Finite Group Databasebeta

← #11885825

Subgroups — #11885825

Order 1152.

1219 conjugacy classes of subgroups.

The subgroup lattice has 963 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596025C211yesmaximal, characteristic, complemented
2C2×#63936C211yesmaximal, characteristic, complemented
3C2×#63926C211yesmaximal, characteristic, complemented
4#10594005C211yesmaximal, characteristic, complemented
5C3×#5016C211yesmaximal, characteristic, complemented
6C3×C4×#213C211yesmaximal, characteristic, complemented
7#10591467C211yesmaximal, characteristic, complemented
8#10591457C211yesmaximal, characteristic, complemented
9#10590617C211yesmaximal, characteristic, complemented
10#10590597C211yesmaximal, characteristic, complemented
11#10590525C211yesmaximal, characteristic, complemented
12#10590509C211yesmaximal, characteristic, complemented
13#10590370C211yesmaximal, characteristic, complemented
14#10590366C211yesmaximal, characteristic, complemented
15#10590327C211yesmaximal, characteristic, complemented
16#80557—31nomaximal
17#79606—31nomaximal
18C2×#3830C2211yescharacteristic, complemented
19C2×D4×C3⋊D3C2211yescharacteristic
20C2×#3802C2211yescharacteristic
21C2×#3796C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic, complemented
23#64139—21no—
24C2×#3752—21no—
25#64106C2211yescharacteristic
26#64104C2211yescharacteristic, complemented
27#64095—21no—
28#64091—21no—
29#64084C2211yescharacteristic, complemented
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31C2×C3×#214C2211yescharacteristic, complemented
32C2×C3×#213C2211yescharacteristic
33C2×C3×#213C2211yescharacteristic
34C3×#875C2211yescharacteristic, complemented
35C3×C4×D12C2211yescharacteristic, complemented
36#63936—24no—
37#63926—24no—
38#63923—21no—
39D3×(C2×D3)⋊C4—21no—
40#63916C2211yescharacteristic, complemented
41#63906—21no—
42#63891—21no—
43#63871C2211yescharacteristic
44C2×#3719C2211yescharacteristic, complemented
45C2×#3717C2211yescharacteristic, complemented
46C2×#3716C2211yescharacteristic, complemented
47C2×#3716C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic
49C2×#3714C2211yescharacteristic
50C2×#3710C2211yescharacteristic
51C2×#3710C2211yescharacteristic, complemented
52C3×#832C2211yescharacteristic, complemented
53C3×#810C2211yescharacteristic, complemented
54C3×#809C2211yescharacteristic, complemented
55C3×#809C2211yescharacteristic, complemented
56C3×#807C2211yescharacteristic, complemented
57C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
58C3×C4×C3⋊C8C2211yescharacteristic, complemented
59#63567C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63557C2211yescharacteristic
62#63557C2211yescharacteristic, complemented
63C2×#916—31no—
64C2×#912—31no—
65C2×D3×D8—31no—
66C2×D3×D8—31no—
67#5676—31no—
68#5554—31no—
69#5554—31no—
70#5554—31no—
71#5554—61no—
72C3×#463—31no—
73C3×C4×D8—31no—
74#5169—31no—
75#5158—31no—
76#5059—31no—
77#5016—31no—
78#5016D311yescharacteristic, complemented
79C4×#213D311yescharacteristic, complemented
