Finite Group Databasebeta

← #11910365

Subgroups — #11910365

Order 1152.

2242 conjugacy classes of subgroups.

The subgroup lattice has 1259 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596191C211yesmaximal, characteristic, complemented
2C3×#5720C211yesmaximal, characteristic, complemented
3C3×#5716C211yesmaximal, characteristic, complemented
4#10595276C211yesmaximal, characteristic, complemented
5#10595264C212yesmaximal, complemented
6#10595263C212yesmaximal, complemented
7#10595262C211yesmaximal, characteristic, complemented
8#10595260C212yesmaximal, complemented
9#10595257C212yesmaximal, complemented
10#10595214C212yesmaximal, complemented
11#10595187C212yesmaximal, complemented
12#10595159C211yesmaximal, characteristic, complemented
13#10595155C212yesmaximal, complemented
14#10595154C211yesmaximal, characteristic, complemented
15#10595138C212yesmaximal, complemented
16#10595129C212yesmaximal, complemented
17#10595116C212yesmaximal, complemented
18#10593975C212yesmaximal, complemented
19#10593957C212yesmaximal, complemented
20#87070—31nomaximal
21#86248—31nomaximal
22C2×C3×#237C2211yescharacteristic
23C2×C3×#237C2211yescharacteristic, complemented
24C22×#624C2211yescharacteristic, complemented
25C2×#3804C2212yes—
26C22×D3×Dic3C2211yescharacteristic, complemented
27C32×#127C2211yescharacteristic
28#64148C2212yes—
29#64148C2212yes—
30#64148C2212yescomplemented
31#64146C2211yescharacteristic
32#64146C2212yescomplemented
33#64144C2211yescharacteristic
34#64144C2212yescomplemented
35#64085C2212yescomplemented
36C3×#939C2212yes—
37C3×#939C2212yes—
38C3×#939C2212yescomplemented
39C3×#938C2212yescomplemented
40C3×#938C2212yescomplemented
41C3×#937C2211yescharacteristic
42C3×#937C2212yescomplemented
43C3×#936C2211yescharacteristic
44C3×#936C2211yescharacteristic, complemented
45C3×#935C2211yescharacteristic
46C3×#935C2212yescomplemented
47C3×D4×Dic3C2212yescomplemented
48C3×D4×Dic3C2212yescomplemented
49C3×#876C2212yescomplemented
50C3×C42×D3C2211yescharacteristic, complemented
51C3×#869C2211yescharacteristic, complemented
52#63982C2212yescomplemented
53#63982C2212yescomplemented
54#63981C2212yes—
55#63981C2211yescharacteristic, complemented
56#63980C2212yescomplemented
57#63979C2212yes—
58#63978C2212yescomplemented
59#63977C2212yes—
60#63976C2211yescharacteristic, complemented
61#63975C2212yescomplemented
62Dic3×#67C2212yes—
63Dic3×#67C2212yescomplemented
64#63971C2212yes—
65#63970C2212yes—
66#63969C2212yescomplemented
67#63966C2212yescomplemented
68#63964C2212yescomplemented
69#63964C2212yescomplemented
70#63962C2211yescharacteristic, complemented
71#63962C2212yescomplemented
72#63961C2211yescharacteristic, complemented
73#63959C2212yes—
74#63959C2212yescomplemented
75#63958C2212yes—
76#63958C2212yes—
77#63956C2212yescomplemented
78#63956C2212yescomplemented
79#63955C2211yescharacteristic, complemented
80#63955C2211yescharacteristic, complemented
81C2×Dic32C2212yescomplemented
82#63953C2212yes—
83#63952C2212yes—
84#63952C2212yescomplemented
85#63907C2212yes—
86#63906C2212yes—
87#63905C2212yescomplemented
88#63904C2212yescomplemented
89#63899C2212yescomplemented
90#63895C2212yescomplemented
91#63890C2212yes—
92#63888C2212yescomplemented
