Finite Group Databasebeta

← #11872775

Subgroups — #11872775

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#10594604C211yesmaximal, characteristic, complemented
2#10594496C211yesmaximal, characteristic, complemented
3#10592590C211yesmaximal, characteristic, complemented
4C3×#4885C211yesmaximal, characteristic, complemented
5C3×#4872C211yesmaximal, characteristic, complemented
6#10590944C211yesmaximal, characteristic, complemented
7#10590749C211yesmaximal, characteristic, complemented
8#10590745C211yesmaximal, characteristic, complemented
9#10590696C211yesmaximal, characteristic, complemented
10#10590595C211yesmaximal, characteristic, complemented
11#10590589C211yesmaximal, characteristic, complemented
12#10590551C211yesmaximal, characteristic, complemented
13#10590505C211yesmaximal, characteristic, complemented
14#10590474C211yesmaximal, characteristic, complemented
15#10590455C211yesmaximal, characteristic, complemented
16#81354—31nomaximal
17#79596—31nomaximal
18C2×D3×D12C2211yescharacteristic
19#64102C2211yescharacteristic
20#64099C2211yescharacteristic, complemented
21C2×C3×D24C2211yescharacteristic
22C3×#895C2211yescharacteristic
23C3×#893C2211yescharacteristic
24C3×#893C2211yescharacteristic, complemented
25C3×#892C2211yescharacteristic
26#63921—21no—
27D3×(C2×D3)⋊C4—21no—
28#63914C2211yescharacteristic, complemented
29#63908—21no—
30#63908C2211yescharacteristic
31#63905—21no—
32C4×#626—21no—
33#63898C2211yescharacteristic
34#63894C2211yescharacteristic
35Dic3×D12C2211yescharacteristic, complemented
36#63891—21no—
37#63885—21no—
38#63880—21no—
39#63855C2211yescharacteristic
40C2×#3714C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C32×#107C2211yescharacteristic, complemented
44#63648C2211yescharacteristic
45#63641C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47#63635C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×C8×Dic3C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic, complemented
61#5619—31no—
62#5562—31no—
63#5545—31no—
64#5521—31no—
65C3×#482—31no—
66C3×C4×D8—31no—
67#5156—31no—
68#5150—31no—
69#5036—31no—
70#5014—31no—
71#5014—31no—
72#5003—31no—
73#4891—31no—
74#4891—31no—
75#4891—61no—
76#4885D311yescharacteristic, complemented
77#4872D311yescharacteristic, complemented
78#4871—31no—
79#4869—31no—
80#4786—31no—
81#4786—31no—
82#4786—31no—
83#4785—31no—
84#4784—31no—
85#4773—31no—
86#4766—31no—
87#4756—31no—
88#4732—31no—
89#4720—31no—
90C4×D24—31no—
91#4690—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4×C3⋊D3—21no—
95C2×C3×D12—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×#626—21no—
103C2×#625—21no—
104C2×#625—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
113C32×C4⋊C4C2311yescharacteristic
114#3752—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4×Dic3—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)⋊Dic3D411yescharacteristic
137(C2×D3)⋊Dic3D411yescharacteristic
138#3714—22no—
139#3714—22no—
140#3713—22no—
141#3122—91noSylow
142C2×D3×D4—31no—
143C22×D12—31no—
144C2×C3×D8—31no—
145C3×#121—31no—
146C3×C4×D4—31no—
147C3×C4×D4—31no—
148C3×#117—31no—
149#940—31no—
150#940—31no—
151#939—61no—
152#938—31no—
153#938—61no—
154D4×Dic3—31no—
155D4×Dic3—31no—
156C2×#213—31no—
157C2×#213—31no—
158C2×#213—31no—
159C2×#213—31no—
160#930—31no—
161#930—61no—
162#929—61no—
163C4×#67—61no—
164C2×(C2×D3)⋊C4—61no—
165#926—31no—
166C2×D24—31no—
167C2×D24—31no—
168C2×D24C2×D311yescharacteristic
169#895C2×D311yescharacteristic
170#893—31no—
171#893—31no—
172#893—31no—
173#893—31no—
174#893—61no—
175#893C2×D311yescharacteristic
176#893C2×D311yescharacteristic, complemented
177#892C2×D311yescharacteristic
178#890—31no—
179#890—31no—
180#890—61no—
181#886—61no—
182#884—61no—
183#883—61no—
184#883—61no—
185#67⋊C4—61no—
186D3×C22⋊C4—61no—
187D3×C22⋊C4—61no—
188D3×C22⋊C4—61no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—61no—
192C4×D12—61no—
193#872—31no—
194C3×#107—21no—
195C3×#107C2×D311yescharacteristic, complemented
196C3×#107C2×D311yescharacteristic, complemented
197C3×#106—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×C22⋊C8—31no—
203C3×C4×C8—31no—
204#832—31no—
205#832—31no—
206#830—31no—
207#821—31no—
208#821—31no—
209#821—31no—
210#821—61no—
211#821C2×D311yescharacteristic, complemented
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8C2×D311yescharacteristic
214#818—31no—
215#815—31no—
216Dic3⋊C8—31no—
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—61no—
221C8×Dic3C2×D311yescharacteristic, complemented
222#809—31no—
223#809—31no—
224#809—31no—
225#809—61no—
226#809C2×D311yescharacteristic
