Finite Group Databasebeta

← #11883948

Subgroups — #11883948

Order 1152.

1306 conjugacy classes of subgroups.

The subgroup lattice has 985 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596080C211yesmaximal, characteristic, complemented
2C2×#63937C211yesmaximal, characteristic, complemented
3#10594900C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5C3×#5040C211yesmaximal, characteristic, complemented
6C3×#5038C211yesmaximal, characteristic, complemented
7#10591475C211yesmaximal, characteristic, complemented
8#10591467C211yesmaximal, characteristic, complemented
9#10591444C211yesmaximal, characteristic, complemented
10#10591168C211yesmaximal, characteristic, complemented
11#10591157C211yesmaximal, characteristic, complemented
12#10590617C211yesmaximal, characteristic, complemented
13#10590540C211yesmaximal, characteristic, complemented
14#10590522C211yesmaximal, characteristic, complemented
15#10590484C211yesmaximal, characteristic, complemented
16#80727—31nomaximal
17#80060—31nomaximal
18C2×D4×C3⋊D3—21no—
19C2×D4×C3⋊D3C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic, complemented
22C2×#3796C2211yescharacteristic, complemented
23C32×#121C2211yescharacteristic
24#64149C2211yescharacteristic
25#64146—21no—
26C4×#638C2211yescharacteristic
27#64104C2211yescharacteristic
28#64102C2211yescharacteristic
29#64093—21no—
30#64091—21no—
31C2×C3×#214C2211yescharacteristic, complemented
32C2×C3×#214C2211yescharacteristic, complemented
33C2×C3×#213C2211yescharacteristic, complemented
34C3×#930C2211yescharacteristic, complemented
35C22×C3×C3⋊C8C2211yescharacteristic, complemented
36#63978—21no—
37Dic3×#67—21no—
38#63937—24no—
39#63907—21no—
40#63887—21no—
41#63871C2211yescharacteristic, complemented
42#63863C2211yescharacteristic, complemented
43#63843C2211yescharacteristic, complemented
44C2×#3717—24no—
45C2×#3717C2211yescharacteristic
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic, complemented
48C2×#3717C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic
50C2×#3714C2211yescharacteristic, complemented
51C2×#3712C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic, complemented
53C3×#830C2211yescharacteristic, complemented
54C3×#810C2211yescharacteristic, complemented
55C3×#810C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, complemented
57C3×#807C2211yescharacteristic, complemented
58#63572C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62#63555C2211yescharacteristic, complemented
63#5817—31no—
64C22×#215—31no—
65C2×#914—31no—
66C2×#911—31no—
67C22×#204—31no—
68#5609—31no—
69#5609—31no—
70#5609—61no—
71#5598—31no—
72C3×#466—31no—
73C3×#448—31no—
