Finite Group Databasebeta

← #11782580

Subgroups — #11782580

Order 1152.

415 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 415 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592787C211yesmaximal, characteristic
2C3×#5093C211yesmaximal, characteristic, complemented
3C3×#5079C211yesmaximal, characteristic, complemented
4#10590290C211yesmaximal, characteristic, complemented
5#10590281C211yesmaximal, characteristic
6#10590281C211yesmaximal, characteristic
7C3⋊C82C211yesmaximal, characteristic, complemented
8#71215—31nomaximal
9#71215—31nomaximal
10C32×C4⋊Q8C2211yescharacteristic
11#64083C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14#63636—22no—
15C4×C3⋊(C3⋊C8)C2211yescharacteristic
16C3×#835—22no—
17C3×#810—22no—
18C3×C4×C3⋊C8C2211yescharacteristic
19C3×C4×C3⋊C8C2211yescharacteristic
20#63565—22no—
21#63564—22no—
22#63564—22no—
23C3×#487—31no—
24C3×#487—31no—
25#5093—31no—
26#5093D311yescharacteristic, complemented
27#5088—31no—
28#5088—31no—
29#5088—31no—
30#5088—31no—
31#5088—61no—
32#5079—31no—
33#5079D311yescharacteristic, complemented
34#4694—31no—
35#4694—31no—
36C8×C3⋊C8—31no—
37C8×C3⋊C8—31no—
38C2×C32×Q8—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4—21no—
46C32×C42C2311yescharacteristic
47C2×C3⋊(C3⋊C8)D412yes—
48C3×C4⋊Dic3—21no—
49C3×C4⋊Dic3—21no—
50C3×C4⋊Dic3—21no—
51C3×C4⋊Dic3—21no—
52C2×C3×C3⋊C8D412yes—
53C2×C3×C3⋊C8D412yes—
54#1711—91noSylow
55C3×C4⋊Q8—21no—
56C3×C4⋊Q8—31no—
57C3×C4⋊Q8—31no—
58C3×C4⋊Q8C2×D311yescharacteristic
59C3×C4⋊Q8C2×D311yescharacteristic
60#874—31no—
61#874—31no—
62#874—61no—
63#869C2×D311yescharacteristic
64#869C2×D311yescharacteristic
65C3×#103—62no—
66C3×#103—62no—
67C3×C4×C8—31no—
68C3×C4×C8—31no—
69#835—22no—
70#835—62no—
71#821—62no—
72#821—62no—
73#810—22no—
74#810—62no—
75#809—62no—
76#809—62no—
77#809—64no—
78#809—62no—
79#809—62no—
80C4×C3⋊C8—31no—
81C4×C3⋊C8—31no—
82C4×C3⋊C8—61no—
83C4×C3⋊C8C2×D311yescharacteristic
84C4×C3⋊C8C2×D311yescharacteristic
85C22×C3⋊D3—41no—
86C32×Q8—42no—
87C2×C32×C4—41no—
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C4⋊(C3⋊D3)—42no—
92C4⋊(C3⋊D3)—42no—
93C4⋊(C3⋊D3)—42no—
94C2×C3×Dic3—41no—
95C2×C3×Dic3—41no—
96C3×Dic6—42no—
97C3×Dic6—42no—
98C3⋊(C3⋊C8)—22no—
99C3×C3⋊C8—22no—
100C3×C3⋊C8—22no—
101#487—31no—
102#487—31no—
103#487—91no—
104#486—91no—
105#486—91no—
106#486—91no—
107C82—91no—
108C2×C3×Q8—21no—
109C2×C3×Q8—21no—
110C2×C3×Q8—41no—
111C2×C3×Q8—61no—
112C2×C3×Q8—61no—
113C2×D12—62no—
114C2×D12—61no—
115C2×D12—61no—
116C2×D12—61no—
117C2×D12—61no—
118C2×D12—61no—
119C2×D12—61no—
120C2×D12—121no—
121C2×D12—121no—
122C2×Dic6—21no—
123C2×Dic6—21no—
124C2×C3×C8—32no—
125C2×C3×C8—32no—
126C3×C4⋊C4—22no—
127C3×C4⋊C4—21no—
128C3×C4⋊C4—21no—
129C3×C4⋊C4—21no—
130C3×C4⋊C4—21no—
131C3×C4⋊C4—41no—
132C3×C4⋊C4—61no—
133C3×C4⋊C4—61no—
134C3×C4⋊C4—61no—
135C3×C4⋊C4—61no—
136C3×C42—21no—
137C3×C42C22×D311yescharacteristic
138C3×C42C22×D311yescharacteristic
139C4⋊Dic3—21no—
140C4⋊Dic3—21no—
141C4⋊Dic3—21no—
142C4⋊Dic3—21no—
143C2×C3⋊C8—32no—
144C2×C3⋊C8—32no—
145C2×C3⋊C8—62no—
146C2×C3⋊C8#6712yes—
147C2×C3⋊C8#6712yes—
148C22×C32#12711yescharacteristic
149C2×C3⋊D3—81no—
150C2×C3⋊D3—81no—
151C2×C3⋊D3—81no—
152C32×C4—81no—
153C32×C4#13512yes—
154C32×C4#13512yes—
155C32×C4#13512yes—
156C3×Dic3—81no—
157C3×Dic3—81no—
158C4⋊Q8—31no—
159C4⋊Q8—31no—
160C4⋊Q8D3211yescharacteristic
161#127—91no—
