Finite Group Databasebeta

← #11887237

Subgroups — #11887237

Order 1152.

983 conjugacy classes of subgroups.

The subgroup lattice has 843 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596300C211yesmaximal, characteristic
2#10594970C211yesmaximal, characteristic, complemented
3C3×#5239C211yesmaximal, characteristic, complemented
4C3×#5233C211yesmaximal, characteristic, complemented
5#10591601C211yesmaximal, characteristic, complemented
6#10591579C211yesmaximal, characteristic, complemented
7#10591553C211yesmaximal, characteristic, complemented
8#10591539C211yesmaximal, characteristic, complemented
9#10591479C211yesmaximal, characteristic, complemented
10#10591467C211yesmaximal, characteristic, complemented
11#10591445C211yesmaximal, characteristic, complemented
12#10591416C211yesmaximal, characteristic, complemented
13#10591177C211yesmaximal, characteristic, complemented
14#10591148C211yesmaximal, characteristic, complemented
15#10591136C211yesmaximal, characteristic, complemented
16#80246—31nomaximal
17#78845—31nomaximal
18C2×C32×#41C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20#64156C2211yescharacteristic
21#64155C2211yescharacteristic
22#64148—21no—
23#64146—21no—
24D4×C3⋊Dic3C2211yescharacteristic
25#64139C2211yescharacteristic
26#64138—21no—
27C4×#638C2211yescharacteristic
28C2×#3752—21no—
29C2×C3×#216C2211yescharacteristic, complemented
30C2×C3×#214C2211yescharacteristic
31C3×#926C2211yescharacteristic, complemented
32C3×#924C2211yescharacteristic, complemented
33C22×C3×C3⋊C8C2211yescharacteristic, complemented
34#63975—21no—
35#63956—21no—
36#63900C2211yescharacteristic
37#63872C2211yescharacteristic, complemented
38#63871C2211yescharacteristic
39#63867—21no—
40#63843C2211yescharacteristic, complemented
41#63836—21no—
42C2×#3717C2211yescharacteristic
43C2×#3710C2211yescharacteristic
44C3×#835C2211yescharacteristic, complemented
45C3×#835C2211yescharacteristic, complemented
46C3×#835C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#832C2211yescharacteristic
50C3×#830C2211yescharacteristic, complemented
51#63575C2211yescharacteristic, complemented
52#63573C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63557C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61#5829—31no—
62#5829—31no—
63#5829—61no—
64#5639—31no—
65#5529—31no—
66C3×#452—31no—
67C3×#416—31no—
68#5239D311yescharacteristic, complemented
69#5233D311yescharacteristic, complemented
70#5188—31no—
71#5185—31no—
72#5169—31no—
73Dic3×SD16—31no—
74#5114—31no—
75C8×#67—31no—
76#5048—31no—
77#5003—31no—
78#4813—31no—
79#4805—31no—
80#4805—31no—
81#4800—31no—
82#4800—31no—
83#4798—31no—
84#4776—31no—
85D3×#102—31no—
86D3×#102—31no—
87#4766—31no—
88#4763—31no—
89#4758—31no—
90#4737—31no—
91#67⋊C8—31no—
92C23×C3⋊D3—21no—
93C32×#41—22no—
94C32×#41—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4—21no—
99C22×C32×C4C2311yescharacteristic
100C2×#638—21no—
101C2×#638—21no—
102C2×#638D411yescharacteristic
103C22×C3⋊Dic3—21no—
104D4×C3⋊D3—22no—
105D4×C3⋊D3—41no—
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4×C3⋊D3C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#624—21no—
110#3757—21no—
111#3757D411yescharacteristic
112#3752—21no—
113#3752—21no—
114#3752—21no—
115#3752—21no—
116#3752D411yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118#3750—21no—
119#3750D411yescharacteristic
120C4×C3⋊Dic3C2311yescharacteristic
121C3×#217—21no—
122C3×#217—21no—
123C3×#216—41no—
