Finite Group Databasebeta

← #11910743

Subgroups — #11910743

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#10596191C211yesmaximal, characteristic, complemented
2C3×#5715C211yesmaximal, characteristic, complemented
3C3×#5713C211yesmaximal, characteristic, complemented
4#10595276C211yesmaximal, characteristic, complemented
5#10595234C211yesmaximal, characteristic, complemented
6#10595216C212yesmaximal, complemented
7#10595214C212yesmaximal, complemented
8#10595208C211yesmaximal, characteristic, complemented
9#10595207C212yesmaximal, complemented
10#10595204C212yesmaximal, complemented
11#10595192C212yesmaximal, complemented
12#10595184C212yesmaximal, complemented
13#10595176C212yesmaximal, complemented
14#10595149C212yesmaximal, complemented
15D3×#935C211yesmaximal, characteristic, complemented
16#10595135C212yesmaximal, complemented
17#10595129C212yesmaximal, complemented
18#10593927C212yesmaximal, complemented
19#10593916C212yesmaximal, complemented
20#87065—31nomaximal
21#86321—31nomaximal
22C2×C3×#237C2211yescharacteristic, complemented
23C2×C3×D3×D4C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C2×#3804C2212yes—
26C22×D3×Dic3C2211yescharacteristic, complemented
27C32×#127C2211yescharacteristic
28#64148C2212yescomplemented
29#64148C2212yescomplemented
30#64148C2212yescomplemented
31#64146C2211yescharacteristic
32#64146C2212yescomplemented
33#64144C2211yescharacteristic
34#64144C2212yescomplemented
35#64085C2212yescomplemented
36C3×#940C2211yescharacteristic, complemented
37C3×#939C2212yes—
38C3×#939C2212yescomplemented
39C3×#937C2212yes—
40C3×#937C2212yescomplemented
41C3×#936C2211yescharacteristic
42C3×#936C2212yescomplemented
43C3×#936C2212yescomplemented
44C3×#935C2211yescharacteristic
45C3×#935C2211yescharacteristic
46C3×#935C2212yescomplemented
47C3×D4×Dic3C2212yescomplemented
48C3×D4×Dic3C2212yescomplemented
49C3×#875C2211yescharacteristic, complemented
50C3×#872C2211yescharacteristic, complemented
51C3×C4×Dic6C2212yescomplemented
52#63982C2212yescomplemented
53#63981C2211yescharacteristic
54#63978C2212yescomplemented
55#63977C2212yes—
56#63975C2212yescomplemented
57#63974C2212yescomplemented
58#67⋊Dic3C2212yescomplemented
59#67⋊Dic3C2212yescomplemented
60Dic3×#67C2212yescomplemented
61#63971C2212yes—
62#63971C2212yes—
63#63971C2212yescomplemented
64#63969C2212yes—
65#63969C2212yescomplemented
66#63969C2212yescomplemented
67D3×#217C2212yes—
68D3×#217C2211yescharacteristic
69D3×#217C2211yescharacteristic, complemented
70C2×#3724C2212yescomplemented
71#63966C2212yescomplemented
72#63964C2212yescomplemented
73#63964C2212yescomplemented
74#63962C2211yescharacteristic, complemented
75#63962C2212yescomplemented
76#63961C2211yescharacteristic
77#63961C2211yescharacteristic, complemented
78#63958C2212yescomplemented
79#63958C2212yescomplemented
80#63956C2212yescomplemented
81#63956C2212yescomplemented
82#63956C2212yescomplemented
83#63952C2212yescomplemented
84#63952C2212yescomplemented
85#63907C2212yescomplemented
86#63899C2212yescomplemented
87#63890C2212yes—
88#63888C2212yescomplemented
89#63888C2212yescomplemented
90#63887C2212yescomplemented
91#63887C2212yescomplemented
92#63886C2212yes—
