Finite Group Databasebeta

← #11910456

Subgroups — #11910456

Order 1152.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596157C211yesmaximal, characteristic, complemented
2C3×#5699C211yesmaximal, characteristic, complemented
3C3×#5691C211yesmaximal, characteristic, complemented
4#10594586C212yesmaximal, complemented
5#10594586C212yesmaximal, complemented
6#10594507C212yesmaximal, complemented
7#10594497C212yesmaximal, complemented
8#10594495C212yesmaximal, complemented
9#10594492C212yesmaximal, complemented
10#10594445C212yesmaximal, complemented
11#10594444C212yesmaximal, complemented
12#10594405C212yesmaximal, complemented
13#10594405C212yesmaximal, complemented
14#10594404C212yesmaximal, complemented
15#10594386C212yesmaximal, complemented
16#10593985C211yesmaximal, characteristic, complemented
17#10593952C211yesmaximal, characteristic, complemented
18#10593921C211yesmaximal, characteristic, complemented
19#10593874C211yesmaximal, characteristic, complemented
20#87116—31nomaximal
21#86132—31nomaximal
22C32×#125C2211yescharacteristic
23#64099C2212yes—
24#64099C2212yes—
25#64098C2212yes—
26#64098C2212yes—
27#64098C2212yes—
28#64098C2212yes—
29#64079C2211yescharacteristic
30#64079C2211yescharacteristic
31C3×#898C2212yes—
32C3×#898C2212yes—
33C3×#898C2212yes—
34C3×#897C2211yescharacteristic
35C3×#897C2212yes—
36C3×#896C2212yes—
37C3×#895C2211yescharacteristic
38C3×#894C2212yes—
39C3×#894C2212yes—
40C3×#893C2211yescharacteristic
41C3×#893C2212yes—
42C3×#892C2212yes—
43C3×#888C2212yes—
44C3×#887C2211yescharacteristic
45C3×#875C2211yescharacteristic
46C3×#875C2211yescharacteristic
47C3×C42×D3C2211yescharacteristic
48C3×#870C2211yescharacteristic
49#63918C2211yescharacteristic
50#63918C2212yes—
51#63918C2211yescharacteristic
52#63915C2212yes—
53#63915C2212yes—
54#63915C2212yes—
55#63908C2211yescharacteristic
56#63908C2212yes—
57#63905C2212yes—
58#63905C2212yes—
59#63899C2212yes—
60#63899C2212yes—
61#63899C2212yes—
62#63893C2212yes—
63#63893C2212yes—
64#63893C2212yes—
65Dic3×D12C2211yescharacteristic
66#63891C2212yes—
67#63891C2212yes—
68#63891C2212yes—
69#63891C2212yes—
70#63887C2212yes—
71#63887C2212yes—
72#63887C2212yes—
73#63885C2212yes—
74#63885C2212yes—
75#63885C2212yes—
76#63884C2212yes—
77#63884C2212yes—
78#63879C2212yes—
79#63879C2212yes—
80#63879C2212yes—
81#63877C2212yes—
82#63877C2212yes—
83C4×D3×Dic3C2212yes—
84C4×D3×Dic3C2212yes—
85#63872C2212yes—
86#63870C2212yes—
87#63863C2212yes—
88#63861C2212yes—
89#63859C2212yes—
90#63859C2212yes—
91#63859C2212yes—
92#63858C2212yes—
93#63858C2212yes—
94#63858C2212yes—
95#63856C2211yescharacteristic
96#63851C2212yes—
97#63851C2212yes—
98#63851C2212yes—
99Dic3×Dic6C2212yes—
100Dic3×Dic6C2211yescharacteristic
101#63841C2211yescharacteristic
102#63841C2211yescharacteristic
103#63841C2212yes—
104#63839C2212yes—
