Finite Group Databasebeta

← #11872774

Subgroups — #11872774

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#10594604C211yesmaximal, characteristic, complemented
2#10594501C211yesmaximal, characteristic, complemented
3#10592571C211yesmaximal, characteristic, complemented
4C3×#4891C211yesmaximal, characteristic, complemented
5C3×#4885C211yesmaximal, characteristic, complemented
6#10590947C211yesmaximal, characteristic, complemented
7#10590765C211yesmaximal, characteristic, complemented
8#10590740C211yesmaximal, characteristic, complemented
9#10590698C211yesmaximal, characteristic, complemented
10#10590595C211yesmaximal, characteristic, complemented
11#10590547C211yesmaximal, characteristic, complemented
12#10590470C211yesmaximal, characteristic, complemented
13#10590462C211yesmaximal, characteristic, complemented
14#10590462C211yesmaximal, characteristic, complemented
15#10590425C211yesmaximal, characteristic, complemented
16#81354—31nomaximal
17#81146—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3745C2211yescharacteristic
20#64102C2211yescharacteristic
21#64102C2211yescharacteristic, complemented
22C3×#895C2211yescharacteristic
23C3×#893C2211yescharacteristic
24C3×#892C2211yescharacteristic
25C3×#890C2211yescharacteristic, complemented
26#63921—21no—
27D3×(C2×D3)⋊C4—21no—
28#63916—21no—
29#63911C2211yescharacteristic, complemented
30#63909C2211yescharacteristic
31C4×#626—21no—
32#63898C2211yescharacteristic
33#63898C2211yescharacteristic, complemented
34#63894C2211yescharacteristic
35#63890—21no—
36#63886—21no—
37#63880—21no—
38#63855C2211yescharacteristic
39#63853—21no—
40C2×#3714C2211yescharacteristic
41C2×#3714C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C32×#107C2211yescharacteristic, complemented
44C8×C3⋊Dic3C2211yescharacteristic, complemented
45#63636C2211yescharacteristic
46#63636C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic, complemented
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×Dic3⋊C8C2211yescharacteristic, complemented
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic, complemented
53C3×#808C2211yescharacteristic, complemented
54C3×#808C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63555C2211yescharacteristic, complemented
61#5697—31no—
62#5619—31no—
63#5545—31no—
64#5521—31no—
65C3×#482—31no—
66C3×#478—31no—
67#5066—31no—
68#5036—31no—
69#5015—31no—
70#5003—31no—
71#4891D311yescharacteristic, complemented
72#4885D311yescharacteristic, complemented
73#4872—31no—
74#4872—31no—
75#4872—61no—
76#4871—31no—
77#4869—31no—
78#4869—31no—
79#4866—31no—
80#4843—31no—
81#4840—31no—
82#4786—31no—
83#4786—31no—
84#4785—31no—
85#4785—31no—
86#4773—31no—
87#4773—31no—
88#4756—31no—
89#4756—31no—
90#4732—31no—
91#4720—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×C4×C3⋊D3—21no—
96C2×C4×C3⋊D3—21no—
97C2×C3×D12—21no—
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#626—21no—
105C2×#626—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—
115#3752—21no—
116C4×C3⋊Dic3C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118#3745—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130Dic3⋊Dic3D411yescharacteristic
131Dic3⋊Dic3D411yescharacteristic
132#3722—21no—
133#3722—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—
144C3×#125—31no—
145C3×#121—31no—
146C3×C4×D4—31no—
147C3×#117—31no—
148#940—31no—
149#939—61no—
150#938—61no—
151D4×Dic3—31no—
152D4×Dic3—31no—
153C2×#213—31no—
154C2×#213—31no—
155C2×#213—31no—
156C2×#213—31no—
157#930—31no—
158C4×#67—61no—
159C2×(C2×D3)⋊C4—61no—
160#926—31no—
161C2×D24—31no—
162C2×D24—31no—
163C2×D24—31no—
164C2×D24—31no—
165C2×D24—61no—
166#895—31no—
167#895—61no—
168#895—61no—
169#895C2×D311yescharacteristic
170#894—61no—
171#894—61no—
172#893—31no—
173#893—31no—
174#893—31no—
175#893—31no—
176#893—31no—
177#893—31no—
178#893—31no—
179#893—61no—
180#893—61no—
181#893C2×D311yescharacteristic
182#892C2×D311yescharacteristic
183#890C2×D311yescharacteristic, complemented
184#886—61no—
185#883—61no—
186#67⋊C4—61no—
187D3×C22⋊C4—61no—
188D3×C22⋊C4—61no—
189D3×C22⋊C4—61no—
190#874—31no—
191C4×D12—31no—
192C4×D12—61no—
193C4×D12—61no—
194#872—31no—
195C3×#107—21no—
196C3×#107C2×D311yescharacteristic, complemented
197C3×#107C2×D311yescharacteristic, complemented
198C3×#106—31no—
199C3×#106—31no—
200C3×C4⋊C8—31no—
201C3×#102—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×C22⋊C8—31no—
206#830—31no—
207#821—31no—
208#821—31no—
209#821C2×D311yescharacteristic
210#821C2×D311yescharacteristic, complemented
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8C2×D311yescharacteristic
213#815—31no—
214#815—31no—
215Dic3⋊C8—31no—
