Finite Group Databasebeta

← #11910388

Subgroups — #11910388

Order 1152.

2281 conjugacy classes of subgroups.

The subgroup lattice has 1271 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596057C211yesmaximal, characteristic, complemented
2C3×#5595C211yesmaximal, characteristic, complemented
3C3×#5594C211yesmaximal, characteristic, complemented
4#10595505C212yesmaximal, complemented
5#10595501C212yesmaximal, complemented
6#10595276C211yesmaximal, characteristic, complemented
7#10595259C211yesmaximal, characteristic, complemented
8#10595257C212yesmaximal, complemented
9#10595214C212yesmaximal, complemented
10#10595173C212yesmaximal, complemented
11#10595167C211yesmaximal, characteristic, complemented
12#10595160C211yesmaximal, characteristic, complemented
13#10595130C212yesmaximal, complemented
14#10594176C212yesmaximal, complemented
15#10594175C212yesmaximal, complemented
16#10594172C212yesmaximal, complemented
17#10594137C212yesmaximal, complemented
18#10594111C212yesmaximal, complemented
19#10594061C212yesmaximal, complemented
20#87085—31nomaximal
21#87070—31nomaximal
22C23×C3⋊Dic3C2211yescharacteristic, complemented
23C2×#3830C2211yescharacteristic
24C2×#3805C2212yes—
25C22×D3×Dic3C2211yescharacteristic, complemented
26C2×#3796C2211yescharacteristic, complemented
27C32×#120C2211yescharacteristic
28#64162C2211yescharacteristic, complemented
29#64148C2212yes—
30#64144C2211yescharacteristic
31D4×C3⋊Dic3C2212yes—
32#64095C2211yescharacteristic, complemented
33#64090C2212yescomplemented
34#64087C2212yescomplemented
35#64086C2211yescharacteristic, complemented
36C3×#953C2212yes—
37C3×#953C2212yescomplemented
38C3×#940C2211yescharacteristic
39C3×#939C2212yes—
40C3×#938C2212yes—
41C3×#937C2212yes—
42C3×#937C2211yescharacteristic
43C3×#936C2211yescharacteristic
44C3×#936C2212yes—
45C3×#935C2211yescharacteristic
46C3×#885C2212yes—
47C3×#885C2212yes—
48C3×#885C2212yes—
49C3×#884C2212yescomplemented
50C3×#883C2212yescomplemented
51C3×#879C2212yescomplemented
52#63982C2212yescomplemented
53#63982C2212yescomplemented
54#63980C2212yes—
55#63980C2212yes—
56#63979C2212yes—
57#63977C2211yescharacteristic, complemented
58#63976C2212yescomplemented
59#63975C2212yescomplemented
60#67⋊Dic3C2212yes—
61#67⋊Dic3C2212yes—
62#67⋊Dic3C2212yescomplemented
63#67⋊Dic3C2212yescomplemented
64#67⋊Dic3C2212yescomplemented
65#63971C2212yes—
66#63971C2212yescomplemented
67#63970C2212yes—
68#63970C2212yes—
69#63969C2212yes—
70#63969C2212yescomplemented
71#63969C2212yescomplemented
72#63966C2211yescharacteristic, complemented
73#63964C2212yescomplemented
74#63962C2212yes—
75#63962C2212yescomplemented
76#63958C2212yes—
77#63958C2212yescomplemented
78#63958C2212yescomplemented
79#63957C2211yescharacteristic, complemented
80#63957C2212yescomplemented
81#63956C2212yescomplemented
82#63956C2212yescomplemented
83#63956C2212yescomplemented
84#63906C2212yescomplemented
85#63905C2212yescomplemented
86#63902C2212yescomplemented
87#63896C2212yescomplemented
88#63893C2212yescomplemented
89#63891C2212yescomplemented
90#63888C2212yescomplemented
91#63887C2212yescomplemented
92#63885C2212yescomplemented
93C4×#624C2211yescharacteristic, complemented
94#63881C2212yescomplemented
95#63878C2212yescomplemented
96C4×D3×Dic3C2212yescomplemented
97#63869C2212yescomplemented
