Finite Group Databasebeta

← #11872737

Subgroups — #11872737

Order 1152.

903 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595215C211yesmaximal, characteristic, complemented
2#10594501C211yesmaximal, characteristic, complemented
3#10592455C211yesmaximal, characteristic, complemented
4C3×#4773C211yesmaximal, characteristic, complemented
5C3×#4766C211yesmaximal, characteristic, complemented
6#10591481C211yesmaximal, characteristic, complemented
7#10591448C211yesmaximal, characteristic, complemented
8#10591436C211yesmaximal, characteristic, complemented
9#10590777C211yesmaximal, characteristic, complemented
10#10590753C211yesmaximal, characteristic, complemented
11#10590705C211yesmaximal, characteristic, complemented
12#10590698C211yesmaximal, characteristic, complemented
13#10590467C211yesmaximal, characteristic, complemented
14#10590462C211yesmaximal, characteristic, complemented
15#10590449C211yesmaximal, characteristic, complemented
16#81146—31nomaximal
17#79993—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19D4×C3⋊Dic3C2211yescharacteristic
20C2×#3753C2211yescharacteristic
21#64102C2211yescharacteristic, complemented
22C3×D4×Dic3C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×#890C2211yescharacteristic, complemented
27#67⋊Dic3—21no—
28Dic3×#67—21no—
29D3×#217—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63916—21no—
32#63911C2211yescharacteristic, complemented
33#63909C2211yescharacteristic
34#63898C2211yescharacteristic
35#63898C2211yescharacteristic, complemented
36Dic3×D12C2211yescharacteristic
37#63890—21no—
38#63886—21no—
39#63855C2211yescharacteristic
40#63853—21no—
41#63841C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×#102C2211yescharacteristic
44#63648C2211yescharacteristic, complemented
45C8×C3⋊Dic3C2211yescharacteristic, complemented
46#63634C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#818C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#808C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic, complemented
56#63563C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#5798—31no—
62#5697—31no—
63#5619—31no—
64#5545—31no—
65C3×#478—31no—
66C3×#447—31no—
67#5217—31no—
68#5152—31no—
69#5150—31no—
70#5150—31no—
71Dic3×D8—31no—
72#5066—31no—
73#5035—31no—
74#5015—31no—
75#4885—31no—
76#4872—31no—
77#4869—31no—
78#4866—31no—
79#4843—31no—
80#4840—31no—
81#4785—31no—
82#4785—31no—
83#4773—31no—
84#4773D311yescharacteristic, complemented
85#4766D311yescharacteristic, complemented
86#4763—31no—
87#4756—31no—
88#4756—31no—
89#4756—61no—
90#4737—31no—
91#4720—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×#67—21no—
98C22×C3×Dic3—21no—
99C3×D3×D4—22no—
100C3×D3×D4—22no—
101C2×C3×D12—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3757—21no—
114#3753—22no—
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#213—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D24—22no—
130Dic3⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
132#3722—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3D411yescharacteristic
138(C2×D3)⋊Dic3D411yescharacteristic
139Dic32—21no—
140#3714—22no—
141#3122—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C3×#125—31no—
147C3×#121—31no—
148C3×C4×D4—31no—
149C2×#217—61no—
150C2×#217—61no—
151#940—31no—
152#939—61no—
153#938—61no—
154D4×Dic3—31no—
155D4×Dic3—31no—
156D4×Dic3—31no—
157D4×Dic3—31no—
158D4×Dic3—31no—
159D4×Dic3—61no—
160D4×Dic3—61no—
161D4×Dic3—61no—
162D4×Dic3C2×D311yescharacteristic
163C2×#213—31no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—61no—
167C2×#213C2×D311yescharacteristic
168#930—31no—
169C4×#67—61no—
170C2×(C2×D3)⋊C4—61no—
171#926—31no—
172#926—31no—
