Finite Group Databasebeta

← #28293205

Subgroups — #28293205

Order 13568.

11222 conjugacy classes of subgroups.

The subgroup lattice has 1646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811459C211yesmaximal, characteristic, complemented
2C2×#16811458C211yesmaximal, characteristic, complemented
3#20288483C212yesmaximal, complemented
4#20288480C212yesmaximal, complemented
5#20288475C216yesmaximal, complemented
6#20288471C216yesmaximal, complemented
7#20288396C211yesmaximal, characteristic, complemented
8#20288395C211yesmaximal, characteristic, complemented
9#20288394C212yesmaximal, complemented
10#20288390C213yesmaximal, complemented
11#20288387C213yesmaximal, complemented
12#20288386C216yesmaximal, complemented
13#20288383C212yesmaximal, complemented
14#20288382C213yesmaximal, complemented
15#20288380C213yesmaximal, complemented
16#20288377C211yesmaximal, characteristic, complemented
17#20288375C216yesmaximal, complemented
18#20288046C213yesmaximal, complemented
19#20288045C213yesmaximal, complemented
20C2×#16811202C213yesmaximal, complemented
21#537×D53C213yesmaximal, complemented
22#520×D53C211yesmaximal, characteristic, complemented
23C53×#3488C211yesmaximal, characteristic, complemented
24#16811459—216no—
25#16811458—216no—
26C2×#13133265C2211yescharacteristic, complemented
27C2×#13133265C2211yescharacteristic, complemented
28C2×#13133264C2213yescomplemented
29C2×#13133264C2213yescomplemented
30C2×#13133264C2211yescharacteristic, complemented
31C2×#13133264C2211yescharacteristic, complemented
32C2×#13133264C2212yescomplemented
33C2×#13133263C2211yescharacteristic, complemented
34C2×#13133263C2213yescomplemented
35C2×#13133262C2213yescomplemented
36C2×#13133262C2213yescomplemented
37C2×#13133262C2213yescomplemented
38C2×#13133262C2216yescomplemented
39C22×#11719945C2213yescomplemented
40C22×#11719945C2213yescomplemented
41C22×#11719947C2213yescomplemented
42C22×#11719947C2216yescomplemented
43C2×#41×D53C2211yescharacteristic
44C2×#41×D53C2213yescomplemented
45C2×#41×D53C2213yescomplemented
46C2×#41×D53C2211yescharacteristic, complemented
47C2×#41×D53C2213yescomplemented
48C2×#41×D53C2212yescomplemented
49#16811293C2216yescomplemented
50#16811292C2212yescomplemented
51#16811291C2216yescomplemented
52Q8×D212C2212yescomplemented
53D4×Dic106C2216yescomplemented
54Q8×C22⋊D53C2212yescomplemented
55#16811286C2216yescomplemented
56#16811285C2212yescomplemented
57#16811282C2216yescomplemented
58#16811281C2216yescomplemented
59#16811280C2212yescomplemented
60#16811280C2212yescomplemented
61#16811279C2216yescomplemented
62#16811279C2216yescomplemented
63#16811278C2216yescomplemented
64#16811277C2216yescomplemented
65#16811275C2216yescomplemented
66#16811273C22112yescomplemented
67#16811272C2216yescomplemented
68#16811271C22112yescomplemented
69#16811270C2216yescomplemented
70#16811270C2216yescomplemented
71#16811269C2216yescomplemented
72#16811268C2216yescomplemented
73#16811267C2216yescomplemented
74#16811267C2216yescomplemented
75#16811266C2216yescomplemented
76#16811263C22112yescomplemented
77#16811262C22112yescomplemented
78#16811260C22112yescomplemented
79#16811260C22112yescomplemented
80#16811258C2216yescomplemented
81#16811257C2216yescomplemented
82D4×C22⋊D53C2216yescomplemented
83D4×C22⋊D53C22112yescomplemented
84#16811255C22112yescomplemented
85#16811204C2213yescomplemented
86#16811203C2213yescomplemented
87#16811203C2216yescomplemented
88#16811203C2211yescharacteristic, complemented
89#16811202C2216yescomplemented
90#16811202C2216yescomplemented
91#16811202C2213yescomplemented
92#16811202C2216yescomplemented
93#16811202C2216yescomplemented
94#16811202C2216yescomplemented
95#16811202C2216yescomplemented
96#16811202C2216yescomplemented
97#16811202C2216yescomplemented
98#16811202C2213yescomplemented
99#16811201C2213yescomplemented
100#16811201C2213yescomplemented
101#16811200C22112yescomplemented
102#16811199C2213yescomplemented
103#16811196C2213yescomplemented
104#16811196C2213yescomplemented
105#16811195C2216yescomplemented
106#16811194C2213yescomplemented
107#16811193C2216yescomplemented
108#16811190C2213yescomplemented
109#16811189C2213yescomplemented
110#16811189C2213yescomplemented
111#16811188C2216yescomplemented
112#16811186C2216yescomplemented
113#16811184C2216yescomplemented
114#16811183C2216yescomplemented
115#16811183C22112yescomplemented
116#16811172C2216yescomplemented
117#16811171C2216yescomplemented
118#16811170C2216yescomplemented
119#16811170C2216yescomplemented
120#16811135C2213yescomplemented
121#16811134C2213yescomplemented
122#16811133C2216yescomplemented
123#16811133C2216yescomplemented
124#16811132C2216yescomplemented
125#16811132C2216yescomplemented
126#16811130C2213yescomplemented
127#16811129C22112yescomplemented
128C2×#13133197C2213yescomplemented
129C2×#13133196C2213yescomplemented
130C2×#13133194C2216yescomplemented
131C22⋊Q8×D53C2216yescomplemented
132C22⋊Q8×D53C2216yescomplemented
133C2×#13133190C2216yescomplemented
134C2×#13133189C2216yescomplemented
135C2×#13133188C2213yescomplemented
136C2×#13133188C2216yescomplemented
137#121×D53C2216yescomplemented
