Finite Group Databasebeta

← #11883977

Subgroups — #11883977

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×D4×D12C211yesmaximal, characteristic, complemented
2C2×#63932C211yesmaximal, characteristic, complemented
3C2×D3×#214C211yesmaximal, characteristic, complemented
4#10593905C211yesmaximal, characteristic, complemented
5#10592717C211yesmaximal, characteristic, complemented
6C3×#5016C211yesmaximal, characteristic, complemented
7#10591458C211yesmaximal, characteristic, complemented
8#10591447C211yesmaximal, characteristic, complemented
9#10590613C211yesmaximal, characteristic, complemented
10#10590603C211yesmaximal, characteristic, complemented
11#10590515C211yesmaximal, characteristic, complemented
12#10590499C211yesmaximal, characteristic, complemented
13#10590377C211yesmaximal, characteristic, complemented
14#10590354C211yesmaximal, characteristic, complemented
15#10590330C211yesmaximal, characteristic, complemented
16#83491—31nomaximal
17#80553—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×C3×D12—21no—
21C2×#3795C2211yescharacteristic, complemented
22C2×D3×Dic6C2211yescharacteristic, complemented
23C32×C4×D4C2211yescharacteristic
24C2×#3754C2211yescharacteristic
25C4×#634C2211yescharacteristic, complemented
26C2×C3×#214C2211yescharacteristic
27C2×C3×#213C2211yescharacteristic
28C3×#930—21no—
29C3×#895C2211yescharacteristic
30C3×#895C2211yescharacteristic
31C3×#882—21no—
32C3×#882—21no—
33C3×#875C2211yescharacteristic, complemented
34C3×#874C2211yescharacteristic
35C3×C4×D12C2211yescharacteristic
36#63932—24no—
37D3×#214—24no—
38#63915—21no—
39#63908C2211yescharacteristic, complemented
40#63902—21no—
41#63899—21no—
42#63885—21no—
43#63856C2211yescharacteristic, complemented
44C2×#3716C2211yescharacteristic, complemented
45C2×#3716C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic, complemented
48C2×#3713C2211yescharacteristic, complemented
49C2×#3713C2211yescharacteristic, complemented
50C2×#3711C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63659C2211yescharacteristic
53#63637C2211yescharacteristic, complemented
54#63634C2211yescharacteristic, complemented
55#63630C2211yescharacteristic, complemented
56C3×#810C2211yescharacteristic, complemented
57C3×#809C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
62(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
63C3×D42—31no—
64C22×#214—31no—
65C2×#932—31no—
66C2×D3×SD16—31no—
67C2×#911—31no—
68#5677—31no—
69#5552—31no—
70D4×D12D311yescharacteristic, complemented
71C3×#463—31no—
72#5218—31no—
73#5217—31no—
74#5169—31no—
75#5156—31no—
76#5075—31no—
77#5074—31no—
78#5058—31no—
79#5042—31no—
80#5040—31no—
81#5038—31no—
82#5037—31no—
83#5018—31no—
84#5018—31no—
85#5018—61no—
86#5016D311yescharacteristic, complemented
87#5011—31no—
88#4848—31no—
89#4836—31no—
90#4812—31no—
91#4806—31no—
92#4781—31no—
93#4775—31no—
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C2×#634C2311yescharacteristic
99C2×C3×#67—21no—
100C2×C3×#67—21no—
101C3×D3×D4—22no—
102C3×D3×D4—22no—
103C3×D3×D4—41no—
