Finite Group Databasebeta

← #11872777

Subgroups — #11872777

Order 1152.

902 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#10595217C211yesmaximal, characteristic, complemented
2#10594604C211yesmaximal, characteristic, complemented
3#10592484C211yesmaximal, characteristic, complemented
4C3×#4786C211yesmaximal, characteristic, complemented
5C3×#4779C211yesmaximal, characteristic, complemented
6#10591515C211yesmaximal, characteristic, complemented
7#10591435C211yesmaximal, characteristic, complemented
8#10591429C211yesmaximal, characteristic, complemented
9#10590944C211yesmaximal, characteristic, complemented
10#10590781C211yesmaximal, characteristic, complemented
11#10590769C211yesmaximal, characteristic, complemented
12#10590699C211yesmaximal, characteristic, complemented
13#10590542C211yesmaximal, characteristic, complemented
14#10590505C211yesmaximal, characteristic, complemented
15#10590459C211yesmaximal, characteristic, complemented
16#81354—31nomaximal
17#80317—31nomaximal
18C2×D3×D12C2211yescharacteristic
19D4×C3⋊Dic3C2211yescharacteristic, complemented
20C2×#3753C2211yescharacteristic
21#64102C2211yescharacteristic
22C3×#940C2211yescharacteristic, complemented
23C3×#938C2211yescharacteristic
24C2×C3×#213C2211yescharacteristic
25C2×C3×D24C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#892C2211yescharacteristic
28#63980—21no—
29#63970—21no—
30#63969—21no—
31#63962—21no—
32#63921—21no—
33D3×(C2×D3)⋊C4—21no—
34#63908C2211yescharacteristic
35C4×#626—21no—
36#63898C2211yescharacteristic
37#63898C2211yescharacteristic, complemented
38#63894C2211yescharacteristic
39#63880—21no—
40#63869C2211yescharacteristic, complemented
41#63855C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×#102C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45#63642C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic, complemented
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#817C2211yescharacteristic, complemented
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63563C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61#5719—31no—
62#5619—31no—
63#5545—31no—
64#5521—31no—
65C3×#482—31no—
66C3×#459—31no—
67#5156—31no—
68#5156—31no—
69#5152—31no—
70Dic3×D8—31no—
71#5072—31no—
72#5036—31no—
73#5009—31no—
74#5003—31no—
75#4891—31no—
76#4872—31no—
77#4871—31no—
78#4869—31no—
79#4847—31no—
80#4840—31no—
81#4786—31no—
82#4786D311yescharacteristic, complemented
83#4785—31no—
84#4785—31no—
85#4785—61no—
86#4784—31no—
87#4779D311yescharacteristic, complemented
88#4756—31no—
89#4756—31no—
90#4732—31no—
91#4720—31no—
92C22×D32—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C4×C3⋊D3—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×#626—21no—
105C2×#625—21no—
106C2×#624—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109D3×D12—22no—
110D3×D12—22no—
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×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4×Dic3—21no—
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D24—22no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3D411yescharacteristic
139(C2×D3)⋊Dic3D411yescharacteristic
140#3714—22no—
141#3122—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C3×#127—31no—
147C3×#121—31no—
148C3×C4×D4—31no—
149C3×#117—31no—
150#940C2×D311yescharacteristic, complemented
151#939—61no—
152#939—61no—
153#939—61no—
154#938—31no—
155#938—61no—
156#938C2×D311yescharacteristic
157#935—61no—
158#935—61no—
159D4×Dic3—31no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—61no—
164C2×#213—31no—
165C2×#213—31no—
166C2×#213—31no—
167C2×#213—61no—
168C2×#213C2×D311yescharacteristic
169#930—31no—
170C4×#67—61no—
171C2×(C2×D3)⋊C4—61no—
172#926—31no—
173C2×D24—31no—
174C2×D24C2×D311yescharacteristic
175#893—31no—
176#893—31no—
177#893—31no—
178#893—31no—
179#893—31no—
180#893—61no—
181#893C2×D311yescharacteristic
182#892C2×D311yescharacteristic
183#890—31no—
184#886—61no—
185#883—61no—
186#67⋊C4—61no—
187D3×C22⋊C4—61no—
188D3×C22⋊C4—61no—
189D3×C22⋊C4—61no—
190C4×D12—31no—
191C4×D12—61no—
192C4×D12—61no—
193#872—31no—
194#870—31no—
195C3×#107—31no—
196C3×#106—31no—
197C3×C4⋊C8—31no—
198C3×#102—21no—
199C3×#102—31no—
200C3×#102—31no—
201C3×#102C2×D311yescharacteristic, complemented
202C3×#102C2×D311yescharacteristic, complemented
