Finite Group Databasebeta

← #11774337

Subgroups — #11774337

Order 1152.

546 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 92 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×Q8×C3⋊Dic3C211yesmaximal, characteristic
2#10593795C211yesmaximal, characteristic
3#10593795C211yesmaximal, characteristic
4Q8⋊#622C214yesmaximal, complemented
5C22×C32×Q8C411yescharacteristic
6Q8×C3⋊Dic3—21no—
7Q8×C3⋊Dic3—21no—
8Q8×C3⋊Dic3C412yes—
9Q8×C3⋊Dic3C2212yes—
10C2×C4⋊(C3⋊Dic3)—21no—
11C2×C4⋊(C3⋊Dic3)C411yescharacteristic
12C2×C4×C3⋊Dic3—21no—
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C22⋊#622—21no—
15C22⋊#622—21no—
16C4⋊#622—21no—
17C4⋊#622C2212yes—
18C4×#622—21no—
19C4×#622C2212yes—
20C2×Q8×Dic3—62no—
21C2×C32×Q8—21no—
22C2×C32×Q8—22no—
23C2×C32×Q8C814yescomplemented
24C2×C32×Q8C2×C412yes—
25C22×C32×C4—21no—
26C22×C32×C4C2×C411yescharacteristic
27C22×C3⋊Dic3—21no—
28C22×C3⋊Dic3D411yescharacteristic
29C22×C3⋊Dic3D411yescharacteristic
30C2×#622—22no—
31C2×#622—22no—
32C4⋊(C3⋊Dic3)—21no—
33C4⋊(C3⋊Dic3)—22no—
34C4⋊(C3⋊Dic3)—22no—
35C4⋊(C3⋊Dic3)C2×C412yes—
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×C3×Q8—22no—
44Q8×Dic3—64no—
45Q8×Dic3—64no—
46Q8×Dic3—64no—
47Q8×Dic3—64no—
48C2×C4⋊Dic3—62no—
49C2×C4⋊Dic3—64no—
50C2×C4×Dic3—62no—
51C2×C4×Dic3—64no—
52C23×C32C22⋊C411yescharacteristic
53C32×Q8—24no—
54C32×Q8—22no—
55C32×Q8C2×C814yes—
56C2×C32×C4—24no—
57C2×C32×C4—22no—
58C2×C32×C4C22⋊C411yescharacteristic
59C2×C32×C4C2×C812yes—
60C2×C32×C4M1612yes—
61C2×C32×C4C22×C411yescharacteristic
62C2×C3⋊Dic3—22no—
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3—42no—
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C2×D411yescharacteristic
69C2×C3⋊Dic3C2×D411yescharacteristic
70#622—42no—
71#622—42no—
72C2×C4×Q8—91no—
73#431—91no—
74#431—91no—
75Q8⋊C8—94no—
76C2×C3×Q8—24no—
77C2×C3×Q8—28no—
78C2×C3×Q8—28no—
79C2×C3×Q8—24no—
80C22×C3×C4—24no—
81C22×C3×C4—22no—
82C22×Dic3—62no—
83C22×Dic3—62no—
84C22×Dic3—64no—
85C4⋊Dic3—64no—
86C4⋊Dic3—68no—
87C4⋊Dic3—68no—
88C4⋊Dic3—64no—
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—24no—
100C32×C4C22⋊C812yes—
101C32×C4C22×C811yescharacteristic
102C32×C4C2×M1611yescharacteristic
103C3⋊Dic3—21no—
104C3⋊Dic3—21no—
105C3⋊Dic3—21no—
106C3⋊Dic3—42no—
107C3⋊Dic3#13712yes—
108C22×Q8#15711yescharacteristic
109C4×Q8—92no—
110C4×Q8—92no—
111C4×Q8—181no—
112C4×Q8—181no—
113C2×C4⋊C4—91no—
114C2×C4⋊C4—181no—
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—
124C3×Q8—28no—
125C3×Q8—216no—
126C3×Q8—28no—
127C2×C3×C4—28no—
128C2×C3×C4—216no—
129C2×C3×C4—22no—
130C2×C3×C4—24no—
131C2×C3×C4—24no—
132C2×C3×C4—22no—
133C2×Dic3—62no—
134C2×Dic3—62no—
135C2×Dic3—62no—
136C2×Dic3—62no—
137C2×Dic3—68no—
138C2×Dic3—68no—
139C2×Dic3—124no—
140C2×Dic3—128no—
141C2×C32—22no—
142C2×C32C2×C22⋊C811yescharacteristic
143C2×C32#41911yescharacteristic
144C2×C32#42111yescharacteristic
145C2×Q8—22no—
146C2×Q8—21no—
147C2×Q8#62214yescomplemented
148C2×Q8C2×#15712yes—
149C22×C4—21no—
150C22×C4—91no—
151C22×C4—91no—
152C22×C4—181no—
153C22×C4C2×#15711yescharacteristic
154C2×C8—182no—
155C2×C8—182no—
156C4⋊C4—92no—
157C4⋊C4—182no—
158C4⋊C4—182no—
159C4⋊C4—181no—
160C42—91no—
161C42—91no—
162C42—91no—
163C42—91no—
164C42—182no—
165C42—182no—
166C22×C3—24no—
167C22×C3—24no—
168C22×C3—22no—
169C22×C3—24no—
170C3×C4—216no—
171C3×C4—22no—
172C3×C4—22no—
173C3×C4—24no—
174Dic3—64no—
175Dic3—64no—
176Dic3—122no—
177Dic3—122no—
178Dic3—128no—
179C32#147911yescharacteristic, complemented, Sylow
180C23C22⋊#15711yescharacteristic
181Q8—22no—
182Q8—24no—
183Q8C2×#62214yes—
184C2×C4—22no—
185C2×C4—24no—
186C2×C4—91no—
187C2×C4—91no—
188C2×C4—91no—
189C2×C4—91no—
190C2×C4—182no—
191C2×C4—182no—
192C2×C4—361no—
193C2×C4—362no—
194C2×C4C2×#62212yes—
195C2×C4#379212yes—
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—
206C22C22⋊#62212yes—
207C22C2×C22⋊#15711yescharacteristic
208C4—24no—
209C4—92no—
210C4—181no—
211C4—181no—
212C4—181no—
213C4—362no—
214C4C22⋊#62212yes—
215C4C22×#62211yescharacteristic
216C4C2×#379211yescharacteristic
217C3—22no—
218C2—22no—
219C2#1059382911yescharacteristic
220C2#1059383111yescharacteristic
221C2C2×C22⋊#62211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC32×C4C22×C8
FrattiniC2×C4C22×#157
FittingC22×C32×Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×Q8#157
hypocenterC32#1479
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
4. Q8⋊#622C2semidirect
23. C2×C32×Q8C8semidirect
147. C2×Q8#622semidirect
179. C32#1479semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C3⋊Dic32
#105937952
Q8⋊#6222
#14799