Finite Group Databasebeta

← #11911147

Subgroups — #11911147

Order 1152.

2497 conjugacy classes of subgroups.

The subgroup lattice has 1372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596077C211yesmaximal, characteristic, complemented
2C3×#5605C211yesmaximal, characteristic, complemented
3C3×#5597C211yesmaximal, characteristic, complemented
4#10595307C212yesmaximal, complemented
5#10595305C212yesmaximal, complemented
6#10595291C212yesmaximal, complemented
7#10595258C212yesmaximal, complemented
8#10595244C212yesmaximal, complemented
9#10595189C212yesmaximal, complemented
10#10595081C211yesmaximal, characteristic, complemented
11#10594977C211yesmaximal, characteristic, complemented
12#10594973C211yesmaximal, characteristic, complemented
13C2×#63853C211yesmaximal, characteristic, complemented
14#10594653C212yesmaximal, complemented
15#10594590C212yesmaximal, complemented
16#10594263C212yesmaximal, complemented
17#10594173C212yesmaximal, complemented
18#10594151C212yesmaximal, complemented
19#10594041C212yesmaximal, complemented
20#86383—31nomaximal
21#86312—31nomaximal
22C2×#3830C2211yescharacteristic, complemented
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C2×C3×#237C2212yescomplemented
25C2×C3×D3×D4C2212yescomplemented
26C2×#3811C2212yescomplemented
27C2×D3×#67C2212yescomplemented
28C22×#626C2211yescharacteristic
29C2×#3802C2211yescharacteristic, complemented
30C32×#121C2211yescharacteristic, complemented
31#64147C2211yescharacteristic, complemented
32#64146C2212yescomplemented
33D4×C3⋊Dic3C2212yescomplemented
34#64133C2211yescharacteristic, complemented
35#64106C2211yescharacteristic, complemented
36#64101C2211yescharacteristic, complemented
37#64092C2212yescomplemented
38#64090C2212yescomplemented
39C3×#939C2212yescomplemented
40C3×#939C2212yescomplemented
41C3×#939C2212yescomplemented
42C3×#937C2212yescomplemented
43C3×#930C2211yescharacteristic
44C3×#930C2211yescharacteristic, complemented
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
47C3×#896C2212yescomplemented
48C3×#894C2212yescomplemented
49C3×#884C2212yescomplemented
50C3×#883C2212yescomplemented
51C3×#882C2212yescomplemented
52C3×#878C2212yescomplemented
53#63983C2212yescomplemented
54#63980C2212yescomplemented
55#63980C2212yescomplemented
56#63979C2212yescomplemented
57#63978C2212yescomplemented
58#63977C2212yescomplemented
59#63976C2212yescomplemented
60#63976C2212yescomplemented
61#67⋊Dic3C2212yescomplemented
62Dic3×#67C2212yescomplemented
63Dic3×#67C2212yescomplemented
64#63971C2212yescomplemented
65#63970C2212yescomplemented
66C2×Dic3⋊Dic3C2211yescharacteristic, complemented
67C2×#3722C2211yescharacteristic, complemented
68#63962C2212yescomplemented
69#63961C2212yescomplemented
70#63961C2212yescomplemented
71C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
72C2×(C2×D3)⋊Dic3C2212yescomplemented
73#63958C2212yes—
74#63956C2212yescomplemented
75#63952C2212yescomplemented
76#63922C2212yes—
77#63921C2212yescomplemented
78D3×(C2×D3)⋊C4C2212yescomplemented
79#63916C2211yescharacteristic, complemented
80#63916C2211yescharacteristic, complemented
81#63913C2212yescomplemented
82#63912C2212yescomplemented
83#63908C2212yescomplemented
84#63907C2212yescomplemented
85#63906C2212yescomplemented
86#63904C2212yescomplemented
87C4×#625C2212yescomplemented
88#63900C2211yescharacteristic, complemented
89#63896C2212yescomplemented
90#63891C2212yescomplemented
91#63891C2212yescomplemented
92#63888C2212yescomplemented
93#63886C2212yescomplemented
94#63885C2212yescomplemented
95#63884C2212yescomplemented
96#63878C2212yescomplemented
97#63863C2212yescomplemented
98#63862C2212yescomplemented
99#63861C2212yescomplemented
100#63858C2212yescomplemented
101#63856C2212yescomplemented
102#63853C2212yescomplemented
103#63853C2212yescomplemented
