Finite Group Databasebeta

← #11885743

Subgroups — #11885743

Order 1152.

1454 conjugacy classes of subgroups.

The subgroup lattice has 1053 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D4×#638C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3C2×#63926C211yesmaximal, characteristic, complemented
4#10595069C211yesmaximal, characteristic, complemented
5C3×#5217C211yesmaximal, characteristic, complemented
6#10591516C211yesmaximal, characteristic, complemented
7#10591486C211yesmaximal, characteristic, complemented
8#10591484C211yesmaximal, characteristic, complemented
9#10591456C211yesmaximal, characteristic, complemented
10#10591455C211yesmaximal, characteristic, complemented
11#10591435C211yesmaximal, characteristic, complemented
12#10591433C211yesmaximal, characteristic, complemented
13#10591164C211yesmaximal, characteristic, complemented
14#10591162C211yesmaximal, characteristic, complemented
15#10591148C211yesmaximal, characteristic, complemented
16D8×#67—31nomaximal
17#80024—31nomaximal
18C22×C32×D4C2211yescharacteristic, complemented
19C22×#638—21no—
20C2×D4×C3⋊D3C2211yescharacteristic, complemented
21C22×C3×D12C2211yescharacteristic, complemented
22C2×D3×#67—21no—
23C2×#3802C2211yescharacteristic, complemented
24#64162—21no—
25#64149C2211yescharacteristic, complemented
26#64148—21no—
27#64147C2211yescharacteristic, complemented
28#64146—21no—
29D4×C3⋊Dic3C2211yescharacteristic, complemented
30#64139C2211yescharacteristic, complemented
31C4×#638C2211yescharacteristic
32C2×C3×#213—24no—
33C2×C3×#213C2211yescharacteristic
34C2×C3×#213C2211yescharacteristic, complemented
35C2×C3×#213C2211yescharacteristic, complemented
36C2×C3×#213C2211yescharacteristic, complemented
37C2×C3×#213C2211yescharacteristic, complemented
38C2×C3×#213C2211yescharacteristic, complemented
39C3×#930C2211yescharacteristic, complemented
40C22×C3×C3⋊C8C2211yescharacteristic, complemented
41#63976—21no—
42#63926—24no—
43#63922—21no—
44#63916C2211yescharacteristic, complemented
45#63914C2211yescharacteristic, complemented
46#63898C2211yescharacteristic, complemented
47#63885—21no—
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×#3710C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic, complemented
53C3×#832C2211yescharacteristic, complemented
54C3×#830C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63572C2211yescharacteristic, complemented
57#63564C2211yescharacteristic, complemented
58#63563C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62#63553C2211yescharacteristic, complemented
63C22×C3×D8—31no—
64D4×#67—31no—
65D4×#67—31no—
66D4×#67—31no—
67D4×#67—61no—
68C22×#213D311yescharacteristic, complemented
69C2×D3×D8—31no—
70C2×D3×D8—31no—
71#5609—31no—
72C3×#447—31no—
73#5217—31no—
74#5217D311yescharacteristic, complemented
75#5157—31no—
76#5156—31no—
77#5156—31no—
78#5156—31no—
79#5151—31no—
