Finite Group Databasebeta

← #11772903

Subgroups — #11772903

Order 1152.

216 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 40 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
1#10592755C211yesmaximal, characteristic
2C3×#4542C211yesmaximal, characteristic
3C3×#4541C211yesmaximal, characteristic
4#67547—31nomaximal
5#67543—31nomaximal
6C32×#124C2211yescharacteristic
7#64079C411yescharacteristic, complemented
8#63662—21no—
9#63659—21no—
10C4×C3⋊(C3⋊C8)C411yescharacteristic, complemented
11C3×#836—21no—
12C3×#834—21no—
13#5056—31no—
14#5056—31no—
15#5056—61no—
16C3×#355—31no—
17C3×#354—31no—
18#4542D311yescharacteristic
19#4541D311yescharacteristic
20C2×C32×Q8D411yescharacteristic
21C2×C32×D4D411yescharacteristic
22C32×C22⋊C4—41no—
23C32×C42C2×C411yescharacteristic
24C4⋊(C3⋊Dic3)—21no—
25#3750—41no—
26C2×C3⋊(C3⋊C8)—21no—
27C3×#217—41no—
28C3×#208—41no—
29#1414—91noSylow
30C3×#124—21no—
31C3×#124C2×D311yescharacteristic
32C3×#124C2×D311yescharacteristic
33#870—31no—
34#870—31no—
35#870—61no—
36C3×#101—61no—
37C3×#99—61no—
38#836—21no—
39#835—62no—
40#835—61no—
41#835—61no—
42#834—21no—
43#832—62no—
44#832—61no—
45#832—61no—
46C4×C3⋊C8—31no—
47C4×C3⋊C8—31no—
48C4×C3⋊C8—61no—
49C23×C32—21no—
50C32×Q8—41no—
51C32×D4—41no—
52C2×C32×C4—21no—
53C2×C32×C4—21no—
54C2×C32×C4C22⋊C411yescharacteristic
55C2×C3⋊Dic3—41no—
56C2×C3×Dic3—81no—
57C3⋊(C3⋊C8)—41no—
58C3×C3⋊C8—81no—
59#488—91no—
60#355—31no—
61#354—31no—
62C2×C3×Q8—21no—
63C2×C3×Q8D1211yescharacteristic
64C2×C3×Q8#6711yescharacteristic
65C2×C3×D4—21no—
66C2×C3×D4D1211yescharacteristic
67C2×C3×D4#6711yescharacteristic
68C3×M16—121no—
69C3×C22⋊C4—41no—
70C3×C22⋊C4—41no—
71C3×C22⋊C4—42no—
72C3×C22⋊C4—121no—
73C3×C42—21no—
74C3×C42C4×D311yescharacteristic
75C3×C42C4×D311yescharacteristic
76#217—41no—
77C4⋊Dic3—62no—
78C4⋊Dic3—61no—
79C4⋊Dic3—61no—
80Dic3⋊C4—122no—
81Dic3⋊C4—121no—
82Dic3⋊C4—121no—
83#208—41no—
84C2×C3⋊C8—62no—
85C2×C3⋊C8—61no—
86C2×C3⋊C8—61no—
87C22×C32—41no—
88C22×C32—81no—
89C22×C32#9911yescharacteristic
90C32×C4—21no—
91C32×C4—41no—
92C32×C4—41no—
93C3⋊Dic3—81no—
94C3×Dic3—161no—
95#125—91no—
96#124D3211yescharacteristic
97#103—181no—
98#102—181no—
99#101—61no—
100#99—61no—
101C4×C8—91no—
102C23×C3—21no—
103C23×C3—21no—
104C23×C3—41no—
105C3×Q8—41no—
106C3×Q8—41no—
107C3×Q8—42no—
108C3×D4—41no—
109C3×D4—41no—
110C3×D4—42no—
111C2×C3×C4—22no—
112C2×C3×C4—21no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—41no—
118C2×C3×C4—241no—
119C2×C3×C4(C2×D3)⋊C411yescharacteristic
120C2×C3×C4(C2×D3)⋊C411yescharacteristic
121C2×Dic3—81no—
122C2×Dic3—122no—
123C2×Dic3—121no—
124C2×Dic3—121no—
125C3×C8—241no—
126C3⋊C8—81no—
127C3⋊C8—122no—
128C3⋊C8—121no—
129C3⋊C8—121no—
130C2×C32—21no—
131C2×C32—81no—
132C2×C32#35411yescharacteristic
133C2×Q8#62611yescharacteristic
134C2×D4#62611yescharacteristic
135M16—121no—
136C2×C8—181no—
137C4⋊C4—181no—
138C4⋊C4—361no—
139C22⋊C4—41no—
140C22⋊C4—121no—
141C42#62411yescharacteristic
142C22×C3—21no—
143C22×C3—41no—
144C22×C3—41no—
145C22×C3—81no—
146C22×C3—81no—
147C22×C3—81no—
148C22×C3—82no—
149C22×C3#80611yescharacteristic
150C22×C3#80611yescharacteristic
151C3×C4—22no—
152C3×C4—21no—
153C3×C4—21no—
154C3×C4—42no—
155C3×C4—41no—
156C3×C4—41no—
157C3×C4—41no—
158C3×C4—41no—
159C3×C4—81no—
160C3×C4—481no—
161Dic3—161no—
162Dic3—242no—
163Dic3—241no—
164Dic3—241no—
165C32#141411yescharacteristic, complemented, Sylow
166C23—21no—
167Q8—41no—
168D4—41no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—241no—
172C2×C4—361no—
173C2×C4#372211yescharacteristic
174C8—241no—
175C8—361no—
176C2×C3—22no—
177C2×C3—21no—
178C2×C3—21no—
179C2×C3—21no—
180C2×C3—81no—
181C2×C3—81no—
182C2×C3—161no—
183C2×C3#447311yescharacteristic
184C2×C3#447311yescharacteristic
185C22—41no—
186C22—81no—
187C22#6358111yescharacteristic
188C4—21no—
189C4—41no—
190C4—41no—
191C4—481no—
192C4—721no—
193C3—21no—
194C3#6754311yescharacteristic, complemented
195C3#6754711yescharacteristic, complemented
196C2—21no—
197C2—81no—
198C2#1058918111yescharacteristic
subgroupG/H
centerC2#10589181
commutatorC32×C42C2×C4
Frattini, hypercenter#124D32
Fitting, cosocleC32×#124C22
socleC2×C32#354
prime radicalC2×C32×D4D4
hypocenterC32#1414
LCSG ▷ C32×C42 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
7. #64079C4semidirect
10. C4×C3⋊(C3⋊C8)C4semidirect
165. C32#1414semidirect
194. C3#67543semidirect
195. C3#67547semidirect

Maximal subgroups

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

subgroupindex
#105927552
C3×#45422
C3×#45412
#675473
#675433