Finite Group Databasebeta

← #11910753

Subgroups — #11910753

Order 1152.

2291 conjugacy classes of subgroups.

The subgroup lattice has 1281 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3⋊D3×#123C211yesmaximal, characteristic, complemented
2C3×#5666C211yesmaximal, characteristic, complemented
3C3×#5651C211yesmaximal, characteristic, complemented
4#10595242C211yesmaximal, characteristic, complemented
5#10595200C211yesmaximal, characteristic, complemented
6#10595176C211yesmaximal, characteristic, complemented
7#10595168C211yesmaximal, characteristic, complemented
8#10594976C212yesmaximal, complemented
9#10594922C212yesmaximal, complemented
10#10594563C212yesmaximal, complemented
11#10594471C212yesmaximal, complemented
12#10594466C212yesmaximal, complemented
13#10594373C212yesmaximal, complemented
14#10594228C212yesmaximal, complemented
15#10594226C212yesmaximal, complemented
16#10594129C212yesmaximal, complemented
17#10594127C212yesmaximal, complemented
18#10594125C212yesmaximal, complemented
19#10594063C212yesmaximal, complemented
20#87128—31nomaximal
21#87081—31nomaximal
22C2×D4×C3⋊D3C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C22×#626C2211yescharacteristic
25C2×#3796C2212yes—
26C2×#3796C2211yescharacteristic, complemented
27C32×#123C2211yescharacteristic
28#64144C2211yescharacteristic
29#64138C2211yescharacteristic, complemented
30#64103C2212yescomplemented
31C4⋊C4×C3⋊D3C2212yescomplemented
32#64095C2211yescharacteristic, complemented
33#64092C2212yes—
34C22⋊C4×C3⋊D3C2212yes—
35C22⋊C4×C3⋊D3C2211yescharacteristic, complemented
36C3×#940C2211yescharacteristic
37C3×#937C2211yescharacteristic
38C3×#936C2211yescharacteristic
39C3×#935C2211yescharacteristic
40C3×#930C2212yescomplemented
41C3×#924C2212yescomplemented
42C3×#898C2212yescomplemented
43C3×#895C2212yescomplemented
44C3×#889C2212yescomplemented
45C3×#888C2212yescomplemented
46C3×#884C2212yescomplemented
47C3×#883C2212yescomplemented
48C3×#882C2212yescomplemented
49C3×#879C2212yescomplemented
50C3×#879C2212yescomplemented
51C3×#878C2212yescomplemented
52#63981C2212yes—
53#63981C2212yes—
54#63981C2212yescomplemented
55#63977C2211yescharacteristic
56#63974C2211yescharacteristic
57#67⋊Dic3C2212yescomplemented
58#67⋊Dic3C2212yescomplemented
59Dic3×#67C2212yescomplemented
60#63971C2212yes—
61#63971C2212yescomplemented
62#63969C2212yescomplemented
63D3×#217C2212yescomplemented
64#63966C2211yescharacteristic
65#63959C2212yescomplemented
66#63959C2212yescomplemented
67#63958C2212yes—
68#63956C2212yescomplemented
69#63916C2212yes—
70#63916C2212yescomplemented
71#63911C2211yescharacteristic, complemented
72#63910C2212yes—
73#63907C2212yescomplemented
74#63904C2212yescomplemented
75C4×#626C2212yescomplemented
76#63899C2212yescomplemented
77#63895C2212yescomplemented
78Dic3×D12C2212yescomplemented
79#63890C2212yescomplemented
80D3×C4⋊Dic3C2212yescomplemented
81#63887C2212yescomplemented
82#63887C2212yescomplemented
83#63886C2212yescomplemented
84#63886C2212yescomplemented
85#63886C2212yescomplemented
86#63884C2212yescomplemented
87#63884C2212yescomplemented
88#63881C2212yes—
89#63881C2212yescomplemented
90#63881C2212yescomplemented
91#63877C2212yescomplemented
92#63874C2211yescharacteristic, complemented
93#63871C2212yescomplemented
94#63865C2212yescomplemented
