Finite Group Databasebeta

← #11775264

Subgroups — #11775264

Order 1152.

476 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 58 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#10596162C211yesmaximal, characteristic
2C4×C4⋊#157C211yesmaximal, characteristic, complemented
3#10593731C211yesmaximal, characteristic, complemented
4#10590158C212yesmaximal, complemented
5#10590157C212yesmaximal
6C2×C4⋊#157—21no—
7C2×C4×#157—21no—
8C32×#125C411yescharacteristic, complemented
9#64107—21no—
10#64106C2211yescharacteristic
11#64104C2211yescharacteristic
12#64103—21no—
13#64102—21no—
14#64102C411yescharacteristic, complemented
15#64101—21no—
16#64096C411yescharacteristic, complemented
17#64084C411yescharacteristic, complemented
18C42×C3⋊D3C2211yescharacteristic
19#63781C2212yes—
20#63779—21no—
21#63778C2212yes—
22#63777—21no—
23#5691—62no—
24C22×#157—22no—
25C2×C4⋊(C3⋊D3)—21no—
26C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
27C2×C4×C3⋊D3—21no—
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3D411yescharacteristic
30C2×C4×C3⋊D3C2311yescharacteristic
31C2×#634C2×C411yescharacteristic
32C2×#622—22no—
33C4⋊#157—24no—
34C4×#157—42no—
35C32×C4⋊C4—21no—
36C32×C4⋊C4—21no—
37C32×C4⋊C4C2×C411yescharacteristic
38C32×C4⋊C4C2×C411yescharacteristic
39C32×C42C2×C411yescharacteristic
40#3752—21no—
41#3752—21no—
42#3752—21no—
43#3752—21no—
44#3752—21no—
45C4⋊(C3⋊Dic3)—21no—
46#3750—21no—
47C4×C3⋊Dic3—21no—
48C4×C3⋊Dic3C2×C411yescharacteristic
49C4×C3⋊Dic3D411yescharacteristic
50C4×C3⋊Dic3D411yescharacteristic
51#1509—91nomaximal, Sylow
52C3×#125—22no—
53#898—64no—
54#897—62no—
55#895—62no—
56#894—64no—
57#893—62no—
58#893—64no—
59#892—64no—
60#887—62no—
61#875—62no—
62C42×D3—62no—
63C22×C3⋊D3—21no—
64C22×C3⋊D3C2×D411yescharacteristic
65C2×#157—24no—
66C2×#157—42no—
67C2×#157—42no—
68C2×C32×C4—21no—
69C2×C32×C4—21no—
70C2×C32×C4C22⋊C411yescharacteristic
71C2×C32×C4C22⋊C411yescharacteristic
72C2×C32×C4C22×C411yescharacteristic
73C2×C3⋊Dic3—21no—
74C2×C3⋊Dic3C22⋊C411yescharacteristic
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C2×C3⋊Dic3C2×D411yescharacteristic
77C4⋊(C3⋊D3)—41no—
78C4⋊(C3⋊D3)—41no—
79C4⋊(C3⋊D3)—41no—
80C4×C3⋊D3—21no—
81C4×C3⋊D3—21no—
82C4×C3⋊D3—22no—
83C4×C3⋊D3—41no—
84C4×C3⋊D3—42no—
85#634—41no—
86#622—42no—
87#529—91no—
88#432—91no—
89C4×C4⋊C4—91no—
90#328—92no—
91#327—92no—
92C2×D12—62no—
93C2×D12—64no—
94C2×C4×D3—62no—
95C2×C4×D3—62no—
96C2×C4×D3—62no—
97C2×C4×D3—64no—
98C2×Dic6—62no—
99C3×C4⋊C4—24no—
100C3×C4⋊C4—24no—
101C3×C4⋊C4—22no—
102C3×C4⋊C4—22no—
103C3×C42—22no—
104(C2×D3)⋊C4—64no—
105(C2×D3)⋊C4—64no—
106(C2×D3)⋊C4—64no—
107(C2×D3)⋊C4—64no—
108(C2×D3)⋊C4—64no—
109C4⋊Dic3—64no—
110Dic3⋊C4—64no—
111C4×Dic3—62no—
112C4×Dic3—62no—
113C4×Dic3—62no—
114C4×Dic3—64no—
115C22×C32C2×C22⋊C411yescharacteristic
116C2×C3⋊D3—21no—
117C2×C3⋊D3—21no—
118C2×C3⋊D3—41no—
119C2×C3⋊D3—41no—
120C2×C3⋊D3—41no—
121C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
122C2×C3⋊D3#13711yescharacteristic
123#157—44no—
124C32×C4—21no—
125C32×C4—21no—
126C32×C4—21no—
127C32×C4—41no—
128C32×C4—41no—
129C3⋊Dic3—21no—
130C3⋊Dic3—21no—
131C3⋊Dic3—41no—
