Finite Group Databasebeta

← #11910387

Subgroups — #11910387

Order 1152.

2246 conjugacy classes of subgroups.

The subgroup lattice has 1260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596065C211yesmaximal, characteristic, complemented
2C3×#5595C211yesmaximal, characteristic, complemented
3C3×#5586C211yesmaximal, characteristic, complemented
4#10595505C212yesmaximal, complemented
5#10595498C212yesmaximal, complemented
6#10595275C211yesmaximal, characteristic, complemented
7#10595266C211yesmaximal, characteristic, complemented
8#10595264C212yesmaximal, complemented
9#10595213C212yesmaximal, complemented
10#10595172C212yesmaximal, complemented
11#10595159C211yesmaximal, characteristic, complemented
12#10595152C211yesmaximal, characteristic, complemented
13#10595138C212yesmaximal, complemented
14#10594235C212yesmaximal, complemented
15#10594174C212yesmaximal, complemented
16#10594089C212yesmaximal, complemented
17#10594088C212yesmaximal, complemented
18#10594058C212yesmaximal, complemented
19#10594034C212yesmaximal, complemented
20#87070—31nomaximal
21#86048—31nomaximal
22C23×C3×Dic3C2211yescharacteristic, complemented
23C2×C3×#237C2211yescharacteristic
24C22×#624C2211yescharacteristic, complemented
25C2×#3804C2212yes—
26C2×#3795C2211yescharacteristic, complemented
27C32×#120C2211yescharacteristic
28#64162C2212yes—
29#64146C2212yes—
30#64146C2211yescharacteristic
31#64145C2211yescharacteristic
32#64145C2212yes—
33#64094C2212yes—
34#64094C2212yes—
35#64094C2212yes—
36C3×#953C2211yescharacteristic, complemented
37C3×#953C2212yescomplemented
38C3×#940C2211yescharacteristic
39C3×#939C2212yes—
40C3×#939C2212yes—
41C3×#938C2212yes—
42C3×#935C2211yescharacteristic
43C3×#935C2211yescharacteristic
44C3×D4×Dic3C2212yes—
45C3×#886C2211yescharacteristic, complemented
46C3×#884C2212yescomplemented
47C3×#883C2212yescomplemented
48C3×#67⋊C4C2212yescomplemented
49C3×#879C2212yescomplemented
50C3×#878C2212yescomplemented
51C3×#877C2211yescharacteristic, complemented
52#63981C2212yescomplemented
53#63981C2211yescharacteristic, complemented
54#63979C2212yes—
55#63978C2212yes—
56#63978C2212yes—
57#63975C2212yes—
58Dic3×#67C2212yescomplemented
59Dic3×#67C2212yescomplemented
60Dic3×#67C2212yescomplemented
61#63971C2212yes—
62#63971C2212yes—
63#63970C2212yescomplemented
64#63970C2212yescomplemented
65#63970C2212yescomplemented
66#63969C2212yescomplemented
67#63969C2212yescomplemented
68#63969C2212yescomplemented
69#63966C2212yes—
70#63964C2212yescomplemented
71#63964C2212yescomplemented
72#63964C2212yescomplemented
73#63961C2211yescharacteristic, complemented
74#63961C2212yescomplemented
75#63958C2212yes—
76#63958C2212yes—
77#63956C2212yescomplemented
78#63956C2212yescomplemented
79#63956C2212yescomplemented
80#63955C2212yescomplemented
81#63955C2211yescharacteristic, complemented
82#63952C2212yes—
83#63952C2212yes—
84#63915C2212yescomplemented
85#63906C2212yescomplemented
86#63904C2212yescomplemented
87#63896C2212yescomplemented
88#63896C2212yescomplemented
89#63895C2212yescomplemented
90#63890C2212yescomplemented
91#63888C2212yescomplemented
92#63886C2212yescomplemented
93#63880C2212yescomplemented