93#63887C2212yescomplemented
94#63880C2212yes—
95#63879C2212yescomplemented
96#63877C2212yescomplemented
97#63867C2212yescomplemented
98#63858C2212yescomplemented
99#63854C2212yes—
100#63852C2212yes—
101#63851C2212yescomplemented
102#63850C2212yescomplemented
103#63848C2212yescomplemented
104#63847C2212yescomplemented
105#63846C2212yescomplemented
106#63839C2212yescomplemented
107#63837C2212yescomplemented
108#63836C2212yescomplemented
109C3×#560—31no—
110C3×#532—31no—
111#5832—32no—
112#5828—31no—
113#5828—31no—
114#5735—32no—
115#5720—31no—
116#5720—31no—
117#5720—61no—
118#5720D311yescharacteristic, complemented
119#5716D311yescharacteristic, complemented
120#5712—32no—
121#5706—32no—
122#5684—32no—
123#5683—31no—
124#5672—31no—
125#5667—32no—
126#5656—31no—
127#5651—31no—
128#5649—32no—
129#5621—32no—
130#5621—32no—
131#5621—32no—
132#5621—32no—
133#5620—32no—
134#5620—32no—
135#5620—32no—
136#5606—32no—
137#5600—32no—
138#5596—32no—
139#5595—32no—
140#5594—31no—
141#5586—31no—
142#5586—32no—
143#5547—32no—
144#5547—32no—
145#5538—32no—
146#5538—32no—
147#5479—32no—
148C23×C3⋊D3C2311yescharacteristic
149C23×C3×D3C2311yescharacteristic
150C2×C32×D4C2312yes—
151C2×C32×D4C2312yes—
152C2×C32×D4C2311yescharacteristic
153C2×C32×D4C2311yescharacteristic
154C2×#638C2312yes—
155C2×#638C2312yes—
156C2×#638C2312yes—
157C22×C3⋊Dic3C2311yescharacteristic
158C22×C3⋊Dic3C2312yes—
159C2×C3×#67C2312yes—
160C2×C3×#67C2312yes—
161C2×C3×#67C2312yes—
162C2×C3×#67C2311yescharacteristic
163C2×C3×#67C2311yescharacteristic
164C2×C3×#67C2312yes—
165C22×C3×Dic3C2311yescharacteristic
166C22×C3×Dic3C2312yes—
167C22×C3×Dic3C2311yescharacteristic
168C22×C3×Dic3C2311yescharacteristic
169C22×C3×Dic3C2312yes—
170C3×#237—42no—
171C3×#237—42no—
172C2×C3×C4×D3C2311yescharacteristic
173C2×C3×C4×D3C2312yes—
174C2×C3×Dic6C2311yescharacteristic
175C2×C3×Dic6C2311yescharacteristic
176C2×#627C2312yes—
177C2×#627C2312yes—
178C2×#626C2312yes—
179C2×#626C2312yes—
180C2×#626C2312yes—
181C2×#625C2312yes—
182C2×#624—42no—
183C2×#624C2312yes—
184C2×#624C2312yes—
185#3804—44no—
186C2×D3×Dic3—42no—
187C2×D3×Dic3C2312yes—
188C2×D3×Dic3C2312yes—
189C32×C42C2311yescharacteristic
190#3757C2312yes—
191#3757C2311yescharacteristic
192#3757C2311yescharacteristic
193#3757C2312yes—
194#3752C2312yes—
195#3752C2312yes—
196#3752C2312yes—
197#3750C2312yes—
198#3750C2312yes—
199#3750C2312yes—
200C3×#217C2312yes—
201C3×#217C2312yes—
202C3×#217C2312yes—
203C3×#217C2312yes—
204C3×#217C2312yes—
205C3×#217C2311yescharacteristic
206C3×#217C2311yescharacteristic
207C3×#217C2312yes—
208C3×(C2×D3)⋊C4C2312yes—
209C3×(C2×D3)⋊C4C2312yes—
210C3×(C2×D3)⋊C4C2312yes—
211C3×C4⋊Dic3C2312yes—
212C3×C4⋊Dic3C2312yes—
213C3×Dic3⋊C4C2312yes—
214C3×Dic3⋊C4C2312yes—
215C3×Dic3⋊C4C2312yes—
216C3×C4×Dic3C2312yes—
217C3×C4×Dic3C2311yescharacteristic
218#3724C2312yes—
219#3724C2312yes—
220#3724C2312yes—
221Dic3⋊Dic3C2312yes—
222Dic3⋊Dic3C2312yes—
223Dic3⋊Dic3C2312yes—
224Dic3⋊Dic3C2312yes—
225Dic3⋊Dic3C2312yes—
226Dic3⋊Dic3C2312yes—
227Dic3⋊Dic3C2312yes—
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—
236Dic32C2312yes—
237Dic32C2312yes—
238Dic32C2312yes—
239Dic32C2312yes—
240#3529—91noSylow
241C2×C3×#41—31no—
