Finite Group Databasebeta

← #11883979

Subgroups — #11883979

Order 1152.

1154 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×D4×D12C211yesmaximal, characteristic, complemented
2C2×#63934C211yesmaximal, characteristic, complemented
3C2×D3×#214C211yesmaximal, characteristic, complemented
4#10593899C211yesmaximal, characteristic, complemented
5#10592715C211yesmaximal, characteristic, complemented
6C3×#5018C211yesmaximal, characteristic, complemented
7#10591459C211yesmaximal, characteristic, complemented
8#10591448C211yesmaximal, characteristic, complemented
9#10590615C211yesmaximal, characteristic, complemented
10#10590603C211yesmaximal, characteristic, complemented
11#10590588C211yesmaximal, characteristic, complemented
12#10590576C211yesmaximal, characteristic, complemented
13#10590371C211yesmaximal, characteristic, complemented
14#10590364C211yesmaximal, characteristic, complemented
15#10590326C211yesmaximal, characteristic, complemented
16#83491—31nomaximal
17#79794—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×C3×D3×D4C2211yescharacteristic
20C22×C3×D12—21no—
21C2×#3799C2211yescharacteristic, complemented
22C2×D3×Dic6C2211yescharacteristic, complemented
23C32×C4×D4C2211yescharacteristic
24C2×#3754C2211yescharacteristic
25C2×#3753C2211yescharacteristic
26#64084C2211yescharacteristic, complemented
27C2×C3×#214C2211yescharacteristic
28C3×#930—21no—
29C3×#895C2211yescharacteristic
30C3×#895C2211yescharacteristic
31C3×#882—21no—
32C3×#882—21no—
33C3×#874C2211yescharacteristic
34C3×C4×D12C2211yescharacteristic
35C3×C4×Dic6C2211yescharacteristic, complemented
36#63934—24no—
37D3×#214—24no—
38#63909C2211yescharacteristic, complemented
39#63895—21no—
40#63886—21no—
41#63880—21no—
42#63857C2211yescharacteristic, complemented
43#63852—21no—
44C2×#3716C2211yescharacteristic, complemented
45C2×#3716C2211yescharacteristic, complemented
46C2×#3715C2211yescharacteristic, complemented
47C2×#3715C2211yescharacteristic, complemented
48C2×#3714C2211yescharacteristic, complemented
49C2×#3714C2211yescharacteristic, complemented
50C2×#3711C2211yescharacteristic, complemented
51C2×D3×C3⋊C8C2211yescharacteristic, complemented
52#63637C2211yescharacteristic, complemented
53#63636C2211yescharacteristic, complemented
54C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
55C3×#832C2211yescharacteristic
56C3×#810C2211yescharacteristic, complemented
57C3×#807C2211yescharacteristic, complemented
58C3×#803C2211yescharacteristic, complemented
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, 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×#914—31no—
67C2×D3×SD16—31no—
68#5576—31no—
69#5552—31no—
70D4×D12D311yescharacteristic, complemented
71C3×#440—31no—
72#5218—31no—
73#5217—31no—
74#5075—31no—
75#5074—31no—
76#5042—31no—
77#5040—31no—
78#5038—31no—
79#5037—31no—
80#5027—31no—
81#5018D311yescharacteristic, complemented
82#5016—31no—
83#5016—31no—
84#5016—61no—
85#5011—31no—
86#4886—31no—
87#4883—31no—
88#4810—31no—
89#4806—31no—
90#4776—31no—
