Finite Group Databasebeta

← #11885750

Subgroups — #11885750

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
1#10596080C211yesmaximal, characteristic, complemented
2C2×#63926C211yesmaximal, characteristic, complemented
3#10595069C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5C3×#5038C211yesmaximal, characteristic, complemented
6C3×#5036C211yesmaximal, characteristic, complemented
7#10591484C211yesmaximal, characteristic, complemented
8#10591456C211yesmaximal, characteristic, complemented
9#10591433C211yesmaximal, characteristic, complemented
10#10591168C211yesmaximal, characteristic, complemented
11#10591148C211yesmaximal, characteristic, complemented
12#10590598C211yesmaximal, characteristic, complemented
13#10590551C211yesmaximal, characteristic, complemented
14#10590509C211yesmaximal, characteristic, complemented
15#10590459C211yesmaximal, characteristic, complemented
16#80729—31nomaximal
17#80024—31nomaximal
18C2×D4×C3⋊D3—21no—
19C2×D4×C3⋊D3C2211yescharacteristic, complemented
20C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
21C22×C3×D12C2211yescharacteristic, complemented
22C2×D3×#67—21no—
23C2×#3802C2211yescharacteristic, complemented
24C32×#121C2211yescharacteristic, complemented
25#64149C2211yescharacteristic, complemented
26#64146—21no—
27C4×#638C2211yescharacteristic
28#64104C2211yescharacteristic, complemented
29#64102C2211yescharacteristic, complemented
30#64093—21no—
31#64091—21no—
32C2×C3×#213C2211yescharacteristic, complemented
33C2×C3×#213C2211yescharacteristic, complemented
34C2×C3×#213C2211yescharacteristic, complemented
35C3×#930C2211yescharacteristic, complemented
36C22×C3×C3⋊C8C2211yescharacteristic, complemented
37#63976—21no—
38#63926—24no—
39#63922—21no—
40#63916C2211yescharacteristic, complemented
41#63914C2211yescharacteristic, complemented
42#63898C2211yescharacteristic, complemented
43#63885—21no—
44C2×#3714—24no—
45C2×#3714C2211yescharacteristic
46C2×#3714C2211yescharacteristic, complemented
47C2×#3714C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3714C2211yescharacteristic, complemented
51C2×#3710C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic, complemented
53C3×#830C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, complemented
57C3×#807C2211yescharacteristic, complemented
58#63572C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62#63553C2211yescharacteristic, complemented
63D4×#67—31no—
64C22×#213—31no—
65C2×D3×D8—31no—
66C2×D3×D8—31no—
67C22×D24—31no—
68#5609—31no—
69#5609—31no—
70#5609—31no—
71#5609—61no—
72C3×#466—31no—
73C3×#447—31no—
74#5156—31no—
75#5151—31no—
76#5151—31no—
77#5150—31no—
78C8×#67—31no—
79#5038D311yescharacteristic, complemented
80#5036—31no—
81#5036D311yescharacteristic, complemented
82#4883—31no—
83#4872—31no—
84#4786—31no—
85#4786—31no—
86#4786—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×D4—21no—
99C2×C32×D4C2311yescharacteristic
100C22×C32×C4C2311yescharacteristic
