Finite Group Databasebeta

← #28293035

Subgroups — #28293035

Order 13568.

7254 conjugacy classes of subgroups.

The subgroup lattice has 1724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289304C214yesmaximal, complemented
2#20289289C214yesmaximal, complemented
3#20289173C214yesmaximal, complemented
4#20289074C214yesmaximal, complemented
5#20289018C218yesmaximal, complemented
6#20288718C214yesmaximal, complemented
7#20288669C214yesmaximal, complemented
8#20288641C218yesmaximal, complemented
9#20288621C214yesmaximal, complemented
10#20288612C211yesmaximal, characteristic, complemented
11#20288610C211yesmaximal, characteristic, complemented
12#20288596C211yesmaximal, characteristic, complemented
13#20288590C211yesmaximal, characteristic, complemented
14#20288585C214yesmaximal, complemented
15#20288509C211yesmaximal, characteristic, complemented
16#20288507C211yesmaximal, characteristic, complemented
17#20288496C211yesmaximal, characteristic, complemented
18#20288490C211yesmaximal, characteristic, complemented
19#20288369C211yesmaximal, characteristic, complemented
20#20288359C211yesmaximal, characteristic, complemented
21#20288357C211yesmaximal, characteristic, complemented
22#20288007C211yesmaximal, characteristic, complemented
23#20288007C211yesmaximal, characteristic, complemented
24C2×#16811169C211yesmaximal, characteristic, complemented
25C53×#3487C211yesmaximal, characteristic, complemented
26C2×#13133264C2211yescharacteristic, complemented
27C2×#13133263C2211yescharacteristic
28C2×#13133262C2211yescharacteristic
29C22×#11719945C2211yescharacteristic, complemented
30#16811368C2218yescomplemented
31#16811367C2218yescomplemented
32#16811361C2218yescomplemented
33#16811360C2218yescomplemented
34#16811359C2214yescomplemented
35#16811358C2214yescomplemented
36#16811356C2218yescomplemented
37#16811355C2214yescomplemented
38#16811351C2214yescomplemented
39#16811345C2214yescomplemented
40#16811345C2214yescomplemented
41#16811342C2214yescomplemented
42#16811335C2218yescomplemented
43#16811327C2218yescomplemented
44#16811323C2218yescomplemented
45#16811322C2218yescomplemented
46#16811316C2218yescomplemented
47#16811316C2218yescomplemented
48#16811306C2218yescomplemented
49#16811304C2218yescomplemented
50#16811302C2218yescomplemented
51#16811300C2218yescomplemented
52#16811297C2218yescomplemented
53#16811294C2214yescomplemented
54#16811293C2214yescomplemented
55#16811293C2218yescomplemented
56#16811291C2214yescomplemented
57#16811291C2214yescomplemented
58Q8×C22⋊D53C2214yescomplemented
59#16811284C2214yescomplemented
60#16811283C2214yescomplemented
61#16811282C2214yescomplemented
62#16811279C2214yescomplemented
63#16811278C2214yescomplemented
64#16811275C2214yescomplemented
65#16811272C2214yescomplemented
66#16811272C2214yescomplemented
67#16811272C2214yescomplemented
68#16811272C2218yescomplemented
69#16811270C2214yescomplemented
70#16811270C2214yescomplemented
71#16811269C2214yescomplemented
72#16811262C2218yescomplemented
73#16811262C2218yescomplemented
74#16811261C2214yescomplemented
75#16811261C2214yescomplemented
76#16811261C2214yescomplemented
77#16811261C2218yescomplemented
78#16811260C2218yescomplemented
79#16811260C2218yescomplemented
80#16811257C2214yescomplemented
81#16811255C2218yes—
82#16811245C2214yescomplemented
83#16811243C2218yescomplemented
84#16811240C2214yescomplemented
85#16811237C2218yescomplemented
86#16811231C2214yescomplemented
87#16811227C2218yescomplemented
88#16811226C2214yescomplemented
89#16811223C2218yescomplemented
90#16811223C2218yescomplemented
91#16811223C2218yescomplemented
92#16811219C2218yescomplemented
93#16811215C2218yescomplemented
94#16811210C2218yescomplemented
95#16811207C2218yescomplemented
96#16811206C2218yescomplemented
97#16811205C2218yescomplemented
98#16811200C2218yescomplemented
99#16811199C2211yescharacteristic
100#16811197C2211yescharacteristic
101#16811197C2212yescomplemented
102#16811197C2211yescharacteristic, complemented
103#16811197C2212yescomplemented
104#16811194C2212yescomplemented
105#16811194C2211yescharacteristic, complemented
106#16811193C2212yescomplemented
107#16811192C2211yescharacteristic
108#16811191C2212yescomplemented
109#16811188C2214yescomplemented
110#16811187C2212yescomplemented
111#16811187C2211yescharacteristic, complemented
112#16811186C2212yescomplemented
113#16811186C2212yescomplemented
114#16811186C2218yescomplemented
115#16811183C2214yescomplemented
116#16811182C2214yescomplemented
117#16811177C2214yescomplemented
118#16811176C2211yescharacteristic, complemented
119#16811176C2211yescharacteristic, complemented
120#16811175C2212yescomplemented
121#16811175C2212yescomplemented
122#16811172C2212yescomplemented
123#16811171C2212yescomplemented
124#16811169C2211yescharacteristic
125#16811169C2211yescharacteristic
126#16811169C2214yescomplemented
127#16811169C2214yescomplemented
128#16811169C2212yescomplemented
129#16811169C2214yescomplemented
130#16811169C2214yescomplemented
131#16811169C2212yescomplemented
132#16811168C2212yescomplemented
133#16811168C2212yescomplemented
134#16811168C2214yescomplemented
135C2×#13133215C2211yescharacteristic, complemented
136C2×#13133215C2212yescomplemented
137C2×#13133213C2211yescharacteristic
138#127×D53C2212yescomplemented
139#16811160C2214yescomplemented
140#16811159C2212yescomplemented
141#16811159C2212yescomplemented
142#16811154C2212yescomplemented