124C3×#214—22no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3—21no—
130C2×C3×C3⋊C8—41no—
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141Dic32—21no—
142#3717—41no—
143#3710—41no—
144#3296—91noSylow
145C2×C3×#41—21no—
146C2×C3×#41C2×D311yescharacteristic
147C2×C3×#41C2×D311yescharacteristic
148C2×D3×D4—31no—
149C2×D3×D4—31no—
150C2×D3×D4—61no—
151C2×C3×Q16—31no—
152C2×C3×SD16—31no—
153C22×C3×C8—31no—
154C3×C22⋊Q8—31no—
155C3×#117—31no—
156#947—31no—
157#947—31no—
158#947—61no—
159#946—31no—
160#946—31no—
161#946—31no—
162#946—61no—
163Q8×Dic3—31no—
164C2×#216C2×D311yescharacteristic, complemented
165C2×#215—31no—
166#939—61no—
167#939—61no—
168#939—62no—
169#937—61no—
170#937—61no—
171#937—62no—
172D4×Dic3—31no—
173D4×Dic3—31no—
174D4×Dic3—61no—
175C2×#214C2×D311yescharacteristic
176#930—31no—
177#930—31no—
178#930—61no—
179#929—61no—
180#929—61no—
181#929—62no—
182C4×#67—31no—
183C4×#67—31no—
184C4×#67—61no—
185C2×(C2×D3)⋊C4—61no—
186C2×(C2×D3)⋊C4—61no—
187C2×(C2×D3)⋊C4—62no—
188#926C2×D311yescharacteristic, complemented
189#924C2×D311yescharacteristic, complemented
190C22×C3⋊C8C2×D311yescharacteristic, complemented
191C2×#204—31no—
192C2×D3×C8—31no—
193C2×D3×C8—31no—
194#897—31no—
195#892—61no—
196D3×C4⋊C4—31no—
197D3×C4⋊C4—31no—
198#890—31no—
199#890—31no—
200#889—61no—
201#887—31no—
202#883—61no—
203#883—61no—
204#879—61no—
205#879—61no—
206#872—61no—
207#870—61no—
208C3×#103—31no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#102—31no—
212C3×#102—31no—
213C3×#102—31no—
214C3×C22⋊C8—31no—
215#835—31no—
216#835C2×D311yescharacteristic, complemented
217#835C2×D311yescharacteristic, complemented
218#835C2×D311yescharacteristic, complemented
219#832C2×D311yescharacteristic
220#832C2×D311yescharacteristic
221#832C2×D311yescharacteristic
222#830C2×D311yescharacteristic, complemented
223#821—31no—
224#821—31no—
225#821—31no—
226(C2×D3)⋊C8—31no—
227(C2×D3)⋊C8—31no—
228#818—31no—
229#817—31no—
230#817—31no—
231#816—31no—
232Dic3⋊C8—31no—
233Dic3⋊C8—31no—
234C8×Dic3—31no—
235C8×Dic3—31no—
236#809—31no—
237#809—31no—
238#809—31no—
239#808—31no—
240#808—31no—
241#807—31no—
242C23×C32—21no—
243C23×C32C2×D411yescharacteristic
244C22×C3⋊D3—21no—
245C22×C3⋊D3—42no—
246C22×C3⋊D3—42no—
247C22×C3⋊D3—81no—
248C22×C3⋊D3C2×D411yescharacteristic
249C32×Q8—21no—
250C32×Q8—21no—
251C32×D4—21no—
252C32×D4—42no—
253C32×D4#4112yes—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—42no—
258C2×C32×C4C2×D411yescharacteristic
259C2×C32×C4C2411yescharacteristic
260#638—22no—
261#638—42no—
262#638—81no—
263C2×C3⋊Dic3—21no—
264C2×C3⋊Dic3—81no—
265C2×C3⋊Dic3C2×D411yescharacteristic
266C2×C3⋊Dic3C2×D411yescharacteristic
267C2×C3⋊Dic3C2×D411yescharacteristic
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C4×C3⋊D3—21no—
271C4×C3⋊D3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C3×Dic6—21no—
277C3×Dic6—21no—
278#624—42no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283#552—91no—
284#546—91no—
285#488—91no—
286#483—91no—
287#482—91no—
288#478—91no—
289#467—91no—
290#465—91no—
291#464—91no—
292#452—31no—
293#450—91no—
294C4×SD16—91no—
295C8×D4—91no—
296#416—31no—
297C2×#102—91no—
298C23×D3—61no—
299C23×D3—61no—
300C23×D3—62no—
301C3×#41—22no—
302C3×#41—22no—
303C3×#41—42no—
304C3×#41—41no—
305C3×#41—41no—
306C3×#41—42no—
307C2×C3×Q8—21no—
308C2×C3×Q8—31no—
309C2×C3×Q8C22×D311yescharacteristic
310C2×C3×Q8C22×D311yescharacteristic
311C2×C3×D4—22no—