242C2×C3×#41—31no—
243C23×Dic3—31no—
244C2×#237—32no—
245C2×#237C2×D311yescharacteristic
246C2×#237C2×D311yescharacteristic, complemented
247C2×#235—32no—
248C22×C4×D3—31no—
249C22×C4×D3—31no—
250C22×C4×D3—31no—
251C3×C4⋊Q8—31no—
252C3×#127—21no—
253C3×#127C2×D311yescharacteristic
254C3×#127C2×D311yescharacteristic
255C3×#126—32no—
256C3×#124—31no—
257C3×#124—31no—
258C3×#123—32no—
259C3×#123—31no—
260C3×#121—32no—
261C3×#121—32no—
262C3×#121—32no—
263C3×#121—32no—
264C3×#121—32no—
265C3×#120—31no—
266C3×#120—32no—
267C3×C4×D4—32no—
268C3×C4×D4—32no—
269C2×C3×C42—31no—
270#953—31no—
271#953—32no—
272#947—32no—
273#946—32no—
274#946—32no—
275#944—32no—
276#940—32no—
277#940—32no—
278#939—32no—
279#939—32no—
280#939—32no—
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—62no—
290#939—62no—
291#939—62no—
292#939C2×D312yes—
293#939C2×D312yes—
294#939C2×D312yescomplemented
295#938—32no—
296#938—32no—
297#938—32no—
298#938C2×D312yescomplemented
299#938C2×D312yescomplemented
300#937—31no—
301#937—31no—
302#937—31no—
303#937—32no—
304#937—32no—
305#937—31no—
306#937—32no—
307#937—61no—
308#937—62no—
309#937C2×D311yescharacteristic
310#937C2×D312yescomplemented
311#936—32no—
312#936—32no—
313#936C2×D311yescharacteristic
314#936C2×D311yescharacteristic, complemented
315#935—31no—
316#935—31no—
317#935—32no—
318#935—32no—
319#935—31no—
320#935—31no—
321#935—32no—
322#935—32no—
323#935—61no—
324#935—62no—
325#935C2×D311yescharacteristic
326#935C2×D312yescomplemented
327D4×Dic3—32no—
328D4×Dic3—32no—
329D4×Dic3C2×D312yescomplemented
330D4×Dic3C2×D312yescomplemented
331#930—32no—
332#930—32no—
333#929—31no—
334#929—32no—
335#929—32no—
336#929—32no—
337C4×#67—32no—
338C4×#67—32no—
339C4×#67—32no—
340C4×#67—32no—
341C4×#67—32no—
342C4×#67—32no—
343#926—31no—
344#926—31no—
345#924—32no—
346#924—32no—
347#924—32no—
348C2×C4×Dic3—32no—
349C2×C4×Dic3—32no—
350#898—32no—
351#898—32no—
352#898—32no—
353#897—32no—
354#896—32no—
355#896—32no—
356#896—32no—
357#896—32no—
358#894—32no—
359#894—32no—
360#894—32no—
361#893—32no—
362#892—32no—
363#890—32no—
364#889—32no—
365#889—32no—
366#889—32no—
367#889—32no—
368#888—32no—
369#887—32no—
370#886—31no—
371#886—32no—
372#886—32no—
373#886—32no—
374#885—32no—
375#885—32no—
376#885—32no—
377#885—32no—
378#885—32no—
379#885—32no—
380#884—32no—
381#884—32no—
382#884—32no—
383#884—32no—
384#883—32no—
385#883—32no—
386#883—32no—
387#883—32no—
388#883—32no—
389#882—32no—
390#882—31no—
391#882—32no—
392#67⋊C4—32no—
393#67⋊C4—32no—
394#67⋊C4—32no—
395#67⋊C4—32no—
396#879—32no—
397#879—32no—
398#879—32no—
399#879—32no—
400#879—32no—
401#878—32no—
402#878—32no—
403#878—32no—
404#878—32no—
405#878—32no—
406#878—32no—
407#878—32no—
408#878—32no—
409#877—31no—
410#877—31no—
411#877—32no—
412#876—32no—
413#876—32no—
414#876—62no—
415#876C2×D312yescomplemented
416#875—32no—
417C4×D12—32no—
418#872—32no—
419#872—32no—
420C42×D3C2×D311yescharacteristic, complemented
421#870—32no—
422#869C2×D311yescharacteristic, complemented
423C4×Dic6—32no—
424C23×C32C2411yescharacteristic
425C23×C32C2411yescharacteristic
426C23×C32C2412yes—
427C22×C3⋊D3—42no—
428C22×C3⋊D3—41no—
429C22×C3⋊D3C2412yes—
430C22×C3×D3—42no—
431C22×C3×D3—41no—
