Finite Group Databasebeta

← #15686479

Subgroups — #15686479

Order 2944.

356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 113 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#13093136C212yesmaximal, complemented
2#13092808C212yesmaximal, complemented
3#13092636C212yesmaximal, complemented
4#13092630C212yesmaximal
5#13092625C212yesmaximal, complemented
6#13092547C211yesmaximal, characteristic, complemented
7#13092518C212yesmaximal, complemented
8C4×Dic92C211yesmaximal, characteristic, complemented
9C23×#495C211yesmaximal, characteristic
10C2×Q16×C23C2211yescharacteristic
11C2×SD16×C23C2212yes—
12C2×D8×C23C2211yescharacteristic
13C23×#124C2212yes—
14Q8×Dic23C2212yes—
15#10625115C2212yes—
16C2×#67275C2212yes—
17#10625107C2212yes—
18D4×Dic23C2212yes—
19C2×#67273C2212yes—
20C2×Dic92C2211yescharacteristic
21#10625050—22no—
22#10625050—22no—
23#10625049—22no—
24#10625048—22no—
25C4×Dic46C2212yes—
26C4×Dic46C2211yescharacteristic
27C4×C8×C23C2211yescharacteristic
28#10625017C2212yes—
29#10625014C2212yes—
30#10625000C2211yescharacteristic
31#10624998C2212yes—
32#10624997C2212yes—
33Dic23⋊C8C2212yes—
34C4⋊(C23⋊C8)C2211yescharacteristic
35C2×Q8×C23C2312yes—
36C2×D4×C23C2312yes—
37C22×Dic23—22no—
38C2×Dic46D411yescharacteristic
39C2×Dic46C2312yes—
40Q16×C23—41no—
41SD16×C23—24no—
42D8×C23—41no—
43C2×C8×C23C2311yescharacteristic
44C2×C8×C23C2311yescharacteristic
45C22⋊C4×C23—22no—
46C22⋊C4×C23—22no—
47C42×C23C2311yescharacteristic
48C22⋊Dic23—22no—
49C22⋊Dic23—22no—
50C22⋊Dic23—22no—
51#67275—42no—
52#67273—42no—
53C4⋊Dic23—22no—
54C4⋊Dic23D411yescharacteristic
55C4⋊Dic23C2312yes—
56Dic23⋊C4—22no—
57Dic23⋊C4—22no—
58Dic23⋊C4—22no—
59Dic23⋊C4D412yes—
60C4×Dic23—22no—
61C4×Dic23—22no—
62C4×Dic23C2312yes—
63C2×C23⋊C8C2312yes—
64Dic92—22no—
65C23×C23—22no—
66Q8×C23—22no—
67Q8×C23—22no—
68D4×C23—22no—
69D4×C23—22no—
70C2×C4×C23—22no—
71C2×C4×C23C2×D411yescharacteristic
72C2×C4×C23C2×D411yescharacteristic
73C2×C4×C23C2411yescharacteristic
74C2×Dic23—22no—
75C2×Dic23—22no—
76C2×Dic23—44no—
77C2×Dic23C2×D412yes—
78C2×Dic23C2×D412yes—
79Dic46—22no—
80Dic46—22no—
81Dic46—41no—
82C8×C23—21no—
83C8×C23#4112yes—
84C23⋊C8—22no—
85#3402—231nomaximal, Sylow
86C22×C23—42no—
87C22×C23—42no—
88C22×C23—42no—
89C22×C23C22×D411yescharacteristic
90C4×C23—21no—
91C4×C23—21no—
92C4×C23—42no—
93C4×C23C2×#4111yescharacteristic
94C4×C23H(5,𝔽2)11yescharacteristic
95Dic23—22no—
96Dic23—22no—
97Dic23—42no—
98Dic23—42no—
99#556—232no—
100#497—232no—
101#495D2311yescharacteristic
102#464—232no—
103#463—232no—
104#462—232no—
105#446—231no—
106#440—232no—
107C4×Q16—231no—
108C2×C23—82no—
109C2×C23#55011yescharacteristic
110C2×C23#57511yescharacteristic
111C2×C23#57811yescharacteristic
112C2×Q16—232no—
113C2×Q16—231no—
114C2×Q16C2×D2311yescharacteristic
115C2×SD16—232no—
116C2×SD16C2×D2312yes—
117C2×D8C2×D2311yescharacteristic
118C4⋊Q8—232no—
119#126—462no—
120#126—462no—
121#124—232no—
122#124C2×D2312yes—
123C22⋊Q8—462no—
124C4×Q8—231no—
125C4×Q8—232no—
126C4×Q8—232no—
127C4×D4—232no—
128#117—462no—
129#107—231no—
130C4⋊C8—232no—
131C4⋊C8—231no—
132#103—232no—
133#103—232no—
134#102—232no—
135#97—232no—
136C4×C8C2×D2311yescharacteristic
137C23#340211yescharacteristic, complemented, Sylow
138C2×Q8—231no—
139C2×Q8—232no—
140C2×Q8C22×D2312yes—
141C2×D4C22×D2312yes—
142C22×C4—462no—
143Q16—41no—
144Q16—462no—
145Q16—922no—
146SD16—24no—
147SD16—922no—
148D8—41no—
149C2×C8—232no—
150C2×C8C22×D2311yescharacteristic
151C2×C8C22×D2311yescharacteristic
152C4⋊C4—232no—
153C4⋊C4—231no—
154C4⋊C4—232no—
155C4⋊C4—462no—
156C4⋊C4—462no—
157C4⋊C4—462no—
158C4⋊C4—462no—
159C22⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—462no—
162C22⋊C4—462no—
163C22⋊C4—462no—
164C42—232no—
165C42—462no—
166C42—462no—
167C42C22×D2311yescharacteristic
168C23—22no—
169Q8—22no—
170Q8—22no—
171Q8—462no—
172Q8—462no—
173Q8—921no—
174D4—22no—
175D4—22no—
176C2×C4—22no—
177C2×C4—232no—
178C2×C4—232no—
179C2×C4—462no—
180C2×C4—462no—
181C2×C4—924no—
182C2×C4D4×D2311yescharacteristic
183C2×C4D4×D2311yescharacteristic
184C2×C4C23×D2311yescharacteristic
185C8—21no—
186C8—462no—
187C8#6729012yes—
188C22—42no—
189C22—42no—
190C22—42no—
191C22C2×D4×D2311yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—462no—
196C4—462no—
197C4—922no—
198C4—922no—
199C4C2×#6729011yescharacteristic
200C4#1062515511yescharacteristic
201C2—82no—
202C2#1309308711yescharacteristic
203C2#1309321411yescharacteristic
204C2#1309323111yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#495C2
socleC22×C23C22×D4
prime radicalC2×D8×C23C22
hypercenter#495D23
hypocenterC23#3402
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #13093136C2semidirect
2. #13092808C2semidirect
3. #13092636C2semidirect
5. #13092625C2semidirect
6. #13092547C2semidirect
7. #13092518C2semidirect
8. C4×Dic92C2semidirect
137. C23#3402semidirect

Maximal subgroups

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

subgroupindex
#130931362
#130928082
#130926362
#130926302
#130926252
#130925472
#130925182
C4×Dic922
C23×#4952
#340223