Finite Group Databasebeta

← #15673799

Subgroups — #15673799

Order 2944.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C2×#10625046C211yesmaximal, characteristic
2#13092894C211yesmaximal, characteristic, complemented
3#13092423C211yesmaximal, characteristic
4#13092421C211yesmaximal, characteristic
5C2×#10625006C211yesmaximal, characteristic, complemented
6#13092177C211yesmaximal, characteristic, complemented
7C23×#339C211yesmaximal, characteristic, complemented
8C22×D92C2211yescharacteristic
9C22×Dic46C2211yescharacteristic
10C2×M16×C23C2211yescharacteristic
11C23×#117C2211yescharacteristic
12C2×C42×C23C2211yescharacteristic
13C2×(C2×D23)⋊C4—22no—
14#10625097C2211yescharacteristic
15C2×#67267C2211yescharacteristic
16#10625058—22no—
17#10625048—22no—
18#10625046—22no—
19#10625046C414yescomplemented
20C4×Dic46—22no—
21#10625006—22no—
22#10625003—22no—
23#10624991—22no—
24C23×D23—21no—
25C22×C4×C23—21no—
26C22×C4×C23C2311yescharacteristic
27C22×Dic23D412yes—
28C2×D92—21no—
29C2×D92—21no—
30C2×D92—21no—
31C2×D92—21no—
32C2×D92—21no—
33C2×D92C2×C412yes—
34C2×Dic46—21no—
35C2×Dic46—21no—
36C2×Dic46—21no—
37C2×Dic46—21no—
38C2×Dic46C2×C412yes—
39C2×Dic46D412yes—
40M16×C23—21no—
41M16×C23—21no—
42C2×C8×C23—21no—
43C4⋊C4×C23D412yes—
44C22⋊C4×C23—21no—
45C42×C23—21no—
46C42×C23—21no—
47C42×C23C2×C412yes—
48C22⋊Dic23—21no—
49(C2×D23)⋊C4—28no—
50C4⋊Dic23D412yes—
51Dic23⋊C4—24no—
52C4×Dic23—24no—
53C4×Dic23—21no—
54#67267—21no—
55#67267—21no—
56C2×C23⋊C8—21no—
57C23×C23C2×D411yescharacteristic
58C22×D23—22no—
59C22×D23—44no—
60C22×D23—41no—
61C22×D23—41no—
62C2×C4×C23—22no—
63C2×C4×C23—22no—
64C2×C4×C23—42no—
65C2×C4×C23C22×C411yescharacteristic
66C2×C4×C23C2×D411yescharacteristic
67C2×C4×C23C2×D411yescharacteristic
68C2×C4×C23C2×D411yescharacteristic
69C2×C4×C23#4111yescharacteristic
70C2×C4×C23#4111yescharacteristic
71C2×Dic23—22no—
72C2×Dic23—22no—
73C2×Dic23—22no—
74C2×Dic23C22⋊C414yes—
75D92—22no—
76D92—22no—
77D92—41no—
78D92—41no—
79Dic46—22no—
80Dic46—22no—
81Dic46—22no—
82Dic46—22no—
83C8×C23—41no—
84C23⋊C8—41no—
85#1888—231nomaximal, Sylow
86C22×C23—22no—
87C22×C23C2×C22⋊C411yescharacteristic
88C22×C23#12011yescharacteristic
89C22×C23#12311yescharacteristic
90C2×D23—44no—
91C2×D23—42no—
92C2×D23—82no—
93C2×D23—82no—
94C4×C23—42no—
95C4×C23—42no—
96C4×C23C4×D411yescharacteristic
97C4×C23C4×D411yescharacteristic
98C4×C23#12111yescharacteristic
99C4×C23#12111yescharacteristic
100Dic23—24no—
101Dic23—42no—
102C2×#124—231no—
103#519—231no—
104#418—231no—
105#418—231no—
106C2×#101—231no—
107#339—231no—
108#339D2311yescharacteristic, complemented
109C2×C23—21no—
110C2×C23—21no—
111C2×C23#38611yescharacteristic
112C2×C23#45412yes—
113D23—82no—
114C22×Q8—231no—
115C22×D4—231no—
116C2×M16—231no—
117C2×M16C2×D2311yescharacteristic
118#124—234no—
119#124—462no—
120C4×Q8—462no—
121C4×Q8—462no—
122#117—231no—
123#117—462no—
124#117C2×D2311yescharacteristic
125C2×C22⋊C4—462no—
126C2×C42C2×D2311yescharacteristic
127#102—462no—
128#102—462no—
129#101—462no—
130C23#188811yescharacteristic, complemented, Sylow
131C24—461no—
132C2×Q8—232no—
133C2×Q8—232no—
134C2×Q8—461no—
135C2×Q8—461no—
136C2×Q8—461no—
137C2×Q8—461no—
138C2×D4—232no—
139C2×D4—461no—
140C2×D4—461no—
141C2×D4—461no—
142C2×D4—461no—
143C2×D4—461no—
144C22×C4—21no—
145C22×C4—232no—
146C22×C4C22×D2311yescharacteristic
147M16—21no—
148M16—21no—
149M16—461no—
150M16—461no—
151C2×C8—21no—
152C2×C8—461no—
153C4⋊C4—232no—
154C4⋊C4—464no—
155C4⋊C4D9212yes—
156C22⋊C4—21no—
157C22⋊C4—468no—
158C22⋊C4—461no—
159C42—21no—
160C42—21no—
161C42—464no—
162C42—461no—
163C42C4×D2312yes—
164C23—462no—
165C23—924no—
166C23—921no—
167C23—921no—
168C23D4×D2311yescharacteristic
169Q8—462no—
170Q8—462no—
171Q8—462no—
172Q8—462no—
173D4—462no—
174D4—462no—
175D4—921no—
176D4—921no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—234no—
181C2×C4—462no—
182C2×C4—462no—
183C2×C4—462no—
184C2×C4C2×C4×D2311yescharacteristic
185C2×C4C2×D9211yescharacteristic
186C2×C4#6728811yescharacteristic
187C2×C4D4×D2311yescharacteristic
188C2×C4D4×D2311yescharacteristic
189C2×C4#6729211yescharacteristic
190C8—41no—
191C8—921no—
192C22—22no—
193C22—924no—
194C22—922no—
195C22—1842no—
196C22—1842no—
197C22C22⋊C4×D2311yescharacteristic
198C22#1062505311yescharacteristic
199C22#1062506511yescharacteristic
200C4—42no—
201C4—42no—
202C4—464no—
203C4—922no—
204C4C4×D9211yescharacteristic
205C4#1062505511yescharacteristic
206C4#1062506411yescharacteristic
207C4#1062506611yescharacteristic
208C2—21no—
209C2—21no—
210C2—1842no—
211C2#1309229511yescharacteristic
212C2#1309259112yes—
subgroupG/H
centerC22#10625053
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#339C2
socleC22×C23#120
prime radicalC22×D92C22
cosocleC22×C4×C23C23
hypercenter#339D23
hypocenterC23#1888
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #13092894C2semidirect
5. C2×#10625006C2semidirect
6. #13092177C2semidirect
7. C23×#339C2semidirect
19. #10625046C4semidirect
108. #339D23semidirect
130. C23#1888semidirect

Maximal subgroups

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

subgroupindex
C2×#106250462
#130928942
#130924232
#130924212
C2×#106250062
#130921772
C23×#3392
#188823