Finite Group Databasebeta

← #11773811

Subgroups — #11773811

Order 1152.

738 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 80 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
1C2×C4×#638C211yesmaximal, characteristic
2#10593801C212yesmaximal, complemented
3#10590222C212yesmaximal, complemented
4#10590204C212yesmaximal, complemented
5C23×C32×C4C411yescharacteristic
6C22×#638C411yescharacteristic
7C22×C4×C3⋊D3C411yescharacteristic
8C2×#3757C2211yescharacteristic
9C4×#638—22no—
10C4×#638—22no—
11C2×#3752C2211yescharacteristic
12C2×#3750C411yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C22⋊#622C2214yes—
15#63779—22no—
16C4×#622—22no—
17C2×C4×#67—62no—
18C24×C32C2×C411yescharacteristic
19C23×C3⋊D3C2×C411yescharacteristic
20C22×C32×C4—21no—
21C22×C32×C4—21no—
22C22×C32×C4—42no—
23C22×C32×C4C2×C411yescharacteristic
24C22×C32×C4C2×C411yescharacteristic
25C2×#638—22no—
26C2×#638—22no—
27C2×#638C814yescomplemented
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3C2×C411yescharacteristic
30C22×C3⋊Dic3C2311yescharacteristic
31C2×C4×C3⋊D3—21no—
32C2×C4×C3⋊D3—21no—
33C2×C4×C3⋊D3—42no—
34C2×#622—24no—
35#3757—22no—
36#3752—22no—
37#3750—22no—
38C4×C3⋊Dic3D412yes—
39C4×C3⋊Dic3D412yes—
40#1460—91nomaximal, Sylow
41C23×C3×C4—22no—
42C22×#67—62no—
43C22×C4×D3—62no—
44C2×#217—62no—
45C4×#67—68no—
46C4×#67—68no—
47C2×(C2×D3)⋊C4—62no—
48C2×Dic3⋊C4—62no—
49C2×C4×Dic3—62no—
50C23×C32—21no—
51C23×C32—21no—
52C23×C32—41no—
53C23×C32—41no—
54C23×C32C2×C812yes—
55C23×C32C22×C411yescharacteristic
56C22×C3⋊D3—21no—
57C22×C3⋊D3—21no—
58C22×C3⋊D3—41no—
59C22×C3⋊D3—41no—
60C22×C3⋊D3C2×C812yes—
61C2×C32×C4—22no—
62C2×C32×C4—21no—
63C2×C32×C4—42no—
64C2×C32×C4—42no—
65C2×C32×C4—41no—
66C2×C32×C4C22⋊C411yescharacteristic
67C2×C32×C4C22⋊C411yescharacteristic
68#638—28no—
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—41no—
71C2×C3⋊Dic3—41no—
72C2×C3⋊Dic3C22⋊C412yes—
73C2×C3⋊Dic3C2×C812yes—
74C2×C3⋊Dic3M1612yes—
75C2×C3⋊Dic3C2×D412yes—
76C4×C3⋊D3—42no—
77C4×C3⋊D3—42no—
78#622—44no—
79C2×C4×D4—91no—
80#431—92no—
81#323—92no—
82#323—92no—
83C24×C3—22no—
84C23×D3—62no—
85C22×C3×C4—24no—
86C22×C3×C4—24no—
87C22×C3×C4—22no—
88C22×C3×C4—22no—
89C22×C3×C4—48no—
90C2×#67—68no—
91C2×#67—68no—
92C2×#67—68no—
93C22×Dic3—62no—
94C22×Dic3—62no—
95C22×Dic3—62no—
96C2×C4×D3—64no—
97C2×C4×D3—64no—
98C2×C4×D3—128no—
99#217—68no—
100(C2×D3)⋊C4—68no—
101Dic3⋊C4—68no—
102C4×Dic3—64no—
103C4×Dic3—64no—
104C22×C32—21no—
105C22×C32—21no—
106C22×C32—22no—
107C22×C32—42no—
108C22×C32—42no—
109C22×C32—41no—
110C22×C32—41no—
111C22×C32C2×C22⋊C411yescharacteristic
112C22×C32C22×C811yescharacteristic
113C22×C32C2×M1611yescharacteristic
114C2×C3⋊D3—22no—
115C2×C3⋊D3—42no—
116C2×C3⋊D3—41no—
117C2×C3⋊D3—41no—
118C2×C3⋊D3—42no—
119C32×C4—21no—
120C32×C4—41no—
121C32×C4#10012yes—
122C3⋊Dic3—22no—
123C3⋊Dic3—41no—
124C3⋊Dic3C22⋊C814yes—
125C22×D4—91no—
126C23×C4—91no—
127C23×C4#15711yescharacteristic
128C4×D4—182no—
129C4×D4—182no—
130C2×C4⋊C4—91no—
131C2×C22⋊C4—91no—
132C2×C22⋊C4—91no—
133C2×C42—91no—
134C4⋊C8—182no—
