Finite Group Databasebeta

← #11910738

Subgroups — #11910738

Order 1152.

2238 conjugacy classes of subgroups.

The subgroup lattice has 1260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596135C211yesmaximal, characteristic, complemented
2C3×#5653C211yesmaximal, characteristic, complemented
3C3×#5651C211yesmaximal, characteristic, complemented
4#10595261C211yesmaximal, characteristic, complemented
5#10595235C211yesmaximal, characteristic, complemented
6#10595176C211yesmaximal, characteristic, complemented
7D3×#935C211yesmaximal, characteristic, complemented
8#10594968C212yesmaximal, complemented
9#10594889C212yesmaximal, complemented
10#10594563C212yesmaximal, complemented
11#10594494C212yesmaximal, complemented
12#10594430C212yesmaximal, complemented
13#10594372C212yesmaximal, complemented
14#10594217C212yesmaximal, complemented
15#10594174C212yesmaximal, complemented
16#10594126C212yesmaximal, complemented
17#10594126C212yesmaximal, complemented
18#10594094C212yesmaximal, complemented
19#10594055C212yesmaximal, complemented
20#87128—31nomaximal
21#86300—31nomaximal
22C2×C3×D3×D4C2211yescharacteristic
23C22×C3×D12C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic, complemented
25C2×#3799C2211yescharacteristic, complemented
26C2×#3796C2212yes—
27C32×#123C2211yescharacteristic
28#64149C2211yescharacteristic
29#64144C2211yescharacteristic
30C4×#638C2212yescomplemented
31#64103C2212yescomplemented
32#64096C2212yescomplemented
33#64094C2212yescomplemented
34#64094C2212yescomplemented
35#64090C2212yescomplemented
36C3×#937C2211yescharacteristic
37C3×#936C2211yescharacteristic
38C3×#935C2211yescharacteristic
39C3×#929C2211yescharacteristic
40C3×#924C2212yescomplemented
41C3×#895C2212yes—
42C3×#894C2212yes—
43C3×#889C2212yescomplemented
44C3×#888C2212yescomplemented
45C3×#884C2212yes—
46C3×#882C2212yes—
47C3×#882C2211yescharacteristic
48C3×D3×C22⋊C4C2211yescharacteristic
49C3×#879C2212yescomplemented
50C3×#879C2212yescomplemented
51C3×#878C2212yescomplemented
52#63978C2212yescomplemented
53#63977C2212yes—
54#63977C2212yescomplemented
55#63977C2212yescomplemented
56#63975C2212yescomplemented
57#67⋊Dic3C2212yescomplemented
58#63969C2212yes—
59#63969C2212yescomplemented
60D3×#217C2212yes—
61D3×#217C2212yescomplemented
62D3×#217C2211yescharacteristic, complemented
63#63962C2211yescharacteristic, complemented
64#63961C2211yescharacteristic, complemented
65#63958C2212yes—
66#63958C2212yescomplemented
67#63958C2212yescomplemented
68#63956C2212yescomplemented
69#63916C2212yescomplemented
70#63911C2211yescharacteristic, complemented
71#63910C2212yescomplemented
72#63904C2212yescomplemented
73#63898C2212yes—
74#63898C2212yescomplemented
75#63896C2212yescomplemented
76#63896C2212yescomplemented
77#63890C2212yescomplemented
78#63888C2212yescomplemented
79#63887C2212yescomplemented
80#63887C2212yescomplemented
81#63886C2212yes—
82#63886C2212yescomplemented
83#63886C2212yescomplemented
84#63886C2212yescomplemented
85#63884C2212yes—
86#63884C2212yescomplemented
87#63884C2212yescomplemented
88#63883C2212yescomplemented
89#63881C2212yescomplemented
