Finite Group Databasebeta

← #11885739

Subgroups — #11885739

Order 1152.

1409 conjugacy classes of subgroups.

The subgroup lattice has 1030 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D8×C3⋊D3C211yesmaximal, characteristic, complemented
2#10595297C211yesmaximal, characteristic, complemented
3D4×#626C211yesmaximal, characteristic, complemented
4C2×D3×#213C211yesmaximal, characteristic, complemented
5C3×#5156C211yesmaximal, characteristic, complemented
6C3×#5150C211yesmaximal, characteristic, complemented
7#10591482C211yesmaximal, characteristic, complemented
8#10591456C211yesmaximal, characteristic, complemented
9#10591456C211yesmaximal, characteristic, complemented
10#10591449C211yesmaximal, characteristic, complemented
11#10591400C211yesmaximal, characteristic, complemented
12#10590947C211yesmaximal, characteristic, complemented
13#10590906C211yesmaximal, characteristic, complemented
14#10590839C211yesmaximal, characteristic, complemented
15#10590765C211yesmaximal, characteristic, complemented
16#80350—31nomaximal
17#80024—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic, complemented
19C2×D4×C3⋊D3C2211yescharacteristic, complemented
20C2×C3×D3×D4C2211yescharacteristic, complemented
21C2×#3811—21no—
22C22×#626—21no—
23C2×D3×D12C2211yescharacteristic, complemented
24C2×C32×D8C2211yescharacteristic, complemented
25C2×#3753C2211yescharacteristic
26C2×#3753C2211yescharacteristic, complemented
27D8×C3⋊D3—24no—
28C2×#3745C2211yescharacteristic, complemented
29C2×C8×C3⋊D3C2211yescharacteristic, complemented
30C3×#940C2211yescharacteristic, complemented
31C3×#938C2211yescharacteristic, complemented
32C3×D4×Dic3C2211yescharacteristic, complemented
33C2×C3×#213C2211yescharacteristic, complemented
34C2×C3×#213C2211yescharacteristic, complemented
35#63983—21no—
36#63981—21no—
37#63981—21no—
38#63978—21no—
39#63977—21no—
40#63958—21no—
41D3×#213—24no—
42#63916C2211yescharacteristic, complemented
43#63916C2211yescharacteristic, complemented
44#63911C2211yescharacteristic, complemented
45#63909C2211yescharacteristic, complemented
46C4×#626C2211yescharacteristic
47#63894C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3713C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#821C2211yescharacteristic, complemented
56C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58#63576C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62Dic3×C3⋊C8C2211yescharacteristic, complemented
63D4×#67—31no—
64C22×#213—31no—
65C2×D3×D8—31no—
66C2×D3×D8—31no—
67C2×D3×D8—31no—
68C2×D3×D8—61no—
69#5717—31no—
70#5609—31no—
71D4×D12—31no—
72C3×#459—31no—
73C3×#447—31no—
74#5156—31no—
75#5156—31no—
76#5156D311yescharacteristic, complemented
77#5151—31no—
78#5150D311yescharacteristic, complemented
79#5073—31no—
80#5038—31no—
