Finite Group Databasebeta

← #11782577

Subgroups — #11782577

Order 1152.

415 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 415 conjugacy classes of subgroups — too many to draw. Only its 100 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#10592393C211yesmaximal, characteristic
2C3×#4681C211yesmaximal, characteristic, complemented
3#10590288C211yesmaximal, characteristic, complemented
4#10590287C211yesmaximal, characteristic, complemented
5#10590281C211yesmaximal, characteristic
6#10590281C211yesmaximal, characteristic
7C3×C8×C3⋊C8C211yesmaximal, characteristic, complemented
8#71215—31nomaximal
9#68061—31nomaximal
10#64083C2211yescharacteristic
11#64078C2211yescharacteristic
12C3×#869C2211yescharacteristic
13C3×#869C2211yescharacteristic
14C32×C4×C8C2211yescharacteristic
15#63648—22no—
16C3×#816—22no—
17C3×C4×C3⋊C8C2211yescharacteristic
18C3×C4×C3⋊C8C2211yescharacteristic
19#63567—22no—
20#63566—22no—
21#63564—22no—
22#63564—22no—
23C3×#487—31no—
24#5093—31no—
25#5088—31no—
26#5088—31no—
27#5079—31no—
28#4694—31no—
29#4694—31no—
30#4694—31no—
31#4694—31no—
32#4694—61no—
33#4681—31no—
34#4681—31no—
35#4681D311yescharacteristic, complemented
36C3×C82—31no—
37C8×C3⋊C8D311yescharacteristic, complemented
38C2×C4⋊(C3⋊D3)—21no—
39C2×C4⋊(C3⋊D3)—21no—
40C2×C4⋊(C3⋊D3)—21no—
41C2×#634—21no—
42C2×C3×Dic6—21no—
43C2×C3×Dic6—21no—
44C2×C32×C8D412yes—
45C32×C42C2311yescharacteristic
46C4⋊(C3⋊Dic3)—21no—
47C4⋊(C3⋊Dic3)—21no—
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—31no—
56C3×C4⋊Q8—31no—
57#874—31no—
58#874—31no—
59#874—61no—
60#869—31no—
61#869—31no—
62#869—61no—
63#869C2×D311yescharacteristic
64#869C2×D311yescharacteristic
65C3×#103—62no—
66C3×C4×C8—21no—
67C3×C4×C8—31no—
68C3×C4×C8—31no—
69C3×C4×C8C2×D311yescharacteristic
70C3×C4×C8C2×D311yescharacteristic
71#835—62no—
72#821—62no—
73#821—62no—
74#821—64no—
75#821—62no—
76#821—62no—
77#816—22no—
78#816—62no—
79#816—62no—
80#810—62no—
81#809—62no—
82#809—62no—
83C4×C3⋊C8C2×D311yescharacteristic
84C4×C3⋊C8C2×D311yescharacteristic
85C22×C3⋊D3—41no—
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C3⋊Dic3—41no—
90C4⋊(C3⋊D3)—42no—
91C4⋊(C3⋊D3)—42no—
92C4⋊(C3⋊D3)—42no—
93#634—42no—
94C2×C3×Dic3—41no—
95C2×C3×Dic3—41no—
96C3×Dic6—42no—
97C3×Dic6—42no—
98C32×C8—22no—
99C3×C3⋊C8—22no—
100C3×C3⋊C8—22no—
101#487—31no—
102#487—91no—
103#487—91no—
104#486—91no—
105#486—91no—
106#486—91no—
107C82—31no—
108C2×C3×Q8—61no—
109C2×C3×Q8—61no—
110C2×D12—62no—
111C2×D12—61no—
112C2×D12—61no—
113C2×D12—61no—
114C2×D12—61no—
115C2×D12—61no—
116C2×D12—61no—
117C2×D12—121no—
118C2×D12—121no—
119C2×Dic6—21no—
120C2×Dic6—21no—
121C2×Dic6—61no—
122C2×Dic6—61no—
123C2×Dic6—121no—
124C2×C3×C8—22no—
125C2×C3×C8—32no—
126C2×C3×C8—32no—
127C2×C3×C8D1212yes—
128C2×C3×C8#6712yes—
129C3×C4⋊C4—61no—
130C3×C4⋊C4—61no—
131C3×C4⋊C4—61no—
132C3×C4⋊C4—61no—
133C3×C42—21no—
134C3×C42C22×D311yescharacteristic
135C3×C42C22×D311yescharacteristic
136C4⋊Dic3—21no—
137C4⋊Dic3—21no—
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—62no—
141C4⋊Dic3—61no—
142C4⋊Dic3—61no—
143C4⋊Dic3—61no—
144C4⋊Dic3—61no—
145C4⋊Dic3—121no—
146C2×C3⋊C8D1212yes—
147C2×C3⋊C8D1212yes—
148C22×C32#12711yescharacteristic
149C2×C3⋊D3—81no—
150C2×C3⋊D3—81no—
151C2×C3⋊D3—81no—
152C32×C4#13512yes—
153C32×C4#13512yes—
154C32×C4#13512yes—
155C3⋊Dic3—81no—
156C3×Dic3—81no—