93#63884C2212yescomplemented
94#63880C2212yes—
95#63880C2212yescomplemented
96#63877C2212yescomplemented
97#63877C2212yescomplemented
98D3×Dic3⋊C4C2212yescomplemented
99#63868C2212yescomplemented
100#63867C2212yescomplemented
101#63867C2212yescomplemented
102#63859C2212yescomplemented
103#63854C2212yescomplemented
104#63852C2212yescomplemented
105#63850C2212yes—
106#63847C2212yescomplemented
107#63839C2212yescomplemented
108#63836C2212yescomplemented
109C3×#559—31no—
110C3×#535—31no—
111#5824—32no—
112#5804—31no—
113C2×#935—31no—
114#5720—31no—
115#5720—31no—
116#5720—61no—
117#5719—32no—
118#5715D311yescharacteristic, complemented
119#5713D311yescharacteristic, complemented
120#5684—32no—
121#5679—32no—
122#5679—31no—
123#5678—32no—
124#5678—32no—
125#5672—31no—
126#5669—32no—
127#5663—32no—
128#5659—31no—
129#5655—32no—
130#5653—31no—
131D3×#123—31no—
132#5651—31no—
133#5621—32no—
134#5613—32no—
135#5602—32no—
136#5601—32no—
137#5593—32no—
138#5591—32no—
139#5587—32no—
140#5586—32no—
141#5582—32no—
142#5581—32no—
143#5564—32no—
144#5550—32no—
145#5547—32no—
146#5540—32no—
147#5531—32no—
148C23×C3⋊D3C2311yescharacteristic
149C23×C3×D3C2311yescharacteristic
150C23×C3×D3C2311yescharacteristic
151C2×C32×D4C2312yes—
152C2×C32×D4C2312yes—
153C2×C32×D4C2311yescharacteristic
154C2×C32×D4C2311yescharacteristic
155C2×#638C2312yes—
156C2×#638C2312yes—
157C2×#638C2312yes—
158C22×C3⋊Dic3C2311yescharacteristic
159C22×C3⋊Dic3C2312yes—
160C2×C3×#67C2312yes—
161C2×C3×#67C2312yes—
162C2×C3×#67C2312yes—
163C2×C3×#67C2311yescharacteristic
164C2×C3×#67C2311yescharacteristic
165C22×C3×Dic3C2311yescharacteristic
166C22×C3×Dic3C2311yescharacteristic
167C22×C3×Dic3C2312yes—
168C22×C3×Dic3C2312yes—
169C3×#237—42no—
170C3×D3×D4—42no—
171C2×C3×D12C2311yescharacteristic
172C2×C3×C4×D3C2311yescharacteristic
173C2×C3×Dic6C2311yescharacteristic
174C2×C3×Dic6C2312yes—
175C2×#627C2312yes—
176C2×#626—42no—
177C2×#626C2312yes—
178C2×#626C2312yes—
179C2×#626C2312yes—
180C2×#624C2312yes—
181C2×#624C2312yes—
182#3804—44no—
183C2×D3×Dic3—42no—
184C2×D3×Dic3C2312yes—
185C2×D3×Dic3C2312yes—
186C2×D3×Dic3C2312yes—
187C2×D3×Dic3C2312yes—
188C32×C42C2311yescharacteristic
189#3757C2312yes—
190#3757C2311yescharacteristic
191#3757C2311yescharacteristic
192#3757C2312yes—
193#3752C2312yes—
194#3752C2312yes—
195#3752C2312yes—
196#3750C2312yes—
197#3750C2312yes—
198#3750C2312yes—
199C3×#217C2312yes—
200C3×#217C2312yes—
201C3×#217C2312yes—
202C3×#217C2312yes—
203C3×#217C2311yescharacteristic
204C3×#217C2311yescharacteristic
205C3×#217C2312yes—
206C3×#217C2312yes—
207C3×#217C2312yes—
208C3×(C2×D3)⋊C4C2312yes—
209C3×(C2×D3)⋊C4C2312yes—
210C3×(C2×D3)⋊C4C2312yes—
211C3×C4⋊Dic3C2312yes—
212C3×Dic3⋊C4C2312yes—
213C3×Dic3⋊C4C2312yes—
214C3×Dic3⋊C4C2312yes—
215C3×C4×Dic3C2312yes—
216C3×C4×Dic3C2312yes—
217C3×C4×Dic3C2311yescharacteristic
218#3724C2312yes—
219#3724C2312yes—
220#3724C2312yes—
221#3724C2312yes—
222#3724C2312yes—
223Dic3⋊Dic3C2312yes—
224Dic3⋊Dic3C2312yes—
225Dic3⋊Dic3C2312yes—
226Dic3⋊Dic3C2312yes—
227Dic3⋊Dic3C2312yes—
228Dic3⋊Dic3C2312yes—
229Dic3⋊Dic3C2312yes—
230#3722C2312yes—
231#3722C2312yes—
232#3722C2312yes—
233(C2×D3)⋊Dic3C2312yes—
234(C2×D3)⋊Dic3C2312yes—