81C4×#213—31no—
82#4843—31no—
83#4834—31no—
84#4786—31no—
85#4775—31no—
86#4775—31no—
87#4775—31no—
88#4773—31no—
89#4773—31no—
90#4773—31no—
91#4756—31no—
92#4732—31no—
93#67⋊C8—31no—
94C23×C3⋊D3—21no—
95C23×C3⋊D3—21no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C2×C32×D4C2311yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×#638—21no—
101C2×#638—21no—
102D4×C3⋊D3—22no—
103D4×C3⋊D3—22no—
104D4×C3⋊D3—41no—
105D4×C3⋊D3—41no—
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4⋊(C3⋊D3)C2311yescharacteristic
108C2×C4×C3⋊D3C2311yescharacteristic
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C2×C3×#67—21no—
112C2×C3×#67—21no—
113C22×C3×Dic3—21no—
114C3×D3×D4—22no—
115C3×D3×D4—41no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×C4×D3C2311yescharacteristic
119#3811—44no—
120C2×#626—21no—
121C2×#626—21no—
122C2×#626—21no—
123C2×#626—21no—
124C2×#626—21no—
125C2×#626—21no—
126C2×#626—44no—
127C2×#626D411yescharacteristic
128C2×#624—21no—
129D3×D12—22no—
130D3×D12—41no—
131C32×D8—22no—
132C2×C32×C8C2311yescharacteristic
133#3753—22no—
134#3753D414yescomplemented
135C2×C3⋊(C3⋊C8)C2311yescharacteristic
136#3745—22no—
137C8×C3⋊D3—22no—
138C3×#217—21no—
139C3×#217—21no—
140C3×#213—22no—
141C3×#213—41no—
142C3×C4⋊Dic3C2311yescharacteristic
143C3×C4⋊Dic3C2311yescharacteristic
144C3×C4×Dic3C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147Dic3⋊Dic3D411yescharacteristic
148#3722—21no—
149#3722—21no—
150#3722D411yescharacteristic
151(C2×D3)⋊Dic3—21no—
152(C2×D3)⋊Dic3—21no—
153(C2×D3)⋊Dic3D411yescharacteristic
154#3714—22no—
155#3714—41no—
156#3713—22no—
157D3×C3⋊C8—22no—
158D4×D8—91noSylow
159C22×C3×D4—31no—
160C22×#67—61no—
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—31no—
166C2×D3×D4—61no—
167C2×D3×D4—61no—
168C2×D3×D4—61no—
169C2×D3×D4—61no—
170C2×D3×D4C2×D311yescharacteristic, complemented
171C22×D12—31no—
172C22×D12—61no—
173C2×C3×D8—21no—
174C2×C3×D8—31no—
175C2×C3×D8—31no—
176C2×C3×D8C2×D311yescharacteristic, complemented
177C2×C3×D8C2×D311yescharacteristic, complemented
178C3×#127—31no—
179C3×#121—31no—
180C3×C4×D4—31no—
181#953—61no—
182#940—31no—
183#940C2×D311yescharacteristic, complemented
184#939—61no—
185#938—31no—
186#938—31no—
187#938—61no—
188#938C2×D311yescharacteristic, complemented
189#937—61no—
190#937—61no—
191#937—61no—
192#937—61no—
193D4×Dic3C2×D311yescharacteristic, complemented
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—61no—
203C2×#213—61no—
204C2×#213—64no—
205C2×#213C2×D311yescharacteristic, complemented
206C2×#213C2×D311yescharacteristic, complemented
207#930—31no—
208#930—61no—
209C4×#67—31no—
210C22×C3⋊C8—31no—
211D3×D8—64no—
212D3×D8—64no—
213D3×D8—64no—
214D3×D8—68no—
215C2×D24—31no—
216C2×D24—31no—
217C2×D24—31no—
218C2×D24—31no—
