Finite Group Databasebeta

← #11872761

Subgroups — #11872761

Order 1152.

884 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593996C211yesmaximal, characteristic, complemented
2#10593950C211yesmaximal, characteristic, complemented
3#10592539C211yesmaximal, characteristic, complemented
4C3×#4847C211yesmaximal, characteristic, complemented
5C3×#4843C211yesmaximal, characteristic, complemented
6#10590945C211yesmaximal, characteristic, complemented
7#10590945C211yesmaximal, characteristic, complemented
8#10590781C211yesmaximal, characteristic, complemented
9#10590777C211yesmaximal, characteristic, complemented
10#10590741C211yesmaximal, characteristic, complemented
11#10590740C211yesmaximal, characteristic, complemented
12#10590652C211yesmaximal, characteristic, complemented
13#10590651C211yesmaximal, characteristic, complemented
14#10590347C211yesmaximal, characteristic, complemented
15#10590270C211yesmaximal, characteristic, complemented
16#81146—31nomaximal
17#80317—31nomaximal
18C2×#3802C2211yescharacteristic
19#64081C2211yescharacteristic
20C2×C3×D24C2211yescharacteristic
21C2×C3×D24C2211yescharacteristic
22C3×#874C2211yescharacteristic, complemented
23C3×C4×D12C2211yescharacteristic
24C3×C4×D12C2211yescharacteristic
25C3×#870C2211yescharacteristic, complemented
26D3×(C2×D3)⋊C4—21no—
27D3×(C2×D3)⋊C4—21no—
28#63916C2211yescharacteristic
29#63916C2211yescharacteristic
30#63898C2211yescharacteristic
31#63898C2211yescharacteristic
32#63898C2211yescharacteristic, complemented
33#63898C2211yescharacteristic, complemented
34#63886—21no—
35#63886—21no—
36#63884—21no—
37#63884—21no—
38#63879—21no—
39#63879—21no—
40#63849C2211yescharacteristic
41C2×#3713C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C32×C4⋊C8C2211yescharacteristic, complemented
44#63647C2211yescharacteristic
45#63647C2211yescharacteristic
46#63642C2211yescharacteristic, complemented
47C8×C3⋊Dic3C2211yescharacteristic, complemented
48C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic, complemented
52C3×#821C2211yescharacteristic, complemented
53C3×#818C2211yescharacteristic, complemented
54C3×#817C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56#63574C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61#5719—31no—
62#5697—31no—
63#5545—31no—
64#5545—31no—
65C3×#478—31no—
66C3×#459—31no—
67#5156—31no—
68#5156—31no—
69#5152—31no—
70Dic3×D8—31no—
71#5072—31no—
72#5066—31no—
73#5015—31no—
74#5009—31no—
75#4885—31no—
76#4872—31no—
77#4869—31no—
78#4866—31no—
79#4847D311yescharacteristic, complemented
80#4843D311yescharacteristic, complemented
81#4840—31no—
82#4840—31no—
83#4840—61no—
84#4785—31no—
85#4785—31no—
86#4784—31no—
87#4779—31no—
88#4773—31no—
89#4773—31no—
90#4756—31no—
91#4756—31no—
92C22×D32—21no—
93C2×C4×C3⋊D3C2311yescharacteristic
94C2×C3×D12—21no—
95C2×C3×D12—21no—
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×D12C2311yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×#626—21no—
103C2×#626—21no—
104C2×#625—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109#3802—22no—
110#3802—22no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113C32×C42C2311yescharacteristic
114#3752D411yescharacteristic
115#3752D411yescharacteristic
116#3750D411yescharacteristic
117#3750D411yescharacteristic
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×D24—22no—
130C3×D24—22no—
131#3722—21no—
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)⋊Dic3—21no—
138Dic32—21no—
139#3713—22no—
140#3713—22no—
141#3122—91noSylow
142C2×D3×D4—31no—
143C2×D3×D4—31no—
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C3×#127—31no—
147C3×#125—31no—
