Finite Group Databasebeta

← #11895421

Subgroups — #11895421

Order 1152.

838 conjugacy classes of subgroups.

The subgroup lattice has 545 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10593900C211yesmaximal, characteristic
2Dic62C211yesmaximal, characteristic, complemented
3#10592541C211yesmaximal, characteristic, complemented
4C3×#4848C211yesmaximal, characteristic, complemented
5C3×#4830C211yesmaximal, characteristic, complemented
6#10590878C212yesmaximal, complemented
7#10590799C212yesmaximal, complemented
8#10590757C212yesmaximal, complemented
9Dic3×#204C212yesmaximal, complemented
10C4×#3717C211yesmaximal, characteristic, complemented
11#10590273C211yesmaximal, characteristic, complemented
12#80369—31nomaximal
13#79932—31nomaximal
14C2×#3796—21no—
15C4×C4⋊(C3⋊D3)C2211yescharacteristic
16#64078C2211yescharacteristic
17C2×C3×#204C2212yes—
18C3×#874C2211yescharacteristic
19C3×C4×Dic6C2211yescharacteristic
20C3×C4×Dic6C2211yescharacteristic
21#63918—21no—
22#63918C2212yes—
23#63916—21no—
24#63911C2212yes—
25Dic3×D12C2212yes—
26#63886—22no—
27Dic3×Dic6—21no—
28Dic3×Dic6C2212yes—
29#63840—22no—
30C2×#3717C2211yescharacteristic
31C32×C4⋊C8C2211yescharacteristic
32#63648C2212yes—
33#63644C2212yes—
34C3×#821C2212yes—
35C3×Dic3⋊C8C2212yes—
36C3×C8×Dic3C2212yes—
37C3×C4×C3⋊C8C2211yescharacteristic
38#63573C2211yescharacteristic
39#63566C2211yescharacteristic
40#63564C2211yescharacteristic
41#63563C2212yes—
42#63563C2212yes—
43#5718—31no—
44#5577—31no—
45Q8×Dic6—31no—
46Q8×Dic6—31no—
47C3×#460—31no—
48C3×C8×Q8—31no—
49#5163—32no—
50Dic3×SD16—32no—
51#5070—31no—
52C4×#215—31no—
53#4848—32no—
54#4848D311yescharacteristic, complemented
55#4842—31no—
56#4842—31no—
57#4842—32no—
58#4842—61no—
59#4830D311yescharacteristic, complemented
60#4761—32no—
61#4760—32no—
62#4694—31no—
63#4694—32no—
64C4×#204—32no—
65C4×#204—31no—
66C2×C4⋊(C3⋊D3)C2311yescharacteristic
67C2×C4×C3⋊D3—21no—
68C2×#634—21no—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12C2312yes—
72C2×C3×Dic6D411yescharacteristic
73C2×C3×Dic6C2311yescharacteristic
74C2×#627—22no—
75C2×#626—22no—
76C2×#626—22no—
77C2×D3×Dic3—22no—
78#3796—44no—
79C2×C32×C8C2312yes—
80C32×C42C2311yescharacteristic
81#3752—21no—
82C4⋊(C3⋊Dic3)—21no—
83C4⋊(C3⋊Dic3)C2312yes—
84C4⋊(C3⋊Dic3)C2311yescharacteristic
85C3×C4⋊Dic3D411yescharacteristic
86C3×C4⋊Dic3C2311yescharacteristic
87C3×Dic3⋊C4—21no—
88C3×Dic3⋊C4D412yes—
89C3×C4×Dic3—21no—
90C3×C4×Dic3C2312yes—
91C2×C3×C3⋊C8C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93C3×#204—24no—
94Dic3⋊Dic3—22no—
95Dic3⋊Dic3—22no—
96(C2×D3)⋊Dic3—22no—
97Dic32—22no—
98#3717—22no—
99#3362—91noSylow
100C2×#239—61no—
101C2×#237—61no—
102C2×C3×SD16—32no—
103C3×#127—31no—
104C3×C4×Q8—31no—
105C3×C4×Q8—31no—
106Q8×Dic3—32no—
107Q8×Dic3—61no—
108C2×#215—31no—
109#940—32no—
110#939—62no—
111#938—61no—
112D4×Dic3—32no—
113C2×#204—31no—
114C2×#204C2×D312yes—
