Finite Group Databasebeta

← #11785923

Subgroups — #11785923

Order 1152.

610 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 62 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#10595957C211yesmaximal, characteristic
2C2×#63788C212yesmaximal
3#10590156C214yesmaximal, complemented
4C22×#638C2211yescharacteristic
5C2×#3792C2214yes—
6C2×C32×C22⋊C4C411yescharacteristic
7C2×#3757C411yescharacteristic
8C4×#638—22no—
9#64090—22no—
10C22⋊C4×C3⋊D3C412yes—
11#64086C2212yes—
12#63788—22no—
13#63788—22no—
14#5486—62no—
15C24×C32C2×C411yescharacteristic
16C23×C3⋊D3C2×C411yescharacteristic
17C22×C32×C4—21no—
18C2×#638—24no—
19C2×#638D412yes—
20C2×#638D412yes—
21C22×C3⋊Dic3—21no—
22C22×C3⋊Dic3C2311yescharacteristic
23C2×C4×C3⋊D3—22no—
24#3792—24no—
25#3792—24no—
26C2×#622—24no—
27C32×C22⋊C4—21no—
28C32×C22⋊C4C2×C412yes—
29#3757—21no—
30#3757C2×C412yes—
31#3752—22no—
32#3750—22no—
33C4×C3⋊Dic3—22no—
34#1829—91nomaximal, Sylow
35C22×#67—62no—
36C2×C3×C22⋊C4—22no—
37C2×#217—62no—
38C4×#67—68no—
39#67⋊C4—68no—
40D3×C22⋊C4—64no—
41#877—64no—
42C23×C32—22no—
43C23×C32—81no—
44C23×C32C22⋊C411yescharacteristic
45C23×C32C22⋊C411yescharacteristic
46C23×C32C22×C411yescharacteristic
47C22×C3⋊D3—22no—
48C22×C3⋊D3—81no—
49C22×C3⋊D3C22⋊C412yes—
50C2×C32×C4—22no—
51C2×C32×C4—81no—
52#638—24no—
53#638—24no—
54C2×C3⋊Dic3—22no—
55C2×C3⋊Dic3—81no—
56C2×C3⋊Dic3C2×D412yes—
57C2×C3⋊Dic3#4114yes—
58C4×C3⋊D3—82no—
59#622—44no—
60#518—91no—
61C2×#100—92no—
62#344—94no—
63C24×C3—22no—
64C23×D3—62no—
65C22×C3×C4—24no—
66C2×#67—64no—
67C2×#67—64no—
68C2×#67—616no—
69C22×Dic3—62no—
70C22×Dic3—64no—
71C2×C4×D3—68no—
72C3×C22⋊C4—24no—
73C3×C22⋊C4—24no—
74#217—64no—
75#217—64no—
76(C2×D3)⋊C4—68no—
77Dic3⋊C4—68no—
78C4×Dic3—68no—
79C22×C32—21no—
80C22×C32—21no—
81C22×C32—41no—
82C22×C32—41no—
83C22×C32—41no—
84C22×C32—82no—
85C22×C32C2×C22⋊C411yescharacteristic
86C22×C32#11712yes—
87C2×C3⋊D3—22no—
88C2×C3⋊D3—42no—
89C2×C3⋊D3—82no—
90C32×C4—42no—
91C3⋊Dic3—42no—
92C3⋊Dic3#12314yes—
93C22×D4—91no—
94C2×M16—94no—
95C4×D4—182no—
96C4×D4—182no—
97#117—92no—
98C2×C22⋊C4—91no—
99C2×C22⋊C4—92no—
100C2×C22⋊C4#15711yescharacteristic
101#100—182no—
102#100—182no—
103C23×C3—28no—
104C23×C3—22no—
105C23×C3—22no—
106C23×C3—22no—
107C23×C3—84no—
108C22×D3—64no—
109C22×D3—68no—
110C22×D3—244no—
111C2×C3×C4—28no—
112C2×C3×C4—84no—
113#67—616no—
114#67—616no—
115C2×Dic3—64no—
116C2×Dic3—68no—
117C2×Dic3—68no—
118C2×Dic3—244no—
119C4×D3—248no—
120C2×C32—21no—
121C2×C32—22no—
122C2×C32—41no—
123C2×C32—41no—
124C2×C32#38111yescharacteristic
125C3⋊D3—42no—
126C24—91no—
127C24C2×#15711yescharacteristic
128C2×D4—92no—
129C2×D4—92no—
130C2×D4—184no—
131C22×C4—21no—
132C22×C4—91no—
133C22×C4—182no—
134C22×C4—181no—
135M16—184no—
136M16—184no—
137C2×C8—184no—
138C4⋊C4—182no—
139C22⋊C4—21no—
140C22⋊C4—92no—
141C22⋊C4—182no—
142C22⋊C4—181no—
143C22⋊C4C2×#15712yes—
144C42—182no—
145C22×C3—24no—
146C22×C3—24no—
147C22×C3—24no—
148C22×C3—22no—
149C22×C3—44no—
150C22×C3—44no—
151C22×C3—44no—
152C22×C3—88no—
153C2×D3—68no—
154C2×D3—128no—
155C2×D3—248no—
156C3×C4—48no—
157Dic3—68no—
158Dic3—128no—
159C32#182911yescharacteristic, complemented, Sylow
160C23—22no—
161C23—81no—
162C23—92no—
163C23—182no—
164C23—721no—
165C23C22⋊#15711yescharacteristic
166C23C22⋊#15711yescharacteristic
167C23C22×#15711yescharacteristic
168D4—184no—
169D4—184no—
170C2×C4—22no—
171C2×C4—81no—
172C2×C4—94no—
173C2×C4—92no—
174C2×C4—182no—
175C2×C4—722no—
176C2×C4—721no—
177C8—364no—
178C2×C3—24no—
179C2×C3—22no—
180C2×C3—44no—
181C2×C3—44no—
182C2×C3—44no—
183D3—128no—
184C22—21no—
185C22—21no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—82no—
190C22—182no—
191C22—362no—
192C22—722no—
193C22#6428612yes—
194C22C2×C22⋊#15711yescharacteristic
195C4—42no—
196C4—94no—
197C4—362no—
198C3—22no—
199C2—21no—
200C2—22no—
201C2—41no—
202C2—41no—
203C2—362no—
204C2#1059381111yescharacteristic
subgroupG/H
centerC2#10593811
commutatorC23×C32C22×C4
FrattiniC23C22×#157
FittingC2×C32×C22⋊C4C4
socleC2×C32#381
prime radicalC22×#638C22
cosocleC22×C3⋊Dic3C23
hypercenterC2×C22⋊C4#157
hypocenterC32#1829
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #10590156C2semidirect
159. C32#1829semidirect

Maximal subgroups

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

subgroupindex
#105959572
C2×#637882
#105901562
#18299