432C22×C3×D3C2412yes—
433C22×C3×D3C2411yescharacteristic
434C32×D4—41no—
435C32×D4—41no—
436C32×D4—42no—
437C32×D4—42no—
438C2×C32×C4C2412yes—
439C2×C32×C4C2411yescharacteristic
440#638—42no—
441#638—42no—
442#638—42no—
443C2×C3⋊Dic3—41no—
444C2×C3⋊Dic3—42no—
445C2×C3⋊Dic3C2412yes—
446C2×C3⋊Dic3C2412yes—
447C2×C3⋊Dic3C2412yes—
448C3×#67—42no—
449C3×#67—41no—
450C3×#67—41no—
451C3×#67—42no—
452C3×#67—42no—
453C3×#67—42no—
454C2×C3×Dic3—22no—
455C2×C3×Dic3—24no—
456C2×C3×Dic3—22no—
457C2×C3×Dic3—41no—
458C2×C3×Dic3—42no—
459C2×C3×Dic3C2412yes—
460C2×C3×Dic3C2412yes—
461C2×C3×Dic3C2412yes—
462C2×C3×Dic3C2411yescharacteristic
463C2×C3×Dic3C2412yes—
464C2×C3×Dic3C2412yes—
465C2×C3×Dic3C2411yescharacteristic
466C2×C3×Dic3C2411yescharacteristic
467C3×C4×D3—22no—
468C3×C4×D3—42no—
469C3×Dic6—41no—
470C3×Dic6—41no—
471#627—42no—
472#627—42no—
473#626—42no—
474#626—42no—
475#626—42no—
476#625—42no—
477#624—24no—
478#624—42no—
479D3×Dic3—24no—
480D3×Dic3—42no—
481#563—91no—
482#563—92no—
483#562—92no—
484#562—92no—
485#562—92no—
486H(3,𝔽4)—91no—
487#560—31no—
488#560—92no—
489#560—92no—
490#560—91no—
491#532—31no—
492#532—92no—
493#529—92no—
494#529—92no—
495#529—92no—
496#525—92no—
497#525—92no—
498#525—91no—
499#525—91no—
500C24×C3—31no—
501C23×D3—31no—
502C23×D3—31no—
503C23×D3—61no—
504C23×D3C22×D311yescharacteristic
505C3×#41—122no—
506C3×#41—122no—
507C2×C3×Q8—31no—
508C2×C3×Q8—31no—
509C2×C3×D4—22no—
510C2×C3×D4—21no—
511C2×C3×D4—22no—
512C2×C3×D4—21no—
513C2×C3×D4—32no—
514C2×C3×D4—32no—
515C2×C3×D4—31no—
516C2×C3×D4—31no—
517C2×C3×D4—32no—
518C2×C3×D4—32no—
519C2×C3×D4C22×D312yes—
520C2×C3×D4C22×D312yes—
521C2×C3×D4C22×D311yescharacteristic
522C2×C3×D4C22×D311yescharacteristic
523C2×C3×D4C22×D312yes—
524C2×C3×D4C22×D312yes—
525C2×C3×D4C22×D311yescharacteristic
526C2×C3×D4C22×D311yescharacteristic
527C22×C3×C4—32no—
528C22×C3×C4—31no—
529C22×C3×C4—31no—
530C22×C3×C4—32no—
531C22×C3×C4—31no—
532C22×C3×C4—31no—
533C22×C3×C4—32no—
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—32no—
544C2×#67—32no—
545C2×#67—62no—
546C2×#67—62no—
547C2×#67—62no—
548C2×#67C22×D312yes—
549C2×#67C22×D311yescharacteristic
550C2×#67C22×D312yes—
551C2×#67C22×D311yescharacteristic
552C2×#67C22×D312yes—
553C2×#67C22×D312yes—
554C22×Dic3—31no—
555C22×Dic3—31no—
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×D311yescharacteristic
565C22×Dic3C22×D312yes—
566C22×Dic3C22×D311yescharacteristic
567C22×Dic3C22×D312yes—
568#237—42no—
569#237—42no—
570#237—124no—
571#235—124no—
572C2×D12—32no—
573C2×D12—32no—
574C2×D12—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—122no—
582C2×C4×D3—122no—
583C2×C4×D3—122no—
584C2×C4×D3C22×D311yescharacteristic
585C2×C4×D3C22×D312yes—
586C2×Dic6—32no—
587C2×Dic6—32no—
588C2×Dic6—32no—
589C2×Dic6—32no—
590C2×Dic6C22×D311yescharacteristic
591C2×Dic6C22×D311yescharacteristic
592C3×C4⋊C4—32no—
593C3×C4⋊C4—32no—
594C3×C4⋊C4—32no—
595C3×C4⋊C4—32no—
596C3×C4⋊C4—32no—
597C3×C22⋊C4—31no—
598C3×C22⋊C4—31no—
599C3×C22⋊C4—32no—
600C3×C22⋊C4—32no—
601C3×C22⋊C4—32no—
602C3×C22⋊C4—32no—
603C3×C22⋊C4—32no—
604C3×C22⋊C4—32no—
605C3×C22⋊C4—32no—
606C3×C22⋊C4—32no—
607C3×C22⋊C4—32no—
608C3×C42—21no—
609C3×C42—32no—
610C3×C42—31no—
611C3×C42C22×D311yescharacteristic
