Finite Group Databasebeta

← #11796526

Subgroups — #11796526

Order 1152.

500 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 54 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#10596296C211yesmaximal, characteristic
2C2×#63780C212yesmaximal, complemented
3#10590218C212yesmaximal, complemented
4#10590212C212yesmaximal, complemented
5C2×C32×#41C411yescharacteristic
6C22×#634C2211yescharacteristic
7C2×#3792—22no—
8#64153C411yescharacteristic
9#64153C2211yescharacteristic
10#64145C411yescharacteristic
11#64145C2211yescharacteristic
12#64144—22no—
13#64135C411yescharacteristic
14#64133—22no—
15#63780—22no—
16#63780C2214yes—
17#5825—62no—
18C32×#41—42no—
19C2×C32×Q8C2×C411yescharacteristic
20C2×C32×D4—21no—
21C2×C32×D4C2×C411yescharacteristic
22C22×C32×C4—21no—
23C22×C32×C4C2×C411yescharacteristic
24C22×C3⋊Dic3D412yes—
25C2×#634—42no—
26C2×#634C2×C411yescharacteristic
27C2×#634D412yes—
28C2×#634C2311yescharacteristic
29#3792—24no—
30#3792—42no—
31C2×#622—42no—
32#3757—21no—
33#3757—22no—
34#3757—22no—
35C4⋊(C3⋊Dic3)—21no—
36#3750—22no—
37#3750—22no—
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3C2×C411yescharacteristic
40#2133—91nomaximal, Sylow
41C2×C3×#41—22no—
42C22×Dic6—62no—
43#944—62no—
44#944—62no—
45#936—62no—
46#936—62no—
47#935—68no—
48#926—62no—
49#924—68no—
50C23×C32—21no—
51C23×C32C22⋊C411yescharacteristic
52C32×Q8—41no—
53C32×D4—41no—
54C32×D4—42no—
55C2×C32×C4—22no—
56C2×C32×C4—21no—
57C2×C32×C4—42no—
58C2×C32×C4C22⋊C411yescharacteristic
59C2×C32×C4C22×C411yescharacteristic
60C2×C3⋊Dic3—21no—
61C2×C3⋊Dic3—21no—
62C2×C3⋊Dic3—22no—
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3C22⋊C412yes—
65C2×C3⋊Dic3C2×D412yes—
66#634—41no—
67#634—42no—
68#634—41no—
69#622—44no—
70#536—91no—
71C2×#101—92no—
72#356—92no—
73#355—92no—
74C3×#41—48no—
75C2×C3×Q8—22no—
76C2×C3×D4—24no—
77C2×C3×D4—22no—
78C22×C3×C4—24no—
79C22×C3×C4—22no—
80C22×Dic3—64no—
81C2×Dic6—64no—
82C2×Dic6—62no—
83C2×Dic6—62no—
84C2×Dic6—128no—
85#217—68no—
86#217—68no—
87#217—64no—
88C4⋊Dic3—64no—
89Dic3⋊C4—68no—
90Dic3⋊C4—68no—
91C4×Dic3—62no—
92C4×Dic3—62no—
93C22×C32—41no—
94C22×C32—42no—
95C22×C32—41no—
96C22×C32#9912yes—
97C22×C32C2×C22⋊C411yescharacteristic
98C32×C4—21no—
99C32×C4—21no—
100C32×C4—41no—
101C3⋊Dic3—22no—
102C3⋊Dic3—22no—
103C3⋊Dic3—41no—
104C3⋊Dic3—41no—
105C2×#41#15711yescharacteristic
106C22×Q8—91no—
107C2×M16—182no—
108C4⋊Q8—91no—
109C4⋊Q8—91no—
110#124—91no—
111#124—91no—
112#123—182no—
113C22⋊Q8—182no—
114#117—91no—
115#101—94no—
116#101—182no—
117C23×C3—24no—
118C23×C3—22no—
119C3×Q8—44no—
120C3×D4—44no—
121C3×D4—48no—
122C2×C3×C4—28no—
123C2×C3×C4—24no—
124C2×C3×C4—22no—
125C2×C3×C4—22no—
126C2×C3×C4—48no—
127C2×Dic3—64no—
128C2×Dic3—64no—
129C2×Dic3—64no—
130C2×Dic3—64no—
131C2×Dic3—124no—
132C2×Dic3—124no—
133Dic6—128no—
134Dic6—124no—
135Dic6—124no—
136C2×C32—21no—
137C2×C32—22no—
138C2×C32—81no—
139C2×C32C2×#9911yescharacteristic
140#41—42no—
141C2×Q8—91no—
142C2×Q8—91no—
143C2×Q8—92no—
144C2×Q8—362no—
145C2×Q8C2×#15711yescharacteristic
146C2×D4—21no—
147C2×D4C2×#15711yescharacteristic
148C22×C4—21no—
149C22×C4—92no—
150C22×C4C2×#15711yescharacteristic
151M16—184no—
152M16—362no—
153C2×C8—362no—
154C4⋊C4—182no—
155C4⋊C4—182no—
156C4⋊C4—181no—
157C22⋊C4—182no—
158C22⋊C4—182no—
159C22⋊C4—181no—
160C42—91no—
161C42—91no—
162C22×C3—22no—
163C22×C3—24no—
164C22×C3—44no—
165C22×C3—44no—
166C22×C3—48no—
167C3×C4—24no—
168C3×C4—24no—
169C3×C4—44no—
170Dic3—124no—
171Dic3—124no—
172Dic3—124no—
173Dic3—124no—
174C32#213311yescharacteristic, complemented, Sylow
175C23—21no—
176C23C22⋊#15711yescharacteristic
177Q8—41no—
178Q8—362no—
179Q8—361no—
180Q8—361no—
181D4—41no—
182D4—42no—
183C2×C4—22no—
184C2×C4—21no—
185C2×C4—42no—
186C2×C4—92no—
187C2×C4—92no—
188C2×C4—182no—
189C2×C4—182no—
190C2×C4—181no—
191C2×C4—181no—
192C2×C4C22⋊#15711yescharacteristic
193C2×C4C22×#15711yescharacteristic
194C8—364no—
195C2×C3—24no—
196C2×C3—22no—
197C2×C3—44no—
198C2×C3—84no—
199C22—41no—
200C22—42no—
201C22—41no—
202C22#6378612yes—
203C22C2×C22⋊#15711yescharacteristic
204C4—21no—
205C4—21no—
206C4—41no—
207C4—182no—
208C4—182no—
209C4—361no—
210C4—361no—
211C3—22no—
212C2—21no—
213C2—22no—
214C2—81no—
215C2C2×#6378611yescharacteristic
subgroupG/H
centerC2C2×#63786
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
Fitting, prime radicalC2×C32×#41C4
socleC2×C32C2×#99
cosocleC2×#634C23
hypercenterC2×#41#157
hypocenterC32#2133
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#63780C2semidirect
3. #10590218C2semidirect
4. #10590212C2semidirect
174. C32#2133semidirect

Maximal subgroups

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

subgroupindex
#105962962
C2×#637802
#105902182
#105902122
#21339