Finite Group Databasebeta

← #28293030

Subgroups — #28293030

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#20289306C214yesmaximal, complemented
2#20289293C214yesmaximal, complemented
3#20289175C214yesmaximal, complemented
4#20289076C214yesmaximal, complemented
5#20289016C218yesmaximal, complemented
6#20288713C214yesmaximal, complemented
7#20288670C214yesmaximal, complemented
8#20288648C218yesmaximal, complemented
9#20288621C214yesmaximal, complemented
10#20288611C211yesmaximal, characteristic, complemented
11#20288609C211yesmaximal, characteristic, complemented
12#20288600C211yesmaximal, characteristic, complemented
13#20288590C211yesmaximal, characteristic, complemented
14#20288583C214yesmaximal, complemented
15#20288502C211yesmaximal, characteristic, complemented
16#20288496C211yesmaximal, characteristic, complemented
17#20288489C211yesmaximal, characteristic, complemented
18#20288371C211yesmaximal, characteristic, complemented
19#20288370C211yesmaximal, characteristic, complemented
20#20288358C211yesmaximal, characteristic, complemented
21#20288355C211yesmaximal, characteristic, complemented
22#20288010C211yesmaximal, characteristic, complemented
23#20288008C211yesmaximal, characteristic, complemented
24C2×#16811172C211yesmaximal, characteristic, complemented
25C53×#3500C211yesmaximal, characteristic, complemented
26C2×#13133264C2211yescharacteristic, complemented
27C2×#13133263C2211yescharacteristic
28C22×#11719949C2211yescharacteristic, complemented
29C22×#11719947C2211yescharacteristic, complemented
30#16811370C2218yescomplemented
31#16811369C2218yescomplemented
32#16811362C2218yescomplemented
33#16811361C2218yescomplemented
34#16811357C2218yescomplemented
35#16811356C2214yescomplemented
36#16811355C2214yescomplemented
37#16811355C2214yescomplemented
38#16811348C2214yescomplemented
39#16811345C2214yescomplemented
40#16811342C2214yescomplemented
41#16811342C2214yescomplemented
42#16811335C2218yescomplemented
43#16811327C2218yescomplemented
44#16811322C2218yescomplemented
45#16811322C2218yescomplemented
46#16811320C2218yescomplemented
47#16811316C2218yescomplemented
48#16811310C2218yescomplemented
49#16811303C2218yescomplemented
50#16811302C2218yescomplemented
51#16811299C2218yescomplemented
52#16811299C2218yescomplemented
53#16811293C2214yescomplemented
54#16811293C2214yescomplemented
55#16811292C2214yescomplemented
56#16811292C2214yescomplemented
57#16811292C2214yescomplemented
58#16811291C2214yescomplemented
59#16811291C2218yescomplemented
60Q8×C22⋊D53C2214yescomplemented
61#16811284C2214yescomplemented
62#16811284C2214yescomplemented
63#16811282C2214yescomplemented
64#16811281C2214yescomplemented
65#16811279C2214yescomplemented
66#16811276C2214yescomplemented
67#16811275C2214yescomplemented
68#16811272C2214yescomplemented
69#16811272C2214yescomplemented
70#16811272C2214yescomplemented
71#16811272C2218yescomplemented
72#16811269C2214yescomplemented
73#16811267C2214yescomplemented
74#16811267C2214yescomplemented
75#16811266C2214yescomplemented
76#16811264C2214yescomplemented
77#16811263C2218yescomplemented
78#16811262C2218yescomplemented
79#16811260C2218yescomplemented
80#16811260C2218yescomplemented
81D4×C22⋊D53C2218yes—
82D4×C22⋊D53C2214yescomplemented
83#16811244C2214yescomplemented
84#16811243C2218yescomplemented
85#16811242C2214yescomplemented
86#16811237C2218yescomplemented
87#16811233C2214yescomplemented
88#16811226C2214yescomplemented
89#16811225C2218yescomplemented
90#16811224C2218yescomplemented
91#16811223C2218yescomplemented
92#16811223C2218yescomplemented
93#16811222C2218yescomplemented
94#16811216C2218yescomplemented
95#16811211C2218yescomplemented
96#16811208C2218yescomplemented
97#16811207C2218yescomplemented
98#16811205C2218yescomplemented
99#16811200C2218yescomplemented
100#16811198C2212yescomplemented
101#16811197C2212yescomplemented
102#16811197C2211yescharacteristic, complemented
103#16811194C2211yescharacteristic
104#16811194C2212yescomplemented
105#16811194C2211yescharacteristic, complemented
106#16811190C2211yescharacteristic
107#16811190C2212yescomplemented
108#16811188C2218yescomplemented
109#16811188C2214yescomplemented
110#16811187C2211yescharacteristic
111#16811187C2212yescomplemented
112#16811187C2211yescharacteristic, complemented
113#16811187C2214yescomplemented
114#16811186C2212yescomplemented
115#16811184C2214yescomplemented
116#16811182C2214yescomplemented
117#16811180C2211yescharacteristic, complemented
118#16811178C2212yescomplemented
119#16811177C2212yescomplemented
120#16811176C2211yescharacteristic, complemented
121#16811175C2214yescomplemented
122#16811172C2214yescomplemented
123#16811172C2214yescomplemented
124#16811172C2214yescomplemented
125#16811172C2214yescomplemented
126#16811172C2212yescomplemented
127#16811171C2212yescomplemented
128#16811170C2212yescomplemented
129#16811169C2211yescharacteristic
130#16811169C2212yescomplemented
131#16811169C2212yescomplemented
132#16811168C2214yescomplemented
133C2×#13133215C2211yescharacteristic, complemented
134C2×#13133215C2212yescomplemented
135C2×#13133213C2211yescharacteristic
136C2×#13133213C2212yescomplemented
137#16811160C2212yescomplemented
138#16811157C2214yescomplemented
139#16811155C2212yescomplemented
