Finite Group Databasebeta

← #11910752

Subgroups — #11910752

Order 1152.

2246 conjugacy classes of subgroups.

The subgroup lattice has 1267 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596137C211yesmaximal, characteristic, complemented
2C3×D3×#123C211yesmaximal, characteristic, complemented
3C3×#5651C211yesmaximal, characteristic, complemented
4#10595235C211yesmaximal, characteristic, complemented
5#10595234C211yesmaximal, characteristic, complemented
6#10595212C211yesmaximal, characteristic, complemented
7#10595208C211yesmaximal, characteristic, complemented
8#10595005C212yesmaximal, complemented
9#10594978C212yesmaximal, complemented
10#10594517C212yesmaximal, complemented
11#10594467C212yesmaximal, complemented
12#10594458C212yesmaximal, complemented
13#10594331C212yesmaximal, complemented
14#10594232C212yesmaximal, complemented
15#10594199C212yesmaximal, complemented
16#10594187C212yesmaximal, complemented
17#10594157C212yesmaximal, complemented
18#10594093C212yesmaximal, complemented
19#10594041C212yesmaximal, complemented
20#87128—31nomaximal
21#86016—31nomaximal
22C2×C3×D3×D4C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic, complemented
24C22×#626C2211yescharacteristic
25C2×#3799C2212yes—
26C2×#3799C2211yescharacteristic, complemented
27C32×#123C2211yescharacteristic
28#64149C2211yescharacteristic
29#64146C2211yescharacteristic
30#64139C2212yescomplemented
31#64107C2212yescomplemented
32#64104C2212yescomplemented
33#64093C2212yescomplemented
34#64092C2212yescomplemented
35#64091C2212yescomplemented
36C3×#936C2211yescharacteristic
37C3×#935C2211yescharacteristic
38C3×#935C2211yescharacteristic
39C3×#929C2211yescharacteristic, complemented
40C3×#924C2212yescomplemented
41C3×#894C2212yescomplemented
42C3×D3×C4⋊C4C2212yescomplemented
43C3×#889C2212yescomplemented
44C3×#888C2212yescomplemented
45C3×#886C2211yescharacteristic, complemented
46C3×#883C2212yes—
47C3×D3×C22⋊C4C2212yes—
48C3×D3×C22⋊C4C2211yescharacteristic, complemented
49C3×#879C2212yescomplemented
50C3×#879C2212yescomplemented
51C3×#878C2212yescomplemented
52#63981C2211yescharacteristic
53#63977C2212yes—
54#63977C2212yes—
55#63977C2212yescomplemented
56#63975C2212yescomplemented
57#63974C2212yescomplemented
58#63971C2212yes—
59D3×#217C2211yescharacteristic
60#63961C2211yescharacteristic
61#63958C2212yes—
62#63958C2212yescomplemented
63#63956C2212yescomplemented
64#63953C2212yescomplemented
65#63953C2212yescomplemented
66#63952C2212yescomplemented
67#63952C2212yescomplemented
68#63952C2212yescomplemented
69#63911C2211yescharacteristic, complemented
70#63910C2212yescomplemented
71#63910C2212yescomplemented
72#63910C2212yescomplemented
73#63909C2212yes—
74#63909C2212yescomplemented
75#63907C2212yescomplemented
76#63904C2212yes—
77#63904C2212yescomplemented
78#63904C2212yescomplemented
79C4×#626C2212yescomplemented
80#63900C2212yescomplemented
81#63897C2212yescomplemented
82#63897C2212yescomplemented
83#63895C2212yescomplemented
84#63894C2212yescomplemented
85#63893C2212yescomplemented
86#63890C2212yescomplemented
87#63888C2212yescomplemented
88#63888C2212yescomplemented
89#63886C2212yes—
90#63881C2212yescomplemented
91#63877C2212yescomplemented
92#63863C2211yescharacteristic, complemented
93#63858C2212yescomplemented
94#63856C2212yescomplemented
95#63855C2211yescharacteristic, complemented
96#63854C2212yescomplemented
97#63853C2212yescomplemented
98#63852C2212yescomplemented
99#63851C2212yescomplemented