227#809C2×D311yescharacteristic, complemented
228#809C2×D311yescharacteristic, complemented
229#808—31no—
230#808—31no—
231#808—61no—
232#808C2×D311yescharacteristic, complemented
233#807—31no—
234#803—31no—
235C22×C3⋊D3—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—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3C2×D411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)#4112yes—
251C4×C3⋊D3—81no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3C2×D411yescharacteristic
254C2×C3×Dic3C2×D411yescharacteristic
255C2×C3×Dic3C2×D411yescharacteristic
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—81no—
262C3×D12#4112yes—
263C3×C4×D3—21no—
264C3×C4×D3—21no—
265C3×C4×D3—81no—
266C3×C4×D3—81no—
267#626—24no—
268#625—81no—
269#625—81no—
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—91no—
285#459—91no—
286#447—91no—
287#447—91no—
288#442—91no—
289#442—91no—
290C4×D8—31no—
291C4×D8—91no—
292#433—91no—
293C23×D3—61no—
294C23×D3—61no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—61no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C22×C3×C4—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311D3×D4—62no—
312D3×D4—62no—
313C2×D12—21no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—61no—
317C2×D12—62no—
318C2×D12—61no—
319C2×D12—62no—
320C2×D12C22×D311yescharacteristic
321C2×D12C22×D311yescharacteristic
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—121no—
332C2×C4×D3C22×D311yescharacteristic
333C3×D8—62no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C3×C4⋊C4—21no—
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4C22×D311yescharacteristic
343C3×C4⋊C4C22×D311yescharacteristic
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—31no—
351C3×C42—61no—
352#217—31no—
353#217—31no—
354#217—61no—
355#217—61no—
356#217—61no—
357#213—62no—
358#213—62no—
359#213—62no—
360#213—62no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—61no—
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—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—121no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—121no—
383C4⋊Dic3C22×D311yescharacteristic
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—121no—
389C4×Dic3—21no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—61no—
393C4×Dic3C22×D311yescharacteristic
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—61no—
397C2×C3⋊C8C22×D311yescharacteristic
398C2×C3⋊C8C22×D311yescharacteristic
399D24—22no—
400D24—62no—
401D24—62no—
402C22×C32C22×D411yescharacteristic
403C2×C3⋊D3—22no—
404C2×C3⋊D3—41no—
405C2×C3⋊D3—41no—
406C2×C3×D3—22no—
407C2×C3×D3—21no—
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—
418D32—84no—
419C32×C4—41no—
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—
430C22×D4—91no—
431C2×D8—31no—
432C2×D8—91no—
433C2×D8—91no—
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—31no—
452#117—91no—
453C2×C22⋊C4—181no—
454C2×C22⋊C4—181no—
455#107—91no—
456#107D3211yescharacteristic, complemented
457#106—31no—
458#106—91no—
459C4⋊C8—91no—
460C4⋊C8—91no—
461#102—31no—
462#102—31no—
463#102—31no—
464#102—31no—
465#102—91no—
466#102—91no—
467#102—91no—
468#102—91no—
469C22⋊C8—31no—
470C22⋊C8—91no—
471#97—91no—
472C4×C8—31no—
473C23×C3—31no—
474C23×C3—61no—
475C23×C3—61no—
476C23×C3—61no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—64no—
481C22×D3—64no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—121no—
485C22×D3—241no—
486C22×D3—241no—
487C22×D3—241no—
488C22×D3—241no—
489C22×D3D3×D411yescharacteristic
490C3×D4—32no—
491C3×D4—61no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—61no—
495C3×D4—61no—
496C3×D4—241no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—241no—
511C2×C3×C4—241no—
512C2×C3×C4C23×D311yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514#67—64no—
515#67—241no—
516#67—241no—
517#67—241no—
518#67—241no—
519#67—241no—
520#67—241no—
521C2×Dic3—21no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—121no—
531C2×Dic3—241no—
532C2×Dic3—241no—
533C2×Dic3D3×D411yescharacteristic
534C2×Dic3D3×D411yescharacteristic
535C2×Dic3D3×D411yescharacteristic
536D12—21no—
537D12—21no—
538D12—21no—
539D12—21no—
540D12—21no—
541D12—32no—
542D12—32no—
543D12—62no—
544D12—64no—
545D12—61no—
546D12—61no—
547D12—81no—
548D12—121no—
549D12#23512yes—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—81no—
553C4×D3—81no—
554C4×D3—241no—
555C4×D3—241no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—242no—
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#52511yescharacteristic
572C2×C32#57611yescharacteristic
573C2×C32#57611yescharacteristic
