Finite Group Databasebeta

← #11883994

Subgroups — #11883994

Order 1152.

1152 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5633C211yesmaximal, characteristic, complemented
2C2×D3×#215C211yesmaximal, characteristic, complemented
3D12×#67C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592748C211yesmaximal, characteristic, complemented
6C3×#5046C211yesmaximal, characteristic, complemented
7#10591619C211yesmaximal, characteristic, complemented
8#10591583C211yesmaximal, characteristic, complemented
9#10591567C211yesmaximal, characteristic, complemented
10#10591163C211yesmaximal, characteristic, complemented
11#10591151C211yesmaximal, characteristic, complemented
12#10590595C211yesmaximal, characteristic, complemented
13#10590549C211yesmaximal, characteristic, complemented
14#10590499C211yesmaximal, characteristic, complemented
15#10590454C211yesmaximal, characteristic, complemented
16#83542—31nomaximal
17#80156—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic, complemented
19C2×C3×#235C2211yescharacteristic, complemented
20C22×C3×D12C2211yescharacteristic
21C2×D3×#67—21no—
22C2×D3×D12C2211yescharacteristic
23C32×C22⋊Q8C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic, complemented
25#64139C2211yescharacteristic
26C2×#3748C2211yescharacteristic, complemented
27C3×#947C2211yescharacteristic, complemented
28C2×C3×#215C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic, complemented
30C3×C4×#67C2211yescharacteristic
31C3×#896—21no—
32C3×#895C2211yescharacteristic, complemented
33C3×#893—21no—
34C3×#887C2211yescharacteristic, complemented
35C3×#885—21no—
36C3×#884—21no—
37#63977—21no—
38D3×#215—24no—
39#63922—21no—
40#63911C2211yescharacteristic
41#63908C2211yescharacteristic
42Dic3×D12C2211yescharacteristic
43#63886—21no—
44C2×#3717C2211yescharacteristic, complemented
45C2×#3715C2211yescharacteristic
46C2×#3715C2211yescharacteristic, complemented
47C2×#3714C2211yescharacteristic, complemented
48#63823—24no—
49C2×#3713C2211yescharacteristic
50C2×#3713C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55C3×#830C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic
57C3×#809C2211yescharacteristic, complemented
58Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62#63554C2211yescharacteristic, complemented
63C3×#548—31no—
64C2×#949—31no—
65C22×#215—31no—
66D4×#67—31no—
67C2×#932—31no—
68C2×D3×SD16—31no—
69#5633D311yescharacteristic, complemented
70D4×D12—31no—
71C3×#450—31no—
72#5238—31no—
73#5227—31no—
74#5176—31no—
75#5170—31no—
76#5165—31no—
77#5058—31no—
78#5057—31no—
79#5049—31no—
80#5049—31no—
81#5049—61no—
82#5046D311yescharacteristic, complemented
83#5038—31no—
84#5036—31no—
85#5027—31no—
86#5026—31no—
87#5011—31no—
88#4775—31no—
89#4773—31no—
90#4762—31no—
91#4757—31no—
92#4734—31no—
93#4728—31no—
94C23×C3×D3—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4C2311yescharacteristic
98C2×#638—21no—
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C3×D3×Q8—22no—
103C3×D3×Q8—41no—
104C3×#235—22no—
105C3×#235—41no—
106C2×C3×D12—22no—
107C2×C3×D12—21no—
108C2×C3×D12—21no—
109C2×C3×D12—41no—
110C2×C3×D12C2311yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×C4×D3—21no—
114C2×C3×C4×D3—21no—