104#63853C2212yescomplemented
105#63853C2212yescomplemented
106#63850C2212yescomplemented
107#63847C2212yescomplemented
108#63845C2212yescomplemented
109C3×#537—31no—
110C3×#534—31no—
111#5829—32no—
112#5829—32no—
113#5806—32no—
114D4×#67—32no—
115#5667—32no—
116#5663—32no—
117#5660—32no—
118#5659—32no—
119#5647—32no—
120#5644—32no—
121#5638—32no—
122#5637—32no—
123#5620—32no—
124#5618—32no—
125#5617—31no—
126#5615—32no—
127#5610—32no—
128#5610—32no—
129#5609—32no—
130#5606—31no—
131#5606—31no—
132#5606—61no—
133#5605—32no—
134#5605D311yescharacteristic, complemented
135D3×#121—31no—
136D3×#121—31no—
137#5602—31no—
138#5601—32no—
139#5597D311yescharacteristic, complemented
140#5595—32no—
141#5593—32no—
142#5591—32no—
143#5589—32no—
144#5515—31no—
145C2×#894—31no—
146#5494—31no—
147C2×#883—31no—
148C23×C3⋊D3C2311yescharacteristic
149C23×C3×D3C2311yescharacteristic
150C23×C3×D3C2312yes—
151C22×D32C2312yes—
152C2×C32×D4C2312yes—
153C2×C32×D4C2311yescharacteristic
154C22×C32×C4C2311yescharacteristic
155C2×#638C2312yes—
156C2×#638C2312yes—
157C22×C3⋊Dic3C2312yes—
158C22×C3⋊Dic3C2311yescharacteristic
159#3830—42no—
160C2×C4×C3⋊D3—42no—
161C2×C4×C3⋊D3C2311yescharacteristic
162C2×C4×C3⋊D3C2311yescharacteristic
163C2×C4×C3⋊D3C2311yescharacteristic
164C2×C4×C3⋊D3C2311yescharacteristic
165C2×#634C2311yescharacteristic
166C2×C3×#67C2312yes—
167C2×C3×#67C2312yes—
168C2×C3×#67C2312yes—
169C2×C3×#67C2312yes—
170C2×C3×#67C2312yes—
171C2×C3×#67C2312yes—
172C22×C3×Dic3C2311yescharacteristic
173C22×C3×Dic3C2312yes—
174C22×C3×Dic3C2311yescharacteristic
175C22×C3×Dic3C2311yescharacteristic
176C3×#237—44no—
177C3×D3×D4—44no—
178C2×C3×D12C2311yescharacteristic
179C2×C3×D12C2312yes—
180C2×C3×D12C2311yescharacteristic
181C2×C3×C4×D3C2312yes—
182C2×C3×C4×D3C2312yes—
183C2×C3×Dic6C2312yes—
184#3811—44no—
185D3×#67—44no—
186C2×#626—42no—
187C2×#626C2312yes—
188C2×#626C2312yes—
189C2×#626C2312yes—
190C2×#626C2312yes—
191C2×#625C2312yes—
192C2×#625C2312yes—
193C2×#625C2312yes—
194C2×#624C2312yes—
195C2×D3×Dic3C2312yes—
196C2×D3×Dic3C2312yes—
197#3802—42no—
198C32×C4⋊C4C2311yescharacteristic
199C32×C22⋊C4C2312yes—
200#3757C2312yes—
201#3757C2312yes—
202#3752C2312yes—
203#3752C2312yes—
204C4⋊(C3⋊Dic3)C2312yes—
205C4⋊(C3⋊Dic3)C2311yescharacteristic
206#3750C2312yes—
207C4×C3⋊Dic3C2312yes—
208C3×#217C2312yes—
209C3×#217C2312yes—
210C3×(C2×D3)⋊C4C2312yes—
211C3×(C2×D3)⋊C4C2312yes—
212C3×(C2×D3)⋊C4C2312yes—
213C3×(C2×D3)⋊C4C2312yes—
214C3×(C2×D3)⋊C4C2312yes—
215C3×(C2×D3)⋊C4C2312yes—
216C3×C4⋊Dic3C2311yescharacteristic
217C3×C4⋊Dic3C2311yescharacteristic
218C3×Dic3⋊C4C2312yes—
219C3×Dic3⋊C4C2312yes—
220C3×Dic3⋊C4C2312yes—
221C3×Dic3⋊C4C2312yes—
222#3724C2312yes—
223#3724C2312yes—
224#3724C2312yes—
225Dic3⋊Dic3C2312yes—
226Dic3⋊Dic3C2312yes—
227Dic3⋊Dic3C2312yes—
228Dic3⋊Dic3C2312yes—
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—
237(C2×D3)⋊Dic3C2312yes—
238(C2×D3)⋊Dic3C2312yes—
239(C2×D3)⋊Dic3C2312yes—
240(C2×D3)⋊Dic3C2312yes—
241Dic32C2312yes—
242Dic32C2312yes—
243#3534—91noSylow
244C2×C3×#41—32no—
245C22×C3×D4—32no—
246C22×#67—32no—
247C22×#67—31no—
248C2×#237—31no—
249C2×#237—31no—
250C2×#237—61no—
251C2×#237C2×D312yescomplemented
252C2×D3×D4—32no—
253C2×D3×D4—32no—
254C2×D3×D4—32no—
255C2×D3×D4—31no—
256C2×D3×D4—31no—
257C2×D3×D4C2×D312yescomplemented
258C22×D12—31no—
259C22×C4×D3—31no—
260C22×C4×D3—31no—
261C22×C4×D3—61no—
262C3×#123—32no—
263C3×#123—32no—
264C3×C22⋊Q8—32no—
265C3×C22⋊Q8—32no—
266C3×#121—21no—
267C3×#121—32no—
268C3×#121—32no—
269C3×#121—32no—
270C3×#121—31no—
271C3×#121—31no—
272C3×#121—32no—
273C3×#121C2×D311yescharacteristic, complemented
274C3×#121C2×D311yescharacteristic, complemented
275C3×#120—32no—
276C3×#120—32no—
277C2×C3×C4⋊C4—31no—
278C2×C3×C22⋊C4—31no—
279#953—32no—
280#953—32no—
281#953—32no—
282C2×#217—31no—
283C2×#217—32no—