173C2×D24—31no—
174C2×D24C2×D311yescharacteristic
175#895—31no—
176#895—61no—
177#895—61no—
178#895C2×D311yescharacteristic
179#894—61no—
180#894—61no—
181#893—31no—
182#893—31no—
183#893—31no—
184#893—31no—
185#893—61no—
186#892—31no—
187#890C2×D311yescharacteristic, complemented
188#886—61no—
189#883—61no—
190#67⋊C4—61no—
191D3×C22⋊C4—61no—
192#874—31no—
193C4×D12—31no—
194#872—31no—
195C3×#107—31no—
196C3×#106—31no—
197C3×C4⋊C8—31no—
198C3×#102—21no—
199C3×#102—31no—
200C3×#102—31no—
201C3×#102C2×D311yescharacteristic
202C3×#102C2×D311yescharacteristic
203C3×C22⋊C8—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832C2×D311yescharacteristic
208#830—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—61no—
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8C2×D311yescharacteristic
216#818C2×D311yescharacteristic, complemented
217#817—31no—
218#815—31no—
219#815—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8C2×D311yescharacteristic, complemented
222C8×Dic3—31no—
223C8×Dic3—31no—
224C8×Dic3—61no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809C2×D311yescharacteristic
229#808—31no—
230#808C2×D311yescharacteristic, complemented
231#807—31no—
232#807—31no—
233#807—61no—
234C4⋊(C3⋊C8)—31no—
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—24no—
239C22×C3×D3—21no—
240C22×C3×D3—81no—
241C22×C3×D3—81no—
242C22×C3×D3C2×D411yescharacteristic
243C32×D4—21no—
244C32×D4#4112yes—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—81no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C4×C3⋊D3—81no—
254C3×#67—24no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—81no—
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—81no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268#626—81no—
269#626—81no—
270#626—81no—
271D3×Dic3—81no—
272D3×Dic3—81no—
273D3×Dic3—81no—
274C32×C8—21no—
275C3⋊(C3⋊C8)—21no—
276C3×C3⋊C8—21no—
277C3×C3⋊C8—21no—
278#540—91no—
279#518—91no—
280#482—91no—
281#482—91no—
282#478—31no—
283#478—91no—
284#459—91no—
285#459—91no—
286#447—31no—
287#447—91no—
288#442—91no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—91no—
293C24×C3—61no—
294C23×D3—21no—
295C2×C3×D4—21no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C2×C3×D4—62no—
301C2×C3×D4—62no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C2×#67—21no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C22×Dic3—21no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—121no—
317D3×D4—22no—
318D3×D4—22no—
319C2×D12—21no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—61no—
326C2×D12C22×D311yescharacteristic
327C2×D12C22×D311yescharacteristic
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—121no—
334C2×C4×D3C22×D311yescharacteristic
335C3×D8—62no—
336C3×D8—62no—
337C2×C3×C8—21no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C3×C4⋊C4—21no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C42—31no—
352#217—21no—
353#217—31no—
354#217—31no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—121no—
362#213—22no—
363#213—62no—
364#213—64no—
365#213—62no—
366#213—62no—
367(C2×D3)⋊C4—21no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
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—121no—
379C4⋊Dic3—21no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—61no—
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—31no—
389Dic3⋊C4—31no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3C22×D311yescharacteristic
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8C22×D311yescharacteristic
400C2×C3⋊C8C22×D311yescharacteristic
401D24—22no—
402D24—62no—
403C22×C32—22no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32C22×D411yescharacteristic