612C3×C42C22×D311yescharacteristic
613#217—31no—
614#217—31no—
615#217—32no—
616#217—32no—
617#217—31no—
618#217—32no—
619#217—31no—
620#217—32no—
621#217—32no—
622#217—32no—
623#217—32no—
624#217—32no—
625#217—32no—
626#217—61no—
627#217—62no—
628#217—61no—
629#217—62no—
630#217C22×D312yes—
631#217C22×D312yes—
632#217C22×D312yes—
633#217C22×D312yes—
634#217C22×D311yescharacteristic
635#217C22×D312yes—
636#217C22×D312yes—
637#217C22×D311yescharacteristic
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—
669C4⋊Dic3C22×D312yes—
670Dic3⋊C4—32no—
671Dic3⋊C4—32no—
672Dic3⋊C4—32no—
673Dic3⋊C4—32no—
674Dic3⋊C4—32no—
675Dic3⋊C4—32no—
676Dic3⋊C4—32no—
677Dic3⋊C4—32no—
678Dic3⋊C4—32no—
679Dic3⋊C4—32no—
680Dic3⋊C4—32no—
681Dic3⋊C4—32no—
682Dic3⋊C4—32no—
683Dic3⋊C4—32no—
684Dic3⋊C4—32no—
685Dic3⋊C4—32no—
686Dic3⋊C4—32no—
687Dic3⋊C4—32no—
688Dic3⋊C4—32no—
689Dic3⋊C4—62no—
690Dic3⋊C4—62no—
691Dic3⋊C4—62no—
692Dic3⋊C4C22×D312yes—
693Dic3⋊C4C22×D312yes—
694Dic3⋊C4C22×D312yes—
695C4×Dic3—32no—
696C4×Dic3—32no—
697C4×Dic3—32no—
698C4×Dic3—32no—
699C4×Dic3—32no—
700C4×Dic3—32no—
701C4×Dic3—32no—
702C4×Dic3—32no—
703C4×Dic3C22×D312yes—
704C4×Dic3C22×D311yescharacteristic
705C22×C32—21no—
706C22×C32—22no—
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—44no—
717C2×C3×D3—22no—
718C2×C3×D3—21no—
719C2×C3×D3—22no—
720C2×C3×D3—22no—
721C2×C3×D3—22no—
722C2×C3×D3—44no—
723C32×C4—21no—
724C32×C4—22no—
725C3⋊Dic3—22no—
726C3⋊Dic3—22no—
727C3⋊Dic3—22no—
728C3×Dic3—21no—
729C3×Dic3—22no—
730C3×Dic3—21no—
731C3×Dic3—22no—
732C3×Dic3—22no—
733C3×Dic3—22no—
734C3×Dic3—22no—
735C3×Dic3H(5,𝔽2)12yes—
736C2×#41—31no—
737C2×#41—31no—
738C2×#41—92no—
739C23×C4—91no—
740C23×C4—91no—
741C4⋊Q8—31no—
742C4⋊Q8—92no—
743#127—92no—
744#127D3211yescharacteristic
745#126—32no—
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—31no—
756#124—92no—
757#124—92no—
758#124—92no—
759#124—92no—
760#124—92no—
761#123—31no—
762#123—32no—
763#123—92no—
764#123—92no—
765#123—92no—
766#123—92no—
767#123—92no—
768#123—92no—
769#123—91no—
770#123—92no—
771#123—92no—
772#123—91no—
773#123—91no—
774#123—92no—
775C22⋊Q8—92no—
776C22⋊Q8—92no—
777C22⋊Q8—92no—
778C22⋊Q8—92no—
779C22⋊Q8—92no—
780C22⋊Q8—92no—
781C22⋊Q8—92no—
782C22⋊Q8—92no—
783C22⋊Q8—92no—
784#121—32no—
785#121—32no—
786#121—32no—
787#121—32no—
788#121—32no—
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#121—92no—
799#120—32no—
800#120—31no—
801#120—91no—
802#120—92no—
803#120—92no—
804#120—91no—
805#120—92no—
806#120—91no—
807C4×Q8—92no—
808C4×D4—32no—
809C4×D4—32no—
810C4×D4—92no—
811C4×D4—92no—
812C4×D4—92no—
813C4×D4—92no—
814C4×D4—92no—
815C4×D4—92no—
816C4×D4—92no—
817#117—92no—
818#117—92no—
819#117—91no—
820#117—91no—
821C2×C42—31no—
822C2×C42—92no—
823C23×C3—21no—
824C23×C3—21no—
825C23×C3—22no—
826C23×C3—31no—
827C23×C3—32no—
828C23×C3—121no—
829C23×C3—122no—
830C23×C3C23×D311yescharacteristic
831C23×C3C23×D311yescharacteristic
832C23×C3C23×D311yescharacteristic
833C23×C3C23×D311yescharacteristic
834C23×C3C23×D312yes—
835C23×C3C23×D312yes—
836C22×D3—32no—
837C22×D3—32no—
838C22×D3—41no—
839C22×D3—42no—
840C22×D3—62no—
841C22×D3—121no—
842C22×D3—121no—
843C22×D3—122no—
844C22×D3—122no—
845C22×D3—241no—
