Finite Group Databasebeta

← #11884112

Subgroups — #11884112

Order 1152.

1155 conjugacy classes of subgroups.

The subgroup lattice has 919 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596021C211yesmaximal, characteristic
2C3×D4×Dic6C211yesmaximal, characteristic, complemented
3C2×#63833C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5C3×#5011C211yesmaximal, characteristic, complemented
6#10591187C211yesmaximal, characteristic, complemented
7#10591186C211yesmaximal, characteristic, complemented
8#10591184C211yesmaximal, characteristic, complemented
9#10591183C211yesmaximal, characteristic, complemented
10#10591178C211yesmaximal, characteristic, complemented
11#10591174C211yesmaximal, characteristic, complemented
12#10590379C211yesmaximal, characteristic, complemented
13#10590374C211yesmaximal, characteristic, complemented
14#10590368C211yesmaximal, characteristic, complemented
15#10590362C211yesmaximal, characteristic, complemented
16#83559—31nomaximal
17#79495—31nomaximal
18C2×#3828C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic, complemented
22C32×C4×D4C2211yescharacteristic
23#64146—21no—
24#64139C2211yescharacteristic
25#64133C2211yescharacteristic
26#64103—21no—
27#64093—21no—
28C22⋊C4×C3⋊D3—21no—
29#64084C2211yescharacteristic
30C4×C4⋊(C3⋊D3)C2211yescharacteristic
31C3×D4×Dic3—21no—
32C3×#924C2211yescharacteristic
33C3×#924C2211yescharacteristic, complemented
34C2×C3×#208C2211yescharacteristic, complemented
35C22×C3×C3⋊C8C2211yescharacteristic
36C3×#888—21no—
37C3×#878—21no—
38C3×#878—21no—
39C3×#869C2211yescharacteristic, complemented
40C3×C4×Dic6C2211yescharacteristic, complemented
41C2×#3719C2211yescharacteristic, complemented
42C2×#3719C2211yescharacteristic, complemented
43C2×#3719C2211yescharacteristic, complemented
44#63833—24no—
45C2×#3717—24no—
46C2×#3717C2211yescharacteristic
47C2×#3717C2211yescharacteristic
48C2×#3717C2211yescharacteristic
49C2×#3717C2211yescharacteristic
50C2×#3717C2211yescharacteristic
51C2×#3717C2211yescharacteristic
52C3×#830C2211yescharacteristic
53C3×#830C2211yescharacteristic, complemented
54C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
55C3×#803C2211yescharacteristic, complemented
56#63575C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63566C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63564C2211yescharacteristic
62#63564C2211yescharacteristic
63C3×D4×Q8—31no—
64C2×#942—31no—
65C22×#215—31no—
66C2×#909—31no—
67C22×#204—31no—
68#5550—31no—
69#5550—31no—
70#5550—61no—
71D4×Dic6D311yescharacteristic, complemented
72C3×#435—31no—
73#5228—31no—
74#5227—31no—
75#5134—31no—
76#5116—31no—
77#5086—31no—
78#5083—31no—
79#5051—31no—
80#5049—31no—
81#5047—31no—
82#5046—31no—
83#5028—31no—
84#5026—31no—
85#5011D311yescharacteristic, complemented