138#121×D53C2216yescomplemented
139#121×D53C22112yescomplemented
140#16811106C2211yescharacteristic, complemented
141#16811105C2212yescomplemented
142#16811104C2213yescomplemented
143#16811103C2213yescomplemented
144#16811102C2216yescomplemented
145C4×Q8×D53C2212yescomplemented
146C4×D4×D53C2216yescomplemented
147#117×D53C2213yescomplemented
148C2×C4⋊C4×D53C2213yescomplemented
149C2×H(5,𝔽2)×C53C2211yescharacteristic, complemented
150C22×#41×C53C2211yescharacteristic, complemented
151C53×#550C2212yescomplemented
152C53×#548C2212yescomplemented
153C53×#546C2216yescomplemented
154D42×C53C2216yescomplemented
155C53×#537C2213yescomplemented
156C53×#535C2213yescomplemented
157C53×#525C2213yescomplemented
158C2×#121×C53C2213yescomplemented
159C53×#520C2211yescharacteristic, complemented
160#13133265—28no—
161#13133265—28no—
162#13133264—28no—
163#13133264—216no—
164#13133264—28no—
165#13133264—224no—
166#13133264—224no—
167#13133263—28no—
168#13133263—224no—
169#13133262—224no—
170#13133262—248no—
171#13133262—224no—
172#13133262—224no—
173C2×#11719949C2313yes—
174C2×#11719949C2311yescharacteristic
175C2×#11719949C2313yes—
176C2×#11719949C2311yescharacteristic
177C2×#11719949C2311yescharacteristic
178C2×#11719945—224no—
179C2×#11719945—224no—
180C2×#11719945C2316yes—
181C2×#11719945C2313yes—
182C2×#11719945C2316yes—
183C2×#11719945C2313yes—
184C2×#11719945C2313yes—
185C2×#11719945C2313yes—
186C2×#11719945C2313yes—
187C2×#11719945C2316yes—
188C2×#11719945C2313yes—
189C2×#11719945C2313yes—
190C2×#11719945C2313yes—
191C2×#11719945C2313yes—
192C2×#11719945C2313yes—
193C2×#11719945C2313yes—
194C2×#11719945C2311yescharacteristic
195C2×#11719945C2313yes—
196C2×#11719947—248no—
197C2×#11719947—224no—
198C2×#11719947C2313yes—
199C2×#11719947C2316yes—
200C2×#11719947C23112yes—
201C2×#11719947C2316yes—
202C2×#11719947C2313yes—
203C2×#11719947C2316yes—
204C2×#11719947C2316yes—
205C2×#11719947C2316yes—
206C2×#11719947C2313yes—
207C2×#11719947C2316yes—
208C2×#11719947C2316yes—
209C2×#11719947C2316yes—
210C2×#11719947C2313yes—
211C2×#11719947C2313yes—
212#41×D53—28no—
213#41×D53—216no—
214#41×D53—224no—
215#41×D53—224no—
216#41×D53—224no—
217#41×D53D4116yescomplemented
218C22×Dic106C2313yes—
219C22×Dic106C2316yes—
220C22×Dic106C2313yes—
221C22×Dic106C2313yes—
222C2×Q8×D53C2311yescharacteristic
223C2×Q8×D53C2312yes—
224C2×Q8×D53C2313yes—
225C2×Q8×D53C2313yes—
226C2×Q8×D53C2313yes—
227C2×Q8×D53C2311yescharacteristic
228C22×D212C2313yes—
229C22×D212C2313yes—
230C22×C22⋊D53C2313yes—
231C22×C22⋊D53C2316yes—
232C22×C22⋊D53C2313yes—
233C22×C22⋊D53C23112yes—
234C22×C22⋊D53C2316yes—
235C22×C22⋊D53C2316yes—
236C2×D4×D53C2316yes—
237C2×D4×D53C2313yes—
238C2×D4×D53C2313yes—
239C2×D4×D53C2316yes—
240C2×D4×D53C2316yes—
241C2×D4×D53C2313yes—
242C2×D4×D53C2313yes—
243C2×D4×D53C2316yes—
244C2×D4×D53C23112yes—
245C2×D4×D53C2313yes—
246C23×Dic53C2316yes—
247C22×C4×D53C2316yes—
248C22×C4×D53C2316yes—
249C22×C4×D53C2313yes—
250C22×C4×D53C2316yes—
251C22×C4×D53C2313yes—
252#13133217C2316yes—
253#13133216C2316yes—
254#13133216C2316yes—
255#13133215C2316yes—
256#13133213C2316yes—
257#13133213C2316yes—
258#13133213C2316yes—
259#13133205C2316yes—
260#13133204C2316yes—
261#13133204C2316yes—
262#13133203C2316yes—
263#13133203C2316yes—
264#13133203C2316yes—
265#13133203C2316yes—
266#13133202C2316yes—
267#13133202C2316yes—
268#13133201C23112yes—
269#13133201C2316yes—
270#13133200C2316yes—
271#13133199C23112yes—
272#13133199C2316yes—
273#13133199C23112yes—
274#13133199C2316yes—
275#13133198C2316yes—
276#13133198C23112yes—
277#13133197C2316yes—
278#13133197C2316yes—
279#13133197C2316yes—
280#13133197C2316yes—
281#13133197C2313yes—
282#13133197C2313yes—
283#13133196C2316yes—
284#13133196C2316yes—
285#13133196C2316yes—
286#13133196C2316yes—
287#13133196C2313yes—
288#13133196C2313yes—
289#13133195C23112yes—
290#13133195C2316yes—
291#13133195C2312yes—
292#13133194C23112yes—
293#13133194C23112yes—
294#13133194C23112yes—
295#13133194C23112yes—
296#13133194C2316yes—
297#13133194C2316yes—
298#13133193C2316yes—
299#13133193C2313yes—
300#13133193C2311yescharacteristic
301#13133192C2316yes—
302#13133192C2313yes—
303#13133192C2316yes—
304#13133192C2311yescharacteristic
305#13133192C2312yes—
306#13133191C23112yes—
307#13133191C2316yes—
308#13133191C2313yes—
309#13133191C2311yescharacteristic
310#13133190C23112yes—
311#13133190C23112yes—
312#13133190C23112yes—
313#13133190C2316yes—
314#13133190C2316yes—
315#13133190C23112yes—
316#13133190C2316yes—
317#13133190C2312yes—
318#13133190C2312yes—
319#13133190C2316yes—
320#13133189C23112yes—
321#13133189C23112yes—
322#13133189C23112yes—
323#13133189C23112yes—
324#13133189C23112yes—
325#13133189C23112yes—
326#13133189C2316yes—
327#13133189C2316yes—
328#13133188C2316yes—
329#13133188C2316yes—
330#13133188C2316yes—
331#13133188C23112yes—
332#13133188C23112yes—
333#13133188C2316yes—
334#13133188C23112yes—
335#13133188C2313yes—
336#13133188C2316yes—
337#13133188C2313yes—
338#13133188C2316yes—
339#13133187C2316yes—
340#13133187C2316yes—
341#13133187C2316yes—
342#13133186C2316yes—
343#13133186C23112yes—
