Finite Group Databasebeta

← #11790216

Subgroups — #11790216

Order 1152.

410 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 81 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×#63777C211yesmaximal, characteristic
2C2×#63743C211yesmaximal, characteristic
3C2×#63742C211yesmaximal, characteristic
4#10591337C212yesmaximal
5#10590075C212yesmaximal
6C22×#622C2211yescharacteristic
7C22×#622C2211yescharacteristic
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C2×C3×Dic3⋊C4—22no—
10C2×#3724C2212yes—
11C2×#3724C2212yes—
12#63777—22no—
13#63743—22no—
14#63742C414yescomplemented
15#63579—22no—
16#4976—62no—
17C22×C32×C4D411yescharacteristic
18C22×C3⋊Dic3D411yescharacteristic
19C22×C3⋊Dic3C2311yescharacteristic
20C22×C3×Dic3—22no—
21C22×C3×Dic3—22no—
22C2×#622—21no—
23C2×#622—21no—
24C2×#622C2×C412yes—
25C2×#622D412yes—
26C2×#622Q812yes—
27C2×#622Q812yes—
28C4×C3⋊Dic3—21no—
29C4×C3⋊Dic3—21no—
30C3×Dic3⋊C4—44no—
31#3724—22no—
32#3724—22no—
33#3724—22no—
34#3724C2×C414yes—
35#1944—91nomaximal, Sylow
36C2×C3×C4⋊C4—62no—
37C2×Dic3⋊C4—22no—
38C2×Dic3⋊C4—62no—
39C2×Dic3⋊C4—62no—
40C2×C4×Dic3—62no—
41C3⋊#95—62no—
42C3⋊#95—62no—
43C23×C32C2×D411yescharacteristic
44C2×C32×C4—22no—
45C2×C32×C4—21no—
46C2×C3⋊Dic3—22no—
47C2×C3⋊Dic3—21no—
48C2×C3⋊Dic3C22×C411yescharacteristic
49C2×C3⋊Dic3C2×D411yescharacteristic
50C2×C3⋊Dic3C2×Q811yescharacteristic
51C2×C3⋊Dic3C2×Q811yescharacteristic
52C2×C3⋊Dic3#4111yescharacteristic
53C2×C3⋊Dic3#4111yescharacteristic
54C2×C3×Dic3—24no—
55C2×C3×Dic3—42no—
56C2×C3×Dic3—42no—
57C2×C3×Dic3—42no—
58C2×C3×Dic3—42no—
59C2×C3×Dic3—42no—
60#622—22no—
61#622C4⋊C414yescomplemented
62C2×#107—91no—
63C2×#106—91no—
64C2×#97—91no—
65#389—92no—
66#340—92no—
67C22×C3×C4—22no—
68C22×C3×C4—62no—
69C22×C3×C4—62no—
70C22×Dic3—22no—
71C22×Dic3—22no—
72C22×Dic3—62no—
73C22×Dic3—62no—
74C3×C4⋊C4—124no—
75Dic3⋊C4—44no—
76Dic3⋊C4—64no—
77Dic3⋊C4—64no—
78Dic3⋊C4—122no—
79Dic3⋊C4—122no—
80C4×Dic3—122no—
81C4×Dic3—122no—
82C22×C32C4×D411yescharacteristic
83C22×C32#12111yescharacteristic
84C22×C32C4⋊Q811yescharacteristic
85C22×C32AGL(1,ℤ/8)12yes—
86C22×C32#13712yes—
87C32×C4—41no—
88C3⋊Dic3—41no—
89C3⋊Dic3C2×C4⋊C411yescharacteristic
90C3⋊Dic3C4×Q811yescharacteristic
91C3⋊Dic3C22⋊Q811yescharacteristic
92C3⋊Dic3#12511yescharacteristic
93C3×Dic3—44no—
94C3×Dic3—82no—
95C22×C8—91no—
96C22×C8—91no—
97C2×C4⋊C4—62no—
98C2×C4⋊C4—92no—
99C2×C4⋊C4—92no—
100C2×C42—91no—
101#107—182no—
102#106—94no—
103#97—182no—
104#95—182no—
105C23×C3—22no—
106C2×C3×C4—24no—
107C2×C3×C4—42no—
108C2×C3×C4—42no—
109C2×C3×C4—64no—
110C2×C3×C4—122no—
111C2×C3×C4—122no—
112C2×C3×C4—122no—
113C2×C3×C4—122no—
114C2×C3×C4—122no—
115C2×Dic3—24no—
116C2×Dic3—42no—
117C2×Dic3—42no—
118C2×Dic3—42no—
119C2×Dic3—42no—
120C2×Dic3—42no—
121C2×Dic3—62no—
122C2×Dic3—62no—
123C2×Dic3—62no—
124C2×Dic3—62no—
125C2×Dic3—62no—
126C2×Dic3—62no—
127C2×Dic3—64no—
128C2×Dic3—122no—
129C2×Dic3—122no—
130C2×C32#38911yescharacteristic
131C2×C32#44012yes—
132C2×C32#46911yescharacteristic
133C2×C32#47011yescharacteristic
134C2×C32#50112yes—
135C22×C4—62no—
136C22×C4—62no—
137C22×C4—91no—
138C22×C4—91no—
139C22×C4GO+(4,𝔽2)11yescharacteristic
140C2×C8—92no—
141C2×C8—92no—
142C2×C8—92no—
143C2×C8—92no—
144C2×C8—181no—
145C2×C8—181no—
146C4⋊C4—94no—
147C4⋊C4—124no—
148C4⋊C4—182no—
149C4⋊C4—182no—
150C4⋊C4—182no—
151C42—181no—
152C42—181no—
153C22×C3—22no—
154C22×C3—22no—
155C22×C3—22no—
156C22×C3—22no—
157C22×C3—22no—
158C22×C3—22no—
159C22×C3—22no—
160C3×C4—44no—
161C3×C4—124no—
162C3×C4—242no—
163Dic3—44no—
164Dic3—62no—
165Dic3—62no—
166Dic3—62no—
167Dic3—62no—
168Dic3—82no—
169Dic3—124no—
170C32#194411yescharacteristic, complemented, Sylow
171C23C2×GO+(4,𝔽2)11yescharacteristic
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—64no—
175C2×C4—91no—
176C2×C4—91no—
177C2×C4—91no—
178C2×C4—91no—
179C2×C4—91no—
180C2×C4—91no—
181C2×C4—122no—
182C2×C4—122no—
183C2×C4—122no—
184C2×C4—122no—
185C2×C4—122no—
186C2×C4—182no—
187C2×C4—181no—
188C8—94no—
189C8—182no—
190C2×C3—22no—
191C2×C3—22no—
192C2×C3—22no—
193C2×C3—22no—
194C2×C3—22no—
195C2×C3—22no—
196C2×C3—22no—
197C22#6422211yescharacteristic
198C22#6422612yes—
199C22C4×GO+(4,𝔽2)11yescharacteristic
200C22#6423612yes—
201C22#6424211yescharacteristic
202C4—41no—
203C4—91no—
204C4—91no—
205C4—91no—
206C4—91no—
207C4—124no—
208C4—242no—
209C4—361no—
210C3—22no—
211C2#1059339212yes—
212C2#1059341011yescharacteristic
213C2#1059343112yes—
214C2#1059344911yescharacteristic
215C2#1059352211yescharacteristic
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#1944
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
14. #63742C4semidirect
61. #622C4⋊C4semidirect
170. C32#1944semidirect

Maximal subgroups

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

subgroupindex
C2×#637772
C2×#637432
C2×#637422
#105913372
#105900752
#19449