Finite Group Databasebeta

← #28293208

Subgroups — #28293208

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×#16811460C211yesmaximal, characteristic, complemented
2C2×#16811459C211yesmaximal, characteristic, complemented
3#20288485C212yesmaximal, complemented
4#20288483C212yesmaximal, complemented
5#20288475C216yesmaximal, complemented
6#20288473C216yesmaximal, complemented
7#20288393C213yesmaximal, complemented
8#20288392C212yesmaximal, complemented
9#20288391C213yesmaximal, complemented
10#20288389C216yesmaximal, complemented
11#20288388C211yesmaximal, characteristic, complemented
12#20288385C211yesmaximal, characteristic, complemented
13#20288384C211yesmaximal, characteristic, complemented
14#20288381C212yesmaximal, complemented
15#20288379C213yesmaximal, complemented
16#20288378C216yesmaximal, complemented
17#20288376C213yesmaximal, complemented
18#20288047C213yesmaximal, complemented
19#20288045C213yesmaximal, complemented
20C2×#16811203C213yesmaximal, complemented
21#537×D53C213yesmaximal, complemented
22#520×D53C211yesmaximal, characteristic, complemented
23C53×#3489C211yesmaximal, characteristic, complemented
24#16811460—216no—
25#16811459—216no—
26C2×#13133265C2213yescomplemented
27C2×#13133265C2211yescharacteristic, complemented
28C2×#13133265C2212yescomplemented
29C2×#13133265C2211yescharacteristic, complemented
30C2×#13133264C2213yescomplemented
31C2×#13133264C2211yescharacteristic, complemented
32C2×#13133263C2213yescomplemented
33C2×#13133263C2211yescharacteristic, complemented
34C2×#13133263C2211yescharacteristic, complemented
35C2×#13133263C2213yescomplemented
36C2×#13133263C2216yescomplemented
37C2×#13133262C2213yescomplemented
38C2×#13133262C2213yescomplemented
39C22×#11719949C2213yescomplemented
40C22×#11719949C2212yescomplemented
41C22×#11719945C2213yescomplemented
42C22×#11719945C2213yescomplemented
43C2×#41×D53C2211yescharacteristic
44C2×#41×D53C2213yescomplemented
45C2×#41×D53C2213yescomplemented
46C2×#41×D53C2216yescomplemented
47C2×#41×D53C2213yescomplemented
48C2×#41×D53C2211yescharacteristic, complemented
49#16811295C2212yescomplemented
50#16811294C2216yescomplemented
51#16811292C2212yescomplemented
52#16811291C2216yescomplemented
53#16811288C2216yescomplemented
54Q8×C22⋊D53C2212yescomplemented
55#16811286C2216yescomplemented
56#16811285C2212yescomplemented
57#16811284C2212yescomplemented
58#16811284C2212yescomplemented
59#16811283C2216yescomplemented
60#16811283C2216yescomplemented
61#16811282C2216yescomplemented
62#16811281C2216yescomplemented
63#16811276C2216yescomplemented
64#16811275C2216yescomplemented
65#16811274C22112yescomplemented
66#16811272C2216yescomplemented
67#16811271C22112yescomplemented
68#16811269C2216yescomplemented
69#16811268C2216yescomplemented
70#16811266C2216yescomplemented
71#16811265C22112yescomplemented
72#16811265C22112yescomplemented
73#16811264C2216yescomplemented
74#16811264C2216yescomplemented
75#16811263C22112yescomplemented
76#16811262C22112yescomplemented
77#16811261C2216yescomplemented
78#16811261C2216yescomplemented
79D4×D212C2216yescomplemented
80D4×D212C2216yescomplemented
81#16811257C22112yescomplemented
82#16811257C2216yescomplemented
83D4×C22⋊D53C2216yescomplemented
84#16811255C22112yescomplemented
85#16811204C2213yescomplemented
86#16811203C2216yescomplemented
87#16811203C2216yescomplemented
88#16811203C2213yescomplemented
89#16811203C2216yescomplemented
90#16811203C2216yescomplemented
91#16811203C2216yescomplemented
92#16811203C2216yescomplemented
93#16811203C2216yescomplemented
94#16811203C2216yescomplemented
95#16811203C2213yescomplemented
96#16811202C2213yescomplemented
97#16811202C2216yescomplemented
98#16811202C2211yescharacteristic, complemented
99#16811201C2213yescomplemented
100#16811201C2213yescomplemented
101#16811200C22112yescomplemented
102#16811198C2216yescomplemented
103#16811197C2213yescomplemented
104#16811196C2213yescomplemented
105#16811196C2213yescomplemented
106#16811195C2216yescomplemented
107#16811192C2213yescomplemented
108#16811191C2216yescomplemented
109#16811189C2213yescomplemented
110#16811189C2213yescomplemented
111#16811188C2216yescomplemented
112#16811187C2213yescomplemented
113#16811184C2216yescomplemented
114#16811184C22112yescomplemented
115#16811183C2216yescomplemented
116#16811174C2216yescomplemented
117#16811172C2216yescomplemented
118#16811170C2216yescomplemented
119#16811170C2216yescomplemented
120#16811136C2216yescomplemented
121#16811136C2216yescomplemented
122#16811135C2213yescomplemented
123#16811134C2213yescomplemented
124#16811132C2216yescomplemented
125#16811132C2216yescomplemented
126#16811131C22112yescomplemented
127#16811130C2213yescomplemented
