Finite Group Databasebeta

← #11887449

Subgroups — #11887449

Order 1152.

888 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594003C211yesmaximal, characteristic, complemented
2#10593923C211yesmaximal, characteristic, complemented
3#10592396C211yesmaximal, characteristic, complemented
4C3×C4×D24C211yesmaximal, characteristic, complemented
5C3×C8×D12C211yesmaximal, characteristic, complemented
6#10590962C211yesmaximal, characteristic, complemented
7#10590954C211yesmaximal, characteristic, complemented
8#10590944C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590826C211yesmaximal, characteristic, complemented
11#10590825C211yesmaximal, characteristic, complemented
12#10590705C211yesmaximal, characteristic, complemented
13#10590684C211yesmaximal, characteristic, complemented
14#10590366C211yesmaximal, characteristic, complemented
15#10590271C211yesmaximal, characteristic, complemented
16#79609—31nomaximal
17#79441—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20#64084C2211yescharacteristic
21#64079C2211yescharacteristic, complemented
22C2×C3×D24C2211yescharacteristic
23C2×C3×D3×C8C2211yescharacteristic
24C2×C3×D3×C8C2211yescharacteristic, complemented
25C3×C4×D12C2211yescharacteristic
26C3×C4×D12C2211yescharacteristic
27C3×C4×D12C2211yescharacteristic, complemented
28#63922—21no—
29D3×(C2×D3)⋊C4—21no—
30#63909C2211yescharacteristic
31#63908C2211yescharacteristic
32#63908C2211yescharacteristic, complemented
33#63906—21no—
34#63905—21no—
35#63890—21no—
36D3×C4⋊Dic3C2211yescharacteristic
37#63885—21no—
38#63879—21no—
39#63858—21no—
40#63857C2211yescharacteristic
41#63841C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic, complemented
43C2×#3714C2211yescharacteristic
44C32×C4×C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic
47#63643C2211yescharacteristic, complemented
48#63643C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×#818C2211yescharacteristic, complemented
54C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5565—31no—
62#5558—31no—
63#5554—31no—
64#5550—31no—
65C3×C4×D8—31no—
66C3×C8×D4—31no—
67#5158—31no—
68#5156—31no—
69#5115—31no—
70#5114—31no—
71#5113—31no—
72C2×#821—31no—
73#5016—31no—
74#5009—31no—
75#4885—31no—
76#4884—31no—
77#4847—31no—
78#4844—31no—
79#4778—31no—
80#4775—31no—
81#4772—31no—
82D3×#102—31no—
83#4737—31no—
84#4734—31no—
85#4732—31no—
86#4722—31no—
87#4697—31no—
88#4697—31no—
89#4697—61no—
90C4×D24D311yescharacteristic, complemented
91C8×D12D311yescharacteristic, complemented
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×C3×D12D411yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#625—21no—
105C2×#625—21no—
106C2×#625—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109D3×D12—22no—
110D3×D12—41no—
111#3795—22no—
112#3795—41no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115C32×C42C2311yescharacteristic
116#3752—21no—
117#3752—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121#3750—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4D411yescharacteristic
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3D411yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D24—22no—
132C3×D3×C8—41no—
133C3×D3×C8—41no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3716—41no—
143#3714—41no—
144#3297—91noSylow
145C2×#237—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C2×C3×D8—31no—
150C22×C3×C8—31no—
151C22×C3×C8—31no—
152C3×C4×D4—31no—
153C3×C4×D4—31no—
154C3×C4×D4—31no—
155#939—61no—
156#938—31no—
157#938—31no—
158#937—61no—
159C2×#214—31no—
160C2×#213—31no—
161#930—31no—
162#930—31no—
163#930—31no—
164#930—61no—
165#929—61no—
166C4×#67—61no—