284#947—32no—
285#947—32no—
286#946—32no—
287#946—32no—
288#940—32no—
289#940—32no—
290#939—32no—
291#939—32no—
292#939—32no—
293#939—32no—
294#939—32no—
295#939—32no—
296#939—32no—
297#939—32no—
298#939—32no—
299#939C2×D312yescomplemented
300#939C2×D312yescomplemented
301#939C2×D312yescomplemented
302#938—31no—
303#938—31no—
304#938—32no—
305#938—32no—
306#938—32no—
307#938—31no—
308#938—31no—
309#938—61no—
310#937—32no—
311#937—32no—
312#937—32no—
313#937—32no—
314#937—32no—
315#937—32no—
316#937—32no—
317#937—62no—
318#937C2×D312yescomplemented
319#936—32no—
320#935—32no—
321#935—32no—
322#935—32no—
323#935—32no—
324D4×Dic3—32no—
325D4×Dic3—32no—
326D4×Dic3—32no—
327D4×Dic3—32no—
328D4×Dic3—32no—
329D4×Dic3—62no—
330#930—32no—
331#930—32no—
332#930—32no—
333#930C2×D311yescharacteristic
334#930C2×D311yescharacteristic, complemented
335#929—32no—
336#929—32no—
337#929—32no—
338C4×#67—32no—
339C4×#67—32no—
340C4×#67—32no—
341C4×#67—32no—
342C4×#67—32no—
343C4×#67—32no—
344C2×(C2×D3)⋊C4—32no—
345C2×(C2×D3)⋊C4—31no—
346C2×(C2×D3)⋊C4—31no—
347C2×(C2×D3)⋊C4—31no—
348C2×(C2×D3)⋊C4—32no—
349C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
350C2×C4⋊Dic3—31no—
351#924—31no—
352#924—31no—
353#924—32no—
354#924—61no—
355C2×Dic3⋊C4—31no—
356C2×Dic3⋊C4C2×D311yescharacteristic, complemented
357#898—32no—
358#898—32no—
359#898—32no—
360#897—31no—
361#897—31no—
362#897—61no—
363#896—32no—
364#896—32no—
365#896C2×D312yescomplemented
366#895—31no—
367#895—32no—
368#895—31no—
369#894—32no—
370#894—32no—
371#894—32no—
372#894—32no—
373#894—32no—
374#894—32no—
375#894C2×D312yescomplemented
376#893—32no—
377#892—31no—
378#892—31no—
379#892—32no—
380#892—61no—
381D3×C4⋊C4—31no—
382D3×C4⋊C4—31no—
383#890—32no—
384#889—32no—
385#889—32no—
386#889—32no—
387#886—32no—
388#886—32no—
389#886—32no—
390#885—32no—
391#885—32no—
392#885—32no—
393#884—32no—
394#884—32no—
395#884—32no—
396#884—32no—
397#884—32no—
398#884—32no—
399#884C2×D312yescomplemented
400#883—32no—
401#883—32no—
402#883—32no—
403#883—32no—
404#883—32no—
405#883—32no—
406#883—32no—
407#883—32no—
408#883—62no—
409#883C2×D312yescomplemented
410#882—32no—
411#882—32no—
412#882C2×D312yescomplemented
413#67⋊C4—32no—
414#67⋊C4—32no—
415#67⋊C4—32no—
416#67⋊C4—32no—
417#67⋊C4—62no—
418D3×C22⋊C4—32no—
419D3×C22⋊C4—32no—
420D3×C22⋊C4—32no—
421#879—32no—
422#879—32no—
423#879—32no—
424#879—32no—
425#879—32no—
426#878—32no—
427#878C2×D312yescomplemented
428#877—32no—
429C23×C32C2412yes—
430C23×C32C2411yescharacteristic
431C22×C3⋊D3—22no—
432C22×C3⋊D3—22no—
433C22×C3⋊D3—41no—
434C22×C3⋊D3C2411yescharacteristic
435C22×C3⋊D3C2411yescharacteristic
436C22×C3×D3—22no—
437C22×C3×D3—41no—
438C22×C3×D3—42no—
439C22×C3×D3—41no—
440C22×C3×D3—42no—
441C22×C3×D3—42no—
442C22×C3×D3C2412yes—
443C22×C3×D3C2412yes—
444C22×C3×D3C2412yes—
445C2×D32—24no—
446C2×D32—42no—
447C2×D32—42no—
448C32×D4—24no—
449C32×D4—41no—
450C2×C32×C4—41no—
451C2×C32×C4C2411yescharacteristic
452C2×C32×C4C2411yescharacteristic
453C2×C32×C4C2412yes—
454#638—24no—
455#638—42no—
456C2×C3⋊Dic3—41no—
457C2×C3⋊Dic3—42no—
458C2×C3⋊Dic3C2412yes—
459C2×C3⋊Dic3C2412yes—
460C2×C3⋊Dic3C2411yescharacteristic
461C2×C3⋊Dic3C2411yescharacteristic
462C4×C3⋊D3—22no—
463C4×C3⋊D3—22no—
464C4×C3⋊D3—41no—
465C4×C3⋊D3—41no—
466#634—41no—
467C3×#67—24no—
468C3×#67—24no—
469C3×#67—42no—
470C3×#67—42no—
471C3×#67—42no—
472C3×#67—42no—
473C2×C3×Dic3—22no—
474C2×C3×Dic3—41no—
475C2×C3×Dic3—42no—
476C2×C3×Dic3—41no—
477C2×C3×Dic3C2412yes—
478C2×C3×Dic3C2412yes—
479C2×C3×Dic3C2412yes—
480C2×C3×Dic3C2412yes—
481C2×C3×Dic3C2412yes—
482C3×D12—41no—
483C3×D12—41no—
484C3×D12—42no—
485C3×C4×D3—42no—
486C3×C4×D3—42no—
487C3×Dic6—42no—
488#626—24no—
489#626—42no—
490#626—42no—
491#626—42no—
492#625—42no—
493#625—42no—
494#625—42no—
495#624—42no—
496D3×Dic3—42no—
