Finite Group Databasebeta

← #11771025

Subgroups — #11771025

Order 1152.

284 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 55 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#10593728C211yesmaximal, characteristic
2#10590340C211yesmaximal, characteristic
3#10590331C211yesmaximal, characteristic
4C2×#3788—21no—
5C42×C3⋊D3C2211yescharacteristic
6C2×#3712—21no—
7C2×#3710C412yes—
8C4⋊#622—21no—
9C4⋊#622C412yes—
10C3×C4⋊(C3⋊C8)—21no—
11C3×C4⋊(C3⋊C8)—21no—
12#63572—21no—
13#63572C412yes—
14#4837—61no—
15D3×C4⋊C8—61no—
16C2×C4×C3⋊D3C2×C411yescharacteristic
17C2×C4×C3⋊D3D411yescharacteristic
18C2×C4×C3⋊D3Q811yescharacteristic
19C2×#622—22no—
20#3788—41no—
21#3788—41no—
22C32×C42D411yescharacteristic
23C4×C3⋊Dic3C2×C411yescharacteristic
24C4×C3⋊Dic3C2×C411yescharacteristic
25C4×C3⋊Dic3D411yescharacteristic
26C2×C3×C3⋊C8—22no—
27C2×C3×C3⋊C8—22no—
28#3712—41no—
29#3712—41no—
30#3710—42no—
31#1292—91nomaximal, Sylow
32C2×ΓL(1,𝔽25)—62no—
33C2×D3×C8—62no—
34C42×D3—61no—
35C42×D3—61no—
36C3×C4⋊C8—61no—
37C3×C4⋊C8—61no—
38Dic3⋊C8—62no—
39Dic3⋊C8—62no—
40C4⋊(C3⋊C8)—21no—
41C4⋊(C3⋊C8)—21no—
42C22×C3⋊D3C4⋊C411yescharacteristic
43C2×C32×C4C22⋊C411yescharacteristic
44C2×C32×C4C22⋊C411yescharacteristic
45C2×C32×C4C4⋊C411yescharacteristic
46C2×C3⋊Dic3C4211yescharacteristic
47C2×C3⋊Dic3C22⋊C411yescharacteristic
48C2×C3⋊Dic3C4⋊C411yescharacteristic
49C4×C3⋊D3—21no—
50C4×C3⋊D3—21no—
51C4×C3⋊D3—41no—
52C4×C3⋊D3D811yescharacteristic
53C4×C3⋊D3SD1611yescharacteristic
54C4×C3⋊D3SD1611yescharacteristic
55C4×C3⋊D3Q1611yescharacteristic
56#622—42no—
57C3×C3⋊C8—42no—
58C3×C3⋊C8—42no—
59#423—91no—
60#423—91no—
61C2×C4⋊C8—91no—
62C2×C4×D3—61no—
63C2×C4×D3—61no—
64C2×C4×D3—61no—
65C2×C4×D3—61no—
66C2×C4×D3—61no—
67C2×C4×D3—61no—
68C2×C3×C8—62no—
69C2×C3×C8—62no—
70C3×C42—21no—
71C3×C42—21no—
72C4×Dic3—61no—
73C4×Dic3—61no—
74C4×Dic3—61no—
75C4×Dic3—61no—
76C4×Dic3—61no—
77C4×Dic3—61no—
78C2×C3⋊C8—22no—
79C2×C3⋊C8—22no—
80ΓL(1,𝔽25)—122no—
81ΓL(1,𝔽25)—122no—
82D3×C8—124no—
83C22×C32#9511yescharacteristic
84C2×C3⋊D3—21no—
85C2×C3⋊D3—21no—
86C2×C3⋊D3#10611yescharacteristic
87C2×C3⋊D3#10711yescharacteristic
88C32×C4—21no—
89C32×C4#10011yescharacteristic
90C32×C4#10111yescharacteristic
91C32×C4#10211yescharacteristic
92C32×C4#10311yescharacteristic
93C3⋊Dic3—21no—
94C3⋊Dic3—21no—
95C3⋊Dic3#10211yescharacteristic
96C3⋊Dic3#10311yescharacteristic
97C2×M16—181no—
98C2×M16—181no—
99C22×C8—92no—
100C2×C42—91no—
101C4⋊C8—61no—
102C4⋊C8—61no—
103C4⋊C8—92no—
104C4⋊C8—92no—
105C4⋊C8—181no—
106C4⋊C8—181no—
107C22×D3—61no—
108C22×D3—61no—
