Finite Group Databasebeta

← #11872738

Subgroups — #11872738

Order 1152.

887 conjugacy classes of subgroups.

The subgroup lattice has 799 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595215C211yesmaximal, characteristic, complemented
2#10594496C211yesmaximal, characteristic, complemented
3#10592465C211yesmaximal, characteristic, complemented
4C3×#4773C211yesmaximal, characteristic, complemented
5C3×#4756C211yesmaximal, characteristic, complemented
6#10591486C211yesmaximal, characteristic, complemented
7#10591447C211yesmaximal, characteristic, complemented
8#10591430C211yesmaximal, characteristic, complemented
9#10590834C211yesmaximal, characteristic, complemented
10Dic3×D24C211yesmaximal, characteristic, complemented
11#10590749C211yesmaximal, characteristic, complemented
12#10590696C211yesmaximal, characteristic, complemented
13#10590473C211yesmaximal, characteristic, complemented
14#10590455C211yesmaximal, characteristic, complemented
15#10590446C211yesmaximal, characteristic, complemented
16#79993—31nomaximal
17#79596—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19D4×C3⋊Dic3C2211yescharacteristic
20#64099C2211yescharacteristic, complemented
21C3×D4×Dic3C2211yescharacteristic
22C2×C3×#213C2211yescharacteristic
23C2×C3×#213C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25C3×#895C2211yescharacteristic
26C3×#893C2211yescharacteristic, complemented
27#67⋊Dic3—21no—
28Dic3×#67—21no—
29D3×#217—21no—
30C2×(C2×D3)⋊Dic3—21no—
31#63914C2211yescharacteristic, complemented
32#63908—21no—
33#63908C2211yescharacteristic
34#63905—21no—
35#63898C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37Dic3×D12C2211yescharacteristic, complemented
38#63891—21no—
39#63885—21no—
40#63855C2211yescharacteristic
41#63841C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C32×#102C2211yescharacteristic
44#63659C2211yescharacteristic
45#63645C2211yescharacteristic, complemented
46#63641C2211yescharacteristic, complemented
47#63635C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#807C2211yescharacteristic, complemented
53#63573C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63563C2211yescharacteristic
56#63563C2211yescharacteristic, complemented
57#63563C2211yescharacteristic, complemented
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5798—31no—
62#5619—31no—
63#5562—31no—
64#5545—31no—
65C3×#447—31no—
66C3×C4×D8—31no—
67#5217—31no—
68#5156—31no—
69#5152—31no—
70#5150—31no—
71#5150—31no—
72#5150—31no—
73Dic3×D8—31no—
74#5035—31no—
75#5014—31no—
76#5014—31no—
77#4891—31no—
78#4885—31no—
79#4786—31no—
80#4785—31no—
81#4784—31no—
82#4773D311yescharacteristic, complemented
83#4766—31no—
84#4766—31no—
85#4766—61no—
86#4763—31no—
87#4756D311yescharacteristic, complemented
88#4737—31no—
89#4720—31no—
90C4×D24—31no—
91#4690—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C3×#67—21no—
96C22×C3×Dic3—21no—
97C3×D3×D4—22no—
98C3×D3×D4—22no—
99C2×C3×D12—21no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×#625—21no—
106C2×#625—21no—
107C2×#625—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3757—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#213—22no—
122C3×#213—22no—
123C3×(C2×D3)⋊C4—21no—
124C3×(C2×D3)⋊C4—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D24—22no—
130Dic3⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
132(C2×D3)⋊Dic3—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#3713—22no—
141#3122—91noSylow
142C22×C3×D4—31no—
143C2×D3×D4C2×D311yescharacteristic
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C2×C3×D8—31no—
147C3×#121—31no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150C2×#217—61no—
151C2×#217—61no—
152#940—31no—
153#940—31no—
154#939—61no—
155#938—31no—
156#938—61no—
157D4×Dic3—31no—
158D4×Dic3—31no—
159D4×Dic3—31no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—61no—
163D4×Dic3—61no—
164D4×Dic3—61no—
165D4×Dic3C2×D311yescharacteristic
166C2×#213—31no—
167C2×#213—31no—
168C2×#213C2×D311yescharacteristic
169C2×#213C2×D311yescharacteristic
170#930—31no—
171#930—61no—
172#929—61no—
173C4×#67—61no—
174C2×(C2×D3)⋊C4—61no—
175#926—31no—
176#926—31no—
177C2×D24C2×D311yescharacteristic
178#895C2×D311yescharacteristic
179#893—31no—
180#893C2×D311yescharacteristic, complemented
181#892—31no—
182#890—31no—
183#890—31no—
184#890—61no—
185#886—61no—
186#884—61no—
187#883—61no—
188#883—61no—
189#67⋊C4—61no—
190D3×C22⋊C4—61no—
191C4×D12—31no—
192C4×D12—31no—
193#872—31no—
194C3×#107—31no—
195C3×#102—21no—
196C3×#102—31no—
197C3×#102—31no—
198C3×#102C2×D311yescharacteristic
199C3×#102C2×D311yescharacteristic
200C3×C22⋊C8—31no—
201C3×C4×C8—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#832—61no—
