Finite Group Databasebeta

← #11791441

Subgroups — #11791441

Order 1152.

486 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 81 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×#64222C211yesmaximal, characteristic
2C4⋊C4×#157C211yesmaximal, characteristic
3C2×#63732C211yesmaximal, characteristic
4C2×#63730C212yesmaximal
5#10590601C212yesmaximal
6C2×#3797C2212yes—
7C2×C4⋊#157C2211yescharacteristic
8C2×C4×#157—21no—
9C2×C4×#157C2211yescharacteristic
10C2×#3773—21no—
11C2×#3773—21no—
12#64222—22no—
13#64222C414yescomplemented
14C4⋊C4×C3⋊D3C2211yescharacteristic
15C2×#3710C2212yes—
16#63781—21no—
17#63732—22no—
18#63730—24no—
19C3×#810—22no—
20#63566—22no—
21D3×#103—62no—
22C22×#157—21no—
23C22×#157D411yescharacteristic
24C22×#157D411yescharacteristic
25C2×C4×C3⋊D3—21no—
26C2×C4×C3⋊D3C2311yescharacteristic
27C2×C3×Dic6—22no—
28C2×#627—22no—
29C2×#624—22no—
30#3797—22no—
31#3797—22no—
32#3797—22no—
33#3797C2×C414yes—
34C4⋊#157—21no—
35C4⋊#157D412yes—
36C4×#157—42no—
37C4×#157C2×C412yes—
38C4×#157D412yes—
39#3773—24no—
40#3773—24no—
41C32×C4⋊C4D411yescharacteristic
42C4⋊(C3⋊Dic3)D411yescharacteristic
43#3750—21no—
44C2×C3×C3⋊C8—22no—
45#3710—22no—
46#3710—22no—
47#1981—91nomaximal, Sylow
48C2×D3×Q8—62no—
49C2×D3×C8—62no—
50D3×C4⋊C4—62no—
51C3×#103—62no—
52#835—62no—
53#816—62no—
54#810—22no—
55C22×C3⋊D3C2×D411yescharacteristic
56C2×#157—21no—
57C2×#157—21no—
58C2×#157—22no—
59C2×#157—41no—
60C2×#157—41no—
61C2×#157C22⋊C412yes—
62C2×#157C22⋊C412yes—
63C2×#157SD1612yes—
64C2×#157Q1612yes—
65C2×C32×C4—21no—
66C2×C32×C4C2×D411yescharacteristic
67C2×C3⋊Dic3—21no—
68C2×C3⋊Dic3#4111yescharacteristic
69C4×C3⋊D3—41no—
70C4×C3⋊D3—41no—
71C4×C3⋊D3C22×C411yescharacteristic
72C4×C3⋊D3C2×D411yescharacteristic
73C4×C3⋊D3C2×D411yescharacteristic
74C4×C3⋊D3#4111yescharacteristic
75C2×C3×Dic3—42no—
76C3×Dic6—24no—
77C3×Dic6—42no—
78#627—24no—
79#627—42no—
80#624—24no—
81#624—42no—
82C3×C3⋊C8—42no—
83C2×C4⋊Q8—91no—
84C2×C4⋊C8—91no—
85C2×#103—92no—
86C2×#103—92no—
87C4×C4⋊C4—91no—
88C2×C3×Q8—62no—
89D3×Q8—64no—
90D3×Q8—64no—
91D3×Q8—122no—
92D3×Q8—122no—
93C2×C4×D3—62no—
94C2×C4×D3—122no—
95C2×C4×D3—122no—
96C2×Dic6—22no—
97C2×Dic6—122no—
98C2×C3×C8—62no—
99C3×C4⋊C4—22no—
100C4⋊Dic3—62no—
101Dic3⋊C4—122no—
102C2×C3⋊C8—22no—
103D3×C8—122no—
104D3×C8—122no—
105C22×C32#12111yescharacteristic
106C2×C3⋊D3C2×C22⋊C411yescharacteristic
107C2×C3⋊D3#12111yescharacteristic
108C2×C3⋊D3C2×SD1611yescharacteristic
109C2×C3⋊D3C2×Q1611yescharacteristic
110C2×C3⋊D3#13711yescharacteristic
111C2×C3⋊D3#13711yescharacteristic
112#157—22no—
113#157—42no—
114#157#10314yescomplemented
115C32×C4—41no—
116C32×C4C4×D411yescharacteristic
117C32×C4#12711yescharacteristic
118C3⋊Dic3—41no—
119C3⋊Dic3C4×D411yescharacteristic
120C3⋊Dic3#12411yescharacteristic
121C3×Dic3—44no—
122C22×Q8—92no—
123C22×C8—92no—
124C4⋊Q8—94no—
125C4⋊Q8—182no—
126C2×C4⋊C4—91no—