203C3×C22⋊C8—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832C2×D311yescharacteristic, complemented
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#818—31no—
217#817C2×D311yescharacteristic, complemented
218#815—31no—
219#815—31no—
220#815—61no—
221Dic3⋊C8—31no—
222Dic3⋊C8C2×D311yescharacteristic, complemented
223C8×Dic3—31no—
224C8×Dic3—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809C2×D311yescharacteristic, complemented
229#808—31no—
230#808—31no—
231#808—61no—
232#807—31no—
233#807C2×D311yescharacteristic, complemented
234C4⋊(C3⋊C8)—31no—
235C23×C32—21no—
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3C2×D411yescharacteristic
240C2×D32—24no—
241C2×D32—81no—
242C2×D32—81no—
243C32×D4—21no—
244C32×D4—21no—
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)#4112yes—
253C4×C3⋊D3—81no—
254C3×#67—81no—
255C3×#67—81no—
256C3×#67—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—81no—
269#626—24no—
270#625—81no—
271#624—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—31no—
281#482—91no—
282#478—91no—
283#478—91no—
284#459—31no—
285#459—91no—
286#447—91no—
287#447—91no—
288#442—91no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—91no—
293C23×D3—61no—
294C23×D3—61no—
295C2×C3×D4—21no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4C22×D311yescharacteristic
302C2×C3×D4C22×D311yescharacteristic
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C2×#67—21no—
306C2×#67—21no—
307C2×#67—21no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—121no—
316D3×D4—62no—
317D3×D4—62no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—61no—
321C2×D12—62no—
322C2×D12—61no—
323C2×D12—62no—
324C2×D12C22×D311yescharacteristic
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—21no—
327C2×C4×D3—61no—
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⋊C4C22×D311yescharacteristic
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—31no—
351C3×C42—61no—
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—121no—
361#213—22no—
362#213—62no—
363#213—62no—
364#213—62no—
365#213—64no—
366(C2×D3)⋊C4—21no—
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—121no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391C4×Dic3—21no—
392C4×Dic3—31no—
393C4×Dic3—31no—
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—41no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32C22×D411yescharacteristic
407C2×C3⋊D3—22no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3×D3—22no—
411C2×C3×D3—21no—
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—
419D32—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—91no—
432C2×D8—31no—
433C2×D8—31no—
434C2×D8—91no—
435C2×D8—91no—
436#127—31no—
437#125—91no—
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—31no—
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, complemented
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—61no—
479C23×C3—61no—
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—64no—
483C22×D3—64no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—121no—
487C22×D3—241no—
488C22×D3—241no—
489C22×D3—241no—
490C22×D3—241no—
491C22×D3D3×D411yescharacteristic
492C3×D4—22no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—32no—
498C3×D4—41no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4—61no—
502C3×D4—241no—
503C3×D4—241no—
504C3×D4—241no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—41no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—241no—
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519#67—64no—
520#67—81no—
521#67—81no—
522#67—81no—
523#67—241no—
524#67—241no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—121no—
536C2×Dic3—241no—
537C2×Dic3—241no—
538C2×Dic3—241no—
539C2×Dic3—241no—
540C2×Dic3—242no—
541C2×Dic3D3×D411yescharacteristic
542C2×Dic3D3×D411yescharacteristic
543C2×Dic3D3×D411yescharacteristic
544D12—21no—
545D12—21no—
546D12—21no—
547D12—32no—
548D12—32no—
549D12—62no—
550D12—64no—
551D12—61no—
552D12—61no—
553D12—121no—
554D12#23712yes—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—81no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—241no—
561C4×D3—241no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—242no—
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—81no—
576C2×C32#52511yescharacteristic
577C2×C32#57611yescharacteristic
578C2×C32#57611yescharacteristic
579C3⋊D3—42no—