128C2×#13133195C2216yescomplemented
129C2×#13133193C2213yescomplemented
130C22⋊Q8×D53C2216yescomplemented
131C22⋊Q8×D53C2216yescomplemented
132C2×#13133192C2213yescomplemented
133C2×#13133192C2216yescomplemented
134C2×#13133191C2213yescomplemented
135C2×#13133190C2216yescomplemented
136C2×#13133190C2216yescomplemented
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
149C2×2−1+4×C53C2211yescharacteristic, complemented
150C22×#41×C53C2211yescharacteristic, complemented
151D4×Q8×C53C2212yescomplemented
152C53×#548C2212yescomplemented
153C53×#547C2216yescomplemented
154C53×#546C2216yescomplemented
155C53×#537C2213yescomplemented
156C53×#536C2213yescomplemented
157C53×#525C2213yescomplemented
158C2×C22⋊Q8×C53C2213yescomplemented
159C53×#520C2211yescharacteristic, complemented
160#13133265—28no—
161#13133265—28no—
162#13133265—216no—
163#13133265—224no—
164#13133264—28no—
165#13133264—224no—
166#13133263—28no—
167#13133263—28no—
168#13133263—224no—
169#13133263—248no—
170#13133263—224no—
171#13133262—224no—
172#13133262—224no—
173C2×#11719949—216no—
174C2×#11719949—224no—
175C2×#11719949C2313yes—
176C2×#11719949C2316yes—
177C2×#11719949C2311yescharacteristic
178C2×#11719949C2312yes—
179C2×#11719949C2316yes—
180C2×#11719949C2316yes—
181C2×#11719949C2313yes—
182C2×#11719949C2316yes—
183C2×#11719949C2313yes—
184C2×#11719949C2311yescharacteristic
185C2×#11719945—224no—
186C2×#11719945—224no—
187C2×#11719945C2316yes—
188C2×#11719945C23112yes—
189C2×#11719945C2313yes—
190C2×#11719945C2316yes—
191C2×#11719945C2313yes—
192C2×#11719945C2313yes—
193C2×#11719945C2313yes—
194C2×#11719945C2313yes—
195C2×#11719945C2316yes—
196C2×#11719945C2313yes—
197C2×#11719945C2313yes—
198C2×#11719945C2313yes—
199C2×#11719945C2313yes—
200C2×#11719945C2313yes—
201C2×#11719945C2313yes—
202C2×#11719945C2311yescharacteristic
203C2×#11719945C2313yes—
204C2×#11719947C2313yes—
205C2×#11719947C2316yes—
206C2×#11719947C2313yes—
207C2×#11719947C2316yes—
208C2×#11719947C2313yes—
209C2×#11719947C2316yes—
210C2×#11719947C2311yescharacteristic
211C2×#11719947C2313yes—
212#41×D53—28no—
213#41×D53—248no—
214#41×D53—224no—
215#41×D53—224no—
216#41×D53—224no—
217#41×D53D4116yescomplemented
218C22×Dic106C2313yes—
219C22×Dic106C2313yes—
220C2×Q8×D53C2316yes—
221C2×Q8×D53C2313yes—
222C2×Q8×D53C2311yescharacteristic
223C2×Q8×D53C2313yes—
224C2×Q8×D53C2313yes—
225C2×Q8×D53C2311yescharacteristic
226C22×D212C2313yes—
227C22×D212C2316yes—
228C22×D212C2316yes—
229C22×D212C2313yes—
230C22×D212C2313yes—
231C22×D212C2316yes—
232C22×C22⋊D53C2313yes—
233C22×C22⋊D53C2313yes—
234C22×C22⋊D53C2316yes—
235C22×C22⋊D53C2316yes—
236C2×D4×D53C2316yes—
237C2×D4×D53C23112yes—
238C2×D4×D53C2313yes—
239C2×D4×D53C2316yes—
240C2×D4×D53C2316yes—
241C2×D4×D53C2316yes—
242C2×D4×D53C2313yes—
243C2×D4×D53C2313yes—
244C2×D4×D53C2313yes—
245C2×D4×D53C23112yes—
246C2×D4×D53C2313yes—
247C22×C4×D53C2316yes—
248C22×C4×D53C2316yes—
249C22×C4×D53C2316yes—
250C22×C4×D53C2313yes—
251C22×C4×D53C2316yes—
252C22×C4×D53C2313yes—
253#13133216C2316yes—
254#13133216C2316yes—
255#13133215C2316yes—
256#13133214C2316yes—
257#13133213C2316yes—
258#13133213C2316yes—
259#13133213C2316yes—
260#13133206C2316yes—
261#13133206C2316yes—
262#13133205C2316yes—
263#13133203C2316yes—
264#13133203C2316yes—
265#13133203C2316yes—
266#13133203C2316yes—
267#13133202C2316yes—
268#13133202C23112yes—
269#13133202C2316yes—
270#13133202C23112yes—
271#13133201C2316yes—
272#13133200C23112yes—
273#13133200C2316yes—
274#13133199C2316yes—
275#13133199C2316yes—
276#13133198C2316yes—
277#13133197C2316yes—
278#13133197C2313yes—
279#13133197C2311yescharacteristic
280#13133196C2316yes—
281#13133196C2313yes—
282#13133196C2311yescharacteristic
283#13133195C23112yes—
284#13133195C23112yes—
285#13133195C23112yes—
286#13133195C23112yes—
287#13133195C2316yes—
288#13133195C2316yes—
289#13133194C23112yes—
290#13133194C2316yes—
291#13133194C2312yes—
292#13133193C2316yes—
293#13133193C2316yes—
294#13133193C2316yes—
295#13133193C2316yes—
296#13133193C2313yes—
297#13133193C2313yes—
298#13133192C23112yes—
299#13133192C23112yes—
300#13133192C2316yes—
301#13133192C2316yes—
302#13133192C2316yes—
303#13133192C2316yes—
304#13133192C23112yes—
305#13133192C2313yes—
306#13133192C2316yes—
307#13133192C2313yes—
308#13133192C2316yes—
309#13133191C23112yes—
310#13133191C2316yes—
311#13133191C2316yes—
312#13133191C2316yes—
313#13133191C2316yes—
314#13133191C2313yes—
315#13133191C2313yes—
316#13133190C23112yes—
317#13133190C23112yes—
318#13133190C23112yes—
319#13133190C23112yes—
320#13133190C23112yes—
321#13133190C2316yes—
322#13133190C23112yes—
323#13133190C23112yes—
324#13133190C2316yes—
325#13133190C2316yes—
326#13133190C2316yes—
327#13133190C2312yes—