91#4773—31no—
92#4712—31no—
93#4706—31no—
94C23×C3×D3—21no—
95C23×C3×D3—21no—
96C2×C32×D4C2311yescharacteristic
97C22×C32×C4—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67—21no—
102C3×D3×D4—22no—
103C3×D3×D4—22no—
104C3×D3×D4—41no—
105C3×D3×D4—41no—
106C2×C3×D12—21no—
107C2×C3×D12—21no—
108C2×C3×D12—21no—
109C2×C3×D12—21no—
110C2×C3×D12—44no—
111C2×C3×D12D411yescharacteristic
112C2×C3×D12C2311yescharacteristic
113C2×C3×D12C2311yescharacteristic
114C2×C3×C4×D3C2311yescharacteristic
115C2×C3×C4×D3C2311yescharacteristic
116C2×C3×Dic6C2311yescharacteristic
117C2×#627—21no—
118C2×#626—21no—
119C2×#626—21no—
120C2×#624—21no—
121C2×D3×Dic3—21no—
122#3799—22no—
123#3799—41no—
124D3×Dic6—22no—
125D3×Dic6—41no—
126C32×C4⋊C4C2311yescharacteristic
127C32×C22⋊C4—21no—
128C32×C42C2311yescharacteristic
129#3754—22no—
130#3753—22no—
131#3752—21no—
132#3752—21no—
133C2×C3⋊(C3⋊C8)C2311yescharacteristic
134C2×C3⋊(C3⋊C8)C2311yescharacteristic
135C3×#214D414yescomplemented
136C3×(C2×D3)⋊C4—21no—
137C3×(C2×D3)⋊C4—21no—
138C3×(C2×D3)⋊C4D411yescharacteristic
139C3×(C2×D3)⋊C4D411yescharacteristic
140C3×C4⋊Dic3D411yescharacteristic
141C3×C4⋊Dic3C2311yescharacteristic
142C3×Dic3⋊C4—21no—
143C3×C4×Dic3—21no—
144C2×C3×C3⋊C8C2311yescharacteristic
145C2×C3×C3⋊C8C2311yescharacteristic
146Dic3⋊Dic3—21no—
147#3722—21no—
148(C2×D3)⋊Dic3—21no—
149#3716—22no—
150#3716—41no—
151#3715—22no—
152#3715—22no—
153#3714—22no—
154#3714—41no—
155#3711—22no—
156D3×C3⋊C8—22no—
157#3265—91noSylow
158C22×C3×D4—31no—
159C22×C3×D4—31no—
160C22×C3×D4—61no—
161C2×#239—31no—
162C2×D3×Q8—31no—
163C2×D3×D4C2×D311yescharacteristic
164C2×D3×D4C2×D311yescharacteristic
165C2×#235—31no—
166C22×D12—21no—
167C22×Dic6—31no—
168C2×C3×SD16—31no—
169C3×#127—31no—
170C3×#121—31no—
171C3×#121—31no—
172C3×#121—61no—
173C3×#120—61no—
174C3×#120—61no—
175C3×C4×Q8—31no—
176C3×C4×D4—21no—
177C3×C4×D4—31no—
178C3×C4×D4C2×D311yescharacteristic
179C3×C4×D4C2×D311yescharacteristic
180C2×#215—31no—
181C2×#215—31no—
182#939—61no—
183C2×#214—31no—
184C2×#214—31no—
185C2×#214—31no—
186C2×#214—31no—
187C2×#214—31no—
188C2×#214—31no—
189C2×#214—61no—
190C2×#214—64no—
191C2×#214C2×D311yescharacteristic
192#932—64no—
193C2×#213—31no—
194C2×#213—31no—
195C2×#213—31no—
196C2×#213—31no—
197C2×#213—61no—
198#930—21no—
199#930—31no—
200#924—31no—
201C2×#208—31no—
202C22×C3⋊C8—31no—
203#914—64no—
204D3×SD16—64no—
205C2×D24—31no—
206C2×D24—31no—
207C2×#204—31no—
208C2×#204—31no—
209C2×ΓL(1,𝔽25)—31no—
210C2×D3×C8—31no—
211#897—31no—
212#897—61no—
213#896—61no—
214#895—31no—
215#895—61no—
216#895C2×D311yescharacteristic
217#895C2×D311yescharacteristic
218#885—61no—
219#882—21no—
220#882—21no—
221#67⋊C4—61no—
222#875—31no—
223#875—31no—
224#875—61no—
225#875—61no—
226#874C2×D311yescharacteristic
227C4×D12—61no—
228C4×D12C2×D311yescharacteristic
229C4×Dic6C2×D311yescharacteristic, complemented
230C3×#107—31no—
231C3×#103—31no—
232C3×#102—31no—
233C3×#97—31no—
234#832—31no—
235#832—31no—
236#832C2×D311yescharacteristic
237#830—31no—
