Finite Group Databasebeta

← #11777387

Subgroups — #11777387

Order 1152.

316 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 56 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#10593752C211yesmaximal, characteristic, complemented
2#10593749C211yesmaximal, characteristic, complemented
3#10592571C211yesmaximal, characteristic
4#10590173C211yesmaximal, characteristic, complemented
5#10590169C211yesmaximal, characteristic, complemented
6#10590160C211yesmaximal, characteristic, complemented
7#10590160C211yesmaximal, characteristic, complemented
8C2×#3788—21no—
9C2×#3787—21no—
10C2×#3745C411yescharacteristic
11#64102C2211yescharacteristic
12#64102C2211yescharacteristic
13#63778—21no—
14#63778—21no—
15C4⋊#622C2211yescharacteristic
16C4⋊#622C2211yescharacteristic
17C4×#622C2211yescharacteristic
18C4×#622C2211yescharacteristic
19C32×#107C411yescharacteristic
20C8×C3⋊Dic3C2211yescharacteristic
21#63636C411yescharacteristic
22#63636C411yescharacteristic
23#4872—62no—
24C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
25C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
26C2×C4×C3⋊D3—21no—
27C2×C4×C3⋊D3—21no—
28C2×#622—21no—
29C2×#622—21no—
30C2×#622—21no—
31C2×#622D411yescharacteristic
32C2×#622D411yescharacteristic
33#3788—42no—
34#3787—42no—
35C2×C32×C8C2×C411yescharacteristic
36C32×C4⋊C4C2×C411yescharacteristic
37C32×C4⋊C4C2×C411yescharacteristic
38#3752—21no—
39#3752—21no—
40C4×C3⋊Dic3C2311yescharacteristic
41C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
42#3745—22no—
43#1581—91nomaximal, Sylow
44C2×D24—62no—
45#893—62no—
46#893—62no—
47C3×#107—22no—
48C8×Dic3—62no—
49#809—62no—
50#809—62no—
51C22×C3⋊D3—21no—
52C22×C3⋊D3—21no—
53C2×C32×C4—21no—
54C2×C32×C4—21no—
55C2×C32×C4C22×C411yescharacteristic
56C2×C3⋊Dic3C2×D411yescharacteristic
57C2×C3⋊Dic3#4111yescharacteristic
58C4⋊(C3⋊D3)—21no—
59C4⋊(C3⋊D3)—21no—
60C4⋊(C3⋊D3)—21no—
61C4⋊(C3⋊D3)M1612yescomplemented
62C4×C3⋊D3—41no—
63C4×C3⋊D3—41no—
64C4×C3⋊D3—41no—
65C4×C3⋊D3—41no—
66#622—21no—
67#622—41no—
68#622—41no—
69#622—41no—
70#622D812yescomplemented
71C32×C8—21no—
72C3⋊(C3⋊C8)—21no—
73C4×D8—91no—
74#436—91no—
75C8×D4—91no—
76#335—91no—
77D4⋊C8—91no—
78D4⋊C8—91no—
79#322—91no—
80C2×D12—62no—
81C2×D12—62no—
82C2×C4×D3—122no—
83C2×C4×D3—122no—
84C2×C3×C8—22no—
85C3×C4⋊C4—22no—
86C3×C4⋊C4—22no—
87(C2×D3)⋊C4—122no—
88(C2×D3)⋊C4—122no—
89C4×Dic3—62no—
90C2×C3⋊C8—62no—
91D24—68no—
92C22×C32C4×D411yescharacteristic
93C2×C3⋊D3—22no—
94C2×C3⋊D3—41no—
95C2×C3⋊D3—41no—
96C2×C3⋊D3—41no—
97C2×C3⋊D3—41no—
98C2×C3⋊D3—41no—
99C32×C4—41no—
100C32×C4—41no—
101C32×C4C2×M1611yescharacteristic
102C32×C4#13111yescharacteristic
103C3⋊Dic3—21no—
104C3⋊Dic3C2×D811yescharacteristic
105C3⋊Dic3#13511yescharacteristic
