Finite Group Databasebeta

← #11784259

Subgroups — #11784259

Order 1152.

434 conjugacy classes of subgroups; only the 124 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 124 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×C8×#157C212yesmaximal
2C4×C4⋊#157C211yesmaximal, characteristic
3C4×#3787C211yesmaximal, characteristic
4C3⋊D3×C4⋊C8C211yesmaximal, characteristic
5#10590181C212yesmaximal
6C2×C4⋊#157C412yes—
7C2×C4×#157C2212yes—
8C2×#3787C2211yescharacteristic
9C2×#3787C2211yescharacteristic
10C2×C8×C3⋊D3C2212yes—
11C42×C3⋊D3C2211yescharacteristic
12#63781C412yes—
13C4×#622C412yescomplemented
14C4×#622C412yescomplemented
15C8×#157—24no—
16C32×C4⋊C8C411yescharacteristic, complemented
17#63641C412yescomplemented
18C4⋊(C3⋊(C3⋊C8))C411yescharacteristic, complemented
19D3×C4⋊C8—62no—
20C22×#157C2×C414yes—
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3C2311yescharacteristic
24C2×#622C2×C412yes—
25C2×#622C2×C412yes—
26C4⋊#157C818yescomplemented
27C4×#157—22no—
28C4×#157—22no—
29#3787—21no—
30#3787—21no—
31#3787D412yes—
32#3787Q812yes—
33C2×C32×C8C2×C412yes—
34C32×C42C2×C411yescharacteristic
35C4×C3⋊Dic3C2×C411yescharacteristic
36C4×C3⋊Dic3C2×C411yescharacteristic
37C4×C3⋊Dic3C2×C411yescharacteristic
38C2×C3⋊(C3⋊C8)C2×C412yes—
39C8×C3⋊D3—22no—
40C8×C3⋊D3—22no—
41C8×C4⋊C4—91nomaximal, Sylow
42C2×D3×C8—64no—
43C42×D3—62no—
44C3×C4⋊C8—22no—
45Dic3⋊C8—64no—
46C4⋊(C3⋊C8)—62no—
47C22×C3⋊D3C22×C411yescharacteristic
48C2×#157—24no—
49C2×#157—24no—
50C2×#157C2×C818yes—
51C2×C32×C4C4211yescharacteristic
52C2×C32×C4C4211yescharacteristic
53C2×C32×C4C22×C411yescharacteristic
54C2×C3⋊Dic3C4211yescharacteristic
55C2×C3⋊Dic3C4211yescharacteristic
56C2×C3⋊Dic3C22×C411yescharacteristic
57C4×C3⋊D3—22no—
58C4×C3⋊D3C2×C814yes—
59C4×C3⋊D3C2×D411yescharacteristic
60C4×C3⋊D3C2×Q811yescharacteristic
61C4×C3⋊D3#4111yescharacteristic
62C4×C3⋊D3#4111yescharacteristic
63#622—22no—
64#622C4⋊C414yescomplemented
65C32×C8—22no—
66C3⋊(C3⋊C8)—22no—
67C2×C4⋊C8—91no—
68C2×C4×C8—91no—
69C2×C4×C8—92no—
70C4×C4⋊C4—91no—
71#336—92no—
72C2×C4×D3—62no—
73C2×C4×D3—62no—
74C2×C4×D3—62no—
75C2×C3×C8—24no—
76C3×C42—22no—
77C4×Dic3—62no—
78C4×Dic3—62no—
79C4×Dic3—62no—
80C2×C3⋊C8—64no—
81D3×C8—124no—
82D3×C8—124no—
83C22×C32C2×C4211yescharacteristic
84C2×C3⋊D3C4×D411yescharacteristic
85C2×C3⋊D3C4×Q811yescharacteristic
86C2×C3⋊D3C22×C812yes—
87C2×C3⋊D3#13112yes—
88#157—28no—
89C32×C4—21no—
90C32×C4C4×C812yescomplemented
91C32×C4C4×D411yescharacteristic
92C32×C4C4×Q811yescharacteristic
93C3⋊Dic3—21no—
94C3⋊Dic3C4×C812yescomplemented
95C3⋊Dic3C2×C4⋊C411yescharacteristic
96C3⋊Dic3#11711yescharacteristic
97C22×C8—91no—
98C22×C8—91no—