98#63867C2212yescomplemented
99#63867C2212yescomplemented
100#63866C2211yescharacteristic, complemented
101#63860C2211yescharacteristic, complemented
102#63859C2212yescomplemented
103#63858C2212yescomplemented
104#63856C2212yescomplemented
105#63854C2212yescomplemented
106#63852C2212yescomplemented
107#63843C2212yescomplemented
108#63839C2212yescomplemented
109C3×H(3,𝔽4)—31no—
110C3×#560—31no—
111#5720—31no—
112#5716—31no—
113#5712—32no—
114#5706—32no—
115#5684—32no—
116#5684—32no—
117#5684—32no—
118#5680—32no—
119#5680—32no—
120#5680—32no—
121#5672—31no—
122#5672—32no—
123#5668—31no—
124#5668—32no—
125#5667—32no—
126#5656—31no—
127#5651—31no—
128#5649—32no—
129#5621—32no—
130#5621—32no—
131#5620—32no—
132#5606—32no—
133#5600—32no—
134#5596—32no—
135#5595—32no—
136#5595—32no—
137#5595—31no—
138#5595—32no—
139#5595D311yescharacteristic, complemented
140#5594D311yescharacteristic, complemented
141#5586—31no—
142#5586—31no—
143#5586—32no—
144#5586—32no—
145#5586—32no—
146#5586—31no—
147#5586—61no—
148C24×C32C2311yescharacteristic
149C23×C3×D3C2311yescharacteristic
150C2×C32×D4C2311yescharacteristic
151C2×C32×D4C2312yes—
152C2×#638C2312yes—
153C2×#638C2311yescharacteristic
154C2×#638C2311yescharacteristic
155C22×C3⋊Dic3—42no—
156C22×C3⋊Dic3C2311yescharacteristic
157C22×C3⋊Dic3C2312yes—
158C22×C3⋊Dic3C2311yescharacteristic
159C22×C3⋊Dic3C2312yes—
160C22×C3⋊Dic3C2311yescharacteristic
161#3830—42no—
162C2×C4×C3⋊D3C2311yescharacteristic
163C2×#634C2311yescharacteristic
164C2×C3×#67C2312yes—
165C2×C3×#67C2312yes—
166C2×C3×#67C2312yes—
167C2×C3×#67C2312yes—
168C2×C3×#67C2312yes—
169C2×C3×#67C2312yes—
170C2×C3×#67C2312yes—
171C22×C3×Dic3C2311yescharacteristic
172C2×C3×D12C2311yescharacteristic
173C2×C3×C4×D3C2312yes—
174C2×C3×Dic6C2311yescharacteristic
175C2×C3×Dic6C2312yes—
176C2×#627C2312yes—
177C2×#626C2312yes—
178C2×#626C2312yes—
179C2×#625C2312yes—
180C2×#625C2312yes—
181C2×#624C2312yes—
182#3805—44no—
183C2×D3×Dic3—42no—
184C2×D3×Dic3C2312yes—
185C2×D3×Dic3C2312yes—
186C2×D3×Dic3C2312yes—
187C2×D3×Dic3C2312yes—
188#3796—42no—
189C32×C22⋊C4C2312yes—
190C32×C22⋊C4C2311yescharacteristic
191#3757C2311yescharacteristic
192#3757C2312yes—
193#3757C2312yes—
194#3752C2312yes—
195C4⋊(C3⋊Dic3)C2312yes—
196#3750C2312yes—
197#3750C2312yes—
198C4×C3⋊Dic3C2312yes—
199C3×#217C2312yes—
200C3×#217C2312yes—
201C3×#217C2312yes—
202C3×#217C2312yes—
203C3×#217C2312yes—
204C3×#217C2312yes—
205C3×#217C2311yescharacteristic
206C3×#217C2312yes—
207C3×#217C2311yescharacteristic
208C3×(C2×D3)⋊C4C2312yes—
209C3×(C2×D3)⋊C4C2312yes—
210C3×(C2×D3)⋊C4C2312yes—
211C3×(C2×D3)⋊C4C2312yes—
212C3×C4⋊Dic3C2312yes—
213C3×Dic3⋊C4C2312yes—
214C3×Dic3⋊C4C2312yes—
215C3×C4×Dic3C2311yescharacteristic
216C3×C4×Dic3C2312yes—
217C3×C4×Dic3C2311yescharacteristic
218#3724C2312yes—
219#3724C2312yes—
220#3724C2312yes—
221#3724C2312yes—
222Dic3⋊Dic3C2312yes—
223Dic3⋊Dic3C2312yes—
224Dic3⋊Dic3C2312yes—
225Dic3⋊Dic3C2312yes—
226Dic3⋊Dic3C2312yes—
227Dic3⋊Dic3C2312yes—
228Dic3⋊Dic3C2312yes—
229Dic3⋊Dic3C2312yes—
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#3529—91noSylow
241C23×Dic3—31no—
242C23×Dic3—31no—
243C23×Dic3—31no—
244C23×Dic3—61no—
245C2×#239—31no—
246C2×#237—31no—
247C2×#237—31no—
248C2×#237—32no—
249C2×#237—32no—
250C2×#237—31no—
251C2×#237—61no—
252C22×C4×D3—31no—
253C3×#127—31no—
