Finite Group Databasebeta

← #15673597

Subgroups — #15673597

Order 2944.

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

normal subgroups only

This group has 316 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
1C2×#10625063C211yesmaximal, characteristic
2C2×#10624989C211yesmaximal, characteristic, complemented
3C2×#10624999C211yesmaximal, characteristic, complemented
4C2×(C2×D23)⋊C8C211yesmaximal, characteristic
5#13092274C211yesmaximal, characteristic
6#13092179C211yesmaximal, characteristic, complemented
7C23×#340C211yesmaximal, characteristic, complemented
8C22×C4×D23C2211yescharacteristic
9C22×C8×C23C2211yescharacteristic
10C2×C4⋊C4×C23C2211yescharacteristic
11C2×C4⋊C4×C23C2211yescharacteristic
12C2×(C2×D23)⋊C4—21no—
13C2×(C2×D23)⋊C4—21no—
14C2×C4⋊Dic23C2211yescharacteristic
15C2×C4⋊Dic23C2211yescharacteristic
16C2×C4×Dic23—21no—
17C22×C23⋊C8C2211yescharacteristic
18#10625063—22no—
19#10625063—22no—
20C23⋊#95—21no—
21(C2×D23)⋊C8C414yescomplemented
22#10624999—22no—
23#10624989—22no—
24C23×D23D411yescharacteristic
25C22×C4×C23—21no—
26C22×C4×C23—21no—
27C22×C4×C23C2311yescharacteristic
28C22×Dic23—21no—
29C22×Dic23—21no—
30C22×Dic23D411yescharacteristic
31C2×C4×D23—21no—
32C2×C4×D23—21no—
33C2×C4×D23—21no—
34C2×C4×D23—21no—
35C2×C4×D23C2×C412yes—
36C2×C4×D23Q812yes—
37C2×C8×C23—21no—
38C2×C8×C23—21no—
39C2×C8×C23C2×C412yes—
40C4⋊C4×C23—21no—
41C4⋊C4×C23—21no—
42C4⋊C4×C23—21no—
43C4⋊C4×C23D412yes—
44(C2×D23)⋊C4—24no—
45(C2×D23)⋊C4—42no—
46C4⋊Dic23—21no—
47C4⋊Dic23—21no—
48C4⋊Dic23—21no—
49C4⋊Dic23D412yes—
50C4×Dic23—24no—
51C2×C23⋊C8—21no—
52C2×C23⋊C8—21no—
53C2×C23⋊C8C2×C412yes—
54C23×C23C2×D411yescharacteristic
55C22×D23—21no—
56C22×D23—21no—
57C22×D23—21no—
58C22×D23—21no—
59C22×D23—21no—
60C22×D23—21no—
61C22×D23C4⋊C412yes—
62C2×C4×C23—22no—
63C2×C4×C23—41no—
64C2×C4×C23—41no—
65C2×C4×C23—41no—
66C2×C4×C23—41no—
67C2×C4×C23—41no—
68C2×C4×C23C22×C411yescharacteristic
69C2×C4×C23C2×D411yescharacteristic
70C2×C4×C23C2×D411yescharacteristic
71C2×C4×C23C2×Q811yescharacteristic
72C2×C4×C23#4111yescharacteristic
73C2×C4×C23#4111yescharacteristic
74C2×Dic23—21no—
75C2×Dic23—21no—
76C2×Dic23—22no—
77C2×Dic23—41no—
78C2×Dic23—41no—
79C2×Dic23—41no—
80C2×Dic23—41no—
81C2×Dic23—41no—
82C2×Dic23C4⋊C412yes—
83C4×D23—22no—
84C4×D23—22no—
85C4×D23—22no—
86C4×D23—22no—
87C8×C23—22no—
88C23⋊C8—22no—
89#1854—231nomaximal, Sylow
90C22×C23C2×C4⋊C411yescharacteristic
91C22×C23#12011yescharacteristic
92C22×C23#12311yescharacteristic
93C22×C23#13511yescharacteristic
94C22×C23#13511yescharacteristic
95C22×C23AGL(1,ℤ/8)11yescharacteristic
96C22×C23#13711yescharacteristic
97C2×D23—22no—
98C2×D23—22no—
99C2×D23—22no—
100C2×D23—41no—
101C2×D23—41no—
102C2×D23—41no—
103C2×D23—41no—
104C4×C23—42no—
105C4×C23—81no—
106C4×C23C4×D411yescharacteristic
107C4×C23C4×D411yescharacteristic
108C4×C23C22⋊Q811yescharacteristic
109C4×C23C22⋊Q811yescharacteristic
110Dic23—22no—
111Dic23—42no—
112Dic23—81no—
113C2×#117—231no—
114C2×#107—231no—
115C2×#106—231no—
116C2×C22⋊C8—231no—
117#380—231no—
118#340—231no—
119#340D2311yescharacteristic, complemented
120C2×C23#38511yescharacteristic
