Finite Group Databasebeta

← #11887384

Subgroups — #11887384

Order 1152.

919 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595078C211yesmaximal, characteristic, complemented
2#10594945C211yesmaximal, characteristic, complemented
3#10592812C211yesmaximal, characteristic, complemented
4C3×#5115C211yesmaximal, characteristic, complemented
5C3×C8×#67C211yesmaximal, characteristic, complemented
6#10591182C211yesmaximal, characteristic, complemented
7#10591093C211yesmaximal, characteristic, complemented
8#10590944C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590863C211yesmaximal, characteristic, complemented
11#10590825C211yesmaximal, characteristic, complemented
12#10590774C211yesmaximal, characteristic, complemented
13#10590755C211yesmaximal, characteristic, complemented
14#10590745C211yesmaximal, characteristic, complemented
15#10590684C211yesmaximal, characteristic, complemented
16#80725—31nomaximal
17#79441—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic, complemented
21#64135C2211yescharacteristic, complemented
22C3×#930C2211yescharacteristic
23C3×#930C2211yescharacteristic, complemented
24C3×C4×#67C2211yescharacteristic
25C2×C3×D24C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic
27#63983—21no—
28#63970—21no—
29#63969—21no—
30#63958—21no—
31#63921—21no—
32#63908C2211yescharacteristic
33#63902—21no—
34#63894C2211yescharacteristic
35Dic3×D12C2211yescharacteristic, complemented
36D3×C4⋊Dic3C2211yescharacteristic
37#63869C2211yescharacteristic, complemented
38#63862—21no—
39#63860C2211yescharacteristic
40#63857C2211yescharacteristic
41#63853—21no—
42C2×#3716C2211yescharacteristic, complemented
43C2×#3714C2211yescharacteristic
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic
46#63643C2211yescharacteristic, complemented
47#63643C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×#818C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5614—31no—
62#5612—31no—
63#5565—31no—
64#5550—31no—
65C3×#466—31no—
66C3×C8×D4—31no—
67#5156—31no—
68#5153—31no—
69#5115D311yescharacteristic, complemented
70#5114—31no—
71#5113—31no—
72#5113—31no—
73#5113—61no—
74C2×#821—31no—
75C8×#67D311yescharacteristic, complemented
76#5037—31no—
77#5035—31no—
78#4891—31no—
79#4884—31no—
80#4847—31no—
81#4844—31no—
82#4778—31no—
83D3×#102—31no—
84#4768—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—
95#3828—22no—
96#3828—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C2×C3×#67D411yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×#626—21no—
107C2×#625—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#3757—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4×C3⋊Dic3—21no—
120C3×#217D411yescharacteristic
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4D411yescharacteristic
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D24—41no—
131C3×D3×C8—41no—
132#3724—21no—
133Dic3⋊Dic3—21no—
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—
141(C2×D3)⋊Dic3—21no—
142#3716—41no—
143#3714—22no—
144#3297—91noSylow
145C2×D3×D4—31no—
146C2×#235—31no—
147C2×#235—31no—
148C2×#235—61no—
149C22×D12—31no—
150C2×C3×D8—31no—
151C22×C3×C8—21no—
152C22×C3×C8—31no—
153C22×C3×C8C2×D311yescharacteristic, complemented
154C22×C3×C8C2×D311yescharacteristic, complemented
155C3×#121—31no—
156C3×#121—31no—
157C3×C4×D4—31no—
158#939—61no—
159#938—31no—
160#938—61no—
161#938—61no—
162#937—61no—
163#937—61no—
164#936—31no—
165#935—61no—
166D4×Dic3—31no—
167C2×#214—31no—
168C2×#213—31no—
169#930—31no—
170#930C2×D311yescharacteristic
171#930C2×D311yescharacteristic, complemented
172C4×#67C2×D311yescharacteristic
173#926—31no—
174#926—31no—
175#926—61no—
176C2×C4⋊Dic3—31no—
177#924—31no—
178C2×D24—31no—