148C3×C4×D4—31no—
149C3×C4×D4—31no—
150#939—61no—
151#939—61no—
152#938—31no—
153#938—31no—
154#935—61no—
155#935—61no—
156D4×Dic3—31no—
157D4×Dic3—31no—
158D4×Dic3—31no—
159D4×Dic3—31no—
160C2×#213—31no—
161C2×#213—31no—
162C2×#213—31no—
163C2×#213—31no—
164C4×#67—61no—
165C4×#67—61no—
166C2×(C2×D3)⋊C4—61no—
167C2×(C2×D3)⋊C4—61no—
168C2×D24C2×D311yescharacteristic
169C2×D24C2×D311yescharacteristic
170#895—31no—
171#895—31no—
172#895—61no—
173#895—61no—
174#894—61no—
175#894—61no—
176#893—31no—
177#893—31no—
178#893—31no—
179#893—31no—
180#892—31no—
181#892—31no—
182#67⋊C4—61no—
183#67⋊C4—61no—
184D3×C22⋊C4—61no—
185D3×C22⋊C4—61no—
186#874C2×D311yescharacteristic, complemented
187C4×D12C2×D311yescharacteristic
188C4×D12C2×D311yescharacteristic
189#872—31no—
190#872—31no—
191#872—61no—
192#870C2×D311yescharacteristic, complemented
193C3×#107—31no—
194C3×#106—31no—
195C3×C4⋊C8—21no—
196C3×C4⋊C8C2×D311yescharacteristic, complemented
197C3×C4⋊C8C2×D311yescharacteristic, complemented
198C3×#102—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×#102—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#821C2×D311yescharacteristic
207#821C2×D311yescharacteristic
208#821C2×D311yescharacteristic, complemented
209#821C2×D311yescharacteristic, complemented
210(C2×D3)⋊C8—31no—
211(C2×D3)⋊C8—31no—
212(C2×D3)⋊C8—31no—
213(C2×D3)⋊C8—31no—
214(C2×D3)⋊C8—61no—
215(C2×D3)⋊C8—61no—
216#818C2×D311yescharacteristic, complemented
217#817C2×D311yescharacteristic, complemented
218#815—31no—
219#815—31no—
220#815—61no—
221C8×Dic3—31no—
222C8×Dic3—31no—
223C8×Dic3—61no—
224#809—31no—
225#809—31no—
226#809—31no—
227#809—31no—
228#808—31no—
229#808—31no—
230#807—31no—
231#807—31no—
232C4⋊(C3⋊C8)—31no—
233C4⋊(C3⋊C8)—31no—
234C4⋊(C3⋊C8)—61no—
235C22×C3⋊D3C2×D411yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C2×D32—24no—
241C2×D32—81no—
242C2×D32—81no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2×D411yescharacteristic
245C2×C32×C4C2411yescharacteristic
246C2×C3⋊Dic3C2×D411yescharacteristic
247C2×C3⋊Dic3C2×D411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249C4×C3⋊D3—21no—
250C4×C3⋊D3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C3×D12—21no—
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—81no—
262C3×D12—81no—
263C3×D12#4112yes—
264C3×D12#4112yes—
265C3×C4×D3—81no—
266C3×C4×D3—81no—
267#626—81no—
268#626—81no—
269#625—24no—
270D3×Dic3—81no—
271D3×Dic3—81no—
272D3×Dic3—81no—
273D3×Dic3—81no—
274C32×C8—21no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3⋊(C3⋊C8)—21no—
278#540—91no—
279#518—91no—
280#482—91no—
281#482—91no—
282#478—31no—
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—31no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C22×C3×C4—61no—
302C22×C3×C4—61no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C22×Dic3—61no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311D3×D4—62no—
312D3×D4—62no—
313D3×D4—62no—
314D3×D4—62no—
315C2×D12—21no—
316C2×D12—21no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12C22×D311yescharacteristic
320C2×D12C22×D311yescharacteristic
321C2×D12C22×D311yescharacteristic
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—21no—
325C2×C4×D3—31no—
326C2×C4×D3—31no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C3×D8—62no—
333C3×D8—62no—
334C2×C3×C8—21no—
335C2×C3×C8—21no—
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—21no—
349C3×C42C22×D311yescharacteristic
350C3×C42C22×D311yescharacteristic
351#217—61no—
352#217—61no—
353#217—61no—
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—31no—
364(C2×D3)⋊C4—31no—