80#5151—31no—
81#5150—31no—
82#5150—31no—
83#5150—31no—
84Dic3×D8—31no—
85#5115—31no—
86C8×#67—31no—
87#5038—31no—
88#4786—31no—
89#4775—31no—
90#4773—31no—
91#4756—31no—
92#4732—31no—
93#67⋊C8—31no—
94C24×C32—21no—
95C23×C3⋊D3—21no—
96C23×C3×D3—21no—
97C22×D32—21no—
98C2×C32×D4—22no—
99C2×C32×D4—21no—
100C2×C32×D4—41no—
101C2×C32×D4C2311yescharacteristic
102C2×C32×D4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C2×#638—21no—
105C2×#638—21no—
106C2×#638—21no—
107C2×#638—21no—
108C2×#638—21no—
109C2×#638—44no—
110C2×#638D411yescharacteristic
111C22×C3⋊Dic3—21no—
112D4×C3⋊D3—22no—
113D4×C3⋊D3—41no—
114C2×C4⋊(C3⋊D3)C2311yescharacteristic
115C2×C4×C3⋊D3C2311yescharacteristic
116C2×C3×#67—21no—
117C2×C3×D12—22no—
118C2×C3×D12—21no—
119C2×C3×D12—41no—
120C2×C3×D12C2311yescharacteristic
121C2×C3×D12C2311yescharacteristic
122C2×C3×D12C2311yescharacteristic
123D3×#67—44no—
124C2×#626—21no—
125C2×#625—21no—
126C2×#625—21no—
127C2×#625—21no—
128C2×D3×Dic3—21no—
129#3802—22no—
130#3802—41no—
131#3757—21no—
132#3757—21no—
133#3757D411yescharacteristic
134#3752—21no—
135#3752D411yescharacteristic
136C4⋊(C3⋊Dic3)C2311yescharacteristic
137#3750D411yescharacteristic
138C4×C3⋊Dic3C2311yescharacteristic
139C3×#213—22no—
140C3×#213—22no—
141C3×#213—22no—
142C3×#213—22no—
143C3×#213—41no—
144C3×#213D414yescomplemented
145C3×(C2×D3)⋊C4—21no—
146C3×C4⋊Dic3C2311yescharacteristic
147C2×C3×C3⋊C8—22no—
148C2×C3×C3⋊C8C2311yescharacteristic
149C2×C3×C3⋊C8C2311yescharacteristic
150C2×C3×C3⋊C8C2311yescharacteristic
151C2×C3×C3⋊C8C2311yescharacteristic
152(C2×D3)⋊Dic3—21no—
153(C2×D3)⋊Dic3—21no—
154#3714—22no—
155#3714—22no—
156#3714—41no—
157#3710—22no—
158D4×D8—91noSylow
159C22×C3×D4—21no—
160C22×C3×D4—31no—
161C22×C3×D4C2×D311yescharacteristic, complemented
162C22×C3×D4C2×D311yescharacteristic, complemented
163C22×#67—61no—
164C22×#67—61no—
165C22×#67—61no—
166C22×#67—62no—
167C2×D3×D4—31no—
168C2×D3×D4—31no—
169C2×D3×D4—31no—
170C2×D3×D4—31no—
171C2×D3×D4—61no—
172C2×D3×D4—61no—
173C22×D12C2×D311yescharacteristic, complemented
174C2×C3×D8—31no—
175C2×C3×D8—31no—
176C2×C3×D8—31no—
177C2×C3×D8—31no—
178C2×C3×D8—31no—
179C2×C3×D8—31no—
180C2×C3×D8—64no—
181C22×C3×C8—31no—
182C3×#121—31no—
183#953—61no—
184#953—61no—
185#953—61no—
186#953—62no—
187#940—31no—
188#940—31no—
189#940—31no—
190#940—31no—
191#940—61no—
192#939—61no—
193#939—61no—
194#939—61no—
195#939—62no—
196#938—31no—
197#938—31no—
198#938—31no—
199#938—61no—
200#937—61no—
201#937—61no—
202#937—61no—
203#937—61no—
204#937—62no—
205D4×Dic3—31no—
206D4×Dic3—31no—
207D4×Dic3—31no—
208D4×Dic3—61no—
209C2×#213—24no—
210C2×#213—31no—
211C2×#213—31no—
212C2×#213—31no—
213C2×#213C2×D311yescharacteristic
214C2×#213C2×D311yescharacteristic, complemented
215C2×#213C2×D311yescharacteristic, complemented
216C2×#213C2×D311yescharacteristic, complemented
217C2×#213C2×D311yescharacteristic, complemented
