Finite Group Databasebeta

← #11790591

Subgroups — #11790591

Order 1152.

810 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 94 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
1C2×D4×C3⋊Dic3C211yesmaximal, characteristic
2C2×C22⋊#622C214yesmaximal, complemented
3C2×#63779C211yesmaximal, characteristic, complemented
4C2×#63777C211yesmaximal, characteristic, complemented
5C22×C32×D4C411yescharacteristic
6C23×C3⋊Dic3C2212yes—
7C22×#622C2212yes—
8C22×#622C2212yes—
9C2×#3757C412yes—
10D4×C3⋊Dic3—22no—
11D4×C3⋊Dic3—22no—
12C2×C4⋊(C3⋊Dic3)C411yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C22⋊#622—28no—
15#63779—22no—
16#63777—22no—
17C2×D4×Dic3—62no—
18C24×C32C2×C412yes—
19C2×C32×D4—24no—
20C2×C32×D4—22no—
21C22×C32×C4C2×C411yescharacteristic
22C22×C3⋊Dic3—22no—
23C22×C3⋊Dic3—22no—
24C22×C3⋊Dic3—24no—
25C22×C3⋊Dic3—24no—
26C22×C3⋊Dic3C2×C412yes—
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3C2311yescharacteristic
29C2×#622—22no—
30C2×#622—22no—
31C2×#622—22no—
32C2×#622—24no—
33C2×#622D414yescomplemented
34#3757—24no—
35C4⋊(C3⋊Dic3)—22no—
36C4×C3⋊Dic3D412yes—
37C4×C3⋊Dic3D412yes—
38#1955—91nomaximal, Sylow
39C22×C3×D4—22no—
40C23×Dic3—64no—
41C2×#217—64no—
42D4×Dic3—68no—
43D4×Dic3—68no—
44C2×C4⋊Dic3—62no—
45C2×C4×Dic3—62no—
46C23×C32—22no—
47C23×C32—22no—
48C23×C32—24no—
49C23×C32—24no—
50C23×C32M1614yes—
51C23×C32C22×C411yescharacteristic
52C32×D4—28no—
53C2×C32×C4—22no—
54C2×C32×C4C22⋊C412yes—
55C2×C3⋊Dic3—22no—
56C2×C3⋊Dic3—22no—
57C2×C3⋊Dic3—24no—
58C2×C3⋊Dic3—44no—
59C2×C3⋊Dic3—42no—
60C2×C3⋊Dic3—42no—
61C2×C3⋊Dic3C22⋊C412yes—
62C2×C3⋊Dic3C2×D411yescharacteristic
63C2×C3⋊Dic3C2×D412yes—
64C2×C3⋊Dic3C2×D411yescharacteristic
65C2×C3⋊Dic3#4112yes—
66#622—24no—
67#622—42no—
68C2×C4×D4—91no—
69C2×C4⋊C8—91no—
70C2×C22⋊C8—94no—
71C2×#97—91no—
72C24×C3—24no—
73C2×C3×D4—28no—
74C2×C3×D4—216no—
75C22×C3×C4—22no—
76C22×Dic3—62no—
77C22×Dic3—62no—
78C22×Dic3—64no—
79C22×Dic3—68no—
80C22×Dic3—68no—
81C22×Dic3—128no—
82C22×Dic3—128no—
83#217—616no—
84C4⋊Dic3—68no—
85C4×Dic3—64no—
86C4×Dic3—64no—
87C22×C32—24no—
88C22×C32—28no—
89C22×C32—42no—
90C22×C32—42no—
91C22×C32—44no—
92C22×C32C2×C22⋊C411yescharacteristic
93C22×C32C4×D412yes—
94C22×C32C2×M1612yes—
95C22×C32#13112yes—
96C32×C4—22no—
97C3⋊Dic3—22no—
98C3⋊Dic3—42no—
99C3⋊Dic3#12112yes—
100C3⋊Dic3#12411yescharacteristic
101C3⋊Dic3#12711yescharacteristic
102C22×D4#15711yescharacteristic
103C23×C4—92no—
104C22×C8—92no—
105C22×C8—92no—
106C4×D4—182no—