219C2×D24—61no—
220C2×D3×C8—31no—
221C2×D3×C8—31no—
222C2×D3×C8—31no—
223C2×D3×C8—61no—
224#895—31no—
225#895—31no—
226#895—31no—
227#893—31no—
228#884—61no—
229#882—61no—
230#882—61no—
231#882—61no—
232#874—31no—
233C4×D12—31no—
234C4×D12—31no—
235C3×C4⋊C8—31no—
236C3×#102—31no—
237C3×#102—31no—
238C3×#102—31no—
239C3×#102—31no—
240C3×C22⋊C8—31no—
241#832C2×D311yescharacteristic, complemented
242#832C2×D311yescharacteristic, complemented
243#821—31no—
244#821—31no—
245#821C2×D311yescharacteristic, complemented
246#821C2×D311yescharacteristic, complemented
247(C2×D3)⋊C8—31no—
248(C2×D3)⋊C8—31no—
249(C2×D3)⋊C8C2×D311yescharacteristic, complemented
250Dic3⋊C8C2×D311yescharacteristic, complemented
251C8×Dic3—31no—
252#809—31no—
253#809—31no—
254#807—31no—
255#807—31no—
256C4×C3⋊C8—31no—
257C23×C32—21no—
258C23×C32—21no—
259C22×C3⋊D3—21no—
260C22×C3⋊D3—21no—
261C22×C3⋊D3—42no—
262C22×C3⋊D3—42no—
263C22×C3⋊D3—42no—
264C22×C3⋊D3—42no—
265C22×C3⋊D3—81no—
266C22×C3⋊D3—81no—
267C22×C3⋊D3C2×D411yescharacteristic
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3—42no—
271C22×C3×D3—42no—
272C22×C3×D3—81no—
273C22×C3×D3C2×D411yescharacteristic
274C2×D32—42no—
275C2×D32—42no—
276C2×D32—81no—
277C32×D4—21no—
278C32×D4—21no—
279C32×D4—21no—
280C32×D4C2×D412yescomplemented
281C2×C32×C4C2411yescharacteristic
282#638—42no—
283#638—42no—
284C2×C3⋊Dic3C2×D411yescharacteristic
285C4⋊(C3⋊D3)—21no—
286C4⋊(C3⋊D3)—21no—
287C4⋊(C3⋊D3)—21no—
288C4⋊(C3⋊D3)C2×D412yescomplemented
289C4×C3⋊D3—21no—
290C4×C3⋊D3—21no—
291C3×#67—42no—
292C3×#67—42no—
293C3×#67—42no—
294C3×#67—81no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—42no—
298C2×C3×Dic3C2×D411yescharacteristic
299C2×C3×Dic3C2×D411yescharacteristic
300C2×C3×Dic3C2×D411yescharacteristic
301C3×D12—21no—
302C3×D12—21no—
303C3×D12—21no—
304C3×D12—21no—
305C3×C4×D3—21no—
306C3×C4×D3—21no—
307#626—42no—
308#626—42no—
309#626—42no—
310#626—42no—
311#626—42no—
312#626—81no—
313#626D814yescomplemented
314#624—42no—
315C32×C8—21no—
316C3⋊(C3⋊C8)C2×D412yescomplemented
317C3×C3⋊C8—21no—
318C3×C3⋊C8—21no—
319C22×D8—91no—
320C22×D8—91no—
321D42—91no—
322D42—91no—
323#493—91no—
324#466—91no—
325#466—91no—
326#459—31no—
327#459—91no—
328#447—31no—
329#447—91no—
330#447—91no—
331#447—91no—
332C4×D8—91no—
333C8×D4—91no—
334C24×C3—61no—
335C23×D3—21no—
336C23×D3—61no—
337C23×D3—61no—
338C23×D3—61no—
339C23×D3—61no—
340C23×D3—61no—
341C23×D3—61no—
342C23×D3—121no—
343C23×D3—121no—
344C2×C3×D4—21no—
345C2×C3×D4—21no—
346C2×C3×D4—31no—
347C2×C3×D4—31no—
348C2×C3×D4—61no—
349C2×C3×D4—61no—
350C2×C3×D4—61no—
351C2×C3×D4—62no—
352C2×C3×D4—61no—
353C2×C3×D4—121no—
354C2×C3×D4C22×D311yescharacteristic
355C2×C3×D4C22×D311yescharacteristic
356C2×C3×D4C22×D311yescharacteristic
357C2×C3×D4C22×D311yescharacteristic