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3×D3—21no—
411C2×C3×D3—22no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—84no—
420C32×C4—41no—
421C32×C4C2×#4111yescharacteristic
422C32×C4C2×#4111yescharacteristic
423C3⋊Dic3—21no—
424C3⋊Dic3—21no—
425C3⋊Dic3—41no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C22×D4—31no—
432C2×D8—31no—
433C2×D8—31no—
434C2×D8—91no—
435C2×D8—91no—
436#127—91no—
437#125—31no—
438#123—181no—
439#123—181no—
440#121—31no—
441#121—91no—
442#121—181no—
443#121—181no—
444C4×D4—31no—
445C4×D4—91no—
446C4×D4—91no—
447C4×D4—91no—
448C4×D4—91no—
449C4×D4—91no—
450C4×D4—181no—
451C4×D4—181no—
452#117—91no—
453#117—91no—
454C2×C22⋊C4—181no—
455C2×C22⋊C4—181no—
456#107—31no—
457#107—91no—
458#106—31no—
459#106—91no—
460C4⋊C8—31no—
461C4⋊C8—91no—
462#102—31no—
463#102—31no—
464#102—91no—
465#102—91no—
466#102—91no—
467#102—91no—
468#102—91no—
469#102D3211yescharacteristic
470C22⋊C8—31no—
471C22⋊C8—91no—
472#97—91no—
473C4×C8—91no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—31no—
477C23×C3—41no—
478C23×C3—64no—
479C23×C3—61no—
480C23×C3—61no—
481C23×C3—241no—
482C23×C3—241no—
483C22×D3—21no—
484C22×D3—24no—
485C22×D3—21no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—81no—
489C22×D3—81no—
490C22×D3—121no—
491C22×D3D3×D411yescharacteristic
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—22no—
495C3×D4—32no—
496C3×D4—41no—
497C3×D4—64no—
498C3×D4—61no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4—241no—
502C3×D4#23712yes—
503C3×D4#23912yes—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—241no—
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—24no—
519#67—241no—
520#67—241no—
521#67—241no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—81no—
533C2×Dic3—121no—
534C2×Dic3—241no—
535C2×Dic3—241no—
536C2×Dic3—241no—
537C2×Dic3—241no—
538C2×Dic3—241no—
539C2×Dic3—242no—
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542C2×Dic3D3×D411yescharacteristic
543D12—21no—
544D12—21no—
545D12—21no—
546D12—62no—
547D12—61no—
548D12—61no—
549D12—61no—
550D12—61no—
551D12—81no—
552D12—121no—
553D12—241no—
554D12—241no—
555D12—241no—
556D12#23712yes—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—241no—
560C4×D3—241no—
561C4×D3—242no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—241no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—41no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—62no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C2×C32—42no—
576C2×C32#52511yescharacteristic
577C2×C32#57611yescharacteristic
578C2×C32#57611yescharacteristic
579C3⋊D3—81no—
580C3×D3—41no—
581C3×D3—42no—
582C3×D3—81no—
583C24—61no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—62no—
589C2×D4—62no—
590C2×D4—91no—
591C2×D4—181no—
592C2×D4—181no—
593C2×D4—181no—
594C2×D4C2×D3211yescharacteristic
595C22×C4—31no—
596C22×C4—61no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4—181no—
600C22×C4—181no—
601C22×C4—181no—
602D8—62no—
603D8—62no—
604D8—182no—
605D8—182no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—91no—
609C2×C8C2×D3211yescharacteristic
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—91no—
615C4⋊C4—91no—
616C4⋊C4—91no—
617C4⋊C4C2×D3211yescharacteristic
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—91no—
621C22⋊C4—91no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C42—31no—
630C42—91no—
631C42—181no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—42no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—62no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—244no—
652C22×C3C2×D3×D411yescharacteristic
653C22×C3C2×D3×D411yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—22no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—84no—