235(C2×D3)⋊Dic3C2312yes—
236(C2×D3)⋊Dic3C2312yes—
237(C2×D3)⋊Dic3C2312yes—
238Dic32C2312yes—
239Dic32C2312yes—
240#3533—91noSylow
241C2×C3×#41—31no—
242C22×C3×D4—31no—
243C22×#67—31no—
244C23×Dic3—31no—
245C2×#237—32no—
246C2×#237C2×D311yescharacteristic, complemented
247C2×D3×D4C2×D311yescharacteristic
248C2×#235—32no—
249C22×D12—31no—
250C22×C4×D3—31no—
251C3×#127—21no—
252C3×#127—31no—
253C3×#127C2×D311yescharacteristic
254C3×#127C2×D311yescharacteristic
255C3×#124—32no—
256C3×#124—32no—
257C3×#124—31no—
258C3×#124—31no—
259C3×#123—31no—
260C3×#123—31no—
261C3×#123—32no—
262C3×#121—32no—
263C3×#121—32no—
264C3×#120—32no—
265C3×#120—32no—
266C3×C4×Q8—32no—
267C3×C4×D4—32no—
268C3×C4×D4—32no—
269C3×#117—31no—
270#953—32no—
271C2×#217—32no—
272C2×#217—31no—
273C2×#217—31no—
274#947—32no—
275#946—32no—
276#946—32no—
277#946—32no—
278#946—32no—
279#944—32no—
280#940C2×D311yescharacteristic, complemented
281#939—32no—
282#939—32no—
283#939—32no—
284#939—32no—
285#939—32no—
286#939—32no—
287#939—32no—
288#939—32no—
289#939—32no—
290#939—32no—
291#939—32no—
292#939—62no—
293#939—62no—
294#939—62no—
295#939C2×D312yes—
296#939C2×D312yescomplemented
297#938—32no—
298#938—32no—
299#937—31no—
300#937—32no—
301#937—31no—
302#937—32no—
303#937—31no—
304#937—61no—
305#937—62no—
306#937C2×D312yes—
307#937C2×D312yescomplemented
308#936C2×D311yescharacteristic
309#936C2×D312yescomplemented
310#936C2×D312yescomplemented
311#935—31no—
312#935—31no—
313#935—32no—
314#935—32no—
315#935—31no—
316#935—31no—
317#935—32no—
318#935—32no—
319#935—31no—
320#935—32no—
321#935—32no—
322#935—32no—
323#935—61no—
324#935—62no—
325#935C2×D311yescharacteristic
326#935C2×D311yescharacteristic
327#935C2×D312yescomplemented
328D4×Dic3—32no—
329D4×Dic3—32no—
330D4×Dic3—32no—
331D4×Dic3C2×D312yescomplemented
332D4×Dic3C2×D312yescomplemented
333#930—32no—
334#929—31no—
335#929—31no—
336#929—32no—
337#929—32no—
338C4×#67—32no—
339C4×#67—32no—
340C4×#67—32no—
341#924—32no—
342#924—32no—
343C2×Dic3⋊C4—32no—
344C2×Dic3⋊C4—32no—
345C2×Dic3⋊C4—32no—
346#898—32no—
347#896—32no—
348#896—32no—
349#896—32no—
350#895—32no—
351#894—32no—
352#894—32no—
353#894—32no—
354#894—32no—
355#892—32no—
356D3×C4⋊C4—32no—
357#889—32no—
358#889—32no—
359#889—32no—
360#889—32no—
361#888—32no—
362#886—31no—
363#886—32no—
364#886—32no—
365#886—32no—
366#885—32no—
367#885—32no—
368#884—32no—
369#884—32no—
370#884—32no—
371#884—32no—
372#884—32no—
373#883—32no—
374#883—32no—
375#883—32no—
376#883—32no—
377#883—32no—
378#883—32no—
379#882—32no—
380#882—31no—
381#67⋊C4—32no—
382#67⋊C4—32no—
383#67⋊C4—32no—
384#67⋊C4—32no—
385#67⋊C4—32no—
386#67⋊C4—32no—
387D3×C22⋊C4—31no—
388D3×C22⋊C4—32no—
389D3×C22⋊C4—31no—
390D3×C22⋊C4—32no—
391D3×C22⋊C4—32no—
392#879—32no—
393#879—32no—
394#879—32no—
395#879—32no—
396#879—32no—
397#879—32no—
398#879—32no—
399#878—32no—
400#878—32no—
401#878—32no—
402#878—32no—
403#878—32no—
404#878—32no—
405#878—32no—
406#877—32no—
407#877—32no—
408#876—32no—
409#876—32no—
410#876—32no—
411#876—32no—
412#876—62no—
413#875—32no—
414#875C2×D311yescharacteristic, complemented
415C4×D12—32no—
416C4×D12—32no—
417#872—32no—
418#872—32no—
419#872—32no—
