Finite Group Databasebeta

← #11783609

Subgroups — #11783609

Order 1152.

666 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 666 conjugacy classes of subgroups — too many to draw. Only its 108 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×#64086C211yesmaximal, characteristic
2C2×C22⋊#622C212yesmaximal
3C2×#63777C211yesmaximal, characteristic, complemented
4C2×C4×#622C211yesmaximal, characteristic, complemented
5#10590207C212yesmaximal, complemented
6C23×C3⋊Dic3C2211yescharacteristic
7C22×#622C2212yes—
8C22×#622C2212yes—
9C2×C32×C22⋊C4C411yescharacteristic
10C2×#3757C411yescharacteristic
11C2×#3750C411yescharacteristic
12C2×#3750C411yescharacteristic
13C2×C4×C3⋊Dic3C2211yescharacteristic
14C2×C4×C3⋊Dic3C2211yescharacteristic
15#64086—22no—
16#64086—22no—
17C22⋊#622C418yescomplemented
18#63777—22no—
19C4×#622—22no—
20C2×#877—62no—
21C24×C32C2×C411yescharacteristic
22C22×C32×C4C2×C411yescharacteristic
23C22×C32×C4C2×C411yescharacteristic
24C22×C3⋊Dic3—21no—
25C22×C3⋊Dic3—21no—
26C22×C3⋊Dic3—22no—
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3C2×C414yes—
30C22×C3⋊Dic3C2×C411yescharacteristic
31C22×C3⋊Dic3C2311yescharacteristic
32C2×#622—22no—
33C2×#622—22no—
34C2×#622—22no—
35C2×#622—22no—
36C2×#622C2×C414yes—
37C2×#622C2×C414yes—
38C32×C22⋊C4—22no—
39#3757—22no—
40#3750—22no—
41#3750—22no—
42C4×C3⋊Dic3—21no—
43C4×C3⋊Dic3—21no—
44C4×C3⋊Dic3D412yes—
45C4×C3⋊Dic3D412yes—
46#1750—91nomaximal, Sylow
47C23×Dic3—62no—
48C2×C3×C22⋊C4—22no—
49C2×#217—62no—
50C2×Dic3⋊C4—62no—
51C2×Dic3⋊C4—62no—
52C2×C4×Dic3—62no—
53C2×C4×Dic3—62no—
54#877—68no—
55#877—68no—
56C23×C32—21no—
57C23×C32—21no—
58C23×C32—22no—
59C23×C32—22no—
60C23×C32C4212yes—
61C23×C32C22×C411yescharacteristic
62C2×C32×C4—21no—
63C2×C32×C4—22no—
64C2×C32×C4—22no—
65C2×C32×C4C22⋊C412yes—
66C2×C3⋊Dic3—21no—
67C2×C3⋊Dic3—21no—
68C2×C3⋊Dic3—24no—
69C2×C3⋊Dic3—24no—
70C2×C3⋊Dic3—21no—
71C2×C3⋊Dic3—22no—
72C2×C3⋊Dic3—22no—
73C2×C3⋊Dic3C4212yes—
74C2×C3⋊Dic3C22⋊C412yes—
75C2×C3⋊Dic3C22×C412yes—
76C2×C3⋊Dic3C2×D411yescharacteristic
77C2×C3⋊Dic3C2×D411yescharacteristic
78C2×C3⋊Dic3#4112yes—
79#622—24no—
80#622—24no—
81C2×#117—91no—
82C2×C22⋊C8—92no—
83C2×#97—91no—
84C2×C4×C8—91no—
85#336—92no—
86C24×C3—22no—
87C22×C3×C4—22no—
88C22×C3×C4—22no—
89C22×Dic3—62no—
90C22×Dic3—62no—
91C22×Dic3—68no—
92C22×Dic3—62no—
93C22×Dic3—62no—
94C22×Dic3—64no—
95C22×Dic3—64no—
96C22×Dic3—68no—
97C3×C22⋊C4—28no—
98#217—68no—
99Dic3⋊C4—68no—
100Dic3⋊C4—68no—
101C4×Dic3—64no—
102C4×Dic3—64no—
103C4×Dic3—64no—
104C4×Dic3—64no—
105C22×C32—22no—
106C22×C32—24no—
107C22×C32—41no—
108C22×C32—41no—
109C22×C32—42no—
110C22×C32C2×C4211yescharacteristic
111C22×C32C2×C22⋊C411yescharacteristic
112C22×C32#11711yescharacteristic
113C22×C32#13112yes—
114C22×C32#13112yes—
115C32×C4—22no—
116C32×C4—41no—
117C3⋊Dic3—22no—
118C3⋊Dic3—22no—
119C3⋊Dic3—41no—
120C3⋊Dic3C4×D412yes—
121C3⋊Dic3C4×D412yes—
122C23×C4—91no—
123C22×C8—92no—
124C22×C8—92no—
125#117—182no—
126#117—182no—