95#63864C2211yescharacteristic, complemented
96#63861C2212yescomplemented
97#63854C2212yescomplemented
98#63853C2212yes—
99#63853C2212yes—
100#63853C2212yescomplemented
101#63852C2212yescomplemented
102#63850C2212yescomplemented
103#63849C2212yescomplemented
104#63848C2212yescomplemented
105#63847C2212yescomplemented
106#63845C2212yescomplemented
107#63837C2212yescomplemented
108#63836C2212yescomplemented
109C3×#563—31no—
110C3×#560—31no—
111#5733—32no—
112#5726—32no—
113#5715—31no—
114#5713—31no—
115#5710—32no—
116#5709—32no—
117#5708—32no—
118#5705—32no—
119#5704—32no—
120#5704—32no—
121#5697—32no—
122#5693—32no—
123#5679—31no—
124#5674—31no—
125#5666D311yescharacteristic, complemented
126#5665—32no—
127#5664—31no—
128#5659—32no—
129#5653—31no—
130D3×#123—31no—
131D3×#123—31no—
132D3×#123—61no—
133#5651D311yescharacteristic, complemented
134#5647—32no—
135#5638—32no—
136#5630—32no—
137#5627—32no—
138#5621—32no—
139#5618—32no—
140#5615—32no—
141#5613—32no—
142#5611—32no—
143#5606—32no—
144#5593—32no—
145#5591—32no—
146#5589—31no—
147#5587—31no—
148C23×C3⋊D3C2311yescharacteristic
149C23×C3⋊D3C2311yescharacteristic
150C23×C3×D3C2311yescharacteristic
151C2×C32×D4C2311yescharacteristic
152C22×C32×C4C2311yescharacteristic
153C2×#638C2311yescharacteristic
154C2×#638C2311yescharacteristic
155C22×C3⋊Dic3C2311yescharacteristic
156D4×C3⋊D3—42no—
157C2×C4⋊(C3⋊D3)C2311yescharacteristic
158C2×C4×C3⋊D3—42no—
159C2×C4×C3⋊D3C2312yes—
160C2×C4×C3⋊D3C2311yescharacteristic
161C2×C4×C3⋊D3C2312yes—
162C2×C4×C3⋊D3C2312yes—
163C2×C3×#67C2312yes—
164C2×C3×#67C2312yes—
165C2×C3×#67C2312yes—
166C22×C3×Dic3C2311yescharacteristic
167C2×C3×D12C2312yes—
168C2×C3×D12C2312yes—
169C2×C3×D12C2311yescharacteristic
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×D3×Dic3C2312yes—
183C2×D3×Dic3C2312yes—
184C2×D3×Dic3C2312yes—
185C2×D3×Dic3C2312yes—
186#3796—44no—
187#3796—42no—
188C32×C4⋊C4C2312yes—
189C32×C22⋊C4C2312yes—
190C32×C22⋊C4C2311yescharacteristic
191#3757C2312yes—
192#3757C2311yescharacteristic
193#3752C2312yes—
194#3752C2312yes—
195#3752C2312yes—
196C4⋊(C3⋊Dic3)C2312yes—
197#3750C2312yes—
198#3750C2312yes—
199C3×#217C2312yes—
200C3×#217C2311yescharacteristic
201C3×#217C2312yes—
202C3×#217C2312yes—
203C3×#217C2311yescharacteristic
204C3×(C2×D3)⋊C4C2312yes—
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×C4×Dic3C2312yes—
218C3×C4×Dic3C2311yescharacteristic
219C3×C4×Dic3C2311yescharacteristic
220#3724C2312yes—
221#3724C2312yes—
222Dic3⋊Dic3C2312yes—
223Dic3⋊Dic3C2312yes—
224Dic3⋊Dic3C2312yes—
225Dic3⋊Dic3C2312yes—
226#3722C2312yes—
227#3722C2312yes—
228#3722C2312yes—
229#3722C2312yes—
230#3722C2312yes—
231(C2×D3)⋊Dic3C2312yes—
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×#67—31no—
242C2×#239—32no—
243C2×#239—31no—
244C2×#237—32no—
245C2×#237—31no—
246C2×D3×D4—31no—
247C2×D3×D4—31no—
248C2×D3×D4—61no—
249C22×D12—31no—
250C22×C4×D3—31no—
251C22×C4×D3—31no—
252C22×C4×D3—61no—
253C3×C4⋊Q8—32no—
254C3×#127—31no—
255C3×#126—32no—
256C3×#126—32no—
257C3×#126—32no—
258C3×#125—32no—
259C3×#124—31no—
260C3×#123—21no—
261C3×#123—31no—
262C3×#123—32no—
263C3×#123C2×D311yescharacteristic
264C3×#123C2×D311yescharacteristic
265C3×C22⋊Q8—32no—
266C3×C22⋊Q8—32no—
267C3×#121—32no—
268C3×#121—32no—
269C3×#121—32no—
270C3×#120—31no—
271C3×#120—32no—
272#953—31no—
273C2×#217—32no—
