Finite Group Databasebeta

← #11872776

Subgroups — #11872776

Order 1152.

906 conjugacy classes of subgroups.

The subgroup lattice has 813 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595125C211yesmaximal, characteristic, complemented
2#10594604C211yesmaximal, characteristic, complemented
3#10592485C211yesmaximal, characteristic, complemented
4C3×#4785C211yesmaximal, characteristic, complemented
5C3×#4779C211yesmaximal, characteristic, complemented
6#10591515C211yesmaximal, characteristic, complemented
7#10591433C211yesmaximal, characteristic, complemented
8#10591400C211yesmaximal, characteristic, complemented
9#10590947C211yesmaximal, characteristic, complemented
10#10590782C211yesmaximal, characteristic, complemented
11#10590768C211yesmaximal, characteristic, complemented
12#10590697C211yesmaximal, characteristic, complemented
13#10590456C211yesmaximal, characteristic, complemented
14#10590435C211yesmaximal, characteristic, complemented
15#10590425C211yesmaximal, characteristic, complemented
16#81354—31nomaximal
17#79874—31nomaximal
18C2×D3×D12C2211yescharacteristic
19#64149C2211yescharacteristic, complemented
20C2×#3753C2211yescharacteristic
21C2×#3745C2211yescharacteristic
22#64102C2211yescharacteristic
23C3×#938C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic, complemented
25C2×C3×#213C2211yescharacteristic
26C3×#893C2211yescharacteristic
27C3×#892C2211yescharacteristic
28#63978—21no—
29#63975—21no—
30#63966—21no—
31#63958—21no—
32#63921—21no—
33D3×(C2×D3)⋊C4—21no—
34#63909C2211yescharacteristic
35C4×#626—21no—
36#63898C2211yescharacteristic
37#63894C2211yescharacteristic
38#63894C2211yescharacteristic, complemented
39#63880—21no—
40#63872C2211yescharacteristic, complemented
41#63855C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×#102C2211yescharacteristic, complemented
44#63641C2211yescharacteristic, complemented
45#63636C2211yescharacteristic, complemented
46C3×#832C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#817C2211yescharacteristic, complemented
50C3×#815C2211yescharacteristic, complemented
51C3×#808C2211yescharacteristic, complemented
52C3×#807C2211yescharacteristic, complemented
53#63576C2211yescharacteristic, complemented
54#63572C2211yescharacteristic, complemented
55#63564C2211yescharacteristic
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61#5619—31no—
62#5562—31no—
63#5545—31no—
64#5521—31no—
65C3×#482—31no—
66C3×#442—31no—
67#5156—31no—
68#5150—31no—
69#5036—31no—
70C4×#213—31no—
71C4×#213—31no—
72#5003—31no—
73#4891—31no—
74#4872—31no—
75#4871—31no—
76#4871—31no—
77#4869—31no—
78#4866—31no—
79#4786—31no—
80#4786—31no—
81#4786—31no—
82#4786—61no—
83#4785D311yescharacteristic, complemented
84#4779D311yescharacteristic, complemented
85#4773—31no—
86#4763—31no—
87#4756—31no—
88#4732—31no—
89#4720—31no—
90#4711—31no—
91#4709—31no—
92C22×D32—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×#638—21no—
96C2×C4⋊(C3⋊D3)C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×C3×#67—21no—
100C22×C3×Dic3—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#624—21no—
107C2×#624—21no—
108C2×D3×Dic3—21no—
109D3×D12—22no—
110D3×D12—22no—
111C2×C32×C8C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3753—22no—
114#3752—21no—
115C4×C3⋊Dic3C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117#3745—22no—
118C3×#217—21no—
119C3×#217—21no—
120C3×#213—22no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3D411yescharacteristic
133Dic3⋊Dic3D411yescharacteristic
134#3722—21no—
135#3722—21no—
136#3722—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—
145C3×#121—31no—
146C3×C4×D4—31no—
147C3×C4×D4—31no—