358C22×C3×C4—31no—
359C22×C3×C4—61no—
360C2×#67—21no—
361C2×#67—21no—
362C2×#67—21no—
363C2×#67—21no—
364C2×#67—31no—
365C2×#67—61no—
366C2×#67—61no—
367C2×#67—61no—
368C2×#67—61no—
369C2×#67—61no—
370C2×#67—61no—
371C2×#67—61no—
372C2×#67—61no—
373C2×#67—61no—
374C2×#67—61no—
375C2×#67—121no—
376C2×#67—121no—
377C2×#67—124no—
378C22×Dic3—21no—
379D3×D4—22no—
380D3×D4—41no—
381D3×D4—62no—
382D3×D4—62no—
383D3×D4—62no—
384D3×D4—64no—
385D3×D4—64no—
386D3×D4—62no—
387D3×D4—62no—
388D3×D4—121no—
389D3×D4—121no—
390D3×D4—121no—
391D3×D4—121no—
392D3×D4—121no—
393D3×D4—122no—
394D3×D4—122no—
395D3×D4—124no—
396D3×D4—124no—
397C2×D12—31no—
398C2×D12—31no—
399C2×D12—31no—
400C2×D12—31no—
401C2×D12—31no—
402C2×D12—61no—
403C2×D12—61no—
404C2×D12—62no—
405C2×D12—61no—
406C2×D12—61no—
407C2×D12—61no—
408C2×D12—61no—
409C2×D12—61no—
410C2×D12—61no—
411C2×D12—121no—
412C2×D12—124no—
413C2×D12C22×D311yescharacteristic
414C2×D12C22×D311yescharacteristic
415C2×C4×D3—31no—
416C2×C4×D3—31no—
417C2×C4×D3—61no—
418C2×C4×D3—61no—
419C2×C4×D3—61no—
420C2×C4×D3C22×D311yescharacteristic
421C3×D8—24no—
422C3×D8—22no—
423C3×D8—22no—
424C3×D8—62no—
425C3×D8—121no—
426C2×C3×C8—21no—
427C2×C3×C8—31no—
428C2×C3×C8—31no—
429C2×C3×C8C22×D311yescharacteristic
430C2×C3×C8C22×D311yescharacteristic
431C3×C4⋊C4—31no—
432C3×C4⋊C4—31no—
433C3×C22⋊C4—61no—
434C3×C22⋊C4—61no—
435C3×C42—31no—
436#217—21no—
437#217—21no—
438#217—31no—
439#217—61no—
440#217—61no—
441#213—22no—
442#213—34no—
443#213—34no—
444#213—41no—
445#213—64no—
446#213—62no—
447#213—62no—
448#213—62no—
449#213—62no—
450#213—62no—
451#213—64no—
452#213—121no—
453(C2×D3)⋊C4—31no—
454(C2×D3)⋊C4—31no—
455(C2×D3)⋊C4—31no—
456(C2×D3)⋊C4—61no—
457(C2×D3)⋊C4—61no—
458(C2×D3)⋊C4—61no—
459(C2×D3)⋊C4—61no—
460(C2×D3)⋊C4—61no—
461(C2×D3)⋊C4—61no—
462C4⋊Dic3—31no—
463C4⋊Dic3C22×D311yescharacteristic
464C4⋊Dic3C22×D311yescharacteristic
465Dic3⋊C4—31no—
466C4×Dic3C22×D311yescharacteristic
467C2×C3⋊C8—31no—
468C2×C3⋊C8—31no—
469C2×C3⋊C8—61no—
470C2×C3⋊C8—62no—
471C2×C3⋊C8C22×D311yescharacteristic
472C2×C3⋊C8C22×D311yescharacteristic
473D24—62no—
474D24—62no—
475D24—64no—
476D24—62no—
477D24—121no—
478D3×C8—62no—
479D3×C8—62no—
480D3×C8—62no—
481D3×C8—64no—
482C22×C32—22no—
483C22×C32—41no—
484C22×C32—41no—
485C22×C32—41no—
486C22×C32—41no—
487C22×C32—41no—
488C22×C32C22×D411yescharacteristic
489C2×C3⋊D3—21no—
490C2×C3⋊D3—21no—
491C2×C3⋊D3—22no—
492C2×C3⋊D3—41no—
493C2×C3⋊D3—41no—
494C2×C3⋊D3—41no—
495C2×C3⋊D3—41no—
496C2×C3⋊D3—41no—
497C2×C3⋊D3—84no—
498C2×C3⋊D3—84no—
499C2×C3⋊D3C2×D812yescomplemented
500C2×C3×D3—21no—
501C2×C3×D3—21no—
502C2×C3×D3—41no—
503C2×C3×D3—41no—
504C2×C3×D3—41no—
505C2×C3×D3—41no—
506C2×C3×D3—41no—
507C2×C3×D3—41no—
508C2×C3×D3—84no—
509C2×C3×D3C2×D812yescomplemented