99C22×C8—92no—
100C2×C4⋊C4—92no—
101C2×C42—91no—
102C2×C42—92no—
103C4⋊C8—92no—
104C4⋊C8—91no—
105C4⋊C8#15711yescharacteristic, complemented
106C4×C8—92no—
107C4×C8—92no—
108C4×C8—184no—
109#95—92no—
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—62no—
119C4×D3—62no—
120C4×D3—62no—
121C4×D3—62no—
122C4×D3—124no—
123C3×C8—44no—
124C3⋊C8—124no—
125C2×C32C4×C4⋊C411yescharacteristic
126C2×C32C2×C4×C811yescharacteristic
127C2×C32#40511yescharacteristic
128C3⋊D3C8×D412yes—
129C3⋊D3C8×Q812yes—
130C22×C4—91no—
131C22×C4—91no—
132C22×C4—94no—
133C22×C4—91no—
134C2×C8—92no—
135C2×C8—92no—
136C2×C8—92no—
137C2×C8—92no—
138C2×C8—92no—
139C2×C8—182no—
140C2×C8—182no—
141C2×C8—181no—
142C2×C8—181no—
143C2×C8C2×#15712yes—
144C4⋊C4—98no—
145C42—91no—
146C42—91no—
147C42—91no—
148C42—182no—
149C42—182no—
150C42C2×#15711yescharacteristic
151C22×C3—22no—
152C2×D3—62no—
153C2×D3—62no—
154C2×D3—64no—
155C2×D3—64no—
156C3×C4—24no—
157C3×C4—22no—
158C3×C4—22no—
159C3×C4—42no—
160Dic3—64no—
161Dic3—62no—
162Dic3—62no—
163Dic3—122no—
164C32C8×C4⋊C411yescharacteristic, complemented, Sylow
165C23—91no—
166C2×C4—91no—
167C2×C4—91no—
168C2×C4—94no—
169C2×C4—91no—
170C2×C4—91no—
171C2×C4—91no—
172C2×C4—91no—
173C2×C4—98no—
174C2×C4—91no—
175C2×C4—182no—
176C2×C4—184no—
177C2×C4—184no—
178C2×C4C4×#15711yescharacteristic
179C2×C4C4×#15711yescharacteristic
180C2×C4C22×#15711yescharacteristic
181C8—22no—
182C8—94no—
183C8—182no—
184C8—182no—
185C2×C3—22no—
186C2×C3—22no—
187C2×C3—22no—
188D3—64no—
189D3—64no—
190C22—91no—
191C22—91no—
192C22—92no—
193C22—92no—
194C22C2×C4×#15711yescharacteristic
195C4—21no—
196C4—91no—
197C4—91no—
198C4—92no—
199C4—188no—
200C4—181no—
201C4C8×#15712yescomplemented
202C4D4×#15711yescharacteristic
203C4Q8×#15711yescharacteristic
204C3—22no—
205C2—92no—
206C2—92no—
207C2C4⋊C4×#15711yescharacteristic
208C2C2×C8×#15711yescharacteristic
209C2#1059377511yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×#157
commutatorC2×C32C2×C4×C8
FittingC32×C4⋊C8C4
socleC22×C32C2×C42
prime radicalC22×C3⋊D3C22×C4
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊C8#157
hypocenterC32C8×C4⋊C4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
13. C4×#622C4semidirect
14. C4×#622C4semidirect
16. C32×C4⋊C8C4semidirect
17. #63641C4semidirect
18. C4⋊(C3⋊(C3⋊C8))C4semidirect
26. C4⋊#157C8semidirect
64. #622C4⋊C4semidirect
90. C32×C4C4×C8semidirect
94. C3⋊Dic3C4×C8semidirect
105. C4⋊C8#157semidirect
164. C32C8×C4⋊C4semidirect
201. C4C8×#157semidirect

Maximal subgroups

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

subgroupindex
C2×C8×#1572
C4×C4⋊#1572
C4×#37872
C3⋊D3×C4⋊C82
#105901812
C8×C4⋊C49