Finite Group Databasebeta

← #15672424

Subgroups — #15672424

Order 2944.

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

normal subgroups only

This group has 236 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#13093043C211yesmaximal, characteristic
2#13092753C212yesmaximal, complemented
3#13092353C211yesmaximal, characteristic
4#13092155C212yesmaximal, complemented
5C23×#323C211yesmaximal, characteristic
6C2×C22⋊C4×C23C2211yescharacteristic
7C2×C22⋊Dic23—21no—
8C2×C22⋊Dic23—21no—
9C2×C4⋊Dic23C2211yescharacteristic
10#10625095—21no—
11#10625095C2212yes—
12C2×Dic23⋊C4—21no—
13#10625049—22no—
14#10625049—22no—
15C23×C22⋊C8C2212yes—
16C23⋊#95C2211yescharacteristic
17#10625000—22no—
18#10624998—22no—
19C24×C23D411yescharacteristic
20C22×C4×C23D411yescharacteristic
21C22×C4×C23C2311yescharacteristic
22C22×Dic23—21no—
23C22×Dic23—21no—
24C22×Dic23—21no—
25C22×Dic23—21no—
26C2×Dic46—21no—
27C2×Dic46D412yes—
28C2×C8×C23—22no—
29C22⋊C4×C23—22no—
30C22⋊Dic23—22no—
31C22⋊Dic23—22no—
32C22⋊Dic23—42no—
33C4⋊Dic23—21no—
34C4⋊Dic23—22no—
35C4⋊Dic23D412yes—
36Dic23⋊C4—22no—
37Dic23⋊C4—22no—
38Dic23⋊C4—42no—
39C23×C23—21no—
40C23×C23—21no—
41C23×C23—41no—
42C23×C23—41no—
43C23×C23Q1612yes—
44C23×C23C2×D411yescharacteristic
45C2×C4×C23—21no—
46C2×C4×C23—41no—
47C2×C4×C23—41no—
48C2×C4×C23C2×D412yes—
49C2×Dic23—22no—
50C2×Dic23—22no—
51C2×Dic23—22no—
52C2×Dic23—41no—
53C2×Dic23—41no—
54C2×Dic23—41no—
55C2×Dic23—41no—
56C2×Dic23—41no—
57C2×Dic23—81no—
58C2×Dic23—81no—
59Dic46—42no—
60Dic46—81no—
61C8×C23—42no—
62#1614—231nomaximal, Sylow
63C22×C23—21no—
64C22×C23—21no—
65C22×C23—22no—
66C22×C23—42no—
67C22×C23—41no—
68C22×C23—41no—
69C22×C23—81no—
70C22×C23#12011yescharacteristic
71C22×C23C2×Q1611yescharacteristic
72C22×C23#13711yescharacteristic
73C4×C23—22no—
74C4×C23—41no—
75Dic23—42no—
76Dic23—42no—
77Dic23—42no—
78Dic23—81no—
79#543—231no—
80#484—232no—
81#399—231no—
82#328—232no—
83#323D2311yescharacteristic
84C2×C23—21no—
85C2×C23—21no—
86C2×C23—42no—
87C2×C23#45111yescharacteristic
88C2×C23#45311yescharacteristic
89C2×C23#45811yescharacteristic
90C22⋊Q8—232no—
91C22⋊Q8—462no—
92C22⋊Q8—462no—
93C22⋊Q8—461no—
94C2×C4⋊C4—231no—
95C2×C4⋊C4—461no—
96C2×C22⋊C4—461no—
97C2×C22⋊C4—461no—
98C2×C22⋊C4C2×D2311yescharacteristic
99#107—462no—
100#103—462no—
101C22⋊C8C2×D2312yes—
102#95—231no—
103C23#161411yescharacteristic, complemented, Sylow
104C24D9211yescharacteristic
105C2×Q8—232no—
106C2×Q8—461no—
107C22×C4—461no—
108C22×C4—461no—
109C22×C4—461no—
110C22×C4—461no—
111C22×C4D9211yescharacteristic
112C22×C4C22×D2311yescharacteristic
113C2×C8—22no—
114C4⋊C4—232no—
115C4⋊C4—462no—
116C4⋊C4—461no—
117C4⋊C4—462no—
118C4⋊C4—462no—
119C4⋊C4—922no—
120C22⋊C4—22no—
121C22⋊C4—462no—
122C22⋊C4—462no—
123C22⋊C4—922no—
124C23—21no—
125C23—21no—
126C23—41no—
127C23—41no—
128C23Dic9212yes—
129C23C2×D9211yescharacteristic
130Q8—922no—
131Q8—1841no—
132C2×C4—21no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—462no—
136C2×C4—462no—
137C2×C4—462no—
138C2×C4—921no—
139C2×C4—921no—
140C2×C4—921no—
141C2×C4—921no—
142C2×C4—921no—
143C2×C4—1841no—
144C2×C4—1841no—
145C2×C4D4×D2312yes—
146C8—42no—
147C22—21no—
148C22—21no—
149C22—22no—
150C22—42no—
151C22—41no—
152C22—41no—
153C22—81no—
154C22#1062505311yescharacteristic
155C22C2×Dic9211yescharacteristic
156C22#1062508011yescharacteristic
157C4—22no—
158C4—41no—
159C4—922no—
160C4—922no—
161C4—922no—
162C4—1841no—
163C2—21no—
164C2—21no—
165C2—42no—
166C2#1309257511yescharacteristic
167C2#1309258711yescharacteristic
168C2#1309260811yescharacteristic
subgroupG/H
centerC22#10625053
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#323C2
socleC22×C23#120
prime radicalC24×C23D4
hypercenter#323D23
hypocenterC23#1614
LCSG ▷ C22×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #13092753C2semidirect
4. #13092155C2semidirect
103. C23#1614semidirect

Maximal subgroups

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

subgroupindex
#130930432
#130927532
#130923532
#130921552
C23×#3232
#161423