328#13133190C2316yes—
329#13133189C23112yes—
330#13133189C23112yes—
331#13133189C23112yes—
332#13133189C2316yes—
333#13133189C2312yes—
334#13133188C2316yes—
335#13133188C2313yes—
336#13133188C2316yes—
337#13133188C2311yescharacteristic
338#13133188C2312yes—
339#13133187C2316yes—
340#13133187C23112yes—
341#13133187C2316yes—
342#13133187C2316yes—
343#13133187C23112yes—
344#13133187C23112yes—
345#13133186C2316yes—
346#13133185C2316yes—
347#13133185C2316yes—
348#13133185C23112yes—
349#13133185C2316yes—
350Q8×Dic53C2312yes—
351C4×Dic106C2316yes—
352#13133182C2316yes—
353C4×D212C2316yes—
354C4×D212C2316yes—
355C4×D212C2316yes—
356D4×Dic53C2316yes—
357#13133179C2316yes—
358#13133179C23112yes—
359#13133179C23112yes—
360C4×C22⋊D53C2316yes—
361C4×C22⋊D53C2316yes—
362C4×C22⋊D53C2316yes—
363C4×C22⋊D53C23112yes—
364C4×C22⋊D53C2316yes—
365#13133177C23112yes—
366#13133177C23112yes—
367#13133177C23112yes—
368#13133176C2313yes—
369#13133175C2313yes—
370#13133175C2313yes—
371#13133174C2316yes—
372#13133173C2316yes—
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×#11719921C2316yes—
383C2×#11719921C2316yes—
384C2×#11719921C2316yes—
385C22⋊C4×D53C23112yes—
386C22⋊C4×D53C23112yes—
387C22⋊C4×D53C2316yes—
388C42×D53C2316yes—
3892−1+4×C53—28no—
390C2×#41×C53—28no—
391C2×#41×C53C2316yes—
392C2×#41×C53C2311yescharacteristic
393C2×#41×C53C2313yes—
394C2×#41×C53C2313yes—
395C2×#41×C53C2313yes—
396C2×#41×C53C2311yescharacteristic
397C22×Q8×C53C2311yescharacteristic
398C22×Q8×C53C2312yes—
399C22×Q8×C53C2313yes—
400C22×D4×C53C2313yes—
401C23×C4×C53C2313yes—
402C4⋊Q8×C53C2316yes—
403#124×C53C2316yes—
404#123×C53C2316yes—
405#123×C53C23112yes—
406C22⋊Q8×C53C2316yes—
407C22⋊Q8×C53C2316yes—
408C22⋊Q8×C53C2316yes—
409C22⋊Q8×C53C2313yes—
410C22⋊Q8×C53C2316yes—
411C22⋊Q8×C53C2313yes—
412#121×C53C2316yes—
413#121×C53C2311yescharacteristic
414#121×C53C2313yes—
415#121×C53C23112yes—
416#120×C53C2316yes—
417C4×Q8×C53C2312yes—
418C4×D4×C53C2316yes—
419C4×D4×C53C2316yes—
420C4×D4×C53C2316yes—
421#117×C53C2313yes—
422C2×C4⋊C4×C53C2316yes—
423C2×C4⋊C4×C53C2313yes—
424C2×C22⋊C4×C53C2316yes—
425C24×C53C2413yes—
426C23×D53C2416yes—
427C23×D53C2416yes—
428C23×D53C2416yes—
429C23×D53C2413yes—
430C23×D53C2413yes—
431#41×C53—24no—
432#41×C53—212no—
433#41×C53—224no—
434#41×C53—212no—
435#41×C53—212no—
436#41×C53C2×D418yescomplemented
437C2×Q8×C53—24no—
438C2×Q8×C53—28no—
439C2×Q8×C53—212no—
440C2×Q8×C53C2413yes—
441C2×Q8×C53C2416yes—
442C2×Q8×C53C2413yes—
443C2×Q8×C53C2411yescharacteristic
444C2×D4×C53—212no—
445C2×D4×C53C2416yes—
446C2×D4×C53C2411yescharacteristic
447C2×D4×C53C2416yes—
448C2×D4×C53C2413yes—
449C2×D4×C53C2412yes—
450C2×D4×C53C2416yes—
451C2×D4×C53C2413yes—
452C22×C4×C53—212no—
453C22×C4×C53C2416yes—
454C22×C4×C53C2413yes—
455C22×C4×C53C2416yes—
456C22×C4×C53C2413yes—
457C22×C4×C53C2413yes—
458C22×C4×C53C2411yescharacteristic
459C22×C4×C53C2413yes—
460C22×C4×C53C2416yes—
461C22×C4×C53C2413yes—
462C2×C22⋊D53—212no—
463C2×C22⋊D53—224no—
464C2×C22⋊D53—212no—
465C2×C22⋊D53—86no—
466C2×C22⋊D53C2413yes—
467C2×C22⋊D53C2413yes—
468C2×C22⋊D53C2416yes—
469C2×C22⋊D53C2416yes—
470C2×C22⋊D53C2412yes—
471C2×C22⋊D53C2413yes—
472C2×C22⋊D53C2411yescharacteristic
473C2×C22⋊D53C2413yes—
474C2×C22⋊D53C2411yescharacteristic
475C2×C22⋊D53C2416yes—
476C2×C22⋊D53C2413yes—
477C2×C22⋊D53C2413yes—
478C2×C22⋊D53C2416yes—
479C2×C22⋊D53C24112yes—
480C2×C22⋊D53C2412yes—
481C2×C22⋊D53C2416yes—
482C2×C22⋊D53C2416yes—
483C2×C22⋊D53C2416yes—
484C22×Dic53C2413yes—
485C22×Dic53C2416yes—
486C22×Dic53C2412yes—
487C22×Dic53C2416yes—
488C22×Dic53C2413yes—
489#11719949—24no—
490#11719949—28no—
491#11719949—212no—
492#11719949—224no—
493#11719949—224no—
494#11719949—212no—
495#11719949—212no—
496#11719949—224no—
497#11719949—224no—
498#11719949C2×D418yescomplemented
499Q8×D53—24no—
500Q8×D53—212no—
501Q8×D53—212no—
502Q8×D53—212no—
503Q8×D53—224no—
504Q8×D53C2×D418yescomplemented
505#11719947—212no—
506#11719947—224no—
507#11719947—224no—
508#11719947—224no—
509#11719947—24no—
510#11719947—212no—
511#11719947—212no—
512#11719947C2×D4124yescomplemented
513D4×D53—224no—
514D4×D53—224no—
515D4×D53—212no—
516D4×D53—224no—
517D4×D53—224no—
518D4×D53—248no—
519D4×D53—212no—
520D4×D53—212no—
521D4×D53—212no—
522D4×D53—812no—
523D4×D53C2×D4124yescomplemented
524#11719945—212no—
525#11719945—212no—
526#11719945—248no—
527#11719945—224no—
528#11719945—212no—
529#11719945—212no—
530#11719945—212no—
531#11719945—224no—
532#11719945—212no—
533#11719945—24no—
534#11719945—212no—
535#11719945—212no—
536#11719945—212no—
537#11719945—212no—
538#11719945—224no—
539#11719945—212no—
540#11719945C2×D4124yescomplemented
541C2×D212—212no—
542C2×D212—224no—
543C2×D212—212no—
544C2×D212—212no—