90#63880C2212yescomplemented
91#63880C2212yescomplemented
92#63878C2212yescomplemented
93#63877C2212yescomplemented
94D3×Dic3⋊C4C2212yescomplemented
95#63870C2212yescomplemented
96#63863C2212yescomplemented
97#63863C2211yescharacteristic, complemented
98#63862C2212yescomplemented
99#63862C2212yescomplemented
100#63862C2212yescomplemented
101#63860C2212yescomplemented
102#63857C2212yescomplemented
103#63855C2212yescomplemented
104#63855C2211yescharacteristic, complemented
105#63854C2212yescomplemented
106#63854C2212yescomplemented
107#63850C2212yescomplemented
108#63846C2212yescomplemented
109C3×#563—31no—
110C3×#534—31no—
111#5806—32no—
112#5805—31no—
113C2×#935—31no—
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#5666—31no—
125#5664—31no—
126#5664—31no—
127#5664—61no—
128#5660—32no—
129#5655—32no—
130#5653D311yescharacteristic, complemented
131D3×#123—31no—
132#5651D311yescharacteristic, complemented
133#5650—32no—
134#5647—32no—
135#5638—32no—
136#5630—32no—
137#5627—32no—
138#5621—32no—
139#5615—32no—
140#5614—32no—
141#5603—32no—
142#5595—31no—
143#5593—32no—
144#5593—32no—
145#5587—31no—
146#5586—32no—
147#5495—32no—
148C23×C3×D3C2311yescharacteristic
149C23×C3×D3C2311yescharacteristic
150C23×C3×D3C2311yescharacteristic
151C2×C32×D4C2311yescharacteristic
152C22×C32×C4C2311yescharacteristic
153C2×#638C2312yes—
154C2×#638C2312yes—
155C22×C3⋊Dic3C2311yescharacteristic
156C2×C4⋊(C3⋊D3)C2311yescharacteristic
157C2×C4×C3⋊D3C2312yes—
158C2×#634C2312yes—
159C2×C3×#67C2312yes—
160C2×C3×#67C2311yescharacteristic
161C2×C3×#67C2311yescharacteristic
162C22×C3×Dic3C2311yescharacteristic
163C3×D3×D4—42no—
164C2×C3×D12—42no—
165C2×C3×D12C2312yes—
166C2×C3×D12C2312yes—
167C2×C3×D12C2312yes—
168C2×C3×D12C2311yescharacteristic
169C2×C3×C4×D3C2311yescharacteristic
170C2×C3×C4×D3C2312yes—
171C2×C3×Dic6C2312yes—
172C2×C3×Dic6C2311yescharacteristic
173C2×#626C2312yes—
174C2×#626C2312yes—
175C2×#626C2312yes—
176C2×#626C2312yes—
177C2×#626C2312yes—
178C2×#624C2312yes—
179C2×#624C2312yes—
180C2×D3×Dic3—42no—
181C2×D3×Dic3C2312yes—
182C2×D3×Dic3C2312yes—
183C2×D3×Dic3C2312yes—
184C2×D3×Dic3C2312yes—
185C2×D3×Dic3C2312yes—
186#3799—42no—
187#3796—44no—
188C32×C4⋊C4C2312yes—
189C32×C22⋊C4C2312yes—
190C32×C22⋊C4C2311yescharacteristic
191#3757C2311yescharacteristic
192#3757C2312yes—
193#3752C2312yes—
194#3752C2312yes—
195#3752C2312yes—
196#3750C2312yes—
197#3750C2312yes—
198C4×C3⋊Dic3C2312yes—
199C4×C3⋊Dic3C2312yes—
200C4×C3⋊Dic3C2311yescharacteristic
201C3×#217C2312yes—
202C3×#217C2311yescharacteristic
203C3×#217C2312yes—
204C3×#217C2312yes—
205C3×#217C2311yescharacteristic
206C3×(C2×D3)⋊C4C2312yes—
207C3×(C2×D3)⋊C4C2312yes—
208C3×(C2×D3)⋊C4C2312yes—
209C3×(C2×D3)⋊C4C2312yes—
210C3×C4⋊Dic3C2312yes—
211C3×C4⋊Dic3C2312yes—
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—
222Dic3⋊Dic3C2312yes—
223Dic3⋊Dic3C2312yes—
224Dic3⋊Dic3C2312yes—
225Dic3⋊Dic3C2312yes—
226Dic3⋊Dic3C2312yes—
227Dic3⋊Dic3C2312yes—
228#3722C2312yes—
229(C2×D3)⋊Dic3C2312yes—
230(C2×D3)⋊Dic3C2312yes—
231(C2×D3)⋊Dic3C2312yes—
232(C2×D3)⋊Dic3C2312yes—
233(C2×D3)⋊Dic3C2312yes—
234(C2×D3)⋊Dic3C2312yes—
