13133174C2312yes—
421#13133173C2318yes—
422C2×#11719919C2318yes—
423C4⋊C4×D53C2318yes—
424C4⋊C4×D53C2314yes—
425C4⋊C4×D53C2314yes—
426C2×#11719921C2318yes—
427C22⋊C4×D53C2318yes—
428C22⋊C4×D53C2318yes—
429C22⋊C4×D53C2318yes—
430C22⋊C4×D53C2318yes—
431C2×C4×Dic53C2312yes—
432C2×C4×Dic53C2311yescharacteristic
433C42×D53C2312yes—
434C42×D53C2312yes—
435C42×D53C2312yes—
436C42×D53C2312yes—
437C42×D53C2312yes—
438C2×#41×C53C2314yes—
439C2×#41×C53C2314yes—
440C2×#41×C53C2311yescharacteristic
441C22×D4×C53C2312yes—
442C22×D4×C53C2314yes—
443C4⋊Q8×C53C2312yes—
444#127×C53C2312yes—
445#127×C53C2314yes—
446#127×C53C2312yes—
447#127×C53C2314yes—
448#125×C53C2312yes—
449#124×C53C2314yes—
450#124×C53C2314yes—
451#124×C53C2314yes—
452#123×C53C2318yes—
453#123×C53C2318yes—
454C22⋊Q8×C53C2314yes—
455#121×C53C2314yes—
456#121×C53C2318yes—
457#121×C53C2314yes—
458#121×C53C2314yes—
459#121×C53C2314yes—
460#121×C53C2318yes—
461#120×C53C2314yes—
462#120×C53C2314yes—
463C4×Q8×C53C2314yes—
464C4×Q8×C53C2312yes—
465C4×D4×C53C2314yes—
466C4×D4×C53C2312yes—
467C4×D4×C53C2312yes—
468C4×D4×C53C2318yes—
469C4×D4×C53C2312yes—
470C4×D4×C53C2314yes—
471C4×D4×C53C2314yes—
472C4×D4×C53C2314yes—
473#117×C53C2311yescharacteristic
474#117×C53C2311yescharacteristic
475#117×C53C2311yescharacteristic
476#117×C53C2312yes—
477C2×C22⋊C4×C53C2318yes—
478C2×C42×C53C2311yescharacteristic
479C2×C42×C53C2311yescharacteristic
480C2×C42×C53C2311yescharacteristic
481C24×C53C2414yes—
482C23×D53C2411yescharacteristic
483C23×D53C2418yes—
484C23×D53C2414yes—
485C23×D53C2418yes—
486#41×C53—42no—
487#41×C53—48no—
488#41×C53—48no—
489C2×Q8×C53C2414yes—
490C2×Q8×C53C2411yescharacteristic
491C2×D4×C53—44no—
492C2×D4×C53—48no—
493C2×D4×C53C2414yes—
494C2×D4×C53C2414yes—
495C2×D4×C53C2414yes—
496C2×D4×C53C2411yescharacteristic
497C2×D4×C53C2411yescharacteristic
498C2×D4×C53C2414yes—
499C2×D4×C53C2411yescharacteristic
500C2×D4×C53C2418yes—
501C2×D4×C53C2418yes—
502C2×D4×C53C2418yes—
503C22×C4×C53C2411yescharacteristic
504C22×C4×C53C2411yescharacteristic
505C22×C4×C53C2411yescharacteristic
506C22×C4×C53C2412yes—
507C22×C4×C53C2412yes—
508C22×C4×C53C2412yes—
509C22×C4×C53C2418yes—
510C22×C4×C53C2418yes—
511C2×C22⋊D53—416no—
512C2×C22⋊D53—416no—
513C2×C22⋊D53C2418yes—
514C2×C22⋊D53C2418yes—
515C2×C22⋊D53C2412yes—
516C2×C22⋊D53C2412yes—
517C2×C22⋊D53C2412yes—
518C2×C22⋊D53C2412yes—
519C2×C22⋊D53C2418yes—
520C2×C22⋊D53C2418yes—
521C2×C22⋊D53C2412yes—
522C2×C22⋊D53C2418yes—
523C2×C22⋊D53C2418yes—
524C2×C22⋊D53C2418yes—
525C2×C22⋊D53C2418yes—
526C2×C22⋊D53C2418yes—
527C2×C22⋊D53C2418yes—
528C22×Dic53C2412yes—
529C22×Dic53C2418yes—
530C22×Dic53C2411yescharacteristic
531C22×Dic53C2418yes—
532#11719949—216no—
533#11719949—48no—
534Q8×D53—48no—
535#11719947—216no—
536#11719947—48no—
537#11719947—416no—
538#11719947—416no—
539D4×D53—216no—
540D4×D53—48no—
541D4×D53—48no—
542D4×D53—48no—
543D4×D53—48no—
544D4×D53—48no—
545D4×D53—416no—
546D4×D53—416no—
547D4×D53—416no—
548D4×D53—416no—
549#11719945—28no—
550#11719945—28no—
551#11719945—416no—
552#11719945—48no—
553#11719945—48no—
554#11719945—42no—
555#11719945—416no—
556C2×D212—44no—
557C2×D212—48no—
558C2×D212—416no—
559C2×D212C2414yes—
560C2×D212C2418yes—
561C2×D212C2414yes—
562C2×D212C2414yes—
563C2×D212C2412yes—
564C2×D212C2412yes—
565C2×D212C2414yes—
566C2×D212C2411yescharacteristic
567C2×D212C2418yes—
568C2×D212C2418yes—
569C2×C4×D53—28no—
570C2×C4×D53—416no—
571C2×C4×D53—42no—
572C2×C4×D53C2412yes—
573C2×C4×D53C2412yes—
574C2×C4×D53C2412yes—
575C2×C4×D53C2412yes—
576C2×C4×D53C2412yes—
577C2×C4×D53C2412yes—
578C2×C4×D53C2412yes—
579C2×C4×D53C2418yes—
580C2×C4×D53C2412yes—
581C2×C4×D53C2418yes—
582C2×C4×D53C2418yes—
