Finite Group Databasebeta

← #11872743

Subgroups — #11872743

Order 1152.

902 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#10595217C211yesmaximal, characteristic, complemented
2#10595215C211yesmaximal, characteristic, complemented
3#10592851C211yesmaximal, characteristic, complemented
4C3×#5156C211yesmaximal, characteristic, complemented
5C3×#5150C211yesmaximal, characteristic, complemented
6#10591447C211yesmaximal, characteristic, complemented
7#10591435C211yesmaximal, characteristic, complemented
8#10591435C211yesmaximal, characteristic, complemented
9#10591428C211yesmaximal, characteristic, complemented
10#10591423C211yesmaximal, characteristic, complemented
11#10591411C211yesmaximal, characteristic, complemented
12#10590837C211yesmaximal, characteristic, complemented
13#10590772C211yesmaximal, characteristic, complemented
14#10590741C211yesmaximal, characteristic, complemented
15#10590699C211yesmaximal, characteristic, complemented
16#80317—31nomaximal
17#79993—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C32×D8C2211yescharacteristic
20D4×C3⋊Dic3C2211yescharacteristic
21D4×C3⋊Dic3C2211yescharacteristic, complemented
22C3×#940C2211yescharacteristic, complemented
23C3×#938C2211yescharacteristic
24C3×D4×Dic3C2211yescharacteristic
25C2×C3×#213C2211yescharacteristic
26C2×C3×#213C2211yescharacteristic
27#63980—21no—
28#67⋊Dic3—21no—
29Dic3×#67—21no—
30#63970—21no—
31#63969—21no—
32D3×#217—21no—
33#63962—21no—
34C2×(C2×D3)⋊Dic3—21no—
35#63908C2211yescharacteristic
36#63898C2211yescharacteristic
37#63898C2211yescharacteristic, complemented
38Dic3×D12C2211yescharacteristic
39#63869C2211yescharacteristic, complemented
40#63855C2211yescharacteristic
41#63841C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43#63659C2211yescharacteristic
44#63659C2211yescharacteristic, complemented
45#63644C2211yescharacteristic, complemented
46#63642C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic, complemented
51C3×(C2×D3)⋊C8C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic, complemented
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic, complemented
61#5798—31no—
62#5719—31no—
63#5619—31no—
64#5545—31no—
65C3×#459—31no—
66C3×#447—31no—
67#5217—31no—
68#5156—31no—
69#5156D311yescharacteristic, complemented
70#5152—31no—
71#5152—31no—
72#5152—61no—
73#5150—31no—
74#5150D311yescharacteristic, complemented
75Dic3×D8—31no—
76Dic3×D8—31no—
77#5072—31no—
78#5035—31no—
79#5009—31no—
80#4847—31no—
81#4840—31no—
82#4785—31no—
83#4785—31no—
84#4784—31no—
85#4779—31no—
86#4766—31no—
87#4763—31no—
88#4756—31no—
89#4756—31no—
90#4737—31no—
91#4720—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×C32×D4C2311yescharacteristic
95C22×C3⋊Dic3—21no—
96C22×C3⋊Dic3—21no—
97C2×C3×#67—21no—
98C2×C3×#67—21no—
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C22×C3×Dic3—21no—
102C3×D3×D4—22no—
103C3×D3×D4—22no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×D12C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×#625—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C32×D8—22no—
112C2×C32×C8C2311yescharacteristic
113#3757—21no—
114#3757—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#217—21no—
120C3×#217—21no—
121C3×#213—22no—
122C3×#213—22no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128#3724—21no—
129Dic3⋊Dic3—21no—
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—21no—
145C2×C3×D8—31no—
146C2×C3×D8—31no—
147C2×C3×D8C2×D311yescharacteristic
148C2×C3×D8C2×D311yescharacteristic
149C3×#127—31no—
150C3×#121—31no—
151C3×C4×D4—31no—
152C2×#217—61no—