235(C2×D3)⋊Dic3C2312yes—
236(C2×D3)⋊Dic3C2312yes—
237(C2×D3)⋊Dic3C2312yes—
238(C2×D3)⋊Dic3C2312yes—
239Dic32C2312yes—
240#3533—91noSylow
241C22×C3×D4—31no—
242C22×C3×D4—31no—
243C23×Dic3—31no—
244C2×#239—32no—
245C2×#239—31no—
246C2×#237—32no—
247C2×D3×D4C2×D311yescharacteristic
248C2×#235—31no—
249C22×D12C2×D311yescharacteristic
250C22×C4×D3—31no—
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—32no—
260C3×#123C2×D311yescharacteristic
261C3×#123C2×D311yescharacteristic
262C3×C22⋊Q8—32no—
263C3×C22⋊Q8—32no—
264C3×#121—32no—
265C3×#121—32no—
266C3×#120—31no—
267C3×#120—32no—
268C3×#120—31no—
269C2×C3×C22⋊C4—31no—
270#953—32no—
271#953—32no—
272#953—32no—
273C2×#217—32no—
274C2×#217—31no—
275C2×#217—32no—
276#947—32no—
277#947—31no—
278#946—32no—
279#946—32no—
280#946—32no—
281#940—31no—
282#940—31no—
283#940—31no—
284#940—61no—
285#939—32no—
286#939—32no—
287#939—32no—
288#939—32no—
289#939—32no—
290#938—32no—
291#938—32no—
292#938—32no—
293#938—32no—
294#937C2×D311yescharacteristic
295#936—31no—
296#936—32no—
297#936—32no—
298#936C2×D311yescharacteristic
299#935—31no—
300#935—31no—
301#935—31no—
302#935—32no—
303#935—31no—
304#935—32no—
305#935—32no—
306#935—32no—
307#935—32no—
308#935—61no—
309#935C2×D311yescharacteristic
310D4×Dic3—32no—
311D4×Dic3—32no—
312D4×Dic3—32no—
313#930—32no—
314#929—31no—
315#929—32no—
316#929C2×D311yescharacteristic
317C4×#67—32no—
318C4×#67—32no—
319C4×#67—32no—
320C4×#67—62no—
321#926—31no—
322#926—32no—
323#924—32no—
324#924C2×D312yescomplemented
325C2×Dic3⋊C4—32no—
326#898—32no—
327#898—32no—
328#898—32no—
329#897—32no—
330#896—32no—
331#896—32no—
332#896—32no—
333#895—32no—
334#895—32no—
335#895—32no—
336#895—32no—
337#895—32no—
338#895—32no—
339#895C2×D312yes—
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#894—62no—
350#894C2×D312yes—
351#893—32no—
352#893—32no—
353#893—32no—
354#893—32no—
355#892—32no—
356D3×C4⋊C4—32no—
357D3×C4⋊C4—32no—
358D3×C4⋊C4—32no—
359#890—32no—
360#889—32no—
361#889—32no—
362#889—32no—
363#889C2×D312yescomplemented
364#888C2×D312yescomplemented
365#887—32no—
366#887—32no—
367#887—62no—
368#886—31no—
369#886—32no—
370#885—32no—
371#885—32no—
372#885—32no—
373#885—32no—
374#885—62no—
375#885—62no—
376#884—32no—
377#884—32no—
378#884—32no—
379#884—32no—
380#884C2×D312yes—
381#883—32no—
382#883—32no—
383#883—32no—
384#883—32no—
385#883—32no—
386#883—32no—
387#882—32no—
388#882—32no—
389#882—32no—
390#882C2×D311yescharacteristic
391#882C2×D312yes—
392#67⋊C4—32no—
393#67⋊C4—32no—
394#67⋊C4—32no—
395#67⋊C4—32no—
396#67⋊C4—32no—
397#67⋊C4—32no—
398#67⋊C4—62no—
399D3×C22⋊C4—31no—
400D3×C22⋊C4—32no—
401D3×C22⋊C4—32no—
402D3×C22⋊C4C2×D311yescharacteristic
403#879—32no—
404#879—32no—
405#879—32no—
406#879—32no—
407#879—32no—
408#879C2×D312yescomplemented
409#879C2×D312yescomplemented
410#878—32no—
411#878—32no—
412#878—32no—
413#878—32no—
414#878C2×D312yescomplemented
415#877—32no—
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⋊D3C2412yes—
427C22×C3×D3—22no—
428C22×C3×D3—22no—
429C22×C3×D3—42no—
430C22×C3×D3—42no—
431C22×C3×D3—42no—
432C22×C3×D3—41no—
433C22×C3×D3C2411yescharacteristic
