Finite Group Databasebeta

← #15673677

Subgroups — #15673677

Order 2944.

374 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 89 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#13092892C211yesmaximal, characteristic
2C2×#10625016C211yesmaximal, characteristic
3#13092290C212yesmaximal, complemented
4#13092183C212yesmaximal, complemented
5C23×#386C211yesmaximal, characteristic
6C22×D4×C23C2211yescharacteristic
7C23×C4×C23C2211yescharacteristic
8C2×C22⋊C4×C23—21no—
9C2×C22⋊C4×C23C2211yescharacteristic
10C2×C22⋊Dic23—21no—
11C2×C22⋊Dic23C2212yes—
12C2×C22⋊Dic23C2212yes—
13D4×Dic23—22no—
14D4×Dic23—22no—
15#10625097—21no—
16C2×Dic23⋊C4—22no—
17C23×#95—21no—
18#10625016C414yescomplemented
19C23⋊#95—22no—
20C24×C23D411yescharacteristic
21C24×C23C2311yescharacteristic
22C2×D4×C23—22no—
23C2×D4×C23—22no—
24C2×D4×C23C2×C412yes—
25C2×D4×C23Q812yes—
26C22×C4×C23—22no—
27C22×C4×C23—21no—
28C22×C4×C23—21no—
29C22×C4×C23—42no—
30C22×C4×C23D411yescharacteristic
31C22×Dic23—22no—
32C22×Dic23—21no—
33C22×Dic23—21no—
34C22×Dic23D412yes—
35C22×Dic23D412yes—
36C22⋊C4×C23—22no—
37C22⋊C4×C23—42no—
38C22⋊Dic23—22no—
39C22⋊Dic23—22no—
40C22⋊Dic23—22no—
41C22⋊Dic23—22no—
42C22⋊Dic23C2×C414yescomplemented
43C4⋊Dic23—21no—
44C4⋊Dic23—21no—
45Dic23⋊C4—44no—
46C4×Dic23—22no—
47C23×C23—21no—
48C23×C23—21no—
49C23×C23—41no—
50C23×C23—41no—
51C23×C23—41no—
52C23×C23—41no—
53C23×C23C4⋊C412yescomplemented
54C23×C23C22×C411yescharacteristic
55C23×C23C2×D412yes—
56C23×C23C2×D411yescharacteristic
57C23×C23C2×Q811yescharacteristic
58C23×C23#4112yes—
59D4×C23—24no—
60D4×C23—24no—
61C2×C4×C23—21no—
62C2×C4×C23—21no—
63C2×C4×C23—24no—
64C2×C4×C23—22no—
65C2×C4×C23—42no—
66C2×C4×C23—41no—
67C2×C4×C23—41no—
68C2×C4×C23—41no—
69C2×C4×C23—41no—
70C2×C4×C23—41no—
71C2×C4×C23C4⋊C412yescomplemented
72C2×Dic23—24no—
73C2×Dic23—22no—
74C2×Dic23—22no—
75C2×Dic23—42no—
76C2×Dic23—42no—
77C2×Dic23—42no—
78C2×Dic23—42no—
79C2×Dic23—81no—
80C2×Dic23—81no—
81#1867—231nomaximal, Sylow
82C22×C23—22no—
83C22×C23—21no—
84C22×C23—22no—
85C22×C23—21no—
86C22×C23—22no—
87C22×C23—41no—
88C22×C23—41no—
89C22×C23—42no—
90C22×C23—42no—
91C22×C23—41no—
92C22×C23—41no—
93C22×C23—81no—
94C22×C23C2×C4⋊C411yescharacteristic
95C22×C23C4×D412yes—
96C22×C23#12011yescharacteristic
97C22×C23C22⋊Q812yes—
98C22×C23#12311yescharacteristic
99C4×C23—22no—
100C4×C23—42no—
101C4×C23—81no—
102Dic23—44no—
103Dic23—42no—
104Dic23—42no—
105#518—231no—
106C2×#99—231no—
107#386D2311yescharacteristic
108#385—232no—
109#342—232no—
110C2×C23—22no—
111C2×C23—21no—
112C2×C23—21no—
113C2×C23—22no—
114C2×C23—42no—
115C2×C23#38511yescharacteristic
116C2×C23B(4,𝔽2)11yescharacteristic
117C2×C23#45811yescharacteristic