100#63850C2212yes—
101#63850C2212yes—
102#63850C2212yescomplemented
103#63848C2212yescomplemented
104#63847C2212yescomplemented
105#63845C2212yescomplemented
106#63841C2212yescomplemented
107#63838C2212yescomplemented
108#63836C2212yescomplemented
109C3×#563—31no—
110C2×C3×#123—31no—
111#5805—31no—
112#5804—31no—
113#5791—32no—
114#5733—32no—
115#5726—32no—
116#5709—32no—
117#5705—32no—
118#5704—32no—
119#5704—32no—
120#5697—32no—
121#5693—32no—
122#5679—31no—
123#5674—31no—
124#5667—32no—
125#5666—31no—
126#5666—31no—
127#5666—61no—
128#5664—31no—
129#5664—31no—
130#5663—32no—
131#5662—32no—
132#5661—32no—
133#5660—32no—
134#5659—31no—
135#5657—32no—
136#5653—31no—
137D3×#123D311yescharacteristic, complemented
138#5651D311yescharacteristic, complemented
139#5647—32no—
140#5638—32no—
141#5630—32no—
142#5627—32no—
143#5513—32no—
144#5507—32no—
145#5495—32no—
146#5494—32no—
147#5490—32no—
148C23×C3⋊D3C2311yescharacteristic
149C23×C3×D3C2311yescharacteristic
150C23×C3×D3C2311yescharacteristic
151C2×C32×D4C2311yescharacteristic
152C22×C32×C4C2311yescharacteristic
153C2×#638C2312yes—
154C2×#638C2312yes—
155C2×#638C2312yes—
156C2×C4⋊(C3⋊D3)C2312yes—
157C2×C4⋊(C3⋊D3)C2311yescharacteristic
158C2×C4⋊(C3⋊D3)C2312yes—
159C2×C4×C3⋊D3C2312yes—
160C2×C3×#67C2311yescharacteristic
161C2×C3×#67C2311yescharacteristic
162C22×C3×Dic3C2311yescharacteristic
163C22×C3×Dic3C2311yescharacteristic
164C3×D3×D4—42no—
165C2×C3×D12C2311yescharacteristic
166C2×C3×C4×D3—42no—
167C2×C3×C4×D3C2312yes—
168C2×C3×C4×D3C2311yescharacteristic
169C2×C3×C4×D3C2312yes—
170C2×C3×C4×D3C2312yes—
171C2×C3×Dic6C2312yes—
172C2×C3×Dic6C2311yescharacteristic
173C2×#627C2312yes—
174C2×#626—42no—
175C2×#626C2312yes—
176C2×#626C2312yes—
177C2×#626C2312yes—
178C2×#626C2312yes—
179C2×#626C2312yes—
180C2×#626C2312yes—
181C2×#624C2312yes—
182C2×#624C2312yes—
183C2×#624C2312yes—
184C2×#624C2312yes—
185C2×D3×Dic3C2312yes—
186#3799—44no—
187#3799—42no—
188C32×C4⋊C4C2312yes—
189C32×C22⋊C4C2312yes—
190C32×C22⋊C4C2311yescharacteristic
191#3757C2311yescharacteristic
192#3752C2312yes—
193#3752C2312yes—
194#3752C2312yes—
195#3752C2312yes—
196C4⋊(C3⋊Dic3)C2312yes—
197#3750C2312yes—
198C4×C3⋊Dic3C2311yescharacteristic
199C3×#217C2312yes—
200C3×#217C2311yescharacteristic
201C3×#217C2312yes—
202C3×#217C2312yes—
203C3×#217C2312yes—
204C3×#217C2311yescharacteristic
205C3×(C2×D3)⋊C4C2312yes—
206C3×(C2×D3)⋊C4C2312yes—
207C3×(C2×D3)⋊C4C2312yes—
208C3×C4⋊Dic3C2312yes—
209C3×C4⋊Dic3C2312yes—
210C3×C4⋊Dic3C2312yes—
211C3×Dic3⋊C4C2312yes—
212C3×Dic3⋊C4C2312yes—
213C3×Dic3⋊C4C2312yes—
214C3×Dic3⋊C4C2312yes—
215C3×Dic3⋊C4C2312yes—
216C3×Dic3⋊C4C2312yes—
217C3×Dic3⋊C4C2312yes—
218C3×C4×Dic3C2312yes—
219C3×C4×Dic3C2311yescharacteristic
220#3724C2312yes—
221#3724C2312yes—
222#3724C2312yes—
223Dic3⋊Dic3C2312yes—
224Dic3⋊Dic3C2312yes—
225Dic3⋊Dic3C2312yes—
226#3722C2312yes—
227#3722C2312yes—
228#3722C2312yes—
229#3722C2312yes—
230#3722C2312yes—
231#3722C2312yes—
232(C2×D3)⋊Dic3C2312yes—
233(C2×D3)⋊Dic3C2312yes—
234(C2×D3)⋊Dic3C2312yes—
235(C2×D3)⋊Dic3C2312yes—
236(C2×D3)⋊Dic3C2312yes—
237Dic32C2312yes—
238Dic32C2312yes—
239Dic32C2312yes—
240#3533—91noSylow
241C22×C3×D4—31no—
242C23×C3×C4—31no—
243C22×#67—31no—
244C2×#239—31no—
245C2×#239—32no—
246C2×D3×D4C2×D311yescharacteristic
247C2×#235—32no—
248C2×#235—31no—
249C22×D12—31no—
250C22×C4×D3C2×D311yescharacteristic, complemented
251C3×C4⋊Q8—32no—
252C3×#126—32no—
253C3×#126—32no—
254C3×#125—32no—
255C3×#124—31no—
256C3×#123—21no—