94C4×D3×Dic3C2212yescomplemented
95C4×D3×Dic3C2211yescharacteristic, complemented
96#63872C2212yescomplemented
97#63870C2212yescomplemented
98#63870C2212yescomplemented
99#63868C2212yescomplemented
100#63866C2211yescharacteristic, complemented
101#63863C2211yescharacteristic, complemented
102#63857C2212yescomplemented
103#63854C2212yescomplemented
104#63850C2212yescomplemented
105#63848C2212yescomplemented
106#63844C2212yescomplemented
107#63840C2212yescomplemented
108#63836C2212yescomplemented
109C3×#560—31no—
110C3×#525—31no—
111#5832—31no—
112#5828—31no—
113#5791—32no—
114#5720—31no—
115#5716—31no—
116#5712—32no—
117#5706—32no—
118#5667—32no—
119#5667—32no—
120#5666—31no—
121#5656—31no—
122#5651—31no—
123#5651—31no—
124#5649—32no—
125#5647—32no—
126#5646—32no—
127#5621—32no—
128#5621—32no—
129#5621—32no—
130#5620—32no—
131#5620—32no—
132#5606—32no—
133#5600—32no—
134#5596—32no—
135#5595—32no—
136#5595—32no—
137#5595D311yescharacteristic, complemented
138#5594—31no—
139#5594—31no—
140#5594—61no—
141#5586—32no—
142#5586D311yescharacteristic, complemented
143#5557—32no—
144#5548—32no—
145#5547—32no—
146#5538—32no—
147#5528—32no—
148C24×C32C2311yescharacteristic
149C23×C3⋊D3C2311yescharacteristic
150C2×C32×D4C2312yes—
151C2×C32×D4C2311yescharacteristic
152C2×#638C2312yes—
153C2×#638C2312yes—
154C2×#638C2312yes—
155C2×#634C2311yescharacteristic
156C2×#634C2312yes—
157C2×C3×#67C2312yes—
158C2×C3×#67C2312yes—
159C2×C3×#67C2312yes—
160C2×C3×#67C2312yes—
161C2×C3×#67C2311yescharacteristic
162C2×C3×#67C2312yes—
163C2×C3×#67C2311yescharacteristic
164C22×C3×Dic3—42no—
165C22×C3×Dic3C2311yescharacteristic
166C22×C3×Dic3C2312yes—
167C22×C3×Dic3C2311yescharacteristic
168C22×C3×Dic3C2312yes—
169C22×C3×Dic3C2311yescharacteristic
170C22×C3×Dic3C2311yescharacteristic
171C3×#237—42no—
172C2×C3×D12C2311yescharacteristic
173C2×C3×C4×D3C2311yescharacteristic
174C2×C3×C4×D3C2312yes—
175C2×C3×Dic6C2311yescharacteristic
176C2×#627C2312yes—
177C2×#626C2312yes—
178C2×#626C2312yes—
179C2×#626C2312yes—
180C2×#625C2312yes—
181C2×#624—42no—
182C2×#624C2312yes—
183C2×#624C2312yes—
184#3804—44no—
185C2×D3×Dic3C2312yes—
186C2×D3×Dic3C2312yes—
187C2×D3×Dic3C2312yes—
188#3795—42no—
189C32×C22⋊C4C2311yescharacteristic
190C32×C22⋊C4C2312yes—
191#3757C2312yes—
192#3757C2312yes—
193#3757C2312yes—
194#3757C2311yescharacteristic
195#3757C2312yes—
196#3752C2312yes—
197#3752C2312yes—
198#3752C2312yes—
199C4×C3⋊Dic3C2311yescharacteristic
200C4×C3⋊Dic3C2312yes—
201C3×#217C2311yescharacteristic
202C3×#217C2312yes—
203C3×#217C2312yes—
204C3×#217C2312yes—
205C3×#217C2312yes—
206C3×#217C2312yes—
207C3×#217C2311yescharacteristic
208C3×(C2×D3)⋊C4C2312yes—
209C3×(C2×D3)⋊C4C2312yes—
210C3×C4⋊Dic3C2312yes—
211C3×C4⋊Dic3C2312yes—
212C3×Dic3⋊C4C2312yes—
213C3×Dic3⋊C4C2312yes—
214C3×Dic3⋊C4C2312yes—
215C3×Dic3⋊C4C2312yes—
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#3722C2312yes—
232#3722C2312yes—
233(C2×D3)⋊Dic3C2312yes—
234(C2×D3)⋊Dic3C2312yes—
235(C2×D3)⋊Dic3C2312yes—
236(C2×D3)⋊Dic3C2312yes—
237Dic32C2312yes—
238Dic32C2312yes—
239Dic32C2312yes—
240#3529—91noSylow
241C2×C3×#41—31no—
242C23×C3×C4—31no—
