Finite Group Databasebeta

← #11772640

Subgroups — #11772640

Order 1152.

320 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 39 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#10593808C211yesmaximal, characteristic
2#10591232C211yesmaximal, characteristic
3#10591153C211yesmaximal, characteristic
4C2×#3828C2211yescharacteristic
5#64283—21no—
6C3×#926—21no—
7C2×#3712C411yescharacteristic, complemented
8C2×#3710C411yescharacteristic, complemented
9#63788—21no—
10#63780C412yescomplemented
11C3×#830—21no—
12#63581—21no—
13#63581C412yes—
14#63557—21no—
15#5006—61no—
16#4727—61no—
17C22×C32×C4D411yescharacteristic
18C2×#638C2×C411yescharacteristic
19C2×#638D411yescharacteristic
20#3828—41no—
21#3828—41no—
22C2×C4⋊(C3⋊D3)Q811yescharacteristic
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×#634C2×C411yescharacteristic
26#3792—22no—
27#3788—41no—
28#3787—41no—
29C3×#217—22no—
30C3×C4⋊Dic3—41no—
31C3×C4×Dic3—41no—
32C2×C3×C3⋊C8—21no—
33C2×C3×C3⋊C8—21no—
34#3712—41no—
35#3710—41no—
36#1395—91nomaximal, Sylow
37C2×#235—61no—
38C2×#235—61no—
39C3×#117—61no—
40#926—21no—
41C2×ΓL(1,𝔽25)—61no—
42C2×D3×C8—61no—
43C3×C22⋊C8—61no—
44#830—21no—
45(C2×D3)⋊C8—61no—
46(C2×D3)⋊C8—61no—
47#806—62no—
48#806—62no—
49C23×C32C22⋊C411yescharacteristic
50C22×C3⋊D3C4⋊C411yescharacteristic
51C22×C3⋊D3C4⋊C411yescharacteristic
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4C22⋊C411yescharacteristic
55C2×C32×C4C4⋊C411yescharacteristic
56#638—41no—
57#638—41no—
58C2×C3⋊Dic3C4211yescharacteristic
59C2×C3⋊Dic3C22⋊C411yescharacteristic
60C4⋊(C3⋊D3)—41no—
61C4×C3⋊D3—21no—
62C4×C3⋊D3—21no—
63C4×C3⋊D3—21no—
64C4×C3⋊D3—21no—
65#634—41no—
66C2×C3×Dic3—42no—
67#622—42no—
68C3×C3⋊C8—41no—
69C3×C3⋊C8—41no—
70#413—91no—
71#410—91no—
72#408—91no—
73C22×C3×C4—21no—
74C22×C3×C4—21no—
75C2×#67—61no—
76C2×#67—61no—
77C2×#67—61no—
78C2×#67—61no—
79#235—122no—
80#235—122no—
81#235—121no—
82#235—121no—
83#235—121no—
84#235—121no—
85C2×D12—61no—
86C2×D12—61no—
87C2×C4×D3—61no—
88C2×C4×D3—61no—
89C2×C4×D3—61no—
90C2×C4×D3—61no—
91C2×Dic6—61no—
92C2×Dic6—61no—
93C2×C3×C8—61no—
94C2×C3×C8—61no—
95C3×C4⋊C4—121no—
96C3×C22⋊C4—62no—
97C3×C42—121no—
98#217—22no—
99C4⋊Dic3—41no—
100C4×Dic3—41no—
101C2×C3⋊C8—21no—
102C2×C3⋊C8—21no—
103ΓL(1,𝔽25)—122no—
104D3×C8—122no—
105C22×C32—21no—
106C22×C32—41no—
107C22×C32#9511yescharacteristic
108C2×C3⋊D3—21no—
109C2×C3⋊D3—21no—
110C2×C3⋊D3—41no—
111C2×C3⋊D3—41no—
112C32×C4—21no—
113C32×C4#9911yescharacteristic
114C32×C4#9911yescharacteristic
115C3⋊Dic3—21no—
116C3⋊Dic3—21no—
117C3×Dic3—82no—
118C2×#41—91no—
119C2×M16—91no—
120C2×M16—181no—
121C22×C8—91no—
122#117—61no—
123#101—92no—
124#100—181no—
125#99—92no—
126#99—181no—
127C22⋊C8—61no—
128C22⋊C8—181no—
129C23×C3—21no—
130C23×C3—21no—
131C22×D3—61no—
132C22×D3—61no—
133C22×D3—61no—
