Finite Group Databasebeta

← #11895434

Subgroups — #11895434

Order 1152.

940 conjugacy classes of subgroups.

The subgroup lattice has 349 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596048C211yesmaximal, characteristic
2C3×Q8×Dic6C211yesmaximal, characteristic, complemented
3C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4#10590367C213yesmaximal, complemented
5C4×#3717C213yesmaximal, complemented
6#10590300C213yesmaximal, complemented
7#10590281C213yesmaximal, complemented
8#83703—31nomaximal
9#79932—31nomaximal
10C2×#3832—21no—
11C32×C4×Q8C2211yescharacteristic
12#64104—23no—
13#64083C2213yes—
14C4×C4⋊(C3⋊D3)C2213yes—
15C3×Q8×Dic3—21no—
16C3×#888—23no—
17C3×#869C2213yes—
18C3×C4×Dic6C2213yes—
19C2×#3717C2213yes—
20C3×C4⋊(C3⋊C8)C2213yes—
21C3×C4×C3⋊C8C2213yes—
22#63573C2213yes—
23#63566C2211yescharacteristic
24#63564C2213yes—
25#63564C2216yes—
26C3×Q82—31no—
27#5577—31no—
28#5577—31no—
29#5577—61no—
30Q8×Dic6D311yescharacteristic, complemented
31C3×C8×Q8—31no—
32#5088—33no—
33#5084—33no—
34#5027—33no—
35C4×#215—33no—
36Q8×C3⋊C8D311yescharacteristic, complemented
37#4848—33no—
38#4842—33no—
39#4694—33no—
40C4×#204—33no—
41C2×C32×Q8D411yescharacteristic
42#3832—44no—
43C2×C4⋊(C3⋊D3)—23no—
44C2×C4⋊(C3⋊D3)—23no—
45C2×C4⋊(C3⋊D3)C2313yes—
46C2×C4×C3⋊D3—23no—
47C2×C3×Dic6—23no—
48C2×C3×Dic6C2311yescharacteristic
49C32×C4⋊C4D413yes—
50C32×C42C2313yes—
51#3752—23no—
52C4⋊(C3⋊Dic3)C2311yescharacteristic
53C3×C4⋊Dic3—23no—
54C3×C4⋊Dic3C2313yes—
55C3×Dic3⋊C4—23no—
56C3×C4×Dic3—23no—
57C2×C3×C3⋊C8C2311yescharacteristic
58C2×C3×C3⋊C8C2313yes—
59#3717—26no—
60#3362—91noSylow
61C2×#239—62no—
62C2×#239—61no—
63C2×#239—61no—
64C3×C4⋊Q8—33no—
65C3×C4⋊Q8—63no—
66C3×C4×Q8—21no—
67C3×C4×Q8—33no—
68C3×C4×Q8—61no—
69C3×C4×Q8C2×D311yescharacteristic
70C3×C4×Q8C2×D311yescharacteristic
71Q8×Dic3—21no—
72C2×#215—33no—
73C2×#204—33no—
74#895—66no—
75#895—63no—
76#895—63no—
77#888—23no—
78#874—33no—
79#874—33no—
80#874—63no—
81C4×D12—33no—
82C4×D12—33no—
83C4×D12—63no—
84#869C2×D313yes—
85C4×Dic6C2×D313yes—
86C3×C4⋊C8—33no—
87C3×C4×C8—33no—
88#835—31no—
89#821—33no—
90#821—36no—
91#817—33no—
92#816—31no—
93#809—33no—
94#809—36no—
95#808—33no—
96C4⋊(C3⋊C8)C2×D313yes—
97C4×C3⋊C8C2×D313yes—
98C22×C3⋊D3—23no—
99C32×Q8SD1614yescomplemented
100C2×C32×C4C2×D413yes—
101C2×C32×C4C2×D413yes—
102C2×C32×C4C2411yescharacteristic
103C2×C3⋊Dic3—21no—
104C4⋊(C3⋊D3)—23no—
105C4⋊(C3⋊D3)—23no—
106C4⋊(C3⋊D3)—46no—
107C4⋊(C3⋊D3)—83no—
108C4×C3⋊D3—46no—
109C2×C3×Dic3—21no—
110C2×C3×Dic3—23no—
111C3×Dic6—21no—
112C3×Dic6—83no—
113C3×Dic6#4112yescomplemented
114C3×C3⋊C8—23no—
115C3×C3⋊C8—21no—
116Q82—31no—