209#830—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821C2×D311yescharacteristic, complemented
214(C2×D3)⋊C8—31no—
215(C2×D3)⋊C8C2×D311yescharacteristic
216#818—31no—
217#818—31no—
218#818—61no—
219#817—31no—
220#815—31no—
221Dic3⋊C8—31no—
222Dic3⋊C8—31no—
223Dic3⋊C8—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—61no—
226C8×Dic3C2×D311yescharacteristic, complemented
227#809—31no—
228#809C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808—31no—
232#808—61no—
233#807C2×D311yescharacteristic, complemented
234#803—31no—
235C23×C32—21no—
236C22×C3×D3—21no—
237C22×C3×D3—24no—
238C22×C3×D3—21no—
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—21no—
249C2×C3⋊Dic3—81no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252C3×#67—24no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—81no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—81no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—81no—
268#625—81no—
269#625—81no—
270#625—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—91no—
283#478—91no—
284#459—91no—
285#459—91no—
286#447—31no—
287#447—91no—
288#442—91no—
289#442—91no—
290C4×D8—31no—
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—31no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4—62no—
302C2×C3×D4—62no—
303C2×C3×D4C22×D311yescharacteristic
304C2×C3×D4C22×D311yescharacteristic
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C2×#67—21no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67—61no—
315C22×Dic3—21no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—121no—
322D3×D4—22no—
323D3×D4—22no—
324C2×D12—21no—
325C2×D12C22×D311yescharacteristic
326C2×D12C22×D311yescharacteristic
327C2×D12C22×D311yescharacteristic
328C2×C4×D3—21no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3C22×D311yescharacteristic
333C3×D8—62no—
334C3×D8—62no—
335C3×D8—62no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—31no—
349#217—21no—
350#217—31no—
351#217—31no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—121no—
360#213—22no—
361#213—22no—
362#213—62no—
363#213—62no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—121no—
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—121no—
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—
402C22×C32—22no—
403C22×C32—41no—
404C22×C32—41no—
405C22×C32C22×D411yescharacteristic
406C2×C3×D3—21no—
407C2×C3×D3—22no—
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3—84no—
419C32×C4—41no—
420C32×C4C2×#4111yescharacteristic
421C32×C4C2×#4111yescharacteristic
422C3⋊Dic3—21no—
423C3⋊Dic3—21no—
424C3⋊Dic3—41no—
425C3⋊Dic3—41no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C22×D4—31no—
431C2×D8—31no—
432C2×D8—31no—
433C2×D8—31no—
434C2×D8—91no—
435#127—91no—
436#125—91no—
437#123—181no—
438#123—181no—
439#121—31no—
440#121—91no—
441#121—181no—
442#121—181no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—91no—
446C4×D4—91no—
447C4×D4—91no—
448C4×D4—91no—
449C4×D4—181no—
450C4×D4—181no—
451#117—91no—
452#117—91no—
453C2×C22⋊C4—181no—
454C2×C22⋊C4—181no—
455#107—31no—
456#107—91no—
457#106—91no—
458#106—91no—
459C4⋊C8—91no—
460C4⋊C8—91no—
461#102—31no—
462#102—31no—
463#102—91no—
464#102—91no—
465#102—91no—
466#102—91no—
467#102—91no—
468#102D3211yescharacteristic
469C22⋊C8—31no—
470C22⋊C8—91no—
471#97—91no—
472C4×C8—31no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—31no—
476C23×C3—41no—
477C23×C3—64no—
478C23×C3—61no—
479C23×C3—61no—
480C23×C3—61no—
481C23×C3—241no—
482C23×C3—241no—
483C22×D3—21no—
484C22×D3—24no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—81no—
488C22×D3—81no—
489C22×D3D3×D411yescharacteristic
490C3×D4—21no—
491C3×D4—21no—
492C3×D4—22no—
493C3×D4—32no—
494C3×D4—41no—
495C3×D4—64no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4—241no—
502C3×D4#23512yes—
503C3×D4#23712yes—
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—241no—
515C2×C3×C4—241no—
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—24no—
519#67—241no—
520#67—241no—
521#67—241no—
522#67—241no—
523#67—241no—
524#67—241no—
525C2×Dic3—21no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—81no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—241no—
540C2×Dic3—241no—
541C2×Dic3—241no—
542C2×Dic3—241no—
543C2×Dic3—241no—
544C2×Dic3—242no—
545C2×Dic3D3×D411yescharacteristic
546C2×Dic3D3×D411yescharacteristic
547C2×Dic3D3×D411yescharacteristic
548D12—21no—
549D12—21no—
550D12—21no—
551D12—21no—
552D12—21no—
553D12—81no—
554D12#23712yes—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—81no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—241no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—41no—