846C22×D3—242no—
847C22×D3C23×D311yescharacteristic
848C22×D3C23×D312yes—
849C3×Q8—121no—
850C3×Q8—121no—
851C3×D4—41no—
852C3×D4—41no—
853C3×D4—42no—
854C3×D4—42no—
855C3×D4—42no—
856C3×D4—42no—
857C3×D4—41no—
858C3×D4—41no—
859C3×D4—81no—
860C3×D4—81no—
861C3×D4—82no—
862C3×D4—82no—
863C3×D4—122no—
864C3×D4—122no—
865C3×D4—122no—
866C3×D4—122no—
867C3×D4—121no—
868C3×D4—121no—
869C2×C3×C4—22no—
870C2×C3×C4—21no—
871C2×C3×C4—31no—
872C2×C3×C4—32no—
873C2×C3×C4—32no—
874C2×C3×C4—32no—
875C2×C3×C4—32no—
876C2×C3×C4—32no—
877C2×C3×C4—31no—
878C2×C3×C4—31no—
879C2×C3×C4—62no—
880C2×C3×C4—62no—
881C2×C3×C4—62no—
882C2×C3×C4—64no—
883C2×C3×C4—122no—
884C2×C3×C4—121no—
885C2×C3×C4—122no—
886C2×C3×C4C23×D312yes—
887C2×C3×C4C23×D311yescharacteristic
888C2×C3×C4C23×D312yes—
889C2×C3×C4C23×D311yescharacteristic
890#67—42no—
891#67—42no—
892#67—41no—
893#67—41no—
894#67—42no—
895#67—42no—
896#67—122no—
897#67—122no—
898#67—122no—
899#67—122no—
900#67—122no—
901#67—122no—
902#67—122no—
903#67—122no—
904#67—122no—
905#67—122no—
906#67—122no—
907#67—242no—
908#67—242no—
909#67—242no—
910C2×Dic3—22no—
911C2×Dic3—24no—
912C2×Dic3—22no—
913C2×Dic3—32no—
914C2×Dic3—32no—
915C2×Dic3—32no—
916C2×Dic3—32no—
917C2×Dic3—32no—
918C2×Dic3—32no—
919C2×Dic3—41no—
920C2×Dic3—42no—
921C2×Dic3—62no—
922C2×Dic3—62no—
923C2×Dic3—62no—
924C2×Dic3—64no—
925C2×Dic3—122no—
926C2×Dic3—121no—
927C2×Dic3—122no—
928C2×Dic3—122no—
929C2×Dic3—121no—
930C2×Dic3—241no—
931C2×Dic3—242no—
932C2×Dic3C23×D312yes—
933C2×Dic3C23×D312yes—
934C2×Dic3C23×D312yes—
935C2×Dic3C23×D312yes—
936C2×Dic3C23×D311yescharacteristic
937C2×Dic3C23×D312yes—
938C2×Dic3C23×D311yescharacteristic
939C2×Dic3C23×D311yescharacteristic
940D12—122no—
941D12—122no—
942D12—122no—
943C4×D3—22no—
944C4×D3—42no—
945C4×D3—64no—
946C4×D3—64no—
947C4×D3—64no—
948C4×D3—122no—
949C4×D3—122no—
950C4×D3—122no—
951Dic6—41no—
952Dic6—41no—
953Dic6—122no—
954Dic6—122no—
955Dic6—122no—
956Dic6—122no—
957C2×C32—41no—
958C2×C32—41no—
959C2×C32—42no—
960C2×C32C2×H(5,𝔽2)11yescharacteristic
961C2×C32#58512yes—
962C3⋊D3—42no—
963C3×D3—41no—
964C3×D3—42no—
965C24—31no—
966C24—91no—
967#41—122no—
968#41—122no—
969#41—364no—
970C2×Q8—31no—
971C2×Q8—31no—
972C2×Q8—92no—
973C2×Q8—92no—
974C2×D4—32no—
975C2×D4—32no—
976C2×D4—32no—
977C2×D4—31no—
978C2×D4—31no—
979C2×D4—32no—
980C2×D4—92no—
981C2×D4—92no—
982C2×D4—92no—
983C2×D4—92no—
984C2×D4—92no—
985C2×D4—92no—
986C2×D4—92no—
987C2×D4C2×D3212yes—
988C2×D4C2×D3212yes—
989C2×D4C2×D3211yescharacteristic
990C2×D4C2×D3211yescharacteristic
991C22×C4—32no—
992C22×C4—31no—
993C22×C4—31no—
994C22×C4—32no—
995C22×C4—31no—
996C22×C4—31no—
997C22×C4—32no—
998C22×C4—92no—
999C22×C4—92no—
1000C22×C4—92no—
1001C22×C4—92no—
1002C22×C4—92no—
1003C22×C4—91no—
1004C22×C4—362no—
1005C22×C4—362no—
1006C4⋊C4—32no—
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—
1024C22⋊C4—31no—
1025C22⋊C4—31no—
1026C22⋊C4—32no—
1027C22⋊C4—32no—
1028C22⋊C4—32no—
1029C22⋊C4—32no—
1030C22⋊C4—32no—
1031C22⋊C4—32no—
1032C22⋊C4—32no—
1033C22⋊C4—32no—
1034C22⋊C4—32no—
1035C22⋊C4—92no—
1036C22⋊C4—92no—
1037C22⋊C4—92no—
1038C22⋊C4—92no—
1039C22⋊C4—92no—
1040C22⋊C4—92no—
1041C22⋊C4—92no—
1042C22⋊C4—92no—
1043C22⋊C4—91no—
