Finite Group Databasebeta

← #11790810

Subgroups — #11790810

Order 1152.

630 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 70 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#10596187C211yesmaximal, characteristic
2C2×#63783C214yesmaximal, complemented
3#10593733C211yesmaximal, characteristic, complemented
4#10593729C211yesmaximal, characteristic, complemented
5C2×#3830C2212yes—
6C2×C4×#157C2212yes—
7C2×#3788C2212yes—
8C32×#127C411yescharacteristic, complemented
9#64147—22no—
10#64145C412yescomplemented
11D4×C3⋊Dic3—22no—
12C42×C3⋊D3C2211yescharacteristic
13#64078C411yescharacteristic, complemented
14#63783—28no—
15#63781—22no—
16#63779—22no—
17#5716—62no—
18C22×#157—22no—
19C2×C32×D4—22no—
20C2×C32×D4C2×C412yes—
21C2×#638—22no—
22C22×C3⋊Dic3—22no—
23#3830—24no—
24#3830—24no—
25C2×C4×C3⋊D3D412yes—
26C2×C4×C3⋊D3C2311yescharacteristic
27C2×#634C2×C412yes—
28C2×#622—22no—
29C4×#157—22no—
30C4×#157D414yescomplemented
31#3788—24no—
32C32×C42C2×C411yescharacteristic
33#3757—24no—
34C4⋊(C3⋊Dic3)—22no—
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3D412yes—
37#1963—91nomaximal, Sylow
38C2×#237—64no—
39C3×#127—22no—
40#938—68no—
41#936—64no—
42D4×Dic3—68no—
43C42×D3—62no—
44#869—62no—
45C23×C32—22no—
46C22×C3⋊D3C2×D411yescharacteristic
47C2×#157—24no—
48C2×#157—44no—
49C32×D4—24no—
50C32×D4—44no—
51C2×C32×C4C22⋊C412yes—
52C2×C32×C4C22×C411yescharacteristic
53#638—44no—
54C2×C3⋊Dic3—22no—
55C2×C3⋊Dic3—42no—
56C2×C3⋊Dic3—42no—
57C2×C3⋊Dic3C22⋊C412yes—
58C2×C3⋊Dic3C2×D411yescharacteristic
59C4×C3⋊D3—42no—
60C4×C3⋊D3C2×D412yes—
61C4×C3⋊D3#4112yes—
62#634—24no—
63#622—42no—
64#532—91no—
65#423—91no—
66C2×#104—94no—
67#376—91no—
68C2×C3×D4—28no—
69C2×C3×D4—24no—
70C2×#67—68no—
71C22×Dic3—68no—
72#237—128no—
73#237—128no—
74C2×C4×D3—62no—
75C2×C4×D3—64no—
76C2×Dic6—64no—
77C3×C42—22no—
78#217—616no—
79C4⋊Dic3—68no—
80C4×Dic3—62no—
81C4×Dic3—64no—
82C22×C32—42no—
83C22×C32—44no—
84C22×C32C2×C22⋊C411yescharacteristic
85C2×C3⋊D3—22no—
86C2×C3⋊D3#12112yes—
87#157—44no—
88C32×C4—22no—
89C32×C4C4×D412yes—
90C3⋊Dic3—22no—
91C3⋊Dic3—42no—
92C3⋊Dic3#12411yescharacteristic
93C3⋊Dic3#12711yescharacteristic
94C2×#41—92no—
95C2×M16—92no—
96C4⋊Q8—91no—
97#127#15711yescharacteristic, complemented
98#124—92no—
99#121—182no—
100C4×D4—182no—
101C2×C42—91no—
102C2×C42—92no—
103C4⋊C8—182no—
104#104—188no—
105#95—182no—
106C23×C3—28no—
107C22×D3—62no—
108C3×D4—48no—
109C3×D4—416no—
110C2×C3×C4—22no—
111C2×C3×C4—24no—
112#67—1216no—
113C2×Dic3—62no—
114C2×Dic3—64no—
115C2×Dic3—68no—
116C2×Dic3—128no—
117C2×Dic3—128no—
118C4×D3—64no—
119C4×D3—64no—
120C4×D3—128no—
121Dic6—128no—
122C2×C32—82no—
123C2×C32#39011yescharacteristic
124C2×C32#42112yes—
125C3⋊D3—22no—
126#41—184no—
127#41—184no—
128C2×Q8—92no—
129C2×D4—22no—
130C2×D4—182no—
131C2×D4C2×#15712yes—
132C22×C4—91no—
133C22×C4—92no—
134C22×C4—182no—
135C22×C4—182no—
136M16—184no—
137C2×C8—182no—
138C4⋊C4—182no—
139C22⋊C4—184no—
140C42—91no—
141C42—92no—
142C42—94no—
143C42—182no—
144C42C2×#15711yescharacteristic
145C22×C3—22no—
146C22×C3—48no—
147C22×C3—416no—
148C2×D3—64no—
149C2×D3—124no—
150C3×C4—28no—
151C3×C4—24no—
152Dic3—62no—
153Dic3—62no—
154Dic3—124no—
155Dic3—128no—
156C32#196311yescharacteristic, complemented, Sylow
157C23—22no—
158C23—91no—
159Q8—184no—
160D4—24no—
161D4—44no—
162D4—364no—
163C2×C4—91no—
164C2×C4—92no—
165C2×C4—92no—
166C2×C4—92no—
167C2×C4—184no—
168C2×C4—182no—
169C2×C4—362no—
170C2×C4—362no—
171C2×C4—362no—
172C2×C4—364no—
173C2×C4C22⋊#15712yes—
174C2×C4C22×#15711yescharacteristic
175C8—362no—
176C2×C3—24no—
177C2×C3—22no—
178C2×C3—88no—
179D3—124no—
180C22—44no—
181C22—42no—
182C22—92no—
183C22—182no—
184C22C2×C22⋊#15711yescharacteristic
185C4—22no—
186C4—91no—
187C4—91no—
188C4—182no—
189C4—364no—
190C4—362no—
191C4D4×#15712yes—
192C3—22no—
193C2—82no—
194C2—182no—
195C2#1059381612yes—
196C2#1059382711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#127C4
socleC22×C32C2×C22⋊C4
prime radical#10596187C2
cosocleC2×C4×C3⋊D3C23
hypercenter#127#157
hypocenterC32#1963
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. C2×#63783C2semidirect
3. #10593733C2semidirect
4. #10593729C2semidirect
8. C32×#127C4semidirect
10. #64145C4semidirect
13. #64078C4semidirect
30. C4×#157D4semidirect
97. #127#157semidirect
156. C32#1963semidirect

Maximal subgroups

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

subgroupindex
#105961872
C2×#637832
#105937332
#105937292
#19639