105#63839C2212yes—
106#63837C2212yes—
107#63837C2212yes—
108#63837C2212yes—
109C3×#563—31no—
110C3×#529—31no—
111#5735—32no—
112#5728—32no—
113#5712—32no—
114#5712—32no—
115#5712—32no—
116#5712—32no—
117#5706—32no—
118#5706—32no—
119#5699—31no—
120#5699D311yescharacteristic, complemented
121#5691D311yescharacteristic, complemented
122#5688—31no—
123C3⋊#564—31no—
124C3⋊#564—31no—
125C3⋊#564—61no—
126#5684—31no—
127#5684—31no—
128#5680—31no—
129#5672—31no—
130#5667—32no—
131#5667—32no—
132#5651—32no—
133#5649—32no—
134#5647—32no—
135#5646—32no—
136#5646—32no—
137#5624—32no—
138#5622—32no—
139#5621—32no—
140#5578—32no—
141#5557—32no—
142#5538—32no—
143#5538—32no—
144#5528—32no—
145#5517—32no—
146#5479—31no—
147#5470—31no—
148C2×C3×D12C2312yes—
149C2×C3×D12C2311yescharacteristic
150C2×C3×D12C2311yescharacteristic
151C2×C3×C4×D3C2312yes—
152C2×C3×C4×D3C2311yescharacteristic
153C2×C3×C4×D3C2311yescharacteristic
154C2×C3×C4×D3C2312yes—
155C2×C3×C4×D3C2311yescharacteristic
156C2×C3×Dic6C2311yescharacteristic
157C2×C3×Dic6C2311yescharacteristic
158C2×C3×Dic6C2312yes—
159C2×#627C2312yes—
160C2×#627C2312yes—
161C2×#627C2312yes—
162C2×#625C2312yes—
163C2×#625C2312yes—
164C2×#625C2312yes—
165C2×D3×Dic3C2312yes—
166C2×D3×Dic3C2312yes—
167C2×D3×Dic3C2312yes—
168C2×D3×Dic3C2312yes—
169C32×C4⋊C4C2311yescharacteristic
170C32×C4⋊C4C2312yes—
171C32×C4⋊C4C2311yescharacteristic
172C32×C4⋊C4C2312yes—
173C32×C42C2311yescharacteristic
174C4⋊(C3⋊Dic3)C2311yescharacteristic
175C4⋊(C3⋊Dic3)C2311yescharacteristic
176C4⋊(C3⋊Dic3)C2311yescharacteristic
177C4⋊(C3⋊Dic3)C2311yescharacteristic
178C4⋊(C3⋊Dic3)C2312yes—
179C4⋊(C3⋊Dic3)C2312yes—
180#3750C2312yes—
181#3750C2312yes—
182#3750C2312yes—
183#3750C2312yes—
184#3750C2312yes—
185#3750C2312yes—
186#3750C2312yes—
187#3750C2312yes—
188C4×C3⋊Dic3C2312yes—
189C4×C3⋊Dic3C2312yes—
190C3×(C2×D3)⋊C4C2312yes—
191C3×(C2×D3)⋊C4C2312yes—
192C3×(C2×D3)⋊C4C2312yes—
193C3×(C2×D3)⋊C4C2312yes—
194C3×(C2×D3)⋊C4C2312yes—
195C3×(C2×D3)⋊C4C2312yes—
196C3×(C2×D3)⋊C4C2312yes—
197C3×(C2×D3)⋊C4C2312yes—
198C3×(C2×D3)⋊C4C2312yes—
199C3×(C2×D3)⋊C4C2312yes—
200C3×C4⋊Dic3C2312yes—
201C3×C4⋊Dic3C2312yes—
202C3×C4⋊Dic3C2311yescharacteristic
203C3×C4⋊Dic3C2311yescharacteristic
204C3×Dic3⋊C4C2312yes—
205C3×Dic3⋊C4C2312yes—
206C3×Dic3⋊C4C2312yes—
207C3×Dic3⋊C4C2312yes—
208C3×C4×Dic3C2312yes—
209C3×C4×Dic3C2311yescharacteristic
210C3×C4×Dic3C2312yes—
211C3×C4×Dic3C2311yescharacteristic
212C3×C4×Dic3C2311yescharacteristic
213#3724C2312yes—
214#3724C2312yes—
215Dic3⋊Dic3C2312yes—
216Dic3⋊Dic3C2312yes—
217Dic3⋊Dic3C2312yes—
218Dic3⋊Dic3C2312yes—
219Dic3⋊Dic3C2312yes—
220Dic3⋊Dic3C2312yes—
221(C2×D3)⋊Dic3C2312yes—
222(C2×D3)⋊Dic3C2312yes—
223(C2×D3)⋊Dic3C2312yes—
224(C2×D3)⋊Dic3C2312yes—
225(C2×D3)⋊Dic3C2312yes—
226(C2×D3)⋊Dic3C2312yes—
227(C2×D3)⋊Dic3C2312yes—