583C2×C4×D53C2418yes—
584C2×C4×D53C2418yes—
585C2×C4×D53C2412yes—
586C2×Dic106C2414yes—
587C2×Dic106C2412yes—
588C2×Dic106C2412yes—
589C2×Dic106C2411yescharacteristic
590C2×Dic106C2418yes—
591C4⋊C4×C53C2412yes—
592C4⋊C4×C53C2414yes—
593C4⋊C4×C53C2412yes—
594C4⋊C4×C53C2412yes—
595C4⋊C4×C53C2414yes—
596C4⋊C4×C53C2418yes—
597C22⋊C4×C53C2412yes—
598C22⋊C4×C53C2414yes—
599C22⋊C4×C53C2418yes—
600C22⋊C4×C53C2418yes—
601C22⋊C4×C53C2412yes—
602C22⋊C4×C53C2412yes—
603C22⋊C4×C53C2418yes—
604C22⋊C4×C53C2418yes—
605C42×C53C2411yescharacteristic
606C42×C53C2411yescharacteristic
607C42×C53C2411yescharacteristic
608C42×C53C2411yescharacteristic
609C42×C53C2412yes—
610C42×C53C2412yes—
611C42×C53C2412yes—
612C42×C53C2414yes—
613C22⋊Dic53C2414yes—
614C22⋊Dic53C2418yes—
615C22⋊Dic53C2418yes—
616C22⋊Dic53C2418yes—
617C22⋊Dic53C2418yes—
618C22⋊Dic53C2412yes—
619C22⋊Dic53C2412yes—
620C22⋊Dic53C2411yescharacteristic
621C22⋊Dic53C2411yescharacteristic
622C22⋊Dic53C2412yes—
623C22⋊Dic53C2412yes—
624#11719921C2412yes—
625#11719921C2418yes—
626#11719921C2418yes—
627#11719921C2418yes—
628#11719921C2418yes—
629#11719921C2418yes—
630#11719921C2418yes—
631#11719921C2412yes—
632#11719921C2418yes—
633#11719921C2412yes—
634#11719921C2412yes—
635#11719921C2412yes—
636#11719921C2412yes—
637#11719921C2412yes—
638#11719921C2412yes—
639#11719921C2412yes—
640#11719921C2412yes—
641#11719921C2418yes—
642#11719921C2418yes—
643C4⋊Dic53C2414yes—
644C4⋊Dic53C2414yes—
645C4⋊Dic53C2418yes—
646C4⋊Dic53C2412yes—
647C4⋊Dic53C2412yes—
648C4⋊Dic53C2412yes—
649C4⋊Dic53C2412yes—
650C4⋊Dic53C2412yes—
651#11719919C2412yes—
652#11719919C2418yes—
653#11719919C2418yes—
654#11719919C2412yes—
655#11719919C2418yes—
656#11719919C2418yes—
657#11719919C2412yes—
658#11719919C2412yes—
659#11719919C2412yes—
660#11719919C2412yes—
661#11719919C2412yes—
662#11719919C2412yes—
663#11719919C2412yes—
664#11719919C2412yes—
665C4×Dic53C2412yes—
666C4×Dic53C2411yescharacteristic
667C4×Dic53C2412yes—
668C4×Dic53C2412yes—
669C4×Dic53C2412yes—
670C4×Dic53C2412yes—
671C4×Dic53C2411yescharacteristic
672C4×Dic53C2412yes—
673C4×Dic53C2412yes—
674C4×Dic53C2412yes—
675C4×Dic53C2414yes—
676C4×Dic53C2418yes—
677C23×C53—48no—
678C23×C53—44no—
679C23×C53C2511yescharacteristic
680C23×C53C2518yes—
681C23×C53C2511yescharacteristic
682C23×C53C2511yescharacteristic
683C22×D53—24no—
684C22×D53—216no—
685C22×D53—41no—
686C22×D53—48no—
687C22×D53—48no—
688C22×D53—48no—
689C22×D53—48no—
690C22×D53—44no—
691C22×D53—48no—
692C22×D53—48no—
693C22×D53C2518yes—
694C22×D53C2512yes—
695C22×D53C2512yes—
696Q8×C53—28no—
697Q8×C53—41no—
698D4×C53—28no—
699D4×C53—28no—
700D4×C53—28no—
701D4×C53—48no—
702D4×C53—48no—
703D4×C53—48no—
704D4×C53—44no—
705D4×C53—41no—
706D4×C53—41no—
707D4×C53—41no—
708C2×C4×C53—24no—
709C2×C4×C53—24no—
710C2×C4×C53—24no—
711C2×C4×C53—22no—
712C2×C4×C53—22no—
713C2×C4×C53—22no—
714C2×C4×C53—48no—
715C2×C4×C53—48no—
716C2×C4×C53C2512yes—
717C2×C4×C53C2518yes—
718C2×C4×C53C2511yescharacteristic
719C2×C4×C53C2512yes—
720C2×C4×C53C2512yes—
721C2×C4×C53C2511yescharacteristic
722C2×C4×C53C2511yescharacteristic
723C2×C4×C53C2512yes—
724C2×C4×C53C2511yescharacteristic
725C22⋊D53—24no—
726C22⋊D53—24no—
727C22⋊D53—216no—
728C22⋊D53—24no—
729C22⋊D53—24no—
730C22⋊D53—216no—
731C22⋊D53—48no—
732C22⋊D53—48no—
733C22⋊D53—48no—
734C22⋊D53—48no—
735C22⋊D53—42no—
736C22⋊D53—48no—
737C22⋊D53—48no—
738C22⋊D53—48no—
739C22⋊D53—48no—
740C2×Dic53—24no—
741C2×Dic53—216no—
742C2×Dic53—41no—
743C2×Dic53—48no—
744C2×Dic53C2512yes—
745C2×Dic53C2518yes—
746C2×Dic53C2512yes—
747C2×Dic53C2512yes—
748C2×Dic53C2512yes—
749C2×Dic53C2512yes—
750C2×Dic53C2512yes—
751D212—24no—
752D212—216no—
753D212—24no—
754D212—28no—
755D212—28no—