118C22×D4C2×D2311yescharacteristic
119C23×C4C2×D2311yescharacteristic
120C4×D4—462no—
121C4×D4—462no—
122#117—461no—
123C2×C4⋊C4—462no—
124C2×C22⋊C4—21no—
125C2×C22⋊C4—232no—
126C2×C22⋊C4—232no—
127C2×C22⋊C4—461no—
128C2×C22⋊C4C2×D2311yescharacteristic
129#99—234no—
130#95—21no—
131#95—462no—
132C23#186711yescharacteristic, complemented, Sylow
133C24C22⋊D2311yescharacteristic
134C24C22×D2311yescharacteristic
135C2×D4—22no—
136C2×D4—22no—
137C2×D4Dic4612yes—
138C2×D4C4×D2312yes—
139C22×C4—22no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—42no—
143C22×C4—232no—
144C22×C4—232no—
145C22×C4—462no—
146C22×C4—461no—
147C22×C4—461no—
148C22×C4C22⋊D2311yescharacteristic
149C4⋊C4—461no—
150C4⋊C4—461no—
151C4⋊C4—924no—
152C22⋊C4—22no—
153C22⋊C4—42no—
154C22⋊C4—234no—
155C22⋊C4—462no—
156C22⋊C4—462no—
157C22⋊C4—462no—
158C22⋊C4—462no—
159C42—462no—
160C23—21no—
161C23—21no—
162C23—41no—
163C23—41no—
164C23—41no—
165C23—41no—
166C23Dic23⋊C412yescomplemented
167C23C2×Dic4611yescharacteristic
168C23C2×C4×D2311yescharacteristic
169C23D4×D2312yes—
170C23#6729012yes—
171C23C2×C22⋊D2311yescharacteristic
172D4—24no—
173D4—24no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—41no—
179C2×C4—42no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—464no—
185C2×C4—462no—
186C2×C4—462no—
187C2×C4—922no—
188C2×C4—922no—
189C2×C4—922no—
190C2×C4—922no—
191C2×C4—1841no—
192C2×C4—1841no—
193C2×C4Dic23⋊C412yescomplemented
194C22—21no—
195C22—22no—
196C22—21no—
197C22—22no—
198C22—22no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22#1062504912yes—
207C22(C22⋊D23)⋊C412yes—
208C22C2×Dic23⋊C411yescharacteristic
209C22#1062510611yescharacteristic
210C22#1062510811yescharacteristic
211C4—22no—
212C4—42no—
213C4—81no—
214C4—924no—
215C4—922no—
216C4—922no—
217C2—21no—
218C2—22no—
219C2—21no—
220C2—22no—
221C2—42no—
222C2#1309228911yescharacteristic
223C2#1309260311yescharacteristic
224C2#1309260611yescharacteristic
subgroupG/H
centerC22#10625108
commutatorC23×C23C22×C4
FrattiniC24C22×D23
FittingC23×#386C2
socleC22×C23#120
prime radicalC22×D4×C23C22
cosocleC24×C23C23
hypercenter#386D23
hypocenterC23#1867
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #386

Complements

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

NH ≅ G/Ntype
3. #13092290C2semidirect
4. #13092183C2semidirect
18. #10625016C4semidirect
42. C22⋊Dic23C2×C4semidirect
53. C23×C23C4⋊C4semidirect
71. C2×C4×C23C4⋊C4semidirect
132. C23#1867semidirect
166. C23Dic23⋊C4semidirect
193. C2×C4Dic23⋊C4semidirect

Maximal subgroups

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

subgroupindex
#130928922
C2×#106250162
#130922902
#130921832
C23×#3862
#186723