243C23×Dic3C2×D311yescharacteristic, complemented
244C2×#237—32no—
245C2×#237—31no—
246C2×#237C2×D311yescharacteristic
247C2×#235—32no—
248C2×#235—31no—
249C22×C4×D3—31no—
250C22×C4×D3—31no—
251C3×#127—31no—
252C3×#126—32no—
253C3×#123—31no—
254C3×#123—31no—
255C3×#123—32no—
256C3×#123—31no—
257C3×C22⋊Q8—32no—
258C3×#121—32no—
259C3×#121—32no—
260C3×#121—32no—
261C3×#121—32no—
262C3×#120—21no—
263C3×#120—32no—
264C3×#120—31no—
265C3×#120C2×D311yescharacteristic
266C3×#120C2×D311yescharacteristic
267C3×C4×D4—32no—
268C3×C4×D4—32no—
269C3×#117—31no—
270#953—32no—
271#953—32no—
272#953—62no—
273#953C2×D312yescomplemented
274#953C2×D311yescharacteristic, complemented
275#947—31no—
276#946—32no—
277#944—31no—
278#940—32no—
279#940—32no—
280#940C2×D311yescharacteristic
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#939C2×D312yes—
290#939C2×D312yes—
291#938—32no—
292#938—32no—
293#938—32no—
294#938—32no—
295#938—32no—
296#938C2×D312yes—
297#937—31no—
298#937—31no—
299#937—32no—
300#937—32no—
301#937—32no—
302#937—31no—
303#937—62no—
304#937—61no—
305#936—31no—
306#936—31no—
307#936—32no—
308#936—32no—
309#936—31no—
310#936—62no—
311#936—61no—
312#935—31no—
313#935—32no—
314#935—32no—
315#935—32no—
316#935—32no—
317#935C2×D311yescharacteristic
318#935C2×D311yescharacteristic
319D4×Dic3—32no—
320D4×Dic3—32no—
321D4×Dic3—32no—
322D4×Dic3C2×D312yes—
323#930—32no—
324#930—32no—
325#930—32no—
326#929—32no—
327#929—31no—
328#929—32no—
329#929—32no—
330C4×#67—32no—
331C4×#67—32no—
332C4×#67—32no—
333C4×#67—32no—
334C4×#67—32no—
335C4×#67—32no—
336#926—32no—
337#926—31no—
338#924—32no—
339#924—32no—
340#924—32no—
341#924—32no—
342C2×C4×Dic3—32no—
343C2×C4×Dic3—31no—
344#898—32no—
345#898—32no—
346#898—32no—
347#897—32no—
348#897—32no—
349#896—32no—
350#896—32no—
351#896—32no—
352#896—32no—
353#895—32no—
354#894—32no—
355#894—32no—
356#894—32no—
357#893—32no—
358#892—32no—
359#890—32no—
360#890—32no—
361#889—32no—
362#889—32no—
363#889—32no—
364#889—32no—
365#888—32no—
366#888—32no—
367#887—32no—
368#886—32no—
369#886—32no—
370#886C2×D311yescharacteristic, complemented
371#885—32no—
372#885—32no—
373#885—32no—
374#885—32no—
375#885—32no—
376#885—32no—
377#885—32no—
378#885—32no—
379#885—62no—
380#885—62no—
381#885—62no—
382#884—32no—
383#884—32no—
384#884—32no—
385#884—32no—
386#884—32no—
387#884C2×D312yescomplemented
388#883—32no—
389#883—32no—
390#883—32no—
391#883—32no—
392#883—32no—
393#883—32no—
394#883C2×D312yescomplemented
395#882—31no—
396#882—32no—
397#67⋊C4—32no—
398#67⋊C4—32no—
399#67⋊C4—32no—
400#67⋊C4C2×D312yescomplemented
401#879—32no—
402#879—32no—
403#879—32no—
404#879—32no—
405#879—32no—
406#879—32no—
407#879C2×D312yescomplemented
408#878—32no—
409#878—32no—
410#878—32no—
411#878—32no—
412#878—32no—
413#878C2×D312yescomplemented
414#877—31no—
415#877—32no—
416#877C2×D311yescharacteristic, complemented
417#876—32no—
418C4×D12—32no—
419#872—32no—
420C42×D3—31no—
421C42×D3—32no—
422#869—31no—
423C4×Dic6—32no—
424C23×C32—42no—
425C23×C32—41no—
426C23×C32C2411yescharacteristic
427C23×C32C2412yes—
428C23×C32C2411yescharacteristic
429C22×C3⋊D3—42no—
430C22×C3⋊D3—41no—
431C22×C3⋊D3C2412yes—
