Finite Group Databasebeta

← #11790135

Subgroups — #11790135

Order 1152.

378 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 82 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×#63769C211yesmaximal, characteristic
2C2×C8×#157C211yesmaximal, characteristic
3#10593759C212yesmaximal
4C3⋊D3×#107C211yesmaximal, characteristic
5#10590163C212yesmaximal
6C2×C4⋊#157—22no—
7C2×C4⋊#157C2212yes—
8C2×C4×#157C2211yescharacteristic
9C2×#3787C2211yescharacteristic
10C2×C8×C3⋊D3C2211yescharacteristic
11C4⋊C4×C3⋊D3C2212yes—
12#63781—22no—
13#63769—22no—
14C8×#157—22no—
15C32×#107C411yescharacteristic, complemented
16#63645C411yescharacteristic, complemented
17#63634C412yescomplemented
18D3×#107—62no—
19C22×#157—22no—
20C22×#157D411yescharacteristic
21C22×#157D411yescharacteristic
22C2×C4×C3⋊D3—22no—
23C2×C4×C3⋊D3C2311yescharacteristic
24C2×#622—21no—
25C4⋊#157—22no—
26C4⋊#157—22no—
27C4⋊#157—44no—
28C4×#157—21no—
29C4×#157—21no—
30#3787—21no—
31#3787Q812yes—
32C2×C32×C8C2×C411yescharacteristic
33C32×C4⋊C4C2×C412yes—
34C4⋊(C3⋊Dic3)C2×C412yes—
35#3750—22no—
36C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
37C8×C3⋊D3D412yes—
38C8×C3⋊D3Q812yes—
39#1942—91nomaximal, Sylow
40C2×D3×C8—62no—
41D3×C4⋊C4—64no—
42C3×#107—22no—
43#818—62no—
44#807—64no—
45C22×C3⋊D3C2×D411yescharacteristic
46C2×#157—21no—
47C2×#157—21no—
48C2×#157—21no—
49C2×#157—21no—
50C2×#157—42no—
51C2×#157—42no—
52C2×#157—42no—
53C2×#157D812yes—
54C2×#157Q1612yes—
55C2×C32×C4—22no—
56C2×C32×C4C22×C411yescharacteristic
57C2×C3⋊Dic3—22no—
58C2×C3⋊Dic3#4111yescharacteristic
59C4×C3⋊D3—42no—
60C4×C3⋊D3—42no—
61C4×C3⋊D3C2×D411yescharacteristic
62C4×C3⋊D3C2×Q811yescharacteristic
63C4×C3⋊D3C2×Q811yescharacteristic
64C4×C3⋊D3#4111yescharacteristic
65#622—22no—
66C32×C8C4⋊C412yescomplemented
67C3⋊(C3⋊C8)C4⋊C412yescomplemented
68C2×#107—91no—
69C2×#107—91no—
70C2×C4×C8—91no—
71#389—92no—
72#340—92no—
73C2×C4×D3—62no—
74C2×C4×D3—124no—
75C2×C3×C8—22no—
76C3×C4⋊C4—24no—
77C4⋊Dic3—64no—
78Dic3⋊C4—124no—
79C2×C3⋊C8—62no—
80D3×C8—64no—
81D3×C8—64no—
82C22×C32C4×D411yescharacteristic
83C2×C3⋊D3#12111yescharacteristic
84C2×C3⋊D3C4⋊Q811yescharacteristic
85C2×C3⋊D3C2×D811yescharacteristic
86C2×C3⋊D3C2×Q1611yescharacteristic
87C2×C3⋊D3#13511yescharacteristic
88C2×C3⋊D3#13511yescharacteristic
89#157—22no—
90#157—22no—
91#157—82no—
92C32×C4—42no—
93C32×C4C2×C4⋊C411yescharacteristic
94C32×C4C4×Q811yescharacteristic
95C3⋊Dic3—42no—
96C3⋊Dic3C22⋊Q811yescharacteristic
97C3⋊Dic3#12511yescharacteristic
98C22×C8—91no—
99C22×C8—91no—
100C2×C4⋊C4—92no—
101C2×C4⋊C4—92no—
102C2×C4⋊C4—182no—
103C2×C42—91no—
104#107—91no—
105#107—92no—