756D212—28no—
757D212—48no—
758D212—44no—
759D212—48no—
760D212—41no—
761C4×D53—24no—
762C4×D53—24no—
763C4×D53—24no—
764C4×D53—24no—
765C4×D53—24no—
766C4×D53—24no—
767C4×D53—24no—
768C4×D53—216no—
769C4×D53—42no—
770C4×D53—48no—
771C4×D53—48no—
772C4×D53—48no—
773C4×D53—48no—
774C4×D53H(5,𝔽2)18yescomplemented
775Dic106—28no—
776Dic106—24no—
777Dic106—24no—
778Dic106—41no—
779Dic106—48no—
780#62834—531nomaximal, Sylow
781C22×C53—28no—
782C22×C53—22no—
783C22×C53—28no—
784C22×C53—22no—
785C22×C53—22no—
786C22×C53—21no—
787C22×C53—28no—
788C22×C53—21no—
789C22×C53—21no—
790C22×C53—164no—
791C22×C53C2611yescharacteristic
792C2×D53—22no—
793C2×D53—22no—
794C2×D53—28no—
795C2×D53—22no—
796C2×D53—22no—
797C2×D53—28no—
798C2×D53—22no—
799C2×D53—28no—
800C2×D53—44no—
801C2×D53—816no—
802C2×D53—164no—
803C2×D53—168no—
804C2×D53C2×H(5,𝔽2)14yes—
805C4×C53—22no—
806C4×C53—22no—
807C4×C53—28no—
808C4×C53—22no—
809C4×C53—21no—
810C4×C53—21no—
811C4×C53—21no—
812C4×C53C2×H(5,𝔽2)14yes—
813C4×C53#58512yes—
814Dic53—28no—
815Dic53—22no—
816Dic53—22no—
817Dic53—22no—
818Dic53—22no—
819Dic53—22no—
820Dic53C2×H(5,𝔽2)14yes—
821#3558—534no—
822#3558—534no—
823#3549—532no—
824#3548—532no—
825#3546—534no—
826#3546—534no—
827#3537—532no—
828#3537—532no—
829#3519—534no—
830#3519—534no—
831#3511—532no—
832#3511—532no—
833#3508—532no—
834#3508—531no—
835#3508D5311yescharacteristic, complemented
836#3506—534no—
837#3498—532no—
838#3498—532no—
839#3496—534no—
840#3488—534no—
841#3488—534no—
842#3444—531no—
843C2×#532—532no—
844C2×C53—41no—
845C2×C53—48no—
846C2×C53—41no—
847C2×C53—41no—
848C2×C53C22×H(5,𝔽2)12yes—
849C2×C53C2×#58511yescharacteristic
850D53—24no—
851D53—48no—
852D53—42no—
853C2×H(5,𝔽2)—534no—
854C2×H(5,𝔽2)—534no—
855C22×#41—534no—
856#562—538no—
857H(3,𝔽4)—534no—
858H(3,𝔽4)—534no—
859#560—534no—
860#560—538no—
861#560—534no—
862#559—534no—
863#559—534no—
864#559—534no—
865#559C2×D5314yescomplemented
866#556—534no—
867#556—534no—
868#555—534no—
869#555—534no—
870#555—534no—
871#554—534no—
872#554—534no—
873#553—534no—
874#553—538no—
875#553—534no—
876#553—538no—
877#553—534no—
878#553—534no—
879#550—534no—
880#550—534no—
881#550—534no—
882#550—534no—
883#550—534no—
884#550—534no—
885#550—534no—
886#550C2×D5314yescomplemented
887#548—534no—
888#548—534no—
889#548—534no—
890#548—534no—
891#547—534no—
892#547—538no—
893#547—534no—
894#546—534no—
895#546—534no—
896#546—538no—
897#546—534no—
898#546—538no—
899#546—538no—
900#546—534no—
901#546—534no—
902#546—538no—
903#546—534no—
904#546—538no—
905#546—538no—
906#546C2×D5314yescomplemented
907#546C2×D5314yescomplemented
908D42—534no—
909D42—534no—
910D42—534no—
911D42—534no—
912D42—534no—
913D42—534no—
914D42—534no—
915D42—538no—
916D42—534no—
917D42—534no—
918D42—534no—
919D42—534no—
920D42—534no—
921D42—534no—
922D42—534no—
923D42—534no—
924#542—534no—
925#542—534no—
926#542—534no—
927#542—534no—
928#540—534no—
929#540—534no—
930#540—532no—
931#540—532no—
932#540C2×D5312yescomplemented
933#540C2×D5312yescomplemented
934#538—538no—
935#538—538no—
936#538—538no—
937#538—538no—
938#538—538no—
939#538—538no—
940#537—534no—
941#537—534no—
942#537—538no—
943#537—538no—
944#535—534no—
945#535—532no—
946#535—534no—
947#535—534no—
948#535—538no—
949#535—534no—
950#535—534no—
951#535—534no—
952#535—534no—
953#535—538no—
954#535C2×D5312yescomplemented
955#534—538no—
956#534—538no—
957#533—532no—
958#533—532no—
959#533—531no—
960#533—531no—
961#533C2×D5311yescharacteristic, complemented
962#532—534no—
963#532—531no—
964#532—532no—
965#532—532no—
966#532—532no—
967#532—532no—
968#532—534no—
969#532—534no—
970#532—534no—
971#532—534no—
972#532—534no—
973#532—532no—
974#532—532no—