312C2×C3×D4—21no—
313C2×C3×D4—21no—
314C2×C3×D4—21no—
315C2×C3×D4C22×D311yescharacteristic
316C2×C3×D4C22×D311yescharacteristic
317C22×C3×C4—22no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C2×#67—31no—
324C2×#67—31no—
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—62no—
329C2×#67—62no—
330C2×#67—61no—
331C2×#67—61no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3—62no—
335D3×D4—62no—
336D3×D4—62no—
337D3×D4—122no—
338D3×D4—121no—
339D3×D4—121no—
340D3×D4—122no—
341C2×D12—31no—
342C2×D12—31no—
343C2×D12—61no—
344C2×C4×D3—31no—
345C2×C4×D3—31no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×Dic6C22×D311yescharacteristic
350C3×Q16—121no—
351C3×SD16—62no—
352C2×C3×C8—31no—
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355C2×C3×C8—31no—
356C2×C3×C8—121no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C42—61no—
364#217—21no—
365#217—21no—
366#217—31no—
367#217—31no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—62no—
372#216—41no—
373#215—121no—
374#214—22no—
375(C2×D3)⋊C4—31no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—62no—
387(C2×D3)⋊C4—62no—
388(C2×D3)⋊C4—62no—
389(C2×D3)⋊C4—62no—
390(C2×D3)⋊C4—61no—
391(C2×D3)⋊C4—61no—
392C4⋊Dic3—31no—
393C4⋊Dic3—31no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3—61no—
398C4⋊Dic3—61no—
399C4⋊Dic3C22×D311yescharacteristic
400C4⋊Dic3C22×D311yescharacteristic
401C4⋊Dic3C22×D311yescharacteristic
402Dic3⋊C4—21no—
403Dic3⋊C4—31no—
404Dic3⋊C4—31no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—61no—
414Dic3⋊C4—62no—
415C4×Dic3—21no—
416C4×Dic3—31no—
417C4×Dic3—31no—
418C4×Dic3—61no—
419C4×Dic3—61no—
420C4×Dic3—61no—
421C2×C3⋊C8—41no—
422C2×C3⋊C8C22×D311yescharacteristic
423C2×C3⋊C8C22×D311yescharacteristic
424C2×C3⋊C8C22×D311yescharacteristic
425C2×C3⋊C8C22×D311yescharacteristic
426#204—121no—
427D3×C8—121no—
428D3×C8—121no—
429C22×C32—22no—
430C22×C32—21no—
431C22×C32—21no—
432C22×C32—21no—
433C22×C32—41no—
434C22×C32—41no—
435C22×C32C22×D411yescharacteristic
436C2×C3⋊D3—21no—
437C2×C3⋊D3—21no—
438C2×C3⋊D3—41no—
439C2×C3⋊D3—41no—
440C2×C3⋊D3—41no—
441C2×C3⋊D3—84no—
442C2×C3⋊D3#13512yes—
443C32×C4—21no—
444C32×C4—41no—
445C32×C4C2×#4111yescharacteristic
446C32×C4H(5,𝔽2)11yescharacteristic
447C3⋊Dic3—21no—
448C3⋊Dic3—21no—
449C3⋊Dic3—21no—
450C3⋊Dic3—41no—
451C3×Dic3—41no—
452C3×Dic3—41no—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C2×#41D3211yescharacteristic
456C22×D4—91no—
457C2×Q16—31no—
458C2×SD16—31no—
459C2×SD16—91no—
460C22×C8—31no—
461C22×C8—91no—
462#126—181no—
463#125—91no—
464#125—181no—
465#124—91no—
466#123—181no—
467#123—181no—
468C22⋊Q8—31no—
469C22⋊Q8—91no—
470C22⋊Q8—91no—
471#121—91no—
472#121—181no—
473#120—181no—
474C4×Q8—91no—
475C4×D4—91no—
476C4×D4—91no—
477#117—31no—
478#117—181no—
479C2×C4⋊C4—91no—
480C2×C22⋊C4—181no—
481#107—91no—
482#106—91no—
483#106—91no—
484C4⋊C8—91no—
485#103—31no—
486#103—31no—
487#103—31no—
488#103—91no—
489#102—31no—
490#102—31no—
491#102—31no—
492#102—91no—
493#102—91no—
494#102—91no—
495C22⋊C8—31no—
496C22⋊C8—91no—
497C4×C8—91no—
498C23×C3—22no—
499C23×C3—21no—
500C23×C3—21no—
501C23×C3—21no—
502C23×C3D3×D411yescharacteristic
503C23×C3D3×D411yescharacteristic
504C22×D3—31no—
505C22×D3—31no—
506C22×D3—61no—
507C22×D3—62no—
508C22×D3—61no—
509C22×D3—61no—
510C22×D3—122no—
511C22×D3—122no—
512C22×D3—122no—
513C22×D3—122no—
514C22×D3—124no—
515C22×D3—124no—
516C22×D3—241no—
517C22×D3—241no—
518C22×D3—242no—
519C3×Q8—21no—