257C3×#123—31no—
258C3×#123—31no—
259C3×#123—31no—
260C3×#123—32no—
261C3×#123—32no—
262C3×#123—31no—
263C3×#123C2×D311yescharacteristic
264C3×#123C2×D311yescharacteristic
265C3×C22⋊Q8—32no—
266C3×C22⋊Q8—32no—
267C2×C3×C4⋊C4—32no—
268C2×C3×C22⋊C4—32no—
269C2×C3×C22⋊C4—31no—
270#953—32no—
271#953—32no—
272#953—32no—
273C2×#217—31no—
274#947—31no—
275#947—32no—
276#946—32no—
277#946—32no—
278#946—32no—
279#940—31no—
280#940—31no—
281#940—31no—
282#940—61no—
283#939—32no—
284#939—32no—
285#938—32no—
286#938—32no—
287#937—31no—
288#937—31no—
289#937—31no—
290#937—61no—
291#936—31no—
292#936C2×D311yescharacteristic
293#935—31no—
294#935C2×D311yescharacteristic
295#935C2×D311yescharacteristic
296#930—32no—
297#930—32no—
298#930—32no—
299#930—32no—
300#930—62no—
301#929—31no—
302#929—32no—
303#929—32no—
304#929—32no—
305#929C2×D311yescharacteristic, complemented
306C4×#67—32no—
307C4×#67—32no—
308C4×#67—32no—
309C4×#67—32no—
310C4×#67—32no—
311C4×#67—32no—
312C4×#67—32no—
313#926—32no—
314#926—31no—
315#924—32no—
316#924—32no—
317#924C2×D312yescomplemented
318#898—32no—
319#898—32no—
320#898—32no—
321#898—32no—
322#898—32no—
323#898—62no—
324#897—32no—
325#897—32no—
326#896—32no—
327#896—32no—
328#896—32no—
329#896—32no—
330#895—32no—
331#895—32no—
332#895—32no—
333#895—32no—
334#895—32no—
335#895—32no—
336#895—32no—
337#895—32no—
338#895—62no—
339#894—32no—
340#894—32no—
341#894—32no—
342#894—32no—
343#894—32no—
344#894—32no—
345#894—32no—
346#894—32no—
347#894—32no—
348#894—32no—
349#894C2×D312yescomplemented
350#893—32no—
351#893—32no—
352#893—32no—
353#893—32no—
354#893—32no—
355#892—32no—
356#892—32no—
357D3×C4⋊C4—32no—
358D3×C4⋊C4—32no—
359D3×C4⋊C4C2×D312yescomplemented
360#890—32no—
361#889—32no—
362#889—32no—
363#889—32no—
364#889C2×D312yescomplemented
365#888C2×D312yescomplemented
366#887—32no—
367#887—32no—
368#886—32no—
369#886C2×D311yescharacteristic, complemented
370#885—32no—
371#885—32no—
372#885—32no—
373#885—32no—
374#885—32no—
375#885—32no—
376#884—32no—
377#884—32no—
378#884—32no—
379#884—32no—
380#884—32no—
381#884—32no—
382#884—32no—
383#884—32no—
384#884—62no—
385#883—32no—
386#883—32no—
387#883—32no—
388#883—32no—
389#883—32no—
390#883—32no—
391#883—62no—
392#883C2×D312yes—
393#882—32no—
394#882—32no—
395#882—32no—
396#882—31no—
397#882—32no—
398#882—32no—
399#882—62no—
400#67⋊C4—32no—
401#67⋊C4—32no—
402#67⋊C4—32no—
403#67⋊C4—32no—
404D3×C22⋊C4—31no—
405D3×C22⋊C4—32no—
406D3×C22⋊C4—32no—
407D3×C22⋊C4C2×D312yes—
408D3×C22⋊C4C2×D311yescharacteristic, complemented
409#879—32no—
410#879—32no—
411#879—32no—
412#879C2×D312yescomplemented
413#879C2×D312yescomplemented
414#878—32no—
415#878C2×D312yescomplemented
416#877—32no—
417#875—32no—
418#874—31no—
419C4×D12—32no—
420C4×D12—32no—
421#872—31no—
422#872—32no—
423#872—32no—
424C23×C32C2411yescharacteristic
425C23×C32C2411yescharacteristic
426C22×C3⋊D3—42no—
427C22×C3⋊D3—41no—
428C22×C3⋊D3C2412yes—
429C22×C3⋊D3C2412yes—
430C22×C3×D3—22no—
431C22×C3×D3—22no—
432C22×C3×D3—42no—
433C22×C3×D3—42no—
434C22×C3×D3C2411yescharacteristic
435C22×C3×D3C2411yescharacteristic
436C22×C3×D3C2411yescharacteristic
437C32×D4—41no—
438C2×C32×C4—41no—
439C2×C32×C4C2411yescharacteristic
440C2×C32×C4C2412yes—
441C2×C32×C4C2412yes—
442#638—42no—
443#638—42no—
444#638—42no—
445C2×C3⋊Dic3C2412yes—
446C2×C3⋊Dic3C2412yes—
447C4⋊(C3⋊D3)—42no—
448C4⋊(C3⋊D3)—41no—
449C4⋊(C3⋊D3)—42no—
450C4×C3⋊D3—42no—
451C3×#67—41no—
452C3×#67—41no—
453C2×C3×Dic3—41no—