274#947—32no—
275#947—31no—
276#946—32no—
277#946—32no—
278#946—32no—
279#940—31no—
280#940C2×D311yescharacteristic
281#939—32no—
282#939—32no—
283#939—32no—
284#939—32no—
285#939—32no—
286#938—32no—
287#938—32no—
288#938—32no—
289#937—32no—
290#937—32no—
291#937—32no—
292#937C2×D311yescharacteristic
293#936—32no—
294#936—32no—
295#936C2×D311yescharacteristic
296#935—31no—
297#935—31no—
298#935—32no—
299#935—32no—
300#935—32no—
301#935—61no—
302#935C2×D311yescharacteristic
303D4×Dic3—32no—
304D4×Dic3—32no—
305D4×Dic3—32no—
306D4×Dic3—32no—
307#930C2×D312yescomplemented
308#929—31no—
309#929—31no—
310#929—31no—
311#929—32no—
312#929—61no—
313C4×#67—32no—
314C4×#67—32no—
315C4×#67—32no—
316C2×C4⋊Dic3—32no—
317#924C2×D312yescomplemented
318#898—32no—
319#898—32no—
320#898—32no—
321#898C2×D312yescomplemented
322#897—32no—
323#897—32no—
324#896—32no—
325#896—32no—
326#896—32no—
327#896—32no—
328#895—32no—
329#895—32no—
330#895—32no—
331#895—32no—
332#895—32no—
333#895—32no—
334#895C2×D312yescomplemented
335#894—32no—
336#894—32no—
337#894—32no—
338#894—32no—
339#894—32no—
340#894—32no—
341#894—32no—
342#894—32no—
343#894—32no—
344#894—32no—
345#894—62no—
346#893—32no—
347#893—32no—
348#893—32no—
349#893—32no—
350#892—32no—
351#892—32no—
352#892—32no—
353D3×C4⋊C4—32no—
354D3×C4⋊C4—32no—
355D3×C4⋊C4—32no—
356D3×C4⋊C4—62no—
357#890—32no—
358#889—32no—
359#889—32no—
360#889—32no—
361#889C2×D312yescomplemented
362#888C2×D312yescomplemented
363#887—32no—
364#886—31no—
365#886—31no—
366#886—31no—
367#886—32no—
368#886—61no—
369#885—32no—
370#885—32no—
371#885—32no—
372#885—32no—
373#884—32no—
374#884—32no—
375#884—32no—
376#884—32no—
377#884C2×D312yescomplemented
378#883—32no—
379#883—32no—
380#883—32no—
381#883—32no—
382#883—32no—
383#883—32no—
384#883—32no—
385#883—62no—
386#883C2×D312yescomplemented
387#882—31no—
388#882—32no—
389#882—32no—
390#882—32no—
391#882C2×D312yescomplemented
392#67⋊C4—32no—
393#67⋊C4—32no—
394#67⋊C4—32no—
395#67⋊C4—32no—
396#67⋊C4—32no—
397D3×C22⋊C4—32no—
398D3×C22⋊C4—32no—
399D3×C22⋊C4—31no—
400D3×C22⋊C4—32no—
401D3×C22⋊C4—31no—
402D3×C22⋊C4—31no—
403D3×C22⋊C4—31no—
404D3×C22⋊C4—62no—
405D3×C22⋊C4—61no—
406#879—32no—
407#879—32no—
408#879—32no—
409#879C2×D312yescomplemented
410#879C2×D312yescomplemented
411#878—32no—
412#878—32no—
413#878—32no—
414#878C2×D312yescomplemented
415#877—32no—
416#875—31no—
417#875—32no—
418#874—31no—
419C4×D12—32no—
420C4×D12—32no—
421#872—32no—
422#872—32no—
423#872—31no—
424#872—31no—
425C4×Dic6—32no—
426C23×C32C2411yescharacteristic
427C23×C32C2411yescharacteristic
428C22×C3⋊D3—22no—
429C22×C3⋊D3—22no—
430C22×C3⋊D3—42no—
431C22×C3⋊D3—42no—
432C22×C3⋊D3C2411yescharacteristic
433C22×C3⋊D3C2411yescharacteristic
434C22×C3⋊D3C2411yescharacteristic
435C22×C3×D3—42no—
436C22×C3×D3—41no—
437C22×C3×D3C2412yes—
438C22×C3×D3C2412yes—
439C32×D4—41no—
440C2×C32×C4—41no—
441C2×C32×C4C2411yescharacteristic
442C2×C32×C4C2412yes—
443C2×C32×C4C2412yes—
444#638—41no—
445#638—41no—
446C2×C3⋊Dic3—41no—
447C2×C3⋊Dic3C2412yes—
448C2×C3⋊Dic3C2412yes—
449C2×C3⋊Dic3C2411yescharacteristic
450C4⋊(C3⋊D3)—41no—
451C4×C3⋊D3—24no—
452C4×C3⋊D3—22no—
453C4×C3⋊D3—42no—
454C4×C3⋊D3—42no—
455C3×#67—42no—
456C3×#67—42no—
457C3×#67—42no—
458C2×C3×Dic3—41no—
459C2×C3×Dic3C2412yes—
460C2×C3×Dic3C2412yes—
461C2×C3×Dic3C2412yes—
