Finite Group Databasebeta

← #15672541

Subgroups — #15672541

Order 2944.

218 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 53 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#13093132C211yesmaximal, characteristic
2#13092796C211yesmaximal, characteristic, complemented
3#13092704C211yesmaximal, characteristic, complemented
4#13092165C211yesmaximal, characteristic, complemented
5D4⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
6#13092144C211yesmaximal, characteristic, complemented
7C23×#476C211yesmaximal, characteristic, complemented
8C23×C4⋊Q8C2211yescharacteristic
9C4×D4×C23C2211yescharacteristic
10C2×#67275—22no—
11#10625109—21no—
12#10625101—21no—
13#10625097—21no—
14#10625063—21no—
15#10625056—22no—
16C4×D92C2211yescharacteristic
17#10625040C2211yescharacteristic
18C23×#106—21no—
19C23×C4⋊C8C2211yescharacteristic
20C23×#102—21no—
21#10624991—21no—
22#10624990—21no—
23C4⋊(C23⋊C8)C2211yescharacteristic
24C4×C23⋊C8C2211yescharacteristic
25C2×Q8×C23—21no—
26C2×D4×C23D411yescharacteristic
27C22×C4×C23—21no—
28C2×C22⋊D23—22no—
29C2×D92D411yescharacteristic
30C2×C4×D23—21no—
31C2×Dic46D412yes—
32C2×C8×C23—21no—
33C4⋊C4×C23—21no—
34C4⋊C4×C23—21no—
35C4⋊C4×C23D411yescharacteristic
36C22⋊C4×C23—21no—
37C42×C23C2311yescharacteristic
38C22⋊Dic23—22no—
39#67275—44no—
40(C2×D23)⋊C4—22no—
41(C2×D23)⋊C4—21no—
42C4⋊Dic23—21no—
43C4⋊Dic23—21no—
44C4⋊Dic23D411yescharacteristic
45C4×Dic23—22no—
46C2×C23⋊C8—21no—
47C2×C23⋊C8—21no—
48C23×C23—21no—
49C22×D23—21no—
50Q8×C23—42no—
51D4×C23—21no—
52D4×C23—21no—
53C2×C4×C23—21no—
54C2×C4×C23—41no—
55C2×C4×C23—41no—
56C2×C4×C23—41no—
57C2×C4×C23C2×D411yescharacteristic
58C2×C4×C23C2×D411yescharacteristic
59C2×C4×C23C2×D411yescharacteristic
60C22⋊D23—82no—
61C2×Dic23—21no—
62C2×Dic23—22no—
63D92—21no—
64D92—21no—
65C4×D23—41no—
66C4×D23—41no—
67Dic46—42no—
68C8×C23—41no—
69C23⋊C8—22no—
70C23⋊C8—41no—
71#1634—231nomaximal, Sylow
72C22×C23—41no—
73C22×C23—41no—
74C22×C23—41no—
75C22×C23#12011yescharacteristic
76C2×D23—41no—
77C2×D23—41no—
78C2×D23—41no—
79C4×C23—21no—
80C4×C23—41no—
81C4×C23—81no—
82C4×C23#13511yescharacteristic
83C4×C23#13511yescharacteristic
84C4×C23#13711yescharacteristic
85C4×C23#13711yescharacteristic
86Dic23—41no—
87Dic23—42no—
88#555—231no—
89#494—231no—
90#476—231no—
91#476D2311yescharacteristic, complemented
92#333—231no—
93D4⋊C8—231no—
94D4⋊C8—231no—
95C2×C23—81no—
96C2×C23#45211yescharacteristic
97C2×C23#45211yescharacteristic
98C2×C23#45311yescharacteristic
99D23—81no—
100C2×Q16—462no—
101C4⋊Q8—231no—
102C4⋊Q8C2×D2311yescharacteristic
103#124—462no—
104#121—461no—
105#121—461no—
106C4×D4—231no—
107C4×D4C2×D2311yescharacteristic
108#117—461no—
109#117—461no—
110#106—21no—
111#106—461no—
112C4⋊C8—231no—
113C4⋊C8C2×D2311yescharacteristic
114#102—21no—
115#102—461no—
116C4×C8—231no—
117C23#163411yescharacteristic, complemented, Sylow
118C2×Q8—21no—
119C2×Q8—232no—
120C2×D4—231no—
121C2×D4—462no—
122C2×D4C22⋊D2311yescharacteristic
123C22×C4—21no—
124C22×C4—461no—
125Q16—924no—
126C2×C8—21no—
127C2×C8—461no—
128C2×C8—461no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—231no—
132C4⋊C4—461no—
133C4⋊C4—461no—
134C4⋊C4C22⋊D2311yescharacteristic
135C22⋊C4—21no—
136C22⋊C4—462no—
137C22⋊C4—462no—
138C22⋊C4—461no—
139C42—462no—
140C42C22×D2311yescharacteristic
141C23—21no—
142C23—461no—
143Q8—42no—
144Q8—922no—
145D4—21no—
146D4—21no—
147D4—461no—
148D4—461no—
149D4—1842no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—461no—
155C2×C4—462no—
156C2×C4—921no—
157C2×C4—921no—
158C2×C4D4×D2311yescharacteristic
159C2×C4D4×D2311yescharacteristic
160C2×C4C2×C22⋊D2311yescharacteristic
161C8—41no—
162C8—462no—
163C8—921no—
164C22—41no—
165C22—41no—
166C22—41no—
167C22—921no—
168C22—921no—
169C22—921no—
170C22#1062510811yescharacteristic
171C4—21no—
172C4—41no—
173C4—81no—
174C4—921no—
175C4—922no—
176C4#1062508611yescharacteristic
177C4#1062508711yescharacteristic
178C4#1062511311yescharacteristic
179C4#1062512111yescharacteristic
180C2—81no—
181C2—1841no—
182C2#1309257611yescharacteristic
183C2#1309257711yescharacteristic
184C2#1309258311yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#476C2
socleC22×C23#120
prime radical#13093132C2
hypercenter#476D23
hypocenterC23#1634
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #13092796C2semidirect
3. #13092704C2semidirect
4. #13092165C2semidirect
5. D4⋊(C23⋊C8)C2semidirect
6. #13092144C2semidirect
7. C23×#476C2semidirect
91. #476D23semidirect
117. C23#1634semidirect

Maximal subgroups

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

subgroupindex
#130931322
#130927962
#130927042
#130921652
D4⋊(C23⋊C8)2
#130921442
C23×#4762
#163423