254C3×#126—32no—
255C3×#124—31no—
256C3×#124—32no—
257C3×#124—32no—
258C3×#124—32no—
259C3×#124—32no—
260C3×#123—31no—
261C3×#123—32no—
262C3×#121—32no—
263C3×#121—32no—
264C3×#121—32no—
265C3×#120—21no—
266C3×#120—32no—
267C3×#120—32no—
268C3×#120—31no—
269C3×#120—32no—
270C3×#120C2×D311yescharacteristic
271C3×#120C2×D311yescharacteristic
272#953—31no—
273#953—31no—
274#953—32no—
275#953—31no—
276#953—61no—
277#953C2×D312yes—
278#953C2×D312yescomplemented
279#946—32no—
280#946—32no—
281#946—32no—
282Q8×Dic3—32no—
283#944—32no—
284#944—31no—
285#940—32no—
286#940—32no—
287#940C2×D311yescharacteristic
288#939—32no—
289#939—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#939—62no—
300#939C2×D312yes—
301#938—32no—
302#938—32no—
303#938—32no—
304#938—32no—
305#938—32no—
306#938C2×D312yes—
307#937—32no—
308#937C2×D311yescharacteristic
309#937C2×D312yes—
310#936—31no—
311#936C2×D311yescharacteristic
312#936C2×D312yes—
313#935—31no—
314#935—31no—
315#935—32no—
316#935—32no—
317#935—32no—
318#935—32no—
319#935—32no—
320#935—61no—
321#935C2×D311yescharacteristic
322D4×Dic3—32no—
323D4×Dic3—32no—
324D4×Dic3—32no—
325D4×Dic3—32no—
326D4×Dic3—32no—
327D4×Dic3—32no—
328D4×Dic3—32no—
329D4×Dic3—62no—
330#930—32no—
331#929—31no—
332#929—32no—
333#924—32no—
334#924—32no—
335C2×C4×Dic3—32no—
336#898—32no—
337#897—32no—
338#896—32no—
339#896—32no—
340#894—32no—
341#893—32no—
342#892—32no—
343#890—32no—
344#889—32no—
345#889—32no—
346#888—32no—
347#887—32no—
348#886—32no—
349#886—32no—
350#886—31no—
351#886—31no—
352#886—31no—
353#886—32no—
354#886—61no—
355#885—32no—
356#885C2×D312yes—
357#885C2×D312yes—
358#885C2×D312yes—
359#884—32no—
360#884—32no—
361#884—32no—
362#884—32no—
363#884—32no—
364#884—32no—
365#884—32no—
366#884C2×D312yescomplemented
367#883—32no—
368#883—32no—
369#883—32no—
370#883—32no—
371#883—32no—
372#883—32no—
373#883—32no—
374#883—32no—
375#883C2×D312yescomplemented
376#882—31no—
377#67⋊C4—32no—
378#67⋊C4—32no—
379#67⋊C4—32no—
380#67⋊C4—32no—
381#67⋊C4—32no—
382#67⋊C4—32no—
383#67⋊C4—32no—
384#67⋊C4—32no—
385#67⋊C4—32no—
386#67⋊C4—32no—
387#67⋊C4—62no—
388#879—32no—
389#879—32no—
390#879—32no—
391#879—32no—
392#879—32no—
393#879—32no—
394#879—32no—
395#879—32no—
396#879C2×D312yescomplemented
397#878—32no—
398#878—32no—
399#878—32no—
400#878—32no—
401#878—32no—
402#878—32no—
403#878—32no—
404#878—32no—
405#878—32no—
406#878—32no—
407#878—62no—
408#877—31no—
409#877—31no—
410#877—31no—
411#877—31no—
412#877—32no—
413#877—32no—
414#877—32no—
415#877—61no—
416#876—32no—
417#875—31no—
418#875—32no—
419C42×D3—32no—
420C42×D3—31no—
421C42×D3—31no—
422#870—32no—
423#870—32no—
424#870—32no—
425#869—31no—
426C23×C32—42no—
427C23×C32—41no—
428C23×C32C2411yescharacteristic
429C23×C32C2411yescharacteristic
430C23×C32C2412yes—
431C22×C3⋊D3C2411yescharacteristic
432C22×C3×D3—42no—
433C22×C3×D3—41no—
434C22×C3×D3C2412yes—
435C22×C3×D3C2412yes—
436C32×D4—41no—
437C32×D4—42no—
438C2×C32×C4C2411yescharacteristic
439C2×C32×C4C2412yes—
440#638—41no—
441#638—41no—
442#638—42no—
443C2×C3⋊Dic3—22no—
444C2×C3⋊Dic3—22no—
445C2×C3⋊Dic3—24no—
446C2×C3⋊Dic3—42no—
447C2×C3⋊Dic3—41no—
448C2×C3⋊Dic3C2412yes—
449C2×C3⋊Dic3C2411yescharacteristic
450C2×C3⋊Dic3C2412yes—
451C2×C3⋊Dic3C2411yescharacteristic
452C2×C3⋊Dic3C2411yescharacteristic
453C4×C3⋊D3—22no—
454#634—41no—