975#532—532no—
976#532C2×D5312yescomplemented
977#532C2×D5312yescomplemented
978C2×C4⋊Q8—532no—
979C2×#127—532no—
980C2×#127—532no—
981C2×#127—531no—
982C2×#127C2×D5311yescharacteristic, complemented
983#529—532no—
984#529—532no—
985#529—532no—
986#529—532no—
987#529—532no—
988#529—532no—
989C2×#124—534no—
990#525—531no—
991#525—538no—
992#525—532no—
993#525—532no—
994#525—538no—
995#525—531no—
996C2×#121—534no—
997C2×#121—534no—
998C2×#121—538no—
999C2×#121—538no—
1000#520—534no—
1001#520—534no—
1002#518—534no—
1003#518—532no—
1004#518C2×D5312yescomplemented
1005C4×#41—532no—
1006C4×#41—532no—
1007C4×#41—531no—
1008C4×#41C2×D5311yescharacteristic, complemented
1009C2×C4×D4—534no—
1010C2×C4×D4—534no—
1011C22×C42—531no—
1012C53#6283411yescharacteristic, complemented, Sylow
1013H(5,𝔽2)—21216no—
1014H(5,𝔽2)—21216no—
1015C2×#41—534no—
1016C2×#41—534no—
1017C2×#41—534no—
1018C2×#41—538no—
1019C2×#41—538no—
1020C2×#41—534no—
1021C2×#41—532no—
1022C2×#41—532no—
1023C2×#41—531no—
1024C2×#41—538no—
1025C2×#41—538no—
1026C2×#41—534no—
1027C2×#41—534no—
1028C2×#41—21216no—
1029C2×#41C22×D5311yescharacteristic
1030C2×#41C22×D5314yes—
1031C2×#41C22×D5314yes—
1032C22×Q8—534no—
1033C22×D4—538no—
1034C22×D4—538no—
1035C22×D4—534no—
1036C22×D4—534no—
1037C22×D4—534no—
1038C22×D4—538no—
1039C22×D4—538no—
1040C22×D4—538no—
1041C22×D4—538no—
1042C22×D4—534no—
1043C22×D4—534no—
1044C22×D4—534no—
1045C22×D4—532no—
1046C22×D4—538no—
1047C22×D4—534no—
1048C22×D4C22×D5312yes—
1049C22×D4C22×D5314yes—
1050C23×C4—532no—
1051C23×C4—538no—
1052C23×C4—531no—
1053C4⋊Q8—534no—
1054C4⋊Q8—531no—
1055C4⋊Q8—534no—
1056C4⋊Q8—534no—
1057C4⋊Q8—532no—
1058C4⋊Q8—532no—
1059C4⋊Q8C22×D5312yes—
1060#127—534no—
1061#127—534no—
1062#127—534no—
1063#127—534no—
1064#127—534no—
1065#127—534no—
1066#127—531no—
1067#127—538no—
1068#127—534no—
1069#127—532no—
1070#127—534no—
1071#127—532no—
1072#127C22×D5312yes—
1073#127C22×D5314yes—
1074#127C22×D5312yes—
1075#127C22×D5314yes—
1076#126—532no—
1077#126—532no—
1078#126—538no—
1079#126—532no—
1080#126—532no—
1081#126—538no—
1082#126—538no—
1083#126—538no—
1084#125—532no—
1085#125—532no—
1086#125—532no—
1087#125—534no—
1088#125—532no—
1089#125C22×D5312yes—
1090#124—534no—
1091#124—531no—
1092#124—534no—
1093#124—534no—
1094#124—534no—
1095#124—531no—
1096#124—534no—
1097#124—538no—
1098#124—538no—
1099#124—538no—
1100#124—532no—
1101#124—532no—
1102#124—538no—
1103#124—538no—
1104#124—538no—
1105#124—534no—
1106#124—534no—
1107#124—538no—
1108#124C22×D5314yes—
1109#124C22×D5314yes—
1110#124C22×D5314yes—
1111#123—531no—
1112#123—531no—
1113#123—538no—
1114#123—538no—
1115#123—538no—
1116#123—532no—
1117#123—532no—
1118#123—538no—
1119#123—538no—
1120#123—538no—
1121#123—532no—
1122#123—532no—
1123#123—532no—
1124#123—538no—
1125#123—538no—
1126#123—538no—
1127#123—538no—
1128#123C22×D5318yes—
1129#123C22×D5318yes—
1130C22⋊Q8—532no—
1131C22⋊Q8—534no—
1132C22⋊Q8—534no—
1133C22⋊Q8—538no—
1134C22⋊Q8—532no—
1135C22⋊Q8—532no—
1136C22⋊Q8—532no—
1137C22⋊Q8—538no—
1138C22⋊Q8—534no—
1139C22⋊Q8—538no—
1140C22⋊Q8—538no—
1141C22⋊Q8—532no—
1142C22⋊Q8—532no—
1143C22⋊Q8—538no—
1144C22⋊Q8—538no—
1145C22⋊Q8C22×D5314yes—
1146#121—538no—
1147#121—534no—
1148#121—534no—
1149#121—538no—
1150#121—538no—
1151#121—538no—
1152#121—538no—
1153#121—532no—
1154#121—532no—
1155#121—532no—
1156#121—538no—
1157#121—534no—
1158#121—534no—
1159#121—538no—
1160#121—538no—
1161#121—538no—
1162#121—538no—
1163#121—538no—
1164#121—538no—
1165#121—534no—
1166#121—534no—
1167#121—538no—
1168#121—534no—
1169#121—534no—
1170#121—538no—
1171#121—538no—
1172#121—534no—
1173#121—534no—
1174#121—538no—
1175#121—532no—
1176#121—534no—
1177#121—534no—
1178#121—532no—
