Finite Group Databasebeta

← #11883837

Subgroups — #11883837

Order 1152.

1303 conjugacy classes of subgroups.

The subgroup lattice has 1003 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596083C211yesmaximal, characteristic, complemented
2C2×#63926C211yesmaximal, characteristic, complemented
3#10595069C211yesmaximal, characteristic, complemented
4C2×#63830C211yesmaximal, characteristic, complemented
5C3×#5039C211yesmaximal, characteristic, complemented
6C3×#5036C211yesmaximal, characteristic, complemented
7#10591485C211yesmaximal, characteristic, complemented
8#10591456C211yesmaximal, characteristic, complemented
9#10591434C211yesmaximal, characteristic, complemented
10#10591182C211yesmaximal, characteristic, complemented
11#10591149C211yesmaximal, characteristic, complemented
12#10590597C211yesmaximal, characteristic, complemented
13#10590551C211yesmaximal, characteristic, complemented
14#10590507C211yesmaximal, characteristic, complemented
15#10590462C211yesmaximal, characteristic, complemented
16#80881—31nomaximal
17#80012—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic, complemented
19C2×#3828C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic, complemented
21C2×D3×#67—21no—
22C2×#3802C2211yescharacteristic
23C32×#121C2211yescharacteristic, complemented
24#64147—21no—
25#64146—21no—
26#64145C2211yescharacteristic, complemented
27C4×#638C2211yescharacteristic
28#64106C2211yescharacteristic, complemented
29#64102C2211yescharacteristic, complemented
30#64092—21no—
31C22⋊C4×C3⋊D3—21no—
32C2×C3×#213C2211yescharacteristic
33C2×C3×#213C2211yescharacteristic, complemented
34C2×C3×#213C2211yescharacteristic, complemented
35C3×#930C2211yescharacteristic, complemented
36C2×C3×#208C2211yescharacteristic, complemented
37#63976—21no—
38#63926—24no—
39#63922—21no—
40#63916C2211yescharacteristic
41#63914C2211yescharacteristic, complemented
42#63898C2211yescharacteristic, complemented
43#63885—21no—
44#63830—24no—
45C2×#3716C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
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×#808C2211yescharacteristic, complemented
58#63572C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62#63555C2211yescharacteristic, complemented
63D4×#67—31no—
64C2×#932—31no—
65C2×D3×D8—31no—
66C2×D3×D8—31no—
67C2×#908—31no—
68#5612—31no—
69#5612—31no—
70#5612—61no—
71#5609—31no—
72C3×#469—31no—
73C3×#447—31no—
74#5156—31no—
75#5154—31no—
76#5154—31no—
77#5153—31no—
78#5127—31no—
79#5039D311yescharacteristic, complemented
80#5037—31no—
81#5036D311yescharacteristic, complemented
82#4869—31no—
83#4864—31no—
84#4787—31no—
85#4786—31no—
86#4786—31no—
87#4785—31no—
88#4778—31no—
89#4776—31no—
90#4776—31no—
91#4773—31no—
92#4734—31no—
93#4728—31no—
94C23×C3⋊D3—21no—
95C23×C3×D3—21no—
96C22×D32—21no—
97C2×C32×D4—21no—
98C2×C32×D4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C2×#638—21no—
101C2×#638—21no—
102C2×#638D411yescharacteristic
103D4×C3⋊D3—22no—
104D4×C3⋊D3—41no—
