Finite Group Databasebeta

← #11887386

Subgroups — #11887386

Order 1152.

907 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595067C211yesmaximal, characteristic, complemented
2#10594946C211yesmaximal, characteristic, complemented
3#10592814C211yesmaximal, characteristic, complemented
4C3×#5113C211yesmaximal, characteristic, complemented
5C3×C8×#67C211yesmaximal, characteristic, complemented
6#10591163C211yesmaximal, characteristic, complemented
7#10591136C211yesmaximal, characteristic, complemented
8#10590947C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590872C211yesmaximal, characteristic, complemented
11#10590847C211yesmaximal, characteristic, complemented
12#10590770C211yesmaximal, characteristic, complemented
13#10590767C211yesmaximal, characteristic, complemented
14#10590745C211yesmaximal, characteristic, complemented
15#10590682C211yesmaximal, characteristic, complemented
16#79441—31nomaximal
17#78846—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic, complemented
21#64139C2211yescharacteristic
22#64139C2211yescharacteristic, complemented
23C2×#3745C2211yescharacteristic
24C3×C4×#67C2211yescharacteristic
25C3×#926C2211yescharacteristic, complemented
26C2×C3×D3×C8C2211yescharacteristic
27#63983—21no—
28#63975—21no—
29#63971—21no—
30#63971—21no—
31D3×(C2×D3)⋊C4—21no—
32#63909C2211yescharacteristic
33#63894C2211yescharacteristic, complemented
34Dic3×D12C2211yescharacteristic
35D3×C4⋊Dic3C2211yescharacteristic
36#63880—21no—
37#63869C2211yescharacteristic, complemented
38#63868—21no—
39#63864C2211yescharacteristic
40#63856C2211yescharacteristic
41#63850—21no—
42C2×#3717C2211yescharacteristic, complemented
43C2×#3714C2211yescharacteristic
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic, complemented
46#63645C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63563C2211yescharacteristic
61#5829—31no—
62#5565—31no—
63#5550—31no—
64#5530—31no—
65C3×C8×D4—31no—
66C3×#416—31no—
67#5238—31no—
68#5115—31no—
69#5115—31no—
70#5115—61no—
71#5114—31no—
72#5113D311yescharacteristic, complemented
73C2×#821—31no—
74C8×#67D311yescharacteristic, complemented
75#5003—31no—
76#4847—31no—
77#4844—31no—
78#4819—31no—
79#4811—31no—
80#4807—31no—
81#4800—31no—
82#4773—31no—
83D3×#102—31no—
84#4766—31no—
85#4756—31no—
86#4737—31no—
87#4734—31no—
88#4732—31no—
89#4722—31no—
90#4697—31no—
91C4×D24—31no—
92C22×D32—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×#638—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C3×#67—21no—
99C2×C3×#67D411yescharacteristic
100C3×#235—22no—
101C3×#235—41no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#624—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111D3×D12—22no—
112D3×D12—41no—
113C2×C32×C8—41no—
114C2×C32×C8C2311yescharacteristic
115C2×C32×C8C2311yescharacteristic
116#3752—21no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3745—41no—
121C3×#217—21no—
122C3×#217D411yescharacteristic
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4D411yescharacteristic
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—41no—
132#3724—21no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137#3722—21no—
138#3722—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142#3717—41no—
143#3714—22no—
144#3297—91noSylow
145C2×C3×#41—31no—
146C2×D3×D4—31no—
147C2×#235C2×D311yescharacteristic
148C22×D12—31no—
149C22×C3×C8—21no—
150C22×C3×C8—31no—
151C22×C3×C8C2×D311yescharacteristic, complemented
152C22×C3×C8C2×D311yescharacteristic, complemented
153C3×C4×D4—31no—
154C3×#117—31no—
155#947—31no—
156#946—31no—
157C2×#215—31no—
158#939—61no—
159#939—61no—
160#937—61no—
161#937—61no—
162D4×Dic3—31no—
163C2×#213—31no—
164#930—31no—
165#930—31no—
166#930—31no—
167#930—31no—
168#930—31no—
169#930—61no—
170#930—61no—
171#929—61no—
172C4×#67C2×D311yescharacteristic
173C2×(C2×D3)⋊C4—61no—