238#830—31no—
239(C2×D3)⋊C8—31no—
240(C2×D3)⋊C8—31no—
241#810—31no—
242#810—31no—
243#810—61no—
244#810C2×D311yescharacteristic, complemented
245#809—31no—
246#809—31no—
247#809—31no—
248#809—31no—
249#809—61no—
250#807C2×D311yescharacteristic, complemented
251C4⋊(C3⋊C8)—31no—
252C4⋊(C3⋊C8)—31no—
253C4⋊(C3⋊C8)—61no—
254#803C2×D311yescharacteristic, complemented
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—
275C4⋊(C3⋊D3)—21no—
276C4⋊(C3⋊D3)—21no—
277#634—21no—
278#634—21no—
279C3×#67—42no—
280C3×#67—42no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3C2×D411yescharacteristic
284C2×C3×Dic3C2×D411yescharacteristic
285C3×D12—22no—
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×Dic6C2×D412yescomplemented
300#627—42no—
301#626—42no—
302#626—42no—
303#624—42no—
304D3×Dic3—42no—
305C3⋊(C3⋊C8)—21no—
306C3⋊(C3⋊C8)—21no—
307C3×C3⋊C8—21no—
308C3×C3⋊C8C2×D412yescomplemented
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—91no—
317#460—91no—
318#450—91no—
319#449—91no—
320#448—91no—
321#447—91no—
322#440—31no—
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—61no—
334C2×C3×D4—61no—
335C2×C3×D4—61no—
336C2×C3×D4—61no—
337C2×C3×D4—62no—
338C2×C3×D4—62no—
339C2×C3×D4—61no—
340C2×C3×D4—61no—
341C2×C3×D4—124no—
342C2×C3×D4—121no—
343C2×C3×D4—121no—
344C2×C3×D4C22×D311yescharacteristic
345C2×C3×D4C22×D311yescharacteristic
346C22×C3×C4—21no—
347C22×C3×C4—21no—
348C22×C3×C4—31no—
349C22×C3×C4—31no—
350C22×C3×C4—41no—
351C2×#67—21no—
352C2×#67—21no—
353C2×#67—61no—
354C2×#67—61no—
355C22×Dic3—61no—
356#239—62no—
357#239—121no—
358D3×Q8—62no—
359D3×Q8—121no—
360D3×D4—22no—
361D3×D4—22no—
362D3×D4—41no—
363D3×D4—41no—
364#235—62no—
365#235—121no—
366C2×D12—21no—
367C2×D12—21no—
368C2×D12—21no—
369C2×D12—21no—
370C2×D12—31no—
371C2×D12—31no—
372C2×D12—44no—
373C2×D12—61no—
374C2×D12—61no—
375C2×D12—61no—
376C2×D12#6711yescharacteristic
377C2×D12C22×D311yescharacteristic
378C2×D12C22×D311yescharacteristic
379C2×C4×D3—61no—
380C2×C4×D3—61no—
381C2×C4×D3—61no—
382C2×C4×D3C22×D311yescharacteristic
383C2×C4×D3C22×D311yescharacteristic
384C2×Dic6—31no—
385C2×Dic6—31no—
386C2×Dic6—61no—
387C2×Dic6—62no—
388C2×Dic6—61no—
389C2×Dic6—61no—
390C2×Dic6—121no—
391C2×Dic6C22×D311yescharacteristic
392C3×SD16—34no—
393C2×C3×C8—31no—
394C2×C3×C8—31no—
395C3×C4⋊C4—21no—
396C3×C4⋊C4—31no—
397C3×C4⋊C4—31no—
398C3×C4⋊C4—61no—
399C3×C4⋊C4C22×D311yescharacteristic
400C3×C4⋊C4C22×D311yescharacteristic
401C3×C22⋊C4—21no—
402C3×C22⋊C4—21no—
403C3×C22⋊C4—31no—
404C3×C22⋊C4—31no—
405C3×C22⋊C4—41no—
406C3×C22⋊C4—61no—
407C3×C22⋊C4—61no—
408C3×C42—21no—
409C3×C42—61no—
410C3×C42C22×D311yescharacteristic
411C3×C42C22×D311yescharacteristic
412#217—61no—
413#215—62no—
414#215—62no—
415#214—62no—
416#214—62no—
417#214—62no—
418#214—62no—
419#214—62no—
420#214—122no—
421#214—121no—
422#214D1214yescomplemented
423#213—62no—
424#213—62no—
425#213—62no—
426#213—122no—
427#213—121no—
428(C2×D3)⋊C4—21no—
429(C2×D3)⋊C4—21no—
430(C2×D3)⋊C4—61no—
431(C2×D3)⋊C4—61no—
432(C2×D3)⋊C4—61no—