432C22×C3×D3C2412yes—
433C22×C3×D3C2411yescharacteristic
434C32×D4—41no—
435C32×D4—42no—
436C2×C32×C4C2411yescharacteristic
437C2×C32×C4C2412yes—
438#638—42no—
439#638—42no—
440#638—42no—
441C2×C3⋊Dic3C2412yes—
442C2×C3⋊Dic3C2412yes—
443C2×C3⋊Dic3C2412yes—
444#634—41no—
445#634—42no—
446C3×#67—42no—
447C3×#67—41no—
448C3×#67—41no—
449C3×#67—42no—
450C3×#67—42no—
451C3×#67—42no—
452C3×#67—42no—
453C2×C3×Dic3—24no—
454C2×C3×Dic3—22no—
455C2×C3×Dic3—22no—
456C2×C3×Dic3—41no—
457C2×C3×Dic3—41no—
458C2×C3×Dic3—42no—
459C2×C3×Dic3C2412yes—
460C2×C3×Dic3C2412yes—
461C2×C3×Dic3C2412yes—
462C2×C3×Dic3C2411yescharacteristic
463C2×C3×Dic3C2411yescharacteristic
464C2×C3×Dic3C2412yes—
465C2×C3×Dic3C2412yes—
466C2×C3×Dic3C2411yescharacteristic
467C3×D12—41no—
468C3×C4×D3—22no—
469C3×C4×D3—42no—
470C3×Dic6—41no—
471#627—42no—
472#626—42no—
473#626—42no—
474#626—42no—
475#625—42no—
476#624—24no—
477#624—42no—
478D3×Dic3—24no—
479D3×Dic3—42no—
480D3×Dic3—42no—
481#563—92no—
482#563—91no—
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—92no—
492#532—91no—
493#529—92no—
494#529—92no—
495#529—92no—
496#525—31no—
497#525—92no—
498#525—92no—
499#525—91no—
500C24×C3—21no—
501C24×C3C22×D311yescharacteristic
502C24×C3C22×D311yescharacteristic
503C23×D3—31no—
504C23×D3—31no—
505C23×D3—61no—
506C3×#41—122no—
507C2×C3×Q8—31no—
508C2×C3×D4—22no—
509C2×C3×D4—21no—
510C2×C3×D4—32no—
511C2×C3×D4—32no—
512C2×C3×D4—32no—
513C2×C3×D4—31no—
514C2×C3×D4—32no—
515C2×C3×D4—32no—
516C2×C3×D4—31no—
517C2×C3×D4—31no—
518C2×C3×D4C22×D312yes—
519C2×C3×D4C22×D311yescharacteristic
520C2×C3×D4C22×D311yescharacteristic
521C2×C3×D4C22×D312yes—
522C22×C3×C4—31no—
523C22×C3×C4—32no—
524C22×C3×C4—31no—
525C22×C3×C4—31no—
526C22×C3×C4—31no—
527C22×C3×C4—32no—
528C22×C3×C4—31no—
529C22×C3×C4—32no—
530C22×C3×C4—122no—
531C2×#67—32no—
532C2×#67—32no—
533C2×#67—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—62no—
543C2×#67—62no—
544C2×#67—62no—
545C2×#67C22×D312yes—
546C2×#67C22×D312yes—
547C2×#67C22×D311yescharacteristic
548C2×#67C22×D312yes—
549C2×#67C22×D312yes—
550C2×#67C22×D311yescharacteristic
551C2×#67C22×D312yes—
552C22×Dic3—32no—
553C22×Dic3—32no—
554C22×Dic3—32no—
555C22×Dic3—42no—
556C22×Dic3C22×D312yes—
557C22×Dic3C22×D311yescharacteristic
558C22×Dic3C22×D311yescharacteristic
559C22×Dic3C22×D311yescharacteristic
560C22×Dic3C22×D311yescharacteristic
561C22×Dic3C22×D312yes—
562#237—42no—
563#237—122no—
564#237—124no—
565#235—122no—
566#235—124no—
567C2×D12—32no—
568C2×D12—32no—
569C2×D12—32no—
570C2×D12C22×D311yescharacteristic
571C2×C4×D3—32no—
572C2×C4×D3—32no—
573C2×C4×D3—32no—
574C2×C4×D3—32no—
575C2×C4×D3—32no—
576C2×C4×D3—32no—
577C2×C4×D3—32no—
578C2×C4×D3—122no—
579C2×C4×D3—122no—
580C2×C4×D3C22×D311yescharacteristic
581C2×C4×D3C22×D312yes—
582C2×Dic6—32no—
583C2×Dic6—31no—
584C2×Dic6—32no—
585C2×Dic6—31no—
586C2×Dic6—32no—
587C2×Dic6—32no—
588C2×Dic6—62no—
589C2×Dic6—61no—
590C2×Dic6C22×D311yescharacteristic
591C3×C4⋊C4—32no—
592C3×C4⋊C4—32no—
593C3×C4⋊C4—32no—
594C3×C4⋊C4—32no—
595C3×C4⋊C4—32no—
596C3×C4⋊C4—32no—
597C3×C22⋊C4—21no—
598C3×C22⋊C4—22no—
599C3×C22⋊C4—31no—
600C3×C22⋊C4—32no—
601C3×C22⋊C4—32no—