462C2×C3×Dic3C2412yes—
463C2×C3×Dic3C2412yes—
464C2×C3×Dic3C2412yes—
465C3×D12—42no—
466C3×D12—41no—
467C3×D12—42no—
468C3×C4×D3—42no—
469C3×Dic6—41no—
470C3×Dic6—42no—
471#627—42no—
472#626—24no—
473#626—24no—
474#626—42no—
475#626—42no—
476#626—42no—
477#626—42no—
478#624—42no—
479D3×Dic3—42no—
480D3×Dic3—42no—
481D3×Dic3—42no—
482D3×Dic3—42no—
483#563—31no—
484#562—92no—
485#560—31no—
486#559—91no—
487#553—92no—
488#552—92no—
489#551—91no—
490#551—92no—
491#547—92no—
492#546—92no—
493#542—92no—
494#540—92no—
495#539—92no—
496#538—92no—
497#538—92no—
498#535—91no—
499#534—91no—
500#525—92no—
501C2×#123—91no—
502C24×C3—31no—
503C23×D3—31no—
504C23×D3—31no—
505C23×D3—31no—
506C23×D3—31no—
507C23×D3—61no—
508C23×D3—61no—
509C23×D3C22×D311yescharacteristic
510C2×C3×Q8—32no—
511C2×C3×Q8—31no—
512C2×C3×D4—21no—
513C2×C3×D4—32no—
514C2×C3×D4—32no—
515C2×C3×D4—32no—
516C2×C3×D4—32no—
517C2×C3×D4—31no—
518C2×C3×D4—32no—
519C2×C3×D4C22×D311yescharacteristic
520C2×C3×D4C22×D311yescharacteristic
521C22×C3×C4—21no—
522C22×C3×C4—31no—
523C22×C3×C4—32no—
524C22×C3×C4C22×D311yescharacteristic
525C22×C3×C4C22×D311yescharacteristic
526C2×#67—31no—
527C2×#67—31no—
528C2×#67—31no—
529C2×#67—31no—
530C2×#67—32no—
531C2×#67—32no—
532C2×#67—32no—
533C2×#67—32no—
534C2×#67—32no—
535C2×#67—32no—
536C2×#67—61no—
537C2×#67—61no—
538C2×#67—122no—
539C2×#67C22×D312yes—
540C2×#67C22×D312yes—
541C2×#67C22×D312yes—
542C22×Dic3—31no—
543C22×Dic3—31no—
544C22×Dic3—32no—
545C22×Dic3—32no—
546C22×Dic3—32no—
547C22×Dic3—32no—
548C22×Dic3—61no—
549C22×Dic3C22×D311yescharacteristic
550#239—124no—
551#239—122no—
552#237—124no—
553#237—122no—
554D3×D4—122no—
555D3×D4—122no—
556D3×D4—124no—
557C2×D12—32no—
558C2×D12—32no—
559C2×D12—32no—
560C2×D12—32no—
561C2×D12—32no—
562C2×D12—32no—
563C2×D12—31no—
564C2×D12—31no—
565C2×D12—61no—
566C2×D12—122no—
567C2×D12C22×D312yes—
568C2×D12C22×D311yescharacteristic
569C2×D12C22×D312yes—
570C2×C4×D3—31no—
571C2×C4×D3—31no—
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—32no—
581C2×C4×D3—32no—
582C2×C4×D3—32no—
583C2×C4×D3—32no—
584C2×C4×D3—62no—
585C2×C4×D3—62no—
586C2×C4×D3—62no—
587C2×C4×D3—61no—
588C2×C4×D3—122no—
589C2×C4×D3—122no—
590C2×C4×D3—124no—
591C2×C4×D3C22×D312yes—
592C2×Dic6—32no—
593C2×Dic6—32no—
594C2×Dic6C22×D311yescharacteristic
595C2×Dic6C22×D312yes—
596C3×C4⋊C4—22no—
597C3×C4⋊C4—32no—
598C3×C4⋊C4—32no—
599C3×C4⋊C4—32no—
600C3×C4⋊C4—32no—
601C3×C4⋊C4—32no—
602C3×C4⋊C4—32no—
603C3×C4⋊C4—32no—
604C3×C4⋊C4—32no—
605C3×C4⋊C4—32no—
606C3×C4⋊C4C22×D312yes—
607C3×C4⋊C4C22×D312yes—
608C3×C22⋊C4—22no—
609C3×C22⋊C4—21no—
610C3×C22⋊C4—31no—
611C3×C22⋊C4—32no—
612C3×C22⋊C4—31no—
613C3×C22⋊C4—32no—
614C3×C22⋊C4—32no—
615C3×C22⋊C4—32no—
616C3×C22⋊C4—32no—
617C3×C22⋊C4—32no—
618C3×C22⋊C4—32no—
619C3×C22⋊C4C22×D312yes—
620C3×C22⋊C4C22×D311yescharacteristic
621C3×C22⋊C4C22×D312yes—
622C3×C22⋊C4C22×D311yescharacteristic
623C3×C42—31no—
624C3×C42—31no—
625C3×C42—32no—
626#217—32no—
627#217—32no—
628#217—31no—
629#217—31no—
630#217—32no—
631#217—32no—
632#217—32no—
633#217—32no—
634#217—32no—
635#217—32no—
636#217—62no—
637#217—61no—
638#217C22×D312yes—
639#217C22×D311yescharacteristic
640#217C22×D311yescharacteristic
641#217C22×D312yes—
642#217C22×D312yes—
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—32no—
660(C2×D3)⋊C4—32no—