455C3×#67—42no—
456C3×#67—42no—
457C3×#67—42no—
458C3×#67—42no—
459C3×#67—42no—
460C3×#67—42no—
461C3×#67—42no—
462C2×C3×Dic3—41no—
463C2×C3×Dic3C2412yes—
464C2×C3×Dic3C2412yes—
465C2×C3×Dic3C2412yes—
466C2×C3×Dic3C2412yes—
467C2×C3×Dic3C2412yes—
468C2×C3×Dic3C2412yes—
469C3×D12—41no—
470C3×C4×D3—42no—
471C3×Dic6—41no—
472C3×Dic6—42no—
473#627—42no—
474#626—42no—
475#626—42no—
476#625—42no—
477#625—42no—
478#624—42no—
479D3×Dic3—24no—
480D3×Dic3—24no—
481D3×Dic3—42no—
482D3×Dic3—42no—
483#563—91no—
484#563—92no—
485#562—92no—
486#562—92no—
487#562—92no—
488H(3,𝔽4)—31no—
489#560—31no—
490#560—92no—
491#560—92no—
492#560—91no—
493#532—92no—
494#532—91no—
495#529—92no—
496#529—92no—
497#529—92no—
498#525—92no—
499#525—92no—
500#525—91no—
501#525—91no—
502C24×C3—21no—
503C24×C3—31no—
504C24×C3C22×D311yescharacteristic
505C24×C3C22×D311yescharacteristic
506C23×D3C22×D311yescharacteristic
507C2×C3×Q8—31no—
508C2×C3×Q8—32no—
509C2×C3×D4—22no—
510C2×C3×D4—21no—
511C2×C3×D4—32no—
512C2×C3×D4—32no—
513C2×C3×D4—32no—
514C2×C3×D4—32no—
515C2×C3×D4—32no—
516C2×C3×D4—32no—
517C2×C3×D4—32no—
518C2×C3×D4—31no—
519C2×C3×D4C22×D312yes—
520C2×C3×D4C22×D312yes—
521C2×C3×D4C22×D311yescharacteristic
522C2×C3×D4C22×D311yescharacteristic
523C22×C3×C4—31no—
524C22×C3×C4—32no—
525C2×#67—32no—
526C2×#67—32no—
527C2×#67—31no—
528C2×#67—31no—
529C2×#67—31no—
530C2×#67—31no—
531C2×#67—32no—
532C2×#67—32no—
533C2×#67—32no—
534C2×#67—32no—
535C2×#67—32no—
536C2×#67—32no—
537C2×#67—62no—
538C2×#67—61no—
539C2×#67—61no—
540C2×#67C22×D312yes—
541C2×#67C22×D312yes—
542C2×#67C22×D312yes—
543C2×#67C22×D312yes—
544C2×#67C22×D312yes—
545C2×#67C22×D312yes—
546C2×#67C22×D312yes—
547C22×Dic3—31no—
548C22×Dic3—31no—
549C22×Dic3—31no—
550C22×Dic3—32no—
551C22×Dic3—32no—
552C22×Dic3—31no—
553C22×Dic3—32no—
554C22×Dic3—32no—
555C22×Dic3—31no—
556C22×Dic3—31no—
557C22×Dic3—32no—
558C22×Dic3—32no—
559C22×Dic3—32no—
560C22×Dic3—32no—
561C22×Dic3—61no—
562C22×Dic3—62no—
563C22×Dic3—62no—
564C22×Dic3—61no—
565C22×Dic3—61no—
566C22×Dic3—122no—
567C22×Dic3—122no—
568C22×Dic3—122no—
569C22×Dic3—124no—
570C22×Dic3C22×D311yescharacteristic
571#239—122no—
572#237—122no—
573#237—124no—
574#237—124no—
575#237—122no—
576#237—122no—
577#237—124no—
578C2×D12—32no—
579C2×D12—32no—
580C2×D12C22×D311yescharacteristic
581C2×C4×D3—32no—
582C2×C4×D3—32no—
583C2×C4×D3—31no—
584C2×C4×D3—31no—
585C2×C4×D3—32no—
586C2×C4×D3—32no—
587C2×C4×D3—32no—
588C2×C4×D3—32no—
589C2×C4×D3—61no—
590C2×C4×D3—122no—
591C2×C4×D3C22×D312yes—
592C2×Dic6—31no—
593C2×Dic6—31no—
594C2×Dic6—32no—
595C2×Dic6—32no—
596C2×Dic6—61no—
597C2×Dic6C22×D311yescharacteristic
598C2×Dic6C22×D312yes—
599C3×C4⋊C4—32no—
600C3×C4⋊C4—32no—
601C3×C4⋊C4—32no—
602C3×C22⋊C4—21no—
603C3×C22⋊C4—22no—
604C3×C22⋊C4—31no—
605C3×C22⋊C4—32no—
606C3×C22⋊C4—31no—
607C3×C22⋊C4—32no—
608C3×C22⋊C4—32no—
609C3×C22⋊C4—32no—
610C3×C22⋊C4—32no—
611C3×C22⋊C4—32no—
612C3×C22⋊C4—32no—
613C3×C22⋊C4—32no—
614C3×C22⋊C4—32no—
615C3×C22⋊C4—32no—
616C3×C22⋊C4—32no—
617C3×C22⋊C4C22×D311yescharacteristic
618C3×C22⋊C4C22×D311yescharacteristic
619C3×C22⋊C4C22×D312yes—
620C3×C22⋊C4C22×D312yes—
621C3×C42—31no—
622C3×C42—32no—
623C3×C42—31no—
624#217—31no—
625#217—31no—
626#217—32no—
627#217—32no—
628#217—32no—
629#217—32no—
630#217—32no—
631#217—32no—
632#217—32no—
633#217—32no—