104C3×D3×D4—41no—
105C2×C3×D12—21no—
106C2×C3×D12—21no—
107C2×C3×D12—21no—
108C2×C3×D12—21no—
109C2×C3×D12—44no—
110C2×C3×D12D411yescharacteristic
111C2×C3×D12C2311yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#627—21no—
118C2×#625—21no—
119C2×#625—21no—
120C2×D3×Dic3—21no—
121C2×D3×Dic3—21no—
122#3795—22no—
123#3795—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C32×C4⋊C4C2311yescharacteristic
127C32×C22⋊C4—21no—
128C32×C42C2311yescharacteristic
129#3754D414yescomplemented
130C4⋊(C3⋊Dic3)C2311yescharacteristic
131#3750—21no—
132C4×C3⋊Dic3—21no—
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C3×#214—22no—
136C3×#213—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⋊Dic3D411yescharacteristic
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146#3724—21no—
147(C2×D3)⋊Dic3—21no—
148(C2×D3)⋊Dic3—21no—
149#3716—22no—
150#3716—22no—
151#3715—22no—
152#3715—41no—
153#3713—22no—
154#3713—41no—
155#3711—22no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C22×C3×D4—31no—
159C22×C3×D4—31no—
160C22×C3×D4—61no—
161C2×D3×Q8—31no—
162C2×#237—31no—
163C2×D3×D4C2×D311yescharacteristic
164C2×D3×D4C2×D311yescharacteristic
165C2×#235—31no—
166C22×D12—21no—
167C22×Dic6—31no—
168C2×C3×SD16—31no—
169C2×C3×D8—31no—
170C3×#127—31no—
171C3×#124—31no—
172C3×#121—31no—
173C3×#121—31no—
174C3×#121—61no—
175C3×#120—61no—
176C3×#120—61no—
177C3×C4×D4—21no—
178C3×C4×D4—31no—
179C3×C4×D4C2×D311yescharacteristic
180C3×C4×D4C2×D311yescharacteristic
181#946—31no—
182C2×#215—31no—
183C2×#215—31no—
184#939—61no—
185#938—31no—
186C2×#214—31no—
187C2×#214—31no—
188C2×#214—31no—
189C2×#214—31no—
190C2×#214—31no—
191C2×#214—31no—
192C2×#214—61no—
193C2×#214—64no—
194C2×#214C2×D311yescharacteristic
195#932—64no—
196C2×#213—31no—
197C2×#213—31no—
198C2×#213—31no—
199C2×#213—31no—
200C2×#213C2×D311yescharacteristic
201#930—21no—
202#930—31no—
203#924—31no—
204C2×#208—31no—
205C22×C3⋊C8—31no—
206D3×SD16—64no—
207#911—64no—
208C2×#204—31no—
209C2×#204—31no—
210C2×ΓL(1,𝔽25)—31no—
211C2×D3×C8—31no—
212#896—61no—
213#895C2×D311yescharacteristic
214#895C2×D311yescharacteristic
215#885—61no—
216#885—61no—
217#884—61no—
218#882—21no—
219#882—21no—
220#67⋊C4—61no—
221#67⋊C4—61no—
222#878—61no—
223#875C2×D311yescharacteristic, complemented
224#874C2×D311yescharacteristic
225C4×D12C2×D311yescharacteristic
226C4×Dic6—31no—
227C4×Dic6—31no—
228C4×Dic6—61no—
229C3×C4⋊C8—31no—
230C3×#103—31no—
231C3×#102—31no—
232#832—31no—
233#832—31no—
234#832—31no—
235#832—31no—
236#832—61no—
237#830—31no—
238#830—31no—
239#821—31no—
240#821—31no—
241(C2×D3)⋊C8—31no—
242(C2×D3)⋊C8—31no—
243#810—31no—
244#810—31no—
245#810—61no—
246#810C2×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—
255C23×C32—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—42no—
260C22×C3×D3—42no—
261C22×C3×D3—42no—
262C22×C3×D3—42no—
263C22×C3×D3—81no—
264C22×C3×D3—81no—
265C22×C3×D3C2×D411yescharacteristic
266C22×C3×D3C2×D411yescharacteristic
267C32×D4—21no—
268C32×D4C2×D412yes—
269C2×C32×C4—21no—
270C2×C32×C4—42no—
271C2×C32×C4C2×D411yescharacteristic
