Finite Group Databasebeta

← #11772573

Subgroups — #11772573

Order 1152.

324 conjugacy classes of subgroups; only the 38 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 38 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#10593822C211yesmaximal, characteristic
2#10593818C211yesmaximal, characteristic
3#10592439C211yesmaximal, characteristic
4C2×#3830C2211yescharacteristic
5C2×#3792C411yescharacteristic, complemented
6C22×#622C411yescharacteristic, complemented
7#64286—21no—
8#64086—21no—
9C22⋊#622—21no—
10#63786—21no—
11#63786C412yescomplemented
12#63778—21no—
13C32×#99C411yescharacteristic, complemented
14#63661C411yescharacteristic, complemented
15#63633—21no—
16#4740—62no—
17C2×C32×D4C2×C411yescharacteristic
18C2×#638C2×C411yescharacteristic
19C2×#638D411yescharacteristic
20C22×C3⋊Dic3C2×C411yescharacteristic
21C22×C3⋊Dic3D411yescharacteristic
22#3830—41no—
23#3830—41no—
24C2×C4×C3⋊D3D411yescharacteristic
25C2×#634Q811yescharacteristic
26C22⋊#157—22no—
27#3792—41no—
28C2×#622—21no—
29C2×#622—21no—
30C2×#622—41no—
31C4⋊#157—41no—
32C4×#157—41no—
33C32×C22⋊C4—21no—
34#3757—21no—
35#3750—41no—
36C4×C3⋊Dic3—41no—
37#1391—91nomaximal, Sylow
38C2×#237—62no—
39#877—64no—
40C3×#99—22no—
41#834—62no—
42#806—64no—
43C23×C32C4211yescharacteristic
44C23×C32C22⋊C411yescharacteristic
45C22×C3⋊D3C22⋊C411yescharacteristic
46C2×#157—42no—
47C32×D4—41no—
48C2×C32×C4—41no—
49C2×C32×C4C4⋊C411yescharacteristic
50#638—41no—
51#638—41no—
52C2×C3⋊Dic3—21no—
53C2×C3⋊Dic3—21no—
54C2×C3⋊Dic3—21no—
55C2×C3⋊Dic3—21no—
56C2×C3⋊Dic3—41no—
57C2×C3⋊Dic3C22⋊C411yescharacteristic
58C2×C3⋊Dic3C4⋊C411yescharacteristic
59C2×C3⋊Dic3C4⋊C411yescharacteristic
60C4×C3⋊D3—21no—
61C4×C3⋊D3—21no—
62#634—41no—
63#622—41no—
64#622—41no—
65#410—91no—
66#410—91no—
67#408—91no—
68C2×C3×D4—22no—
69C2×#67—62no—
70C2×#67—62no—
71C22×Dic3—62no—
72C22×Dic3—62no—
73#237—124no—
74#237—124no—
75C2×C4×D3—62no—
76C2×Dic6—62no—
77C3×C22⋊C4—24no—
78#217—64no—
79Dic3⋊C4—124no—
80C4×Dic3—124no—
81C22×C32—21no—
82C22×C32—21no—
83C22×C32—41no—
84C22×C32—41no—
85C22×C32#9511yescharacteristic
86C2×C3⋊D3—21no—
87C2×C3⋊D3—41no—
88#157—82no—
89C32×C4—21no—
90C32×C4—81no—
91C3⋊Dic3—21no—
92C3⋊Dic3—21no—
93C3⋊Dic3—81no—
94C3⋊Dic3#9911yescharacteristic
95C3⋊Dic3#9911yescharacteristic
96C2×#41—91no—
97C2×M16—91no—
98C22×C8—91no—
99#117—181no—
100#117—181no—
101#99—92no—
102#99—91no—
103#99—181no—
104#99—181no—
105#99#15711yescharacteristic, complemented
106C22⋊C8—181no—
107C22⋊C8—181no—
108C23×C3—22no—
109C23×C3—22no—
110C22×D3—62no—
111C3×D4—44no—
112C2×C3×C4—22no—
113C2×C3×C4—44no—
114#67—124no—
115#67—124no—
116C2×Dic3—62no—
117C2×Dic3—62no—
118C2×Dic3—62no—
119C2×Dic3—64no—
120C2×Dic3—64no—
121C2×Dic3—122no—
122C2×Dic3—122no—
123C2×Dic3—124no—
124C4×D3—122no—
125C4×D3—122no—
126Dic6—124no—
127C2×C32—21no—
128C2×C32—41no—
129C2×C32—41no—
130C2×C32#34211yescharacteristic
131C3⋊D3—41no—
132#41—361no—
133#41—361no—
134C2×Q8—91no—
135C2×D4—91no—
136C2×D4—91no—
137C2×D4C2×#15711yescharacteristic
138C22×C4—91no—
139C22×C4—91no—
140C22×C4—91no—
141M16—361no—
142C2×C8—181no—
143C2×C8—181no—
144C2×C8—361no—
145C4⋊C4—361no—
146C4⋊C4—361no—
147C22⋊C4—21no—
148C22⋊C4—182no—
149C22⋊C4—181no—
150C42—361no—
151C42—361no—
152C22×C3—24no—
153C22×C3—22no—
154C22×C3—42no—
155C22×C3—82no—
156C22×C3—82no—
157C2×D3—122no—
158C2×D3—242no—
159C3×C4—42no—
160C3×C4—84no—
161Dic3—62no—
162Dic3—62no—
163Dic3—64no—
164Dic3—122no—
165Dic3—244no—
166C32#139111yescharacteristic, complemented, Sylow
167C23—91no—
168C23C4×#15711yescharacteristic
169C23C22⋊#15711yescharacteristic
170Q8—361no—
171D4—41no—
172D4—361no—
173D4—361no—
174C2×C4—41no—
175C2×C4—91no—
176C2×C4—91no—
177C2×C4—91no—
178C2×C4—181no—
179C2×C4—181no—
180C2×C4—181no—
181C2×C4—181no—
182C2×C4—181no—
183C2×C4—181no—
184C2×C4—361no—
185C2×C4—362no—
186C2×C4C4⋊#15711yescharacteristic
187C8—361no—
188C8—361no—
189C2×C3—22no—
190C2×C3—42no—
191C2×C3—44no—
192C2×C3—82no—
193D3—242no—
194C22—21no—
195C22—21no—
196C22—41no—
197C22—41no—
198C22—181no—
199C22—361no—
200C22#6378111yescharacteristic
201C4—21no—
202C4—81no—
203C4—91no—
204C4—91no—
205C4—181no—
206C4—181no—
207C4—721no—
208C4—722no—
209C3—22no—
210C2—21no—
211C2—41no—
212C2—41no—
213C2—361no—
214C2#1059015511yescharacteristic
subgroupG/H
centerC2#10590155
commutatorC23×C32C42
FrattiniC2×D4C2×#157
FittingC32×#99C4
socleC2×C32#342
prime radical, cosocleC2×#3830C22
hypercenter#99#157
hypocenterC32#1391
LCSG ▷ C23×C32 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
5. C2×#3792C4semidirect
6. C22×#622C4semidirect
11. #63786C4semidirect
13. C32×#99C4semidirect
14. #63661C4semidirect
105. #99#157semidirect
166. C32#1391semidirect

Maximal subgroups

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

subgroupindex
#105938222
#105938182
#105924392
#13919