86#4845—31no—
87#4841—31no—
88#4739—31no—
89#4738—31no—
90#4733—31no—
91#4731—31no—
92#4715—31no—
93#4710—31no—
94C23×C3⋊D3—21no—
95C2×C32×D4D411yescharacteristic
96C22×C32×C4C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×#638—21no—
99C2×#638—21no—
100#3828—22no—
101#3828—41no—
102C2×C4⋊(C3⋊D3)—22no—
103C2×C4⋊(C3⋊D3)—21no—
104C2×C4⋊(C3⋊D3)—41no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4⋊(C3⋊D3)C2311yescharacteristic
107C2×C4×C3⋊D3—21no—
108C2×C4×C3⋊D3—21no—
109C2×#634C2311yescharacteristic
110C22×C3×Dic3—21no—
111C22×C3×Dic3—21no—
112C2×C3×Dic6—22no—
113C2×C3×Dic6—22no—
114C2×C3×Dic6—21no—
115C2×C3×Dic6—21no—
116C2×C3×Dic6—41no—
117C2×C3×Dic6—41no—
118C2×C3×Dic6C2311yescharacteristic
119C2×C3×Dic6C2311yescharacteristic
120C2×C3×Dic6C2311yescharacteristic
121C32×C4⋊C4D411yescharacteristic
122C32×C22⋊C4D411yescharacteristic
123C32×C22⋊C4D411yescharacteristic
124C32×C42C2311yescharacteristic
125#3757—21no—
126#3752—21no—
127#3752—21no—
128#3752—21no—
129#3752—21no—
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131#3750—21no—
132C3×#217—21no—
133C3×#217—21no—
134C3×C4⋊Dic3—21no—
135C3×C4⋊Dic3—21no—
136C3×C4⋊Dic3C2311yescharacteristic
137C3×Dic3⋊C4—21no—
138C3×Dic3⋊C4—21no—
139C3×Dic3⋊C4—21no—
140C3×C4×Dic3—21no—
141C3×#208—22no—
142C2×C3×C3⋊C8—22no—
143C2×C3×C3⋊C8C2311yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147#3719—22no—
148#3719—22no—
149#3719—41no—
150#3717—22no—
151#3717—22no—
152#3717—22no—
153#3717—22no—
154#3717—41no—
155#3717D414yescomplemented
156#3266—91noSylow
157C22×C3×Q8—31no—
158C22×C3×Q8—31no—
159C2×#235—31no—
160C2×#235—31no—
161C2×#235—61no—
162C22×D12—31no—
163C22×D12—31no—
164C22×D12—61no—
165C22×Dic6C2×D311yescharacteristic
166C22×Dic6C2×D311yescharacteristic, complemented
167C2×C3×M16—31no—
168C22×C3×C8—31no—
169C3×C4⋊Q8—31no—
170C3×C4⋊Q8—61no—
171C3×C22⋊Q8—31no—
172C3×C22⋊Q8—31no—
173C3×C22⋊Q8—61no—
174C3×C22⋊Q8—61no—
175C3×C4×Q8—31no—
176C3×C4×D4—21no—
177C3×C4×D4—61no—
178C3×C4×D4C2×D311yescharacteristic
179C3×C4×D4C2×D311yescharacteristic
180C2×#216—31no—
181C2×#216—31no—
182C2×#216—31no—
183#942—64no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—31no—
190C2×#215—64no—
191#937—62no—
192#937—61no—
193#937—61no—
194D4×Dic3—21no—
195#930—31no—
196#930—31no—
197#930—61no—
198#924—31no—
199#924—31no—
200#924—61no—
201#924C2×D311yescharacteristic
202#924C2×D311yescharacteristic, complemented
203C2×#208C2×D311yescharacteristic, complemented
204C22×C3⋊C8C2×D311yescharacteristic
205#909—64no—
206C2×Dic12—31no—
207C2×Dic12—31no—
208C2×Dic12—31no—
209C2×#204—31no—
210C2×#204—31no—
211C2×#204—31no—
212C2×#204—31no—
213C2×#204—31no—
214C2×#204—31no—
215C2×#204—64no—
216#894—62no—
217#894—61no—
218#894—61no—
219#888—21no—
220#884—62no—
221#884—61no—
222#884—61no—