143#16811154C2212yescomplemented
144#16811154C2214yescomplemented
145#16811153C2214yescomplemented
146#16811153C2214yescomplemented
147#16811150C2214yescomplemented
148#16811150C2214yescomplemented
149C2×#13133206C2211yescharacteristic, complemented
150C2×#13133206C2212yescomplemented
151C2×#13133204C2211yescharacteristic, complemented
152#124×D53C2212yescomplemented
153#16811134C2211yescharacteristic
154#16811134C2211yescharacteristic, complemented
155#16811131C2214yescomplemented
156#16811129C2214yescomplemented
157#16811129C2214yescomplemented
158C2×#13133200C2214yescomplemented
159#123×D53C2214yescomplemented
160C2×#13133189C2214yescomplemented
161#16811102C2218yescomplemented
162#16811100C2211yescharacteristic, complemented
163#16811098C2211yescharacteristic, complemented
164#16811097C2211yescharacteristic, complemented
165#16811095C2218yescomplemented
166#41×Dic53C2211yescharacteristic, complemented
167#41×Dic53C2211yescharacteristic, complemented
168#16811091C2211yescharacteristic
169#16811091C2211yescharacteristic, complemented
170C4×#11719947C2214yescomplemented
171C4×#11719947C2214yescomplemented
172C2×C4×C22⋊D53C2214yescomplemented
173C22×C4×Dic53C2211yescharacteristic, complemented
174C2×2−1+4×C53C2211yescharacteristic, complemented
175C22×#41×C53C2211yescharacteristic, complemented
176C53×#550C2214yescomplemented
177C53×#550C2214yescomplemented
178C53×#548C2214yescomplemented
179C53×#548C2214yescomplemented
180C53×#535C2211yescharacteristic
181C53×#535C2211yescharacteristic, complemented
182C53×#535C2214yescomplemented
183C53×#525C2211yescharacteristic, complemented
184C53×#525C2211yescharacteristic, complemented
185C53×#525C2214yescomplemented
186C53×#519C2211yescharacteristic, complemented
187#13133264—44no—
188#13133263—44no—
189#13133262—44no—
190C2×#11719949C2312yes—
191C2×#11719945—44no—
192C2×#11719945C2311yescharacteristic
193C2×#11719945C2311yescharacteristic
194C2×#11719945C2314yes—
195C2×#11719945C2312yes—
196C2×#11719945C2314yes—
197C2×#11719945C2312yes—
198C2×#11719947C2312yes—
199C2×#11719947C2312yes—
200C2×#11719947C2312yes—
201C2×#11719947C2314yes—
202C2×#11719947C2314yes—
203C2×#11719947C2318yes—
204C2×#11719947C2314yes—
205C22×Dic106C2311yescharacteristic
206C22×Dic106C2312yes—
207C2×Q8×D53C2312yes—
208C22×D212C2311yescharacteristic
209C22×D212C2312yes—
210C22×C22⋊D53C2314yes—
211C22×C22⋊D53C2312yes—
212C22×C22⋊D53C2314yes—
213C2×D4×D53C2312yes—
214C2×D4×D53C2312yes—
215C2×D4×D53C2318yes—
216C2×D4×D53C2314yes—
217C2×D4×D53C2312yes—
218C23×Dic53C2312yes—
219C22×C4×D53C2312yes—
220#13133217C2312yes—
221#13133216C2312yes—
222#13133216C2312yes—
223#13133215C2312yes—
224#13133215C2312yes—
225#13133215C2318yes—
226#13133215C2314yes—
227#13133215C2312yes—
228#13133215C2311yescharacteristic
229#13133215C2312yes—
230#13133215C2312yes—
231#13133215C2311yescharacteristic
232#13133214C2312yes—
233#13133213C2312yes—
234#13133213C2318yes—
235#13133213C2314yes—
236#13133213C2318yes—
237#13133213C2311yescharacteristic
238#13133213C2312yes—
239#13133213C2312yes—
240#13133213C2311yescharacteristic
241#13133212C2318yes—
242#13133212C2314yes—
243#13133212C2318yes—
244#13133212C2314yes—
245#13133211C2318yes—
246#13133211C2318yes—
247#13133210C2318yes—
248#13133210C2318yes—
249#13133210C2314yes—
250#13133210C2314yes—
251#13133209C2318yes—
252#13133208C2312yes—
253#13133208C2312yes—
254#13133207C2318yes—
255#13133207C2318yes—
256#13133207C2314yes—
257#13133207C2314yes—
258#13133206C2312yes—
259#13133206C2318yes—
260#13133206C2314yes—
261#13133206C2312yes—
262#13133206C2312yes—
263#13133206C2311yescharacteristic
264#13133206C2312yes—
265#13133206C2312yes—
266#13133206C2311yescharacteristic
267#13133205C2312yes—
268#13133205C2312yes—
269#13133205C2318yes—
270#13133204C2312yes—
271#13133204C2314yes—
272#13133204C2318yes—
273#13133204C2312yes—
274#13133204C2312yes—
275#13133204C2311yescharacteristic
276#13133204C2311yescharacteristic
277#13133203C2318yes—
278#13133203C2318yes—
279#13133203C2318yes—
280#13133203C2314yes—
281#13133203C2314yes—
282#13133202C2318yes—
283#13133202C2318yes—
284#13133202C2318yes—
285#13133201C2318yes—
286#13133201C2314yes—
287#13133201C2314yes—
288#13133201C2314yes—
289#13133200C2314yes—
290#13133200C2318yes—
291#13133200C2318yes—
292#13133200C2318yes—
293#13133200C2314yes—
294#13133200C2318yes—
295#13133200C2312yes—
296#13133200C2312yes—
297#13133199C2318yes—
298#13133199C2318yes—
299#13133199C2318yes—
300#13133199C2318yes—
301#13133198C2314yes—
302#13133198C2318yes—
303#13133198C2318yes—
304#13133198C2318yes—
305#13133198C2318yes—
306#13133198C2314yes—
307#13133198C2314yes—
308#13133197C2314yes—
309#13133196C2314yes—
310#13133196C2312yes—
311#13133196C2312yes—
312#13133196C2318yes—
313#13133195C2318yes—
314#13133195C2318yes—
315#13133195C2318yes—
316#13133194C2318yes—
317#13133194C2314yes—
318#13133194C2318yes—
319#13133194C2314yes—
320#13133194C2314yes—
321#13133194C2314yes—
322#13133193C2314yes—
323#13133193C2314yes—
324#13133193C2318yes—
325#13133193C2318yes—
326#13133192C2314yes—
327#13133191C2312yes—
328#13133191C2314yes—
329#13133191C2318yes—
330#13133191C2312yes—
331#13133190C2318yes—
332#13133190C2318yes—
333#13133190C2318yes—
334#13133190C2318yes—
335#13133190C2318yes—
336#13133189C2318yes—
337#13133189C2314yes—
338#13133189C2318yes—
339#13133189C2318yes—
340#13133189C2318yes—
341#13133189C2318yes—