272C2×C32×C4C2×D411yescharacteristic
273C2×C32×C4C2411yescharacteristic
274C2×C3⋊Dic3—21no—
275C2×C3⋊Dic3—21no—
276#634—21no—
277#634C2×D412yescomplemented
278C3×#67—42no—
279C3×#67—42no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3C2×D411yescharacteristic
282C2×C3×Dic3C2×D411yescharacteristic
283C3×D12—22no—
284C3×D12—21no—
285C3×D12—21no—
286C3×D12—21no—
287C3×D12—21no—
288C3×D12—21no—
289C3×D12—21no—
290C3×D12—42no—
291C3×D12—42no—
292C3×D12—42no—
293C3×D12—81no—
294C3×C4×D3—21no—
295C3×C4×D3—21no—
296C3×C4×D3—21no—
297C3×C4×D3—21no—
298C3×Dic6—21no—
299C3×Dic6—21no—
300#627—42no—
301#625—42no—
302#625—42no—
303D3×Dic3—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—91no—
312D42—31no—
313#496—91no—
314#468—91no—
315#466—91no—
316#463—31no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—91no—
323#435—91no—
324C24×C3—61no—
325C24×C3—61no—
326C23×D3—21no—
327C23×D3—21no—
328C2×C3×Q8—31no—
329C2×C3×D4—21no—
330C2×C3×D4—31no—
331C2×C3×D4—31no—
332C2×C3×D4—31no—
333C2×C3×D4—31no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—61no—
338C2×C3×D4—62no—
339C2×C3×D4—62no—
340C2×C3×D4—61no—
341C2×C3×D4—61no—
342C2×C3×D4—124no—
343C2×C3×D4—121no—
344C2×C3×D4—121no—
345C2×C3×D4C22×D311yescharacteristic
346C2×C3×D4C22×D311yescharacteristic
347C22×C3×C4—21no—
348C22×C3×C4—21no—
349C22×C3×C4—31no—
350C22×C3×C4—31no—
351C22×C3×C4—41no—
352C2×#67—21no—
353C2×#67—21no—
354C2×#67—61no—
355C2×#67—61no—
356C2×#67—61no—
357C2×#67—61no—
358C22×Dic3—61no—
359C22×Dic3—61no—
360D3×Q8—62no—
361D3×Q8—121no—
362#237—62no—
363#237—121no—
364D3×D4—22no—
365D3×D4—22no—
366D3×D4—41no—
367D3×D4—41no—
368#235—62no—
369#235—121no—
370C2×D12—21no—
371C2×D12—21no—
372C2×D12—21no—
373C2×D12—21no—
374C2×D12—44no—
375C2×D12#6711yescharacteristic
376C2×D12C22×D311yescharacteristic
377C2×D12C22×D311yescharacteristic
378C2×D12C22×D311yescharacteristic
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3C22×D311yescharacteristic
382C2×C4×D3C22×D311yescharacteristic
383C2×Dic6—31no—
384C2×Dic6—31no—
385C2×Dic6—61no—
386C2×Dic6—62no—
387C2×Dic6—61no—
388C2×Dic6—61no—
389C2×Dic6—121no—
390C2×Dic6C22×D311yescharacteristic
391C3×SD16—62no—
392C3×D8—62no—
393C2×C3×C8—31no—
394C2×C3×C8—31no—
395C3×C4⋊C4—21no—
396C3×C4⋊C4—31no—
397C3×C4⋊C4C22×D311yescharacteristic
398C3×C4⋊C4C22×D311yescharacteristic
399C3×C22⋊C4—21no—
400C3×C22⋊C4—21no—
401C3×C22⋊C4—31no—
402C3×C22⋊C4—31no—
403C3×C22⋊C4—41no—
404C3×C22⋊C4—61no—
405C3×C22⋊C4—61no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C42—21no—
409C3×C42C22×D311yescharacteristic
410C3×C42C22×D311yescharacteristic
411#217—61no—
412#217—61no—
413#215—62no—
414#215—121no—
415#214—22no—
416#214—34no—
417#214—34no—
418#214—64no—
419#214—62no—
420#214—62no—
421#214—62no—
422#214—121no—
423#213—22no—
424#213—62no—
425#213—62no—
426#213—121no—
427#213—121no—
428(C2×D3)⋊C4—21no—
429(C2×D3)⋊C4—21no—
430(C2×D3)⋊C4—21no—
431(C2×D3)⋊C4—21no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4#6711yescharacteristic
435(C2×D3)⋊C4#6711yescharacteristic