135C22⋊C8—94no—
136C4×C8—182no—
137C23×C3—24no—
138C23×C3—24no—
139C23×C3—22no—
140C23×C3—24no—
141C23×C3—44no—
142C23×C3—44no—
143C22×D3—64no—
144C22×D3—64no—
145C22×D3—64no—
146C22×D3—124no—
147C22×D3—124no—
148C2×C3×C4—28no—
149C2×C3×C4—24no—
150C2×C3×C4—22no—
151C2×C3×C4—22no—
152C2×C3×C4—48no—
153C2×C3×C4—48no—
154C2×C3×C4—44no—
155#67—632no—
156C2×Dic3—64no—
157C2×Dic3—64no—
158C2×Dic3—64no—
159C2×Dic3—64no—
160C2×Dic3—64no—
161C2×Dic3—124no—
162C2×Dic3—124no—
163C4×D3—128no—
164C4×D3—128no—
165C2×C32—21no—
166C2×C32—21no—
167C2×C32—42no—
168C2×C32C2×C22⋊C811yescharacteristic
169C2×C32#41011yescharacteristic
170C2×C32C2×#10011yescharacteristic
171C3⋊D3—42no—
172C24—91no—
173C24C2×#15711yescharacteristic
174C2×D4—94no—
175C2×D4—182no—
176C2×D4—182no—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4—42no—
180C22×C4—91no—
181C22×C4—91no—
182C22×C4—91no—
183C22×C4—181no—
184C22×C4—181no—
185C22×C4—362no—
186C22×C4C2×#15711yescharacteristic
187C22×C4C2×#15711yescharacteristic
188C2×C8—184no—
189C4⋊C4—182no—
190C22⋊C4—182no—
191C22⋊C4—182no—
192C42—92no—
193C42—92no—
194C22×C3—24no—
195C22×C3—24no—
196C22×C3—28no—
197C22×C3—22no—
198C22×C3—22no—
199C22×C3—22no—
200C22×C3—44no—
201C22×C3—48no—
202C22×C3—48no—
203C22×C3—44no—
204C2×D3—68no—
205C2×D3—124no—
206C2×D3—128no—
207C2×D3—128no—
208C2×D3—124no—
209C3×C4—24no—
210C3×C4—24no—
211C3×C4—44no—
212Dic3—68no—
213Dic3—124no—
214Dic3—124no—
215C32#146011yescharacteristic, complemented, Sylow
216C23—21no—
217C23—21no—
218C23—41no—
219C23—41no—
220C23—92no—
221C23—181no—
222C23—181no—
223C23—361no—
224C23—361no—
225C23#378712yes—
226C23C22×#15711yescharacteristic
227D4—188no—
228C2×C4—22no—
229C2×C4—21no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—41no—
233C2×C4—92no—
234C2×C4—92no—
235C2×C4—92no—
236C2×C4—92no—
237C2×C4—181no—
238C2×C4—362no—
239C2×C4—361no—
240C2×C4—362no—
241C2×C4—361no—
242C2×C4C22⋊#15711yescharacteristic
243C2×C4C22⋊#15711yescharacteristic
244C8—364no—
245C2×C3—24no—
246C2×C3—24no—
247C2×C3—22no—
248C2×C3—22no—
249C2×C3—22no—
250C2×C3—48no—
251D3—128no—
252C22—21no—
253C22—21no—
254C22—22no—
255C22—42no—
256C22—42no—
257C22—41no—
258C22—41no—
259C22—182no—
260C22—362no—
261C22—362no—
262C22—361no—
263C22—361no—
264C22C2×#378711yescharacteristic
265C22#6428311yescharacteristic
266C22C2×C22⋊#15711yescharacteristic
267C4—21no—
268C4—41no—
269C4—94no—
270C4—182no—
271C4—361no—
272C4#6378812yes—
273C3—22no—
274C2—21no—
275C2—21no—
276C2—42no—
277C2—362no—
278C2#1059379211yescharacteristic
279C2#1059380011yescharacteristic
280C2C2×#6378811yescharacteristic
subgroupG/H
centerC2×C4C22⋊#157
commutatorC22×C32C22×C8
FrattiniC23C22×#157
FittingC23×C32×C4C4
socleC22×C32C2×C22⋊C4
prime radicalC22×#638C4
cosocleC22×C3⋊Dic3C23
hypercenterC23×C4#157
hypocenterC32#1460
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #10593801C2semidirect
3. #10590222C2semidirect
4. #10590204C2semidirect
27. C2×#638C8semidirect
215. C32#1460semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6382
#105938012
#105902222
#105902042
#14609