Finite Group Databasebeta

← #11887435

Subgroups — #11887435

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#10595431C211yesmaximal, characteristic, complemented
2#10594437C211yesmaximal, characteristic, complemented
3#10592503C211yesmaximal, characteristic, complemented
4C3×#4807C211yesmaximal, characteristic, complemented
5C3×#4800C211yesmaximal, characteristic, complemented
6#10591593C211yesmaximal, characteristic, complemented
7#10591567C211yesmaximal, characteristic, complemented
8#10591551C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590839C211yesmaximal, characteristic, complemented
11#10590745C211yesmaximal, characteristic, complemented
12C8×#626C211yesmaximal, characteristic, complemented
13#10590595C211yesmaximal, characteristic, complemented
14#10590513C211yesmaximal, characteristic, complemented
15#10590470C211yesmaximal, characteristic, complemented
16#81653—31nomaximal
17#80681—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic, complemented
21#64101C2211yescharacteristic, complemented
22C3×#947C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic, complemented
25C2×C3×D3×C8C2211yescharacteristic
26C3×#895C2211yescharacteristic
27C3×#890C2211yescharacteristic, complemented
28#63923—21no—
29#63921—21no—
30#63916C2211yescharacteristic
31#63916C2211yescharacteristic, complemented
32#63910—21no—
33C4×#626C2211yescharacteristic
34#63898—21no—
35#63894C2211yescharacteristic
36Dic3×D12C2211yescharacteristic, complemented
37#63890—21no—
38D3×C4⋊Dic3C2211yescharacteristic
39#63886—21no—
40#63862—21no—
41#63853—21no—
42C2×#3714C2211yescharacteristic
43C2×#3713C2211yescharacteristic
44C32×#103C2211yescharacteristic, complemented
45#63662C2211yescharacteristic, complemented
46#63648C2211yescharacteristic
47#63636C2211yescharacteristic
48C3×#835C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×C8×Dic3C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#808C2211yescharacteristic, complemented
54#63576C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63563C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5695—31no—
62#5676—31no—
63#5630—31no—
64#5618—31no—
65C3×#488—31no—
66C3×#465—31no—
67#5172—31no—
68#5165—31no—
69C2×#821—31no—
70C8×#67—31no—
71#5066—31no—
72#5057—31no—
73#5044—31no—
74#5036—31no—
75#4871—31no—
76#4866—31no—
77#4811—31no—
78#4810—31no—
79#4807D311yescharacteristic, complemented
80#4804—31no—
81#4804—31no—
82#4804—61no—
83#4800D311yescharacteristic, complemented
84#4784—31no—
85#4775—31no—
86#4775—31no—
87#4773—31no—
88D3×#102—31no—
89#4756—31no—
90C4×D24—31no—
91C8×D12—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94#3832—22no—
95#3832—41no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C4×C3⋊D3C2311yescharacteristic
100C2×C3×D12—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#626—21no—
107C2×#626D411yescharacteristic
108C2×#624—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111D3×D12—22no—
112D3×D12—41no—
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊Dic3—21no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C8×C3⋊D3—41no—
120C3×#215—41no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C2×C3×C3⋊C8C2311yescharacteristic
133C3×D3×C8—41no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3D411yescharacteristic
136#3722—21no—
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3D411yescharacteristic
142#3714—22no—
143#3713—41no—
144#3297—91noSylow
145C2×#239—31no—
146C2×#239—31no—
147C2×#239—61no—
148C2×D3×D4—31no—
149C22×D12—31no—
150C2×C3×SD16—31no—
151C22×C3×C8—31no—
152C3×#125—31no—
153C3×#124—31no—
154C3×C22⋊Q8—31no—
155C3×#121—31no—
156#947C2×D311yescharacteristic
157#946C2×D311yescharacteristic
158C2×#215C2×D311yescharacteristic, complemented
159#939—61no—
160#938—31no—
161#938—31no—
162D4×Dic3—31no—
163D4×Dic3—61no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—31no—