344#13133185C23112yes—
345#13133185C2316yes—
346#13133185C23112yes—
347#13133185C2316yes—
348#13133185C2316yes—
349Q8×Dic53C2312yes—
350C4×Dic106C2316yes—
351#13133182C2316yes—
352C4×D212C2316yes—
353C4×D212C2316yes—
354C4×D212C2316yes—
355D4×Dic53C2316yes—
356D4×Dic53C23112yes—
357D4×Dic53C23112yes—
358#13133179C2316yes—
359C4×C22⋊D53C2316yes—
360C4×C22⋊D53C2316yes—
361C4×C22⋊D53C2316yes—
362C4×C22⋊D53C23112yes—
363C4×C22⋊D53C2316yes—
364#13133177C23112yes—
365#13133177C23112yes—
366#13133177C23112yes—
367#13133176C2313yes—
368#13133175C2313yes—
369#13133175C2313yes—
370#13133174C2316yes—
371#13133173C2316yes—
372C2×C4⋊Dic53C2316yes—
373C2×C4⋊Dic53C2313yes—
374C2×#11719919C2316yes—
375C2×#11719919C2316yes—
376C4⋊C4×D53C23112yes—
377C4⋊C4×D53C2313yes—
378C4⋊C4×D53C2316yes—
379C4⋊C4×D53C2316yes—
380C4⋊C4×D53C2316yes—
381C4⋊C4×D53C2311yescharacteristic
382C2×C22⋊Dic53C2316yes—
383C2×C22⋊Dic53C2316yes—
384C2×#11719921C2316yes—
385C22⋊C4×D53C23112yes—
386C22⋊C4×D53C23112yes—
387C22⋊C4×D53C2316yes—
388C42×D53C2316yes—
389H(5,𝔽2)×C53—28no—
390C2×#41×C53—28no—
391C2×#41×C53C2313yes—
392C2×#41×C53C2311yescharacteristic
393C2×#41×C53C2312yes—
394C2×#41×C53C2313yes—
395C2×#41×C53C2313yes—
396C2×#41×C53C2311yescharacteristic
397C22×Q8×C53C2311yescharacteristic
398C22×D4×C53C2313yes—
399C22×D4×C53C2316yes—
400C22×D4×C53C2313yes—
401C22×D4×C53C2316yes—
402C23×C4×C53C2313yes—
403#127×C53C2316yes—
404#124×C53C2316yes—
405#123×C53C2316yes—
406C22⋊Q8×C53C2316yes—
407C22⋊Q8×C53C2311yescharacteristic
408C22⋊Q8×C53C2313yes—
409#121×C53C2316yes—
410#121×C53C2316yes—
411#121×C53C23112yes—
412#121×C53C2316yes—
413#121×C53C2313yes—
414#121×C53C2316yes—
415#121×C53C2313yes—
416#120×C53C2316yes—
417#120×C53C23112yes—
418C4×Q8×C53C2312yes—
419C4×D4×C53C2316yes—
420C4×D4×C53C2316yes—
421C4×D4×C53C2316yes—
422#117×C53C2313yes—
423C2×C4⋊C4×C53C2313yes—
424C2×C22⋊C4×C53C2316yes—
425C24×C53C2416yes—
426C24×C53C2413yes—
427C23×D53C2416yes—
428C23×D53C2416yes—
429C23×D53C2413yes—
430C23×D53C2413yes—
431#41×C53—24no—
432#41×C53—28no—
433#41×C53—212no—
434#41×C53—212no—
435#41×C53—212no—
436#41×C53C2×D418yescomplemented
437C2×Q8×C53—24no—
438C2×Q8×C53C2411yescharacteristic
439C2×Q8×C53C2413yes—
440C2×Q8×C53C2411yescharacteristic
441C2×D4×C53—212no—
442C2×D4×C53—224no—
443C2×D4×C53—212no—
444C2×D4×C53—86no—
445C2×D4×C53C2416yes—
446C2×D4×C53C2416yes—
447C2×D4×C53C2413yes—
448C2×D4×C53C2416yes—
449C2×D4×C53C2413yes—
450C2×D4×C53C2416yes—
451C2×D4×C53C2416yes—
452C2×D4×C53C24112yes—
453C2×D4×C53C2413yes—
454C22×C4×C53—212no—
455C22×C4×C53C2413yes—
456C22×C4×C53C2413yes—
457C22×C4×C53C2413yes—
458C22×C4×C53C2416yes—
459C22×C4×C53C2411yescharacteristic
460C22×C4×C53C2413yes—
461C22×C4×C53C2416yes—
462C22×C4×C53C2413yes—
463C2×C22⋊D53—224no—
464C2×C22⋊D53—212no—
465C2×C22⋊D53—248no—
466C2×C22⋊D53—224no—
467C2×C22⋊D53—212no—
468C2×C22⋊D53—86no—
469C2×C22⋊D53C2413yes—
470C2×C22⋊D53C2413yes—
471C2×C22⋊D53C24112yes—
472C2×C22⋊D53C2416yes—
473C2×C22⋊D53C2416yes—
474C2×C22⋊D53C2413yes—
475C2×C22⋊D53C2411yescharacteristic
476C2×C22⋊D53C2416yes—
477C2×C22⋊D53C2413yes—
478C2×C22⋊D53C2411yescharacteristic
479C2×C22⋊D53C2413yes—
480C2×C22⋊D53C2413yes—
481C2×C22⋊D53C2416yes—
482C2×C22⋊D53C2416yes—
483C2×C22⋊D53C24112yes—
484C2×C22⋊D53C2412yes—
485C2×C22⋊D53C2416yes—
486C2×C22⋊D53C2416yes—
487C2×C22⋊D53C2416yes—
488C22×Dic53—224no—
489C22×Dic53C2416yes—
490C22×Dic53C2413yes—
491C22×Dic53C24112yes—
492C22×Dic53C2416yes—
493C22×Dic53C2416yes—
494C22×Dic53C2416yes—
495C22×Dic53C2413yes—
496#11719949—24no—
497#11719949—212no—
498#11719949—24no—
499#11719949—212no—
500#11719949C2×D418yescomplemented
501Q8×D53—28no—
502Q8×D53—24no—
503Q8×D53—212no—
504Q8×D53—212no—
505Q8×D53—212no—
506Q8×D53C2×D418yescomplemented
507#11719947—212no—
508#11719947—224no—
509#11719947—224no—
510#11719947—248no—
511#11719947—224no—
512#11719947—224no—
513#11719947—224no—
514#11719947—212no—
515#11719947—212no—
516#11719947—224no—
517#11719947—224no—
518#11719947—212no—
519#11719947—224no—
520#11719947C2×D4124yescomplemented
521D4×D53—224no—
522D4×D53—224no—
523D4×D53—212no—
524D4×D53—224no—
525D4×D53—224no—
526D4×D53—212no—
527D4×D53—212no—
528D4×D53—212no—
529D4×D53—812no—
530D4×D53C2×D4124yescomplemented
531#11719945—212no—
532#11719945—212no—
533#11719945—224no—
534#11719945—224no—
535#11719945—212no—
536#11719945—212no—
537#11719945—212no—
538#11719945—224no—
539#11719945—212no—
540#11719945—24no—
541#11719945—212no—
542#11719945—212no—
543#11719945—212no—
544#11719945—212no—
545#11719945—212no—
546#11719945C2×D4124yescomplemented
547C2×D212—212no—
548C2×D212—212no—
549C2×D212C2413yes—
550C2×D212C2413yes—
551C2×D212C2413yes—
552C2×D212C2411yescharacteristic
553C2×D212C2412yes—
554C2×D212C2411yescharacteristic
555C2×D212C2413yes—
556C2×D212C2412yes—
557C2×D212C2416yes—
558C2×D212C2413yes—
559C2×C4×D53—212no—
560C2×C4×D53—224no—
561C2×C4×D53—224no—
562C2×C4×D53—86no—
563C2×C4×D53C2×D4124yescomplemented
564C2×C4×D53C2416yes—
565C2×C4×D53C2416yes—
566C2×C4×D53C2416yes—
567C2×C4×D53C2413yes—
568C2×C4×D53C2413yes—
569C2×C4×D53C2416yes—
570C2×C4×D53C2413yes—