140#16811155C2214yescomplemented
141#16811154C2214yescomplemented
142#16811153C2214yescomplemented
143#16811152C2212yescomplemented
144#16811152C2212yescomplemented
145#16811152C2214yescomplemented
146#16811151C2214yescomplemented
147C2×#13133205C2211yescharacteristic, complemented
148#124×D53C2212yescomplemented
149#16811135C2211yescharacteristic, complemented
150#16811133C2214yescomplemented
151#16811132C2214yescomplemented
152#16811130C2211yescharacteristic
153#16811130C2211yescharacteristic, complemented
154#16811130C2211yescharacteristic, complemented
155#16811130C2214yescomplemented
156#16811129C2214yescomplemented
157C2×#13133198C2214yescomplemented
158#123×D53C2214yescomplemented
159C2×#13133190C2214yescomplemented
160#16811102C2218yescomplemented
161#16811101C2211yescharacteristic, complemented
162#16811100C2211yescharacteristic, complemented
163#16811098C2211yescharacteristic, complemented
164#16811097C2211yescharacteristic, complemented
165#16811096C2218yescomplemented
166#41×Dic53C2211yescharacteristic
167#41×Dic53C2211yescharacteristic, complemented
168C4×#11719945C2211yescharacteristic, complemented
169C4×#11719945C2214yescomplemented
170C4×#11719947C2214yescomplemented
171C2×#13133177C2214yescomplemented
172C2×C42×D53C2211yescharacteristic, complemented
173C2×2−1+4×C53C2211yescharacteristic, complemented
174C2×H(5,𝔽2)×C53C2211yescharacteristic
175C53×#548C2214yescomplemented
176C53×#546C2214yescomplemented
177C53×#546C2218yescomplemented
178C53×#536C2211yescharacteristic
179C53×#536C2212yescomplemented
180C53×#535C2212yescomplemented
181C53×#535C2211yescharacteristic, complemented
182C53×#532C2211yescharacteristic
183C53×#532C2212yescomplemented
184C2×#124×C53C2211yescharacteristic, complemented
185C2×#124×C53C2212yescomplemented
186C4×#41×C53C2211yescharacteristic, complemented
187#13133264—44no—
188#13133263—44no—
189C2×#11719949—44no—
190C2×#11719949C2314yes—
191C2×#11719949C2314yes—
192C2×#11719949C2312yes—
193C2×#11719945C2311yescharacteristic
194C2×#11719945C2312yes—
195C2×#11719945C2312yes—
196C2×#11719945C2314yes—
197C2×#11719947—44no—
198C2×#11719947C2314yes—
199C2×#11719947C2314yes—
200C2×#11719947C2312yes—
201C2×#11719947C2314yes—
202C2×#11719947C2318yes—
203C2×#11719947C2314yes—
204C22×Dic106C2311yescharacteristic
205C22×Dic106C2312yes—
206C2×Q8×D53C2312yes—
207C22×D212C2311yescharacteristic
208C22×D212C2312yes—
209C22×D212C2312yes—
210C22×C22⋊D53C2314yes—
211C22×C22⋊D53C2318yes—
212C22×C22⋊D53C2312yes—
213C2×D4×D53C2312yes—
214C2×D4×D53C2314yes—
215C23×Dic53C2312yes—
216C22×C4×D53C2311yescharacteristic
217C22×C4×D53C2312yes—
218C22×C4×D53C2312yes—
219#13133217C2312yes—
220#13133216C2312yes—
221#13133215C2312yes—
222#13133215C2312yes—
223#13133215C2318yes—
224#13133215C2314yes—
225#13133215C2312yes—
226#13133215C2311yescharacteristic
227#13133215C2312yes—
228#13133215C2312yes—
229#13133213C2318yes—
230#13133213C2312yes—
231#13133213C2318yes—
232#13133213C2318yes—
233#13133213C2312yes—
234#13133213C2312yes—
235#13133213C2314yes—
236#13133213C2312yes—
237#13133213C2312yes—
238#13133213C2311yescharacteristic
239#13133212C2318yes—
240#13133212C2314yes—
241#13133211C2318yes—
242#13133210C2314yes—
243#13133210C2318yes—
244#13133210C2318yes—
245#13133210C2318yes—
246#13133210C2318yes—
247#13133210C2314yes—
248#13133210C2314yes—
249#13133209C2312yes—
250#13133208C2318yes—
251#13133208C2314yes—
252#13133208C2312yes—
253#13133207C2318yes—
254#13133207C2318yes—
255#13133207C2314yes—
256#13133206C2312yes—
257#13133206C2318yes—
258#13133206C2312yes—
259#13133206C2312yes—
260#13133206C2311yescharacteristic
261#13133205C2314yes—
262#13133205C2312yes—
263#13133205C2312yes—
264#13133204C2312yes—
265#13133204C2312yes—
266#13133204C2312yes—
267#13133204C2314yes—
268#13133204C2311yescharacteristic
269#13133203C2318yes—
270#13133203C2318yes—
271#13133203C2318yes—
272#13133203C2318yes—
273#13133203C2318yes—
274#13133203C2314yes—
275#13133202C2318yes—
276#13133202C2318yes—
277#13133202C2318yes—
278#13133202C2314yes—
279#13133201C2318yes—
280#13133201C2318yes—
281#13133201C2312yes—
282#13133200C2314yes—
283#13133200C2318yes—
284#13133200C2318yes—
285#13133200C2318yes—
286#13133199C2318yes—
287#13133199C2318yes—
288#13133199C2318yes—
289#13133199C2318yes—
290#13133199C2314yes—
291#13133199C2314yes—
292#13133199C2314yes—
293#13133198C2318yes—
294#13133198C2318yes—
295#13133198C2314yes—
296#13133198C2318yes—
297#13133198C2314yes—
298#13133198C2312yes—
299#13133198C2312yes—
300#13133198C2312yes—
301#13133197C2312yes—
302#13133197C2314yes—
303#13133196C2314yes—
304#13133196C2314yes—
305#13133196C2318yes—
306#13133196C2314yes—
307#13133195C2318yes—
308#13133195C2318yes—
309#13133195C2314yes—
310#13133194C2318yes—
311#13133194C2318yes—
312#13133194C2314yes—
313#13133194C2318yes—
314#13133193C2314yes—
315#13133193C2312yes—
316#13133193C2312yes—
317#13133193C2318yes—
318#13133193C2312yes—
319#13133193C2318yes—
320#13133192C2312yes—
321#13133192C2318yes—
322#13133191C2314yes—
323#13133191C2314yes—
324#13133191C2318yes—
325#13133191C2318yes—
326#13133191C2318yes—
327#13133190C2318yes—
328#13133190C2318yes—
329#13133190C2318yes—
330#13133190C2318yes—
331#13133190C2318yes—
332#13133190C2318yes—
333#13133190C2318yes—
334#13133190C2314yes—