148C3×#117—31no—
149#940—31no—
150#940—31no—
151#940—61no—
152#939—61no—
153#938—61no—
154#938C2×D311yescharacteristic
155D4×Dic3—31no—
156D4×Dic3C2×D311yescharacteristic, complemented
157C2×#213—31no—
158C2×#213—31no—
159C2×#213—31no—
160C2×#213—61no—
161C2×#213C2×D311yescharacteristic
162#930—31no—
163#930—61no—
164#929—61no—
165C4×#67—61no—
166C2×(C2×D3)⋊C4—61no—
167#926—31no—
168C2×D24—31no—
169C2×D24—31no—
170C2×D24—31no—
171C2×D24—61no—
172#895—31no—
173#893—31no—
174#893—31no—
175#893—31no—
176#893—31no—
177#893—31no—
178#893—61no—
179#893C2×D311yescharacteristic
180#892C2×D311yescharacteristic
181#890—31no—
182#890—31no—
183#886—61no—
184#884—61no—
185#883—61no—
186#883—61no—
187#67⋊C4—61no—
188D3×C22⋊C4—61no—
189D3×C22⋊C4—61no—
190D3×C22⋊C4—61no—
191C4×D12—31no—
192C4×D12—31no—
193C4×D12—61no—
194C4×D12—61no—
195#872—31no—
196C3×#107—31no—
197C3×#106—31no—
198C3×#106—31no—
199C3×#102—21no—
200C3×#102—31no—
201C3×#102—31no—
202C3×#102C2×D311yescharacteristic, complemented
203C3×#102C2×D311yescharacteristic, complemented
204C3×C22⋊C8—31no—
205C3×#97—31no—
206#832—31no—
207#832C2×D311yescharacteristic, complemented
208#830—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821C2×D311yescharacteristic
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8C2×D311yescharacteristic
215#817C2×D311yescharacteristic, complemented
216#815C2×D311yescharacteristic, complemented
217Dic3⋊C8—31no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8—61no—
222C8×Dic3—31no—
223#809—31no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#809—31no—
229#809—61no—
230#808C2×D311yescharacteristic, complemented
231#807—31no—
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
247#638—81no—
248#638—81no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)#4112yes—
255C4×C3⋊D3—81no—
256C3×#67—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—81no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—81no—
269#626—24no—
270#626—81no—
271#624—81no—
272#624—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—31no—
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—61no—
298C2×C3×D4C22×D311yescharacteristic
299C2×C3×D4C22×D311yescharacteristic
300C22×C3×C4—31no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C2×#67—21no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—121no—
311C2×#67—121no—
312C22×Dic3—21no—
313C22×Dic3—61no—
314D3×D4—62no—
315D3×D4—62no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—62no—
323C2×D12—61no—
324C2×D12—62no—
325C2×D12—61no—
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—121no—
336C2×C4×D3C22×D311yescharacteristic
337C3×D8—62no—
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—21no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—31no—
354C3×C42—61no—
355#217—21no—
356#217—21no—
357#217—31no—
358#217—31no—
359#217—61no—
360#213—22no—
361#213—62no—
362#213—62no—
363#213—62no—
364#213—122no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
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—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—31no—
387Dic3⋊C4—31no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390C4×Dic3—21no—
391C4×Dic3—31no—
392C4×Dic3—31no—
393C4×Dic3—61no—
394C4×Dic3C22×D311yescharacteristic
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—61no—
398C2×C3⋊C8C22×D311yescharacteristic
399C2×C3⋊C8C22×D311yescharacteristic
400D24—62no—
401D24—62no—
402D24—62no—
403D24—122no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32C22×D411yescharacteristic
408C2×C3⋊D3—22no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3×D3—22no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420D32—84no—