218C2×#213C2×D311yescharacteristic, complemented
219#930—31no—
220#930—31no—
221#930—61no—
222#930C2×D311yescharacteristic, complemented
223C4×#67—31no—
224C4×#67—31no—
225C4×#67—61no—
226C22×C3⋊C8C2×D311yescharacteristic, complemented
227D3×D8—64no—
228D3×D8—64no—
229C2×D24—31no—
230C2×D24—31no—
231C2×D24—31no—
232C2×D3×C8—31no—
233C2×D3×C8—31no—
234#895—31no—
235#893—31no—
236#884—61no—
237#882—61no—
238C3×#102—31no—
239C3×#102—31no—
240C3×C22⋊C8—31no—
241#832—31no—
242#832—31no—
243#832—31no—
244#832C2×D311yescharacteristic, complemented
245#832C2×D311yescharacteristic, complemented
246#830C2×D311yescharacteristic, complemented
247#821—31no—
248#821—31no—
249#821—31no—
250#821—31no—
251(C2×D3)⋊C8—31no—
252(C2×D3)⋊C8—31no—
253#818—31no—
254Dic3⋊C8—31no—
255Dic3⋊C8—31no—
256C8×Dic3—31no—
257C8×Dic3—31no—
258#809—31no—
259#807—31no—
260C23×C32—21no—
261C23×C32—21no—
262C23×C32—42no—
263C23×C32—42no—
264C23×C32—81no—
265C23×C32C2×D411yescharacteristic
266C22×C3⋊D3—21no—
267C22×C3⋊D3—42no—
268C22×C3⋊D3—42no—
269C22×C3⋊D3—81no—
270C22×C3⋊D3C2×D411yescharacteristic
271C22×C3×D3—21no—
272C22×C3×D3—21no—
273C22×C3×D3—21no—
274C22×C3×D3—42no—
275C22×C3×D3—42no—
276C22×C3×D3—81no—
277C2×D32—42no—
278C2×D32—42no—
279C2×D32—81no—
280C32×D4—21no—
281C32×D4—21no—
282C32×D4—21no—
283C32×D4—42no—
284C32×D4C2×D412yescomplemented
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4C2×D411yescharacteristic
288C2×C32×C4C2411yescharacteristic
289#638—42no—
290#638—42no—
291#638—42no—
292#638—42no—
293#638—81no—
294#638D814yescomplemented
295C2×C3⋊Dic3—21no—
296C2×C3⋊Dic3—42no—
297C2×C3⋊Dic3C2×D411yescharacteristic
298C2×C3⋊Dic3C2×D411yescharacteristic
299C2×C3⋊Dic3C2×D411yescharacteristic
300C4⋊(C3⋊D3)—21no—
301C4⋊(C3⋊D3)—21no—
302C4×C3⋊D3—21no—
303C4×C3⋊D3—21no—
304C3×#67—42no—
305C2×C3×Dic3—21no—
306C3×D12—21no—
307C3×D12—21no—
308C3×D12—21no—
309C3×D12—21no—
310C3×D12—21no—
311C3×D12—42no—
312C3×D12C2×D412yescomplemented
313#626—42no—
314#625—42no—
315#625—42no—
316#625—81no—
317D3×Dic3—42no—
318C3×C3⋊C8—21no—
319C3×C3⋊C8—21no—
320C3×C3⋊C8—21no—
321C3×C3⋊C8C2×D412yescomplemented
322C22×D8—31no—
323C22×D8—91no—
324D42—91no—
325D42—91no—
326#493—91no—
327#466—91no—
328#466—91no—
329#459—91no—
330#459—91no—
331#447—31no—
332#447—91no—
333#447—91no—
334#447—91no—
335C4×D8—91no—
336C8×D4—91no—
337C24×C3—22no—
338C24×C3—21no—
339C24×C3—21no—
340C24×C3—61no—
341C23×D3—21no—
342C23×D3—61no—
343C23×D3—61no—
344C23×D3—61no—
345C23×D3—61no—
346C23×D3—62no—
347C2×C3×D4—22no—
348C2×C3×D4—22no—
349C2×C3×D4—22no—
350C2×C3×D4—21no—
351C2×C3×D4—21no—
352C2×C3×D4—21no—
353C2×C3×D4—21no—
354C2×C3×D4—31no—
355C2×C3×D4—31no—
356C2×C3×D4—31no—
357C2×C3×D4—42no—
358C2×C3×D4—41no—
359C2×C3×D4—41no—
360C2×C3×D4—42no—
361C2×C3×D4—62no—
362C2×C3×D4—61no—
363C2×C3×D4—61no—
364C2×C3×D4—121no—
365C2×C3×D4C22×D311yescharacteristic
