Finite Group Databasebeta

← #11790562

Subgroups — #11790562

Order 1152.

822 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 118 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×C4⋊#622C211yesmaximal, characteristic, complemented
4C2×C4×#622C211yesmaximal, 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—
15C4⋊#622—22no—
16C4×#622—22no—
17C2×D4×Dic3—62no—
18C24×C32C2×C412yes—
19C2×C32×D4—22no—
20C2×C32×D4—22no—
21C2×C32×D4C814yescomplemented
22C22×C32×C4C2×C411yescharacteristic
23C22×C3⋊Dic3—22no—
24C22×C3⋊Dic3—22no—
25C22×C3⋊Dic3—24no—
26C22×C3⋊Dic3—24no—
27C22×C3⋊Dic3C2×C412yes—
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3C2311yescharacteristic
30C2×#622—22no—
31C2×#622—22no—
32C2×#622—22no—
33C2×#622—24no—
34C2×#622D414yescomplemented
35#3757—24no—
36C4⋊(C3⋊Dic3)—22no—
37C4×C3⋊Dic3D412yes—
38C4×C3⋊Dic3D412yes—
39#1954—91nomaximal, Sylow
40C22×C3×D4—22no—
41C23×Dic3—64no—
42C2×#217—64no—
43D4×Dic3—68no—
44D4×Dic3—68no—
45C2×C4⋊Dic3—62no—
46C2×C4×Dic3—62no—
47C23×C32—22no—
48C23×C32—22no—
49C23×C32—24no—
50C23×C32—24no—
51C23×C32C2×C814yes—
52C23×C32C22×C411yescharacteristic
53C32×D4—28no—
54C2×C32×C4C22⋊C412yes—
55C2×C32×C4C2×C812yes—
56C2×C32×C4M1612yes—
57C2×C3⋊Dic3—22no—
58C2×C3⋊Dic3—22no—
59C2×C3⋊Dic3—24no—
60C2×C3⋊Dic3—44no—
61C2×C3⋊Dic3—42no—
62C2×C3⋊Dic3—42no—
63C2×C3⋊Dic3C22⋊C412yes—
64C2×C3⋊Dic3C2×D411yescharacteristic
65C2×C3⋊Dic3C2×D412yes—
66C2×C3⋊Dic3C2×D411yescharacteristic
67C2×C3⋊Dic3#4112yes—
68#622—24no—
69#622—42no—
70C2×C4×D4—91no—
71C2×C4⋊C8—91no—
72C2×C22⋊C8—94no—
73C2×C4×C8—91no—
74C24×C3—24no—
75C2×C3×D4—28no—
76C2×C3×D4—28no—
77C2×C3×D4—28no—
78C22×C3×C4—22no—
79C22×Dic3—62no—
80C22×Dic3—62no—
81C22×Dic3—64no—
82C22×Dic3—68no—
83C22×Dic3—68no—
84C22×Dic3—128no—
85C22×Dic3—128no—
86#217—616no—
87C4⋊Dic3—68no—
88C4×Dic3—64no—
89C4×Dic3—64no—
90C22×C32—24no—
91C22×C32—28no—
92C22×C32—42no—
93C22×C32—42no—
94C22×C32—44no—
95C22×C32C2×C22⋊C411yescharacteristic
96C22×C32C4×D412yes—
97C22×C32C22×C811yescharacteristic
98C22×C32C2×M1611yescharacteristic
99C22×C32#13112yes—
100C32×C4C22⋊C814yescomplemented
101C3⋊Dic3—22no—
102C3⋊Dic3—42no—
103C3⋊Dic3#12112yes—
104C3⋊Dic3#12411yescharacteristic
105C3⋊Dic3#12711yescharacteristic
106C22×D4#15711yescharacteristic
107C23×C4—92no—
108C22×C8—92no—
109C22×C8—92no—
110C4×D4—182no—
111C4×D4—182no—
112C2×C4⋊C4—91no—
113C2×C22⋊C4—92no—
114C2×C42—91no—
115C4⋊C8—182no—
116C22⋊C8—188no—
117C4×C8—182no—
118C23×C3—28no—
119C23×C3—28no—
120C23×C3—22no—
121C23×C3—28no—
122C23×C3—48no—
123C23×C3—48no—
124C3×D4—232no—