497D3×Dic3—42no—
498#562—92no—
499#560—92no—
500#553—92no—
501#551—92no—
502#546—92no—
503#546—92no—
504#546—92no—
505D42—92no—
506#540—92no—
507#539—91no—
508#539—92no—
509#538—91no—
510#538—92no—
511#537—31no—
512#534—31no—
513#534—92no—
514#525—91no—
515C2×#123—91no—
516C2×#121—91no—
517C24×C3—31no—
518C24×C3—32no—
519C23×D3—31no—
520C23×D3—31no—
521C23×D3—32no—
522C23×D3—32no—
523C23×D3—61no—
524C23×D3C22×D311yescharacteristic
525C23×D3C22×D312yes—
526C3×#41—124no—
527C2×C3×Q8—32no—
528C2×C3×D4—22no—
529C2×C3×D4—21no—
530C2×C3×D4—32no—
531C2×C3×D4—32no—
532C2×C3×D4—32no—
533C2×C3×D4—32no—
534C2×C3×D4—32no—
535C2×C3×D4—32no—
536C2×C3×D4—31no—
537C2×C3×D4—32no—
538C2×C3×D4—31no—
539C2×C3×D4—124no—
540C2×C3×D4C22×D312yes—
541C2×C3×D4C22×D312yes—
542C2×C3×D4C22×D311yescharacteristic
543C2×C3×D4C22×D311yescharacteristic
544C22×C3×C4—21no—
545C22×C3×C4—31no—
546C22×C3×C4—31no—
547C22×C3×C4—31no—
548C22×C3×C4—32no—
549C22×C3×C4—32no—
550C22×C3×C4—32no—
551C22×C3×C4C22×D311yescharacteristic
552C22×C3×C4C22×D311yescharacteristic
553C2×#67—32no—
554C2×#67—32no—
555C2×#67—32no—
556C2×#67—32no—
557C2×#67—32no—
558C2×#67—32no—
559C2×#67—32no—
560C2×#67—32no—
561C2×#67—32no—
562C2×#67—32no—
563C2×#67—32no—
564C2×#67—32no—
565C2×#67—32no—
566C2×#67—32no—
567C2×#67—62no—
568C2×#67—62no—
569C2×#67—122no—
570C2×#67—124no—
571C2×#67C22×D312yes—
572C2×#67C22×D312yes—
573C2×#67C22×D312yes—
574C2×#67C22×D312yes—
575C2×#67C22×D312yes—
576C2×#67C22×D312yes—
577C22×Dic3—32no—
578C22×Dic3—32no—
579C22×Dic3—31no—
580C22×Dic3—31no—
581C22×Dic3—32no—
582C22×Dic3—32no—
583C22×Dic3—62no—
584C22×Dic3—61no—
585C22×Dic3C22×D311yescharacteristic
586C22×Dic3C22×D312yes—
587C22×Dic3C22×D311yescharacteristic
588C22×Dic3C22×D311yescharacteristic
589#237—44no—
590#237—122no—
591#237—122no—
592#237—124no—
593D3×D4—44no—
594D3×D4—122no—
595D3×D4—122no—
596D3×D4—124no—
597D3×D4—124no—
598D3×D4—124no—
599C2×D12—32no—
600C2×D12—32no—
601C2×D12—32no—
602C2×D12—32no—
603C2×D12—122no—
604C2×D12C22×D312yes—
605C2×D12C22×D311yescharacteristic
606C2×D12C22×D311yescharacteristic
607C2×C4×D3—31no—
608C2×C4×D3—31no—
609C2×C4×D3—31no—
610C2×C4×D3—31no—
611C2×C4×D3—32no—
612C2×C4×D3—32no—
613C2×C4×D3—31no—
614C2×C4×D3—31no—
615C2×C4×D3—31no—
616C2×C4×D3—31no—
617C2×C4×D3—32no—
618C2×C4×D3—32no—
619C2×C4×D3—61no—
620C2×C4×D3—61no—
621C2×C4×D3—61no—
622C2×C4×D3—61no—
623C2×C4×D3—122no—
624C2×C4×D3—122no—
625C2×C4×D3—124no—
626C2×C4×D3C22×D312yes—
627C2×C4×D3C22×D312yes—
628C2×Dic6—31no—
629C2×Dic6—31no—
630C2×Dic6—61no—
631C2×Dic6C22×D312yes—
632C3×C4⋊C4—21no—
633C3×C4⋊C4—31no—
634C3×C4⋊C4—32no—
635C3×C4⋊C4—32no—
636C3×C4⋊C4—32no—
637C3×C4⋊C4—31no—
638C3×C4⋊C4—32no—
639C3×C4⋊C4C22×D311yescharacteristic
640C3×C4⋊C4C22×D311yescharacteristic
641C3×C22⋊C4—22no—
642C3×C22⋊C4—32no—
643C3×C22⋊C4—32no—
644C3×C22⋊C4—32no—
645C3×C22⋊C4—32no—
646C3×C22⋊C4—32no—
647C3×C22⋊C4—32no—
648C3×C22⋊C4—32no—
649C3×C22⋊C4—32no—
650C3×C22⋊C4C22×D312yes—
651C3×C22⋊C4C22×D312yes—
652#217—32no—
653#217—32no—
654#217—32no—
655#217—32no—
656#217—32no—
657#217—32no—
658#217—32no—
659#217—32no—
660#217—32no—
661#217—32no—
662#217—32no—
663#217—32no—
664#217—32no—
665#217—32no—
666#217—62no—
667#217—62no—
668#217C22×D312yes—
669#217C22×D312yes—
670(C2×D3)⋊C4—32no—
671(C2×D3)⋊C4—32no—
672(C2×D3)⋊C4—32no—
673(C2×D3)⋊C4—32no—
674(C2×D3)⋊C4—32no—
675(C2×D3)⋊C4—32no—
676(C2×D3)⋊C4—32no—
677(C2×D3)⋊C4—32no—
678(C2×D3)⋊C4—32no—
679(C2×D3)⋊C4—32no—
680(C2×D3)⋊C4—32no—
681(C2×D3)⋊C4—32no—
682(C2×D3)⋊C4—32no—
683(C2×D3)⋊C4—32no—
684(C2×D3)⋊C4—32no—
685(C2×D3)⋊C4—32no—
686(C2×D3)⋊C4—32no—
687(C2×D3)⋊C4—32no—
688(C2×D3)⋊C4—62no—
689(C2×D3)⋊C4—62no—
690(C2×D3)⋊C4C22×D312yes—
691(C2×D3)⋊C4C22×D312yes—
692(C2×D3)⋊C4C22×D312yes—
693(C2×D3)⋊C4C22×D312yes—
694(C2×D3)⋊C4C22×D312yes—
695(C2×D3)⋊C4C22×D312yes—
696C4⋊Dic3—31no—