454C2×C3×Dic3—41no—
455C2×C3×Dic3C2412yes—
456C2×C3×Dic3C2412yes—
457C2×C3×Dic3C2412yes—
458C2×C3×Dic3C2412yes—
459C2×C3×Dic3C2412yes—
460C2×C3×Dic3C2412yes—
461C2×C3×Dic3C2411yescharacteristic
462C3×D12—41no—
463C3×C4×D3—24no—
464C3×C4×D3—22no—
465C3×C4×D3—42no—
466C3×C4×D3—42no—
467C3×Dic6—41no—
468C3×Dic6—42no—
469#627—42no—
470#626—24no—
471#626—24no—
472#626—42no—
473#626—42no—
474#626—42no—
475#626—42no—
476#624—42no—
477#624—42no—
478#624—42no—
479#624—42no—
480D3×Dic3—42no—
481#563—31no—
482#562—92no—
483#560—91no—
484#559—91no—
485#553—92no—
486#552—92no—
487#551—92no—
488#551—91no—
489#547—92no—
490#546—92no—
491#542—92no—
492#540—92no—
493#539—92no—
494#538—92no—
495#538—92no—
496#535—91no—
497#534—91no—
498#525—92no—
499C2×#123—31no—
500C24×C3—31no—
501C24×C3—31no—
502C23×D3—31no—
503C23×D3—31no—
504C23×D3—61no—
505C23×D3C22×D311yescharacteristic
506C23×D3C22×D311yescharacteristic
507C2×C3×Q8—32no—
508C2×C3×Q8—31no—
509C2×C3×D4—21no—
510C2×C3×D4—31no—
511C2×C3×D4—31no—
512C2×C3×D4—31no—
513C2×C3×D4—122no—
514C2×C3×D4C22×D311yescharacteristic
515C2×C3×D4C22×D311yescharacteristic
516C22×C3×C4—21no—
517C22×C3×C4—31no—
518C22×C3×C4—31no—
519C22×C3×C4—32no—
520C22×C3×C4—31no—
521C22×C3×C4—32no—
522C22×C3×C4—32no—
523C22×C3×C4—122no—
524C22×C3×C4C22×D311yescharacteristic
525C22×C3×C4C22×D311yescharacteristic
526C2×#67—32no—
527C2×#67—32no—
528C2×#67—32no—
529C2×#67—32no—
530C2×#67—32no—
531C2×#67—32no—
532C2×#67—32no—
533C2×#67—32no—
534C2×#67—32no—
535C2×#67—32no—
536C2×#67—32no—
537C2×#67—32no—
538C2×#67—62no—
539C2×#67—62no—
540C2×#67—62no—
541C2×#67—122no—
542C2×#67C22×D311yescharacteristic
543C2×#67C22×D311yescharacteristic
544C22×Dic3—32no—
545C22×Dic3C22×D311yescharacteristic
546C22×Dic3C22×D311yescharacteristic
547#239—124no—
548#239—122no—
549D3×D4—42no—
550#235—122no—
551#235—124no—
552C2×D12—32no—
553C2×D12—32no—
554C2×D12—32no—
555C2×D12—32no—
556C2×D12—32no—
557C2×D12—32no—
558C2×D12—32no—
559C2×D12—31no—
560C2×D12—32no—
561C2×D12—32no—
562C2×D12—32no—
563C2×D12—31no—
564C2×D12—62no—
565C2×D12—62no—
566C2×D12—61no—
567C2×D12—122no—
568C2×D12C22×D311yescharacteristic
569C2×C4×D3—32no—
570C2×C4×D3—32no—
571C2×C4×D3—32no—
572C2×C4×D3—32no—
573C2×C4×D3—32no—
574C2×C4×D3—32no—
575C2×C4×D3—32no—
576C2×C4×D3—32no—
577C2×C4×D3—32no—
578C2×C4×D3—32no—
579C2×C4×D3—32no—
580C2×C4×D3—42no—
581C2×C4×D3—62no—
582C2×C4×D3C22×D311yescharacteristic
583C2×C4×D3C22×D312yes—
584C2×C4×D3C22×D312yes—
585C2×C4×D3C22×D312yes—
586C2×Dic6—32no—
587C2×Dic6—32no—
588C2×Dic6C22×D312yes—
589C2×Dic6C22×D311yescharacteristic
590C3×C4⋊C4—22no—
591C3×C4⋊C4—32no—
592C3×C4⋊C4—32no—
593C3×C4⋊C4—32no—
594C3×C4⋊C4—32no—
595C3×C4⋊C4—32no—
596C3×C4⋊C4—32no—
597C3×C4⋊C4—32no—
598C3×C4⋊C4—32no—
599C3×C4⋊C4—32no—
600C3×C4⋊C4—32no—
601C3×C4⋊C4C22×D312yes—
602C3×C4⋊C4C22×D312yes—
603C3×C22⋊C4—22no—
604C3×C22⋊C4—21no—
605C3×C22⋊C4—32no—
606C3×C22⋊C4—32no—
607C3×C22⋊C4—31no—
608C3×C22⋊C4—32no—
609C3×C22⋊C4—32no—
610C3×C22⋊C4—31no—
611C3×C22⋊C4—32no—
612C3×C22⋊C4—32no—
613C3×C22⋊C4—32no—
614C3×C22⋊C4C22×D312yes—
615C3×C22⋊C4C22×D311yescharacteristic
616C3×C22⋊C4C22×D312yes—
617C3×C22⋊C4C22×D311yescharacteristic
618C3×C42—31no—
619C3×C42—32no—
620#217—31no—
621#217—31no—
622#217—32no—
623#217—32no—
624#217—32no—
625#217—32no—
626#217—32no—
627#217—61no—
628#217C22×D312yes—
629#217C22×D312yes—
630#217C22×D311yescharacteristic
631#217C22×D312yes—
632#217C22×D312yes—
633#217C22×D311yescharacteristic
634(C2×D3)⋊C4—32no—
