Finite Group Databasebeta

← #11796529

Subgroups — #11796529

Order 1152.

500 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 52 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#10596195C211yesmaximal, characteristic
2#10593836C212yesmaximal, complemented
3#10590218C212yesmaximal, complemented
4#10590145C212yesmaximal, complemented
5C2×#3832C411yescharacteristic
6C2×Q8×C3⋊D3C2211yescharacteristic
7#64283—22no—
8C32×C4⋊Q8C411yescharacteristic
9#64156C411yescharacteristic
10#64153C2211yescharacteristic
11#64105—22no—
12#64103—22no—
13#64084C2211yescharacteristic
14#64081C411yescharacteristic
15#63780—22no—
16#63780C2214yes—
17#5724—62no—
18C2×C32×Q8C2×C411yescharacteristic
19C2×C32×Q8C2×C411yescharacteristic
20#3832—42no—
21Q8×C3⋊D3—42no—
22C2×C4⋊(C3⋊D3)—21no—
23C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
24C2×C4×C3⋊D3—21no—
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×C4×C3⋊D3D412yes—
27C2×#634D412yes—
28C2×#634C2311yescharacteristic
29#3792—24no—
30#3788—42no—
31#3787—42no—
32C32×C4⋊C4—22no—
33C32×C42C2×C411yescharacteristic
34#3752—21no—
35#3752—22no—
36#3752—22no—
37#3750—21no—
38#3750—22no—
39C4×C3⋊Dic3C2×C411yescharacteristic
40#2133—91nomaximal, Sylow
41C2×#239—62no—
42C2×D3×Q8—62no—
43C3×C4⋊Q8—22no—
44#947—62no—
45#944—62no—
46#896—68no—
47#894—68no—
48#875—62no—
49#872—62no—
50C22×C3⋊D3—21no—
51C22×C3⋊D3C22⋊C411yescharacteristic
52C32×Q8—41no—
53C32×Q8—41no—
54C2×C32×C4—21no—
55C2×C32×C4—21no—
56C2×C32×C4C22⋊C412yes—
57C2×C32×C4C22×C411yescharacteristic
58C2×C3⋊Dic3—21no—
59C2×C3⋊Dic3C22⋊C411yescharacteristic
60C2×C3⋊Dic3C2×D412yes—
61C4⋊(C3⋊D3)—41no—
62C4⋊(C3⋊D3)—42no—
63C4×C3⋊D3—22no—
64C4×C3⋊D3—22no—
65C4×C3⋊D3—22no—
66C4×C3⋊D3—42no—
67#634—42no—
68#634—41no—
69#622—44no—
70#536—91no—
71C2×#101—92no—
72#356—92no—
73#355—92no—
74C2×C3×Q8—22no—
75C2×C3×Q8—22no—
76#239—128no—
77D3×Q8—128no—
78C2×D12—62no—
79C2×D12—64no—
80C2×C4×D3—62no—
81C2×C4×D3—64no—
82C2×C4×D3—64no—
83C2×Dic6—62no—
84C2×Dic6—64no—
85C3×C4⋊C4—28no—
86C3×C42—22no—
87(C2×D3)⋊C4—64no—
88(C2×D3)⋊C4—68no—
89(C2×D3)⋊C4—68no—
90Dic3⋊C4—64no—
91Dic3⋊C4—68no—
92C4×Dic3—62no—
93C22×C32C2×C22⋊C411yescharacteristic
94C2×C3⋊D3—41no—
95C2×C3⋊D3—42no—
96C2×C3⋊D3—41no—
97C2×C3⋊D3#9912yes—
98C32×C4—21no—
99C32×C4—22no—
100C32×C4—41no—
101C32×C4—41no—
102C3⋊Dic3—21no—
103C3⋊Dic3—22no—
104C3⋊Dic3—41no—
105C2×#41—91no—
106C22×Q8—91no—
107C2×M16—182no—
108C4⋊Q8—91no—
109C4⋊Q8#15711yescharacteristic
110#124—91no—
111#124—91no—
112#123—182no—
113C22⋊Q8—182no—
114#117—91no—
115#101—94no—
116#101—182no—
117C22×D3—62no—
118C22×D3—64no—
119C3×Q8—44no—
120C3×Q8—44no—
121C2×C3×C4—24no—
122C2×C3×C4—24no—
123C2×C3×C4—22no—
124C2×C3×C4—24no—
125C2×Dic3—62no—
126C2×Dic3—64no—
127C2×Dic3—64no—
128D12—124no—
129D12—128no—
130C4×D3—68no—
131C4×D3—124no—
132C4×D3—124no—
133C4×D3—128no—
134Dic6—128no—
135Dic6—124no—
136C2×C32—21no—
137C2×C32C2×#9911yescharacteristic
138C3⋊D3—22no—
139C3⋊D3—81no—
140#41—362no—
141C2×Q8—91no—
142C2×Q8—92no—
143C2×Q8—362no—
144C2×Q8C2×#15711yescharacteristic
145C2×Q8C2×#15711yescharacteristic
146C2×D4—91no—
147C2×D4—181no—
148C22×C4—91no—
149C22×C4—92no—
150C22×C4—181no—
151M16—184no—
152M16—362no—
153C2×C8—362no—
154C4⋊C4—22no—
155C4⋊C4—181no—
156C4⋊C4—182no—
157C22⋊C4—182no—
158C22⋊C4—181no—
159C22⋊C4—182no—
160C42—91no—
161C42C2×#15711yescharacteristic
162C22×C3—22no—
163C2×D3—64no—
164C2×D3—124no—
165C2×D3—124no—
166C2×D3—128no—
167C3×C4—24no—
168C3×C4—44no—
169C3×C4—44no—
170C3×C4—44no—
171Dic3—64no—
172Dic3—124no—
173Dic3—124no—
174C32#213311yescharacteristic, complemented, Sylow
175C23—91no—
176C23—181no—
177Q8—41no—
178Q8—41no—
179Q8—361no—
180Q8—362no—
181D4—361no—
182D4—362no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—92no—
186C2×C4—91no—
187C2×C4—182no—
188C2×C4—182no—
189C2×C4—182no—
190C2×C4—181no—
191C2×C4—362no—
192C2×C4C22⋊#15712yes—
193C2×C4C22×#15711yescharacteristic
194C8—364no—
195C2×C3—24no—
196C2×C3—22no—
197D3—124no—
198D3—244no—
199C22—92no—
200C22—361no—
201C22—362no—
202C22—361no—
203C22C2×C22⋊#15711yescharacteristic
204C4—21no—
205C4—22no—
206C4—41no—
207C4—41no—
208C4—182no—
209C4—181no—
210C4—361no—
211C3—22no—
212C2—21no—
213C2—182no—
214C2—721no—
215C2#1059381711yescharacteristic
subgroupG/H
centerC2#10593817
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4⋊Q8C4
socleC2×C32C2×#99
prime radicalC2×#3832C4
cosocleC2×#634C23
hypercenterC4⋊Q8#157
hypocenterC32#2133
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10593836C2semidirect
3. #10590218C2semidirect
4. #10590145C2semidirect
174. C32#2133semidirect

Maximal subgroups

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

subgroupindex
#105961952
#105938362
#105902182
#105901452
#21339