80#4887—31no—
81#4883—31no—
82#4844—31no—
83#4834—31no—
84#4813—31no—
85#4810—31no—
86#4781—31no—
87#4781—31no—
88#4776—31no—
89#4776—31no—
90#4776—31no—
91#4775—31no—
92#4696—31no—
93C8×D12—31no—
94C23×C3⋊D3—21no—
95C22×D32—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C2×#638—21no—
99C2×#638—21no—
100C22×C3⋊Dic3—21no—
101#3830—22no—
102#3830—41no—
103D4×C3⋊D3—22no—
104D4×C3⋊D3—41no—
105C2×C4⋊(C3⋊D3)—21no—
106C2×C4⋊(C3⋊D3)D411yescharacteristic
107C2×C4⋊(C3⋊D3)C2311yescharacteristic
108C2×C4×C3⋊D3C2311yescharacteristic
109C2×C4×C3⋊D3C2311yescharacteristic
110C2×#634C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×Dic6C2311yescharacteristic
115C2×#626—21no—
116C2×#626—21no—
117C2×#625—21no—
118C2×D3×Dic3—21no—
119#3802—22no—
120#3802—41no—
121#3796—22no—
122#3796—41no—
123C32×C4⋊C4C2311yescharacteristic
124C32×C22⋊C4—21no—
125C32×C42C2311yescharacteristic
126#3752—21no—
127#3752—21no—
128#3752—21no—
129#3752—21no—
130#3752D411yescharacteristic
131#3752D411yescharacteristic
132C4⋊(C3⋊Dic3)—21no—
133C4⋊(C3⋊Dic3)D411yescharacteristic
134C3×#214—22no—
135C3×#213—22no—
136C3×#213D414yescomplemented
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×C4⋊Dic3C2311yescharacteristic
141C2×C3×C3⋊C8C2311yescharacteristic
142C2×C3×C3⋊C8C2311yescharacteristic
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145Dic3⋊Dic3—21no—
146#3722—21no—
147(C2×D3)⋊Dic3—21no—
148#3719—22no—
149#3717—41no—
150#3716—22no—
151#3716—41no—
152#3714—22no—
153#3714—22no—
154#3710—22no—
155#3710—22no—
156#3280—91noSylow
157C2×#239—31no—
158C2×#237—31no—
159C2×#237—31no—
160C2×#237—31no—
161C2×#237—61no—
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—31no—
165C2×D3×D4—31no—
166C2×D3×D4—61no—
167C2×C3×SD16—31no—
168C2×C3×D8—31no—
169C2×C3×D8—31no—
170C3×#124—31no—
171C3×C4×D4—21no—
172C3×C4×D4—31no—
173C3×C4×D4C2×D311yescharacteristic, complemented
174C3×C4×D4C2×D311yescharacteristic, complemented
175#946—31no—
176C2×#216—31no—
177C2×#215—31no—
178#938—31no—
179C2×#214—31no—
180C2×#214—31no—
181C2×#214C2×D311yescharacteristic, complemented
182C2×#213—31no—
183C2×#213—31no—
184C2×#213C2×D311yescharacteristic
185C2×#213C2×D311yescharacteristic
186#930—61no—
187#930—61no—
188#930—61no—
189#930—62no—
190C2×(C2×D3)⋊C4—61no—
191C2×(C2×D3)⋊C4—61no—
192C2×(C2×D3)⋊C4—61no—
193C2×(C2×D3)⋊C4—62no—
194#916—64no—
195#912—64no—
196D3×D8—64no—
197D3×D8—64no—
198C2×Dic12—31no—
199C2×D24—31no—
200C2×D24—31no—
201C2×#204—31no—
202C2×#204—31no—
203C2×#204—31no—
204C2×D3×C8—31no—
205C2×D3×C8—31no—
206C2×D3×C8—31no—
207C2×D3×C8—31no—
208#897—31no—
209#897—31no—
210#897—31no—
211#897—61no—
212#895—31no—
213#895—31no—
214#895—31no—
215#895—61no—
216#886—61no—
217#886—61no—
218#886—61no—
219#886—62no—
220#884—61no—
221#883—61no—
222#882—61no—
223#882—61no—
224#882—61no—
225#882—61no—
226#882—62no—
227D3×C22⋊C4—61no—
228#875—31no—
229#875—31no—
230#875—61no—
231#875C2×D311yescharacteristic, complemented
232C4×D12—31no—
233C4×D12—31no—