571C2×C4×D53C2411yescharacteristic
572C2×C4×D53C2412yes—
573C2×C4×D53C2412yes—
574C2×C4×D53C2416yes—
575C2×C4×D53C24112yes—
576C2×C4×D53C2413yes—
577C2×C4×D53C2411yescharacteristic
578C2×C4×D53C2413yes—
579C2×C4×D53C2413yes—
580C2×Dic106—212no—
581C2×Dic106—212no—
582C2×Dic106—224no—
583C2×Dic106—212no—
584C2×Dic106C2413yes—
585C2×Dic106C2411yescharacteristic
586C2×Dic106C2413yes—
587C2×Dic106C2413yes—
588C2×Dic106C2416yes—
589C2×Dic106C2413yes—
590C2×Dic106C2413yes—
591C2×Dic106C2416yes—
592C2×Dic106C2413yes—
593C4⋊C4×C53C2413yes—
594C4⋊C4×C53C2416yes—
595C4⋊C4×C53C2411yescharacteristic
596C4⋊C4×C53C2412yes—
597C4⋊C4×C53C2416yes—
598C22⋊C4×C53C2416yes—
599C22⋊C4×C53C24112yes—
600C22⋊C4×C53C2416yes—
601C22⋊C4×C53C2412yes—
602C22⋊C4×C53C2416yes—
603C22⋊C4×C53C2416yes—
604C42×C53C2416yes—
605C22⋊Dic53C24112yes—
606C22⋊Dic53C24112yes—
607C22⋊Dic53C2416yes—
608C22⋊Dic53C2416yes—
609C22⋊Dic53C2416yes—
610C22⋊Dic53C2416yes—
611C22⋊Dic53C2416yes—
612#11719921C2416yes—
613#11719921C2416yes—
614#11719921C2416yes—
615#11719921C24112yes—
616#11719921C2416yes—
617#11719921C2416yes—
618#11719921C2416yes—
619#11719921C2416yes—
620#11719921C2412yes—
621#11719921C2412yes—
622#11719921C2412yes—
623C4⋊Dic53C2413yes—
624C4⋊Dic53C2416yes—
625C4⋊Dic53C24112yes—
626C4⋊Dic53C2411yescharacteristic
627C4⋊Dic53C2416yes—
628C4⋊Dic53C2416yes—
629#11719919C2416yes—
630#11719919C24112yes—
631#11719919C2416yes—
632#11719919C24112yes—
633#11719919C2412yes—
634#11719919C2416yes—
635#11719919C2416yes—
636#11719919C2412yes—
637C4×Dic53C2416yes—
638C4×Dic53C2416yes—
639C4×Dic53C2416yes—
640C23×C53—212no—
641C23×C53—26no—
642C23×C53—46no—
643C23×C53—43no—
644C23×C53—43no—
645C23×C53—46no—
646C23×C53C2516yes—
647C23×C53C2513yes—
648C23×C53C2511yescharacteristic
649C23×C53C2513yes—
650C22×D53—26no—
651C22×D53—212no—
652C22×D53—212no—
653C22×D53—43no—
654C22×D53—43no—
655C22×D53—46no—
656C22×D53—46no—
657C22×D53—43no—
658C22×D53—46no—
659C22×D53—46no—
660C22×D53—43no—
661C22×D53C22×D4112yes—
662C22×D53C2513yes—
663C22×D53C2511yescharacteristic
664C22×D53C2512yes—
665C22×D53C2511yescharacteristic
666C22×D53C2513yes—
667Q8×C53—22no—
668Q8×C53—26no—
669Q8×C53C22×D414yes—
670D4×C53—212no—
671D4×C53—212no—
672D4×C53—26no—
673D4×C53—212no—
674D4×C53—26no—
675D4×C53—412no—
676D4×C53—46no—
677D4×C53—46no—
678D4×C53C22×D4112yes—
679C2×C4×C53—26no—
680C2×C4×C53—212no—
681C2×C4×C53—26no—
682C2×C4×C53—26no—
683C2×C4×C53—22no—
684C2×C4×C53—26no—
685C2×C4×C53—46no—
686C2×C4×C53C22×D4112yes—
687C2×C4×C53C2511yescharacteristic
688C2×C4×C53C2512yes—
689C2×C4×C53C2513yes—
690C2×C4×C53C2516yes—
691C2×C4×C53C2512yes—
692C2×C4×C53C2513yes—
693C2×C4×C53C2511yescharacteristic
694C22⋊D53—212no—
695C22⋊D53—212no—
696C22⋊D53—26no—
697C22⋊D53—22no—
698C22⋊D53—26no—
699C22⋊D53—26no—
700C22⋊D53—224no—
701C22⋊D53—212no—
702C22⋊D53—26no—
703C22⋊D53—22no—
704C22⋊D53—26no—
705C22⋊D53—26no—
706C22⋊D53—212no—
707C22⋊D53—46no—
708C22⋊D53—412no—
709C22⋊D53—46no—
710C22⋊D53—42no—
711C22⋊D53—46no—
712C22⋊D53C22×D4124yes—
713C2×Dic53—26no—
714C2×Dic53—212no—
715C2×Dic53—212no—
716C2×Dic53—224no—
717C2×Dic53—212no—
718C2×Dic53—46no—
719C2×Dic53C22×D4112yes—
720C2×Dic53C2513yes—
721C2×Dic53C2511yescharacteristic
722C2×Dic53C2516yes—
723C2×Dic53C2516yes—
724C2×Dic53C2512yes—
725C2×Dic53C2513yes—
726C2×Dic53C2511yescharacteristic
727D212—26no—
728D212—22no—
729D212—26no—
730D212—26no—
731D212—24no—
732D212—26no—
733D212—22no—
734D212—42no—
735D212—46no—
736D212C22×D4112yes—
737C4×D53—212no—
738C4×D53—212no—
739C4×D53—22no—
740C4×D53—26no—
741C4×D53—212no—
742C4×D53—26no—
743C4×D53—26no—
744C4×D53—24no—
745C4×D53—212no—
746C4×D53—46no—
747C4×D53—412no—
748C4×D53—42no—
749C4×D53C22×D4112yes—
750C4×D53C22×D4112yes—
751C4×D53C22×D414yes—
752C4×D53C22×D4112yes—
753Dic106—212no—
754Dic106—26no—
755Dic106—26no—
756Dic106—26no—
757Dic106—22no—
758Dic106—212no—
759Dic106—26no—
760Dic106—26no—
761Dic106C22×D4112yes—
762#62853—531nomaximal, Sylow
763C22×C53—23no—
764C22×C53—23no—
765C22×C53—26no—
766C22×C53—23no—
767C22×C53—21no—
768C22×C53—26no—
769C22×C53—23no—
770C22×C53—21no—
771C22×C53—21no—
772C22×C53—26no—
773C22×C53—23no—
774C22×C53—86no—
775C22×C53—812no—
776C22×C53C23×D416yes—
777C22×C53C2611yescharacteristic
778C2×D53—21no—
779C2×D53—23no—
780C2×D53—21no—
781C2×D53—23no—
782C2×D53—21no—
783C2×D53—23no—
784C2×D53—22no—
785C2×D53—22no—
786C2×D53—23no—
787C2×D53—21no—
788C2×D53—21no—
789C2×D53—22no—
790C2×D53—23no—
791C2×D53—412no—
792C2×D53—812no—
793C2×D53—812no—
794C2×D53—86no—
795C2×D53C23×D416yes—
796C2×D53C23×D412yes—
797C4×C53—21no—
798C4×C53—22no—
799C4×C53—23no—
800C4×C53—26no—
801C4×C53—22no—
802C4×C53C23×D416yes—
803C4×C53C23×D412yes—
804Dic53—23no—
805Dic53—21no—
806Dic53—26no—
807Dic53—26no—
808Dic53—22no—
809Dic53C23×D416yes—
810Dic53C23×D412yes—
811C2×#585—531no—
812C2×#585—531no—
813#3497—532no—
814#3497—532no—
815#3496—536no—
816#3496—536no—
817#3489—531no—
818#3489—532no—
819#3489—536no—
820#3489—533no—
821#3489—533no—
822#3489—531no—
823#3488—531no—
824#3488—532no—
825#3488—536no—
826#3488—533no—
827#3488—533no—
828#3488D5311yescharacteristic, complemented