153C2×#217—61no—
154#940C2×D311yescharacteristic, complemented
155#939—61no—
156#939—61no—
157#939—61no—
158#938—31no—
159#938—61no—
160#938C2×D311yescharacteristic
161#935—61no—
162#935—61no—
163D4×Dic3—31no—
164D4×Dic3—31no—
165D4×Dic3—31no—
166D4×Dic3—31no—
167D4×Dic3—31no—
168D4×Dic3—31no—
169D4×Dic3—31no—
170D4×Dic3—61no—
171D4×Dic3—61no—
172D4×Dic3—61no—
173D4×Dic3—61no—
174D4×Dic3C2×D311yescharacteristic
175C2×#213—31no—
176C2×#213—31no—
177C2×#213C2×D311yescharacteristic
178C2×#213C2×D311yescharacteristic
179#930—31no—
180C4×#67—61no—
181C2×(C2×D3)⋊C4—61no—
182#926—31no—
183#926—31no—
184#893—31no—
185#893—31no—
186#892—31no—
187#890—31no—
188#886—61no—
189#883—61no—
190#67⋊C4—61no—
191D3×C22⋊C4—61no—
192C4×D12—31no—
193#872—31no—
194#870—31no—
195C3×C4⋊C8—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×#102—31no—
199C3×#102—31no—
200C3×C22⋊C8—31no—
201#832—31no—
202#832—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—61no—
208#832—61no—
209#832C2×D311yescharacteristic
210#832C2×D311yescharacteristic, complemented
211#830—31no—
212#821—31no—
213#821—31no—
214#821C2×D311yescharacteristic
215#821C2×D311yescharacteristic, complemented
216(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8C2×D311yescharacteristic
218#818—31no—
219#818—31no—
220#817—31no—
221#817—31no—
222#817—61no—
223#815—31no—
224#815—31no—
225#815—61no—
226Dic3⋊C8—31no—
227Dic3⋊C8C2×D311yescharacteristic, complemented
228C8×Dic3—31no—
229C8×Dic3—31no—
230#808—31no—
231#808—31no—
232#807—31no—
233#807—31no—
234C4⋊(C3⋊C8)—31no—
235C23×C32—21no—
236C23×C32—21no—
237C22×C3×D3—21no—
238C22×C3×D3—24no—
239C22×C3×D3—21no—
240C22×C3×D3—81no—
241C22×C3×D3—81no—
242C22×C3×D3C2×D411yescharacteristic
243C32×D4—21no—
244C32×D4—21no—
245C32×D4—21no—
246C32×D4#4112yes—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—81no—
251C2×C3⋊Dic3—81no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C2×C3⋊Dic3C2×D411yescharacteristic
254C3×#67—24no—
255C3×#67—81no—
256C3×#67—81no—
257C3×#67—81no—
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—21no—
266C3×D12—21no—
267C3×D12#4112yes—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
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—31no—
285#459—91no—
286#447—31no—
287#447—91no—
288#442—91no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—91no—
293C24×C3—61no—
294C23×D3—21no—
295C2×C3×D4—21no—
296C2×C3×D4—21no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C2×C3×D4—62no—
303C2×C3×D4—62no—
304C2×C3×D4—61no—
305C2×C3×D4C22×D311yescharacteristic
306C2×C3×D4C22×D311yescharacteristic
307C2×C3×D4C22×D311yescharacteristic
308C2×C3×D4C22×D311yescharacteristic
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C2×#67—21no—
312C2×#67—21no—
313C2×#67—21no—
314C2×#67—21no—
315C2×#67—61no—
316C2×#67—61no—
317C22×Dic3—21no—
318C22×Dic3—61no—
319C22×Dic3—61no—
320C22×Dic3—61no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—121no—
326C22×Dic3—121no—
327D3×D4—22no—
328D3×D4—22no—
329C2×D12C22×D311yescharacteristic
330C2×D12C22×D311yescharacteristic
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3C22×D311yescharacteristic
335C3×D8—24no—
336C3×D8—22no—
337C3×D8—22no—
338C3×D8—62no—
339C3×D8—62no—
340C2×C3×C8—21no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—31no—
350#217—21no—
351#217—21no—
352#217—31no—
353#217—31no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—121no—
364#217—121no—
365#213—22no—
366#213—22no—
367#213—62no—
368#213—62no—
369(C2×D3)⋊C4—31no—
370(C2×D3)⋊C4—31no—
