Finite Group Databasebeta

← #11883945

Subgroups — #11883945

Order 1152.

1152 conjugacy classes of subgroups.

The subgroup lattice has 926 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5576C211yesmaximal, characteristic, complemented
2C2×#63939C211yesmaximal, characteristic, complemented
3C2×D3×#215C211yesmaximal, characteristic, complemented
4#10594004C211yesmaximal, characteristic, complemented
5#10592725C211yesmaximal, characteristic, complemented
6C3×#5027C211yesmaximal, characteristic, complemented
7#10591586C211yesmaximal, characteristic, complemented
8#10591583C211yesmaximal, characteristic, complemented
9#10590596C211yesmaximal, characteristic, complemented
10#10590595C211yesmaximal, characteristic, complemented
11#10590503C211yesmaximal, characteristic, complemented
12#10590499C211yesmaximal, characteristic, complemented
13#10590356C211yesmaximal, characteristic, complemented
14#10590354C211yesmaximal, characteristic, complemented
15#10590330C211yesmaximal, characteristic, complemented
16#83542—31nomaximal
17#80404—31nomaximal
18C2×C3×#239C2211yescharacteristic, complemented
19C2×C3×D3×Q8C2211yescharacteristic, complemented
20C2×#3802—21no—
21C2×D3×D12C2211yescharacteristic
22C2×D3×D12C2211yescharacteristic
23C32×C4×Q8C2211yescharacteristic, complemented
24C2×#3755C2211yescharacteristic
25C4×C4⋊(C3⋊D3)C2211yescharacteristic
26C2×C3×#215C2211yescharacteristic, complemented
27C2×C3×#215C2211yescharacteristic, complemented
28C3×#897—21no—
29C3×#897C2211yescharacteristic, complemented
30C3×#895—21no—
31C3×#895C2211yescharacteristic, complemented
32C3×#875—21no—
33C3×#875C2211yescharacteristic, complemented
34C3×#874C2211yescharacteristic
35C3×C4×D12—21no—
36C3×C4×D12C2211yescharacteristic
37#63939—24no—
38D3×#215—24no—
39#63922—21no—
40#63922—21no—
41#63916—21no—
42#63908C2211yescharacteristic
43#63908C2211yescharacteristic
44C2×#3717C2211yescharacteristic
45C2×#3715C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, complemented
47C2×#3714C2211yescharacteristic
48C2×#3713C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50C2×#3711C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63662C2211yescharacteristic, complemented
53#63636C2211yescharacteristic
54#63634C2211yescharacteristic, complemented
55#63630C2211yescharacteristic, complemented
56C3×#809C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×#548—31no—
64C2×#949—31no—
65C22×#215—31no—
66C2×#914—31no—
67C2×D3×SD16—31no—
68#5717—31no—
69#5576D311yescharacteristic, complemented
70D4×D12—31no—
71C3×#460—31no—
72#5238—31no—
73#5227—31no—
74#5172—31no—
75#5170—31no—
76#5074—31no—
77#5058—31no—
78#5057—31no—
79#5049—31no—
80#5046—31no—
81#5038—31no—
82#5036—31no—
83#5027D311yescharacteristic, complemented
84#5026—31no—
85#5026—31no—
86#5026—61no—
87#5011—31no—
88#4844—31no—
89#4836—31no—
90#4780—31no—
91#4776—31no—
92#4775—31no—
93#4773—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C32×Q8C2311yescharacteristic
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C3×#239—22no—
100C3×#239—41no—
101C3×D3×Q8—22no—
102C3×D3×Q8—41no—
103C2×C3×D12—21no—
104C2×C3×D12—21no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12D411yescharacteristic
108C2×C3×D12C2311yescharacteristic
109C2×C3×D12C2311yescharacteristic