174#926C2×D311yescharacteristic, complemented
175C2×C4⋊Dic3—31no—
176#924—31no—
177C2×D24—31no—
178C2×D24—31no—
179C2×D24—31no—
180C2×D24—61no—
181C2×#204—31no—
182C2×D3×C8C2×D311yescharacteristic
183#898—61no—
184#895—31no—
185#894—61no—
186#893—31no—
187D3×C4⋊C4—31no—
188#890—31no—
189#884—61no—
190#884—61no—
191#883—61no—
192#883—61no—
193#67⋊C4—61no—
194D3×C22⋊C4—61no—
195#876—61no—
196#875—31no—
197C4×D12—31no—
198C4×D12—31no—
199C4×D12—61no—
200#870—31no—
201C3×C4⋊C8—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—31no—
207C3×C22⋊C8—31no—
208C3×C4×C8—31no—
209#835—31no—
210#832—31no—
211#830C2×D311yescharacteristic, complemented
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—61no—
220#821—61no—
221#821C2×D311yescharacteristic
222#821C2×D311yescharacteristic
223(C2×D3)⋊C8C2×D311yescharacteristic
224#818—31no—
225#818—31no—
226#818—31no—
227#818—61no—
228#817—31no—
229#816—31no—
230#816C2×D311yescharacteristic, complemented
231#816C2×D311yescharacteristic, complemented
232Dic3⋊C8C2×D311yescharacteristic, complemented
233C8×Dic3C2×D311yescharacteristic, complemented
234#809—31no—
235#809—31no—
236#808—31no—
237#807—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3C2×D411yescharacteristic
243C2×D32—42no—
244C2×D32—42no—
245C2×D32—81no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250#638—81no—
251#638—81no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—21no—
258C3×#67—22no—
259C3×#67—42no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12#4112yes—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×C4×D3—42no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273#626—42no—
274#626—42no—
275#624—81no—
276D3×Dic3—81no—
277D3×Dic3—81no—
278C32×C8—21no—
279C32×C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—91no—
284#488—91no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—31no—
295#416—31no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C3×#41—62no—
300C3×#41—121no—
301C2×C3×Q8—31no—
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—61no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—61no—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C2×#67—21no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—121no—
318C2×#67—121no—
319C2×#67D1211yescharacteristic
320C22×Dic3—61no—
321C22×Dic3—61no—
322D3×D4—62no—
323D3×D4—121no—
324#235—22no—
325#235—41no—
326C2×D12—31no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—31no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12—62no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—121no—
336C2×D12C22×D311yescharacteristic
337C2×C4×D3—21no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3C22×D311yescharacteristic
343C2×Dic6C22×D311yescharacteristic
344C2×C3×C8—21no—
345C2×C3×C8—21no—
346C2×C3×C8—31no—
347C2×C3×C8—31no—
348C2×C3×C8—41no—
349C2×C3×C8—41no—
350C2×C3×C8—42no—
351C2×C3×C8—121no—
352C2×C3×C8C22×D311yescharacteristic
353C2×C3×C8C22×D311yescharacteristic
354C2×C3×C8C22×D311yescharacteristic
355C2×C3×C8C22×D311yescharacteristic
356C3×C4⋊C4—31no—
357C3×C4⋊C4—31no—
358C3×C4⋊C4—31no—
359C3×C22⋊C4—31no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—61no—
362C3×C42—31no—
363C3×C42—61no—
364#217—21no—
365#217—61no—
366#217—61no—
367#217D1211yescharacteristic
368#215—121no—
369#213—62no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
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—121no—
385(C2×D3)⋊C4—121no—
386(C2×D3)⋊C4D1211yescharacteristic
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4D1211yescharacteristic
404C4×Dic3—21no—
405C4×Dic3C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D24—62no—
409D24—121no—
410D24—121no—
411D24—122no—
412#204—121no—
413D3×C8—41no—
414C22×C32—21no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32C22×D411yescharacteristic