117#550—91no—
118#486—93no—
119#476—93no—
120#460—93no—
121C8×Q8—31no—
122C4×SD16—93no—
123C2×C3×Q8—21no—
124C2×C3×Q8—31no—
125C2×C3×Q8—63no—
126C2×C3×Q8D1211yescharacteristic
127C2×C3×Q8#6711yescharacteristic
128#239—128no—
129#239—124no—
130#239—124no—
131C2×D12—33no—
132C2×D12—33no—
133C2×D12—63no—
134C2×D12—66no—
135C2×D12—63no—
136C2×D12—63no—
137C2×D12—66no—
138C2×D12—63no—
139C2×D12—63no—
140C2×C4×D3—66no—
141C2×C4×D3—63no—
142C2×C4×D3—63no—
143C2×Dic6—23no—
144C2×Dic6C22×D311yescharacteristic
145C2×C3×C8—31no—
146C2×C3×C8—33no—
147C3×C4⋊C4—23no—
148C3×C4⋊C4—33no—
149C3×C4⋊C4—63no—
150C3×C4⋊C4—63no—
151C3×C4⋊C4D1213yes—
152C3×C4⋊C4#6713yes—
153C3×C42—23no—
154C3×C42—63no—
155C3×C42C22×D313yes—
156C3×C42C22×D313yes—
157#215—66no—
158(C2×D3)⋊C4—66no—
159(C2×D3)⋊C4—63no—
160(C2×D3)⋊C4—63no—
161C4⋊Dic3—23no—
162C4⋊Dic3—31no—
163C4⋊Dic3—31no—
164C4⋊Dic3—61no—
165C4⋊Dic3C22×D313yes—
166Dic3⋊C4—23no—
167C4×Dic3—23no—
168C2×C3⋊C8C22×D311yescharacteristic
169C2×C3⋊C8C22×D313yes—
170#204—66no—
171C22×C32C22×D411yescharacteristic
172C2×C3⋊D3—43no—
173C2×C3⋊D3—43no—
174C2×C3⋊D3—43no—
175C32×C4—23no—
176C32×C4C2×SD1616yes—
177C32×C4C2×#4111yescharacteristic
178C32×C42−1+411yescharacteristic
179C3⋊Dic3—41no—
180C3×Dic3—22no—
181C3×Dic3—43no—
182C2×#41—181no—
183C2×SD16—93no—
184C4⋊Q8—33no—
185C4⋊Q8—63no—
186#127—93no—
187#121—183no—
188C4×Q8—33no—
189C4×Q8—61no—
190C4×Q8D3211yescharacteristic
191C4×D4—93no—
192#106—93no—
193C4⋊C8—33no—
194#103—91no—
195#102—93no—
196#102—96no—
197C4×C8—33no—
198C22×D3—66no—
199C22×D3—63no—
200C22×D3—63no—
201C3×Q8—24no—
202C3×Q8—32no—
203C3×Q8—61no—
204C3×Q8—243no—
205C3×Q8#20414yescomplemented
206C3×Q8#21514yescomplemented
207C2×C3×C4—21no—
208C2×C3×C4—23no—
209C2×C3×C4—23no—
210C2×C3×C4—61no—
211C2×C3×C4—63no—
212C2×C3×C4C2×D1213yes—
213C2×C3×C4C2×D1213yes—
214C2×C3×C4C2×#6713yes—
215C2×C3×C4C2×#6713yes—
216C2×C3×C4C23×D311yescharacteristic
217C2×C3×C4C23×D311yescharacteristic
218C2×Dic3—21no—
219C2×Dic3—23no—
220C2×Dic3—62no—
221C2×Dic3—61no—
222C2×Dic3—61no—
223D12—63no—
224D12—63no—
225D12—63no—
226D12—63no—
227D12—123no—
228D12—123no—
229D12—1212no—
230D12—126no—
231D12—126no—
232D12—243no—
233D12—243no—
234D12—246no—
235C4×D3—1212no—
236C4×D3—126no—
237C4×D3—126no—
238Dic6—21no—
239Dic6—83no—
240Dic6#23912yescomplemented
241C3×C8—63no—
242C3×C8—61no—
243C3⋊C8—21no—
244C3⋊C8—23no—
245C2×C32#54811yescharacteristic
246C2×C32C22×SD1611yescharacteristic
247C2×C32#57611yescharacteristic
248C3⋊D3—83no—
249#41—364no—
250C2×Q8—31no—
251C2×Q8—63no—
252C2×Q8#62611yescharacteristic
253C2×D4—93no—
254C2×D4—183no—
255C2×D4—183no—
256C22×C4—183no—