697C4⋊Dic3—32no—
698C4⋊Dic3—32no—
699C4⋊Dic3—31no—
700C4⋊Dic3—32no—
701C4⋊Dic3—32no—
702C4⋊Dic3—32no—
703C4⋊Dic3—32no—
704C4⋊Dic3—62no—
705C4⋊Dic3—61no—
706C4⋊Dic3C22×D311yescharacteristic
707C4⋊Dic3C22×D311yescharacteristic
708Dic3⋊C4—32no—
709Dic3⋊C4—32no—
710Dic3⋊C4—32no—
711Dic3⋊C4—32no—
712Dic3⋊C4—32no—
713Dic3⋊C4—32no—
714Dic3⋊C4—32no—
715Dic3⋊C4—32no—
716Dic3⋊C4—32no—
717Dic3⋊C4—32no—
718Dic3⋊C4—32no—
719Dic3⋊C4—32no—
720Dic3⋊C4—62no—
721Dic3⋊C4C22×D312yes—
722Dic3⋊C4C22×D312yes—
723Dic3⋊C4C22×D312yes—
724Dic3⋊C4C22×D312yes—
725C4×Dic3—32no—
726C4×Dic3—32no—
727C4×Dic3—32no—
728C4×Dic3—32no—
729C4×Dic3—32no—
730C4×Dic3—32no—
731C4×Dic3—62no—
732C22×C32—21no—
733C22×C32—21no—
734C22×C32—22no—
735C22×C32—22no—
736C22×C32—22no—
737C22×C32H(5,𝔽2)12yes—
738C22×C32C2511yescharacteristic
739C2×C3⋊D3—21no—
740C2×C3⋊D3—21no—
741C2×C3⋊D3—21no—
742C2×C3⋊D3—21no—
743C2×C3⋊D3—21no—
744C2×C3⋊D3—44no—
745C2×C3⋊D3H(5,𝔽2)12yes—
746C2×C3×D3—22no—
747C2×C3×D3—22no—
748C2×C3×D3—22no—
749C2×C3×D3—22no—
750C2×C3×D3—22no—
751C2×C3×D3—22no—
752C2×C3×D3—22no—
753C2×C3×D3—22no—
754C2×C3×D3—22no—
755C2×C3×D3—82no—
756C2×C3×D3—84no—
757D32—84no—
758C32×C4—21no—
759C32×C4—22no—
760C32×C4—21no—
761C3⋊Dic3—21no—
762C3⋊Dic3—22no—
763C3⋊Dic3—21no—
764C3⋊Dic3—22no—
765C3×Dic3—22no—
766C3×Dic3—22no—
767C3×Dic3—22no—
768C3×Dic3—22no—
769C3×Dic3—22no—
770C2×#41—32no—
771C2×#41—91no—
772C22×D4—32no—
773C22×D4—91no—
774C22×D4—91no—
775C22×D4—92no—
776C22×D4—92no—
777C23×C4—91no—
778#127—92no—
779#126—92no—
780#126—92no—
781#126—92no—
782#126—92no—
783#125—92no—
784#125—92no—
785#124—92no—
786#124—92no—
787#124—92no—
788#123—32no—
789#123—32no—
790#123—92no—
791#123—92no—
792#123—92no—
793#123—92no—
794#123—92no—
795#123—92no—
796#123—92no—
797#123—92no—
798#123—92no—
799#123—92no—
800#123—92no—
801#123—92no—
802C22⋊Q8—32no—
803C22⋊Q8—32no—
804C22⋊Q8—92no—
805C22⋊Q8—92no—
806C22⋊Q8—92no—
807C22⋊Q8—91no—
808C22⋊Q8—91no—
809#121—32no—
810#121—32no—
811#121—32no—
812#121—31no—
813#121—31no—
814#121—32no—
815#121—92no—
816#121—92no—
817#121—92no—
818#121—92no—
819#121—92no—
820#121—91no—
821#121—91no—
822#121—92no—
823#121—92no—
824#121—92no—
825#121—92no—
826#121—92no—
827#121—92no—
828#121—91no—
829#121D3211yescharacteristic, complemented
830#120—32no—
831#120—32no—
832#120—92no—
833#120—92no—
834#120—92no—
835#120—92no—
836#120—92no—
837#120—92no—
838C4×D4—92no—
839C4×D4—92no—
840C4×D4—92no—
841C4×D4—92no—
842C4×D4—92no—
843C4×D4—92no—
844C4×D4—92no—
845C4×D4—92no—
846#117—92no—
847#117—91no—
848C2×C4⋊C4—31no—
849C2×C4⋊C4—91no—
850C2×C4⋊C4—91no—
851C2×C22⋊C4—31no—
852C2×C22⋊C4—92no—
853C2×C22⋊C4—92no—
854C2×C22⋊C4—91no—
855C2×C22⋊C4—91no—
856C2×C22⋊C4—92no—
857C23×C3—21no—
858C23×C3—22no—
859C23×C3—32no—
860C23×C3—32no—
861C23×C3—32no—
862C23×C3—62no—
863C23×C3—121no—
864C23×C3—122no—
865C23×C3—122no—
866C23×C3—121no—
867C23×C3—122no—
868C23×C3C23×D312yes—
869C23×C3C23×D312yes—
870C23×C3C23×D311yescharacteristic
871C23×C3C23×D311yescharacteristic
872C22×D3—22no—
873C22×D3—31no—
874C22×D3—31no—
875C22×D3—31no—
876C22×D3—31no—
877C22×D3—41no—
878C22×D3—42no—
879C22×D3—42no—
880C22×D3—42no—
881C22×D3—41no—
882C22×D3—61no—
883C22×D3—61no—
884C22×D3—64no—
885C22×D3—64no—
886C22×D3—62no—
887C22×D3—62no—
888C22×D3—62no—
889C22×D3—62no—
890C22×D3—122no—
891C22×D3—122no—
892C22×D3—122no—
893C22×D3—122no—
894C22×D3—122no—
895C22×D3—122no—
896C22×D3—121no—
897C22×D3—121no—
898C22×D3—122no—
899C22×D3C23×D312yes—
900C22×D3C23×D312yes—
901C22×D3C23×D312yes—
902C3×Q8—122no—
903C3×D4—24no—
904C3×D4—24no—
905C3×D4—44no—
906C3×D4—41no—
907C3×D4—41no—
908C3×D4—42no—
909C3×D4—64no—
910C3×D4—64no—
911C3×D4—121no—
912C3×D4—121no—
913C3×D4—122no—
914C3×D4—122no—
915C3×D4—122no—
916C3×D4—122no—
917C3×D4—122no—
918C2×C3×C4—21no—
919C2×C3×C4—22no—
920C2×C3×C4—21no—
921C2×C3×C4—32no—