520C3×Q8—21no—
521C3×Q8—21no—
522C3×Q8—21no—
523C3×Q8—41no—
524C3×Q8—41no—
525C3×Q8—61no—
526C3×Q8—61no—
527C3×D4—22no—
528C3×D4—21no—
529C3×D4—21no—
530C3×D4—22no—
531C3×D4—42no—
532C3×D4—42no—
533C3×D4—44no—
534C3×D4#23512yes—
535C3×D4#23712yes—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—22no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—42no—
548C2×C3×C4—42no—
549C2×C3×C4—44no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4D3×D411yescharacteristic
555C2×C3×C4D3×D411yescharacteristic
556C2×C3×C4C23×D311yescharacteristic
557C2×C3×C4C23×D311yescharacteristic
558#67—62no—
559#67—62no—
560#67—122no—
561#67—122no—
562#67—122no—
563#67—124no—
564#67—241no—
565#67—241no—
566#67—242no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—31no—
572C2×Dic3—31no—
573C2×Dic3—31no—
574C2×Dic3—31no—
575C2×Dic3—31no—
576C2×Dic3—31no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—62no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—241no—
584C2×Dic3—241no—
585C2×Dic3—242no—
586D12—61no—
587D12—61no—
588D12—61no—
589D12—61no—
590D12—121no—
591D12—121no—
592C4×D3—61no—
593C4×D3—61no—
594C4×D3—61no—
595C4×D3—61no—
596C4×D3—121no—
597C4×D3—121no—
598C4×D3—122no—
599C4×D3—122no—
600Dic6—21no—
601Dic6—21no—
602C3×C8—61no—
603C3×C8—61no—
604C3×C8—61no—
605C3×C8—61no—
606C3⋊C8—21no—
607C3⋊C8—21no—
608C3⋊C8—21no—
609C3⋊C8—21no—
610C2×C32—42no—
611C2×C32—41no—
612C2×C32#54611yescharacteristic
613C2×C32C2×#13511yescharacteristic
614C2×C32#57711yescharacteristic
615C3⋊D3—22no—
616C3⋊D3—81no—
617C24—181no—
618#41—22no—
619#41—41no—
620C2×Q8—31no—
621C2×Q8C2×D3211yescharacteristic
622C2×D4—21no—
623C2×D4—91no—
624C2×D4—91no—
625C2×D4—181no—
626C2×D4—182no—
627C2×D4—181no—
628C2×D4—361no—
629C2×D4C2×D3211yescharacteristic
630C22×C4—21no—
631C22×C4—91no—
632C22×C4—181no—
633C22×C4—181no—
634C22×C4C2×D3211yescharacteristic
635Q16—121no—
636SD16—62no—
637SD16—361no—
638C2×C8—31no—
639C2×C8—31no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—121no—
643C2×C8—361no—
644C4⋊C4—31no—
645C4⋊C4—31no—
646C4⋊C4—31no—
647C4⋊C4—61no—
648C4⋊C4—91no—
649C4⋊C4—91no—
650C4⋊C4—181no—
651C4⋊C4—181no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4—181no—
656C22⋊C4—61no—
657C22⋊C4—61no—
658C22⋊C4—91no—
659C22⋊C4—91no—
660C22⋊C4—181no—
661C22⋊C4—181no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C42—61no—
667C42—91no—
668C42—181no—
669C22×C3—24no—
670C22×C3—22no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—21no—
674C22×C3—21no—
675C22×C3—21no—
676C22×C3—22no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—41no—
680C22×C3—41no—
681C22×C3—41no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3—41no—
687C22×C3—41no—
688C22×C3C2×D3×D411yescharacteristic
689C22×C3C2×D3×D411yescharacteristic
690C2×D3—32no—
691C2×D3—32no—
692C2×D3—62no—
693C2×D3—61no—
694C2×D3—61no—
695C2×D3—61no—
696C2×D3—61no—
697C2×D3—121no—
698C2×D3—121no—
699C2×D3—122no—
700C2×D3—122no—
701C2×D3—122no—
702C2×D3—121no—
703C2×D3—121no—
704C2×D3—121no—
705C2×D3—121no—
706C2×D3—121no—
707C2×D3—121no—
708C2×D3—244no—
709C2×D3—244no—
710C2×D3—248no—
711C3×C4—21no—
712C3×C4—21no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—41no—
716C3×C4—42no—
717C3×C4—41no—
718C3×C4—41no—
719C3×C4—121no—
720C3×C4—121no—
721C3×C4—121no—
722C3×C4—121no—
723C3×C4C2×#23511yescharacteristic
724C3×C4C2×#23711yescharacteristic
725C3×C4#100411yescharacteristic
726C3×C4#100411yescharacteristic
727Dic3—41no—