420#872C2×D311yescharacteristic, complemented
421#870—32no—
422#870—32no—
423C4×Dic6C2×D312yescomplemented
424C23×C32C2411yescharacteristic
425C23×C32C2411yescharacteristic
426C23×C32C2412yes—
427C22×C3⋊D3—42no—
428C22×C3⋊D3—41no—
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—
438C32×D4—41no—
439C32×D4—42no—
440C32×D4—42no—
441C2×C32×C4C2412yes—
442C2×C32×C4C2411yescharacteristic
443#638—42no—
444#638—42no—
445#638—42no—
446C2×C3⋊Dic3—41no—
447C2×C3⋊Dic3—42no—
448C2×C3⋊Dic3C2412yes—
449C2×C3⋊Dic3C2412yes—
450C2×C3⋊Dic3C2412yes—
451C3×#67—24no—
452C3×#67—41no—
453C3×#67—41no—
454C3×#67—42no—
455C3×#67—42no—
456C2×C3×Dic3—41no—
457C2×C3×Dic3—42no—
458C2×C3×Dic3—41no—
459C2×C3×Dic3—42no—
460C2×C3×Dic3C2412yes—
461C2×C3×Dic3C2412yes—
462C2×C3×Dic3C2412yes—
463C2×C3×Dic3C2412yes—
464C2×C3×Dic3C2412yes—
465C2×C3×Dic3C2412yes—
466C2×C3×Dic3C2411yescharacteristic
467C3×D12—41no—
468C3×C4×D3—22no—
469C3×Dic6—42no—
470C3×Dic6—41no—
471#627—42no—
472#626—24no—
473#626—42no—
474#626—42no—
475#624—42no—
476#624—42no—
477D3×Dic3—24no—
478D3×Dic3—42no—
479D3×Dic3—42no—
480D3×Dic3—42no—
481#563—91no—
482#562—92no—
483#560—91no—
484#559—31no—
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—31no—
497#534—91no—
498#525—92no—
499C2×#123—91no—
500C24×C3—31no—
501C24×C3—31no—
502C23×D3—31no—
503C23×D3—31no—
504C23×D3—61no—
505C23×D3C22×D311yescharacteristic
506C23×D3C22×D311yescharacteristic
507C3×#41—122no—
508C2×C3×Q8—31no—
509C2×C3×Q8—32no—
510C2×C3×D4—22no—
511C2×C3×D4—21no—
512C2×C3×D4—22no—
513C2×C3×D4—21no—
514C2×C3×D4—32no—
515C2×C3×D4—32no—
516C2×C3×D4—32no—
517C2×C3×D4—31no—
518C2×C3×D4—31no—
519C2×C3×D4—31no—
520C2×C3×D4—122no—
521C2×C3×D4C22×D312yes—
522C2×C3×D4C22×D312yes—
523C2×C3×D4C22×D311yescharacteristic
524C2×C3×D4C22×D311yescharacteristic
525C2×C3×D4C22×D312yes—
526C2×C3×D4C22×D311yescharacteristic
527C2×C3×D4C22×D312yes—
528C2×C3×D4C22×D311yescharacteristic
529C22×C3×C4—32no—
530C22×C3×C4—32no—
531C22×C3×C4—31no—
532C22×C3×C4—31no—
533C22×C3×C4—31no—
534C2×#67—32no—
535C2×#67—32no—
536C2×#67—32no—
537C2×#67—32no—
538C2×#67—32no—
539C2×#67—32no—
540C2×#67—32no—
541C2×#67—32no—
542C2×#67—32no—
543C2×#67—62no—
544C2×#67—62no—
545C2×#67—62no—
546C2×#67—122no—
547C2×#67C22×D312yes—
548C2×#67C22×D312yes—
549C2×#67C22×D311yescharacteristic
550C2×#67C22×D312yes—
551C2×#67C22×D311yescharacteristic
552C22×Dic3—31no—
553C22×Dic3—31no—
554C22×Dic3—32no—
555C22×Dic3—32no—
556C22×Dic3—32no—
557C22×Dic3—32no—
558C22×Dic3—32no—
559C22×Dic3—32no—
560C22×Dic3—62no—
561C22×Dic3—61no—
562C22×Dic3—122no—
563C22×Dic3C22×D311yescharacteristic
564C22×Dic3C22×D312yes—
565C22×Dic3C22×D311yescharacteristic
566C22×Dic3C22×D312yes—
567#237—42no—
568#237—124no—
569D3×D4—42no—
570#235—124no—
571C2×D12—32no—
572C2×D12—32no—
573C2×D12—32no—
574C2×D12—122no—
575C2×D12C22×D311yescharacteristic
576C2×C4×D3—32no—
577C2×C4×D3—32no—
578C2×C4×D3—32no—
579C2×C4×D3—32no—
580C2×C4×D3—32no—
581C2×C4×D3—32no—
582C2×C4×D3—32no—
583C2×C4×D3—32no—
584C2×C4×D3—122no—
585C2×C4×D3C22×D311yescharacteristic
586C2×Dic6—32no—
587C2×Dic6—32no—
588C2×Dic6C22×D312yes—
589C2×Dic6C22×D311yescharacteristic
590C3×C4⋊C4—32no—
591C3×C4⋊C4—32no—
592C3×C4⋊C4—32no—
593C3×C4⋊C4—32no—