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—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—31no—
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—31no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8—61no—
400D24—22no—
401D24—22no—
402C22×C32C22×D411yescharacteristic
403C2×C3⋊D3—21no—
404C2×C3⋊D3—21no—
405C2×C3⋊D3—21no—
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
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—21no—
420C32×C4—21no—
421C32×C4C2×#4111yescharacteristic
422C32×C4C2×#4111yescharacteristic
423C3⋊Dic3—21no—
424C3⋊Dic3—21no—
425C3⋊Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C22×D4—91no—
431C2×D8—31no—
432C2×D8—31no—
433C2×D8—91no—
434C2×D8—91no—
435#127—31no—
436#125—31no—
437#123—181no—
438#123—181no—
439#121—91no—
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—31no—
458#106—91no—
459C4⋊C8—91no—
460C4⋊C8D3211yescharacteristic, complemented
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—91no—
470C22⋊C8—91no—
471#97—91no—
472C4×C8—91no—
473C23×C3—61no—
474C23×C3—61no—
475C23×C3—61no—
476C23×C3—61no—
477C22×D3—21no—
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—31no—
482C22×D3—31no—
483C22×D3—61no—
484C22×D3—64no—
485C22×D3—64no—
486C22×D3—241no—
487C22×D3—241no—
488C22×D3—241no—
489C22×D3—241no—
490C3×D4—32no—
491C3×D4—32no—
492C3×D4—61no—
493C3×D4—61no—
494C3×D4—61no—
495C3×D4—61no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—241no—
499C3×D4—241no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—241no—
508C2×C3×C4—241no—
509C2×C3×C4D3×D411yescharacteristic
510C2×C3×C4D3×D411yescharacteristic
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4D3×D411yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515#67—64no—
516#67—64no—
517#67—241no—
518#67—241no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—31no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—241no—
533C2×Dic3—241no—
534C2×Dic3—241no—
535C2×Dic3—241no—
536D12—21no—
537D12—21no—
538D12—21no—
539D12—21no—
540D12—21no—
541D12—21no—
542D12—81no—
543D12—81no—
544D12—241no—
545D12—241no—
546D12#23712yes—
547D12#23912yes—
548C4×D3—61no—
549C4×D3—61no—
550C4×D3—61no—
551C4×D3—61no—
552C4×D3—81no—
553C4×D3—81no—
554C4×D3—121no—
555C4×D3—121no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3—241no—
560C3×C8—21no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—41no—
565C3×C8—41no—
566C3⋊C8—61no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—121no—
571C3⋊C8—121no—
572C2×C32#52511yescharacteristic
573C2×C32#57611yescharacteristic
574C2×C32#57611yescharacteristic
575C3⋊D3—41no—
576C3×D3—42no—
577C3×D3—42no—
578C3×D3—81no—
579C3×D3—81no—
580C24—181no—
581C2×D4—31no—
582C2×D4—31no—
583C2×D4—31no—
584C2×D4—31no—
585C2×D4—61no—
586C2×D4—61no—
587C2×D4—181no—
588C2×D4—181no—
589C2×D4—181no—
590C2×D4—182no—
591C2×D4—182no—
592C22×C4—61no—
593C22×C4—61no—
594C22×C4—91no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4—181no—
599D8—62no—
600D8—62no—
601D8—182no—
602D8—182no—
603C2×C8—91no—
604C2×C8—91no—
605C2×C8C2×D3211yescharacteristic
606C2×C8C2×D3211yescharacteristic
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—91no—
614C4⋊C4—91no—
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—
625C22⋊C4—181no—
626C42—91no—
627C42—181no—
628C42C2×D3211yescharacteristic
629C22×C3—21no—
630C22×C3—62no—
631C22×C3—62no—
632C22×C3—121no—
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×C3—121no—
642C22×C3C2×D3×D411yescharacteristic
643C22×C3C2×D3×D411yescharacteristic
644C2×D3—22no—
645C2×D3—22no—
646C2×D3—41no—
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—41no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—61no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—244no—