216Dic3⋊C8C2×D311yescharacteristic, complemented
217C8×Dic3—31no—
218C8×Dic3—31no—
219C8×Dic3—61no—
220#809—31no—
221#809—31no—
222#809—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—61no—
227#809—61no—
228#809C2×D311yescharacteristic
229#809C2×D311yescharacteristic, complemented
230#808C2×D311yescharacteristic, complemented
231#808C2×D311yescharacteristic, complemented
232#807—31no—
233#807—31no—
234C4⋊(C3⋊C8)—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⋊Dic3C2×D411yescharacteristic
247C2×C3⋊Dic3C2×D411yescharacteristic
248C4⋊(C3⋊D3)—21no—
249C4⋊(C3⋊D3)—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)#4112yes—
252C4×C3⋊D3—81no—
253C4×C3⋊D3—81no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—81no—
263C3×D12#4112yes—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—81no—
267#626—24no—
268#626—81no—
269#626—81no—
270#626—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—31no—
283#478—91no—
284#459—91no—
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—31no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C22×C3×C4—31no—
299C22×C3×C4—61no—
300C2×#67—61no—
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—61no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306D3×D4—62no—
307D3×D4—62no—
308C2×D12—21no—
309C2×D12—31no—
310C2×D12—31no—
311C2×D12—31no—
312C2×D12—31no—
313C2×D12—61no—
314C2×D12—61no—
315C2×D12—62no—
316C2×D12—61no—
317C2×D12—62no—
318C2×D12—61no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12C22×D311yescharacteristic
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—61no—
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—61no—
332C2×C4×D3—121no—
333C2×C4×D3—121no—
334C2×C4×D3C22×D311yescharacteristic
335C2×C3×C8—21no—
336C2×C3×C8—31no—
337C2×C3×C8—31no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—21no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—31no—
354C3×C42—61no—
355#217—31no—
356#217—31no—
357#217—61no—
358#217—61no—
359#213—62no—
360#213—62no—
361#213—62no—
362#213—62no—
363(C2×D3)⋊C4—21no—
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—
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—
379(C2×D3)⋊C4—121no—
380C4⋊Dic3—21no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388C4×Dic3—21no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—61no—
392C4×Dic3C22×D311yescharacteristic
393C2×C3⋊C8—31no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398D24—62no—
399D24—62no—
400D24—64no—
401D24—62no—
402D24—62no—
403C22×C32C22×D411yescharacteristic
404C2×C3⋊D3—22no—
405C2×C3⋊D3—41no—
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
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×C4—41no—
422C32×C4C2×#4111yescharacteristic
423C32×C4C2×#4111yescharacteristic
424C3⋊Dic3—21no—
425C3⋊Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C22×D4—91no—
432C2×D8—91no—
433C2×D8—91no—
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—31no—
453#117—91no—
454C2×C22⋊C4—181no—
455C2×C22⋊C4—181no—
456#107—91no—
457#107D3211yescharacteristic, complemented
458#106—31no—
459#106—31no—
460C4⋊C8—31no—
461C4⋊C8—91no—
462#102—31no—
463#102—31no—
464#102—31no—
465#102—31no—
466#102—91no—
467#102—91no—
468#102—91no—
469#102—91no—
470C22⋊C8—31no—
471C22⋊C8—91no—
472#97—91no—
473C4×C8—91no—
474C23×C3—31no—
475C23×C3—61no—
476C23×C3—61no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—64no—
480C22×D3—64no—
481C22×D3—61no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—121no—
486C22×D3—121no—
487C22×D3—241no—
488C22×D3—241no—
489C22×D3—241no—
490C22×D3—241no—
491C22×D3D3×D411yescharacteristic
492C3×D4—32no—
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—61no—
511C2×C3×C4—241no—
512C2×C3×C4C23×D311yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514#67—64no—
515#67—241no—
516#67—241no—
517#67—241no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—31no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—31no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—241no—
527C2×Dic3—241no—
528C2×Dic3D3×D411yescharacteristic
529C2×Dic3D3×D411yescharacteristic
530C2×Dic3D3×D411yescharacteristic
531D12—21no—
532D12—21no—
533D12—21no—
534D12—32no—
535D12—32no—
536D12—62no—
537D12—62no—
538D12—64no—
539D12—61no—
540D12—61no—
541D12—61no—
542D12—61no—
543D12—61no—
544D12—61no—
545D12—81no—
546D12—121no—
547D12—121no—
548D12—241no—
549D12—241no—
550D12—241no—
551D12#23912yes—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—81no—
555C4×D3—241no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—241no—
561C4×D3—242no—
562C4×D3—242no—
563C4×D3—241no—
564C4×D3—241no—
565C3×C8—22no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—61no—
