Finite Group Databasebeta

← #11774338

Subgroups — #11774338

Order 1152.

546 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 84 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×#64096C211yesmaximal, characteristic
2#10593795C211yesmaximal, characteristic
3#10593795C211yesmaximal, characteristic
4#10590161C214yesmaximal, complemented
5C22×#634C411yescharacteristic
6C2×C32×C4⋊C4C411yescharacteristic
7C2×#3750—21no—
8C2×C4×C3⋊Dic3—21no—
9C2×C4×C3⋊Dic3C2211yescharacteristic
10#64096—21no—
11#64096—21no—
12#64096C412yes—
13#64096C2212yes—
14C22⋊#622—21no—
15C22⋊#622—21no—
16C4⋊#622—21no—
17C4⋊#622C2212yes—
18C4×#622—21no—
19C4×#622C2212yes—
20C2×#887—62no—
21C22×C32×C4—21no—
22C22×C32×C4C2×C411yescharacteristic
23C22×C3⋊Dic3—21no—
24C22×C3⋊Dic3D411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C2×#634—21no—
27C2×#634—22no—
28C2×#634C814yescomplemented
29C2×#634C2×C412yes—
30C2×#622—22no—
31C2×#622—22no—
32C32×C4⋊C4—21no—
33C32×C4⋊C4C2×C412yes—
34#3750—22no—
35#3750—22no—
36C4×C3⋊Dic3—22no—
37C4×C3⋊Dic3—22no—
38C4×C3⋊Dic3C2×C411yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3C2311yescharacteristic
42#1479—91nomaximal, Sylow
43C22×Dic6—62no—
44C2×C3×C4⋊C4—22no—
45C2×Dic3⋊C4—64no—
46C2×C4×Dic3—62no—
47C2×C4×Dic3—64no—
48#887—64no—
49#887—64no—
50#887—64no—
51#887—64no—
52C23×C32C22⋊C411yescharacteristic
53C2×C32×C4—22no—
54C2×C32×C4—42no—
55C2×C32×C4C22⋊C411yescharacteristic
56C2×C32×C4C2×C812yes—
57C2×C32×C4M1612yes—
58C2×C32×C4C22×C411yescharacteristic
59C2×C3⋊Dic3—24no—
60C2×C3⋊Dic3—22no—
61C2×C3⋊Dic3—22no—
62C2×C3⋊Dic3—41no—
63C2×C3⋊Dic3C22⋊C411yescharacteristic
64C2×C3⋊Dic3C22⋊C411yescharacteristic
65C2×C3⋊Dic3C2×D411yescharacteristic
66C2×C3⋊Dic3C2×D411yescharacteristic
67#634—24no—
68#634—22no—
69#634C2×C814yes—
70#622—42no—
71#622—42no—
72C2×C4×Q8—91no—
73#431—91no—
74#431—91no—
75Q8⋊C8—94no—
76C22×C3×C4—24no—
77C22×C3×C4—22no—
78C22×Dic3—62no—
79C22×Dic3—62no—
80C22×Dic3—64no—
81C2×Dic6—64no—
82C2×Dic6—68no—
83C2×Dic6—64no—
84C2×Dic6—68no—
85C3×C4⋊C4—24no—
86C3×C4⋊C4—24no—
87Dic3⋊C4—68no—
88Dic3⋊C4—68no—
89C4×Dic3—62no—
90C4×Dic3—62no—
91C4×Dic3—62no—
92C4×Dic3—62no—
93C4×Dic3—68no—
94C4×Dic3—68no—
95C22×C32—21no—
96C22×C32—21no—
97C22×C32C22⋊C812yes—
98C22×C32C2×C22⋊C411yescharacteristic
99C32×C4—42no—
100C32×C4C22⋊C812yes—
101C32×C4C22×C811yescharacteristic
102C32×C4C2×M1611yescharacteristic
103C3⋊Dic3—24no—
104C3⋊Dic3—21no—
105C3⋊Dic3—21no—
106C3⋊Dic3—21no—
107C3⋊Dic3#13712yes—
108C22×Q8—91no—