109C2×C3×C4—21no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×Dic3—61no—
116C2×Dic3—61no—
117C2×Dic3—61no—
118C2×Dic3—61no—
119C2×Dic3—61no—
120C2×Dic3—61no—
121C4×D3—61no—
122C4×D3—61no—
123C4×D3—61no—
124C4×D3—61no—
125C4×D3—61no—
126C4×D3—61no—
127C4×D3—61no—
128C4×D3—61no—
129C4×D3—62no—
130C4×D3—62no—
131C4×D3—121no—
132C4×D3—121no—
133C4×D3—122no—
134C4×D3—122no—
135C3×C8—122no—
136C3×C8—122no—
137C3⋊C8—42no—
138C3⋊C8—42no—
139C2×C32#33811yescharacteristic
140C2×C32#34011yescharacteristic
141C2×C32#34311yescharacteristic
142C3⋊D3—21no—
143C3⋊D3—21no—
144C22×C4—91no—
145C22×C4—91no—
146C22×C4—91no—
147M16—361no—
148M16—361no—
149M16—361no—
150M16—361no—
151C2×C8—62no—
152C2×C8—62no—
153C2×C8—182no—
154C2×C8—362no—
155C42—91no—
156C42—91no—
157C42—91no—
158C42GO+(4,𝔽2)11yescharacteristic
159C22×C3—21no—
160C22×C3—21no—
161C2×D3—61no—
162C2×D3—61no—
163C2×D3—61no—
164C2×D3—61no—
165C2×D3—62no—
166C2×D3—62no—
167C2×D3—121no—
168C2×D3—121no—
169C3×C4—21no—
170C3×C4—21no—
171C3×C4—21no—
172C3×C4—21no—
173C3×C4—21no—
174C3×C4—21no—
175C3×C4—21no—
176C3×C4—21no—
177C3×C4—41no—
178C3×C4—41no—
179Dic3—61no—
180Dic3—61no—
181Dic3—61no—
182Dic3—61no—
183Dic3—62no—
184Dic3—62no—
185Dic3—121no—
186Dic3—121no—
187C32#129211yescharacteristic, complemented, Sylow
188C23—91no—
189C2×C4—91no—
190C2×C4—91no—
191C2×C4—91no—
192C2×C4—91no—
193C2×C4—91no—
194C2×C4—91no—
195C2×C4—91no—
196C2×C4—181no—
197C2×C4—181no—
198C2×C4—361no—
199C2×C4D32⋊C411yescharacteristic
200C2×C4D32⋊C411yescharacteristic
201C2×C4#377311yescharacteristic
202C8—122no—
203C8—122no—
204C8—362no—
205C2×C3—21no—
206C2×C3—21no—
207C2×C3—21no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3—21no—
211D3—62no—
212D3—62no—
213D3—121no—
214D3—121no—
215C22—91no—
216C22—91no—
217C22—181no—
218C22—181no—
219C22#6373711yescharacteristic
220C4—21no—
221C4—91no—
222C4—91no—
223C4—181no—
224C4—181no—
225C4#6372711yescharacteristic
226C4#6372811yescharacteristic
227C4#6372911yescharacteristic
228C4#6373011yescharacteristic
229C3—21no—
230C3—21no—
231C2—181no—
232C2—181no—
233C2#1059004611yescharacteristic
234C2#1059004911yescharacteristic
235C2#1059005211yescharacteristic
subgroupG/H
centerC22#63737
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC42GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32#95
prime radicalC22×C3⋊D3C4⋊C4
cosocleC42×C3⋊D3C22
hypocenterC32#1292
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
187. C32#1292semidirect

Maximal subgroups

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

subgroupindex
#105937282
#105903402
#105903312
#12929