228(C2×D3)⋊Dic3C2312yes—
229(C2×D3)⋊Dic3C2312yes—
230(C2×D3)⋊Dic3C2312yes—
231Dic32C2312yes—
232Dic32C2312yes—
233Dic32C2312yes—
234Dic32C2312yes—
235#3531—91noSylow
236C3×C4⋊Q8—32no—
237C3×#126—32no—
238C3×#126—32no—
239C3×#126—32no—
240C3×#125—21no—
241C3×#125—31no—
242C3×#125C2×D311yescharacteristic
243C3×#125C2×D311yescharacteristic
244C3×#124—31no—
245C3×#124—31no—
246C3×#123—32no—
247C3×#123—32no—
248C3×C22⋊Q8—32no—
249C3×C22⋊Q8—32no—
250C3×C22⋊Q8—31no—
251C3×#121—31no—
252C3×C4×Q8—31no—
253C3×C4×D4—31no—
254C3×C4×D4—32no—
255C3×#117—32no—
256C2×C3×C42—31no—
257#947—32no—
258#946—31no—
259#946—32no—
260#946—32no—
261#946—32no—
262Q8×Dic3—31no—
263Q8×Dic3—32no—
264#944—32no—
265#944—32no—
266#939—32no—
267#939—32no—
268#939—32no—
269#938—31no—
270#938—32no—
271#936—32no—
272#935—32no—
273#935—32no—
274D4×Dic3—31no—
275#930—32no—
276#930—31no—
277#929—32no—
278#929—32no—
279C4×#67—32no—
280C4×#67—32no—
281C4×#67—32no—
282#926—31no—
283#926—31no—
284#926—32no—
285#924—31no—
286#924—32no—
287#924—32no—
288#924—32no—
289C2×C4×Dic3—32no—
290C2×C4×Dic3—32no—
291#898—32no—
292#898—32no—
293#898—32no—
294#898—32no—
295#898C2×D312yes—
296#898C2×D312yes—
297#898C2×D312yes—
298#897—32no—
299#897—32no—
300#897—32no—
301#897C2×D311yescharacteristic
302#897C2×D312yes—
303#896—32no—
304#896—32no—
305#896—32no—
306#896—32no—
307#896—32no—
308#896—32no—
309#896C2×D312yes—
310#895C2×D311yescharacteristic
311#894—32no—
312#894—32no—
313#894C2×D312yes—
314#894C2×D312yes—
315#893C2×D311yescharacteristic
316#893C2×D312yes—
317#892—31no—
318#892—31no—
319#892—32no—
320#892C2×D312yes—
321#890—32no—
322#890—32no—
323#890—32no—
324#890—32no—
325#890—32no—
326#890—32no—
327#890—62no—
328#890—62no—
329#889—32no—
330#889—32no—
331#889—32no—
332#889—32no—
333#889—32no—
334#889—32no—
335#889—32no—
336#889—32no—
337#889—32no—
338#889—32no—
339#889—62no—
340#889—62no—
341#889—62no—
342#889—62no—
343#888—32no—
344#888—32no—
345#888—31no—
346#888—32no—
347#888—31no—
348#888C2×D312yes—
349#887—32no—
350#887—32no—
351#887—32no—
352#887C2×D311yescharacteristic
353#886—32no—
354#886—32no—
355#886—32no—
356#886—32no—
357#885—32no—
358#885—32no—
359#885—32no—
360#885—32no—
361#885—32no—
362#885—32no—
363#884—32no—
364#884—32no—
365#884—32no—
366#883—32no—
367#883—32no—
368#883—32no—
369#883—32no—
370#883—32no—
371#883—32no—
372#67⋊C4—32no—
373#67⋊C4—32no—
374#67⋊C4—32no—
375#879—32no—
376#879—32no—
377#879—32no—
378#879—32no—
379#879—32no—
380#879—32no—
381#879—32no—
382#878—32no—
383#878—32no—
384#878—32no—
385#878—32no—
386#878—32no—
387#878—32no—
388#878—32no—
389#878—32no—
390#878—32no—
391#877—32no—
392#877—32no—
393#876—32no—
394#876—32no—
395#876—32no—
396#875C2×D311yescharacteristic
397#875C2×D311yescharacteristic
398C4×D12—31no—
399#872—32no—
400#872—32no—
401C42×D3—32no—
402C42×D3—32no—