179C2×D24C2×D311yescharacteristic
180C2×#204—31no—
181C2×D3×C8C2×D311yescharacteristic
182#898—61no—
183#897—31no—
184#894—61no—
185#893—31no—
186D3×C4⋊C4—31no—
187#890—31no—
188#884—61no—
189#883—61no—
190#883—61no—
191#67⋊C4—61no—
192#67⋊C4—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196#875—31no—
197C4×D12—31no—
198C4×D12—31no—
199#870—31no—
200C3×#107—31no—
201C3×C4⋊C8—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8—31no—
206C3×C4×C8—31no—
207#832—31no—
208#832—31no—
209#830C2×D311yescharacteristic, complemented
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#818—31no—
223#818C2×D311yescharacteristic, complemented
224#817—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—61no—
231#816—61no—
232Dic3⋊C8C2×D311yescharacteristic, complemented
233C8×Dic3C2×D311yescharacteristic, complemented
234#810—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—42no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)#4112yes—
256C4×C3⋊D3—42no—
257#634—21no—
258#634—21no—
259C3×#67—22no—
260C3×#67—81no—
261C3×#67—81no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×D12—21no—
270C3×D12—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273#626—42no—
274#625—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—31no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
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—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C22×C3×C4—21no—
305C22×C3×C4—31no—
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C2×#67—21no—
309C2×#67—21no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C2×#67—121no—
316C2×#67D1211yescharacteristic
317C22×Dic3—61no—
318C22×Dic3—61no—
319D3×D4—62no—
320D3×D4—121no—
321#235—62no—
322#235—62no—
323#235—64no—
324#235—121no—
325#235—121no—
326#235—122no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12—62no—
331C2×D12—61no—
332C2×D12—121no—
333C2×D12C22×D311yescharacteristic
334C2×D12C22×D311yescharacteristic
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—121no—
342C2×C4×D3C22×D311yescharacteristic
343C2×Dic6—31no—
344C2×Dic6—31no—
345C2×Dic6—61no—
346C3×D8—121no—
347C2×C3×C8—21no—
348C2×C3×C8—21no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8—41no—
352C2×C3×C8—41no—
353C2×C3×C8—42no—
354C2×C3×C8—121no—
355C2×C3×C8C22×D311yescharacteristic
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C2×C3×C8C22×D311yescharacteristic
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C22⋊C4—31no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C42—31no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217—61no—
373#217—61no—
374#217—121no—
375#217D1211yescharacteristic
376#214—121no—
377#213—62no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
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—61no—
387(C2×D3)⋊C4D1211yescharacteristic
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—61no—
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4D1211yescharacteristic
405C4×Dic3—61no—
406C4×Dic3—61no—
407C4×Dic3—121no—
408C4×Dic3C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410C2×C3⋊C8C22×D311yescharacteristic
411D24—41no—
412D24—62no—
413#204—121no—
414D3×C8—41no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—22no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—41no—
425C2×C3×D3—41no—
426C2×C3×D3—41no—
427C2×C3×D3—41no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3#13512yes—
431D32—84no—
432C32×C4—21no—
433C32×C4C2×#4111yescharacteristic
434C32×C4H(5,𝔽2)11yescharacteristic
435C3⋊Dic3—41no—
436C3⋊Dic3—41no—
437C3⋊Dic3—41no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—21no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C2×#41—91no—
444C22×D4—91no—
445C2×SD16—91no—
446C2×D8—31no—
