Finite Group Databasebeta

← #11775902

Subgroups — #11775902

Order 1152.

434 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 60 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#10595988C211yesmaximal, characteristic
2#10593804C211yesmaximal, characteristic
3C2×#63777C211yesmaximal, characteristic
4#10590159C212yesmaximal, complemented
5#10590159C212yesmaximal, complemented
6C22×#622—21no—
7C32×#117C411yescharacteristic
8#64135C411yescharacteristic
9C2×C4×C3⋊Dic3C2211yescharacteristic
10#64099C2211yescharacteristic
11#64099C2211yescharacteristic
12#64097C411yescharacteristic
13#64097C411yescharacteristic
14#64087—21no—
15#64087—21no—
16C4×#634—21no—
17C4×#634—21no—
18C22⋊#622—21no—
19#63779—21no—
20#63777—21no—
21#63777C2212yes—
22#63777C2212yes—
23#5517—62no—
24C22×C32×C4C2×C411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C22×C3⋊Dic3D411yescharacteristic
27C2×#634—21no—
28C2×#634—21no—
29C2×#622—24no—
30C2×#622—22no—
31C2×#622—22no—
32C32×C4⋊C4C2×C411yescharacteristic
33C32×C4⋊C4C2×C411yescharacteristic
34C32×C22⋊C4—21no—
35C32×C42—21no—
36#3757—21no—
37C4⋊(C3⋊Dic3)—21no—
38C4⋊(C3⋊Dic3)—21no—
39C4⋊(C3⋊Dic3)C2×C411yescharacteristic
40C4⋊(C3⋊Dic3)C2×C411yescharacteristic
41#3750—21no—
42#3750—21no—
43#3750—21no—
44#3750—21no—
45C4×C3⋊Dic3—21no—
46C4×C3⋊Dic3C2×C411yescharacteristic
47C4×C3⋊Dic3D411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3C2311yescharacteristic
50#1531—91nomaximal, Sylow
51C3×#117—22no—
52#926—62no—
53C2×C4×Dic3—62no—
54#890—62no—
55#890—62no—
56#888—62no—
57#888—62no—
58#878—64no—
59#878—64no—
60C4×Dic6—64no—
61C4×Dic6—64no—
62C23×C32C22⋊C411yescharacteristic
63C2×C32×C4—22no—
64C2×C32×C4—21no—
65C2×C32×C4—21no—
66C2×C32×C4C22⋊C411yescharacteristic
67C2×C32×C4C22×C411yescharacteristic
68C2×C3⋊Dic3—21no—
69C2×C3⋊Dic3—21no—
70C2×C3⋊Dic3—22no—
71C2×C3⋊Dic3—41no—
72C2×C3⋊Dic3C22⋊C411yescharacteristic
73C2×C3⋊Dic3C22⋊C411yescharacteristic
74C2×C3⋊Dic3C2×D411yescharacteristic
75C2×C3⋊Dic3C2×D411yescharacteristic
76#634—42no—
77#634—42no—
78#622—24no—
79#622—42no—
80#533—91no—
81#432—91no—
82C2×#97—91no—
83#330—92no—
84#330—92no—
85C22×C3×C4—22no—
86C22×Dic3—62no—
87C22×Dic3—62no—
88C2×Dic6—64no—
89C2×Dic6—64no—
90C3×C4⋊C4—22no—
91C3×C4⋊C4—22no—
92C3×C22⋊C4—24no—
93C3×C42—24no—
94#217—64no—
95C4⋊Dic3—62no—
96C4⋊Dic3—62no—
97C4⋊Dic3—64no—
98C4⋊Dic3—64no—
99Dic3⋊C4—64no—
100Dic3⋊C4—64no—
101Dic3⋊C4—64no—
102Dic3⋊C4—64no—
103C4×Dic3—62no—
104C4×Dic3—62no—
105C4×Dic3—62no—
106C4×Dic3—62no—
107C4×Dic3—64no—
108C22×C32—21no—
109C22×C32—21no—
110C22×C32#10112yes—
111C22×C32C2×C22⋊C411yescharacteristic
112C32×C4—21no—
113C32×C4—21no—
114C32×C4—41no—
