Finite Group Databasebeta

← #11796713

Subgroups — #11796713

Order 1152.

577 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 577 conjugacy classes of subgroups — too many to draw. Only its 98 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×#63797C211yesmaximal, characteristic
2#10592579C211yesmaximal, characteristic, complemented
3C2×#63544C211yesmaximal, characteristic, complemented
4C3×#4491C212yesmaximal, complemented
5#10589115C212yesmaximal, complemented
6#69190—32nomaximal
7C2×#3802—21no—
8C2×C8×C3⋊D3C2211yescharacteristic
9#64101—21no—
10C2×C3×D24C2212yes—
11C2×#3713—21no—
12#63797—22no—
13#63797C414yescomplemented
14C32×#107C2211yescharacteristic, complemented
15#63645C2211yescharacteristic, complemented
16#63635—21no—
17C2×C3×C3⋊C16C2212yescomplemented
18#63544—22no—
19C2×D3×D8—32no—
20C2×#798—32no—
21#4880—32no—
22#4880—61no—
23C3×#357—32no—
24#4562—32no—
25#4509—32no—
26#4491D312yescomplemented
27C22×D32—41no—
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C3×D12—22no—
30C2×#625—41no—
31#3802—24no—
32#3802—42no—
33C2×C32×C8C2311yescharacteristic
34C32×C4⋊C4—21no—
35#3752—41no—
36C4⋊(C3⋊Dic3)—21no—
37C4×C3⋊Dic3—41no—
38C2×C3⋊(C3⋊C8)D411yescharacteristic
39C8×C3⋊D3C2×C412yes—
40C8×C3⋊D3D412yes—
41C3×D24—22no—
42C3×D24C2×C414yes—
43#3713—24no—
44C3×C3⋊C16—22no—
45#2140—91noSylow
46C2×D3×D4—62no—
47C2×C3×D8—32no—
48C2×#213—62no—
49D3×D8—38no—
50D3×D8—64no—
51C2×D24C2×D312yes—
52C2×D3×C8—32no—
53C2×D3×C8—61no—
54#892—62no—
55#892—62no—
56C2×C3×C16—32no—
57C3×#107—21no—
58C3×#107C2×D312yescomplemented
59#818—32no—
60#818—61no—
61C2×C3⋊C16C2×D312yescomplemented
62#808—62no—
63#808—62no—
64#798—64no—
65C22×C3⋊D3D811yescharacteristic
66C22×C3×D3—42no—
67C2×D32—44no—
68C2×D32—82no—
69C2×D32—82no—
70C2×C32×C4—41no—
71C2×C32×C4C2×D411yescharacteristic
72C2×C3⋊Dic3—41no—
73C2×C3⋊Dic3D811yescharacteristic
74C4×C3⋊D3C22⋊C412yes—
75C4×C3⋊D3SD1612yes—
76C3×D12—24no—
77C3×D12—42no—
78#625—44no—
79C32×C8C22×C411yescharacteristic
80C32×C8C2×D411yescharacteristic
81C3⋊(C3⋊C8)C22⋊C412yes—
82C22×D8—91no—
83C2×M32—91no—
84#427—91no—
85#357—32no—
86#357—92no—
87C23×D3—122no—
88C2×C3×D4—62no—
89C2×#67—122no—
90D3×D4—68no—
91D3×D4—124no—
92C2×D12—22no—
93C2×C4×D3—32no—
94C2×C4×D3—61no—
95C3×D8—34no—
96C3×D8—62no—
97C2×C3×C8—21no—
98C2×C3×C8C22×D312yes—
99C3×C4⋊C4—22no—
100C3×C4⋊C4—22no—
101#213—68no—
102(C2×D3)⋊C4—122no—
103(C2×D3)⋊C4—122no—
104C4⋊Dic3—62no—
105C4⋊Dic3—62no—
106C4×Dic3—122no—
107C4×Dic3—122no—
108C2×C3⋊C8—32no—
109C2×C3⋊C8—61no—
110D24—22no—
111D24C4×D314yes—
112D3×C8—34no—
113D3×C8—34no—
114D3×C8—62no—
115D3×C8—62no—
116C3×C16—62no—
117C3⋊C16—22no—
118C22×C32C2×D811yescharacteristic
119C2×C3⋊D3—21no—
120C2×C3⋊D3—21no—
121C2×C3⋊D3#10212yes—
122C2×C3×D3—44no—
123C2×C3×D3—82no—
124C2×C3×D3—82no—
125D32—88no—
126C32×C4—81no—
127C32×C4C2×C22⋊C411yescharacteristic
128C32×C4C2×SD1611yescharacteristic
129C3⋊Dic3—81no—
130C3⋊Dic3#10212yes—
131C22×D4—181no—
132C2×D8—32no—
133C2×D8—94no—
134C2×D8—182no—
135C2×D8—181no—
136C22×C8—91no—
137#117—181no—
138M32—182no—
139C2×C16—32no—
