Finite Group Databasebeta

← #11775178

Subgroups — #11775178

Order 1152.

450 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 58 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#10596049C211yesmaximal, characteristic
2#10593733C211yesmaximal, characteristic
3#10593731C211yesmaximal, characteristic
4#10590215C212yesmaximal
5#10590158C212yesmaximal
6C2×C4×#157—21no—
7C32×C4×Q8C411yescharacteristic, complemented
8#64155C2211yescharacteristic
9#64153C411yescharacteristic, complemented
10#64106C2211yescharacteristic
11#64105—21no—
12#64098—21no—
13#64097C411yescharacteristic, complemented
14#64081—21no—
15C42×C3⋊D3C2211yescharacteristic
16C4×#634—21no—
17C4×#634C411yescharacteristic, complemented
18#63781—21no—
19#63781C2212yes—
20#63779—21no—
21#63778C2212yes—
22#63777—21no—
23#5578—62no—
24C22×#157—22no—
25C2×C32×Q8C2×C411yescharacteristic
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3C2311yescharacteristic
29C2×#634—21no—
30C2×#634C2×C411yescharacteristic
31C2×#622—22no—
32C4×#157—24no—
33C32×C4⋊C4—21no—
34C32×C4⋊C4C2×C411yescharacteristic
35C32×C42—21no—
36C32×C42C2×C411yescharacteristic
37#3752—21no—
38#3752—21no—
39C4⋊(C3⋊Dic3)—21no—
40C4⋊(C3⋊Dic3)C2×C411yescharacteristic
41#3750—21no—
42#3750—21no—
43#3750—21no—
44#3750—21no—
45#3750—21no—
46C4×C3⋊Dic3—21no—
47C4×C3⋊Dic3C2×C411yescharacteristic
48C4×C3⋊Dic3D411yescharacteristic
49C4×C3⋊Dic3D411yescharacteristic
50#1506—91nomaximal, Sylow
51C3×C4×Q8—22no—
52#946—62no—
53#944—62no—
54#897—62no—
55#896—64no—
56#889—64no—
57#888—62no—
58#872—64no—
59C42×D3—62no—
60C4×Dic6—62no—
61C4×Dic6—64no—
62C22×C3⋊D3C2×D411yescharacteristic
63C2×#157—24no—
64C2×#157—42no—
65C2×#157—42no—
66C32×Q8—41no—
67C2×C32×C4—21no—
68C2×C32×C4—21no—
69C2×C32×C4C22⋊C411yescharacteristic
70C2×C32×C4C22⋊C411yescharacteristic
71C2×C32×C4C22×C411yescharacteristic
72C2×C3⋊Dic3—21no—
73C2×C3⋊Dic3—21no—
74C2×C3⋊Dic3C22⋊C411yescharacteristic
75C2×C3⋊Dic3C22⋊C411yescharacteristic
76C2×C3⋊Dic3C2×D411yescharacteristic
77C4×C3⋊D3—22no—
78C4×C3⋊D3—22no—
79C4×C3⋊D3—41no—
80#634—42no—
81#634—41no—
82#622—42no—
83#533—91no—
84#432—91no—
85#376—91no—
86#328—92no—
87#328—92no—
88C2×C3×Q8—22no—
89C2×C4×D3—62no—
90C2×C4×D3—62no—
91C2×C4×D3—62no—
92C2×Dic6—62no—
93C2×Dic6—64no—
94C3×C4⋊C4—24no—
95C3×C4⋊C4—22no—
96C3×C42—24no—
97C3×C42—22no—
98(C2×D3)⋊C4—64no—
99(C2×D3)⋊C4—64no—
100C4⋊Dic3—62no—
101C4⋊Dic3—64no—
102Dic3⋊C4—64no—
103Dic3⋊C4—64no—
104Dic3⋊C4—64no—
105Dic3⋊C4—64no—
106Dic3⋊C4—64no—
107C4×Dic3—62no—
108C4×Dic3—62no—
109C4×Dic3—62no—
110C4×Dic3—64no—
111C22×C32C2×C22⋊C411yescharacteristic
112C2×C3⋊D3—21no—
113C2×C3⋊D3—21no—
114C2×C3⋊D3#13712yes—
115#157—44no—
116C32×C4—21no—
117C32×C4—21no—
118C32×C4—21no—
119C32×C4—41no—
120C32×C4—41no—
121C3⋊Dic3—21no—
122C3⋊Dic3—21no—