234C4×D12—61no—
235C4×D12C2×D311yescharacteristic, complemented
236C3×#107—31no—
237C3×C4⋊C8—31no—
238C3×#103—31no—
239C3×#102—31no—
240C3×#102—31no—
241C3×#102—31no—
242C3×C4×C8—31no—
243#832C2×D311yescharacteristic, complemented
244#821—31no—
245(C2×D3)⋊C8—31no—
246(C2×D3)⋊C8—31no—
247(C2×D3)⋊C8—31no—
248(C2×D3)⋊C8—31no—
249#816—31no—
250#810—31no—
251#810C2×D311yescharacteristic, complemented
252#809—31no—
253#809C2×D311yescharacteristic, complemented
254#809C2×D311yescharacteristic, complemented
255#807C2×D311yescharacteristic, complemented
256C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
257C4×C3⋊C8C2×D311yescharacteristic, complemented
258C23×C32—21no—
259C22×C3⋊D3—21no—
260C22×C3⋊D3—42no—
261C22×C3⋊D3—42no—
262C22×C3⋊D3—81no—
263C22×C3⋊D3C2×D411yescharacteristic
264C22×C3⋊D3C2×D411yescharacteristic
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C2×D32—42no—
268C2×D32—42no—
269C2×D32—81no—
270C32×D4—21no—
271C32×D4C2×D412yes—
272C2×C32×C4—21no—
273C2×C32×C4—81no—
274C2×C32×C4C2×D411yescharacteristic
275C2×C32×C4C2×D411yescharacteristic
276C2×C32×C4C2411yescharacteristic
277#638—42no—
278#638—42no—
279C2×C3⋊Dic3—21no—
280C2×C3⋊Dic3—42no—
281C2×C3⋊Dic3C2×D411yescharacteristic
282C2×C3⋊Dic3C2×D411yescharacteristic
283C4⋊(C3⋊D3)—22no—
284C4⋊(C3⋊D3)—21no—
285C4⋊(C3⋊D3)—21no—
286C4⋊(C3⋊D3)—81no—
287C4×C3⋊D3—21no—
288C4×C3⋊D3—21no—
289C4×C3⋊D3—21no—
290C4×C3⋊D3—21no—
291#634—21no—
292#634—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3—21no—
295C3×D12—21no—
296C3×D12—21no—
297C3×D12—21no—
298C3×D12C2×D412yes—
299C3×C4×D3—81no—
300C3×Dic6—21no—
301C3×Dic6—21no—
302#626—42no—
303#626—81no—
304#625—42no—
305D3×Dic3—42no—
306C3×C3⋊C8—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C3×C3⋊C8C2×D412yes—
310C2×#135—91no—
311C22×D8—91no—
312#546—91no—
313#546—91no—
314#495—91no—
315#467—91no—
316#466—91no—
317#463—31no—
318#463—91no—
319#450—91no—
320#450—91no—
321#449—91no—
322#449—91no—
323C4×D8—31no—
324C8×D4—91no—
325C23×D3—61no—
326C23×D3—61no—
327C23×D3—61no—
328C23×D3—61no—
329C23×D3—62no—
330C2×C3×Q8—31no—
331C2×C3×D4—21no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4C22×D311yescharacteristic
335C2×C3×D4C22×D311yescharacteristic
336C22×C3×C4—22no—
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—61no—
340C2×#67—61no—
341C2×#67—61no—
342C2×#67—61no—
343C2×#67—61no—
344C2×#67—61no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—61no—
348C2×#67—62no—
349C2×#67—62no—
350C22×Dic3—61no—
351C22×Dic3—61no—
352C22×Dic3—61no—
353C22×Dic3—62no—
354#239—62no—
355#239—121no—
356#237—62no—
357#237—62no—
358#237—62no—
359#237—122no—
360#237—121no—
361#237—121no—
362#237—121no—
363#237—122no—
364D3×D4—62no—
365D3×D4—62no—
366D3×D4—62no—
367D3×D4—62no—
368D3×D4—122no—
369D3×D4—121no—
370D3×D4—121no—
371D3×D4—121no—
372D3×D4—121no—
373D3×D4—122no—
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—62no—
384C2×D12—61no—
385C2×D12C22×D311yescharacteristic
386C2×D12C22×D311yescharacteristic
387C2×C4×D3—21no—