140#107—91no—
141#107D3211yescharacteristic, complemented
142#106—181no—
143C23×C3—122no—
144C22×D3—32no—
145C22×D3—42no—
146C22×D3—61no—
147C22×D3—128no—
148C22×D3—244no—
149C22×D3—244no—
150C3×D4—64no—
151C3×D4—122no—
152C2×C3×C4—21no—
153C2×C3×C4—42no—
154C2×C3×C4—42no—
155C2×C3×C4D3×D412yes—
156#67—128no—
157C2×Dic3—32no—
158C2×Dic3—61no—
159C2×Dic3—122no—
160C2×Dic3—122no—
161D12—24no—
162D12—42no—
163C4×D3—34no—
164C4×D3—34no—
165C4×D3—62no—
166C4×D3—62no—
167C3×C8—21no—
168C3×C8—21no—
169C3×C8C2×C4×D312yes—
170C3×C8D3×D412yes—
171C3⋊C8—34no—
172C3⋊C8—62no—
173C2×C32C2×#10211yescharacteristic
174C2×C32#50911yescharacteristic
175C2×C32#50911yescharacteristic
176C3⋊D3—22no—
177C3×D3—84no—
178C24—361no—
179C2×D4—62no—
180C2×D4—184no—
181C2×D4—362no—
182C2×D4—361no—
183C22×C4—91no—
184D8—34no—
185D8—62no—
186D8—184no—
187C2×C8—91no—
188C2×C8—92no—
189C2×C8—92no—
190C2×C8C2×D3211yescharacteristic
191C4⋊C4—21no—
192C4⋊C4—181no—
193C22⋊C4—361no—
194C42—361no—
195C16—62no—
196C22×C3—21no—
197C22×C3—124no—
198C22×C3—242no—
199C22×C3—242no—
200C22×C3D3×D812yes—
201C2×D3—34no—
202C2×D3—44no—
203C2×D3—62no—
204C2×D3—62no—
205C2×D3—62no—
206C2×D3—82no—
207C2×D3—82no—
208C2×D3—121no—
209C2×D3—121no—
210C2×D3—2416no—
211C3×C4—21no—
212C3×C4—21no—
213C3×C4—82no—
214C3×C4—82no—
215C3×C4D3×C22⋊C412yes—
216C3×C4D3×SD1612yes—
217Dic3—34no—
218Dic3—62no—
219Dic3—242no—
220Dic3—242no—
221C32#214011yescharacteristic, complemented, Sylow
222C23—91no—
223C23—122no—
224C23—364no—
225C23—722no—
226C23—722no—
227D4—64no—
228D4—122no—
229D4—364no—
230C2×C4—41no—
231C2×C4—91no—
232C2×C4—92no—
233C2×C4—92no—
234C2×C4—361no—
235C2×C4#381111yescharacteristic
236C8—92no—
237C8C4×D3211yescharacteristic
238C8#380211yescharacteristic
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—244no—
243C2×C3D3×#10212yes—
244C2×C3#491112yes—
245C2×C3#491412yes—
246D3—64no—
247D3—84no—
248D3—122no—
249C22—92no—
250C22—124no—
251C22—181no—
252C22—181no—
253C22—242no—
254C22—242no—
255C22—728no—
256C22#6392611yescharacteristic
257C4—81no—
258C4—92no—
259C4—721no—
260C4#6392111yescharacteristic
261C4#6394011yescharacteristic
262C3—21no—
263C3#6919012yescomplemented
264C2—182no—
265C2—244no—
266C2#1059059311yescharacteristic
267C2#1059102611yescharacteristic
268C2#1059104011yescharacteristic
subgroupG/H
centerC22#63926
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#107C22
socleC22×C32C2×D8
prime radicalC2×#63797C2
cosocleC2×C32×C8C23
hypercenter#107D32
hypocenterC32#2140
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
2. #10592579C2semidirect
3. C2×#63544C2semidirect
4. C3×#4491C2semidirect
5. #10589115C2semidirect
13. #63797C4semidirect
14. C32×#107C22semidirect
15. #63645C22semidirect
17. C2×C3×C3⋊C16C22semidirect
26. #4491D3semidirect
58. C3×#107C2×D3semidirect
61. C2×C3⋊C16C2×D3semidirect
141. #107D32semidirect
221. C32#2140semidirect
263. C3#69190semidirect

Maximal subgroups

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

subgroupindex
C2×#637972
#105925792
C2×#635442
C3×#44912
#105891152
#691903