335#13133189C2318yes—
336#13133189C2318yes—
337#13133189C2318yes—
338#13133189C2314yes—
339#13133189C2318yes—
340#13133189C2318yes—
341#13133189C2318yes—
342#13133189C2318yes—
343#13133189C2318yes—
344#13133189C2318yes—
345#13133188C2312yes—
346#13133188C2312yes—
347#13133188C2314yes—
348#13133188C2312yes—
349#13133188C2318yes—
350#13133188C2318yes—
351#13133188C2318yes—
352#13133188C2314yes—
353#13133187C2318yes—
354#13133187C2312yes—
355#13133186C2318yes—
356#13133186C2314yes—
357#13133186C2318yes—
358#13133185C2318yes—
359#13133185C2314yes—
360#13133185C2318yes—
361#13133185C2312yes—
362#13133185C2312yes—
363#13133185C2312yes—
364#13133185C2314yes—
365Q8×Dic53C2314yes—
366Q8×Dic53C2314yes—
367Q8×Dic53C2312yes—
368Q8×Dic53C2312yes—
369C4×Dic106C2314yes—
370C4×Dic106C2312yes—
371C4×Dic106C2314yes—
372C4×Dic106C2314yes—
373C4×Dic106C2314yes—
374#13133182C2314yes—
375#13133182C2318yes—
376#13133182C2314yes—
377C4×D212C2314yes—
378C4×D212C2314yes—
379C4×D212C2312yes—
380C4×D212C2314yes—
381D4×Dic53C2314yes—
382D4×Dic53C2314yes—
383D4×Dic53C2312yes—
384D4×Dic53C2314yes—
385D4×Dic53C2318yes—
386D4×Dic53C2314yes—
387D4×Dic53C2314yes—
388D4×Dic53C2312yes—
389#13133179C2314yes—
390C4×C22⋊D53C2314yes—
391C4×C22⋊D53C2314yes—
392C4×C22⋊D53C2314yes—
393C4×C22⋊D53C2318yes—
394C4×C22⋊D53C2314yes—
395C4×C22⋊D53C2318yes—
396C4×C22⋊D53C2318yes—
397C4×C22⋊D53C2318yes—
398C4×C22⋊D53C2318yes—
399C4×C22⋊D53C2314yes—
400C4×C22⋊D53C2314yes—
401C4×C22⋊D53C2314yes—
402#13133177C2318yes—
403#13133177C2318yes—
404#13133177C2314yes—
405#13133177C2318yes—
406#13133177C2318yes—
407#13133177C2318yes—
408#13133177C2318yes—
409#13133177C2314yes—
410#13133177C2318yes—
411#13133177C2318yes—
412#13133176C2314yes—
413#13133176C2314yes—
414#13133176C2311yescharacteristic
415#13133176C2311yescharacteristic
416#13133176C2312yes—
417#13133176C2311yescharacteristic
418#13133176C2312yes—
419#13133175C2314yes—
420#13133174C2318yes—
421#13133174C2314yes—
422#13133174C2314yes—
423#13133174C2312yes—
424#13133173C2318yes—
425#13133173C2314yes—
426#13133173C2318yes—
427#13133173C2314yes—
428#13133173C2314yes—
429C2×#11719919C2314yes—
430C2×#11719919C2318yes—
431C2×#11719919C2318yes—
432C4⋊C4×D53C2318yes—
433C2×C22⋊Dic53C2318yes—
434C2×C22⋊Dic53C2314yes—
435C2×#11719921C2314yes—
436C22⋊C4×D53C2318yes—
437C22⋊C4×D53C2318yes—
438C22⋊C4×D53C2314yes—
439C2×C4×Dic53C2312yes—
440C2×C4×Dic53C2311yescharacteristic
441C2×C4×Dic53C2312yes—
442C2×C4×Dic53C2312yes—
443C42×D53C2312yes—
444C42×D53C2312yes—
445C42×D53C2312yes—
446C42×D53C2312yes—
447C42×D53C2312yes—
4482−1+4×C53—44no—
449H(5,𝔽2)×C53—44no—
450C2×#41×C53C2311yescharacteristic
451C2×#41×C53C2311yescharacteristic
452C2×#41×C53C2311yescharacteristic
453C2×#41×C53C2312yes—
454C2×#41×C53C2312yes—
455C2×#41×C53C2314yes—
456C2×#41×C53C2312yes—
457C2×#41×C53C2312yes—
458C22×Q8×C53C2311yescharacteristic
459C22×Q8×C53C2312yes—
460C22×Q8×C53C2312yes—
461C22×D4×C53C2311yescharacteristic
462C22×D4×C53C2312yes—
463C22×D4×C53C2312yes—
464C22×D4×C53C2314yes—
465C4⋊Q8×C53C2312yes—
466C4⋊Q8×C53C2311yescharacteristic
467#127×C53C2312yes—
468#127×C53C2311yescharacteristic
469#124×C53C2312yes—
470#124×C53C2312yes—
471#124×C53C2318yes—
472#124×C53C2311yescharacteristic
473#124×C53C2312yes—
474#124×C53C2312yes—
475#124×C53C2314yes—
476#124×C53C2311yescharacteristic
477#123×C53C2314yes—
478#123×C53C2318yes—
479C22⋊Q8×C53C2314yes—
480C22⋊Q8×C53C2318yes—
481#121×C53C2314yes—
482#121×C53C2318yes—
483#121×C53C2314yes—
484#121×C53C2318yes—
485#120×C53C2318yes—
486#120×C53C2314yes—
487C4×Q8×C53C2312yes—
488C4×D4×C53C2314yes—
489C4×D4×C53C2314yes—
490C4×D4×C53C2312yes—
491C4×D4×C53C2318yes—
492#117×C53C2311yescharacteristic
493#117×C53C2312yes—
494C2×C22⋊C4×C53C2314yes—
495C2×C22⋊C4×C53C2318yes—
496C2×C42×C53C2311yescharacteristic
497C2×C42×C53C2312yes—
498C24×C53C2412yes—
499C24×C53C2414yes—
500C23×D53C2412yes—
501C23×D53C2411yescharacteristic
502C23×D53C2414yes—
503#41×C53—24no—
504#41×C53—24no—
505#41×C53—24no—
506#41×C53—48no—
507#41×C53—44no—
508#41×C53—44no—
509#41×C53—44no—
510#41×C53—44no—
511C2×Q8×C53—24no—
512C2×Q8×C53—44no—
513C2×Q8×C53—44no—
514C2×Q8×C53C2411yescharacteristic
515C2×Q8×C53C2412yes—
516C2×Q8×C53C2411yescharacteristic
517C2×Q8×C53C2412yes—
518C2×Q8×C53C2411yescharacteristic
519C2×Q8×C53C2414yes—
520C2×D4×C53—24no—
521C2×D4×C53—44no—
522C2×D4×C53—44no—
523C2×D4×C53—48no—
524C2×D4×C53C2412yes—
525C2×D4×C53C2411yescharacteristic
526C2×D4×C53C2412yes—
527C2×D4×C53C2412yes—
528C2×D4×C53C2412yes—
529C2×D4×C53C2411yescharacteristic
530C2×D4×C53C2412yes—
531C2×D4×C53C2411yescharacteristic
532C2×D4×C53C2414yes—
533C2×D4×C53C2418yes—
534C2×D4×C53C2414yes—
535C2×D4×C53C2414yes—
536C2×D4×C53C2414yes—
537C22×C4×C53C2412yes—
538C22×C4×C53C2412yes—
539C22×C4×C53C2412yes—
540C22×C4×C53C2412yes—
541C22×C4×C53C2412yes—
542C22×C4×C53C2414yes—
543C22×C4×C53C2414yes—
544C22×C4×C53C2414yes—
545C22×C4×C53C2414yes—
546C22×C4×C53C2411yescharacteristic
547C2×C22⋊D53—48no—
548C2×C22⋊D53—416no—
549C2×C22⋊D53—44no—
550C2×C22⋊D53C2418yes—
551C2×C22⋊D53C2414yes—
552C2×C22⋊D53C2412yes—
553C2×C22⋊D53C2418yes—
554C2×C22⋊D53C2418yes—
555C2×C22⋊D53C2418yes—
556C2×C22⋊D53C2414yes—
557C2×C22⋊D53C2414yes—
558C2×C22⋊D53C2414yes—
559C2×C22⋊D53C2418yes—
560C2×C22⋊D53C2414yes—