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—
431C3×Dic3—41no—
432C22×D4—91no—
433C2×D8—31no—
434C2×D8—91no—
435C2×D8—91no—
436C2×D8—91no—
437#127—91no—
438#125—91no—
439#123—181no—
440#123—181no—
441#121—31no—
442#121—91no—
443#121—181no—
444#121—181no—
445C4×D4—31no—
446C4×D4—31no—
447C4×D4—91no—
448C4×D4—91no—
449C4×D4—91no—
450C4×D4—91no—
451C4×D4—181no—
452C4×D4—181no—
453#117—31no—
454#117—91no—
455C2×C22⋊C4—181no—
456C2×C22⋊C4—181no—
457#107—31no—
458#107—91no—
459#106—31no—
460#106—31no—
461C4⋊C8—91no—
462C4⋊C8—91no—
463#102—31no—
464#102—31no—
465#102—91no—
466#102—91no—
467#102—91no—
468#102—91no—
469#102—91no—
470#102D3211yescharacteristic, complemented
471C22⋊C8—31no—
472C22⋊C8—91no—
473#97—31no—
474C4×C8—91no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—31no—
478C23×C3—41no—
479C23×C3—61no—
480C22×D3—21no—
481C22×D3—64no—
482C22×D3—64no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—121no—
488C22×D3—121no—
489C22×D3—241no—
490C22×D3—241no—
491C22×D3—241no—
492C22×D3—241no—
493C22×D3D3×D411yescharacteristic
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—32no—
499C3×D4—41no—
500C3×D4—41no—
501C3×D4—61no—
502C3×D4—241no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—41no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—241no—
516C2×C3×C4—241no—
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519#67—64no—
520#67—81no—
521#67—241no—
522#67—241no—
523#67—241no—
524#67—241no—
525#67—241no—
526#67—242no—
527#67—242no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—81no—
538C2×Dic3—241no—
539C2×Dic3D3×D411yescharacteristic
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542D12—21no—
543D12—32no—
544D12—32no—
545D12—62no—
546D12—64no—
547D12—61no—
548D12—61no—
549D12—61no—
550D12—61no—
551D12—61no—
552D12—61no—
553D12—121no—
554D12—121no—
555D12—121no—
556D12—241no—
557D12#23512yes—
558C4×D3—21no—
559C4×D3—21no—
560C4×D3—81no—
561C4×D3—241no—
562C4×D3—241no—
563C4×D3—241no—
564C4×D3—241no—
565C4×D3—241no—
566C4×D3—241no—
567C4×D3—242no—
568C4×D3—241no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—41no—
572C3×C8—61no—
573C3×C8—61no—
574C3⋊C8—21no—
575C3⋊C8—21no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C3⋊C8—121no—
579C2×C32—81no—
580C2×C32#52511yescharacteristic
581C2×C32#57611yescharacteristic
582C2×C32#57611yescharacteristic
583C3⋊D3—42no—
584C3⋊D3—81no—
585C3×D3—41no—
586C3×D3—42no—
587C24—181no—
588C2×D4—31no—
589C2×D4—61no—
590C2×D4—91no—
591C2×D4—91no—
592C2×D4—181no—
593C2×D4—182no—
594C2×D4—182no—
595C2×D4—181no—
596C2×D4—181no—
597C2×D4—181no—
598C2×D4C2×D3211yescharacteristic
599C22×C4—31no—
600C22×C4—61no—
601C22×C4—61no—
602C22×C4—181no—
603C22×C4—181no—
604C22×C4—181no—
605C22×C4—181no—
606D8—62no—
607D8—182no—
608D8—182no—
609D8—182no—
610C2×C8—31no—
611C2×C8—31no—
612C2×C8—91no—
613C2×C8C2×D3211yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—91no—
618C4⋊C4—91no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4C2×D3211yescharacteristic
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C42—31no—
634C42—61no—
635C42—91no—
636C22×C3—21no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—62no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—81no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3—121no—
651C22×C3—121no—
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—62no—
661C2×D3—62no—
662C2×D3—122no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—241no—
674C2×D3—241no—
675C2×D3—241no—
676C2×D3—241no—
677C2×D3—241no—
678C2×D3—244no—
679C2×D3—244no—
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—41no—
