Finite Group Databasebeta

← #15684868

Subgroups — #15684868

Order 2944.

346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 117 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#13093038C212yesmaximal, complemented
2#13092708C212yesmaximal, complemented
3#13092703C212yesmaximal, complemented
4#13092675C211yesmaximal, characteristic, complemented
5#13092670C211yesmaximal, characteristic
6#13092646C212yesmaximal, complemented
7#13092640C212yesmaximal, complemented
8#13092633C212yesmaximal, complemented
9C23×#424C211yesmaximal, characteristic, complemented
10C2×M16×C23C2211yescharacteristic
11C22×C8×C23C2211yescharacteristic
12C23×#117C2211yescharacteristic
13#10625101C2212yes—
14#10625095C2212yes—
15C2×Dic92C2211yescharacteristic
16C2×D184C2211yescharacteristic
17C2×#67263C2212yes—
18#10625069—22no—
19#10625067—22no—
20#10625056—22no—
21#10625054—22no—
22#10625046C2212yes—
23C4×D92C2212yes—
24#10625040C2212yes—
25C4×Dic46C2212yes—
26C23×C4⋊C8C2212yes—
27C23×C4⋊C8C2212yes—
28#10625003C2212yes—
29#10625003C2212yes—
30#10624999C2212yes—
31#10624999C2211yescharacteristic
32#10624999C2211yescharacteristic
33#10624998C2212yes—
34#10624998C2212yes—
35C22×C4×C23C2311yescharacteristic
36C2×C22⋊D23—22no—
37C2×D92C2312yes—
38C2×C4×D23—22no—
39C2×Dic46—22no—
40C2×Dic46C2312yes—
41M16×C23—41no—
42C2×C8×C23—41no—
43C2×C8×C23C2312yes—
44C2×C8×C23C2311yescharacteristic
45C2×C8×C23C2311yescharacteristic
46C4⋊C4×C23D412yes—
47C22⋊C4×C23D411yescharacteristic
48C22⋊C4×C23D411yescharacteristic
49C42×C23C2312yes—
50C22⋊Dic23—22no—
51(C2×D23)⋊C4—22no—
52(C2×D23)⋊C4—22no—
53(C2×D23)⋊C4—22no—
54(C2×D23)⋊C4—22no—
55C4⋊Dic23—22no—
56C4⋊Dic23C2312yes—
57C4⋊Dic23C2312yes—
58Dic23⋊C4—22no—
59Dic23⋊C4—22no—
60C4×Dic23—22no—
61Dic92—41no—
62D184—41no—
63#67263—42no—
64C23×C23C2×D411yescharacteristic
65C22×D23—22no—
66C2×C4×C23—21no—
67C2×C4×C23—21no—
68C2×C4×C23C2×D412yes—
69C2×C4×C23C2×D411yescharacteristic
70C2×C4×C23C2×D412yes—
71C2×C4×C23C2411yescharacteristic
72C22⋊D23—82no—
73C2×Dic23—22no—
74C2×Dic23—22no—
75C2×Dic23—22no—
76D92—22no—
77D92—22no—
78C4×D23—82no—
79Dic46—22no—
80Dic46—22no—
81Dic46—82no—
82C8×C23—22no—
83C8×C23—21no—
84C8×C23—21no—
85#3263—231nomaximal, Sylow
86C22×C23—21no—
87C22×C23—22no—
88C22×C23C22×D411yescharacteristic
89C2×D23—42no—
90C2×D23—42no—
91C2×D23—42no—
92C4×C23—21no—
93C4×C23—22no—
94C4×C23—22no—
95C4×C23H(5,𝔽2)11yescharacteristic
96C4×C232−1+411yescharacteristic
97Dic23—42no—
98Dic23—42no—
99Dic23—42no—
100#542—232no—
101#476—232no—
102#475—232no—
103#470—231no—
104#469—231no—
105#465—232no—
106#464—232no—
107#463—232no—
108#424D2311yescharacteristic, complemented
109C2×C23—41no—
110C2×C23#53711yescharacteristic
111C2×C23#57712yes—
112D23—82no—
113C2×Q16—231no—
114C2×SD16—232no—
115C2×D8—231no—
116C2×M16C2×D2311yescharacteristic
117C22×C8C2×D2311yescharacteristic
118C4⋊Q8—232no—
119#126—462no—
120#124—232no—
121#124—462no—
122#123—462no—
123C22⋊Q8—232no—
124C22⋊Q8—462no—
125#121—232no—
126C4×Q8—232no—
127C4×D4—232no—
128#117C2×D2311yescharacteristic
129#106—232no—
130#106—231no—
131#106—231no—
132C4⋊C8C2×D2312yes—
133C4⋊C8C2×D2312yes—
134#103—232no—
135#103—232no—
136#102—232no—
137#102—232no—
138C23#326311yescharacteristic, complemented, Sylow
139C2×Q8—232no—
140C2×Q8—462no—
141C2×D4—232no—
142C2×D4—462no—
143C22×C4—462no—
144C22×C4C22×D2311yescharacteristic
145Q16—921no—
146SD16—922no—
147D8—921no—
148M16—41no—
149C2×C8—41no—
150C2×C8C22×D2311yescharacteristic
151C2×C8C22×D2312yes—
152C2×C8C22×D2311yescharacteristic
153C4⋊C4—232no—
154C4⋊C4—232no—
155C4⋊C4—462no—
156C4⋊C4—462no—
157C4⋊C4—462no—
158C4⋊C4D9212yes—
159C22⋊C4—462no—
160C22⋊C4—462no—
161C22⋊C4—462no—
162C22⋊C4—462no—
163C22⋊C4—462no—
164C22⋊C4D9211yescharacteristic
165C22⋊C4D9211yescharacteristic
166C42—462no—
167C42C22×D2312yes—
168C23—462no—
169C23C2×D9211yescharacteristic
170Q8—462no—
171Q8—462no—
172Q8—1842no—
173D4—462no—
174D4—462no—
175D4—1842no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—462no—
179C2×C4—462no—
180C2×C4—462no—
181C2×C4—1842no—
182C2×C4C2×D9212yes—
183C2×C4C2×D9212yes—
184C2×C4C2×D9211yescharacteristic
185C2×C4C23×D2311yescharacteristic
186C8—22no—
187C8—21no—
188C8—21no—
189C22—22no—
190C22—21no—
191C22—922no—
192C22—922no—
193C22—922no—
194C22C22×D9211yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—922no—
199C4—922no—
200C4—922no—
201C4#1062515511yescharacteristic
202C4#1062515811yescharacteristic
203C2—41no—
204C2—1842no—
205C2#1309299811yescharacteristic
206C2#1309322912yes—
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#424C2
socleC22×C23C22×D4
prime radical#13092670C2
hypercenter#424D23
hypocenterC23#3263
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
1. #13093038C2semidirect
2. #13092708C2semidirect
3. #13092703C2semidirect
4. #13092675C2semidirect
6. #13092646C2semidirect
7. #13092640C2semidirect
8. #13092633C2semidirect
9. C23×#424C2semidirect
108. #424D23semidirect
138. C23#3263semidirect

Maximal subgroups

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

subgroupindex
#130930382
#130927082
#130927032
#130926752
#130926702
#130926462
#130926402
#130926332
C23×#4242
#326323