661(C2×D3)⋊C4—32no—
662(C2×D3)⋊C4—32no—
663(C2×D3)⋊C4—32no—
664(C2×D3)⋊C4—32no—
665(C2×D3)⋊C4—62no—
666(C2×D3)⋊C4—62no—
667(C2×D3)⋊C4—62no—
668(C2×D3)⋊C4C22×D312yes—
669(C2×D3)⋊C4C22×D312yes—
670(C2×D3)⋊C4C22×D312yes—
671(C2×D3)⋊C4C22×D312yes—
672C4⋊Dic3—32no—
673C4⋊Dic3—32no—
674C4⋊Dic3—32no—
675C4⋊Dic3—32no—
676C4⋊Dic3—32no—
677C4⋊Dic3—32no—
678C4⋊Dic3—62no—
679C4⋊Dic3C22×D312yes—
680C4⋊Dic3C22×D312yes—
681C4⋊Dic3C22×D312yes—
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—32no—
693Dic3⋊C4—32no—
694Dic3⋊C4—62no—
695Dic3⋊C4—62no—
696Dic3⋊C4C22×D312yes—
697Dic3⋊C4C22×D312yes—
698Dic3⋊C4C22×D312yes—
699Dic3⋊C4C22×D312yes—
700Dic3⋊C4C22×D312yes—
701Dic3⋊C4C22×D312yes—
702C4×Dic3—32no—
703C4×Dic3—32no—
704C4×Dic3—32no—
705C4×Dic3—32no—
706C4×Dic3—32no—
707C4×Dic3—32no—
708C4×Dic3C22×D311yescharacteristic
709C4×Dic3C22×D311yescharacteristic
710C4×Dic3C22×D312yes—
711C22×C32—21no—
712C22×C32—21no—
713C22×C32—22no—
714C22×C32—22no—
715C22×C32C2511yescharacteristic
716C2×C3⋊D3—22no—
717C2×C3⋊D3—21no—
718C2×C3⋊D3—21no—
719C2×C3⋊D3—22no—
720C2×C3⋊D3—22no—
721C2×C3⋊D3—44no—
722C2×C3⋊D3—82no—
723C2×C3⋊D3H(5,𝔽2)12yes—
724C2×C3×D3—22no—
725C2×C3×D3—22no—
726C2×C3×D3—22no—
727C2×C3×D3—22no—
728C2×C3×D3—22no—
729C2×C3×D3—22no—
730C2×C3×D3—82no—
731C32×C4—22no—
732C32×C4—21no—
733C32×C4—22no—
734C3⋊Dic3—22no—
735C3⋊Dic3—21no—
736C3⋊Dic3—22no—
737C3×Dic3—22no—
738C3×Dic3—22no—
739C3×Dic3—22no—
740C3×Dic3—22no—
741C3×Dic3—22no—
742C3×Dic3—22no—
743C2×#41—92no—
744C2×#41—91no—
745C22×D4—91no—
746C22×D4—91no—
747C23×C4—91no—
748C4⋊Q8—32no—
749#127—31no—
750#127—91no—
751#126—32no—
752#126—32no—
753#126—32no—
754#126—92no—
755#126—92no—
756#126—92no—
757#125—32no—
758#125—92no—
759#125—92no—
760#124—31no—
761#124—92no—
762#124—91no—
763#124—92no—
764#124—92no—
765#124—92no—
766#123—31no—
767#123—32no—
768#123—92no—
769#123—92no—
770#123—92no—
771#123—92no—
772#123—92no—
773#123—91no—
774#123—92no—
775#123—92no—
776#123—92no—
777#123—92no—
778#123—91no—
779#123—91no—
780#123—92no—
781#123—92no—
782#123—91no—
783#123D3211yescharacteristic
784C22⋊Q8—32no—
785C22⋊Q8—32no—
786C22⋊Q8—92no—
787C22⋊Q8—92no—
788C22⋊Q8—92no—
789C22⋊Q8—92no—
790C22⋊Q8—92no—
791C22⋊Q8—92no—
792#121—32no—
793#121—32no—
794#121—32no—
795#121—92no—
796#121—92no—
797#121—92no—
798#121—92no—
799#121—92no—
800#121—92no—
801#121—92no—
802#121—92no—
803#121—92no—
804#120—31no—
805#120—32no—
806#120—92no—
807#120—92no—
808#120—92no—
809#120—91no—
810C4×Q8—92no—
811C4×D4—92no—
812C4×D4—92no—
813C4×D4—92no—
814C4×D4—92no—
815C4×D4—92no—
816C4×D4—92no—
817C4×D4—92no—
818C4×D4—92no—
819C4×D4—92no—
820#117—91no—
821#117—92no—
822#117—92no—
823#117—92no—
824C2×C4⋊C4—92no—
825C2×C4⋊C4—92no—
826C2×C22⋊C4—91no—
827C2×C22⋊C4—92no—
828C2×C22⋊C4—91no—
829C2×C22⋊C4—92no—
830C23×C3—21no—
831C23×C3—21no—
832C23×C3—32no—
833C23×C3—32no—
834C23×C3—121no—
835C23×C3—122no—
836C23×C3C23×D311yescharacteristic
837C23×C3C23×D311yescharacteristic
838C23×C3C23×D311yescharacteristic
839C23×C3C23×D311yescharacteristic
840C22×D3—31no—
841C22×D3—31no—
842C22×D3—31no—
843C22×D3—31no—
844C22×D3—31no—
845C22×D3—31no—
846C22×D3—41no—
847C22×D3—42no—
848C22×D3—61no—
849C22×D3—61no—
850C22×D3—61no—
851C22×D3—62no—
852C22×D3—62no—
853C22×D3—62no—
854C22×D3—62no—
855C22×D3—64no—
856C22×D3—122no—
857C22×D3—122no—
858C22×D3—122no—
