Finite Group Databasebeta

← #11883978

Subgroups — #11883978

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
1D4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
2C2×#63937C211yesmaximal, characteristic, complemented
3C2×#63930C211yesmaximal, characteristic, complemented
4#10593901C211yesmaximal, characteristic, complemented
5C3×#5018C211yesmaximal, characteristic, complemented
6C3×#5016C211yesmaximal, characteristic, complemented
7#10591467C211yesmaximal, characteristic, complemented
8#10591456C211yesmaximal, characteristic, complemented
9#10590617C211yesmaximal, characteristic, complemented
10#10590606C211yesmaximal, characteristic, complemented
11#10590522C211yesmaximal, characteristic, complemented
12#10590509C211yesmaximal, characteristic, complemented
13#10590367C211yesmaximal, characteristic, complemented
14#10590351C211yesmaximal, characteristic, complemented
15#10590328C211yesmaximal, characteristic, complemented
16#80553—31nomaximal
17#79794—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×D4×C3⋊D3C2211yescharacteristic
20C22×C4⋊(C3⋊D3)—21no—
21C2×#3797C2211yescharacteristic, complemented
22C2×#3796C2211yescharacteristic, complemented
23C32×C4×D4C2211yescharacteristic
24#64139—21no—
25#64104C2211yescharacteristic
26#64104C2211yescharacteristic
27#64091—21no—
28#64091—21no—
29#64083C2211yescharacteristic
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic
32C2×C3×#214C2211yescharacteristic
33C2×C3×#213C2211yescharacteristic
34C3×#875C2211yescharacteristic, complemented
35C3×C4×Dic6C2211yescharacteristic, complemented
36#63937—24no—
37#63930—24no—
38#63916C2211yescharacteristic, complemented
39#63910—21no—
40#63893—21no—
41#63880—21no—
42#63871C2211yescharacteristic, complemented
43#63852—21no—
44C2×#3717C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic, complemented
46C2×#3717C2211yescharacteristic, complemented
47C2×#3717C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3712C2211yescharacteristic, complemented
51C2×#3710C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic
53C3×#810C2211yescharacteristic, complemented
54C3×#810C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic, complemented
56C3×#807C2211yescharacteristic, complemented
57C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
58C3×#803C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63557C2211yescharacteristic, complemented
62#63557C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×D3×SD16—31no—
65C2×D3×SD16—31no—
66C2×#911—31no—
67#5677—31no—
68#5576—31no—
69D4×D12—31no—
70D4×D12—31no—
71D4×D12—61no—
72C3×#463—31no—
73C3×#440—31no—
74#5169—31no—
75#5156—31no—
76#5058—31no—
77#5027—31no—
78#5018D311yescharacteristic, complemented
79#5016D311yescharacteristic, complemented
80#4886—31no—
81#4883—31no—
82#4848—31no—
83#4836—31no—
84#4812—31no—
85#4810—31no—
86#4806—31no—
87#4806—31no—
88#4781—31no—
