Finite Group Databasebeta

← #11878416

Subgroups — #11878416

Order 1152.

1134 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 249 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#10596296C212yesmaximal
2C32×#408C211yesmaximal, characteristic
3#10592836C212yesmaximal, complemented
4#10592815C212yesmaximal, complemented
5#10592438C214yesmaximal, complemented
6#10592422C214yesmaximal, complemented
7#78682—34nomaximal
8C2×C32×#41C2211yescharacteristic
9C22×#634C2212yes—
10C2×C32×M16C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12#64153—22no—
13#64145—22no—
14#64144—22no—
15#64144—22no—
16#64135C2212yes—
17#64133C2214yes—
18#64133C2214yes—
19C2×#3746C2212yes—
20C2×#3746C2212yes—
21C32×C22⋊C8C2214yes—
22#63645C2212yes—
23#63644C2212yes—
24#63643C2214yes—
25#63643C2214yes—
26#5825—38no—
27C3×#408D314yes—
28#5137—38no—
29#5116—38no—
30#4739—316no—
31#4723—316no—
32C32×#41—41no—
33C32×#41—41no—
34C2×C32×Q8D411yescharacteristic
35C2×C32×D4D411yescharacteristic
36C2×C32×D4D412yes—
37C22×C32×C4C2312yes—
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3—22no—
40C2×#634—22no—
41C2×#634—42no—
42C2×#634—42no—
43C2×#634C2314yes—
44C32×M16—41no—
45C2×C32×C8—41no—
46C2×C32×C8C2312yes—
47C2×C32×C8C2312yes—
48#3757—24no—
49#3757—24no—
50#3757—22no—
51C4⋊(C3⋊Dic3)C2314yes—
52#3750—24no—
53#3750—24no—
54C4×C3⋊Dic3—22no—
55#3746—42no—
56#3746—42no—
57#3202—91noSylow
58C2×C3×#41C2×D314yes—
59C22×Dic6—38no—
60C2×C3×M16C2×D314yes—
61C22×C3×C8C2×D314yes—
62#944—68no—
63#936—68no—
64#935—68no—
65#935—68no—
66#926—38no—
67#924—316no—
68#924—316no—
69C2×Dic12—38no—
70C2×Dic12—38no—
71C3×C22⋊C8C2×D3116yes—
72#818—38no—
73#817—38no—
74#816—316no—
75#816—316no—
76C23×C32C2×D411yescharacteristic
77C23×C32C2×D412yes—
78C32×Q8—41no—
79C32×D4—42no—
80C32×D4—41no—
81C2×C32×C4—21no—
82C2×C32×C4—21no—
83C2×C32×C4—22no—
84C2×C32×C4—22no—
85C2×C32×C4C2×D412yes—
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2411yescharacteristic
88C2×C3⋊Dic3—24no—
89C2×C3⋊Dic3—24no—
90C2×C3⋊Dic3—44no—
91#634—24no—
92#634—24no—
93#634—44no—
94C32×C8—22no—
95C32×C8—22no—
96#536—92no—
97#485—94no—
98#470—92no—
99#467—92no—
100#451—94no—
101#408C3⋊D311yescharacteristic
102C3×#41—44no—
103C3×#41—44no—
104C2×C3×Q8D1214yes—
105C2×C3×D4D1214yes—
106C2×C3×D4D1218yes—
107C22×C3×C4C22×D318yes—
108C22×C3×C4C22×D314yes—
109C22×Dic3—68no—
110C2×Dic6—316no—
111C2×Dic6—68no—
112C2×Dic6—128no—
113C2×Dic6—128no—
114C3×M16—44no—
115C2×C3×C8—44no—
116C2×C3×C8C22×D318yes—
117C2×C3×C8C22×D318yes—
118#217—616no—
119#217—616no—
120#217—68no—
121C4⋊Dic3—316no—
122Dic3⋊C4—616no—
123Dic3⋊C4—616no—
124C4×Dic3—68no—
125Dic12—128no—
126Dic12—128no—
127C22×C32—22no—
128C22×C32—21no—
129C22×C32—22no—
130C22×C32—24no—
131C22×C32C22×D411yescharacteristic
132C32×C4—22no—
133C32×C4—21no—
134C32×C4H(5,𝔽2)11yescharacteristic
135C32×C4H(5,𝔽2)11yescharacteristic
136C3⋊Dic3—44no—