436C4⋊Dic3—31no—
437C4⋊Dic3—31no—
438C4⋊Dic3—61no—
439C4⋊Dic3#6711yescharacteristic
440Dic3⋊C4—61no—
441Dic3⋊C4—61no—
442Dic3⋊C4—61no—
443Dic3⋊C4—61no—
444Dic3⋊C4—121no—
445C4×Dic3—61no—
446C4×Dic3—61no—
447C4×Dic3—121no—
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
458#204—62no—
459#204—62no—
460ΓL(1,𝔽25)—62no—
461D3×C8—62no—
462C22×C32—22no—
463C22×C32—41no—
464C22×C32—41no—
465C22×C32C22×D411yescharacteristic
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×D3—84no—
481C2×C3×D3—84no—
482C2×C3×D3AGL(1,ℤ/8)12yescomplemented
483C32×C4—21no—
484C32×C4—21no—
485C32×C4—41no—
486C32×C4C22×D411yescharacteristic
487C32×C4H(5,𝔽2)11yescharacteristic
488C3⋊Dic3—22no—
489C3⋊Dic3—41no—
490C3×Dic3—21no—
491C3×Dic3—21no—
492C3×Dic3—41no—
493C2×#41—91no—
494C22×Q8—91no—
495C22×D4—31no—
496C22×D4—31no—
497C22×D4—61no—
498AGL(1,ℤ/8)—184no—
499C2×SD16—31no—
500C2×SD16—91no—
501C2×SD16—91no—
502C2×SD16—91no—
503C2×SD16—91no—
504C2×SD16—91no—
505C2×SD16—184no—
506C2×D8—31no—
507C2×D8—91no—
508C2×D8—91no—
509C2×M16—91no—
510C22×C8—91no—
511#127—31no—
512#124—31no—
513#124—181no—
514C22⋊Q8—91no—
515C22⋊Q8—181no—
516#121—31no—
517#121—31no—
518#121—61no—
519#121—91no—
520#121—181no—
521#120—61no—
522#120—61no—
523C4×Q8—91no—
524C4×D4—31no—
525C4×D4—181no—
526C4×D4D3211yescharacteristic
527#107—91no—
528C4⋊C8—31no—
529#103—31no—
530#103—91no—
531#102—31no—
532#102—91no—
533#102—91no—
534#102—91no—
535C22⋊C8—91no—
536C22⋊C8—91no—
537#97—91no—
538C23×C3—21no—
539C23×C3—21no—
540C23×C3—31no—
541C23×C3—31no—
542C23×C3—41no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—122no—
547C23×C3—122no—
548C23×C3—122no—
549C23×C3—122no—
550C23×C3—241no—
551C23×C3—241no—
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—42no—
556C22×D3—42no—
557C22×D3—42no—
558C22×D3—42no—
559C22×D3—81no—
560C22×D3—81no—
561C22×D3C2×#6711yescharacteristic
562C22×D3C2×#6711yescharacteristic
563C3×Q8—61no—
564C3×Q8—61no—
565C3×D4—21no—
566C3×D4—21no—
567C3×D4—22no—
568C3×D4—41no—
569C3×D4—62no—
570C3×D4—61no—
571C3×D4—61no—
572C3×D4—61no—
573C3×D4—61no—
574C3×D4—61no—
575C3×D4—61no—
576C3×D4—122no—
577C3×D4—122no—
578C3×D4—122no—
579C3×D4—122no—
580C3×D4—122no—
581C3×D4—241no—
582C3×D4D3×D412yes—
583C3×D4D3×D412yes—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—31no—
590C2×C3×C4—31no—
591C2×C3×C4—41no—
592C2×C3×C4—42no—
593C2×C3×C4—42no—
594C2×C3×C4—61no—
595C2×C3×C4—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—82no—
600C2×C3×C4D3×D411yescharacteristic
601C2×C3×C4D3×D411yescharacteristic
602C2×C3×C4C2×#6711yescharacteristic
603C2×C3×C4C2×#6711yescharacteristic
604C2×C3×C4C23×D311yescharacteristic
605C2×C3×C4C23×D311yescharacteristic
606#67—42no—
607#67—42no—
608#67—122no—
609#67—122no—
610#67—122no—
611#67—122no—
612C2×Dic3—21no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—121no—
618C2×Dic3—121no—
619C2×Dic3—122no—
620C2×Dic3—122no—
621C2×Dic3C2×#6711yescharacteristic
622C2×Dic3C2×#6711yescharacteristic
623D12—22no—
624D12—21no—
625D12—21no—
626D12—21no—
627D12—21no—
628D12—21no—
629D12—21no—
