Finite Group Databasebeta

← #15674267

Subgroups — #15674267

Order 2944.

304 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C22×#67275C211yesmaximal, characteristic
2C2×#10624990C211yesmaximal, characteristic
3C2×#10625017C211yesmaximal, characteristic
4C2×#10624992C211yesmaximal, characteristic
5C2×#10624985C211yesmaximal, characteristic
6#13092323C211yesmaximal, characteristic
7C23×#391C211yesmaximal, characteristic
8C22×Q8×C23C2211yescharacteristic
9C22×Dic46C2211yescharacteristic
10C2×C4⋊C4×C23C2211yescharacteristic
11C2×C42×C23C2211yescharacteristic
12C2×#67275—22no—
13C2×#67275—22no—
14C2×#67275C414yescomplemented
15C2×C4⋊Dic23C2211yescharacteristic
16C22×C23⋊C8C2211yescharacteristic
17C22×C23⋊C8C2211yescharacteristic
18C23×#95—22no—
19#10625017—22no—
20C23⋊#95—22no—
21#10624992—22no—
22#10624990—22no—
23#10624985—22no—
24C2×Q8×C23—21no—
25C2×Q8×C23—21no—
26C2×Q8×C23—21no—
27C2×Q8×C23—21no—
28C2×Q8×C23—21no—
29C2×Q8×C23C2×C412yes—
30C22×C4×C23—21no—
31C22×C4×C23—21no—
32C22×C4×C23D412yes—
33C22×C4×C23C2311yescharacteristic
34C22×Dic23—21no—
35C22×Dic23—21no—
36C2×Dic46—21no—
37C2×Dic46—21no—
38C2×Dic46—21no—
39C2×Dic46—21no—
40C2×Dic46—21no—
41C2×Dic46C2×C412yes—
42C4⋊C4×C23—21no—
43C4⋊C4×C23—21no—
44C42×C23—21no—
45C42×C23—21no—
46#67275—28no—
47C4⋊Dic23—21no—
48C4⋊Dic23—21no—
49C2×C23⋊C8—21no—
50C2×C23⋊C8—21no—
51C2×C23⋊C8C2×C412yes—
52C2×C23⋊C8D412yes—
53C2×C23⋊C8D412yes—
54C2×C23⋊C8D412yes—
55C23×C23C2×D411yescharacteristic
56Q8×C23—22no—
57Q8×C23—22no—
58Q8×C23—41no—
59Q8×C23—41no—
60C2×C4×C23—22no—
61C2×C4×C23—22no—
62C2×C4×C23—22no—
63C2×C4×C23—22no—
64C2×C4×C23—41no—
65C2×C4×C23—41no—
66C2×C4×C23—41no—
67C2×C4×C23—42no—
68C2×C4×C23C22×C411yescharacteristic
69C2×C4×C23C2×D411yescharacteristic
70C2×C4×C23C2×D411yescharacteristic
71C2×C4×C23C2×D411yescharacteristic
72C2×C4×C23#4111yescharacteristic
73C2×C4×C23#4111yescharacteristic
74C2×Dic23—22no—
75C2×Dic23—41no—
76C2×Dic23—41no—
77C2×Dic23—41no—
78C2×Dic23—42no—
79Dic46—22no—
80Dic46—22no—
81Dic46—41no—
82Dic46—41no—
83C23⋊C8—22no—
84C23⋊C8C22⋊C414yes—
85#1971—231nomaximal, Sylow
86C22×C23C4×D411yescharacteristic
87C22×C23#12111yescharacteristic
88C22×C23#12711yescharacteristic
89C22×C23#13712yes—
90C22×C23#13712yes—
91C4×C23—42no—
92C4×C23—42no—
93C4×C23—81no—
94C4×C23C2×C22⋊C411yescharacteristic
95C4×C23C4×D411yescharacteristic
96C4×C23#12111yescharacteristic
97C4×C23#12411yescharacteristic
98Dic23—42no—
99Dic23—81no—
100C22×Q16—231no—
101C2×#106—231no—
102C2×#103—231no—
103C2×#103—231no—
104C2×#97—231no—
105#391—231no—
106#391D2311yescharacteristic
107C2×C23#39011yescharacteristic
108C2×C23#44112yes—
109C2×C23#47012yes—
110C2×C23#49711yescharacteristic
111C2×C23#49711yescharacteristic
112C22×Q8—231no—
113C22×Q8C2×D2311yescharacteristic
114C2×Q16—234no—
115C2×Q16—462no—
116C2×Q16—462no—
117C22×C8—231no—
118C22×C8—231no—
119C2×C4⋊C4—231no—
120C2×C4⋊C4C2×D2311yescharacteristic
121C2×C42C2×D2311yescharacteristic
122#106—462no—
123#103—462no—
124#103—462no—
125#97—462no—
126#95—22no—
127#95—462no—
128C23#197111yescharacteristic, complemented, Sylow
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—232no—
135C2×Q8—461no—
136C2×Q8—461no—
137C2×Q8—461no—
138C2×Q8—461no—
139C2×Q8—461no—
140C2×Q8C4×D2312yes—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—461no—
144C22×C4—461no—
145C22×C4C22⋊D2312yes—
146C22×C4C22×D2311yescharacteristic
147Q16—468no—
148C2×C8—232no—
149C2×C8—232no—
150C2×C8—232no—
151C2×C8—232no—
152C2×C8—461no—
153C2×C8—461no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—461no—
157C4⋊C4—461no—
158C42—21no—
159C42—21no—
160C23C2×C22⋊D2311yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165Q8—462no—
166Q8—462no—
167Q8—921no—
168Q8—921no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—462no—
178C2×C4—921no—
179C2×C4—921no—
180C2×C4—921no—
181C2×C4—922no—
182C2×C4C2×C4×D2311yescharacteristic
183C2×C4#6728811yescharacteristic
184C2×C4D4×D2311yescharacteristic
185C2×C4D4×D2311yescharacteristic
186C2×C4D4×D2311yescharacteristic
187C2×C4#6729011yescharacteristic
188C8—234no—
189C8—462no—
190C22C4×C22⋊D2311yescharacteristic
191C22#1062511011yescharacteristic
192C22#1062511111yescharacteristic
193C22#1062511312yes—
194C22#1062512212yes—
195C4—42no—
196C4—42no—
197C4—81no—
198C4—922no—
199C4—1841no—
200C4C22⋊C4×D2311yescharacteristic
201C4(C22⋊D23)⋊C411yescharacteristic
202C4#1062505511yescharacteristic
203C4#1062505611yescharacteristic
204C2#1309231711yescharacteristic
205C2#1309252212yes—
206C2#1309267312yes—
207C2#1309280911yescharacteristic
208C2#1309281211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#391C2
socle, prime radicalC23×C23C2×D4
cosocleC22×C4×C23C23
hypercenter#391D23
hypocenterC23#1971
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
14. C2×#67275C4semidirect
128. C23#1971semidirect

Maximal subgroups

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

subgroupindex
C22×#672752
C2×#106249902
C2×#106250172
C2×#106249922
C2×#106249852
#130923232
C23×#3912
#197123