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—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—31no—
388Dic3⋊C4—31no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392C4×Dic3—31no—
393C4×Dic3—31no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3C22×D311yescharacteristic
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403C22×C32—22no—
404C22×C32—41no—
405C22×C32—41no—
406C22×C32—41no—
407C22×C32—41no—
408C22×C32—41no—
409C22×C32C22×D411yescharacteristic
410C2×C3×D3—21no—
411C2×C3×D3—22no—
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—
419C2×C3×D3—84no—
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—
430C3×Dic3—41no—
431C22×D4—31no—
432C2×D8—31no—
433C2×D8—31no—
434C2×D8—91no—
435C2×D8D3211yescharacteristic
436#127—31no—
437#125—91no—
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—91no—
453#117—91no—
454C2×C22⋊C4—181no—
455C2×C22⋊C4—181no—
456#107—91no—
457#107—91no—
458#106—91no—
459#106—91no—
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—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—31no—
479C23×C3—41no—
480C23×C3—41no—
481C23×C3—64no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—241no—
485C23×C3—241no—
486C22×D3—21no—
487C22×D3—24no—
488C22×D3—21no—
489C22×D3—81no—
490C22×D3—81no—
491C22×D3D3×D411yescharacteristic
492C3×D4—22no—
493C3×D4—21no—
494C3×D4—21no—
495C3×D4—21no—
496C3×D4—21no—
497C3×D4—21no—
498C3×D4—21no—
499C3×D4—22no—
500C3×D4—32no—
501C3×D4—41no—
502C3×D4—41no—
503C3×D4—64no—
504C3×D4—61no—
505C3×D4—61no—
506C3×D4—61no—
507C3×D4—241no—
508C3×D4—241no—
509C3×D4—241no—
510C3×D4#23712yes—
511C3×D4#23712yes—
512C2×C3×C4—21no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—241no—
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—24no—
524#67—81no—
525#67—81no—
526#67—81no—
527#67—241no—
528#67—241no—
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—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—81no—
542C2×Dic3—121no—
543C2×Dic3—121no—
544C2×Dic3—241no—
545C2×Dic3—241no—
546C2×Dic3—241no—
547C2×Dic3—241no—
548C2×Dic3—241no—
549C2×Dic3—241no—
550C2×Dic3—241no—
551C2×Dic3—242no—
552C2×Dic3—242no—
553C2×Dic3D3×D411yescharacteristic
554C2×Dic3D3×D411yescharacteristic
555C2×Dic3D3×D411yescharacteristic
556D12—21no—
557D12—21no—
558D12—21no—
559D12#23712yes—
560C4×D3—21no—
561C4×D3—21no—
562C4×D3—241no—
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—42no—
576C2×C32—81no—
577C2×C32#52511yescharacteristic
578C2×C32#57611yescharacteristic
579C2×C32#57611yescharacteristic
580C3×D3—41no—
581C3×D3—42no—
582C3×D3—81no—
583C24—61no—
584C2×D4—31no—
585C2×D4—31no—
586C2×D4—61no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—62no—
590C2×D4—62no—
591C2×D4—61no—
592C2×D4—181no—
593C2×D4C2×D3211yescharacteristic
594C2×D4C2×D3211yescharacteristic
595C22×C4—31no—
596C22×C4—61no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4—181no—
600C22×C4—181no—
601C22×C4—181no—
602D8—22no—
603D8—62no—
604D8—62no—
605D8—182no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—91no—
609C2×C8C2×D3211yescharacteristic
610C4⋊C4—31no—
611C4⋊C4—31no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—91no—
615C4⋊C4—91no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—91no—
621C22⋊C4—91no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C42—31no—
630C42—91no—
631C42—181no—
632C22×C3—22no—
633C22×C3—22no—
634C22×C3—21no—
635C22×C3—42no—
636C22×C3—42no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—41no—
646C22×C3—41no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—61no—
650C22×C3—62no—
651C22×C3—81no—
652C22×C3—81no—
653C22×C3—81no—