157C3×Dic3—81no—
158C4⋊Q8—31no—
159C4⋊Q8—31no—
160C4⋊Q8—91no—
161#127—91no—
162#103—62no—
163#103—182no—
164#103—182no—
165#102—182no—
166#102—182no—
167#102—182no—
168C4×C8—31no—
169C4×C8—31no—
170C4×C8D3211yescharacteristic
171C22×D3—122no—
172C22×D3—121no—
173C22×D3—121no—
174C3×Q8—122no—
175C3×Q8—122no—
176C2×C3×C4—21no—
177C2×C3×C4—21no—
178C2×C3×C4—21no—
179C2×C3×C4—121no—
180C2×C3×C4—121no—
181C2×C3×C4C2×D1211yescharacteristic
182C2×C3×C4C2×D1211yescharacteristic
183C2×C3×C4C2×D1211yescharacteristic
184C2×C3×C4D3×D411yescharacteristic
185C2×C3×C4D3×D411yescharacteristic
186C2×C3×C4C2×#6711yescharacteristic
187C2×Dic3—41no—
188C2×Dic3—41no—
189C2×Dic3—122no—
190C2×Dic3—121no—
191C2×Dic3—121no—
192D12—124no—
193D12—122no—
194D12—122no—
195D12—122no—
196D12—122no—
197D12—122no—
198D12—122no—
199D12—242no—
200D12—242no—
201Dic6—42no—
202Dic6—42no—
203Dic6—122no—
204Dic6—122no—
205Dic6—242no—
206C3×C8—22no—
207C3×C8—22no—
208C3×C8—42no—
209C3×C8—62no—
210C3×C8—62no—
211C3⋊C8—22no—
212C3⋊C8—22no—
213C2×C32#49511yescharacteristic
214C2×C32#49511yescharacteristic
215C2×C32#49511yescharacteristic
216C3⋊D3—161no—
217C2×Q8—61no—
218C2×Q8—61no—
219C2×Q8—181no—
220C2×D4—181no—
221C2×D4—181no—
222C2×D4—181no—
223C2×C8—32no—
224C2×C8—32no—
225C2×C8#62612yes—
226C4⋊C4—61no—
227C4⋊C4—61no—
228C4⋊C4—61no—
229C4⋊C4—61no—
230C4⋊C4—181no—
231C4⋊C4—181no—
232C42C2×D3211yescharacteristic
233C22×C3—21no—
234C22×C3#87411yescharacteristic
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—241no—
249C3×C4—241no—
250C3×C4#90412yes—
251C3×C4#90412yes—
252C3×C4#90412yes—
253C3×C4#91612yes—
254C3×C4#91912yes—
255C3×C4#95012yes—
256Dic3—81no—
257Dic3—81no—
258Dic3—242no—
259Dic3—241no—
260Dic3—241no—
261C32#171111yescharacteristic, complemented, Sylow
262C23—361no—
263Q8—122no—
264Q8—122no—
265Q8—362no—
266D4—362no—
267D4—362no—
268D4—362no—
269C2×C4—121no—
270C2×C4—121no—
271C2×C4—361no—
272C2×C4D3×D1211yescharacteristic
273C2×C4D3×D1211yescharacteristic
274C2×C4C2×#62611yescharacteristic
275C8—22no—
276C8—62no—
277C8—62no—
278C2×C3—21no—
279C2×C3—21no—
280C2×C3—21no—
281C2×C3#469611yescharacteristic
282C2×C3#469611yescharacteristic
283C2×C3#469611yescharacteristic
284C2×C3#505911yescharacteristic
285C2×C3#516811yescharacteristic
286C2×C3#519111yescharacteristic
287D3—482no—
288D3—481no—
289D3—481no—
290C22—721no—
291C22—721no—
292C22—721no—
293C22#6391111yescharacteristic
294C4—241no—
295C4—241no—
296C4—721no—
297C4#6380612yes—
298C4#6380812yes—
299C4#6382912yes—
300C3—21no—
301C3#6806111yescharacteristic, complemented
302C3#7121511yescharacteristic, complemented
303C2—1441no—
304C2#1059037011yescharacteristic
305C2#1059086211yescharacteristic
306C2#1059086511yescharacteristic
subgroupG/H
centerC22#63911
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×C8C22
socleC22×C32#127
prime radical#64083C22
hypercenterC4×C8D32
hypocenterC32#1711
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. C3×#4681C2semidirect
3. #10590288C2semidirect
4. #10590287C2semidirect
7. C3×C8×C3⋊C8C2semidirect
35. #4681D3semidirect
37. C8×C3⋊C8D3semidirect
261. C32#1711semidirect
301. C3#68061semidirect
302. C3#71215semidirect

Maximal subgroups

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

subgroupindex
#105923932
C3×#46812
#105902882
#105902872
#105902812
C3×C8×C3⋊C82
#712153
#680613