388C2×C4×D3—31no—
389C2×C4×D3—31no—
390C2×C4×D3—31no—
391C2×C4×D3—31no—
392C2×C4×D3—61no—
393C2×C4×D3—61no—
394C2×C4×D3—61no—
395C2×Dic6—31no—
396C2×Dic6—31no—
397C2×Dic6—61no—
398C2×Dic6C22×D311yescharacteristic
399C3×SD16—62no—
400C3×D8—34no—
401C3×D8—62no—
402C2×C3×C8—31no—
403C2×C3×C8—31no—
404C2×C3×C8—31no—
405C2×C3×C8—31no—
406C3×C4⋊C4—21no—
407C3×C4⋊C4—31no—
408C3×C4⋊C4C22×D311yescharacteristic
409C3×C4⋊C4C22×D311yescharacteristic
410C3×C22⋊C4—22no—
411C3×C22⋊C4—21no—
412C3×C22⋊C4—21no—
413C3×C22⋊C4—61no—
414C3×C22⋊C4—61no—
415C3×C22⋊C4—61no—
416C3×C42—21no—
417C3×C42C22×D311yescharacteristic
418C3×C42C22×D311yescharacteristic
419#217—61no—
420#216—62no—
421#215—121no—
422#214—22no—
423#214—62no—
424#214—121no—
425#213—22no—
426#213—62no—
427#213—62no—
428#213D1214yescomplemented
429(C2×D3)⋊C4—21no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—31no—
433(C2×D3)⋊C4—31no—
434(C2×D3)⋊C4—31no—
435(C2×D3)⋊C4—31no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—61no—
441(C2×D3)⋊C4—61no—
442(C2×D3)⋊C4—61no—
443(C2×D3)⋊C4—61no—
444(C2×D3)⋊C4—61no—
445(C2×D3)⋊C4—62no—
446(C2×D3)⋊C4—62no—
447(C2×D3)⋊C4—62no—
448(C2×D3)⋊C4—62no—
449(C2×D3)⋊C4—61no—
450(C2×D3)⋊C4—61no—
451(C2×D3)⋊C4—61no—
452(C2×D3)⋊C4—61no—
453C4⋊Dic3—31no—
454C4⋊Dic3—31no—
455C4⋊Dic3—61no—
456C4⋊Dic3—61no—
457C4⋊Dic3—61no—
458C4⋊Dic3—61no—
459C4⋊Dic3—62no—
460C4⋊Dic3C22×D311yescharacteristic
461Dic3⋊C4—61no—
462C2×C3⋊C8C22×D311yescharacteristic
463C2×C3⋊C8C22×D311yescharacteristic
464C2×C3⋊C8C22×D311yescharacteristic
465C2×C3⋊C8C22×D311yescharacteristic
466Dic12—62no—
467D24—62no—
468D24—62no—
469#204—62no—
470#204—121no—
471#204—121no—
472D3×C8—62no—
473D3×C8—62no—
474D3×C8—62no—
475D3×C8—62no—
476C22×C32—22no—
477C22×C32—41no—
478C22×C32—41no—
479C22×C32C22×D411yescharacteristic
480C2×C3⋊D3—21no—
481C2×C3⋊D3—21no—
482C2×C3⋊D3—21no—
483C2×C3⋊D3—21no—
484C2×C3⋊D3—21no—
485C2×C3⋊D3—41no—
486C2×C3⋊D3—41no—
487C2×C3⋊D3—41no—
488C2×C3⋊D3—84no—
489C2×C3⋊D3#13512yescomplemented
490C2×C3×D3—22no—
491C2×C3×D3—41no—
492C2×C3×D3—41no—
493C2×C3×D3—41no—
494C2×C3×D3—41no—
495C2×C3×D3—41no—
496D32—84no—
497C32×C4—21no—
498C32×C4—21no—
499C32×C4—41no—
500C32×C4C22×D411yescharacteristic
501C32×C4H(5,𝔽2)11yescharacteristic
502C3⋊Dic3—21no—
503C3⋊Dic3—21no—
504C3⋊Dic3—41no—
505C3×Dic3—41no—
506C3×Dic3—41no—
507C2×#41—91no—
508C2×#41—91no—
509C22×D4—91no—
510C22×D4—91no—
511#135—184no—
512C2×Q16—91no—
513C2×SD16—31no—
514C2×SD16—91no—
515C2×SD16—91no—
516C2×SD16—91no—
517C2×D8—31no—
518C2×D8—31no—
519C2×D8—91no—
520C2×D8—91no—
521C2×D8—184no—
522C22×C8—91no—
523C22×C8—91no—
524#124—31no—
525#124—91no—
526#123—181no—
527#123—181no—
528C22⋊Q8—91no—
529C22⋊Q8—91no—
530#121—91no—
531#121—91no—
532#121—181no—
533#121—181no—
534#120—181no—
535#120—181no—
536C4×D4—31no—
537C4×D4—91no—
538C4×D4D3211yescharacteristic, complemented
539C2×C22⋊C4—181no—
540C2×C22⋊C4—181no—
541#107—31no—
542C4⋊C8—31no—
543#103—31no—
544#103—91no—
545#102—31no—
546#102—31no—
547#102—31no—