107C4×D4—182no—
108C2×C4⋊C4—91no—
109C2×C22⋊C4—92no—
110C2×C42—91no—
111C4⋊C8—182no—
112C22⋊C8—188no—
113#97—182no—
114C23×C3—28no—
115C23×C3—28no—
116C23×C3—22no—
117C23×C3—28no—
118C23×C3—48no—
119C23×C3—48no—
120C3×D4—232no—
121C2×C3×C4—28no—
122C2×C3×C4—24no—
123C2×Dic3—62no—
124C2×Dic3—62no—
125C2×Dic3—64no—
126C2×Dic3—64no—
127C2×Dic3—64no—
128C2×Dic3—68no—
129C2×Dic3—124no—
130C2×Dic3—128no—
131C2×Dic3—1216no—
132C2×Dic3—128no—
133C2×Dic3—128no—
134C2×C32—44no—
135C2×C32#39011yescharacteristic
136C2×C32#40711yescharacteristic
137C2×C32#40811yescharacteristic
138C2×C32#43514yes—
139C24C2×#15712yes—
140C2×D4—24no—
141C2×D4—22no—
142C22×C4—91no—
143C22×C4—91no—
144C22×C4—92no—
145C22×C4—184no—
146C22×C4—182no—
147C22×C4—182no—
148C22×C4—184no—
149C22×C4C2×#15711yescharacteristic
150C2×C8—94no—
151C2×C8—182no—
152C2×C8—182no—
153C2×C8—184no—
154C2×C8—182no—
155C4⋊C4—182no—
156C22⋊C4—184no—
157C42—92no—
158C42—92no—
159C22×C3—216no—
160C22×C3—24no—
161C22×C3—24no—
162C22×C3—24no—
163C22×C3—22no—
164C22×C3—416no—
165C22×C3—48no—
166C22×C3—416no—
167C22×C3—48no—
168C3×C4—28no—
169Dic3—64no—
170Dic3—62no—
171Dic3—62no—
172Dic3—124no—
173Dic3—128no—
174C32#195511yescharacteristic, complemented, Sylow
175C23—24no—
176C23—24no—
177C23—22no—
178C23—22no—
179C23#379214yes—
180C23C22×#15711yescharacteristic
181D4—28no—
182C2×C4—22no—
183C2×C4—92no—
184C2×C4—92no—
185C2×C4—91no—
186C2×C4—91no—
187C2×C4—92no—
188C2×C4—182no—
189C2×C4—184no—
190C2×C4—182no—
191C2×C4—364no—
192C2×C4—362no—
193C2×C4—362no—
194C2×C4C22⋊#15712yes—
195C8—184no—
196C8—362no—
197C2×C3—28no—
198C2×C3—22no—
199C2×C3—22no—
200C2×C3—22no—
201C2×C3—416no—
202C22—28no—
203C22—24no—
204C22—44no—
205C22—42no—
206C22—42no—
207C22#6428712yes—
208C22D4×#15712yes—
209C22C2×#379212yes—
210C22C2×C22⋊#15711yescharacteristic
211C4—22no—
212C4—92no—
213C4—91no—
214C4—91no—
215C4—182no—
216C4—362no—
217C3—22no—
218C2—44no—
219C2#1059382014yes—
220C2#1059382311yescharacteristic
221C2#1059382711yescharacteristic
222C2#1059384511yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutator, socleC23×C32C22×C4
Fitting, prime radicalC22×C32×D4C4
cosocleC22×C3⋊Dic3C23
hypercenterC22×D4#157
hypocenterC32#1955
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊#622C2semidirect
3. C2×#63779C2semidirect
4. C2×#63777C2semidirect
33. C2×#622D4semidirect
174. C32#1955semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C3⋊Dic32
C2×C22⋊#6222
C2×#637792
C2×#637772
#19559