106#107—182no—
107#107#15711yescharacteristic, complemented
108C4×C8—182no—
109#95—182no—
110C22×D3—62no—
111C2×C3×C4—22no—
112C2×C3×C4—44no—
113C2×Dic3—62no—
114C2×Dic3—124no—
115C4×D3—62no—
116C4×D3—62no—
117C4×D3—62no—
118C4×D3—62no—
119C4×D3—244no—
120C4×D3—244no—
121C3×C8—24no—
122C3⋊C8—64no—
123C2×C32#38911yescharacteristic
124C2×C32C4×D811yescharacteristic
125C2×C32C4×Q1611yescharacteristic
126C3⋊D3#46611yescharacteristic
127C3⋊D3#46711yescharacteristic
128C3⋊D3#49911yescharacteristic
129C3⋊D3#50011yescharacteristic
130C22×C4—91no—
131C22×C4—91no—
132C22×C4—91no—
133C22×C4—182no—
134C22×C4—182no—
135C2×C8—91no—
136C2×C8—92no—
137C2×C8—92no—
138C2×C8—92no—
139C2×C8—181no—
140C2×C8—181no—
141C2×C8C2×#15711yescharacteristic
142C4⋊C4—92no—
143C4⋊C4—182no—
144C4⋊C4—182no—
145C4⋊C4—182no—
146C4⋊C4—364no—
147C4⋊C4C2×#15712yes—
148C42—181no—
149C42—181no—
150C22×C3—22no—
151C2×D3—62no—
152C2×D3—62no—
153C2×D3—62no—
154C2×D3—62no—
155C2×D3—62no—
156C2×D3—62no—
157C3×C4—22no—
158C3×C4—22no—
159C3×C4—84no—
160Dic3—62no—
161Dic3—62no—
162Dic3—244no—
163C32#194211yescharacteristic, complemented, Sylow
164C23—91no—
165C2×C4—22no—
166C2×C4—91no—
167C2×C4—91no—
168C2×C4—91no—
169C2×C4—91no—
170C2×C4—91no—
171C2×C4—92no—
172C2×C4—92no—
173C2×C4—181no—
174C2×C4—181no—
175C2×C4—181no—
176C2×C4—181no—
177C2×C4—182no—
178C2×C4—362no—
179C2×C4—362no—
180C2×C4—362no—
181C2×C4—362no—
182C2×C4—362no—
183C2×C4C22×#15711yescharacteristic
184C8—92no—
185C8—182no—
186C8C4⋊#15712yescomplemented
187C2×C3—22no—
188C2×C3—22no—
189C2×C3—22no—
190D3—62no—
191D3—62no—
192D3—62no—
193D3—62no—
194C22—91no—
195C22—91no—
196C22—91no—
197C22—91no—
198C22—91no—
199C22—91no—
200C22D4×#15711yescharacteristic
201C4—42no—
202C4—91no—
203C4—91no—
204C4—182no—
205C4—182no—
206C4—362no—
207C4—722no—
208C4C2×C4⋊#15711yescharacteristic
209C4Q8×#15711yescharacteristic
210C3—22no—
211C2—91no—
212C2—91no—
213C2—91no—
214C2—91no—
215C2#1059375911yescharacteristic
216C2D8×#15711yescharacteristic
217C2Q16×#15711yescharacteristic
subgroupG/H
centerC22D4×#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#107C4
socleC22×C32C4×D4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenter#107#157
hypocenterC32#1942
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
15. C32×#107C4semidirect
16. #63645C4semidirect
17. #63634C4semidirect
66. C32×C8C4⋊C4semidirect
67. C3⋊(C3⋊C8)C4⋊C4semidirect
107. #107#157semidirect
163. C32#1942semidirect
186. C8C4⋊#157semidirect

Maximal subgroups

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

subgroupindex
C2×#637692
C2×C8×#1572
#105937592
C3⋊D3×#1072
#105901632
#19429