635(C2×D3)⋊C4—32no—
636(C2×D3)⋊C4—32no—
637(C2×D3)⋊C4—32no—
638(C2×D3)⋊C4—32no—
639(C2×D3)⋊C4—32no—
640(C2×D3)⋊C4—32no—
641(C2×D3)⋊C4—32no—
642(C2×D3)⋊C4—32no—
643(C2×D3)⋊C4—32no—
644(C2×D3)⋊C4—32no—
645(C2×D3)⋊C4—32no—
646(C2×D3)⋊C4—32no—
647(C2×D3)⋊C4—32no—
648(C2×D3)⋊C4—32no—
649(C2×D3)⋊C4—32no—
650(C2×D3)⋊C4—32no—
651(C2×D3)⋊C4—32no—
652(C2×D3)⋊C4—32no—
653(C2×D3)⋊C4—32no—
654(C2×D3)⋊C4—32no—
655(C2×D3)⋊C4—32no—
656(C2×D3)⋊C4—32no—
657(C2×D3)⋊C4—32no—
658(C2×D3)⋊C4—32no—
659(C2×D3)⋊C4—62no—
660(C2×D3)⋊C4—62no—
661(C2×D3)⋊C4—62no—
662(C2×D3)⋊C4—62no—
663(C2×D3)⋊C4C22×D312yes—
664(C2×D3)⋊C4C22×D312yes—
665(C2×D3)⋊C4C22×D312yes—
666C4⋊Dic3—32no—
667C4⋊Dic3—32no—
668C4⋊Dic3—32no—
669C4⋊Dic3—32no—
670C4⋊Dic3—32no—
671C4⋊Dic3—62no—
672C4⋊Dic3C22×D312yes—
673C4⋊Dic3C22×D312yes—
674C4⋊Dic3C22×D312yes—
675Dic3⋊C4—32no—
676Dic3⋊C4—32no—
677Dic3⋊C4—32no—
678Dic3⋊C4—32no—
679Dic3⋊C4—32no—
680Dic3⋊C4—32no—
681Dic3⋊C4—32no—
682Dic3⋊C4—32no—
683Dic3⋊C4—32no—
684Dic3⋊C4—32no—
685Dic3⋊C4—32no—
686Dic3⋊C4—62no—
687Dic3⋊C4C22×D312yes—
688Dic3⋊C4C22×D312yes—
689Dic3⋊C4C22×D312yes—
690Dic3⋊C4C22×D312yes—
691Dic3⋊C4C22×D312yes—
692Dic3⋊C4C22×D312yes—
693Dic3⋊C4C22×D312yes—
694C4×Dic3—31no—
695C4×Dic3—31no—
696C4×Dic3—32no—
697C4×Dic3—32no—
698C4×Dic3—32no—
699C4×Dic3—32no—
700C4×Dic3—32no—
701C4×Dic3—32no—
702C4×Dic3—61no—
703C4×Dic3C22×D312yes—
704C4×Dic3C22×D311yescharacteristic
705C22×C32—21no—
706C22×C32—21no—
707C22×C32—22no—
708C22×C32—22no—
709C22×C32C2511yescharacteristic
710C2×C3⋊D3—22no—
711C2×C3⋊D3—22no—
712C2×C3⋊D3—22no—
713C2×C3⋊D3—22no—
714C2×C3⋊D3—22no—
715C2×C3⋊D3—22no—
716C2×C3⋊D3—82no—
717C2×C3×D3—22no—
718C2×C3×D3—21no—
719C2×C3×D3—21no—
720C2×C3×D3—22no—
721C2×C3×D3—22no—
722C2×C3×D3—44no—
723C2×C3×D3—82no—
724C2×C3×D3H(5,𝔽2)12yes—
725C32×C4—22no—
726C32×C4—21no—
727C32×C4—22no—
728C3⋊Dic3—22no—
729C3⋊Dic3—22no—
730C3×Dic3—22no—
731C3×Dic3—22no—
732C3×Dic3—21no—
733C3×Dic3—22no—
734C3×Dic3—22no—
735C3×Dic3—22no—
736C3×Dic3—22no—
737C2×#41—92no—
738C2×#41—91no—
739C22×D4—31no—
740C22×D4—91no—
741C23×C4—31no—
742C4⋊Q8—32no—
743#127—91no—
744#127—91no—
745#126—32no—
746#126—32no—
747#126—92no—
748#126—92no—
749#126—92no—
750#126—92no—
751#125—32no—
752#125—92no—
753#125—92no—
754#124—31no—
755#124—92no—
756#124—92no—
757#124—92no—
758#124—92no—
759#124—91no—
760#123—31no—
761#123—31no—
762#123—31no—
763#123—32no—
764#123—32no—
765#123—31no—
766#123—92no—
767#123—92no—
768#123—92no—
769#123—92no—
770#123—92no—
771#123—92no—
772#123—92no—
773#123—92no—
774#123—92no—
775#123—91no—
776#123—92no—
777#123D3211yescharacteristic
778C22⋊Q8—32no—
779C22⋊Q8—32no—
780C22⋊Q8—92no—
781C22⋊Q8—92no—
782C22⋊Q8—92no—
783C22⋊Q8—92no—
784C22⋊Q8—92no—
785C22⋊Q8—92no—
786#121—92no—
787#121—92no—
788#121—92no—
789#121—92no—
790#121—92no—
791#121—92no—
792#121—92no—
793#121—92no—
794#121—92no—
795#121—92no—
796#121—92no—
797#121—92no—
798#120—91no—
799#120—92no—
800#120—92no—
801#120—92no—
802#120—91no—
803#120—92no—
804C4×Q8—92no—
805C4×D4—92no—
806C4×D4—92no—
807C4×D4—92no—
808C4×D4—92no—
809C4×D4—92no—
810C4×D4—92no—
811C4×D4—92no—
812C4×D4—92no—
813C4×D4—92no—
814#117—92no—
815#117—92no—
816#117—91no—
817#117—92no—
818C2×C4⋊C4—32no—
819C2×C4⋊C4—92no—
820C2×C22⋊C4—31no—
821C2×C22⋊C4—32no—
822C2×C22⋊C4—92no—
823C2×C22⋊C4—91no—
824C23×C3—21no—
825C23×C3—21no—
826C23×C3—31no—
827C23×C3—31no—
828C23×C3—31no—
829C23×C3—62no—
830C23×C3—62no—
831C23×C3—122no—
832C23×C3—122no—
833C23×C3C23×D311yescharacteristic