74#5176—31no—
75#5169—31no—
76#5163—31no—
77#5154—31no—
78#5111—31no—
79#5040D311yescharacteristic, complemented
80#5038D311yescharacteristic, complemented
81#5036—31no—
82#4889—31no—
83#4886—31no—
84#4819—31no—
85#4817—31no—
86#4812—31no—
87#4810—31no—
88#4787—31no—
89#4781—31no—
90#4776—31no—
91#4762—31no—
92#4732—31no—
93#4730—31no—
94C23×C3⋊D3—21no—
95C23×C3⋊D3—21no—
96C2×C32×D4—21no—
97C2×C32×D4C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C2×#638—21no—
100C2×#638—21no—
101C2×#638—21no—
102C2×#638D411yescharacteristic
103D4×C3⋊D3—22no—
104D4×C3⋊D3—41no—
105D4×C3⋊D3—44no—
106C2×C4⋊(C3⋊D3)—22no—
107C2×C4⋊(C3⋊D3)—21no—
108C2×C4⋊(C3⋊D3)—21no—
109C2×C4⋊(C3⋊D3)—41no—
110C2×C4⋊(C3⋊D3)C2311yescharacteristic
111C2×C4⋊(C3⋊D3)C2311yescharacteristic
112C2×C4×C3⋊D3—21no—
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×C3×#67—21no—
115C22×C3×Dic3—21no—
116C2×C3×D12C2311yescharacteristic
117C2×C3×Dic6—22no—
118C2×C3×Dic6—21no—
119C2×C3×Dic6—41no—
120C2×C3×Dic6C2311yescharacteristic
121C2×C3×Dic6C2311yescharacteristic
122C2×#626—21no—
123C2×D3×Dic3—21no—
124#3796—22no—
125#3796—41no—
126C32×C4⋊C4C2311yescharacteristic
127C32×C22⋊C4—21no—
128#3757D411yescharacteristic
129#3752—21no—
130#3752—21no—
131#3752D411yescharacteristic
132#3750D411yescharacteristic
133C4×C3⋊Dic3C2311yescharacteristic
134C3×#214—22no—
135C3×#214—41no—
136C3×#213—22no—
137C3×(C2×D3)⋊C4—21no—
138C3×C4⋊Dic3C2311yescharacteristic
139C2×C3×C3⋊C8—22no—
140C2×C3×C3⋊C8C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144Dic3⋊Dic3—21no—
145Dic3⋊Dic3—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149Dic32—21no—
150#3717—22no—
151#3717—22no—
152#3717—22no—
153#3717D414yescomplemented
154#3714—22no—
155#3714—41no—
156#3712—22no—
157#3265—91noSylow
158C22×C3×Q8—31no—
159C2×#239—31no—
160C2×#237—31no—
161C2×D3×D4—31no—
162C2×D3×D4—31no—
163C2×D3×D4—61no—
164C2×D3×D4—61no—
165C2×D3×D4—61no—
166C2×D3×D4—62no—
167C22×D12—31no—
168C22×D12—31no—
169C22×D12—61no—
170C22×Dic6C2×D311yescharacteristic, complemented
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×D8—31no—
174C22×C3×C8—31no—
175C3×#121—21no—
176C3×#121—31no—
177C3×#121C2×D311yescharacteristic
178C3×#121C2×D311yescharacteristic
179#947—31no—
180#947—61no—
181#946—31no—
182#946—61no—
183Q8×Dic3—31no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—64no—
189#940—31no—
190#940—31no—
191#940—61no—
192#939—61no—
193#937—61no—
194#937—61no—
195#937—62no—
196#936—31no—
197D4×Dic3—61no—
198C2×#214C2×D311yescharacteristic, complemented
199C2×#214C2×D311yescharacteristic, complemented
200C2×#213—31no—
201C2×#213—31no—
202C2×#213C2×D311yescharacteristic, complemented