561C2×C22⋊D53C2414yes—
562C2×C22⋊D53C2418yes—
563C22×Dic53—44no—
564C22×Dic53C2412yes—
565C22×Dic53C2411yescharacteristic
566C22×Dic53C2414yes—
567C22×Dic53C2414yes—
568C22×Dic53C2412yes—
569C22×Dic53C2418yes—
570C22×Dic53C2418yes—
571C22×Dic53C2414yes—
572#11719949—48no—
573#11719949—48no—
574#11719949—44no—
575Q8×D53—44no—
576#11719947—48no—
577#11719947—48no—
578#11719947—44no—
579#11719947—416no—
580#11719947—48no—
581#11719947—48no—
582D4×D53—44no—
583D4×D53—48no—
584#11719945—24no—
585#11719945—48no—
586#11719945—44no—
587#11719945—44no—
588C2×D212—24no—
589C2×D212—44no—
590C2×D212—44no—
591C2×D212C2412yes—
592C2×D212C2412yes—
593C2×D212C2411yescharacteristic
594C2×D212C2414yes—
595C2×D212C2418yes—
596C2×D212C2414yes—
597C2×C4×D53—24no—
598C2×C4×D53—44no—
599C2×C4×D53—44no—
600C2×C4×D53C2412yes—
601C2×C4×D53C2412yes—
602C2×C4×D53C2412yes—
603C2×C4×D53C2412yes—
604C2×C4×D53C2412yes—
605C2×C4×D53C2412yes—
606C2×C4×D53C2412yes—
607C2×C4×D53C2414yes—
608C2×C4×D53C2418yes—
609C2×C4×D53C2414yes—
610C2×C4×D53C2418yes—
611C2×C4×D53C2414yes—
612C2×Dic106—24no—
613C2×Dic106—44no—
614C2×Dic106C2414yes—
615C2×Dic106C2412yes—
616C2×Dic106C2412yes—
617C2×Dic106C2411yescharacteristic
618C2×Dic106C2414yes—
619C2×Dic106C2414yes—
620C4⋊C4×C53C2412yes—
621C4⋊C4×C53C2414yes—
622C4⋊C4×C53C2418yes—
623C4⋊C4×C53C2414yes—
624C22⋊C4×C53C2414yes—
625C22⋊C4×C53C2418yes—
626C22⋊C4×C53C2418yes—
627C22⋊C4×C53C2418yes—
628C22⋊C4×C53C2418yes—
629C22⋊C4×C53C2412yes—
630C22⋊C4×C53C2414yes—
631C22⋊C4×C53C2414yes—
632C42×C53C2411yescharacteristic
633C42×C53C2411yescharacteristic
634C42×C53C2412yes—
635C42×C53C2412yes—
636C42×C53C2414yes—
637C22⋊Dic53C2414yes—
638C22⋊Dic53C2412yes—
639C22⋊Dic53C2418yes—
640C22⋊Dic53C2412yes—
641C22⋊Dic53C2414yes—
642C22⋊Dic53C2418yes—
643C22⋊Dic53C2418yes—
644C22⋊Dic53C2412yes—
645C22⋊Dic53C2414yes—
646C22⋊Dic53C2418yes—
647C22⋊Dic53C2414yes—
648C22⋊Dic53C2414yes—
649C22⋊Dic53C2414yes—
650#11719921C2414yes—
651#11719921C2418yes—
652#11719921C2418yes—
653#11719921C2418yes—
654#11719921C2418yes—
655#11719921C2418yes—
656#11719921C2418yes—
657#11719921C2414yes—
658#11719921C2414yes—
659#11719921C2414yes—
660#11719921C2414yes—
661#11719921C2414yes—
662#11719921C2414yes—
663C4⋊Dic53C2414yes—
664C4⋊Dic53C2414yes—
665C4⋊Dic53C2412yes—
666C4⋊Dic53C2412yes—
667C4⋊Dic53C2412yes—
668C4⋊Dic53C2414yes—
669C4⋊Dic53C2414yes—
670C4⋊Dic53C2414yes—
671C4⋊Dic53C2418yes—
672#11719919C2414yes—
673#11719919C2418yes—
674#11719919C2418yes—
675#11719919C2414yes—
676#11719919C2414yes—
677#11719919C2418yes—
678#11719919C2418yes—
679#11719919C2418yes—
680#11719919C2414yes—
681#11719919C2414yes—
682#11719919C2414yes—
683#11719919C2414yes—
684#11719919C2418yes—
685#11719919C2414yes—
686#11719919C2414yes—
687C4×Dic53C2411yescharacteristic
688C4×Dic53C2412yes—
689C4×Dic53C2412yes—
690C4×Dic53C2411yescharacteristic
691C4×Dic53C2412yes—
692C4×Dic53C2412yes—
693C4×Dic53C2412yes—
694C4×Dic53C2414yes—
695C4×Dic53C2412yes—
696C4×Dic53C2414yes—
697C4×Dic53C2414yes—
698C4×Dic53C2412yes—
699C4×Dic53C2412yes—
700C4×Dic53C2418yes—
701C4×Dic53C2418yes—
702C23×C53—24no—
703C23×C53—44no—
704C23×C53—48no—
705C23×C53—44no—
706C23×C53C2512yes—
707C23×C53C2514yes—
708C23×C53C2512yes—
709C23×C53C2512yes—
710C23×C53C2511yescharacteristic
711C22×D53—22no—
712C22×D53—24no—
713C22×D53—42no—
714C22×D53—44no—
715C22×D53—44no—
716C22×D53—48no—
717C22×D53C2512yes—
718C22×D53C2512yes—
719C22×D53C2514yes—
720Q8×C53—22no—
721Q8×C53—24no—
722Q8×C53—24no—
723Q8×C53—22no—
724Q8×C53—22no—
725Q8×C53—44no—
726D4×C53—24no—
727D4×C53—24no—
728D4×C53—24no—
729D4×C53—22no—
730D4×C53—24no—
731D4×C53—24no—
732D4×C53—22no—
733D4×C53—22no—
734D4×C53—48no—
735D4×C53—44no—
736D4×C53—44no—
737D4×C53—44no—
738D4×C53—44no—
739C2×C4×C53—24no—
740C2×C4×C53—24no—
741C2×C4×C53—24no—
742C2×C4×C53—24no—
743C2×C4×C53—42no—
744C2×C4×C53—44no—
745C2×C4×C53—44no—
746C2×C4×C53—44no—
747C2×C4×C53—44no—
748C2×C4×C53H(5,𝔽2)14yes—
749C2×C4×C53C2512yes—
750C2×C4×C53C2512yes—
751C2×C4×C53C2514yes—
752C2×C4×C53C2512yes—
753C2×C4×C53C2512yes—
754C2×C4×C53C2514yes—
755C2×C4×C53C2512yes—
756C2×C4×C53C2511yescharacteristic
757C2×C4×C53C2511yescharacteristic
758C22⋊D53—24no—
759C22⋊D53—28no—
760C22⋊D53—216no—
761C22⋊D53—44no—
762C22⋊D53—44no—
763C22⋊D53—44no—
764C22⋊D53—48no—
765C22⋊D53—48no—
766C22⋊D53—44no—
767C22⋊D53—44no—
768C22⋊D53—48no—
769C22⋊D53—48no—
770C22⋊D53—48no—
771C2×Dic53—24no—
772C2×Dic53—22no—
773C2×Dic53—24no—
774C2×Dic53—28no—
775C2×Dic53—28no—
776C2×Dic53—44no—
777C2×Dic53—48no—
778C2×Dic53—48no—
779C2×Dic53C2512yes—
780C2×Dic53C2514yes—
781C2×Dic53C2514yes—
782C2×Dic53C2514yes—
783C2×Dic53C2514yes—
784C2×Dic53C2512yes—
785C2×Dic53C2512yes—
786C2×Dic53C2512yes—
787D212—24no—
788D212—24no—
789D212—22no—
790D212—44no—
791D212—48no—
792D212—44no—
793C4×D53—24no—
794C4×D53—24no—
795C4×D53—24no—
796C4×D53—24no—
797C4×D53—24no—
798C4×D53—42no—
799C4×D53—42no—
800C4×D53—48no—
801C4×D53—44no—
802C4×D53—44no—
803C4×D53—44no—
804C4×D53—48no—
805Dic106—24no—
806Dic106—24no—
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—24no—
818C22×C53—24no—
819C22×C53—28no—
820C22×C53—24no—
821C22×C53—84no—
822C22×C53—164no—
823C22×C53C2×H(5,𝔽2)12yes—
824C22×C53C2611yescharacteristic
825C2×D53—22no—
826C2×D53—22no—