110C2×C3×D12C2311yescharacteristic
111C2×C3×C4×D3—21no—
112C2×C3×C4×D3—21no—
113C2×C3×C4×D3C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×Dic6—21no—
116C2×C3×Dic6C2311yescharacteristic
117C2×#626—21no—
118C2×#626—21no—
119C2×#625—21no—
120C2×#625—21no—
121#3802—44no—
122D3×D12—22no—
123D3×D12—22no—
124D3×D12—41no—
125D3×D12—41no—
126C32×C4⋊C4—21no—
127C32×C4⋊C4C2311yescharacteristic
128C32×C42—21no—
129C32×C42C2311yescharacteristic
130#3755D414yescomplemented
131#3752—21no—
132C4⋊(C3⋊Dic3)C2311yescharacteristic
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C3×#215—22no—
136C3×#215—22no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4—21no—
139C3×(C2×D3)⋊C4—21no—
140C3×(C2×D3)⋊C4—21no—
141C3×(C2×D3)⋊C4D411yescharacteristic
142C3×(C2×D3)⋊C4D411yescharacteristic
143C3×C4⋊Dic3—21no—
144C3×C4⋊Dic3D411yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146C2×C3×C3⋊C8C2311yescharacteristic
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3717—22no—
150#3715—22no—
151#3715—41no—
152#3714—22no—
153#3713—22no—
154#3713—41no—
155#3711—22no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C2×C3×#41—31no—
159C22×C3×Q8—31no—
160C2×#239C2×D311yescharacteristic, complemented
161C2×D3×Q8C2×D311yescharacteristic, complemented
162C2×D3×D4—31no—
163C2×D3×D4—31no—
164C2×D3×D4—61no—
165C2×D3×D4—61no—
166C22×D12—31no—
167C22×D12—31no—
168C2×C3×SD16—31no—
169C2×C3×SD16—31no—
170C3×#127—31no—
171C3×#124—31no—
172C3×#124—61no—
173C3×C22⋊Q8—31no—
174C3×C22⋊Q8—61no—
175C3×#121—31no—
176C3×#121—61no—
177C3×C4×Q8—21no—
178C3×C4×Q8C2×D311yescharacteristic, complemented
179C3×C4×Q8C2×D311yescharacteristic, complemented
180C3×C4×D4—31no—
181C3×C4×D4—61no—
182#949—64no—
183C2×#215—31no—
184C2×#215—31no—
185C2×#215—31no—
186C2×#215—31no—
187C2×#215—31no—
188C2×#215—61no—
189C2×#215—64no—
190C2×#215C2×D311yescharacteristic, complemented
191C2×#215C2×D311yescharacteristic, complemented
192#938—31no—
193#938—31no—
194#938—61no—
195#937—61no—
196#937—61no—
197C2×#214—31no—
198C2×#214—31no—
199C2×#213—31no—
200C2×#213—31no—
201C2×#213—31no—
202C2×#213—31no—
203C2×#213—31no—
204#930—31no—
205#930—31no—
206C2×#208—31no—
207C22×C3⋊C8—31no—
208#914—64no—
209D3×SD16—64no—
210C2×D24—31no—
211C2×#204—31no—
212C2×ΓL(1,𝔽25)—31no—
213C2×D3×C8—31no—
214#897—21no—
215#897C2×D311yescharacteristic, complemented
216#895—21no—
217#895—61no—
218#895C2×D311yescharacteristic, complemented
219#882—61no—
220#882—61no—
221#875—21no—
222#875C2×D311yescharacteristic, complemented
223#874C2×D311yescharacteristic
224C4×D12—21no—
225C4×D12—31no—
226C4×D12—31no—
227C4×D12—61no—
228C4×D12C2×D311yescharacteristic
229C3×C4⋊C8—31no—
230C3×#102—31no—
231C3×#102—31no—
232#835—31no—
233#835—31no—
234#835—31no—
235#835—61no—
236#832—31no—
237#830—31no—
238#830—31no—
239#821—31no—
240(C2×D3)⋊C8—31no—
241(C2×D3)⋊C8—31no—
242#816—31no—
243#809—31no—
244#809—31no—
245#809—61no—
246#809C2×D311yescharacteristic, complemented
247#809C2×D311yescharacteristic, complemented
248#807—31no—
249#807—31no—
250#807—61no—
251C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
252#803—31no—
253#803—31no—
254#803—61no—
255C22×C3⋊D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3C2×D411yescharacteristic
260C22×C3×D3C2×D411yescharacteristic