433(C2×D3)⋊C4—61no—
434(C2×D3)⋊C4—61no—
435(C2×D3)⋊C4—61no—
436(C2×D3)⋊C4—61no—
437(C2×D3)⋊C4—121no—
438(C2×D3)⋊C4—121no—
439(C2×D3)⋊C4#6711yescharacteristic
440(C2×D3)⋊C4#6711yescharacteristic
441C4⋊Dic3—61no—
442C4⋊Dic3#6711yescharacteristic
443C4⋊Dic3C22×D311yescharacteristic
444Dic3⋊C4—21no—
445Dic3⋊C4—61no—
446C4×Dic3—21no—
447#208—62no—
448C2×C3⋊C8—31no—
449C2×C3⋊C8—31no—
450C2×C3⋊C8—31no—
451C2×C3⋊C8—31no—
452C2×C3⋊C8—61no—
453C2×C3⋊C8—61no—
454C2×C3⋊C8—62no—
455C2×C3⋊C8C22×D311yescharacteristic
456C2×C3⋊C8C22×D311yescharacteristic
457D24—62no—
458D24—121no—
459#204—62no—
460#204—121no—
461ΓL(1,𝔽25)—62no—
462D3×C8—62no—
463C22×C32—22no—
464C22×C32—41no—
465C22×C32—41no—
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—21no—
473C2×C3×D3—21no—
474C2×C3×D3—21no—
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×D3—84no—
483C2×C3×D3AGL(1,ℤ/8)12yescomplemented
484C32×C4—21no—
485C32×C4—21no—
486C32×C4—41no—
487C32×C4C22×D411yescharacteristic
488C32×C4H(5,𝔽2)11yescharacteristic
489C3⋊Dic3—41no—
490C3×Dic3—22no—
491C3×Dic3—21no—
492C3×Dic3—21no—
493C3×Dic3—41no—
494C2×#41—91no—
495C22×Q8—91no—
496C22×D4—31no—
497C22×D4—31no—
498C22×D4—61no—
499AGL(1,ℤ/8)—184no—
500C2×SD16—31no—
501C2×SD16—91no—
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—31no—
513#124—91no—
514#124—181no—
515C22⋊Q8—91no—
516C22⋊Q8—181no—
517#121—31no—
518#121—31no—
519#121—61no—
520#121—91no—
521#121—181no—
522#120—61no—
523#120—61no—
524C4×Q8—31no—
525C4×D4—31no—
526C4×D4—181no—
527C4×D4D3211yescharacteristic
528#107—31no—
529C4⋊C8—91no—
530#103—31no—
531#103—91no—
532#102—31no—
533#102—91no—
534#102—91no—
535#102—91no—
536C22⋊C8—91no—
537C22⋊C8—91no—
538#97—31no—
539C23×C3—21no—
540C23×C3—21no—
541C23×C3—31no—
542C23×C3—31no—
543C23×C3—41no—
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—42no—
555C22×D3—42no—
556C22×D3—42no—
557C22×D3—42no—
558C22×D3—61no—
559C22×D3—61no—
560C22×D3—81no—
561C22×D3—81no—
562C22×D3—121no—
563C22×D3C2×#6711yescharacteristic
564C22×D3C2×#6711yescharacteristic
565C3×Q8—32no—
566C3×Q8—61no—
567C3×D4—21no—
568C3×D4—21no—
569C3×D4—22no—
570C3×D4—41no—
571C3×D4—62no—
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×D4C2×D1212yes—
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—61no—
600C2×C3×C4—82no—
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—42no—
608#67—42no—
609#67—122no—
610#67—122no—
611C2×Dic3—21no—
612C2×Dic3—21no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—121no—
616C2×Dic3—122no—
617C2×Dic3C2×#6711yescharacteristic
618C2×Dic3C2×#6711yescharacteristic
619D12—22no—
620D12—21no—
621D12—21no—
622D12—21no—
623D12—21no—
624D12—42no—
625D12—42no—
626D12—42no—
627D12—61no—
628D12—61no—
629D12—61no—
630D12—61no—
631D12—81no—
632D12—121no—
633D12—121no—
634D12—122no—
635D12—122no—
636C4×D3—21no—
637C4×D3—21no—
638C4×D3—21no—
639C4×D3—21no—
640C4×D3—122no—
641C4×D3—122no—
642C4×D3—122no—
643Dic6—21no—
644Dic6—61no—
645Dic6—61no—
646Dic6—61no—
647Dic6—61no—
648Dic6—121no—
649Dic6—121no—