109C4×Q8—92no—
110C4×Q8—92no—
111C4×Q8—181no—
112C4×Q8—181no—
113C2×C4⋊C4—181no—
114C2×C4⋊C4#15711yescharacteristic
115C2×C42—91no—
116C2×C42—181no—
117C4⋊C8—92no—
118C4⋊C8—181no—
119C22⋊C8—181no—
120C22⋊C8—181no—
121C4×C8—92no—
122C4×C8—181no—
123C23×C3—22no—
124C2×C3×C4—28no—
125C2×C3×C4—22no—
126C2×C3×C4—24no—
127C2×C3×C4—24no—
128C2×C3×C4—22no—
129C2×C3×C4—48no—
130C2×Dic3—62no—
131C2×Dic3—62no—
132C2×Dic3—62no—
133C2×Dic3—62no—
134C2×Dic3—68no—
135C2×Dic3—616no—
136C2×Dic3—68no—
137C2×Dic3—124no—
138Dic6—68no—
139Dic6—68no—
140Dic6—616no—
141C2×C32—22no—
142C2×C32C2×C22⋊C811yescharacteristic
143C2×C32#41911yescharacteristic
144C2×C32#42111yescharacteristic
145C2×Q8—92no—
146C2×Q8—94no—
147C2×Q8—182no—
148C2×Q8—181no—
149C22×C4—21no—
150C22×C4—91no—
151C22×C4—91no—
152C22×C4—181no—
153C22×C4C2×#15711yescharacteristic
154C2×C8—182no—
155C2×C8—182no—
156C4⋊C4—21no—
157C4⋊C4—182no—
158C4⋊C4—182no—
159C4⋊C4C2×#15712yes—
160C42—91no—
161C42—91no—
162C42—91no—
163C42—91no—
164C42—182no—
165C42—182no—
166C22×C3—24no—
167C22×C3—24no—
168C22×C3—24no—
169C22×C3—22no—
170C3×C4—22no—
171C3×C4—22no—
172C3×C4—24no—
173C3×C4—48no—
174Dic3—64no—
175Dic3—616no—
176Dic3—64no—
177Dic3—122no—
178Dic3—122no—
179C32#147911yescharacteristic, complemented, Sylow
180C23C22⋊#15711yescharacteristic
181Q8—94no—
182Q8—182no—
183Q8—184no—
184C2×C4—22no—
185C2×C4—42no—
186C2×C4—91no—
187C2×C4—91no—
188C2×C4—91no—
189C2×C4—91no—
190C2×C4—182no—
191C2×C4—184no—
192C2×C4—182no—
193C2×C4—361no—
194C2×C4#378712yes—
195C2×C4#378812yes—
196C2×C4C22⋊#15711yescharacteristic
197C2×C4C22×#15711yescharacteristic
198C8—362no—
199C8—362no—
200C2×C3—28no—
201C2×C3—22no—
202C2×C3—22no—
203C2×C3—22no—
204C22—21no—
205C22—21no—
206C22#6377812yes—
207C22C2×C22⋊#15711yescharacteristic
208C4—42no—
209C4—92no—
210C4—184no—
211C4—181no—
212C4—181no—
213C4—181no—
214C4#6377812yes—
215C4C2×#378711yescharacteristic
216C4C2×#378811yescharacteristic
217C3—22no—
218C2—22no—
219C2C2×#6377811yescharacteristic
220C2#1059381611yescharacteristic
221C2#1059382911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC32×C4C22×C8
FrattiniC2×C4C22×#157
FittingC2×C32×C4⋊C4C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC2×C4⋊C4#157
hypocenterC32#1479
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10590161C2semidirect
28. C2×#634C8semidirect
179. C32#1479semidirect

Maximal subgroups

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

subgroupindex
C2×#640962
#105937952
#105901612
#14799