510D32—84no—
511C32×C4C22×D411yescharacteristic
512C32×C4H(5,𝔽2)11yescharacteristic
513C3⋊Dic3—21no—
514C3×Dic3—21no—
515C3×Dic3—21no—
516C3×Dic3—41no—
517C3×Dic3—41no—
518C3×Dic3C2×D812yescomplemented
519C22×D4—31no—
520C22×D4—91no—
521C22×D4—91no—
522C22×D4—91no—
523C22×D4—181no—
524C22×D4—181no—
525C2×D8—31no—
526C2×D8—31no—
527C2×D8—91no—
528C2×D8—91no—
529C2×D8—91no—
530C2×D8—91no—
531C2×D8—91no—
532C2×D8—91no—
533C2×D8—184no—
534C2×D8—184no—
535C2×D8D3211yescharacteristic, complemented
536C22×C8—91no—
537C22×C8—91no—
538#127—31no—
539#127—91no—
540#121—31no—
541#121—91no—
542#121—91no—
543#121—91no—
544#121—181no—
545#121—181no—
546#120—181no—
547#120—181no—
548#120—181no—
549#120—181no—
550C4×D4—31no—
551C4×D4—91no—
552C4×D4—91no—
553#107—91no—
554C4⋊C8—31no—
555#102—31no—
556#102—31no—
557#102—31no—
558#102—31no—
559#102—91no—
560#102—91no—
561C22⋊C8—31no—
562C22⋊C8—91no—
563C4×C8—91no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—31no—
569C23×C3—41no—
570C23×C3—41no—
571C23×C3—61no—
572C23×C3—61no—
573C23×C3—122no—
574C23×C3—122no—
575C23×C3—241no—
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—31no—
579C22×D3—31no—
580C22×D3—42no—
581C22×D3—42no—
582C22×D3—61no—
583C22×D3—61no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—61no—
587C22×D3—81no—
588C22×D3—121no—
589C22×D3—121no—
590C22×D3—122no—
591C22×D3—122no—
592C22×D3—122no—
593C22×D3—122no—
594C22×D3—122no—
595C22×D3—122no—
596C22×D3—122no—
597C22×D3—122no—
598C22×D3—122no—
599C22×D3—122no—
600C22×D3—122no—
601C22×D3—124no—
602C22×D3—124no—
603C22×D3—122no—
604C22×D3—242no—
605C22×D3—242no—
606C22×D3—241no—
607C22×D3—241no—
608C22×D3—241no—
609C22×D3—241no—
610C22×D3—241no—
611C22×D3—241no—
612C22×D3—242no—
613C22×D3—242no—
614C22×D3D3×D411yescharacteristic
615C3×D4—22no—
616C3×D4—21no—
617C3×D4—21no—
618C3×D4—21no—
619C3×D4—21no—
620C3×D4—21no—
621C3×D4—21no—
622C3×D4—22no—
623C3×D4—41no—
624C3×D4—41no—
625C3×D4—61no—
626C3×D4—61no—
627C3×D4—61no—
628C3×D4—61no—
629C3×D4—122no—
630C3×D4—122no—
631C3×D4—122no—
632C3×D4—241no—
633C3×D4D3×D412yescomplemented
634C3×D4D3×D412yescomplemented
635C2×C3×C4—21no—
636C2×C3×C4—31no—
637C2×C3×C4—31no—
638C2×C3×C4—31no—
639C2×C3×C4—61no—
640C2×C3×C4—61no—
641C2×C3×C4—61no—
642C2×C3×C4—61no—
643C2×C3×C4—122no—
644C2×C3×C4C23×D311yescharacteristic
645C2×C3×C4C23×D311yescharacteristic
646#67—34no—
647#67—42no—
648#67—42no—
649#67—42no—
650#67—81no—
651#67—122no—
652#67—122no—
653#67—122no—
654#67—122no—
655#67—122no—
656#67—122no—
657#67—122no—
658#67—122no—
659#67—124no—
660#67—124no—
661#67—122no—
662#67—241no—
663C2×Dic3—21no—
664C2×Dic3—21no—
665C2×Dic3—31no—
666C2×Dic3—31no—
667C2×Dic3—42no—
668C2×Dic3—61no—
669C2×Dic3D3×D411yescharacteristic
670C2×Dic3D3×D411yescharacteristic