548#102—91no—
549C22⋊C8—91no—
550C22⋊C8—91no—
551C4×C8—31no—
552C23×C3—22no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—61no—
556C23×C3—61no—
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—31no—
560C22×D3—31no—
561C22×D3—31no—
562C22×D3—31no—
563C22×D3—61no—
564C22×D3—61no—
565C22×D3—62no—
566C22×D3—61no—
567C22×D3—61no—
568C22×D3—122no—
569C22×D3—122no—
570C22×D3—122no—
571C22×D3—122no—
572C22×D3—122no—
573C22×D3—122no—
574C22×D3—122no—
575C22×D3—122no—
576C22×D3—124no—
577C22×D3—124no—
578C22×D3—241no—
579C22×D3—241no—
580C22×D3—241no—
581C22×D3—241no—
582C22×D3—242no—
583C3×Q8—61no—
584C3×Q8—61no—
585C3×D4—22no—
586C3×D4—21no—
587C3×D4—21no—
588C3×D4—22no—
589C3×D4—32no—
590C3×D4—61no—
591C3×D4—61no—
592C3×D4—61no—
593C3×D4C2×D1212yes—
594C3×D4D3×D412yes—
595C2×C3×C4—22no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—21no—
600C2×C3×C4—21no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—81no—
604C2×C3×C4—81no—
605C2×C3×C4—82no—
606C2×C3×C4—241no—
607C2×C3×C4D3×D411yescharacteristic
608C2×C3×C4D3×D411yescharacteristic
609C2×C3×C4D3×D411yescharacteristic
610C2×C3×C4D3×D411yescharacteristic
611C2×C3×C4C23×D311yescharacteristic
612C2×C3×C4C23×D311yescharacteristic
613#67—122no—
614#67—122no—
615#67—122no—
616#67—122no—
617#67—122no—
618#67—122no—
619#67—122no—
620#67—124no—
621#67—124no—
622#67—241no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—31no—
626C2×Dic3—31no—
627C2×Dic3—31no—
628C2×Dic3—31no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—62no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—122no—
635C2×Dic3—122no—
636C2×Dic3—122no—
637C2×Dic3—124no—
638D12—21no—
639D12—21no—
640D12—21no—
641D12—62no—
642D12—62no—
643D12—61no—
644D12—61no—
645D12—61no—
646D12—61no—
647D12—121no—
648D12—121no—
649D12—122no—
650D12—122no—
651D12—241no—
652D12—241no—
653D12—242no—
654D12—241no—
655D12C2×D1212yes—
656C4×D3—61no—
657C4×D3—61no—
658C4×D3—61no—
659C4×D3—61no—
660C4×D3—61no—
661C4×D3—61no—
662C4×D3—61no—
663C4×D3—61no—
664C4×D3—81no—
665C4×D3—121no—
666C4×D3—121no—
667C4×D3—121no—
668C4×D3—121no—
669C4×D3—122no—
670Dic6—21no—
671Dic6—21no—
672Dic6—61no—
673Dic6—61no—
674Dic6—61no—
675Dic6—61no—
676Dic6—121no—
677Dic6—121no—
678C3×C8—32no—
679C3×C8—61no—
680C3×C8—61no—
681C3×C8—61no—
682C3⋊C8—21no—
683C3⋊C8—21no—
684C3⋊C8—21no—
685C3⋊C8C2×D1212yes—
686C2×C32—42no—
687C2×C32D4211yescharacteristic
688C2×C32C2×#13511yescharacteristic
689C2×C32#57611yescharacteristic
690C3⋊D3—22no—
691C3⋊D3—41no—
692C3⋊D3—81no—
693C3×D3—42no—
694C3×D3—81no—
695C24—181no—
696C24—181no—
697#41—182no—
698#41—182no—
699#41—361no—
700#41—361no—
701C2×Q8—31no—
702C2×Q8—91no—
703C2×D4—31no—
704C2×D4—31no—
705C2×D4—91no—
706C2×D4—91no—
707C2×D4—181no—
708C2×D4—181no—
709C2×D4—181no—
710C2×D4—181no—
711C2×D4—181no—
712C2×D4—182no—
713C2×D4—182no—
714C2×D4—181no—
715C2×D4—361no—
716C2×D4—361no—
717C2×D4C2×D3211yescharacteristic
718C22×C4—21no—
719C22×C4—61no—
720C22×C4—91no—
721C22×C4—91no—
722C22×C4—181no—