634#217—32no—
635#217—32no—
636#217—61no—
637#217—62no—
638#217—62no—
639#217C22×D311yescharacteristic
640#217C22×D312yes—
641#217C22×D312yes—
642#217C22×D311yescharacteristic
643#217C22×D312yes—
644#217C22×D312yes—
645#217C22×D312yes—
646#217C22×D312yes—
647#217C22×D312yes—
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—62no—
659(C2×D3)⋊C4C22×D312yes—
660(C2×D3)⋊C4C22×D312yes—
661(C2×D3)⋊C4C22×D312yes—
662(C2×D3)⋊C4C22×D312yes—
663C4⋊Dic3—32no—
664C4⋊Dic3—32no—
665C4⋊Dic3—32no—
666C4⋊Dic3—32no—
667C4⋊Dic3—32no—
668C4⋊Dic3—32no—
669C4⋊Dic3—32no—
670C4⋊Dic3—32no—
671C4⋊Dic3—32no—
672C4⋊Dic3—32no—
673C4⋊Dic3—62no—
674C4⋊Dic3C22×D312yes—
675Dic3⋊C4—32no—
676Dic3⋊C4—32no—
677Dic3⋊C4—32no—
678Dic3⋊C4—32no—
679Dic3⋊C4—32no—
680Dic3⋊C4—32no—
681Dic3⋊C4—32no—
682Dic3⋊C4—32no—
683Dic3⋊C4—32no—
684Dic3⋊C4—32no—
685Dic3⋊C4—32no—
686Dic3⋊C4—32no—
687Dic3⋊C4—32no—
688Dic3⋊C4—32no—
689Dic3⋊C4—32no—
690Dic3⋊C4—32no—
691Dic3⋊C4—32no—
692Dic3⋊C4—32no—
693Dic3⋊C4—32no—
694Dic3⋊C4—32no—
695Dic3⋊C4—62no—
696Dic3⋊C4—62no—
697Dic3⋊C4C22×D312yes—
698Dic3⋊C4C22×D312yes—
699C4×Dic3—32no—
700C4×Dic3—32no—
701C4×Dic3—32no—
702C4×Dic3—32no—
703C4×Dic3—32no—
704C4×Dic3—32no—
705C4×Dic3—32no—
706C4×Dic3—32no—
707C4×Dic3—62no—
708C4×Dic3C22×D311yescharacteristic
709C4×Dic3C22×D311yescharacteristic
710C4×Dic3C22×D312yes—
711C22×C32—21no—
712C22×C32—22no—
713C22×C32—21no—
714C22×C32—22no—
715C22×C32—22no—
716C22×C32—22no—
717C22×C32—22no—
718C22×C32—44no—
719C22×C32C2511yescharacteristic
720C2×C3⋊D3—21no—
721C2×C3⋊D3—22no—
722C2×C3×D3—22no—
723C2×C3×D3—22no—
724C2×C3×D3—22no—
725C2×C3×D3—22no—
726C2×C3×D3—22no—
727C2×C3×D3—22no—
728C2×C3×D3—44no—
729C32×C4—21no—
730C32×C4—22no—
731C3⋊Dic3—21no—
732C3⋊Dic3—21no—
733C3⋊Dic3—22no—
734C3⋊Dic3—22no—
735C3⋊Dic3H(5,𝔽2)12yes—
736C3×Dic3—22no—
737C3×Dic3—22no—
738C3×Dic3—22no—
739C3×Dic3—22no—
740C3×Dic3—22no—
741C3×Dic3—22no—
742C2×#41—92no—
743C2×#41—91no—
744C2×#41—91no—
745C23×C4—91no—
746C23×C4—91no—
747C4⋊Q8—91no—
748C4⋊Q8—92no—
749#127—31no—
750#127—92no—
751#126—32no—
752#126—92no—
753#126—92no—
754#126—92no—
755#126—92no—
756#126—92no—
757#125—92no—
758#125—92no—
759#125—92no—
760#124—32no—
761#124—31no—
762#124—32no—
763#124—32no—
764#124—32no—
765#124—92no—
766#124—91no—
767#123—31no—
768#123—32no—
769#123—92no—
770#123—92no—
771#123—92no—
772#123—91no—
773#123—92no—
774#123—92no—
775#123—92no—
776#123—92no—
777#123—92no—
778#123—92no—
779#123—91no—
780#123—91no—
781C22⋊Q8—92no—
782C22⋊Q8—92no—
783C22⋊Q8—92no—
784C22⋊Q8—92no—
785C22⋊Q8—92no—
786C22⋊Q8—92no—
787C22⋊Q8—92no—
788C22⋊Q8—92no—
789C22⋊Q8—92no—
790#121—32no—
791#121—32no—
792#121—32no—
793#121—92no—
794#121—92no—
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#121—92no—
805#120—32no—
806#120—32no—
807#120—31no—
808#120—32no—
809#120—91no—
810#120—92no—
811#120—91no—
812#120D3211yescharacteristic
813C4×Q8—92no—
814C4×D4—92no—
815C4×D4—92no—
816C4×D4—92no—
817C4×D4—92no—
818C4×D4—92no—
819C4×D4—92no—
820C4×D4—92no—
821C4×D4—92no—
822C4×D4—92no—
823#117—92no—
824#117—91no—
825#117—92no—
826#117—91no—
827C2×C42—91no—
828C2×C42—92no—
829C23×C3—21no—
830C23×C3—22no—
831C23×C3—21no—
832C23×C3—32no—
833C23×C3—32no—
834C23×C3—41no—
835C23×C3—41no—
836C23×C3—42no—
837C23×C3—42no—
838C23×C3—42no—
839C23×C3—44no—
840C23×C3—121no—
841C23×C3—122no—