134C22×D3—61no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—21no—
140C2×C3×C4—21no—
141C2×C3×C4—21no—
142C2×C3×C4—21no—
143C2×C3×C4—41no—
144C2×C3×C4—41no—
145C2×C3×C4—122no—
146#67—122no—
147#67—122no—
148#67—121no—
149#67—121no—
150#67—121no—
151#67—121no—
152C2×Dic3—42no—
153C2×Dic3—61no—
154C2×Dic3—61no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157D12—121no—
158D12—121no—
159D12—122no—
160C4×D3—62no—
161C4×D3—62no—
162C4×D3—121no—
163C4×D3—121no—
164C4×D3—121no—
165C4×D3—121no—
166C4×D3—121no—
167C4×D3—121no—
168Dic6—122no—
169Dic6—121no—
170Dic6—121no—
171C3×C8—121no—
172C3×C8—121no—
173C3⋊C8—41no—
174C3⋊C8—41no—
175C2×C32—21no—
176C2×C32—41no—
177C2×C32#34211yescharacteristic
178C3⋊D3—41no—
179C3⋊D3—41no—
180#41—361no—
181#41—361no—
182C2×Q8—91no—
183C2×D4—91no—
184C2×D4—91no—
185C2×D4—91no—
186C22×C4—91no—
187C22×C4—91no—
188C22×C4GO+(4,𝔽2)11yescharacteristic
189M16—182no—
190M16—361no—
191M16—361no—
192C2×C8—61no—
193C2×C8—61no—
194C2×C8—361no—
195C2×C8—361no—
196C4⋊C4—121no—
197C22⋊C4—62no—
198C42—121no—
199C22×C3—21no—
200C22×C3—21no—
201C22×C3—21no—
202C22×C3—21no—
203C22×C3—41no—
204C22×C3—42no—
205C22×C3—81no—
206C2×D3—62no—
207C2×D3—121no—
208C2×D3—121no—
209C2×D3—121no—
210C2×D3—122no—
211C2×D3—122no—
212C2×D3—241no—
213C2×D3—241no—
214C3×C4—21no—
215C3×C4—21no—
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—21no—
219C3×C4—21no—
220C3×C4—41no—
221C3×C4—242no—
222Dic3—62no—
223Dic3—82no—
224Dic3—121no—
225Dic3—121no—
226Dic3—121no—
227C32#139511yescharacteristic, complemented, Sylow
228C23—91no—
229C23—91no—
230C23D32⋊C411yescharacteristic
231Q8—361no—
232D4—361no—
233D4—361no—
234D4—361no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—91no—
238C2×C4—91no—
239C2×C4—122no—
240C2×C4—181no—
241C2×C4—181no—
242C2×C4—181no—
243C2×C4—181no—
244C2×C4D32⋊C411yescharacteristic
245C2×C4#377311yescharacteristic
246C8—121no—
247C8—121no—
248C8—362no—
249C2×C3—22no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—41no—
253C2×C3—41no—
254C2×C3—41no—
255C2×C3—81no—
256D3—122no—
257D3—241no—
258D3—241no—
259D3—241no—
260C22—21no—
261C22—41no—
262C22—181no—
263C22—181no—
264C22—361no—
265C22—361no—
266C22#6373711yescharacteristic
267C4—21no—
268C4—181no—
269C4—181no—
270C4—242no—
271C4#6373811yescharacteristic
272C4#6373811yescharacteristic
273C3—21no—
274C3—21no—
275C2—21no—
276C2—41no—
277C2—361no—
278C2—361no—
279C2#1059007611yescharacteristic
subgroupG/H
centerC4#63738
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC2×C32#342
prime radical, cosocleC2×#3828C22
hypocenterC32#1395
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
7. C2×#3712C4semidirect
8. C2×#3710C4semidirect
10. #63780C4semidirect
227. C32#1395semidirect

Maximal subgroups

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

subgroupindex
#105938082
#105912322
#105911532
#13959