Finite Group Databasebeta

← #11791638

Subgroups — #11791638

Order 1152.

534 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 91 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×#63919C211yesmaximal, characteristic
2C2×#63779C211yesmaximal, characteristic
3#10591257C211yesmaximal, characteristic
4#10590075C214yesmaximal
5C22×#627—21no—
6C22×#622C2212yes—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×C3×C4⋊Dic3—21no—
9C2×#3724C2212yes—
10C2×#3724C2212yes—
11C2×Dic32—21no—
12#63919—22no—
13#63919C414yescomplemented
14#63779—22no—
15C3×C3⋊#95—21no—
16C2×#888—61no—
17#4649—61no—
18C22×C32×C4D411yescharacteristic
19C22×C3⋊Dic3D411yescharacteristic
20C22×C3⋊Dic3C2311yescharacteristic
21C22×C3×Dic3—22no—
22C22×C3×Dic3—22no—
23C2×#627—24no—
24C2×#627—42no—
25C2×#627—42no—
26C2×#622—22no—
27C2×#622—24no—
28C4×C3⋊Dic3C2×C412yes—
29C4×C3⋊Dic3D412yes—
30C3×C4⋊Dic3—24no—
31#3724—22no—
32#3724—22no—
33#3724C2×C414yes—
34#3724Q814yescomplemented
35Dic32—42no—
36#1988—91nomaximal, Sylow
37C22×Dic6—62no—
38C2×C3×C4⋊C4—61no—
39C2×C4⋊Dic3—21no—
40C2×Dic3⋊C4—62no—
41C2×Dic3⋊C4—62no—
42C2×C4×Dic3—61no—
43C2×C4×Dic3—61no—
44C2×C4×Dic3—62no—
45#888—64no—
46#888—64no—
47C3×#95—61no—
48C3⋊#95—21no—
49C23×C32C2×D411yescharacteristic
50C2×C32×C4—22no—
51C2×C32×C4C22⋊C412yes—
52C2×C3⋊Dic3C22⋊C412yes—
53C2×C3⋊Dic3D812yes—
54C2×C3⋊Dic3SD1612yes—
55C2×C3⋊Dic3C22×C411yescharacteristic
56C2×C3⋊Dic3C2×D411yescharacteristic
57C2×C3⋊Dic3C2×Q812yes—
58C2×C3⋊Dic3#4112yes—
59C2×C3×Dic3—24no—
60C2×C3×Dic3—24no—
61C2×C3×Dic3—42no—
62C2×C3×Dic3—42no—
63C2×C3×Dic3—42no—
64C2×C3×Dic3—42no—
65#627—48no—
66#622—42no—
67C2×C4⋊Q8—91no—
68C2×C4⋊C8—91no—
69C4×C4⋊C4—91no—
70#340—94no—
71C22×C3×C4—21no—
72C22×C3×C4—21no—
73C22×C3×C4—62no—
74C22×C3×C4—62no—
75C22×Dic3—22no—
76C22×Dic3—22no—
77C22×Dic3—61no—
78C22×Dic3—61no—
79C22×Dic3—61no—
80C22×Dic3—61no—
81C2×Dic6—68no—
82C2×Dic6—124no—
83C2×Dic6—124no—
84C3×C4⋊C4—64no—
85C4⋊Dic3—24no—
86Dic3⋊C4—64no—
87Dic3⋊C4—64no—
88Dic3⋊C4—64no—
89Dic3⋊C4—64no—
90C4×Dic3—62no—
91C4×Dic3—62no—
92C4×Dic3—62no—
93C4×Dic3—62no—
94C4×Dic3—124no—
95C22×C32C2×C22⋊C411yescharacteristic
96C22×C32C22⋊Q812yes—
97C22×C32C2×D811yescharacteristic
98C22×C32C2×SD1611yescharacteristic
99C22×C32#13712yes—
100C32×C4—22no—
101C3⋊Dic3#10214yes—
102C3⋊Dic3C4×Q812yes—
103C3⋊Dic3#12411yescharacteristic
104C3⋊Dic3C4⋊Q811yescharacteristic
105C3×Dic3—44no—
106C3×Dic3—44no—
107C22×Q8—181no—
108C22×C8—92no—
109C4⋊Q8—94no—
110C4⋊Q8—182no—
111C2×C4⋊C4—61no—
112C2×C4⋊C4—92no—
113C2×C4⋊C4—92no—
114C2×C42—91no—
115C2×C42—181no—
116C4⋊C8—182no—
117#95—61no—
