Finite Group Databasebeta

← #15672716

Subgroups — #15672716

Order 2944.

208 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 45 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#13093165C211yesmaximal, characteristic
2#13092827C211yesmaximal, characteristic, complemented
3#13092811C211yesmaximal, characteristic, complemented
4#13092777C211yesmaximal, characteristic, complemented
5#13092156C211yesmaximal, characteristic, complemented
6#13092156C211yesmaximal, characteristic, complemented
7C23×#330C211yesmaximal, characteristic, complemented
8C23×#125C2211yescharacteristic
9C2×Dic92—21no—
10C2×#67263—21no—
11#10625067—21no—
12#10625067—21no—
13#10625066—21no—
14#10625066—21no—
15#10625065—21no—
16#10625065—21no—
17#10625046C2211yescharacteristic
18#10625046C2211yescharacteristic
19#10625040C2211yescharacteristic
20C23×#97C2211yescharacteristic
21C23×#97C2211yescharacteristic
22#10625003—21no—
23#10624998—21no—
24#10624990—21no—
25#10624989—21no—
26#10624985C2211yescharacteristic
27C2×D92—21no—
28C2×D92—21no—
29C2×D92D411yescharacteristic
30C2×D92D411yescharacteristic
31C2×C4×D23—21no—
32C2×C4×D23—21no—
33C2×Dic46—21no—
34C2×Dic46D411yescharacteristic
35C2×Dic46D411yescharacteristic
36C2×C8×C23—21no—
37C2×C8×C23—21no—
38C4⋊C4×C23—21no—
39C4⋊C4×C23—21no—
40C4⋊C4×C23D411yescharacteristic
41C4⋊C4×C23D411yescharacteristic
42C42×C23C2311yescharacteristic
43(C2×D23)⋊C4—21no—
44(C2×D23)⋊C4—21no—
45(C2×D23)⋊C4—21no—
46(C2×D23)⋊C4—21no—
47(C2×D23)⋊C4—21no—
48(C2×D23)⋊C4—21no—
49C4⋊Dic23—21no—
50C4⋊Dic23—21no—
51Dic23⋊C4—21no—
52Dic23⋊C4—21no—
53C2×C23⋊C8—21no—
54Dic92—42no—
55#67263—42no—
56C22×D23—21no—
57C22×D23—21no—
58C2×C4×C23—21no—
59C2×C4×C23—21no—
60C2×C4×C23C2×D411yescharacteristic
61C2×C4×C23C2×D411yescharacteristic
62C2×C4×C23C2×D411yescharacteristic
63C2×Dic23—21no—
64C2×Dic23—21no—
65C2×Dic23—41no—
66D92—41no—
67D92—41no—
68D92—81no—
69D92—81no—
70C4×D23—81no—
71C4×D23—81no—
72Dic46—41no—
73Dic46—41no—
74Dic46—41no—
75Dic46—41no—
76C8×C23—22no—
77C8×C23—41no—
78C23⋊C8—22no—
79#1661—231nomaximal, Sylow
80C22×C23#12011yescharacteristic
81C2×D23—41no—
82C2×D23—41no—
83C2×D23—41no—
84C2×D23—41no—
85C2×D23—41no—
86C2×D23—41no—
87C4×C23—21no—
88C4×C23—21no—
89C4×C23—21no—
90C4×C23—41no—
91C4×C23—41no—
92Dic23—41no—
93Dic23—41no—
94Dic23—81no—
95#562—231no—
96#501—231no—
97#497—231no—
98#489—231no—
99#330D2311yescharacteristic, complemented
100#329—231no—
101#329—231no—
102C2×C23#45311yescharacteristic
103C2×C23#45511yescharacteristic
104C2×C23#45611yescharacteristic
105D23—81no—
106D23—81no—
107C2×Q16—461no—
108C2×SD16—461no—
109C4⋊Q8—231no—
110#125C2×D2311yescharacteristic
111#124—231no—
112#124—231no—
113#123—461no—
114#123—461no—
115C22⋊Q8—461no—
116C22⋊Q8—461no—
117#121—461no—
118#121—461no—
119#107—461no—
120#106—461no—
121#103—461no—
122#102—461no—
123#97—231no—
124#97C2×D2311yescharacteristic
125#97C2×D2311yescharacteristic
126C23#166111yescharacteristic, complemented, Sylow
127C2×Q8—231no—
128C2×Q8—231no—
129C2×Q8—461no—
130C2×D4—231no—
131C2×D4—231no—
132C2×D4—461no—
133C2×D4—461no—
134C22×C4—461no—
135C22×C4—461no—
136Q16—922no—
137SD16—922no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—461no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—461no—
144C4⋊C4—461no—
145C4⋊C4—461no—
146C4⋊C4—461no—
147C4⋊C4D9211yescharacteristic
148C4⋊C4D9211yescharacteristic
149C22⋊C4—461no—
150C22⋊C4—461no—
151C22⋊C4—461no—
152C22⋊C4—461no—
153C22⋊C4—461no—
154C22⋊C4—461no—
155C42C22×D2311yescharacteristic
156C23—461no—
157C23—461no—
158Q8—921no—
159Q8—921no—
160Q8—921no—
161Q8—921no—
162D4—921no—
163D4—921no—
164D4—1841no—
165D4—1841no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—461no—
169C2×C4—461no—
170C2×C4—921no—
171C2×C4—1841no—
172C2×C4—1841no—
173C2×C4C2×D9211yescharacteristic
174C2×C4D4×D2311yescharacteristic
175C2×C4D4×D2311yescharacteristic
176C8—22no—
177C8—41no—
178C8—462no—
179C22—921no—
180C22—921no—
181C22—921no—
182C22—921no—
183C22—921no—
184C22—921no—
185C22#1062505311yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4—921no—
192C4—921no—
193C4—1841no—
194C2—1841no—
195C2—1841no—
196C2#1309258611yescharacteristic
197C2#1309259611yescharacteristic
198C2#1309260211yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#330C2
socleC22×C23#120
prime radical#13093165C2
hypercenter#330D23
hypocenterC23#1661
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
2. #13092827C2semidirect
3. #13092811C2semidirect
4. #13092777C2semidirect
5. #13092156C2semidirect
6. #13092156C2semidirect
7. C23×#330C2semidirect
99. #330D23semidirect
126. C23#1661semidirect

Maximal subgroups

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

subgroupindex
#130931652
#130928272
#130928112
#130927772
#130921562
C23×#3302
#166123