167C4×#67—31no—
168C2×C4⋊Dic3—31no—
169C2×D24—31no—
170C2×D3×C8—31no—
171C2×D3×C8—31no—
172C2×D3×C8—61no—
173C2×D3×C8C2×D311yescharacteristic
174#898—61no—
175#895—31no—
176#895—31no—
177#895—61no—
178#895—61no—
179#895C2×D311yescharacteristic
180#894—61no—
181#894—61no—
182#893—31no—
183#893—61no—
184#892—31no—
185#892—31no—
186#892—61no—
187D3×C4⋊C4—31no—
188#890C2×D311yescharacteristic, complemented
189#886—61no—
190#884—61no—
191#883—61no—
192#882—61no—
193#882—61no—
194D3×C22⋊C4—61no—
195D3×C22⋊C4—61no—
196#879—61no—
197C4×D12—31no—
198C4×D12—31no—
199C4×D12—31no—
200C3×#106—31no—
201C3×#103—21no—
202C3×#103—31no—
203C3×#103C2×D311yescharacteristic, complemented
204C3×#103C2×D311yescharacteristic, complemented
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×C4×C8—31no—
209#835—31no—
210#835—31no—
211#835—61no—
212#835C2×D311yescharacteristic, complemented
213#832—31no—
214#830—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—61no—
220#821C2×D311yescharacteristic
221#821C2×D311yescharacteristic, complemented
222(C2×D3)⋊C8—31no—
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#818—31no—
226Dic3⋊C8—31no—
227C8×Dic3C2×D311yescharacteristic, complemented
228#809—31no—
229#809—31no—
230#809—31no—
231#809—61no—
232#809C2×D311yescharacteristic
233#808C2×D311yescharacteristic, complemented
234#807—31no—
235#807—31no—
236#807—31no—
237C4⋊(C3⋊C8)—31no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3C2×D411yescharacteristic
243C2×D32—42no—
244C2×D32—42no—
245C2×D32—81no—
246C32×Q8—21no—
247C32×Q8—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2411yescharacteristic
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—42no—
255C4⋊(C3⋊D3)#4112yes—
256C4×C3⋊D3—21no—
257C4×C3⋊D3—21no—
258C4×C3⋊D3—42no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—21no—
268C3×D12—42no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271#626—22no—
272#626—42no—
273#626—81no—
274#626—81no—
275#624—81no—
276D3×Dic3—81no—
277D3×Dic3—81no—
278C32×C8—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—91no—
284#488—31no—
285#484—91no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—31no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—91no—
295#416—91no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C2×C3×Q8—21no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—31no—
303C2×C3×D4—31no—
304C2×C3×D4—61no—
305C22×C3×C4—31no—
306C2×#67—31no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312#239—62no—
313#239—62no—
314#239—64no—
315#239—121no—
316#239—121no—
317#239—122no—
318D3×D4—62no—
319D3×D4—121no—
320C2×D12—21no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—61no—
325C2×D12—62no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—121no—
332C2×D12—121no—
333C2×D12C22×D311yescharacteristic
334C2×D12C22×D311yescharacteristic
335C2×C4×D3—31no—
336C2×C4×D3—31no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—121no—
345C2×C4×D3C22×D311yescharacteristic
346C3×SD16—121no—
347C2×C3×C8—21no—
348C2×C3×C8—31no—
349C2×C3×C8—31no—
350C2×C3×C8—121no—
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C3×C4⋊C4—21no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C4⋊C4C22×D311yescharacteristic
361C3×C22⋊C4—61no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C42—31no—
366#217—31no—
367#217—61no—
368#217—61no—
369#217—61no—
370#215—41no—
371#213—62no—
372#213—121no—
373#213—121no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—31no—
379(C2×D3)⋊C4—31no—
380(C2×D3)⋊C4—31no—
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)⋊C4—61no—
388(C2×D3)⋊C4—121no—
389C4⋊Dic3—21no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—31no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—31no—
400Dic3⋊C4—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—121no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8C22×D311yescharacteristic