105#3828—22no—
106#3828—41no—
107C2×C4⋊(C3⋊D3)C2311yescharacteristic
108C2×C4×C3⋊D3—21no—
109C2×C4×C3⋊D3—21no—
110C2×C4×C3⋊D3C2311yescharacteristic
111C2×#634C2311yescharacteristic
112C2×C3×#67—21no—
113C2×C3×D12—22no—
114C2×C3×D12—21no—
115C2×C3×D12—41no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×D12C2311yescharacteristic
118C2×C3×D12C2311yescharacteristic
119D3×#67—44no—
120C2×#626—21no—
121C2×#625—21no—
122C2×#625—21no—
123C2×#625—21no—
124C2×D3×Dic3—21no—
125#3802—22no—
126#3802—41no—
127C32×C4⋊C4C2311yescharacteristic
128C32×C22⋊C4—21no—
129#3757—21no—
130#3757—21no—
131#3757D411yescharacteristic
132#3752—21no—
133#3752—21no—
134#3752D411yescharacteristic
135C4⋊(C3⋊Dic3)—21no—
136#3750D411yescharacteristic
137C4×C3⋊Dic3C2311yescharacteristic
138C3×#213—22no—
139C3×#213—22no—
140C3×#213—41no—
141C3×(C2×D3)⋊C4—21no—
142C3×C4⋊Dic3C2311yescharacteristic
143C3×#208—22no—
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150#3716—22no—
151#3716—22no—
152#3716—41no—
153#3714—22no—
154#3714—22no—
155#3714D414yescomplemented
156#3710—22no—
157#3264—91noSylow
158C22×C3×D4—31no—
159C22×#67—61no—
160C2×D3×D4—31no—
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—61no—
165C2×D3×D4—61no—
166C2×#235—31no—
167C2×#235—31no—
168C2×#235—61no—
169C22×D12C2×D311yescharacteristic, complemented
170C2×C3×D8—31no—
171C2×C3×D8—31no—
172C2×C3×D8—31no—
173C2×C3×M16—31no—
174C3×#121—21no—
175C3×#121—31no—
176C3×#121C2×D311yescharacteristic, complemented
177C3×#121C2×D311yescharacteristic, complemented
178#953—61no—
179#940—31no—
180#940—31no—
181#939—61no—
182#938—31no—
183#938—61no—
184#938—61no—
185#938—62no—
186#937—61no—
187#937—61no—
188#937—61no—
189#937—61no—
190#937—62no—
191#936—31no—
192#936—31no—
193#936—61no—
194D4×Dic3—31no—
195C2×#214—31no—
196C2×#214—31no—
197C2×#214—31no—
198#932—64no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213C2×D311yescharacteristic
203C2×#213C2×D311yescharacteristic, complemented
204C2×#213C2×D311yescharacteristic, complemented
205#930C2×D311yescharacteristic, complemented
206C4×#67—31no—
207C4×#67—31no—
208C4×#67—61no—
209C2×#208C2×D311yescharacteristic, complemented
210D3×D8—64no—
211D3×D8—64no—
212#908—64no—
213C2×D24—31no—
214C2×D24—31no—
215C2×D24—31no—
216C2×#204—31no—
217C2×#204—31no—
218C2×#204—31no—
219C2×D3×C8—31no—
220C2×D3×C8—31no—
221#897—31no—
222#897—31no—
223#897—61no—
224#895—31no—
225#893—31no—
226#893—31no—
227#893—31no—
228#893—61no—
229#884—61no—
230#883—61no—
231#883—61no—
232#883—62no—
233#882—61no—
234D3×C22⋊C4—61no—
235D3×C22⋊C4—61no—
236D3×C22⋊C4—62no—
237C3×#106—31no—
238C3×#102—31no—
239C3×#102—31no—
240C3×#102—31no—
241C3×#102—31no—
242C3×C22⋊C8—31no—
243#832C2×D311yescharacteristic, complemented
244#830C2×D311yescharacteristic, complemented
245#821—31no—
246(C2×D3)⋊C8—31no—
247(C2×D3)⋊C8—31no—
248#816—31no—
249#815—31no—
250#815—31no—
251Dic3⋊C8—31no—
252Dic3⋊C8—31no—
253#810—31no—
254#809—31no—
255#809C2×D311yescharacteristic, complemented
