Finite Group Databasebeta

← #11791429

Subgroups — #11791429

Order 1152.

614 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 614 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
2C2×#63784C214yesmaximal
3C4×C4⋊#157C211yesmaximal, characteristic
4#10593726C211yesmaximal, characteristic
5C2×Q8×C3⋊D3C2212yes—
6C2×C4⋊#157C2212yes—
7C2×C4×#157—21no—
8C2×#3787C2212yes—
9C32×C4⋊Q8C411yescharacteristic, complemented
10#64153C412yescomplemented
11C4⋊C4×C3⋊D3—21no—
12C4⋊C4×C3⋊D3—21no—
13#64097—21no—
14#64097—21no—
15C42×C3⋊D3C2211yescharacteristic
16#64078C411yescharacteristic, complemented
17#63784—28no—
18#63781—21no—
19#63779—21no—
20C4⋊#622—21no—
21D3×C4⋊Q8—62no—
22C22×#157—22no—
23C2×C32×Q8C2×C412yes—
24Q8×C3⋊D3—24no—
25Q8×C3⋊D3—24no—
26C2×C4×C3⋊D3—22no—
27C2×C4×C3⋊D3D411yescharacteristic
28C2×C4×C3⋊D3D411yescharacteristic
29C2×C4×C3⋊D3C2311yescharacteristic
30C2×#634—22no—
31C2×#634C2×C412yes—
32C2×#622—22no—
33C4⋊#157—22no—
34C4⋊#157D414yes—
35C4×#157—42no—
36#3787—24no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4—21no—
39C32×C42C2×C411yescharacteristic
40C4⋊(C3⋊Dic3)—21no—
41C4⋊(C3⋊Dic3)—21no—
42#3750—22no—
43#3750—22no—
44C4×C3⋊Dic3C2×C411yescharacteristic
45C4×C3⋊Dic3D411yescharacteristic
46C4×C3⋊Dic3D411yescharacteristic
47#1981—91nomaximal, Sylow
48C2×D3×Q8—64no—
49C3×C4⋊Q8—22no—
50#944—64no—
51D3×C4⋊C4—64no—
52D3×C4⋊C4—64no—
53#888—64no—
54#888—64no—
55C42×D3—62no—
56#869—62no—
57C22×C3⋊D3C2×D411yescharacteristic
58C2×#157—24no—
59C2×#157—42no—
60C2×#157—42no—
61C32×Q8—24no—
62C2×C32×C4—22no—
63C2×C32×C4C22⋊C411yescharacteristic
64C2×C32×C4C22⋊C411yescharacteristic
65C2×C32×C4C22×C411yescharacteristic
66C2×C3⋊Dic3—22no—
67C2×C3⋊Dic3C22⋊C411yescharacteristic
68C2×C3⋊Dic3C22⋊C411yescharacteristic
69C2×C3⋊Dic3C2×D411yescharacteristic
70C4×C3⋊D3—22no—
71C4×C3⋊D3—44no—
72C4×C3⋊D3SD1612yes—
73C4×C3⋊D3Q1612yes—
74C4×C3⋊D3C2×D412yes—
75C4×C3⋊D3#4112yes—
76#634—24no—
77#634—42no—
78#634—42no—
79#622—42no—
80C2×C4⋊Q8—91no—
81C2×C4⋊C8—91no—
82C2×#103—94no—
83C4×C4⋊C4—91no—
84C2×C3×Q8—24no—
85D3×Q8—128no—
86D3×Q8—128no—
87C2×C4×D3—62no—
88C2×C4×D3—62no—
89C2×C4×D3—62no—
90C2×C4×D3—68no—
91C2×Dic6—64no—
92C2×Dic6—68no—
93C3×C4⋊C4—24no—
94C3×C4⋊C4—24no—
95C3×C42—22no—
96C4⋊Dic3—64no—
97C4⋊Dic3—64no—
98Dic3⋊C4—68no—
99Dic3⋊C4—68no—
100C4×Dic3—62no—
101C4×Dic3—62no—
102C4×Dic3—62no—
103C22×C32C2×C22⋊C411yescharacteristic
104C2×C3⋊D3#12112yes—
105C2×C3⋊D3C2×SD1611yescharacteristic
106C2×C3⋊D3C2×Q1611yescharacteristic
107C2×C3⋊D3#13712yes—
108#157—44no—
109C32×C4—21no—
110C32×C4—42no—
111C32×C4#10312yescomplemented
112C32×C4C4×D412yes—
113C3⋊Dic3—21no—
114C3⋊Dic3—42no—
115C3⋊Dic3#10312yescomplemented
116C3⋊Dic3#12411yescharacteristic
117C3⋊Dic3#12711yescharacteristic
