Finite Group Databasebeta

← #11775713

Subgroups — #11775713

Order 1152.

468 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 60 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#10596095C211yesmaximal, characteristic
2C4×#3792C211yesmaximal, characteristic, complemented
3C2×#63777C211yesmaximal, characteristic, complemented
4#10590216C212yesmaximal, complemented
5#10590159C212yesmaximal, complemented
6C2×#3792—21no—
7C22×#622—21no—
8C32×C22⋊Q8C411yescharacteristic
9#64156C2211yescharacteristic
10Q8×C3⋊Dic3C411yescharacteristic
11#64139C411yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13#64107—21no—
14#64102C411yescharacteristic
15#64101—21no—
16#64099C2211yescharacteristic
17#64095—21no—
18#64090—21no—
19#63777—21no—
20#63777C2212yes—
21#63777C2212yes—
22C4×#622—21no—
23#5624—62no—
24C2×C32×Q8C2×C411yescharacteristic
25C22×C32×C4C2×C411yescharacteristic
26C2×#638—21no—
27C22×C3⋊Dic3D411yescharacteristic
28C22×C3⋊Dic3D411yescharacteristic
29C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
30C2×C4×C3⋊D3—21no—
31#3792—24no—
32C2×#622—24no—
33C2×#622—22no—
34C2×#622—22no—
35C32×C4⋊C4—21no—
36C32×C4⋊C4C2×C411yescharacteristic
37C32×C22⋊C4—21no—
38#3752—21no—
39#3752—21no—
40#3752—21no—
41#3752—21no—
42C4⋊(C3⋊Dic3)—21no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)C2×C411yescharacteristic
45#3750—21no—
46C4×C3⋊Dic3—21no—
47C4×C3⋊Dic3C2×C411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3D411yescharacteristic
50C4×C3⋊Dic3C2311yescharacteristic
51#1524—91nomaximal, Sylow
52C3×C22⋊Q8—22no—
53#947—62no—
54Q8×Dic3—62no—
55#930—62no—
56C2×C4×Dic3—62no—
57#898—64no—
58#893—62no—
59#892—64no—
60#890—62no—
61#886—64no—
62#67⋊C4—64no—
63C23×C32C22⋊C411yescharacteristic
64C22×C3⋊D3—21no—
65C32×Q8—41no—
66C2×C32×C4—21no—
67C2×C32×C4—21no—
68C2×C32×C4—41no—
69C2×C32×C4C22⋊C411yescharacteristic
70C2×C32×C4C22×C411yescharacteristic
71#638—42no—
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3—22no—
74C2×C3⋊Dic3—22no—
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C2×C3⋊Dic3C22⋊C411yescharacteristic
77C2×C3⋊Dic3C2×D411yescharacteristic
78C2×C3⋊Dic3C2×D411yescharacteristic
79C4⋊(C3⋊D3)—41no—
80C4×C3⋊D3—42no—
81#622—24no—
82#622—24no—
83#529—91no—
84C4×M16—91no—
85C2×#97—91no—
86#330—92no—
87#329—92no—
88C2×C3×Q8—22no—
89C22×C3×C4—22no—
90C2×#67—64no—
91C22×Dic3—62no—
92C22×Dic3—62no—
93C2×D12—62no—
94C2×C4×D3—64no—
95C3×C4⋊C4—24no—
96C3×C4⋊C4—22no—
97C3×C22⋊C4—24no—
98(C2×D3)⋊C4—64no—
99(C2×D3)⋊C4—64no—
100(C2×D3)⋊C4—64no—
101(C2×D3)⋊C4—64no—
102C4⋊Dic3—62no—
103C4⋊Dic3—64no—
104C4⋊Dic3—64no—
105Dic3⋊C4—64no—
106C4×Dic3—62no—
107C4×Dic3—62no—
108C4×Dic3—62no—
109C4×Dic3—62no—
110C4×Dic3—64no—
111C22×C32—21no—
112C22×C32—21no—
113C22×C32#10412yes—
114C22×C32C2×C22⋊C411yescharacteristic
115C2×C3⋊D3—41no—
116C2×C3⋊D3—41no—
117C2×C3⋊D3—41no—
118C32×C4—21no—
119C32×C4—21no—
120C32×C4—41no—