261C2×D32—42no—
262C2×D32—42no—
263C2×D32—42no—
264C2×D32—42no—
265C2×D32—81no—
266C2×D32—81no—
267C32×Q8—21no—
268C32×Q8C2×D412yescomplemented
269C2×C32×C4—21no—
270C2×C32×C4—21no—
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2411yescharacteristic
274C2×C3⋊Dic3—21no—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)C2×D412yes—
277C4×C3⋊D3—42no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C3×D12—22no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—42no—
289C3×D12—42no—
290C3×D12—42no—
291C3×D12—81no—
292C3×C4×D3—21no—
293C3×C4×D3—21no—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×C4×D3—42no—
297C3×C4×D3—42no—
298C3×Dic6—21no—
299C3×Dic6—21no—
300C3×Dic6—42no—
301#626—42no—
302#626—42no—
303#625—42no—
304#625—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—31no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C23×D3—61no—
325C23×D3—61no—
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—61no—
342C2×C3×D4—61no—
343C2×C3×D4—61no—
344C2×C3×D4—61no—
345C22×C3×C4—31no—
346C22×C3×C4—31no—
347C22×C3×C4—61no—
348C22×C3×C4—61no—
349C2×#67—61no—
350C2×#67—61no—
351C2×#67—61no—
352C2×#67—61no—
353C2×#67—61no—
354C2×#67—61no—
355#239—22no—
356#239—41no—
357D3×Q8—22no—
358D3×Q8—41no—
359D3×D4—62no—
360D3×D4—62no—
361D3×D4—121no—
362D3×D4—121no—
363D3×D4—124no—
364D3×D4—124no—
365C2×D12—21no—
366C2×D12—21no—
367C2×D12—21no—
368C2×D12—21no—
369C2×D12—31no—
370C2×D12—31no—
371C2×D12—61no—
372C2×D12—62no—
373C2×D12—62no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12—121no—
377C2×D12—121no—
378C2×D12#6711yescharacteristic
379C2×D12C22×D311yescharacteristic
380C2×D12C22×D311yescharacteristic
381C2×D12C22×D311yescharacteristic
382C2×C4×D3—21no—
383C2×C4×D3—21no—
384C2×C4×D3—61no—
385C2×C4×D3—61no—
386C2×C4×D3—121no—
387C2×C4×D3C22×D311yescharacteristic
388C2×C4×D3C22×D311yescharacteristic
389C2×Dic6—21no—
390C2×Dic6C22×D311yescharacteristic
391C3×SD16—62no—
392C3×SD16—62no—
393C2×C3×C8—31no—
394C2×C3×C8—31no—
395C3×C4⋊C4—21no—
396C3×C4⋊C4—21no—
397C3×C4⋊C4—21no—
398C3×C4⋊C4—31no—
399C3×C4⋊C4—41no—
400C3×C4⋊C4—61no—
401C3×C4⋊C4C22×D311yescharacteristic
402C3×C4⋊C4C22×D311yescharacteristic
403C3×C22⋊C4—31no—
404C3×C22⋊C4—31no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C22⋊C4—61no—
409C3×C42—21no—
410C3×C42—21no—
411C3×C42—21no—
412C3×C42—41no—
413C3×C42C22×D311yescharacteristic
414C3×C42C22×D311yescharacteristic
415#217—61no—
416#217—61no—
417#215—22no—
418#215—22no—
419#215—34no—
420#215—34no—
421#215—64no—
422#215—62no—
423#215—62no—
424#215—121no—
425#214—62no—
426#214—121no—
427#213—62no—
428#213—62no—
429#213—62no—
430#213—121no—
431#213—121no—
432(C2×D3)⋊C4—21no—
433(C2×D3)⋊C4—21no—
434(C2×D3)⋊C4—21no—
435(C2×D3)⋊C4—21no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—61no—
438(C2×D3)⋊C4—61no—
439(C2×D3)⋊C4—61no—
440(C2×D3)⋊C4—121no—
441(C2×D3)⋊C4#6711yescharacteristic
442(C2×D3)⋊C4#6711yescharacteristic
443C4⋊Dic3—21no—
444C4⋊Dic3—31no—
445C4⋊Dic3—31no—
446C4⋊Dic3—61no—
447C4⋊Dic3#6711yescharacteristic
448#208—62no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—31no—
453C2×C3⋊C8—61no—
454C2×C3⋊C8—61no—
455C2×C3⋊C8—62no—
456C2×C3⋊C8C22×D311yescharacteristic
457C2×C3⋊C8C22×D311yescharacteristic
458D24—62no—
459#204—62no—