101C2×#638—21no—
102C2×#638—21no—
103C2×#638—21no—
104C2×#638D411yescharacteristic
105D4×C3⋊D3—22no—
106D4×C3⋊D3—41no—
107D4×C3⋊D3—44no—
108C2×C4⋊(C3⋊D3)—22no—
109C2×C4⋊(C3⋊D3)—21no—
110C2×C4⋊(C3⋊D3)—21no—
111C2×C4⋊(C3⋊D3)—41no—
112C2×C4⋊(C3⋊D3)C2311yescharacteristic
113C2×C4⋊(C3⋊D3)C2311yescharacteristic
114C2×C4×C3⋊D3—21no—
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—
131C32×C4⋊C4C2311yescharacteristic
132C32×C22⋊C4—21no—
133#3757D411yescharacteristic
134#3752—21no—
135#3752—21no—
136#3752D411yescharacteristic
137#3750D411yescharacteristic
138C4×C3⋊Dic3C2311yescharacteristic
139C3×#213—22no—
140C3×#213—22no—
141C3×#213—41no—
142C3×(C2×D3)⋊C4—21no—
143C3×C4⋊Dic3C2311yescharacteristic
144C2×C3×C3⋊C8—22no—
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148C2×C3×C3⋊C8C2311yescharacteristic
149(C2×D3)⋊Dic3—21no—
150(C2×D3)⋊Dic3—21no—
151#3714—22no—
152#3714—22no—
153#3714—22no—
154#3714—22no—
155#3714—41no—
156#3714D414yescomplemented
157#3710—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—61no—
166C2×D3×D4—61no—
167C2×D3×D4—61no—
168C2×D3×D4—61no—
169C2×D3×D4—62no—
170C22×D12—31no—
171C22×D12—31no—
172C22×D12—61no—
173C22×D12C2×D311yescharacteristic, complemented
174C2×C3×D8—31no—
175C2×C3×D8—31no—
176C2×C3×D8—31no—
177C22×C3×C8—31no—
178C3×#121—21no—
179C3×#121—31no—
180C3×#121C2×D311yescharacteristic, complemented
181C3×#121C2×D311yescharacteristic, complemented
182#953—61no—
183#940—31no—
184#940—31no—
185#940—31no—
186#940—31no—
187#940—61no—
188#939—61no—
189#938—31no—
190#937—61no—
191#937—61no—
192#937—61no—
193#937—61no—
194#937—62no—
195D4×Dic3—31no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—64no—
203C2×#213C2×D311yescharacteristic, complemented
204C2×#213C2×D311yescharacteristic, complemented
205C2×#213C2×D311yescharacteristic, complemented
206#930C2×D311yescharacteristic, complemented
207C4×#67—31no—
208C4×#67—31no—
209C4×#67—61no—
210C22×C3⋊C8C2×D311yescharacteristic, complemented
211D3×D8—64no—
212D3×D8—64no—
213C2×D24—31no—
214C2×D24—31no—
215C2×D24—31no—
216C2×D24—31no—
217C2×D24—31no—
218C2×D24—31no—
219C2×D24—64no—
220C2×D3×C8—31no—
221C2×D3×C8—31no—
222#895—31no—
223#895—31no—
224#895—31no—
225#895—61no—
226#893—31no—
227#893—31no—
228#893—31no—
229#893—61no—
230#884—61no—
231#884—61no—
232#884—61no—
233#884—62no—
234#882—61no—
235#882—61no—
236#882—61no—
237#882—62no—
238C3×#107—31no—
239C3×#102—31no—
240C3×#102—31no—
241C3×#102—31no—
242C3×#102—31no—
243C3×C22⋊C8—31no—
244#832C2×D311yescharacteristic, complemented
245#830C2×D311yescharacteristic, complemented
246#821—31no—
247#821—31no—
248(C2×D3)⋊C8—31no—
249(C2×D3)⋊C8—31no—
250Dic3⋊C8—31no—
251Dic3⋊C8—31no—
252C8×Dic3—31no—
253C8×Dic3—31no—
254#809—31no—
255#809—31no—
256#809C2×D311yescharacteristic, complemented
257#809C2×D311yescharacteristic, complemented
258#809C2×D311yescharacteristic, complemented
259#807C2×D311yescharacteristic, complemented
260C23×C32—21no—
