Finite Group Databasebeta

← #11790149

Subgroups — #11790149

Order 1152.

418 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 87 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×C4×#622C211yesmaximal, characteristic
2C2×#63743C211yesmaximal, characteristic
3C2×#63743C211yesmaximal, characteristic
4#10591337C212yesmaximal
5#10590075C212yesmaximal
6C22×#622C2211yescharacteristic
7C22×#622C2211yescharacteristic
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C2×C3×Dic3⋊C4—22no—
10C2×#3724C2212yes—
11C2×#3724C2212yes—
12C4×#622—22no—
13#63743—22no—
14#63743C414yescomplemented
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#1942—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—21no—
45C2×C32×C4—21no—
46C2×C32×C4D812yes—
47C2×C3⋊Dic3—21no—
48C2×C3⋊Dic3—21no—
49C2×C3⋊Dic3Q1612yes—
50C2×C3⋊Dic3C22×C411yescharacteristic
51C2×C3⋊Dic3C2×D411yescharacteristic
52C2×C3⋊Dic3C2×Q811yescharacteristic
53C2×C3⋊Dic3C2×Q811yescharacteristic
54C2×C3⋊Dic3#4111yescharacteristic
55C2×C3⋊Dic3#4111yescharacteristic
56C2×C3×Dic3—24no—
57C2×C3×Dic3—42no—
58C2×C3×Dic3—42no—
59C2×C3×Dic3—42no—
60C2×C3×Dic3—42no—
61C2×C3×Dic3—42no—
62#622—22no—
63#622C4⋊C414yescomplemented
64C2×#107—91no—
65C2×#107—91no—
66C2×C4×C8—91no—
67#389—92no—
68#340—92no—
69C22×C3×C4—22no—
70C22×C3×C4—62no—
71C22×C3×C4—62no—
72C22×Dic3—22no—
73C22×Dic3—22no—
74C22×Dic3—62no—
75C22×Dic3—62no—
76C3×C4⋊C4—124no—
77Dic3⋊C4—44no—
78Dic3⋊C4—64no—
79Dic3⋊C4—64no—
80Dic3⋊C4—122no—
81Dic3⋊C4—122no—
82C4×Dic3—122no—
83C4×Dic3—122no—
84C22×C32C4×D411yescharacteristic
85C22×C32#12111yescharacteristic
86C22×C32C4⋊Q811yescharacteristic
87C22×C32C2×D811yescharacteristic
88C22×C32C2×Q1611yescharacteristic
89C22×C32#13511yescharacteristic
90C22×C32#13511yescharacteristic
91C32×C4—22no—
92C3⋊Dic3—22no—
93C3⋊Dic3C2×C4⋊C411yescharacteristic
94C3⋊Dic3C4×Q811yescharacteristic
95C3⋊Dic3C22⋊Q811yescharacteristic
96C3⋊Dic3#12511yescharacteristic
97C3×Dic3—44no—
98C3×Dic3—82no—
99C22×C8—91no—
100C22×C8—91no—
101C2×C4⋊C4—62no—
102C2×C4⋊C4—92no—
103C2×C4⋊C4—92no—
104C2×C42—91no—
105#107—94no—
106#107—182no—
107C4×C8—182no—
108#95—182no—
109C23×C3—22no—
110C2×C3×C4—24no—
111C2×C3×C4—42no—
112C2×C3×C4—42no—
113C2×C3×C4—64no—
114C2×C3×C4—122no—
115C2×C3×C4—122no—
116C2×C3×C4—122no—
117C2×C3×C4—122no—
118C2×C3×C4—122no—
119C2×Dic3—24no—
120C2×Dic3—42no—
121C2×Dic3—42no—
122C2×Dic3—42no—
123C2×Dic3—42no—
124C2×Dic3—42no—
125C2×Dic3—62no—
126C2×Dic3—62no—
127C2×Dic3—62no—
128C2×Dic3—62no—
129C2×Dic3—62no—
130C2×Dic3—62no—
131C2×Dic3—64no—
132C2×Dic3—122no—
133C2×Dic3—122no—
134C2×C32#38911yescharacteristic
135C2×C32C4×D811yescharacteristic
136C2×C32C4×Q1611yescharacteristic
137C2×C32#46611yescharacteristic
138C2×C32#46711yescharacteristic
139C2×C32#49911yescharacteristic
140C2×C32#50011yescharacteristic
141C22×C4—62no—
142C22×C4—62no—
143C22×C4—91no—
144C22×C4—91no—
145C22×C4GO+(4,𝔽2)11yescharacteristic
146C2×C8—92no—
147C2×C8—92no—
148C2×C8—92no—
149C2×C8—92no—
150C2×C8—181no—
151C2×C8—181no—
152C4⋊C4—94no—
153C4⋊C4—124no—
154C4⋊C4—182no—
155C4⋊C4—182no—
156C4⋊C4—182no—
157C42—181no—
158C42—181no—
159C22×C3—22no—
160C22×C3—22no—
161C22×C3—22no—
162C22×C3—22no—
163C22×C3—22no—
164C22×C3—22no—
165C22×C3—22no—
166C3×C4—44no—
167C3×C4—124no—
168C3×C4—242no—
169Dic3—44no—
170Dic3—62no—
171Dic3—62no—
172Dic3—62no—
173Dic3—62no—
174Dic3—82no—
175Dic3—124no—
176C32#194211yescharacteristic, complemented, Sylow
177C23C2×GO+(4,𝔽2)11yescharacteristic
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—64no—
181C2×C4—91no—
182C2×C4—91no—
183C2×C4—91no—
184C2×C4—91no—
185C2×C4—91no—
186C2×C4—91no—
187C2×C4—92no—
188C2×C4—122no—
189C2×C4—122no—
190C2×C4—122no—
191C2×C4—122no—
192C2×C4—122no—
193C2×C4—181no—
194C2×C4—181no—
195C2×C4#377412yes—
196C8—94no—
197C8—182no—
198C2×C3—22no—
199C2×C3—22no—
200C2×C3—22no—
201C2×C3—22no—
202C2×C3—22no—
203C2×C3—22no—
204C2×C3—22no—
205C22#6422211yescharacteristic
206C22#6422311yescharacteristic
207C22#6422811yescharacteristic
208C22C4×GO+(4,𝔽2)11yescharacteristic
209C22C2×#377411yescharacteristic
210C22#6423711yescharacteristic
211C22#6424211yescharacteristic
212C4—22no—
213C4—91no—
214C4—91no—
215C4—91no—
216C4—91no—
217C4—124no—
218C4—182no—
219C4—242no—
220C3—22no—
221C2#1059338811yescharacteristic
222C2#1059339011yescharacteristic
223C2#1059341011yescharacteristic
224C2C4×#377411yescharacteristic
225C2#1059344511yescharacteristic
226C2#1059344611yescharacteristic
227C2#1059352011yescharacteristic
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#1942
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. #63743C4semidirect
63. #622C4⋊C4semidirect
176. C32#1942semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#6222
C2×#637432
#105913372
#105900752
#19429