827C2×D53—24no—
828C2×D53—22no—
829C2×D53—22no—
830C2×D53—24no—
831C2×D53—28no—
832C2×D53—44no—
833C2×D53—84no—
834C2×D53—164no—
835C4×C53—22no—
836C4×C53—22no—
837C4×C53—24no—
838C4×C53—22no—
839C4×C53—24no—
840C4×C53—22no—
841C4×C53—22no—
842C4×C53C2×H(5,𝔽2)12yes—
843C4×C53C2×H(5,𝔽2)12yes—
844Dic53—24no—
845Dic53—22no—
846Dic53—22no—
847Dic53—24no—
848Dic53—24no—
849Dic53—24no—
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#3500D5311yescharacteristic, complemented
868#3499—531no—
869#3498—531no—
870#3487—531no—
871#3487—531no—
872#3485—531no—
873#3485—531no—
874#3444—531no—
875#3444—531no—
876C2×#532—531no—
877C2×C53—22no—
878C2×C53—42no—
879C2×C53—42no—
880C2×C53—44no—
881C2×C53—42no—
882C2×C53C22×H(5,𝔽2)11yescharacteristic
883C2×C53C2×#58512yes—
884D53—42no—
885D53—44no—
886D53—42no—
887C2×2−1+4—531no—
888C2×2−1+4C2×D5311yescharacteristic, complemented
889C2×H(5,𝔽2)—531no—
890C2×H(5,𝔽2)C2×D5311yescharacteristic
891C22×#41—531no—
892C22×#41—531no—
893#562—538no—
894#562—538no—
895#560—538no—
896#560—538no—
897#559—534no—
898#559—534no—
899#559—538no—
900#559—534no—
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—534no—
917#550—534no—
918#550—534no—
919#550—534no—
920#550—534no—
921#550—534no—
922#550—538no—
923D4×Q8—534no—
924#548—534no—
925#548—534no—
926#548—534no—
927#548—534no—
928#548—534no—
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—534no—
940#546—538no—
941#546—538no—
942#546—538no—
943#546—534no—
944#546—538no—
945#546C2×D5314yescomplemented
946#546C2×D5318yescomplemented
947D42—538no—
948D42—534no—
949#542—534no—
950#542—538no—
951#542—538no—
952#542—534no—
953#541—534no—
954#540—538no—
955#540—538no—
956#540—534no—
957#540—538no—
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—531no—
968#536—532no—
969#536—531no—
970#536—532no—
971#536—532no—
972#536C2×D5311yescharacteristic
973#536C2×D5312yescomplemented
974#535—531no—
975#535—531no—
976#535—534no—
977#535—532no—
978#535—531no—
979#535—532no—
980#535—532no—
981#535—534no—
982#535—538no—
983#535C2×D5311yescharacteristic, complemented
984#535C2×D5312yescomplemented
985#534—534no—
986#534—534no—
987#533—532no—
988#533—534no—
989#533—532no—
990#533—531no—
991#533—531no—
992#532—531no—
993#532—532no—
994#532—532no—
995#532—532no—
996#532—534no—
997#532—534no—
998#532—534no—
999#532—534no—
1000#532—532no—
1001#532—534no—
1002#532—532no—
1003#532C2×D5311yescharacteristic
1004#532C2×D5312yescomplemented
1005C2×C4⋊Q8—531no—
1006C2×C4⋊Q8—532no—
1007C2×#127—531no—
1008C2×#127—532no—
1009#529—532no—
1010#529—532no—
1011#529—534no—
1012#529—534no—
1013#529—532no—
1014#529—534no—
1015#529—534no—
1016#529—532no—
1017#529—534no—
1018#529—534no—
1019C2×#124—532no—
1020C2×#124—531no—
1021C2×#124C2×D5311yescharacteristic, complemented
1022C2×#124C2×D5312yescomplemented
1023#525—531no—
1024#525—531no—
1025#525—531no—
1026#525—534no—
1027#525—534no—
1028#525—534no—
1029#525—534no—
1030#525—531no—
1031C2×#123—534no—
1032C2×#123—534no—
1033C2×#121—534no—
1034#520—538no—
1035#519—531no—
1036#519—531no—
1037#518—531no—
1038#518—531no—
1039#518—538no—
1040C4×#41—531no—
1041C4×#41—531no—
1042C4×#41—534no—
1043C4×#41—531no—
1044C4×#41—534no—
1045C4×#41C2×D5311yescharacteristic, complemented
1046C2×C4×D4—534no—
1047C22×C42—531no—
1048C53#6283611yescharacteristic, complemented, Sylow
10492−1+4—44no—
10502−1+4—2124no—
1051H(5,𝔽2)—44no—
1052H(5,𝔽2)—2124no—
1053C2×#41—534no—
1054C2×#41—534no—
1055C2×#41—532no—
1056C2×#41—534no—
1057C2×#41—538no—
1058C2×#41—534no—
1059C2×#41—534no—
1060C2×#41—534no—
1061C2×#41—532no—
1062C2×#41—531no—
1063C2×#41—534no—
1064C2×#41—532no—
1065C2×#41—532no—
1066C2×#41—2124no—
1067C2×#41—2124no—
1068C2×#41C22×D5311yescharacteristic
1069C2×#41C22×D5311yescharacteristic
1070C2×#41C22×D5311yescharacteristic
1071C2×#41C22×D5314yes—
1072C2×#41C22×D5312yes—
1073C2×#41C22×D5312yes—
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—538no—
1084C22×D4—532no—
1085C22×D4—534no—
1086C22×D4—532no—
1087C22×D4—531no—
1088C22×D4—532no—
1089C22×D4—532no—
1090C22×D4C22×D5311yescharacteristic
1091C22×D4C22×D5314yes—
1092C22×D4C22×D5312yes—
1093C22×D4C22×D5312yes—
1094C23×C4—532no—
1095C23×C4—531no—
1096C23×C4—532no—
1097C23×C4—532no—
1098C4⋊Q8—532no—
1099C4⋊Q8—531no—
1100C4⋊Q8—532no—
1101C4⋊Q8—534no—
1102C4⋊Q8—532no—
1103C4⋊Q8—532no—
1104C4⋊Q8—538no—
1105C4⋊Q8—532no—
1106C4⋊Q8—532no—
1107C4⋊Q8—532no—
1108C4⋊Q8C22×D5311yescharacteristic
1109C4⋊Q8C22×D5312yes—
1110#127—532no—
1111#127—531no—
1112#127—532no—
1113#127—534no—
1114#127—532no—
1115#127—532no—
1116#127—538no—
1117#127—532no—
1118#127—538no—
1119#127—538no—
1120#127C22×D5311yescharacteristic
1121#127C22×D5312yes—
1122#126—534no—
1123#126—538no—
1124#126—534no—
1125#126—534no—
1126#126—534no—
1127#126—538no—
1128#126—538no—
1129#126—538no—
1130#126—538no—
1131#126—538no—
1132#125—534no—
1133#125—532no—
1134#125—534no—
1135#125—538no—
1136#125—538no—
1137#125—538no—
1138#125—532no—
1139#124—532no—
1140#124—531no—
1141#124—532no—
1142#124—532no—
1143#124—538no—
1144#124—532no—
1145#124—531no—
1146#124—534no—
1147#124—532no—
1148#124—532no—
1149#124—538no—
1150#124—534no—
1151#124—538no—
1152#124—538no—
1153#124—538no—
1154#124—538no—
1155#124—532no—
1156#124—532no—
1157#124—534no—