127C2×C4⋊C4—91no—
128C2×C4⋊C4—181no—
129C2×C4⋊C4—181no—
130C2×C42—91no—
131C2×C42—181no—
132C4⋊C8—182no—
133#103—62no—
134#103—182no—
135#103—184no—
136#95—181no—
137C22×D3—62no—
138C3×Q8—64no—
139C3×Q8—122no—
140C2×C3×C4—22no—
141C2×C3×C4—42no—
142C2×C3×C4—122no—
143C2×Dic3—42no—
144C2×Dic3—62no—
145C2×Dic3—122no—
146C4×D3—62no—
147C4×D3—62no—
148C4×D3—62no—
149C4×D3—62no—
150C4×D3—124no—
151C4×D3—124no—
152C4×D3—242no—
153C4×D3—242no—
154Dic6—24no—
155Dic6—42no—
156Dic6—124no—
157Dic6—124no—
158C3×C8—122no—
159C3⋊C8—42no—
160C2×C32#39011yescharacteristic
161C2×C32#46111yescharacteristic
162C2×C32#46211yescharacteristic
163C3⋊D3C2×#10311yescharacteristic
164C3⋊D3#41911yescharacteristic
165C3⋊D3#46111yescharacteristic
166C3⋊D3#46211yescharacteristic
167C2×Q8—62no—
168C2×Q8—94no—
169C2×Q8—182no—
170C2×Q8—182no—
171C2×Q8—182no—
172C2×Q8—182no—
173C22×C4—91no—
174C22×C4—91no—
175C22×C4—91no—
176C22×C4—181no—
177C22×C4—182no—
178C22×C4—181no—
179C2×C8—62no—
180C2×C8—182no—
181C2×C8—182no—
182C4⋊C4—92no—
183C4⋊C4—91no—
184C4⋊C4—181no—
185C4⋊C4—181no—
186C4⋊C4—184no—
187C4⋊C4—184no—
188C4⋊C4GO+(4,𝔽2)11yescharacteristic
189C42—92no—
190C42—92no—
191C42—362no—
192C22×C3—22no—
193C2×D3—62no—
194C2×D3—62no—
195C2×D3—62no—
196C2×D3—62no—
197C2×D3—62no—
198C2×D3—62no—
199C3×C4—22no—
200C3×C4—22no—
201C3×C4—82no—
202C3×C4—124no—
203Dic3—44no—
204Dic3—62no—
205Dic3—62no—
206Dic3—242no—
207C32#198111yescharacteristic, complemented, Sylow
208C23—91no—
209Q8—64no—
210Q8—122no—
211Q8—184no—
212Q8—362no—
213C2×C4—21no—
214C2×C4—92no—
215C2×C4—92no—
216C2×C4—92no—
217C2×C4—91no—
218C2×C4—91no—
219C2×C4—91no—
220C2×C4—91no—
221C2×C4—91no—
222C2×C4—92no—
223C2×C4—122no—
224C2×C4—184no—
225C2×C4—181no—
226C2×C4—181no—
227C2×C4—182no—
228C2×C4—181no—
229C2×C4—361no—
230C2×C4—361no—
231C2×C4—362no—
232C2×C4—361no—
233C2×C4—361no—
234C2×C4C2×GO+(4,𝔽2)11yescharacteristic
235C8—122no—
236C2×C3—22no—
237C2×C3—22no—
238C2×C3—22no—
239D3—62no—
240D3—62no—
241D3—62no—
242D3—62no—
243C22—91no—
244C22—91no—
245C22—91no—
246C22—91no—
247C22—91no—
248C22—91no—
249C22#6424211yescharacteristic
250C4—41no—
251C4—94no—
252C4—91no—
253C4—91no—
254C4—124no—
255C4—182no—
256C4—362no—
257C4—361no—
258C4C4×GO+(4,𝔽2)11yescharacteristic
259C4#6423111yescharacteristic
260C3—22no—
261C2—91no—
262C2—91no—
263C2—91no—
264C2—91no—
265C2#1059345411yescharacteristic
266C2#1059346511yescharacteristic
267C2#1059347711yescharacteristic
subgroupG/H
centerC22#64242
commutatorC4×C3⋊D3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#121
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#1981
LCSG ▷ C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
13. #64222C4semidirect
114. #157#103semidirect
207. C32#1981semidirect

Maximal subgroups

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

subgroupindex
C2×#642222
C4⋊C4×#1572
C2×#637322
C2×#637302
#105906012
#19819