829#3449—533no—
830#3449—533no—
831C2×#537—533no—
832C2×#537—533no—
833C2×#520—531no—
834C2×C53—26no—
835C2×C53—43no—
836C2×C53—46no—
837C2×C53—41no—
838C2×C53C24×D411yescharacteristic
839C2×C53H(7,𝔽2)11yescharacteristic
840C2×C532−1+611yescharacteristic
841D53—22no—
842D53—26no—
843D53—43no—
844D53—41no—
845D53—42no—
846#585—10616no—
847#585—10616no—
848C2×2−1+4—533no—
849C2×2−1+4—533no—
850C2×2−1+4—531no—
851C2×2−1+4—531no—
852C2×2−1+4—532no—
853C2×2−1+4—531no—
854C2×2−1+4—531no—
855C2×H(5,𝔽2)—531no—
856C2×H(5,𝔽2)—533no—
857C2×H(5,𝔽2)—533no—
858C2×H(5,𝔽2)—533no—
859C2×H(5,𝔽2)—536no—
860C2×H(5,𝔽2)—533no—
861C2×H(5,𝔽2)C2×D5311yescharacteristic, complemented
862C22×#41—531no—
863C22×#41—533no—
864C22×#41—533no—
865C22×#41—532no—
866C22×#41—533no—
867C22×#41—531no—
868C22×#41—533no—
869C22×#41—536no—
870C22×#41—533no—
871C22×#41—533no—
872C22×#41C2×D5311yescharacteristic, complemented
873#550—532no—
874#550—536no—
875#550—536no—
876#550C2×D5312yescomplemented
877D4×Q8—532no—
878D4×Q8—536no—
879D4×Q8—532no—
880D4×Q8—536no—
881#548—532no—
882#548—532no—
883#548—536no—
884#548—536no—
885#548—536no—
886#548—532no—
887#548—536no—
888#548C2×D5312yescomplemented
889#547—536no—
890#547—5312no—
891#547—536no—
892#547—5312no—
893#547—536no—
894#547—536no—
895#546—536no—
896#546—536no—
897#546—536no—
898#546—536no—
899#546—536no—
900#546—5312no—
901#546—5312no—
902#546—5312no—
903#546—536no—
904#546—536no—
905#546—5312no—
906#546C2×D5316yescomplemented
907D42—536no—
908D42—5312no—
909D42—536no—
910D42—536no—
911D42—5312no—
912D42C2×D5316yescomplemented
913#537—533no—
914#537—533no—
915#537—533no—
916#537—536no—
917#537—531no—
918#537—536no—
919#537—533no—
920#537—5312no—
921#537—536no—
922#537—536no—
923#537—536no—
924#537—536no—
925#537—536no—
926#537—536no—
927#537—536no—
928#537—533no—
929#537—533no—
930#537C2×D5313yescomplemented
931#536—533no—
932#536—536no—
933#536—536no—
934#536—533no—
935#536—533no—
936#536—533no—
937#535—533no—
938#535—536no—
939#535—533no—
940#535—533no—
941#535—536no—
942#535C2×D5313yescomplemented
943#534—536no—
944#534—5312no—
945#534—536no—
946#532—536no—
947#532—536no—
948#532—536no—
949#532—536no—
950#525—533no—
951#525—533no—
952#525—536no—
953#525—536no—
954#525—5312no—
955#525—536no—
956#525—536no—
957#525—533no—
958#525C2×D5313yescomplemented
959C2×C22⋊Q8—533no—
960C2×C22⋊Q8—536no—
961C2×C22⋊Q8—536no—
962C2×C22⋊Q8—533no—
963C2×C22⋊Q8—536no—
964C2×#121—533no—
965C2×#121—536no—
966C2×#121—536no—
967C2×#121—536no—
968C2×#121—536no—
969C2×#121—5312no—
970C2×#121—536no—
971C2×#121C2×D5313yescomplemented
972#520—531no—
973#520—532no—
974#520—536no—
975#520—533no—
976#520—533no—
977#520C2×D5311yescharacteristic, complemented
978C2×C4×Q8—532no—
979C2×C4×D4—536no—
980C2×#117—533no—
981C22×C4⋊C4—533no—
982C53#6285311yescharacteristic, complemented, Sylow
9832−1+4—1068no—
9842−1+4—1068no—
9852−1+4—1068no—
9862−1+4—10616no—
9872−1+4—10624no—
9882−1+4—10624no—
9892−1+4—1068no—
990H(5,𝔽2)—28no—
991H(5,𝔽2)—10624no—
992H(5,𝔽2)—10648no—
993H(5,𝔽2)—10624no—
994H(5,𝔽2)—10624no—
995H(5,𝔽2)—10624no—
996H(5,𝔽2)—1068no—
997C2×#41—28no—
998C2×#41—5316no—
999C2×#41—531no—
1000C2×#41—533no—
1001C2×#41—531no—
1002C2×#41—533no—
1003C2×#41—531no—
1004C2×#41—533no—
1005C2×#41—536no—
1006C2×#41—536no—
1007C2×#41—533no—
1008C2×#41—536no—
1009C2×#41—536no—
1010C2×#41—536no—
1011C2×#41—533no—
1012C2×#41—533no—
1013C2×#41—536no—
1014C2×#41—5312no—
1015C2×#41—536no—
1016C2×#41—533no—
1017C2×#41—536no—
1018C2×#41—533no—
1019C2×#41—533no—
1020C2×#41—533no—
1021C2×#41—533no—
1022C2×#41—536no—
1023C2×#41—533no—
1024C2×#41—533no—
1025C2×#41—533no—
1026C2×#41—533no—
1027C2×#41—533no—
1028C2×#41—533no—
1029C2×#41—531no—
1030C2×#41—536no—
1031C2×#41—533no—
1032C2×#41—536no—
1033C2×#41—533no—
1034C2×#41—10624no—
1035C2×#41—10624no—
1036C2×#41—10624no—
1037C2×#41—10624no—
1038C2×#41—10624no—
1039C2×#41—10648no—
1040C2×#41—10616no—
1041C2×#41—10624no—
1042C2×#41—1068no—
1043C2×#41C22×D5313yes—
1044C2×#41C22×D5313yes—
1045C2×#41C22×D5313yes—
1046C2×#41C22×D5311yescharacteristic
1047C2×#41C22×D5312yes—
1048C2×#41C22×D5311yescharacteristic
1049C22×Q8—531no—
1050C22×Q8—533no—
1051C22×Q8—533no—
1052C22×Q8—533no—
1053C22×Q8—531no—
1054C22×Q8—532no—
1055C22×Q8—533no—
1056C22×Q8—533no—
1057C22×Q8—536no—
1058C22×Q8—533no—
1059C22×Q8C22×D5311yescharacteristic
1060C22×D4—533no—
1061C22×D4—533no—
1062C22×D4—536no—
1063C22×D4—533no—
1064C22×D4—536no—
1065C22×D4—5312no—
1066C22×D4—536no—
1067C22×D4—536no—
1068C22×D4—536no—
1069C22×D4—533no—
1070C22×D4—533no—
1071C22×D4—536no—
1072C22×D4—533no—
1073C22×D4—536no—
1074C22×D4—533no—
1075C22×D4—5312no—
1076C22×D4—533no—
1077C22×D4—533no—
1078C22×D4C22×D5313yes—
1079C22×D4C22×D5316yes—
1080C22×D4C22×D5313yes—
1081C22×D4C22×D5316yes—
1082C23×C4—533no—
1083C23×C4—536no—
1084C23×C4—536no—
1085C23×C4—536no—
1086C23×C4—533no—
1087C23×C4—536no—
1088C23×C4C22×D5313yes—
1089C4⋊Q8—536no—
1090C4⋊Q8—536no—
1091C4⋊Q8—536no—
1092C4⋊Q8—536no—
1093#127—536no—
1094#127—536no—
1095#127—536no—
1096#127C22×D5316yes—
1097#124—536no—
1098#124—536no—
1099#124—536no—
1100#124—536no—