723C22×C4—181no—
724Q16—182no—
725SD16—62no—
726SD16—182no—
727SD16—361no—
728SD16—361no—
729D8—34no—
730D8—62no—
731D8—182no—
732D8—182no—
733C2×C8—31no—
734C2×C8—31no—
735C2×C8—31no—
736C2×C8—31no—
737C2×C8—182no—
738C2×C8—182no—
739C4⋊C4—31no—
740C4⋊C4—91no—
741C4⋊C4—181no—
742C4⋊C4—181no—
743C4⋊C4C2×D3211yescharacteristic
744C22⋊C4—21no—
745C22⋊C4—61no—
746C22⋊C4—61no—
747C22⋊C4—61no—
748C22⋊C4—91no—
749C22⋊C4—91no—
750C22⋊C4—181no—
751C22⋊C4—181no—
752C22⋊C4—181no—
753C22⋊C4—181no—
754C22⋊C4—181no—
755C22⋊C4—181no—
756C42C2×D3211yescharacteristic
757C22×C3—24no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—21no—
761C22×C3—42no—
762C22×C3—42no—
763C22×C3—41no—
764C22×C3—41no—
765C22×C3—41no—
766C22×C3—41no—
767C22×C3—62no—
768C22×C3—121no—
769C22×C3—121no—
770C22×C3—121no—
771C22×C3—121no—
772C22×C3—121no—
773C22×C3C2×D3×D411yescharacteristic
774C22×C3C2×D3×D411yescharacteristic
775C2×D3—22no—
776C2×D3—32no—
777C2×D3—32no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—62no—
784C2×D3—61no—
785C2×D3—61no—
786C2×D3—61no—
787C2×D3—61no—
788C2×D3—61no—
789C2×D3—61no—
790C2×D3—61no—
791C2×D3—61no—
792C2×D3—61no—
793C2×D3—61no—
794C2×D3—121no—
795C2×D3—121no—
796C2×D3—121no—
797C2×D3—121no—
798C2×D3—121no—
799C2×D3—122no—
800C2×D3—122no—
801C2×D3—122no—
802C2×D3—121no—
803C2×D3—121no—
804C2×D3—121no—
805C2×D3—121no—
806C2×D3—121no—
807C2×D3—121no—
808C2×D3—244no—
809C2×D3—244no—
810C2×D3—244no—
811C2×D3—244no—
812C2×D3—248no—
813C3×C4—21no—
814C3×C4—21no—
815C3×C4—21no—
816C3×C4—21no—
817C3×C4—21no—
818C3×C4—21no—
819C3×C4—41no—
820C3×C4—41no—
821C3×C4—42no—
822C3×C4—41no—
823C3×C4—41no—
824C3×C4—121no—
825C3×C4—121no—
826C3×C4C22×D1211yescharacteristic
827C3×C4C2×D3×D411yescharacteristic
828C3×C4#100911yescharacteristic
829C3×C4#100911yescharacteristic
830Dic3—41no—
831Dic3—41no—
832Dic3—61no—
833Dic3—61no—
834Dic3—61no—
835Dic3—61no—
836Dic3—121no—
837Dic3—121no—
838Dic3—122no—
839Dic3—121no—
840Dic3—121no—
841C32#328011yescharacteristic, complemented, Sylow
842C23—21no—
843C23—61no—
844C23—61no—
845C23—91no—
846C23—91no—
847C23—181no—
848C23—362no—
849C23—362no—
850C23—362no—
851C23—362no—
852C23—721no—
853C23—721no—
854Q8—61no—
855Q8—61no—
856Q8—181no—
857Q8—181no—
858D4—21no—
859D4—32no—
860D4—61no—
861D4—61no—
862D4—61no—
863D4—182no—
864D4—181no—
865D4—181no—
866D4—362no—
867D4—362no—
868D4—362no—
869D4—362no—
870D4—721no—
871D4—721no—
872D4D3×D1212yes—
873C2×C4—21no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—81no—
877C2×C4—91no—
878C2×C4—91no—
879C2×C4—181no—
880C2×C4—181no—
881C2×C4—181no—
882C2×C4—181no—
883C2×C4—181no—
884C2×C4—241no—
885C2×C4—362no—
886C2×C4—362no—
887C2×C4#381111yescharacteristic
888C2×C4#381111yescharacteristic
889C2×C4C22×D3211yescharacteristic
890C8—32no—
891C8—61no—
892C8—61no—
893C8—61no—
894C2×C3—21no—
895C2×C3—21no—
896C2×C3—21no—
897C2×C3—44no—
898C2×C3—42no—
899C2×C3—42no—
900C2×C3—122no—
901C2×C3—241no—
902C2×C3D4×D1211yescharacteristic
903C2×C3#560911yescharacteristic