342#13133189C2318yes—
343#13133189C2318yes—
344#13133189C2318yes—
345#13133189C2318yes—
346#13133189C2318yes—
347#13133189C2314yes—
348#13133189C2318yes—
349#13133189C2318yes—
350#13133189C2318yes—
351#13133189C2314yes—
352#13133189C2314yes—
353#13133188C2318yes—
354#13133188C2318yes—
355#13133188C2318yes—
356#13133187C2314yes—
357#13133187C2318yes—
358#13133186C2312yes—
359#13133186C2312yes—
360#13133185C2318yes—
361#13133185C2318yes—
362#13133185C2318yes—
363#13133185C2318yes—
364#13133185C2318yes—
365#13133185C2314yes—
366Q8×Dic53C2312yes—
367Q8×Dic53C2312yes—
368C4×Dic106C2314yes—
369C4×Dic106C2318yes—
370C4×Dic106C2314yes—
371C4×Dic106C2314yes—
372#13133182C2312yes—
373#13133182C2314yes—
374#13133182C2312yes—
375#13133182C2314yes—
376#13133182C2314yes—
377C4×D212C2314yes—
378C4×D212C2318yes—
379D4×Dic53C2312yes—
380D4×Dic53C2314yes—
381D4×Dic53C2314yes—
382D4×Dic53C2314yes—
383D4×Dic53C2318yes—
384D4×Dic53C2314yes—
385D4×Dic53C2318yes—
386D4×Dic53C2314yes—
387D4×Dic53C2314yes—
388D4×Dic53C2312yes—
389#13133179C2312yes—
390#13133179C2314yes—
391#13133179C2318yes—
392#13133179C2312yes—
393C4×C22⋊D53C2314yes—
394C4×C22⋊D53C2314yes—
395C4×C22⋊D53C2314yes—
396C4×C22⋊D53C2314yes—
397C4×C22⋊D53C2318yes—
398C4×C22⋊D53C2318yes—
399C4×C22⋊D53C2318yes—
400C4×C22⋊D53C2318yes—
401C4×C22⋊D53C2318yes—
402C4×C22⋊D53C2318yes—
403#13133177C2318yes—
404#13133177C2318yes—
405#13133177C2314yes—
406#13133177C2314yes—
407#13133177C2314yes—
408#13133177C2318yes—
409#13133177C2314yes—
410#13133177C2314yes—
411#13133177C2314yes—
412#13133176C2311yescharacteristic
413#13133176C2311yescharacteristic
414#13133176C2312yes—
415#13133176C2312yes—
416#13133175C2314yes—
417#13133175C2314yes—
418#13133174C2318yes—
419#13133174C2318yes—
420#13133174C2312yes—
421#13133174C2312yes—
422#13133173C2318yes—
423#13133173C2314yes—
424#13133173C2314yes—
425#13133173C2314yes—
426#13133173C2314yes—
427#13133173C2314yes—
428C2×#11719919C2314yes—
429C2×#11719919C2318yes—
430C2×#11719919C2318yes—
431C4⋊C4×D53C2318yes—
432C2×C22⋊Dic53C2314yes—
433C2×C22⋊Dic53C2314yes—
434C2×#11719921C2314yes—
435C2×#11719921C2318yes—
436C2×#11719921C2318yes—
437C22⋊C4×D53C2318yes—
438C22⋊C4×D53C2318yes—
439C22⋊C4×D53C2314yes—
440C2×C4×Dic53C2312yes—
441C2×C4×Dic53C2312yes—
442C2×C4×Dic53C2312yes—
443C2×C4×Dic53C2311yescharacteristic
444C2×C4×Dic53C2311yescharacteristic
445C2×C4×Dic53C2312yes—
446C2×C4×Dic53C2312yes—
447C2×C4×Dic53C2312yes—
448C2×C4×Dic53C2312yes—
449C42×D53C2312yes—
450C42×D53C2312yes—
4512−1+4×C53—44no—
452C2×#41×C53—44no—
453C2×#41×C53C2311yescharacteristic
454C2×#41×C53C2311yescharacteristic
455C2×#41×C53C2314yes—
456C2×#41×C53C2312yes—
457C2×#41×C53C2314yes—
458C2×#41×C53C2314yes—
459C2×#41×C53C2312yes—
460C22×Q8×C53C2311yescharacteristic
461C22×Q8×C53C2312yes—
462C22×Q8×C53C2312yes—
463C22×D4×C53C2311yescharacteristic
464C22×D4×C53C2312yes—
465C23×C4×C53C2311yescharacteristic
466C23×C4×C53C2312yes—
467#127×C53C2312yes—
468#127×C53C2318yes—
469#127×C53C2312yes—
470#124×C53C2312yes—
471#124×C53C2318yes—
472#124×C53C2312yes—
473#123×C53C2312yes—
474#123×C53C2312yes—
475C22⋊Q8×C53C2312yes—
476C22⋊Q8×C53C2312yes—
477C22⋊Q8×C53C2318yes—
478#121×C53C2312yes—
479#121×C53C2314yes—
480#121×C53C2312yes—
481#121×C53C2314yes—
482#121×C53C2318yes—
483#121×C53C2318yes—
484#121×C53C2318yes—
485#120×C53C2314yes—
486#120×C53C2312yes—
487#120×C53C2312yes—
488#120×C53C2314yes—
489C4×Q8×C53C2314yes—
490C4×Q8×C53C2314yes—
491C4×D4×C53C2314yes—
492C4×D4×C53C2314yes—
493C4×D4×C53C2318yes—
494C4×D4×C53C2318yes—
495#117×C53C2314yes—
496#117×C53C2311yescharacteristic
497#117×C53C2311yescharacteristic
498C24×C53C2412yes—
499C24×C53C2411yescharacteristic
500C23×D53C2412yes—
501C23×D53C2414yes—
502C23×D53C2414yes—
503#41×C53—24no—
504#41×C53—24no—
505#41×C53—48no—
506#41×C53—48no—
507#41×C53—48no—
508#41×C53—44no—
509#41×C53—44no—
510C2×Q8×C53—24no—
511C2×Q8×C53—44no—
512C2×Q8×C53—44no—
513C2×Q8×C53C2412yes—
514C2×Q8×C53C2412yes—
515C2×Q8×C53C2411yescharacteristic
516C2×Q8×C53C2411yescharacteristic
517C2×Q8×C53C2414yes—
518C2×D4×C53—24no—
519C2×D4×C53—44no—
520C2×D4×C53C2412yes—
521C2×D4×C53C2412yes—
522C2×D4×C53C2412yes—
523C2×D4×C53C2412yes—
524C2×D4×C53C2411yescharacteristic
525C2×D4×C53C2411yescharacteristic
526C2×D4×C53C2414yes—
527C2×D4×C53C2418yes—
528C2×D4×C53C2418yes—
529C2×D4×C53C2414yes—
530C2×D4×C53C2418yes—
531C2×D4×C53C2414yes—
532C22×C4×C53—24no—
533C22×C4×C53—44no—
534C22×C4×C53C2412yes—
535C22×C4×C53C2412yes—
536C22×C4×C53C2412yes—
537C22×C4×C53C2412yes—
538C22×C4×C53C2412yes—
539C22×C4×C53C2411yescharacteristic
540C22×C4×C53C2414yes—
541C22×C4×C53C2414yes—
542C22×C4×C53C2418yes—
543C22×C4×C53C2411yescharacteristic
544C2×C22⋊D53—48no—
545C2×C22⋊D53—44no—
546C2×C22⋊D53—48no—
547C2×C22⋊D53C2418yes—
548C2×C22⋊D53C2412yes—
549C2×C22⋊D53C2412yes—
550C2×C22⋊D53C2414yes—
551C2×C22⋊D53C2414yes—
552C2×C22⋊D53C2414yes—
553C2×C22⋊D53C2414yes—
554C2×C22⋊D53C2418yes—
555C2×C22⋊D53C2418yes—
556C2×C22⋊D53C2414yes—
557C2×C22⋊D53C2414yes—
558C2×C22⋊D53C2418yes—
559C2×C22⋊D53C2414yes—
560C2×C22⋊D53C2414yes—
561C22×Dic53—44no—
562C22×Dic53C2412yes—
563C22×Dic53C2412yes—
564C22×Dic53C2412yes—
565C22×Dic53C2414yes—
566C22×Dic53C2412yes—
567C22×Dic53C2412yes—
568C22×Dic53C2412yes—
569C22×Dic53C2412yes—
570C22×Dic53C2414yes—
571C22×Dic53C2418yes—
572C22×Dic53C2414yes—
573C22×Dic53C2414yes—
574#11719949—44no—
575Q8×D53—44no—
576#11719947—44no—