545C2×D212—224no—
546C2×D212—86no—
547C2×D212C24112yes—
548C2×D212C2413yes—
549C2×D212C2413yes—
550C2×D212C2416yes—
551C2×D212C2413yes—
552C2×D212C2411yescharacteristic
553C2×D212C2413yes—
554C2×D212C2416yes—
555C2×D212C2413yes—
556C2×D212C2416yes—
557C2×D212C24112yes—
558C2×D212C2416yes—
559C2×D212C2413yes—
560C2×C4×D53—212no—
561C2×C4×D53—224no—
562C2×C4×D53—224no—
563C2×C4×D53—224no—
564C2×C4×D53—86no—
565C2×C4×D53C2×D4124yescomplemented
566C2×C4×D53C2416yes—
567C2×C4×D53C2416yes—
568C2×C4×D53C24112yes—
569C2×C4×D53C2416yes—
570C2×C4×D53C2413yes—
571C2×C4×D53C2413yes—
572C2×C4×D53C2416yes—
573C2×C4×D53C2413yes—
574C2×C4×D53C2411yescharacteristic
575C2×C4×D53C2416yes—
576C2×C4×D53C2412yes—
577C2×C4×D53C2416yes—
578C2×C4×D53C24112yes—
579C2×C4×D53C2413yes—
580C2×C4×D53C2411yescharacteristic
581C2×C4×D53C2413yes—
582C2×C4×D53C2413yes—
583C2×Dic106—212no—
584C2×Dic106—212no—
585C2×Dic106C2413yes—
586C2×Dic106C2411yescharacteristic
587C2×Dic106C2416yes—
588C2×Dic106C2413yes—
589C2×Dic106C2413yes—
590C2×Dic106C2411yescharacteristic
591C2×Dic106C2413yes—
592C2×Dic106C2413yes—
593C4⋊C4×C53C2413yes—
594C4⋊C4×C53C2416yes—
595C4⋊C4×C53C2416yes—
596C4⋊C4×C53C24112yes—
597C4⋊C4×C53C2411yescharacteristic
598C4⋊C4×C53C2416yes—
599C22⋊C4×C53C2416yes—
600C22⋊C4×C53C24112yes—
601C22⋊C4×C53C2416yes—
602C22⋊C4×C53C2412yes—
603C22⋊C4×C53C2416yes—
604C22⋊C4×C53C2416yes—
605C42×C53C2416yes—
606C22⋊Dic53C2416yes—
607C22⋊Dic53C2416yes—
608C22⋊Dic53C2416yes—
609C22⋊Dic53C2412yes—
610C22⋊Dic53C2412yes—
611#11719921C2416yes—
612#11719921C24112yes—
613#11719921C24112yes—
614#11719921C24112yes—
615#11719921C2416yes—
616#11719921C2416yes—
617#11719921C2416yes—
618#11719921C2416yes—
619#11719921C2416yes—
620#11719921C2416yes—
621#11719921C2416yes—
622#11719921C2416yes—
623#11719921C2412yes—
624C4⋊Dic53C2413yes—
625C4⋊Dic53C2416yes—
626C4⋊Dic53C2416yes—
627C4⋊Dic53C2411yescharacteristic
628C4⋊Dic53C2412yes—
629#11719919C2416yes—
630#11719919C24112yes—
631#11719919C2416yes—
632#11719919C24112yes—
633#11719919C2412yes—
634#11719919C2416yes—
635#11719919C2416yes—
636#11719919C2412yes—
637C4×Dic53C2416yes—
638C4×Dic53C2416yes—
639C4×Dic53C2416yes—
640C23×C53—26no—
641C23×C53—43no—
642C23×C53—43no—
643C23×C53C2513yes—
644C23×C53C2512yes—
645C23×C53C2511yescharacteristic
646C23×C53C2513yes—
647C22×D53—212no—
648C22×D53—26no—
649C22×D53—212no—
650C22×D53—212no—
651C22×D53—43no—
652C22×D53—43no—
653C22×D53—43no—
654C22×D53—46no—
655C22×D53—46no—
656C22×D53—46no—
657C22×D53—46no—
658C22×D53—46no—
659C22×D53—43no—
660C22×D53—46no—
661C22×D53C22×D4112yes—
662C22×D53C2516yes—
663C22×D53C2511yescharacteristic
664C22×D53C2513yes—
665C22×D53C2511yescharacteristic
666C22×D53C2513yes—
667Q8×C53—26no—
668Q8×C53—212no—
669Q8×C53—26no—
670Q8×C53C22×D414yes—
671D4×C53—212no—
672D4×C53—212no—
673D4×C53—22no—
674D4×C53—26no—
675D4×C53—46no—
676D4×C53—42no—
677D4×C53C22×D4112yes—
678C2×C4×C53—26no—
679C2×C4×C53—212no—
680C2×C4×C53—26no—
681C2×C4×C53—26no—
682C2×C4×C53—212no—
683C2×C4×C53—22no—
684C2×C4×C53—26no—
685C2×C4×C53—46no—
686C2×C4×C53C22×D4112yes—
687C2×C4×C53C2511yescharacteristic
688C2×C4×C53C2513yes—
689C2×C4×C53C2516yes—
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—24no—
699C22⋊D53—26no—
700C22⋊D53—26no—
701C22⋊D53—26no—
702C22⋊D53—22no—
703C22⋊D53—212no—
704C22⋊D53—26no—
705C22⋊D53—26no—
706C22⋊D53—46no—
707C22⋊D53—412no—
708C22⋊D53—46no—
709C22⋊D53—46no—
710C22⋊D53—42no—
711C22⋊D53C22×D4124yes—
712C2×Dic53—26no—
713C2×Dic53—212no—
714C2×Dic53—24no—
715C2×Dic53—46no—
716C2×Dic53C22×D4112yes—
717C2×Dic53C2512yes—
718C2×Dic53C2513yes—
719C2×Dic53C2511yescharacteristic
720C2×Dic53C2516yes—
721C2×Dic53C2512yes—
722C2×Dic53C2513yes—
723C2×Dic53C2511yescharacteristic
724D212—26no—
725D212—22no—
726D212—224no—
727D212—212no—
728D212—26no—
729D212—26no—
730D212—212no—
731D212—26no—
732D212—26no—
733D212—46no—
734D212—412no—
735D212—46no—
736D212C22×D4112yes—
737C4×D53—212no—
738C4×D53—212no—
739C4×D53—22no—
740C4×D53—26no—
741C4×D53—26no—
742C4×D53—26no—
743C4×D53—212no—
744C4×D53—212no—
745C4×D53—212no—
746C4×D53—224no—
747C4×D53—46no—
748C4×D53—412no—
749C4×D53—42no—
750C4×D53C22×D4112yes—
751C4×D53C22×D4112yes—
752C4×D53C22×D414yes—
753C4×D53C22×D4112yes—
754Dic106—26no—
755Dic106—22no—
756Dic106—26no—
757Dic106—22no—
758Dic106—26no—
759Dic106—26no—
760Dic106—212no—
761Dic106C22×D4112yes—
762#62853—531nomaximal, Sylow
763C22×C53—23no—
764C22×C53—23no—
765C22×C53—23no—
766C22×C53—22no—
767C22×C53—21no—
768C22×C53—21no—
769C22×C53—23no—
770C22×C53—22no—
771C22×C53—23no—
772C22×C53—22no—
773C22×C53—21no—
774C22×C53—86no—
775C22×C53C23×D416yes—
776C22×C53C2611yescharacteristic
777C2×D53—21no—
778C2×D53—23no—
779C2×D53—21no—