574C3⋊D3—42no—
575C3×D3—41no—
576C3×D3—42no—
577C3×D3—81no—
578C3×D3—81no—
579C24—181no—
580C2×D4—31no—
581C2×D4—31no—
582C2×D4—31no—
583C2×D4—61no—
584C2×D4—91no—
585C2×D4—181no—
586C2×D4—182no—
587C2×D4—182no—
588C2×D4—181no—
589C2×D4—181no—
590C2×D4—181no—
591C22×C4—31no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598D8—62no—
599D8—182no—
600D8—182no—
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—181no—
611C4⋊C4—181no—
612C4⋊C4C2×D3211yescharacteristic
613C4⋊C4C2×D3211yescharacteristic
614C22⋊C4—61no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—91no—
619C22⋊C4—91no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C42—31no—
626C42—61no—
627C42—91no—
628C22×C3—21no—
629C22×C3—62no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3—121no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3C2×D3×D411yescharacteristic
642C22×C3C2×D3×D411yescharacteristic
643C2×D3—21no—
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—22no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—62no—
656C2×D3—62no—
657C2×D3—122no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—241no—
663C2×D3—241no—
664C2×D3—244no—
665C2×D3—244no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—61no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—81no—
676C3×C4—81no—
677C3×C4—121no—
678C3×C4C2×#23511yescharacteristic
679C3×C4D3×#4111yescharacteristic
680C3×C4D3×#4111yescharacteristic
681C3×C4D3×#4111yescharacteristic
682Dic3—21no—
683Dic3—21no—
684Dic3—21no—
685Dic3—41no—
686Dic3—61no—
687Dic3—61no—
688Dic3—61no—
689Dic3—61no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—241no—
695C32#312211yescharacteristic, complemented, Sylow
696C23—31no—
697C23—61no—
698C23—61no—
699C23—61no—
700C23—184no—
701C23—181no—
702C23—721no—
703C23—721no—
704D4—32no—
705D4—61no—
706D4—61no—
707D4—61no—
708D4—61no—
709D4—61no—
710D4—92no—
711D4—184no—
712D4—181no—
713D4—241no—
714D4—721no—
715D4—721no—
716D4—721no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—91no—
726C2×C4—91no—
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—122no—
743C2×C3—121no—
744C2×C3—241no—
745C2×C3—241no—
746C2×C3#554711yescharacteristic
747C2×C3#565611yescharacteristic
748C2×C3#575711yescharacteristic
749C2×C3#576911yescharacteristic
750C2×C3#576911yescharacteristic
751C2×C3#577411yescharacteristic
752D3—41no—
753D3—42no—
754D3—81no—
755D3—81no—
756D3—122no—
757D3—122no—
758D3—242no—
759C22—61no—
760C22—62no—
761C22—61no—
762C22—61no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—182no—
772C22—361no—
773C22—361no—
774C22—724no—
775C22D32×D411yescharacteristic
776C4—41no—
777C4—41no—
778C4—61no—
779C4—61no—
780C4—61no—
781C4—121no—
782C4—181no—
783C4—181no—
784C4—361no—
785C4D3×#23511yescharacteristic
786C4#6431911yescharacteristic
787C3—21no—
788C3#7959611yescharacteristic, complemented
789C3#8135411yescharacteristic, complemented
790C2—121no—
791C2—122no—
792C2—241no—
793C2—241no—
794C2—362no—
795C2#1059461411yescharacteristic
796C2#1059473211yescharacteristic
797C2#1059477111yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#107C22
socleC22×C32C22×D4
hypercenter#107D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #10594604C2semidirect
2. #10594496C2semidirect
3. #10592590C2semidirect
4. C3×#4885C2semidirect
5. C3×#4872C2semidirect
6. #10590944C2semidirect
7. #10590749C2semidirect
8. #10590745C2semidirect
9. #10590696C2semidirect
10. #10590595C2semidirect
11. #10590589C2semidirect
12. #10590551C2semidirect
13. #10590505C2semidirect
14. #10590474C2semidirect
15. #10590455C2semidirect
20. #64099C22semidirect
24. C3×#893C22semidirect
28. #63914C22semidirect
35. Dic3×D12C22semidirect
43. C32×#107C22semidirect
45. #63641C22semidirect
47. #63635C22semidirect
48. C3×#821C22semidirect
50. C3×C8×Dic3C22semidirect
52. C3×#809C22semidirect
53. C3×#809C22semidirect
54. C3×#808C22semidirect
55. #63575C22semidirect
56. #63572C22semidirect
58. #63562C22semidirect
60. #63554C22semidirect
76. #4885D3semidirect
77. #4872D3semidirect
176. #893C2×D3semidirect
195. C3×#107C2×D3semidirect
196. C3×#107C2×D3semidirect
211. #821C2×D3semidirect
221. C8×Dic3C2×D3semidirect
227. #809C2×D3semidirect
228. #809C2×D3semidirect
232. #808C2×D3semidirect
456. #107D32semidirect
695. C32#3122semidirect
788. C3#79596semidirect
789. C3#81354semidirect

Maximal subgroups

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

subgroupindex
#105946042
#105944962
#105925902
C3×#48852
C3×#48722
#105909442
#105907492
#105907452
#105906962
#105905952
#105905892
#105905512
#105905052
#105904742
#105904552
#813543
#795963