577#11719947—44no—
578#11719947—44no—
579#11719947—416no—
580#11719947—48no—
581#11719947—48no—
582#11719947—48no—
583D4×D53—44no—
584D4×D53—44no—
585D4×D53—44no—
586D4×D53—416no—
587D4×D53—48no—
588#11719945—24no—
589#11719945—24no—
590#11719945—48no—
591#11719945—48no—
592#11719945—44no—
593#11719945—44no—
594C2×D212—24no—
595C2×D212—44no—
596C2×D212C2411yescharacteristic
597C2×D212C2412yes—
598C2×D212C2411yescharacteristic
599C2×D212C2412yes—
600C2×D212C2418yes—
601C2×D212C2414yes—
602C2×C4×D53—44no—
603C2×C4×D53C2414yes—
604C2×C4×D53C2412yes—
605C2×C4×D53C2412yes—
606C2×C4×D53C2414yes—
607C2×C4×D53C2418yes—
608C2×C4×D53C2414yes—
609C2×C4×D53C2418yes—
610C2×C4×D53C2414yes—
611C2×Dic106—24no—
612C2×Dic106—44no—
613C2×Dic106C2412yes—
614C2×Dic106C2411yescharacteristic
615C2×Dic106C2411yescharacteristic
616C2×Dic106C2414yes—
617C2×Dic106C2412yes—
618C2×Dic106C2414yes—
619C2×Dic106C2414yes—
620C4⋊C4×C53C2412yes—
621C4⋊C4×C53C2412yes—
622C4⋊C4×C53C2418yes—
623C4⋊C4×C53C2414yes—
624C4⋊C4×C53C2414yes—
625C22⋊C4×C53C2412yes—
626C22⋊C4×C53C2412yes—
627C22⋊C4×C53C2414yes—
628C22⋊C4×C53C2414yes—
629C22⋊C4×C53C2418yes—
630C22⋊C4×C53C2418yes—
631C22⋊C4×C53C2414yes—
632C22⋊C4×C53C2414yes—
633C42×C53C2412yes—
634C42×C53C2412yes—
635C42×C53C2418yes—
636C22⋊Dic53C2412yes—
637C22⋊Dic53C2418yes—
638C22⋊Dic53C2418yes—
639C22⋊Dic53C2412yes—
640C22⋊Dic53C2418yes—
641C22⋊Dic53C2418yes—
642C22⋊Dic53C2414yes—
643C22⋊Dic53C2414yes—
644C22⋊Dic53C2414yes—
645C22⋊Dic53C2414yes—
646C22⋊Dic53C2414yes—
647C22⋊Dic53C2414yes—
648#11719921C2414yes—
649#11719921C2414yes—
650#11719921C2418yes—
651#11719921C2418yes—
652#11719921C2418yes—
653#11719921C2418yes—
654#11719921C2414yes—
655#11719921C2418yes—
656#11719921C2418yes—
657#11719921C2418yes—
658#11719921C2418yes—
659#11719921C2414yes—
660#11719921C2414yes—
661#11719921C2414yes—
662C4⋊Dic53C2418yes—
663C4⋊Dic53C2414yes—
664C4⋊Dic53C2414yes—
665C4⋊Dic53C2412yes—
666C4⋊Dic53C2412yes—
667C4⋊Dic53C2414yes—
668C4⋊Dic53C2414yes—
669#11719919C2414yes—
670#11719919C2418yes—
671#11719919C2414yes—
672#11719919C2414yes—
673#11719919C2418yes—
674#11719919C2418yes—
675#11719919C2418yes—
676#11719919C2418yes—
677#11719919C2414yes—
678#11719919C2414yes—
679#11719919C2414yes—
680#11719919C2414yes—
681#11719919C2414yes—
682#11719919C2418yes—
683#11719919C2414yes—
684#11719919C2414yes—
685C4×Dic53C2411yescharacteristic
686C4×Dic53C2411yescharacteristic
687C4×Dic53C2414yes—
688C4×Dic53C2414yes—
689C4×Dic53C2412yes—
690C4×Dic53C2412yes—
691C4×Dic53C2411yescharacteristic
692C4×Dic53C2411yescharacteristic
693C4×Dic53C2412yes—
694C4×Dic53C2412yes—
695C4×Dic53C2412yes—
696C4×Dic53C2412yes—
697C4×Dic53C2414yes—
698C4×Dic53C2414yes—
699C4×Dic53C2412yes—
700C4×Dic53C2412yes—
701C4×Dic53C2418yes—
702C23×C53—22no—
703C23×C53—24no—
704C23×C53—42no—
705C23×C53—44no—
706C23×C53C2512yes—
707C23×C53C2512yes—
708C23×C53C2514yes—
709C23×C53C2512yes—
710C23×C53C2511yescharacteristic
711C22×D53—24no—
712C22×D53—44no—
713C22×D53—44no—
714C22×D53—44no—
715C22×D53—48no—
716C22×D53—48no—
717C22×D53C2512yes—
718C22×D53C2514yes—
719C22×D53C2512yes—
720Q8×C53—22no—
721Q8×C53—22no—
722Q8×C53—24no—
723Q8×C53—24no—
724Q8×C53—44no—
725D4×C53—24no—
726D4×C53—24no—
727D4×C53—22no—
728D4×C53—24no—
729D4×C53—24no—
730D4×C53—22no—
731D4×C53—48no—
732D4×C53—44no—
733D4×C53—48no—
734D4×C53—44no—
735D4×C53—48no—
736D4×C53—44no—
737C2×C4×C53—22no—
738C2×C4×C53—24no—
739C2×C4×C53—24no—
740C2×C4×C53—24no—
741C2×C4×C53—24no—
742C2×C4×C53—24no—
743C2×C4×C53—48no—
744C2×C4×C53—44no—
745C2×C4×C53—44no—
746C2×C4×C53H(5,𝔽2)14yes—
747C2×C4×C53C2512yes—
748C2×C4×C53C2514yes—
749C2×C4×C53C2514yes—
750C2×C4×C53C2512yes—
751C2×C4×C53C2512yes—
752C2×C4×C53C2514yes—
753C2×C4×C53C2511yescharacteristic
754C2×C4×C53C2511yescharacteristic
755C22⋊D53—24no—
756C22⋊D53—24no—
757C22⋊D53—28no—
758C22⋊D53—216no—
759C22⋊D53—48no—
760C22⋊D53—44no—
761C22⋊D53—44no—
762C22⋊D53—44no—
763C22⋊D53—44no—
764C22⋊D53—44no—
765C22⋊D53—48no—
766C22⋊D53—44no—
767C22⋊D53—44no—
768C22⋊D53—48no—
769C2×Dic53—24no—
770C2×Dic53—28no—
771C2×Dic53—24no—
772C2×Dic53—24no—
773C2×Dic53—24no—
774C2×Dic53—44no—
775C2×Dic53—44no—
776C2×Dic53—48no—
777C2×Dic53—44no—
778C2×Dic53—42no—
779C2×Dic53—42no—
780C2×Dic53—42no—
781C2×Dic53C2514yes—
782C2×Dic53C2512yes—
783C2×Dic53C2512yes—
784C2×Dic53C2512yes—
785C2×Dic53C2514yes—
786C2×Dic53C2514yes—
787C2×Dic53C2512yes—
788C2×Dic53C2512yes—
789C2×Dic53C2512yes—
790D212—24no—
791D212—24no—
792D212—22no—
793D212—22no—
794D212—44no—
795D212—48no—
796C4×D53—24no—
797C4×D53—24no—
798C4×D53—28no—
799C4×D53—48no—
800C4×D53—44no—
801C4×D53—44no—
802C4×D53—48no—
803C4×D53—44no—
804Dic106—24no—
805Dic106—24no—
806Dic106—22no—
807Dic106—22no—
808Dic106—28no—
809Dic106—44no—
810Dic106—44no—
811#62836—531nomaximal, Sylow
812C22×C53—22no—
813C22×C53—22no—
814C22×C53—24no—
815C22×C53—22no—
816C22×C53—22no—
817C22×C53—22no—
818C22×C53—22no—
819C22×C53—24no—
820C22×C53—28no—
821C22×C53—24no—
822C22×C53—44no—
823C22×C53—84no—
824C22×C53C2×H(5,𝔽2)12yes—
825C22×C53C2611yescharacteristic
826C2×D53—22no—
827C2×D53—22no—
828C2×D53—24no—
829C2×D53—24no—
830C2×D53—24no—
831C2×D53—28no—
832C2×D53—84no—
833C2×D53—164no—
834C2×D53—164no—
835C4×C53—22no—
836C4×C53—22no—
837C4×C53—22no—
838C4×C53—24no—
839C4×C53—24no—
840C4×C53—24no—
841C4×C53C2×H(5,𝔽2)12yes—
842C4×C53C2×H(5,𝔽2)12yes—
843Dic53—24no—
844Dic53—22no—
845Dic53—22no—