89#4776—31no—
90#4775—31no—
91#4773—31no—
92#4712—31no—
93#4706—31no—
94C23×C3⋊D3—21no—
95C23×C3⋊D3—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C2×#638—21no—
99C2×#638—21no—
100D4×C3⋊D3—22no—
101D4×C3⋊D3—22no—
102D4×C3⋊D3—41no—
103D4×C3⋊D3—41no—
104C2×C4⋊(C3⋊D3)—21no—
105C2×C4⋊(C3⋊D3)—21no—
106C2×C4⋊(C3⋊D3)—21no—
107C2×C4⋊(C3⋊D3)—21no—
108C2×C4⋊(C3⋊D3)—44no—
109C2×C4⋊(C3⋊D3)D411yescharacteristic
110C2×C4⋊(C3⋊D3)C2311yescharacteristic
111C2×C4⋊(C3⋊D3)C2311yescharacteristic
112C2×C4×C3⋊D3C2311yescharacteristic
113C2×C4×C3⋊D3C2311yescharacteristic
114C2×C3×D12C2311yescharacteristic
115C2×C3×Dic6C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#627—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#624—21no—
121C2×D3×Dic3—21no—
122#3797—22no—
123#3797—41no—
124#3796—22no—
125#3796—41no—
126C32×C4⋊C4C2311yescharacteristic
127C32×C22⋊C4—21no—
128C32×C42C2311yescharacteristic
129#3752—21no—
130#3752—21no—
131#3752D411yescharacteristic
132#3752D411yescharacteristic
133C4⋊(C3⋊Dic3)D411yescharacteristic
134C3×#214—22no—
135C3×#214D414yescomplemented
136C3×#213—22no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×C4⋊Dic3C2311yescharacteristic
140C3×Dic3⋊C4—21no—
141C3×C4×Dic3—21no—
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146Dic3⋊Dic3—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149#3717—22no—
150#3717—22no—
151#3717—22no—
152#3717—41no—
153#3714—22no—
154#3714—41no—
155#3712—22no—
156#3710—22no—
157#3265—91noSylow
158C2×#239—31no—
159C2×D3×Q8—31no—
160C2×D3×Q8—31no—
161C2×#237—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—
168C22×D12—61no—
169C22×D12—61no—
170C22×D12—62no—
171C2×C3×SD16—31no—
172C2×C3×SD16—31no—
173C2×C3×D8—31no—
174C3×#124—31no—
175C3×C4×Q8—31no—
176C3×C4×D4—21no—
177C3×C4×D4C2×D311yescharacteristic
178C3×C4×D4C2×D311yescharacteristic
179#946—31no—
180C2×#215—31no—
181C2×#215—31no—
182C2×#215—31no—
183C2×#215—31no—
184#938—31no—
185C2×#214C2×D311yescharacteristic
186C2×#214C2×D311yescharacteristic
187C2×#213—31no—
188C2×#213—31no—
189C2×#213C2×D311yescharacteristic
190#930—61no—
191#930—61no—
192#930—62no—
193#914—64no—
194D3×SD16—64no—
195D3×SD16—64no—
196#911—64no—
197C2×D24—31no—
198C2×D24—31no—
199C2×#204—31no—
200C2×#204—31no—
201C2×#204—31no—
202C2×#204—31no—
203C2×ΓL(1,𝔽25)—31no—
204C2×ΓL(1,𝔽25)—31no—
205C2×D3×C8—31no—
206C2×D3×C8—31no—
207#897—31no—
208#897—61no—
209#895—31no—
210#895—31no—
211#895—31no—
212#895—31no—
213#895—31no—
214#895—61no—
215#895—61no—
216#895—61no—
217#885—61no—
218#884—61no—
219#882—61no—
220#882—61no—
221#882—61no—
222#882—61no—
223#882—62no—
224#882—62no—
225#67⋊C4—61no—
226#878—61no—
227#875—61no—
228#875C2×D311yescharacteristic, complemented
229#874—31no—
230#874—31no—
231#874—61no—
232C4×D12—31no—
233C4×D12—31no—
234C4×D12—61no—
235C4×D12—61no—
236C4×Dic6C2×D311yescharacteristic, complemented
237C3×#107—31no—
238C3×C4⋊C8—31no—