256#809C2×D311yescharacteristic, complemented
257#809C2×D311yescharacteristic, complemented
258#808C2×D311yescharacteristic, complemented
259C23×C32—21no—
260C23×C32C2×D411yescharacteristic
261C22×C3⋊D3—21no—
262C22×C3⋊D3—42no—
263C22×C3⋊D3—42no—
264C22×C3⋊D3—81no—
265C22×C3⋊D3C2×D411yescharacteristic
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—21no—
269C22×C3×D3—42no—
270C22×C3×D3—42no—
271C22×C3×D3—81no—
272C2×D32—42no—
273C2×D32—42no—
274C2×D32—81no—
275C32×D4—21no—
276C32×D4—21no—
277C32×D4—81no—
278C2×C32×C4—21no—
279C2×C32×C4—21no—
280C2×C32×C4—21no—
281C2×C32×C4C2×D411yescharacteristic
282C2×C32×C4C2411yescharacteristic
283#638—22no—
284#638—42no—
285#638—42no—
286C2×C3⋊Dic3—21no—
287C2×C3⋊Dic3C2×D411yescharacteristic
288C2×C3⋊Dic3C2×D411yescharacteristic
289C2×C3⋊Dic3C2×D411yescharacteristic
290C4⋊(C3⋊D3)—21no—
291C4⋊(C3⋊D3)C2×D412yescomplemented
292C4×C3⋊D3—21no—
293C4×C3⋊D3—21no—
294C4×C3⋊D3—42no—
295C4×C3⋊D3—81no—
296#634—21no—
297#634—21no—
298C3×#67—42no—
299C2×C3×Dic3—21no—
300C3×D12—21no—
301C3×D12—21no—
302C3×D12—21no—
303C3×D12—21no—
304C3×D12—21no—
305C3×D12—42no—
306C3×D12C2×D412yes—
307#626—42no—
308#625—42no—
309#625—42no—
310#625—81no—
311D3×Dic3—42no—
312C3×C3⋊C8—21no—
313C3×C3⋊C8—21no—
314C3×C3⋊C8—21no—
315C3×C3⋊C8C2×D412yescomplemented
316C2×AGL(1,ℤ/8)—91no—
317C22×D8—91no—
318#546—91no—
319D42—91no—
320#496—91no—
321#469—31no—
322#465—91no—
323#463—91no—
324#459—91no—
325#450—91no—
326#449—91no—
327#447—31no—
328#447—91no—
329#442—91no—
330#435—91no—
331C24×C3—61no—
332C23×D3—21no—
333C23×D3—61no—
334C23×D3—61no—
335C23×D3—61no—
336C23×D3—61no—
337C23×D3—62no—
338C2×C3×D4—22no—
339C2×C3×D4—21no—
340C2×C3×D4—21no—
341C2×C3×D4—21no—
342C2×C3×D4—31no—
343C2×C3×D4—31no—
344C2×C3×D4—31no—
345C2×C3×D4—62no—
346C2×C3×D4—61no—
347C2×C3×D4—61no—
348C2×C3×D4—121no—
349C2×C3×D4C22×D311yescharacteristic
350C2×C3×D4C22×D311yescharacteristic
351C22×C3×C4—21no—
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C2×#67—21no—
355C2×#67—31no—
356C2×#67—31no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—61no—
363C2×#67—61no—
364C2×#67—61no—
365C2×#67—61no—
366C2×#67—61no—
367C2×#67—62no—
368C2×#67—62no—
369C2×#67—61no—
370C2×#67—61no—
371C2×#67—124no—
372C22×Dic3—61no—
373D3×D4—62no—
374D3×D4—62no—
375D3×D4—62no—
376D3×D4—62no—
377D3×D4—122no—
378D3×D4—121no—
379D3×D4—121no—
380D3×D4—121no—
381D3×D4—121no—
382D3×D4—122no—
383D3×D4—124no—
384#235—62no—
385#235—62no—
386#235—122no—
387#235—121no—
388#235—121no—
389#235—122no—
390C2×D12—22no—
391C2×D12—21no—
392C2×D12—31no—
393C2×D12—31no—
394C2×D12—41no—
395C2×D12—61no—
396C2×D12—61no—
397C2×D12C22×D311yescharacteristic
398C2×D12C22×D311yescharacteristic
399C2×D12C22×D311yescharacteristic
400C2×C4×D3—31no—
401C2×C4×D3—31no—
402C2×C4×D3—61no—
403C2×C4×D3—61no—
404C2×C4×D3—62no—
405C2×C4×D3—61no—
406C2×C4×D3—61no—
407C2×C4×D3—61no—
408C2×C4×D3—61no—
409C2×C4×D3—62no—
410C2×Dic6—31no—
411C2×Dic6—31no—
412C2×Dic6—61no—
413C3×D8—62no—
414C3×D8—62no—
415C3×D8—121no—