846Dic53—24no—
847Dic53—22no—
848Dic53—24no—
849Dic53—22no—
850Dic53—22no—
851Dic53#58514yes—
852#3562—534no—
853#3562—534no—
854#3554—534no—
855#3546—534no—
856#3542—538no—
857#3517—534no—
858#3514—534no—
859#3513—538no—
860#3511—534no—
861#3510—531no—
862#3510—531no—
863#3509—531no—
864#3508—534no—
865#3508—531no—
866#3500—531no—
867#3500—531no—
868#3499—531no—
869#3498—531no—
870#3487—531no—
871#3487D5311yescharacteristic, complemented
872#3485—531no—
873#3485—531no—
874#3444—531no—
875#3444—531no—
876C2×#532—531no—
877C2×C53—22no—
878C2×C53—42no—
879C2×C53—44no—
880C2×C53—42no—
881C2×C53—42no—
882C2×C53C22×H(5,𝔽2)11yescharacteristic
883C2×C53C2×#58512yes—
884D53—44no—
885D53—42no—
886D53—42no—
887C2×2−1+4—531no—
888C2×2−1+4C2×D5311yescharacteristic, complemented
889C2×H(5,𝔽2)—531no—
890C2×H(5,𝔽2)—531no—
891C22×#41—531no—
892C22×#41C2×D5311yescharacteristic, complemented
893#562—538no—
894#562—538no—
895#560—538no—
896#560—538no—
897#559—534no—
898#559—534no—
899#559—534no—
900#559—538no—
901#557—534no—
902#556—534no—
903#556—534no—
904#556—534no—
905#555—538no—
906#554—538no—
907#553—538no—
908#553—538no—
909#553—538no—
910#553—538no—
911#552—538no—
912#551—538no—
913#551—538no—
914#551—538no—
915#551—538no—
916#550—538no—
917#550—534no—
918#550—534no—
919#550—534no—
920#550—534no—
921#550C2×D5314yescomplemented
922#550C2×D5314yescomplemented
923D4×Q8—534no—
924#548—534no—
925#548—534no—
926#548—534no—
927#548—534no—
928#548C2×D5314yescomplemented
929#548C2×D5314yescomplemented
930#547—534no—
931#547—534no—
932#547—538no—
933#547—534no—
934#547—534no—
935#547—534no—
936#546—534no—
937#546—534no—
938#546—534no—
939#546—538no—
940#546—534no—
941#546—534no—
942#546—538no—
943#546—538no—
944#546—538no—
945#546—538no—
946#546—534no—
947D42—534no—
948D42—538no—
949#542—538no—
950#542—538no—
951#542—534no—
952#542—534no—
953#541—534no—
954#540—538no—
955#540—538no—
956#540—538no—
957#540—534no—
958#540—538no—
959#539—538no—
960#539—538no—
961#538—538no—
962#538—538no—
963#538—538no—
964#538—538no—
965#537—538no—
966#536—531no—
967#536—532no—
968#536—531no—
969#536—531no—
970#536—532no—
971#536—532no—
972#536—532no—
973#536—531no—
974#535—531no—
975#535—532no—
976#535—532no—
977#535—532no—
978#535—538no—
979#535—532no—
980#535—534no—
981#535—531no—
982#535C2×D5311yescharacteristic
983#535C2×D5311yescharacteristic, complemented
984#535C2×D5314yescomplemented
985#534—534no—
986#534—534no—
987#533—532no—
988#533—532no—
989#533—534no—
990#533—531no—
991#533—531no—
992#532—534no—
993#532—534no—
994#532—534no—
995#532—534no—
996#532—531no—
997#532—531no—
998#532—532no—
999#532—532no—
1000#532—532no—
1001#532—532no—
1002#532—532no—
1003#532—532no—
1004#532—534no—
1005C2×C4⋊Q8—531no—
1006C2×C4⋊Q8—532no—
1007C2×#127—531no—
1008C2×#127—532no—
1009#529—534no—
1010#529—534no—
1011#529—532no—
1012#529—532no—
1013#529—532no—
1014#529—532no—
1015#529—534no—
1016#529—534no—
1017#529—534no—
1018#529—534no—
1019C2×#124—531no—
1020C2×#124—532no—
1021C2×#124—531no—
1022C2×#124—532no—
1023#525—531no—
1024#525—531no—
1025#525—534no—
1026#525—534no—
1027#525—534no—
1028#525C2×D5311yescharacteristic, complemented
1029#525C2×D5311yescharacteristic, complemented
1030#525C2×D5314yescomplemented
1031C2×#123—534no—
1032C2×#123—534no—
1033C2×#121—534no—
1034#520—538no—
1035#519—531no—
1036#519C2×D5311yescharacteristic, complemented
1037#518—531no—
1038#518—538no—
1039#518—531no—
1040C4×#41—531no—
1041C4×#41—531no—
1042C4×#41—534no—
1043C4×#41—534no—
1044C4×#41—531no—
1045C4×#41—531no—
1046C2×C4×D4—534no—
1047C22×C42—531no—
1048C53#6283611yescharacteristic, complemented, Sylow
10492−1+4—44no—
10502−1+4—2124no—
1051H(5,𝔽2)—2124no—
1052H(5,𝔽2)—2124no—
1053C2×#41—44no—
1054C2×#41—532no—
1055C2×#41—534no—
1056C2×#41—534no—
1057C2×#41—538no—
1058C2×#41—534no—
1059C2×#41—532no—
1060C2×#41—532no—
1061C2×#41—532no—
1062C2×#41—531no—
1063C2×#41—531no—
1064C2×#41—534no—
1065C2×#41—534no—
1066C2×#41—532no—
1067C2×#41—532no—
1068C2×#41—2124no—
1069C2×#41C22×D5311yescharacteristic
1070C2×#41C22×D5311yescharacteristic
1071C2×#41C22×D5314yes—
1072C2×#41C22×D5314yes—
1073C2×#41C22×D5314yes—
1074C2×#41C22×D5312yes—
1075C2×#41C22×D5312yes—
1076C22×Q8—532no—
1077C22×Q8—531no—
1078C22×Q8—532no—
1079C22×Q8C22×D5311yescharacteristic
1080C22×Q8C22×D5312yes—
1081C22×Q8C22×D5312yes—
1082C22×D4—534no—
1083C22×D4—532no—
1084C22×D4—534no—
1085C22×D4—538no—
1086C22×D4—534no—
1087C22×D4—532no—
1088C22×D4—532no—
1089C22×D4—532no—
1090C22×D4—531no—
1091C22×D4—532no—
1092C22×D4C22×D5311yescharacteristic
1093C22×D4C22×D5312yes—
1094C23×C4—532no—
1095C23×C4—532no—
1096C23×C4C22×D5311yescharacteristic
1097C23×C4C22×D5312yes—
1098C4⋊Q8—531no—
1099C4⋊Q8—532no—
1100C4⋊Q8—532no—
1101C4⋊Q8—534no—
1102C4⋊Q8—532no—
1103C4⋊Q8—532no—
1104C4⋊Q8—538no—
1105C4⋊Q8—531no—
1106C4⋊Q8—532no—
1107C4⋊Q8—532no—
1108C4⋊Q8—532no—
1109C4⋊Q8—532no—
1110#127—531no—
1111#127—532no—
1112#127—532no—
1113#127—534no—
1114#127—538no—
1115#127—531no—
1116#127—532no—
1117#127—538no—
1118#127—532no—
1119#127C22×D5312yes—
1120#127C22×D5312yes—
1121#127C22×D5318yes—
1122#126—534no—
1123#126—534no—
1124#126—538no—
1125#126—538no—
1126#126—534no—
1127#126—534no—
1128#126—538no—
1129#126—538no—
1130#126—538no—
1131#126—538no—
1132#125—532no—
1133#125—534no—
1134#125—532no—
1135#125—534no—
1136#125—538no—
1137#125—538no—
1138#125—538no—
1139#124—531no—
1140#124—532no—