671C2×Dic3D3×D411yescharacteristic
672D12—21no—
673D12—21no—
674D12—21no—
675D12—21no—
676D12—34no—
677D12—32no—
678D12—32no—
679D12—62no—
680D12—62no—
681D12—61no—
682D12—61no—
683D12—61no—
684D12—61no—
685D12—61no—
686D12—61no—
687D12—121no—
688D12—121no—
689D12—122no—
690D12—122no—
691D12—122no—
692D12—122no—
693D12—122no—
694D12—241no—
695C4×D3—21no—
696C4×D3—21no—
697C4×D3—62no—
698C4×D3—62no—
699C4×D3—61no—
700C4×D3—61no—
701C4×D3—61no—
702C4×D3—61no—
703C4×D3—122no—
704C4×D3—122no—
705C3×C8—22no—
706C3×C8—21no—
707C3×C8—21no—
708C3×C8—61no—
709C3×C8—61no—
710C3⋊C8—21no—
711C3⋊C8—21no—
712C3⋊C8—32no—
713C3⋊C8—32no—
714C3⋊C8—62no—
715C2×C32—42no—
716C2×C32—81no—
717C2×C32D4211yescharacteristic
718C2×C32C22×D811yescharacteristic
719C2×C32#57611yescharacteristic
720C3⋊D3—22no—
721C3⋊D3—42no—
722C3⋊D3—81no—
723C3×D3—22no—
724C3×D3—81no—
725C3×D3—81no—
726C24—61no—
727C24—181no—
728C24—181no—
729C24—181no—
730C2×D4—31no—
731C2×D4—31no—
732C2×D4—61no—
733C2×D4—61no—
734C2×D4—61no—
735C2×D4—62no—
736C2×D4—61no—
737C2×D4—91no—
738C2×D4—91no—
739C2×D4—91no—
740C2×D4—121no—
741C2×D4—181no—
742C2×D4—181no—
743C2×D4—181no—
744C2×D4—182no—
745C2×D4—181no—
746C2×D4—181no—
747C2×D4—181no—
748C2×D4—181no—
749C2×D4—181no—
750C2×D4—182no—
751C2×D4—182no—
752C2×D4—361no—
753C2×D4—364no—
754C2×D4—361no—
755C2×D4—361no—
756C2×D4—364no—
757C2×D4C2×D3211yescharacteristic
758C2×D4C2×D3211yescharacteristic
759C22×C4—31no—
760C22×C4—61no—
761C22×C4—91no—
762C22×C4—181no—
763D8—22no—
764D8—62no—
765D8—94no—
766D8—121no—
767D8—182no—
768D8—182no—
769D8—182no—
770D8—182no—
771D8—361no—
772C2×C8—31no—
773C2×C8—31no—
774C2×C8—91no—
775C2×C8—182no—
776C2×C8—182no—
777C2×C8C2×D3211yescharacteristic
778C4⋊C4—31no—
779C4⋊C4—31no—
780C4⋊C4—91no—
781C22⋊C4—61no—
782C22⋊C4—61no—
783C22⋊C4—91no—
784C22⋊C4—91no—
785C22⋊C4—181no—
786C22⋊C4—181no—
787C22⋊C4—181no—
788C22⋊C4—181no—
789C42—31no—
790C22×C3—22no—
791C22×C3—22no—
792C22×C3—21no—
793C22×C3—32no—
794C22×C3—42no—
795C22×C3—42no—
796C22×C3—41no—
797C22×C3—41no—
798C22×C3—41no—
799C22×C3—41no—
800C22×C3—41no—
801C22×C3—41no—
802C22×C3—41no—
803C22×C3—41no—
804C22×C3—41no—
805C22×C3—41no—
806C22×C3—61no—
807C22×C3—61no—
808C22×C3—81no—
809C22×C3—81no—
810C22×C3—81no—
811C22×C3—81no—
812C22×C3—121no—
813C22×C3—121no—
814C22×C3—121no—
815C22×C3—121no—
816C22×C3—121no—
817C22×C3—121no—
818C22×C3—244no—
819C22×C3C2×D3×D411yescharacteristic
820C22×C3C2×D3×D411yescharacteristic
821C2×D3—21no—
822C2×D3—21no—
823C2×D3—32no—
824C2×D3—32no—
825C2×D3—41no—
826C2×D3—41no—
827C2×D3—41no—
828C2×D3—41no—
829C2×D3—41no—
830C2×D3—41no—
831C2×D3—62no—
832C2×D3—62no—
833C2×D3—62no—
834C2×D3—61no—
835C2×D3—61no—
836C2×D3—61no—
837C2×D3—61no—
838C2×D3—62no—
839C2×D3—62no—
840C2×D3—84no—
841C2×D3—122no—