460ΓL(1,𝔽25)—62no—
461D3×C8—62no—
462C22×C32C22×D411yescharacteristic
463C2×C3⋊D3—22no—
464C2×C3⋊D3—41no—
465C2×C3⋊D3—41no—
466C2×C3×D3—21no—
467C2×C3×D3—21no—
468C2×C3×D3—21no—
469C2×C3×D3—21no—
470C2×C3×D3—21no—
471C2×C3×D3—41no—
472C2×C3×D3—41no—
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×D3AGL(1,ℤ/8)12yescomplemented
481D32—84no—
482D32—84no—
483C32×C4—22no—
484C32×C4—21no—
485C32×C4—21no—
486C32×C4—41no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—41no—
490C3×Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—41no—
493C2×#41—31no—
494C22×Q8—31no—
495C22×D4—91no—
496C22×D4—91no—
497C22×D4—181no—
498AGL(1,ℤ/8)—184no—
499C2×SD16—31no—
500C2×SD16—31no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—184no—
506C2×D8—91no—
507C2×D8—91no—
508C2×D8—91no—
509C2×M16—91no—
510C22×C8—91no—
511#127—31no—
512#124—31no—
513#124—61no—
514C22⋊Q8—31no—
515C22⋊Q8—61no—
516#121—31no—
517#121—61no—
518#121—91no—
519#121—91no—
520#121—181no—
521#120—181no—
522#120—181no—
523C4×Q8D3211yescharacteristic, complemented
524C4×D4—31no—
525C4×D4—61no—
526C4×D4—91no—
527#107—91no—
528C4⋊C8—31no—
529#103—91no—
530#103—91no—
531#102—31no—
532#102—31no—
533#102—91no—
534#102—91no—
535C22⋊C8—91no—
536C22⋊C8—91no—
537#97—91no—
538C23×C3—31no—
539C23×C3—31no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—21no—
546C22×D3—61no—
547C22×D3—61no—
548C22×D3—121no—
549C22×D3—122no—
550C22×D3—122no—
551C22×D3—122no—
552C22×D3—122no—
553C22×D3—122no—
554C22×D3—122no—
555C22×D3—122no—
556C22×D3—122no—
557C22×D3—241no—
558C22×D3—241no—
559C22×D3—241no—
560C22×D3—241no—
561C22×D3C2×#6711yescharacteristic
562C22×D3C2×#6711yescharacteristic
563C3×Q8—21no—
564C3×Q8—21no—
565C3×Q8—22no—
566C3×Q8—41no—
567C3×Q8—61no—
568C3×Q8—61no—
569C3×Q8—122no—
570C3×Q8D3×D412yescomplemented
571C3×Q8D3×D412yescomplemented
572C3×D4—62no—
573C3×D4—61no—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—61no—
577C3×D4—61no—
578C3×D4—61no—
579C3×D4—122no—
580C3×D4—122no—
581C3×D4—122no—
582C3×D4—241no—
583C2×C3×C4—21no—
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—31no—
591C2×C3×C4—31no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—122no—
600C2×C3×C4—122no—
601C2×C3×C4D3×D411yescharacteristic
602C2×C3×C4D3×D411yescharacteristic
603C2×C3×C4C2×#6711yescharacteristic
604C2×C3×C4C2×#6711yescharacteristic
605C2×C3×C4C23×D311yescharacteristic
606C2×C3×C4C23×D311yescharacteristic
607#67—122no—
608#67—122no—
609#67—122no—
610#67—122no—
611#67—122no—
612#67—122no—
613C2×Dic3—21no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—121no—
617C2×Dic3C2×#6711yescharacteristic
618C2×Dic3C2×#6711yescharacteristic
619D12—22no—
620D12—21no—
621D12—21no—
622D12—21no—
623D12—21no—
624D12—21no—
625D12—21no—
626D12—32no—
627D12—32no—
628D12—42no—
629D12—42no—
630D12—42no—
631D12—62no—
632D12—61no—
633D12—61no—
634D12—81no—
635D12—121no—
636D12—122no—
637D12—122no—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—21no—
641C4×D3—21no—
642C4×D3—42no—
643C4×D3—42no—
644C4×D3—122no—
645C4×D3—122no—
646C4×D3—242no—
647Dic6—21no—
648Dic6—21no—
649Dic6—42no—
650C3×C8—61no—
651C3×C8—61no—
652C3⋊C8—21no—
653C3⋊C8—21no—
654C3⋊C8—32no—
655C3⋊C8—32no—
656C3⋊C8—62no—
657C3⋊C8—61no—
658C3⋊C8—61no—
659C3⋊C8—121no—
660C2×C32D4211yescharacteristic