115#895—62no—
116#895—61no—
117#888—32no—
118#888—61no—
119#888—62no—
120#888—62no—
121#874—32no—
122#874C2×D311yescharacteristic
123C4×D12—32no—
124C4×D12—31no—
125C4×D12—31no—
126C4×D12—61no—
127#869—31no—
128#869—31no—
129#869—32no—
130#869—61no—
131#869—61no—
132C4×Dic6—32no—
133C4×Dic6—61no—
134C4×Dic6C2×D311yescharacteristic
135C4×Dic6C2×D311yescharacteristic
136C3×C4⋊C8—21no—
137C3×C4⋊C8—32no—
138C3×C4⋊C8C2×D311yescharacteristic
139C3×C4⋊C8C2×D311yescharacteristic
140C3×#102—32no—
141C3×C4×C8—32no—
142C3×C4×C8—31no—
143#835—31no—
144#832—32no—
145#832—32no—
146#821—32no—
147#821—32no—
148#821—32no—
149#821—32no—
150#821—31no—
151#821—62no—
152#821C2×D312yes—
153#817—32no—
154#817—32no—
155#817—31no—
156#817—62no—
157#816—31no—
158Dic3⋊C8C2×D312yes—
159C8×Dic3C2×D312yes—
160#809—31no—
161#808—31no—
162C4×C3⋊C8C2×D311yescharacteristic
163C22×C3⋊D3—21no—
164C22×C3×D3—22no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—21no—
170C4⋊(C3⋊D3)—21no—
171C4⋊(C3⋊D3)—21no—
172C4×C3⋊D3—42no—
173#634—81no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3C2×D412yes—
177C2×C3×Dic3C2×D412yes—
178C3×D12—22no—
179C3×D12—22no—
180C3×D12—42no—
181C3×D12—81no—
182C3×Dic6—21no—
183C3×Dic6SD1614yescomplemented
184C3×Dic6#4112yescomplemented
185#627—82no—
186#626—44no—
187#626—82no—
188D3×Dic3—44no—
189C32×C8—22no—
190C3×C3⋊C8—21no—
191C3×C3⋊C8—21no—
192Q82—91no—
193#550—91no—
194#486—92no—
195#486—91no—
196#476—92no—
197#476—91no—
198#460—31no—
199#460—92no—
200C8×Q8—31no—
201C4×SD16—91no—
202C4×SD16—92no—
203C2×C3×Q8—31no—
204C2×C3×Q8—31no—
205C2×C3×D4—32no—
206C2×C3×D4—61no—
207C2×C3×D4—61no—
208C2×#67—62no—
209C2×#67—62no—
210C22×Dic3—62no—
211#239—124no—
212#237—124no—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12—31no—
216C2×D12—31no—
217C2×D12—61no—
218C2×D12—62no—
219C2×D12—62no—
220C2×D12C22×D312yes—
221C2×C4×D3—62no—
222C2×C4×D3—61no—
223C2×C4×D3—61no—
224C2×C4×D3—121no—
225C2×Dic6—62no—
226C2×Dic6—61no—
227C2×Dic6—61no—
228C2×Dic6—62no—
229C2×Dic6—121no—
230C2×Dic6D1211yescharacteristic
231C2×Dic6C22×D311yescharacteristic
232C3×SD16—64no—
233C2×C3×C8—22no—
234C2×C3×C8—31no—
235C2×C3×C8—31no—
236C2×C3×C8C22×D312yes—
237C2×C3×C8C22×D312yes—
238C3×C4⋊C4—32no—
239C3×C4⋊C4—31no—
240C3×C4⋊C4—31no—
241C3×C4⋊C4—61no—
242C3×C42—21no—
243C3×C42—32no—
244C3×C42—61no—
245C3×C42C22×D311yescharacteristic
246C3×C42C22×D311yescharacteristic
247#217—62no—
248#215—62no—
249(C2×D3)⋊C4—62no—
250(C2×D3)⋊C4—61no—
251(C2×D3)⋊C4—61no—
252(C2×D3)⋊C4—121no—
253C4⋊Dic3—31no—
254C4⋊Dic3—31no—
255C4⋊Dic3—32no—
256C4⋊Dic3—32no—
257C4⋊Dic3—61no—
258C4⋊Dic3—62no—
259C4⋊Dic3—62no—
260C4⋊Dic3—61no—
261C4⋊Dic3—61no—
262C4⋊Dic3—62no—
263C4⋊Dic3—121no—
264C4⋊Dic3D1211yescharacteristic
265C4⋊Dic3C22×D311yescharacteristic
266Dic3⋊C4—21no—
267Dic3⋊C4—62no—
268Dic3⋊C4—62no—
269Dic3⋊C4D1212yes—
270C4×Dic3—21no—
271C4×Dic3—62no—
272C4×Dic3—62no—
273C4×Dic3C22×D312yes—