834C23×C3C23×D311yescharacteristic
835C23×C3C23×D311yescharacteristic
836C23×C3C23×D311yescharacteristic
837C22×D3—22no—
838C22×D3—22no—
839C22×D3—32no—
840C22×D3—32no—
841C22×D3—32no—
842C22×D3—32no—
843C22×D3—42no—
844C22×D3—42no—
845C22×D3—62no—
846C22×D3—62no—
847C22×D3—121no—
848C22×D3—121no—
849C22×D3—122no—
850C22×D3—122no—
851C22×D3—241no—
852C22×D3—242no—
853C22×D3C23×D311yescharacteristic
854C22×D3C23×D311yescharacteristic
855C22×D3C23×D311yescharacteristic
856C3×Q8—122no—
857C3×Q8—121no—
858C3×D4—41no—
859C3×D4—41no—
860C3×D4—81no—
861C3×D4—121no—
862C3×D4—121no—
863C3×D4—121no—
864C2×C3×C4—21no—
865C2×C3×C4—22no—
866C2×C3×C4—22no—
867C2×C3×C4—32no—
868C2×C3×C4—32no—
869C2×C3×C4—32no—
870C2×C3×C4—32no—
871C2×C3×C4—32no—
872C2×C3×C4—31no—
873C2×C3×C4—32no—
874C2×C3×C4—41no—
875C2×C3×C4—41no—
876C2×C3×C4—64no—
877C2×C3×C4—62no—
878C2×C3×C4—81no—
879C2×C3×C4—122no—
880C2×C3×C4—122no—
881C2×C3×C4—121no—
882C2×C3×C4—121no—
883C2×C3×C4C23×D311yescharacteristic
884C2×C3×C4C23×D311yescharacteristic
885C2×C3×C4C23×D312yes—
886C2×C3×C4C23×D312yes—
887C2×C3×C4C23×D312yes—
888C2×C3×C4C23×D312yes—
889#67—41no—
890#67—41no—
891#67—64no—
892#67—64no—
893#67—122no—
894#67—122no—
895#67—122no—
896#67—122no—
897#67—122no—
898#67—122no—
899#67—122no—
900#67—122no—
901#67—122no—
902#67—122no—
903#67—242no—
904#67—242no—
905#67—242no—
906C2×Dic3—32no—
907C2×Dic3—32no—
908C2×Dic3—32no—
909C2×Dic3—32no—
910C2×Dic3—41no—
911C2×Dic3—41no—
912C2×Dic3—62no—
913C2×Dic3—62no—
914C2×Dic3—122no—
915C2×Dic3C23×D312yes—
916C2×Dic3C23×D312yes—
917C2×Dic3C23×D312yes—
918C2×Dic3C23×D312yes—
919C2×Dic3C23×D312yes—
920C2×Dic3C23×D312yes—
921C2×Dic3C23×D311yescharacteristic
922D12—41no—
923D12—64no—
924D12—64no—
925D12—122no—
926D12—122no—
927D12—122no—
928D12—121no—
929D12—122no—
930D12—121no—
931D12—122no—
932D12—122no—
933D12—122no—
934D12—122no—
935D12—242no—
936D12—241no—
937D12—242no—
938C4×D3—24no—
939C4×D3—22no—
940C4×D3—42no—
941C4×D3—42no—
942C4×D3—122no—
943C4×D3—122no—
944C4×D3—122no—
945C4×D3—122no—
946C4×D3—122no—
947C4×D3—122no—
948C4×D3—122no—
949C4×D3—122no—
950C4×D3—122no—
951C4×D3—122no—
952C4×D3—122no—
953C4×D3—242no—
954Dic6—41no—
955Dic6—42no—
956Dic6—122no—
957Dic6—122no—
958C2×C32—41no—
959C2×C32—41no—
960C2×C32C2×H(5,𝔽2)11yescharacteristic
961C2×C32#58512yes—
962C3⋊D3—42no—
963C3⋊D3—42no—
964C3×D3—22no—
965C3×D3—41no—
966C3×D3—41no—
967C24—31no—
968C24—31no—
969C24—91no—
970#41—364no—
971#41—362no—
972C2×Q8—32no—
973C2×Q8—31no—
974C2×Q8—92no—
975C2×D4—31no—
976C2×D4—31no—
977C2×D4—31no—
978C2×D4—92no—
979C2×D4—92no—
980C2×D4—92no—
981C2×D4—92no—
982C2×D4—92no—
983C2×D4—92no—
984C2×D4—92no—
985C2×D4—92no—
986C2×D4—92no—
987C2×D4—92no—
988C2×D4—92no—
989C2×D4—91no—
990C2×D4—122no—
991C2×D4—362no—
992C2×D4C2×D3211yescharacteristic
993C22×C4—31no—
994C22×C4—31no—
995C22×C4—32no—
996C22×C4—31no—
997C22×C4—32no—
998C22×C4—32no—
999C22×C4—92no—
1000C22×C4—92no—
1001C22×C4—92no—
1002C22×C4—92no—
1003C22×C4—92no—
1004C22×C4—92no—
1005C22×C4—122no—
1006C22×C4C2×D3211yescharacteristic
1007C4⋊C4—32no—
1008C4⋊C4—32no—
1009C4⋊C4—32no—
1010C4⋊C4—32no—
1011C4⋊C4—32no—
1012C4⋊C4—32no—
1013C4⋊C4—32no—
1014C4⋊C4—32no—
1015C4⋊C4—32no—
1016C4⋊C4—32no—
1017C4⋊C4—92no—
1018C4⋊C4—92no—
1019C4⋊C4—92no—
1020C4⋊C4—92no—
1021C4⋊C4—92no—
1022C4⋊C4—92no—
1023C4⋊C4—92no—
1024C4⋊C4—92no—
1025C4⋊C4C2×D3212yes—
1026C22⋊C4—32no—
1027C22⋊C4—31no—
1028C22⋊C4—32no—
1029C22⋊C4—31no—
1030C22⋊C4—32no—
1031C22⋊C4—32no—
1032C22⋊C4—32no—