167C2×(C2×D3)⋊C4—61no—
168#926—31no—
169C2×C4⋊Dic3—31no—
170#924—31no—
171C2×D24—31no—
172C2×D24C2×D311yescharacteristic
173C2×#204—31no—
174C2×D3×C8C2×D311yescharacteristic
175C2×D3×C8C2×D311yescharacteristic, complemented
176#898—61no—
177#897—31no—
178#895—31no—
179#894—61no—
180#892—31no—
181D3×C4⋊C4—31no—
182#886—61no—
183#884—61no—
184#884—61no—
185#883—61no—
186#882—61no—
187#67⋊C4—61no—
188D3×C22⋊C4—61no—
189#879—61no—
190#875—31no—
191#875—31no—
192#875—61no—
193C4×D12C2×D311yescharacteristic
194C4×D12C2×D311yescharacteristic
195C4×D12C2×D311yescharacteristic, complemented
196#870—31no—
197#870—31no—
198#870—61no—
199C3×#107—31no—
200C3×C4⋊C8—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×C22⋊C8—31no—
204C3×C22⋊C8—31no—
205C3×C4×C8—21no—
206C3×C4×C8C2×D311yescharacteristic, complemented
207C3×C4×C8C2×D311yescharacteristic, complemented
208#832—31no—
209#832—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—61no—
218#821—61no—
219#821C2×D311yescharacteristic
220#821C2×D311yescharacteristic, complemented
221(C2×D3)⋊C8C2×D311yescharacteristic
222(C2×D3)⋊C8C2×D311yescharacteristic, complemented
223#818—31no—
224#818C2×D311yescharacteristic, complemented
225#817—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—31no—
231#816—61no—
232#816—61no—
233#810—31no—
234#809—31no—
235#808—31no—
236#807—31no—
237C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C2×D32—42no—
244C2×D32—42no—
245C2×D32—81no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254#634—21no—
255#634—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—22no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—81no—
270C3×C4×D3—81no—
271#626—42no—
272#626—81no—
273#625—42no—
274#625—42no—
275#625—81no—
276D3×Dic3—42no—
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—31no—
294C8×D4—31no—
295#416—91no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316#237—62no—
317#237—121no—
318D3×D4—62no—
319D3×D4—121no—
320#235—62no—
321#235—121no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—61no—
325C2×D12—62no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—121no—
329C2×D12D1211yescharacteristic
330C2×D12C22×D311yescharacteristic
331C2×D12C22×D311yescharacteristic
332C2×C4×D3—21no—
333C2×C4×D3—21no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3C22×D311yescharacteristic
337C2×C4×D3C22×D311yescharacteristic
338C2×Dic6—31no—
339C2×Dic6—31no—
340C2×Dic6—61no—
341C3×D8—62no—
342C2×C3×C8—21no—
343C2×C3×C8—21no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—121no—
347C2×C3×C8—121no—
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C2×C3×C8C22×D311yescharacteristic
351C2×C3×C8C22×D311yescharacteristic
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—31no—
357C3×C22⋊C4—61no—
358C3×C22⋊C4—61no—
359C3×C42—21no—
360C3×C42C22×D311yescharacteristic
361C3×C42C22×D311yescharacteristic
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#214—121no—
367#213—121no—
368(C2×D3)⋊C4—21no—
369(C2×D3)⋊C4—21no—
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—121no—
381(C2×D3)⋊C4—121no—
382(C2×D3)⋊C4D1211yescharacteristic
383(C2×D3)⋊C4D1211yescharacteristic
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3D1211yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—121no—
402Dic3⋊C4—121no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407D24—22no—
408D24—121no—
409#204—121no—
410D3×C8—41no—
411D3×C8—41no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—22no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3#13512yes—
428D32—84no—
429C32×C4—21no—
430C32×C4—21no—
431C32×C4C2×#4111yescharacteristic
432C32×C4H(5,𝔽2)11yescharacteristic