403C42×D3C2×D311yescharacteristic
404#870—31no—
405#870—31no—
406#870—31no—
407#870—31no—
408#870—61no—
409#870—61no—
410#870C2×D311yescharacteristic
411#869—31no—
412#869—31no—
413#869—32no—
414C4×Dic6—31no—
415C4×Dic6—32no—
416C4×Dic6—32no—
417C4×Dic6—32no—
418C4×Dic6—32no—
419C22×C3×D3C2411yescharacteristic
420C22×C3×D3C2412yes—
421C22×C3×D3C2412yes—
422C2×C32×C4C2412yes—
423C2×C32×C4C2411yescharacteristic
424C2×C32×C4C2411yescharacteristic
425C2×C32×C4C2412yes—
426C2×C32×C4C2411yescharacteristic
427C2×C3⋊Dic3C2412yes—
428C2×C3⋊Dic3C2412yes—
429C2×C3⋊Dic3C2412yes—
430C2×C3⋊Dic3C2412yes—
431C2×C3×Dic3C2412yes—
432C2×C3×Dic3C2412yes—
433C2×C3×Dic3C2412yes—
434C2×C3×Dic3C2412yes—
435C2×C3×Dic3C2411yescharacteristic
436C2×C3×Dic3C2411yescharacteristic
437C2×C3×Dic3C2411yescharacteristic
438C3×D12—41no—
439C3×D12—42no—
440C3×D12—41no—
441C3×C4×D3—24no—
442C3×C4×D3—22no—
443C3×C4×D3—41no—
444C3×C4×D3—41no—
445C3×C4×D3—42no—
446C3×Dic6—41no—
447C3×Dic6—41no—
448C3×Dic6—42no—
449#627—42no—
450#627—42no—
451#627—42no—
452#625—42no—
453#625—42no—
454#625—42no—
455D3×Dic3—24no—
456D3×Dic3—42no—
457D3×Dic3—42no—
458D3×Dic3—42no—
459#564—91no—
460#563—31no—
461#563—92no—
462#563—92no—
463#563—92no—
464#563—91no—
465#563—92no—
466#562—92no—
467#562—92no—
468#562—91no—
469#533—91no—
470#533—92no—
471#533—92no—
472#529—31no—
473#529—91no—
474#529—92no—
475#529—92no—
476#529—92no—
477#529—92no—
478C2×C3×Q8—31no—
479C2×C3×Q8—32no—
480C2×C3×Q8—31no—
481C2×C3×D4—31no—
482C2×C3×D4—31no—
483C2×C3×D4—32no—
484C22×C3×C4—32no—
485C22×C3×C4—31no—
486C22×C3×C4—32no—
487C22×C3×C4—31no—
488C22×C3×C4—31no—
489C2×#67—32no—
490C2×#67—32no—
491C2×#67—32no—
492C2×#67—32no—
493C2×#67—32no—
494C2×#67—32no—
495C22×Dic3—32no—
496C22×Dic3—32no—
497C22×Dic3—32no—
498C22×Dic3—32no—
499C2×D12C22×D311yescharacteristic
500C2×D12C22×D311yescharacteristic
501C2×D12C22×D312yes—
502C2×C4×D3—32no—
503C2×C4×D3—32no—
504C2×C4×D3—32no—
505C2×C4×D3—32no—
506C2×C4×D3C22×D312yes—
507C2×C4×D3C22×D311yescharacteristic
508C2×C4×D3C22×D312yes—
509C2×C4×D3C22×D311yescharacteristic
510C2×C4×D3C22×D311yescharacteristic
511C2×Dic6—32no—
512C2×Dic6—32no—
513C2×Dic6—32no—
514C2×Dic6—32no—
515C2×Dic6—32no—
516C2×Dic6—32no—
517C2×Dic6C22×D311yescharacteristic
518C2×Dic6C22×D312yes—
519C2×Dic6C22×D311yescharacteristic
520C3×C4⋊C4—21no—
521C3×C4⋊C4—21no—
522C3×C4⋊C4—22no—
523C3×C4⋊C4—22no—
524C3×C4⋊C4—32no—
525C3×C4⋊C4—32no—
526C3×C4⋊C4—32no—
527C3×C4⋊C4—32no—
528C3×C4⋊C4—32no—
529C3×C4⋊C4—31no—
530C3×C4⋊C4—31no—
531C3×C4⋊C4—32no—
532C3×C4⋊C4C22×D311yescharacteristic
533C3×C4⋊C4C22×D312yes—
534C3×C4⋊C4C22×D311yescharacteristic
535C3×C4⋊C4C22×D311yescharacteristic
536C3×C4⋊C4C22×D311yescharacteristic
537C3×C4⋊C4C22×D312yes—
538C3×C4⋊C4C22×D312yes—
539C3×C4⋊C4C22×D312yes—
540C3×C22⋊C4—32no—
541C3×C22⋊C4—32no—
542C3×C22⋊C4—32no—
