Finite Group Databasebeta

← #11773679

Subgroups — #11773679

Order 1152.

296 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 78 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#10593727C211yesmaximal, characteristic
2#10593725C211yesmaximal, characteristic
3#10592532C211yesmaximal, characteristic
4#10590169C211yesmaximal, characteristic, complemented
5#10590169C211yesmaximal, characteristic, complemented
6#10590168C211yesmaximal, characteristic, complemented
7C8×#622C211yesmaximal, characteristic, complemented
8C42×C3⋊D3C2211yescharacteristic
9#63779C412yes—
10#63778C412yes—
11#63778C412yes—
12C4⋊#622C412yes—
13C4×#622C2211yescharacteristic
14C4×#622C2211yescharacteristic
15C4×#622C2211yescharacteristic
16C4×#622C2211yescharacteristic
17C32×C4⋊C8C411yescharacteristic
18#63647C411yescharacteristic
19#63647C411yescharacteristic
20C8×C3⋊Dic3C2211yescharacteristic
21C8×C3⋊Dic3C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C411yescharacteristic
23#4833—62no—
24C2×C4×C3⋊D3C2×C411yescharacteristic
25C2×C4×C3⋊D3C2×C411yescharacteristic
26C2×C4×C3⋊D3C2×C411yescharacteristic
27C2×#622C2×C412yes—
28C2×#622C2×C412yes—
29C2×#622C2×C412yes—
30C2×#622C2×C412yes—
31C2×C32×C8C2×C411yescharacteristic
32C2×C32×C8C2×C411yescharacteristic
33C32×C42C2×C411yescharacteristic
34C4×C3⋊Dic3C2×C411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3C2311yescharacteristic
37C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
38C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
39#1454—91nomaximal, Sylow
40C42×D3—62no—
41C3×C4⋊C8—22no—
42(C2×D3)⋊C8—62no—
43(C2×D3)⋊C8—62no—
44C8×Dic3—62no—
45C8×Dic3—62no—
46C4⋊(C3⋊C8)—62no—
47C22×C3⋊D3C4211yescharacteristic
48C2×C32×C4C4211yescharacteristic
49C2×C32×C4C4211yescharacteristic
50C2×C32×C4C22×C411yescharacteristic
51C2×C3⋊Dic3C4211yescharacteristic
52C2×C3⋊Dic3C22×C411yescharacteristic
53C2×C3⋊Dic3C22×C411yescharacteristic
54C4×C3⋊D3—22no—
55C4×C3⋊D3—21no—
56C4×C3⋊D3—21no—
57C4×C3⋊D3—22no—
58#622—22no—
59#622—22no—
60#622—22no—
61#622—22no—
62C32×C8—21no—
63C32×C8—21no—
64C3⋊(C3⋊C8)—21no—
65C3⋊(C3⋊C8)—21no—
66#431—91no—
67#431—91no—
68#431—91no—
69#322—91no—
70#322—91no—
71#322—91no—
72C82—91no—
73C2×C4×D3—62no—
74C2×C4×D3—62no—
75C2×C4×D3—62no—
76C2×C3×C8—22no—
77C2×C3×C8—22no—
78C3×C42—22no—
79C4×Dic3—62no—
80C4×Dic3—62no—
81C4×Dic3—62no—
82C2×C3⋊C8—62no—
83C2×C3⋊C8—62no—
84C22×C32C2×C4211yescharacteristic
85C2×C3⋊D3—21no—
86C2×C3⋊D3—21no—
87C2×C3⋊D3—21no—
88C32×C4—21no—
89C32×C4—21no—
90C32×C4#13111yescharacteristic
91C32×C4#13111yescharacteristic
92C3⋊Dic3—21no—
93C3⋊Dic3#13112yes—
94C3⋊Dic3#13112yes—
95C2×C42—91no—
96C4⋊C8—92no—
97C4⋊C8—92no—
98C4⋊C8—91no—
99C4⋊C8#15711yescharacteristic
100C22⋊C8—92no—
101C22⋊C8—92no—
102C22⋊C8—91no—
103C22⋊C8—91no—
104C4×C8—91no—
105C4×C8—91no—
106C4×C8—91no—
107C4×C8—91no—
108C4×C8—91no—
109C4×C8—91no—
110C22×D3—62no—
111C2×C3×C4—22no—
112C2×C3×C4—22no—
113C2×C3×C4—22no—
114C2×Dic3—62no—
115C2×Dic3—62no—
116C2×Dic3—62no—
117C4×D3—68no—
118C4×D3—124no—
119C4×D3—122no—
120C4×D3—122no—
121C3×C8—42no—
122C3×C8—42no—
123C3⋊C8—122no—
124C3⋊C8—122no—
125C2×C32#40511yescharacteristic
126C2×C32#40511yescharacteristic
127C2×C32#40511yescharacteristic
128C3⋊D3—41no—
129C22×C4—91no—
130C22×C4—91no—
131C22×C4—91no—
132C2×C8—92no—
133C2×C8—92no—
134C2×C8—92no—
135C2×C8—92no—
136C2×C8—91no—
137C2×C8—91no—
138C2×C8C2×#15711yescharacteristic
139C2×C8C2×#15711yescharacteristic
140C42—91no—
141C42—91no—
142C42—91no—
143C42C2×#15711yescharacteristic
144C22×C3—22no—
145C2×D3—64no—
146C2×D3—122no—
147C2×D3—122no—
148C3×C4—24no—
149C3×C4—22no—
150C3×C4—22no—
151C3×C4—42no—
152Dic3—64no—
153Dic3—64no—
154Dic3—122no—
155C32#145411yescharacteristic, complemented, Sylow
156C23—91no—
157C2×C4—91no—
158C2×C4—91no—
159C2×C4—91no—
160C2×C4—182no—
161C2×C4—182no—
162C2×C4—181no—
163C2×C4—181no—
164C2×C4C4×#15711yescharacteristic
165C2×C4C4×#15711yescharacteristic
166C2×C4C22×#15711yescharacteristic
167C8—21no—
168C8—21no—
169C8—182no—
170C8—182no—
171C8—182no—
172C8—182no—
173C8—181no—
174C8—181no—
175C2×C3—22no—
176C2×C3—22no—
177C2×C3—22no—
178D3—124no—
179C22—181no—
180C22—181no—
181C22—181no—
182C22C2×C4×#15711yescharacteristic
183C4—21no—
184C4—21no—
185C4—92no—
186C4—92no—
187C4—181no—
188C4#6428711yescharacteristic
189C4#6428911yescharacteristic
190C3—22no—
191C2—361no—
192C2#1059374811yescharacteristic
193C2#1059376511yescharacteristic
194C2#1059377511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#157
commutator, socleC22×C32C2×C42
FittingC32×C4⋊C8C4
prime radicalC22×C3⋊D3C42
cosocleC4×C3⋊Dic3C23
hypercenterC4⋊C8#157
hypocenterC32#1454
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
4. #10590169C2semidirect
5. #10590169C2semidirect
6. #10590168C2semidirect
7. C8×#622C2semidirect
155. C32#1454semidirect

Maximal subgroups

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

subgroupindex
#105937272
#105937252
#105925322
#105901692
#105901682
C8×#6222
#14549