1158#124C22×D5311yescharacteristic
1159#124C22×D5312yes—
1160#124C22×D5312yes—
1161#124C22×D5314yes—
1162#124C22×D5312yes—
1163#124C22×D5312yes—
1164#124C22×D5318yes—
1165#124C22×D5311yescharacteristic
1166#123—532no—
1167#123—532no—
1168#123—534no—
1169#123—534no—
1170#123—538no—
1171#123—538no—
1172#123—532no—
1173#123—538no—
1174#123—534no—
1175#123—538no—
1176#123—538no—
1177#123—538no—
1178#123—538no—
1179#123—534no—
1180#123—538no—
1181#123—538no—
1182#123—532no—
1183#123—538no—
1184#123—534no—
1185#123—534no—
1186#123—534no—
1187#123—538no—
1188#123—538no—
1189#123—538no—
1190#123—538no—
1191#123—538no—
1192#123C22×D5314yes—
1193#123C22×D5318yes—
1194C22⋊Q8—532no—
1195C22⋊Q8—532no—
1196C22⋊Q8—532no—
1197C22⋊Q8—538no—
1198C22⋊Q8—534no—
1199C22⋊Q8—538no—
1200C22⋊Q8—534no—
1201C22⋊Q8—534no—
1202C22⋊Q8—534no—
1203C22⋊Q8—538no—
1204C22⋊Q8—534no—
1205C22⋊Q8—532no—
1206C22⋊Q8—534no—
1207C22⋊Q8—538no—
1208C22⋊Q8—538no—
1209C22⋊Q8—534no—
1210C22⋊Q8—538no—
1211C22⋊Q8—538no—
1212C22⋊Q8—538no—
1213C22⋊Q8C22×D5314yes—
1214C22⋊Q8C22×D5318yes—
1215#121—534no—
1216#121—532no—
1217#121—532no—
1218#121—532no—
1219#121—534no—
1220#121—538no—
1221#121—538no—
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—534no—
1234#121—534no—
1235#121—538no—
1236#121—538no—
1237#121—538no—
1238#121—532no—
1239#121—538no—
1240#121—538no—
1241#121—538no—
1242#121—538no—
1243#121—538no—
1244#121—534no—
1245#121—538no—
1246#121—538no—
1247#121—538no—
1248#121C22×D5314yes—
1249#121C22×D5314yes—
1250#121C22×D5318yes—
1251#121C22×D5318yes—
1252#120—534no—
1253#120—538no—
1254#120—538no—
1255#120—532no—
1256#120—532no—
1257#120—532no—
1258#120—534no—
1259#120—534no—
1260#120—538no—
1261#120—538no—
1262#120—532no—
1263#120—538no—
1264#120C22×D5314yes—
1265#120C22×D5318yes—
1266C4×Q8—532no—
1267C4×Q8—532no—
1268C4×Q8—534no—
1269C4×Q8—534no—
1270C4×Q8—534no—
1271C4×Q8—534no—
1272C4×Q8—538no—
1273C4×Q8—534no—
1274C4×Q8—532no—
1275C4×Q8—534no—
1276C4×Q8—534no—
1277C4×Q8—534no—
1278C4×Q8C22×D5312yes—
1279C4×D4—534no—
1280C4×D4—534no—
1281C4×D4—532no—
1282C4×D4—534no—
1283C4×D4—532no—
1284C4×D4—534no—
1285C4×D4—534no—
1286C4×D4—538no—
1287C4×D4—534no—
1288C4×D4—534no—
1289C4×D4—534no—
1290C4×D4—534no—
1291C4×D4—534no—
1292C4×D4—534no—
1293C4×D4—534no—
1294C4×D4—538no—
1295C4×D4—538no—
1296C4×D4—538no—
1297C4×D4—538no—
1298C4×D4—538no—
1299C4×D4—534no—
1300C4×D4—538no—
1301C4×D4—538no—
1302C4×D4—538no—
1303C4×D4—538no—
1304C4×D4—534no—
1305C4×D4—534no—
1306C4×D4—538no—
1307C4×D4—538no—
1308C4×D4—538no—
1309C4×D4—538no—
1310C4×D4—534no—
1311C4×D4—534no—
1312C4×D4—532no—
1313C4×D4—534no—
1314C4×D4C22×D5314yes—
1315C4×D4C22×D5314yes—
1316C4×D4C22×D5312yes—
1317C4×D4C22×D5318yes—
1318#117—531no—
1319#117—531no—
1320#117—531no—
1321#117—532no—
1322#117—532no—
1323#117—534no—
1324#117—534no—
1325#117—534no—
1326#117—534no—
1327#117—534no—
1328#117—538no—
1329#117—534no—
1330#117—538no—
1331#117—534no—
1332#117—532no—
1333#117—534no—
1334#117—538no—
1335#117C22×D5311yescharacteristic
1336#117C22×D5312yes—
1337C2×C4⋊C4—534no—
1338C2×C4⋊C4—538no—
1339C2×C4⋊C4—538no—
1340C2×C4⋊C4—538no—
1341C2×C22⋊C4—534no—
1342C2×C22⋊C4—538no—
1343C2×C22⋊C4—534no—
1344C2×C22⋊C4—534no—
1345C2×C22⋊C4—538no—
1346C2×C22⋊C4—538no—
1347C2×C22⋊C4C22×D5314yes—
1348C2×C22⋊C4C22×D5318yes—
1349C2×C42—532no—
1350C2×C42—532no—
1351C2×C42—532no—
1352C2×C42—531no—
1353C2×C42—532no—
1354C2×C42—532no—
1355C2×C42—532no—
1356C2×C42—532no—
1357C2×C42—532no—
1358C2×C42C22×D5312yes—
1359C2×C42C22×D5311yescharacteristic
1360C24—532no—
1361C24—531no—
1362C24—534no—
1363C24C23×D5312yes—
1364C24C23×D5314yes—
1365#41—24no—
1366#41—24no—
1367#41—24no—
1368#41—48no—
1369#41—44no—
1370#41—44no—
1371#41—44no—
1372#41—44no—
1373#41—1064no—
1374#41—2124no—
1375#41—2124no—
1376#41—2128no—
1377#41—2128no—
1378#41—2128no—
1379#41—2128no—
1380#41—2128no—
1381#41—2124no—
1382#41—21216no—
1383#41—2128no—
1384#41—2128no—
1385#41—2124no—
1386C2×Q8—24no—
1387C2×Q8—44no—
1388C2×Q8—44no—
1389C2×Q8—534no—
1390C2×Q8—532no—
1391C2×Q8—531no—
1392C2×Q8—532no—
1393C2×Q8—534no—
1394C2×Q8—534no—
1395C2×Q8—1064no—
1396C2×Q8—2124no—
1397C2×Q8—2124no—
1398C2×Q8C23×D5311yescharacteristic
1399C2×Q8C23×D5312yes—
1400C2×Q8C23×D5311yescharacteristic
1401C2×Q8C23×D5312yes—
1402C2×Q8C23×D5311yescharacteristic
1403C2×Q8C23×D5314yes—
1404C2×D4—24no—
1405C2×D4—44no—
1406C2×D4—44no—
1407C2×D4—48no—
1408C2×D4—534no—
1409C2×D4—538no—
1410C2×D4—532no—
1411C2×D4—534no—
1412C2×D4—534no—
1413C2×D4—538no—
1414C2×D4—538no—
1415C2×D4—538no—
1416C2×D4—538no—
1417C2×D4—534no—
1418C2×D4—534no—
1419C2×D4—534no—
1420C2×D4—538no—
1421C2×D4—532no—
1422C2×D4—531no—
1423C2×D4—532no—
1424C2×D4—534no—
1425C2×D4—538no—
1426C2×D4—534no—
1427C2×D4—1064no—
1428C2×D4—2124no—
1429C2×D4—2124no—
1430C2×D4—2124no—
1431C2×D4—2128no—
1432C2×D4—21216no—
1433C2×D4—2124no—
1434C2×D4—2128no—
1435C2×D4C23×D5312yes—
1436C2×D4C23×D5312yes—
1437C2×D4C23×D5311yescharacteristic
1438C2×D4C23×D5312yes—
1439C2×D4C23×D5311yescharacteristic
1440C2×D4C23×D5312yes—
1441C2×D4C23×D5312yes—
1442C2×D4C23×D5311yescharacteristic
1443C2×D4C23×D5314yes—
1444C2×D4C23×D5318yes—
1445C2×D4C23×D5314yes—
1446C2×D4C23×D5314yes—
1447C2×D4C23×D5314yes—
1448C22×C4—532no—
1449C22×C4—531no—
1450C22×C4—534no—
1451C22×C4—534no—
