Finite Group Databasebeta

← #11774408

Subgroups — #11774408

Order 1152.

396 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 65 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#10593882C211yesmaximal, characteristic
2#10593725C211yesmaximal, characteristic
3#10590331C211yesmaximal, characteristic
4#10590032C214yesmaximal, complemented
5C42×C3⋊D3C2211yescharacteristic
6C3×C4×Dic6—21no—
7#63919C411yescharacteristic
8C4×#627C2212yes—
9#63874—21no—
10#63873C411yescharacteristic
11#63871—21no—
12#63870—21no—
13#63865C412yes—
14C2×#3710—21no—
15#63779—21no—
16#63778—21no—
17C4×#622C2212yes—
18C3×C4⋊(C3⋊C8)—21no—
19#63572C2212yes—
20#5578—61no—
21D3×C4⋊C8—61no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C3×Dic6—21no—
26C2×#627C2×C412yes—
27C2×#622—22no—
28C32×C42D411yescharacteristic
29C4×C3⋊Dic3C2×C411yescharacteristic
30C4×C3⋊Dic3D411yescharacteristic
31C4×C3⋊Dic3C2311yescharacteristic
32C3×C4⋊Dic3—21no—
33C3×Dic3⋊C4—22no—
34C3×C4×Dic3—22no—
35C2×C3×C3⋊C8—22no—
36#3724—21no—
37#3724—21no—
38#3724C2×C412yes—
39Dic3⋊Dic3—22no—
40#3722—22no—
41#3710—42no—
42#1481—91nomaximal, Sylow
43C3×C4×Q8—61no—
44#946—61no—
45#944—61no—
46C2×D3×C8—62no—
47#897—61no—
48#896—62no—
49#889—62no—
50#888—61no—
51#872—62no—
52C42×D3—61no—
53C42×D3—61no—
54C4×Dic6—21no—
55C4×Dic6—62no—
56C3×C4⋊C8—61no—
57Dic3⋊C8—62no—
58C4⋊(C3⋊C8)—21no—
59C22×C3⋊D3C22⋊C411yescharacteristic
60C2×C32×C4C22⋊C411yescharacteristic
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C2×D411yescharacteristic
63C2×C3⋊Dic3C22⋊C411yescharacteristic
64C2×C3⋊Dic3C22×C411yescharacteristic
65C2×C3⋊Dic3C2×D411yescharacteristic
66C4×C3⋊D3—22no—
67C4×C3⋊D3—41no—
68C4×C3⋊D3SD1612yes—
69C4×C3⋊D3Q1612yes—
70C2×C3×Dic3—22no—
71C2×C3×Dic3—22no—
72C3×Dic6—42no—
73#627—24no—
74#622—42no—
75C3×C3⋊C8—42no—
76#533—91no—
77#431—91no—
78C2×C4⋊C8—91no—
79Q8⋊C8—94no—
80C2×C3×Q8—61no—
81C2×C4×D3—61no—
82C2×C4×D3—61no—
83C2×C4×D3—61no—
84C2×C4×D3—61no—
85C2×C4×D3—61no—
86C2×C4×D3—61no—
87C2×Dic6—21no—
88C2×Dic6—62no—
89C2×C3×C8—62no—
90C3×C4⋊C4—61no—
91C3×C4⋊C4—62no—
92C3×C42—21no—
93C3×C42—21no—
94C3×C42—62no—
95(C2×D3)⋊C4—62no—
96(C2×D3)⋊C4—62no—
97C4⋊Dic3—21no—
98C4⋊Dic3—62no—
99Dic3⋊C4—22no—
100Dic3⋊C4—62no—
101Dic3⋊C4—62no—
102Dic3⋊C4—62no—
103Dic3⋊C4—62no—
104C4×Dic3—22no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C2×C3⋊C8—22no—
112D3×C8—124no—
113C22×C32C2×C22⋊C411yescharacteristic
114C2×C3⋊D3—21no—
115C2×C3⋊D3—21no—
116C2×C3⋊D3#10312yes—
117C32×C4—21no—
118C32×C4—21no—
119C32×C4C2×SD1611yescharacteristic
120C32×C4C2×Q1611yescharacteristic
121C3⋊Dic3—21no—
122C3⋊Dic3#10312yes—
123C3⋊Dic3#13112yes—
124C3×Dic3—42no—