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6—21no—
117C2×C3×Dic6C2311yescharacteristic
118D3×#67—44no—
119C2×#626—21no—
120C2×#626—21no—
121C2×#626—21no—
122C2×#625—21no—
123C2×D3×Dic3—21no—
124D3×D12—22no—
125D3×D12—41no—
126C32×C4⋊C4—21no—
127C32×C4⋊C4C2311yescharacteristic
128C32×C22⋊C4—21no—
129#3755—22no—
130#3752—21no—
131C4⋊(C3⋊Dic3)C2311yescharacteristic
132#3748—22no—
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C3×#217D411yescharacteristic
136C3×#215—22no—
137C3×#215—41no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×Dic3⋊C4—21no—
143C3×Dic3⋊C4D411yescharacteristic
144C3×C4×Dic3—21no—
145C3×C4×Dic3C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147C2×C3×C3⋊C8C2311yescharacteristic
148(C2×D3)⋊Dic3—21no—
149(C2×D3)⋊Dic3—21no—
150#3717—22no—
151#3715—22no—
152#3715D414yescomplemented
153#3714—41no—
154#3713—22no—
155#3713—22no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C22×C3×Q8—31no—
160C22×C3×D4—31no—
161C22×#67—61no—
162C2×D3×Q8C2×D311yescharacteristic, complemented
163C2×D3×D4—31no—
164C2×D3×D4—61no—
165C2×#235C2×D311yescharacteristic, complemented
166C22×D12—31no—
167C22×D12C2×D311yescharacteristic
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C3×#124—31no—
171C3×#124—61no—
172C3×C22⋊Q8—21no—
173C3×C22⋊Q8—61no—
174C3×C22⋊Q8C2×D311yescharacteristic, complemented
175C3×C22⋊Q8C2×D311yescharacteristic, complemented
176C3×#121—31no—
177C3×#121—61no—
178C3×C4×Q8—31no—
179C3×C4×D4—31no—
180C3×C4×D4—61no—
181#953—61no—
182#949—64no—
183#947C2×D311yescharacteristic, complemented
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—31no—
189C2×#215—61no—
190C2×#215—64no—
191C2×#215C2×D311yescharacteristic
192C2×#215C2×D311yescharacteristic, complemented
193#940—31no—
194#939—61no—
195#938—31no—
196#937—61no—
197D4×Dic3—31no—
198C2×#214—31no—
199C2×#214—31no—
200#932—64no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—31no—
204C2×#213—31no—
205C2×#213—31no—
206#930—31no—
207#930—31no—
208#930—31no—
209#930—61no—
210C4×#67C2×D311yescharacteristic
211C2×#208—31no—
212C2×#208—31no—
213C2×#208—61no—
214C22×C3⋊C8—31no—
215D3×SD16—64no—
216C2×D24—31no—
217C2×#204—31no—
218C2×D3×C8—31no—
219#896—21no—
220#895—61no—
221#895C2×D311yescharacteristic, complemented
222#893—21no—
223#887C2×D311yescharacteristic, complemented
224#885—21no—
225#884—21no—
226#882—61no—
227#882—61no—
228#874—31no—
229C4×D12—31no—
230C3×#102—31no—
231C3×#102—31no—
232C3×C22⋊C8—31no—
233#835—31no—
234#835—31no—
235#835—31no—
236#835—61no—
237#832—31no—
238#830—31no—
239#830C2×D311yescharacteristic, complemented
240#821—31no—
241(C2×D3)⋊C8—31no—
242#816—31no—
243#815—31no—
244Dic3⋊C8—31no—
245#809—31no—
246#809—31no—
247#809—61no—
248#809C2×D311yescharacteristic
249#809C2×D311yescharacteristic, complemented
250#807—31no—
251#807—31no—
252#807—61no—
253C4⋊(C3⋊C8)—31no—
254#803—31no—
255C23×C32C2×D411yescharacteristic
256C22×C3⋊D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—81no—
263C22×C3×D3C2×D411yescharacteristic
264C2×D32—42no—
265C2×D32—42no—
266C2×D32—81no—
267C32×Q8—21no—
268C32×Q8—21no—
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4—21no—
272C2×C32×C4—21no—
273C2×C32×C4C2×D411yescharacteristic
274C2×C32×C4C2411yescharacteristic
