Finite Group Databasebeta

← #15672488

Subgroups — #15672488

Order 2944.

256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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#13093071C211yesmaximal, characteristic, complemented
2#13092764C211yesmaximal, characteristic, complemented
3#13092613C211yesmaximal, characteristic, complemented
4#13092612C211yesmaximal, characteristic, complemented
5#13092162C211yesmaximal, characteristic, complemented
6#13092146C211yesmaximal, characteristic, complemented
7C23×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#67290—21no—
9C4×D4×C23C2211yescharacteristic
10C2×#67272—21no—
11#10625101—21no—
12C2×C4⋊Dic23—21no—
13C2×D184—21no—
14#10625068—21no—
15#10625057—22no—
16#10625045C2211yescharacteristic
17C4×D92C2211yescharacteristic
18#10625040C2211yescharacteristic
19C23×C4⋊C8C2211yescharacteristic
20C4×C8×C23C2211yescharacteristic
21#10625003—21no—
22#10625003—22no—
23#10624991—21no—
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×D4×C23D411yescharacteristic
26C22×C4×C23—21no—
27C2×C22⋊D23—22no—
28C22×Dic23—22no—
29#67290—42no—
30#67290—42no—
31C2×D92—21no—
32C2×D92—21no—
33C2×D92—21no—
34C2×D92D411yescharacteristic
35C2×C4×D23—21no—
36C2×Dic46—21no—
37C2×C8×C23—21no—
38C2×C8×C23—21no—
39C4⋊C4×C23D411yescharacteristic
40C22⋊C4×C23—21no—
41C42×C23C2311yescharacteristic
42#67272—42no—
43(C2×D23)⋊C4—22no—
44(C2×D23)⋊C4—21no—
45C4⋊Dic23—22no—
46C4⋊Dic23—21no—
47C4⋊Dic23D412yes—
48C4⋊Dic23D411yescharacteristic
49C2×C23⋊C8—21no—
50D184—42no—
51C23×C23—21no—
52C22×D23—21no—
53C22×D23—41no—
54D4×C23—21no—
55D4×C23D812yescomplemented
56C2×C4×C23—21no—
57C2×C4×C23—41no—
58C2×C4×C23—41no—
59C2×C4×C23C2×D411yescharacteristic
60C2×C4×C23C2×D411yescharacteristic
61C2×C4×C23C2×D411yescharacteristic
62C22⋊D23—44no—
63C2×Dic23—22no—
64C2×Dic23—21no—
65C2×Dic23—44no—
66D92—21no—
67D92—21no—
68D92—42no—
69D92—41no—
70D92—41no—
71D92—41no—
72D92—41no—
73C4×D23—41no—
74C4×D23—41no—
75Dic46—41no—
76Dic46—41no—
77C8×C23—41no—
78C8×C23—41no—
79C23⋊C8—41no—
80#1625—231nomaximal, Sylow
81C22×C23—22no—
82C22×C23—41no—
83C22×C23—41no—
84C22×C23#12011yescharacteristic
85C2×D23—41no—
86C2×D23—41no—
87C2×D23—41no—
88C2×D23—81no—
89C2×D23—81no—
90C2×D23—81no—
91C4×C23—21no—
92C4×C23—41no—
93C4×C23C2×D811yescharacteristic
94C4×C23#13511yescharacteristic
95C4×C23AGL(1,ℤ/8)11yescharacteristic
96C4×C23AGL(1,ℤ/8)11yescharacteristic
97Dic23—42no—
98Dic23—41no—
99#547—231no—
100#486—231no—
101#459—231no—
102#459—231no—
103#332—231no—
104D4⋊C8—231no—
105D4⋊C8D2311yescharacteristic, complemented
106C2×C23—42no—
107C2×C23#44711yescharacteristic
108C2×C23#44911yescharacteristic
109C2×C23#45411yescharacteristic
110D23—81no—
111D23—161no—
112C2×#41—461no—
113C2×D8—461no—
114C2×D8—461no—
115C4⋊Q8—231no—
116#127—231no—
117#123—462no—
118C22⋊Q8—461no—
119#121—461no—
120C4×D4—231no—
121C4×D4C2×D2311yescharacteristic
122C2×C4⋊C4—461no—
123C4⋊C8—231no—
124C4⋊C8C2×D2311yescharacteristic
125#102—461no—
126#102—462no—
127#102—461no—
128C4×C8C2×D2311yescharacteristic
129C23#162511yescharacteristic, complemented, Sylow
130#41—922no—
131#41—922no—
132C2×Q8—461no—
133C2×D4—231no—
134C2×D4—462no—
135C2×D4—461no—
136C2×D4—461no—
137C2×D4—461no—
138C2×D4D9211yescharacteristic
139C22×C4—21no—
140C22×C4—462no—
141C22×C4—461no—
142D8—922no—
143D8—922no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—461no—
147C4⋊C4—231no—
148C4⋊C4—232no—
149C4⋊C4—462no—
150C4⋊C4—461no—
151C4⋊C4D9211yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—462no—
154C22⋊C4—461no—
155C42C22×D2311yescharacteristic
156C23—21no—
157C23—461no—
158C23—921no—
159Q8—921no—
160Q8—921no—
161D4—21no—
162D4—461no—
163D4—461no—
164D4—922no—
165D4—924no—
166D4—921no—
167D4—921no—
168D4—921no—
169D4—921no—
170D4D18412yescomplemented
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—461no—
175C2×C4—462no—
176C2×C4—924no—
177C2×C4—921no—
178C2×C4—921no—
179C2×C4C2×D9211yescharacteristic
180C2×C4D4×D2311yescharacteristic
181C2×C4D4×D2311yescharacteristic
182C8—41no—
183C8—41no—
184C8—921no—
185C22—22no—
186C22—41no—
187C22—41no—
188C22—921no—
189C22—921no—
190C22—921no—
191C22—1841no—
192C22—1841no—
193C22—1841no—
194C22#1062505311yescharacteristic
195C4—21no—
196C4—41no—
197C4—921no—
198C4—922no—
199C4C2×D18411yescharacteristic
200C4#1062507911yescharacteristic
201C4#1062508211yescharacteristic
202C4#1062508711yescharacteristic
203C2—42no—
204C2—3681no—
205C2—1841no—
206C2#1309255311yescharacteristic
207C2#1309256311yescharacteristic
208C2#1309259111yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×D4⋊C8C2
socleC22×C23#120
hypercenterD4⋊C8D23
hypocenterC23#1625
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #13093071C2semidirect
2. #13092764C2semidirect
3. #13092613C2semidirect
4. #13092612C2semidirect
5. #13092162C2semidirect
6. #13092146C2semidirect
7. C23×D4⋊C8C2semidirect
55. D4×C23D8semidirect
105. D4⋊C8D23semidirect
129. C23#1625semidirect
170. D4D184semidirect

Maximal subgroups

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

subgroupindex
#130930712
#130927642
#130926132
#130926122
#130921622
#130921462
C23×D4⋊C82
#162523