Finite Group Databasebeta

← #15671864

Subgroups — #15671864

Order 2944.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#13092964C211yesmaximal, characteristic
2#13092473C211yesmaximal, characteristic, complemented
3#13092468C211yesmaximal, characteristic, complemented
4#13092146C211yesmaximal, characteristic, complemented
5D4⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
6#13092144C211yesmaximal, characteristic, complemented
7C23×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#67288—21no—
9C4×D4×C23C2211yescharacteristic
10#10625111C411yescharacteristic
11#10625109C411yescharacteristic
12C4×C22⋊D23—21no—
13#10625066C411yescharacteristic
14#10625059C411yescharacteristic
15#10625056—21no—
16#10625055—21no—
17C4×D92C2211yescharacteristic
18C42×D23C2211yescharacteristic
19C23×C4⋊C8C2211yescharacteristic
20C4×C8×C23C2211yescharacteristic
21(C2×D23)⋊C8—21no—
22(C2×D23)⋊C8—21no—
23#10624997—21no—
24Dic23⋊C8—21no—
25C4⋊(C23⋊C8)C2211yescharacteristic
26C4×C23⋊C8C2211yescharacteristic
27C2×D4×C23C2×C411yescharacteristic
28C22×C4×C23—21no—
29C2×C22⋊D23—21no—
30C2×C22⋊D23—21no—
31C2×C22⋊D23—21no—
32#67288—42no—
33#67288—42no—
34C2×D92—21no—
35C2×D92C2×C411yescharacteristic
36C2×C4×D23—21no—
37C2×C4×D23C2×C411yescharacteristic
38C2×C4×D23D411yescharacteristic
39C2×C4×D23D411yescharacteristic
40C2×Dic46—21no—
41C2×C8×C23—21no—
42C2×C8×C23—21no—
43C4⋊C4×C23C2×C411yescharacteristic
44C22⋊C4×C23—21no—
45C42×C23C2311yescharacteristic
46C22⋊Dic23—21no—
47(C2×D23)⋊C4—21no—
48(C2×D23)⋊C4—21no—
49C4⋊Dic23C2×C411yescharacteristic
50Dic23⋊C4—21no—
51C4×Dic23C2×C411yescharacteristic
52C4×Dic23D411yescharacteristic
53C4×Dic23D411yescharacteristic
54C2×C23⋊C8—21no—
55C2×C23⋊C8—21no—
56C23×C23—21no—
57C22×D23—21no—
58C22×D23C22⋊C411yescharacteristic
59D4×C23—21no—
60D4×C23—21no—
61C2×C4×C23—21no—
62C2×C4×C23—41no—
63C2×C4×C23—41no—
64C2×C4×C23C22×C411yescharacteristic
65C2×C4×C23C2×D411yescharacteristic
66C2×C4×C23C2×D411yescharacteristic
67C22⋊D23—42no—
68C22⋊D23—42no—
69C22⋊D23—42no—
70C2×Dic23—21no—
71C2×Dic23C22⋊C411yescharacteristic
72C2×Dic23C22⋊C411yescharacteristic
73C2×Dic23C22⋊C411yescharacteristic
74D92—21no—
75D92—21no—
76D92—42no—
77C4×D23—21no—
78C4×D23—21no—
79C4×D23—21no—
80C4×D23—21no—
81C4×D23—41no—
82C4×D23—41no—
83C4×D23—41no—
84Dic46—42no—
85C8×C23—41no—
86C8×C23—41no—
87C23⋊C8—41no—
88C23⋊C8—41no—
89#1496—231nomaximal, Sylow
90C22×C23—41no—
91C22×C23—41no—
92C22×C23—41no—
93C22×C23C2×C22⋊C411yescharacteristic
94C2×D23—21no—
95C2×D23—21no—
96C2×D23—21no—
97C2×D23—41no—
98C2×D23—41no—
99C2×D23—41no—
100C4×C23—21no—
101C4×C23—41no—
102C4×C23#13111yescharacteristic
103C4×C23#13111yescharacteristic
104C4×C23AGL(1,ℤ/8)11yescharacteristic
105C4×C23AGL(1,ℤ/8)11yescharacteristic
106Dic23—21no—
107Dic23—21no—
108Dic23—21no—
109Dic23—41no—
110#532—231no—
111#432—231no—
112#431—231no—