842C23×C3C23×D311yescharacteristic
843C23×C3C23×D311yescharacteristic
844C23×C3C23×D312yes—
845C23×C3C23×D312yes—
846C23×C3C23×D311yescharacteristic
847C23×C3C23×D311yescharacteristic
848C22×D3—31no—
849C22×D3—31no—
850C22×D3—41no—
851C22×D3—42no—
852C22×D3—61no—
853C22×D3C23×D312yes—
854C22×D3C23×D312yes—
855C3×Q8—121no—
856C3×Q8—122no—
857C3×D4—41no—
858C3×D4—41no—
859C3×D4—42no—
860C3×D4—42no—
861C3×D4—42no—
862C3×D4—44no—
863C3×D4—121no—
864C3×D4—122no—
865C3×D4—122no—
866C3×D4—122no—
867C3×D4—122no—
868C3×D4—122no—
869C3×D4—122no—
870C3×D4—122no—
871C2×C3×C4—22no—
872C2×C3×C4—21no—
873C2×C3×C4—32no—
874C2×C3×C4—32no—
875C2×C3×C4—32no—
876C2×C3×C4—32no—
877C2×C3×C4—32no—
878C2×C3×C4—32no—
879C2×C3×C4—122no—
880C2×C3×C4—121no—
881C2×C3×C4C23×D312yes—
882C2×C3×C4C23×D312yes—
883C2×C3×C4C23×D311yescharacteristic
884C2×C3×C4C23×D311yescharacteristic
885#67—42no—
886#67—42no—
887#67—42no—
888#67—42no—
889#67—42no—
890#67—42no—
891#67—42no—
892#67—122no—
893#67—122no—
894#67—122no—
895#67—122no—
896#67—122no—
897#67—122no—
898#67—121no—
899#67—121no—
900#67—121no—
901#67—121no—
902#67—122no—
903#67—122no—
904#67—122no—
905#67—122no—
906#67—124no—
907C2×Dic3—31no—
908C2×Dic3—31no—
909C2×Dic3—32no—
910C2×Dic3—32no—
911C2×Dic3—31no—
912C2×Dic3—31no—
913C2×Dic3—32no—
914C2×Dic3—32no—
915C2×Dic3—31no—
916C2×Dic3—31no—
917C2×Dic3—41no—
918C2×Dic3—61no—
919C2×Dic3—61no—
920C2×Dic3—62no—
921C2×Dic3—62no—
922C2×Dic3—61no—
923C2×Dic3—64no—
924C2×Dic3—64no—
925C2×Dic3—62no—
926C2×Dic3—62no—
927C2×Dic3—62no—
928C2×Dic3—62no—
929C2×Dic3—64no—
930C2×Dic3—64no—
931C2×Dic3—64no—
932C2×Dic3—122no—
933C2×Dic3—124no—
934C2×Dic3—122no—
935C2×Dic3—122no—
936C2×Dic3—122no—
937C2×Dic3—122no—
938C2×Dic3—121no—
939C2×Dic3—121no—
940C2×Dic3—124no—
941C2×Dic3—122no—
942C2×Dic3C23×D312yes—
943C2×Dic3C23×D312yes—
944C2×Dic3C23×D312yes—
945C2×Dic3C23×D312yes—
946C2×Dic3C23×D312yes—
947C2×Dic3C23×D312yes—
948D12—41no—
949D12—122no—
950D12—122no—
951C4×D3—42no—
952C4×D3—62no—
953C4×D3—62no—
954C4×D3—64no—
955C4×D3—64no—
956C4×D3—122no—
957C4×D3—122no—
958C4×D3—122no—
959C4×D3—122no—
960C4×D3—122no—
961Dic6—42no—
962Dic6—41no—
963Dic6—122no—
964Dic6—122no—
965Dic6—121no—
966Dic6—121no—
967Dic6—122no—
968C2×C32—41no—
969C2×C32—42no—
970C2×C32—41no—
971C2×C32C2×H(5,𝔽2)11yescharacteristic
972C2×C32#58512yes—
973C3⋊D3—41no—
974C3×D3—42no—
975C3×D3—42no—
976C24—31no—
977C24C2×D3211yescharacteristic
978#41—362no—
979#41—364no—
980#41—362no—
981C2×Q8—32no—
982C2×Q8—31no—
983C2×Q8—92no—
984C2×Q8—91no—
985C2×D4—32no—
986C2×D4—32no—
987C2×D4—32no—
988C2×D4—32no—
989C2×D4—32no—
990C2×D4—32no—
991C2×D4—32no—
992C2×D4—31no—
993C2×D4—92no—
994C2×D4—92no—
995C2×D4—92no—
996C2×D4—92no—
997C2×D4—92no—
998C2×D4—91no—
999C2×D4—91no—
1000C2×D4C2×D3212yes—
1001C2×D4C2×D3211yescharacteristic
1002C22×C4—31no—
1003C22×C4—32no—
1004C22×C4—92no—
1005C22×C4—92no—
1006C22×C4—92no—
1007C22×C4—92no—
1008C22×C4—92no—
1009C22×C4—91no—
1010C22×C4—91no—
1011C22×C4—92no—
1012C22×C4—91no—
1013C22×C4—92no—
1014C22×C4—91no—
1015C22×C4—362no—
1016C22×C4—362no—
1017C4⋊C4—32no—
1018C4⋊C4—32no—
1019C4⋊C4—32no—
1020C4⋊C4—92no—
1021C4⋊C4—92no—
1022C4⋊C4—92no—
1023C4⋊C4—92no—
1024C4⋊C4—92no—
1025C4⋊C4—92no—
1026C4⋊C4—92no—
1027C4⋊C4—92no—
1028C4⋊C4—92no—
1029C4⋊C4—92no—
1030C4⋊C4—92no—
1031C4⋊C4—92no—
1032C4⋊C4—92no—
1033C4⋊C4—92no—