594C3×C22⋊C4—32no—
595C3×C22⋊C4—32no—
596C3×C22⋊C4—32no—
597C3×C22⋊C4—32no—
598C3×C22⋊C4—31no—
599C3×C22⋊C4—32no—
600C3×C22⋊C4—31no—
601C3×C22⋊C4—32no—
602C3×C22⋊C4—32no—
603C3×C22⋊C4—32no—
604C3×C22⋊C4—32no—
605C3×C22⋊C4—32no—
606C3×C42—21no—
607C3×C42—31no—
608C3×C42—32no—
609C3×C42—32no—
610C3×C42C22×D311yescharacteristic
611C3×C42C22×D311yescharacteristic
612#217—32no—
613#217—32no—
614#217—31no—
615#217—31no—
616#217—31no—
617#217—31no—
618#217—32no—
619#217—32no—
620#217—32no—
621#217—32no—
622#217—32no—
623#217—32no—
624#217—32no—
625#217—62no—
626#217—61no—
627#217—61no—
628#217—62no—
629#217C22×D312yes—
630#217C22×D312yes—
631#217C22×D312yes—
632#217C22×D311yescharacteristic
633#217C22×D312yes—
634#217C22×D311yescharacteristic
635#217C22×D312yes—
636#217C22×D312yes—
637#217C22×D312yes—
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—
661C4⋊Dic3—32no—
662C4⋊Dic3—32no—
663C4⋊Dic3—32no—
664C4⋊Dic3—32no—
665C4⋊Dic3—32no—
666C4⋊Dic3—32no—
667C4⋊Dic3—32no—
668C4⋊Dic3C22×D312yes—
669Dic3⋊C4—32no—
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—32no—
685Dic3⋊C4—32no—
686Dic3⋊C4—32no—
687Dic3⋊C4—32no—
688Dic3⋊C4—32no—
689Dic3⋊C4—32no—
690Dic3⋊C4—32no—
691Dic3⋊C4—32no—
692Dic3⋊C4—62no—
693Dic3⋊C4—62no—
694Dic3⋊C4—62no—
695Dic3⋊C4C22×D312yes—
696Dic3⋊C4C22×D312yes—
697Dic3⋊C4C22×D312yes—
698C4×Dic3—32no—
699C4×Dic3—32no—
700C4×Dic3—32no—
701C4×Dic3—32no—
702C4×Dic3C22×D312yes—
703C4×Dic3C22×D312yes—
704C4×Dic3C22×D311yescharacteristic
705C22×C32—22no—
706C22×C32—21no—
707C22×C32—21no—
708C22×C32—22no—
709C22×C32—22no—
710C22×C32—22no—
711C22×C32—22no—
712C22×C32C2511yescharacteristic
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—21no—
726C32×C4—22no—
727C3⋊Dic3—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—31no—
738C2×#41—92no—
739C22×D4—31no—
740C22×D4—91no—
741C23×C4—91no—
742C4⋊Q8—92no—
743#127—31no—
744#127D3211yescharacteristic
745#126—92no—
746#126—92no—
747#126—92no—
748#126—92no—
749#126—92no—
750#126—92no—
751#125—92no—
752#125—92no—
753#125—92no—
754#124—31no—
755#124—32no—
756#124—32no—
757#124—31no—
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—91no—
777#123—92no—
778C22⋊Q8—92no—
779C22⋊Q8—92no—
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—32no—
799#120—32no—
800#120—91no—
801#120—92no—
802#120—91no—
803#120—92no—
804C4×Q8—32no—
805C4×D4—32no—
806C4×D4—32no—
807C4×D4—92no—
808C4×D4—92no—
809C4×D4—92no—
810C4×D4—92no—
811C4×D4—92no—
812C4×D4—92no—
813C4×D4—92no—
814#117—31no—
815#117—92no—
816#117—92no—
817#117—92no—
818C2×C4⋊C4—92no—
819C2×C4⋊C4—92no—
820C2×C22⋊C4—92no—
821C2×C22⋊C4—91no—
822C2×C22⋊C4—92no—
823C2×C22⋊C4—91no—
824C23×C3—21no—
825C23×C3—21no—
826C23×C3—22no—
827C23×C3—31no—
828C23×C3—31no—
829C23×C3—31no—
830C23×C3—62no—
831C23×C3—62no—
832C23×C3—122no—
833C23×C3—122no—
834C23×C3C23×D311yescharacteristic
835C23×C3C23×D311yescharacteristic
836C23×C3C23×D311yescharacteristic
837C23×C3C23×D312yes—
838C23×C3C23×D311yescharacteristic
839C23×C3C23×D312yes—
840C22×D3—22no—
841C22×D3—22no—
842C22×D3—32no—
843C22×D3—32no—
844C22×D3—42no—
845C22×D3—42no—
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—41no—
861C3×D4—42no—
862C3×D4—42no—
863C3×D4—42no—