261C23×C32C2×D411yescharacteristic
262C22×C3⋊D3—21no—
263C22×C3⋊D3—21no—
264C22×C3⋊D3—42no—
265C22×C3⋊D3—42no—
266C22×C3⋊D3—42no—
267C22×C3⋊D3—42no—
268C22×C3⋊D3—81no—
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—42no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
285C2×C32×C4—21no—
286C2×C32×C4C2×D411yescharacteristic
287C2×C32×C4C2411yescharacteristic
288#638—42no—
289#638—42no—
290#638—81no—
291#638D814yescomplemented
292C2×C3⋊Dic3C2×D411yescharacteristic
293C2×C3⋊Dic3C2×D411yescharacteristic
294C2×C3⋊Dic3C2×D411yescharacteristic
295C4⋊(C3⋊D3)—21no—
296C4⋊(C3⋊D3)—21no—
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)—42no—
299C4⋊(C3⋊D3)—42no—
300C4⋊(C3⋊D3)C2×D412yescomplemented
301C4×C3⋊D3—21no—
302C4×C3⋊D3—21no—
303C4×C3⋊D3—42no—
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—91no—
323C22×D8—91no—
324D42—91no—
325D42—91no—
326#493—91no—
327#466—31no—
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—61no—
338C23×D3—21no—
339C23×D3—61no—
340C23×D3—61no—
341C23×D3—61no—
342C23×D3—61no—
343C23×D3—62no—
344C23×D3—62no—
345C23×D3—61no—
346C23×D3—61no—
347C2×C3×D4—22no—
348C2×C3×D4—21no—
349C2×C3×D4—21no—
350C2×C3×D4—21no—
351C2×C3×D4—31no—
352C2×C3×D4—31no—
353C2×C3×D4—31no—
354C2×C3×D4—62no—
355C2×C3×D4—61no—
356C2×C3×D4—61no—
357C2×C3×D4—121no—
358C2×C3×D4C22×D311yescharacteristic
359C2×C3×D4C22×D311yescharacteristic
360C22×C3×C4—21no—
361C22×C3×C4C22×D311yescharacteristic
362C22×C3×C4C22×D311yescharacteristic
363C2×#67—21no—
364C2×#67—31no—
365C2×#67—31no—
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—61no—
376C2×#67—61no—
377C2×#67—61no—
378C2×#67—61no—
379C2×#67—61no—
380C2×#67—62no—
381C2×#67—62no—
382C2×#67—62no—
383C2×#67—124no—
384C22×Dic3—61no—
385D3×D4—62no—
386D3×D4—62no—
387D3×D4—62no—
388D3×D4—62no—
389D3×D4—122no—
390D3×D4—121no—
391D3×D4—121no—
392D3×D4—121no—
393D3×D4—121no—
394D3×D4—122no—
395D3×D4—124no—
396D3×D4—124no—
397D3×D4—124no—
398D3×D4—128no—
399C2×D12—22no—
400C2×D12—21no—
401C2×D12—31no—
402C2×D12—31no—
403C2×D12—31no—
404C2×D12—31no—
405C2×D12—41no—
406C2×D12—61no—
407C2×D12—61no—
408C2×D12—62no—
409C2×D12—62no—
410C2×D12—61no—
411C2×D12—61no—
412C2×D12—62no—
413C2×D12—62no—
414C2×D12—61no—
415C2×D12—61no—
416C2×D12—61no—
417C2×D12—122no—
418C2×D12—121no—
419C2×D12—121no—
420C2×D12—122no—
421C2×D12C22×D311yescharacteristic
422C2×D12C22×D311yescharacteristic
423C2×D12C22×D311yescharacteristic
424C2×C4×D3—31no—
425C2×C4×D3—31no—
426C2×C4×D3—61no—
427C2×C4×D3—61no—
428C2×C4×D3—61no—
429C2×C4×D3—61no—
430C2×C4×D3—62no—
431C3×D8—62no—
432C3×D8—62no—
433C3×D8—121no—
434C2×C3×C8—31no—
435C2×C3×C8—31no—
436C2×C3×C8—31no—
437C2×C3×C8—31no—
438C2×C3×C8—62no—
439C3×C4⋊C4—21no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4C22×D311yescharacteristic
442C3×C4⋊C4C22×D311yescharacteristic
443C3×C22⋊C4—22no—
444C3×C22⋊C4—21no—
445C3×C22⋊C4—21no—
446C3×C22⋊C4—61no—
447#217—31no—
448#217—31no—
449#217—61no—
450#217—61no—