203#930—61no—
204#930C2×D311yescharacteristic, complemented
205C4×#67—31no—
206C4×#67—31no—
207C4×#67—61no—
208C4×#67—61no—
209C22×C3⋊C8C2×D311yescharacteristic, complemented
210#914—64no—
211#911—64no—
212C2×D24—31no—
213C2×D24—31no—
214C2×#204—31no—
215C2×#204—31no—
216C2×#204—31no—
217C2×#204—31no—
218C2×#204—64no—
219C2×ΓL(1,𝔽25)—31no—
220C2×ΓL(1,𝔽25)—31no—
221#897—31no—
222#895—31no—
223#895—31no—
224#895—61no—
225#893—31no—
226#893—31no—
227#893—61no—
228#887—31no—
229#885—61no—
230#884—61no—
231#884—61no—
232#884—62no—
233#882—61no—
234#882—61no—
235#882—62no—
236#878—61no—
237C3×#107—31no—
238C3×#103—31no—
239C3×#103—31no—
240C3×#102—31no—
241C3×#102—31no—
242C3×C22⋊C8—31no—
243#832C2×D311yescharacteristic, complemented
244#830C2×D311yescharacteristic, complemented
245#821—31no—
246#821—31no—
247(C2×D3)⋊C8—31no—
248(C2×D3)⋊C8—31no—
249#815—31no—
250#815—31no—
251Dic3⋊C8—31no—
252Dic3⋊C8—31no—
253#810C2×D311yescharacteristic, complemented
254#810C2×D311yescharacteristic, complemented
255#809—31no—
256#809—31no—
257#809C2×D311yescharacteristic, complemented
258#807C2×D311yescharacteristic, complemented
259C23×C32—21no—
260C23×C32C2×D411yescharacteristic
261C22×C3⋊D3—21no—
262C22×C3⋊D3—21no—
263C22×C3⋊D3—42no—
264C22×C3⋊D3—42no—
265C22×C3⋊D3—42no—
266C22×C3⋊D3—42no—
267C22×C3⋊D3—81no—
268C22×C3⋊D3—81no—
269C22×C3⋊D3C2×D411yescharacteristic
270C22×C3×D3—21no—
271C32×D4—21no—
272C32×D4—21no—
273C32×D4—42no—
274C2×C32×C4—21no—
275C2×C32×C4—21no—
276C2×C32×C4—21no—
277C2×C32×C4C2×D411yescharacteristic
278C2×C32×C4C2411yescharacteristic
279#638—22no—
280#638—42no—
281#638—42no—
282#638—81no—
283C2×C3⋊Dic3C2×D411yescharacteristic
284C2×C3⋊Dic3C2×D411yescharacteristic
285C2×C3⋊Dic3C2×D411yescharacteristic
286C4⋊(C3⋊D3)—21no—
287C4⋊(C3⋊D3)—21no—
288C4⋊(C3⋊D3)—21no—
289C4⋊(C3⋊D3)—42no—
290C4⋊(C3⋊D3)—42no—
291C4⋊(C3⋊D3)C2×D412yes—
292C4×C3⋊D3—21no—
293C4×C3⋊D3—21no—
294C4×C3⋊D3—42no—
295C3×#67—42no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C2×C3×Dic3—21no—
299C2×C3×Dic3—42no—
300C3×D12—21no—
301C3×D12—21no—
302C3×Dic6—21no—
303C3×Dic6—21no—
304C3×Dic6—21no—
305C3×Dic6—42no—
306C3×Dic6C2×D412yescomplemented
307#626—42no—
308D3×Dic3—42no—
309C3×C3⋊C8—21no—
310C3×C3⋊C8—21no—
311C3×C3⋊C8—21no—
312C3×C3⋊C8C2×D412yescomplemented
313C2×AGL(1,ℤ/8)—91no—
314C22×SD16—91no—
315#548—91no—
316D42—91no—
317#496—91no—
318#468—91no—
319#466—31no—
320#463—91no—
321#460—91no—
322#450—91no—
323#449—91no—
324#448—31no—
325#447—91no—
326#440—91no—
327#435—91no—
328C23×D3—61no—
329C23×D3—61no—
330C23×D3—62no—
331C23×D3—62no—
332C23×D3—61no—
333C23×D3—61no—
334C2×C3×Q8—31no—
335C2×C3×Q8—31no—
336C2×C3×Q8—62no—