543C3×C22⋊C4—32no—
544C3×C22⋊C4—32no—
545C3×C22⋊C4—32no—
546C3×C22⋊C4—32no—
547C3×C22⋊C4—32no—
548C3×C22⋊C4—32no—
549C3×C22⋊C4—32no—
550C3×C42—21no—
551C3×C42—31no—
552C3×C42—32no—
553C3×C42—31no—
554C3×C42—31no—
555C3×C42—32no—
556C3×C42C22×D311yescharacteristic
557C3×C42C22×D311yescharacteristic
558#217—32no—
559#217—32no—
560#217—32no—
561#217—32no—
562#217—32no—
563#217—32no—
564#217—32no—
565#217—32no—
566#217—32no—
567#217—32no—
568(C2×D3)⋊C4—32no—
569(C2×D3)⋊C4—32no—
570(C2×D3)⋊C4—32no—
571(C2×D3)⋊C4—32no—
572(C2×D3)⋊C4—32no—
573(C2×D3)⋊C4—32no—
574(C2×D3)⋊C4—32no—
575(C2×D3)⋊C4—32no—
576(C2×D3)⋊C4—32no—
577(C2×D3)⋊C4—32no—
578(C2×D3)⋊C4C22×D312yes—
579(C2×D3)⋊C4C22×D312yes—
580(C2×D3)⋊C4C22×D312yes—
581(C2×D3)⋊C4C22×D312yes—
582(C2×D3)⋊C4C22×D312yes—
583(C2×D3)⋊C4C22×D312yes—
584(C2×D3)⋊C4C22×D312yes—
585(C2×D3)⋊C4C22×D312yes—
586(C2×D3)⋊C4C22×D312yes—
587(C2×D3)⋊C4C22×D312yes—
588C4⋊Dic3—31no—
589C4⋊Dic3—32no—
590C4⋊Dic3—31no—
591C4⋊Dic3—31no—
592C4⋊Dic3—32no—
593C4⋊Dic3—31no—
594C4⋊Dic3—31no—
595C4⋊Dic3—31no—
596C4⋊Dic3—31no—
597C4⋊Dic3—31no—
598C4⋊Dic3—32no—
599C4⋊Dic3—32no—
600C4⋊Dic3—32no—
601C4⋊Dic3—32no—
602C4⋊Dic3—32no—
603C4⋊Dic3—32no—
604C4⋊Dic3—32no—
605C4⋊Dic3—32no—
606C4⋊Dic3—61no—
607C4⋊Dic3—61no—
608C4⋊Dic3—61no—
609C4⋊Dic3—61no—
610C4⋊Dic3—62no—
611C4⋊Dic3—62no—
612C4⋊Dic3C22×D311yescharacteristic
613C4⋊Dic3C22×D311yescharacteristic
614C4⋊Dic3C22×D312yes—
615C4⋊Dic3C22×D312yes—
616Dic3⋊C4—32no—
617Dic3⋊C4—32no—
618Dic3⋊C4—32no—
619Dic3⋊C4—32no—
620Dic3⋊C4—32no—
621Dic3⋊C4—32no—
622Dic3⋊C4—32no—
623Dic3⋊C4—32no—
624Dic3⋊C4—32no—
625Dic3⋊C4—32no—
626Dic3⋊C4—32no—
627Dic3⋊C4—32no—
628Dic3⋊C4—32no—
629Dic3⋊C4—32no—
630Dic3⋊C4—32no—
631Dic3⋊C4—32no—
632Dic3⋊C4—32no—
633Dic3⋊C4—32no—
634Dic3⋊C4—32no—
635Dic3⋊C4—32no—
636Dic3⋊C4—32no—
637Dic3⋊C4—32no—
638Dic3⋊C4—32no—
639Dic3⋊C4—32no—
640Dic3⋊C4—32no—
641Dic3⋊C4—32no—
642Dic3⋊C4—62no—
643Dic3⋊C4—62no—
644Dic3⋊C4—62no—
645Dic3⋊C4—62no—
646Dic3⋊C4—62no—
647Dic3⋊C4—62no—
648Dic3⋊C4—62no—
649Dic3⋊C4—62no—
650Dic3⋊C4C22×D312yes—
651Dic3⋊C4C22×D312yes—
652Dic3⋊C4C22×D312yes—
653Dic3⋊C4C22×D312yes—
654C4×Dic3—32no—
655C4×Dic3—32no—
656C4×Dic3—32no—
657C4×Dic3—32no—
658C4×Dic3—32no—
659C4×Dic3—32no—
660C4×Dic3—32no—
661C4×Dic3—32no—
662C4×Dic3—32no—
663C4×Dic3—32no—
664C4×Dic3—32no—
665C4×Dic3—32no—
666C4×Dic3—62no—
667C4×Dic3—62no—
668C4×Dic3C22×D311yescharacteristic
669C4×Dic3C22×D311yescharacteristic
670C4×Dic3C22×D311yescharacteristic
671C4×Dic3C22×D312yes—
672C4×Dic3C22×D312yes—
673C22×C32C2511yescharacteristic
674C2×C3×D3—22no—
675C2×C3×D3—21no—
676C2×C3×D3—22no—
677C2×C3×D3—22no—
678C2×C3×D3—22no—
679C2×C3×D3—22no—
680C2×C3×D3—21no—
681C2×C3×D3—22no—
682C2×C3×D3—21no—
683C32×C4—22no—
684C32×C4—21no—
685C32×C4—21no—
686C32×C4—21no—
687C32×C4—22no—
688C3⋊Dic3—22no—
689C3⋊Dic3—22no—
690C3⋊Dic3—22no—