366C2×C3×D4C22×D311yescharacteristic
367C2×C3×D4C22×D311yescharacteristic
368C2×C3×D4C22×D311yescharacteristic
369C22×C3×C4—21no—
370C22×C3×C4C22×D311yescharacteristic
371C22×C3×C4C22×D311yescharacteristic
372C2×#67—21no—
373C2×#67—31no—
374C2×#67—31no—
375C2×#67—61no—
376C2×#67—61no—
377C2×#67—61no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—61no—
381C2×#67—61no—
382C2×#67—61no—
383C2×#67—61no—
384C2×#67—61no—
385C2×#67—61no—
386C2×#67—61no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—61no—
391C2×#67—62no—
392C2×#67—62no—
393C2×#67—62no—
394C2×#67—62no—
395C2×#67—61no—
396C2×#67—61no—
397C2×#67—62no—
398C2×#67—124no—
399C2×#67—124no—
400C2×#67—124no—
401C2×#67—128no—
402C22×Dic3—61no—
403C22×Dic3—61no—
404C22×Dic3—61no—
405C22×Dic3—62no—
406D3×D4—62no—
407D3×D4—62no—
408D3×D4—62no—
409D3×D4—62no—
410D3×D4—122no—
411D3×D4—121no—
412D3×D4—121no—
413D3×D4—121no—
414D3×D4—121no—
415D3×D4—124no—
416D3×D4—122no—
417C2×D12—22no—
418C2×D12—21no—
419C2×D12—31no—
420C2×D12—31no—
421C2×D12—41no—
422C2×D12—61no—
423C2×D12—61no—
424C2×D12C22×D311yescharacteristic
425C2×D12C22×D311yescharacteristic
426C2×D12C22×D311yescharacteristic
427C2×C4×D3—31no—
428C2×C4×D3—31no—
429C2×C4×D3—61no—
430C2×C4×D3—61no—
431C3×D8—34no—
432C3×D8—62no—
433C3×D8—62no—
434C3×D8—62no—
435C3×D8—62no—
436C3×D8—121no—
437C2×C3×C8—31no—
438C2×C3×C8—31no—
439C2×C3×C8—31no—
440C2×C3×C8—31no—
441C2×C3×C8—62no—
442C3×C4⋊C4—31no—
443C3×C22⋊C4—61no—
444#217—31no—
445#217—31no—
446#217—61no—
447#217—61no—
448#217—61no—
449#217—61no—
450#217—61no—
451#217—61no—
452#217—61no—
453#217—62no—
454#217—62no—
455#213—22no—
456#213—22no—
457#213—22no—
458#213—22no—
459#213—41no—
460#213—62no—
461#213—62no—
462#213—121no—
463#213#6714yescomplemented
464(C2×D3)⋊C4—21no—
465(C2×D3)⋊C4—31no—
466(C2×D3)⋊C4—31no—
467(C2×D3)⋊C4—61no—
468(C2×D3)⋊C4—61no—
469(C2×D3)⋊C4—61no—
470(C2×D3)⋊C4—62no—
471(C2×D3)⋊C4—61no—
472(C2×D3)⋊C4—61no—
473C4⋊Dic3—31no—
474C4⋊Dic3—31no—
475C4⋊Dic3—61no—
476C4⋊Dic3C22×D311yescharacteristic
477Dic3⋊C4—31no—
478Dic3⋊C4—31no—
479Dic3⋊C4—61no—
480C4×Dic3—31no—
481C4×Dic3—31no—
482C4×Dic3—61no—
483C2×C3⋊C8—22no—
484C2×C3⋊C8C22×D311yescharacteristic
485C2×C3⋊C8C22×D311yescharacteristic
486C2×C3⋊C8C22×D311yescharacteristic
487C2×C3⋊C8C22×D311yescharacteristic
488D24—62no—
489D24—62no—
490D24—121no—
491D3×C8—62no—
492D3×C8—62no—
493C22×C32—22no—
494C22×C32—21no—
495C22×C32—21no—
496C22×C32—41no—
497C22×C32—41no—
498C22×C32—41no—
499C22×C32—41no—
500C22×C32—41no—
501C22×C32—84no—
502C22×C32C2×D812yescomplemented
503C22×C32C22×D411yescharacteristic
504C2×C3⋊D3—21no—
505C2×C3⋊D3—21no—
506C2×C3⋊D3—41no—
507C2×C3⋊D3—41no—
508C2×C3⋊D3—41no—
509C2×C3⋊D3—84no—
510C2×C3⋊D3C2×D812yescomplemented
511C2×C3×D3—22no—
512C2×C3×D3—41no—
513C2×C3×D3—41no—
514C2×C3×D3—41no—
515C2×C3×D3—41no—
516C2×C3×D3—41no—
517C2×C3×D3—41no—