337C2×C3×Q8—61no—
338C2×C3×Q8—121no—
339C2×C3×D4—22no—
340C2×C3×D4—21no—
341C2×C3×D4—21no—
342C2×C3×D4—21no—
343C2×C3×D4—31no—
344C2×C3×D4—61no—
345C2×C3×D4C22×D311yescharacteristic
346C2×C3×D4C22×D311yescharacteristic
347C22×C3×C4—21no—
348C22×C3×C4—61no—
349C22×C3×C4C22×D311yescharacteristic
350C22×C3×C4C22×D311yescharacteristic
351C2×#67—21no—
352C2×#67—31no—
353C2×#67—31no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—61no—
361C2×#67—61no—
362C2×#67—62no—
363C2×#67—62no—
364C2×#67—62no—
365C22×Dic3—21no—
366C22×Dic3—61no—
367#239—62no—
368#239—121no—
369#237—62no—
370#237—121no—
371D3×D4—62no—
372D3×D4—62no—
373D3×D4—122no—
374D3×D4—121no—
375D3×D4—121no—
376D3×D4—122no—
377D3×D4—128no—
378D3×D4—124no—
379D3×D4—124no—
380C2×D12—31no—
381C2×D12—31no—
382C2×D12—31no—
383C2×D12—31no—
384C2×D12—61no—
385C2×D12—61no—
386C2×D12—62no—
387C2×D12—62no—
388C2×D12—61no—
389C2×D12—61no—
390C2×D12—62no—
391C2×D12—62no—
392C2×D12—61no—
393C2×D12—61no—
394C2×D12—61no—
395C2×D12—122no—
396C2×D12—121no—
397C2×D12—121no—
398C2×D12—122no—
399C2×D12C22×D311yescharacteristic
400C2×C4×D3—31no—
401C2×C4×D3—31no—
402C2×C4×D3—61no—
403C2×C4×D3—61no—
404C2×C4×D3—61no—
405C2×C4×D3—61no—
406C2×C4×D3—62no—
407C2×Dic6—22no—
408C2×Dic6—21no—
409C2×Dic6—41no—
410C2×Dic6C22×D311yescharacteristic
411C2×Dic6C22×D311yescharacteristic
412C3×SD16—62no—
413C3×SD16—121no—
414C3×D8—62no—
415C2×C3×C8—31no—
416C2×C3×C8—31no—
417C2×C3×C8—31no—
418C2×C3×C8—31no—
419C2×C3×C8—62no—
420C3×C4⋊C4—21no—
421C3×C4⋊C4—31no—
422C3×C4⋊C4C22×D311yescharacteristic
423C3×C4⋊C4C22×D311yescharacteristic
424C3×C22⋊C4—22no—
425C3×C22⋊C4—21no—
426C3×C22⋊C4—21no—
427C3×C22⋊C4—61no—
428#217—31no—
429#217—31no—
430#217—61no—
431#217—61no—
432#217—61no—
433#215—34no—
434#215—62no—
435#215—62no—
436#215—62no—
437#214—22no—
438#214—41no—
439#213—22no—
440#213—62no—
441#213—121no—
442(C2×D3)⋊C4—21no—
443(C2×D3)⋊C4—31no—
444(C2×D3)⋊C4—31no—
445(C2×D3)⋊C4—61no—
446(C2×D3)⋊C4—61no—
447(C2×D3)⋊C4—61no—
448(C2×D3)⋊C4—61no—
449(C2×D3)⋊C4—61no—
450(C2×D3)⋊C4—61no—
451(C2×D3)⋊C4—61no—
452(C2×D3)⋊C4—61no—
453(C2×D3)⋊C4—61no—
454(C2×D3)⋊C4—62no—
455(C2×D3)⋊C4—62no—
456C4⋊Dic3—61no—
457C4⋊Dic3—61no—
458C4⋊Dic3C22×D311yescharacteristic
459Dic3⋊C4—31no—
460Dic3⋊C4—31no—
461Dic3⋊C4—61no—
462Dic3⋊C4—61no—
463Dic3⋊C4—61no—
464C4×Dic3—31no—
465C4×Dic3—31no—
466C4×Dic3—61no—
467C4×Dic3—61no—
468C4×Dic3—61no—
469C2×C3⋊C8—22no—
470C2×C3⋊C8C22×D311yescharacteristic
471C2×C3⋊C8C22×D311yescharacteristic
472C2×C3⋊C8C22×D311yescharacteristic
473C2×C3⋊C8C22×D311yescharacteristic
474D24—62no—
475D24—121no—
476#204—34no—
477#204—62no—
478#204—62no—
479#204—62no—