137C3⋊Dic3—44no—
138C2×#41C2×C3⋊D311yescharacteristic
139C22×Q8—92no—
140C2×Q16—92no—
141C2×Q16—92no—
142C2×M16C2×C3⋊D311yescharacteristic
143C22×C8C2×C3⋊D311yescharacteristic
144C4⋊Q8—182no—
145#124—182no—
146#123—182no—
147#123—182no—
148C22⋊Q8—94no—
149C22⋊Q8—94no—
150#117—92no—
151#107—92no—
152#106—92no—
153#103—94no—
154#103—94no—
155C22⋊C8C2×C3⋊D314yes—
156C23×C3C2×D1214yes—
157C23×C3C2×D1218yes—
158C3×Q8—44no—
159C3×D4—48no—
160C3×D4—44no—
161C2×C3×C4—24no—
162C2×C3×C4—24no—
163C2×C3×C4—28no—
164C2×C3×C4—28no—
165C2×C3×C4C2×D1218yes—
166C2×C3×C4C2×D1214yes—
167C2×C3×C4C23×D314yes—
168C2×Dic3—616no—
169C2×Dic3—616no—
170C2×Dic3—1216no—
171Dic6—616no—
172Dic6—616no—
173Dic6—1216no—
174C3×C8—28no—
175C3×C8—28no—
176C2×C32—42no—
177C2×C32—41no—
178C2×C32#53411yescharacteristic
179C2×C32#57812yes—
180#41—41no—
181#41—41no—
182C2×Q8—94no—
183C2×Q8—182no—
184C2×Q8—362no—
185C2×Q8—362no—
186C2×Q8C4⋊(C3⋊D3)11yescharacteristic
187C2×D4C4⋊(C3⋊D3)11yescharacteristic
188C2×D4C4⋊(C3⋊D3)12yes—
189C22×C4—182no—
190C22×C4C22×C3⋊D312yes—
191C22×C4C22×C3⋊D311yescharacteristic
192Q16—362no—
193Q16—362no—
194M16—41no—
195C2×C8—41no—
196C2×C8C22×C3⋊D312yes—
197C2×C8C22×C3⋊D312yes—
198C4⋊C4—94no—
199C4⋊C4—184no—
200C4⋊C4—184no—
201C22⋊C4—182no—
202C22⋊C4—184no—
203C22⋊C4—184no—
204C42—182no—
205C22×C3—28no—
206C22×C3—24no—
207C22×C3—28no—
208C22×C3—216no—
209C22×C3C22×D1214yes—
210C3×C4—28no—
211C3×C4—24no—
212C3×C4#100414yes—
213C3×C4#100414yes—
214Dic3—1216no—
215Dic3—1216no—
216C32#320211yescharacteristic, complemented, Sylow
217C23C2×C4⋊(C3⋊D3)11yescharacteristic
218C23C2×C4⋊(C3⋊D3)12yes—
219Q8—41no—
220Q8—184no—
221Q8—184no—
222Q8—364no—
223D4—42no—
224D4—41no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—184no—
230C2×C4—184no—
231C2×C4—364no—
232C2×C4C2×C4⋊(C3⋊D3)12yes—
233C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
234C2×C4C23×C3⋊D311yescharacteristic
235C8—22no—
236C8—22no—
237C2×C3—48no—
238C2×C3—44no—
239C2×C3#549314yes—
240C2×C3#575318yes—
241C22—22no—
242C22—21no—
243C22—22no—
244C22—24no—
245C22C22×C4⋊(C3⋊D3)11yescharacteristic
246C4—22no—
247C4—21no—
248C4—364no—
249C4—364no—
250C4#6436111yescharacteristic
251C4#6436111yescharacteristic
252C3#7868214yescomplemented
253C2—42no—
254C2—41no—
255C2#1059596411yescharacteristic
256C2#1059622412yes—
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#408C2
socleC22×C32C22×D4
prime radicalC2×C32×#41C22
hypercenter#408C3⋊D3
hypocenterC32#3202
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

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

NH ≅ G/Ntype
3. #10592836C2semidirect
4. #10592815C2semidirect
5. #10592438C2semidirect
6. #10592422C2semidirect
216. C32#3202semidirect
252. C3#78682semidirect

Maximal subgroups

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

subgroupindex
#105962962
C32×#4082
#105928362
#105928152
#105924382
#105924222
#786823