602C3×C22⋊C4—32no—
603C3×C22⋊C4—32no—
604C3×C22⋊C4—31no—
605C3×C22⋊C4—32no—
606C3×C22⋊C4—32no—
607C3×C22⋊C4—32no—
608C3×C22⋊C4C22×D311yescharacteristic
609C3×C22⋊C4C22×D312yes—
610C3×C22⋊C4C22×D312yes—
611C3×C22⋊C4C22×D311yescharacteristic
612C3×C42—32no—
613C3×C42—31no—
614#217—32no—
615#217—31no—
616#217—32no—
617#217—32no—
618#217—32no—
619#217—32no—
620#217—32no—
621#217—32no—
622#217—31no—
623#217—32no—
624#217—32no—
625#217—32no—
626#217—32no—
627#217—32no—
628#217—62no—
629#217—62no—
630#217—62no—
631#217—61no—
632#217—62no—
633#217C22×D311yescharacteristic
634#217C22×D312yes—
635#217C22×D311yescharacteristic
636#217C22×D312yes—
637#217C22×D312yes—
638#217C22×D312yes—
639#217C22×D312yes—
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—32no—
656(C2×D3)⋊C4—62no—
657(C2×D3)⋊C4—62no—
658(C2×D3)⋊C4—62no—
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⋊Dic3—32no—
669C4⋊Dic3C22×D312yes—
670C4⋊Dic3C22×D312yes—
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⋊C4C22×D312yes—
688Dic3⋊C4C22×D312yes—
689Dic3⋊C4C22×D312yes—
690Dic3⋊C4C22×D312yes—
691C4×Dic3—32no—
692C4×Dic3—31no—
693C4×Dic3—32no—
694C4×Dic3—31no—
695C4×Dic3—32no—
696C4×Dic3—32no—
697C4×Dic3—32no—
698C4×Dic3—32no—
699C4×Dic3—32no—
700C4×Dic3—32no—
701C4×Dic3—61no—
702C4×Dic3—62no—
703C4×Dic3C22×D312yes—
704C4×Dic3C22×D311yescharacteristic
705C22×C32—22no—
706C22×C32—21no—
707C22×C32—21no—
708C22×C32—22no—
709C22×C32—22no—
710C22×C32—22no—
711C22×C32—22no—
712C22×C32—44no—
713C22×C32C2511yescharacteristic
714C2×C3⋊D3—22no—
715C2×C3⋊D3—22no—
716C2×C3⋊D3—22no—
717C2×C3⋊D3—44no—
718C2×C3×D3—22no—
719C2×C3×D3—21no—
720C2×C3×D3—22no—
721C2×C3×D3—22no—
722C2×C3×D3—22no—
723C32×C4—21no—
724C32×C4—22no—
725C3⋊Dic3—22no—
726C3⋊Dic3—22no—
727C3⋊Dic3—22no—
728C3×Dic3—22no—
729C3×Dic3—21no—
730C3×Dic3—22no—
731C3×Dic3—21no—
732C3×Dic3—22no—
733C3×Dic3—22no—
734C3×Dic3—22no—
735C3×Dic3H(5,𝔽2)12yes—
736C2×#41—31no—
737C2×#41—92no—
738C2×#41—91no—
739C23×C4—31no—
740C23×C4—91no—
741C4⋊Q8—91no—
742C4⋊Q8—92no—
743#127—31no—
744#127—92no—
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—92no—
755#124—91no—
756#124—92no—
757#124—91no—
758#124—92no—
759#124—92no—
760#124—92no—
761#123—31no—
762#123—31no—
763#123—31no—
764#123—32no—
765#123—92no—
766#123—92no—
767#123—92no—
768#123—92no—
769#123—92no—
770#123—92no—
771#123—92no—
772#123—92no—
773#123—91no—
774#123—92no—
775C22⋊Q8—32no—
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—92no—
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—31no—
800#120—32no—
801#120—91no—
802#120—92no—
803#120—92no—
804#120—91no—
805#120—92no—
806#120D3211yescharacteristic
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—31no—
818#117—92no—
819#117—92no—
820#117—91no—
821C2×C42—92no—
822C2×C42—91no—
823C23×C3—21no—
824C23×C3—21no—
825C23×C3—22no—
826C23×C3—32no—
827C23×C3—31no—
828C23×C3—41no—
829C23×C3—41no—
830C23×C3—42no—
831C23×C3—42no—
832C23×C3—81no—
833C23×C3—82no—
834C23×C3C23×D311yescharacteristic
835C23×C3C23×D311yescharacteristic
836C23×C3C23×D312yes—
837C23×C3C23×D311yescharacteristic
838C23×C3C23×D311yescharacteristic
839C23×C3C23×D312yes—
840C22×D3—32no—
841C22×D3—32no—