480ΓL(1,𝔽25)—62no—
481ΓL(1,𝔽25)—62no—
482C22×C32—21no—
483C22×C32—21no—
484C22×C32—41no—
485C22×C32—41no—
486C22×C32—41no—
487C22×C32AGL(1,ℤ/8)12yescomplemented
488C22×C32C22×D411yescharacteristic
489C2×C3⋊D3—22no—
490C2×C3⋊D3—21no—
491C2×C3⋊D3—21no—
492C2×C3⋊D3—21no—
493C2×C3⋊D3—41no—
494C2×C3⋊D3—41no—
495C2×C3⋊D3—41no—
496C2×C3⋊D3—41no—
497C2×C3⋊D3—41no—
498C2×C3⋊D3—84no—
499C2×C3⋊D3—84no—
500C2×C3×D3—41no—
501C2×C3×D3—41no—
502C2×C3×D3—41no—
503C32×C4—21no—
504C32×C4—41no—
505C32×C4C22×D411yescharacteristic
506C32×C4H(5,𝔽2)11yescharacteristic
507C3⋊Dic3—21no—
508C3⋊Dic3—21no—
509C3⋊Dic3—21no—
510C3×Dic3—22no—
511C3×Dic3—41no—
512C3×Dic3—41no—
513C2×#41—91no—
514C22×Q8—31no—
515C22×D4—91no—
516C22×D4—91no—
517C22×D4—181no—
518AGL(1,ℤ/8)—184no—
519C2×SD16—31no—
520C2×SD16—31no—
521C2×SD16—91no—
522C2×SD16—91no—
523C2×SD16—91no—
524C2×SD16—91no—
525C2×SD16—184no—
526C2×D8—31no—
527C2×D8—91no—
528C2×D8—91no—
529C2×M16—91no—
530C22×C8—31no—
531#127—91no—
532#124—91no—
533#124—181no—
534C22⋊Q8—91no—
535C22⋊Q8—181no—
536#121—31no—
537#121—91no—
538#121—181no—
539#121—181no—
540#121D3211yescharacteristic
541#120—181no—
542#120—181no—
543C4×Q8—91no—
544C4×D4—91no—
545C4×D4—91no—
546C4×D4—181no—
547#107—31no—
548C4⋊C8—91no—
549#103—31no—
550#103—31no—
551#102—31no—
552#102—31no—
553#102—91no—
554#102—91no—
555C22⋊C8—31no—
556C22⋊C8—91no—
557#97—91no—
558C23×C3—22no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—21no—
562C23×C3—61no—
563C23×C3D3×D411yescharacteristic
564C23×C3D3×D411yescharacteristic
565C22×D3—21no—
566C22×D3—31no—
567C22×D3—31no—
568C22×D3—61no—
569C22×D3—62no—
570C22×D3—61no—
571C22×D3—61no—
572C22×D3—62no—
573C22×D3—61no—
574C22×D3—61no—
575C22×D3—122no—
576C22×D3—122no—
577C22×D3—122no—
578C22×D3—122no—
579C22×D3—124no—
580C22×D3—124no—
581C22×D3—124no—
582C22×D3—122no—
583C22×D3—122no—
584C22×D3—124no—
585C22×D3—122no—
586C22×D3—122no—
587C22×D3—241no—
588C22×D3—241no—
589C22×D3—241no—
590C22×D3—241no—
591C22×D3—242no—
592C22×D3—242no—
593C3×Q8—32no—
594C3×Q8—61no—
595C3×Q8—61no—
596C3×Q8—61no—
597C3×Q8—122no—
598C3×D4—21no—
599C3×D4—21no—
600C3×D4—21no—
601C3×D4—21no—
602C3×D4—41no—
603C3×D4—41no—
604C3×D4—44no—
605C3×D4—42no—
606C3×D4—42no—
607C3×D4—61no—
608C3×D4—61no—
609C3×D4—122no—
610C2×C3×C4—21no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—22no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—41no—
620C2×C3×C4—41no—
621C2×C3×C4—61no—
622C2×C3×C4—61no—
623C2×C3×C4—61no—
624C2×C3×C4—122no—
625C2×C3×C4D3×D411yescharacteristic
626C2×C3×C4D3×D411yescharacteristic
627C2×C3×C4C23×D311yescharacteristic
628C2×C3×C4C23×D311yescharacteristic
629#67—42no—
630#67—64no—