666C2×D3—244no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4C2×#23711yescharacteristic
680C3×C4C2×#23911yescharacteristic
681C3×C4D3×#4111yescharacteristic
682C3×C4D3×#4111yescharacteristic
683Dic3—41no—
684Dic3—41no—
685Dic3—41no—
686Dic3—41no—
687Dic3—61no—
688Dic3—61no—
689Dic3—61no—
690Dic3—61no—
691Dic3—61no—
692Dic3—61no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696C32#312211yescharacteristic, complemented, Sylow
697C23—61no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23—91no—
702C23—184no—
703C23—721no—
704C23—721no—
705D4—32no—
706D4—32no—
707D4—61no—
708D4—61no—
709D4—61no—
710D4—61no—
711D4—61no—
712D4—61no—
713D4—184no—
714D4—241no—
715D4—241no—
716D4—721no—
717D4—721no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—91no—
723C2×C4—91no—
724C2×C4—91no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4—241no—
728C2×C4—241no—
729C2×C4—721no—
730C2×C4—721no—
731C2×C4—721no—
732C2×C4—721no—
733C2×C4#380211yescharacteristic
734C2×C4#380211yescharacteristic
735C2×C4C22×D3211yescharacteristic
736C8—21no—
737C8—21no—
738C8—181no—
739C8—181no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—122no—
744C2×C3—122no—
745C2×C3—241no—
746C2×C3—241no—
747C2×C3#560611yescharacteristic
748C2×C3#562711yescharacteristic
749C2×C3#575711yescharacteristic
750C2×C3#576911yescharacteristic
751C2×C3#577411yescharacteristic
752C2×C3#577411yescharacteristic
753D3—42no—
754D3—42no—
755D3—81no—
756D3—81no—
757D3—121no—
758D3—121no—
759D3—241no—
760C22—62no—
761C22—62no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—181no—
773C22—181no—
774C22—181no—
775C22—724no—
776C22C2×#380211yescharacteristic
777C4—21no—
778C4—21no—
779C4—121no—
780C4—121no—
781C4—121no—
782C4—121no—
783C4—181no—
784C4—181no—
785C4—181no—
786C4D3×#23711yescharacteristic
787C4D3×#23911yescharacteristic
788C3—21no—
789C3#8031711yescharacteristic, complemented
790C3#8114611yescharacteristic, complemented
791C2—122no—
792C2—122no—
793C2—241no—
794C2—241no—
795C2—361no—
796C2#1059463211yescharacteristic
797C2#1059468711yescharacteristic
798C2#1059472011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #10593996C2semidirect
2. #10593950C2semidirect
3. #10592539C2semidirect
4. C3×#4847C2semidirect
5. C3×#4843C2semidirect
6. #10590945C2semidirect
7. #10590945C2semidirect
8. #10590781C2semidirect
9. #10590777C2semidirect
10. #10590741C2semidirect
11. #10590740C2semidirect
12. #10590652C2semidirect
13. #10590651C2semidirect
14. #10590347C2semidirect
15. #10590270C2semidirect
22. C3×#874C22semidirect
25. C3×#870C22semidirect
32. #63898C22semidirect
33. #63898C22semidirect
43. C32×C4⋊C8C22semidirect
46. #63642C22semidirect
47. C8×C3⋊Dic3C22semidirect
48. C4⋊(C3⋊(C3⋊C8))C22semidirect
51. C3×#821C22semidirect
52. C3×#821C22semidirect
53. C3×#818C22semidirect
54. C3×#817C22semidirect
55. #63576C22semidirect
56. #63574C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
79. #4847D3semidirect
80. #4843D3semidirect
186. #874C2×D3semidirect
192. #870C2×D3semidirect
196. C3×C4⋊C8C2×D3semidirect
197. C3×C4⋊C8C2×D3semidirect
208. #821C2×D3semidirect
209. #821C2×D3semidirect
216. #818C2×D3semidirect
217. #817C2×D3semidirect
460. C4⋊C8D32semidirect
696. C32#3122semidirect
789. C3#80317semidirect
790. C3#81146semidirect

Maximal subgroups

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

subgroupindex
#105939962
#105939502
#105925392
C3×#48472
C3×#48432
#105909452
#105907812
#105907772
#105907412
#105907402
#105906522
#105906512
#105903472
#105902702
#811463
#803173