922C2×C3×C4—32no—
923C2×C3×C4—32no—
924C2×C3×C4—32no—
925C2×C3×C4—32no—
926C2×C3×C4—41no—
927C2×C3×C4—41no—
928C2×C3×C4—42no—
929C2×C3×C4—62no—
930C2×C3×C4—122no—
931C2×C3×C4—122no—
932C2×C3×C4—121no—
933C2×C3×C4—121no—
934C2×C3×C4—122no—
935C2×C3×C4C23×D312yes—
936C2×C3×C4C23×D312yes—
937C2×C3×C4C23×D311yescharacteristic
938C2×C3×C4C23×D311yescharacteristic
939C2×C3×C4C23×D311yescharacteristic
940C2×C3×C4C23×D311yescharacteristic
941#67—24no—
942#67—24no—
943#67—42no—
944#67—42no—
945#67—42no—
946#67—42no—
947#67—64no—
948#67—64no—
949#67—64no—
950#67—124no—
951#67—122no—
952#67—122no—
953#67—122no—
954#67—122no—
955#67—122no—
956#67—122no—
957#67—122no—
958#67—122no—
959#67—122no—
960#67—122no—
961#67—122no—
962#67—124no—
963C2×Dic3—22no—
964C2×Dic3—32no—
965C2×Dic3—32no—
966C2×Dic3—31no—
967C2×Dic3—31no—
968C2×Dic3—32no—
969C2×Dic3—32no—
970C2×Dic3—31no—
971C2×Dic3—31no—
972C2×Dic3—42no—
973C2×Dic3—41no—
974C2×Dic3—41no—
975C2×Dic3—61no—
976C2×Dic3—62no—
977C2×Dic3—62no—
978C2×Dic3—61no—
979C2×Dic3—122no—
980C2×Dic3—122no—
981C2×Dic3—121no—
982C2×Dic3—121no—
983C2×Dic3—122no—
984C2×Dic3—122no—
985C2×Dic3—122no—
986C2×Dic3—124no—
987C2×Dic3C23×D312yes—
988C2×Dic3C23×D312yes—
989C2×Dic3C23×D312yes—
990C2×Dic3C23×D312yes—
991C2×Dic3C23×D312yes—
992D12—42no—
993D12—41no—
994D12—41no—
995D12—64no—
996D12—122no—
997D12—122no—
998D12—122no—
999C4×D3—42no—
1000C4×D3—42no—
1001C4×D3—62no—
1002C4×D3—62no—
1003C4×D3—62no—
1004C4×D3—62no—
1005C4×D3—64no—
1006C4×D3—122no—
1007C4×D3—122no—
1008C4×D3—122no—
1009C4×D3—121no—
1010C4×D3—121no—
1011C4×D3—121no—
1012C4×D3—121no—
1013C4×D3—122no—
1014C4×D3—122no—
1015C4×D3—122no—
1016C4×D3—122no—
1017Dic6—42no—
1018Dic6—121no—
1019Dic6—121no—
1020Dic6—122no—
1021C2×C32—22no—
1022C2×C32—42no—
1023C2×C32C2×H(5,𝔽2)11yescharacteristic
1024C2×C32C2×H(5,𝔽2)11yescharacteristic
1025C2×C32#58511yescharacteristic
1026C3⋊D3—22no—
1027C3⋊D3—41no—
1028C3×D3—42no—
1029C3×D3—42no—
1030C3×D3—42no—
1031C24—31no—
1032C24—32no—
1033C24—92no—
1034C24—91no—
1035#41—124no—
1036#41—362no—
1037C2×Q8—32no—
1038C2×Q8—91no—
1039C2×D4—32no—
1040C2×D4—32no—
1041C2×D4—32no—
1042C2×D4—32no—
1043C2×D4—32no—
1044C2×D4—32no—
1045C2×D4—31no—
1046C2×D4—32no—
1047C2×D4—31no—
1048C2×D4—92no—
1049C2×D4—92no—
1050C2×D4—92no—
1051C2×D4—92no—
1052C2×D4—92no—
1053C2×D4—92no—
1054C2×D4—92no—
1055C2×D4—92no—
1056C2×D4—92no—
1057C2×D4—124no—
1058C2×D4—362no—
1059C2×D4—362no—
1060C2×D4—364no—
1061C2×D4—364no—
1062C2×D4C2×D3212yes—
1063C2×D4C2×D3211yescharacteristic
1064C22×C4—31no—
1065C22×C4—31no—
1066C22×C4—32no—
1067C22×C4—31no—
1068C22×C4—32no—
1069C22×C4—32no—
1070C22×C4—92no—
1071C22×C4—92no—
1072C22×C4—92no—
1073C22×C4—91no—
1074C22×C4—92no—
1075C22×C4—91no—
1076C22×C4—91no—
1077C22×C4—91no—
1078C22×C4—91no—
1079C22×C4—362no—
1080C22×C4C2×D3211yescharacteristic
1081C4⋊C4—32no—
1082C4⋊C4—32no—
1083C4⋊C4—31no—
1084C4⋊C4—31no—
1085C4⋊C4—32no—
1086C4⋊C4—32no—
1087C4⋊C4—92no—
1088C4⋊C4—92no—
1089C4⋊C4—92no—
1090C4⋊C4—92no—
1091C4⋊C4—92no—
1092C4⋊C4—92no—
1093C4⋊C4—92no—
1094C4⋊C4—91no—
1095C4⋊C4—92no—
1096C4⋊C4—92no—
1097C4⋊C4C2×D3211yescharacteristic
1098C22⋊C4—32no—
1099C22⋊C4—32no—
1100C22⋊C4—32no—
1101C22⋊C4—32no—
1102C22⋊C4—32no—
1103C22⋊C4—32no—
1104C22⋊C4—32no—
1105C22⋊C4—32no—
1106C22⋊C4—92no—
1107C22⋊C4—92no—
1108C22⋊C4—92no—
1109C22⋊C4—92no—
1110C22⋊C4—92no—
1111C22⋊C4—92no—
1112C22⋊C4—92no—
1113C22⋊C4—92no—
1114C22⋊C4—92no—
1115C22⋊C4—92no—
1116C22⋊C4—92no—
1117C22⋊C4—92no—
1118C22⋊C4—92no—
1119C22⋊C4—92no—
1120C22⋊C4—92no—
1121C22⋊C4—92no—
1122C22⋊C4C2×D3212yes—
1123C42—92no—
1124C42—92no—
1125C42—92no—
1126C22×C3—21no—
1127C22×C3—21no—
1128C22×C3—21no—
1129C22×C3—21no—
1130C22×C3—22no—
1131C22×C3—22no—
1132C22×C3—22no—
1133C22×C3—22no—
1134C22×C3—22no—
1135C22×C3—22no—
1136C22×C3—22no—
1137C22×C3—21no—
1138C22×C3—41no—
1139C22×C3—41no—