842C2×D3—121no—
843C2×D3—121no—
844C2×D3—121no—
845C2×D3—121no—
846C2×D3—122no—
847C2×D3—121no—
848C2×D3—121no—
849C2×D3—121no—
850C2×D3—121no—
851C2×D3—121no—
852C2×D3—121no—
853C2×D3—241no—
854C2×D3—241no—
855C2×D3—241no—
856C2×D3—241no—
857C2×D3—244no—
858C2×D3—244no—
859C2×D3—244no—
860C2×D3—244no—
861C2×D3—244no—
862C2×D3—248no—
863C2×D3—248no—
864C2×D3—244no—
865C2×D3D3×D812yescomplemented
866C3×C4—21no—
867C3×C4—21no—
868C3×C4—32no—
869C3×C4—61no—
870C3×C4—61no—
871C3×C4—121no—
872C3×C4—121no—
873C3×C4C2×D3×D411yescharacteristic
874C3×C4C2×D3×D411yescharacteristic
875C3×C4#100411yescharacteristic
876C3×C4#100911yescharacteristic
877Dic3—21no—
878Dic3—21no—
879Dic3—41no—
880Dic3—41no—
881Dic3—62no—
882Dic3—61no—
883Dic3—61no—
884Dic3D3×D812yescomplemented
885C32D4×D811yescharacteristic, complemented, Sylow
886C23—21no—
887C23—21no—
888C23—31no—
889C23—61no—
890C23—61no—
891C23—91no—
892C23—122no—
893C23—122no—
894C23—181no—
895C23—181no—
896C23—241no—
897C23—362no—
898C23—362no—
899C23—362no—
900C23—362no—
901C23—362no—
902C23—362no—
903C23—721no—
904C23—721no—
905C23—721no—
906D4—21no—
907D4—21no—
908D4—21no—
909D4—61no—
910D4—61no—
911D4—61no—
912D4—61no—
913D4—94no—
914D4—92no—
915D4—122no—
916D4—122no—
917D4—122no—
918D4—181no—
919D4—181no—
920D4—181no—
921D4—241no—
922D4—362no—
923D4—362no—
924D4—362no—
925D4—362no—
926D4—362no—
927D4—362no—
928D4—362no—
929D4—721no—
930D4#381112yescomplemented
931C2×C4—31no—
932C2×C4—31no—
933C2×C4—31no—
934C2×C4—61no—
935C2×C4—61no—
936C2×C4—61no—
937C2×C4—61no—
938C2×C4—91no—
939C2×C4—122no—
940C2×C4—181no—
941C2×C4—181no—
942C2×C4—362no—
943C2×C4C22×D3211yescharacteristic
944C8—21no—
945C8—61no—
946C8—61no—
947C8—92no—
948C2×C3—21no—
949C2×C3—21no—
950C2×C3—21no—
951C2×C3—42no—
952C2×C3—42no—
953C2×C3—62no—
954C2×C3—82no—
955C2×C3—82no—
956C2×C3—81no—
957C2×C3—81no—
958C2×C3—241no—
959C2×C3—241no—
960C2×C3#559011yescharacteristic
961C2×C3#560911yescharacteristic
962C2×C3C2×D3×D811yescharacteristic
963C2×C3C2×D3×D811yescharacteristic
964C2×C3#577411yescharacteristic
965C2×C3#577411yescharacteristic
966D3—22no—
967D3—64no—
968D3—62no—
969D3—62no—
970D3—81no—
971D3—81no—
972D3—122no—
973D3—122no—
974D3—242no—
975D3—242no—
976D3—241no—
977D3—241no—
978C22—22no—
979C22—32no—
980C22—41no—
981C22—41no—
982C22—41no—
983C22—41no—
984C22—41no—
985C22—61no—
986C22—61no—
987C22—92no—
988C22—121no—
989C22—121no—
990C22—121no—
991C22—121no—
992C22—121no—
993C22—121no—
994C22—181no—
995C22—181no—
996C22—182no—
997C22—244no—
998C22—361no—
999C22—361no—
1000C22—361no—
1001C22—361no—
1002C22—361no—
1003C22—724no—
1004C22—724no—
1005C22—724no—
1006C22D32×D411yescharacteristic
1007C4—32no—
1008C4—61no—
1009C4—61no—
1010C4—121no—
1011C4—121no—
1012C4—181no—
1013C4#6431411yescharacteristic