842C22×D3—62no—
843C22×D3—121no—
844C22×D3—121no—
845C22×D3—122no—
846C22×D3—122no—
847C22×D3—241no—
848C22×D3—242no—
849C22×D3C23×D312yes—
850C22×D3C23×D311yescharacteristic
851C3×Q8—121no—
852C3×D4—41no—
853C3×D4—42no—
854C3×D4—42no—
855C3×D4—41no—
856C3×D4—81no—
857C3×D4—82no—
858C3×D4—121no—
859C3×D4—122no—
860C3×D4—122no—
861C3×D4—122no—
862C3×D4—122no—
863C3×D4—122no—
864C3×D4—121no—
865C3×D4—121no—
866C2×C3×C4—22no—
867C2×C3×C4—21no—
868C2×C3×C4—31no—
869C2×C3×C4—32no—
870C2×C3×C4—32no—
871C2×C3×C4—32no—
872C2×C3×C4—31no—
873C2×C3×C4—32no—
874C2×C3×C4—32no—
875C2×C3×C4—31no—
876C2×C3×C4—62no—
877C2×C3×C4—62no—
878C2×C3×C4—64no—
879C2×C3×C4—62no—
880C2×C3×C4—122no—
881C2×C3×C4—121no—
882C2×C3×C4—121no—
883C2×C3×C4—122no—
884C2×C3×C4C23×D311yescharacteristic
885C2×C3×C4C23×D312yes—
886C2×C3×C4C23×D311yescharacteristic
887C2×C3×C4C23×D312yes—
888#67—42no—
889#67—41no—
890#67—41no—
891#67—42no—
892#67—42no—
893#67—42no—
894#67—42no—
895#67—122no—
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—242no—
907#67—242no—
908#67—242no—
909C2×Dic3—22no—
910C2×Dic3—22no—
911C2×Dic3—24no—
912C2×Dic3—32no—
913C2×Dic3—32no—
914C2×Dic3—32no—
915C2×Dic3—32no—
916C2×Dic3—32no—
917C2×Dic3—32no—
918C2×Dic3—41no—
919C2×Dic3—42no—
920C2×Dic3—41no—
921C2×Dic3—62no—
922C2×Dic3—62no—
923C2×Dic3—62no—
924C2×Dic3—64no—
925C2×Dic3—122no—
926C2×Dic3—122no—
927C2×Dic3C23×D312yes—
928C2×Dic3C23×D312yes—
929C2×Dic3C23×D312yes—
930C2×Dic3C23×D312yes—
931C2×Dic3C23×D312yes—
932C2×Dic3C23×D311yescharacteristic
933C2×Dic3C23×D311yescharacteristic
934C2×Dic3C23×D311yescharacteristic
935D12—41no—
936D12—122no—
937D12—122no—
938D12—122no—
939C4×D3—22no—
940C4×D3—42no—
941C4×D3—64no—
942C4×D3—64no—
943C4×D3—64no—
944C4×D3—122no—
945C4×D3—122no—
946C4×D3—122no—
947C4×D3—122no—
948Dic6—41no—
949Dic6—122no—
950Dic6—122no—
951Dic6—122no—
952Dic6—122no—
953Dic6—121no—
954Dic6—121no—
955Dic6—241no—
956Dic6—242no—
957C2×C32—41no—
958C2×C32—42no—
959C2×C32—41no—
960C2×C32C2×H(5,𝔽2)11yescharacteristic
961C2×C32#58512yes—
962C3⋊D3—42no—
963C3×D3—42no—
964C3×D3—41no—
965C24—91no—
966C24C2×D3211yescharacteristic
967#41—122no—
968#41—362no—
969#41—364no—
970C2×Q8—31no—
971C2×Q8—92no—
972C2×Q8—92no—
973C2×Q8—91no—
974C2×D4—32no—
975C2×D4—32no—
976C2×D4—32no—
977C2×D4—32no—
978C2×D4—32no—
979C2×D4—31no—
980C2×D4—31no—
981C2×D4—31no—
982C2×D4—92no—
983C2×D4—92no—
984C2×D4—92no—
985C2×D4—92no—
986C2×D4—92no—
987C2×D4—92no—
988C2×D4—92no—
989C2×D4C2×D3212yes—
990C2×D4C2×D3211yescharacteristic
991C22×C4—31no—
992C22×C4—32no—
993C22×C4—31no—
994C22×C4—31no—
995C22×C4—32no—
996C22×C4—31no—
997C22×C4—31no—
998C22×C4—32no—
999C22×C4—92no—
1000C22×C4—92no—
1001C22×C4—92no—
1002C22×C4—92no—
1003C22×C4—92no—
1004C22×C4—122no—
1005C22×C4—362no—
1006C4⋊C4—32no—
1007C4⋊C4—32no—
1008C4⋊C4—32no—
1009C4⋊C4—32no—
1010C4⋊C4—32no—
1011C4⋊C4—32no—
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—32no—
1026C22⋊C4—31no—
1027C22⋊C4—32no—
1028C22⋊C4—32no—
1029C22⋊C4—32no—
1030C22⋊C4—32no—
1031C22⋊C4—32no—
1032C22⋊C4—32no—
1033C22⋊C4—92no—
1034C22⋊C4—92no—
1035C22⋊C4—92no—
1036C22⋊C4—92no—
1037C22⋊C4—92no—
1038C22⋊C4—92no—
1039C22⋊C4—92no—