451#217—61no—
452#213—22no—
453#213—22no—
454#213—34no—
455#213—41no—
456#213—62no—
457#213—62no—
458#213—62no—
459#213—62no—
460#213—121no—
461(C2×D3)⋊C4—21no—
462(C2×D3)⋊C4—31no—
463(C2×D3)⋊C4—31no—
464(C2×D3)⋊C4—61no—
465(C2×D3)⋊C4—61no—
466(C2×D3)⋊C4—61no—
467(C2×D3)⋊C4—61no—
468(C2×D3)⋊C4—61no—
469(C2×D3)⋊C4—61no—
470(C2×D3)⋊C4—61no—
471(C2×D3)⋊C4—62no—
472(C2×D3)⋊C4—62no—
473C4⋊Dic3C22×D311yescharacteristic
474Dic3⋊C4—31no—
475Dic3⋊C4—31no—
476Dic3⋊C4—61no—
477C4×Dic3—31no—
478C4×Dic3—31no—
479C4×Dic3—61no—
480C2×C3⋊C8—22no—
481C2×C3⋊C8C22×D311yescharacteristic
482C2×C3⋊C8C22×D311yescharacteristic
483C2×C3⋊C8C22×D311yescharacteristic
484C2×C3⋊C8C22×D311yescharacteristic
485D24—34no—
486D24—62no—
487D24—62no—
488D24—62no—
489D24—62no—
490D24—121no—
491D3×C8—62no—
492D3×C8—62no—
493C22×C32—21no—
494C22×C32—21no—
495C22×C32—41no—
496C22×C32—41no—
497C22×C32—41no—
498C22×C32C2×D812yescomplemented
499C22×C32C22×D411yescharacteristic
500C2×C3⋊D3—22no—
501C2×C3⋊D3—21no—
502C2×C3⋊D3—21no—
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⋊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×C4—41no—
524C32×C4C22×D411yescharacteristic
525C32×C4H(5,𝔽2)11yescharacteristic
526C3⋊Dic3—21no—
527C3⋊Dic3—21no—
528C3⋊Dic3C2×D812yescomplemented
529C3×Dic3—41no—
530C22×D4—31no—
531C22×D4—91no—
532C22×D4—91no—
533C22×D4—91no—
534C22×D4—181no—
535C22×D4—181no—
536C2×D8—31no—
537C2×D8—31no—
538C2×D8—31no—
539C2×D8—91no—
540C2×D8—91no—
541C2×D8—91no—
542C2×D8—91no—
543C2×D8—91no—
544C2×D8—91no—
545C2×D8—184no—
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—181no—
555#121—181no—
556#121D3211yescharacteristic, complemented
557#120—181no—
558#120—181no—
559#120—181no—
560#120—181no—
561C4×D4—91no—
562C4×D4—91no—
563C4×D4—91no—
564#107—31no—
565C4⋊C8—91no—
566#102—31no—
567#102—31no—
568#102—31no—
569#102—31no—
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—21no—
579C23×C3—61no—
580C23×C3—61no—
581C23×C3—61no—
582C23×C3—122no—
583C23×C3—122no—
584C23×C3—241no—
585C23×C3D3×D411yescharacteristic
586C23×C3D3×D411yescharacteristic
587C22×D3—21no—
588C22×D3—21no—
589C22×D3—21no—
590C22×D3—31no—
591C22×D3—31no—
592C22×D3—42no—
593C22×D3—42no—
594C22×D3—61no—
595C22×D3—62no—
596C22×D3—61no—
597C22×D3—61no—
598C22×D3—62no—
599C22×D3—61no—
600C22×D3—61no—
601C22×D3—81no—
602C22×D3—122no—
603C22×D3—122no—
604C22×D3—122no—
605C22×D3—122no—
606C22×D3—122no—
607C22×D3—122no—
608C22×D3—122no—
609C22×D3—122no—
610C22×D3—122no—
611C22×D3—122no—
612C22×D3—124no—
613C22×D3—124no—
614C22×D3—124no—
615C22×D3—124no—
616C22×D3—122no—
617C22×D3—122no—
618C22×D3—241no—
619C22×D3—241no—
620C22×D3—241no—
621C22×D3—241no—
622C22×D3—241no—
623C22×D3—241no—
624C22×D3—242no—
625C22×D3—242no—
626C3×D4—21no—
627C3×D4—21no—
628C3×D4—21no—
629C3×D4—21no—
630C3×D4—32no—
631C3×D4—41no—
632C3×D4—41no—
633C3×D4—44no—
634C3×D4—42no—
635C3×D4—42no—
636C3×D4—61no—
637C3×D4—61no—
638C3×D4—61no—
639C3×D4—61no—
640C3×D4—61no—