569C3×C8—61no—
570C3⋊C8—21no—
571C3⋊C8—21no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—121no—
575C2×C32#52511yescharacteristic
576C2×C32#57611yescharacteristic
577C2×C32#57611yescharacteristic
578C3⋊D3—42no—
579C3⋊D3—81no—
580C3×D3—41no—
581C3×D3—42no—
582C3×D3—81no—
583C24—181no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—91no—
588C2×D4—91no—
589C2×D4—181no—
590C2×D4—181no—
591C2×D4—181no—
592C2×D4—182no—
593C2×D4—182no—
594C2×D4—181no—
595C22×C4—31no—
596C22×C4—61no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4—181no—
600C22×C4—181no—
601C22×C4—181no—
602D8—182no—
603D8—182no—
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⋊C4C2×D3211yescharacteristic
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—62no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3—61no—
637C22×C3—121no—
638C22×C3—121no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C2×D3×D411yescharacteristic
644C2×D3—21no—
645C2×D3—21no—
646C2×D3—21no—
647C2×D3—22no—
648C2×D3—41no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—122no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—122no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—241no—
668C2×D3—241no—
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—41no—
678C3×C4—41no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—81no—
683C3×C4—81no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4C2×#23911yescharacteristic
687C3×C4D3×#4111yescharacteristic
688C3×C4D3×#4111yescharacteristic
689C3×C4D3×#4111yescharacteristic
690Dic3—21no—
691Dic3—21no—
692Dic3—21no—
693Dic3—41no—
694Dic3—41no—
695Dic3—62no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699Dic3—61no—
700Dic3—121no—
701C32#312211yescharacteristic, complemented, Sylow
702C23—31no—
703C23—61no—
704C23—61no—
705C23—184no—
706C23—181no—
707C23—181no—
708C23—721no—
709C23—721no—
710D4—32no—
711D4—61no—
712D4—61no—
713D4—61no—
714D4—92no—
715D4—184no—
716D4—181no—
717D4—181no—
718D4—181no—
719D4—241no—
720D4—721no—
721D4—721no—
722D4—721no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—31no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—91no—
733C2×C4—91no—
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—122no—
749C2×C3—121no—
750C2×C3—241no—
751C2×C3#562711yescharacteristic
752C2×C3#565611yescharacteristic
753C2×C3#576911yescharacteristic
754C2×C3#576911yescharacteristic
755C2×C3#577411yescharacteristic
756C2×C3#577411yescharacteristic
757D3—41no—
758D3—42no—
759D3—81no—
760D3—122no—
761D3—122no—
762D3—242no—
763D3—242no—
764D3—241no—
765D3—241no—
766C22—61no—
767C22—62no—
768C22—61no—
769C22—61no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—182no—
776C22—361no—
777C22—361no—
778C22—361no—
779C22—361no—
780C22—361no—
781C22—724no—
782C22D32×D411yescharacteristic
783C4—41no—
784C4—41no—
785C4—61no—
786C4—61no—
787C4—61no—
788C4—121no—
789C4—121no—
790C4—181no—
791C4—181no—
792C4#6430611yescharacteristic
793C4D3×#23911yescharacteristic
794C3—21no—
795C3#8114611yescharacteristic, complemented
796C3#8135411yescharacteristic, complemented
797C2—121no—
798C2—122no—
799C2—241no—
800C2—362no—
801C2—721no—
802C2#1059461511yescharacteristic
803C2#1059473511yescharacteristic
804C2#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. #10594501C2semidirect
3. #10592571C2semidirect
4. C3×#4891C2semidirect
5. C3×#4885C2semidirect
6. #10590947C2semidirect
7. #10590765C2semidirect
8. #10590740C2semidirect
9. #10590698C2semidirect
10. #10590595C2semidirect
11. #10590547C2semidirect
12. #10590470C2semidirect
13. #10590462C2semidirect
14. #10590462C2semidirect
15. #10590425C2semidirect
21. #64102C22semidirect
25. C3×#890C22semidirect
29. #63911C22semidirect
33. #63898C22semidirect
43. C32×#107C22semidirect
44. C8×C3⋊Dic3C22semidirect
46. #63636C22semidirect
48. C3×#821C22semidirect
50. C3×Dic3⋊C8C22semidirect
52. C3×#809C22semidirect
53. C3×#808C22semidirect
54. C3×#808C22semidirect
55. #63576C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
58. #63564C22semidirect
60. #63555C22semidirect
71. #4891D3semidirect
72. #4885D3semidirect
183. #890C2×D3semidirect
196. C3×#107C2×D3semidirect
197. C3×#107C2×D3semidirect
210. #821C2×D3semidirect
216. Dic3⋊C8C2×D3semidirect
229. #809C2×D3semidirect
230. #808C2×D3semidirect
231. #808C2×D3semidirect
457. #107D32semidirect
701. C32#3122semidirect
795. C3#81146semidirect
796. C3#81354semidirect

Maximal subgroups

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

subgroupindex
#105946042
#105945012
#105925712
C3×#48912
C3×#48852
#105909472
#105907652
#105907402
#105906982
#105905952
#105905472
#105904702
#105904622
#105904252
#813543
#811463