691C3⋊Dic3—22no—
692C3×Dic3—22no—
693C3×Dic3—22no—
694C3×Dic3—22no—
695C3×Dic3—21no—
696C3×Dic3—21no—
697C3×Dic3—22no—
698C3×Dic32−1+412yes—
699C4⋊Q8—32no—
700C4⋊Q8—91no—
701C4⋊Q8—91no—
702C4⋊Q8—92no—
703C4⋊Q8—92no—
704C4⋊Q8—92no—
705#126—32no—
706#126—32no—
707#126—32no—
708#126—92no—
709#126—92no—
710#126—92no—
711#126—92no—
712#126—92no—
713#126—92no—
714#126—92no—
715#125—31no—
716#125—92no—
717#125—92no—
718#125—92no—
719#125—92no—
720#125—92no—
721#125—92no—
722#125—92no—
723#125—92no—
724#125—91no—
725#125—91no—
726#125D3211yescharacteristic
727#124—31no—
728#124—31no—
729#124—92no—
730#124—92no—
731#124—92no—
732#124—92no—
733#123—32no—
734#123—32no—
735#123—92no—
736#123—92no—
737#123—92no—
738#123—92no—
739#123—92no—
740#123—92no—
741#123—92no—
742#123—92no—
743C22⋊Q8—31no—
744C22⋊Q8—32no—
745C22⋊Q8—32no—
746C22⋊Q8—92no—
747C22⋊Q8—92no—
748C22⋊Q8—92no—
749C22⋊Q8—92no—
750C22⋊Q8—92no—
751C22⋊Q8—92no—
752C22⋊Q8—92no—
753C22⋊Q8—92no—
754C22⋊Q8—92no—
755C22⋊Q8—92no—
756C22⋊Q8—92no—
757C22⋊Q8—92no—
758C22⋊Q8—91no—
759#121—31no—
760#121—92no—
761#121—92no—
762#121—92no—
763#121—91no—
764#121—92no—
765C4×Q8—31no—
766C4×Q8—92no—
767C4×Q8—92no—
768C4×Q8—92no—
769C4×Q8—91no—
770C4×Q8—92no—
771C4×D4—31no—
772C4×D4—32no—
773C4×D4—91no—
774C4×D4—92no—
775C4×D4—92no—
776C4×D4—92no—
777#117—32no—
778#117—92no—
779#117—92no—
780#117—91no—
781#117—92no—
782#117—91no—
783C2×C42—31no—
784C2×C42—92no—
785C2×C42—92no—
786C23×C3—31no—
787C23×C3—32no—
788C23×C3—32no—
789C22×D3C23×D311yescharacteristic
790C22×D3C23×D312yes—
791C22×D3C23×D312yes—
792C3×Q8—121no—
793C3×Q8—122no—
794C3×Q8—121no—
795C3×D4—121no—
796C3×D4—122no—
797C3×D4—121no—
798C2×C3×C4—22no—
799C2×C3×C4—22no—
800C2×C3×C4—21no—
801C2×C3×C4—21no—
802C2×C3×C4—21no—
803C2×C3×C4—31no—
804C2×C3×C4—32no—
805C2×C3×C4—32no—
806C2×C3×C4—32no—
807C2×C3×C4—32no—
808C2×C3×C4—31no—
809C2×C3×C4—31no—
810C2×C3×C4—64no—
811C2×C3×C4—62no—
812C2×C3×C4—122no—
813C2×C3×C4—121no—
814C2×C3×C4—121no—
815C2×C3×C4C23×D312yes—
816C2×C3×C4C23×D312yes—
817C2×C3×C4C23×D312yes—
818C2×C3×C4C23×D312yes—
819C2×C3×C4C23×D311yescharacteristic
820C2×C3×C4C23×D311yescharacteristic
821C2×C3×C4C23×D311yescharacteristic
822C2×C3×C4C23×D311yescharacteristic
823C2×C3×C4C23×D311yescharacteristic
824C2×C3×C4C23×D311yescharacteristic
825#67—122no—
826#67—122no—
827#67—122no—
828#67—122no—
829#67—122no—
830#67—122no—
831C2×Dic3—32no—
832C2×Dic3—32no—
833C2×Dic3—32no—
834C2×Dic3—32no—
835C2×Dic3—32no—
836C2×Dic3—32no—
837C2×Dic3—32no—
838C2×Dic3—32no—
839C2×Dic3—62no—
840C2×Dic3—62no—
841C2×Dic3—62no—
842C2×Dic3—62no—
843C2×Dic3—64no—
844C2×Dic3—122no—
845C2×Dic3—122no—
846C2×Dic3—122no—
847C2×Dic3C23×D312yes—
848C2×Dic3C23×D312yes—
849C2×Dic3C23×D312yes—
850C2×Dic3C23×D312yes—
851C2×Dic3C23×D311yescharacteristic
852C2×Dic3C23×D311yescharacteristic