162#103—62no—
163#103—62no—
164#103—182no—
165#102—182no—
166#102—182no—
167#102—182no—
168C4×C8—31no—
169C4×C8—31no—
170C4×C8—91no—
171C22×D3—122no—
172C22×D3—121no—
173C22×D3—121no—
174C3×Q8—42no—
175C3×Q8—42no—
176C3×Q8—82no—
177C3×Q8—122no—
178C3×Q8—122no—
179C2×C3×C4—21no—
180C2×C3×C4—21no—
181C2×C3×C4—21no—
182C2×C3×C4—42no—
183C2×C3×C4—41no—
184C2×C3×C4—41no—
185C2×C3×C4—121no—
186C2×C3×C4—121no—
187C2×C3×C4D3×D411yescharacteristic
188C2×C3×C4D3×D411yescharacteristic
189C2×C3×C4D3×D411yescharacteristic
190C2×C3×C4D3×D411yescharacteristic
191C2×C3×C4C2×#6711yescharacteristic
192C2×C3×C4C2×#6711yescharacteristic
193C2×Dic3—41no—
194C2×Dic3—41no—
195D12—124no—
196D12—122no—
197D12—122no—
198D12—122no—
199D12—122no—
200D12—122no—
201D12—122no—
202D12—242no—
203D12—242no—
204Dic6—42no—
205Dic6—42no—
206C3×C8—62no—
207C3×C8—62no—
208C3⋊C8—22no—
209C3⋊C8—22no—
210C3⋊C8—62no—
211C3⋊C8—62no—
212C3⋊C8—122no—
213C2×C32#49511yescharacteristic
214C2×C32#49511yescharacteristic
215C2×C32#49511yescharacteristic
216C3⋊D3—161no—
217C2×Q8—21no—
218C2×Q8—61no—
219C2×Q8—61no—
220C2×D4—181no—
221C2×D4—181no—
222C2×D4—181no—
223C2×C8—32no—
224C2×C8—32no—
225C2×C8—92no—
226C4⋊C4—21no—
227C4⋊C4—21no—
228C4⋊C4—61no—
229C4⋊C4—61no—
230C4⋊C4—61no—
231C4⋊C4—61no—
232C42C2×D3211yescharacteristic
233C22×C3—21no—
234C22×C3#94011yescharacteristic
235C22×C3#94011yescharacteristic
236C2×D3—242no—
237C2×D3—242no—
238C2×D3—242no—
239C2×D3—241no—
240C2×D3—241no—
241C2×D3—241no—
242C2×D3—241no—
243C2×D3—241no—
244C2×D3—241no—
245C3×C4—22no—
246C3×C4—22no—
247C3×C4—22no—
248C3×C4—82no—
249C3×C4—81no—
250C3×C4—81no—
251C3×C4—241no—
252C3×C4—241no—
253C3×C4#91612yes—
254C3×C4#91612yes—
255C3×C4#91912yes—
256C3×C4#91912yes—
257C3×C4#95012yes—
258C3×C4#95012yes—
259Dic3—81no—
260Dic3—81no—
261C32#171111yescharacteristic, complemented, Sylow
262C23—361no—
263Q8—42no—
264Q8—122no—
265Q8—122no—
266D4—362no—
267D4—362no—
268D4—362no—
269C2×C4—41no—
270C2×C4—121no—
271C2×C4—121no—
272C2×C4D3×#6711yescharacteristic
273C2×C4D3×#6711yescharacteristic
274C2×C4#381111yescharacteristic
275C8—62no—
276C8—62no—
277C8—182no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3#505911yescharacteristic
282C2×C3#505911yescharacteristic
283C2×C3#516811yescharacteristic
284C2×C3#516811yescharacteristic
285C2×C3#519111yescharacteristic
286C2×C3#519111yescharacteristic
287D3—482no—
288D3—481no—
289D3—481no—
290C22—721no—
291C22—721no—
292C22—721no—
293C22#6397911yescharacteristic
294C4—81no—
295C4—241no—
296C4—241no—
297C4#6393512yes—
298C4#6394912yes—
299C4#6395012yes—
300C3—21no—
301C3#7121511yescharacteristic, complemented
302C3#7121511yescharacteristic, complemented
303C2—1441no—
304C2#1059147311yescharacteristic
305C2#1059160911yescharacteristic
306C2#1059161011yescharacteristic
subgroupG/H
centerC22#63979
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊Q8C22
socleC22×C32#127
prime radical#64083C22
hypercenterC4⋊Q8D32
hypocenterC32#1711
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5093C2semidirect
3. C3×#5079C2semidirect
4. #10590290C2semidirect
7. C3⋊C82C2semidirect
26. #5093D3semidirect
33. #5079D3semidirect
261. C32#1711semidirect
301. C3#71215semidirect
302. C3#71215semidirect

Maximal subgroups

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

subgroupindex
#105927872
C3×#50932
C3×#50792
#105902902
#105902812
C3⋊C822
#712153