125C2×C3×C4—24no—
126C2×C3×C4—24no—
127C2×C3×C4—24no—
128C2×Dic3—62no—
129C2×Dic3—62no—
130C2×Dic3—64no—
131C2×Dic3—64no—
132C2×Dic3—64no—
133C2×Dic3—68no—
134C2×Dic3—124no—
135C2×Dic3—128no—
136C2×Dic3—1216no—
137C2×Dic3—128no—
138C2×Dic3—128no—
139C2×C32—44no—
140C2×C32#39011yescharacteristic
141C2×C32C2×C22⋊C811yescharacteristic
142C2×C32#40811yescharacteristic
143C2×C32C8×D412yes—
144C2×C32#43612yes—
145C24C2×#15712yes—
146C2×D4—22no—
147C2×D4—22no—
148C2×D4#62214yescomplemented
149C22×C4—91no—
150C22×C4—91no—
151C22×C4—92no—
152C22×C4—184no—
153C22×C4—182no—
154C22×C4—182no—
155C22×C4—184no—
156C22×C4C2×#15711yescharacteristic
157C2×C8—94no—
158C2×C8—182no—
159C2×C8—182no—
160C2×C8—184no—
161C2×C8—182no—
162C4⋊C4—182no—
163C22⋊C4—184no—
164C42—92no—
165C42—92no—
166C22×C3—216no—
167C22×C3—24no—
168C22×C3—24no—
169C22×C3—22no—
170C22×C3—22no—
171C22×C3—22no—
172C22×C3—416no—
173C22×C3—48no—
174C22×C3—416no—
175C22×C3—48no—
176C3×C4—28no—
177Dic3—64no—
178Dic3—62no—
179Dic3—62no—
180Dic3—124no—
181Dic3—128no—
182C32#195411yescharacteristic, complemented, Sylow
183C23—24no—
184C23—24no—
185C23—22no—
186C23—22no—
187C23C2×#62214yes—
188C23C22×#15711yescharacteristic
189D4—28no—
190C2×C4—92no—
191C2×C4—92no—
192C2×C4—91no—
193C2×C4—91no—
194C2×C4—92no—
195C2×C4—182no—
196C2×C4—184no—
197C2×C4—182no—
198C2×C4—364no—
199C2×C4—362no—
200C2×C4—362no—
201C2×C4C2×#62212yes—
202C2×C4#379212yes—
203C2×C4C22⋊#15712yes—
204C8—184no—
205C8—362no—
206C2×C3—24no—
207C2×C3—24no—
208C2×C3—22no—
209C2×C3—22no—
210C2×C3—22no—
211C2×C3—416no—
212C22—28no—
213C22—24no—
214C22—44no—
215C22—42no—
216C22—42no—
217C22#6428712yes—
218C22D4×#15712yes—
219C22C22×#62211yescharacteristic
220C22C2×#379211yescharacteristic
221C22C2×C22⋊#15711yescharacteristic
222C4—92no—
223C4—91no—
224C4—91no—
225C4—182no—
226C4—362no—
227C4C22⋊#62214yescomplemented
228C3—22no—
229C2—44no—
230C2D4×#62212yes—
231C2#1059382112yes—
232C2#1059382311yescharacteristic
233C2#1059382711yescharacteristic
234C2C2×C22⋊#62211yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C22×C8
Fitting, prime radicalC22×C32×D4C4
socleC23×C32C22×C4
cosocleC22×C3⋊Dic3C23
hypercenterC22×D4#157
hypocenterC32#1954
LCSG ▷ C22×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×C4⋊#622C2semidirect
4. C2×C4×#622C2semidirect
21. C2×C32×D4C8semidirect
34. C2×#622D4semidirect
100. C32×C4C22⋊C8semidirect
148. C2×D4#622semidirect
182. C32#1954semidirect
227. C4C22⋊#622semidirect

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×C4⋊#6222
C2×C4×#6222
#19549