904C2×C3#575711yescharacteristic
905C2×C3D3×#13511yescharacteristic
906C2×C3D3×#13511yescharacteristic
907C2×C3#577411yescharacteristic
908D3—42no—
909D3—62no—
910D3—62no—
911D3—81no—
912D3—122no—
913D3—121no—
914D3—121no—
915D3—241no—
916D3—242no—
917D3—241no—
918D3—241no—
919C22—22no—
920C22—41no—
921C22—41no—
922C22—62no—
923C22—92no—
924C22—121no—
925C22—121no—
926C22—121no—
927C22—121no—
928C22—121no—
929C22—181no—
930C22—181no—
931C22—181no—
932C22—181no—
933C22—181no—
934C22—361no—
935C22—361no—
936C22—361no—
937C22—724no—
938C22—724no—
939C22C2×#381111yescharacteristic
940C4—21no—
941C4—21no—
942C4—41no—
943C4—121no—
944C4—121no—
945C4—181no—
946C4—181no—
947C4—361no—
948C4C2×D3×D1211yescharacteristic
949C4#6430811yescharacteristic
950C3—21no—
951C3#7960611yescharacteristic, complemented
952C3#8055711yescharacteristic, complemented
953C2—42no—
954C2—122no—
955C2—182no—
956C2—241no—
957C2—361no—
958C2—721no—
959C2#1059507411yescharacteristic
960C2#1059510211yescharacteristic
961C2#1059545911yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
hypercenterC4×D4D32
hypocenterC32#3280
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. #10596025C2semidirect
2. C2×#63936C2semidirect
3. C2×#63926C2semidirect
4. #10594005C2semidirect
5. C3×#5016C2semidirect
6. C3×C4×#213C2semidirect
7. #10591467C2semidirect
8. #10591457C2semidirect
9. #10590617C2semidirect
10. #10590597C2semidirect
11. #10590525C2semidirect
12. #10590509C2semidirect
13. #10590370C2semidirect
14. #10590366C2semidirect
15. #10590327C2semidirect
18. C2×#3830C22semidirect
21. C2×#3796C22semidirect
22. C32×C4×D4C22semidirect
26. #64104C22semidirect
29. #64084C22semidirect
31. C2×C3×#214C22semidirect
34. C3×#875C22semidirect
35. C3×C4×D12C22semidirect
40. #63916C22semidirect
44. C2×#3719C22semidirect
45. C2×#3717C22semidirect
46. C2×#3716C22semidirect
47. C2×#3716C22semidirect
51. C2×#3710C22semidirect
52. C3×#832C22semidirect
53. C3×#810C22semidirect
54. C3×#809C22semidirect
55. C3×#809C22semidirect
56. C3×#807C22semidirect
57. C3×C4⋊(C3⋊C8)C22semidirect
58. C3×C4×C3⋊C8C22semidirect
59. #63567C22semidirect
60. #63564C22semidirect
62. #63557C22semidirect
78. #5016D3semidirect
79. C4×#213D3semidirect
136. C3×#213D4semidirect
173. C3×C4×D4C2×D3semidirect
174. C3×C4×D4C2×D3semidirect
181. C2×#214C2×D3semidirect
231. #875C2×D3semidirect
235. C4×D12C2×D3semidirect
243. #832C2×D3semidirect
251. #810C2×D3semidirect
253. #809C2×D3semidirect
254. #809C2×D3semidirect
255. #807C2×D3semidirect
256. C4⋊(C3⋊C8)C2×D3semidirect
257. C4×C3⋊C8C2×D3semidirect
428. #213D12semidirect
489. C2×C3⋊D3#135semidirect
538. C4×D4D32semidirect
841. C32#3280semidirect
951. C3#79606semidirect
952. C3#80557semidirect

Maximal subgroups

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

subgroupindex
#105960252
C2×#639362
C2×#639262
#105940052
C3×#50162
C3×C4×#2132
#105914672
#105914572
#105906172
#105905972
#105905252
#105905092
#105903702
#105903662
#105903272
#805573
#796063