Finite Group Databasebeta

← #11791657

Subgroups — #11791657

Order 1152.

486 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 78 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
1C3⋊D3×#125C211yesmaximal, characteristic
2C4×C4⋊#157C211yesmaximal, characteristic
3#10593726C211yesmaximal, characteristic
4#10590163C212yesmaximal
5#10590163C212yesmaximal
6C2×C4⋊#157C2212yes—
7C2×C4×#157—21no—
8C2×#3787C2212yes—
9C32×#125C411yescharacteristic, complemented
10C4⋊C4×C3⋊D3—21no—
11C4⋊C4×C3⋊D3—21no—
12C4⋊C4×C3⋊D3C2211yescharacteristic
13C4⋊C4×C3⋊D3C2211yescharacteristic
14#64099C411yescharacteristic, complemented
15#64099C411yescharacteristic, complemented
16#64098—21no—
17#64098—21no—
18C42×C3⋊D3C2211yescharacteristic
19#64079C411yescharacteristic, complemented
20#63781—21no—
21#63779—21no—
22C4⋊#622—21no—
23D3×#125—62no—
24C22×#157—22no—
25C2×C4×C3⋊D3—21no—
26C2×C4×C3⋊D3—21no—
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3C2311yescharacteristic
30C2×#622—22no—
31C4⋊#157—22no—
32C4⋊#157Q814yes—
33C4×#157—42no—
34#3787—24no—
35C32×C4⋊C4—21no—
36C32×C4⋊C4—21no—
37C32×C4⋊C4C2×C411yescharacteristic
38C32×C4⋊C4C2×C411yescharacteristic
39C32×C42C2×C411yescharacteristic
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)—21no—
42C4⋊(C3⋊Dic3)C2×C411yescharacteristic
43C4⋊(C3⋊Dic3)C2×C411yescharacteristic
44#3750—21no—
45#3750—21no—
46#3750—21no—
47#3750—21no—
48#3750—21no—
49#3750—21no—
50C4×C3⋊Dic3C2×C411yescharacteristic
51C4×C3⋊Dic3D411yescharacteristic
52C4×C3⋊Dic3D411yescharacteristic
53#1989—91nomaximal, Sylow
54C3×#125—22no—
55D3×C4⋊C4—62no—
56D3×C4⋊C4—62no—
57D3×C4⋊C4—64no—
58D3×C4⋊C4—64no—
59#890—62no—
60#890—62no—
61#889—64no—
62#889—64no—
63C42×D3—62no—
64#870—62no—
65C22×C3⋊D3C2×D411yescharacteristic
66C2×#157—24no—
67C2×#157—42no—
68C2×#157—42no—
69C2×C32×C4—21no—
70C2×C32×C4—21no—
71C2×C32×C4C22⋊C411yescharacteristic
72C2×C32×C4C22⋊C411yescharacteristic
73C2×C32×C4C22×C411yescharacteristic
74C2×C3⋊Dic3—21no—
75C2×C3⋊Dic3—21no—
76C2×C3⋊Dic3C22⋊C411yescharacteristic
77C2×C3⋊Dic3C22⋊C411yescharacteristic
78C2×C3⋊Dic3C2×D411yescharacteristic
79C4×C3⋊D3—22no—
80C4×C3⋊D3—21no—
81C4×C3⋊D3—21no—
82C4×C3⋊D3—42no—
83C4×C3⋊D3—41no—
84C4×C3⋊D3—41no—
85C4×C3⋊D3C2×Q812yes—
86C4×C3⋊D3#4112yes—
87#622—42no—
88C2×#125—91no—
89C2×C4⋊C8—91no—
90C4×C4⋊C4—91no—
91#340—92no—
92#340—92no—
93C2×C4×D3—62no—
94C2×C4×D3—62no—
95C2×C4×D3—62no—
96C2×C4×D3—64no—
97C2×C4×D3—64no—
98C3×C4⋊C4—24no—
99C3×C4⋊C4—24no—
100C3×C4⋊C4—22no—
101C3×C4⋊C4—22no—
102C3×C42—22no—
103C4⋊Dic3—62no—
104C4⋊Dic3—62no—
105C4⋊Dic3—64no—
106C4⋊Dic3—64no—
107Dic3⋊C4—64no—
108Dic3⋊C4—64no—
109Dic3⋊C4—64no—
110Dic3⋊C4—64no—
111Dic3⋊C4—64no—
112Dic3⋊C4—64no—
113C4×Dic3—62no—
114C4×Dic3—62no—
115C4×Dic3—62no—
116C22×C32C2×C22⋊C411yescharacteristic
117C2×C3⋊D3C22⋊Q812yes—
118C2×C3⋊D3#13512yes—
119C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
120C2×C3⋊D3#13711yescharacteristic
121#157—44no—
122C32×C4—21no—
123C32×C4—21no—
124C32×C4—41no—
125C32×C4—41no—
126C32×C4C4×Q812yes—