434C22×C3×D3C2411yescharacteristic
435C22×C3×D3C2412yes—
436C22×C3×D3C2411yescharacteristic
437C32×D4—41no—
438C2×C32×C4—41no—
439C2×C32×C4C2412yes—
440C2×C32×C4C2411yescharacteristic
441C2×C32×C4C2412yes—
442#638—42no—
443#638—42no—
444C2×C3⋊Dic3—41no—
445C2×C3⋊Dic3C2412yes—
446C2×C3⋊Dic3C2412yes—
447C2×C3⋊Dic3C2412yes—
448C4⋊(C3⋊D3)—41no—
449C4×C3⋊D3—42no—
450#634—42no—
451C3×#67—41no—
452C3×#67—41no—
453C3×#67—42no—
454C2×C3×Dic3—41no—
455C2×C3×Dic3C2412yes—
456C2×C3×Dic3C2412yes—
457C2×C3×Dic3C2412yes—
458C2×C3×Dic3C2412yes—
459C2×C3×Dic3C2412yes—
460C2×C3×Dic3C2411yescharacteristic
461C3×D12—24no—
462C3×D12—42no—
463C3×D12—42no—
464C3×D12—41no—
465C3×C4×D3—22no—
466C3×C4×D3—42no—
467C3×Dic6—42no—
468C3×Dic6—41no—
469#626—24no—
470#626—42no—
471#626—42no—
472#626—42no—
473#626—42no—
474#624—42no—
475#624—42no—
476D3×Dic3—24no—
477D3×Dic3—42no—
478D3×Dic3—42no—
479D3×Dic3—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—31no—
498#525—92no—
499C2×#123—91no—
500C24×C3—31no—
501C24×C3—31no—
502C24×C3—31no—
503C23×D3C22×D311yescharacteristic
504C23×D3C22×D311yescharacteristic
505C23×D3C22×D311yescharacteristic
506C2×C3×Q8—32no—
507C2×C3×Q8—31no—
508C2×C3×D4—21no—
509C2×C3×D4—32no—
510C2×C3×D4—31no—
511C2×C3×D4—31no—
512C2×C3×D4—32no—
513C2×C3×D4—32no—
514C2×C3×D4—31no—
515C2×C3×D4—32no—
516C2×C3×D4—122no—
517C2×C3×D4—122no—
518C2×C3×D4C22×D311yescharacteristic
519C2×C3×D4C22×D311yescharacteristic
520C22×C3×C4—21no—
521C22×C3×C4—31no—
522C22×C3×C4—31no—
523C22×C3×C4—32no—
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—62no—
536C2×#67—62no—
537C2×#67C22×D312yes—
538C2×#67C22×D311yescharacteristic
539C2×#67C22×D311yescharacteristic
540C22×Dic3—31no—
541C22×Dic3—31no—
542C22×Dic3—32no—
543C22×Dic3—32no—
544C22×Dic3—32no—
545C22×Dic3—32no—
546C22×Dic3—32no—
547C22×Dic3—61no—
548C22×Dic3—122no—
549C22×Dic3C22×D311yescharacteristic
550#239—122no—
551#239—124no—
552#237—124no—
553D3×D4—42no—
554#235—122no—
555C2×D12—32no—
556C2×D12—32no—
557C2×D12—32no—
558C2×D12—32no—
559C2×D12—32no—
560C2×D12—31no—
561C2×D12—31no—
562C2×D12—42no—
563C2×D12—61no—
564C2×D12C22×D312yes—
565C2×D12C22×D311yescharacteristic
566C2×D12C22×D312yes—
567C2×D12C22×D312yes—
568C2×C4×D3—32no—
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—62no—
580C2×C4×D3—122no—
581C2×C4×D3C22×D311yescharacteristic
582C2×C4×D3C22×D312yes—
583C2×Dic6—32no—
584C2×Dic6—32no—
585C2×Dic6—62no—
586C2×Dic6C22×D311yescharacteristic
587C2×Dic6C22×D312yes—
588C3×C4⋊C4—22no—
589C3×C4⋊C4—32no—
590C3×C4⋊C4—32no—
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⋊C4C22×D312yes—
598C3×C4⋊C4C22×D312yes—
599C3×C22⋊C4—22no—
600C3×C22⋊C4—21no—
601C3×C22⋊C4—31no—
602C3×C22⋊C4—32no—
603C3×C22⋊C4—32no—
604C3×C22⋊C4—31no—
605C3×C22⋊C4—32no—
606C3×C22⋊C4—32no—
607C3×C22⋊C4—32no—
608C3×C22⋊C4—32no—
609C3×C22⋊C4—32no—
610C3×C22⋊C4C22×D312yes—
611C3×C22⋊C4C22×D311yescharacteristic
612C3×C22⋊C4C22×D311yescharacteristic
613C3×C22⋊C4C22×D312yes—
614C3×C42—31no—
615C3×C42—32no—
616#217—32no—
617#217—32no—
618#217—31no—
619#217—31no—
620#217—32no—
621#217—32no—
622#217—32no—
623#217—32no—