1044C22⋊C4—91no—
1045C22⋊C4—92no—
1046C22⋊C4—92no—
1047C22⋊C4—92no—
1048C22⋊C4—92no—
1049C22⋊C4—92no—
1050C42—32no—
1051C42—31no—
1052C42—92no—
1053C42—92no—
1054C42—92no—
1055C42—92no—
1056C42C2×D3211yescharacteristic
1057C22×C3—21no—
1058C22×C3—22no—
1059C22×C3—21no—
1060C22×C3—22no—
1061C22×C3—22no—
1062C22×C3—22no—
1063C22×C3—22no—
1064C22×C3—21no—
1065C22×C3—21no—
1066C22×C3—22no—
1067C22×C3—22no—
1068C22×C3—22no—
1069C22×C3—22no—
1070C22×C3—22no—
1071C22×C3—21no—
1072C22×C3—41no—
1073C22×C3—42no—
1074C22×C3—42no—
1075C22×C3—42no—
1076C22×C3—42no—
1077C22×C3—41no—
1078C22×C3—42no—
1079C22×C3—62no—
1080C22×C3—62no—
1081C22×C3—62no—
1082C22×C3—61no—
1083C22×C3—62no—
1084C22×C3—124no—
1085C22×C3C24×D311yescharacteristic
1086C22×C3C24×D311yescharacteristic
1087C2×D3—21no—
1088C2×D3—22no—
1089C2×D3—22no—
1090C2×D3—22no—
1091C2×D3—22no—
1092C2×D3—44no—
1093C2×D3—62no—
1094C2×D3—62no—
1095C2×D3—62no—
1096C2×D3—62no—
1097C2×D3—62no—
1098C2×D3—62no—
1099C2×D3—122no—
1100C2×D3—122no—
1101C2×D3—122no—
1102C2×D3—124no—
1103C2×D3—124no—
1104C2×D3—244no—
1105C3×C4—21no—
1106C3×C4—22no—
1107C3×C4—21no—
1108C3×C4—22no—
1109C3×C4—32no—
1110C3×C4—41no—
1111C3×C4—42no—
1112C3×C4—62no—
1113C3×C4—62no—
1114C3×C4—62no—
1115C3×C4—62no—
1116C3×C4—61no—
1117C3×C4—61no—
1118C3×C4—62no—
1119Dic3—22no—
1120Dic3—21no—
1121Dic3—21no—
1122Dic3—22no—
1123Dic3—22no—
1124Dic3—22no—
1125Dic3—22no—
1126Dic3—62no—
1127Dic3—62no—
1128Dic3—62no—
1129Dic3—62no—
1130Dic3—62no—
1131Dic3—62no—
1132Dic3—122no—
1133Dic3—122no—
1134Dic3—122no—
1135Dic3#100412yes—
1136C32#352911yescharacteristic, complemented, Sylow
1137C23—32no—
1138C23—31no—
1139C23—92no—
1140C23—121no—
1141C23—122no—
1142C23—361no—
1143C23—362no—
1144C23C22×D3211yescharacteristic
1145C23C22×D3211yescharacteristic
1146C23C22×D3212yes—
1147Q8—121no—
1148Q8—121no—
1149Q8—362no—
1150Q8—362no—
1151D4—41no—
1152D4—41no—
1153D4—42no—
1154D4—42no—
1155D4—121no—
1156D4—121no—
1157D4—122no—
1158D4—122no—
1159D4—122no—
1160D4—122no—
1161D4—362no—
1162D4—362no—
1163D4—362no—
1164D4—362no—
1165D4—362no—
1166D4—362no—
1167D4—362no—
1168C2×C4—31no—
1169C2×C4—32no—
1170C2×C4—32no—
1171C2×C4—32no—
1172C2×C4—32no—
1173C2×C4—32no—
1174C2×C4—31no—
1175C2×C4—31no—
1176C2×C4—62no—
1177C2×C4—62no—
1178C2×C4—62no—
1179C2×C4—64no—
1180C2×C4—92no—
1181C2×C4—92no—
1182C2×C4—92no—
1183C2×C4—122no—
1184C2×C4—121no—
1185C2×C4—122no—
1186C2×C4—184no—
1187C2×C4—184no—
1188C2×C4—362no—
1189C2×C4—362no—
1190C2×C4—361no—
1191C2×C4—362no—
1192C2×C4C22×D3212yes—
1193C2×C4C22×D3211yescharacteristic
1194C2×C3—21no—
1195C2×C3—22no—
1196C2×C3—41no—
1197C2×C3—41no—
1198C2×C3—42no—
1199C2×C3—41no—
1200C2×C3—41no—
1201C2×C3—42no—
1202C2×C3—81no—
1203C2×C3—81no—
1204C2×C3—82no—
1205C2×C3—121no—
1206C2×C3—122no—
1207C2×C3C2×#100411yescharacteristic
1208C2×C3#596412yes—
1209C2×C3D3×H(5,𝔽2)11yescharacteristic
1210C2×C3#596612yes—
1211D3—42no—
1212D3—41no—
1213D3—122no—
1214D3—122no—
1215D3—242no—
1216C22—21no—
1217C22—21no—
1218C22—22no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—61no—
1224C22—62no—
1225C22—62no—
1226C22—62no—
1227C22—62no—
1228C22—124no—
1229C22—182no—
1230C22—182no—
1231C22—182no—
1232C22—364no—
1233C22C23×D3211yescharacteristic