1101#124—536no—
1102#124—536no—
1103#124—536no—
1104#124C22×D5316yes—
1105#123—536no—
1106#123—5312no—
1107#123—536no—
1108#123—536no—
1109#123—536no—
1110#123—5312no—
1111#123—536no—
1112#123—536no—
1113#123—5312no—
1114#123—5312no—
1115#123—536no—
1116#123C22×D5316yes—
1117C22⋊Q8—533no—
1118C22⋊Q8—536no—
1119C22⋊Q8—531no—
1120C22⋊Q8—536no—
1121C22⋊Q8—533no—
1122C22⋊Q8—536no—
1123C22⋊Q8—536no—
1124C22⋊Q8—536no—
1125C22⋊Q8—533no—
1126C22⋊Q8—536no—
1127C22⋊Q8—536no—
1128C22⋊Q8—533no—
1129C22⋊Q8—5312no—
1130C22⋊Q8—536no—
1131C22⋊Q8—536no—
1132C22⋊Q8—536no—
1133C22⋊Q8—532no—
1134C22⋊Q8—533no—
1135C22⋊Q8—5312no—
1136C22⋊Q8—536no—
1137C22⋊Q8—5312no—
1138C22⋊Q8—5312no—
1139C22⋊Q8—5312no—
1140C22⋊Q8—536no—
1141C22⋊Q8C22×D5313yes—
1142C22⋊Q8C22×D5316yes—
1143C22⋊Q8C22×D5311yescharacteristic
1144#121—533no—
1145#121—536no—
1146#121—5312no—
1147#121—536no—
1148#121—5312no—
1149#121—536no—
1150#121—5312no—
1151#121—5312no—
1152#121—5312no—
1153#121—5312no—
1154#121—536no—
1155#121—536no—
1156#121—536no—
1157#121—5312no—
1158#121—5312no—
1159#121—5312no—
1160#121—533no—
1161#121—536no—
1162#121—536no—
1163#121—533no—
1164#121—5312no—
1165#121—536no—
1166#121—531no—
1167#121—533no—
1168#121—536no—
1169#121—536no—
1170#121—531no—
1171#121—532no—
1172#121—536no—
1173#121—536no—
1174#121—5312no—
1175#121—536no—
1176#121—5312no—
1177#121—5312no—
1178#121—5312no—
1179#121—532no—
1180#121—536no—
1181#121—532no—
1182#121C22×D5316yes—
1183#121C22×D53112yes—
1184#121C22×D5316yes—
1185#121C22×D5313yes—
1186#121C22×D5316yes—
1187#121C22×D5316yes—
1188#121C22×D5313yes—
1189#120—536no—
1190#120—5312no—
1191#120—5312no—
1192#120—536no—
1193#120—536no—
1194#120—5312no—
1195#120—536no—
1196#120—536no—
1197#120—536no—
1198#120—536no—
1199#120C22×D53112yes—
1200#120C22×D5316yes—
1201C4×Q8—532no—
1202C4×Q8—536no—
1203C4×Q8—536no—
1204C4×Q8C22×D5312yes—
1205C4×D4—536no—
1206C4×D4—5312no—
1207C4×D4—5312no—
1208C4×D4—5312no—
1209C4×D4—536no—
1210C4×D4—536no—
1211C4×D4—536no—
1212C4×D4—536no—
1213C4×D4—536no—
1214C4×D4—5312no—
1215C4×D4—5312no—
1216C4×D4—5312no—
1217C4×D4—536no—
1218C4×D4—536no—
1219C4×D4—536no—
1220C4×D4C22×D5316yes—
1221C4×D4C22×D5316yes—
1222C4×D4C22×D5316yes—
1223#117—533no—
1224#117—533no—
1225#117—533no—
1226#117—536no—
1227#117—536no—
1228#117C22×D5313yes—
1229C2×C4⋊C4—536no—
1230C2×C4⋊C4—533no—
1231C2×C4⋊C4—536no—
1232C2×C4⋊C4—536no—
1233C2×C4⋊C4—533no—
1234C2×C4⋊C4—536no—
1235C2×C4⋊C4—536no—
1236C2×C4⋊C4—536no—
1237C2×C4⋊C4—531no—
1238C2×C4⋊C4—5312no—
1239C2×C4⋊C4C22×D5313yes—
1240C2×C22⋊C4—536no—
1241C2×C22⋊C4—536no—
1242C2×C22⋊C4—536no—
1243C2×C22⋊C4—536no—
1244C2×C22⋊C4—5312no—
1245C2×C22⋊C4—5312no—
1246C2×C22⋊C4C22×D5316yes—
1247C2×C42—536no—
1248C24—533no—
1249C24—536no—
1250C24—536no—
1251C24—533no—
1252C24C23×D5313yes—
1253C24C23×D5316yes—
1254#41—24no—
1255#41—28no—
1256#41—212no—
1257#41—212no—
1258#41—212no—
1259#41—538no—
1260#41—5324no—
1261#41—5324no—
1262#41—1064no—
1263#41—10612no—
1264#41—10612no—
1265#41—10612no—
1266#41—10612no—
1267#41—10612no—
1268#41—10612no—
1269#41—10612no—
1270#41—10624no—
1271#41—10624no—
1272#41—10612no—
1273#41—10624no—
1274#41—10612no—
1275#41—10624no—
1276#41—10612no—
1277#41—10624no—
1278#41—10624no—
1279#41—10624no—
1280#41—10624no—
1281#41—10612no—
1282#41—1064no—
1283#41—10612no—
1284#41—10648no—
1285#41—10624no—
1286#41—10624no—
1287#41—10612no—
1288#41—10612no—
1289#41—1064no—
1290#41—10612no—
1291#41—10624no—
1292#41—10612no—
1293#41—10612no—
1294#41D4×D5318yescomplemented
1295C2×Q8—24no—
1296C2×Q8—538no—
1297C2×Q8—533no—
1298C2×Q8—533no—
1299C2×Q8—531no—
1300C2×Q8—533no—
1301C2×Q8—536no—
1302C2×Q8—533no—
1303C2×Q8—533no—
1304C2×Q8—533no—
1305C2×Q8—536no—
1306C2×Q8—10612no—
1307C2×Q8—10612no—
1308C2×Q8—10624no—
1309C2×Q8—10612no—
1310C2×Q8—10612no—
1311C2×Q8—10612no—
1312C2×Q8—1068no—
1313C2×Q8—1064no—
1314C2×Q8—10612no—
1315C2×Q8C23×D5311yescharacteristic
1316C2×Q8C23×D5313yes—
1317C2×Q8C23×D5311yescharacteristic
1318C2×D4—212no—
1319C2×D4—224no—
1320C2×D4—212no—
1321C2×D4—86no—
1322C2×D4—536no—
1323C2×D4—5324no—
1324C2×D4—533no—
1325C2×D4—533no—
1326C2×D4—5312no—
1327C2×D4—536no—
1328C2×D4—536no—
1329C2×D4—533no—
1330C2×D4—531no—
1331C2×D4—533no—
1332C2×D4—531no—
1333C2×D4—536no—
1334C2×D4—533no—
1335C2×D4—533no—
1336C2×D4—536no—
1337C2×D4—532no—
1338C2×D4—536no—
1339C2×D4—536no—
1340C2×D4—5312no—
1341C2×D4—536no—
1342C2×D4—533no—
1343C2×D4—533no—
1344C2×D4—533no—
1345C2×D4—532no—
1346C2×D4—533no—
1347C2×D4—531no—
1348C2×D4—531no—
1349C2×D4—533no—
1350C2×D4—532no—
1351C2×D4—536no—
1352C2×D4—10612no—
1353C2×D4—10612no—
1354C2×D4—10612no—
1355C2×D4—10612no—
1356C2×D4—10612no—
1357C2×D4—10624no—
1358C2×D4—10624no—
1359C2×D4—10612no—
1360C2×D4—10624no—
1361C2×D4—10624no—
1362C2×D4—10624no—
1363C2×D4—10648no—
1364C2×D4—10612no—
1365C2×D4—10624no—
1366C2×D4—10612no—
1367C2×D4—42412no—
1368C2×D4—4246no—
1369C2×D4C23×D5316yes—
1370C2×D4C23×D5316yes—
1371C2×D4C23×D5313yes—
1372C2×D4C23×D5313yes—
1373C2×D4C23×D5316yes—
1374C2×D4C23×D5316yes—
1375C2×D4C23×D53112yes—
1376C2×D4C23×D5316yes—
1377C2×D4C23×D5313yes—
1378C22×C4—212no—
1379C22×C4—533no—