641C3×D4—122no—
642C3×D4—122no—
643C2×C3×C4—21no—
644C2×C3×C4—21no—
645C2×C3×C4—21no—
646C2×C3×C4—21no—
647C2×C3×C4—22no—
648C2×C3×C4—21no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—41no—
653C2×C3×C4—41no—
654C2×C3×C4—61no—
655C2×C3×C4D3×D411yescharacteristic
656C2×C3×C4D3×D411yescharacteristic
657C2×C3×C4C23×D311yescharacteristic
658C2×C3×C4C23×D311yescharacteristic
659#67—34no—
660#67—34no—
661#67—42no—
662#67—64no—
663#67—122no—
664#67—122no—
665#67—122no—
666#67—122no—
667#67—122no—
668#67—122no—
669#67—122no—
670#67—122no—
671#67—122no—
672#67—124no—
673#67—124no—
674#67—241no—
675#67—241no—
676#67—241no—
677#67—241no—
678#67—242no—
679C2×Dic3—21no—
680C2×Dic3—31no—
681C2×Dic3—31no—
682C2×Dic3—31no—
683C2×Dic3—31no—
684C2×Dic3—31no—
685C2×Dic3—31no—
686C2×Dic3—61no—
687C2×Dic3—61no—
688C2×Dic3—61no—
689C2×Dic3—122no—
690D12—21no—
691D12—21no—
692D12—21no—
693D12—21no—
694D12—21no—
695D12—32no—
696D12—32no—
697D12—42no—
698D12—62no—
699D12—62no—
700D12—61no—
701D12—61no—
702D12—61no—
703D12—61no—
704D12—61no—
705D12—61no—
706D12—121no—
707D12—121no—
708D12—122no—
709D12—122no—
710D12—122no—
711D12—122no—
712D12—124no—
713D12—124no—
714D12—122no—
715D12D3×D412yescomplemented
716C4×D3—61no—
717C4×D3—61no—
718C4×D3—61no—
719C4×D3—61no—
720C4×D3—121no—
721C4×D3—121no—
722C4×D3—122no—
723C4×D3—122no—
724C4×D3—122no—
725C4×D3—124no—
726C3×C8—32no—
727C3×C8—61no—
728C3×C8—61no—
729C3×C8—61no—
730C3⋊C8—21no—
731C3⋊C8—21no—
732C3⋊C8—21no—
733C3⋊C8D3×D412yescomplemented
734C2×C32—22no—
735C2×C32—81no—
736C2×C32D4211yescharacteristic
737C2×C32C22×D811yescharacteristic
738C2×C32#57611yescharacteristic
739C3⋊D3—22no—
740C3⋊D3—42no—
741C3⋊D3—81no—
742C3×D3—42no—
743C3×D3—81no—
744C3×D3—81no—
745C24—61no—
746C24—181no—
747C24—181no—
748C24—181no—
749C2×D4—21no—
750C2×D4—31no—
751C2×D4—31no—
752C2×D4—31no—
753C2×D4—62no—
754C2×D4—61no—
755C2×D4—61no—
756C2×D4—91no—
757C2×D4—91no—
758C2×D4—91no—
759C2×D4—121no—
760C2×D4—182no—
761C2×D4—181no—
762C2×D4—181no—
763C2×D4—181no—
764C2×D4—181no—
765C2×D4—181no—
766C2×D4—181no—
767C2×D4—181no—
768C2×D4—181no—
769C2×D4—182no—
770C2×D4—182no—
771C2×D4—181no—
772C2×D4—361no—
773C2×D4—361no—
774C2×D4—361no—
775C2×D4—364no—
776C2×D4—364no—
777C2×D4C2×D3211yescharacteristic
778C22×C4—91no—
779C22×C4—181no—
780C22×C4—181no—
781C22×C4C2×D3211yescharacteristic
782D8—62no—
783D8—62no—
784D8—94no—
785D8—121no—
786D8—182no—
787D8—182no—
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⋊C4C2×D3211yescharacteristic
800C22⋊C4—21no—
801C22⋊C4—61no—
802C22⋊C4—91no—
803C22⋊C4—91no—
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—21no—
814C22×C3—22no—
815C22×C3—41no—
816C22×C3—41no—
817C22×C3—42no—
818C22×C3—42no—
819C22×C3—42no—
820C22×C3—41no—
821C22×C3—41no—
822C22×C3—41no—
823C22×C3—41no—
824C22×C3—41no—
825C22×C3—41no—
826C22×C3—62no—
827C22×C3—121no—
828C22×C3—121no—
829C22×C3—121no—
830C22×C3—121no—
831C22×C3—121no—
832C22×C3—121no—
833C22×C3—121no—