1179#121—532no—
1180#121—538no—
1181#121—538no—
1182#121—538no—
1183#121—538no—
1184#121—538no—
1185#121—538no—
1186#121—538no—
1187#121—538no—
1188#121—538no—
1189#121—538no—
1190#121—538no—
1191#121—538no—
1192#121C22×D5314yes—
1193#121C22×D5314yes—
1194#121C22×D5318yes—
1195#121C22×D5314yes—
1196#121C22×D5314yes—
1197#121C22×D5318yes—
1198#120—538no—
1199#120—538no—
1200#120—531no—
1201#120—531no—
1202#120—538no—
1203#120—538no—
1204#120—534no—
1205#120—538no—
1206#120—538no—
1207#120—534no—
1208#120—538no—
1209#120—538no—
1210#120—538no—
1211#120—532no—
1212#120—538no—
1213#120—538no—
1214#120—538no—
1215#120—538no—
1216#120—538no—
1217#120C22×D5314yes—
1218#120C22×D5314yes—
1219C4×Q8—534no—
1220C4×Q8—534no—
1221C4×Q8—532no—
1222C4×Q8—532no—
1223C4×Q8—532no—
1224C4×Q8—532no—
1225C4×Q8—532no—
1226C4×Q8—534no—
1227C4×Q8C22×D5312yes—
1228C4×Q8C22×D5314yes—
1229C4×D4—534no—
1230C4×D4—534no—
1231C4×D4—534no—
1232C4×D4—534no—
1233C4×D4—538no—
1234C4×D4—538no—
1235C4×D4—532no—
1236C4×D4—532no—
1237C4×D4—532no—
1238C4×D4—532no—
1239C4×D4—532no—
1240C4×D4—532no—
1241C4×D4—532no—
1242C4×D4—532no—
1243C4×D4—532no—
1244C4×D4—532no—
1245C4×D4—538no—
1246C4×D4—538no—
1247C4×D4—534no—
1248C4×D4—534no—
1249C4×D4—538no—
1250C4×D4—534no—
1251C4×D4—538no—
1252C4×D4—534no—
1253C4×D4—538no—
1254C4×D4—538no—
1255C4×D4—538no—
1256C4×D4—538no—
1257C4×D4—534no—
1258C4×D4—534no—
1259C4×D4—532no—
1260C4×D4—532no—
1261C4×D4—532no—
1262C4×D4—532no—
1263C4×D4—532no—
1264C4×D4—534no—
1265C4×D4—538no—
1266C4×D4—534no—
1267C4×D4C22×D5314yes—
1268C4×D4C22×D5314yes—
1269C4×D4C22×D5312yes—
1270C4×D4C22×D5312yes—
1271C4×D4C22×D5312yes—
1272C4×D4C22×D5318yes—
1273C4×D4C22×D5314yes—
1274C4×D4C22×D5314yes—
1275#117—531no—
1276#117—532no—
1277#117—532no—
1278#117—532no—
1279#117—534no—
1280#117—538no—
1281#117—532no—
1282#117—532no—
1283#117—532no—
1284#117—532no—
1285#117—532no—
1286#117—538no—
1287#117C22×D5311yescharacteristic
1288#117C22×D5311yescharacteristic
1289#117C22×D5311yescharacteristic
1290#117C22×D5312yes—
1291C2×C4⋊C4—538no—
1292C2×C4⋊C4—534no—
1293C2×C4⋊C4—534no—
1294C2×C4⋊C4—538no—
1295C2×C22⋊C4—538no—
1296C2×C22⋊C4—538no—
1297C2×C22⋊C4—538no—
1298C2×C22⋊C4—538no—
1299C2×C22⋊C4—538no—
1300C2×C22⋊C4C22×D5318yes—
1301C2×C42—532no—
1302C2×C42—531no—
1303C2×C42—532no—
1304C2×C42—532no—
1305C2×C42—532no—
1306C2×C42—532no—
1307C2×C42—532no—
1308C2×C42C22×D5311yescharacteristic
1309C2×C42C22×D5311yescharacteristic
1310C2×C42C22×D5311yescharacteristic
1311C24—531no—
1312C24—538no—
1313C24—538no—
1314C24—534no—
1315C24C23×D5314yes—
1316#41—42no—
1317#41—48no—
1318#41—48no—
1319#41—1068no—
1320#41—1068no—
1321#41—10616no—
1322#41—10616no—
1323#41—2122no—
1324#41—2128no—
1325#41—2128no—
1326#41—21216no—
1327#41—21216no—
1328#41—21216no—
1329#41—2128no—
1330#41—21216no—
1331#41—2128no—
1332C2×Q8—532no—
1333C2×Q8—532no—
1334C2×Q8—534no—
1335C2×Q8—531no—
1336C2×Q8—538no—
1337C2×Q8—2128no—
1338C2×Q8C23×D5314yes—
1339C2×Q8C23×D5311yescharacteristic
1340C2×D4—44no—
1341C2×D4—48no—
1342C2×D4—538no—
1343C2×D4—532no—
1344C2×D4—532no—
1345C2×D4—532no—
1346C2×D4—532no—
1347C2×D4—538no—
1348C2×D4—532no—
1349C2×D4—538no—
1350C2×D4—538no—
1351C2×D4—538no—
1352C2×D4—538no—
1353C2×D4—538no—
1354C2×D4—538no—
1355C2×D4—538no—
1356C2×D4—538no—
1357C2×D4—534no—
1358C2×D4—538no—
1359C2×D4—532no—
1360C2×D4—532no—
1361C2×D4—534no—
1362C2×D4—534no—
1363C2×D4—531no—
1364C2×D4—534no—
1365C2×D4—538no—
1366C2×D4—538no—
1367C2×D4—10616no—
1368C2×D4—2124no—
1369C2×D4—2128no—
1370C2×D4—21216no—
1371C2×D4—2128no—
1372C2×D4—2128no—
1373C2×D4—2128no—
1374C2×D4—2128no—
1375C2×D4—2128no—
1376C2×D4—21216no—
1377C2×D4—21216no—
1378C2×D4—21216no—
1379C2×D4—21216no—