1380C22×C4—5324no—
1381C22×C4—533no—
1382C22×C4—531no—
1383C22×C4—533no—
1384C22×C4—533no—
1385C22×C4—536no—
1386C22×C4—533no—
1387C22×C4—536no—
1388C22×C4—5312no—
1389C22×C4—536no—
1390C22×C4—536no—
1391C22×C4—536no—
1392C22×C4—536no—
1393C22×C4—536no—
1394C22×C4—533no—
1395C22×C4—533no—
1396C22×C4—536no—
1397C22×C4—532no—
1398C22×C4—531no—
1399C22×C4—533no—
1400C22×C4—532no—
1401C22×C4—536no—
1402C22×C4—5312no—
1403C22×C4—10624no—
1404C22×C4—10624no—
1405C22×C4—10624no—
1406C22×C4—10612no—
1407C22×C4—4246no—
1408C22×C4C23×D5313yes—
1409C22×C4C23×D5316yes—
1410C22×C4C23×D5313yes—
1411C22×C4C23×D5313yes—
1412C22×C4C23×D5313yes—
1413C22×C4C23×D5311yescharacteristic
1414C22×C4C23×D5316yes—
1415C22×C4C23×D5313yes—
1416C4⋊C4—536no—
1417C4⋊C4—533no—
1418C4⋊C4—5312no—
1419C4⋊C4—536no—
1420C4⋊C4—536no—
1421C4⋊C4—5312no—
1422C4⋊C4—536no—
1423C4⋊C4—536no—
1424C4⋊C4—5312no—
1425C4⋊C4—532no—
1426C4⋊C4—531no—
1427C4⋊C4—532no—
1428C4⋊C4—536no—
1429C4⋊C4—536no—
1430C4⋊C4C23×D5313yes—
1431C4⋊C4C23×D5316yes—
1432C4⋊C4C23×D5316yes—
1433C4⋊C4C23×D5311yescharacteristic
1434C4⋊C4C23×D5312yes—
1435C22⋊C4—5312no—
1436C22⋊C4—536no—
1437C22⋊C4—536no—
1438C22⋊C4—5312no—
1439C22⋊C4—536no—
1440C22⋊C4—536no—
1441C22⋊C4—536no—
1442C22⋊C4—536no—
1443C22⋊C4—536no—
1444C22⋊C4—536no—
1445C22⋊C4—5312no—
1446C22⋊C4—536no—
1447C22⋊C4—536no—
1448C22⋊C4—536no—
1449C22⋊C4—532no—
1450C22⋊C4—532no—
1451C22⋊C4—536no—
1452C22⋊C4—532no—
1453C22⋊C4C23×D5316yes—
1454C22⋊C4C23×D53112yes—
1455C22⋊C4C23×D5316yes—
1456C22⋊C4C23×D5316yes—
1457C22⋊C4C23×D5316yes—
1458C22⋊C4C23×D5312yes—
1459C42—536no—
1460C42—536no—
1461C42—536no—
1462C42C23×D5316yes—
1463C23—26no—
1464C23—212no—
1465C23—43no—
1466C23—46no—
1467C23—43no—
1468C23—46no—
1469C23—533no—
1470C23—531no—
1471C23—5312no—
1472C23—532no—
1473C23—533no—
1474C23—531no—
1475C23—10612no—
1476C23—10612no—
1477C23—1066no—
1478C23—2123no—
1479C23—2126no—
1480C23—2126no—
1481C23—2123no—
1482C23—2126no—
1483C23—2126no—
1484C23—2123no—
1485C23—2123no—
1486C23C24×D5313yes—
1487C23C24×D5311yescharacteristic
1488C23C24×D5316yes—
1489C23C24×D5313yes—
1490Q8—26no—
1491Q8—22no—
1492Q8—5312no—
1493Q8—1062no—
1494Q8—1066no—
1495Q8—10612no—
1496Q8—1066no—
1497Q8—1066no—
1498Q8—1066no—
1499Q8—10612no—
1500Q8—1066no—
1501Q8C2×D4×D5314yes—
1502D4—212no—
1503D4—212no—
1504D4—26no—
1505D4—212no—
1506D4—26no—
1507D4—46no—
1508D4—412no—
1509D4—46no—
1510D4—5324no—
1511D4—5312no—
1512D4—1062no—
1513D4—1066no—
1514D4—1064no—
1515D4—1066no—
1516D4—1066no—
1517D4—1062no—
1518D4—1066no—
1519D4—1066no—
1520D4—1066no—
1521D4—10612no—
1522D4—1062no—
1523D4—1066no—
1524D4—1066no—
1525D4—1066no—
1526D4—10612no—
1527D4—10624no—
1528D4—10612no—
1529D4—10612no—
1530D4—1062no—
1531D4—1066no—
1532D4—2122no—
1533D4—2126no—
1534D4—2126no—
1535D4—2122no—
1536D4—2126no—
1537D4—21212no—
1538D4—2126no—
1539D4C2×D4×D53112yes—
1540C2×C4—26no—
1541C2×C4—22no—
1542C2×C4—26no—
1543C2×C4—26no—
1544C2×C4—26no—
1545C2×C4—212no—
1546C2×C4—46no—
1547C2×C4—5312no—
1548C2×C4—533no—
1549C2×C4—531no—
1550C2×C4—534no—
1551C2×C4—5312no—
1552C2×C4—5312no—
1553C2×C4—5312no—
1554C2×C4—532no—
1555C2×C4—536no—
1556C2×C4—531no—
1557C2×C4—533no—
1558C2×C4—536no—
1559C2×C4—1064no—
1560C2×C4—10612no—
1561C2×C4—10612no—
1562C2×C4—10612no—
1563C2×C4—10612no—
1564C2×C4—10612no—
1565C2×C4—10624no—
1566C2×C4—1066no—
1567C2×C4—10612no—
1568C2×C4—1066no—
1569C2×C4—1062no—
1570C2×C4—10612no—
1571C2×C4—1066no—
1572C2×C4—1066no—
1573C2×C4—2122no—
1574C2×C4—2126no—
1575C2×C4—21212no—
1576C2×C4—2126no—
1577C2×C4C2×D4×D53112yes—
1578C2×C4C24×D5312yes—
1579C2×C4C24×D5316yes—
1580C2×C4C24×D5312yes—
1581C2×C4C24×D5313yes—
1582C2×C4C24×D5311yescharacteristic
1583C2×C4C24×D5313yes—
1584C2×C4C24×D5311yescharacteristic
1585C22—23no—
1586C22—23no—
1587C22—21no—
1588C22—23no—
1589C22—26no—
1590C22—21no—
1591C22—23no—
1592C22—26no—
1593C22—23no—
1594C22—26no—
1595C22—21no—
1596C22—86no—
1597C22—812no—
1598C22—532no—
1599C22—536no—
1600C22—1061no—
1601C22—1063no—
1602C22—1061no—
1603C22—1063no—
1604C22—1062no—
1605C22—1063no—
1606C22—1061no—
1607C22—1062no—
1608C22—1063no—
1609C22—1061no—
1610C22—1061no—
1611C22—1062no—
1612C22—1063no—
1613C22—4246no—
1614C22—42412no—
1615C22—42412no—
1616C22—21212no—
1617C22C22×D4×D5316yes—
1618C22C25×D5311yescharacteristic
1619C4—21no—
1620C4—22no—
1621C4—23no—
1622C4—26no—
1623C4—22no—
1624C4—532no—
1625C4—536no—
1626C4—1063no—
1627C4—1066no—
1628C4—1061no—
1629C4—1066no—
1630C4—1062no—
1631C4C22×D4×D5312yes—
1632C4C22×D4×D5316yes—
1633C2—26no—
1634C2—41no—
1635C2—46no—
1636C2—43no—
1637C2—1066no—
1638C2—1062no—
1639C2—2121no—
1640C2—2123no—
1641C2—2122no—
1642C2C23×D4×D5311yescharacteristic
1643C2#2028952511yescharacteristic
1644C2#2028952811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3488C2
hypercenter#3488D53
hypocenterC53#62853
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3488

Complements

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

NH ≅ G/Ntype
1. C2×#16811459C2semidirect
2. C2×#16811458C2semidirect
3. #20288483C2semidirect
4. #20288480C2semidirect
5. #20288475C2semidirect
6. #20288471C2semidirect