650Dic6—122no—
651Dic6—122no—
652Dic6C2×D1212yescomplemented
653C3×C8—32no—
654C3×C8—61no—
655C3⋊C8—21no—
656C3⋊C8—61no—
657C3⋊C8—61no—
658C3⋊C8—61no—
659C3⋊C8—61no—
660C3⋊C8—121no—
661C3⋊C8—121no—
662C3⋊C8C2×D1212yescomplemented
663C2×C32—42no—
664C2×C32D4211yescharacteristic
665C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
666C2×C32#57711yescharacteristic
667C3⋊D3—81no—
668C3×D3—22no—
669C3×D3—41no—
670C3×D3—81no—
671C3×D3—81no—
672C24—61no—
673C24—61no—
674#41—182no—
675#41—361no—
676C2×Q8—31no—
677C2×Q8—91no—
678C2×Q8—181no—
679C2×Q8—182no—
680C2×Q8—361no—
681C2×D4—31no—
682C2×D4—31no—
683C2×D4—31no—
684C2×D4—61no—
685C2×D4—61no—
686C2×D4—61no—
687C2×D4—61no—
688C2×D4—62no—
689C2×D4—62no—
690C2×D4—61no—
691C2×D4—61no—
692C2×D4—91no—
693C2×D4—124no—
694C2×D4—121no—
695C2×D4—121no—
696C2×D4—181no—
697C2×D4—181no—
698C2×D4C2×D3211yescharacteristic
699C22×C4—21no—
700C22×C4—31no—
701C22×C4—31no—
702C22×C4—181no—
703C22×C4—181no—
704SD16—34no—
705SD16—182no—
706SD16—182no—
707SD16—182no—
708SD16—182no—
709SD16—361no—
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—31no—
720C4⋊C4—31no—
721C4⋊C4—61no—
722C4⋊C4—181no—
723C4⋊C4C2×D3211yescharacteristic
724C22⋊C4—21no—
725C22⋊C4—31no—
726C22⋊C4—31no—
727C22⋊C4—61no—
728C22⋊C4—61no—
729C22⋊C4—181no—
730C22⋊C4—181no—
731C22⋊C4—181no—
732C22⋊C4—181no—
733C42—61no—
734C42C2×D3211yescharacteristic
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—21no—
738C22×C3—32no—
739C22×C3—42no—
740C22×C3—41no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—41no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—61no—
747C22×C3—61no—
748C22×C3—61no—
749C22×C3—81no—
750C22×C3—81no—
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—84no—
773C2×D3—84no—
774C2×D3—121no—
775C2×D3—121no—
776C2×D3—121no—
777C2×D3—121no—
778C2×D3—121no—
779C2×D3—121no—
780C2×D3—241no—
781C2×D3—241no—
782C2×D3—241no—
783C2×D3#93212yescomplemented
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—61no—
796C3×C4—61no—
797C3×C4—81no—
798C3×C4—121no—
799C3×C4C22×D1211yescharacteristic
800C3×C4C2×D3×D411yescharacteristic
801C3×C4#100411yescharacteristic
802C3×C4#100911yescharacteristic
803Dic3—21no—
804Dic3—21no—
805Dic3—22no—
806Dic3—41no—
807Dic3—121no—
808Dic3—121no—
809Dic3—241no—
810C32#326511yescharacteristic, complemented, Sylow
811C23—21no—
812C23—31no—
813C23—31no—
814C23—61no—
815C23—61no—
816C23—122no—
817C23—122no—
818C23—122no—
819C23—122no—
820C23—181no—
821C23—241no—
822C23—241no—
823Q8—32no—
824Q8—61no—
825Q8—181no—
826Q8—181no—
827Q8—362no—
828D4—21no—
829D4—62no—
830D4—61no—
831D4—61no—
832D4—61no—
833D4—61no—
834D4—122no—
835D4—122no—
836D4—122no—
837D4—122no—
838D4—122no—
839D4—181no—
840D4—181no—
841D4—241no—
842D4—362no—
843D4—362no—
844D4D3×D1212yes—
845C2×C4—21no—
846C2×C4—31no—
847C2×C4—31no—
848C2×C4—42no—
849C2×C4—61no—
850C2×C4—61no—
851C2×C4—61no—
852C2×C4—61no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—181no—
856C2×C4—362no—
857C2×C4—362no—
858C2×C4D3×#6711yescharacteristic