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—22no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3#13512yes—
430D32—84no—
431C32×C4—21no—
432C32×C4C2×#4111yescharacteristic
433C32×C4H(5,𝔽2)11yescharacteristic
434C3⋊Dic3—41no—
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C2×#41—31no—
443C22×D4—91no—
444C2×SD16—91no—
445C2×D8—91no—
446C2×D8—91no—
447C22×C8—31no—
448C22×C8D3211yescharacteristic, complemented
449#126—181no—
450#125—91no—
451#124—91no—
452#123—181no—
453#123—181no—
454C22⋊Q8—91no—
455#121—91no—
456#121—91no—
457#121—91no—
458#121—181no—
459#121—181no—
460#120—181no—
461C4×D4—31no—
462C4×D4—91no—
463C4×D4—91no—
464C4×D4—181no—
465#117—31no—
466C2×C4⋊C4—91no—
467C2×C22⋊C4—181no—
468#107—91no—
469#107—91no—
470#106—91no—
471C4⋊C8—31no—
472#103—31no—
473#103—31no—
474#103—91no—
475#102—31no—
476#102—31no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482C22⋊C8—31no—
483C22⋊C8—31no—
484C4×C8—31no—
485C23×C3—21no—
486C23×C3—31no—
487C23×C3—61no—
488C23×C3C2×D1211yescharacteristic
489C23×C3D3×D411yescharacteristic
490C22×D3—21no—
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—121no—
496C22×D3—121no—
497C22×D3—122no—
498C22×D3—122no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3—241no—
502C22×D3—241no—
503C22×D3C2×D1211yescharacteristic
504C3×Q8—61no—
505C3×Q8—61no—
506C3×D4—32no—
507C3×D4—62no—
508C3×D4—61no—
509C3×D4—122no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—122no—
527C2×C3×C4C2×D1211yescharacteristic
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531#67—22no—
532#67—42no—
533#67—122no—
534#67—122no—
535#67—241no—
536#67—241no—
537#67—241no—
538#67—241no—
539#67—242no—
540#67—242no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—121no—
549C2×Dic3—121no—
550C2×Dic3—241no—
551C2×Dic3—241no—
552C2×Dic3C2×D1211yescharacteristic
553C2×Dic3C2×D1211yescharacteristic
554C2×Dic3C2×D1211yescharacteristic
555D12—21no—
556D12—61no—
557D12—61no—
558D12—61no—
559D12—61no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—61no—
564D12—121no—
565D12—121no—
566D12—121no—
567D12—121no—
568D12—122no—
569D12—122no—
570D12#23512yes—
571C4×D3—21no—
572C4×D3—21no—
573C4×D3—42no—
574C4×D3—241no—
575C4×D3—241no—
576C4×D3—241no—
577C4×D3—241no—
578Dic6—21no—
579Dic6—21no—
580C3×C8—22no—
581C3×C8—21no—
582C3×C8—21no—
583C3×C8—21no—
584C3×C8—21no—
585C3×C8—41no—
586C3×C8—61no—
587C3×C8—61no—
588C3⋊C8—21no—
589C3⋊C8—21no—
590C2×C32—41no—
591C2×C32#54611yescharacteristic
592C2×C32C2×#13511yescharacteristic
593C2×C32#57611yescharacteristic
594C3⋊D3—81no—
595C3⋊D3—81no—
596C3×D3—22no—
597C3×D3—42no—
598C24—181no—
599#41—62no—
600#41—121no—
601C2×Q8—31no—
602C2×D4—31no—
603C2×D4—31no—
604C2×D4—61no—
605C2×D4—91no—
606C2×D4—91no—
607C2×D4—181no—
608C2×D4—182no—
609C2×D4—181no—
610C2×D4—181no—
611C2×D4—181no—
612C2×D4—361no—
613C22×C4—31no—
614C22×C4—61no—
615C22×C4—181no—
616C22×C4—181no—
617C22×C4—181no—
618C22×C4C2×D3211yescharacteristic
619SD16—361no—
620D8—182no—
621D8—361no—
622C2×C8—31no—
623C2×C8—31no—
624C2×C8—41no—
625C2×C8—121no—
626C2×C8C2×D3211yescharacteristic
627C2×C8C2×D3211yescharacteristic
628C4⋊C4—31no—
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—91no—
632C4⋊C4—91no—
633C4⋊C4—181no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C22⋊C4—31no—
638C22⋊C4—31no—
639C22⋊C4—61no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C42—31no—
649C42—61no—
650C22×C3—22no—
651C22×C3—21no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—32no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3—61no—
662C22×C3—61no—
663C22×C3—62no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3C22×D1211yescharacteristic
667C22×C3C2×D3×D411yescharacteristic
668C2×D3—21no—
669C2×D3—21no—
670C2×D3—22no—
671C2×D3—41no—
672C2×D3—41no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—241no—
686C2×D3—241no—
687C2×D3—241no—
688C2×D3—241no—
689C2×D3—241no—