1040C22⋊C4—91no—
1041C22⋊C4—92no—
1042C22⋊C4—92no—
1043C22⋊C4—92no—
1044C22⋊C4—92no—
1045C22⋊C4—92no—
1046C22⋊C4—92no—
1047C22⋊C4—92no—
1048C22⋊C4C2×D3211yescharacteristic
1049C22⋊C4C2×D3212yes—
1050C42—32no—
1051C42—31no—
1052C42—92no—
1053C42—92no—
1054C42—92no—
1055C42—91no—
1056C42—92no—
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—22no—
1066C22×C3—21no—
1067C22×C3—22no—
1068C22×C3—22no—
1069C22×C3—22no—
1070C22×C3—22no—
1071C22×C3—21no—
1072C22×C3—42no—
1073C22×C3—42no—
1074C22×C3—42no—
1075C22×C3—41no—
1076C22×C3—42no—
1077C22×C3—41no—
1078C22×C3—42no—
1079C22×C3—44no—
1080C22×C3—44no—
1081C22×C3—62no—
1082C22×C3—62no—
1083C22×C3—62no—
1084C22×C3—61no—
1085C22×C3—62no—
1086C22×C3—84no—
1087C22×C3C24×D311yescharacteristic
1088C22×C3C24×D311yescharacteristic
1089C2×D3—21no—
1090C2×D3—22no—
1091C2×D3—22no—
1092C2×D3—22no—
1093C2×D3—22no—
1094C2×D3—62no—
1095C2×D3—62no—
1096C2×D3—62no—
1097C2×D3—62no—
1098C2×D3—62no—
1099C2×D3—62no—
1100C2×D3—122no—
1101C2×D3—122no—
1102C2×D3—122no—
1103C2×D3—124no—
1104C2×D3—124no—
1105C2×D3—244no—
1106C3×C4—21no—
1107C3×C4—22no—
1108C3×C4—21no—
1109C3×C4—22no—
1110C3×C4—32no—
1111C3×C4—41no—
1112C3×C4—42no—
1113C3×C4—62no—
1114C3×C4—62no—
1115C3×C4—62no—
1116C3×C4—62no—
1117C3×C4—61no—
1118C3×C4—61no—
1119C3×C4—62no—
1120Dic3—21no—
1121Dic3—21no—
1122Dic3—22no—
1123Dic3—22no—
1124Dic3—22no—
1125Dic3—22no—
1126Dic3—22no—
1127Dic3—62no—
1128Dic3—62no—
1129Dic3—62no—
1130Dic3—62no—
1131Dic3—62no—
1132Dic3—62no—
1133Dic3—122no—
1134Dic3—122no—
1135Dic3—122no—
1136Dic3#100412yes—
1137C32#352911yescharacteristic, complemented, Sylow
1138C23—31no—
1139C23—32no—
1140C23—41no—
1141C23—42no—
1142C23—92no—
1143C23—361no—
1144C23—362no—
1145C23C22×D3211yescharacteristic
1146C23C22×D3211yescharacteristic
1147C23C22×D3212yes—
1148Q8—121no—
1149Q8—361no—
1150Q8—362no—
1151Q8—362no—
1152D4—41no—
1153D4—42no—
1154D4—121no—
1155D4—121no—
1156D4—121no—
1157D4—122no—
1158D4—122no—
1159D4—122no—
1160D4—122no—
1161D4—122no—
1162D4—362no—
1163D4—362no—
1164D4—362no—
1165D4—362no—
1166D4—362no—
1167D4—362no—
1168D4—362no—
1169C2×C4—31no—
1170C2×C4—32no—
1171C2×C4—32no—
1172C2×C4—32no—
1173C2×C4—32no—
1174C2×C4—32no—
1175C2×C4—31no—
1176C2×C4—31no—
1177C2×C4—62no—
1178C2×C4—62no—
1179C2×C4—64no—
1180C2×C4—62no—
1181C2×C4—92no—
1182C2×C4—92no—
1183C2×C4—92no—
1184C2×C4—122no—
1185C2×C4—122no—
1186C2×C4—121no—
1187C2×C4—121no—
1188C2×C4—184no—
1189C2×C4—184no—
1190C2×C4—362no—
1191C2×C4—362no—
1192C2×C4—362no—
1193C2×C4C22×D3212yes—
1194C2×C4C22×D3211yescharacteristic
1195C2×C3—21no—
1196C2×C3—22no—
1197C2×C3—41no—
1198C2×C3—42no—
1199C2×C3—41no—
1200C2×C3—41no—
1201C2×C3—41no—
1202C2×C3—42no—
1203C2×C3—81no—
1204C2×C3—81no—
1205C2×C3—82no—
1206C2×C3—121no—
1207C2×C3—122no—
1208C2×C3C2×#100411yescharacteristic
1209C2×C3#596412yes—
1210C2×C3D3×H(5,𝔽2)11yescharacteristic
1211C2×C3#596612yes—
1212D3—42no—
1213D3—41no—
1214D3—122no—
1215D3—122no—
1216D3—242no—
1217C22—21no—
1218C22—21no—
1219C22—22no—
1220C22—22no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—44no—
1225C22—61no—
1226C22—62no—
1227C22—62no—
1228C22—62no—
1229C22—62no—
1230C22—182no—
1231C22—182no—
