Finite Group Databasebeta

← #15672713

Subgroups — #15672713

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#13093161C211yesmaximal, characteristic
2#13092823C211yesmaximal, characteristic, complemented
3#13092809C211yesmaximal, characteristic, complemented
4#13092158C211yesmaximal, characteristic, complemented
5#13092157C211yesmaximal, characteristic, complemented
6#13092156C211yesmaximal, characteristic, complemented
7C23×#489C211yesmaximal, characteristic, complemented
8C23×C4⋊Q8C2211yescharacteristic
9C23×#124C2211yescharacteristic
10#10625117—21no—
11C2×#67275—21no—
12C2×#67274—21no—
13#10625110—21no—
14#10625057—21no—
15#10625055—21no—
16#10625054—21no—
17#10625049—21no—
18#10625046C2211yescharacteristic
19#10625041C2211yescharacteristic
20C23×#103—21no—
21C23×#102—21no—
22C23×#97C2211yescharacteristic
23#10624990—21no—
24#10624989—21no—
25#10624985C2211yescharacteristic
26#10624985C2211yescharacteristic
27C2×Q8×C23—21no—
28C2×Q8×C23D411yescharacteristic
29C2×D4×C23D411yescharacteristic
30C2×C22⋊D23—21no—
31C2×C22⋊D23—21no—
32C22×Dic23—21no—
33C2×D92D411yescharacteristic
34C2×C4×D23—21no—
35C2×Dic46D411yescharacteristic
36C2×C8×C23—21no—
37C4⋊C4×C23—21no—
38C4⋊C4×C23—21no—
39C22⋊C4×C23—21no—
40C22⋊C4×C23—21no—
41C42×C23C2311yescharacteristic
42C22⋊Dic23—21no—
43#67275—42no—
44#67274—42no—
45(C2×D23)⋊C4—21no—
46(C2×D23)⋊C4—21no—
47(C2×D23)⋊C4—21no—
48C4⋊Dic23—21no—
49C4⋊Dic23D411yescharacteristic
50C4⋊Dic23D411yescharacteristic
51Dic23⋊C4—21no—
52Dic23⋊C4—21no—
53Dic23⋊C4—21no—
54C2×C23⋊C8—21no—
55C2×C23⋊C8—21no—
56C23×C23—21no—
57C22×D23—21no—
58Q8×C23—41no—
59Q8×C23—41no—
60Q8×C23—41no—
61D4×C23—41no—
62C2×C4×C23—21no—
63C2×C4×C23—41no—
64C2×C4×C23C2×D411yescharacteristic
65C2×C4×C23C2×D411yescharacteristic
66C2×C4×C23C2×D411yescharacteristic
67C22⋊D23—81no—
68C22⋊D23—81no—
69C2×Dic23—21no—
70C2×Dic23—21no—
71C2×Dic23—21no—
72C2×Dic23—81no—
73D92—41no—
74C4×D23—81no—
75Dic46—41no—
76C8×C23—41no—
77C23⋊C8—22no—
78C23⋊C8—22no—
79#1661—231nomaximal, Sylow
80C22×C23—41no—
81C22×C23—41no—
82C22×C23—41no—
83C22×C23#12011yescharacteristic
84C2×D23—41no—
85C2×D23—41no—
86C2×D23—41no—
87C4×C23—21no—
88C4×C23—21no—
89C4×C23—21no—
90C4×C23—41no—
91C4×C23—81no—
92Dic23—41no—
93Dic23—41no—
94Dic23—41no—
95#562—231no—
96#501—231no—
97#497—231no—
98#489D2311yescharacteristic, complemented
99#330—231no—
100#329—231no—
101#329—231no—
102C2×C23—81no—
103C2×C23#45311yescharacteristic
104C2×C23#45511yescharacteristic
105C2×C23#45611yescharacteristic
106D23—81no—
107C2×Q16—461no—
108C2×SD16—461no—
109C4⋊Q8C2×D2311yescharacteristic
110#125—231no—
111#124—231no—
112#124C2×D2311yescharacteristic
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—21no—
122#102—21no—
123#97—231no—
124#97—231no—
125#97C2×D2311yescharacteristic
126C23#166111yescharacteristic, complemented, Sylow
127C2×Q8—21no—
128C2×Q8—231no—
129C2×Q8C22⋊D2311yescharacteristic
130C2×D4—231no—
131C2×D4—461no—
132C2×D4—461no—
133C2×D4C22⋊D2311yescharacteristic
134C22×C4—461no—
135C22×C4—461no—
136Q16—922no—
137SD16—922no—
138C2×C8—21no—
139C2×C8—461no—
140C2×C8—461no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—231no—
144C4⋊C4—231no—
145C4⋊C4—461no—
146C4⋊C4—461no—
147C4⋊C4—461no—
148C4⋊C4—461no—
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—461no—
152C22⋊C4—461no—
153C22⋊C4—461no—
154C22⋊C4—461no—
155C42C22×D2311yescharacteristic
156C23—21no—
157C23—461no—
158Q8—41no—
159Q8—41no—
160Q8—41no—
161Q8—921no—
162D4—41no—
163D4—921no—
164D4—1841no—
165D4—1841no—
166C2×C4—21no—
167C2×C4—41no—
168C2×C4—461no—
169C2×C4—461no—
170C2×C4—461no—
171C2×C4—1841no—
172C2×C4—1841no—
173C2×C4D4×D2311yescharacteristic
174C2×C4D4×D2311yescharacteristic
175C2×C4C2×C22⋊D2311yescharacteristic
176C8—41no—
177C8—462no—
178C8—462no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—921no—
183C22—921no—
184C22—921no—
185C22#1062510811yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—81no—
191C4—921no—
192C4—921no—
193C4—921no—
194C2—81no—
195C2—1841no—
196C2#1309258311yescharacteristic
197C2#1309259411yescharacteristic
198C2#1309259811yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#489C2
socleC22×C23#120
prime radical#13093161C2
hypercenter#489D23
hypocenterC23#1661
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
2. #13092823C2semidirect
3. #13092809C2semidirect
4. #13092158C2semidirect
5. #13092157C2semidirect
6. #13092156C2semidirect
7. C23×#489C2semidirect
98. #489D23semidirect
126. C23#1661semidirect

Maximal subgroups

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

subgroupindex
#130931612
#130928232
#130928092
#130921582
#130921572
#130921562
C23×#4892
#166123