416C3×M16—62no—
417C2×C3×C8—31no—
418C2×C3×C8—31no—
419C2×C3×C8—31no—
420C2×C3×C8—31no—
421C3×C4⋊C4—21no—
422C3×C4⋊C4—31no—
423C3×C4⋊C4C22×D311yescharacteristic
424C3×C4⋊C4C22×D311yescharacteristic
425C3×C22⋊C4—22no—
426C3×C22⋊C4—21no—
427C3×C22⋊C4—21no—
428C3×C22⋊C4—61no—
429#217—31no—
430#217—31no—
431#217—61no—
432#217—61no—
433#217—61no—
434#217—61no—
435#217—61no—
436#217—61no—
437#217—61no—
438#217—62no—
439#217—62no—
440#214—62no—
441#214—62no—
442#214—121no—
443#213—22no—
444#213—22no—
445#213—34no—
446#213—41no—
447#213—62no—
448#213—62no—
449(C2×D3)⋊C4—21no—
450(C2×D3)⋊C4—31no—
451(C2×D3)⋊C4—31no—
452(C2×D3)⋊C4—61no—
453(C2×D3)⋊C4—61no—
454(C2×D3)⋊C4—61no—
455(C2×D3)⋊C4—61no—
456(C2×D3)⋊C4—61no—
457(C2×D3)⋊C4—61no—
458(C2×D3)⋊C4—61no—
459(C2×D3)⋊C4—62no—
460(C2×D3)⋊C4—62no—
461C4⋊Dic3—61no—
462C4⋊Dic3—61no—
463C4⋊Dic3—62no—
464C4⋊Dic3C22×D311yescharacteristic
465Dic3⋊C4—31no—
466Dic3⋊C4—31no—
467Dic3⋊C4—61no—
468C4×Dic3—31no—
469C4×Dic3—31no—
470C4×Dic3—61no—
471#208—22no—
472C2×C3⋊C8C22×D311yescharacteristic
473C2×C3⋊C8C22×D311yescharacteristic
474C2×C3⋊C8C22×D311yescharacteristic
475C2×C3⋊C8C22×D311yescharacteristic
476D24—34no—
477D24—62no—
478D24—62no—
479#204—62no—
480#204—62no—
481#204—121no—
482D3×C8—62no—
483D3×C8—62no—
484C22×C32—21no—
485C22×C32—21no—
486C22×C32—21no—
487C22×C32—41no—
488C22×C32—41no—
489C22×C32—41no—
490C22×C32C22×D411yescharacteristic
491C2×C3⋊D3—22no—
492C2×C3⋊D3—21no—
493C2×C3⋊D3—21no—
494C2×C3⋊D3—41no—
495C2×C3⋊D3—41no—
496C2×C3⋊D3—84no—
497C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
498C2×C3×D3—22no—
499C2×C3×D3—41no—
500C2×C3×D3—41no—
501C2×C3×D3—41no—
502C2×C3×D3—41no—
503C2×C3×D3—41no—
504C2×C3×D3—41no—
505C2×C3×D3—41no—
506C2×C3×D3—41no—
507C2×C3×D3—84no—
508D32—84no—
509C32×C4—21no—
510C32×C4—41no—
511C32×C4C22×D411yescharacteristic
512C32×C4H(5,𝔽2)11yescharacteristic
513C3⋊Dic3—21no—
514C3⋊Dic3—21no—
515C3⋊Dic3—21no—
516C3⋊Dic3—41no—
517C3×Dic3—41no—
518C2×#41—91no—
519C22×D4—31no—
520C22×D4—91no—
521C22×D4—91no—
522C22×D4—181no—
523AGL(1,ℤ/8)—184no—
524C2×SD16—91no—
525C2×SD16—91no—
526C2×SD16—91no—
527C2×D8—31no—
528C2×D8—31no—
529C2×D8—31no—
530C2×D8—91no—
531C2×D8—91no—
532C2×D8—91no—
533C2×D8—184no—
534C2×M16—31no—
535C22×C8—91no—
536#127—91no—
537#124—91no—
538#123—181no—
539C22⋊Q8—91no—
540#121—31no—
541#121—91no—
542#121—181no—
543#121—181no—
544#121D3211yescharacteristic, complemented
545#120—181no—
546#120—181no—
547#120—181no—
548C4×D4—91no—
549C4×D4—91no—
550C4×D4—91no—
551C2×C22⋊C4—181no—
552#106—31no—
553C4⋊C8—91no—
554#103—91no—
555#102—31no—
556#102—31no—
557#102—31no—
558#102—31no—
559#102—91no—
560C22⋊C8—31no—
561C22⋊C8—91no—
562#97—91no—
563C23×C3—22no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—61no—
568C23×C3—61no—
569C23×C3—61no—
570C23×C3—122no—
571C23×C3—122no—
572C23×C3—241no—
573C23×C3D3×D411yescharacteristic
574C23×C3D3×D411yescharacteristic
575C22×D3—21no—
576C22×D3—21no—
577C22×D3—21no—
578C22×D3—31no—
579C22×D3—31no—