683C3×C4—41no—
684C3×C4—61no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—81no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4C2×#23511yescharacteristic
692C3×C4D3×#4111yescharacteristic
693C3×C4D3×#4111yescharacteristic
694C3×C4D3×#4111yescharacteristic
695Dic3—21no—
696Dic3—21no—
697Dic3—21no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—62no—
702Dic3—61no—
703Dic3—61no—
704Dic3—61no—
705Dic3—61no—
706Dic3—121no—
707C32#312211yescharacteristic, complemented, Sylow
708C23—21no—
709C23—31no—
710C23—61no—
711C23—184no—
712C23—181no—
713C23—181no—
714C23—721no—
715C23—721no—
716D4—21no—
717D4—21no—
718D4—32no—
719D4—61no—
720D4—92no—
721D4—184no—
722D4—181no—
723D4—181no—
724D4—181no—
725D4—241no—
726D4—721no—
727D4—721no—
728D4—721no—
729C2×C4—21no—
730C2×C4—31no—
731C2×C4—31no—
732C2×C4—31no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—91no—
739C2×C4—91no—
740C2×C4—241no—
741C2×C4—241no—
742C2×C4—721no—
743C2×C4—721no—
744C2×C4—721no—
745C2×C4—721no—
746C2×C4C22×D3211yescharacteristic
747C8—21no—
748C8—61no—
749C8—61no—
750C8—181no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—81no—
755C2×C3—81no—
756C2×C3—121no—
757C2×C3—122no—
758C2×C3—161no—
759C2×C3#554711yescharacteristic
760C2×C3#565611yescharacteristic
761C2×C3#576911yescharacteristic
762C2×C3#577411yescharacteristic
763C2×C3#577411yescharacteristic
764C2×C3#577411yescharacteristic
765D3—42no—
766D3—41no—
767D3—122no—
768D3—122no—
769D3—242no—
770D3—241no—
771D3—241no—
772D3—481no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—61no—
777C22—61no—
778C22—61no—
779C22—62no—
780C22—121no—
781C22—121no—
782C22—182no—
783C22—361no—
784C22—361no—
785C22—361no—
786C22—361no—
787C22—361no—
788C22—724no—
789C22D32×D411yescharacteristic
790C4—41no—
791C4—61no—
792C4—61no—
793C4—61no—
794C4—121no—
795C4—121no—
796C4—121no—
797C4—181no—
798C4—181no—
799C4D3×#23511yescharacteristic
800C4#6431211yescharacteristic
801C3—21no—
802C3#7987411yescharacteristic, complemented
803C3#8135411yescharacteristic, complemented
804C2—81no—
805C2—121no—
806C2—122no—
807C2—362no—
808C2—721no—
809C2#1059426611yescharacteristic
810C2#1059473511yescharacteristic
811C2#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. #10595125C2semidirect
2. #10594604C2semidirect
3. #10592485C2semidirect
4. C3×#4785C2semidirect
5. C3×#4779C2semidirect
6. #10591515C2semidirect
7. #10591433C2semidirect
8. #10591400C2semidirect
9. #10590947C2semidirect
10. #10590782C2semidirect
11. #10590768C2semidirect
12. #10590697C2semidirect
13. #10590456C2semidirect
14. #10590435C2semidirect
15. #10590425C2semidirect
19. #64149C22semidirect
24. C3×D4×Dic3C22semidirect
38. #63894C22semidirect
40. #63872C22semidirect
43. C32×#102C22semidirect
44. #63641C22semidirect
45. #63636C22semidirect
46. C3×#832C22semidirect
49. C3×#817C22semidirect
50. C3×#815C22semidirect
51. C3×#808C22semidirect
52. C3×#807C22semidirect
53. #63576C22semidirect
54. #63572C22semidirect
57. #63564C22semidirect
60. Dic3×C3⋊C8C22semidirect
83. #4785D3semidirect
84. #4779D3semidirect
156. D4×Dic3C2×D3semidirect
202. C3×#102C2×D3semidirect
203. C3×#102C2×D3semidirect
207. #832C2×D3semidirect
215. #817C2×D3semidirect
216. #815C2×D3semidirect
230. #808C2×D3semidirect
233. #807C2×D3semidirect
470. #102D32semidirect
707. C32#3122semidirect
802. C3#79874semidirect
803. C3#81354semidirect

Maximal subgroups

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

subgroupindex
#105951252
#105946042
#105924852
C3×#47852
C3×#47792
#105915152
#105914332
#105914002
#105909472
#105907822
#105907682
#105906972
#105904562
#105904352
#105904252
#813543
#798743