853C2×Dic3C23×D311yescharacteristic
854D12—41no—
855D12—42no—
856D12—41no—
857C4×D3—24no—
858C4×D3—22no—
859C4×D3—41no—
860C4×D3—41no—
861C4×D3—42no—
862C4×D3—64no—
863C4×D3—122no—
864C4×D3—122no—
865C4×D3—122no—
866Dic6—41no—
867Dic6—41no—
868Dic6—42no—
869Dic6—122no—
870Dic6—122no—
871Dic6—122no—
872Dic6—122no—
873Dic6—122no—
874Dic6—122no—
875C2×C32C2×2−1+411yescharacteristic
876C2×C32#58511yescharacteristic
877C2×C32#58511yescharacteristic
878C3×D3—42no—
879C3×D3—42no—
880C3×D3—41no—
881C2×Q8—31no—
882C2×Q8—32no—
883C2×Q8—31no—
884C2×Q8—92no—
885C2×Q8—92no—
886C2×Q8—92no—
887C2×D4—32no—
888C2×D4—31no—
889C2×D4—31no—
890C2×D4—92no—
891C2×D4—92no—
892C2×D4—92no—
893C22×C4—31no—
894C22×C4—32no—
895C22×C4—31no—
896C22×C4—31no—
897C22×C4—32no—
898C22×C4—92no—
899C22×C4—92no—
900C22×C4—92no—
901C22×C4—92no—
902C4⋊C4—32no—
903C4⋊C4—31no—
904C4⋊C4—32no—
905C4⋊C4—31no—
906C4⋊C4—32no—
907C4⋊C4—32no—
908C4⋊C4—32no—
909C4⋊C4—32no—
910C4⋊C4—92no—
911C4⋊C4—92no—
912C4⋊C4—92no—
913C4⋊C4—92no—
914C4⋊C4—92no—
915C4⋊C4—92no—
916C4⋊C4—92no—
917C4⋊C4—92no—
918C4⋊C4—92no—
919C4⋊C4—92no—
920C4⋊C4—92no—
921C4⋊C4—91no—
922C4⋊C4—91no—
923C4⋊C4—92no—
924C4⋊C4—92no—
925C4⋊C4—92no—
926C4⋊C4—91no—
927C4⋊C4—92no—
928C4⋊C4—92no—
929C4⋊C4—92no—
930C4⋊C4—92no—
931C4⋊C4—91no—
932C4⋊C4C2×D3212yes—
933C4⋊C4C2×D3211yescharacteristic
934C4⋊C4C2×D3212yes—
935C4⋊C4C2×D3211yescharacteristic
936C22⋊C4—32no—
937C22⋊C4—32no—
938C22⋊C4—32no—
939C22⋊C4—32no—
940C22⋊C4—32no—
941C22⋊C4—32no—
942C22⋊C4—32no—
943C22⋊C4—32no—
944C22⋊C4—32no—
945C22⋊C4—32no—
946C22⋊C4—92no—
947C22⋊C4—92no—
948C22⋊C4—92no—
949C22⋊C4—92no—
950C22⋊C4—92no—
951C22⋊C4—92no—
952C22⋊C4—92no—
953C22⋊C4—92no—
954C22⋊C4—92no—
955C22⋊C4—92no—
956C42—31no—
957C42—31no—
958C42—31no—
959C42—32no—
960C42—32no—
961C42—92no—
962C42—92no—
963C42—92no—
964C42—92no—
965C42—92no—
966C42—92no—
967C42C2×D3211yescharacteristic
968C22×C3—21no—
969C22×C3—62no—
970C22×C3—62no—
971C22×C3—62no—
972C22×C3—62no—
973C22×C3—61no—
974C22×C3—61no—
975C22×C3—62no—
976C22×C3—62no—
977C22×C3—61no—
978C22×C3C24×D311yescharacteristic
979C22×C3C24×D311yescharacteristic
980C2×D3—21no—
981C2×D3—22no—
982C2×D3—21no—
983C2×D3—21no—
984C2×D3—22no—
985C2×D3—22no—
986C2×D3—22no—
987C2×D3—22no—
988C2×D3—22no—
989C3×C4—22no—
990C3×C4—21no—
991C3×C4—21no—
992C3×C4—21no—
993C3×C4—22no—
994C3×C4—22no—
995C3×C4—21no—
996C3×C4—22no—
997C3×C4—21no—
998C3×C4—21no—
999C3×C4—32no—
1000C3×C4—41no—
1001C3×C4—42no—
1002C3×C4—41no—
1003C3×C4—42no—
1004C3×C4—41no—
1005C3×C4—62no—
1006C3×C4—62no—
1007C3×C4—62no—
1008C3×C4—61no—
1009C3×C4—61no—
1010C3×C4—62no—
1011Dic3—22no—
1012Dic3—21no—
1013Dic3—21no—
1014Dic3—22no—
1015Dic3—22no—
1016Dic3—22no—
1017Dic3—62no—
1018Dic3—62no—
1019Dic3—62no—
1020Dic3—62no—
1021Dic3—62no—
1022Dic3—62no—
1023Dic3—62no—
1024Dic3—62no—
1025Dic3—122no—
