Finite Group Databasebeta

← #11785131

Subgroups — #11785131

Order 1152.

522 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 522 conjugacy classes of subgroups — too many to draw. Only its 71 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×D4×#157C211yesmaximal, characteristic
2#10593328C212yesmaximal, complemented
3#10591503C212yesmaximal
4#10590053C212yesmaximal, complemented
5C23×#157C412yes—
6C2×D4×C3⋊D3C2211yescharacteristic
7C2×C22⋊#157C412yes—
8D4×#157—22no—
9D4×#157—22no—
10C2×C4⋊#157C2211yescharacteristic
11C2×C4×#157C2211yescharacteristic
12#63818C2214yes—
13#63732—22no—
14#63732—22no—
15C3×#833—22no—
16#63559—22no—
17D3×#100—62no—
18C23×C3⋊D3C2×C412yes—
19C22×#157—22no—
20C22×#157—22no—
21C22×#157—44no—
22C22×#157C2×C411yescharacteristic
23C22×#157C2×C412yes—
24C22×#157C2×C411yescharacteristic
25C2×C32×D4D411yescharacteristic
26C2×#638Q812yes—
27D4×C3⋊D3—22no—
28D4×C3⋊D3—22no—
29C2×C4⋊(C3⋊D3)D411yescharacteristic
30C2×C4×C3⋊D3C2311yescharacteristic
31C22⋊#157—24no—
32C4⋊#157—22no—
33C4×#157D412yes—
34C4×#157D412yes—
35C3×#208—24no—
36#3712—24no—
37#3710—24no—
38#1800—91nomaximal, Sylow
39C2×D3×D4—62no—
40D3×M16—64no—
41C3×#100—62no—
42#833—22no—
43#823—64no—
44C23×C32C4⋊C412yes—
45C22×C3⋊D3—22no—
46C22×C3⋊D3—22no—
47C22×C3⋊D3—42no—
48C22×C3⋊D3—42no—
49C22×C3⋊D3C4⋊C412yes—
50C22×C3⋊D3C22×C411yescharacteristic
51C2×#157—22no—
52C2×#157—22no—
53C2×#157—41no—
54C2×#157—44no—
55C2×#157—44no—
56C2×#157—42no—
57C2×#157C22⋊C411yescharacteristic
58C2×#157C22⋊C412yes—
59C2×#157C22⋊C411yescharacteristic
60C32×D4—22no—
61C2×C32×C4C2×D411yescharacteristic
62#638—24no—
63C2×C3⋊Dic3C2×Q811yescharacteristic
64C4⋊(C3⋊D3)—22no—
65C4×C3⋊D3C2×D412yes—
66C4×C3⋊D3#4112yes—
67C3×C3⋊C8—44no—
68C2×C4×D4—91no—
69#423—92no—
70C2×#100—92no—
71#343—92no—
72C23×D3—64no—
73C2×C3×D4—22no—
74C2×#67—64no—
75D3×D4—124no—
76D3×D4—124no—
77C2×D12—62no—
78C2×C4×D3—62no—
79C3×M16—64no—
80#208—24no—
81ΓL(1,𝔽25)—124no—
82D3×C8—124no—
83C22×C32—22no—
84C22×C32—42no—
85C22×C32C2×C4⋊C411yescharacteristic
86C2×C3⋊D3—21no—
87C2×C3⋊D3—21no—
88C2×C3⋊D3—22no—
89C2×C3⋊D3—44no—
90C2×C3⋊D3—42no—
91C2×C3⋊D3—42no—
92C2×C3⋊D3—42no—
93C2×C3⋊D3C2×C22⋊C411yescharacteristic
94C2×C3⋊D3#11711yescharacteristic
95#157—21no—
96#157—22no—
97#157—42no—
98#157#10012yescomplemented
99C32×C4#12112yes—
100C3⋊Dic3C22⋊Q812yes—
101C22×D4—91no—
102C23×C4—92no—
103C2×M16—94no—
104C4×D4—182no—
105C4×D4—182no—
106C2×C4⋊C4—91no—
107C2×C22⋊C4—92no—
108C2×C42—91no—