624#217—32no—
625#217—32no—
626#217—32no—
627#217—32no—
628#217—32no—
629#217—32no—
630#217—61no—
631#217—62no—
632#217C22×D312yes—
633#217C22×D311yescharacteristic
634#217C22×D312yes—
635#217C22×D311yescharacteristic
636#217C22×D312yes—
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—62no—
656(C2×D3)⋊C4—62no—
657(C2×D3)⋊C4—62no—
658(C2×D3)⋊C4C22×D312yes—
659(C2×D3)⋊C4C22×D312yes—
660(C2×D3)⋊C4C22×D312yes—
661(C2×D3)⋊C4C22×D312yes—
662C4⋊Dic3—32no—
663C4⋊Dic3—32no—
664C4⋊Dic3—32no—
665C4⋊Dic3—32no—
666C4⋊Dic3—32no—
667C4⋊Dic3—32no—
668C4⋊Dic3C22×D312yes—
669C4⋊Dic3C22×D312yes—
670Dic3⋊C4—32no—
671Dic3⋊C4—32no—
672Dic3⋊C4—32no—
673Dic3⋊C4—32no—
674Dic3⋊C4—32no—
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—62no—
685Dic3⋊C4—62no—
686Dic3⋊C4C22×D312yes—
687Dic3⋊C4C22×D312yes—
688Dic3⋊C4C22×D312yes—
689Dic3⋊C4C22×D312yes—
690Dic3⋊C4C22×D312yes—
691Dic3⋊C4C22×D312yes—
692C4×Dic3—32no—
693C4×Dic3—31no—
694C4×Dic3—32no—
695C4×Dic3—31no—
696C4×Dic3—32no—
697C4×Dic3—32no—
698C4×Dic3—32no—
699C4×Dic3—32no—
700C4×Dic3—62no—
701C4×Dic3—62no—
702C4×Dic3—61no—
703C4×Dic3C22×D311yescharacteristic
704C4×Dic3C22×D312yes—
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—21no—
715C2×C3×D3—22no—
716C2×C3×D3—21no—
717C2×C3×D3—22no—
718C2×C3×D3—22no—
719C2×C3×D3—22no—
720C2×C3×D3—22no—
721C2×C3×D3—44no—
722C2×C3×D3—82no—
723C2×C3×D3—82no—
724C2×C3×D3H(5,𝔽2)12yes—
725C32×C4—21no—
726C32×C4—22no—
727C32×C4—22no—
728C3⋊Dic3—22no—
729C3⋊Dic3—22no—
730C3⋊Dic3—22no—
731C3×Dic3—22no—
732C3×Dic3—22no—
733C3×Dic3—21no—
734C3×Dic3—22no—
735C3×Dic3—22no—
736C3×Dic3—22no—
737C2×#41—91no—
738C2×#41—92no—
739C22×D4—31no—
740C22×D4—31no—
741C23×C4—91no—
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—91no—
757#124—92no—
758#124—92no—
759#124—92no—
760#123—31no—
761#123—31no—
762#123—32no—
763#123—92no—
764#123—92no—
765#123—92no—
766#123—92no—
767#123—92no—
768#123—91no—
769#123—92no—
770#123—92no—
771#123—92no—
772#123—92no—
773#123—92no—
774#123—91no—
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—32no—
787#121—32no—
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—31no—
799#120—32no—
800#120—31no—
801#120—92no—
802#120—92no—
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—91no—
816#117—92no—
817#117—92no—
818C2×C4⋊C4—92no—
819C2×C4⋊C4—92no—
820C2×C22⋊C4—31no—
821C2×C22⋊C4—91no—
822C2×C22⋊C4—92no—
823C2×C22⋊C4—92no—
824C23×C3—21no—
825C23×C3—21no—
826C23×C3—31no—
827C23×C3—31no—
828C23×C3—31no—
829C23×C3—32no—
830C23×C3—62no—
831C23×C3—62no—
832C23×C3—122no—
833C23×C3—121no—
834C23×C3—122no—
835C23×C3—122no—
836C23×C3C23×D311yescharacteristic
837C23×C3C23×D311yescharacteristic
838C23×C3C23×D311yescharacteristic
839C23×C3C23×D311yescharacteristic
840C22×D3—22no—
841C22×D3—22no—
842C22×D3—32no—
843C22×D3—32no—
844C22×D3—42no—
845C22×D3—41no—
846C22×D3—42no—
847C22×D3—42no—
848C22×D3—62no—
849C22×D3C23×D311yescharacteristic
850C22×D3C23×D311yescharacteristic
851C22×D3C23×D312yes—
852C22×D3C23×D311yescharacteristic
853C3×Q8—121no—
854C3×Q8—122no—
855C3×D4—41no—
856C3×D4—41no—
857C3×D4—64no—
858C3×D4—81no—
859C3×D4—122no—
860C3×D4—122no—