1141#124—532no—
1142#124—534no—
1143#124—532no—
1144#124—532no—
1145#124—538no—
1146#124—531no—
1147#124—532no—
1148#124—532no—
1149#124—532no—
1150#124—534no—
1151#124—531no—
1152#124—531no—
1153#124—532no—
1154#124—538no—
1155#124—538no—
1156#124—534no—
1157#124—534no—
1158#124—538no—
1159#124—538no—
1160#124—532no—
1161#124—532no—
1162#124—538no—
1163#124C22×D5312yes—
1164#124C22×D5312yes—
1165#124C22×D5318yes—
1166#123—534no—
1167#123—534no—
1168#123—534no—
1169#123—538no—
1170#123—538no—
1171#123—538no—
1172#123—538no—
1173#123—532no—
1174#123—532no—
1175#123—534no—
1176#123—534no—
1177#123—538no—
1178#123—538no—
1179#123—538no—
1180#123—538no—
1181#123—538no—
1182#123—538no—
1183#123—538no—
1184#123—534no—
1185#123—538no—
1186#123—534no—
1187#123—534no—
1188#123—538no—
1189#123—538no—
1190#123—538no—
1191#123—538no—
1192#123C22×D5312yes—
1193#123C22×D5312yes—
1194C22⋊Q8—534no—
1195C22⋊Q8—534no—
1196C22⋊Q8—538no—
1197C22⋊Q8—538no—
1198C22⋊Q8—532no—
1199C22⋊Q8—532no—
1200C22⋊Q8—534no—
1201C22⋊Q8—538no—
1202C22⋊Q8—538no—
1203C22⋊Q8—534no—
1204C22⋊Q8—538no—
1205C22⋊Q8—538no—
1206C22⋊Q8—534no—
1207C22⋊Q8—534no—
1208C22⋊Q8—534no—
1209C22⋊Q8—534no—
1210C22⋊Q8—538no—
1211C22⋊Q8—538no—
1212C22⋊Q8C22×D5312yes—
1213C22⋊Q8C22×D5312yes—
1214C22⋊Q8C22×D5318yes—
1215#121—538no—
1216#121—538no—
1217#121—538no—
1218#121—538no—
1219#121—534no—
1220#121—534no—
1221#121—534no—
1222#121—534no—
1223#121—538no—
1224#121—538no—
1225#121—538no—
1226#121—538no—
1227#121—538no—
1228#121—538no—
1229#121—538no—
1230#121—538no—
1231#121—538no—
1232#121—538no—
1233#121—538no—
1234#121—538no—
1235#121—532no—
1236#121—532no—
1237#121—534no—
1238#121—538no—
1239#121—534no—
1240#121—538no—
1241#121—538no—
1242#121—538no—
1243#121—538no—
1244#121—538no—
1245#121C22×D5312yes—
1246#121C22×D5312yes—
1247#121C22×D5318yes—
1248#121C22×D5314yes—
1249#121C22×D5314yes—
1250#121C22×D5318yes—
1251#121C22×D5318yes—
1252#120—532no—
1253#120—532no—
1254#120—534no—
1255#120—538no—
1256#120—538no—
1257#120—538no—
1258#120—538no—
1259#120—538no—
1260#120—534no—
1261#120—538no—
1262#120C22×D5312yes—
1263#120C22×D5312yes—
1264#120C22×D5314yes—
1265#120C22×D5314yes—
1266C4×Q8—532no—
1267C4×Q8—532no—
1268C4×Q8—534no—
1269C4×Q8—532no—
1270C4×Q8—532no—
1271C4×Q8—534no—
1272C4×Q8—534no—
1273C4×Q8—534no—
1274C4×Q8—534no—
1275C4×Q8—534no—
1276C4×Q8—538no—
1277C4×Q8C22×D5314yes—
1278C4×Q8C22×D5314yes—
1279C4×D4—534no—
1280C4×D4—534no—
1281C4×D4—534no—
1282C4×D4—534no—
1283C4×D4—532no—
1284C4×D4—532no—
1285C4×D4—538no—
1286C4×D4—534no—
1287C4×D4—534no—
1288C4×D4—538no—
1289C4×D4—538no—
1290C4×D4—538no—
1291C4×D4—538no—
1292C4×D4—538no—
1293C4×D4—534no—
1294C4×D4—534no—
1295C4×D4—534no—
1296C4×D4—534no—
1297C4×D4—538no—
1298C4×D4—538no—
1299C4×D4—532no—
1300C4×D4—532no—
1301C4×D4—538no—
1302C4×D4—534no—
1303C4×D4—534no—
1304C4×D4—534no—
1305C4×D4—534no—
1306C4×D4—534no—
1307C4×D4—534no—
1308C4×D4—534no—
1309C4×D4—538no—
1310C4×D4—538no—
1311C4×D4—538no—
1312C4×D4—538no—
1313C4×D4—534no—
1314C4×D4C22×D5314yes—
1315C4×D4C22×D5314yes—
1316C4×D4C22×D5318yes—
1317C4×D4C22×D5318yes—
1318#117—531no—
1319#117—531no—
1320#117—532no—
1321#117—532no—
1322#117—534no—
1323#117—534no—
1324#117—534no—
1325#117—534no—
1326#117—534no—
1327#117—534no—
1328#117—534no—
1329#117—538no—
1330#117—532no—
1331#117—532no—
1332#117—538no—
1333#117—538no—
1334#117C22×D5311yescharacteristic
1335#117C22×D5311yescharacteristic
1336#117C22×D5314yes—
1337C2×C4⋊C4—534no—
1338C2×C4⋊C4—538no—
1339C2×C4⋊C4—538no—
1340C2×C4⋊C4—538no—
1341C2×C22⋊C4—534no—
1342C2×C22⋊C4—534no—
1343C2×C22⋊C4—534no—
1344C2×C22⋊C4—538no—
1345C2×C22⋊C4—538no—
1346C2×C22⋊C4—534no—
1347C2×C22⋊C4—538no—
1348C2×C22⋊C4—538no—
1349C2×C42—532no—
1350C2×C42—532no—
1351C2×C42—532no—
1352C2×C42—531no—
1353C2×C42—532no—
1354C2×C42—531no—
1355C2×C42—532no—
1356C2×C42—532no—
1357C2×C42—532no—
1358C2×C42—532no—
1359C2×C42—532no—
1360C24—532no—
1361C24—534no—
1362C24—534no—
1363C24C23×D5312yes—
1364C24C23×D5311yescharacteristic
1365#41—24no—
1366#41—24no—
1367#41—48no—
1368#41—48no—
1369#41—48no—
1370#41—44no—
1371#41—44no—
1372#41—1064no—
1373#41—1064no—
1374#41—2128no—
1375#41—2128no—
1376#41—2124no—
1377#41—2124no—
1378#41—2128no—
1379#41—2128no—
1380#41—2124no—
1381#41—2124no—
1382#41—2124no—
1383#41—2128no—
1384#41—21216no—
1385#41—2124no—
1386C2×Q8—24no—
1387C2×Q8—44no—
1388C2×Q8—44no—
1389C2×Q8—534no—
1390C2×Q8—532no—
1391C2×Q8—532no—
1392C2×Q8—531no—
1393C2×Q8—531no—
1394C2×Q8—534no—
1395C2×Q8—534no—
1396C2×Q8—1064no—
1397C2×Q8—2124no—
1398C2×Q8—2124no—
1399C2×Q8C23×D5311yescharacteristic
1400C2×Q8C23×D5311yescharacteristic
1401C2×Q8C23×D5312yes—
1402C2×Q8C23×D5312yes—
1403C2×Q8C23×D5314yes—
1404C2×D4—24no—
1405C2×D4—44no—
1406C2×D4—534no—
1407C2×D4—538no—
1408C2×D4—532no—
1409C2×D4—532no—
1410C2×D4—534no—
1411C2×D4—534no—
1412C2×D4—534no—
1413C2×D4—538no—
1414C2×D4—538no—
1415C2×D4—534no—
1416C2×D4—534no—
1417C2×D4—538no—
1418C2×D4—534no—
1419C2×D4—534no—
1420C2×D4—531no—
1421C2×D4—532no—
1422C2×D4—532no—
1423C2×D4—531no—
1424C2×D4—538no—
1425C2×D4—534no—
1426C2×D4—1064no—
1427C2×D4—2124no—
1428C2×D4—2124no—
1429C2×D4—2124no—
1430C2×D4—2124no—
1431C2×D4—21216no—
1432C2×D4—2128no—
1433C2×D4—2124no—
1434C2×D4—2128no—
1435C2×D4—2128no—
1436C2×D4C23×D5312yes—
1437C2×D4C23×D5312yes—
1438C2×D4C23×D5311yescharacteristic
1439C2×D4C23×D5312yes—
1440C2×D4C23×D5312yes—
1441C2×D4C23×D5311yescharacteristic