1234C4—21no—
1235C4—22no—
1236C4—32no—
1237C4—61no—
1238C4—61no—
1239C4—62no—
1240C4—62no—
1241C4—62no—
1242C4—62no—
1243C4—62no—
1244C4—182no—
1245C4—182no—
1246C4—182no—
1247C3—21no—
1248C3#8624811yescharacteristic, complemented
1249C3#8707011yescharacteristic, complemented
1250C2—41no—
1251C2—41no—
1252C2—42no—
1253C2—122no—
1254C2—121no—
1255C2—362no—
1256C2D3×#100411yescharacteristic
1257C2#1059667812yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#127C22
hypercenter#127D32
hypocenterC32#3529
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×#5720C2semidirect
3. C3×#5716C2semidirect
4. #10595276C2semidirect
5. #10595264C2semidirect
6. #10595263C2semidirect
7. #10595262C2semidirect
8. #10595260C2semidirect
9. #10595257C2semidirect
10. #10595214C2semidirect
11. #10595187C2semidirect
12. #10595159C2semidirect
13. #10595155C2semidirect
14. #10595154C2semidirect
15. #10595138C2semidirect
16. #10595129C2semidirect
17. #10595116C2semidirect
18. #10593975C2semidirect
19. #10593957C2semidirect
23. C2×C3×#237C22semidirect
24. C22×#624C22semidirect
26. C22×D3×Dic3C22semidirect
30. #64148C22semidirect
32. #64146C22semidirect
34. #64144C22semidirect
35. #64085C22semidirect
38. C3×#939C22semidirect
39. C3×#938C22semidirect
40. C3×#938C22semidirect
42. C3×#937C22semidirect
44. C3×#936C22semidirect
46. C3×#935C22semidirect
47. C3×D4×Dic3C22semidirect
48. C3×D4×Dic3C22semidirect
49. C3×#876C22semidirect
50. C3×C42×D3C22semidirect
51. C3×#869C22semidirect
52. #63982C22semidirect
53. #63982C22semidirect
55. #63981C22semidirect
56. #63980C22semidirect
58. #63978C22semidirect
60. #63976C22semidirect
61. #63975C22semidirect
63. Dic3×#67C22semidirect
66. #63969C22semidirect
67. #63966C22semidirect
68. #63964C22semidirect
69. #63964C22semidirect
70. #63962C22semidirect
71. #63962C22semidirect
72. #63961C22semidirect
74. #63959C22semidirect
77. #63956C22semidirect
78. #63956C22semidirect
79. #63955C22semidirect
80. #63955C22semidirect
81. C2×Dic32C22semidirect
84. #63952C22semidirect
87. #63905C22semidirect
88. #63904C22semidirect
89. #63899C22semidirect
90. #63895C22semidirect
92. #63888C22semidirect
93. #63887C22semidirect
95. #63879C22semidirect
96. #63877C22semidirect
97. #63867C22semidirect
98. #63858C22semidirect
101. #63851C22semidirect
102. #63850C22semidirect
103. #63848C22semidirect
104. #63847C22semidirect
105. #63846C22semidirect
106. #63839C22semidirect
107. #63837C22semidirect
108. #63836C22semidirect
118. #5720D3semidirect
119. #5716D3semidirect
246. C2×#237C2×D3semidirect
294. #939C2×D3semidirect
298. #938C2×D3semidirect
299. #938C2×D3semidirect
310. #937C2×D3semidirect
314. #936C2×D3semidirect
326. #935C2×D3semidirect
329. D4×Dic3C2×D3semidirect
330. D4×Dic3C2×D3semidirect
415. #876C2×D3semidirect
420. C42×D3C2×D3semidirect
422. #869C2×D3semidirect
1136. C32#3529semidirect
1248. C3#86248semidirect
1249. C3#87070semidirect

Maximal subgroups

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

subgroupindex
#105961912
C3×#57202
C3×#57162
#105952762
#105952642
#105952632
#105952622
#105952602
#105952572
#105952142
#105951872
#105951592
#105951552
#105951542
#105951382
#105951292
#105951162
#105939752
#105939572
#870703
#862483