223D3×C22⋊C4—62no—
224D3×C22⋊C4—61no—
225D3×C22⋊C4—61no—
226#878—21no—
227#878—21no—
228#875—31no—
229#875—31no—
230#875—61no—
231C4×D12—31no—
232C4×D12—31no—
233C4×D12—61no—
234#869C2×D311yescharacteristic, complemented
235C4×Dic6C2×D311yescharacteristic, complemented
236C3×C4⋊C8—31no—
237C3×C22⋊C8—31no—
238C3×C22⋊C8—31no—
239C3×#97—31no—
240#835—31no—
241#835—31no—
242#835—31no—
243#830C2×D311yescharacteristic
244#830C2×D311yescharacteristic, complemented
245#821—31no—
246#821—31no—
247#818—31no—
248#816—31no—
249#816—31no—
250#816—31no—
251#816—31no—
252#810—31no—
253#809—31no—
254#809—31no—
255#807—31no—
256C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
257#803C2×D311yescharacteristic, complemented
258C23×C32C2×D411yescharacteristic
259C23×C32C2×D411yescharacteristic
260C22×C3⋊D3—21no—
261C22×C3⋊D3—21no—
262C22×C3⋊D3—42no—
263C22×C3⋊D3—42no—
264C22×C3⋊D3—81no—
265C32×D4—22no—
266C2×C32×C4—21no—
267C2×C32×C4—21no—
268C2×C32×C4—21no—
269C2×C32×C4—21no—
270C2×C32×C4C2×D411yescharacteristic
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2411yescharacteristic
275#638—42no—
276#638—81no—
277C2×C3⋊Dic3—21no—
278C2×C3⋊Dic3—21no—
279C4⋊(C3⋊D3)—21no—
280C4⋊(C3⋊D3)—21no—
281C4⋊(C3⋊D3)—21no—
282C4⋊(C3⋊D3)—42no—
283C4⋊(C3⋊D3)C2×D412yes—
284C4×C3⋊D3—42no—
285C4×C3⋊D3—81no—
286#634—21no—
287#634—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—42no—
293C2×C3×Dic3—42no—
294C3×Dic6—21no—
295C3×Dic6—21no—
296C3×Dic6—21no—
297C3×Dic6—21no—
298C3×Dic6—21no—
299C3×Dic6—42no—
300C3×Dic6—42no—
301C3×Dic6C2×D412yes—
302C3×C3⋊C8—21no—
303C3×C3⋊C8—21no—
304C3×C3⋊C8—21no—
305C3×C3⋊C8C2×D412yes—
306C2×#137—91no—
307C22×SD16—91no—
308D4×Q8—31no—
309#546—91no—
310#497—91no—
311#468—91no—
312#467—91no—
313#464—91no—
314#461—91no—
315#452—91no—
316#451—91no—
317#450—91no—
318#448—91no—
319#440—91no—
320#435—31no—
321C23×D3—62no—
322C23×D3—61no—
323C23×D3—61no—
324C2×C3×Q8—31no—
325C2×C3×Q8—31no—
326C2×C3×Q8—31no—
327C2×C3×Q8—62no—
328C2×C3×Q8—62no—
329C2×C3×Q8—61no—
330C2×C3×Q8—61no—
331C2×C3×Q8—121no—
332C2×C3×Q8—121no—
333C2×C3×D4—21no—
334C2×C3×D4D1211yescharacteristic
335C2×C3×D4#6711yescharacteristic
336C22×C3×C4—21no—
337C22×C3×C4—21no—
338C22×C3×C4—61no—
339C22×C3×C4—61no—
340C22×C3×C4C22×D311yescharacteristic
341C22×C3×C4C22×D311yescharacteristic
342C22×C3×C4C22×D311yescharacteristic
343C22×C3×C4C22×D311yescharacteristic
344C2×#67—62no—
345C2×#67—61no—
346C2×#67—61no—
347C2×#67—62no—
348C2×#67—61no—
349C2×#67—61no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352#235—62no—
353#235—62no—
354#235—122no—
355#235—121no—
356#235—121no—
357#235—122no—
358C2×D12—31no—
359C2×D12—31no—
360C2×D12—31no—
361C2×D12—31no—
362C2×D12—61no—
363C2×D12—61no—
364C2×D12—62no—
365C2×D12—62no—
366C2×D12—62no—
367C2×D12—61no—
368C2×D12—61no—