580C22×D3—42no—
581C22×D3—42no—
582C22×D3—61no—
583C22×D3—62no—
584C22×D3—61no—
585C22×D3—61no—
586C22×D3—81no—
587C22×D3—122no—
588C22×D3—122no—
589C22×D3—122no—
590C22×D3—122no—
591C22×D3—122no—
592C22×D3—122no—
593C22×D3—122no—
594C22×D3—122no—
595C22×D3—124no—
596C22×D3—124no—
597C22×D3—241no—
598C22×D3—241no—
599C22×D3—241no—
600C22×D3—241no—
601C22×D3—242no—
602C3×D4—21no—
603C3×D4—21no—
604C3×D4—21no—
605C3×D4—21no—
606C3×D4—32no—
607C3×D4—41no—
608C3×D4—41no—
609C3×D4—61no—
610C3×D4—61no—
611C3×D4—61no—
612C3×D4—61no—
613C3×D4—61no—
614C3×D4—81no—
615C3×D4—81no—
616C3×D4—82no—
617C3×D4—122no—
618C3×D4—122no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—22no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—61no—
631C2×C3×C4D3×D411yescharacteristic
632C2×C3×C4D3×D411yescharacteristic
633C2×C3×C4C23×D311yescharacteristic
634C2×C3×C4C23×D311yescharacteristic
635#67—42no—
636#67—62no—
637#67—62no—
638#67—122no—
639#67—122no—
640#67—122no—
641#67—122no—
642#67—122no—
643#67—122no—
644#67—122no—
645#67—122no—
646#67—122no—
647#67—122no—
648#67—124no—
649#67—124no—
650#67—241no—
651#67—241no—
652C2×Dic3—21no—
653C2×Dic3—31no—
654C2×Dic3—31no—
655C2×Dic3—31no—
656C2×Dic3—31no—
657C2×Dic3—31no—
658C2×Dic3—31no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—62no—
663C2×Dic3—61no—
664C2×Dic3—61no—
665C2×Dic3—122no—
666D12—21no—
667D12—21no—
668D12—21no—
669D12—21no—
670D12—21no—
671D12—32no—
672D12—32no—
673D12—42no—
674D12—62no—
675D12—62no—
676D12—61no—
677D12—61no—
678D12—122no—
679D12D3×D412yes—
680C4×D3—61no—
681C4×D3—61no—
682C4×D3—61no—
683C4×D3—61no—
684C4×D3—121no—
685C4×D3—121no—
686C4×D3—122no—
687C4×D3—122no—
688C4×D3—122no—
689C4×D3—124no—
690C4×D3—241no—
691C4×D3—241no—
692C4×D3—242no—
693Dic6—61no—
694Dic6—61no—
695Dic6—61no—
696Dic6—61no—
697Dic6—121no—
698Dic6—121no—
699C3×C8—32no—
700C3×C8—61no—
701C3×C8—61no—
702C3×C8—61no—
703C3⋊C8—21no—
704C3⋊C8—21no—
705C3⋊C8—21no—
706C3⋊C8D3×D412yescomplemented
707C2×C32—41no—
708C2×C32—81no—
709C2×C32D4211yescharacteristic
710C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
711C2×C32#57611yescharacteristic
712C3⋊D3—22no—
713C3⋊D3—42no—
714C3×D3—42no—
715C3×D3—81no—
716C3×D3—81no—
717C24—61no—
718C24—181no—
719C24—181no—
720#41—182no—
721#41—361no—
722C2×Q8—91no—
723C2×D4—21no—
724C2×D4—31no—
725C2×D4—31no—
726C2×D4—31no—
727C2×D4—62no—
728C2×D4—61no—
729C2×D4—61no—
730C2×D4—91no—
731C2×D4—91no—
732C2×D4—121no—
733C2×D4—181no—
734C2×D4—181no—
735C2×D4—181no—
736C2×D4—181no—
737C2×D4—181no—
738C2×D4—182no—
739C2×D4—182no—
740C2×D4—181no—
741C2×D4—361no—
742C2×D4—361no—
743C2×D4—364no—
744C2×D4C2×D3211yescharacteristic
745C22×C4—91no—
746C22×C4—181no—
747C22×C4—181no—
748C22×C4—181no—
749C22×C4C2×D3211yescharacteristic
750SD16—182no—
751SD16—182no—
752SD16—361no—
753D8—62no—
754D8—62no—
755D8—94no—
756D8—121no—
757D8—182no—
758D8—182no—
759M16—62no—
760C2×C8—31no—
761C2×C8—31no—
762C2×C8—31no—
763C2×C8—31no—
764C2×C8—182no—
765C4⋊C4—31no—