630D12—42no—
631D12—42no—
632D12—42no—
633D12—81no—
634C4×D3—21no—
635C4×D3—21no—
636C4×D3—21no—
637C4×D3—21no—
638C4×D3—122no—
639C4×D3—122no—
640Dic6—21no—
641Dic6—21no—
642Dic6—32no—
643Dic6—32no—
644Dic6—62no—
645Dic6—61no—
646Dic6—61no—
647Dic6—121no—
648Dic6—122no—
649Dic6—122no—
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×C32—42no—
661C2×C32D4211yescharacteristic
662C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
663C2×C32#57711yescharacteristic
664C3×D3—22no—
665C3×D3—41no—
666C3×D3—81no—
667C3×D3—81no—
668C3×D3—81no—
669C24—61no—
670C24—61no—
671#41—182no—
672#41—361no—
673C2×Q8—31no—
674C2×Q8—91no—
675C2×Q8—181no—
676C2×Q8—182no—
677C2×Q8—361no—
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—62no—
687C2×D4—62no—
688C2×D4—61no—
689C2×D4—61no—
690C2×D4—124no—
691C2×D4—121no—
692C2×D4—121no—
693C2×D4—181no—
694C2×D4—181no—
695C2×D4C2×D3211yescharacteristic
696C22×C4—21no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—181no—
700C22×C4—181no—
701SD16—62no—
702SD16—94no—
703SD16—182no—
704SD16—182no—
705SD16—182no—
706SD16—361no—
707D8—62no—
708D8—182no—
709D8—361no—
710M16—182no—
711C2×C8—31no—
712C2×C8—31no—
713C2×C8—91no—
714C2×C8—91no—
715C2×C8—182no—
716C4⋊C4—31no—
717C4⋊C4—91no—
718C4⋊C4—181no—
719C4⋊C4—181no—
720C4⋊C4C2×D3211yescharacteristic
721C22⋊C4—21no—
722C22⋊C4—31no—
723C22⋊C4—31no—
724C22⋊C4—61no—
725C22⋊C4—61no—
726C22⋊C4—61no—
727C22⋊C4—61no—
728C22⋊C4—181no—
729C22⋊C4—181no—
730C42—181no—
731C42C2×D3211yescharacteristic
732C22×C3—22no—
733C22×C3—22no—
734C22×C3—21no—
735C22×C3—32no—
736C22×C3—42no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—81no—
747C22×C3—81no—
748C22×C3—121no—
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×C3—244no—
759C22×C3C2×D3×D411yescharacteristic
760C22×C3C22×#6711yescharacteristic
761C2×D3—21no—
762C2×D3—21no—
763C2×D3—21no—
764C2×D3—21no—
765C2×D3—21no—
766C2×D3—41no—
767C2×D3—41no—
768C2×D3—41no—
769C2×D3—41no—
770C2×D3—41no—
771C2×D3—41no—
772C2×D3—41no—
773C2×D3—41no—
774C2×D3—41no—
775C2×D3—84no—
776C2×D3—84no—
777C2×D3#93212yescomplemented
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—21no—
781C3×C4—21no—
782C3×C4—21no—
783C3×C4—21no—
784C3×C4—41no—
785C3×C4—41no—
786C3×C4—41no—
787C3×C4—41no—
788C3×C4—61no—
789C3×C4—61no—
790C3×C4—81no—
791C3×C4—121no—
792C3×C4C2×D3×D411yescharacteristic
793C3×C4C2×D3×D411yescharacteristic
794C3×C4#100411yescharacteristic
795C3×C4#100911yescharacteristic
796Dic3—21no—
797Dic3—21no—
798Dic3—41no—
799Dic3—62no—
800Dic3—62no—
801Dic3—122no—
802Dic3—121no—
803Dic3—121no—
804Dic3—241no—
805C32#326511yescharacteristic, complemented, Sylow
806C23—21no—
807C23—31no—
808C23—31no—
809C23—61no—
810C23—61no—
811C23—61no—
812C23—122no—
813C23—122no—
814C23—122no—
815C23—122no—
816C23—241no—
817C23—241no—
818Q8—61no—
819Q8—61no—
820Q8—92no—
821Q8—181no—
822Q8—362no—
823D4—21no—
824D4—62no—
825D4—61no—
826D4—61no—
827D4—61no—
828D4—61no—
829D4—61no—
830D4—61no—
831D4—122no—
832D4—122no—
833D4—122no—
834D4—122no—
835D4—122no—
836D4—241no—
837D4—362no—