239C3×#103—31no—
240C3×#103—31no—
241C3×#102—31no—
242C3×#102—31no—
243C3×#97—31no—
244#832C2×D311yescharacteristic
245#821—31no—
246#821—31no—
247(C2×D3)⋊C8—31no—
248(C2×D3)⋊C8—31no—
249(C2×D3)⋊C8—31no—
250(C2×D3)⋊C8—31no—
251#810C2×D311yescharacteristic, complemented
252#810C2×D311yescharacteristic, complemented
253#809—31no—
254#809—31no—
255#809C2×D311yescharacteristic, complemented
256#807C2×D311yescharacteristic, complemented
257C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
258#803C2×D311yescharacteristic, complemented
259C23×C32—21no—
260C22×C3⋊D3—21no—
261C22×C3⋊D3—21no—
262C22×C3⋊D3—42no—
263C22×C3⋊D3—42no—
264C22×C3⋊D3—42no—
265C22×C3⋊D3—42no—
266C22×C3⋊D3—81no—
267C22×C3⋊D3—81no—
268C22×C3⋊D3C2×D411yescharacteristic
269C22×C3⋊D3C2×D411yescharacteristic
270C22×C3×D3—21no—
271C32×D4—21no—
272C32×D4C2×D412yes—
273C2×C32×C4—21no—
274C2×C32×C4—42no—
275C2×C32×C4C2×D411yescharacteristic
276C2×C32×C4C2×D411yescharacteristic
277C2×C32×C4C2411yescharacteristic
278#638—42no—
279#638—42no—
280C2×C3⋊Dic3C2×D411yescharacteristic
281C2×C3⋊Dic3C2×D411yescharacteristic
282C4⋊(C3⋊D3)—22no—
283C4⋊(C3⋊D3)—21no—
284C4⋊(C3⋊D3)—21no—
285C4⋊(C3⋊D3)—21no—
286C4⋊(C3⋊D3)—21no—
287C4⋊(C3⋊D3)—42no—
288C4⋊(C3⋊D3)—42no—
289C4⋊(C3⋊D3)—42no—
290C4⋊(C3⋊D3)—81no—
291C4×C3⋊D3—21no—
292C4×C3⋊D3—21no—
293C4×C3⋊D3—21no—
294C4×C3⋊D3—21no—
295C2×C3×Dic3—21no—
296C2×C3×Dic3—21no—
297C2×C3×Dic3—21no—
298C3×D12—21no—
299C3×D12—21no—
300C3×Dic6—21no—
301C3×Dic6—21no—
302C3×Dic6—21no—
303C3×Dic6C2×D412yescomplemented
304#627—42no—
305#626—42no—
306#626—42no—
307#624—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—91no—
320#463—31no—
321#460—91no—
322#450—91no—
323#449—91no—
324#448—91no—
325#447—91no—
326#440—31no—
327#435—91no—
328C23×D3—61no—
329C23×D3—61no—
330C23×D3—61no—
331C23×D3—61no—
332C23×D3—62no—
333C23×D3—62no—
334C2×C3×Q8—31no—
335C2×C3×Q8—31no—
336C2×C3×D4—21no—
337C2×C3×D4—31no—
338C2×C3×D4C22×D311yescharacteristic
339C2×C3×D4C22×D311yescharacteristic
340C22×C3×C4—22no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—61no—
349C2×#67—62no—
350C2×#67—62no—
351C22×Dic3—61no—
352#239—62no—
353#239—121no—
354D3×Q8—62no—
355D3×Q8—62no—
356D3×Q8—121no—
357D3×Q8—121no—
358#237—62no—
359#237—121no—
360D3×D4—62no—
361D3×D4—62no—
362D3×D4—62no—
363D3×D4—62no—
364D3×D4—122no—
365D3×D4—122no—
366D3×D4—121no—
367D3×D4—121no—
368D3×D4—121no—
369D3×D4—121no—
370D3×D4—122no—
371D3×D4—122no—
372C2×D12—31no—
373C2×D12—31no—
374C2×D12—31no—
375C2×D12—31no—
376C2×D12—31no—
377C2×D12—31no—
378C2×D12—61no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12—61no—
382C2×D12—61no—
383C2×D12—61no—
384C2×D12—61no—
385C2×D12—62no—
386C2×D12—62no—
387C2×D12—62no—
388C2×D12—61no—
389C2×D12—61no—
390C2×D12—61no—
391C2×D12—61no—
392C2×D12—62no—
393C2×D12—61no—
394C2×D12—61no—
395C2×D12—124no—
396C2×D12—124no—
397C2×D12—128no—
398C2×D12C22×D311yescharacteristic