834C22×C3—121no—
835C22×C3—244no—
836C22×C3D3×D812yescomplemented
837C22×C3D3×D812yescomplemented
838C22×C3C2×D3×D411yescharacteristic
839C22×C3C2×D3×D411yescharacteristic
840C2×D3—22no—
841C2×D3—32no—
842C2×D3—32no—
843C2×D3—41no—
844C2×D3—41no—
845C2×D3—41no—
846C2×D3—41no—
847C2×D3—41no—
848C2×D3—41no—
849C2×D3—41no—
850C2×D3—41no—
851C2×D3—62no—
852C2×D3—61no—
853C2×D3—61no—
854C2×D3—61no—
855C2×D3—61no—
856C2×D3—64no—
857C2×D3—62no—
858C2×D3—62no—
859C2×D3—84no—
860C2×D3—121no—
861C2×D3—121no—
862C2×D3—122no—
863C2×D3—122no—
864C2×D3—121no—
865C2×D3—121no—
866C2×D3—121no—
867C2×D3—121no—
868C2×D3—122no—
869C2×D3—122no—
870C2×D3—122no—
871C2×D3—121no—
872C2×D3—121no—
873C2×D3—121no—
874C2×D3—121no—
875C2×D3—121no—
876C2×D3—121no—
877C2×D3—244no—
878C2×D3—244no—
879C2×D3—244no—
880C2×D3—244no—
881C2×D3—248no—
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—42no—
891C3×C4—41no—
892C3×C4—41no—
893C3×C4—121no—
894C3×C4C2×D3×D411yescharacteristic
895C3×C4C2×D3×D411yescharacteristic
896C3×C4#100411yescharacteristic
897C3×C4#100911yescharacteristic
898Dic3—32no—
899Dic3—32no—
900Dic3—41no—
901Dic3—62no—
902Dic3—61no—
903Dic3—61no—
904Dic3—61no—
905Dic3—61no—
906Dic3—121no—
907Dic3—121no—
908C32D4×D811yescharacteristic, complemented, Sylow
909C23—21no—
910C23—61no—
911C23—61no—
912C23—61no—
913C23—91no—
914C23—122no—
915C23—122no—
916C23—181no—
917C23—181no—
918C23—241no—
919C23—362no—
920C23—362no—
921C23—362no—
922C23—362no—
923C23—362no—
924C23—362no—
925C23—721no—
926C23—721no—
927C23—721no—
928C23#381111yescharacteristic
929D4—21no—
930D4—21no—
931D4—32no—
932D4—42no—
933D4—61no—
934D4—61no—
935D4—61no—
936D4—61no—
937D4—61no—
938D4—94no—
939D4—92no—
940D4—122no—
941D4—122no—
942D4—181no—
943D4—181no—
944D4—181no—
945D4—362no—
946D4—362no—
947D4—362no—
948D4—362no—
949D4—362no—
950D4—362no—
951D4—362no—
952D4—721no—
953D4—721no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—21no—
957C2×C4—61no—
958C2×C4—91no—
959C2×C4—91no—
960C2×C4—91no—
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—82no—
978C2×C3—81no—
979C2×C3—81no—
980C2×C3—122no—
981C2×C3—241no—
982C2×C3—241no—
983C2×C3#559011yescharacteristic
984C2×C3#560911yescharacteristic
985C2×C3C2×D3×D811yescharacteristic
986C2×C3C2×D3×D811yescharacteristic
987C2×C3#576911yescharacteristic
988C2×C3#577411yescharacteristic
989D3—42no—
990D3—62no—
991D3—62no—
992D3—81no—
993D3—81no—
994D3—122no—
995D3—124no—
996D3—122no—
997D3—122no—
998D3—242no—
999D3—241no—
1000D3—241no—
1001C22—21no—
1002C22—21no—
1003C22—41no—
1004C22—41no—
1005C22—41no—
1006C22—62no—
1007C22—92no—
1008C22—121no—
1009C22—121no—
1010C22—121no—
1011C22—121no—
1012C22—121no—
1013C22—121no—
1014C22—121no—
1015C22—121no—
1016C22—181no—
1017C22—181no—
1018C22—182no—
1019C22—244no—
1020C22—361no—
1021C22—361no—
1022C22—361no—
1023C22—361no—
1024C22—361no—
1025C22—724no—
1026C22—724no—
1027C22—724no—
1028C22#6392612yescomplemented