859C22×D3—122no—
860C22×D3—122no—
861C22×D3—124no—
862C22×D3—124no—
863C22×D3C23×D312yes—
864C22×D3C23×D312yes—
865C3×Q8—122no—
866C3×Q8—121no—
867C3×D4—41no—
868C3×D4—41no—
869C3×D4—42no—
870C3×D4—122no—
871C3×D4—121no—
872C3×D4—122no—
873C3×D4—122no—
874C3×D4—122no—
875C3×D4—122no—
876C2×C3×C4—21no—
877C2×C3×C4—22no—
878C2×C3×C4—22no—
879C2×C3×C4—32no—
880C2×C3×C4—32no—
881C2×C3×C4—32no—
882C2×C3×C4—32no—
883C2×C3×C4—32no—
884C2×C3×C4—32no—
885C2×C3×C4—41no—
886C2×C3×C4—41no—
887C2×C3×C4—42no—
888C2×C3×C4—122no—
889C2×C3×C4—121no—
890C2×C3×C4C23×D311yescharacteristic
891C2×C3×C4C23×D311yescharacteristic
892C2×C3×C4C23×D312yes—
893C2×C3×C4C23×D312yes—
894C2×C3×C4C23×D312yes—
895C2×C3×C4C23×D312yes—
896#67—42no—
897#67—42no—
898#67—42no—
899#67—64no—
900#67—64no—
901#67—122no—
902#67—122no—
903#67—122no—
904#67—122no—
905#67—121no—
906#67—121no—
907#67—121no—
908#67—121no—
909#67—122no—
910#67—122no—
911C2×Dic3—32no—
912C2×Dic3—32no—
913C2×Dic3—32no—
914C2×Dic3—32no—
915C2×Dic3—31no—
916C2×Dic3—31no—
917C2×Dic3—41no—
918C2×Dic3—61no—
919C2×Dic3—62no—
920C2×Dic3—62no—
921C2×Dic3—122no—
922C2×Dic3—122no—
923C2×Dic3—122no—
924C2×Dic3—122no—
925C2×Dic3—121no—
926C2×Dic3—121no—
927C2×Dic3—122no—
928C2×Dic3C23×D312yes—
929C2×Dic3C23×D312yes—
930C2×Dic3C23×D312yes—
931C2×Dic3C23×D312yes—
932C2×Dic3C23×D312yes—
933C2×Dic3C23×D312yes—
934D12—42no—
935D12—42no—
936D12—41no—
937D12—64no—
938D12—64no—
939D12—121no—
940D12—121no—
941D12—122no—
942D12—122no—
943D12—122no—
944D12—122no—
945D12—122no—
946C4×D3—42no—
947C4×D3—64no—
948C4×D3—64no—
949C4×D3—62no—
950C4×D3—62no—
951C4×D3—124no—
952C4×D3—122no—
953C4×D3—122no—
954C4×D3—122no—
955C4×D3—122no—
956C4×D3—122no—
957C4×D3—122no—
958C4×D3—122no—
959C4×D3—122no—
960C4×D3—122no—
961C4×D3—122no—
962C4×D3—122no—
963C4×D3—124no—
964C4×D3—124no—
965Dic6—41no—
966Dic6—42no—
967Dic6—122no—
968Dic6—122no—
969C2×C32—41no—
970C2×C32—41no—
971C2×C32C2×H(5,𝔽2)11yescharacteristic
972C2×C32#58512yes—
973C3⋊D3—22no—
974C3⋊D3—41no—
975C3⋊D3—41no—
976C3×D3—42no—
977C3×D3—42no—
978C24—31no—
979C24—91no—
980C24—91no—
981#41—364no—
982#41—362no—
983C2×Q8—32no—
984C2×Q8—31no—
985C2×Q8—92no—
986C2×D4—32no—
987C2×D4—32no—
988C2×D4—32no—
989C2×D4—32no—
990C2×D4—32no—
991C2×D4—31no—
992C2×D4—92no—
993C2×D4—92no—
994C2×D4—92no—
995C2×D4—92no—
996C2×D4—92no—
997C2×D4—92no—
998C2×D4—91no—
999C2×D4—91no—
1000C2×D4—91no—
1001C2×D4—362no—
1002C2×D4—362no—
1003C2×D4C2×D3211yescharacteristic
1004C22×C4—31no—
1005C22×C4—32no—
1006C22×C4—92no—
1007C22×C4—92no—
1008C22×C4—92no—
1009C22×C4—92no—
1010C22×C4—92no—
1011C22×C4—91no—
1012C22×C4—92no—
1013C22×C4—91no—
1014C22×C4—92no—
1015C22×C4—92no—
1016C22×C4—362no—
1017C22×C4C2×D3211yescharacteristic
1018C4⋊C4—32no—
1019C4⋊C4—32no—
1020C4⋊C4—32no—
1021C4⋊C4—32no—
1022C4⋊C4—32no—
1023C4⋊C4—32no—
1024C4⋊C4—32no—
1025C4⋊C4—32no—
1026C4⋊C4—32no—
1027C4⋊C4—92no—
1028C4⋊C4—92no—
1029C4⋊C4—92no—
1030C4⋊C4—92no—
1031C4⋊C4—92no—
1032C4⋊C4—92no—
1033C4⋊C4—92no—
1034C4⋊C4—92no—
1035C4⋊C4—92no—
1036C4⋊C4C2×D3212yes—
1037C22⋊C4—31no—
1038C22⋊C4—32no—
1039C22⋊C4—31no—
1040C22⋊C4—32no—
1041C22⋊C4—32no—
1042C22⋊C4—32no—
1043C22⋊C4—32no—
1044C22⋊C4—32no—
1045C22⋊C4—32no—
1046C22⋊C4—92no—
1047C22⋊C4—92no—
1048C22⋊C4—92no—
1049C22⋊C4—92no—
1050C22⋊C4—92no—
1051C22⋊C4—92no—
1052C22⋊C4—92no—
1053C22⋊C4—92no—