132C3⋊Dic3#10412yes—
133#126—181no—
134#125#15711yescharacteristic, complemented
135#124—91no—
136#123—181no—
137C22⋊Q8—91no—
138#121—91no—
139C4×Q8—91no—
140C4×D4—91no—
141C4×D4—181no—
142#117—181no—
143C2×C4⋊C4—181no—
144C2×C42—91no—
145C2×C42—181no—
146C4⋊C8—181no—
147C22⋊C8—92no—
148#97—181no—
149#95—92no—
150C22×D3—62no—
151C22×D3—64no—
152C2×C3×C4—24no—
153C2×C3×C4—24no—
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×C3×C4—22no—
157C2×Dic3—62no—
158C2×Dic3—62no—
159C2×Dic3—62no—
160C2×Dic3—64no—
161D12—124no—
162D12—124no—
163D12—124no—
164C4×D3—124no—
165C4×D3—122no—
166C4×D3—122no—
167C4×D3—128no—
168C4×D3—124no—
169Dic6—124no—
170C2×C32#41011yescharacteristic
171C2×C32#41711yescharacteristic
172C2×C32C2×#10411yescharacteristic
173C3⋊D3—21no—
174C3⋊D3—21no—
175C3⋊D3—81no—
176C2×Q8—91no—
177C2×D4—91no—
178C2×D4—181no—
179C22×C4—91no—
180C22×C4—91no—
181C22×C4—91no—
182C22×C4—181no—
183C22×C4—182no—
184C2×C8—182no—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—181no—
188C4⋊C4—181no—
189C4⋊C4—184no—
190C4⋊C4C2×#15711yescharacteristic
191C4⋊C4C2×#15711yescharacteristic
192C22⋊C4—181no—
193C22⋊C4—181no—
194C22⋊C4—181no—
195C22⋊C4—181no—
196C22⋊C4—181no—
197C42—91no—
198C42—91no—
199C42—91no—
200C42—181no—
201C42—362no—
202C42C2×#15711yescharacteristic
203C22×C3—22no—
204C2×D3—62no—
205C2×D3—62no—
206C2×D3—122no—
207C2×D3—122no—
208C2×D3—124no—
209C2×D3—124no—
210C2×D3—124no—
211C3×C4—24no—
212C3×C4—42no—
213C3×C4—42no—
214C3×C4—44no—
215C3×C4—44no—
216Dic3—64no—
217Dic3—122no—
218Dic3—122no—
219Dic3—124no—
220C32#150911yescharacteristic, complemented, Sylow
221C23—91no—
222C23—181no—
223Q8—361no—
224D4—361no—
225D4—361no—
226D4—361no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—91no—
230C2×C4—91no—
231C2×C4—91no—
232C2×C4—182no—
233C2×C4—181no—
234C2×C4—181no—
235C2×C4—184no—
236C2×C4—181no—
237C2×C4—361no—
238C2×C4—362no—
239C2×C4—362no—
240C2×C4—362no—
241C2×C4C22⋊#15711yescharacteristic
242C2×C4C22⋊#15711yescharacteristic
243C2×C4C22×#15711yescharacteristic
244C8—362no—
245C2×C3—22no—
246C2×C3—22no—
247C2×C3—22no—
248D3—122no—
249D3—122no—
250D3—244no—
251C22—91no—
252C22—91no—
253C22—181no—
254C22—181no—
255C22—361no—
256C22—361no—
257C22—361no—
258C22C2×C22⋊#15711yescharacteristic
259C4—21no—
260C4—21no—
261C4—21no—
262C4—41no—
263C4—41no—
264C4—92no—
265C4—181no—
266C4—181no—
267C4—364no—
268C4—361no—
269C3—22no—
270C2—181no—
271C2—181no—
272C2—721no—
273C2#1059383211yescharacteristic
274C2#1059383911yescharacteristic
275C2#1059384011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#125C4
socleC22×C32C2×C22⋊C4
prime radical#64104C22
cosocleC2×C4×C3⋊D3C23
hypercenter#125#157
hypocenterC32#1509
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. C4×C4⋊#157C2semidirect
3. #10593731C2semidirect
4. #10590158C2semidirect
8. C32×#125C4semidirect
14. #64102C4semidirect
16. #64096C4semidirect
17. #64084C4semidirect
134. #125#157semidirect
220. C32#1509semidirect

Maximal subgroups

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

subgroupindex
#105961622
C4×C4⋊#1572
#105937312
#105901582
#105901572
#15099