Finite Group Databasebeta

← #11795209

Subgroups — #11795209

Order 1152.

394 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 69 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×#63779C211yesmaximal, characteristic
2C2×#63743C211yesmaximal, characteristic
3#10591328C212yesmaximal
4#10590075C212yesmaximal
5#10590075C211yesmaximal, characteristic
6C22×#622C2211yescharacteristic
7C22×#622C2211yescharacteristic
8C2×C4×C3⋊Dic3C2211yescharacteristic
9C2×#3724C2212yes—
10C2×#3724C2212yes—
11C2×Dic3⋊Dic3—22no—
12#63779—22no—
13#63743—22no—
14C3×C3⋊#95—22no—
15#4647—62no—
16C22×C32×C4D411yescharacteristic
17C22×C3⋊Dic3D411yescharacteristic
18C22×C3⋊Dic3C2311yescharacteristic
19C22×C3×Dic3—22no—
20C22×C3×Dic3—22no—
21C2×#622—22no—
22C2×#622—21no—
23C2×#622—22no—
24C2×#622D412yes—
25C4×C3⋊Dic3—21no—
26C4×C3⋊Dic3—21no—
27#3724—22no—
28#3724—22no—
29#3724—22no—
30#3724Q814yes—
31Dic3⋊Dic3—44no—
32#2086—91nomaximal, Sylow
33C2×C4⋊Dic3—62no—
34C2×Dic3⋊C4—62no—
35C2×Dic3⋊C4—62no—
36C2×Dic3⋊C4—62no—
37C2×C4×Dic3—62no—
38C3×#95—62no—
39C3⋊#95—22no—
40C23×C32C2×D411yescharacteristic
41C2×C32×C4—22no—
42C2×C32×C4—21no—
43C2×C3⋊Dic3—21no—
44C2×C3⋊Dic3—21no—
45C2×C3⋊Dic3D812yes—
46C2×C3⋊Dic3C2×D411yescharacteristic
47C2×C3⋊Dic3C2×Q812yes—
48C2×C3⋊Dic3#4112yes—
49C2×C3⋊Dic3#4111yescharacteristic
50C2×C3×Dic3—24no—
51C2×C3×Dic3—42no—
52C2×C3×Dic3—42no—
53C2×C3×Dic3—42no—
54C2×C3×Dic3—42no—
55C2×C3×Dic3—42no—
56#622—22no—
57#622—41no—
58C2×#107—91no—
59C2×C4⋊C8—91no—
60#389—92no—
61#340—91no—
62#340—92no—
63C22×C3×C4—22no—
64C22×C3×C4—62no—
65C22×C3×C4—62no—
66C22×Dic3—22no—
67C22×Dic3—22no—
68C22×Dic3—62no—
69C22×Dic3—62no—
70C4⋊Dic3—124no—
71Dic3⋊C4—64no—
72Dic3⋊C4—64no—
73Dic3⋊C4—122no—
74Dic3⋊C4—122no—
75Dic3⋊C4—124no—
76C4×Dic3—122no—
77C4×Dic3—122no—
78C22×C32#12111yescharacteristic
79C22×C32C22⋊Q812yes—
80C22×C32C2×D811yescharacteristic
81C22×C32#13511yescharacteristic
82C22×C32#13712yes—
83C32×C4—41no—
84C3⋊Dic3—22no—
85C3⋊Dic3#12311yescharacteristic
86C3⋊Dic3#12512yes—
87C3⋊Dic3C4⋊Q811yescharacteristic
88C3×Dic3—44no—
89C3×Dic3—82no—
90C22×C8—91no—
91C22×C8—91no—
92C2×C4⋊C4—92no—
93C2×C4⋊C4—92no—
94C2×C4⋊C4—182no—
95C2×C42—91no—
96#107—182no—
97C4⋊C8—182no—
98#95—62no—
99C23×C3—22no—
100C2×C3×C4—24no—
101C2×C3×C4—42no—
102C2×C3×C4—42no—
103C2×C3×C4—64no—
104C2×C3×C4—122no—
105C2×C3×C4—122no—
106C2×C3×C4—122no—
107C2×C3×C4—122no—
108C2×C3×C4—122no—
109C2×Dic3—24no—
110C2×Dic3—42no—
111C2×Dic3—42no—
112C2×Dic3—42no—
113C2×Dic3—42no—
114C2×Dic3—42no—
115C2×Dic3—62no—
116C2×Dic3—62no—
117C2×Dic3—62no—
118C2×Dic3—62no—
119C2×Dic3—62no—
120C2×Dic3—62no—
121C2×Dic3—64no—
122C2×Dic3—122no—
123C2×Dic3—122no—
124C2×C32#39811yescharacteristic
125C2×C32#46611yescharacteristic
126C2×C32#47011yescharacteristic
127C2×C32#47412yes—
128C2×C32#47912yes—
129C22×C4—62no—
130C22×C4—62no—
131C22×C4—91no—
132C22×C4—91no—
133C22×C4GO+(4,𝔽2)11yescharacteristic
134C2×C8—92no—
135C2×C8—182no—
136C2×C8—181no—
137C2×C8—182no—
138C4⋊C4—94no—
139C4⋊C4—182no—
140C4⋊C4—182no—
141C4⋊C4—182no—
142C4⋊C4—364no—
143C42—181no—
144C42—181no—
145C22×C3—22no—
146C22×C3—22no—
147C22×C3—22no—
148C22×C3—22no—
149C22×C3—22no—
150C22×C3—22no—
151C22×C3—22no—
152C3×C4—44no—
153C3×C4—124no—
154C3×C4—242no—
155Dic3—44no—
156Dic3—62no—
157Dic3—62no—
158Dic3—62no—
159Dic3—62no—
160Dic3—82no—
161Dic3—124no—
162C32#208611yescharacteristic, complemented, Sylow
163C23C2×GO+(4,𝔽2)11yescharacteristic
164C2×C4—22no—
165C2×C4—21no—
166C2×C4—64no—
167C2×C4—92no—
168C2×C4—92no—
169C2×C4—91no—
170C2×C4—91no—
171C2×C4—92no—
172C2×C4—122no—
173C2×C4—122no—
174C2×C4—122no—
175C2×C4—122no—
176C2×C4—122no—
177C2×C4—181no—
178C2×C4—181no—
179C8—182no—
180C8—361no—
181C2×C3—22no—
182C2×C3—22no—
183C2×C3—22no—
184C2×C3—22no—
185C2×C3—22no—
186C2×C3—22no—
187C2×C3—22no—
188C22D32⋊Q812yes—
189C22#6422311yescharacteristic
190C22#6422511yescharacteristic
191C22#6423912yes—
192C22#6424211yescharacteristic
193C4—41no—
194C4—91no—
195C4—91no—
196C4—92no—
197C4—124no—
198C4—182no—
199C4—242no—
200C3—22no—
201C2#1059334011yescharacteristic
202C2#1059336712yes—
203C2#1059338212yes—
204C2#1059342311yescharacteristic
205C2#1059350811yescharacteristic
subgroupG/H
center, FrattiniC23C2×GO+(4,𝔽2)
commutator, cosocleC22×C3⋊Dic3C23
FittingC22×C32×C4D4
socle, prime radicalC23×C32C2×D4
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2086
LCSG ▷ C22×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
162. C32#2086semidirect

Maximal subgroups

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

subgroupindex
C2×#637792
C2×#637432
#105913282
#105900752
#20869