369C2×D12—122no—
370C2×D12—121no—
371C2×D12—121no—
372C2×D12—122no—
373C2×C4×D3—62no—
374C2×C4×D3—61no—
375C2×C4×D3—61no—
376C2×C4×D3—62no—
377C2×C4×D3—61no—
378C2×C4×D3—61no—
379C2×Dic6—22no—
380C2×Dic6—22no—
381C2×Dic6—21no—
382C2×Dic6—21no—
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—41no—
386C2×Dic6—41no—
387C2×Dic6—61no—
388C2×Dic6C22×D311yescharacteristic
389C2×Dic6C22×D311yescharacteristic
390C2×Dic6C22×D311yescharacteristic
391C3×M16—62no—
392C2×C3×C8—31no—
393C2×C3×C8—31no—
394C2×C3×C8—31no—
395C2×C3×C8—31no—
396C2×C3×C8—62no—
397C3×C4⋊C4—21no—
398C3×C4⋊C4—31no—
399C3×C4⋊C4—61no—
400C3×C4⋊C4—61no—
401C3×C4⋊C4—61no—
402C3×C4⋊C4—61no—
403C3×C4⋊C4—61no—
404C3×C4⋊C4D1211yescharacteristic
405C3×C4⋊C4#6711yescharacteristic
406C3×C22⋊C4—21no—
407C3×C22⋊C4—21no—
408C3×C22⋊C4—61no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4D1211yescharacteristic
411C3×C22⋊C4D1211yescharacteristic
412C3×C22⋊C4#6711yescharacteristic
413C3×C22⋊C4#6711yescharacteristic
414C3×C42—21no—
415C3×C42—61no—
416C3×C42C22×D311yescharacteristic
417C3×C42C22×D311yescharacteristic
418#217—21no—
419#217—21no—
420#217—62no—
421#217—61no—
422#217—61no—
423#216—62no—
424#216—62no—
425#216—121no—
426#215—34no—
427#215—62no—
428#215—62no—
429#215—62no—
430#215—62no—
431#215—121no—
432(C2×D3)⋊C4—62no—
433(C2×D3)⋊C4—62no—
434(C2×D3)⋊C4—62no—
435(C2×D3)⋊C4—62no—
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—
444C4⋊Dic3—21no—
445C4⋊Dic3—21no—
446C4⋊Dic3—31no—
447C4⋊Dic3—31no—
448C4⋊Dic3—61no—
449C4⋊Dic3C22×D311yescharacteristic
450Dic3⋊C4—21no—
451Dic3⋊C4—21no—
452Dic3⋊C4—21no—
453Dic3⋊C4—62no—
454Dic3⋊C4—61no—
455Dic3⋊C4—61no—
456C4×Dic3—21no—
457#208—22no—
458C2×C3⋊C8—22no—
459C2×C3⋊C8C22×D311yescharacteristic
460C2×C3⋊C8C22×D311yescharacteristic
461C2×C3⋊C8C22×D311yescharacteristic
462C2×C3⋊C8C22×D311yescharacteristic
463Dic12—62no—
464Dic12—62no—
465Dic12—121no—
466#204—34no—
467#204—62no—
468#204—62no—
469#204—62no—
470#204—62no—
471#204—121no—
472C22×C32—21no—
473C22×C32—21no—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32#13712yescomplemented
478C22×C32C22×D411yescharacteristic
479C2×C3⋊D3—22no—
480C2×C3⋊D3—41no—
481C2×C3⋊D3—41no—
482C2×C3⋊D3—41no—
483C2×C3⋊D3—41no—
484C2×C3⋊D3—41no—
485C2×C3⋊D3—84no—
486C32×C4—21no—
487C32×C4—21no—
488C32×C4—21no—
489C32×C4—21no—
490C32×C4C22×D411yescharacteristic
491C32×C4H(5,𝔽2)11yescharacteristic
492C3⋊Dic3—41no—
493C3⋊Dic3—41no—
494C3×Dic3—22no—
495C3×Dic3—41no—
496C3×Dic3—41no—
497C3×Dic3—41no—
498C2×#41—91no—
499C22×Q8—31no—
500C22×Q8—31no—
501C22×D4—91no—
502#137—184no—
503C2×Q16—91no—
504C2×Q16—91no—
505C2×Q16—91no—
506C2×SD16—91no—
507C2×SD16—91no—
508C2×SD16—91no—
509C2×SD16—91no—
510C2×SD16—91no—
511C2×SD16—91no—
512C2×SD16—184no—
513C2×M16—31no—
514C22×C8—31no—
515C4⋊Q8—31no—