564C3×C8—61no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—21no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—121no—
571C2×C32—42no—
572C2×C32#52511yescharacteristic
573C2×C32#57611yescharacteristic
574C2×C32#57611yescharacteristic
575C3×D3—41no—
576C3×D3—42no—
577C3×D3—81no—
578C3×D3—81no—
579C24—61no—
580C2×D4—31no—
581C2×D4—31no—
582C2×D4—31no—
583C2×D4—61no—
584C2×D4—61no—
585C2×D4—62no—
586C2×D4—62no—
587C2×D4—181no—
588C2×D4—181no—
589C2×D4—181no—
590C2×D4C2×D3211yescharacteristic
591C22×C4—31no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598D8—62no—
599D8—62no—
600D8—62no—
601D8—182no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—91no—
605C2×C8C2×D3211yescharacteristic
606C4⋊C4—31no—
607C4⋊C4—91no—
608C4⋊C4—91no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4C2×D3211yescharacteristic
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—91no—
618C22⋊C4—91no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C42—31no—
626C42—91no—
627C42—181no—
628C22×C3—22no—
629C22×C3—22no—
630C22×C3—21no—
631C22×C3—42no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—62no—
640C22×C3—81no—
641C22×C3—81no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—244no—
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—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—84no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—61no—
673C3×C4—81no—
674C3×C4—121no—
675C3×C4C2×#23511yescharacteristic
676C3×C4C2×#23711yescharacteristic
677C3×C4C2×#23711yescharacteristic
678C3×C4D3×#4111yescharacteristic
679Dic3—21no—
680Dic3—21no—
681Dic3—21no—
682Dic3—41no—
683Dic3—61no—
684Dic3—61no—
685Dic3—61no—
686Dic3—61no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—241no—
694Dic3—241no—
695C32#312211yescharacteristic, complemented, Sylow
696C23—21no—
697C23—31no—
698C23—64no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23—241no—
703C23—241no—
704D4—21no—
705D4—32no—
706D4—64no—
707D4—61no—
708D4—61no—
709D4—61no—
710D4—61no—
711D4—61no—
712D4—241no—
713D4—721no—
714D4—721no—
715D4—721no—
716D4#379512yes—
717C2×C4—21no—
718C2×C4—31no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—91no—
725C2×C4—91no—
726C2×C4—181no—
727C2×C4—181no—
728C2×C4—241no—
729C2×C4—241no—
730C2×C4—721no—
731C2×C4—721no—
732C2×C4—721no—
733C2×C4—721no—
734C2×C4C22×D3211yescharacteristic
735C8—21no—
736C8—61no—
737C8—61no—
738C8—181no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—42no—
743C2×C3—42no—
744C2×C3—82no—
745C2×C3—121no—
746C2×C3—122no—
747C2×C3—241no—
748C2×C3—241no—
749C2×C3#554711yescharacteristic
750C2×C3#558611yescharacteristic
751C2×C3#575711yescharacteristic
752C2×C3#575711yescharacteristic
753C2×C3#576911yescharacteristic
754C2×C3#577411yescharacteristic
755D3—41no—
756D3—42no—
757D3—81no—
758D3—81no—
759C22—22no—
760C22—41no—
761C22—41no—
762C22—61no—
763C22—62no—
764C22—61no—
765C22—61no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—244no—
775C22D32×D411yescharacteristic
776C4—41no—
777C4—61no—
778C4—61no—
779C4—61no—
780C4—121no—
781C4—181no—
782C4—181no—
783C4—361no—
784C4—361no—
785C4C2×#379511yescharacteristic
786C4D3×#23711yescharacteristic
787C3—21no—
788C3#7959611yescharacteristic, complemented
789C3#7999311yescharacteristic, complemented
790C2—42no—
791C2—121no—
792C2—122no—
793C2—241no—
794C2—241no—
795C2#1059405411yescharacteristic
796C2#1059473111yescharacteristic
797C2#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. #10595215C2semidirect
2. #10594496C2semidirect
3. #10592465C2semidirect
4. C3×#4773C2semidirect
5. C3×#4756C2semidirect
6. #10591486C2semidirect
7. #10591447C2semidirect
8. #10591430C2semidirect
9. #10590834C2semidirect
10. Dic3×D24C2semidirect
11. #10590749C2semidirect
12. #10590696C2semidirect
13. #10590473C2semidirect
14. #10590455C2semidirect
15. #10590446C2semidirect
20. #64099C22semidirect
26. C3×#893C22semidirect
31. #63914C22semidirect
37. Dic3×D12C22semidirect
45. #63645C22semidirect
46. #63641C22semidirect
47. #63635C22semidirect
48. C3×#821C22semidirect
50. C3×C8×Dic3C22semidirect
52. C3×#807C22semidirect
53. #63573C22semidirect
54. #63572C22semidirect
56. #63563C22semidirect
57. #63563C22semidirect
58. #63562C22semidirect
60. #63554C22semidirect
82. #4773D3semidirect
87. #4756D3semidirect
180. #893C2×D3semidirect
213. #821C2×D3semidirect
226. C8×Dic3C2×D3semidirect
233. #807C2×D3semidirect
695. C32#3122semidirect
788. C3#79596semidirect
789. C3#79993semidirect

Maximal subgroups

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

subgroupindex
#105952152
#105944962
#105924652
C3×#47732
C3×#47562
#105914862
#105914472
#105914302
#105908342
Dic3×D242
#105907492
#105906962
#105904732
#105904552
#105904462
#799933
#795963