1232C22—182no—
1233C22—364no—
1234C22C23×D3211yescharacteristic
1235C4—21no—
1236C4—22no—
1237C4—32no—
1238C4—61no—
1239C4—62no—
1240C4—61no—
1241C4—62no—
1242C4—62no—
1243C4—62no—
1244C4—62no—
1245C4—182no—
1246C4—182no—
1247C4—182no—
1248C3—21no—
1249C3#8604811yescharacteristic, complemented
1250C3#8707011yescharacteristic, complemented
1251C2—41no—
1252C2—42no—
1253C2—41no—
1254C2—121no—
1255C2—122no—
1256C2—362no—
1257C2D3×#100411yescharacteristic
1258C2#1059667812yes—
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. #10596065C2semidirect
2. C3×#5595C2semidirect
3. C3×#5586C2semidirect
4. #10595505C2semidirect
5. #10595498C2semidirect
6. #10595275C2semidirect
7. #10595266C2semidirect
8. #10595264C2semidirect
9. #10595213C2semidirect
10. #10595172C2semidirect
11. #10595159C2semidirect
12. #10595152C2semidirect
13. #10595138C2semidirect
14. #10594235C2semidirect
15. #10594174C2semidirect
16. #10594089C2semidirect
17. #10594088C2semidirect
18. #10594058C2semidirect
19. #10594034C2semidirect
22. C23×C3×Dic3C22semidirect
24. C22×#624C22semidirect
26. C2×#3795C22semidirect
36. C3×#953C22semidirect
37. C3×#953C22semidirect
45. C3×#886C22semidirect
46. C3×#884C22semidirect
47. C3×#883C22semidirect
48. C3×#67⋊C4C22semidirect
49. C3×#879C22semidirect
50. C3×#878C22semidirect
51. C3×#877C22semidirect
52. #63981C22semidirect
53. #63981C22semidirect
58. Dic3×#67C22semidirect
59. Dic3×#67C22semidirect
60. Dic3×#67C22semidirect
63. #63970C22semidirect
64. #63970C22semidirect
65. #63970C22semidirect
66. #63969C22semidirect
67. #63969C22semidirect
68. #63969C22semidirect
70. #63964C22semidirect
71. #63964C22semidirect
72. #63964C22semidirect
73. #63961C22semidirect
74. #63961C22semidirect
77. #63956C22semidirect
78. #63956C22semidirect
79. #63956C22semidirect
80. #63955C22semidirect
81. #63955C22semidirect
84. #63915C22semidirect
85. #63906C22semidirect
86. #63904C22semidirect
87. #63896C22semidirect
88. #63896C22semidirect
89. #63895C22semidirect
90. #63890C22semidirect
91. #63888C22semidirect
92. #63886C22semidirect
93. #63880C22semidirect
94. C4×D3×Dic3C22semidirect
95. C4×D3×Dic3C22semidirect
96. #63872C22semidirect
97. #63870C22semidirect
98. #63870C22semidirect
99. #63868C22semidirect
100. #63866C22semidirect
101. #63863C22semidirect
102. #63857C22semidirect
103. #63854C22semidirect
104. #63850C22semidirect
105. #63848C22semidirect
106. #63844C22semidirect
107. #63840C22semidirect
108. #63836C22semidirect
137. #5595D3semidirect
142. #5586D3semidirect
243. C23×Dic3C2×D3semidirect
273. #953C2×D3semidirect
274. #953C2×D3semidirect
370. #886C2×D3semidirect
387. #884C2×D3semidirect
394. #883C2×D3semidirect
400. #67⋊C4C2×D3semidirect
407. #879C2×D3semidirect
413. #878C2×D3semidirect
416. #877C2×D3semidirect
1137. C32#3529semidirect
1249. C3#86048semidirect
1250. C3#87070semidirect

Maximal subgroups

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

subgroupindex
#105960652
C3×#55952
C3×#55862
#105955052
#105954982
#105952752
#105952662
#105952642
#105952132
#105951722
#105951592
#105951522
#105951382
#105942352
#105941742
#105940892
#105940882
#105940582
#105940342
#870703
#860483