1452C22×C4—532no—
1453C22×C4—538no—
1454C22×C4—538no—
1455C22×C4—534no—
1456C22×C4—532no—
1457C22×C4—532no—
1458C22×C4—532no—
1459C22×C4—532no—
1460C22×C4—532no—
1461C22×C4—532no—
1462C22×C4—532no—
1463C22×C4—534no—
1464C22×C4—538no—
1465C22×C4—534no—
1466C22×C4—538no—
1467C22×C4—534no—
1468C22×C4—1064no—
1469C22×C4—2124no—
1470C22×C4—2124no—
1471C22×C4—2124no—
1472C22×C4C23×D5312yes—
1473C22×C4C23×D5312yes—
1474C22×C4C23×D5312yes—
1475C22×C4C23×D5312yes—
1476C22×C4C23×D5312yes—
1477C22×C4C23×D5314yes—
1478C22×C4C23×D5314yes—
1479C22×C4C23×D5314yes—
1480C22×C4C23×D5314yes—
1481C22×C4C23×D5311yescharacteristic
1482C4⋊C4—534no—
1483C4⋊C4—538no—
1484C4⋊C4—534no—
1485C4⋊C4—534no—
1486C4⋊C4—534no—
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—534no—
1496C4⋊C4—532no—
1497C4⋊C4—532no—
1498C4⋊C4—534no—
1499C4⋊C4—534no—
1500C4⋊C4—534no—
1501C4⋊C4—534no—
1502C4⋊C4—534no—
1503C4⋊C4—534no—
1504C4⋊C4—538no—
1505C4⋊C4—538no—
1506C4⋊C4C23×D5318yes—
1507C4⋊C4C23×D5314yes—
1508C4⋊C4C23×D5312yes—
1509C4⋊C4C23×D5314yes—
1510C22⋊C4—532no—
1511C22⋊C4—534no—
1512C22⋊C4—532no—
1513C22⋊C4—534no—
1514C22⋊C4—538no—
1515C22⋊C4—538no—
1516C22⋊C4—538no—
1517C22⋊C4—532no—
1518C22⋊C4—534no—
1519C22⋊C4—534no—
1520C22⋊C4—538no—
1521C22⋊C4—534no—
1522C22⋊C4—534no—
1523C22⋊C4—534no—
1524C22⋊C4—538no—
1525C22⋊C4—538no—
1526C22⋊C4—538no—
1527C22⋊C4—538no—
1528C22⋊C4—538no—
1529C22⋊C4—538no—
1530C22⋊C4—534no—
1531C22⋊C4—534no—
1532C22⋊C4—534no—
1533C22⋊C4—534no—
1534C22⋊C4—534no—
1535C22⋊C4—534no—
1536C22⋊C4C23×D5314yes—
1537C22⋊C4C23×D5312yes—
1538C22⋊C4C23×D5318yes—
1539C22⋊C4C23×D5318yes—
1540C22⋊C4C23×D5318yes—
1541C22⋊C4C23×D5318yes—
1542C22⋊C4C23×D5314yes—
1543C22⋊C4C23×D5314yes—
1544C42—531no—
1545C42—532no—
1546C42—532no—
1547C42—531no—
1548C42—532no—
1549C42—532no—
1550C42—532no—
1551C42—534no—
1552C42—534no—
1553C42—532no—
1554C42—532no—
1555C42—534no—
1556C42—532no—
1557C42—538no—
1558C42—538no—
1559C42C23×D5311yescharacteristic
1560C42C23×D5311yescharacteristic
1561C42C23×D5312yes—
1562C42C23×D5314yes—
1563C42C23×D5312yes—
1564C23—24no—
1565C23—44no—
1566C23—44no—
1567C23—48no—
1568C23—532no—
1569C23—534no—
1570C23—532no—
1571C23—1064no—
1572C23—1062no—
1573C23—2124no—
1574C23—2128no—
1575C23—2124no—
1576C23—2122no—
1577C23C24×D5312yes—
1578C23C24×D5312yes—
1579C23C24×D5314yes—
1580C23C24×D5312yes—
1581C23C24×D5311yescharacteristic
1582Q8—24no—
1583Q8—24no—
1584Q8—22no—
1585Q8—22no—
1586Q8—22no—
1587Q8—44no—
1588Q8—1068no—
1589Q8—1064no—
1590Q8—1064no—
1591Q8—1062no—
1592Q8—2124no—
1593Q8—2124no—
1594D4—24no—
1595D4—24no—
1596D4—24no—
1597D4—24no—
1598D4—24no—
1599D4—22no—
1600D4—22no—
1601D4—22no—
1602D4—44no—
1603D4—44no—
1604D4—44no—
1605D4—44no—
1606D4—48no—
1607D4—1068no—
1608D4—10616no—
1609D4—1064no—
1610D4—1064no—
1611D4—1064no—
1612D4—1062no—
1613D4—2124no—
1614D4—2128no—
1615D4—2124no—
1616D4—2128no—
1617D4—2128no—
1618D4—2128no—
1619D4—2124no—
1620D4—2128no—
1621D4—2124no—
1622D4—2124no—
1623D4—2124no—
1624D4—2128no—
1625D4—2124no—
1626C2×C4—24no—
1627C2×C4—24no—
1628C2×C4—24no—
1629C2×C4—24no—
1630C2×C4—42no—
1631C2×C4—44no—
1632C2×C4—44no—
1633C2×C4—44no—
1634C2×C4—44no—
1635C2×C4—532no—
1636C2×C4—534no—
1637C2×C4—534no—
1638C2×C4—532no—
1639C2×C4—532no—
1640C2×C4—534no—
1641C2×C4—532no—
1642C2×C4—534no—
1643C2×C4—1064no—
1644C2×C4—1064no—
1645C2×C4—1064no—
1646C2×C4—1068no—
1647C2×C4—1068no—
1648C2×C4—1062no—
1649C2×C4—1064no—
1650C2×C4—1064no—
1651C2×C4—1064no—
1652C2×C4—1064no—
1653C2×C4—2122no—
1654C2×C4—2122no—
1655C2×C4—2128no—
1656C2×C4—2124no—
1657C2×C4—2124no—
1658C2×C4—2124no—
1659C2×C4—2128no—
1660C2×C4—2128no—
1661C2×C4—2124no—
1662C2×C4—2128no—
1663C2×C4#1313326214yes—
1664C2×C4C24×D5312yes—
1665C2×C4C24×D5312yes—
1666C2×C4C24×D5314yes—
1667C2×C4C24×D5312yes—
1668C2×C4C24×D5314yes—
1669C2×C4C24×D5312yes—
1670C2×C4C24×D5312yes—
1671C2×C4C24×D5311yescharacteristic
1672C2×C4C24×D5311yescharacteristic
1673C22—22no—
1674C22—22no—
1675C22—22no—
1676C22—22no—
1677C22—24no—
1678C22—24no—
1679C22—24no—
1680C22—24no—
1681C22—28no—
1682C22—84no—
1683C22—164no—
1684C22—8484no—
1685C22—1062no—
1686C22—1062no—
1687C22—1064no—
1688C22—1062no—
1689C22—1062no—
1690C22—1064no—
1691C22—1068no—
1692C22—4244no—
1693C22—2124no—
1694C22C2×#1313326212yes—
1695C22C25×D5311yescharacteristic
1696C4—22no—
1697C4—22no—
1698C4—22no—
1699C4—24no—
1700C4—22no—
1701C4—22no—
1702C4—24no—
1703C4—534no—
1704C4—1062no—
1705C4—1062no—
1706C4—1064no—
1707C4—1064no—
1708C4—1062no—
1709C4—1064no—
1710C4—1064no—
1711C4C2×#1313326212yes—
1712C4C2×#1313326212yes—
1713C2—22no—
1714C2—44no—
1715C2—42no—
1716C2—42no—
1717C2—42no—
1718C2—2122no—
1719C2—2124no—
1720C2—2122no—
1721C2C22×#1313326211yescharacteristic
1722C2#585×D5312yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3500C2
hypercenter#3500D53
hypocenterC53#62836
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3500

Complements

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

NH ≅ G/Ntype
1. #20289306C2semidirect
2. #20289293C2semidirect
3. #20289175C2semidirect
4. #20289076C2semidirect
5. #20289016C2semidirect
6. #20288713C2semidirect
7. #20288670C2semidirect
8. #20288648C2semidirect
9. #20288621C2semidirect
10. #20288611C2semidirect
11. #20288609C2semidirect
12. #20288600C2semidirect