1014C4C2×#381111yescharacteristic
1015C3—21no—
1016C3#8002411yescharacteristic, complemented
1017C3#8035011yescharacteristic, complemented
1018C2—42no—
1019C2—62no—
1020C2—81no—
1021C2—182no—
1022C2—241no—
1023C2—241no—
1024C2—362no—
1025C2—721no—
1026C2D32×D811yescharacteristic
1027C2#1059473511yescharacteristic
1028C2#1059529211yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32D4×D8
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. C2×D8×C3⋊D3C2semidirect
2. #10595297C2semidirect
3. D4×#626C2semidirect
4. C2×D3×#213C2semidirect
5. C3×#5156C2semidirect
6. C3×#5150C2semidirect
7. #10591482C2semidirect
8. #10591456C2semidirect
9. #10591456C2semidirect
10. #10591449C2semidirect
11. #10591400C2semidirect
12. #10590947C2semidirect
13. #10590906C2semidirect
14. #10590839C2semidirect
15. #10590765C2semidirect
18. C2×D4×C3⋊D3C22semidirect
19. C2×D4×C3⋊D3C22semidirect
20. C2×C3×D3×D4C22semidirect
23. C2×D3×D12C22semidirect
24. C2×C32×D8C22semidirect
26. C2×#3753C22semidirect
28. C2×#3745C22semidirect
29. C2×C8×C3⋊D3C22semidirect
30. C3×#940C22semidirect
31. C3×#938C22semidirect
32. C3×D4×Dic3C22semidirect
33. C2×C3×#213C22semidirect
34. C2×C3×#213C22semidirect
42. #63916C22semidirect
43. #63916C22semidirect
44. #63911C22semidirect
45. #63909C22semidirect
47. #63894C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. C3×#832C22semidirect
53. C3×#832C22semidirect
54. C3×#821C22semidirect
55. C3×#821C22semidirect
56. C3×(C2×D3)⋊C8C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. #63576C22semidirect
59. #63564C22semidirect
60. #63564C22semidirect
61. #63557C22semidirect
62. Dic3×C3⋊C8C22semidirect
76. #5156D3semidirect
78. #5150D3semidirect
134. #3753D4semidirect
170. C2×D3×D4C2×D3semidirect
176. C2×C3×D8C2×D3semidirect
177. C2×C3×D8C2×D3semidirect
183. #940C2×D3semidirect
188. #938C2×D3semidirect
193. D4×Dic3C2×D3semidirect
205. C2×#213C2×D3semidirect
206. C2×#213C2×D3semidirect
241. #832C2×D3semidirect
242. #832C2×D3semidirect
245. #821C2×D3semidirect
246. #821C2×D3semidirect
249. (C2×D3)⋊C8C2×D3semidirect
250. Dic3⋊C8C2×D3semidirect
280. C32×D4C2×D4semidirect
288. C4⋊(C3⋊D3)C2×D4semidirect
313. #626D8semidirect
316. C3⋊(C3⋊C8)C2×D4semidirect
499. C2×C3⋊D3C2×D8semidirect
509. C2×C3×D3C2×D8semidirect
518. C3×Dic3C2×D8semidirect
535. C2×D8D32semidirect
633. C3×D4D3×D4semidirect
634. C3×D4D3×D4semidirect
865. C2×D3D3×D8semidirect
884. Dic3D3×D8semidirect
885. C32D4×D8semidirect
930. D4#3811semidirect
1016. C3#80024semidirect
1017. C3#80350semidirect

Maximal subgroups

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

subgroupindex
C2×D8×C3⋊D32
#105952972
D4×#6262
C2×D3×#2132
C3×#51562
C3×#51502
#105914822
#105914562
#105914492
#105914002
#105909472
#105909062
#105908392
#105907652
#803503
#800243