766C4⋊C4—91no—
767C4⋊C4—181no—
768C4⋊C4C2×D3211yescharacteristic
769C22⋊C4—21no—
770C22⋊C4—61no—
771C22⋊C4—91no—
772C22⋊C4—91no—
773C22⋊C4—181no—
774C22⋊C4—181no—
775C22⋊C4—181no—
776C22⋊C4—181no—
777C22⋊C4—181no—
778C22⋊C4—181no—
779C42—91no—
780C22×C3—21no—
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—21no—
784C22×C3—21no—
785C22×C3—21no—
786C22×C3—21no—
787C22×C3—41no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—42no—
791C22×C3—42no—
792C22×C3—42no—
793C22×C3—41no—
794C22×C3—41no—
795C22×C3—41no—
796C22×C3—41no—
797C22×C3—41no—
798C22×C3—41no—
799C22×C3—62no—
800C22×C3—121no—
801C22×C3—121no—
802C22×C3—121no—
803C22×C3—121no—
804C22×C3—121no—
805C22×C3—121no—
806C22×C3—121no—
807C22×C3—121no—
808C22×C3—244no—
809C22×C3C2×D3×D411yescharacteristic
810C22×C3C2×D3×D411yescharacteristic
811C2×D3—22no—
812C2×D3—32no—
813C2×D3—32no—
814C2×D3—41no—
815C2×D3—41no—
816C2×D3—41no—
817C2×D3—41no—
818C2×D3—41no—
819C2×D3—41no—
820C2×D3—41no—
821C2×D3—41no—
822C2×D3—62no—
823C2×D3—61no—
824C2×D3—61no—
825C2×D3—61no—
826C2×D3—61no—
827C2×D3—64no—
828C2×D3—62no—
829C2×D3—62no—
830C2×D3—84no—
831C2×D3—121no—
832C2×D3—121no—
833C2×D3—122no—
834C2×D3—122no—
835C2×D3—121no—
836C2×D3—121no—
837C2×D3—121no—
838C2×D3—121no—
839C2×D3—244no—
840C2×D3—244no—
841C2×D3—244no—
842C2×D3—244no—
843C2×D3—248no—
844C3×C4—21no—
845C3×C4—21no—
846C3×C4—21no—
847C3×C4—21no—
848C3×C4—41no—
849C3×C4—42no—
850C3×C4—41no—
851C3×C4—41no—
852C3×C4—121no—
853C3×C4C2×D3×D411yescharacteristic
854C3×C4C2×D3×D411yescharacteristic
855C3×C4#100411yescharacteristic
856C3×C4#100911yescharacteristic
857Dic3—41no—
858Dic3—61no—
859Dic3—61no—
860Dic3—61no—
861Dic3—61no—
862Dic3—61no—
863Dic3—61no—
864Dic3—121no—
865Dic3—121no—
866Dic3—121no—
867Dic3—122no—
868Dic3—121no—
869Dic3—121no—
870C32#326411yescharacteristic, complemented, Sylow
871C23—21no—
872C23—61no—
873C23—61no—
874C23—61no—
875C23—91no—
876C23—122no—
877C23—122no—
878C23—181no—
879C23—241no—
880C23—362no—
881C23—362no—
882C23—362no—
883C23—362no—
884C23—721no—
885C23—721no—
886C23#381111yescharacteristic
887Q8—181no—
888Q8—181no—
889D4—21no—
890D4—21no—
891D4—32no—
892D4—61no—
893D4—61no—
894D4—61no—
895D4—61no—
896D4—61no—
897D4—81no—
898D4—92no—
899D4—122no—
900D4—122no—
901D4—182no—
902D4—181no—
903D4—362no—
904D4—362no—
905D4—362no—
906D4—362no—
907D4—362no—
908D4—721no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—61no—
913C2×C4—91no—
914C2×C4—91no—
915C2×C4—91no—
916C2×C4—181no—
917C2×C4—181no—
918C2×C4—181no—
919C2×C4—362no—
920C2×C4—362no—
921C2×C4—721no—
922C2×C4#381111yescharacteristic
923C2×C4C22×D3211yescharacteristic
924C8—32no—
925C8—61no—
926C8—61no—
927C8—61no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—41no—
932C2×C3—41no—
933C2×C3—81no—
934C2×C3—82no—
935C2×C3—81no—
936C2×C3—81no—
937C2×C3—122no—
938C2×C3—241no—
939C2×C3—241no—
940C2×C3#559011yescharacteristic
941C2×C3#560911yescharacteristic
942C2×C3#575711yescharacteristic
943C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