109C4⋊C8—182no—
110C4⋊C8—182no—
111#100—62no—
112#100—182no—
113C23×C3—24no—
114C22×D3—62no—
115C22×D3—64no—
116C22×D3—124no—
117C22×D3—124no—
118C22×D3—244no—
119C22×D3—244no—
120C3×D4—44no—
121C2×C3×C4—22no—
122#67—128no—
123C2×Dic3—62no—
124D12—124no—
125C4×D3—64no—
126C4×D3—64no—
127C3×C8—124no—
128C3⋊C8—44no—
129C2×C32—21no—
130C2×C32—42no—
131C2×C32#38011yescharacteristic
132C3⋊D3—21no—
133C3⋊D3—42no—
134C3⋊D3C2×#10011yescharacteristic
135C3⋊D3#41311yescharacteristic
136C24—92no—
137C2×D4—92no—
138C2×D4—91no—
139C2×D4—182no—
140C2×D4—182no—
141C2×D4GO+(4,𝔽2)11yescharacteristic
142C22×C4—91no—
143C22×C4—91no—
144C22×C4—91no—
145C22×C4—92no—
146C22×C4—182no—
147C22×C4—182no—
148C22×C4—364no—
149M16—64no—
150M16—184no—
151C2×C8—184no—
152C4⋊C4—182no—
153C22⋊C4—184no—
154C42—92no—
155C42—92no—
156C22×C3—22no—
157C22×C3—44no—
158C22×C3—84no—
159C2×D3—62no—
160C2×D3—62no—
161C2×D3—122no—
162C2×D3—122no—
163C2×D3—124no—
164C2×D3—244no—
165C2×D3—244no—
166C2×D3—248no—
167C2×D3—244no—
168C3×C4—24no—
169Dic3—64no—
170C32#180011yescharacteristic, complemented, Sylow
171C23—91no—
172C23—92no—
173C23—182no—
174C23—182no—
175C23—362no—
176C23—362no—
177C23#377312yes—
178D4—22no—
179D4—184no—
180D4—182no—
181C2×C4—91no—
182C2×C4—91no—
183C2×C4—92no—
184C2×C4—92no—
185C2×C4—92no—
186C2×C4—91no—
187C2×C4—182no—
188C2×C4—182no—
189C2×C4—364no—
190C2×C4—361no—
191C2×C4—364no—
192C2×C4—362no—
193C2×C4C2×GO+(4,𝔽2)11yescharacteristic
194C8—124no—
195C2×C3—22no—
196C2×C3—42no—
197C2×C3—84no—
198D3—62no—
199D3—62no—
200D3—122no—
201D3—244no—
202C22—22no—
203C22—42no—
204C22—91no—
205C22—91no—
206C22—181no—
207C22—181no—
208C22—182no—
209C22—362no—
210C22—362no—
211C22—362no—
212C22—364no—
213C22C2×#377311yescharacteristic
214C4—92no—
215C4—92no—
216C4—181no—
217C4—182no—
218C4—362no—
219C4#6424212yes—
220C3—22no—
221C2—21no—
222C2—42no—
223C2—91no—
224C2—91no—
225C2—181no—
226C2—362no—
227C2#1059351611yescharacteristic
subgroupG/H
centerC2#10593516
commutatorC22×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×D4D4
socleC2×C32#380
prime radicalC2×D4×C3⋊D3C22
cosocleC2×C4×C3⋊D3C23
hypercenterC2×D4GO+(4,𝔽2)
hypocenterC32#1800
LCSG ▷ C22×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #10593328C2semidirect
4. #10590053C2semidirect
98. #157#100semidirect
170. C32#1800semidirect

Maximal subgroups

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

subgroupindex
C2×D4×#1572
#105933282
#105915032
#105900532
#18009