518C2×C3×D3—41no—
519C2×C3×D3—41no—
520C2×C3×D3—84no—
521D32—84no—
522C32×C4—21no—
523C32×C4C22×D411yescharacteristic
524C32×C4H(5,𝔽2)11yescharacteristic
525C3⋊Dic3—21no—
526C3⋊Dic3—21no—
527C3⋊Dic3—41no—
528C3⋊Dic3C2×D812yescomplemented
529C3×Dic3—41no—
530C22×D4—31no—
531C22×D4—91no—
532C22×D4—91no—
533C22×D4—181no—
534C22×D4—181no—
535C22×D4D3211yescharacteristic, complemented
536C2×D8—31no—
537C2×D8—31no—
538C2×D8—31no—
539C2×D8—31no—
540C2×D8—31no—
541C2×D8—31no—
542C2×D8—64no—
543C2×D8—91no—
544C2×D8—91no—
545C2×D8—91no—
546C2×D8—184no—
547C22×C8—31no—
548C22×C8—91no—
549#127—91no—
550#127—91no—
551#121—31no—
552#121—91no—
553#121—91no—
554#121—91no—
555#121—181no—
556#121—181no—
557#120—181no—
558#120—181no—
559#120—181no—
560#120—181no—
561C4×D4—91no—
562C4×D4—91no—
563C4×D4—91no—
564#107—91no—
565C4⋊C8—91no—
566#102—31no—
567#102—31no—
568#102—91no—
569#102—91no—
570#102—91no—
571#102—91no—
572C22⋊C8—31no—
573C22⋊C8—91no—
574C4×C8—91no—
575C23×C3—22no—
576C23×C3—21no—
577C23×C3—21no—
578C23×C3—22no—
579C23×C3—21no—
580C23×C3—21no—
581C23×C3—21no—
582C23×C3—42no—
583C23×C3—42no—
584C23×C3—44no—
585C23×C3—44no—
586C23×C3—42no—
587C23×C3—42no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3—61no—
591C23×C3—81no—
592C23×C3—81no—
593C23×C3—82no—
594C23×C3—122no—
595C23×C3—122no—
596C23×C3—241no—
597C23×C3D3×D411yescharacteristic
598C23×C3D3×D411yescharacteristic
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—31no—
603C22×D3—31no—
604C22×D3—42no—
605C22×D3—42no—
606C22×D3—61no—
607C22×D3—62no—
608C22×D3—61no—
609C22×D3—61no—
610C22×D3—81no—
611C22×D3—122no—
612C22×D3—122no—
613C22×D3—122no—
614C22×D3—122no—
615C22×D3—122no—
616C22×D3—122no—
617C22×D3—122no—
618C22×D3—122no—
619C22×D3—124no—
620C22×D3—124no—
621C22×D3—241no—
622C22×D3—241no—
623C22×D3—241no—
624C22×D3—241no—
625C22×D3—242no—
626C3×D4—22no—
627C3×D4—21no—
628C3×D4—21no—
629C3×D4—21no—
630C3×D4—21no—
631C3×D4—21no—
632C3×D4—21no—
633C3×D4—22no—
634C3×D4—32no—
635C3×D4—41no—
636C3×D4—41no—
637C3×D4—42no—
638C3×D4—42no—
639C3×D4—44no—
640C3×D4—61no—
641C3×D4—61no—
642C3×D4—61no—
643C3×D4—61no—
644C3×D4—61no—
645C3×D4—122no—
646C3×D4—122no—
647C3×D4D3×D412yescomplemented
648C3×D4C2×#6712yescomplemented
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—41no—
656C2×C3×C4—41no—
657C2×C3×C4—61no—
658C2×C3×C4D3×D411yescharacteristic
659C2×C3×C4D3×D411yescharacteristic
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D311yescharacteristic
662#67—34no—
663#67—34no—
664#67—42no—
665#67—64no—
666#67—122no—
667#67—122no—
668#67—122no—
669#67—122no—
670#67—122no—
671#67—122no—
672#67—122no—
673#67—122no—
674#67—122no—
675#67—124no—
676#67—122no—
677#67—122no—
678#67—124no—
679#67—124no—
680#67—124no—
681#67—122no—
682#67—122no—
683#67—241no—
684#67—241no—
685#67—241no—
686#67—241no—
687#67—242no—
688C2×Dic3—21no—
689C2×Dic3—31no—