944C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
945C2×C3#577411yescharacteristic
946D3—42no—
947D3—62no—
948D3—62no—
949D3—81no—
950D3—81no—
951D3—122no—
952D3—124no—
953D3—122no—
954D3—122no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—62no—
962C22—92no—
963C22—121no—
964C22—121no—
965C22—121no—
966C22—121no—
967C22—121no—
968C22—121no—
969C22—121no—
970C22—121no—
971C22—181no—
972C22—181no—
973C22—182no—
974C22—244no—
975C22—361no—
976C22—361no—
977C22—724no—
978C22—724no—
979C22C2×#381111yescharacteristic
980C4—21no—
981C4—41no—
982C4—121no—
983C4—181no—
984C4—181no—
985C4—181no—
986C4—361no—
987C4D32×D411yescharacteristic
988C4#6431411yescharacteristic
989C3—21no—
990C3#8001211yescharacteristic, complemented
991C3#8088111yescharacteristic, complemented
992C2—41no—
993C2—81no—
994C2—122no—
995C2—182no—
996C2—241no—
997C2—241no—
998C2—362no—
999C2#1059510211yescharacteristic
1000C2#1059529211yescharacteristic
1001C2#1059545811yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3264
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. #10596083C2semidirect
2. C2×#63926C2semidirect
3. #10595069C2semidirect
4. C2×#63830C2semidirect
5. C3×#5039C2semidirect
6. C3×#5036C2semidirect
7. #10591485C2semidirect
8. #10591456C2semidirect
9. #10591434C2semidirect
10. #10591182C2semidirect
11. #10591149C2semidirect
12. #10590597C2semidirect
13. #10590551C2semidirect
14. #10590507C2semidirect
15. #10590462C2semidirect
18. C2×D4×C3⋊D3C22semidirect
19. C2×#3828C22semidirect
20. C22×C3×D12C22semidirect
23. C32×#121C22semidirect
26. #64145C22semidirect
28. #64106C22semidirect
29. #64102C22semidirect
33. C2×C3×#213C22semidirect
34. C2×C3×#213C22semidirect
35. C3×#930C22semidirect
36. C2×C3×#208C22semidirect
41. #63914C22semidirect
42. #63898C22semidirect
45. C2×#3716C22semidirect
46. C2×#3716C22semidirect
47. C2×#3716C22semidirect
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×#808C22semidirect
58. #63572C22semidirect
59. #63567C22semidirect
60. #63564C22semidirect
61. #63557C22semidirect
62. #63555C22semidirect
79. #5039D3semidirect
81. #5036D3semidirect
155. #3714D4semidirect
169. C22×D12C2×D3semidirect
176. C3×#121C2×D3semidirect
177. C3×#121C2×D3semidirect
203. C2×#213C2×D3semidirect
204. C2×#213C2×D3semidirect
205. #930C2×D3semidirect
209. C2×#208C2×D3semidirect
243. #832C2×D3semidirect
244. #830C2×D3semidirect
255. #809C2×D3semidirect
256. #809C2×D3semidirect
257. #809C2×D3semidirect
258. #808C2×D3semidirect
291. C4⋊(C3⋊D3)C2×D4semidirect
315. C3×C3⋊C8C2×D4semidirect
497. C2×C3⋊D3AGL(1,ℤ/8)semidirect
544. #121D32semidirect
706. C3⋊C8D3×D4semidirect
870. C32#3264semidirect
990. C3#80012semidirect
991. C3#80881semidirect

Maximal subgroups

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

subgroupindex
#105960832
C2×#639262
#105950692
C2×#638302
C3×#50392
C3×#50362
#105914852
#105914562
#105914342
#105911822
#105911492
#105905972
#105905512
#105905072
#105904622
#808813
#800123