433C3⋊Dic3—41no—
434C3⋊Dic3—41no—
435C3⋊Dic3—41no—
436C3×Dic3—21no—
437C3×Dic3—21no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C2×#41—91no—
441C22×D4—91no—
442C2×SD16—91no—
443C2×D8—31no—
444C2×D8—91no—
445C22×C8—31no—
446C22×C8—31no—
447#126—181no—
448#125—91no—
449#124—91no—
450#123—181no—
451#123—181no—
452C22⋊Q8—91no—
453#121—91no—
454#121—91no—
455#121—91no—
456#121—181no—
457#121—181no—
458#120—181no—
459C4×D4—31no—
460C4×D4—31no—
461C4×D4—31no—
462C4×D4—181no—
463#117—91no—
464C2×C4⋊C4—91no—
465C2×C22⋊C4—181no—
466#107—31no—
467#107—91no—
468#106—91no—
469C4⋊C8—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480C22⋊C8—31no—
481C22⋊C8—31no—
482C4×C8D3211yescharacteristic, complemented
483C23×C3—31no—
484C23×C3—31no—
485C23×C3—61no—
486C23×C3—61no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—121no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—241no—
497C22×D3—241no—
498C22×D3C2×D1211yescharacteristic
499C22×D3C2×D1211yescharacteristic
500C3×D4—32no—
501C3×D4—62no—
502C3×D4—61no—
503C3×D4—61no—
504C3×D4—61no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—241no—
517C2×C3×C4—241no—
518C2×C3×C4C2×D1211yescharacteristic
519C2×C3×C4C2×D1211yescharacteristic
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4D3×D411yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523C2×C3×C4C23×D311yescharacteristic
524#67—122no—
525#67—122no—
526#67—122no—
527#67—122no—
528#67—122no—
529#67—241no—
530#67—241no—
531#67—241no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—121no—
543C2×Dic3—122no—
544C2×Dic3—241no—
545C2×Dic3C2×D1211yescharacteristic
546C2×Dic3C2×D1211yescharacteristic
547D12—22no—
548D12—21no—
549D12—21no—
550D12—21no—
551D12—61no—
552D12—61no—
553D12—61no—
554D12—61no—
555D12—121no—
556D12—121no—
557D12—122no—
558D12—241no—
559D12#23512yes—
560C4×D3—21no—
561C4×D3—21no—
562C4×D3—21no—
563C4×D3—21no—
564C4×D3—81no—
565C4×D3—81no—
566C4×D3—122no—
567C4×D3—241no—
568Dic6—61no—
569Dic6—61no—
570Dic6—61no—
571Dic6—61no—
572Dic6—121no—
573Dic6—121no—
574C3×C8—21no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—21no—
578C3×C8—41no—
579C3×C8—41no—
580C3×C8—61no—
581C3×C8—61no—
582C3⋊C8—21no—
583C3⋊C8—21no—
584C2×C32#54611yescharacteristic
585C2×C32C2×#13511yescharacteristic
586C2×C32#57611yescharacteristic
587C3⋊D3—81no—
588C3×D3—22no—
589C3×D3—42no—
590C3×D3—41no—
591C3×D3—81no—
592C24—181no—
593#41—182no—
594#41—361no—
595C2×Q8—91no—
596C2×D4—31no—
597C2×D4—31no—
598C2×D4—31no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4—182no—
602C2×D4—181no—
603C2×D4—181no—
604C2×D4—181no—
605C2×D4—181no—
606C2×D4—361no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—181no—
612C22×C4—181no—
613SD16—361no—
614D8—62no—
615D8—361no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8—121no—
619C2×C8—121no—
620C2×C8C2×D3211yescharacteristic
621C2×C8C2×D3211yescharacteristic
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—91no—
626C4⋊C4—91no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C22⋊C4—181no—
642C42—181no—
643C42C2×D3211yescharacteristic
644C22×C3—21no—
645C22×C3—32no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—62no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3C22×D1211yescharacteristic
658C22×C3C2×D3×D411yescharacteristic
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—22no—
664C2×D3—21no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—241no—
677C2×D3—241no—
678C2×D3—241no—
679C2×D3—244no—
680C2×D3—244no—
681C2×D3#90412yes—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—21no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—61no—
691C3×C4—61no—