399C2×C4×D3—31no—
400C2×C4×D3—31no—
401C2×C4×D3—31no—
402C2×C4×D3—31no—
403C2×C4×D3—61no—
404C2×C4×D3—61no—
405C2×C4×D3—61no—
406C2×C4×D3—61no—
407C2×C4×D3—61no—
408C2×Dic6—61no—
409C2×Dic6—61no—
410C2×Dic6C22×D311yescharacteristic
411C2×Dic6C22×D311yescharacteristic
412C3×SD16—34no—
413C3×SD16—62no—
414C3×D8—62no—
415C2×C3×C8—31no—
416C2×C3×C8—31no—
417C2×C3×C8—31no—
418C2×C3×C8—31no—
419C3×C4⋊C4—21no—
420C3×C4⋊C4—31no—
421C3×C4⋊C4—61no—
422C3×C4⋊C4C22×D311yescharacteristic
423C3×C4⋊C4C22×D311yescharacteristic
424C3×C22⋊C4—22no—
425C3×C22⋊C4—21no—
426C3×C22⋊C4—21no—
427C3×C22⋊C4—61no—
428C3×C22⋊C4—61no—
429C3×C42—21no—
430C3×C42—61no—
431C3×C42C22×D311yescharacteristic
432C3×C42C22×D311yescharacteristic
433#217—61no—
434#215—62no—
435#215—62no—
436#215—62no—
437#215—121no—
438#214—22no—
439#214D1214yescomplemented
440#213—22no—
441#213—62no—
442#213—121no—
443(C2×D3)⋊C4—21no—
444(C2×D3)⋊C4—21no—
445(C2×D3)⋊C4—31no—
446(C2×D3)⋊C4—31no—
447(C2×D3)⋊C4—31no—
448(C2×D3)⋊C4—31no—
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—61no—
455(C2×D3)⋊C4—61no—
456(C2×D3)⋊C4—61no—
457(C2×D3)⋊C4—61no—
458(C2×D3)⋊C4—62no—
459(C2×D3)⋊C4—62no—
460C4⋊Dic3—31no—
461C4⋊Dic3—31no—
462C4⋊Dic3—61no—
463C4⋊Dic3—61no—
464C4⋊Dic3C22×D311yescharacteristic
465Dic3⋊C4—21no—
466Dic3⋊C4—61no—
467C4×Dic3—21no—
468C2×C3⋊C8C22×D311yescharacteristic
469C2×C3⋊C8C22×D311yescharacteristic
470C2×C3⋊C8C22×D311yescharacteristic
471C2×C3⋊C8C22×D311yescharacteristic
472D24—62no—
473D24—121no—
474#204—62no—
475#204—62no—
476#204—62no—
477#204—121no—
478ΓL(1,𝔽25)—62no—
479ΓL(1,𝔽25)—62no—
480D3×C8—62no—
481D3×C8—62no—
482C22×C32—22no—
483C22×C32—41no—
484C22×C32—41no—
485C22×C32C22×D411yescharacteristic
486C2×C3⋊D3—21no—
487C2×C3⋊D3—21no—
488C2×C3⋊D3—21no—
489C2×C3⋊D3—21no—
490C2×C3⋊D3—21no—
491C2×C3⋊D3—41no—
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⋊D3AGL(1,ℤ/8)12yescomplemented
500C2×C3×D3—41no—
501C2×C3×D3—41no—
502C2×C3×D3—41no—
503C32×C4—21no—
504C32×C4—21no—
505C32×C4—41no—
506C32×C4C22×D411yescharacteristic
507C32×C4H(5,𝔽2)11yescharacteristic
508C3⋊Dic3—21no—
509C3⋊Dic3—21no—
510C3×Dic3—22no—
511C3×Dic3—41no—
512C3×Dic3—41no—
513C2×#41—91no—
514C22×Q8—91no—
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—91no—
531#127—91no—
532#124—31no—
533#124—181no—
534C22⋊Q8—91no—
535C22⋊Q8—181no—
536#121—91no—
537#121—91no—
538#121—91no—
539#121—181no—
540#121—181no—
541#120—181no—
542#120—181no—
543C4×Q8—31no—
544C4×D4—91no—
545C4×D4—181no—
546C4×D4D3211yescharacteristic
547#107—31no—
548C4⋊C8—31no—
549#103—31no—
550#103—31no—
551#102—31no—
552#102—31no—
553#102—91no—
554#102—91no—
555C22⋊C8—91no—
556C22⋊C8—91no—
557#97—31no—
558C23×C3—22no—
559C23×C3—21no—
560C23×C3—21no—
561C23×C3—61no—
562C22×D3—21no—
563C22×D3—31no—
564C22×D3—31no—
565C22×D3—31no—
566C22×D3—31no—
567C22×D3—61no—
568C22×D3—61no—
569C22×D3—62no—
570C22×D3—62no—
571C22×D3—61no—