121C32×C4—41no—
122C3⋊Dic3—21no—
123C3⋊Dic3—21no—
124C3⋊Dic3—21no—
125C3⋊Dic3—41no—
126C3⋊Dic3#10412yes—
127C2×M16—181no—
128C22×C8—181no—
129#126—181no—
130#125—91no—
131#124—91no—
132#123—181no—
133C22⋊Q8#15711yescharacteristic
134#121—91no—
135C4×Q8—91no—
136C4×D4—91no—
137C4×D4—181no—
138#117—181no—
139C2×C42—91no—
140#97—92no—
141#97—92no—
142#97—181no—
143C4×C8—181no—
144C23×C3—22no—
145C22×D3—64no—
146C3×Q8—44no—
147C2×C3×C4—24no—
148C2×C3×C4—24no—
149C2×C3×C4—22no—
150C2×C3×C4—22no—
151C2×C3×C4—44no—
152#67—128no—
153C2×Dic3—62no—
154C2×Dic3—62no—
155C2×Dic3—62no—
156C2×Dic3—62no—
157C2×Dic3—64no—
158C2×Dic3—124no—
159C2×Dic3—124no—
160D12—124no—
161C4×D3—128no—
162C2×C32—22no—
163C2×C32#41311yescharacteristic
164C2×C32C2×#10411yescharacteristic
165C2×C32C2×#10411yescharacteristic
166C3⋊D3—81no—
167C2×Q8C2×#15711yescharacteristic
168C2×D4—91no—
169C2×D4—181no—
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—181no—
173C22×C4C2×#15711yescharacteristic
174M16—184no—
175C2×C8—182no—
176C2×C8—182no—
177C2×C8—184no—
178C4⋊C4—21no—
179C4⋊C4—91no—
180C4⋊C4—181no—
181C4⋊C4—181no—
182C4⋊C4—181no—
183C4⋊C4C2×#15711yescharacteristic
184C22⋊C4—21no—
185C22⋊C4—181no—
186C22⋊C4—181no—
187C22⋊C4—181no—
188C22⋊C4—181no—
189C42—91no—
190C42—91no—
191C42—91no—
192C42—91no—
193C42—181no—
194C22×C3—22no—
195C22×C3—24no—
196C22×C3—42no—
197C22×C3—42no—
198C2×D3—124no—
199C2×D3—124no—
200C2×D3—124no—
201C3×C4—24no—
202C3×C4—42no—
203C3×C4—44no—
204C3×C4—44no—
205Dic3—64no—
206Dic3—122no—
207Dic3—122no—
208Dic3—122no—
209Dic3—124no—
210C32#152411yescharacteristic, complemented, Sylow
211C23—181no—
212C23C22⋊#15711yescharacteristic
213Q8—41no—
214D4—361no—
215D4—362no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—91no—
220C2×C4—91no—
221C2×C4—91no—
222C2×C4—91no—
223C2×C4—182no—
224C2×C4—182no—
225C2×C4—181no—
226C2×C4—362no—
227C2×C4C22⋊#15711yescharacteristic
228C2×C4C22×#15711yescharacteristic
229C8—184no—
230C8—184no—
231C2×C3—22no—
232C2×C3—22no—
233C2×C3—22no—
234C2×C3—44no—
235D3—244no—
236C22—21no—
237C22—21no—
238C22—361no—
239C22—361no—
240C22—361no—
241C22#6378512yes—
242C22C2×C22⋊#15711yescharacteristic
243C4—21no—
244C4—21no—
245C4—41no—
246C4—41no—
247C4—92no—
248C4—181no—
249C4—181no—
250C4—181no—
251C4—361no—
252C3—22no—
253C2—22no—
254C2—721no—
255C2#1059382411yescharacteristic
256C2C2×#6378511yescharacteristic
257C2#1059383911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C22⋊Q8C4
socleC22×C32C2×C22⋊C4
prime radical#64139C4
cosocleC4×C3⋊Dic3C23
hypercenterC22⋊Q8#157
hypocenterC32#1524
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C4×#3792C2semidirect
3. C2×#63777C2semidirect
4. #10590216C2semidirect
5. #10590159C2semidirect
210. C32#1524semidirect

Maximal subgroups

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

subgroupindex
#105960952
C4×#37922
C2×#637772
#105902162
#105901592
#15249