274C2×C3⋊C8C22×D311yescharacteristic
275C2×C3⋊C8C22×D311yescharacteristic
276#204—24no—
277#204—62no—
278C22×C32C22×D411yescharacteristic
279C2×C3⋊D3—41no—
280C2×C3⋊D3—41no—
281C2×C3⋊D3—41no—
282C2×C3×D3—42no—
283C2×C3×D3—42no—
284C2×C3×D3—42no—
285C32×C4—21no—
286C32×C4C2×SD1612yes—
287C32×C4C2×#4111yescharacteristic
288C32×C42−1+411yescharacteristic
289C3⋊Dic3—41no—
290C3⋊Dic3—42no—
291C3×Dic3—22no—
292C3×Dic3—22no—
293C3×Dic3—41no—
294C3×Dic3C2×SD1614yes—
295C2×#41—181no—
296C2×SD16—32no—
297C2×SD16—91no—
298C4⋊Q8—92no—
299C4⋊Q8—91no—
300C4⋊Q8—181no—
301C4⋊Q8—182no—
302#127—31no—
303#127—92no—
304#121—181no—
305#121—182no—
306C4×Q8—31no—
307C4×Q8—31no—
308C4×Q8—92no—
309C4×Q8—181no—
310C4×D4—92no—
311C4×D4—91no—
312#106—91no—
313#106—92no—
314C4⋊C8—32no—
315C4⋊C8D3211yescharacteristic
316#103—91no—
317#102—32no—
318#102—91no—
319#102—92no—
320#102—92no—
321#102—92no—
322C4×C8—32no—
323C4×C8—31no—
324C23×C3—62no—
325C22×D3—22no—
326C22×D3—61no—
327C22×D3—61no—
328C22×D3—121no—
329C3×Q8—34no—
330C3×Q8—32no—
331C3×Q8—61no—
332C3×D4—62no—
333C3×D4—62no—
334C3×D4—122no—
335C3×D4—241no—
336C2×C3×C4—21no—
337C2×C3×C4—21no—
338C2×C3×C4—21no—
339C2×C3×C4—32no—
340C2×C3×C4—32no—
341C2×C3×C4—61no—
342C2×C3×C4—61no—
343C2×C3×C4C2×D1211yescharacteristic
344C2×C3×C4C2×D1211yescharacteristic
345C2×C3×C4D3×D411yescharacteristic
346C2×C3×C4D3×D411yescharacteristic
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D311yescharacteristic
349#67—124no—
350#67—242no—
351C2×Dic3—21no—
352C2×Dic3—21no—
353C2×Dic3—62no—
354C2×Dic3—61no—
355C2×Dic3—62no—
356C2×Dic3—61no—
357C2×Dic3—122no—
358C2×Dic3—121no—
359C2×Dic3—124no—
360C2×Dic3C2×D1212yes—
361C2×Dic3C2×D1212yes—
362D12—22no—
363D12—22no—
364D12—42no—
365D12—62no—
366D12—61no—
367D12—61no—
368D12—61no—
369D12—61no—
370D12—81no—
371D12—121no—
372D12—124no—
373D12—242no—
374C4×D3—124no—
375C4×D3—122no—
376C4×D3—122no—
377C4×D3—242no—
378Dic6—21no—
379Dic6—242no—
380Dic6—242no—
381Dic6—241no—
382Dic6—241no—
383Dic6—242no—
384Dic6#20414yescomplemented
385Dic6#23712yescomplemented
386C3×C8—22no—
387C3×C8—22no—
388C3×C8—42no—
389C3×C8—61no—
390C3×C8—61no—
391C3⋊C8—21no—
392C3⋊C8—21no—
393C2×C32#54811yescharacteristic
394C2×C32C22×SD1611yescharacteristic
395C2×C32#57611yescharacteristic
396C3⋊D3—81no—
397C3×D3—82no—
398#41—364no—
399C2×Q8—31no—
400C2×Q8—31no—
401C2×Q8—182no—
402C2×Q8—181no—
403C2×D4—32no—
404C2×D4—61no—
405C2×D4—61no—
406C2×D4—91no—
407C2×D4—182no—
408C2×D4—182no—
409C22×C4—182no—
410C22×C4—181no—
411SD16—64no—
412SD16—182no—
413C2×C8—31no—
414C2×C8—31no—
415C2×C8C2×D3212yes—
416C4⋊C4—32no—
417C4⋊C4—31no—
418C4⋊C4—31no—
419C4⋊C4—61no—
420C4⋊C4—92no—
421C4⋊C4—91no—
422C4⋊C4—182no—
423C4⋊C4—182no—
424C4⋊C4—181no—
425C22⋊C4—182no—
426C22⋊C4—181no—
427C42—32no—
428C42—61no—
429C42—182no—
430C42C2×D3211yescharacteristic
431C22×C3—21no—
432C22×C3—122no—
433C22×C3—122no—
434C22×C3—122no—