1442C2×D4C23×D5314yes—
1443C2×D4C23×D5318yes—
1444C2×D4C23×D5318yes—
1445C2×D4C23×D5314yes—
1446C2×D4C23×D5314yes—
1447C2×D4C23×D5318yes—
1448C22×C4—24no—
1449C22×C4—44no—
1450C22×C4—532no—
1451C22×C4—532no—
1452C22×C4—532no—
1453C22×C4—534no—
1454C22×C4—532no—
1455C22×C4—532no—
1456C22×C4—532no—
1457C22×C4—532no—
1458C22×C4—534no—
1459C22×C4—538no—
1460C22×C4—534no—
1461C22×C4—534no—
1462C22×C4—534no—
1463C22×C4—532no—
1464C22×C4—532no—
1465C22×C4—534no—
1466C22×C4—538no—
1467C22×C4—534no—
1468C22×C4—538no—
1469C22×C4—534no—
1470C22×C4—2124no—
1471C22×C4—2124no—
1472C22×C4C23×D5312yes—
1473C22×C4C23×D5312yes—
1474C22×C4C23×D5311yescharacteristic
1475C22×C4C23×D5312yes—
1476C22×C4C23×D5312yes—
1477C22×C4C23×D5312yes—
1478C22×C4C23×D5314yes—
1479C22×C4C23×D5318yes—
1480C22×C4C23×D5314yes—
1481C22×C4C23×D5311yescharacteristic
1482C4⋊C4—534no—
1483C4⋊C4—534no—
1484C4⋊C4—538no—
1485C4⋊C4—534no—
1486C4⋊C4—538no—
1487C4⋊C4—538no—
1488C4⋊C4—538no—
1489C4⋊C4—538no—
1490C4⋊C4—538no—
1491C4⋊C4—534no—
1492C4⋊C4—534no—
1493C4⋊C4—532no—
1494C4⋊C4—534no—
1495C4⋊C4—532no—
1496C4⋊C4—534no—
1497C4⋊C4—534no—
1498C4⋊C4—534no—
1499C4⋊C4—534no—
1500C4⋊C4—534no—
1501C4⋊C4—534no—
1502C4⋊C4—534no—
1503C4⋊C4—534no—
1504C4⋊C4—538no—
1505C4⋊C4C23×D5314yes—
1506C4⋊C4C23×D5314yes—
1507C4⋊C4C23×D5312yes—
1508C4⋊C4C23×D5312yes—
1509C4⋊C4C23×D5318yes—
1510C22⋊C4—532no—
1511C22⋊C4—532no—
1512C22⋊C4—538no—
1513C22⋊C4—538no—
1514C22⋊C4—538no—
1515C22⋊C4—538no—
1516C22⋊C4—534no—
1517C22⋊C4—534no—
1518C22⋊C4—534no—
1519C22⋊C4—534no—
1520C22⋊C4—534no—
1521C22⋊C4—534no—
1522C22⋊C4—534no—
1523C22⋊C4—534no—
1524C22⋊C4—534no—
1525C22⋊C4—538no—
1526C22⋊C4—538no—
1527C22⋊C4—538no—
1528C22⋊C4—538no—
1529C22⋊C4—538no—
1530C22⋊C4—538no—
1531C22⋊C4—538no—
1532C22⋊C4—534no—
1533C22⋊C4—538no—
1534C22⋊C4—534no—
1535C22⋊C4—534no—
1536C22⋊C4C23×D5314yes—
1537C22⋊C4C23×D5312yes—
1538C22⋊C4C23×D5318yes—
1539C22⋊C4C23×D5312yes—
1540C22⋊C4C23×D5314yes—
1541C22⋊C4C23×D5318yes—
1542C22⋊C4C23×D5314yes—
1543C22⋊C4C23×D5314yes—
1544C42—531no—
1545C42—531no—
1546C42—532no—
1547C42—532no—
1548C42—531no—
1549C42—531no—
1550C42—532no—
1551C42—532no—
1552C42—532no—
1553C42—532no—
1554C42—534no—
1555C42—534no—
1556C42—534no—
1557C42—532no—
1558C42—532no—
1559C42—534no—
1560C42—538no—
1561C42C23×D5312yes—
1562C42C23×D5312yes—
1563C42C23×D5318yes—
1564C23—22no—
1565C23—24no—
1566C23—42no—
1567C23—44no—
1568C23—532no—
1569C23—532no—
1570C23—534no—
1571C23—1064no—
1572C23—2124no—
1573C23—2124no—
1574C23—2128no—
1575C23—2128no—
1576C23—2124no—
1577C23C24×D5312yes—
1578C23C24×D5314yes—
1579C23C24×D5312yes—
1580C23C24×D5312yes—
1581C23C24×D5311yescharacteristic
1582Q8—24no—
1583Q8—24no—
1584Q8—22no—
1585Q8—22no—
1586Q8—44no—
1587Q8—1068no—
1588Q8—1064no—
1589Q8—1064no—
1590Q8—1062no—
1591Q8—1062no—
1592Q8—2124no—
1593Q8—2124no—
1594D4—24no—
1595D4—24no—
1596D4—24no—
1597D4—24no—
1598D4—22no—
1599D4—22no—
1600D4—48no—
1601D4—48no—
1602D4—44no—
1603D4—44no—
1604D4—44no—
1605D4—48no—
1606D4—1068no—
1607D4—10616no—
1608D4—1064no—
1609D4—1064no—
1610D4—1064no—
1611D4—1064no—
1612D4—1062no—
1613D4—1062no—
1614D4—2128no—
1615D4—2124no—
1616D4—2128no—
1617D4—2124no—
1618D4—2124no—
1619D4—2124no—
1620D4—2128no—
1621D4—2124no—
1622D4—2124no—
1623D4—2124no—
1624D4—2128no—
1625D4—2124no—
1626C2×C4—22no—
1627C2×C4—24no—
1628C2×C4—24no—
1629C2×C4—24no—
1630C2×C4—24no—
1631C2×C4—24no—
1632C2×C4—48no—
1633C2×C4—44no—
1634C2×C4—44no—
1635C2×C4—532no—
1636C2×C4—532no—
1637C2×C4—532no—
1638C2×C4—534no—
1639C2×C4—532no—
1640C2×C4—534no—
1641C2×C4—532no—
1642C2×C4—534no—
1643C2×C4—532no—
1644C2×C4—1068no—
1645C2×C4—1064no—
1646C2×C4—1064no—
1647C2×C4—1064no—
1648C2×C4—1068no—
1649C2×C4—1064no—
1650C2×C4—1064no—
1651C2×C4—1064no—
1652C2×C4—2128no—
1653C2×C4—2124no—
1654C2×C4—2124no—
1655C2×C4—2124no—
1656C2×C4—2128no—
1657C2×C4—2122no—
1658C2×C4—2122no—
1659C2×C4—2122no—
1660C2×C4—2124no—
1661C2×C4—2124no—
1662C2×C4—2124no—
1663C2×C4—2128no—
1664C2×C4#1313326214yes—
1665C2×C4C24×D5312yes—
1666C2×C4C24×D5314yes—
1667C2×C4C24×D5312yes—
1668C2×C4C24×D5312yes—
1669C2×C4C24×D5314yes—
1670C2×C4C24×D5314yes—
1671C2×C4C24×D5311yescharacteristic
1672C2×C4C24×D5311yescharacteristic
1673C22—22no—
1674C22—22no—
1675C22—22no—
1676C22—22no—
1677C22—24no—
1678C22—22no—
1679C22—22no—
1680C22—24no—
1681C22—24no—
1682C22—28no—
1683C22—44no—
1684C22—84no—
1685C22—8484no—
1686C22—8484no—
1687C22—1062no—
1688C22—1062no—
1689C22—1064no—
1690C22—1064no—
1691C22—1064no—
1692C22—1068no—
1693C22—4244no—
1694C22C2×#1313326212yes—
1695C22C25×D5311yescharacteristic
1696C4—22no—
1697C4—24no—
1698C4—22no—
1699C4—22no—
1700C4—24no—
1701C4—24no—
1702C4—534no—
1703C4—1062no—
1704C4—1062no—
1705C4—1064no—
1706C4—1062no—
1707C4—1064no—
1708C4—1062no—
1709C4—1062no—
1710C4—1064no—
1711C4C2×#1313326212yes—
1712C4C2×#1313326212yes—
1713C2—22no—
1714C2—42no—
1715C2—44no—
1716C2—42no—
1717C2—42no—
1718C2—2122no—
1719C2—2122no—
1720C2—2124no—
1721C2C22×#1313326211yescharacteristic
1722C2#585×D5312yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3487C2
hypercenter#3487D53
hypocenterC53#62836
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3487

Complements

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

NH ≅ G/Ntype
1. #20289304C2semidirect
2. #20289289C2semidirect
3. #20289173C2semidirect
4. #20289074C2semidirect
5. #20289018C2semidirect
6. #20288718C2semidirect