861C3×D4—121no—
862C3×D4—122no—
863C3×D4—121no—
864C3×D4—121no—
865C2×C3×C4—21no—
866C2×C3×C4—22no—
867C2×C3×C4—22no—
868C2×C3×C4—32no—
869C2×C3×C4—32no—
870C2×C3×C4—31no—
871C2×C3×C4—32no—
872C2×C3×C4—32no—
873C2×C3×C4—32no—
874C2×C3×C4—41no—
875C2×C3×C4—41no—
876C2×C3×C4—62no—
877C2×C3×C4—81no—
878C2×C3×C4—122no—
879C2×C3×C4—121no—
880C2×C3×C4C23×D311yescharacteristic
881C2×C3×C4C23×D312yes—
882C2×C3×C4C23×D311yescharacteristic
883C2×C3×C4C23×D312yes—
884C2×C3×C4C23×D312yes—
885C2×C3×C4C23×D312yes—
886#67—41no—
887#67—41no—
888#67—42no—
889#67—64no—
890#67—122no—
891#67—122no—
892#67—122no—
893#67—122no—
894#67—122no—
895#67—122no—
896#67—122no—
897#67—122no—
898#67—124no—
899#67—124no—
900C2×Dic3—32no—
901C2×Dic3—32no—
902C2×Dic3—32no—
903C2×Dic3—32no—
904C2×Dic3—32no—
905C2×Dic3—32no—
906C2×Dic3—41no—
907C2×Dic3—62no—
908C2×Dic3—62no—
909C2×Dic3—62no—
910C2×Dic3—64no—
911C2×Dic3—122no—
912C2×Dic3—122no—
913C2×Dic3—122no—
914C2×Dic3—122no—
915C2×Dic3—121no—
916C2×Dic3—121no—
917C2×Dic3—241no—
918C2×Dic3C23×D312yes—
919C2×Dic3C23×D312yes—
920C2×Dic3C23×D312yes—
921C2×Dic3C23×D312yes—
922C2×Dic3C23×D311yescharacteristic
923C2×Dic3C23×D312yes—
924D12—24no—
925D12—42no—
926D12—42no—
927D12—41no—
928D12—64no—
929D12—121no—
930D12—121no—
931D12—122no—
932D12—122no—
933D12—122no—
934D12—122no—
935D12—241no—
936C4×D3—22no—
937C4×D3—42no—
938C4×D3—64no—
939C4×D3—122no—
940C4×D3—122no—
941C4×D3—122no—
942C4×D3—122no—
943C4×D3—122no—
944C4×D3—122no—
945C4×D3—122no—
946C4×D3—122no—
947C4×D3—122no—
948C4×D3—122no—
949C4×D3—242no—
950Dic6—41no—
951Dic6—42no—
952Dic6—122no—
953Dic6—122no—
954Dic6—124no—
955C2×C32—41no—
956C2×C32—41no—
957C2×C32C2×H(5,𝔽2)11yescharacteristic
958C2×C32#58512yes—
959C3⋊D3—42no—
960C3×D3—22no—
961C3×D3—41no—
962C3×D3—42no—
963C3×D3—41no—
964C24—31no—
965C24—31no—
966C24—31no—
967#41—362no—
968#41—364no—
969C2×Q8—32no—
970C2×Q8—31no—
971C2×Q8—92no—
972C2×D4—32no—
973C2×D4—31no—
974C2×D4—31no—
975C2×D4—32no—
976C2×D4—32no—
977C2×D4—32no—
978C2×D4—31no—
979C2×D4—92no—
980C2×D4—92no—
981C2×D4—92no—
982C2×D4—92no—
983C2×D4—92no—
984C2×D4—92no—
985C2×D4—92no—
986C2×D4—91no—
987C2×D4—122no—
988C2×D4—122no—
989C2×D4C2×D3211yescharacteristic
990C22×C4—31no—
991C22×C4—31no—
992C22×C4—32no—
993C22×C4—92no—
994C22×C4—92no—
995C22×C4—92no—
996C22×C4—92no—
997C22×C4—92no—
998C22×C4—92no—
999C22×C4—92no—
1000C22×C4—91no—
1001C22×C4—92no—
1002C22×C4—362no—
1003C22×C4C2×D3211yescharacteristic
1004C4⋊C4—32no—
1005C4⋊C4—32no—
1006C4⋊C4—32no—
1007C4⋊C4—32no—
1008C4⋊C4—32no—
1009C4⋊C4—32no—
1010C4⋊C4—32no—
1011C4⋊C4—32no—
1012C4⋊C4—92no—
1013C4⋊C4—92no—
1014C4⋊C4—92no—
1015C4⋊C4—92no—
1016C4⋊C4—92no—
1017C4⋊C4—92no—
1018C4⋊C4—92no—
1019C4⋊C4—92no—
1020C4⋊C4—92no—
1021C4⋊C4—92no—
1022C4⋊C4C2×D3212yes—
1023C22⋊C4—31no—
1024C22⋊C4—32no—
1025C22⋊C4—32no—
1026C22⋊C4—31no—
1027C22⋊C4—32no—
1028C22⋊C4—32no—
1029C22⋊C4—32no—
1030C22⋊C4—32no—
1031C22⋊C4—32no—
1032C22⋊C4—92no—
1033C22⋊C4—92no—
1034C22⋊C4—92no—
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—91no—
1045C22⋊C4—92no—
1046C22⋊C4—92no—
1047C22⋊C4—92no—
1048C22⋊C4C2×D3211yescharacteristic