516C4⋊Q8—61no—
517#124—91no—
518#123—181no—
519C22⋊Q8—31no—
520C22⋊Q8—31no—
521C22⋊Q8—61no—
522C22⋊Q8—61no—
523C22⋊Q8—91no—
524#121—91no—
525#121—181no—
526#120—181no—
527C4×Q8—31no—
528C4×D4—61no—
529C4×D4—91no—
530C4×D4D3211yescharacteristic
531C2×C22⋊C4—181no—
532#107—91no—
533C4⋊C8—31no—
534#103—91no—
535#103—91no—
536#103—91no—
537#103—91no—
538#102—91no—
539#102—91no—
540C22⋊C8—31no—
541C22⋊C8—31no—
542#97—31no—
543C23×C3—21no—
544C23×C3—21no—
545C23×C3C2×D1211yescharacteristic
546C23×C3C2×D1211yescharacteristic
547C23×C3C2×#6711yescharacteristic
548C23×C3C2×#6711yescharacteristic
549C22×D3—62no—
550C22×D3—61no—
551C22×D3—61no—
552C22×D3—62no—
553C22×D3—61no—
554C22×D3—61no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—124no—
558C22×D3—124no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—241no—
562C22×D3—241no—
563C22×D3—242no—
564C3×Q8—32no—
565C3×Q8—61no—
566C3×Q8—61no—
567C3×Q8—61no—
568C3×Q8—61no—
569C3×Q8—61no—
570C3×Q8—122no—
571C3×Q8—122no—
572C3×D4—22no—
573C3×D4—22no—
574C3×D4—42no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—41no—
589C2×C3×C4—41no—
590C2×C3×C4—41no—
591C2×C3×C4—41no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—122no—
597C2×C3×C4—122no—
598C2×C3×C4C2×D1211yescharacteristic
599C2×C3×C4C2×D1211yescharacteristic
600C2×C3×C4C2×D1211yescharacteristic
601C2×C3×C4C2×D1211yescharacteristic
602C2×C3×C4C2×#6711yescharacteristic
603C2×C3×C4C2×#6711yescharacteristic
604C2×C3×C4C2×#6711yescharacteristic
605C2×C3×C4C2×#6711yescharacteristic
606C2×C3×C4C23×D311yescharacteristic
607C2×C3×C4C23×D311yescharacteristic
608#67—122no—
609#67—122no—
610#67—124no—
611#67—241no—
612#67—241no—
613#67—242no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—42no—
619C2×Dic3—42no—
620C2×Dic3—62no—
621C2×Dic3—62no—
622C2×Dic3—61no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626D12—32no—
627D12—32no—
628D12—62no—
629D12—62no—
630D12—61no—
631D12—61no—
632D12—61no—
633D12—61no—
634D12—61no—
635D12—61no—
636D12—121no—
637D12—121no—
638D12—122no—
639D12—122no—
640D12—124no—
641C4×D3—122no—
642C4×D3—122no—
643C4×D3—124no—
644C4×D3—241no—
645C4×D3—241no—
646C4×D3—242no—
647Dic6—21no—
648Dic6—21no—
649Dic6—21no—
650Dic6—21no—
651Dic6—21no—
652Dic6—42no—
653Dic6—42no—
654Dic6—61no—
655Dic6—61no—
656Dic6—61no—
657Dic6—61no—
658Dic6—121no—
659Dic6—121no—
660Dic6D3×D412yes—
661C3×C8—32no—
662C3×C8—61no—
663C3×C8—61no—
664C3×C8—61no—
665C3⋊C8—21no—
666C3⋊C8—21no—
667C3⋊C8—21no—
668C3⋊C8D3×D412yes—
669C2×C32—22no—
670C2×C32—41no—
671C2×C32D4211yescharacteristic
672C2×C32C2×#13711yescharacteristic
673C2×C32#57711yescharacteristic
674C3⋊D3—42no—
675C3⋊D3—81no—
676C24—181no—
677#41—182no—
678#41—361no—
679C2×Q8—31no—
680C2×Q8—31no—
681C2×Q8—31no—
682C2×Q8—62no—
683C2×Q8—62no—
684C2×Q8—61no—
685C2×Q8—61no—