275#638—42no—
276C2×C3⋊Dic3—21no—
277C4⋊(C3⋊D3)—21no—
278C4⋊(C3⋊D3)—21no—
279C3×#67—22no—
280C3×#67—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3C2×D411yescharacteristic
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—42no—
291C3×D12—42no—
292C3×D12C2×D412yes—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295C3×C4×D3—42no—
296C3×C4×D3—42no—
297C3×Dic6—21no—
298C3×Dic6—42no—
299C3×Dic6C2×D412yescomplemented
300#626—42no—
301#626—42no—
302#626—81no—
303#625—42no—
304D3×Dic3—42no—
305C3⋊(C3⋊C8)—21no—
306C3⋊(C3⋊C8)C2×D412yescomplemented
307C3×C3⋊C8—21no—
308C3×C3⋊C8—21no—
309C2×AGL(1,ℤ/8)—91no—
310C22×SD16—91no—
311#548—31no—
312D42—91no—
313#496—91no—
314#468—91no—
315#466—91no—
316#463—91no—
317#460—91no—
318#450—31no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C24×C3—61no—
325C23×D3—21no—
326C23×D3—61no—
327C23×D3—61no—
328C3×#41—62no—
329C3×#41—121no—
330C2×C3×Q8—21no—
331C2×C3×Q8—31no—
332C2×C3×Q8—61no—
333C2×C3×Q8—62no—
334C2×C3×Q8—121no—
335C2×C3×Q8C22×D311yescharacteristic
336C2×C3×Q8C22×D311yescharacteristic
337C2×C3×D4—31no—
338C2×C3×D4—31no—
339C2×C3×D4—31no—
340C2×C3×D4—31no—
341C2×C3×D4—62no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C2×C3×D4—121no—
346C22×C3×C4—21no—
347C22×C3×C4—31no—
348C22×C3×C4—61no—
349C22×C3×C4—61no—
350C22×C3×C4C22×D311yescharacteristic
351C22×C3×C4C22×D311yescharacteristic
352C2×#67—21no—
353C2×#67—61no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C2×#67—61no—
359C2×#67—61no—
360C2×#67—121no—
361C2×#67—124no—
362C2×#67#6711yescharacteristic
363C22×Dic3—61no—
364D3×Q8—22no—
365D3×Q8—41no—
366D3×D4—62no—
367D3×D4—121no—
368D3×D4—124no—
369#235—22no—
370#235—41no—
371C2×D12—22no—
372C2×D12—21no—
373C2×D12—21no—
374C2×D12—31no—
375C2×D12—31no—
376C2×D12—41no—
377C2×D12—61no—
378C2×D12—62no—
379C2×D12—61no—
380C2×D12—61no—
381C2×D12—61no—
382C2×D12—121no—
383C2×D12C22×D311yescharacteristic
384C2×D12C22×D311yescharacteristic
385C2×D12C22×D311yescharacteristic
386C2×C4×D3—21no—
387C2×C4×D3—21no—
388C2×C4×D3—61no—
389C2×C4×D3C22×D311yescharacteristic
390C2×Dic6—21no—
391C2×Dic6C22×D311yescharacteristic
392C3×SD16—62no—
393C3×SD16—121no—
394C2×C3×C8—31no—
395C2×C3×C8—31no—
396C3×C4⋊C4—21no—
397C3×C4⋊C4—21no—
398C3×C4⋊C4—21no—
399C3×C4⋊C4—31no—
400C3×C4⋊C4—41no—
401C3×C4⋊C4—61no—
402C3×C4⋊C4C22×D311yescharacteristic
403C3×C4⋊C4C22×D311yescharacteristic
404C3×C22⋊C4—21no—
405C3×C22⋊C4—21no—
406C3×C22⋊C4—31no—
407C3×C22⋊C4—31no—
408C3×C22⋊C4—41no—
409C3×C22⋊C4—61no—
410C3×C22⋊C4—61no—
411C3×C22⋊C4—61no—
412C3×C42—31no—
413C3×C42—61no—
414#217—61no—
415#217—61no—
416#217#6711yescharacteristic
417#215—22no—
418#215—34no—
419#215—41no—
420#215—62no—
421#215—62no—
422#215—62no—
423#215—62no—
424#215—122no—
425#214—34no—
426#214—62no—
427#213—62no—
428#213—62no—
429#213—62no—
430#213—62no—
431#213—121no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—121no—
440(C2×D3)⋊C4#6711yescharacteristic
441C4⋊Dic3—31no—
442C4⋊Dic3—31no—
443C4⋊Dic3—61no—
444Dic3⋊C4—21no—
445Dic3⋊C4#6711yescharacteristic
446C4×Dic3—21no—
447C4×Dic3C22×D311yescharacteristic
448#208—62no—
449#208—62no—
450#208—122no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—31no—
454C2×C3⋊C8—31no—
455C2×C3⋊C8—61no—
456C2×C3⋊C8—61no—
