Finite Group Databasebeta

← #15672458

Subgroups — #15672458

Order 2944.

240 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 53 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#13093152C211yesmaximal, characteristic, complemented
2#13092794C211yesmaximal, characteristic
3#13092618C211yesmaximal, characteristic, complemented
4#13092617C211yesmaximal, characteristic, complemented
5#13092160C211yesmaximal, characteristic, complemented
6#13092149C211yesmaximal, characteristic, complemented
7C23×Q8⋊C8C211yesmaximal, characteristic, complemented
8C4×Q8×C23C2211yescharacteristic
9#10625118—21no—
10C2×#67274—21no—
11C2×D184—22no—
12C2×#67263—21no—
13#10625065—22no—
14#10625064—21no—
15#10625046—21no—
16#10625045C2211yescharacteristic
17#10625045C2211yescharacteristic
18C4×D92—21no—
19C4×Dic46C2211yescharacteristic
20C23×C4⋊C8C2211yescharacteristic
21C4×C8×C23C2211yescharacteristic
22#10625003—21no—
23#10624991—21no—
24C4⋊(C23⋊C8)C2211yescharacteristic
25C2×Q8×C23D411yescharacteristic
26C2×D92—21no—
27C2×D92—21no—
28C2×D92—21no—
29C2×D92—21no—
30C2×D92—21no—
31C2×D92D412yes—
32C2×C4×D23—22no—
33C2×Dic46D411yescharacteristic
34C2×C8×C23—21no—
35C2×C8×C23—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23D411yescharacteristic
38C42×C23—21no—
39C42×C23C2311yescharacteristic
40#67274—42no—
41(C2×D23)⋊C4—22no—
42(C2×D23)⋊C4—22no—
43(C2×D23)⋊C4—22no—
44C4⋊Dic23D411yescharacteristic
45Dic23⋊C4—21no—
46C4×Dic23—21no—
47C2×C23⋊C8—21no—
48D184—44no—
49#67263—42no—
50C22×D23—22no—
51C22×D23—41no—
52Q8×C23—21no—
53Q8×C23—21no—
54C2×C4×C23—21no—
55C2×C4×C23—21no—
56C2×C4×C23C2×D411yescharacteristic
57C2×C4×C23C2×D411yescharacteristic
58C2×C4×C23C2×D411yescharacteristic
59C2×Dic23—21no—
60C2×Dic23—21no—
61D92—42no—
62D92—42no—
63D92—41no—
64D92—41no—
65D92—41no—
66D92—41no—
67D92—41no—
68D92—41no—
69D92—41no—
70D92—41no—
71C4×D23—82no—
72Dic46—21no—
73Dic46—21no—
74C8×C23—22no—
75C8×C23—41no—
76C23⋊C8—41no—
77#1620—231nomaximal, Sylow
78C22×C23#12011yescharacteristic
79C2×D23—42no—
80C2×D23—42no—
81C2×D23—42no—
82C2×D23—81no—
83C2×D23—81no—
84C2×D23—81no—
85C4×C23—21no—
86C4×C23—41no—
87C4×C23—41no—
88C4×C23#13511yescharacteristic
89C4×C23#13511yescharacteristic
90C4×C23AGL(1,ℤ/8)11yescharacteristic
91C4×C23AGL(1,ℤ/8)11yescharacteristic
92Dic23—41no—
93Dic23—41no—
94#559—231no—
95#493—231no—
96#460—231no—
97#460—231no—
98#331—231no—
99Q8⋊C8—231no—
100Q8⋊C8D2311yescharacteristic, complemented
101C2×C23#44911yescharacteristic
102C2×C23#44911yescharacteristic
103C2×C23#45311yescharacteristic
104D23—82no—
105D23—161no—
106C2×SD16—461no—
107C2×SD16—461no—
108C2×D8—462no—
109#127—231no—
110#127—231no—
111#124—461no—
112#124—461no—
113#123—462no—
114C4×Q8—231no—
115C4×Q8C2×D2311yescharacteristic
116C4×D4—461no—
117C4×D4—461no—
118C4⋊C8—231no—
119C4⋊C8C2×D2311yescharacteristic
120#102—461no—
121#102—461no—
122C4×C8C2×D2311yescharacteristic
123C23#162011yescharacteristic, complemented, Sylow
124C2×Q8—231no—
125C2×Q8D9211yescharacteristic
126C2×D4—232no—
127C2×D4—461no—
128C2×D4—461no—
129C2×D4—461no—
130C2×D4—461no—
131C2×D4—461no—
132C22×C4—462no—
133SD16—922no—
134SD16—922no—
135D8—924no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—461no—
139C4⋊C4—21no—
140C4⋊C4—231no—
141C4⋊C4—461no—
142C4⋊C4D9211yescharacteristic
143C22⋊C4—462no—
144C22⋊C4—462no—
145C22⋊C4—462no—
146C42—21no—
147C42—461no—
148C42C22×D2311yescharacteristic
149C23—462no—
150C23—921no—
151Q8—21no—
152Q8—21no—
153Q8—461no—
154Q8—461no—
155D4—922no—
156D4—922no—
157D4—921no—
158D4—921no—
159D4—921no—
160D4—921no—
161D4—921no—
162D4—921no—
163D4—921no—
164D4—921no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—461no—
168C2×C4—461no—
169C2×C4—1842no—
170C2×C4C2×D9211yescharacteristic
171C2×C4D4×D2311yescharacteristic
172C2×C4D4×D2311yescharacteristic
173C8—22no—
174C8—41no—
175C8—921no—
176C22—922no—
177C22—922no—
178C22—922no—
179C22—1841no—
180C22—1841no—
181C22—1841no—
182C22#1062505311yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—921no—
187C4—921no—
188C4#1062507511yescharacteristic
189C4#1062507911yescharacteristic
190C4#1062508511yescharacteristic
191C4#1062509011yescharacteristic
192C2—3681no—
193C2—1842no—
194C2#1309256411yescharacteristic
195C2#1309256511yescharacteristic
196C2#1309258611yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×Q8⋊C8C2
socleC22×C23#120
prime radical#13092794C2
hypercenterQ8⋊C8D23
hypocenterC23#1620
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #13093152C2semidirect
3. #13092618C2semidirect
4. #13092617C2semidirect
5. #13092160C2semidirect
6. #13092149C2semidirect
7. C23×Q8⋊C8C2semidirect
100. Q8⋊C8D23semidirect
123. C23#1620semidirect

Maximal subgroups

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

subgroupindex
#130931522
#130927942
#130926182
#130926172
#130921602
#130921492
C23×Q8⋊C82
#162023