780C2×D53—23no—
781C2×D53—26no—
782C2×D53—21no—
783C2×D53—23no—
784C2×D53—21no—
785C2×D53—23no—
786C2×D53—26no—
787C2×D53—23no—
788C2×D53—26no—
789C2×D53—21no—
790C2×D53—412no—
791C2×D53—812no—
792C2×D53—812no—
793C2×D53—812no—
794C2×D53—86no—
795C2×D53C23×D416yes—
796C2×D53C23×D412yes—
797C4×C53—21no—
798C4×C53—23no—
799C4×C53—26no—
800C4×C53—26no—
801C4×C53—22no—
802C4×C53C23×D416yes—
803C4×C53C23×D412yes—
804Dic53—22no—
805Dic53—23no—
806Dic53—21no—
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#3489D5311yescharacteristic, complemented
823#3488—531no—
824#3488—532no—
825#3488—536no—
826#3488—533no—
827#3488—533no—
828#3488—531no—
829#3449—533no—
830#3449—533no—
831C2×#537—533no—
832C2×#537—533no—
833C2×#520—531no—
834C2×C53—26no—
835C2×C53—42no—
836C2×C53—43no—
837C2×C53—41no—
838C2×C53C24×D411yescharacteristic
839C2×C53H(7,𝔽2)11yescharacteristic
840C2×C532−1+611yescharacteristic
841D53—22no—
842D53—26no—
843D53—46no—
844D53—41no—
845D53—43no—
846#585—10616no—
847#585—10616no—
848C2×2−1+4—533no—
849C2×2−1+4—531no—
850C2×2−1+4—531no—
851C2×2−1+4—533no—
852C2×2−1+4—531no—
853C2×2−1+4—532no—
854C2×2−1+4C2×D5311yescharacteristic, complemented
855C2×H(5,𝔽2)—531no—
856C2×H(5,𝔽2)—533no—
857C2×H(5,𝔽2)—531no—
858C2×H(5,𝔽2)—533no—
859C2×H(5,𝔽2)—536no—
860C2×H(5,𝔽2)—533no—
861C2×H(5,𝔽2)—533no—
862C22×#41—531no—
863C22×#41—533no—
864C22×#41—533no—
865C22×#41—536no—
866C22×#41—533no—
867C22×#41—531no—
868C22×#41—533no—
869C22×#41—532no—
870C22×#41—533no—
871C22×#41—533no—
872C22×#41C2×D5311yescharacteristic, complemented
873#550—532no—
874#550—536no—
875#550—532no—
876#550—536no—
877D4×Q8—532no—
878D4×Q8—536no—
879D4×Q8—536no—
880D4×Q8C2×D5312yescomplemented
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—536no—
891#547—5312no—
892#547—536no—
893#547—5312no—
894#547C2×D5316yescomplemented
895#546—536no—
896#546—536no—
897#546—536no—
898#546—5312no—
899#546—5312no—
900#546—536no—
901#546—536no—
902#546—5312no—
903#546—536no—
904#546—536no—
905#546—5312no—
906#546C2×D5316yescomplemented
907D42—536no—
908D42—5312no—
909D42—536no—
910D42—5312no—
911D42—536no—
912D42—536no—
913#537—533no—
914#537—533no—
915#537—536no—
916#537—533no—
917#537—536no—
918#537—536no—
919#537—536no—
920#537—536no—
921#537—536no—
922#537—536no—
923#537—536no—
924#537—533no—
925#537—533no—
926#537—5312no—
927#537—536no—
928#537—531no—
929#537—533no—
930#537C2×D5313yescomplemented
931#536—533no—
932#536—536no—
933#536—536no—
934#536—533no—
935#536—533no—
936#536C2×D5313yescomplemented
937#535—533no—
938#535—536no—
939#535—533no—
940#535—533no—
941#535—536no—
942#535—533no—
943#534—5312no—
944#534—536no—
945#534—536no—
946#532—536no—
947#532—536no—
948#532—536no—
949#532—536no—
950#525—533no—
951#525—533no—
952#525—5312no—
953#525—536no—
954#525—536no—
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—536no—
963C2×C22⋊Q8C2×D5313yescomplemented
964C2×#121—533no—
965C2×#121—536no—
966C2×#121—536no—
967C2×#121—5312no—
968C2×#121—533no—
969C2×#121—536no—
970C2×#121—536no—
971C2×#121—536no—
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—28no—
9842−1+4—1068no—
9852−1+4—10616no—
9862−1+4—1068no—
9872−1+4—10624no—
9882−1+4—1068no—
9892−1+4—10624no—
990H(5,𝔽2)—10624no—
991H(5,𝔽2)—10624no—
992H(5,𝔽2)—10624no—
993H(5,𝔽2)—10648no—
994H(5,𝔽2)—1068no—
995H(5,𝔽2)—10624no—
996H(5,𝔽2)—1068no—
997C2×#41—28no—
998C2×#41—5316no—
999C2×#41—531no—
1000C2×#41—536no—
1001C2×#41—533no—
1002C2×#41—536no—
1003C2×#41—536no—
1004C2×#41—533no—
1005C2×#41—533no—
1006C2×#41—536no—
1007C2×#41—531no—
1008C2×#41—532no—
1009C2×#41—533no—
1010C2×#41—536no—
1011C2×#41—533no—
1012C2×#41—536no—
1013C2×#41—531no—
1014C2×#41—533no—
1015C2×#41—536no—
1016C2×#41—533no—
1017C2×#41—533no—
1018C2×#41—533no—
1019C2×#41—533no—
1020C2×#41—533no—
1021C2×#41—533no—
1022C2×#41—533no—
1023C2×#41—536no—
1024C2×#41—533no—
1025C2×#41—533no—
1026C2×#41—533no—
1027C2×#41—533no—
1028C2×#41—531no—
1029C2×#41—533no—
1030C2×#41—536no—
1031C2×#41—5312no—
1032C2×#41—533no—
1033C2×#41—536no—
1034C2×#41—10624no—
1035C2×#41—10624no—
1036C2×#41—10624no—
1037C2×#41—10624no—
1038C2×#41—10624no—
1039C2×#41—10616no—
1040C2×#41—10648no—
1041C2×#41—10624no—
1042C2×#41—1068no—
1043C2×#41C22×D5313yes—
1044C2×#41C22×D5313yes—
1045C2×#41C22×D5313yes—
1046C2×#41C22×D5316yes—
1047C2×#41C22×D5311yescharacteristic
1048C2×#41C22×D5311yescharacteristic
1049C22×Q8—531no—
1050C22×Q8—533no—
1051C22×Q8—533no—
1052C22×Q8—533no—
1053C22×Q8—536no—
1054C22×Q8—531no—
1055C22×Q8—533no—
1056C22×Q8—533no—
1057C22×Q8C22×D5313yes—
1058C22×Q8C22×D5311yescharacteristic
1059C22×Q8C22×D5312yes—
1060C22×D4—533no—
1061C22×D4—533no—
1062C22×D4—533no—
1063C22×D4—536no—
1064C22×D4—536no—
1065C22×D4—536no—