457C2×C3⋊C8—62no—
458C2×C3⋊C8C22×D311yescharacteristic
459C2×C3⋊C8C22×D311yescharacteristic
460D24—121no—
461#204—62no—
462D3×C8—62no—
463C22×C32—21no—
464C22×C32—21no—
465C22×C32—21no—
466C22×C32C22×D411yescharacteristic
467C2×C3⋊D3—41no—
468C2×C3⋊D3—41no—
469C2×C3⋊D3—41no—
470C2×C3×D3—21no—
471C2×C3×D3—21no—
472C2×C3×D3—22no—
473C2×C3×D3—41no—
474C2×C3×D3—41no—
475C2×C3×D3—41no—
476C2×C3×D3—41no—
477C2×C3×D3—41no—
478C2×C3×D3—41no—
479C2×C3×D3—41no—
480C2×C3×D3—41no—
481C2×C3×D3—84no—
482C2×C3×D3AGL(1,ℤ/8)12yescomplemented
483D32—84no—
484C32×C4—21no—
485C32×C4—41no—
486C32×C4—41no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—41no—
490C3×Dic3—21no—
491C3×Dic3—22no—
492C3×Dic3—21no—
493C3×Dic3—21no—
494C2×#41—31no—
495C22×Q8—31no—
496C22×D4—31no—
497C22×D4—91no—
498C22×D4—181no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—31no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—91no—
506C2×SD16—184no—
507C2×D8—91no—
508C2×D8—91no—
509C2×D8—91no—
510C2×M16—91no—
511C22×C8—91no—
512#127—91no—
513#124—31no—
514#124—61no—
515C22⋊Q8—61no—
516C22⋊Q8D3211yescharacteristic, complemented
517#121—31no—
518#121—61no—
519#121—91no—
520#121—91no—
521#121—181no—
522#120—181no—
523#120—181no—
524C4×Q8—31no—
525C4×D4—31no—
526C4×D4—61no—
527C4×D4—91no—
528#107—91no—
529C4⋊C8—91no—
530#103—91no—
531#103—91no—
532#102—31no—
533#102—31no—
534#102—91no—
535#102—91no—
536C22⋊C8—31no—
537C22⋊C8—91no—
538#97—91no—
539C23×C3—21no—
540C23×C3—31no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—122no—
545C23×C3—122no—
546C23×C3—241no—
547C23×C3D3×D411yescharacteristic
548C23×C3C2×#6711yescharacteristic
549C22×D3—21no—
550C22×D3—21no—
551C22×D3—21no—
552C22×D3—42no—
553C22×D3—42no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—81no—
557C22×D3—121no—
558C22×D3—122no—
559C22×D3—122no—
560C22×D3—122no—
561C22×D3—122no—
562C22×D3—241no—
563C22×D3—241no—
564C22×D3C2×#6711yescharacteristic
565C3×Q8—21no—
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—32no—
570C3×Q8—41no—
571C3×Q8—41no—
572C3×Q8—61no—
573C3×Q8—122no—
574C3×D4—32no—
575C3×D4—62no—
576C3×D4—61no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—61no—
580C3×D4—61no—
581C3×D4—122no—
582C3×D4—122no—
583C3×D4—122no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—31no—
595C2×C3×C4—31no—
596C2×C3×C4—31no—
597C2×C3×C4—41no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
604C2×C3×C4—122no—
605C2×C3×C4—122no—
606C2×C3×C4D3×D411yescharacteristic
607C2×C3×C4C2×#6711yescharacteristic
608C2×C3×C4C23×D311yescharacteristic
609C2×C3×C4C23×D311yescharacteristic
610#67—22no—
611#67—42no—
612#67—122no—
613#67—122no—
614#67—122no—
615#67—122no—
616#67—122no—
617#67—122no—
618#67—242no—
619#67—241no—
620C2×Dic3—21no—
621C2×Dic3—61no—
622C2×Dic3—61no—
623C2×Dic3—121no—
624C2×Dic3—122no—
625C2×Dic3C2×#6711yescharacteristic
626C2×Dic3C2×#6711yescharacteristic
627C2×Dic3C2×#6711yescharacteristic
628D12—21no—
629D12—21no—
630D12—21no—
631D12—21no—
632D12—21no—
633D12—42no—
634D12—42no—
635D12—61no—
636D12—61no—
637D12—61no—
638D12—61no—
639D12—121no—
640D12—121no—
641D12—122no—
642D12—122no—
643D12—241no—
644D12D3×D412yes—
645C4×D3—21no—
646C4×D3—21no—
647C4×D3—42no—
648C4×D3—42no—
649C4×D3—122no—