113D4⋊C8—231no—
114D4⋊C8—231no—
115D4⋊C8—231no—
116D4⋊C8D2311yescharacteristic, complemented
117C2×C23—81no—
118C2×C23#40811yescharacteristic
119C2×C23#41811yescharacteristic
120C2×C23#42111yescharacteristic
121D23—41no—
122D23—81no—
123C2×#41—461no—
124C4⋊Q8—231no—
125#127—231no—
126#124—461no—
127#121—231no—
128#121—231no—
129#121—461no—
130C4×D4—231no—
131C4×D4—461no—
132C4×D4C2×D2311yescharacteristic
133C2×C42—231no—
134C4⋊C8—231no—
135C4⋊C8—461no—
136C4⋊C8C2×D2311yescharacteristic
137C22⋊C8—461no—
138C22⋊C8—461no—
139#97—461no—
140C4×C8—231no—
141C4×C8C2×D2311yescharacteristic
142C23#149611yescharacteristic, complemented, Sylow
143#41—922no—
144#41—922no—
145C2×Q8—461no—
146C2×D4—231no—
147C2×D4—461no—
148C2×D4—461no—
149C2×D4—461no—
150C2×D4—461no—
151C2×D4C4×D2311yescharacteristic
152C22×C4—21no—
153C22×C4—231no—
154C22×C4—231no—
155C22×C4—231no—
156C22×C4—461no—
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—461no—
160C2×C8—461no—
161C4⋊C4—231no—
162C4⋊C4—461no—
163C4⋊C4C4×D2311yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—461no—
166C22⋊C4—461no—
167C22⋊C4—461no—
168C42—231no—
169C42—231no—
170C42—231no—
171C42C22×D2311yescharacteristic
172C23—21no—
173C23—231no—
174C23—461no—
175Q8—922no—
176D4—21no—
177D4—21no—
178D4—461no—
179D4—461no—
180D4—922no—
181D4—922no—
182D4—922no—
183D4—922no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—231no—
188C2×C4—231no—
189C2×C4—231no—
190C2×C4—461no—
191C2×C4—461no—
192C2×C4—461no—
193C2×C4—461no—
194C2×C4—461no—
195C2×C4—921no—
196C2×C4—921no—
197C2×C4—921no—
198C2×C4C2×C4×D2311yescharacteristic
199C2×C4D4×D2311yescharacteristic
200C2×C4D4×D2311yescharacteristic
201C8—41no—
202C8—41no—
203C8—921no—
204C8—921no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—461no—
209C22—461no—
210C22—461no—
211C22—921no—
212C22—921no—
213C22—921no—
214C22C22⋊C4×D2311yescharacteristic
215C4—21no—
216C4—41no—
217C4—461no—
218C4—461no—
219C4—461no—
220C4—921no—
221C4#1062507211yescharacteristic
222C4#1062507811yescharacteristic
223C4#1062508211yescharacteristic
224C4#1062508511yescharacteristic
225C2—81no—
226C2—921no—
227C2—1841no—
228C2#1309238211yescharacteristic
229C2#1309242011yescharacteristic
230C2#1309243211yescharacteristic
subgroupG/H
centerC2×C4D4×D23
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC23×D4⋊C8C2
socleC22×C23C2×C22⋊C4
prime radical#13092964C2
cosocleC42×C23C23
hypercenterD4⋊C8D23
hypocenterC23#1496
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #13092473C2semidirect
3. #13092468C2semidirect
4. #13092146C2semidirect
5. D4⋊(C23⋊C8)C2semidirect
6. #13092144C2semidirect
7. C23×D4⋊C8C2semidirect
116. D4⋊C8D23semidirect
142. C23#1496semidirect

Maximal subgroups

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

subgroupindex
#130929642
#130924732
#130924682
#130921462
D4⋊(C23⋊C8)2
#130921442
C23×D4⋊C82
#149623