864C3×D4—42no—
865C3×D4—41no—
866C3×D4—64no—
867C3×D4—81no—
868C3×D4—81no—
869C3×D4—82no—
870C3×D4—82no—
871C3×D4—121no—
872C3×D4—122no—
873C3×D4—122no—
874C3×D4—121no—
875C3×D4—121no—
876C2×C3×C4—22no—
877C2×C3×C4—21no—
878C2×C3×C4—32no—
879C2×C3×C4—32no—
880C2×C3×C4—32no—
881C2×C3×C4—32no—
882C2×C3×C4—31no—
883C2×C3×C4—32no—
884C2×C3×C4—32no—
885C2×C3×C4—62no—
886C2×C3×C4—121no—
887C2×C3×C4—121no—
888C2×C3×C4—122no—
889C2×C3×C4—122no—
890C2×C3×C4C23×D312yes—
891C2×C3×C4C23×D311yescharacteristic
892C2×C3×C4C23×D311yescharacteristic
893C2×C3×C4C23×D312yes—
894#67—24no—
895#67—41no—
896#67—41no—
897#67—42no—
898#67—42no—
899#67—64no—
900#67—122no—
901#67—122no—
902#67—122no—
903#67—122no—
904#67—122no—
905#67—122no—
906#67—122no—
907#67—122no—
908#67—242no—
909#67—242no—
910#67—242no—
911C2×Dic3—32no—
912C2×Dic3—32no—
913C2×Dic3—32no—
914C2×Dic3—32no—
915C2×Dic3—32no—
916C2×Dic3—32no—
917C2×Dic3—42no—
918C2×Dic3—42no—
919C2×Dic3—41no—
920C2×Dic3—41no—
921C2×Dic3—62no—
922C2×Dic3—62no—
923C2×Dic3—62no—
924C2×Dic3—64no—
925C2×Dic3—122no—
926C2×Dic3—122no—
927C2×Dic3—122no—
928C2×Dic3—121no—
929C2×Dic3—122no—
930C2×Dic3—122no—
931C2×Dic3—121no—
932C2×Dic3—241no—
933C2×Dic3—242no—
934C2×Dic3C23×D312yes—
935C2×Dic3C23×D312yes—
936C2×Dic3C23×D312yes—
937C2×Dic3C23×D312yes—
938C2×Dic3C23×D312yes—
939C2×Dic3C23×D312yes—
940C2×Dic3C23×D311yescharacteristic
941D12—41no—
942D12—64no—
943D12—122no—
944D12—122no—
945C4×D3—22no—
946C4×D3—64no—
947C4×D3—122no—
948C4×D3—122no—
949C4×D3—122no—
950C4×D3—122no—
951C4×D3—122no—
952C4×D3—122no—
953C4×D3—122no—
954Dic6—42no—
955Dic6—41no—
956Dic6—122no—
957Dic6—122no—
958C2×C32—41no—
959C2×C32—41no—
960C2×C32—42no—
961C2×C32C2×H(5,𝔽2)11yescharacteristic
962C2×C32#58512yes—
963C3⋊D3—42no—
964C3×D3—22no—
965C3×D3—41no—
966C3×D3—41no—
967C24—31no—
968C24—31no—
969C24—91no—
970#41—122no—
971#41—364no—
972C2×Q8—32no—
973C2×Q8—31no—
974C2×Q8—92no—
975C2×D4—32no—
976C2×D4—32no—
977C2×D4—32no—
978C2×D4—31no—
979C2×D4—31no—
980C2×D4—31no—
981C2×D4—92no—
982C2×D4—92no—
983C2×D4—92no—
984C2×D4—92no—
985C2×D4—92no—
986C2×D4—92no—
987C2×D4—122no—
988C2×D4—362no—
989C2×D4C2×D3212yes—
990C2×D4C2×D3212yes—
991C2×D4C2×D3211yescharacteristic
992C2×D4C2×D3211yescharacteristic
993C22×C4—32no—
994C22×C4—32no—
995C22×C4—31no—
996C22×C4—31no—
997C22×C4—31no—
998C22×C4—92no—
999C22×C4—92no—
1000C22×C4—92no—
1001C22×C4—92no—
1002C22×C4—92no—
1003C22×C4—92no—
1004C22×C4—92no—
1005C22×C4—91no—
1006C22×C4—362no—
1007C4⋊C4—32no—
1008C4⋊C4—32no—
1009C4⋊C4—32no—
1010C4⋊C4—32no—
1011C4⋊C4—92no—
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⋊C4—92no—
1023C4⋊C4—92no—
1024C4⋊C4—92no—
1025C4⋊C4—92no—
1026C22⋊C4—32no—
1027C22⋊C4—32no—
1028C22⋊C4—31no—
1029C22⋊C4—31no—
1030C22⋊C4—32no—
1031C22⋊C4—32no—
1032C22⋊C4—32no—
1033C22⋊C4—32no—
1034C22⋊C4—32no—
1035C22⋊C4—32no—
1036C22⋊C4—32no—
1037C22⋊C4—32no—
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—92no—
1047C22⋊C4—91no—
1048C22⋊C4—91no—
1049C22⋊C4—92no—
1050C22⋊C4—92no—
1051C22⋊C4—92no—
1052C22⋊C4—92no—
1053C42—31no—
1054C42—32no—
1055C42—32no—
1056C42—92no—
1057C42—92no—
1058C42C2×D3211yescharacteristic
1059C22×C3—22no—
1060C22×C3—21no—
1061C22×C3—21no—
