Finite Group Databasebeta

← #15672705

Subgroups — #15672705

Order 2944.

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

normal subgroups only

This group has 228 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#13093159C211yesmaximal, characteristic
2#13092811C211yesmaximal, characteristic, complemented
3#13092777C211yesmaximal, characteristic, complemented
4#13092776C211yesmaximal, characteristic, complemented
5#13092156C211yesmaximal, characteristic, complemented
6#13092156C211yesmaximal, characteristic, complemented
7C23×#329C211yesmaximal, characteristic, complemented
8C23×#124C2211yescharacteristic
9#10625118—21no—
10#10625108—21no—
11C2×Dic92—21no—
12C2×#67263—21no—
13#10625056—21no—
14#10625056—21no—
15#10625053—21no—
16#10625053—21no—
17#10625046C2211yescharacteristic
18#10625046C2211yescharacteristic
19#10625040C2211yescharacteristic, complemented
20C23×#97C2211yescharacteristic, complemented
21C23×#97C2211yescharacteristic, complemented
22#10625017—21no—
23#10625014—21no—
24#10625003—21no—
25#10624998—21no—
26#10624985C2211yescharacteristic, complemented
27C23×D23—21no—
28C2×Q8×C23D411yescharacteristic
29C2×D4×C23D411yescharacteristic
30C2×C22⋊D23—21no—
31C2×C22⋊D23—21no—
32C2×D92—21no—
33C2×D92D411yescharacteristic
34C2×D92D411yescharacteristic
35C2×Dic46—21no—
36C2×Dic46D411yescharacteristic
37C2×Dic46D411yescharacteristic
38C2×C8×C23—21no—
39C2×C8×C23—21no—
40C22⋊C4×C23—21no—
41C22⋊C4×C23—21no—
42C42×C23C2311yescharacteristic
43C22⋊Dic23—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—
49(C2×D23)⋊C4—21no—
50C4⋊Dic23—21no—
51C4⋊Dic23—21no—
52C4×Dic23—21no—
53C2×C23⋊C8—21no—
54Dic92—42no—
55#67263—42no—
56C23×C23—21no—
57C22×D23—21no—
58C22×D23—21no—
59C22×D23—81no—
60C22×D23—81no—
61C22×D23—81no—
62Q8×C23—41no—
63D4×C23—41no—
64C2×C4×C23—21no—
65C2×C4×C23C2×D411yescharacteristic
66C2×C4×C23C2×D411yescharacteristic
67C2×C4×C23C2×D411yescharacteristic
68C22⋊D23—81no—
69C22⋊D23—81no—
70C2×Dic23—21no—
71C2×Dic23—21no—
72C2×Dic23—41no—
73D92—41no—
74D92—41no—
75D92—81no—
76Dic46—41no—
77Dic46—41no—
78Dic46—41no—
79Dic46—41no—
80C8×C23—22no—
81C8×C23—41no—
82C23⋊C8—41no—
83#1659—231nomaximal, Sylow
84C22×C23—41no—
85C22×C23—41no—
86C22×C23—41no—
87C22×C23#12011yescharacteristic
88C2×D23—41no—
89C2×D23—41no—
90C2×D23—41no—
91C2×D23—41no—
92C2×D23—41no—
93C2×D23—41no—
94C2×D23—84no—
95C4×C23—21no—
96C4×C23—21no—
97C4×C23—21no—
98C4×C23—41no—
99Dic23—41no—
100Dic23—41no—
101Dic23—81no—
102H(3,𝔽4)—231no—
103#497—231no—
104#489—231no—
105#489—231no—
106#329—231no—
107#329—231no—
108#329D2311yescharacteristic, complemented
109C2×C23—81no—
110C2×C23#45311yescharacteristic
111C2×C23#45511yescharacteristic
112C2×C23#45511yescharacteristic
113D23—81no—
114D23—81no—
115C2×Q16—461no—
116C2×SD16—461no—
117C4⋊Q8—231no—
118#124—231no—
119#124—231no—
120#124—461no—
121#124—461no—
122#124—461no—
123#124C2×D2311yescharacteristic
124#120—461no—
125#120—461no—
126#120—461no—
127#103—461no—
128#103—461no—
129#102—461no—
130#102—461no—
131#97—231no—
132#97C2×D2311yescharacteristic, complemented
133#97C2×D2311yescharacteristic, complemented
134C23#165911yescharacteristic, complemented, Sylow
135C24—461no—
136C2×Q8—231no—
137C2×Q8—231no—
138C2×Q8—461no—
139C2×Q8D9211yescharacteristic
140C2×D4—231no—
141C2×D4—231no—
142C2×D4—461no—
143C2×D4—461no—
144C2×D4—461no—
145C2×D4D9211yescharacteristic
146Q16—922no—
147SD16—922no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—461no—
151C4⋊C4—461no—
152C4⋊C4—461no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—461no—
156C22⋊C4—461no—
157C22⋊C4—461no—
158C22⋊C4—461no—
159C22⋊C4—461no—
160C22⋊C4—461no—
161C22⋊C4—461no—
162C42—461no—
163C42C22×D2311yescharacteristic
164C23—21no—
165C23—461no—
166C23—461no—
167C23—1841no—
168C23—1841no—
169C23—1841no—
170Q8—41no—
171Q8—921no—
172Q8—921no—
173Q8—921no—
174Q8—921no—
175D4—41no—
176D4—921no—
177D4—921no—
178D4—1841no—
179D4—1841no—
180D4—1841no—
181C2×C4—21no—
182C2×C4—461no—
183C2×C4—461no—
184C2×C4—921no—
185C2×C4C2×D9211yescharacteristic
186C2×C4D4×D2311yescharacteristic
187C2×C4D4×D2311yescharacteristic
188C8—22no—
189C8—41no—
190C8—921no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—921no—
195C22—921no—
196C22—921no—
197C22—921no—
198C22—921no—
199C22—921no—
200C22—1844no—
201C22#1062505311yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—921no—
207C4—921no—
208C4—1841no—
209C2—81no—
210C2—1841no—
211C2—1841no—
212C2#1309258611yescharacteristic
213C2#1309259611yescharacteristic
214C2#1309259711yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#329C2
socleC22×C23#120
prime radical#13093159C2
hypercenter#329D23
hypocenterC23#1659
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #13092811C2semidirect
3. #13092777C2semidirect
4. #13092776C2semidirect
5. #13092156C2semidirect
6. #13092156C2semidirect
7. C23×#329C2semidirect
19. #10625040C22semidirect
20. C23×#97C22semidirect
21. C23×#97C22semidirect
26. #10624985C22semidirect
108. #329D23semidirect
132. #97C2×D23semidirect
133. #97C2×D23semidirect
134. C23#1659semidirect

Maximal subgroups

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

subgroupindex
#130931592
#130928112
#130927772
#130927762
#130921562
C23×#3292
#165923