13. #20288590C2semidirect
14. #20288583C2semidirect
15. #20288502C2semidirect
16. #20288496C2semidirect
17. #20288489C2semidirect
18. #20288371C2semidirect
19. #20288370C2semidirect
20. #20288358C2semidirect
21. #20288355C2semidirect
22. #20288010C2semidirect
23. #20288008C2semidirect
24. C2×#16811172C2semidirect
25. C53×#3500C2semidirect
26. C2×#13133264C22semidirect
28. C22×#11719949C22semidirect
29. C22×#11719947C22semidirect
30. #16811370C22semidirect
31. #16811369C22semidirect
32. #16811362C22semidirect
33. #16811361C22semidirect
34. #16811357C22semidirect
35. #16811356C22semidirect
36. #16811355C22semidirect
37. #16811355C22semidirect
38. #16811348C22semidirect
39. #16811345C22semidirect
40. #16811342C22semidirect
41. #16811342C22semidirect
42. #16811335C22semidirect
43. #16811327C22semidirect
44. #16811322C22semidirect
45. #16811322C22semidirect
46. #16811320C22semidirect
47. #16811316C22semidirect
48. #16811310C22semidirect
49. #16811303C22semidirect
50. #16811302C22semidirect
51. #16811299C22semidirect
52. #16811299C22semidirect
53. #16811293C22semidirect
54. #16811293C22semidirect
55. #16811292C22semidirect
56. #16811292C22semidirect
57. #16811292C22semidirect
58. #16811291C22semidirect
59. #16811291C22semidirect
60. Q8×C22⋊D53C22semidirect
61. #16811284C22semidirect
62. #16811284C22semidirect
63. #16811282C22semidirect
64. #16811281C22semidirect
65. #16811279C22semidirect
66. #16811276C22semidirect
67. #16811275C22semidirect
68. #16811272C22semidirect
69. #16811272C22semidirect
70. #16811272C22semidirect
71. #16811272C22semidirect
72. #16811269C22semidirect
73. #16811267C22semidirect
74. #16811267C22semidirect
75. #16811266C22semidirect
76. #16811264C22semidirect
77. #16811263C22semidirect
78. #16811262C22semidirect
79. #16811260C22semidirect
80. #16811260C22semidirect
82. D4×C22⋊D53C22semidirect
83. #16811244C22semidirect
84. #16811243C22semidirect
85. #16811242C22semidirect
86. #16811237C22semidirect
87. #16811233C22semidirect
88. #16811226C22semidirect
89. #16811225C22semidirect
90. #16811224C22semidirect
91. #16811223C22semidirect
92. #16811223C22semidirect
93. #16811222C22semidirect
94. #16811216C22semidirect
95. #16811211C22semidirect
96. #16811208C22semidirect
97. #16811207C22semidirect
98. #16811205C22semidirect
99. #16811200C22semidirect
100. #16811198C22semidirect
101. #16811197C22semidirect
102. #16811197C22semidirect
104. #16811194C22semidirect
105. #16811194C22semidirect
107. #16811190C22semidirect
108. #16811188C22semidirect
109. #16811188C22semidirect
111. #16811187C22semidirect
112. #16811187C22semidirect
113. #16811187C22semidirect
114. #16811186C22semidirect
115. #16811184C22semidirect
116. #16811182C22semidirect
117. #16811180C22semidirect
118. #16811178C22semidirect
119. #16811177C22semidirect
120. #16811176C22semidirect
121. #16811175C22semidirect
122. #16811172C22semidirect
123. #16811172C22semidirect
124. #16811172C22semidirect
125. #16811172C22semidirect
126. #16811172C22semidirect
127. #16811171C22semidirect
128. #16811170C22semidirect
130. #16811169C22semidirect
131. #16811169C22semidirect
132. #16811168C22semidirect
133. C2×#13133215C22semidirect
134. C2×#13133215C22semidirect
136. C2×#13133213C22semidirect
137. #16811160C22semidirect
138. #16811157C22semidirect
139. #16811155C22semidirect
140. #16811155C22semidirect
141. #16811154C22semidirect
142. #16811153C22semidirect
143. #16811152C22semidirect
144. #16811152C22semidirect
145. #16811152C22semidirect
146. #16811151C22semidirect
147. C2×#13133205C22semidirect
148. #124×D53C22semidirect
149. #16811135C22semidirect
150. #16811133C22semidirect
151. #16811132C22semidirect
153. #16811130C22semidirect
154. #16811130C22semidirect
155. #16811130C22semidirect
156. #16811129C22semidirect
157. C2×#13133198C22semidirect
158. #123×D53C22semidirect
159. C2×#13133190C22semidirect
160. #16811102C22semidirect
161. #16811101C22semidirect
162. #16811100C22semidirect
163. #16811098C22semidirect
164. #16811097C22semidirect
165. #16811096C22semidirect
167. #41×Dic53C22semidirect
168. C4×#11719945C22semidirect
169. C4×#11719945C22semidirect
170. C4×#11719947C22semidirect
171. C2×#13133177C22semidirect
172. C2×C42×D53C22semidirect
173. C2×2−1+4×C53C22semidirect
175. C53×#548C22semidirect
176. C53×#546C22semidirect
177. C53×#546C22semidirect
179. C53×#536C22semidirect
180. C53×#535C22semidirect
181. C53×#535C22semidirect
183. C53×#532C22semidirect
184. C2×#124×C53C22semidirect
185. C2×#124×C53C22semidirect
186. C4×#41×C53C22semidirect
867. #3500D53semidirect
888. C2×2−1+4C2×D53semidirect
929. #548C2×D53semidirect
945. #546C2×D53semidirect
946. #546C2×D53semidirect
973. #536C2×D53semidirect
983. #535C2×D53semidirect
984. #535C2×D53semidirect
1004. #532C2×D53semidirect
1021. C2×#124C2×D53semidirect
1022. C2×#124C2×D53semidirect
1045. C4×#41C2×D53semidirect
1048. C53#62836semidirect

Maximal subgroups

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

subgroupindex
#202893062
#202892932
#202891752
#202890762
#202890162
#202887132
#202886702
#202886482
#202886212
#202886112
#202886092
#202886002
#202885902
#202885832
#202885022
#202884962
#202884892
#202883712
#202883702
#202883582
#202883552
#202880102
#202880082
C2×#168111722
C53×#35002
#6283653