Finite Group Databasebeta

← #11771113

Subgroups — #11771113

Order 1152.

386 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 49 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#10593800C211yesmaximal, characteristic
2#10591159C211yesmaximal, characteristic
3C2×#63557C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×#3787—21no—
6C22×C3×C3⋊C8—21no—
7C2×#3712C412yes—
8C22⋊#622C412yes—
9#63778—21no—
10C3×#830—21no—
11#63557—21no—
12#63557—21no—
13#63557C412yes—
14C2×(C2×D3)⋊C8—61no—
15#4726—61no—
16C23×C3⋊D3Q811yescharacteristic
17C22×C32×C4D411yescharacteristic
18C22×C3⋊Dic3C2×C411yescharacteristic
19C2×C4×C3⋊D3—42no—
20C2×C4×C3⋊D3C2×C411yescharacteristic
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×#622—22no—
25#3787—42no—
26C2×C3×C3⋊C8—22no—
27C2×C3×C3⋊C8—22no—
28C2×C3×C3⋊C8—42no—
29#3712—42no—
30#1298—91nomaximal, Sylow
31C22×C4×D3—61no—
32C22×C4×D3—61no—
33C22×C3×C8—61no—
34C22×C3⋊C8—21no—
35C2×ΓL(1,𝔽25)—62no—
36C3×C22⋊C8—61no—
37#830—21no—
38(C2×D3)⋊C8—62no—
39(C2×D3)⋊C8—62no—
40(C2×D3)⋊C8—62no—
41C23×C32C4⋊C411yescharacteristic
42C22×C3⋊D3—22no—
43C22×C3⋊D3—22no—
44C22×C3⋊D3—41no—
45C22×C3⋊D3C4⋊C411yescharacteristic
46C22×C3⋊D3C4⋊C411yescharacteristic
47C2×C32×C4—22no—
48C2×C32×C4C22⋊C411yescharacteristic
49C2×C32×C4C22⋊C411yescharacteristic
50C2×C3⋊Dic3—41no—
51C2×C3⋊Dic3C4211yescharacteristic
52C2×C3⋊Dic3C22⋊C411yescharacteristic
53C4×C3⋊D3—22no—
54C4×C3⋊D3—22no—
55C4×C3⋊D3—41no—
56C4×C3⋊D3—41no—
57#622—42no—
58C3×C3⋊C8—42no—
59C3×C3⋊C8—42no—
60#407—91no—
61C2×C22⋊C8—91no—
62C2×C22⋊C8—91no—
63C23×D3—61no—
64C23×D3—61no—
65C22×C3×C4—21no—
66C22×C3×C4—21no—
67C22×Dic3—61no—
68C22×Dic3—61no—
69C2×C4×D3—61no—
70C2×C4×D3—61no—
71C2×C4×D3—61no—
72C2×C4×D3—61no—
73C2×C4×D3—61no—
74C2×C4×D3—61no—
75C2×C4×D3—61no—
76C2×C4×D3—61no—
77C2×C4×D3—124no—
78C2×C4×D3—122no—
79C2×C4×D3—122no—
80C2×C3×C8—62no—
81C2×C3×C8—62no—
82C2×C3×C8—122no—
83C2×C3⋊C8—22no—
84C2×C3⋊C8—22no—
85C2×C3⋊C8—42no—
86ΓL(1,𝔽25)—124no—
87C22×C32—21no—
88C22×C32—21no—
89C22×C32#9511yescharacteristic
90C22×C32#10812yes—
91C2×C3⋊D3—21no—
92C2×C3⋊D3—21no—
93C2×C3⋊D3—21no—
94C2×C3⋊D3—21no—
95C2×C3⋊D3—21no—
96C2×C3⋊D3—44no—
97C2×C3⋊D3#10812yes—
98C32×C4—21no—
99C32×C4#9912yes—
100C3⋊Dic3—21no—
101C3⋊Dic3—21no—
102C23×C4—91no—
103C2×M16—92no—
104C22×C8—61no—
105C22×C8—181no—
106C22⋊C8—61no—
107C22⋊C8—92no—
108C22⋊C8—92no—
109C22⋊C8—181no—
110C22⋊C8—181no—
111C22⋊C8—181no—
112C23×C3—21no—
113C23×C3—21no—
114C22×D3—61no—
115C22×D3—61no—
116C22×D3—61no—
117C22×D3—61no—
118C22×D3—64no—
119C22×D3—122no—
120C22×D3—122no—
121C22×D3—122no—
122C22×D3—122no—
123C22×D3—122no—
124C2×C3×C4—22no—
125C2×C3×C4—22no—