631#67—62no—
632#67—62no—
633#67—122no—
634#67—122no—
635#67—122no—
636#67—124no—
637#67—122no—
638#67—122no—
639#67—124no—
640#67—241no—
641#67—241no—
642#67—242no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—31no—
647C2×Dic3—31no—
648C2×Dic3—31no—
649C2×Dic3—31no—
650C2×Dic3—31no—
651C2×Dic3—31no—
652C2×Dic3—42no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3—122no—
657D12—21no—
658D12—21no—
659D12—32no—
660D12—32no—
661D12—62no—
662D12—62no—
663D12—61no—
664D12—61no—
665D12—61no—
666D12—61no—
667D12—61no—
668D12—61no—
669D12—121no—
670D12—121no—
671D12—122no—
672D12—122no—
673D12—124no—
674D12—124no—
675D12—122no—
676D12—122no—
677D12—122no—
678C4×D3—61no—
679C4×D3—61no—
680C4×D3—61no—
681C4×D3—61no—
682C4×D3—121no—
683C4×D3—121no—
684C4×D3—124no—
685C4×D3—122no—
686C4×D3—122no—
687C4×D3—122no—
688Dic6—21no—
689Dic6—21no—
690Dic6—21no—
691Dic6—42no—
692Dic6D3×D412yescomplemented
693C3×C8—32no—
694C3×C8—61no—
695C3×C8—61no—
696C3×C8—61no—
697C3⋊C8—21no—
698C3⋊C8—21no—
699C3⋊C8—21no—
700C3⋊C8D3×D412yescomplemented
701C2×C32—22no—
702C2×C32—81no—
703C2×C32D4211yescharacteristic
704C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
705C2×C32#57711yescharacteristic
706C3⋊D3—41no—
707C3⋊D3—42no—
708C3⋊D3—81no—
709C3×D3—81no—
710C24—181no—
711C24—181no—
712#41—182no—
713#41—361no—
714C2×Q8—31no—
715C2×Q8—31no—
716C2×Q8—62no—
717C2×Q8—61no—
718C2×Q8—121no—
719C2×D4—21no—
720C2×D4—31no—
721C2×D4—61no—
722C2×D4—91no—
723C2×D4—91no—
724C2×D4—91no—
725C2×D4—182no—
726C2×D4—181no—
727C2×D4—181no—
728C2×D4—181no—
729C2×D4—181no—
730C2×D4—181no—
731C2×D4—182no—
732C2×D4—181no—
733C2×D4—361no—
734C2×D4—361no—
735C2×D4—364no—
736C2×D4C2×D3211yescharacteristic
737C22×C4—61no—
738C22×C4—91no—
739C22×C4—181no—
740C22×C4—181no—
741C22×C4C2×D3211yescharacteristic
742SD16—62no—
743SD16—94no—
744SD16—121no—
745SD16—182no—
746SD16—182no—
747SD16—182no—
748D8—62no—
749D8—182no—
750D8—361no—
751M16—182no—
752C2×C8—31no—
753C2×C8—31no—
754C2×C8—31no—
755C2×C8—31no—
756C2×C8—62no—
757C4⋊C4—31no—
758C4⋊C4—91no—
759C4⋊C4—181no—
760C4⋊C4—181no—
761C4⋊C4C2×D3211yescharacteristic
762C22⋊C4—21no—
763C22⋊C4—61no—
764C22⋊C4—91no—
765C22⋊C4—91no—
766C22⋊C4—181no—
767C22⋊C4—181no—
768C22⋊C4—181no—
769C22⋊C4—181no—
770C22⋊C4—181no—
771C42—91no—
772C42—181no—
773C22×C3—21no—
774C22×C3—21no—
775C22×C3—21no—
776C22×C3—21no—
777C22×C3—21no—
778C22×C3—22no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—42no—
782C22×C3—42no—
783C22×C3—42no—
784C22×C3—41no—
785C22×C3—41no—
786C22×C3—41no—
787C22×C3—41no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—121no—
791C22×C3—121no—
792C22×C3—121no—
