Finite Group Databasebeta

← #11790744

Subgroups — #11790744

Order 1152.

530 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 83 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×#63777C211yesmaximal, characteristic
3C2×#63740C214yesmaximal
4#10591360C211yesmaximal, characteristic
5C22×#627C2212yes—
6C22×#622C2212yes—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C2×C3×C4⋊Dic3—21no—
9C2×#3724—21no—
10C2×#3724C2212yes—
11#63919—22no—
12#63919C414yescomplemented
13#63777—22no—
14#63740—28no—
15C3×C3⋊#95—21no—
16#63579—21no—
17C2×#888—61no—
18#4650—61no—
19C22×C32×C4D411yescharacteristic
20C22×C3⋊Dic3D411yescharacteristic
21C22×C3⋊Dic3C2311yescharacteristic
22C22×C3×Dic3—22no—
23C22×C3×Dic3—22no—
24C2×#627—24no—
25C2×#627—24no—
26C2×#627—22no—
27C2×#627C2×C414yes—
28C2×#622—22no—
29C2×#622—22no—
30C2×#622D414yes—
31C4×C3⋊Dic3C2×C412yes—
32C4×C3⋊Dic3D412yes—
33C3×C4⋊Dic3—24no—
34#3724—24no—
35#3724—24no—
36#1960—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—
44#888—64no—
45#888—64no—
46C3×#95—61no—
47C3⋊#95—21no—
48C3⋊#95—62no—
49C23×C32C2×D411yescharacteristic
50C2×C32×C4—22no—
51C2×C32×C4C22⋊C412yes—
52C2×C3⋊Dic3—22no—
53C2×C3⋊Dic3C22⋊C412yes—
54C2×C3⋊Dic3C22×C411yescharacteristic
55C2×C3⋊Dic3C2×D412yes—
56C2×C3⋊Dic3C2×D411yescharacteristic
57C2×C3⋊Dic3#4112yes—
58C2×C3×Dic3—24no—
59C2×C3×Dic3—42no—
60C2×C3×Dic3—42no—
61C2×C3×Dic3—42no—
62C2×C3×Dic3—42no—
63C2×C3×Dic3—42no—
64#627—28no—
65#627—44no—
66#622—24no—
67C2×C4⋊Q8—91no—
68C2×#103—94no—
69C2×#97—91no—
70#382—91no—
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—64no—
82C2×Dic6—64no—
83C2×Dic6—124no—
84C2×Dic6—124no—
85C3×C4⋊C4—64no—
86C4⋊Dic3—24no—
87Dic3⋊C4—68no—
88Dic3⋊C4—124no—
89C4×Dic3—62no—
90C4×Dic3—62no—
91C4×Dic3—62no—
92C4×Dic3—62no—
93C22×C32C2×C22⋊C411yescharacteristic
94C22×C32#12411yescharacteristic
95C22×C32#12711yescharacteristic
96C22×C32#13712yes—
97C22×C32#13712yes—
98C32×C4—22no—
99C3⋊Dic3—22no—
100C3⋊Dic3C4×D412yes—
101C3⋊Dic3#12112yes—
102C3×Dic3—44no—
103C3×Dic3—82no—
104C22×Q8—92no—
105C22×C8—92no—
106C4⋊Q8—94no—
107C4⋊Q8—182no—
108C2×C4⋊C4—61no—
109C2×C4⋊C4—92no—
110C2×C4⋊C4—181no—
111C2×C42—91no—
112#103—188no—
113#97—182no—
114#95—61no—
115#95—181no—
116C23×C3—21no—
117C23×C3—21no—
118C2×C3×C4—24no—
119C2×C3×C4—22no—
120C2×C3×C4—22no—
121C2×C3×C4—42no—
122C2×C3×C4—64no—
123C2×C3×C4—122no—
124C2×C3×C4—122no—
125C2×C3×C4—122no—
126C2×C3×C4—122no—
127C2×C3×C4—122no—
128C2×Dic3—24no—
129C2×Dic3—42no—
130C2×Dic3—42no—
131C2×Dic3—42no—
132C2×Dic3—42no—
133C2×Dic3—42no—
134C2×Dic3—62no—
135C2×Dic3—61no—
136C2×Dic3—61no—
137C2×Dic3—61no—
138C2×Dic3—61no—
139C2×Dic3—62no—
140C2×Dic3—62no—
141C2×Dic3—62no—
142C2×Dic3—62no—
143C2×Dic3—62no—
144C2×Dic3—64no—
145C2×Dic3—122no—
146Dic6—128no—
147Dic6—128no—
148C2×C32#39011yescharacteristic
149C2×C32#41911yescharacteristic
150C2×C32#41911yescharacteristic
151C2×C32#49112yes—
152C2×C32#49712yes—
153C2×Q8—94no—
154C2×Q8—182no—
155C2×Q8—184no—
156C2×Q8—184no—
157C22×C4—62no—
158C22×C4—62no—
159C22×C4—91no—
160C22×C4—91no—
161C22×C4GO+(4,𝔽2)11yescharacteristic
162C2×C8—94no—
163C2×C8—182no—
164C2×C8—182no—
165C4⋊C4—64no—
166C4⋊C4—184no—
167C4⋊C4—184no—
168C42—92no—
169C42—92no—
170C22×C3—21no—
171C22×C3—21no—
172C22×C3—22no—
173C22×C3—22no—
174C22×C3—21no—
175C22×C3—21no—
176C22×C3—21no—
177C22×C3—21no—
178C22×C3—22no—
179C22×C3—22no—
180C3×C4—24no—
181C3×C4—42no—
182C3×C4—124no—
183C3×C4—242no—
184Dic3—44no—
185Dic3—62no—
186Dic3—62no—
187Dic3—62no—
188Dic3—62no—
189Dic3—64no—
190Dic3—82no—
191Dic3—122no—
192C32#196011yescharacteristic, complemented, Sylow
193C23C2×GO+(4,𝔽2)11yescharacteristic
194Q8—188no—
195Q8—364no—
196C2×C4—22no—
197C2×C4—64no—
198C2×C4—92no—
199C2×C4—92no—
200C2×C4—91no—
201C2×C4—91no—
202C2×C4—92no—
203C2×C4—122no—
204C2×C4—122no—
205C2×C4—122no—
206C2×C4—122no—
207C2×C4—122no—
208C2×C4—182no—
209C2×C4D32⋊C412yes—
210C8—184no—
211C2×C3—21no—
212C2×C3—21no—
213C2×C3—22no—
214C2×C3—22no—
215C2×C3—21no—
216C2×C3—21no—
217C2×C3—22no—
218C2×C3—22no—
219C2×C3—21no—
220C2×C3—21no—
221C22#6422111yescharacteristic
222C22#6422612yes—
223C22#6423111yescharacteristic
224C22C2×D32⋊C411yescharacteristic
225C22#6423912yes—
226C4—22no—
227C4—92no—
228C4—92no—
229C4—124no—
230C4—182no—
231C4—242no—
232C3—21no—
233C3—21no—
234C2#1059337411yescharacteristic
235C2#1059337812yes—
236C2#1059340711yescharacteristic
237C2#1059344312yes—
238C2#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#1960
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
12. #63919C4semidirect
192. C32#1960semidirect

Maximal subgroups

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

subgroupindex
C2×#639192
C2×#637772
C2×#637402
#105913602
#19609