1066C22×D4—536no—
1067C22×D4—533no—
1068C22×D4—533no—
1069C22×D4—536no—
1070C22×D4—5312no—
1071C22×D4—533no—
1072C22×D4—536no—
1073C22×D4—533no—
1074C22×D4—5312no—
1075C22×D4—533no—
1076C22×D4—536no—
1077C22×D4—533no—
1078C22×D4—533no—
1079C22×D4—536no—
1080C22×D4—536no—
1081C22×D4C22×D5313yes—
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⋊Q8C22×D5316yes—
1093#127—536no—
1094#127—536no—
1095#127—536no—
1096#127—536no—
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—536no—
1107#123—5312no—
1108#123—5312no—
1109#123—536no—
1110#123—5312no—
1111#123—536no—
1112#123—536no—
1113#123—536no—
1114#123—536no—
1115#123C22×D53112yes—
1116#123C22×D5316yes—
1117C22⋊Q8—533no—
1118C22⋊Q8—536no—
1119C22⋊Q8—536no—
1120C22⋊Q8—536no—
1121C22⋊Q8—536no—
1122C22⋊Q8—533no—
1123C22⋊Q8—533no—
1124C22⋊Q8—536no—
1125C22⋊Q8—531no—
1126C22⋊Q8—5312no—
1127C22⋊Q8—536no—
1128C22⋊Q8—533no—
1129C22⋊Q8—5312no—
1130C22⋊Q8—5312no—
1131C22⋊Q8—5312no—
1132C22⋊Q8—536no—
1133C22⋊Q8—536no—
1134C22⋊Q8—531no—
1135C22⋊Q8—536no—
1136C22⋊Q8—5312no—
1137C22⋊Q8—532no—
1138C22⋊Q8C22×D5316yes—
1139C22⋊Q8C22×D5316yes—
1140C22⋊Q8C22×D5313yes—
1141C22⋊Q8C22×D5316yes—
1142C22⋊Q8C22×D5316yes—
1143C22⋊Q8C22×D5313yes—
1144#121—533no—
1145#121—536no—
1146#121—536no—
1147#121—5312no—
1148#121—5312no—
1149#121—536no—
1150#121—5312no—
1151#121—531no—
1152#121—532no—
1153#121—532no—
1154#121—536no—
1155#121—533no—
1156#121—5312no—
1157#121—536no—
1158#121—536no—
1159#121—536no—
1160#121—533no—
1161#121—536no—
1162#121—533no—
1163#121—5312no—
1164#121—536no—
1165#121—5312no—
1166#121—5312no—
1167#121—536no—
1168#121—536no—
1169#121—536no—
1170#121—533no—
1171#121—536no—
1172#121—5312no—
1173#121—536no—
1174#121—536no—
1175#121—5312no—
1176#121—536no—
1177#121—5312no—
1178#121—5312no—
1179#121—5312no—
1180#121—5312no—
1181#121—5312no—
1182#121—536no—
1183#121—536no—
1184#121—532no—
1185#121C22×D5313yes—
1186#121C22×D53112yes—
1187#121C22×D5316yes—
1188#121C22×D5311yescharacteristic
1189#120—536no—
1190#120—536no—
1191#120—5312no—
1192#120—536no—
1193#120—536no—
1194#120—5312no—
1195#120—536no—
1196#120—5312no—
1197#120—536no—
1198#120—536no—
1199#120—5312no—
1200#120C22×D5316yes—
1201C4×Q8—532no—
1202C4×Q8—536no—
1203C4×Q8—536no—
1204C4×Q8C22×D5312yes—
1205C4×D4—536no—
1206C4×D4—5312no—
1207C4×D4—536no—
1208C4×D4—536no—
1209C4×D4—536no—
1210C4×D4—536no—
1211C4×D4—536no—
1212C4×D4—5312no—
1213C4×D4—5312no—
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—533no—
1233C2×C4⋊C4—536no—
1234C2×C4⋊C4—536no—
1235C2×C4⋊C4—536no—
1236C2×C4⋊C4—531no—
1237C2×C4⋊C4—5312no—
1238C2×C4⋊C4C22×D5313yes—
1239C2×C4⋊C4C22×D5316yes—
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—
1252C24—536no—
1253C24C23×D5313yes—
1254#41—24no—
1255#41—212no—
1256#41—224no—
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—10648no—
1273#41—10612no—
1274#41—10612no—
1275#41—10624no—
1276#41—10624no—
1277#41—1064no—
1278#41—10624no—
1279#41—10612no—
1280#41—10612no—
1281#41—10624no—
1282#41—10624no—
1283#41—10624no—
1284#41—10612no—
1285#41—10624no—
1286#41—10612no—
1287#41—10624no—
1288#41—10612no—
1289#41—1064no—
1290#41—1068no—
1291#41—10612no—
1292#41—10612no—
1293#41—10612no—
1294#41D4×D5318yescomplemented
1295C2×Q8—24no—
1296C2×Q8—28no—
1297C2×Q8—212no—
1298C2×Q8—538no—
1299C2×Q8—533no—
1300C2×Q8—533no—
1301C2×Q8—531no—
1302C2×Q8—531no—
1303C2×Q8—533no—
1304C2×Q8—533no—
1305C2×Q8—536no—
1306C2×Q8—533no—
1307C2×Q8—10612no—
1308C2×Q8—10612no—
1309C2×Q8—10612no—
1310C2×Q8—10612no—
1311C2×Q8—10624no—
1312C2×Q8—10612no—
1313C2×Q8—1064no—
1314C2×Q8C23×D5313yes—
1315C2×Q8C23×D5313yes—
1316C2×Q8C23×D5316yes—
1317C2×Q8C23×D5311yescharacteristic
1318C2×D4—212no—
1319C2×D4—536no—
1320C2×D4—5324no—
1321C2×D4—533no—
1322C2×D4—533no—
1323C2×D4—536no—
1324C2×D4—536no—
1325C2×D4—533no—
1326C2×D4—531no—
1327C2×D4—532no—
1328C2×D4—533no—
1329C2×D4—531no—
1330C2×D4—536no—
1331C2×D4—533no—
1332C2×D4—533no—
1333C2×D4—532no—
1334C2×D4—536no—
1335C2×D4—536no—
1336C2×D4—5312no—
1337C2×D4—536no—
1338C2×D4—533no—
1339C2×D4—533no—
1340C2×D4—533no—
1341C2×D4—5312no—
1342C2×D4—533no—
1343C2×D4—531no—
1344C2×D4—536no—
1345C2×D4—533no—
1346C2×D4—536no—
1347C2×D4—533no—
1348C2×D4—536no—
1349C2×D4—5312no—
1350C2×D4—536no—
1351C2×D4—10612no—
1352C2×D4—10624no—
1353C2×D4—10612no—
1354C2×D4—10624no—
1355C2×D4—10612no—
1356C2×D4—10612no—
1357C2×D4—10612no—
1358C2×D4—10624no—
1359C2×D4—10648no—
1360C2×D4—10612no—
1361C2×D4—10624no—
1362C2×D4—10624no—
1363C2×D4—10624no—
1364C2×D4—10612no—
1365C2×D4—10612no—
1366C2×D4—10624no—
1367C2×D4—10612no—
1368C2×D4—4246no—
1369C2×D4—42412no—
1370C2×D4—4246no—
1371C2×D4C23×D5316yes—
1372C2×D4C23×D5316yes—
1373C2×D4C23×D5311yescharacteristic