664C2×D3—122no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—241no—
672C2×D3—241no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—81no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4C2×#23711yescharacteristic
684C3×C4C2×#23711yescharacteristic
685C3×C4C2×#23911yescharacteristic
686C3×C4D3×#4111yescharacteristic
687Dic3—21no—
688Dic3—21no—
689Dic3—21no—
690Dic3—41no—
691Dic3—41no—
692Dic3—62no—
693Dic3—61no—
694Dic3—61no—
695Dic3—61no—
696Dic3—61no—
697Dic3—121no—
698Dic3—121no—
699Dic3—121no—
700Dic3—241no—
701C32#312211yescharacteristic, complemented, Sylow
702C23—21no—
703C23—31no—
704C23—64no—
705C23—61no—
706C23—61no—
707C23—181no—
708C23—241no—
709C23—241no—
710D4—21no—
711D4—32no—
712D4—64no—
713D4—61no—
714D4—61no—
715D4—61no—
716D4—181no—
717D4—181no—
718D4—241no—
719D4—721no—
720D4—721no—
721D4—721no—
722D4#379612yes—
723C2×C4—21no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—91no—
732C2×C4—91no—
733C2×C4—181no—
734C2×C4—241no—
735C2×C4—721no—
736C2×C4—721no—
737C2×C4—721no—
738C2×C4—721no—
739C2×C4—721no—
740C2×C4C22×D3211yescharacteristic
741C8—21no—
742C8—61no—
743C8—61no—
744C8—181no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—42no—
749C2×C3—42no—
750C2×C3—82no—
751C2×C3—121no—
752C2×C3—122no—
753C2×C3—241no—
754C2×C3#558611yescharacteristic
755C2×C3#562711yescharacteristic
756C2×C3#575711yescharacteristic
757C2×C3#576911yescharacteristic
758C2×C3#577411yescharacteristic
759C2×C3#577411yescharacteristic
760D3—41no—
761D3—42no—
762D3—81no—
763D3—242no—
764D3—241no—
765D3—241no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—61no—
770C22—62no—
771C22—61no—
772C22—61no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—244no—
779C22—361no—
780C22—361no—
781C22—361no—
782C22D32×D411yescharacteristic
783C4—41no—
784C4—61no—
785C4—61no—
786C4—61no—
787C4—121no—
788C4—121no—
789C4—181no—
790C4—181no—
791C4—361no—
792C4C2×#379611yescharacteristic
793C4D3×#23711yescharacteristic
794C3—21no—
795C3#7999311yescharacteristic, complemented
796C3#8114611yescharacteristic, complemented
797C2—42no—
798C2—121no—
799C2—122no—
800C2—241no—
801C2—721no—
802C2#1059405511yescharacteristic
803C2#1059473411yescharacteristic
804C2#1059475011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
hypercenter#102D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
1. #10595215C2semidirect
2. #10594501C2semidirect
3. #10592455C2semidirect
4. C3×#4773C2semidirect
5. C3×#4766C2semidirect
6. #10591481C2semidirect
7. #10591448C2semidirect
8. #10591436C2semidirect
9. #10590777C2semidirect
10. #10590753C2semidirect
11. #10590705C2semidirect
12. #10590698C2semidirect
13. #10590467C2semidirect
14. #10590462C2semidirect
15. #10590449C2semidirect
21. #64102C22semidirect
26. C3×#890C22semidirect
32. #63911C22semidirect
35. #63898C22semidirect
44. #63648C22semidirect
45. C8×C3⋊Dic3C22semidirect
46. #63634C22semidirect
49. C3×#818C22semidirect
50. C3×Dic3⋊C8C22semidirect
52. C3×#808C22semidirect
53. #63573C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63564C22semidirect
56. #63563C22semidirect
58. #63562C22semidirect
60. #63555C22semidirect
84. #4773D3semidirect
85. #4766D3semidirect
187. #890C2×D3semidirect
216. #818C2×D3semidirect
221. Dic3⋊C8C2×D3semidirect
230. #808C2×D3semidirect
701. C32#3122semidirect
795. C3#79993semidirect
796. C3#81146semidirect

Maximal subgroups

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

subgroupindex
#105952152
#105945012
#105924552
C3×#47732
C3×#47662
#105914812
#105914482
#105914362
#105907772
#105907532
#105907052
#105906982
#105904672
#105904622
#105904492
#811463
#799933