692C3×C4—121no—
693C3×C4—121no—
694C3×C4C2×#23511yescharacteristic
695C3×C4#100411yescharacteristic
696C3×C4D3×#4111yescharacteristic
697C3×C4#100911yescharacteristic
698Dic3—21no—
699Dic3—21no—
700Dic3—41no—
701Dic3—41no—
702Dic3—121no—
703Dic3—121no—
704Dic3—121no—
705Dic3—121no—
706Dic3—121no—
707Dic3—121no—
708Dic3—241no—
709Dic3—241no—
710Dic3—241no—
711C32#329711yescharacteristic, complemented, Sylow
712C23—31no—
713C23—31no—
714C23—61no—
715C23—61no—
716C23—181no—
717C23—362no—
718C23—362no—
719C23—721no—
720Q8—181no—
721Q8—181no—
722D4—32no—
723D4—62no—
724D4—61no—
725D4—61no—
726D4—61no—
727D4—181no—
728D4—181no—
729D4—362no—
730D4—362no—
731D4—362no—
732D4—721no—
733D4—721no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—181no—
743C2×C4—181no—
744C2×C4—181no—
745C2×C4—241no—
746C2×C4—241no—
747C2×C4—362no—
748C2×C4—721no—
749C2×C4D3×D1211yescharacteristic
750C2×C4D3×D1211yescharacteristic
751C2×C4C22×D3211yescharacteristic
752C8—21no—
753C8—21no—
754C8—61no—
755C8—61no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—62no—
760C2×C3—122no—
761C2×C3—121no—
762C2×C3—241no—
763C2×C3#555011yescharacteristic
764C2×C3#555411yescharacteristic
765C2×C3C2×#90411yescharacteristic
766C2×C3#575211yescharacteristic
767C2×C3#575711yescharacteristic
768C2×C3D3×#13511yescharacteristic
769D3—22no—
770D3—41no—
771D3—42no—
772D3—81no—
773D3—241no—
774D3—241no—
775D3—481no—
776C22—32no—
777C22—61no—
778C22—61no—
779C22—61no—
780C22—61no—
781C22—61no—
782C22—62no—
783C22—121no—
784C22—121no—
785C22—121no—
786C22—121no—
787C22—121no—
788C22—361no—
789C22—361no—
790C22—361no—
791C22—724no—
792C22C2×D3×D1211yescharacteristic
793C4—21no—
794C4—21no—
795C4—61no—
796C4—61no—
797C4—121no—
798C4—121no—
799C4—361no—
800C4—361no—
801C4—361no—
802C4D3×#23511yescharacteristic
803C4#6430711yescharacteristic
804C3—21no—
805C3#7944111yescharacteristic, complemented
806C3#7960911yescharacteristic, complemented
807C2—62no—
808C2—121no—
809C2—122no—
810C2—241no—
811C2—721no—
812C2#1059400311yescharacteristic
813C2D3×#90411yescharacteristic
814C2#1059467811yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
hypercenterC4×C8D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. #10594003C2semidirect
2. #10593923C2semidirect
3. #10592396C2semidirect
4. C3×C4×D24C2semidirect
5. C3×C8×D12C2semidirect
6. #10590962C2semidirect
7. #10590954C2semidirect
8. #10590944C2semidirect
9. D3×#821C2semidirect
10. #10590826C2semidirect
11. #10590825C2semidirect
12. #10590705C2semidirect
13. #10590684C2semidirect
14. #10590366C2semidirect
15. #10590271C2semidirect
21. #64079C22semidirect
24. C2×C3×D3×C8C22semidirect
27. C3×C4×D12C22semidirect
32. #63908C22semidirect
41. #63841C22semidirect
42. C2×#3716C22semidirect
44. C32×C4×C8C22semidirect
47. #63643C22semidirect
48. #63643C22semidirect
50. C3×#821C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×#818C22semidirect
54. C3×C4⋊(C3⋊C8)C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
57. #63567C22semidirect
90. C4×D24D3semidirect
91. C8×D12D3semidirect
175. C2×D3×C8C2×D3semidirect
195. C4×D12C2×D3semidirect
206. C3×C4×C8C2×D3semidirect
207. C3×C4×C8C2×D3semidirect
220. #821C2×D3semidirect
222. (C2×D3)⋊C8C2×D3semidirect
224. #818C2×D3semidirect
237. C4⋊(C3⋊C8)C2×D3semidirect
482. C4×C8D32semidirect
711. C32#3297semidirect
805. C3#79441semidirect
806. C3#79609semidirect

Maximal subgroups

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

subgroupindex
#105940032
#105939232
#105923962
C3×C4×D242
C3×C8×D122
#105909622
#105909542
#105909442
D3×#8212
#105908262
#105908252
#105907052
#105906842
#105903662
#105902712
#796093
#794413