7. #20288669C2semidirect
8. #20288641C2semidirect
9. #20288621C2semidirect
10. #20288612C2semidirect
11. #20288610C2semidirect
12. #20288596C2semidirect
13. #20288590C2semidirect
14. #20288585C2semidirect
15. #20288509C2semidirect
16. #20288507C2semidirect
17. #20288496C2semidirect
18. #20288490C2semidirect
19. #20288369C2semidirect
20. #20288359C2semidirect
21. #20288357C2semidirect
22. #20288007C2semidirect
23. #20288007C2semidirect
24. C2×#16811169C2semidirect
25. C53×#3487C2semidirect
26. C2×#13133264C22semidirect
29. C22×#11719945C22semidirect
30. #16811368C22semidirect
31. #16811367C22semidirect
32. #16811361C22semidirect
33. #16811360C22semidirect
34. #16811359C22semidirect
35. #16811358C22semidirect
36. #16811356C22semidirect
37. #16811355C22semidirect
38. #16811351C22semidirect
39. #16811345C22semidirect
40. #16811345C22semidirect
41. #16811342C22semidirect
42. #16811335C22semidirect
43. #16811327C22semidirect
44. #16811323C22semidirect
45. #16811322C22semidirect
46. #16811316C22semidirect
47. #16811316C22semidirect
48. #16811306C22semidirect
49. #16811304C22semidirect
50. #16811302C22semidirect
51. #16811300C22semidirect
52. #16811297C22semidirect
53. #16811294C22semidirect
54. #16811293C22semidirect
55. #16811293C22semidirect
56. #16811291C22semidirect
57. #16811291C22semidirect
58. Q8×C22⋊D53C22semidirect
59. #16811284C22semidirect
60. #16811283C22semidirect
61. #16811282C22semidirect
62. #16811279C22semidirect
63. #16811278C22semidirect
64. #16811275C22semidirect
65. #16811272C22semidirect
66. #16811272C22semidirect
67. #16811272C22semidirect
68. #16811272C22semidirect
69. #16811270C22semidirect
70. #16811270C22semidirect
71. #16811269C22semidirect
72. #16811262C22semidirect
73. #16811262C22semidirect
74. #16811261C22semidirect
75. #16811261C22semidirect
76. #16811261C22semidirect
77. #16811261C22semidirect
78. #16811260C22semidirect
79. #16811260C22semidirect
80. #16811257C22semidirect
82. #16811245C22semidirect
83. #16811243C22semidirect
84. #16811240C22semidirect
85. #16811237C22semidirect
86. #16811231C22semidirect
87. #16811227C22semidirect
88. #16811226C22semidirect
89. #16811223C22semidirect
90. #16811223C22semidirect
91. #16811223C22semidirect
92. #16811219C22semidirect
93. #16811215C22semidirect
94. #16811210C22semidirect
95. #16811207C22semidirect
96. #16811206C22semidirect
97. #16811205C22semidirect
98. #16811200C22semidirect
101. #16811197C22semidirect
102. #16811197C22semidirect
103. #16811197C22semidirect
104. #16811194C22semidirect
105. #16811194C22semidirect
106. #16811193C22semidirect
108. #16811191C22semidirect
109. #16811188C22semidirect
110. #16811187C22semidirect
111. #16811187C22semidirect
112. #16811186C22semidirect
113. #16811186C22semidirect
114. #16811186C22semidirect
115. #16811183C22semidirect
116. #16811182C22semidirect
117. #16811177C22semidirect
118. #16811176C22semidirect
119. #16811176C22semidirect
120. #16811175C22semidirect
121. #16811175C22semidirect
122. #16811172C22semidirect
123. #16811171C22semidirect
126. #16811169C22semidirect
127. #16811169C22semidirect
128. #16811169C22semidirect
129. #16811169C22semidirect
130. #16811169C22semidirect
131. #16811169C22semidirect
132. #16811168C22semidirect
133. #16811168C22semidirect
134. #16811168C22semidirect
135. C2×#13133215C22semidirect
136. C2×#13133215C22semidirect
138. #127×D53C22semidirect
139. #16811160C22semidirect
140. #16811159C22semidirect
141. #16811159C22semidirect
142. #16811154C22semidirect
143. #16811154C22semidirect
144. #16811154C22semidirect
145. #16811153C22semidirect
146. #16811153C22semidirect
147. #16811150C22semidirect
148. #16811150C22semidirect
149. C2×#13133206C22semidirect
150. C2×#13133206C22semidirect
151. C2×#13133204C22semidirect
152. #124×D53C22semidirect
154. #16811134C22semidirect
155. #16811131C22semidirect
156. #16811129C22semidirect
157. #16811129C22semidirect
158. C2×#13133200C22semidirect
159. #123×D53C22semidirect
160. C2×#13133189C22semidirect
161. #16811102C22semidirect
162. #16811100C22semidirect
163. #16811098C22semidirect
164. #16811097C22semidirect
165. #16811095C22semidirect
166. #41×Dic53C22semidirect
167. #41×Dic53C22semidirect
169. #16811091C22semidirect
170. C4×#11719947C22semidirect
171. C4×#11719947C22semidirect
172. C2×C4×C22⋊D53C22semidirect
173. C22×C4×Dic53C22semidirect
174. C2×2−1+4×C53C22semidirect
175. C22×#41×C53C22semidirect
176. C53×#550C22semidirect
177. C53×#550C22semidirect
178. C53×#548C22semidirect
179. C53×#548C22semidirect
181. C53×#535C22semidirect
182. C53×#535C22semidirect
183. C53×#525C22semidirect
184. C53×#525C22semidirect
185. C53×#525C22semidirect
186. C53×#519C22semidirect
871. #3487D53semidirect
888. C2×2−1+4C2×D53semidirect
892. C22×#41C2×D53semidirect
921. #550C2×D53semidirect
922. #550C2×D53semidirect
928. #548C2×D53semidirect
929. #548C2×D53semidirect
983. #535C2×D53semidirect
984. #535C2×D53semidirect
1028. #525C2×D53semidirect
1029. #525C2×D53semidirect
1030. #525C2×D53semidirect
1036. #519C2×D53semidirect
1048. C53#62836semidirect

Maximal subgroups

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

subgroupindex
#202893042
#202892892
#202891732
#202890742
#202890182
#202887182
#202886692
#202886412
#202886212
#202886122
#202886102
#202885962
#202885902
#202885852
#202885092
#202885072
#202884962
#202884902
#202883692
#202883592
#202883572
#202880072
C2×#168111692
C53×#34872
#6283653