409C2×C3⋊C8C22×D311yescharacteristic
410D24—62no—
411D3×C8—41no—
412D3×C8—121no—
413D3×C8—121no—
414D3×C8—122no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—21no—
417C2×C3⋊D3—22no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
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—41no—
433C32×C4—41no—
434C32×C4C2×#4111yescharacteristic
435C32×C4H(5,𝔽2)11yescharacteristic
436C3⋊Dic3—21no—
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—31no—
446C2×D8—91no—
447C2×D8—91no—
448C22×C8—31no—
449C22×C8—91no—
450#126—181no—
451#125—31no—
452#124—31no—
453#123—181no—
454#123—181no—
455C22⋊Q8—31no—
456#121—31no—
457#121—91no—
458#121—91no—
459#121—181no—
460#121—181no—
461#120—181no—
462C4×D4—91no—
463C4×D4—91no—
464C4×D4—91no—
465C4×D4—181no—
466#117—91no—
467C2×C4⋊C4—91no—
468C2×C22⋊C4—181no—
469#107—91no—
470#107—91no—
471#106—31no—
472C4⋊C8—91no—
473#103—31no—
474#103—91no—
475#103D3211yescharacteristic, complemented
476#102—31no—
477#102—31no—
478#102—31no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483C22⋊C8—91no—
484C22⋊C8—91no—
485C4×C8—31no—
486C23×C3—31no—
487C23×C3—61no—
488C23×C3—61no—
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—31no—
492C22×D3—31no—
493C22×D3—61no—
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×D3D3×D411yescharacteristic
504C3×Q8—22no—
505C3×Q8—21no—
506C3×Q8—21no—
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—41no—
510C3×D4—61no—
511C3×D4—61no—
512C3×D4—61no—
513C3×D4—61no—
514C3×D4—122no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4C23×D311yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531#67—62no—
532#67—122no—
533#67—241no—
534#67—241no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—31no—
538C2×Dic3—31no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—121no—
543C2×Dic3—241no—
544C2×Dic3—241no—
545C2×Dic3D3×D411yescharacteristic
546C2×Dic3D3×D411yescharacteristic
547C2×Dic3D3×D411yescharacteristic
548D12—21no—
549D12—21no—
550D12—21no—
551D12—21no—
552D12—32no—
553D12—32no—
554D12—42no—
555D12—62no—
556D12—62no—
557D12—61no—
558D12—61no—
559D12—121no—
560D12—122no—
561D12—122no—
562D12—124no—
563D12—122no—
564D12—241no—
565D12—241no—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—62no—
569C4×D3—62no—
570C4×D3—61no—
571C4×D3—61no—
572C4×D3—61no—
573C4×D3—61no—
574C4×D3—122no—
575C4×D3—122no—
576C4×D3—124no—
577C4×D3—241no—
578C4×D3—241no—
579C4×D3—241no—
580C4×D3—241no—
581C3×C8—21no—
582C3×C8—21no—
583C3×C8—41no—
584C3×C8—61no—
585C3×C8—61no—
586C3⋊C8—21no—
587C3⋊C8—21no—
588C3⋊C8—61no—
589C3⋊C8—61no—
590C3⋊C8—121no—
591C2×C32#54611yescharacteristic
592C2×C32C2×#13511yescharacteristic
593C2×C32#57611yescharacteristic
594C3⋊D3—41no—
595C3⋊D3—42no—
596C3×D3—22no—
597C3×D3—81no—
598C3×D3—81no—
599C24—181no—
600#41—182no—
601#41—361no—
602C2×Q8C2×D3211yescharacteristic
603C2×D4—31no—
604C2×D4—31no—
605C2×D4—61no—
606C2×D4—91no—
607C2×D4—91no—
608C2×D4—181no—
609C2×D4—181no—
610C2×D4—182no—
611C2×D4—181no—
612C2×D4—181no—
613C2×D4—361no—
614C22×C4—31no—
615C22×C4—91no—
616C22×C4—181no—
617C22×C4—181no—
618C22×C4—181no—
619C22×C4—181no—
620SD16—121no—
621D8—182no—
622D8—361no—
623C2×C8—31no—
624C2×C8—31no—
625C2×C8—91no—
626C2×C8—121no—
627C2×C8—361no—
628C2×C8C2×D3211yescharacteristic
629C4⋊C4—31no—
630C4⋊C4—31no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4—91no—
635C4⋊C4—91no—
636C4⋊C4—181no—
637C4⋊C4C2×D3211yescharacteristic
638C22⋊C4—61no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—61no—
642C22⋊C4—91no—
643C22⋊C4—91no—
644C22⋊C4—181no—
645C22⋊C4—181no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C42—31no—
650C42—181no—
651C22×C3—21no—
652C22×C3—32no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3C2×D3×D411yescharacteristic
662C22×C3C2×D3×D411yescharacteristic
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—62no—
672C2×D3—61no—