1380C2×D4—21216no—
1381C2×D4—21216no—
1382C2×D4C23×D5314yes—
1383C2×D4C23×D5314yes—
1384C2×D4C23×D5314yes—
1385C2×D4C23×D5311yescharacteristic
1386C2×D4C23×D5311yescharacteristic
1387C2×D4C23×D5314yes—
1388C2×D4C23×D5311yescharacteristic
1389C2×D4C23×D5318yes—
1390C2×D4C23×D5318yes—
1391C2×D4C23×D5318yes—
1392C22×C4—532no—
1393C22×C4—532no—
1394C22×C4—538no—
1395C22×C4—531no—
1396C22×C4—538no—
1397C22×C4—532no—
1398C22×C4—532no—
1399C22×C4—532no—
1400C22×C4—532no—
1401C22×C4—532no—
1402C22×C4—532no—
1403C22×C4—532no—
1404C22×C4—538no—
1405C22×C4—532no—
1406C22×C4—538no—
1407C22×C4—538no—
1408C22×C4—538no—
1409C22×C4—538no—
1410C22×C4—1068no—
1411C22×C4—2122no—
1412C22×C4—21216no—
1413C22×C4C23×D5311yescharacteristic
1414C22×C4C23×D5312yes—
1415C22×C4C23×D5311yescharacteristic
1416C22×C4C23×D5312yes—
1417C22×C4C23×D5312yes—
1418C22×C4C23×D5311yescharacteristic
1419C22×C4C23×D5318yes—
1420C22×C4C23×D5318yes—
1421C4⋊C4—532no—
1422C4⋊C4—532no—
1423C4⋊C4—538no—
1424C4⋊C4—534no—
1425C4⋊C4—534no—
1426C4⋊C4—538no—
1427C4⋊C4—538no—
1428C4⋊C4—538no—
1429C4⋊C4—538no—
1430C4⋊C4—532no—
1431C4⋊C4—532no—
1432C4⋊C4—532no—
1433C4⋊C4—532no—
1434C4⋊C4—532no—
1435C4⋊C4—532no—
1436C4⋊C4—532no—
1437C4⋊C4—532no—
1438C4⋊C4—532no—
1439C4⋊C4—532no—
1440C4⋊C4—532no—
1441C4⋊C4—532no—
1442C4⋊C4—532no—
1443C4⋊C4C23×D5314yes—
1444C4⋊C4C23×D5314yes—
1445C4⋊C4C23×D5318yes—
1446C4⋊C4C23×D5312yes—
1447C4⋊C4C23×D5312yes—
1448C4⋊C4C23×D5312yes—
1449C22⋊C4—534no—
1450C22⋊C4—538no—
1451C22⋊C4—538no—
1452C22⋊C4—538no—
1453C22⋊C4—532no—
1454C22⋊C4—532no—
1455C22⋊C4—532no—
1456C22⋊C4—532no—
1457C22⋊C4—538no—
1458C22⋊C4—531no—
1459C22⋊C4—531no—
1460C22⋊C4—532no—
1461C22⋊C4—532no—
1462C22⋊C4—538no—
1463C22⋊C4—538no—
1464C22⋊C4—538no—
1465C22⋊C4—538no—
1466C22⋊C4—538no—
1467C22⋊C4—538no—
1468C22⋊C4—538no—
1469C22⋊C4—532no—
1470C22⋊C4—532no—
1471C22⋊C4—532no—
1472C22⋊C4—532no—
1473C22⋊C4—532no—
1474C22⋊C4—532no—
1475C22⋊C4—532no—
1476C22⋊C4—532no—
1477C22⋊C4—538no—
1478C22⋊C4—538no—
1479C22⋊C4C23×D5312yes—
1480C22⋊C4C23×D5318yes—
1481C22⋊C4C23×D5318yes—
1482C22⋊C4C23×D5312yes—
1483C22⋊C4C23×D5314yes—
1484C22⋊C4C23×D5318yes—
1485C22⋊C4C23×D5318yes—
1486C22⋊C4C23×D5312yes—
1487C42—532no—
1488C42—532no—
1489C42—531no—
1490C42—532no—
1491C42—532no—
1492C42—532no—
1493C42—531no—
1494C42—532no—
1495C42—532no—
1496C42—532no—
1497C42—538no—
1498C42—534no—
1499C42C23×D5311yescharacteristic
1500C42C23×D5311yescharacteristic
1501C42C23×D5312yes—
1502C42C23×D5312yes—
1503C42C23×D5312yes—
1504C42C23×D5311yescharacteristic
1505C42C23×D5311yescharacteristic
1506C42C23×D5314yes—
1507C23—48no—
1508C23—44no—
1509C23—532no—
1510C23—532no—
1511C23—538no—
1512C23—10616no—
1513C23—1064no—
1514C23—2128no—
1515C23—2128no—
1516C23—2128no—
1517C23—2124no—
1518C23—2128no—
1519C23—2128no—
1520C23—2128no—
1521C23—2121no—
1522C23C24×D5311yescharacteristic
1523C23C24×D5311yescharacteristic
1524C23C24×D5318yes—
1525C23C24×D5311yescharacteristic
1526Q8—28no—
1527Q8—41no—
1528Q8—1064no—
1529Q8—1064no—
1530Q8—1068no—
1531Q8—2128no—
1532Q8—2121no—
1533D4—28no—
1534D4—28no—
1535D4—28no—
1536D4—48no—
1537D4—44no—
1538D4—48no—
1539D4—48no—
1540D4—41no—
1541D4—41no—
1542D4—41no—
1543D4—1064no—
1544D4—1064no—
1545D4—10616no—
1546D4—10616no—
1547D4—1064no—
1548D4—1064no—
1549D4—1064no—
1550D4—1064no—
1551D4—10616no—
1552D4—1068no—
1553D4—1068no—
1554D4—1068no—
1555D4—2124no—
1556D4—2128no—
1557D4—2128no—
1558D4—2121no—
1559D4—2128no—
1560D4—2128no—
1561D4—2128no—
1562D4—2128no—
1563D4—2128no—
1564D4—2128no—
1565D4—2128no—
1566D4—2128no—
1567D4—2122no—
1568C2×C4—24no—
1569C2×C4—24no—
1570C2×C4—24no—
1571C2×C4—22no—
1572C2×C4—22no—
1573C2×C4—22no—
1574C2×C4—48no—
1575C2×C4—48no—
1576C2×C4—532no—