661C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
662C2×C32#57711yescharacteristic
663C3⋊D3—42no—
664C3×D3—22no—
665C3×D3—41no—
666C3×D3—81no—
667C3×D3—81no—
668C3×D3—81no—
669C24—181no—
670C24—181no—
671#41—62no—
672#41—121no—
673C2×Q8—31no—
674C2×Q8—61no—
675C2×Q8—62no—
676C2×Q8—121no—
677C2×Q8C2×D3211yescharacteristic
678C2×D4—31no—
679C2×D4—31no—
680C2×D4—31no—
681C2×D4—31no—
682C2×D4—61no—
683C2×D4—61no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—91no—
687C2×D4—181no—
688C2×D4—181no—
689C2×D4—182no—
690C2×D4—182no—
691C2×D4—181no—
692C2×D4—181no—
693C2×D4—361no—
694C2×D4—361no—
695C2×D4—364no—
696C22×C4—31no—
697C22×C4—31no—
698C22×C4—61no—
699C22×C4—61no—
700C22×C4—181no—
701SD16—62no—
702SD16—62no—
703SD16—94no—
704SD16—182no—
705SD16—182no—
706SD16—361no—
707D8—182no—
708D8—182no—
709D8—361no—
710M16—182no—
711C2×C8—31no—
712C2×C8—31no—
713C2×C8—91no—
714C2×C8—91no—
715C2×C8—182no—
716C4⋊C4—21no—
717C4⋊C4—31no—
718C4⋊C4—61no—
719C4⋊C4—91no—
720C4⋊C4C2×D3211yescharacteristic
721C22⋊C4—31no—
722C22⋊C4—31no—
723C22⋊C4—61no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—181no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C42—21no—
731C42C2×D3211yescharacteristic
732C22×C3—21no—
733C22×C3—32no—
734C22×C3—61no—
735C22×C3—61no—
736C22×C3—61no—
737C22×C3—61no—
738C22×C3—61no—
739C22×C3—121no—
740C22×C3—121no—
741C22×C3—121no—
742C22×C3—121no—
743C22×C3—121no—
744C22×C3—121no—
745C22×C3—121no—
746C22×C3—121no—
747C22×C3—121no—
748C22×C3C2×D3×D411yescharacteristic
749C22×C3C22×#6711yescharacteristic
750C2×D3—21no—
751C2×D3—21no—
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—41no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—62no—
765C2×D3—62no—
766C2×D3—122no—
767C2×D3—121no—
768C2×D3—121no—
769C2×D3—121no—
770C2×D3—121no—
771C2×D3—241no—
772C2×D3—241no—
773C2×D3—244no—
774C2×D3—244no—
775C2×D3—244no—
776C2×D3—244no—
777C2×D3#94912yescomplemented
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—22no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—22no—
784C3×C4—21no—
785C3×C4—21no—
786C3×C4—41no—
787C3×C4—41no—
788C3×C4—42no—
789C3×C4—41no—
790C3×C4—41no—
791C3×C4—61no—
792C3×C4—61no—
793C3×C4—81no—
794C3×C4—121no—
795C3×C4C2×D3×D411yescharacteristic
796C3×C4C2×D3×D411yescharacteristic
797C3×C4#100411yescharacteristic
798C3×C4#100911yescharacteristic
799Dic3—21no—
800Dic3—21no—
801Dic3—41no—
802Dic3—121no—
803Dic3—121no—
804Dic3—241no—
805C32#326511yescharacteristic, complemented, Sylow
806C23—31no—
807C23—31no—
808C23—61no—
809C23—61no—
810C23—61no—
811C23—181no—
812C23—362no—
813C23—362no—
814C23—362no—
815C23—362no—
816C23—721no—
817C23—721no—
818Q8—21no—
819Q8—61no—
820Q8—61no—
821Q8—122no—
822Q8#380212yescomplemented
823D4—62no—
824D4—61no—
825D4—61no—
826D4—61no—
827D4—61no—
828D4—61no—
829D4—61no—
830D4—92no—
831D4—122no—
832D4—122no—
833D4—122no—
834D4—181no—
835D4—241no—
836D4—362no—
837D4—362no—
838D4—362no—
839D4—362no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—31no—
843C2×C4—31no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—122no—
850C2×C4—122no—
851C2×C4—181no—
852C2×C4—362no—
853C2×C4D3×#6711yescharacteristic
854C2×C4D3×#6711yescharacteristic
855C2×C4C22×D3211yescharacteristic
856C8—61no—
857C8—61no—