686C2×Q8—91no—
687C2×Q8—121no—
688C2×Q8—121no—
689C2×D4—91no—
690C2×D4—91no—
691C2×D4—182no—
692C2×D4—181no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4—361no—
696C2×D4#62611yescharacteristic
697C22×C4—61no—
698C22×C4—61no—
699C22×C4—181no—
700C22×C4—181no—
701C22×C4C2×D3211yescharacteristic
702C22×C4C2×D3211yescharacteristic
703Q16—182no—
704Q16—182no—
705Q16—361no—
706SD16—94no—
707SD16—182no—
708SD16—182no—
709SD16—182no—
710SD16—182no—
711SD16—361no—
712M16—62no—
713C2×C8—31no—
714C2×C8—31no—
715C2×C8—31no—
716C2×C8—31no—
717C2×C8—62no—
718C4⋊C4—31no—
719C4⋊C4—61no—
720C4⋊C4—61no—
721C4⋊C4—61no—
722C4⋊C4—61no—
723C4⋊C4—61no—
724C4⋊C4—91no—
725C4⋊C4—181no—
726C4⋊C4#62611yescharacteristic
727C22⋊C4—61no—
728C22⋊C4—61no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C22⋊C4—181no—
734C22⋊C4#62611yescharacteristic
735C22⋊C4#62611yescharacteristic
736C42—61no—
737C42C2×D3211yescharacteristic
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—22no—
750C22×C3—41no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3#90912yescomplemented
756C22×C3#94212yescomplemented
757C22×C3C22×D1211yescharacteristic
758C22×C3C22×#6711yescharacteristic
759C2×D3—64no—
760C2×D3—62no—
761C2×D3—62no—
762C2×D3—122no—
763C2×D3—122no—
764C2×D3—121no—
765C2×D3—121no—
766C2×D3—121no—
767C2×D3—121no—
768C2×D3—122no—
769C2×D3—122no—
770C2×D3—122no—
771C2×D3—121no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—244no—
778C2×D3—244no—
779C2×D3—248no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—21no—
789C3×C4—21no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—41no—
794C3×C4—62no—
795C3×C4—121no—
796C3×C4—121no—
797C3×C4—121no—
798C3×C4C2×D3×D411yescharacteristic
799C3×C4C2×D3×D411yescharacteristic
800C3×C4#100411yescharacteristic
801C3×C4#100911yescharacteristic
802Dic3—22no—
803Dic3—41no—
804Dic3—41no—
805Dic3—41no—
806Dic3—122no—
807Dic3—122no—
808Dic3—121no—
809Dic3—121no—
810Dic3—121no—
811Dic3—121no—
812C32#326611yescharacteristic, complemented, Sylow
813C23—181no—
814C23—181no—
815C23—362no—
816C23—362no—
817C23—721no—
818C23C2×#62611yescharacteristic
819C23C2×#62611yescharacteristic
820Q8—32no—
821Q8—61no—
822Q8—61no—
823Q8—61no—
824Q8—61no—
825Q8—61no—
826Q8—122no—
827Q8—122no—
828Q8—181no—
829Q8—181no—
830D4—22no—
831D4—92no—
832D4—181no—
833D4—181no—
834D4—181no—
835D4—362no—
836D4—362no—
837D4—721no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—61no—
843C2×C4—61no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—122no—
847C2×C4—122no—
848C2×C4—181no—
849C2×C4—181no—
850C2×C4—362no—
851C2×C4—721no—
852C2×C4C2×#62611yescharacteristic
853C2×C4C2×#62611yescharacteristic
854C2×C4C2×#62611yescharacteristic
855C2×C4C2×#62611yescharacteristic
856C2×C4C22×D3211yescharacteristic
857C8—32no—
858C8—61no—