1054C22⋊C4—92no—
1055C22⋊C4—92no—
1056C22⋊C4—92no—
1057C22⋊C4—92no—
1058C22⋊C4—91no—
1059C22⋊C4—92no—
1060C22⋊C4—92no—
1061C22⋊C4—92no—
1062C22⋊C4C2×D3212yes—
1063C22⋊C4C2×D3211yescharacteristic
1064C42—31no—
1065C42—32no—
1066C42—31no—
1067C42—92no—
1068C42—92no—
1069C42—92no—
1070C22×C3—22no—
1071C22×C3—21no—
1072C22×C3—21no—
1073C22×C3—21no—
1074C22×C3—21no—
1075C22×C3—22no—
1076C22×C3—22no—
1077C22×C3—22no—
1078C22×C3—22no—
1079C22×C3—21no—
1080C22×C3—42no—
1081C22×C3—41no—
1082C22×C3—42no—
1083C22×C3—62no—
1084C22×C3—62no—
1085C22×C3—62no—
1086C22×C3—62no—
1087C22×C3—62no—
1088C22×C3—62no—
1089C22×C3—242no—
1090C22×C3C24×D311yescharacteristic
1091C22×C3C24×D311yescharacteristic
1092C2×D3—22no—
1093C2×D3—22no—
1094C2×D3—22no—
1095C2×D3—22no—
1096C2×D3—22no—
1097C2×D3—22no—
1098C2×D3—32no—
1099C2×D3—32no—
1100C2×D3—62no—
1101C2×D3—64no—
1102C2×D3—62no—
1103C2×D3—62no—
1104C2×D3—62no—
1105C2×D3—61no—
1106C2×D3—61no—
1107C2×D3—61no—
1108C2×D3—61no—
1109C2×D3—62no—
1110C2×D3—62no—
1111C2×D3—62no—
1112C2×D3—62no—
1113C2×D3—82no—
1114C2×D3—122no—
1115C2×D3—121no—
1116C2×D3—122no—
1117C2×D3—128no—
1118C2×D3—124no—
1119C2×D3—124no—
1120C2×D3—242no—
1121C2×D3—242no—
1122C2×D3—244no—
1123C3×C4—22no—
1124C3×C4—21no—
1125C3×C4—22no—
1126C3×C4—21no—
1127C3×C4—22no—
1128C3×C4—22no—
1129C3×C4—42no—
1130C3×C4—41no—
1131C3×C4—42no—
1132C3×C4—62no—
1133C3×C4—62no—
1134C3×C4—62no—
1135C3×C4—62no—
1136C3×C4—62no—
1137C3×C4—62no—
1138Dic3—22no—
1139Dic3—22no—
1140Dic3—22no—
1141Dic3—22no—
1142Dic3—22no—
1143Dic3—22no—
1144Dic3—62no—
1145Dic3—61no—
1146Dic3—62no—
1147Dic3—61no—
1148Dic3—62no—
1149Dic3—62no—
1150Dic3—122no—
1151Dic3—121no—
1152Dic3—122no—
1153C32#353311yescharacteristic, complemented, Sylow
1154C23—32no—
1155C23—32no—
1156C23—91no—
1157C23—91no—
1158C23—91no—
1159C23—121no—
1160C23—122no—
1161C23—182no—
1162C23—182no—
1163C23—362no—
1164C23—362no—
1165C23C22×D3211yescharacteristic
1166C23C22×D3211yescharacteristic
1167Q8—122no—
1168Q8—121no—
1169Q8—362no—
1170D4—41no—
1171D4—122no—
1172D4—121no—
1173D4—122no—
1174D4—122no—
1175D4—122no—
1176D4—122no—
1177D4—184no—
1178D4—184no—
1179D4—361no—
1180D4—362no—
1181D4—362no—
1182D4—362no—
1183D4—362no—
1184D4—361no—
1185D4—361no—
1186C2×C4—32no—
1187C2×C4—32no—
1188C2×C4—32no—
1189C2×C4—32no—
1190C2×C4—32no—
1191C2×C4—32no—
1192C2×C4—41no—
1193C2×C4—92no—
1194C2×C4—92no—
1195C2×C4—91no—
1196C2×C4—122no—
1197C2×C4—121no—
1198C2×C4—184no—
1199C2×C4—182no—
1200C2×C4—362no—
1201C2×C4—362no—
1202C2×C4—362no—
1203C2×C4—362no—
1204C2×C4—362no—
1205C2×C4—362no—
1206C2×C4—362no—
1207C2×C4—361no—
1208C2×C4C22×D3211yescharacteristic
1209C2×C4C22×D3212yes—
1210C2×C4C22×D3212yes—
1211C2×C3—21no—
1212C2×C3—22no—
1213C2×C3—42no—
1214C2×C3—41no—
1215C2×C3—41no—
1216C2×C3—41no—
1217C2×C3—41no—
1218C2×C3—81no—
1219C2×C3—122no—
1220C2×C3—122no—
1221C2×C3D3×H(5,𝔽2)11yescharacteristic
1222C2×C3D3×H(5,𝔽2)11yescharacteristic
1223C2×C3#596612yes—
1224C2×C3#596812yes—
1225D3—42no—
1226D3—42no—
1227D3—64no—
1228D3—62no—
1229D3—62no—
1230D3—122no—
1231D3—121no—
1232D3—121no—
1233D3—121no—
1234D3—121no—
1235D3—241no—
1236C22—21no—
1237C22—21no—
1238C22—22no—
1239C22—22no—
1240C22—62no—
1241C22—62no—
1242C22—62no—
1243C22—62no—
1244C22—62no—
1245C22—62no—
1246C22—92no—
1247C22—182no—
1248C22—181no—
1249C22—181no—
1250C22—182no—