1374C2×D4C23×D5313yes—
1375C2×D4C23×D5312yes—
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—533no—
1386C22×C4—536no—
1387C22×C4—532no—
1388C22×C4—536no—
1389C22×C4—536no—
1390C22×C4—536no—
1391C22×C4—536no—
1392C22×C4—5312no—
1393C22×C4—536no—
1394C22×C4—533no—
1395C22×C4—533no—
1396C22×C4—536no—
1397C22×C4—533no—
1398C22×C4—531no—
1399C22×C4—532no—
1400C22×C4—536no—
1401C22×C4—5312no—
1402C22×C4—10624no—
1403C22×C4—10624no—
1404C22×C4—10624no—
1405C22×C4—10612no—
1406C22×C4—4246no—
1407C22×C4C23×D5313yes—
1408C22×C4C23×D5316yes—
1409C22×C4C23×D5313yes—
1410C22×C4C23×D5313yes—
1411C22×C4C23×D5316yes—
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—536no—
1422C4⋊C4—5312no—
1423C4⋊C4—536no—
1424C4⋊C4—532no—
1425C4⋊C4—531no—
1426C4⋊C4—532no—
1427C4⋊C4—536no—
1428C4⋊C4—532no—
1429C4⋊C4C23×D5313yes—
1430C4⋊C4C23×D5316yes—
1431C4⋊C4C23×D53112yes—
1432C4⋊C4C23×D5311yescharacteristic
1433C4⋊C4C23×D5316yes—
1434C4⋊C4C23×D5316yes—
1435C22⋊C4—536no—
1436C22⋊C4—536no—
1437C22⋊C4—536no—
1438C22⋊C4—532no—
1439C22⋊C4—532no—
1440C22⋊C4—5312no—
1441C22⋊C4—536no—
1442C22⋊C4—536no—
1443C22⋊C4—5312no—
1444C22⋊C4—536no—
1445C22⋊C4—5312no—
1446C22⋊C4—536no—
1447C22⋊C4—536no—
1448C22⋊C4—536no—
1449C22⋊C4—536no—
1450C22⋊C4—536no—
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—43no—
1465C23—43no—
1466C23—533no—
1467C23—531no—
1468C23—5312no—
1469C23—533no—
1470C23—536no—
1471C23—531no—
1472C23—10612no—
1473C23—10612no—
1474C23—10612no—
1475C23—1066no—
1476C23—2123no—
1477C23—2126no—
1478C23—2126no—
1479C23—2126no—
1480C23—2123no—
1481C23—2126no—
1482C23—2126no—
1483C23—2126no—
1484C23—2123no—
1485C23—2123no—
1486C23C24×D5312yes—
1487C23C24×D5313yes—
1488C23C24×D5311yescharacteristic
1489C23C24×D5313yes—
1490Q8—26no—
1491Q8—212no—
1492Q8—26no—
1493Q8—5312no—
1494Q8—1062no—
1495Q8—1066no—
1496Q8—1066no—
1497Q8—1066no—
1498Q8—10612no—
1499Q8—1062no—
1500Q8—1066no—
1501Q8C2×D4×D5314yes—
1502D4—212no—
1503D4—212no—
1504D4—26no—
1505D4—22no—
1506D4—46no—
1507D4—42no—
1508D4—5324no—
1509D4—5312no—
1510D4—1062no—
1511D4—1066no—
1512D4—1066no—
1513D4—1066no—
1514D4—10612no—
1515D4—10624no—
1516D4—1062no—
1517D4—1066no—
1518D4—1066no—
1519D4—10612no—
1520D4—1066no—
1521D4—1062no—
1522D4—1066no—
1523D4—1064no—
1524D4—1066no—
1525D4—1066no—
1526D4—10612no—
1527D4—10612no—
1528D4—1066no—
1529D4—10612no—
1530D4—1066no—
1531D4—2126no—
1532D4—2126no—
1533D4—21212no—
1534D4—2122no—
1535D4—2126no—
1536D4—2126no—
1537D4—21212no—
1538D4—2126no—
1539D4C2×D4×D53112yes—
1540C2×C4—26no—
1541C2×C4—212no—
1542C2×C4—22no—
1543C2×C4—26no—
1544C2×C4—26no—
1545C2×C4—26no—
1546C2×C4—212no—
1547C2×C4—46no—
1548C2×C4—5312no—
1549C2×C4—533no—
1550C2×C4—531no—
1551C2×C4—534no—
1552C2×C4—5312no—
1553C2×C4—5312no—
1554C2×C4—5312no—
1555C2×C4—532no—
1556C2×C4—536no—
1557C2×C4—532no—
1558C2×C4—533no—
1559C2×C4—531no—
1560C2×C4—10612no—
1561C2×C4—10612no—
1562C2×C4—10624no—
1563C2×C4—10612no—
1564C2×C4—10612no—
1565C2×C4—1064no—
1566C2×C4—10612no—
1567C2×C4—1066no—
1568C2×C4—1066no—
1569C2×C4—1062no—
1570C2×C4—1066no—
1571C2×C4—1066no—
1572C2×C4—10612no—
1573C2×C4—2122no—
1574C2×C4—2126no—
1575C2×C4—21212no—
1576C2×C4—2126no—
1577C2×C4C2×D4×D53112yes—
1578C2×C4C24×D5312yes—
1579C2×C4C24×D5316yes—
1580C2×C4C24×D5313yes—
1581C2×C4C24×D5311yescharacteristic
1582C2×C4C24×D5316yes—
1583C2×C4C24×D5313yes—
1584C2×C4C24×D5311yescharacteristic
1585C22—23no—
1586C22—23no—
1587C22—21no—
1588C22—22no—
1589C22—23no—
1590C22—22no—
1591C22—23no—
1592C22—21no—
1593C22—21no—
1594C22—22no—
1595C22—23no—
1596C22—86no—
1597C22—532no—
1598C22—536no—
1599C22—1061no—
1600C22—1063no—
1601C22—1061no—
1602C22—1063no—
1603C22—1066no—
1604C22—1063no—
1605C22—1061no—
1606C22—1061no—
1607C22—1063no—
1608C22—1066no—
1609C22—1063no—
1610C22—1066no—
1611C22—1061no—
1612C22—4246no—
1613C22—42412no—
1614C22—42412no—
1615C22—42412no—
1616C22—21212no—
1617C22C22×D4×D5316yes—
1618C22C25×D5311yescharacteristic
1619C4—21no—
1620C4—23no—
1621C4—26no—
1622C4—26no—
1623C4—22no—
1624C4—532no—
1625C4—536no—
1626C4—1062no—
1627C4—1063no—
1628C4—1061no—
1629C4—1066no—
1630C4—1062no—
1631C4C22×D4×D5312yes—
1632C4C22×D4×D5316yes—
1633C2—26no—
1634C2—41no—
1635C2—43no—
1636C2—42no—
1637C2—1066no—
1638C2—1062no—
1639C2—2121no—
1640C2—2126no—
1641C2—2123no—
1642C2C23×D4×D5311yescharacteristic
1643C2#2028952611yescharacteristic
1644C2#2028952711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3489C2
hypercenter#3489D53
hypocenterC53#62853
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. C2×#16811460C2semidirect
2. C2×#16811459C2semidirect
3. #20288485C2semidirect
4. #20288483C2semidirect
5. #20288475C2semidirect
6. #20288473C2semidirect
7. #20288393C2semidirect
8. #20288392C2semidirect