859C2×C4D3×#6711yescharacteristic
860C2×C4C22×D3211yescharacteristic
861C8—32no—
862C8—61no—
863C8—181no—
864C8—181no—
865C2×C3—21no—
866C2×C3—21no—
867C2×C3—21no—
868C2×C3—42no—
869C2×C3—42no—
870C2×C3—62no—
871C2×C3—82no—
872C2×C3—121no—
873C2×C3—241no—
874C2×C3—241no—
875C2×C3D4×D1211yescharacteristic
876C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
877C2×C3#577811yescharacteristic
878C2×C3C2×#93211yescharacteristic
879C2×C3D4×#6711yescharacteristic
880C2×C3#583611yescharacteristic
881D3—22no—
882D3—41no—
883D3—81no—
884D3—81no—
885D3—241no—
886D3—241no—
887D3—481no—
888C22—22no—
889C22—32no—
890C22—41no—
891C22—41no—
892C22—61no—
893C22—61no—
894C22—61no—
895C22—61no—
896C22—61no—
897C22—121no—
898C22—121no—
899C22—121no—
900C22—121no—
901C22—121no—
902C22—121no—
903C22—244no—
904C22—244no—
905C22—361no—
906C22—361no—
907C22—361no—
908C22C2×D3×#6711yescharacteristic
909C4—21no—
910C4—21no—
911C4—41no—
912C4—61no—
913C4—61no—
914C4—62no—
915C4—121no—
916C4—361no—
917C4C2×D3×D1211yescharacteristic
918C4#6430711yescharacteristic
919C3—21no—
920C3#7979411yescharacteristic, complemented
921C3#8349111yescharacteristic, complemented
922C2—42no—
923C2—62no—
924C2—121no—
925C2—241no—
926C2—241no—
927C2—721no—
928C2D12×#6711yescharacteristic
929C2D3×#93211yescharacteristic
930C2#1059546411yescharacteristic
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×#63934C2semidirect
3. C2×D3×#214C2semidirect
4. #10593899C2semidirect
5. #10592715C2semidirect
6. C3×#5018C2semidirect
7. #10591459C2semidirect
8. #10591448C2semidirect
9. #10590615C2semidirect
10. #10590603C2semidirect
11. #10590588C2semidirect
12. #10590576C2semidirect
13. #10590371C2semidirect
14. #10590364C2semidirect
15. #10590326C2semidirect
21. C2×#3799C22semidirect
22. C2×D3×Dic6C22semidirect
26. #64084C22semidirect
35. C3×C4×Dic6C22semidirect
38. #63909C22semidirect
42. #63857C22semidirect
44. C2×#3716C22semidirect
45. C2×#3716C22semidirect
46. C2×#3715C22semidirect
47. C2×#3715C22semidirect
48. C2×#3714C22semidirect
49. C2×#3714C22semidirect
50. C2×#3711C22semidirect
51. C2×D3×C3⋊C8C22semidirect
52. #63637C22semidirect
53. #63636C22semidirect
54. C4⋊(C3⋊(C3⋊C8))C22semidirect
56. C3×#810C22semidirect
57. C3×#807C22semidirect
58. C3×#803C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
61. (C2×D3)⋊(C3⋊C8)C22semidirect
62. (C2×D3)⋊(C3⋊C8)C22semidirect
70. D4×D12D3semidirect
81. #5018D3semidirect
135. C3×#214D4semidirect
229. C4×Dic6C2×D3semidirect
244. #810C2×D3semidirect
250. #807C2×D3semidirect
254. #803C2×D3semidirect
299. C3×Dic6C2×D4semidirect
308. C3×C3⋊C8C2×D4semidirect
422. #214D12semidirect
483. C2×C3×D3AGL(1,ℤ/8)semidirect
652. Dic6C2×D12semidirect
662. C3⋊C8C2×D12semidirect
783. C2×D3#932semidirect
810. C32#3265semidirect
920. C3#79794semidirect
921. 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×#639342
C2×D3×#2142
#105938992
#105927152
C3×#50182
#105914592
#105914482
#105906152
#105906032
#105905882
#105905762
#105903712
#105903642
#105903262
#834913
#797943