859C8—61no—
860C8—61no—
861C2×C3—22no—
862C2×C3—22no—
863C2×C3—21no—
864C2×C3—21no—
865C2×C3—21no—
866C2×C3—42no—
867C2×C3—41no—
868C2×C3—41no—
869C2×C3—81no—
870C2×C3D4×D1211yescharacteristic
871C2×C3C2×#90911yescharacteristic
872C2×C3#575111yescharacteristic
873C2×C3D4×#6711yescharacteristic
874C2×C3C2×#94211yescharacteristic
875C2×C3#583711yescharacteristic
876D3—124no—
877D3—122no—
878D3—122no—
879D3—242no—
880D3—241no—
881D3—241no—
882C22—21no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—182no—
888C22—361no—
889C22—361no—
890C22—361no—
891C22—361no—
892C22—361no—
893C22—724no—
894C22#6383312yescomplemented
895C22C22×#62611yescharacteristic
896C4—21no—
897C4—21no—
898C4—21no—
899C4—21no—
900C4—62no—
901C4—121no—
902C4—121no—
903C4—121no—
904C4—361no—
905C4—361no—
906C4D32×D411yescharacteristic
907C4#6431411yescharacteristic
908C3—21no—
909C3#7949511yescharacteristic, complemented
910C3#8355911yescharacteristic, complemented
911C2—22no—
912C2—41no—
913C2—362no—
914C2—721no—
915C2C2×#6383311yescharacteristic
916C2D4×#62611yescharacteristic
917C2#1059544811yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×D4C22
socleC22×C32C22×D4
prime radical#10596021C2
hypercenterC4×D4D32
hypocenterC32#3266
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×D4×Dic6C2semidirect
3. C2×#63833C2semidirect
4. C22×#3717C2semidirect
5. C3×#5011C2semidirect
6. #10591187C2semidirect
7. #10591186C2semidirect
8. #10591184C2semidirect
9. #10591183C2semidirect
10. #10591178C2semidirect
11. #10591174C2semidirect
12. #10590379C2semidirect
13. #10590374C2semidirect
14. #10590368C2semidirect
15. #10590362C2semidirect
21. C22×C3×Dic6C22semidirect
33. C3×#924C22semidirect
34. C2×C3×#208C22semidirect
39. C3×#869C22semidirect
40. C3×C4×Dic6C22semidirect
41. C2×#3719C22semidirect
42. C2×#3719C22semidirect
43. C2×#3719C22semidirect
53. C3×#830C22semidirect
54. C3×C4⋊(C3⋊C8)C22semidirect
55. C3×#803C22semidirect
56. #63575C22semidirect
57. #63567C22semidirect
58. #63566C22semidirect
59. #63566C22semidirect
60. #63566C22semidirect
71. D4×Dic6D3semidirect
85. #5011D3semidirect
155. #3717D4semidirect
166. C22×Dic6C2×D3semidirect
202. #924C2×D3semidirect
203. C2×#208C2×D3semidirect
234. #869C2×D3semidirect
235. C4×Dic6C2×D3semidirect
244. #830C2×D3semidirect
256. C4⋊(C3⋊C8)C2×D3semidirect
257. #803C2×D3semidirect
477. C22×C32#137semidirect
755. C22×C3#909semidirect
756. C22×C3#942semidirect
812. C32#3266semidirect
894. C22#63833semidirect
909. C3#79495semidirect
910. C3#83559semidirect

Maximal subgroups

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

subgroupindex
#105960212
C3×D4×Dic62
C2×#638332
C22×#37172
C3×#50112
#105911872
#105911862
#105911842
#105911832
#105911782
#105911742
#105903792
#105903742
#105903682
#105903622
#835593
#794953