728Dic3—41no—
729Dic3—41no—
730Dic3—41no—
731Dic3—61no—
732Dic3—61no—
733Dic3—61no—
734Dic3—61no—
735Dic3—61no—
736Dic3—61no—
737Dic3—121no—
738Dic3—121no—
739Dic3—121no—
740Dic3—122no—
741Dic3—121no—
742Dic3—121no—
743C32#329611yescharacteristic, complemented, Sylow
744C23—21no—
745C23—91no—
746C23—181no—
747C23—362no—
748C23—362no—
749C23—721no—
750C23#381111yescharacteristic
751Q8—21no—
752Q8—21no—
753Q8—61no—
754Q8—61no—
755D4—21no—
756D4—42no—
757D4—182no—
758D4—181no—
759D4—181no—
760D4—362no—
761D4—721no—
762D4#380412yes—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—42no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—91no—
772C2×C4—91no—
773C2×C4—91no—
774C2×C4—181no—
775C2×C4—181no—
776C2×C4—181no—
777C2×C4—362no—
778C2×C4—721no—
779C2×C4#381111yescharacteristic
780C2×C4C22×D3211yescharacteristic
781C8—61no—
782C8—61no—
783C8—61no—
784C8—61no—
785C2×C3—21no—
786C2×C3—21no—
787C2×C3—21no—
788C2×C3—44no—
789C2×C3—42no—
790C2×C3—41no—
791C2×C3—42no—
792C2×C3—41no—
793C2×C3—81no—
794C2×C3#549011yescharacteristic
795C2×C3#559111yescharacteristic
796C2×C3D3×#13511yescharacteristic
797C2×C3D3×#13511yescharacteristic
798C2×C3#577011yescharacteristic
799C2×C3#577811yescharacteristic
800D3—62no—
801D3—62no—
802D3—122no—
803D3—242no—
804D3—241no—
805D3—241no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—22no—
810C22—41no—
811C22—41no—
812C22—92no—
813C22—181no—
814C22—181no—
815C22—361no—
816C22—361no—
817C22—361no—
818C22—724no—
819C22C2×#381111yescharacteristic
820C4—21no—
821C4—41no—
822C4—121no—
823C4—121no—
824C4—121no—
825C4—121no—
826C4—181no—
827C4—181no—
828C4—181no—
829C4—361no—
830C4C2×#380411yescharacteristic
831C4#6433011yescharacteristic
832C3—21no—
833C3#7884511yescharacteristic, complemented
834C3#8024611yescharacteristic, complemented
835C2—41no—
836C2—42no—
837C2—182no—
838C2—721no—
839C2#1059545911yescharacteristic
840C2#1059547311yescharacteristic
841C2#1059550011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
prime radical#10596300C2
hypercenterC2×#41D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10594970C2semidirect
3. C3×#5239C2semidirect
4. C3×#5233C2semidirect
5. #10591601C2semidirect
6. #10591579C2semidirect
7. #10591553C2semidirect
8. #10591539C2semidirect
9. #10591479C2semidirect
10. #10591467C2semidirect
11. #10591445C2semidirect
12. #10591416C2semidirect
13. #10591177C2semidirect
14. #10591148C2semidirect
15. #10591136C2semidirect
29. C2×C3×#216C22semidirect
31. C3×#926C22semidirect
32. C3×#924C22semidirect
33. C22×C3×C3⋊C8C22semidirect
37. #63872C22semidirect
40. #63843C22semidirect
44. C3×#835C22semidirect
45. C3×#835C22semidirect
46. C3×#835C22semidirect
50. C3×#830C22semidirect
51. #63575C22semidirect
52. #63573C22semidirect
53. #63573C22semidirect
54. #63572C22semidirect
55. #63566C22semidirect
60. #63553C22semidirect
68. #5239D3semidirect
69. #5233D3semidirect
164. C2×#216C2×D3semidirect
188. #926C2×D3semidirect
189. #924C2×D3semidirect
190. C22×C3⋊C8C2×D3semidirect
216. #835C2×D3semidirect
217. #835C2×D3semidirect
218. #835C2×D3semidirect
222. #830C2×D3semidirect
743. C32#3296semidirect
833. C3#78845semidirect
834. C3#80246semidirect

Maximal subgroups

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

subgroupindex
#105963002
#105949702
C3×#52392
C3×#52332
#105916012
#105915792
#105915532
#105915392
#105914792
#105914672
#105914452
#105914162
#105911772
#105911482
#105911362
#802463
#788453