1034C4⋊C4—92no—
1035C22⋊C4—32no—
1036C22⋊C4—31no—
1037C22⋊C4—32no—
1038C22⋊C4—31no—
1039C22⋊C4—32no—
1040C22⋊C4—32no—
1041C22⋊C4—32no—
1042C22⋊C4—32no—
1043C22⋊C4—32no—
1044C22⋊C4—32no—
1045C22⋊C4—32no—
1046C22⋊C4—32no—
1047C22⋊C4—32no—
1048C22⋊C4—92no—
1049C22⋊C4—92no—
1050C22⋊C4—92no—
1051C22⋊C4—92no—
1052C22⋊C4—92no—
1053C22⋊C4—92no—
1054C22⋊C4—92no—
1055C22⋊C4—91no—
1056C22⋊C4—92no—
1057C22⋊C4—92no—
1058C22⋊C4—92no—
1059C22⋊C4C2×D3211yescharacteristic
1060C22⋊C4C2×D3212yes—
1061C42—31no—
1062C42—32no—
1063C42—31no—
1064C42—92no—
1065C42—92no—
1066C42—92no—
1067C42—92no—
1068C22×C3—22no—
1069C22×C3—24no—
1070C22×C3—21no—
1071C22×C3—22no—
1072C22×C3—22no—
1073C22×C3—21no—
1074C22×C3—21no—
1075C22×C3—21no—
1076C22×C3—22no—
1077C22×C3—22no—
1078C22×C3—22no—
1079C22×C3—22no—
1080C22×C3—22no—
1081C22×C3—22no—
1082C22×C3—22no—
1083C22×C3—22no—
1084C22×C3—21no—
1085C22×C3—42no—
1086C22×C3—42no—
1087C22×C3—42no—
1088C22×C3—41no—
1089C22×C3—42no—
1090C22×C3—48no—
1091C22×C3—44no—
1092C22×C3—44no—
1093C22×C3—62no—
1094C22×C3—62no—
1095C22×C3—62no—
1096C22×C3—62no—
1097C22×C3—62no—
1098C22×C3—62no—
1099C22×C3—124no—
1100C22×C3C24×D311yescharacteristic
1101C22×C3C24×D311yescharacteristic
1102C2×D3—22no—
1103C2×D3—22no—
1104C2×D3—22no—
1105C2×D3—22no—
1106C2×D3—22no—
1107C2×D3—22no—
1108C2×D3—44no—
1109C2×D3—61no—
1110C2×D3—61no—
1111C2×D3—62no—
1112C2×D3—62no—
1113C2×D3—121no—
1114C2×D3—122no—
1115C3×C4—21no—
1116C3×C4—21no—
1117C3×C4—22no—
1118C3×C4—22no—
1119C3×C4—41no—
1120C3×C4—42no—
1121C3×C4—62no—
1122C3×C4—62no—
1123C3×C4—62no—
1124C3×C4—62no—
1125C3×C4—62no—
1126C3×C4—62no—
1127Dic3—22no—
1128Dic3—22no—
1129Dic3—22no—
1130Dic3—22no—
1131Dic3—22no—
1132Dic3—22no—
1133Dic3—32no—
1134Dic3—32no—
1135Dic3—62no—
1136Dic3—62no—
1137Dic3—61no—
1138Dic3—61no—
1139Dic3—61no—
1140Dic3—62no—
1141Dic3—61no—
1142Dic3—62no—
1143Dic3—62no—
1144Dic3—62no—
1145Dic3—121no—
1146Dic3—122no—
1147Dic3—122no—
1148C32#352911yescharacteristic, complemented, Sylow
1149C23—32no—
1150C23—32no—
1151C23—41no—
1152C23—42no—
1153C23—91no—
1154C23—121no—
1155C23—122no—
1156C23C22×D3211yescharacteristic
1157C23C22×D3211yescharacteristic
1158C23C22×D3212yes—
1159Q8—121no—
1160Q8—122no—
1161Q8—361no—
1162Q8—362no—
1163D4—41no—
1164D4—42no—
1165D4—121no—
1166D4—122no—
1167D4—122no—
1168D4—122no—
1169D4—122no—
1170D4—122no—
1171D4—122no—
1172D4—122no—
1173D4—362no—
1174D4—362no—
1175D4—361no—
1176D4—361no—
1177D4—362no—
1178D4—362no—
1179D4—362no—
1180C2×C4—32no—
1181C2×C4—32no—
1182C2×C4—32no—
1183C2×C4—32no—
1184C2×C4—32no—
1185C2×C4—32no—
1186C2×C4—91no—
1187C2×C4—92no—
1188C2×C4—91no—
1189C2×C4—92no—
1190C2×C4—91no—
1191C2×C4—122no—
1192C2×C4—121no—
1193C2×C4—182no—
1194C2×C4—184no—
1195C2×C4—184no—
1196C2×C4—182no—
1197C2×C4—182no—
1198C2×C4—184no—
1199C2×C4—362no—
1200C2×C4—362no—
1201C2×C4—362no—
1202C2×C4—362no—
1203C2×C4—361no—
1204C2×C4C22×D3211yescharacteristic
1205C2×C4C22×D3212yes—
1206C2×C3—21no—
1207C2×C3—22no—
1208C2×C3—42no—
1209C2×C3—44no—
1210C2×C3—42no—
1211C2×C3—41no—
1212C2×C3—41no—
1213C2×C3—41no—
1214C2×C3—42no—
1215C2×C3—41no—
1216C2×C3—81no—
1217C2×C3—122no—
1218C2×C3—122no—
1219C2×C3D3×H(5,𝔽2)11yescharacteristic
1220C2×C3D3×H(5,𝔽2)11yescharacteristic
1221C2×C3#596612yes—
1222C2×C3#596612yes—
1223D3—42no—
1224D3—42no—
1225D3—121no—
1226D3—121no—