650Dic6—21no—
651Dic6—42no—
652Dic6D3×D412yescomplemented
653C3×C8—61no—
654C3×C8—61no—
655C3⋊C8—21no—
656C3⋊C8—21no—
657C3⋊C8—32no—
658C3⋊C8—32no—
659C3⋊C8—62no—
660C3⋊C8—61no—
661C3⋊C8—61no—
662C3⋊C8—121no—
663C2×C32—41no—
664C2×C32D4211yescharacteristic
665C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
666C2×C32#57711yescharacteristic
667C3⋊D3—81no—
668C3×D3—22no—
669C3×D3—42no—
670C3×D3—81no—
671C3×D3—81no—
672C24—61no—
673C24—181no—
674#41—62no—
675#41—121no—
676C2×Q8—31no—
677C2×Q8—61no—
678C2×Q8—62no—
679C2×Q8—121no—
680C2×Q8C2×D3211yescharacteristic
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—31no—
685C2×D4—62no—
686C2×D4—61no—
687C2×D4—61no—
688C2×D4—61no—
689C2×D4—91no—
690C2×D4—121no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—181no—
694C2×D4—182no—
695C2×D4—181no—
696C2×D4—181no—
697C2×D4—361no—
698C2×D4—364no—
699C22×C4—31no—
700C22×C4—61no—
701C22×C4—61no—
702C22×C4—181no—
703C22×C4C2×D3211yescharacteristic
704SD16—62no—
705SD16—94no—
706SD16—121no—
707SD16—182no—
708SD16—182no—
709SD16—182no—
710D8—182no—
711D8—182no—
712D8—361no—
713M16—182no—
714C2×C8—31no—
715C2×C8—31no—
716C2×C8—91no—
717C2×C8—91no—
718C2×C8—182no—
719C4⋊C4—21no—
720C4⋊C4—31no—
721C4⋊C4—61no—
722C4⋊C4—91no—
723C4⋊C4C2×D3211yescharacteristic
724C22⋊C4—21no—
725C22⋊C4—31no—
726C22⋊C4—31no—
727C22⋊C4—61no—
728C22⋊C4—61no—
729C22⋊C4—61no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C42—31no—
734C42—61no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—32no—
743C22×C3—41no—
744C22×C3—41no—
745C22×C3—41no—
746C22×C3—61no—
747C22×C3—61no—
748C22×C3—62no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—244no—
758C22×C3C2×D3×D411yescharacteristic
759C22×C3C22×#6711yescharacteristic
760C2×D3—21no—
761C2×D3—21no—
762C2×D3—22no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—84no—
772C2×D3—121no—
773C2×D3—121no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—241no—
779C2×D3—241no—
780C2×D3—241no—
781C2×D3—244no—
782C2×D3—244no—
783C2×D3#94912yescomplemented
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—21no—
787C3×C4—21no—
788C3×C4—41no—
789C3×C4—41no—
790C3×C4—41no—
791C3×C4—41no—
792C3×C4—41no—
793C3×C4—61no—
794C3×C4—61no—
795C3×C4—61no—
796C3×C4—62no—
797C3×C4—81no—
798C3×C4—81no—
799C3×C4C2×D3×D411yescharacteristic
800C3×C4C2×D3×D411yescharacteristic
801C3×C4#100411yescharacteristic
802C3×C4#100411yescharacteristic
803Dic3—22no—
804Dic3—21no—
805Dic3—21no—
806Dic3—21no—
807Dic3—121no—
808Dic3—121no—
809Dic3—241no—
810C32#326511yescharacteristic, complemented, Sylow
811C23—31no—
812C23—61no—
813C23—61no—
814C23—61no—
815C23—122no—
816C23—122no—
817C23—181no—
818C23—241no—
819C23—362no—
820C23—362no—
821C23—721no—
822C23D3×#6711yescharacteristic
823Q8—21no—
824Q8—21no—
825Q8—32no—
826Q8—61no—
827Q8—122no—
828D4—32no—
829D4—62no—
830D4—61no—
831D4—61no—
832D4—61no—
833D4—61no—
834D4—61no—
835D4—122no—
836D4—122no—
837D4—122no—
838D4—181no—
839D4—181no—
840D4—362no—
841D4—362no—
842D4—362no—
843D4—362no—
844D4—721no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—31no—
850C2×C4—31no—
851C2×C4—31no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—122no—
856C2×C4—122no—
857C2×C4—181no—
858C2×C4—362no—