447C2×D8—91no—
448C22×C8—31no—
449C22×C8D3211yescharacteristic, complemented
450#126—181no—
451#125—91no—
452#124—91no—
453#123—181no—
454#123—181no—
455C22⋊Q8—91no—
456#121—31no—
457#121—31no—
458#121—91no—
459#121—181no—
460#121—181no—
461#120—181no—
462C4×D4—31no—
463C4×D4—91no—
464C4×D4—91no—
465C4×D4—181no—
466#117—91no—
467C2×C4⋊C4—91no—
468C2×C22⋊C4—181no—
469#107—31no—
470#107—91no—
471#106—91no—
472C4⋊C8—31no—
473#103—91no—
474#103—91no—
475#103—91no—
476#102—31no—
477#102—31no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483C22⋊C8—31no—
484C22⋊C8—31no—
485C4×C8—31no—
486C23×C3—21no—
487C23×C3—31no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3C2×D1211yescharacteristic
491C23×C3D3×D411yescharacteristic
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—61no—
495C22×D3—61no—
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×D4—62no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—61no—
508C3×D4—61no—
509C3×D4—241no—
510C3×D4—241no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—31no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4C2×D1211yescharacteristic
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530#67—22no—
531#67—81no—
532#67—81no—
533#67—122no—
534#67—122no—
535#67—122no—
536#67—122no—
537#67—124no—
538#67—122no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—121no—
550C2×Dic3—241no—
551C2×Dic3—241no—
552C2×Dic3C2×D1211yescharacteristic
553C2×Dic3C2×D1211yescharacteristic
554C2×Dic3C2×D1211yescharacteristic
555D12—21no—
556D12—21no—
557D12—21no—
558D12—21no—
559D12—32no—
560D12—32no—
561D12—62no—
562D12—61no—
563D12—61no—
564D12—121no—
565D12—122no—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—122no—
569C4×D3—122no—
570C4×D3—124no—
571C4×D3—241no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—241no—
575Dic6—62no—
576Dic6—61no—
577Dic6—61no—
578Dic6—61no—
579Dic6—61no—
580Dic6—121no—
581C3×C8—21no—
582C3×C8—21no—
583C3×C8—21no—
584C3×C8—21no—
585C3×C8—41no—
586C3×C8—41no—
587C3×C8—61no—
588C3×C8—61no—
589C3⋊C8—21no—
590C3⋊C8—21no—
591C2×C32—41no—
592C2×C32#54611yescharacteristic
593C2×C32C2×#13511yescharacteristic
594C2×C32#57611yescharacteristic
595C3⋊D3—42no—
596C3×D3—22no—
597C3×D3—81no—
598C3×D3—81no—
599C24—181no—
600#41—182no—
601#41—361no—
602C2×Q8—91no—
603C2×D4—31no—
604C2×D4—31no—
605C2×D4—31no—
606C2×D4—61no—
607C2×D4—61no—
608C2×D4—91no—
609C2×D4—181no—
610C2×D4—182no—
611C2×D4—181no—
612C2×D4—181no—
613C2×D4—361no—
614C22×C4—31no—
615C22×C4—181no—
616C22×C4—181no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4C2×D3211yescharacteristic
620SD16—361no—
621D8—121no—
622D8—182no—
623C2×C8—31no—
624C2×C8—31no—
625C2×C8—41no—
626C2×C8—121no—
627C2×C8C2×D3211yescharacteristic
628C2×C8C2×D3211yescharacteristic
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—31no—
632C4⋊C4—91no—
633C4⋊C4—91no—
634C4⋊C4—181no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C4⋊C4—181no—
638C22⋊C4—31no—
639C22⋊C4—31no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C42—31no—
650C42—181no—
651C22×C3—22no—
652C22×C3—21no—
653C22×C3—21no—
654C22×C3—21no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—32no—
660C22×C3—41no—
661C22×C3—41no—
662C22×C3—61no—
663C22×C3—61no—
664C22×C3—121no—
665C22×C3—121no—
666C22×C3—121no—
667C22×C3—121no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3C22×D1211yescharacteristic
671C22×C3C2×D3×D411yescharacteristic
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—41no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—41no—
679C2×D3—41no—
680C2×D3—62no—
681C2×D3—62no—
682C2×D3—122no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—241no—
688C2×D3—241no—
689C2×D3—244no—
690C2×D3—244no—
691C2×D3#90412yes—