121C2×C23#42711yescharacteristic
122C2×C23#42811yescharacteristic
123C2×C23#44911yescharacteristic
124C2×C23#45211yescharacteristic
125C2×C23#48211yescharacteristic
126C2×C23#48511yescharacteristic
127D23—42no—
128C23×C4—231no—
129C22×C8—231no—
130C22×C8C2×D2311yescharacteristic
131#117—462no—
132#117—462no—
133C2×C4⋊C4—231no—
134C2×C4⋊C4—231no—
135C2×C4⋊C4C2×D2311yescharacteristic
136C2×C4⋊C4C2×D2311yescharacteristic
137C2×C22⋊C4—461no—
138C2×C22⋊C4—461no—
139C2×C42—461no—
140#107—462no—
141#106—462no—
142C22⋊C8—234no—
143#95—461no—
144C23#185411yescharacteristic, complemented, Sylow
145C24—231no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—231no—
149C22×C4—232no—
150C22×C4—232no—
151C22×C4—461no—
152C22×C4—461no—
153C22×C4—461no—
154C22×C4—461no—
155C22×C4—461no—
156C22×C4—461no—
157C22×C4C22×D2311yescharacteristic
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—232no—
161C2×C8—461no—
162C2×C8—461no—
163C2×C8C4×D2312yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—232no—
168C4⋊C4—461no—
169C4⋊C4—461no—
170C4⋊C4—461no—
171C4⋊C4D9212yes—
172C22⋊C4—464no—
173C22⋊C4—922no—
174C42—464no—
175C23—232no—
176C23—461no—
177C23—461no—
178C23—461no—
179C23—461no—
180C23—461no—
181C23—461no—
182C23D4×D2311yescharacteristic
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—232no—
190C2×C4—461no—
191C2×C4—461no—
192C2×C4—462no—
193C2×C4—462no—
194C2×C4—462no—
195C2×C4—462no—
196C2×C4—462no—
197C2×C4—921no—
198C2×C4—921no—
199C2×C4—921no—
200C2×C4—921no—
201C2×C4—921no—
202C2×C4C2×C4×D2311yescharacteristic
203C2×C4C2×D9211yescharacteristic
204C2×C4#6728811yescharacteristic
205C2×C4D4×D2311yescharacteristic
206C2×C4#6729011yescharacteristic
207C2×C4Q8×D2311yescharacteristic
208C8—22no—
209C8—462no—
210C22—462no—
211C22—462no—
212C22—462no—
213C22—921no—
214C22—921no—
215C22—921no—
216C22—921no—
217C22#1062505311yescharacteristic
218C22#1062505411yescharacteristic
219C22C4⋊C4×D2311yescharacteristic
220C22#1062508211yescharacteristic
221C22#1062508711yescharacteristic
222C22#1062508711yescharacteristic
223C22#1062508911yescharacteristic
224C4—42no—
225C4—81no—
226C4—462no—
227C4—922no—
228C4—1841no—
229C4C4×D9211yescharacteristic
230C4(C22⋊D23)⋊C411yescharacteristic
231C4#1062506711yescharacteristic
232C4#1062506811yescharacteristic
233C2—922no—
234C2#1309229111yescharacteristic
235C2#1309245211yescharacteristic
236C2#1309245811yescharacteristic
237C2#1309256311yescharacteristic
238C2#1309258211yescharacteristic
239C2#1309274011yescharacteristic
240C2#1309275611yescharacteristic
subgroupG/H
centerC23D4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#340C2
socleC23×C23C2×D4
prime radicalC23×D23D4
cosocleC22×C4×C23C23
hypercenter#340D23
hypocenterC23#1854
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#10624989C2semidirect
3. C2×#10624999C2semidirect
6. #13092179C2semidirect
7. C23×#340C2semidirect
21. (C2×D23)⋊C8C4semidirect
119. #340D23semidirect
144. C23#1854semidirect

Maximal subgroups

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

subgroupindex
C2×#106250632
C2×#106249892
C2×#106249992
C2×(C2×D23)⋊C82
#130922742
#130921792
C23×#3402
#185423