793C22×C3#91112yescomplemented
794C22×C3#91412yescomplemented
795C22×C3C2×D3×D411yescharacteristic
796C22×C3C2×D3×D411yescharacteristic
797C2×D3—41no—
798C2×D3—41no—
799C2×D3—41no—
800C2×D3—64no—
801C2×D3—62no—
802C2×D3—61no—
803C2×D3—61no—
804C2×D3—61no—
805C2×D3—61no—
806C2×D3—61no—
807C2×D3—62no—
808C2×D3—61no—
809C2×D3—62no—
810C2×D3—121no—
811C2×D3—121no—
812C2×D3—122no—
813C2×D3—122no—
814C2×D3—121no—
815C2×D3—121no—
816C2×D3—121no—
817C2×D3—121no—
818C2×D3—122no—
819C2×D3—122no—
820C2×D3—122no—
821C2×D3—121no—
822C2×D3—121no—
823C2×D3—121no—
824C2×D3—121no—
825C2×D3—121no—
826C2×D3—121no—
827C2×D3—248no—
828C2×D3—244no—
829C2×D3—244no—
830C2×D3—244no—
831C2×D3—244no—
832C2×D3—248no—
833C3×C4—21no—
834C3×C4—21no—
835C3×C4—21no—
836C3×C4—21no—
837C3×C4—41no—
838C3×C4—42no—
839C3×C4—41no—
840C3×C4—41no—
841C3×C4—62no—
842C3×C4—121no—
843C3×C4—121no—
844C3×C4C2×D3×D411yescharacteristic
845C3×C4C2×D3×D411yescharacteristic
846C3×C4#100411yescharacteristic
847C3×C4#100911yescharacteristic
848Dic3—22no—
849Dic3—41no—
850Dic3—41no—
851Dic3—62no—
852Dic3—61no—
853Dic3—61no—
854Dic3—61no—
855Dic3—61no—
856Dic3—61no—
857Dic3—61no—
858Dic3—121no—
859Dic3—121no—
860C32#326511yescharacteristic, complemented, Sylow
861C23—21no—
862C23—61no—
863C23—91no—
864C23—181no—
865C23—181no—
866C23—362no—
867C23—362no—
868C23—362no—
869C23—362no—
870C23—721no—
871C23—721no—
872C23#381111yescharacteristic
873Q8—32no—
874Q8—61no—
875Q8—61no—
876Q8—61no—
877Q8—122no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—61no—
882D4—61no—
883D4—92no—
884D4—122no—
885D4—182no—
886D4—181no—
887D4—181no—
888D4—181no—
889D4—362no—
890D4—362no—
891D4—362no—
892D4—362no—
893D4—362no—
894D4—721no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—91no—
902C2×C4—91no—
903C2×C4—91no—
904C2×C4—122no—
905C2×C4—181no—
906C2×C4—181no—
907C2×C4—362no—
908C2×C4—362no—
909C2×C4#381111yescharacteristic
910C2×C4C22×D3211yescharacteristic
911C8—32no—
912C8—61no—
913C8—61no—
914C8—61no—
915C2×C3—22no—
916C2×C3—22no—
917C2×C3—21no—
918C2×C3—21no—
919C2×C3—21no—
920C2×C3—42no—
921C2×C3—82no—
922C2×C3—81no—
923C2×C3—81no—
924C2×C3—241no—
925C2×C3#559011yescharacteristic
926C2×C3#560911yescharacteristic
927C2×C3C2×#91111yescharacteristic
928C2×C3C2×#91411yescharacteristic
929C2×C3#577011yescharacteristic
930C2×C3#577811yescharacteristic
931D3—81no—
932D3—122no—
933D3—124no—
934D3—121no—
935D3—122no—
936D3—121no—
937D3—122no—
938D3—242no—
939D3—241no—
940D3—241no—
941C22—21no—
942C22—21no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—121no—
947C22—121no—
948C22—121no—
949C22—181no—
950C22—181no—
951C22—181no—
952C22—182no—
953C22—361no—