126C2×C3×C4—21no—
127C2×C3×C4—21no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—42no—
131C2×Dic3—61no—
132C2×Dic3—61no—
133C2×Dic3—61no—
134C2×Dic3—61no—
135C2×Dic3—122no—
136C2×Dic3—122no—
137C4×D3—64no—
138C4×D3—122no—
139C4×D3—122no—
140C4×D3—122no—
141C4×D3—122no—
142C4×D3—121no—
143C4×D3—121no—
144C4×D3—121no—
145C4×D3—121no—
146C4×D3—122no—
147C3×C8—122no—
148C3×C8—122no—
149C3⋊C8—42no—
150C3⋊C8—42no—
151C2×C32—22no—
152C2×C32#34111yescharacteristic
153C2×C32#34111yescharacteristic
154C2×C32#34211yescharacteristic
155C3⋊D3—22no—
156C3⋊D3—41no—
157C24—91no—
158C22×C4—91no—
159C22×C4—91no—
160C22×C4—91no—
161C22×C4—91no—
162C22×C4—91no—
163C22×C4—362no—
164C22×C4GO+(4,𝔽2)11yescharacteristic
165M16—362no—
166C2×C8—62no—
167C2×C8—62no—
168C2×C8—122no—
169C2×C8—182no—
170C2×C8—362no—
171C22×C3—22no—
172C22×C3—22no—
173C22×C3—22no—
174C22×C3—22no—
175C22×C3—21no—
176C22×C3—21no—
177C22×C3—41no—
178C22×C3—41no—
179C2×D3—62no—
180C2×D3—62no—
181C2×D3—62no—
182C2×D3—62no—
183C2×D3—121no—
184C2×D3—121no—
185C2×D3—121no—
186C2×D3—121no—
187C2×D3—121no—
188C2×D3—121no—
189C2×D3—121no—
190C2×D3—121no—
191C2×D3—128no—
192C2×D3—128no—
193C3×C4—21no—
194C3×C4—21no—
195C3×C4—22no—
196C3×C4—22no—
197C3×C4—41no—
198Dic3—62no—
199Dic3—121no—
200Dic3—121no—
201Dic3—121no—
202C32#129811yescharacteristic, complemented, Sylow
203C23—91no—
204C23—91no—
205C23—182no—
206C23—182no—
207C23—361no—
208C23#377311yescharacteristic
209C2×C4—22no—
210C2×C4—91no—
211C2×C4—91no—
212C2×C4—182no—
213C2×C4—182no—
214C2×C4—361no—
215C2×C4—361no—
216C2×C4—361no—
217C2×C4D32⋊C411yescharacteristic
218C2×C4D32⋊C411yescharacteristic
219C8—122no—
220C8—122no—
221C8—362no—
222C2×C3—24no—
223C2×C3—21no—
224C2×C3—21no—
225C2×C3—21no—
226C2×C3—21no—
227C2×C3—21no—
228C2×C3—21no—
229C2×C3—42no—
230D3—122no—
231D3—122no—
232D3—122no—
233D3—122no—
234C22—21no—
235C22—21no—
236C22—92no—
237C22—181no—
238C22—181no—
239C22—181no—
240C22—181no—
241C22—181no—
242C22—364no—
243C22#6373312yes—
244C22#6373711yescharacteristic
245C4—21no—
246C4—181no—
247C4—181no—
248C4#6373812yes—
249C3—21no—
250C3—21no—
251C2—22no—
252C2—182no—
253C2—361no—
254C2#1059005011yescharacteristic
255C2#1059005111yescharacteristic
256C2#1059007611yescharacteristic
subgroupG/H
centerC2×C4D32⋊C4
commutatorC2×C3⋊Dic3C42
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#95
prime radicalC23×C3⋊D3Q8
cosocleC22×C4×C3⋊D3C22
hypocenterC32#1298
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
202. C32#1298semidirect

Maximal subgroups

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

subgroupindex
#105938002
#105911592
C2×#635572
#12989