580C3×D3—41no—
581C3×D3—42no—
582C3×D3—81no—
583C24—181no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—91no—
590C2×D4—181no—
591C2×D4—182no—
592C2×D4—182no—
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—91no—
613C4⋊C4—91no—
614C4⋊C4—91no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4C2×D3211yescharacteristic
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—61no—
621C22⋊C4—91no—
622C22⋊C4—91no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C42—31no—
630C42—61no—
631C42—91no—
632C22×C3—21no—
633C22×C3—42no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—62no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—81no—
645C22×C3—81no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3C2×D3×D411yescharacteristic
652C22×C3C2×D3×D411yescharacteristic
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—22no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—62no—
663C2×D3—62no—
664C2×D3—122no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—241no—
670C2×D3—241no—
671C2×D3—244no—
672C2×D3—244no—
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×C4D3×#4111yescharacteristic
685C3×C4D3×#4111yescharacteristic
686C3×C4D3×#4111yescharacteristic
687Dic3—21no—
688Dic3—21no—
689Dic3—21no—
690Dic3—41no—
691Dic3—41no—
692Dic3—61no—
693Dic3—61no—
694Dic3—61no—
695Dic3—61no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—121no—
700Dic3—241no—
701C32#312211yescharacteristic, complemented, Sylow
702C23—21no—
703C23—31no—
704C23—61no—
705C23—61no—
706C23—184no—
707C23—181no—
708C23—721no—
709C23—721no—
710D4—21no—
711D4—21no—
712D4—32no—
713D4—61no—
714D4—61no—
715D4—61no—
716D4—92no—
717D4—184no—
718D4—181no—
719D4—241no—
720D4—241no—
721D4—241no—
722D4—721no—
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—82no—
749C2×C3—81no—
750C2×C3—81no—
751C2×C3—121no—
752C2×C3—122no—
753C2×C3—241no—
754C2×C3#560611yescharacteristic
755C2×C3#565611yescharacteristic
756C2×C3#575711yescharacteristic
757C2×C3#576911yescharacteristic
758C2×C3#577411yescharacteristic
759C2×C3#577411yescharacteristic
760D3—42no—
761D3—41no—
762D3—81no—
763D3—122no—
764D3—122no—
765D3—242no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—61no—
770C22—61no—
771C22—61no—
772C22—62no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—121no—
777C22—121no—
778C22—182no—
779C22—361no—
780C22—361no—
781C22—724no—
782C22D32×D411yescharacteristic
783C4—41no—
784C4—61no—
785C4—61no—
786C4—61no—
787C4—121no—
788C4—121no—
789C4—181no—
790C4—181no—
791C4—361no—
792C4#6430611yescharacteristic
793C4D3×#23711yescharacteristic
794C3—21no—
795C3#8031711yescharacteristic, complemented
796C3#8135411yescharacteristic, complemented
797C2—81no—
798C2—121no—
799C2—122no—
800C2—241no—
801C2—362no—
802C2#1059426711yescharacteristic
803C2#1059473211yescharacteristic
804C2#1059475511yescharacteristic
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. #10595217C2semidirect
2. #10594604C2semidirect
3. #10592484C2semidirect
4. C3×#4786C2semidirect
5. C3×#4779C2semidirect
6. #10591515C2semidirect
7. #10591435C2semidirect
8. #10591429C2semidirect
9. #10590944C2semidirect
10. #10590781C2semidirect
11. #10590769C2semidirect
12. #10590699C2semidirect
13. #10590542C2semidirect
14. #10590505C2semidirect
15. #10590459C2semidirect
19. D4×C3⋊Dic3C22semidirect
22. C3×#940C22semidirect
37. #63898C22semidirect
40. #63869C22semidirect
43. C32×#102C22semidirect
45. #63642C22semidirect
46. #63635C22semidirect
47. C3×#832C22semidirect
49. C3×#817C22semidirect
50. C3×Dic3⋊C8C22semidirect
51. C3×#809C22semidirect
52. C3×#807C22semidirect
53. #63575C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
58. #63562C22semidirect
60. #63553C22semidirect
82. #4786D3semidirect
87. #4779D3semidirect
150. #940C2×D3semidirect
201. C3×#102C2×D3semidirect
202. C3×#102C2×D3semidirect
207. #832C2×D3semidirect
217. #817C2×D3semidirect
222. Dic3⋊C8C2×D3semidirect
228. #809C2×D3semidirect
233. #807C2×D3semidirect
469. #102D32semidirect
701. C32#3122semidirect
795. C3#80317semidirect
796. C3#81354semidirect

Maximal subgroups

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

subgroupindex
#105952172
#105946042
#105924842
C3×#47862
C3×#47792
#105915152
#105914352
#105914292
#105909442
#105907812
#105907692
#105906992
#105905422
#105905052
#105904592
#813543
#803173