858C8—92no—
859C8—181no—
860C2×C3—21no—
861C2×C3—21no—
862C2×C3—21no—
863C2×C3—62no—
864C2×C3—121no—
865C2×C3—241no—
866C2×C3—241no—
867C2×C3—241no—
868C2×C3#560911yescharacteristic
869C2×C3#576211yescharacteristic
870C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
871C2×C3D4×#6711yescharacteristic
872C2×C3C2×#94911yescharacteristic
873C2×C3#583711yescharacteristic
874D3—22no—
875D3—41no—
876D3—81no—
877D3—81no—
878D3—81no—
879D3—122no—
880D3—122no—
881D3—242no—
882C22—32no—
883C22—61no—
884C22—61no—
885C22—61no—
886C22—61no—
887C22—61no—
888C22—121no—
889C22—121no—
890C22—121no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—182no—
898C22—361no—
899C22—361no—
900C22—724no—
901C22—724no—
902C22C2×D3×#6711yescharacteristic
903C4—21no—
904C4—21no—
905C4—22no—
906C4—41no—
907C4—61no—
908C4—61no—
909C4—121no—
910C4—361no—
911C4C2×#380211yescharacteristic
912C4#6430711yescharacteristic
913C3—21no—
914C3#8040411yescharacteristic, complemented
915C3#8354211yescharacteristic, complemented
916C2—62no—
917C2—121no—
918C2—241no—
919C2—241no—
920C2—241no—
921C2—362no—
922C2#1059506911yescharacteristic
923C2#1059531811yescharacteristic
924C2D3×#94911yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
hypercenterC4×Q8D32
hypocenterC32#3265
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×#5576C2semidirect
2. C2×#63939C2semidirect
3. C2×D3×#215C2semidirect
4. #10594004C2semidirect
5. #10592725C2semidirect
6. C3×#5027C2semidirect
7. #10591586C2semidirect
8. #10591583C2semidirect
9. #10590596C2semidirect
10. #10590595C2semidirect
11. #10590503C2semidirect
12. #10590499C2semidirect
13. #10590356C2semidirect
14. #10590354C2semidirect
15. #10590330C2semidirect
18. C2×C3×#239C22semidirect
19. C2×C3×D3×Q8C22semidirect
23. C32×C4×Q8C22semidirect
26. C2×C3×#215C22semidirect
27. C2×C3×#215C22semidirect
29. C3×#897C22semidirect
31. C3×#895C22semidirect
33. C3×#875C22semidirect
45. C2×#3715C22semidirect
46. C2×#3715C22semidirect
48. C2×#3713C22semidirect
49. C2×#3713C22semidirect
50. C2×#3711C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63662C22semidirect
54. #63634C22semidirect
55. #63630C22semidirect
56. C3×#809C22semidirect
57. C3×#809C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63563C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
69. #5576D3semidirect
83. #5027D3semidirect
130. #3755D4semidirect
160. C2×#239C2×D3semidirect
161. C2×D3×Q8C2×D3semidirect
178. C3×C4×Q8C2×D3semidirect
179. C3×C4×Q8C2×D3semidirect
190. C2×#215C2×D3semidirect
191. C2×#215C2×D3semidirect
215. #897C2×D3semidirect
218. #895C2×D3semidirect
222. #875C2×D3semidirect
246. #809C2×D3semidirect
247. #809C2×D3semidirect
251. C4⋊(C3⋊C8)C2×D3semidirect
268. C32×Q8C2×D4semidirect
306. C3⋊(C3⋊C8)C2×D4semidirect
480. C2×C3×D3AGL(1,ℤ/8)semidirect
523. C4×Q8D32semidirect
570. C3×Q8D3×D4semidirect
571. C3×Q8D3×D4semidirect
777. C2×D3#949semidirect
805. C32#3265semidirect
822. Q8#3802semidirect
914. C3#80404semidirect
915. C3#83542semidirect

Maximal subgroups

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

subgroupindex
C3×#55762
C2×#639392
C2×D3×#2152
#105940042
#105927252
C3×#50272
#105915862
#105915832
#105905962
#105905952
#105905032
#105904992
#105903562
#105903542
#105903302
#835423
#804043