690C2×D3—241no—
691C2×D3—244no—
692C2×D3—244no—
693C2×D3#90412yes—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—21no—
698C3×C4—41no—
699C3×C4—61no—
700C3×C4—61no—
701C3×C4—61no—
702C3×C4—121no—
703C3×C4—121no—
704C3×C4—121no—
705C3×C4C2×#23511yescharacteristic
706C3×C4#100411yescharacteristic
707C3×C4#100411yescharacteristic
708C3×C4D3×#4111yescharacteristic
709Dic3—21no—
710Dic3—21no—
711Dic3—21no—
712Dic3—41no—
713Dic3—41no—
714Dic3—41no—
715Dic3—121no—
716Dic3—121no—
717Dic3—121no—
718Dic3—121no—
719Dic3—241no—
720Dic3—241no—
721C32#329711yescharacteristic, complemented, Sylow
722C23—31no—
723C23—61no—
724C23—181no—
725C23—181no—
726C23—362no—
727C23—362no—
728C23—721no—
729C23D3×D1211yescharacteristic
730Q8—61no—
731Q8—61no—
732D4—32no—
733D4—62no—
734D4—61no—
735D4—122no—
736D4—181no—
737D4—181no—
738D4—181no—
739D4—181no—
740D4—362no—
741D4—362no—
742D4—721no—
743D4—721no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—31no—
747C2×C4—31no—
748C2×C4—31no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—122no—
755C2×C4—181no—
756C2×C4—181no—
757C2×C4—721no—
758C2×C4—721no—
759C2×C4—721no—
760C2×C4D3×D1211yescharacteristic
761C2×C4C22×D3211yescharacteristic
762C8—21no—
763C8—21no—
764C8—61no—
765C8—61no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—42no—
770C2×C3—41no—
771C2×C3—41no—
772C2×C3—62no—
773C2×C3—122no—
774C2×C3#549011yescharacteristic
775C2×C3#555411yescharacteristic
776C2×C3C2×#90411yescharacteristic
777C2×C3#575211yescharacteristic
778C2×C3D3×#13511yescharacteristic
779C2×C3#576911yescharacteristic
780D3—22no—
781D3—42no—
782D3—241no—
783D3—241no—
784D3—241no—
785D3—241no—
786D3—481no—
787D3—481no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—32no—
792C22—61no—
793C22—61no—
794C22—62no—
795C22—121no—
796C22—121no—
797C22—361no—
798C22—361no—
799C22—361no—
800C22—361no—
801C22—361no—
802C22—361no—
803C22—724no—
804C22C2×D3×D1211yescharacteristic
805C4—21no—
806C4—61no—
807C4—61no—
808C4—61no—
809C4—121no—
810C4—121no—
811C4—121no—
812C4—361no—
813C4—361no—
814C4D3×#23511yescharacteristic
815C4#6433011yescharacteristic
816C3—21no—
817C3#7884611yescharacteristic, complemented
818C3#7944111yescharacteristic, complemented
819C2—41no—
820C2—62no—
821C2—122no—
822C2—721no—
823C2—721no—
824C2D3×#90411yescharacteristic
825C2#1059468011yescharacteristic
826C2#1059507311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
hypercenterC22×C8D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. #10595067C2semidirect
2. #10594946C2semidirect
3. #10592814C2semidirect
4. C3×#5113C2semidirect
5. C3×C8×#67C2semidirect
6. #10591163C2semidirect
7. #10591136C2semidirect
8. #10590947C2semidirect
9. D3×#821C2semidirect
10. #10590872C2semidirect
11. #10590847C2semidirect
12. #10590770C2semidirect
13. #10590767C2semidirect
14. #10590745C2semidirect
15. #10590682C2semidirect
20. C22×C32×C8C22semidirect
22. #64139C22semidirect
25. C3×#926C22semidirect
33. #63894C22semidirect
37. #63869C22semidirect
42. C2×#3717C22semidirect
45. #63648C22semidirect
46. #63645C22semidirect
47. C3×#830C22semidirect
51. C3×#816C22semidirect
52. C3×#816C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
57. #63566C22semidirect
72. #5113D3semidirect
74. C8×#67D3semidirect
151. C22×C3×C8C2×D3semidirect
152. C22×C3×C8C2×D3semidirect
174. #926C2×D3semidirect
211. #830C2×D3semidirect
230. #816C2×D3semidirect
231. #816C2×D3semidirect
232. Dic3⋊C8C2×D3semidirect
233. C8×Dic3C2×D3semidirect
448. C22×C8D32semidirect
721. C32#3297semidirect
817. C3#78846semidirect
818. C3#79441semidirect

Maximal subgroups

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

subgroupindex
#105950672
#105949462
#105928142
C3×#51132
C3×C8×#672
#105911632
#105911362
#105909472
D3×#8212
#105908722
#105908472
#105907702
#105907672
#105907452
#105906822
#794413
#788463