125C3×Dic3—42no—
126C22×C8—181no—
127C4⋊Q8—91no—
128C4⋊Q8—91no—
129#125—181no—
130C22⋊Q8—92no—
131C22⋊Q8—181no—
132C4×Q8—61no—
133C4×Q8—92no—
134#117—181no—
135C2×C42—91no—
136C4⋊C8—61no—
137C4⋊C8—92no—
138C4⋊C8—181no—
139C22⋊C8—181no—
140C4×C8—92no—
141C22×D3—61no—
142C22×D3—61no—
143C3×Q8—122no—
144C2×C3×C4—21no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—62no—
151C2×C3×C4—62no—
152C2×Dic3—22no—
153C2×Dic3—22no—
154C2×Dic3—61no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159C2×Dic3—61no—
160C4×D3—62no—
161C4×D3—62no—
162C4×D3—62no—
163C4×D3—62no—
164C4×D3—64no—
165C4×D3—122no—
166C4×D3—122no—
167C4×D3—122no—
168Dic6—42no—
169Dic6—124no—
170C3×C8—122no—
171C3⋊C8—42no—
172C2×C32#40811yescharacteristic
173C2×C32C2×#10311yescharacteristic
174C2×C32#42111yescharacteristic
175C3⋊D3—22no—
176C2×Q8—61no—
177C2×Q8—92no—
178C22×C4—91no—
179C22×C4—91no—
180C22×C4—91no—
181C2×C8—62no—
182C2×C8—182no—
183C2×C8—362no—
184C4⋊C4—62no—
185C4⋊C4—61no—
186C4⋊C4—92no—
187C4⋊C4—181no—
188C4⋊C4—181no—
189C4⋊C4—182no—
190C22⋊C4—182no—
191C42—62no—
192C42—91no—
193C42—91no—
194C42—91no—
195C42GO+(4,𝔽2)11yescharacteristic
196C22×C3—21no—
197C22×C3—21no—
198C2×D3—62no—
199C2×D3—62no—
200C2×D3—62no—
201C2×D3—62no—
202C2×D3—121no—
203C2×D3—121no—
204C3×C4—22no—
205C3×C4—22no—
206C3×C4—21no—
207C3×C4—21no—
208C3×C4—21no—
209C3×C4—21no—
210C3×C4—41no—
211C3×C4—41no—
212C3×C4—122no—
213C3×C4—122no—
214Dic3—42no—
215Dic3—42no—
216Dic3—62no—
217Dic3—62no—
218Dic3—62no—
219Dic3—62no—
220Dic3—121no—
221Dic3—121no—
222C32#148111yescharacteristic, complemented, Sylow
223C23—91no—
224Q8—122no—
225Q8—184no—
226C2×C4—62no—
227C2×C4—62no—
228C2×C4—91no—
229C2×C4—91no—
230C2×C4—92no—
231C2×C4—92no—
232C2×C4—91no—
233C2×C4—182no—
234C2×C4—361no—
235C2×C4D32⋊C411yescharacteristic
236C2×C4D32⋊C411yescharacteristic
237C2×C4C2×GO+(4,𝔽2)11yescharacteristic
238C8—122no—
239C8—362no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—21no—
246D3—64no—
247D3—122no—
248C22—92no—
249C22—181no—
250C22—181no—
251C22C2×D32⋊C411yescharacteristic
252C4—21no—
253C4—21no—
254C4—92no—
255C4—92no—
256C4—122no—
257C4—122no—
258C4—181no—
259C4#6422711yescharacteristic
260C4#6422811yescharacteristic
261C3—21no—
262C3—21no—
263C2—182no—
264C2#1059330811yescharacteristic
265C2#1059332311yescharacteristic
266C2#1059337511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1481
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10590032C2semidirect
222. C32#1481semidirect

Maximal subgroups

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

subgroupindex
#105938822
#105937252
#105903312
#105900322
#14819