859C2×C4D3×#6711yescharacteristic
860C2×C4C22×D3211yescharacteristic
861C8—61no—
862C8—61no—
863C8—92no—
864C8—181no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—41no—
869C2×C3—41no—
870C2×C3—62no—
871C2×C3—81no—
872C2×C3—122no—
873C2×C3—241no—
874C2×C3—241no—
875C2×C3#559011yescharacteristic
876C2×C3#576211yescharacteristic
877C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
878C2×C3D4×#6711yescharacteristic
879C2×C3C2×#94911yescharacteristic
880C2×C3#583711yescharacteristic
881D3—22no—
882D3—42no—
883D3—81no—
884D3—81no—
885D3—241no—
886D3—241no—
887D3—481no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—32no—
892C22—61no—
893C22—61no—
894C22—62no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—244no—
904C22—361no—
905C22—361no—
906C22—361no—
907C22—724no—
908C22C2×D3×#6711yescharacteristic
909C4—21no—
910C4—41no—
911C4—41no—
912C4—61no—
913C4—61no—
914C4—62no—
915C4—61no—
916C4—361no—
917C4D32×D411yescharacteristic
918C4#6431311yescharacteristic
919C3—21no—
920C3#8015611yescharacteristic, complemented
921C3#8354211yescharacteristic, complemented
922C2—41no—
923C2—62no—
924C2—122no—
925C2—241no—
926C2—241no—
927C2—721no—
928C2#1059528711yescharacteristic
929C2#1059531811yescharacteristic
930C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
hypercenterC22⋊Q8D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5633C2semidirect
2. C2×D3×#215C2semidirect
3. D12×#67C2semidirect
4. C2×#63823C2semidirect
5. #10592748C2semidirect
6. C3×#5046C2semidirect
7. #10591619C2semidirect
8. #10591583C2semidirect
9. #10591567C2semidirect
10. #10591163C2semidirect
11. #10591151C2semidirect
12. #10590595C2semidirect
13. #10590549C2semidirect
14. #10590499C2semidirect
15. #10590454C2semidirect
18. C2×C3×D3×Q8C22semidirect
19. C2×C3×#235C22semidirect
23. C32×C22⋊Q8C22semidirect
24. C2×#3755C22semidirect
26. C2×#3748C22semidirect
27. C3×#947C22semidirect
29. C2×C3×#215C22semidirect
32. C3×#895C22semidirect
34. C3×#887C22semidirect
44. C2×#3717C22semidirect
46. C2×#3715C22semidirect
47. C2×#3714C22semidirect
50. C2×#3713C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63662C22semidirect
53. #63636C22semidirect
54. #63634C22semidirect
55. C3×#830C22semidirect
57. C3×#809C22semidirect
58. Dic3⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63563C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. #63554C22semidirect
69. #5633D3semidirect
82. #5046D3semidirect
152. #3715D4semidirect
162. C2×D3×Q8C2×D3semidirect
165. C2×#235C2×D3semidirect
174. C3×C22⋊Q8C2×D3semidirect
175. C3×C22⋊Q8C2×D3semidirect
183. #947C2×D3semidirect
192. C2×#215C2×D3semidirect
221. #895C2×D3semidirect
223. #887C2×D3semidirect
239. #830C2×D3semidirect
249. #809C2×D3semidirect
299. C3×Dic6C2×D4semidirect
306. C3⋊(C3⋊C8)C2×D4semidirect
482. C2×C3×D3AGL(1,ℤ/8)semidirect
516. C22⋊Q8D32semidirect
652. Dic6D3×D4semidirect
783. C2×D3#949semidirect
810. C32#3265semidirect
920. C3#80156semidirect
921. C3#83542semidirect

Maximal subgroups

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

subgroupindex
C3×#56332
C2×D3×#2152
D12×#672
C2×#638232
#105927482
C3×#50462
#105916192
#105915832
#105915672
#105911632
#105911512
#105905952
#105905492
#105904992
#105904542
#835423
#801563