1049C22⋊C4C2×D3212yes—
1050C42—31no—
1051C42—32no—
1052C42—92no—
1053C42—92no—
1054C42—91no—
1055C42—92no—
1056C22×C3—21no—
1057C22×C3—21no—
1058C22×C3—21no—
1059C22×C3—21no—
1060C22×C3—22no—
1061C22×C3—22no—
1062C22×C3—22no—
1063C22×C3—22no—
1064C22×C3—21no—
1065C22×C3—32no—
1066C22×C3—41no—
1067C22×C3—42no—
1068C22×C3—42no—
1069C22×C3—41no—
1070C22×C3—62no—
1071C22×C3—61no—
1072C22×C3—62no—
1073C22×C3—61no—
1074C22×C3—62no—
1075C22×C3—62no—
1076C22×C3—62no—
1077C22×C3—62no—
1078C22×C3—124no—
1079C22×C3—242no—
1080C22×C3—242no—
1081C22×C3C24×D311yescharacteristic
1082C22×C3C24×D311yescharacteristic
1083C2×D3—22no—
1084C2×D3—21no—
1085C2×D3—22no—
1086C2×D3—21no—
1087C2×D3—22no—
1088C2×D3—22no—
1089C2×D3—22no—
1090C2×D3—22no—
1091C2×D3—44no—
1092C2×D3—62no—
1093C2×D3—62no—
1094C2×D3—62no—
1095C2×D3—62no—
1096C2×D3—62no—
1097C2×D3—62no—
1098C2×D3—82no—
1099C2×D3—82no—
1100C2×D3—122no—
1101C2×D3—122no—
1102C2×D3—122no—
1103C2×D3#100412yes—
1104C3×C4—21no—
1105C3×C4—22no—
1106C3×C4—22no—
1107C3×C4—21no—
1108C3×C4—22no—
1109C3×C4—22no—
1110C3×C4—42no—
1111C3×C4—42no—
1112C3×C4—41no—
1113C3×C4—62no—
1114C3×C4—62no—
1115C3×C4—61no—
1116C3×C4—62no—
1117C3×C4—62no—
1118C3×C4—62no—
1119Dic3—21no—
1120Dic3—22no—
1121Dic3—22no—
1122Dic3—22no—
1123Dic3—22no—
1124Dic3—22no—
1125Dic3—64no—
1126Dic3—62no—
1127Dic3—62no—
1128Dic3—62no—
1129Dic3—62no—
1130Dic3—62no—
1131Dic3—62no—
1132Dic3—122no—
1133Dic3—122no—
1134C32#353311yescharacteristic, complemented, Sylow
1135C23—31no—
1136C23—31no—
1137C23—32no—
1138C23—31no—
1139C23—62no—
1140C23—62no—
1141C23—92no—
1142C23—122no—
1143C23—121no—
1144C23—122no—
1145C23—122no—
1146C23C22×D3211yescharacteristic
1147C23C22×D3211yescharacteristic
1148Q8—122no—
1149Q8—121no—
1150Q8—362no—
1151D4—41no—
1152D4—64no—
1153D4—122no—
1154D4—121no—
1155D4—122no—
1156D4—121no—
1157D4—121no—
1158D4—122no—
1159D4—184no—
1160D4—361no—
1161D4—362no—
1162D4—362no—
1163D4—362no—
1164D4—362no—
1165D4—362no—
1166D4—362no—
1167C2×C4—32no—
1168C2×C4—32no—
1169C2×C4—32no—
1170C2×C4—32no—
1171C2×C4—31no—
1172C2×C4—32no—
1173C2×C4—41no—
1174C2×C4—62no—
1175C2×C4—92no—
1176C2×C4—92no—
1177C2×C4—92no—
1178C2×C4—122no—
1179C2×C4—121no—
1180C2×C4—184no—
1181C2×C4—362no—
1182C2×C4—362no—
1183C2×C4—362no—
1184C2×C4—362no—
1185C2×C4—362no—
1186C2×C4—362no—
1187C2×C4—362no—
1188C2×C4—361no—
1189C2×C4C22×D3212yes—
1190C2×C4C22×D3211yescharacteristic
1191C2×C4C22×D3212yes—
1192C2×C3—21no—
1193C2×C3—22no—
1194C2×C3—41no—
1195C2×C3—41no—
1196C2×C3—41no—
1197C2×C3—41no—
1198C2×C3—62no—
1199C2×C3—81no—
1200C2×C3—81no—
1201C2×C3—121no—
1202C2×C3—122no—
1203C2×C3—121no—
1204C2×C3C2×#100411yescharacteristic
1205C2×C3D3×H(5,𝔽2)11yescharacteristic
1206C2×C3#596612yes—
1207C2×C3#596812yes—
1208D3—22no—
1209D3—41no—
1210D3—42no—
1211D3—41no—
1212D3—122no—
1213D3—122no—
1214D3—242no—
1215C22—21no—
1216C22—21no—
1217C22—22no—
1218C22—22no—
1219C22—32no—
1220C22—62no—
1221C22—61no—
1222C22—62no—
1223C22—61no—
1224C22—62no—
1225C22—62no—
1226C22—62no—
1227C22—62no—
1228C22—124no—
1229C22—182no—
1230C22—182no—
1231C22—182no—
1232C22—242no—
1233C22—242no—
1234C22C23×D3211yescharacteristic