1227D3—241no—
1228C22—21no—
1229C22—21no—
1230C22—22no—
1231C22—22no—
1232C22—22no—
1233C22—22no—
1234C22—22no—
1235C22—44no—
1236C22—62no—
1237C22—62no—
1238C22—62no—
1239C22—62no—
1240C22—62no—
1241C22—62no—
1242C22—124no—
1243C22—181no—
1244C22—182no—
1245C22C23×D3211yescharacteristic
1246C4—21no—
1247C4—22no—
1248C4—62no—
1249C4—62no—
1250C4—62no—
1251C4—62no—
1252C4—62no—
1253C4—62no—
1254C4—92no—
1255C4—181no—
1256C4—181no—
1257C4—182no—
1258C4—182no—
1259C3—21no—
1260C3#8707011yescharacteristic, complemented
1261C3#8708511yescharacteristic, complemented
1262C2—41no—
1263C2—42no—
1264C2—41no—
1265C2—122no—
1266C2—122no—
1267C2—361no—
1268C2#1059667511yescharacteristic
1269C2#1059667912yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×#120C22
hypercenter#120D32
hypocenterC32#3529
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. #10596057C2semidirect
2. C3×#5595C2semidirect
3. C3×#5594C2semidirect
4. #10595505C2semidirect
5. #10595501C2semidirect
6. #10595276C2semidirect
7. #10595259C2semidirect
8. #10595257C2semidirect
9. #10595214C2semidirect
10. #10595173C2semidirect
11. #10595167C2semidirect
12. #10595160C2semidirect
13. #10595130C2semidirect
14. #10594176C2semidirect
15. #10594175C2semidirect
16. #10594172C2semidirect
17. #10594137C2semidirect
18. #10594111C2semidirect
19. #10594061C2semidirect
22. C23×C3⋊Dic3C22semidirect
25. C22×D3×Dic3C22semidirect
26. C2×#3796C22semidirect
28. #64162C22semidirect
32. #64095C22semidirect
33. #64090C22semidirect
34. #64087C22semidirect
35. #64086C22semidirect
37. C3×#953C22semidirect
49. C3×#884C22semidirect
50. C3×#883C22semidirect
51. C3×#879C22semidirect
52. #63982C22semidirect
53. #63982C22semidirect
57. #63977C22semidirect
58. #63976C22semidirect
59. #63975C22semidirect
62. #67⋊Dic3C22semidirect
63. #67⋊Dic3C22semidirect
64. #67⋊Dic3C22semidirect
66. #63971C22semidirect
70. #63969C22semidirect
71. #63969C22semidirect
72. #63966C22semidirect
73. #63964C22semidirect
75. #63962C22semidirect
77. #63958C22semidirect
78. #63958C22semidirect
79. #63957C22semidirect
80. #63957C22semidirect
81. #63956C22semidirect
82. #63956C22semidirect
83. #63956C22semidirect
84. #63906C22semidirect
85. #63905C22semidirect
86. #63902C22semidirect
87. #63896C22semidirect
88. #63893C22semidirect
89. #63891C22semidirect
90. #63888C22semidirect
91. #63887C22semidirect
92. #63885C22semidirect
93. C4×#624C22semidirect
94. #63881C22semidirect
95. #63878C22semidirect
96. C4×D3×Dic3C22semidirect
97. #63869C22semidirect
98. #63867C22semidirect
99. #63867C22semidirect
100. #63866C22semidirect
101. #63860C22semidirect
102. #63859C22semidirect
103. #63858C22semidirect
104. #63856C22semidirect
105. #63854C22semidirect
106. #63852C22semidirect
107. #63843C22semidirect
108. #63839C22semidirect
139. #5595D3semidirect
140. #5594D3semidirect
278. #953C2×D3semidirect
366. #884C2×D3semidirect
375. #883C2×D3semidirect
396. #879C2×D3semidirect
1148. C32#3529semidirect
1260. C3#87070semidirect
1261. C3#87085semidirect

Maximal subgroups

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

subgroupindex
#105960572
C3×#55952
C3×#55942
#105955052
#105955012
#105952762
#105952592
#105952572
#105952142
#105951732
#105951672
#105951602
#105951302
#105941762
#105941752
#105941722
#105941372
#105941112
#105940612
#870853
#870703