690C2×Dic3—31no—
691C2×Dic3—31no—
692C2×Dic3—31no—
693C2×Dic3—31no—
694C2×Dic3—31no—
695C2×Dic3—61no—
696C2×Dic3—61no—
697C2×Dic3—61no—
698C2×Dic3—62no—
699C2×Dic3—61no—
700C2×Dic3—61no—
701C2×Dic3—122no—
702C2×Dic3—122no—
703C2×Dic3—122no—
704C2×Dic3—124no—
705D12—21no—
706D12—21no—
707D12—21no—
708D12—21no—
709D12—21no—
710D12—42no—
711D12—61no—
712D12—61no—
713D12—61no—
714D12—61no—
715D12—121no—
716D12—121no—
717D12—122no—
718D12C2×#6712yescomplemented
719C4×D3—61no—
720C4×D3—61no—
721C4×D3—61no—
722C4×D3—61no—
723C4×D3—121no—
724C4×D3—121no—
725C4×D3—122no—
726C3×C8—32no—
727C3×C8—61no—
728C3×C8—61no—
729C3×C8—61no—
730C3⋊C8—21no—
731C3⋊C8—21no—
732C3⋊C8—21no—
733C3⋊C8C2×#6712yescomplemented
734C2×C32—22no—
735C2×C32—42no—
736C2×C32—81no—
737C2×C32D4211yescharacteristic
738C2×C32C22×D811yescharacteristic
739C2×C32#57611yescharacteristic
740C3⋊D3—22no—
741C3⋊D3—81no—
742C3×D3—42no—
743C3×D3—81no—
744C3×D3—81no—
745C24—21no—
746C24—61no—
747C24—181no—
748C24—181no—
749C2×D4—22no—
750C2×D4—21no—
751C2×D4—31no—
752C2×D4—31no—
753C2×D4—31no—
754C2×D4—41no—
755C2×D4—62no—
756C2×D4—61no—
757C2×D4—61no—
758C2×D4—91no—
759C2×D4—91no—
760C2×D4—121no—
761C2×D4—181no—
762C2×D4—181no—
763C2×D4—181no—
764C2×D4—181no—
765C2×D4—181no—
766C2×D4—181no—
767C2×D4—181no—
768C2×D4—182no—
769C2×D4—182no—
770C2×D4—181no—
771C2×D4—181no—
772C2×D4—361no—
773C2×D4—361no—
774C2×D4—364no—
775C2×D4—364no—
776C2×D4C2×D3211yescharacteristic
777C2×D4C2×D3211yescharacteristic
778C22×C4—91no—
779C22×C4—181no—
780C22×C4—181no—
781C22×C4C2×D3211yescharacteristic
782D8—34no—
783D8—62no—
784D8—62no—
785D8—62no—
786D8—62no—
787D8—121no—
788D8—182no—
789D8—182no—
790D8—361no—
791C2×C8—31no—
792C2×C8—31no—
793C2×C8—31no—
794C2×C8—31no—
795C2×C8—62no—
796C2×C8—182no—
797C4⋊C4—31no—
798C4⋊C4—91no—
799C4⋊C4—91no—
800C22⋊C4—61no—
801C22⋊C4—91no—
802C22⋊C4—91no—
803C22⋊C4—181no—
804C22⋊C4—181no—
805C22⋊C4—181no—
806C22⋊C4—181no—
807C22⋊C4—181no—
808C42—91no—
809C22×C3—21no—
810C22×C3—21no—
811C22×C3—21no—
812C22×C3—21no—
813C22×C3—24no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—21no—
817C22×C3—22no—
818C22×C3—41no—
819C22×C3—41no—
820C22×C3—42no—
821C22×C3—42no—
822C22×C3—42no—
823C22×C3—42no—
824C22×C3—42no—
825C22×C3—41no—
826C22×C3—41no—
827C22×C3—41no—
828C22×C3—41no—
829C22×C3—41no—
830C22×C3—41no—
831C22×C3—41no—
832C22×C3—41no—
833C22×C3—41no—
834C22×C3—41no—
835C22×C3—62no—
836C22×C3—84no—
837C22×C3—84no—
838C22×C3—88no—
839C22×C3—121no—
840C22×C3—121no—
841C22×C3—121no—
842C22×C3—121no—
843C22×C3—121no—
844C22×C3—121no—
845C22×C3—121no—
846C22×C3—121no—
847C22×C3—244no—
848C22×C3D3×D812yescomplemented
849C22×C3D3×D812yescomplemented
850C22×C3C2×D3×D411yescharacteristic
851C22×C3C2×D3×D411yescharacteristic
852C2×D3—22no—
853C2×D3—32no—
854C2×D3—32no—
855C2×D3—41no—
856C2×D3—41no—
857C2×D3—41no—
858C2×D3—41no—
859C2×D3—41no—