1062C22×C3—22no—
1063C22×C3—22no—
1064C22×C3—22no—
1065C22×C3—22no—
1066C22×C3—21no—
1067C22×C3—22no—
1068C22×C3—21no—
1069C22×C3—22no—
1070C22×C3—22no—
1071C22×C3—22no—
1072C22×C3—22no—
1073C22×C3—21no—
1074C22×C3—32no—
1075C22×C3—41no—
1076C22×C3—42no—
1077C22×C3—42no—
1078C22×C3—42no—
1079C22×C3—42no—
1080C22×C3—41no—
1081C22×C3—42no—
1082C22×C3—62no—
1083C22×C3—62no—
1084C22×C3—62no—
1085C22×C3—61no—
1086C22×C3—61no—
1087C22×C3—124no—
1088C22×C3—242no—
1089C22×C3C24×D311yescharacteristic
1090C22×C3C24×D311yescharacteristic
1091C2×D3—22no—
1092C2×D3—21no—
1093C2×D3—21no—
1094C2×D3—22no—
1095C2×D3—22no—
1096C2×D3—44no—
1097C2×D3—62no—
1098C2×D3—62no—
1099C2×D3—62no—
1100C2×D3—62no—
1101C2×D3—62no—
1102C2×D3—62no—
1103C2×D3—82no—
1104C2×D3—122no—
1105C2×D3—122no—
1106C2×D3—122no—
1107C2×D3—242no—
1108C2×D3—242no—
1109C2×D3—244no—
1110C2×D3#100412yes—
1111C3×C4—21no—
1112C3×C4—22no—
1113C3×C4—21no—
1114C3×C4—22no—
1115C3×C4—41no—
1116C3×C4—42no—
1117C3×C4—62no—
1118C3×C4—62no—
1119C3×C4—62no—
1120C3×C4—62no—
1121C3×C4—61no—
1122C3×C4—62no—
1123C3×C4—62no—
1124Dic3—22no—
1125Dic3—21no—
1126Dic3—22no—
1127Dic3—22no—
1128Dic3—22no—
1129Dic3—22no—
1130Dic3—22no—
1131Dic3—62no—
1132Dic3—62no—
1133Dic3—62no—
1134Dic3—62no—
1135Dic3—62no—
1136Dic3—62no—
1137Dic3—122no—
1138Dic3—122no—
1139Dic3—122no—
1140C32#353311yescharacteristic, complemented, Sylow
1141C23—31no—
1142C23—31no—
1143C23—31no—
1144C23—62no—
1145C23—62no—
1146C23—92no—
1147C23—122no—
1148C23—122no—
1149C23—361no—
1150C23—362no—
1151C23C22×D3211yescharacteristic
1152C23C22×D3211yescharacteristic
1153C23C22×D3212yes—
1154Q8—121no—
1155Q8—122no—
1156Q8—362no—
1157D4—41no—
1158D4—41no—
1159D4—42no—
1160D4—42no—
1161D4—64no—
1162D4—121no—
1163D4—121no—
1164D4—121no—
1165D4—122no—
1166D4—122no—
1167D4—184no—
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—62no—
1181C2×C4—92no—
1182C2×C4—92no—
1183C2×C4—92no—
1184C2×C4—121no—
1185C2×C4—121no—
1186C2×C4—122no—
1187C2×C4—122no—
1188C2×C4—184no—
1189C2×C4—362no—
1190C2×C4—362no—
1191C2×C4—362no—
1192C2×C4—362no—
1193C2×C4—362no—
1194C2×C4—361no—
1195C2×C4—362no—
1196C2×C4C22×D3212yes—
1197C2×C4C22×D3211yescharacteristic
1198C2×C3—21no—
1199C2×C3—22no—
1200C2×C3—41no—
1201C2×C3—41no—
1202C2×C3—42no—
1203C2×C3—41no—
1204C2×C3—41no—
1205C2×C3—42no—
1206C2×C3—62no—
1207C2×C3—81no—
1208C2×C3—81no—
1209C2×C3—82no—
1210C2×C3—121no—
1211C2×C3—121no—
1212C2×C3C2×#100411yescharacteristic
1213C2×C3#596412yes—
1214C2×C3D3×H(5,𝔽2)11yescharacteristic
1215C2×C3#596612yes—
1216D3—22no—
1217D3—41no—
1218D3—41no—
1219D3—122no—
1220D3—122no—
1221D3—242no—
1222C22—22no—
1223C22—21no—
1224C22—21no—
1225C22—22no—
1226C22—22no—
1227C22—22no—
1228C22—22no—
1229C22—32no—
1230C22—62no—
1231C22—61no—
1232C22—61no—
1233C22—62no—
1234C22—62no—
1235C22—124no—
1236C22—182no—
1237C22—182no—
1238C22—182no—
1239C22—242no—
1240C22—722no—
1241C22C23×D3211yescharacteristic
1242C4—21no—
1243C4—22no—
1244C4—61no—
1245C4—62no—
1246C4—62no—
1247C4—62no—
1248C4—62no—
1249C4—62no—
1250C4—62no—
1251C4—182no—
1252C4—182no—
1253C4—182no—
1254C3—21no—
1255C3#8632111yescharacteristic, complemented
1256C3#8706511yescharacteristic, complemented
1257C2—41no—
1258C2—41no—