1140C22×C3—42no—
1141C22×C3—42no—
1142C22×C3—42no—
1143C22×C3—62no—
1144C22×C3—62no—
1145C22×C3—62no—
1146C22×C3—62no—
1147C22×C3—62no—
1148C22×C3—62no—
1149C22×C3—62no—
1150C22×C3—62no—
1151C22×C3—62no—
1152C22×C3—242no—
1153C22×C3—244no—
1154C22×C3#100412yes—
1155C22×C3#100412yes—
1156C22×C3C24×D311yescharacteristic
1157C22×C3C24×D311yescharacteristic
1158C2×D3—22no—
1159C2×D3—22no—
1160C2×D3—22no—
1161C2×D3—22no—
1162C2×D3—22no—
1163C2×D3—22no—
1164C2×D3—22no—
1165C2×D3—22no—
1166C2×D3—22no—
1167C2×D3—32no—
1168C2×D3—32no—
1169C2×D3—62no—
1170C2×D3—61no—
1171C2×D3—61no—
1172C2×D3—61no—
1173C2×D3—61no—
1174C2×D3—62no—
1175C2×D3—61no—
1176C2×D3—61no—
1177C2×D3—61no—
1178C2×D3—61no—
1179C2×D3—61no—
1180C2×D3—61no—
1181C2×D3—82no—
1182C2×D3—84no—
1183C2×D3—121no—
1184C2×D3—121no—
1185C2×D3—121no—
1186C2×D3—121no—
1187C2×D3—124no—
1188C2×D3—124no—
1189C2×D3—128no—
1190C2×D3—244no—
1191C2×D3—244no—
1192C3×C4—22no—
1193C3×C4—22no—
1194C3×C4—22no—
1195C3×C4—21no—
1196C3×C4—21no—
1197C3×C4—21no—
1198C3×C4—21no—
1199C3×C4—41no—
1200C3×C4—42no—
1201C3×C4—62no—
1202C3×C4—62no—
1203C3×C4—62no—
1204C3×C4—62no—
1205C3×C4—62no—
1206Dic3—22no—
1207Dic3—22no—
1208Dic3—22no—
1209Dic3—22no—
1210Dic3—22no—
1211Dic3—62no—
1212Dic3—62no—
1213Dic3—62no—
1214Dic3—61no—
1215Dic3—61no—
1216Dic3—61no—
1217Dic3—61no—
1218Dic3—62no—
1219Dic3—62no—
1220Dic3—122no—
1221Dic3—121no—
1222Dic3—122no—
1223C32#353411yescharacteristic, complemented, Sylow
1224C23—32no—
1225C23—32no—
1226C23—32no—
1227C23—62no—
1228C23—91no—
1229C23—91no—
1230C23—122no—
1231C23—121no—
1232C23—122no—
1233C23—121no—
1234C23—122no—
1235C23—182no—
1236C23—184no—
1237C23—182no—
1238C23—361no—
1239C23—362no—
1240C23—362no—
1241C23C22×D3212yes—
1242C23C22×D3211yescharacteristic
1243Q8—122no—
1244Q8—361no—
1245D4—24no—
1246D4—41no—
1247D4—64no—
1248D4—64no—
1249D4—122no—
1250D4—121no—
1251D4—121no—
1252D4—122no—
1253D4—122no—
1254D4—122no—
1255D4—122no—
1256D4—184no—
1257D4—184no—
1258D4—362no—
1259D4—362no—
1260D4—362no—
1261D4—362no—
1262D4—362no—
1263D4—362no—
1264D4—362no—
1265C2×C4—32no—
1266C2×C4—32no—
1267C2×C4—32no—
1268C2×C4—32no—
1269C2×C4—32no—
1270C2×C4—41no—
1271C2×C4—62no—
1272C2×C4—92no—
1273C2×C4—91no—
1274C2×C4—92no—
1275C2×C4—91no—
1276C2×C4—122no—
1277C2×C4—122no—
1278C2×C4—121no—
1279C2×C4—122no—
1280C2×C4—121no—
1281C2×C4—182no—
1282C2×C4—182no—
1283C2×C4—361no—
1284C2×C4—361no—
1285C2×C4—362no—
1286C2×C4—362no—
1287C2×C4—362no—
1288C2×C4—361no—
1289C2×C4—362no—
1290C2×C4C22×D3212yes—
1291C2×C4C22×D3211yescharacteristic
1292C2×C4C22×D3211yescharacteristic
1293C2×C3—22no—
1294C2×C3—22no—
1295C2×C3—21no—
1296C2×C3—21no—
1297C2×C3—21no—
1298C2×C3—42no—
1299C2×C3—42no—
1300C2×C3—42no—
1301C2×C3—82no—
1302C2×C3—122no—
1303C2×C3—122no—
1304C2×C3—122no—
1305C2×C3C2×#100411yescharacteristic
1306C2×C3C2×#100411yescharacteristic
1307C2×C3D3×H(5,𝔽2)11yescharacteristic
1308C2×C3D3×H(5,𝔽2)11yescharacteristic
1309C2×C3#596611yescharacteristic
1310C2×C3#596811yescharacteristic
1311D3—42no—
1312D3—42no—
1313D3—42no—
1314D3—62no—
1315D3—62no—
1316D3—122no—
1317D3—122no—
1318D3—121no—
1319D3—121no—
1320C22—21no—
1321C22—21no—
1322C22—22no—
1323C22—22no—
1324C22—22no—
1325C22—62no—
1326C22—62no—
1327C22—62no—
1328C22—62no—
1329C22—62no—
1330C22—62no—
1331C22—62no—
1332C22—62no—
1333C22—62no—
1334C22—92no—
1335C22—181no—
1336C22—181no—
1337C22—181no—
1338C22—181no—
1339C22—181no—
1340C22—242no—
1341C22—244no—
1342C22—364no—
1343C22—724no—
1344C22#6431312yes—
1345C22C23×D3211yescharacteristic
1346C4—21no—
1347C4—21no—
1348C4—22no—
1349C4—62no—
1350C4—62no—
1351C4—62no—
1352C4—62no—
1353C4—62no—
1354C4—181no—
1355C4—181no—
1356C4—182no—
1357C4—182no—
1358C3—21no—
1359C3#8631211yescharacteristic, complemented
1360C3#8638311yescharacteristic, complemented
1361C2—22no—
1362C2—42no—