118C23×C3—21no—
119C23×C3—21no—
120C2×C3×C4—24no—
121C2×C3×C4—22no—
122C2×C3×C4—22no—
123C2×C3×C4—42no—
124C2×C3×C4—64no—
125C2×C3×C4—64no—
126C2×C3×C4—122no—
127C2×C3×C4—122no—
128C2×C3×C4—122no—
129C2×C3×C4—122no—
130C2×Dic3—24no—
131C2×Dic3—24no—
132C2×Dic3—42no—
133C2×Dic3—42no—
134C2×Dic3—42no—
135C2×Dic3—42no—
136C2×Dic3—62no—
137C2×Dic3—62no—
138C2×Dic3—62no—
139C2×Dic3—62no—
140C2×Dic3—62no—
141C2×Dic3—62no—
142C2×Dic3—61no—
143C2×Dic3—61no—
144C2×Dic3—61no—
145C2×Dic3—61no—
146C2×Dic3—62no—
147C2×Dic3—62no—
148C2×Dic3—62no—
149C2×Dic3—62no—
150Dic6—1216no—
151C2×C32#39111yescharacteristic
152C2×C32C2×#10211yescharacteristic
153C2×C32#41911yescharacteristic
154C2×C32#47412yes—
155C2×C32#47512yes—
156C2×Q8—184no—
157C2×Q8—362no—
158C2×Q8—362no—
159C22×C4—62no—
160C22×C4—62no—
161C22×C4—91no—
162C22×C4—91no—
163C22×C4GO+(4,𝔽2)11yescharacteristic
164C2×C8—182no—
165C2×C8—184no—
166C4⋊C4—64no—
167C4⋊C4—94no—
168C4⋊C4—94no—
169C4⋊C4—182no—
170C4⋊C4—182no—
171C42—92no—
172C42—92no—
173C42—362no—
174C22×C3—22no—
175C22×C3—22no—
176C22×C3—21no—
177C22×C3—21no—
178C22×C3—21no—
179C22×C3—21no—
180C22×C3—21no—
181C22×C3—21no—
182C22×C3—22no—
183C22×C3—22no—
184C3×C4—24no—
185C3×C4—42no—
186C3×C4—124no—
187C3×C4—124no—
188Dic3—44no—
189Dic3—44no—
190Dic3—64no—
191Dic3—64no—
192Dic3—62no—
193Dic3—62no—
194Dic3—61no—
195Dic3—61no—
196Dic3—61no—
197Dic3—61no—
198C32#198811yescharacteristic, complemented, Sylow
199C23C2×GO+(4,𝔽2)11yescharacteristic
200Q8—368no—
201C2×C4—22no—
202C2×C4—64no—
203C2×C4—64no—
204C2×C4—92no—
205C2×C4—92no—
206C2×C4—92no—
207C2×C4—92no—
208C2×C4—91no—
209C2×C4—91no—
210C2×C4—92no—
211C2×C4—122no—
212C2×C4—122no—
213C2×C4—122no—
214C2×C4—122no—
215C2×C4D32⋊C412yes—
216C8—362no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3—21no—
221C2×C3—22no—
222C2×C3—22no—
223C2×C3—22no—
224C2×C3—22no—
225C2×C3—21no—
226C2×C3—21no—
227C22D32⋊Q812yes—
228C22#6422511yescharacteristic
229C22#6422711yescharacteristic
230C22C2×D32⋊C411yescharacteristic
231C22#6423912yes—
232C4—22no—
233C4—91no—
234C4—91no—
235C4—92no—
236C4—94no—
237C4—124no—
238C4—124no—
239C3—21no—
240C3—21no—
241C2#1059334111yescharacteristic
242C2#1059336511yescharacteristic
243C2#1059336712yes—
244C2#1059338512yes—
245C2#1059350311yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1988
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
13. #63919C4semidirect
34. #3724Q8semidirect
198. C32#1988semidirect

Maximal subgroups

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

subgroupindex
C2×#639192
C2×#637792
#105912572
#105900752
#19889