654C22×C3—81no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3—121no—
658C22×C3—121no—
659C22×C3—121no—
660C22×C3—244no—
661C22×C3C2×D3×D411yescharacteristic
662C22×C3C2×D3×D411yescharacteristic
663C2×D3—21no—
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—22no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C2×D3—84no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4C2×#23711yescharacteristic
681C3×C4C2×#23711yescharacteristic
682C3×C4C2×#23711yescharacteristic
683C3×C4D3×#4111yescharacteristic
684Dic3—21no—
685Dic3—21no—
686Dic3—21no—
687Dic3—41no—
688Dic3—41no—
689Dic3—61no—
690Dic3—61no—
691Dic3—61no—
692Dic3—61no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—241no—
700Dic3—241no—
701C32#312211yescharacteristic, complemented, Sylow
702C23—21no—
703C23—21no—
704C23—31no—
705C23—64no—
706C23—61no—
707C23—61no—
708C23—241no—
709C23—241no—
710D4—21no—
711D4—21no—
712D4—21no—
713D4—32no—
714D4—64no—
715D4—61no—
716D4—61no—
717D4—61no—
718D4—241no—
719D4—241no—
720D4—241no—
721D4—721no—
722D4#380512yes—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—91no—
731C2×C4—91no—
732C2×C4—181no—
733C2×C4—181no—
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—42no—
749C2×C3—42no—
750C2×C3—82no—
751C2×C3—82no—
752C2×C3—81no—
753C2×C3—81no—
754C2×C3—121no—
755C2×C3—122no—
756C2×C3—241no—
757C2×C3#558611yescharacteristic
758C2×C3#560611yescharacteristic
759C2×C3#575711yescharacteristic
760C2×C3#575711yescharacteristic
761C2×C3#577411yescharacteristic
762C2×C3#577411yescharacteristic
763D3—41no—
764D3—42no—
765D3—81no—
766C22—22no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—61no—
773C22—62no—
774C22—61no—
775C22—61no—
776C22—121no—
777C22—121no—
778C22—121no—
779C22—121no—
780C22—121no—
781C22—244no—
782C22D32×D411yescharacteristic
783C4—61no—
784C4—61no—
785C4—61no—
786C4—121no—
787C4—121no—
788C4—181no—
789C4—181no—
790C4—361no—
791C4—361no—
792C4D3×#23711yescharacteristic
793C4C2×#380511yescharacteristic
794C3—21no—
795C3#7999311yescharacteristic, complemented
796C3#8031711yescharacteristic, complemented
797C2—42no—
798C2—81no—
799C2—121no—
800C2—122no—
801C2—241no—
802C2#1059473211yescharacteristic
803C2#1059473211yescharacteristic
804C2#1059513011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. #10595217C2semidirect
2. #10595215C2semidirect
3. #10592851C2semidirect
4. C3×#5156C2semidirect
5. C3×#5150C2semidirect
6. #10591447C2semidirect
7. #10591435C2semidirect
8. #10591435C2semidirect
9. #10591428C2semidirect
10. #10591423C2semidirect
11. #10591411C2semidirect
12. #10590837C2semidirect
13. #10590772C2semidirect
14. #10590741C2semidirect
15. #10590699C2semidirect
21. D4×C3⋊Dic3C22semidirect
22. C3×#940C22semidirect
37. #63898C22semidirect
39. #63869C22semidirect
44. #63659C22semidirect
45. #63644C22semidirect
46. #63642C22semidirect
48. C3×#832C22semidirect
50. C3×#821C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. #63575C22semidirect
54. #63575C22semidirect
55. #63574C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
58. #63563C22semidirect
60. #63553C22semidirect
69. #5156D3semidirect
74. #5150D3semidirect
154. #940C2×D3semidirect
210. #832C2×D3semidirect
215. #821C2×D3semidirect
227. Dic3⋊C8C2×D3semidirect
701. C32#3122semidirect
795. C3#79993semidirect
796. C3#80317semidirect

Maximal subgroups

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

subgroupindex
#105952172
#105952152
#105928512
C3×#51562
C3×#51502
#105914472
#105914352
#105914282
#105914232
#105914112
#105908372
#105907722
#105907412
#105906992
#803173
#799933