Finite Group Databasebeta

← #15672714

Subgroups — #15672714

Order 2944.

208 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 49 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#13092827C211yesmaximal, characteristic, complemented
2#13092812C211yesmaximal, characteristic, complemented
3#13092776C211yesmaximal, characteristic, complemented
4#13092159C211yesmaximal, characteristic, complemented
5#13092157C211yesmaximal, characteristic, complemented
6#13092157C211yesmaximal, characteristic, complemented
7C23×#562C211yesmaximal, characteristic
8C23×#125C2211yescharacteristic
9C23×#124C2211yescharacteristic
10C23×#124C2211yescharacteristic
11C23×#123—21no—
12C23×#123—21no—
13C23×C22⋊Q8—21no—
14C23×C22⋊Q8—21no—
15C23×#121—21no—
16C23×#121—21no—
17C2×#67275—21no—
18C2×#67273—21no—
19#10625040C2211yescharacteristic
20#10625017—21no—
21#10625014—21no—
22#10624990—21no—
23#10624989—21no—
24#10624985C2211yescharacteristic
25#10624985C2211yescharacteristic
26#10624985C2211yescharacteristic
27C2×Q8×C23D411yescharacteristic
28C2×Q8×C23D411yescharacteristic
29C2×D4×C23—21no—
30C2×D4×C23—21no—
31C2×D4×C23D411yescharacteristic
32C2×D4×C23D411yescharacteristic
33C22×C4×C23—21no—
34C22×C4×C23—21no—
35C2×Dic46—21no—
36C4⋊C4×C23—21no—
37C4⋊C4×C23—21no—
38C4⋊C4×C23—21no—
39C4⋊C4×C23—21no—
40C4⋊C4×C23D411yescharacteristic
41C4⋊C4×C23D411yescharacteristic
42C22⋊C4×C23—21no—
43C22⋊C4×C23—21no—
44C22⋊C4×C23—21no—
45C22⋊C4×C23—21no—
46C22⋊C4×C23—21no—
47C22⋊C4×C23—21no—
48C42×C23C2311yescharacteristic
49#67275—42no—
50#67273—42no—
51C4⋊Dic23—21no—
52C4⋊Dic23—21no—
53C2×C23⋊C8—21no—
54C2×C23⋊C8—21no—
55C2×C23⋊C8—21no—
56C23×C23—21no—
57C23×C23—21no—
58Q8×C23—41no—
59Q8×C23—41no—
60D4×C23—41no—
61D4×C23—41no—
62D4×C23—81no—
63D4×C23—81no—
64C2×C4×C23—21no—
65C2×C4×C23—21no—
66C2×C4×C23—21no—
67C2×C4×C23—21no—
68C2×C4×C23—81no—
69C2×C4×C23—81no—
70C2×C4×C23C2×D411yescharacteristic
71C2×C4×C23C2×D411yescharacteristic
72C2×C4×C23C2×D411yescharacteristic
73C2×Dic23—41no—
74Dic46—41no—
75Dic46—41no—
76C23⋊C8—22no—
77C23⋊C8—22no—
78C23⋊C8—41no—
79#1661—231nomaximal, Sylow
80C22×C23—41no—
81C22×C23—41no—
82C22×C23—41no—
83C22×C23—41no—
84C22×C23—41no—
85C22×C23—41no—
86C22×C23#12011yescharacteristic
87C4×C23—21no—
88C4×C23—21no—
89C4×C23—21no—
90C4×C23—41no—
91C4×C23—41no—
92C4×C23—41no—
93C4×C23—41no—
94Dic23—81no—
95#562D2311yescharacteristic
96#501—231no—
97#497—231no—
98#489—231no—
99#330—231no—
100#329—231no—
101#329—231no—
102C2×C23—81no—
103C2×C23—81no—
104C2×C23#45311yescharacteristic
105C2×C23#45511yescharacteristic
106C2×C23#45611yescharacteristic
107C2×Q16—461no—
108C2×SD16—461no—
109C4⋊Q8—231no—
110#125C2×D2311yescharacteristic
111#124C2×D2311yescharacteristic
112#124C2×D2311yescharacteristic
113#123—21no—
114#123—21no—
115C22⋊Q8—21no—
116C22⋊Q8—21no—
117#121—21no—
118#121—21no—
119#107—461no—
120#106—461no—
121#103—461no—
122#102—461no—
123#97—231no—
124#97—231no—
125#97—231no—
126C23#166111yescharacteristic, complemented, Sylow
127C2×Q8—461no—
128C2×Q8C22⋊D2311yescharacteristic
129C2×Q8C22⋊D2311yescharacteristic
130C2×D4—21no—
131C2×D4—21no—
132C2×D4C22⋊D2311yescharacteristic
133C2×D4C22⋊D2311yescharacteristic
134C22×C4—21no—
135C22×C4—21no—
136Q16—922no—
137SD16—922no—
138C2×C8—461no—
139C2×C8—461no—
140C2×C8—461no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—461no—
146C4⋊C4—461no—
147C4⋊C4C22⋊D2311yescharacteristic
148C4⋊C4C22⋊D2311yescharacteristic
149C22⋊C4—21no—
150C22⋊C4—21no—
151C22⋊C4—21no—
152C22⋊C4—21no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C42C22×D2311yescharacteristic
156C23—21no—
157C23—21no—
158Q8—41no—
159Q8—41no—
160Q8—921no—
161Q8—921no—
162D4—41no—
163D4—41no—
164D4—81no—
165D4—81no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—81no—
171C2×C4—81no—
172C2×C4—921no—
173C2×C4C2×C22⋊D2311yescharacteristic
174C2×C4C2×C22⋊D2311yescharacteristic
175C2×C4C2×C22⋊D2311yescharacteristic
176C8—462no—
177C8—462no—
178C8—921no—
179C22—41no—
180C22—41no—
181C22—41no—
182C22—41no—
183C22—41no—
184C22—41no—
185C22#1062512411yescharacteristic
186C4—21no—
187C4—21no—
188C4—21no—
189C4—41no—
190C4—41no—
191C4—41no—
192C4—41no—
193C4—1841no—
194C2—81no—
195C2—81no—
196C2#1309258511yescharacteristic
197C2#1309259511yescharacteristic
198C2#1309260011yescharacteristic
subgroupG/H
centerC22#10625124
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
Fitting, prime radicalC23×#562C2
socleC22×C23#120
hypercenter#562D23
hypocenterC23#1661
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #13092827C2semidirect
2. #13092812C2semidirect
3. #13092776C2semidirect
4. #13092159C2semidirect
5. #13092157C2semidirect
6. #13092157C2semidirect
126. C23#1661semidirect

Maximal subgroups

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

subgroupindex
#130928272
#130928122
#130927762
#130921592
#130921572
C23×#5622
#166123