127C2×C4⋊C4—91no—
128C2×C4⋊C4—91no—
129C2×C22⋊C4—91no—
130C2×C22⋊C4#15711yescharacteristic
131C2×C42—91no—
132C2×C42—91no—
133C22⋊C8—98no—
134#97—182no—
135C4×C8—182no—
136C23×C3—24no—
137C23×C3—24no—
138C23×C3—22no—
139C23×C3—24no—
140C23×C3—44no—
141C23×C3—44no—
142C2×C3×C4—24no—
143C2×C3×C4—24no—
144C2×C3×C4—44no—
145C2×C3×C4—44no—
146C2×Dic3—64no—
147C2×Dic3—64no—
148C2×Dic3—62no—
149C2×Dic3—62no—
150C2×Dic3—64no—
151C2×Dic3—64no—
152C2×Dic3—64no—
153C2×Dic3—616no—
154C2×Dic3—616no—
155C2×Dic3—64no—
156C2×Dic3—64no—
157C2×Dic3—124no—
158C2×Dic3—124no—
159C2×C32—42no—
160C2×C32C4×C22⋊C411yescharacteristic
161C2×C32#40512yes—
162C2×C32#40811yescharacteristic
163C2×C32#40811yescharacteristic
164C2×C32#43312yes—
165C24C2×#15711yescharacteristic
166C22×C4—91no—
167C22×C4—91no—
168C22×C4—91no—
169C22×C4—94no—
170C22×C4—91no—
171C22×C4—181no—
172C22×C4—181no—
173C22×C4—182no—
174C22×C4C2×#15711yescharacteristic
175C22×C4C2×#15711yescharacteristic
176C2×C8—94no—
177C2×C8—94no—
178C2×C8—182no—
179C2×C8—182no—
180C2×C8—182no—
181C2×C8—182no—
182C4⋊C4—182no—
183C4⋊C4—182no—
184C22⋊C4—22no—
185C22⋊C4—182no—
186C42—92no—
187C42—92no—
188C42—181no—
189C42—181no—
190C22×C3—28no—
191C22×C3—22no—
192C22×C3—22no—
193C22×C3—24no—
194C22×C3—24no—
195C22×C3—22no—
196C22×C3—48no—
197C22×C3—44no—
198C22×C3—44no—
199C22×C3—48no—
200C3×C4—44no—
201C3×C4—44no—
202Dic3—64no—
203Dic3—64no—
204Dic3—68no—
205Dic3—124no—
206Dic3—124no—
207C32#175011yescharacteristic, complemented, Sylow
208C23—21no—
209C23—22no—
210C23—22no—
211C23—21no—
212C23C4×#15712yes—
213C23C22×#15711yescharacteristic
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—21no—
217C2×C4—92no—
218C2×C4—92no—
219C2×C4—91no—
220C2×C4—91no—
221C2×C4—92no—
222C2×C4—92no—
223C2×C4—184no—
224C2×C4—184no—
225C2×C4—181no—
226C2×C4—182no—
227C2×C4—181no—
228C2×C4—182no—
229C2×C4—181no—
230C2×C4C22⋊#15712yes—
231C8—184no—
232C8—184no—
233C2×C3—22no—
234C2×C3—22no—
235C2×C3—22no—
236C2×C3—24no—
237C2×C3—24no—
238C2×C3—48no—
239C22—22no—
240C22—24no—
241C22—41no—
242C22—41no—
243C22—42no—
244C22C2×C4×#15711yescharacteristic
245C22#6428611yescharacteristic
246C22#6428712yes—
247C22#6428712yes—
248C22C2×C22⋊#15711yescharacteristic
249C4—22no—
250C4—41no—
251C4—92no—
252C4—92no—
253C4—182no—
254C4—182no—
255C4—361no—
256C3—22no—
257C2—42no—
258C2#1059373812yes—
259C2#1059374412yes—
260C2C4×C22⋊#15711yescharacteristic
261C2#1059382211yescharacteristic
262C2#1059382311yescharacteristic
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C2×C42
FittingC2×C32×C22⋊C4C4
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C22⋊C4#157
hypocenterC32#1750
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63777C2semidirect
4. C2×C4×#622C2semidirect
5. #10590207C2semidirect
17. C22⋊#622C4semidirect
207. C32#1750semidirect

Maximal subgroups

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

subgroupindex
C2×#640862
C2×C22⋊#6222
C2×#637772
C2×C4×#6222
#105902072
#17509