673C2×D3—62no—
674C2×D3—61no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—61no—
678C2×D3—61no—
679C2×D3—62no—
680C2×D3—121no—
681C2×D3—121no—
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#91612yes—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—42no—
695C3×C4—41no—
696C3×C4—41no—
697C3×C4—41no—
698C3×C4—41no—
699C3×C4—61no—
700C3×C4—61no—
701C3×C4—61no—
702C3×C4—81no—
703C3×C4—121no—
704C3×C4—121no—
705C3×C4#100411yescharacteristic
706C3×C4D3×#4111yescharacteristic
707C3×C4D3×#4111yescharacteristic
708C3×C4#100911yescharacteristic
709Dic3—21no—
710Dic3—21no—
711Dic3—21no—
712Dic3—41no—
713Dic3—41no—
714Dic3—62no—
715Dic3—61no—
716Dic3—61no—
717Dic3—121no—
718Dic3—121no—
719Dic3—241no—
720C32#329711yescharacteristic, complemented, Sylow
721C23—31no—
722C23—61no—
723C23—61no—
724C23—91no—
725C23—181no—
726C23—362no—
727C23—362no—
728C23—721no—
729Q8—21no—
730Q8—21no—
731D4—61no—
732D4—61no—
733D4—61no—
734D4—61no—
735D4—92no—
736D4—122no—
737D4—182no—
738D4—181no—
739D4—362no—
740D4—362no—
741D4—721no—
742D4—721no—
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—91no—
753C2×C4—181no—
754C2×C4—181no—
755C2×C4—181no—
756C2×C4—362no—
757C2×C4—721no—
758C2×C4—721no—
759C2×C4—721no—
760C2×C4C22×D3211yescharacteristic
761C8—21no—
762C8—61no—
763C8—61no—
764C8—181no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—62no—
769C2×C3—241no—
770C2×C3—241no—
771C2×C3#561011yescharacteristic
772C2×C3#567611yescharacteristic
773C2×C3C2×#91611yescharacteristic
774C2×C3D3×#13511yescharacteristic
775C2×C3#576911yescharacteristic
776C2×C3#576911yescharacteristic
777D3—22no—
778D3—81no—
779D3—81no—
780D3—122no—
781D3—121no—
782D3—122no—
783D3—121no—
784D3—122no—
785D3—242no—
786C22—32no—
787C22—61no—
788C22—61no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22—121no—
793C22—121no—
794C22—121no—
795C22—181no—
796C22—181no—
797C22—181no—
798C22—182no—
799C22—361no—
800C22—361no—
801C22—724no—
802C22D32×D411yescharacteristic
803C4—41no—
804C4—41no—
805C4—61no—
806C4—61no—
807C4—61no—
808C4—121no—
809C4—121no—
810C4—181no—
811C4—361no—
812C4#6430611yescharacteristic
813C4#6431411yescharacteristic
814C3—21no—
815C3#8068111yescharacteristic, complemented
816C3#8165311yescharacteristic, complemented
817C2—62no—
818C2—241no—
819C2—241no—
820C2—361no—
821C2—362no—
822C2#1059428511yescharacteristic
823C2D3×#91611yescharacteristic
824C2#1059477111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595431C2semidirect
2. #10594437C2semidirect
3. #10592503C2semidirect
4. C3×#4807C2semidirect
5. C3×#4800C2semidirect
6. #10591593C2semidirect
7. #10591567C2semidirect
8. #10591551C2semidirect
9. D3×#821C2semidirect
10. #10590839C2semidirect
11. #10590745C2semidirect
12. C8×#626C2semidirect
13. #10590595C2semidirect
14. #10590513C2semidirect
15. #10590470C2semidirect
20. C2×C8×C3⋊D3C22semidirect
21. #64101C22semidirect
24. C2×C3×#215C22semidirect
27. C3×#890C22semidirect
31. #63916C22semidirect
36. Dic3×D12C22semidirect
44. C32×#103C22semidirect
45. #63662C22semidirect
48. C3×#835C22semidirect
50. C3×#821C22semidirect
51. C3×C8×Dic3C22semidirect
53. C3×#808C22semidirect
54. #63576C22semidirect
55. #63575C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
59. #63557C22semidirect
79. #4807D3semidirect
83. #4800D3semidirect
158. C2×#215C2×D3semidirect
188. #890C2×D3semidirect
203. C3×#103C2×D3semidirect
204. C3×#103C2×D3semidirect
212. #835C2×D3semidirect
221. #821C2×D3semidirect
227. C8×Dic3C2×D3semidirect
233. #808C2×D3semidirect
475. #103D32semidirect
720. C32#3297semidirect
815. C3#80681semidirect
816. C3#81653semidirect

Maximal subgroups

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

subgroupindex
#105954312
#105944372
#105925032
C3×#48072
C3×#48002
#105915932
#105915672
#105915512
D3×#8212
#105908392
#105907452
C8×#6262
#105905952
#105905132
#105904702
#816533
#806813