1235C4—22no—
1236C4—21no—
1237C4—22no—
1238C4—61no—
1239C4—62no—
1240C4—62no—
1241C4—62no—
1242C4—62no—
1243C4—62no—
1244C4—182no—
1245C4—182no—
1246C4—182no—
1247C3—21no—
1248C3#8630011yescharacteristic, complemented
1249C3#8712811yescharacteristic, complemented
1250C2—41no—
1251C2—41no—
1252C2—62no—
1253C2—121no—
1254C2—122no—
1255C2—121no—
1256C2—362no—
1257C2D3×#100411yescharacteristic
1258C2#1059669812yes—
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. #10596135C2semidirect
2. C3×#5653C2semidirect
3. C3×#5651C2semidirect
4. #10595261C2semidirect
5. #10595235C2semidirect
6. #10595176C2semidirect
7. D3×#935C2semidirect
8. #10594968C2semidirect
9. #10594889C2semidirect
10. #10594563C2semidirect
11. #10594494C2semidirect
12. #10594430C2semidirect
13. #10594372C2semidirect
14. #10594217C2semidirect
15. #10594174C2semidirect
16. #10594126C2semidirect
17. #10594126C2semidirect
18. #10594094C2semidirect
19. #10594055C2semidirect
24. C22×D3×Dic3C22semidirect
25. C2×#3799C22semidirect
30. C4×#638C22semidirect
31. #64103C22semidirect
32. #64096C22semidirect
33. #64094C22semidirect
34. #64094C22semidirect
35. #64090C22semidirect
40. C3×#924C22semidirect
43. C3×#889C22semidirect
44. C3×#888C22semidirect
49. C3×#879C22semidirect
50. C3×#879C22semidirect
51. C3×#878C22semidirect
52. #63978C22semidirect
54. #63977C22semidirect
55. #63977C22semidirect
56. #63975C22semidirect
57. #67⋊Dic3C22semidirect
59. #63969C22semidirect
61. D3×#217C22semidirect
62. D3×#217C22semidirect
63. #63962C22semidirect
64. #63961C22semidirect
66. #63958C22semidirect
67. #63958C22semidirect
68. #63956C22semidirect
69. #63916C22semidirect
70. #63911C22semidirect
71. #63910C22semidirect
72. #63904C22semidirect
74. #63898C22semidirect
75. #63896C22semidirect
76. #63896C22semidirect
77. #63890C22semidirect
78. #63888C22semidirect
79. #63887C22semidirect
80. #63887C22semidirect
82. #63886C22semidirect
83. #63886C22semidirect
84. #63886C22semidirect
86. #63884C22semidirect
87. #63884C22semidirect
88. #63883C22semidirect
89. #63881C22semidirect
90. #63880C22semidirect
91. #63880C22semidirect
92. #63878C22semidirect
93. #63877C22semidirect
94. D3×Dic3⋊C4C22semidirect
95. #63870C22semidirect
96. #63863C22semidirect
97. #63863C22semidirect
98. #63862C22semidirect
99. #63862C22semidirect
100. #63862C22semidirect
101. #63860C22semidirect
102. #63857C22semidirect
103. #63855C22semidirect
104. #63855C22semidirect
105. #63854C22semidirect
106. #63854C22semidirect
107. #63850C22semidirect
108. #63846C22semidirect
130. #5653D3semidirect
132. #5651D3semidirect
324. #924C2×D3semidirect
363. #889C2×D3semidirect
364. #888C2×D3semidirect
408. #879C2×D3semidirect
409. #879C2×D3semidirect
414. #878C2×D3semidirect
1134. C32#3533semidirect
1248. C3#86300semidirect
1249. C3#87128semidirect

Maximal subgroups

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

subgroupindex
#105961352
C3×#56532
C3×#56512
#105952612
#105952352
#105951762
D3×#9352
#105949682
#105948892
#105945632
#105944942
#105944302
#105943722
#105942172
#105941742
#105941262
#105940942
#105940552
#871283
#863003