1259C2—42no—
1260C2—62no—
1261C2—121no—
1262C2—121no—
1263C2—362no—
1264C2D3×#100411yescharacteristic
1265C2#1059667812yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#127C22
hypercenter#127D32
hypocenterC32#3533
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #127

Complements

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

NH ≅ G/Ntype
1. #10596191C2semidirect
2. C3×#5715C2semidirect
3. C3×#5713C2semidirect
4. #10595276C2semidirect
5. #10595234C2semidirect
6. #10595216C2semidirect
7. #10595214C2semidirect
8. #10595208C2semidirect
9. #10595207C2semidirect
10. #10595204C2semidirect
11. #10595192C2semidirect
12. #10595184C2semidirect
13. #10595176C2semidirect
14. #10595149C2semidirect
15. D3×#935C2semidirect
16. #10595135C2semidirect
17. #10595129C2semidirect
18. #10593927C2semidirect
19. #10593916C2semidirect
22. C2×C3×#237C22semidirect
26. C22×D3×Dic3C22semidirect
28. #64148C22semidirect
29. #64148C22semidirect
30. #64148C22semidirect
32. #64146C22semidirect
34. #64144C22semidirect
35. #64085C22semidirect
36. C3×#940C22semidirect
38. C3×#939C22semidirect
40. C3×#937C22semidirect
42. C3×#936C22semidirect
43. C3×#936C22semidirect
46. C3×#935C22semidirect
47. C3×D4×Dic3C22semidirect
48. C3×D4×Dic3C22semidirect
49. C3×#875C22semidirect
50. C3×#872C22semidirect
51. C3×C4×Dic6C22semidirect
52. #63982C22semidirect
54. #63978C22semidirect
56. #63975C22semidirect
57. #63974C22semidirect
58. #67⋊Dic3C22semidirect
59. #67⋊Dic3C22semidirect
60. Dic3×#67C22semidirect
63. #63971C22semidirect
65. #63969C22semidirect
66. #63969C22semidirect
69. D3×#217C22semidirect
70. C2×#3724C22semidirect
71. #63966C22semidirect
72. #63964C22semidirect
73. #63964C22semidirect
74. #63962C22semidirect
75. #63962C22semidirect
77. #63961C22semidirect
78. #63958C22semidirect
79. #63958C22semidirect
80. #63956C22semidirect
81. #63956C22semidirect
82. #63956C22semidirect
83. #63952C22semidirect
84. #63952C22semidirect
85. #63907C22semidirect
86. #63899C22semidirect
88. #63888C22semidirect
89. #63888C22semidirect
90. #63887C22semidirect
91. #63887C22semidirect
93. #63884C22semidirect
95. #63880C22semidirect
96. #63877C22semidirect
97. #63877C22semidirect
98. D3×Dic3⋊C4C22semidirect
99. #63868C22semidirect
100. #63867C22semidirect
101. #63867C22semidirect
102. #63859C22semidirect
103. #63854C22semidirect
104. #63852C22semidirect
106. #63847C22semidirect
107. #63839C22semidirect
108. #63836C22semidirect
118. #5715D3semidirect
119. #5713D3semidirect
246. C2×#237C2×D3semidirect
280. #940C2×D3semidirect
296. #939C2×D3semidirect
307. #937C2×D3semidirect
309. #936C2×D3semidirect
310. #936C2×D3semidirect
327. #935C2×D3semidirect
331. D4×Dic3C2×D3semidirect
332. D4×Dic3C2×D3semidirect
414. #875C2×D3semidirect
420. #872C2×D3semidirect
423. C4×Dic6C2×D3semidirect
1140. C32#3533semidirect
1255. C3#86321semidirect
1256. C3#87065semidirect

Maximal subgroups

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

subgroupindex
#105961912
C3×#57152
C3×#57132
#105952762
#105952342
#105952162
#105952142
#105952082
#105952072
#105952042
#105951922
#105951842
#105951762
#105951492
D3×#9352
#105951352
#105951292
#105939272
#105939162
#870653
#863213