123C3⋊Dic3—41no—
124C3⋊Dic3—41no—
125C3⋊Dic3#10412yes—
126C4⋊Q8—91no—
127C4⋊Q8—91no—
128#125—181no—
129C22⋊Q8—91no—
130C22⋊Q8—91no—
131C22⋊Q8—181no—
132C4×Q8—91no—
133C4×Q8—181no—
134C4×Q8#15711yescharacteristic, complemented
135#117—181no—
136C2×C42—91no—
137C2×C42—181no—
138C4⋊C8—181no—
139C22⋊C8—92no—
140#97—181no—
141#95—92no—
142#95—181no—
143C22×D3—62no—
144C3×Q8—44no—
145C2×C3×C4—24no—
146C2×C3×C4—24no—
147C2×C3×C4—22no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150C2×Dic3—62no—
151C2×Dic3—62no—
152C2×Dic3—62no—
153C2×Dic3—64no—
154C2×Dic3—64no—
155C4×D3—68no—
156C4×D3—124no—
157C4×D3—124no—
158Dic6—128no—
159Dic6—124no—
160C2×C32#41011yescharacteristic
161C2×C32#41911yescharacteristic
162C2×C32C2×#10411yescharacteristic
163C3⋊D3—22no—
164C2×Q8—91no—
165C2×Q8—181no—
166C2×Q8C2×#15711yescharacteristic
167C22×C4—91no—
168C22×C4—91no—
169C22×C4—91no—
170C22×C4—182no—
171C2×C8—182no—
172C4⋊C4—21no—
173C4⋊C4—91no—
174C4⋊C4—181no—
175C4⋊C4—181no—
176C4⋊C4—181no—
177C4⋊C4—181no—
178C4⋊C4—181no—
179C4⋊C4—181no—
180C4⋊C4C2×#15711yescharacteristic
181C22⋊C4—181no—
182C22⋊C4—181no—
183C42—21no—
184C42—91no—
185C42—91no—
186C42—91no—
187C42—184no—
188C42—181no—
189C42C2×#15711yescharacteristic
190C22×C3—22no—
191C2×D3—64no—
192C2×D3—122no—
193C2×D3—122no—
194C3×C4—24no—
195C3×C4—24no—
196C3×C4—42no—
197C3×C4—44no—
198C3×C4—44no—
199Dic3—64no—
200Dic3—64no—
201Dic3—122no—
202Dic3—124no—
203Dic3—124no—
204C32#150611yescharacteristic, complemented, Sylow
205C23—91no—
206Q8—41no—
207Q8—361no—
208Q8—362no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—91no—
212C2×C4—91no—
213C2×C4—91no—
214C2×C4—182no—
215C2×C4—182no—
216C2×C4—184no—
217C2×C4—181no—
218C2×C4—181no—
219C2×C4—361no—
220C2×C4—362no—
221C2×C4—362no—
222C2×C4C22⋊#15711yescharacteristic
223C2×C4C22⋊#15711yescharacteristic
224C2×C4C22×#15711yescharacteristic
225C8—362no—
226C2×C3—22no—
227C2×C3—22no—
228C2×C3—22no—
229D3—124no—
230C22—92no—
231C22—181no—
232C22—181no—
233C22C2×C22⋊#15711yescharacteristic
234C4—21no—
235C4—21no—
236C4—21no—
237C4—41no—
238C4—41no—
239C4—92no—
240C4—181no—
241C4—181no—
242C4—364no—
243C4—361no—
244C4—361no—
245C3—22no—
246C2—182no—
247C2#1059379211yescharacteristic
248C2#1059382911yescharacteristic
249C2#1059383911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×C4×Q8C4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenterC4×Q8#157
hypocenterC32#1506
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
7. C32×C4×Q8C4semidirect
9. #64153C4semidirect
13. #64097C4semidirect
17. C4×#634C4semidirect
134. C4×Q8#157semidirect
204. C32#1506semidirect

Maximal subgroups

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

subgroupindex
#105960492
#105937332
#105937312
#105902152
#105901582
#15069