1577C2×C4—538no—
1578C2×C4—532no—
1579C2×C4—532no—
1580C2×C4—532no—
1581C2×C4—538no—
1582C2×C4—532no—
1583C2×C4—532no—
1584C2×C4—1064no—
1585C2×C4—10616no—
1586C2×C4—1064no—
1587C2×C4—1064no—
1588C2×C4—10616no—
1589C2×C4—1064no—
1590C2×C4—1064no—
1591C2×C4—1064no—
1592C2×C4—1064no—
1593C2×C4—1064no—
1594C2×C4—2122no—
1595C2×C4—2128no—
1596C2×C4—2128no—
1597C2×C4—2128no—
1598C2×C4—2128no—
1599C2×C4—2121no—
1600C2×C4—2128no—
1601C2×C4C24×D5311yescharacteristic
1602C2×C4C24×D5311yescharacteristic
1603C2×C4C24×D5312yes—
1604C2×C4C24×D5318yes—
1605C2×C4C24×D5311yescharacteristic
1606C2×C4C24×D5312yes—
1607C2×C4C24×D5312yes—
1608C2×C4C24×D5312yes—
1609C2×C4C24×D5311yescharacteristic
1610C22—22no—
1611C22—22no—
1612C22—22no—
1613C22—28no—
1614C22—28no—
1615C22—21no—
1616C22—21no—
1617C22—21no—
1618C22—28no—
1619C22—164no—
1620C22—534no—
1621C22—8488no—
1622C22—8484no—
1623C22—1062no—
1624C22—1062no—
1625C22—1068no—
1626C22—1062no—
1627C22—1062no—
1628C22—1068no—
1629C22—1062no—
1630C22—1068no—
1631C22—42416no—
1632C22—2124no—
1633C22C25×D5311yescharacteristic
1634C4—22no—
1635C4—22no—
1636C4—22no—
1637C4—28no—
1638C4—21no—
1639C4—21no—
1640C4—21no—
1641C4—534no—
1642C4—1062no—
1643C4—1062no—
1644C4—1062no—
1645C4—1068no—
1646C4—1062no—
1647C4—1062no—
1648C4H(5,𝔽2)×D5314yes—
1649C4#1681145912yes—
1650C2—41no—
1651C2—48no—
1652C2—41no—
1653C2—41no—
1654C2—1064no—
1655C2—2122no—
1656C2—2128no—
1657C2C2×H(5,𝔽2)×D5312yes—
1658C2C2×#1681145911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3508C2
hypercenter#3508D53
hypocenterC53#62834
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #20289235C2semidirect
2. #20289224C2semidirect
3. #20289118C2semidirect
4. #20289109C2semidirect
5. #20289082C2semidirect
6. #20289074C2semidirect
7. #20288953C2semidirect
8. #20288948C2semidirect
9. #20288745C2semidirect
10. #20288737C2semidirect
11. #20288627C2semidirect
12. #20288616C2semidirect
13. #20288591C2semidirect
14. #20288584C2semidirect
15. #20288563C2semidirect
16. #20288491C2semidirect
17. #20288488C2semidirect
18. #20288475C2semidirect
19. #20288383C2semidirect
20. #20288378C2semidirect
21. #20288008C2semidirect
22. #532×D53C2semidirect
23. C53×#3508C2semidirect
24. C2×#13133263C22semidirect
25. C2×#13133262C22semidirect
26. C2×#41×D53C22semidirect
27. #16811370C22semidirect
28. #16811366C22semidirect
29. #16811365C22semidirect
30. #16811362C22semidirect
31. #16811361C22semidirect
32. #16811360C22semidirect
33. #16811358C22semidirect
34. #16811356C22semidirect
35. #16811355C22semidirect
36. #16811345C22semidirect
37. #16811342C22semidirect
38. #16811337C22semidirect
39. #16811336C22semidirect
40. #16811335C22semidirect
41. #16811332C22semidirect
42. #16811329C22semidirect
43. #16811326C22semidirect
44. #16811323C22semidirect
45. #16811322C22semidirect
46. #16811320C22semidirect
47. #16811318C22semidirect
48. #16811317C22semidirect
49. #16811294C22semidirect
50. #16811294C22semidirect
51. #16811294C22semidirect
52. #16811293C22semidirect
53. #16811293C22semidirect
54. #16811292C22semidirect
55. #16811291C22semidirect
56. #16811285C22semidirect
57. #16811283C22semidirect
58. #16811281C22semidirect
59. #16811280C22semidirect
60. #16811275C22semidirect
61. #16811272C22semidirect
62. #16811271C22semidirect
63. #16811270C22semidirect
64. #16811270C22semidirect
65. #16811269C22semidirect
66. #16811269C22semidirect
67. #16811269C22semidirect
68. #16811268C22semidirect
69. #16811266C22semidirect
70. #16811265C22semidirect
71. #16811263C22semidirect
72. #16811263C22semidirect
73. #16811262C22semidirect
74. #16811261C22semidirect
75. D4×D212C22semidirect
76. D4×D212C22semidirect
77. #16811258C22semidirect
78. #16811258C22semidirect