1033C22⋊C4—32no—
1034C22⋊C4—32no—
1035C22⋊C4—92no—
1036C22⋊C4—92no—
1037C22⋊C4—92no—
1038C22⋊C4—92no—
1039C22⋊C4—92no—
1040C22⋊C4—92no—
1041C22⋊C4—92no—
1042C22⋊C4—92no—
1043C22⋊C4—92no—
1044C22⋊C4—92no—
1045C22⋊C4—92no—
1046C22⋊C4—91no—
1047C22⋊C4—92no—
1048C22⋊C4—92no—
1049C22⋊C4—92no—
1050C22⋊C4—92no—
1051C22⋊C4C2×D3212yes—
1052C22⋊C4C2×D3211yescharacteristic
1053C42—31no—
1054C42—32no—
1055C42—92no—
1056C42—92no—
1057C42—92no—
1058C42—91no—
1059C22×C3—21no—
1060C22×C3—21no—
1061C22×C3—22no—
1062C22×C3—22no—
1063C22×C3—21no—
1064C22×C3—21no—
1065C22×C3—22no—
1066C22×C3—22no—
1067C22×C3—21no—
1068C22×C3—32no—
1069C22×C3—42no—
1070C22×C3—42no—
1071C22×C3—41no—
1072C22×C3—41no—
1073C22×C3—62no—
1074C22×C3—61no—
1075C22×C3—61no—
1076C22×C3—62no—
1077C22×C3—62no—
1078C22×C3—124no—
1079C22×C3—242no—
1080C22×C3C24×D311yescharacteristic
1081C22×C3C24×D311yescharacteristic
1082C2×D3—22no—
1083C2×D3—21no—
1084C2×D3—21no—
1085C2×D3—22no—
1086C2×D3—22no—
1087C2×D3—44no—
1088C2×D3—62no—
1089C2×D3—62no—
1090C2×D3—62no—
1091C2×D3—62no—
1092C2×D3—62no—
1093C2×D3—62no—
1094C2×D3—62no—
1095C2×D3—62no—
1096C2×D3—62no—
1097C2×D3—62no—
1098C2×D3—62no—
1099C2×D3—62no—
1100C2×D3—82no—
1101C2×D3—122no—
1102C2×D3—122no—
1103C2×D3—122no—
1104C2×D3—122no—
1105C2×D3—122no—
1106C2×D3—122no—
1107C2×D3—242no—
1108C2×D3—242no—
1109C2×D3—244no—
1110C2×D3#100412yes—
1111C3×C4—22no—
1112C3×C4—21no—
1113C3×C4—22no—
1114C3×C4—22no—
1115C3×C4—21no—
1116C3×C4—22no—
1117C3×C4—42no—
1118C3×C4—42no—
1119C3×C4—41no—
1120C3×C4—62no—
1121C3×C4—62no—
1122C3×C4—62no—
1123C3×C4—62no—
1124C3×C4—62no—
1125C3×C4—61no—
1126C3×C4—62no—
1127Dic3—22no—
1128Dic3—21no—
1129Dic3—22no—
1130Dic3—22no—
1131Dic3—22no—
1132Dic3—22no—
1133Dic3—22no—
1134Dic3—62no—
1135Dic3—62no—
1136Dic3—62no—
1137Dic3—62no—
1138Dic3—122no—
1139Dic3—122no—
1140C32#353311yescharacteristic, complemented, Sylow
1141C23—31no—
1142C23—31no—
1143C23—31no—
1144C23—62no—
1145C23—62no—
1146C23—92no—
1147C23—92no—
1148C23—122no—
1149C23—122no—
1150C23—361no—
1151C23—362no—
1152C23C22×D3211yescharacteristic
1153C23C22×D3211yescharacteristic
1154Q8—122no—
1155Q8—121no—
1156Q8—362no—
1157D4—41no—
1158D4—121no—
1159D4—121no—
1160D4—121no—
1161D4—184no—
1162D4—184no—
1163D4—362no—
1164D4—361no—
1165D4—362no—
1166D4—362no—
1167D4—362no—
1168D4—362no—
1169D4—362no—
1170D4—362no—
1171D4—362no—
1172D4—362no—
1173C2×C4—32no—
1174C2×C4—32no—
1175C2×C4—32no—
1176C2×C4—32no—
1177C2×C4—32no—
1178C2×C4—32no—
1179C2×C4—31no—
1180C2×C4—41no—
1181C2×C4—64no—
1182C2×C4—62no—
1183C2×C4—92no—
1184C2×C4—92no—
1185C2×C4—122no—
1186C2×C4—122no—
1187C2×C4—121no—
1188C2×C4—121no—
1189C2×C4—362no—
1190C2×C4—362no—
1191C2×C4—362no—
1192C2×C4—362no—
1193C2×C4—362no—
1194C2×C4—362no—
1195C2×C4C22×D3211yescharacteristic
1196C2×C4C22×D3212yes—
1197C2×C4C22×D3212yes—
1198C2×C3—21no—
1199C2×C3—22no—
1200C2×C3—41no—
1201C2×C3—41no—
1202C2×C3—41no—
1203C2×C3—41no—
1204C2×C3—62no—
1205C2×C3—81no—
1206C2×C3—81no—
1207C2×C3—121no—
1208C2×C3—121no—
1209C2×C3C2×#100411yescharacteristic
1210C2×C3#596412yes—
1211C2×C3D3×H(5,𝔽2)11yescharacteristic
1212C2×C3#596812yes—
1213D3—22no—
1214D3—41no—
1215D3—41no—
1216D3—122no—
1217D3—122no—
1218D3—122no—
1219D3—122no—
1220D3—242no—
1221D3—242no—
1222C22—21no—
1223C22—21no—
1224C22—22no—
1225C22—22no—
1226C22—32no—
1227C22—62no—
1228C22—61no—
1229C22—61no—
1230C22—62no—
1231C22—62no—
1232C22—124no—
1233C22—182no—
1234C22—182no—
1235C22—182no—
1236C22—182no—
1237C22—182no—