572C22×D3—61no—
573C22×D3—61no—
574C22×D3—61no—
575C22×D3—122no—
576C22×D3—122no—
577C22×D3—122no—
578C22×D3—122no—
579C22×D3—122no—
580C22×D3—122no—
581C22×D3—124no—
582C22×D3—124no—
583C22×D3—122no—
584C22×D3—122no—
585C22×D3—124no—
586C22×D3—124no—
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×D4—22no—
598C3×D4—21no—
599C3×D4—21no—
600C3×D4—22no—
601C3×D4—61no—
602C3×D4—61no—
603C3×D4C2×D1212yes—
604C3×D4D3×D412yes—
605C2×C3×C4—22no—
606C2×C3×C4—21no—
607C2×C3×C4—21no—
608C2×C3×C4—21no—
609C2×C3×C4—21no—
610C2×C3×C4—21no—
611C2×C3×C4—44no—
612C2×C3×C4—42no—
613C2×C3×C4—42no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4D3×D411yescharacteristic
618C2×C3×C4D3×D411yescharacteristic
619C2×C3×C4D3×D411yescharacteristic
620C2×C3×C4D3×D411yescharacteristic
621C2×C3×C4C23×D311yescharacteristic
622C2×C3×C4C23×D311yescharacteristic
623#67—122no—
624#67—122no—
625#67—122no—
626#67—122no—
627#67—122no—
628#67—122no—
629#67—124no—
630#67—124no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—31no—
635C2×Dic3—31no—
636C2×Dic3—31no—
637C2×Dic3—31no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—122no—
641D12—21no—
642D12—21no—
643D12—62no—
644D12—62no—
645D12—64no—
646D12—61no—
647D12—61no—
648D12—61no—
649D12—61no—
650D12—61no—
651D12—61no—
652D12—61no—
653D12—61no—
654D12—121no—
655D12—121no—
656D12—121no—
657D12—121no—
658D12—124no—
659D12—122no—
660D12—122no—
661D12—122no—
662D12—122no—
663D12—124no—
664D12—124no—
665D12—122no—
666D12—122no—
667D12—122no—
668D12—122no—
669D12—241no—
670D12—241no—
671D12—242no—
672C4×D3—61no—
673C4×D3—61no—
674C4×D3—61no—
675C4×D3—61no—
676C4×D3—61no—
677C4×D3—61no—
678C4×D3—61no—
679C4×D3—61no—
680C4×D3—121no—
681C4×D3—121no—
682C4×D3—121no—
683C4×D3—121no—
684C4×D3—122no—
685C4×D3—122no—
686C4×D3—122no—
687Dic6—21no—
688Dic6—21no—
689Dic6—21no—
690Dic6—122no—
691Dic6—122no—
692Dic6C2×D1212yescomplemented
693C3×C8—32no—
694C3×C8—61no—
695C3×C8—61no—
696C3×C8—61no—
697C3⋊C8—21no—
698C3⋊C8—21no—
699C3⋊C8—21no—
700C3⋊C8C2×D1212yescomplemented
701C2×C32—42no—
702C2×C32D4211yescharacteristic
703C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
704C2×C32#57711yescharacteristic
705C3⋊D3—22no—
706C3⋊D3—41no—
707C3⋊D3—81no—
708C3⋊D3—81no—
709C3×D3—81no—
710C24—181no—
711C24—181no—
712#41—182no—
713#41—361no—
714C2×Q8—31no—
715C2×Q8—31no—
716C2×Q8—181no—
717C2×Q8—182no—
718C2×Q8—361no—
719C2×D4—31no—
720C2×D4—91no—
721C2×D4—91no—
722C2×D4—91no—
723C2×D4—181no—
724C2×D4—181no—
725C2×D4—181no—
726C2×D4—181no—
727C2×D4—181no—
728C2×D4—181no—
729C2×D4—182no—
730C2×D4—182no—
731C2×D4—181no—
732C2×D4—181no—
733C2×D4—364no—
734C2×D4—361no—
735C2×D4—361no—
736C2×D4C2×D3211yescharacteristic
737C22×C4—21no—
738C22×C4—91no—
739C22×C4—91no—
740C22×C4—181no—
741C22×C4—181no—
742SD16—34no—
743SD16—62no—
744SD16—182no—
745SD16—182no—
746SD16—182no—
747SD16—361no—
748D8—62no—
749D8—182no—
750D8—361no—