860C2×D3—41no—
861C2×D3—41no—
862C2×D3—41no—
863C2×D3—62no—
864C2×D3—61no—
865C2×D3—61no—
866C2×D3—61no—
867C2×D3—61no—
868C2×D3—84no—
869C2×D3—121no—
870C2×D3—121no—
871C2×D3—122no—
872C2×D3—122no—
873C2×D3—122no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—121no—
878C2×D3—121no—
879C2×D3—121no—
880C2×D3—244no—
881C2×D3—244no—
882C2×D3—244no—
883C2×D3—244no—
884C2×D3—248no—
885C3×C4—21no—
886C3×C4—21no—
887C3×C4—21no—
888C3×C4—21no—
889C3×C4—41no—
890C3×C4—121no—
891C3×C4C2×D3×D411yescharacteristic
892C3×C4#100411yescharacteristic
893C3×C4#100411yescharacteristic
894C3×C4C22×#6711yescharacteristic
895Dic3—32no—
896Dic3—32no—
897Dic3—41no—
898Dic3—62no—
899Dic3—61no—
900Dic3—61no—
901Dic3—61no—
902Dic3—61no—
903Dic3—121no—
904Dic3—121no—
905Dic3—122no—
906Dic3—121no—
907Dic3—121no—
908C32D4×D811yescharacteristic, complemented, Sylow
909C23—21no—
910C23—21no—
911C23—42no—
912C23—42no—
913C23—61no—
914C23—61no—
915C23—61no—
916C23—81no—
917C23—91no—
918C23—122no—
919C23—122no—
920C23—181no—
921C23—241no—
922C23—362no—
923C23—362no—
924C23—362no—
925C23—362no—
926C23—721no—
927C23—721no—
928C23#381111yescharacteristic
929D4—21no—
930D4—21no—
931D4—21no—
932D4—32no—
933D4—42no—
934D4—61no—
935D4—61no—
936D4—61no—
937D4—61no—
938D4—61no—
939D4—94no—
940D4—122no—
941D4—122no—
942D4—181no—
943D4—181no—
944D4—362no—
945D4—362no—
946D4—362no—
947D4—362no—
948D4—362no—
949D4—362no—
950D4—362no—
951D4—721no—
952D4—721no—
953D4D3×#6712yescomplemented
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—61no—
957C2×C4—91no—
958C2×C4—91no—
959C2×C4—91no—
960C2×C4—181no—
961C2×C4—181no—
962C2×C4—181no—
963C2×C4—362no—
964C2×C4—362no—
965C2×C4#381111yescharacteristic
966C2×C4C22×D3211yescharacteristic
967C8—32no—
968C8—61no—
969C8—61no—
970C8—61no—
971C2×C3—22no—
972C2×C3—22no—
973C2×C3—21no—
974C2×C3—21no—
975C2×C3—21no—
976C2×C3—42no—
977C2×C3—44no—
978C2×C3—42no—
979C2×C3—42no—
980C2×C3—82no—
981C2×C3—81no—
982C2×C3—81no—
983C2×C3—122no—
984C2×C3—241no—
985C2×C3—241no—
986C2×C3#559011yescharacteristic
987C2×C3C2×D3×D811yescharacteristic
988C2×C3C2×D3×D811yescharacteristic
989C2×C3#575711yescharacteristic
990C2×C3#577411yescharacteristic
991C2×C3D4×#6711yescharacteristic
992D3—42no—
993D3—62no—
994D3—62no—
995D3—81no—
996D3—81no—
997D3—122no—
998D3—242no—
999D3—241no—
1000D3—241no—
1001C22—21no—
1002C22—21no—
1003C22—22no—
1004C22—41no—
1005C22—41no—
1006C22—41no—
1007C22—41no—
1008C22—41no—
1009C22—62no—
1010C22—84no—
1011C22—92no—
1012C22—121no—
1013C22—121no—
1014C22—121no—
1015C22—121no—
1016C22—121no—
1017C22—121no—
1018C22—121no—
1019C22—121no—
1020C22—181no—
1021C22—181no—
1022C22—244no—
1023C22—361no—
1024C22—361no—
1025C22—361no—
1026C22—724no—
1027C22—724no—
1028C22#6392612yescomplemented
1029C22C2×#381111yescharacteristic
1030C4—21no—
1031C4—92no—
1032C4—121no—
1033C4—181no—
1034C4—181no—
1035C4—361no—