106C2×D8—91no—
107C2×M16—181no—
108C22×C8—181no—
109C4×D4—91no—
110C4×D4—91no—
111#107#15711yescharacteristic
112C4⋊C8—91no—
113C4⋊C8—91no—
114#102—91no—
115#102—91no—
116C22⋊C8—181no—
117C22⋊C8—181no—
118C4×C8—91no—
119C4×C8—91no—
120C4×C8—91no—
121C22×D3—122no—
122C22×D3—122no—
123C2×C3×C4—22no—
124C2×C3×C4—42no—
125C2×C3×C4—42no—
126C2×Dic3—62no—
127C2×Dic3—62no—
128D12—64no—
129D12—64no—
130D12—122no—
131D12—122no—
132C4×D3—242no—
133C4×D3—242no—
134C4×D3—242no—
135C4×D3—242no—
136C3×C8—24no—
137C3⋊C8—122no—
138C2×C32#43511yescharacteristic
139C2×C32C4×D811yescharacteristic
140C2×C32#44411yescharacteristic
141C3⋊D3—42no—
142C3⋊D3—81no—
143C2×D4—91no—
144C2×D4—91no—
145C22×C4—181no—
146C22×C4—181no—
147D8—182no—
148M16—362no—
149C2×C8—91no—
150C2×C8—91no—
151C2×C8—91no—
152C2×C8—181no—
153C2×C8—181no—
154C2×C8—181no—
155C2×C8—362no—
156C2×C8C2×#15711yescharacteristic
157C4⋊C4C2×#15711yescharacteristic
158C4⋊C4C2×#15711yescharacteristic
159C22⋊C4—181no—
160C22⋊C4—181no—
161C42—91no—
162C22×C3—22no—
163C2×D3—124no—
164C2×D3—124no—
165C2×D3—242no—
166C2×D3—242no—
167C2×D3—242no—
168C2×D3—242no—
169C3×C4—22no—
170C3×C4—22no—
171C3×C4—82no—
172C3×C4—82no—
173Dic3—62no—
174Dic3—62no—
175Dic3—122no—
176C32#158111yescharacteristic, complemented, Sylow
177C23—181no—
178C23—181no—
179D4—92no—
180D4—181no—
181D4—181no—
182D4—181no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—91no—
186C2×C4—91no—
187C2×C4—361no—
188C2×C4—361no—
189C2×C4—361no—
190C2×C4—361no—
191C2×C4C22×#15711yescharacteristic
192C8—21no—
193C8—92no—
194C8—181no—
195C8—181no—
196C8—361no—
197C8—361no—
198C8—361no—
199C2×C3—22no—
200C2×C3—22no—
201C2×C3—22no—
202D3—244no—
203D3—244no—
204C22—182no—
205C22—361no—
206C22—361no—
207C22—361no—
208C22—361no—
209C22—361no—
210C22D4×#15711yescharacteristic
211C4—41no—
212C4—41no—
213C4—91no—
214C4—91no—
215C4—181no—
216C4#6428311yescharacteristic
217C4#6428911yescharacteristic
218C3—22no—
219C2—362no—
220C2—721no—
221C2#1059375111yescharacteristic
222C2D8×#15711yescharacteristic
223C2#1059378811yescharacteristic
subgroupG/H
centerC22D4×#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#107C4
socleC22×C32C4×D4
prime radicalC2×#3745C4
cosocleC4×C3⋊Dic3C23
hypercenter#107#157
hypocenterC32#1581
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
1. #10593752C2semidirect
2. #10593749C2semidirect
4. #10590173C2semidirect
5. #10590169C2semidirect
6. #10590160C2semidirect
7. #10590160C2semidirect
61. C4⋊(C3⋊D3)M16semidirect
70. #622D8semidirect
176. C32#1581semidirect

Maximal subgroups

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

subgroupindex
#105937522
#105937492
#105925712
#105901732
#105901692
#105901602
#15819