751M16—182no—
752C2×C8—31no—
753C2×C8—31no—
754C2×C8—31no—
755C2×C8—31no—
756C2×C8—182no—
757C4⋊C4—31no—
758C4⋊C4—61no—
759C4⋊C4—91no—
760C4⋊C4—181no—
761C4⋊C4C2×D3211yescharacteristic
762C22⋊C4—21no—
763C22⋊C4—61no—
764C22⋊C4—61no—
765C22⋊C4—91no—
766C22⋊C4—91no—
767C22⋊C4—181no—
768C22⋊C4—181no—
769C22⋊C4—181no—
770C22⋊C4—181no—
771C42—61no—
772C42C2×D3211yescharacteristic
773C22×C3—24no—
774C22×C3—22no—
775C22×C3—22no—
776C22×C3—21no—
777C22×C3—42no—
778C22×C3—42no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3—121no—
784C22×C3—121no—
785C22×C3—121no—
786C22×C3C2×D3×D411yescharacteristic
787C22×C3C2×D3×D411yescharacteristic
788C2×D3—32no—
789C2×D3—32no—
790C2×D3—41no—
791C2×D3—41no—
792C2×D3—41no—
793C2×D3—62no—
794C2×D3—61no—
795C2×D3—61no—
796C2×D3—61no—
797C2×D3—61no—
798C2×D3—62no—
799C2×D3—61no—
800C2×D3—61no—
801C2×D3—61no—
802C2×D3—61no—
803C2×D3—61no—
804C2×D3—61no—
805C2×D3—121no—
806C2×D3—121no—
807C2×D3—121no—
808C2×D3—121no—
809C2×D3—122no—
810C2×D3—122no—
811C2×D3—122no—
812C2×D3—122no—
813C2×D3—122no—
814C2×D3—122no—
815C2×D3—121no—
816C2×D3—121no—
817C2×D3—121no—
818C2×D3—121no—
819C2×D3—121no—
820C2×D3—121no—
821C2×D3—121no—
822C2×D3—121no—
823C2×D3—121no—
824C2×D3—121no—
825C2×D3—121no—
826C2×D3—121no—
827C2×D3—244no—
828C2×D3—244no—
829C2×D3—248no—
830C2×D3—248no—
831C2×D3—244no—
832C2×D3—244no—
833C3×C4—22no—
834C3×C4—21no—
835C3×C4—21no—
836C3×C4—21no—
837C3×C4—21no—
838C3×C4—21no—
839C3×C4—21no—
840C3×C4—41no—
841C3×C4—42no—
842C3×C4—41no—
843C3×C4—41no—
844C3×C4—62no—
845C3×C4—121no—
846C3×C4—121no—
847C3×C4C22×D1211yescharacteristic
848C3×C4C2×D3×D411yescharacteristic
849C3×C4#100911yescharacteristic
850C3×C4#100911yescharacteristic
851Dic3—22no—
852Dic3—41no—
853Dic3—41no—
854Dic3—61no—
855Dic3—61no—
856Dic3—61no—
857Dic3—61no—
858Dic3—121no—
859Dic3—121no—
860C32#326511yescharacteristic, complemented, Sylow
861C23—21no—
862C23—61no—
863C23—91no—
864C23—91no—
865C23—181no—
866C23—181no—
867C23—362no—
868C23—362no—
869C23—362no—
870C23—362no—
871C23—721no—
872C23—721no—
873Q8—32no—
874Q8—61no—
875Q8—61no—
876Q8—61no—
877Q8—362no—
878D4—21no—
879D4—61no—
880D4—61no—
881D4—182no—
882D4—181no—
883D4—181no—
884D4—181no—
885D4—181no—
886D4—362no—
887D4—362no—
888D4—362no—
889D4—362no—
890D4—362no—
891D4—362no—
892D4—362no—
893D4—721no—
894D4D3×D1212yes—
895C2×C4—21no—
896C2×C4—42no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—91no—
901C2×C4—91no—
902C2×C4—181no—
903C2×C4—181no—
904C2×C4—181no—
905C2×C4—181no—
906C2×C4—362no—
907C2×C4—362no—
908C2×C4#381111yescharacteristic
909C2×C4#381111yescharacteristic
910C2×C4C22×D3211yescharacteristic
911C8—32no—
912C8—61no—
913C8—61no—
914C8—61no—
915C2×C3—21no—
916C2×C3—21no—
917C2×C3—21no—
918C2×C3—44no—
919C2×C3—42no—
920C2×C3—42no—
921C2×C3—241no—
922C2×C3D4×D1211yescharacteristic
923C2×C3#560911yescharacteristic
924C2×C3#577011yescharacteristic