257SD16—186no—
258C2×C8—31no—
259C2×C8—33no—
260C4⋊C4—33no—
261C4⋊C4—63no—
262C4⋊C4—63no—
263C4⋊C4—91no—
264C4⋊C4#62613yes—
265C22⋊C4—183no—
266C42—63no—
267C42C2×D3213yes—
268C22×C3—21no—
269C22×C3C22×D1211yescharacteristic
270C22×C3C22×#6711yescharacteristic
271C2×D3—126no—
272C2×D3—126no—
273C2×D3—126no—
274C2×D3—123no—
275C2×D3—123no—
276C2×D3—123no—
277C2×D3—123no—
278C2×D3—123no—
279C2×D3—123no—
280C3×C4—23no—
281C3×C4—23no—
282C3×C4—21no—
283C3×C4—21no—
284C3×C4—26no—
285C3×C4—43no—
286C3×C4—62no—
287C3×C4—123no—
288C3×C4C2×#20416yes—
289C3×C4C2×#21516yes—
290C3×C4C2×#23911yescharacteristic
291C3×C4#100711yescharacteristic
292C3×C4#100711yescharacteristic
293C3×C4D3×#4111yescharacteristic
294Dic3—22no—
295Dic3—43no—
296Dic3—122no—
297Dic3—121no—
298Dic3—121no—
299C32#336211yescharacteristic, complemented, Sylow
300C23—183no—
301Q8—32no—
302Q8—61no—
303Q8—243no—
304Q8#371714yescomplemented
305D4—183no—
306D4—183no—
307D4—366no—
308D4—723no—
309C2×C4—61no—
310C2×C4—63no—
311C2×C4—181no—
312C2×C4—366no—
313C2×C4C2×#62613yes—
314C2×C4C2×#62613yes—
315C2×C4C22×D3211yescharacteristic
316C8—61no—
317C8—63no—
318C2×C3—21no—
319C2×C3—21no—
320C2×C3—21no—
321C2×C3#557611yescharacteristic
322C2×C3C22×#20411yescharacteristic
323C2×C3#575211yescharacteristic
324C2×C3C22×#21511yescharacteristic
325C2×C3#581711yescharacteristic
326C2×C3#583511yescharacteristic
327D3—246no—
328D3—243no—
329D3—243no—
330C22—363no—
331C22—363no—
332C22—363no—
333C22C22×#62611yescharacteristic
334C4—23no—
335C4—62no—
336C4—123no—
337C4—361no—
338C4C2×#371716yes—
339C4#6431611yescharacteristic
340C4D3×#23911yescharacteristic
341C3—21no—
342C3#7993211yescharacteristic, complemented
343C3#8370311yescharacteristic, complemented
344C2—723no—
345C2C22×#371711yescharacteristic
346C2#1059534211yescharacteristic
347C2#1059544911yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×Q8C22
socleC22×C32C22×D4
prime radical#10596048C2
hypercenterC4×Q8D32
hypocenterC32#3362
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. C3×Q8×Dic6C2semidirect
3. C3×Q8×C3⋊C8C2semidirect
4. #10590367C2semidirect
5. C4×#3717C2semidirect
6. #10590300C2semidirect
7. #10590281C2semidirect
30. Q8×Dic6D3semidirect
36. Q8×C3⋊C8D3semidirect
99. C32×Q8SD16semidirect
113. C3×Dic6#41semidirect
205. C3×Q8#204semidirect
206. C3×Q8#215semidirect
240. Dic6#239semidirect
299. C32#3362semidirect
304. Q8#3717semidirect
342. C3#79932semidirect
343. C3#83703semidirect

Maximal subgroups

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

subgroupindex
#105960482
C3×Q8×Dic62
C3×Q8×C3⋊C82
#105903672
C4×#37172
#105903002
#105902812
#837033
#799323