1238C22—182no—
1239C22—242no—
1240C22—722no—
1241C22C23×D3211yescharacteristic
1242C4—22no—
1243C4—21no—
1244C4—22no—
1245C4—62no—
1246C4—61no—
1247C4—62no—
1248C4—62no—
1249C4—62no—
1250C4—62no—
1251C4—62no—
1252C4—182no—
1253C4—182no—
1254C3—21no—
1255C3#8601611yescharacteristic, complemented
1256C3#8712811yescharacteristic, complemented
1257C2—41no—
1258C2—41no—
1259C2—62no—
1260C2—121no—
1261C2—121no—
1262C2—362no—
1263C2—362no—
1264C2D3×#100411yescharacteristic
1265C2#1059669712yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#123C22
hypercenter#123D32
hypocenterC32#3533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. #10596137C2semidirect
2. C3×D3×#123C2semidirect
3. C3×#5651C2semidirect
4. #10595235C2semidirect
5. #10595234C2semidirect
6. #10595212C2semidirect
7. #10595208C2semidirect
8. #10595005C2semidirect
9. #10594978C2semidirect
10. #10594517C2semidirect
11. #10594467C2semidirect
12. #10594458C2semidirect
13. #10594331C2semidirect
14. #10594232C2semidirect
15. #10594199C2semidirect
16. #10594187C2semidirect
17. #10594157C2semidirect
18. #10594093C2semidirect
19. #10594041C2semidirect
23. C22×C3×C4×D3C22semidirect
26. C2×#3799C22semidirect
30. #64139C22semidirect
31. #64107C22semidirect
32. #64104C22semidirect
33. #64093C22semidirect
34. #64092C22semidirect
35. #64091C22semidirect
39. C3×#929C22semidirect
40. C3×#924C22semidirect
41. C3×#894C22semidirect
42. C3×D3×C4⋊C4C22semidirect
43. C3×#889C22semidirect
44. C3×#888C22semidirect
45. C3×#886C22semidirect
48. C3×D3×C22⋊C4C22semidirect
49. C3×#879C22semidirect
50. C3×#879C22semidirect
51. C3×#878C22semidirect
55. #63977C22semidirect
56. #63975C22semidirect
57. #63974C22semidirect
62. #63958C22semidirect
63. #63956C22semidirect
64. #63953C22semidirect
65. #63953C22semidirect
66. #63952C22semidirect
67. #63952C22semidirect
68. #63952C22semidirect
69. #63911C22semidirect
70. #63910C22semidirect
71. #63910C22semidirect
72. #63910C22semidirect
74. #63909C22semidirect
75. #63907C22semidirect
77. #63904C22semidirect
78. #63904C22semidirect
79. C4×#626C22semidirect
80. #63900C22semidirect
81. #63897C22semidirect
82. #63897C22semidirect
83. #63895C22semidirect
84. #63894C22semidirect
85. #63893C22semidirect
86. #63890C22semidirect
87. #63888C22semidirect
88. #63888C22semidirect
90. #63881C22semidirect
91. #63877C22semidirect
92. #63863C22semidirect
93. #63858C22semidirect
94. #63856C22semidirect
95. #63855C22semidirect
96. #63854C22semidirect
97. #63853C22semidirect
98. #63852C22semidirect
99. #63851C22semidirect
102. #63850C22semidirect
103. #63848C22semidirect
104. #63847C22semidirect
105. #63845C22semidirect
106. #63841C22semidirect
107. #63838C22semidirect
108. #63836C22semidirect
137. D3×#123D3semidirect
138. #5651D3semidirect
250. C22×C4×D3C2×D3semidirect
305. #929C2×D3semidirect
317. #924C2×D3semidirect
349. #894C2×D3semidirect
359. D3×C4⋊C4C2×D3semidirect
364. #889C2×D3semidirect
365. #888C2×D3semidirect
369. #886C2×D3semidirect
408. D3×C22⋊C4C2×D3semidirect
412. #879C2×D3semidirect
413. #879C2×D3semidirect
415. #878C2×D3semidirect
1140. C32#3533semidirect
1255. C3#86016semidirect
1256. C3#87128semidirect

Maximal subgroups

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

subgroupindex
#105961372
C3×D3×#1232
C3×#56512
#105952352
#105952342
#105952122
#105952082
#105950052
#105949782
#105945172
#105944672
#105944582
#105943312
#105942322
#105941992
#105941872
#105941572
#105940932
#105940412
#871283
#860163