838D4—362no—
839D4#380212yes—
840C2×C4—21no—
841C2×C4—31no—
842C2×C4—31no—
843C2×C4—42no—
844C2×C4—61no—
845C2×C4—61no—
846C2×C4—61no—
847C2×C4—61no—
848C2×C4—61no—
849C2×C4—181no—
850C2×C4—181no—
851C2×C4—362no—
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—42no—
864C2×C3—42no—
865C2×C3—62no—
866C2×C3—82no—
867C2×C3—121no—
868C2×C3—241no—
869C2×C3—241no—
870C2×C3—241no—
871C2×C3#560911yescharacteristic
872C2×C3#577011yescharacteristic
873C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
874C2×C3C2×#93211yescharacteristic
875C2×C3D4×#6711yescharacteristic
876C2×C3#583611yescharacteristic
877D3—22no—
878D3—41no—
879D3—81no—
880D3—81no—
881D3—81no—
882C22—22no—
883C22—32no—
884C22—41no—
885C22—41no—
886C22—61no—
887C22—61no—
888C22—61no—
889C22—61no—
890C22—61no—
891C22—121no—
892C22—121no—
893C22—121no—
894C22—121no—
895C22—121no—
896C22—121no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—244no—
901C22—244no—
902C22C2×D3×#6711yescharacteristic
903C4—21no—
904C4—21no—
905C4—41no—
906C4—61no—
907C4—61no—
908C4—121no—
909C4—182no—
910C4—361no—
911C4C2×#380211yescharacteristic
912C4#6430711yescharacteristic
913C3—21no—
914C3#8055311yescharacteristic, complemented
915C3#8349111yescharacteristic, complemented
916C2—42no—
917C2—62no—
918C2—121no—
919C2—241no—
920C2—241no—
921C2—241no—
922C2#1059506911yescharacteristic
923C2D3×#93211yescharacteristic
924C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
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. C3×D4×D12C2semidirect
2. C2×#63932C2semidirect
3. C2×D3×#214C2semidirect
4. #10593905C2semidirect
5. #10592717C2semidirect
6. C3×#5016C2semidirect
7. #10591458C2semidirect
8. #10591447C2semidirect
9. #10590613C2semidirect
10. #10590603C2semidirect
11. #10590515C2semidirect
12. #10590499C2semidirect
13. #10590377C2semidirect
14. #10590354C2semidirect
15. #10590330C2semidirect
21. C2×#3795C22semidirect
22. C2×D3×Dic6C22semidirect
25. C4×#634C22semidirect
33. C3×#875C22semidirect
39. #63908C22semidirect
43. #63856C22semidirect
44. C2×#3716C22semidirect
45. C2×#3716C22semidirect
46. C2×#3715C22semidirect
47. C2×#3715C22semidirect
48. C2×#3713C22semidirect
49. C2×#3713C22semidirect
50. C2×#3711C22semidirect
51. C2×D3×C3⋊C8C22semidirect
53. #63637C22semidirect
54. #63634C22semidirect
55. #63630C22semidirect
56. C3×#810C22semidirect
57. C3×#809C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
70. D4×D12D3semidirect
86. #5016D3semidirect
129. #3754D4semidirect
223. #875C2×D3semidirect
246. #810C2×D3semidirect
247. #809C2×D3semidirect
251. C4⋊(C3⋊C8)C2×D3semidirect
277. #634C2×D4semidirect
306. C3⋊(C3⋊C8)C2×D4semidirect
482. C2×C3×D3AGL(1,ℤ/8)semidirect
777. C2×D3#932semidirect
805. C32#3265semidirect
914. C3#80553semidirect
915. C3#83491semidirect

Maximal subgroups

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

subgroupindex
C3×D4×D122
C2×#639322
C2×D3×#2142
#105939052
#105927172
C3×#50162
#105914582
#105914472
#105906132
#105906032
#105905152
#105904992
#105903772
#105903542
#105903302
#834913
#805533