692C3×C4—22no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—21no—
697C3×C4—61no—
698C3×C4—61no—
699C3×C4—61no—
700C3×C4—121no—
701C3×C4—121no—
702C3×C4#100411yescharacteristic
703C3×C4#100411yescharacteristic
704C3×C4D3×#4111yescharacteristic
705C3×C4D3×#4111yescharacteristic
706Dic3—21no—
707Dic3—21no—
708Dic3—21no—
709Dic3—41no—
710Dic3—41no—
711Dic3—122no—
712Dic3—121no—
713Dic3—121no—
714Dic3—121no—
715Dic3—121no—
716Dic3—121no—
717Dic3—121no—
718Dic3—241no—
719Dic3—241no—
720C32#329711yescharacteristic, complemented, Sylow
721C23—31no—
722C23—61no—
723C23—61no—
724C23—181no—
725C23—362no—
726C23—362no—
727C23—721no—
728C23D3×D1211yescharacteristic
729Q8—181no—
730Q8—181no—
731D4—62no—
732D4—61no—
733D4—61no—
734D4—61no—
735D4—61no—
736D4—92no—
737D4—181no—
738D4—241no—
739D4—241no—
740D4—362no—
741D4—362no—
742D4—362no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—31no—
746C2×C4—31no—
747C2×C4—31no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—181no—
753C2×C4—181no—
754C2×C4—181no—
755C2×C4—362no—
756C2×C4—721no—
757C2×C4—721no—
758C2×C4—721no—
759C2×C4D3×D1211yescharacteristic
760C2×C4C22×D3211yescharacteristic
761C8—21no—
762C8—21no—
763C8—61no—
764C8—61no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—42no—
769C2×C3—41no—
770C2×C3—41no—
771C2×C3—62no—
772C2×C3—241no—
773C2×C3—241no—
774C2×C3#555411yescharacteristic
775C2×C3#561011yescharacteristic
776C2×C3C2×#90411yescharacteristic
777C2×C3#575211yescharacteristic
778C2×C3#575711yescharacteristic
779C2×C3D3×#13511yescharacteristic
780D3—22no—
781D3—81no—
782D3—81no—
783D3—122no—
784D3—122no—
785D3—242no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—32no—
790C22—61no—
791C22—61no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—121no—
798C22—182no—
799C22—361no—
800C22—361no—
801C22—724no—
802C22C2×D3×D1211yescharacteristic
803C4—21no—
804C4—61no—
805C4—61no—
806C4—61no—
807C4—121no—
808C4—121no—
809C4—361no—
810C4—361no—
811C4—361no—
812C4#6430611yescharacteristic
813C4#6433011yescharacteristic
814C3—21no—
815C3#7944111yescharacteristic, complemented
816C3#8072511yescharacteristic, complemented
817C2—41no—
818C2—62no—
819C2—241no—
820C2—241no—
821C2—362no—
822C2D3×#90411yescharacteristic
823C2#1059467811yescharacteristic
824C2#1059507511yescharacteristic
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. #10595078C2semidirect
2. #10594945C2semidirect
3. #10592812C2semidirect
4. C3×#5115C2semidirect
5. C3×C8×#67C2semidirect
6. #10591182C2semidirect
7. #10591093C2semidirect
8. #10590944C2semidirect
9. D3×#821C2semidirect
10. #10590863C2semidirect
11. #10590825C2semidirect
12. #10590774C2semidirect
13. #10590755C2semidirect
14. #10590745C2semidirect
15. #10590684C2semidirect
20. C22×C32×C8C22semidirect
21. #64135C22semidirect
23. C3×#930C22semidirect
35. Dic3×D12C22semidirect
37. #63869C22semidirect
42. C2×#3716C22semidirect
46. #63643C22semidirect
47. #63643C22semidirect
48. C3×#830C22semidirect
50. C3×#821C22semidirect
52. C3×#818C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
57. #63567C22semidirect
69. #5115D3semidirect
75. C8×#67D3semidirect
153. C22×C3×C8C2×D3semidirect
154. C22×C3×C8C2×D3semidirect
171. #930C2×D3semidirect
209. #830C2×D3semidirect
220. #821C2×D3semidirect
223. #818C2×D3semidirect
232. Dic3⋊C8C2×D3semidirect
233. C8×Dic3C2×D3semidirect
449. C22×C8D32semidirect
720. C32#3297semidirect
815. C3#79441semidirect
816. C3#80725semidirect

Maximal subgroups

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

subgroupindex
#105950782
#105949452
#105928122
C3×#51152
C3×C8×#672
#105911822
#105910932
#105909442
D3×#8212
#105908632
#105908252
#105907742
#105907552
#105907452
#105906842
#807253
#794413