7. #20288396C2semidirect
8. #20288395C2semidirect
9. #20288394C2semidirect
10. #20288390C2semidirect
11. #20288387C2semidirect
12. #20288386C2semidirect
13. #20288383C2semidirect
14. #20288382C2semidirect
15. #20288380C2semidirect
16. #20288377C2semidirect
17. #20288375C2semidirect
18. #20288046C2semidirect
19. #20288045C2semidirect
20. C2×#16811202C2semidirect
21. #537×D53C2semidirect
22. #520×D53C2semidirect
23. C53×#3488C2semidirect
26. C2×#13133265C22semidirect
27. C2×#13133265C22semidirect
28. C2×#13133264C22semidirect
29. C2×#13133264C22semidirect
30. C2×#13133264C22semidirect
31. C2×#13133264C22semidirect
32. C2×#13133264C22semidirect
33. C2×#13133263C22semidirect
34. C2×#13133263C22semidirect
35. C2×#13133262C22semidirect
36. C2×#13133262C22semidirect
37. C2×#13133262C22semidirect
38. C2×#13133262C22semidirect
39. C22×#11719945C22semidirect
40. C22×#11719945C22semidirect
41. C22×#11719947C22semidirect
42. C22×#11719947C22semidirect
44. C2×#41×D53C22semidirect
45. C2×#41×D53C22semidirect
46. C2×#41×D53C22semidirect
47. C2×#41×D53C22semidirect
48. C2×#41×D53C22semidirect
49. #16811293C22semidirect
50. #16811292C22semidirect
51. #16811291C22semidirect
52. Q8×D212C22semidirect
53. D4×Dic106C22semidirect
54. Q8×C22⋊D53C22semidirect
55. #16811286C22semidirect
56. #16811285C22semidirect
57. #16811282C22semidirect
58. #16811281C22semidirect
59. #16811280C22semidirect
60. #16811280C22semidirect
61. #16811279C22semidirect
62. #16811279C22semidirect
63. #16811278C22semidirect
64. #16811277C22semidirect
65. #16811275C22semidirect
66. #16811273C22semidirect
67. #16811272C22semidirect
68. #16811271C22semidirect
69. #16811270C22semidirect
70. #16811270C22semidirect
71. #16811269C22semidirect
72. #16811268C22semidirect
73. #16811267C22semidirect
74. #16811267C22semidirect
75. #16811266C22semidirect
76. #16811263C22semidirect
77. #16811262C22semidirect
78. #16811260C22semidirect
79. #16811260C22semidirect
80. #16811258C22semidirect
81. #16811257C22semidirect
82. D4×C22⋊D53C22semidirect
83. D4×C22⋊D53C22semidirect
84. #16811255C22semidirect
85. #16811204C22semidirect
86. #16811203C22semidirect
87. #16811203C22semidirect
88. #16811203C22semidirect
89. #16811202C22semidirect
90. #16811202C22semidirect
91. #16811202C22semidirect
92. #16811202C22semidirect
93. #16811202C22semidirect
94. #16811202C22semidirect
95. #16811202C22semidirect
96. #16811202C22semidirect
97. #16811202C22semidirect
98. #16811202C22semidirect
99. #16811201C22semidirect
100. #16811201C22semidirect
101. #16811200C22semidirect
102. #16811199C22semidirect
103. #16811196C22semidirect
104. #16811196C22semidirect
105. #16811195C22semidirect
106. #16811194C22semidirect
107. #16811193C22semidirect
108. #16811190C22semidirect
109. #16811189C22semidirect
110. #16811189C22semidirect
111. #16811188C22semidirect
112. #16811186C22semidirect
113. #16811184C22semidirect
114. #16811183C22semidirect
115. #16811183C22semidirect
116. #16811172C22semidirect
117. #16811171C22semidirect
118. #16811170C22semidirect
119. #16811170C22semidirect
120. #16811135C22semidirect
121. #16811134C22semidirect
122. #16811133C22semidirect
123. #16811133C22semidirect
124. #16811132C22semidirect
125. #16811132C22semidirect
126. #16811130C22semidirect
127. #16811129C22semidirect
128. C2×#13133197C22semidirect
129. C2×#13133196C22semidirect
130. C2×#13133194C22semidirect
131. C22⋊Q8×D53C22semidirect
132. C22⋊Q8×D53C22semidirect
133. C2×#13133190C22semidirect
134. C2×#13133189C22semidirect
135. C2×#13133188C22semidirect
136. C2×#13133188C22semidirect
137. #121×D53C22semidirect
138. #121×D53C22semidirect
139. #121×D53C22semidirect
140. #16811106C22semidirect
141. #16811105C22semidirect
142. #16811104C22semidirect
143. #16811103C22semidirect
144. #16811102C22semidirect
145. C4×Q8×D53C22semidirect
146. C4×D4×D53C22semidirect
147. #117×D53C22semidirect
148. C2×C4⋊C4×D53C22semidirect
149. C2×H(5,𝔽2)×C53C22semidirect
150. C22×#41×C53C22semidirect
151. C53×#550C22semidirect
152. C53×#548C22semidirect
153. C53×#546C22semidirect
154. D42×C53C22semidirect
155. C53×#537C22semidirect
156. C53×#535C22semidirect
157. C53×#525C22semidirect
158. C2×#121×C53C22semidirect
159. C53×#520C22semidirect
217. #41×D53D4semidirect
436. #41×C53C2×D4semidirect
500. #11719949C2×D4semidirect
506. Q8×D53C2×D4semidirect
520. #11719947C2×D4semidirect
530. D4×D53C2×D4semidirect
546. #11719945C2×D4semidirect
563. C2×C4×D53C2×D4semidirect
828. #3488D53semidirect
861. C2×H(5,𝔽2)C2×D53semidirect
872. C22×#41C2×D53semidirect
876. #550C2×D53semidirect
888. #548C2×D53semidirect
906. #546C2×D53semidirect
912. D42C2×D53semidirect
930. #537C2×D53semidirect
942. #535C2×D53semidirect
958. #525C2×D53semidirect
971. C2×#121C2×D53semidirect
977. #520C2×D53semidirect
982. C53#62853semidirect
1294. #41D4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168114592
C2×#168114582
#202884832
#202884802
#202884752
#202884712
#202883962
#202883952
#202883942
#202883902
#202883872
#202883862
#202883832
#202883822
#202883802
#202883772
#202883752
#202880462
#202880452
C2×#168112022
#537×D532
#520×D532
C53×#34882
#6285353