1036C4C2×D3×#6711yescharacteristic
1037C4#6433011yescharacteristic
1038C3—21no—
1039C3#8002411yescharacteristic, complemented
1040C3D8×#6711yescharacteristic, complemented
1041C2—22no—
1042C2—42no—
1043C2—81no—
1044C2—122no—
1045C2—182no—
1046C2—241no—
1047C2—241no—
1048C2—721no—
1049C2C2×#6392611yescharacteristic
1050C2#1059510211yescharacteristic
1051C2#1059552611yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. D4×#638C2semidirect
2. C22×C3×#213C2semidirect
3. C2×#63926C2semidirect
4. #10595069C2semidirect
5. C3×#5217C2semidirect
6. #10591516C2semidirect
7. #10591486C2semidirect
8. #10591484C2semidirect
9. #10591456C2semidirect
10. #10591455C2semidirect
11. #10591435C2semidirect
12. #10591433C2semidirect
13. #10591164C2semidirect
14. #10591162C2semidirect
15. #10591148C2semidirect
18. C22×C32×D4C22semidirect
20. C2×D4×C3⋊D3C22semidirect
21. C22×C3×D12C22semidirect
23. C2×#3802C22semidirect
25. #64149C22semidirect
27. #64147C22semidirect
29. D4×C3⋊Dic3C22semidirect
30. #64139C22semidirect
34. C2×C3×#213C22semidirect
35. C2×C3×#213C22semidirect
36. C2×C3×#213C22semidirect
37. C2×C3×#213C22semidirect
38. C2×C3×#213C22semidirect
39. C3×#930C22semidirect
40. C22×C3×C3⋊C8C22semidirect
44. #63916C22semidirect
45. #63914C22semidirect
46. #63898C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
50. C2×#3714C22semidirect
51. C2×#3710C22semidirect
52. C3×#832C22semidirect
53. C3×#832C22semidirect
54. C3×#830C22semidirect
55. #63575C22semidirect
56. #63572C22semidirect
57. #63564C22semidirect
58. #63563C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
61. #63557C22semidirect
62. #63553C22semidirect
68. C22×#213D3semidirect
74. #5217D3semidirect
144. C3×#213D4semidirect
161. C22×C3×D4C2×D3semidirect
162. C22×C3×D4C2×D3semidirect
173. C22×D12C2×D3semidirect
214. C2×#213C2×D3semidirect
215. C2×#213C2×D3semidirect
216. C2×#213C2×D3semidirect
217. C2×#213C2×D3semidirect
218. C2×#213C2×D3semidirect
222. #930C2×D3semidirect
226. C22×C3⋊C8C2×D3semidirect
244. #832C2×D3semidirect
245. #832C2×D3semidirect
246. #830C2×D3semidirect
284. C32×D4C2×D4semidirect
294. #638D8semidirect
312. C3×D12C2×D4semidirect
321. C3×C3⋊C8C2×D4semidirect
463. #213#67semidirect
502. C22×C32C2×D8semidirect
510. C2×C3⋊D3C2×D8semidirect
528. C3⋊Dic3C2×D8semidirect
535. C22×D4D32semidirect
647. C3×D4D3×D4semidirect
648. C3×D4C2×#67semidirect
718. D12C2×#67semidirect
733. C3⋊C8C2×#67semidirect
848. C22×C3D3×D8semidirect
849. C22×C3D3×D8semidirect
908. C32D4×D8semidirect
953. D4D3×#67semidirect
1028. C22#63926semidirect
1039. C3#80024semidirect
1040. C3D8×#67semidirect

Maximal subgroups

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

subgroupindex
D4×#6382
C22×C3×#2132
C2×#639262
#105950692
C3×#52172
#105915162
#105914862
#105914842
#105914562
#105914552
#105914352
#105914332
#105911642
#105911622
#105911482
D8×#673
#800243