925C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
926C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
927C2×C3#577811yescharacteristic
928D3—62no—
929D3—62no—
930D3—81no—
931D3—122no—
932D3—122no—
933D3—121no—
934D3—121no—
935D3—242no—
936D3—242no—
937D3—241no—
938D3—241no—
939D3—241no—
940D3—241no—
941C22—22no—
942C22—41no—
943C22—41no—
944C22—92no—
945C22—121no—
946C22—121no—
947C22—121no—
948C22—181no—
949C22—181no—
950C22—181no—
951C22—181no—
952C22—181no—
953C22—361no—
954C22—361no—
955C22—361no—
956C22—361no—
957C22—361no—
958C22—361no—
959C22—724no—
960C22—724no—
961C22C2×#381111yescharacteristic
962C4—21no—
963C4—21no—
964C4—41no—
965C4—62no—
966C4—121no—
967C4—121no—
968C4—181no—
969C4—181no—
970C4C2×D3×D1211yescharacteristic
971C4#6430811yescharacteristic
972C3—21no—
973C3#7979411yescharacteristic, complemented
974C3#8055311yescharacteristic, complemented
975C2—42no—
976C2—182no—
977C2—241no—
978C2—361no—
979C2—721no—
980C2—721no—
981C2#1059507411yescharacteristic
982C2#1059510011yescharacteristic
983C2#1059547311yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. D4×C4⋊(C3⋊D3)C2semidirect
2. C2×#63937C2semidirect
3. C2×#63930C2semidirect
4. #10593901C2semidirect
5. C3×#5018C2semidirect
6. C3×#5016C2semidirect
7. #10591467C2semidirect
8. #10591456C2semidirect
9. #10590617C2semidirect
10. #10590606C2semidirect
11. #10590522C2semidirect
12. #10590509C2semidirect
13. #10590367C2semidirect
14. #10590351C2semidirect
15. #10590328C2semidirect
21. C2×#3797C22semidirect
22. C2×#3796C22semidirect
34. C3×#875C22semidirect
35. C3×C4×Dic6C22semidirect
38. #63916C22semidirect
42. #63871C22semidirect
44. C2×#3717C22semidirect
45. C2×#3717C22semidirect
46. C2×#3717C22semidirect
47. C2×#3717C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
50. C2×#3712C22semidirect
51. C2×#3710C22semidirect
53. C3×#810C22semidirect
54. C3×#810C22semidirect
55. C3×#809C22semidirect
56. C3×#807C22semidirect
57. C3×C4⋊(C3⋊C8)C22semidirect
58. C3×#803C22semidirect
59. #63564C22semidirect
60. #63564C22semidirect
61. #63557C22semidirect
62. #63557C22semidirect
78. #5018D3semidirect
79. #5016D3semidirect
135. C3×#214D4semidirect
228. #875C2×D3semidirect
236. C4×Dic6C2×D3semidirect
251. #810C2×D3semidirect
252. #810C2×D3semidirect
255. #809C2×D3semidirect
256. #807C2×D3semidirect
257. C4⋊(C3⋊C8)C2×D3semidirect
258. #803C2×D3semidirect
303. C3×Dic6C2×D4semidirect
312. C3×C3⋊C8C2×D4semidirect
439. #214D12semidirect
499. C2×C3⋊D3AGL(1,ℤ/8)semidirect
692. Dic6C2×D12semidirect
700. C3⋊C8C2×D12semidirect
860. C32#3265semidirect
973. C3#79794semidirect
974. C3#80553semidirect

Maximal subgroups

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

subgroupindex
D4×C4⋊(C3⋊D3)2
C2×#639372
C2×#639302
#105939012
C3×#50182
C3×#50162
#105914672
#105914562
#105906172
#105906062
#105905222
#105905092
#105903672
#105903512
#105903282
#805533
#797943