1251C22—182no—
1252C22—242no—
1253C22—364no—
1254C22—722no—
1255C22C23×D3211yescharacteristic
1256C4—22no—
1257C4—21no—
1258C4—22no—
1259C4—62no—
1260C4—62no—
1261C4—62no—
1262C4—62no—
1263C4—62no—
1264C4—62no—
1265C4—182no—
1266C4—181no—
1267C4—182no—
1268C3—21no—
1269C3#8708111yescharacteristic, complemented
1270C3#8712811yescharacteristic, complemented
1271C2—41no—
1272C2—41no—
1273C2—122no—
1274C2—122no—
1275C2—182no—
1276C2—361no—
1277C2—361no—
1278C2#1059667511yescharacteristic
1279C2#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. C3⋊D3×#123C2semidirect
2. C3×#5666C2semidirect
3. C3×#5651C2semidirect
4. #10595242C2semidirect
5. #10595200C2semidirect
6. #10595176C2semidirect
7. #10595168C2semidirect
8. #10594976C2semidirect
9. #10594922C2semidirect
10. #10594563C2semidirect
11. #10594471C2semidirect
12. #10594466C2semidirect
13. #10594373C2semidirect
14. #10594228C2semidirect
15. #10594226C2semidirect
16. #10594129C2semidirect
17. #10594127C2semidirect
18. #10594125C2semidirect
19. #10594063C2semidirect
23. C22×C4×C3⋊D3C22semidirect
26. C2×#3796C22semidirect
29. #64138C22semidirect
30. #64103C22semidirect
31. C4⋊C4×C3⋊D3C22semidirect
32. #64095C22semidirect
35. C22⋊C4×C3⋊D3C22semidirect
40. C3×#930C22semidirect
41. C3×#924C22semidirect
42. C3×#898C22semidirect
43. C3×#895C22semidirect
44. C3×#889C22semidirect
45. C3×#888C22semidirect
46. C3×#884C22semidirect
47. C3×#883C22semidirect
48. C3×#882C22semidirect
49. C3×#879C22semidirect
50. C3×#879C22semidirect
51. C3×#878C22semidirect
54. #63981C22semidirect
57. #67⋊Dic3C22semidirect
58. #67⋊Dic3C22semidirect
59. Dic3×#67C22semidirect
61. #63971C22semidirect
62. #63969C22semidirect
63. D3×#217C22semidirect
65. #63959C22semidirect
66. #63959C22semidirect
68. #63956C22semidirect
70. #63916C22semidirect
71. #63911C22semidirect
73. #63907C22semidirect
74. #63904C22semidirect
75. C4×#626C22semidirect
76. #63899C22semidirect
77. #63895C22semidirect
78. Dic3×D12C22semidirect
79. #63890C22semidirect
80. D3×C4⋊Dic3C22semidirect
81. #63887C22semidirect
82. #63887C22semidirect
83. #63886C22semidirect
84. #63886C22semidirect
85. #63886C22semidirect
86. #63884C22semidirect
87. #63884C22semidirect
89. #63881C22semidirect
90. #63881C22semidirect
91. #63877C22semidirect
92. #63874C22semidirect
93. #63871C22semidirect
94. #63865C22semidirect
95. #63864C22semidirect
96. #63861C22semidirect
97. #63854C22semidirect
100. #63853C22semidirect
101. #63852C22semidirect
102. #63850C22semidirect
103. #63849C22semidirect
104. #63848C22semidirect
105. #63847C22semidirect
106. #63845C22semidirect
107. #63837C22semidirect
108. #63836C22semidirect
125. #5666D3semidirect
133. #5651D3semidirect
307. #930C2×D3semidirect
317. #924C2×D3semidirect
321. #898C2×D3semidirect
334. #895C2×D3semidirect
361. #889C2×D3semidirect
362. #888C2×D3semidirect
377. #884C2×D3semidirect
386. #883C2×D3semidirect
391. #882C2×D3semidirect
409. #879C2×D3semidirect
410. #879C2×D3semidirect
414. #878C2×D3semidirect
1153. C32#3533semidirect
1269. C3#87081semidirect
1270. C3#87128semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1232
C3×#56662
C3×#56512
#105952422
#105952002
#105951762
#105951682
#105949762
#105949222
#105945632
#105944712
#105944662
#105943732
#105942282
#105942262
#105941292
#105941272
#105941252
#105940632
#871283
#870813