115C32×C4—41no—
116C3⋊Dic3—21no—
117C3⋊Dic3—21no—
118C3⋊Dic3—21no—
119C3⋊Dic3—41no—
120C3⋊Dic3—41no—
121C3⋊Dic3#10412yes—
122C22×C8—181no—
123C4⋊Q8—91no—
124C4⋊Q8—91no—
125#125—91no—
126#125—91no—
127C22⋊Q8—181no—
128C22⋊Q8—181no—
129C4×Q8—181no—
130C4×Q8—181no—
131#117—91no—
132#117#15711yescharacteristic
133C2×C42—91no—
134C4⋊C8—181no—
135C22⋊C8—181no—
136#97—92no—
137#97—92no—
138#97—181no—
139C23×C3—22no—
140C2×C3×C4—28no—
141C2×C3×C4—24no—
142C2×C3×C4—24no—
143C2×C3×C4—22no—
144C2×C3×C4—22no—
145C2×Dic3—62no—
146C2×Dic3—62no—
147C2×Dic3—62no—
148C2×Dic3—62no—
149C2×Dic3—64no—
150C2×Dic3—64no—
151C2×Dic3—124no—
152C2×Dic3—124no—
153Dic6—128no—
154Dic6—128no—
155C2×C32—22no—
156C2×C32C2×#10111yescharacteristic
157C2×C32C2×#10411yescharacteristic
158C2×C32#42111yescharacteristic
159C2×Q8—181no—
160C2×Q8—181no—
161C22×C4—91no—
162C22×C4—91no—
163C22×C4C2×#15711yescharacteristic
164C2×C8—182no—
165C2×C8—184no—
166C2×C8—182no—
167C4⋊C4—91no—
168C4⋊C4—91no—
169C4⋊C4—181no—
170C4⋊C4—181no—
171C4⋊C4—181no—
172C4⋊C4—181no—
173C4⋊C4—181no—
174C4⋊C4—181no—
175C4⋊C4C2×#15711yescharacteristic
176C4⋊C4C2×#15711yescharacteristic
177C22⋊C4—21no—
178C22⋊C4—181no—
179C42—21no—
180C42—91no—
181C42—91no—
182C42—91no—
183C42—91no—
184C42—181no—
185C22×C3—24no—
186C22×C3—22no—
187C22×C3—42no—
188C22×C3—42no—
189C3×C4—24no—
190C3×C4—24no—
191C3×C4—44no—
192C3×C4—44no—
193Dic3—64no—
194Dic3—64no—
195Dic3—122no—
196Dic3—122no—
197Dic3—124no—
198Dic3—124no—
199C32#153111yescharacteristic, complemented, Sylow
200C23C22⋊#15711yescharacteristic
201Q8—362no—
202Q8—362no—
203C2×C4—22no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—91no—
207C2×C4—91no—
208C2×C4—91no—
209C2×C4—91no—
210C2×C4—182no—
211C2×C4—181no—
212C2×C4—181no—
213C2×C4—361no—
214C2×C4C22⋊#15711yescharacteristic
215C2×C4C22×#15711yescharacteristic
216C8—184no—
217C8—362no—
218C2×C3—22no—
219C2×C3—22no—
220C2×C3—22no—
221C2×C3—44no—
222C22—21no—
223C22—21no—
224C22#6378012yes—
225C22C2×C22⋊#15711yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—41no—
230C4—92no—
231C4—181no—
232C4—181no—
233C4—181no—
234C4—361no—
235C4—361no—
236C3—22no—
237C2—22no—
238C2C2×#6378011yescharacteristic
239C2#1059383911yescharacteristic
240C2#1059384211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#117C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenter#117#157
hypocenterC32#1531
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
4. #10590159C2semidirect
5. #10590159C2semidirect
199. C32#1531semidirect

Maximal subgroups

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

subgroupindex
#105959882
#105938042
C2×#637772
#105901592
#15319