1029C22C2×#381111yescharacteristic
1030C4—21no—
1031C4—41no—
1032C4—92no—
1033C4—121no—
1034C4—181no—
1035C4—181no—
1036C4D32×D411yescharacteristic
1037C4#6431411yescharacteristic
1038C3—21no—
1039C3#8002411yescharacteristic, complemented
1040C3#8072911yescharacteristic, complemented
1041C2—22no—
1042C2—81no—
1043C2—122no—
1044C2—182no—
1045C2—241no—
1046C2—241no—
1047C2—362no—
1048C2—721no—
1049C2C2×#6392611yescharacteristic
1050C2#1059529211yescharacteristic
1051C2#1059546111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32D4×D8
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
1. #10596080C2semidirect
2. C2×#63926C2semidirect
3. #10595069C2semidirect
4. C22×#3714C2semidirect
5. C3×#5038C2semidirect
6. C3×#5036C2semidirect
7. #10591484C2semidirect
8. #10591456C2semidirect
9. #10591433C2semidirect
10. #10591168C2semidirect
11. #10591148C2semidirect
12. #10590598C2semidirect
13. #10590551C2semidirect
14. #10590509C2semidirect
15. #10590459C2semidirect
19. C2×D4×C3⋊D3C22semidirect
20. C22×C4⋊(C3⋊D3)C22semidirect
21. C22×C3×D12C22semidirect
23. C2×#3802C22semidirect
24. C32×#121C22semidirect
25. #64149C22semidirect
28. #64104C22semidirect
29. #64102C22semidirect
32. C2×C3×#213C22semidirect
33. C2×C3×#213C22semidirect
34. C2×C3×#213C22semidirect
35. C3×#930C22semidirect
36. C22×C3×C3⋊C8C22semidirect
40. #63916C22semidirect
41. #63914C22semidirect
42. #63898C22semidirect
46. C2×#3714C22semidirect
47. C2×#3714C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
50. C2×#3714C22semidirect
51. C2×#3710C22semidirect
52. C3×#832C22semidirect
53. C3×#830C22semidirect
54. C3×#809C22semidirect
55. C3×#809C22semidirect
56. C3×#809C22semidirect
57. C3×#807C22semidirect
58. #63572C22semidirect
59. #63564C22semidirect
60. #63564C22semidirect
61. #63557C22semidirect
62. #63553C22semidirect
79. #5038D3semidirect
81. #5036D3semidirect
156. #3714D4semidirect
173. C22×D12C2×D3semidirect
180. C3×#121C2×D3semidirect
181. C3×#121C2×D3semidirect
203. C2×#213C2×D3semidirect
204. C2×#213C2×D3semidirect
205. C2×#213C2×D3semidirect
206. #930C2×D3semidirect
210. C22×C3⋊C8C2×D3semidirect
244. #832C2×D3semidirect
245. #830C2×D3semidirect
256. #809C2×D3semidirect
257. #809C2×D3semidirect
258. #809C2×D3semidirect
259. #807C2×D3semidirect
291. #638D8semidirect
300. C4⋊(C3⋊D3)C2×D4semidirect
312. C3×D12C2×D4semidirect
321. C3×C3⋊C8C2×D4semidirect
498. C22×C32C2×D8semidirect
510. C2×C3⋊D3C2×D8semidirect
528. C3⋊Dic3C2×D8semidirect
556. #121D32semidirect
715. D12D3×D4semidirect
733. C3⋊C8D3×D4semidirect
836. C22×C3D3×D8semidirect
837. C22×C3D3×D8semidirect
908. C32D4×D8semidirect
1028. C22#63926semidirect
1039. C3#80024semidirect
1040. C3#80729semidirect

Maximal subgroups

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

subgroupindex
#105960802
C2×#639262
#105950692
C22×#37142
C3×#50382
C3×#50362
#105914842
#105914562
#105914332
#105911682
#105911482
#105905982
#105905512
#105905092
#105904592
#807293
#800243