127C3⋊Dic3—21no—
128C3⋊Dic3—21no—
129C3⋊Dic3—41no—
130C3⋊Dic3—41no—
131C3⋊Dic3#12411yescharacteristic
132C3⋊Dic3C4⋊Q811yescharacteristic
133C22×C8—92no—
134#125—91no—
135#125—91no—
136#125—91no—
137#125—181no—
138#125—181no—
139#125#15711yescharacteristic, complemented
140C2×C4⋊C4—92no—
141C2×C4⋊C4—91no—
142C2×C4⋊C4—91no—
143C2×C4⋊C4—181no—
144C2×C4⋊C4—181no—
145C2×C42—91no—
146C2×C42—181no—
147C4⋊C8—181no—
148C4⋊C8—181no—
149#95—181no—
150C22×D3—62no—
151C2×C3×C4—24no—
152C2×C3×C4—24no—
153C2×C3×C4—22no—
154C2×C3×C4—22no—
155C2×C3×C4—22no—
156C2×Dic3—62no—
157C2×Dic3—62no—
158C2×Dic3—62no—
159C2×Dic3—64no—
160C2×Dic3—64no—
161C4×D3—64no—
162C4×D3—64no—
163C4×D3—122no—
164C4×D3—124no—
165C4×D3—122no—
166C4×D3—128no—
167C4×D3—124no—
168C4×D3—124no—
169C2×C32#39111yescharacteristic
170C2×C32#41611yescharacteristic
171C2×C32#41711yescharacteristic
172C3⋊D3#47812yes—
173C3⋊D3#47912yes—
174C22×C4—91no—
175C22×C4—91no—
176C22×C4—91no—
177C22×C4—181no—
178C22×C4—181no—
179C22×C4—182no—
180C2×C8—182no—
181C2×C8—184no—
182C4⋊C4—21no—
183C4⋊C4—21no—
184C4⋊C4—94no—
185C4⋊C4—91no—
186C4⋊C4—91no—
187C4⋊C4—181no—
188C4⋊C4—181no—
189C4⋊C4—181no—
190C4⋊C4—181no—
191C4⋊C4—181no—
192C4⋊C4—181no—
193C4⋊C4—182no—
194C4⋊C4—181no—
195C4⋊C4—181no—
196C4⋊C4C2×#15711yescharacteristic
197C4⋊C4C2×#15711yescharacteristic
198C42—91no—
199C42—91no—
200C42—91no—
201C42—362no—
202C42C2×#15711yescharacteristic
203C22×C3—22no—
204C2×D3—64no—
205C2×D3—64no—
206C2×D3—62no—
207C2×D3—62no—
208C3×C4—24no—
209C3×C4—42no—
210C3×C4—42no—
211C3×C4—44no—
212C3×C4—44no—
213Dic3—62no—
214Dic3—62no—
215Dic3—122no—
216Dic3—122no—
217Dic3—124no—
218Dic3—124no—
219C32#198911yescharacteristic, complemented, Sylow
220C23—91no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—91no—
224C2×C4—92no—
225C2×C4—92no—
226C2×C4—91no—
227C2×C4—91no—
228C2×C4—181no—
229C2×C4—181no—
230C2×C4—182no—
231C2×C4—184no—
232C2×C4—181no—
233C2×C4—181no—
234C2×C4—361no—
235C2×C4—361no—
236C2×C4—362no—
237C2×C4—362no—
238C2×C4—362no—
239C2×C4C22⋊#15711yescharacteristic
240C2×C4C22⋊#15711yescharacteristic
241C2×C4C22×#15711yescharacteristic
242C8—362no—
243C2×C3—22no—
244C2×C3—22no—
245C2×C3—22no—
246D3—64no—
247D3—64no—
248C22—92no—
249C22—91no—
250C22—91no—
251C22—92no—
252C22C2×C22⋊#15711yescharacteristic
253C4—21no—
254C4—21no—
255C4—41no—
256C4—41no—
257C4—91no—
258C4—91no—
259C4—181no—
260C4—181no—
261C4—364no—
262C4—361no—
263C4—361no—
264C4Q8×#15712yes—
265C3—22no—
266C2—92no—
267C2—92no—
268C2#1059383711yescharacteristic
269C2#1059384011yescharacteristic
270C2#1059384111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#125C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenter#125#157
hypocenterC32#1989
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
9. C32×#125C4semidirect
14. #64099C4semidirect
15. #64099C4semidirect
19. #64079C4semidirect
139. #125#157semidirect
219. C32#1989semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×#1252
C4×C4⋊#1572
#105937262
#105901632
#19899