9. #20288391C2semidirect
10. #20288389C2semidirect
11. #20288388C2semidirect
12. #20288385C2semidirect
13. #20288384C2semidirect
14. #20288381C2semidirect
15. #20288379C2semidirect
16. #20288378C2semidirect
17. #20288376C2semidirect
18. #20288047C2semidirect
19. #20288045C2semidirect
20. C2×#16811203C2semidirect
21. #537×D53C2semidirect
22. #520×D53C2semidirect
23. C53×#3489C2semidirect
26. C2×#13133265C22semidirect
27. C2×#13133265C22semidirect
28. C2×#13133265C22semidirect
29. C2×#13133265C22semidirect
30. C2×#13133264C22semidirect
31. C2×#13133264C22semidirect
32. C2×#13133263C22semidirect
33. C2×#13133263C22semidirect
34. C2×#13133263C22semidirect
35. C2×#13133263C22semidirect
36. C2×#13133263C22semidirect
37. C2×#13133262C22semidirect
38. C2×#13133262C22semidirect
39. C22×#11719949C22semidirect
40. C22×#11719949C22semidirect
41. C22×#11719945C22semidirect
42. C22×#11719945C22semidirect
44. C2×#41×D53C22semidirect
45. C2×#41×D53C22semidirect
46. C2×#41×D53C22semidirect
47. C2×#41×D53C22semidirect
48. C2×#41×D53C22semidirect
49. #16811295C22semidirect
50. #16811294C22semidirect
51. #16811292C22semidirect
52. #16811291C22semidirect
53. #16811288C22semidirect
54. Q8×C22⋊D53C22semidirect
55. #16811286C22semidirect
56. #16811285C22semidirect
57. #16811284C22semidirect
58. #16811284C22semidirect
59. #16811283C22semidirect
60. #16811283C22semidirect
61. #16811282C22semidirect
62. #16811281C22semidirect
63. #16811276C22semidirect
64. #16811275C22semidirect
65. #16811274C22semidirect
66. #16811272C22semidirect
67. #16811271C22semidirect
68. #16811269C22semidirect
69. #16811268C22semidirect
70. #16811266C22semidirect
71. #16811265C22semidirect
72. #16811265C22semidirect
73. #16811264C22semidirect
74. #16811264C22semidirect
75. #16811263C22semidirect
76. #16811262C22semidirect
77. #16811261C22semidirect
78. #16811261C22semidirect
79. D4×D212C22semidirect
80. D4×D212C22semidirect
81. #16811257C22semidirect
82. #16811257C22semidirect
83. D4×C22⋊D53C22semidirect
84. #16811255C22semidirect
85. #16811204C22semidirect
86. #16811203C22semidirect
87. #16811203C22semidirect
88. #16811203C22semidirect
89. #16811203C22semidirect
90. #16811203C22semidirect
91. #16811203C22semidirect
92. #16811203C22semidirect
93. #16811203C22semidirect
94. #16811203C22semidirect
95. #16811203C22semidirect
96. #16811202C22semidirect
97. #16811202C22semidirect
98. #16811202C22semidirect
99. #16811201C22semidirect
100. #16811201C22semidirect
101. #16811200C22semidirect
102. #16811198C22semidirect
103. #16811197C22semidirect
104. #16811196C22semidirect
105. #16811196C22semidirect
106. #16811195C22semidirect
107. #16811192C22semidirect
108. #16811191C22semidirect
109. #16811189C22semidirect
110. #16811189C22semidirect
111. #16811188C22semidirect
112. #16811187C22semidirect
113. #16811184C22semidirect
114. #16811184C22semidirect
115. #16811183C22semidirect
116. #16811174C22semidirect
117. #16811172C22semidirect
118. #16811170C22semidirect
119. #16811170C22semidirect
120. #16811136C22semidirect
121. #16811136C22semidirect
122. #16811135C22semidirect
123. #16811134C22semidirect
124. #16811132C22semidirect
125. #16811132C22semidirect
126. #16811131C22semidirect
127. #16811130C22semidirect
128. C2×#13133195C22semidirect
129. C2×#13133193C22semidirect
130. C22⋊Q8×D53C22semidirect
131. C22⋊Q8×D53C22semidirect
132. C2×#13133192C22semidirect
133. C2×#13133192C22semidirect
134. C2×#13133191C22semidirect
135. C2×#13133190C22semidirect
136. C2×#13133190C22semidirect
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. C2×2−1+4×C53C22semidirect
150. C22×#41×C53C22semidirect
151. D4×Q8×C53C22semidirect
152. C53×#548C22semidirect
153. C53×#547C22semidirect
154. C53×#546C22semidirect
155. C53×#537C22semidirect
156. C53×#536C22semidirect
157. C53×#525C22semidirect
158. C2×C22⋊Q8×C53C22semidirect
159. C53×#520C22semidirect
217. #41×D53D4semidirect
436. #41×C53C2×D4semidirect
498. #11719949C2×D4semidirect
504. Q8×D53C2×D4semidirect
512. #11719947C2×D4semidirect
523. D4×D53C2×D4semidirect
540. #11719945C2×D4semidirect
565. C2×C4×D53C2×D4semidirect
822. #3489D53semidirect
854. C2×2−1+4C2×D53semidirect
872. C22×#41C2×D53semidirect
880. D4×Q8C2×D53semidirect
888. #548C2×D53semidirect
894. #547C2×D53semidirect
906. #546C2×D53semidirect
930. #537C2×D53semidirect
936. #536C2×D53semidirect
958. #525C2×D53semidirect
963. C2×C22⋊Q8C2×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×#168114602
C2×#168114592
#202884852
#202884832
#202884752
#202884732
#202883932
#202883922
#202883912
#202883892
#202883882
#202883852
#202883842
#202883812
#202883792
#202883782
#202883762
#202880472
#202880452
C2×#168112032
#537×D532
#520×D532
C53×#34892
#6285353