1363C2—122no—
1364C2—122no—
1365C2—122no—
1366C2—182no—
1367C2—361no—
1368C2#1059667511yescharacteristic
1369C2C2×#6431311yescharacteristic
1370C2#1059669811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#121C22
hypercenter#121D32
hypocenterC32#3534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #10596077C2semidirect
2. C3×#5605C2semidirect
3. C3×#5597C2semidirect
4. #10595307C2semidirect
5. #10595305C2semidirect
6. #10595291C2semidirect
7. #10595258C2semidirect
8. #10595244C2semidirect
9. #10595189C2semidirect
10. #10595081C2semidirect
11. #10594977C2semidirect
12. #10594973C2semidirect
13. C2×#63853C2semidirect
14. #10594653C2semidirect
15. #10594590C2semidirect
16. #10594263C2semidirect
17. #10594173C2semidirect
18. #10594151C2semidirect
19. #10594041C2semidirect
22. C2×#3830C22semidirect
23. C22×C4×C3⋊D3C22semidirect
24. C2×C3×#237C22semidirect
25. C2×C3×D3×D4C22semidirect
26. C2×#3811C22semidirect
27. C2×D3×#67C22semidirect
29. C2×#3802C22semidirect
30. C32×#121C22semidirect
31. #64147C22semidirect
32. #64146C22semidirect
33. D4×C3⋊Dic3C22semidirect
34. #64133C22semidirect
35. #64106C22semidirect
36. #64101C22semidirect
37. #64092C22semidirect
38. #64090C22semidirect
39. C3×#939C22semidirect
40. C3×#939C22semidirect
41. C3×#939C22semidirect
42. C3×#937C22semidirect
44. C3×#930C22semidirect
45. C2×C3×(C2×D3)⋊C4C22semidirect
46. C2×C3×Dic3⋊C4C22semidirect
47. C3×#896C22semidirect
48. C3×#894C22semidirect
49. C3×#884C22semidirect
50. C3×#883C22semidirect
51. C3×#882C22semidirect
52. C3×#878C22semidirect
53. #63983C22semidirect
54. #63980C22semidirect
55. #63980C22semidirect
56. #63979C22semidirect
57. #63978C22semidirect
58. #63977C22semidirect
59. #63976C22semidirect
60. #63976C22semidirect
61. #67⋊Dic3C22semidirect
62. Dic3×#67C22semidirect
63. Dic3×#67C22semidirect
64. #63971C22semidirect
65. #63970C22semidirect
66. C2×Dic3⋊Dic3C22semidirect
67. C2×#3722C22semidirect
68. #63962C22semidirect
69. #63961C22semidirect
70. #63961C22semidirect
71. C2×(C2×D3)⋊Dic3C22semidirect
72. C2×(C2×D3)⋊Dic3C22semidirect
74. #63956C22semidirect
75. #63952C22semidirect
77. #63921C22semidirect
78. D3×(C2×D3)⋊C4C22semidirect
79. #63916C22semidirect
80. #63916C22semidirect
81. #63913C22semidirect
82. #63912C22semidirect
83. #63908C22semidirect
84. #63907C22semidirect
85. #63906C22semidirect
86. #63904C22semidirect
87. C4×#625C22semidirect
88. #63900C22semidirect
89. #63896C22semidirect
90. #63891C22semidirect
91. #63891C22semidirect
92. #63888C22semidirect
93. #63886C22semidirect
94. #63885C22semidirect
95. #63884C22semidirect
96. #63878C22semidirect
97. #63863C22semidirect
98. #63862C22semidirect
99. #63861C22semidirect
100. #63858C22semidirect
101. #63856C22semidirect
102. #63853C22semidirect
103. #63853C22semidirect
104. #63853C22semidirect
105. #63853C22semidirect
106. #63850C22semidirect
107. #63847C22semidirect
108. #63845C22semidirect
134. #5605D3semidirect
139. #5597D3semidirect
251. C2×#237C2×D3semidirect
257. C2×D3×D4C2×D3semidirect
273. C3×#121C2×D3semidirect
274. C3×#121C2×D3semidirect
299. #939C2×D3semidirect
300. #939C2×D3semidirect
301. #939C2×D3semidirect
318. #937C2×D3semidirect
334. #930C2×D3semidirect
349. C2×(C2×D3)⋊C4C2×D3semidirect
356. C2×Dic3⋊C4C2×D3semidirect
365. #896C2×D3semidirect
375. #894C2×D3semidirect
399. #884C2×D3semidirect
409. #883C2×D3semidirect
412. #882C2×D3semidirect
427. #878C2×D3semidirect
829. #121D32semidirect
1223. C32#3534semidirect
1359. C3#86312semidirect
1360. C3#86383semidirect

Maximal subgroups

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

subgroupindex
#105960772
C3×#56052
C3×#55972
#105953072
#105953052
#105952912
#105952582
#105952442
#105951892
#105950812
#105949772
#105949732
C2×#638532
#105946532
#105945902
#105942632
#105941732
#105941512
#105940412
#863833
#863123