118C22×Q8—92no—
119C22×C8—92no—
120C4⋊Q8—92no—
121C4⋊Q8—91no—
122C4⋊Q8—181no—
123C4⋊Q8—181no—
124C4⋊Q8#15711yescharacteristic, complemented
125C2×C4⋊C4—92no—
126C2×C4⋊C4—181no—
127C2×C4⋊C4—181no—
128C2×C42—91no—
129C2×C42—181no—
130C4⋊C8—181no—
131C4⋊C8—181no—
132#103—188no—
133#95—181no—
134C22×D3—62no—
135C3×Q8—48no—
136C2×C3×C4—28no—
137C2×C3×C4—22no—
138C2×C3×C4—22no—
139C2×C3×C4—22no—
140C2×Dic3—62no—
141C2×Dic3—62no—
142C2×Dic3—62no—
143C2×Dic3—68no—
144C4×D3—64no—
145C4×D3—64no—
146C4×D3—64no—
147C4×D3—64no—
148C4×D3—68no—
149C4×D3—1216no—
150Dic6—128no—
151Dic6—128no—
152Dic6—128no—
153C2×C32#39011yescharacteristic
154C2×C32C2×#10311yescharacteristic
155C2×C32#41911yescharacteristic
156C3⋊D3#46112yes—
157C3⋊D3#46212yes—
158C2×Q8—92no—
159C2×Q8—182no—
160C2×Q8—184no—
161C2×Q8—184no—
162C2×Q8C2×#15712yes—
163C22×C4—91no—
164C22×C4—91no—
165C22×C4—91no—
166C22×C4—182no—
167C22×C4—182no—
168C2×C8—184no—
169C2×C8—182no—
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—94no—
173C4⋊C4—182no—
174C4⋊C4—182no—
175C4⋊C4—182no—
176C4⋊C4—181no—
177C4⋊C4—181no—
178C42—91no—
179C42—91no—
180C42—91no—
181C42—362no—
182C42C2×#15711yescharacteristic
183C22×C3—22no—
184C2×D3—64no—
185C2×D3—62no—
186C2×D3—62no—
187C2×D3—64no—
188C3×C4—24no—
189C3×C4—24no—
190C3×C4—24no—
191C3×C4—48no—
192Dic3—62no—
193Dic3—62no—
194Dic3—64no—
195Dic3—64no—
196Dic3—128no—
197C32#198111yescharacteristic, complemented, Sylow
198C23—91no—
199Q8—24no—
200Q8—184no—
201Q8—362no—
202Q8—362no—
203C2×C4—22no—
204C2×C4—91no—
205C2×C4—91no—
206C2×C4—92no—
207C2×C4—92no—
208C2×C4—92no—
209C2×C4—92no—
210C2×C4—91no—
211C2×C4—182no—
212C2×C4—184no—
213C2×C4—182no—
214C2×C4—364no—
215C2×C4—362no—
216C2×C4—362no—
217C2×C4C22⋊#15711yescharacteristic
218C2×C4C22⋊#15711yescharacteristic
219C2×C4C22×#15711yescharacteristic
220C8—362no—
221C2×C3—22no—
222C2×C3—22no—
223C2×C3—22no—
224D3—64no—
225D3—64no—
226C22—92no—
227C22—91no—
228C22—91no—
229C22—92no—
230C22C2×C22⋊#15711yescharacteristic
231C4—21no—
232C4—42no—
233C4—91no—
234C4—91no—
235C4—92no—
236C4—181no—
237C4—364no—
238C4—362no—
239C4#6378412yescomplemented
240C4D4×#15712yes—
241C3—22no—
242C2—92no—
243C2—92no—
244C2#1059382711yescharacteristic
245C2C2×#6378411yescharacteristic
246C2#1059382911yescharacteristic
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#1981
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
9. C32×C4⋊Q8C4semidirect
10. #64153C4semidirect
16. #64078C4semidirect
111. C32×C4#103semidirect
115. C3⋊Dic3#103semidirect
124. C4⋊Q8#157semidirect
197. C32#1981semidirect
239. C4#63784semidirect

Maximal subgroups

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

subgroupindex
C3⋊D3×C4⋊Q82
C2×#637842
C4×C4⋊#1572
#105937262
#19819