954C22—361no—
955C22—361no—
956C22—361no—
957C22—361no—
958C22—724no—
959C22—724no—
960C22#6393712yescomplemented
961C22C2×#381111yescharacteristic
962C4—21no—
963C4—41no—
964C4—62no—
965C4—121no—
966C4—121no—
967C4—181no—
968C4—181no—
969C4—181no—
970C4D32×D411yescharacteristic
971C4#6431411yescharacteristic
972C3—21no—
973C3#8006011yescharacteristic, complemented
974C3#8072711yescharacteristic, complemented
975C2—22no—
976C2—81no—
977C2—241no—
978C2—361no—
979C2—362no—
980C2—721no—
981C2C2×#6393711yescharacteristic
982C2#1059529211yescharacteristic
983C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#121C22
socleC22×C32C22×D4
hypercenter#121D32
hypocenterC32#3265
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×#63937C2semidirect
3. #10594900C2semidirect
4. C22×#3717C2semidirect
5. C3×#5040C2semidirect
6. C3×#5038C2semidirect
7. #10591475C2semidirect
8. #10591467C2semidirect
9. #10591444C2semidirect
10. #10591168C2semidirect
11. #10591157C2semidirect
12. #10590617C2semidirect
13. #10590540C2semidirect
14. #10590522C2semidirect
15. #10590484C2semidirect
21. C22×C3×Dic6C22semidirect
22. C2×#3796C22semidirect
31. C2×C3×#214C22semidirect
32. C2×C3×#214C22semidirect
33. C2×C3×#213C22semidirect
34. C3×#930C22semidirect
35. C22×C3×C3⋊C8C22semidirect
41. #63871C22semidirect
42. #63863C22semidirect
43. #63843C22semidirect
47. C2×#3717C22semidirect
48. C2×#3717C22semidirect
50. C2×#3714C22semidirect
51. C2×#3712C22semidirect
52. C3×#832C22semidirect
53. C3×#830C22semidirect
54. C3×#810C22semidirect
55. C3×#810C22semidirect
56. C3×#809C22semidirect
57. C3×#807C22semidirect
58. #63572C22semidirect
60. #63564C22semidirect
61. #63557C22semidirect
62. #63555C22semidirect
79. #5040D3semidirect
80. #5038D3semidirect
153. #3717D4semidirect
170. C22×Dic6C2×D3semidirect
198. C2×#214C2×D3semidirect
199. C2×#214C2×D3semidirect
202. C2×#213C2×D3semidirect
204. #930C2×D3semidirect
209. C22×C3⋊C8C2×D3semidirect
243. #832C2×D3semidirect
244. #830C2×D3semidirect
253. #810C2×D3semidirect
254. #810C2×D3semidirect
257. #809C2×D3semidirect
258. #807C2×D3semidirect
306. C3×Dic6C2×D4semidirect
312. C3×C3⋊C8C2×D4semidirect
487. C22×C32AGL(1,ℤ/8)semidirect
692. Dic6D3×D4semidirect
700. C3⋊C8D3×D4semidirect
793. C22×C3#911semidirect
794. C22×C3#914semidirect
860. C32#3265semidirect
960. C22#63937semidirect
973. C3#80060semidirect
974. C3#80727semidirect

Maximal subgroups

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

subgroupindex
#105960802
C2×#639372
#105949002
C22×#37172
C3×#50402
C3×#50382
#105914752
#105914672
#105914442
#105911682
#105911572
#105906172
#105905402
#105905222
#105904842
#807273
#800603