79. #16811258C22semidirect
80. #16811257C22semidirect
81. #16811257C22semidirect
82. #16811257C22semidirect
83. #16811257C22semidirect
84. #16811257C22semidirect
85. D4×C22⋊D53C22semidirect
86. D4×C22⋊D53C22semidirect
87. D4×C22⋊D53C22semidirect
88. D4×C22⋊D53C22semidirect
89. #16811255C22semidirect
90. #16811255C22semidirect
91. #16811246C22semidirect
92. #16811245C22semidirect
93. #16811240C22semidirect
94. #16811238C22semidirect
95. #16811228C22semidirect
96. #16811228C22semidirect
97. #16811226C22semidirect
98. #16811224C22semidirect
99. #16811211C22semidirect
100. #16811209C22semidirect
101. #16811209C22semidirect
102. #16811207C22semidirect
103. #16811206C22semidirect
104. #16811205C22semidirect
105. #16811203C22semidirect
106. #16811202C22semidirect
107. #16811202C22semidirect
108. #16811200C22semidirect
109. #16811191C22semidirect
110. #16811191C22semidirect
111. #16811190C22semidirect
112. #16811189C22semidirect
113. #16811188C22semidirect
114. #16811187C22semidirect
115. #16811187C22semidirect
116. #16811186C22semidirect
117. #16811186C22semidirect
118. #16811186C22semidirect
119. #16811184C22semidirect
120. #16811183C22semidirect
121. #16811180C22semidirect
122. #16811178C22semidirect
123. #16811177C22semidirect
124. #16811176C22semidirect
125. #16811174C22semidirect
126. #16811174C22semidirect
127. #16811173C22semidirect
128. #16811173C22semidirect
129. #16811172C22semidirect
130. #16811171C22semidirect
131. #16811171C22semidirect
132. #16811170C22semidirect
133. #16811170C22semidirect
134. #16811170C22semidirect
135. #16811169C22semidirect
136. #16811169C22semidirect
137. #16811168C22semidirect
138. #16811168C22semidirect
139. C4⋊Q8×D53C22semidirect
140. C2×#13133214C22semidirect
141. #127×D53C22semidirect
142. #127×D53C22semidirect
143. #16811160C22semidirect
144. #16811155C22semidirect
145. #16811153C22semidirect
146. #16811153C22semidirect
147. #16811151C22semidirect
148. #16811151C22semidirect
149. #124×D53C22semidirect
150. #16811135C22semidirect
151. #16811132C22semidirect
152. #16811132C22semidirect
153. #16811132C22semidirect
154. #16811131C22semidirect
155. #16811130C22semidirect
156. C2×#13133190C22semidirect
157. #121×D53C22semidirect
158. #121×D53C22semidirect
159. #121×D53C22semidirect
160. #16811105C22semidirect
161. #16811102C22semidirect
162. #16811097C22semidirect
163. #16811095C22semidirect
164. C4×#11719945C22semidirect
165. C4×#11719945C22semidirect
166. C4×#11719945C22semidirect
167. C4×D4×D53C22semidirect
168. C4×D4×D53C22semidirect
169. C2×C42×D53C22semidirect
170. C53×#559C22semidirect
171. C53×#550C22semidirect
172. C53×#546C22semidirect
173. C53×#546C22semidirect
174. C53×#540C22semidirect
175. C53×#540C22semidirect
176. C53×#535C22semidirect
177. C53×#533C22semidirect
178. C53×#532C22semidirect
179. C53×#532C22semidirect
180. C2×#127×C53C22semidirect
181. C53×#518C22semidirect
182. C4×#41×C53C22semidirect
774. C4×D53H(5,𝔽2)semidirect
835. #3508D53semidirect
865. #559C2×D53semidirect
886. #550C2×D53semidirect
906. #546C2×D53semidirect
907. #546C2×D53semidirect
932. #540C2×D53semidirect
933. #540C2×D53semidirect
954. #535C2×D53semidirect
961. #533C2×D53semidirect
976. #532C2×D53semidirect
977. #532C2×D53semidirect
982. C2×#127C2×D53semidirect
1004. #518C2×D53semidirect
1008. C4×#41C2×D53semidirect
1012. C53#62834semidirect

Maximal subgroups

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

subgroupindex
#202892352
#202892242
#202891182
#202891092
#202890822
#202890742
#202889532
#202889482
#202887452
#202887372
#202886272
#202886162
#202885912
#202885842
#202885632
#202884912
#202884882
#202884752
#202883832
#202883782
#202880082
#532×D532
C53×#35082
#6283453