1026Dic3—122no—
1027Dic3—122no—
1028Dic3—122no—
1029Dic3#101012yes—
1030C32#353111yescharacteristic, complemented, Sylow
1031C23—32no—
1032C23—32no—
1033C23—31no—
1034Q8—121no—
1035Q8—122no—
1036Q8—121no—
1037Q8—362no—
1038Q8—362no—
1039Q8—362no—
1040D4—121no—
1041D4—122no—
1042D4—121no—
1043D4—362no—
1044D4—362no—
1045D4—362no—
1046C2×C4—31no—
1047C2×C4—31no—
1048C2×C4—31no—
1049C2×C4—32no—
1050C2×C4—32no—
1051C2×C4—32no—
1052C2×C4—32no—
1053C2×C4—62no—
1054C2×C4—64no—
1055C2×C4—92no—
1056C2×C4—92no—
1057C2×C4—92no—
1058C2×C4—92no—
1059C2×C4—121no—
1060C2×C4—122no—
1061C2×C4—121no—
1062C2×C4—184no—
1063C2×C4—362no—
1064C2×C4—362no—
1065C2×C4—362no—
1066C2×C4C22×D3212yes—
1067C2×C4C22×D3212yes—
1068C2×C4C22×D3211yescharacteristic
1069C2×C4C22×D3211yescharacteristic
1070C2×C4C22×D3211yescharacteristic
1071C2×C3—21no—
1072C2×C3—21no—
1073C2×C3—21no—
1074C2×C3—122no—
1075C2×C3—121no—
1076C2×C3—122no—
1077C2×C3C2×#101011yescharacteristic
1078C2×C3#596411yescharacteristic
1079C2×C3#596411yescharacteristic
1080C2×C3#596611yescharacteristic
1081C2×C3D3×2−1+411yescharacteristic
1082C2×C3#596811yescharacteristic
1083D3—42no—
1084D3—41no—
1085D3—42no—
1086C22—61no—
1087C22—62no—
1088C22—62no—
1089C22—62no—
1090C22—61no—
1091C22—62no—
1092C22—61no—
1093C22—62no—
1094C22—62no—
1095C22C23×D3211yescharacteristic
1096C4—21no—
1097C4—22no—
1098C4—21no—
1099C4—22no—
1100C4—21no—
1101C4—32no—
1102C4—61no—
1103C4—62no—
1104C4—62no—
1105C4—62no—
1106C4—61no—
1107C4—62no—
1108C4—182no—
1109C4—182no—
1110C4—182no—
1111C4—182no—
1112C3—21no—
1113C3#8613211yescharacteristic, complemented
1114C3#8711611yescharacteristic, complemented
1115C2—121no—
1116C2—122no—
1117C2—122no—
1118C2#1059668811yescharacteristic
1119C2D3×#101011yescharacteristic
1120C2#1059669611yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#125C22
hypercenter#125D32
hypocenterC32#3531
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #10596157C2semidirect
2. C3×#5699C2semidirect
3. C3×#5691C2semidirect
4. #10594586C2semidirect
5. #10594586C2semidirect
6. #10594507C2semidirect
7. #10594497C2semidirect
8. #10594495C2semidirect
9. #10594492C2semidirect
10. #10594445C2semidirect
11. #10594444C2semidirect
12. #10594405C2semidirect
13. #10594405C2semidirect
14. #10594404C2semidirect
15. #10594386C2semidirect
16. #10593985C2semidirect
17. #10593952C2semidirect
18. #10593921C2semidirect
19. #10593874C2semidirect
120. #5699D3semidirect
121. #5691D3semidirect
1030. C32#3531semidirect
1113. C3#86132semidirect
1114. C3#87116semidirect

Maximal subgroups

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

subgroupindex
#105961572
C3×#56992
C3×#56912
#105945862
#105945072
#105944972
#105944952
#105944922
#105944452
#105944442
#105944052
#105944042
#105943862
#105939852
#105939522
#105939212
#105938742
#871163
#861323