435C22×C3C22×D1211yescharacteristic
436C22×C3C2×D3×D411yescharacteristic
437C2×D3—42no—
438C2×D3—42no—
439C2×D3—42no—
440C2×D3—122no—
441C2×D3—121no—
442C2×D3—121no—
443C2×D3—121no—
444C2×D3—121no—
445C2×D3—121no—
446C2×D3—121no—
447C2×D3—241no—
448C2×D3—241no—
449C3×C4—21no—
450C3×C4—21no—
451C3×C4—22no—
452C3×C4—21no—
453C3×C4—21no—
454C3×C4—34no—
455C3×C4—41no—
456C3×C4—62no—
457C3×C4—62no—
458C3×C4—121no—
459C3×C4C2×#20412yes—
460C3×C4D3×SD1612yes—
461C3×C4C2×#23711yescharacteristic
462C3×C4#100711yescharacteristic
463C3×C4D3×#4111yescharacteristic
464C3×C4#101011yescharacteristic
465Dic3—22no—
466Dic3—22no—
467Dic3—41no—
468Dic3—121no—
469Dic3—122no—
470Dic3—121no—
471Dic3—122no—
472Dic3—242no—
473Dic3—241no—
474Dic3C2×#20414yes—
475C32#336211yescharacteristic, complemented, Sylow
476C23—62no—
477C23—181no—
478Q8—34no—
479Q8—32no—
480Q8—61no—
481Q8—721no—
482Q8—722no—
483D4—62no—
484D4—62no—
485D4—122no—
486D4—181no—
487D4—181no—
488D4—241no—
489D4—364no—
490D4—722no—
491C2×C4—32no—
492C2×C4—32no—
493C2×C4—61no—
494C2×C4—61no—
495C2×C4—182no—
496C2×C4—181no—
497C2×C4—364no—
498C2×C4—362no—
499C2×C4D3×D1211yescharacteristic
500C2×C4D3×D1211yescharacteristic
501C2×C4C22×D3211yescharacteristic
502C8—22no—
503C8—61no—
504C8—61no—
505C2×C3—21no—
506C2×C3—21no—
507C2×C3—21no—
508C2×C3—242no—
509C2×C3#557611yescharacteristic
510C2×C3#559811yescharacteristic
511C2×C3C22×#20411yescharacteristic
512C2×C3#575211yescharacteristic
513C2×C3C2×D3×SD1611yescharacteristic
514C2×C3#577411yescharacteristic
515D3—82no—
516D3—242no—
517D3—241no—
518D3—241no—
519C22—122no—
520C22—122no—
521C22—122no—
522C22—361no—
523C22—361no—
524C22—361no—
525C22C2×D3×D1211yescharacteristic
526C4—21no—
527C4—34no—
528C4—62no—
529C4—62no—
530C4—121no—
531C4—361no—
532C4—362no—
533C4D3×#20412yes—
534C4D3×#23711yescharacteristic
535C4#6431511yescharacteristic
536C3—21no—
537C3#7993211yescharacteristic, complemented
538C3#8036911yescharacteristic, complemented
539C2—242no—
540C2—721no—
541C2#1059438211yescharacteristic
542C2C2×D3×#20411yescharacteristic
543C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10593900C2
hypercenterC4⋊C8D32
hypocenterC32#3362
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. Dic62C2semidirect
3. #10592541C2semidirect
4. C3×#4848C2semidirect
5. C3×#4830C2semidirect
6. #10590878C2semidirect
7. #10590799C2semidirect
8. #10590757C2semidirect
9. Dic3×#204C2semidirect
10. C4×#3717C2semidirect
11. #10590273C2semidirect
54. #4848D3semidirect
59. #4830D3semidirect
183. C3×Dic6SD16semidirect
184. C3×Dic6#41semidirect
384. Dic6#204semidirect
385. Dic6#237semidirect
475. C32#3362semidirect
537. C3#79932semidirect
538. C3#80369semidirect

Maximal subgroups

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

subgroupindex
#105939002
Dic622
#105925412
C3×#48482
C3×#48302
#105908782
#105907992
#105907572
Dic3×#2042
C4×#37172
#105902732
#803693
#799323