Finite Group Databasebeta

← #15673753

Subgroups — #15673753

Order 2944.

374 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 101 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×#67263C211yesmaximal, characteristic
2C2×#10625058C211yesmaximal, characteristic, complemented
3C2×#10624992C211yesmaximal, characteristic, complemented
4C2×#10624991C211yesmaximal, characteristic
5#13092318C211yesmaximal, characteristic
6#13092171C211yesmaximal, characteristic, complemented
7C23×#340C211yesmaximal, characteristic, complemented
8C22×D92C2211yescharacteristic
9C22×Dic46C2211yescharacteristic
10C22×C8×C23C2211yescharacteristic
11C2×C4⋊C4×C23C2211yescharacteristic
12C2×C4⋊C4×C23C2211yescharacteristic
13C2×(C2×D23)⋊C4—21no—
14C2×(C2×D23)⋊C4—21no—
15C2×Dic23⋊C4—21no—
16C2×C4×Dic23—21no—
17C2×C4×Dic23C2211yescharacteristic
18C22×C23⋊C8C2211yescharacteristic
19C2×#67263—22no—
20C2×#67263—22no—
21C2×#67263C414yescomplemented
22#10625058—22no—
23#10625058—22no—
24#10624992—22no—
25#10624991—22no—
26C23×D23—21no—
27C22×C4×C23—21no—
28C22×C4×C23—21no—
29C22×C4×C23C2311yescharacteristic
30C22×Dic23—21no—
31C22×Dic23D411yescharacteristic
32C22×Dic23D411yescharacteristic
33C2×D92—21no—
34C2×D92—21no—
35C2×D92—21no—
36C2×D92—21no—
37C2×D92—21no—
38C2×D92C2×C412yes—
39C2×Dic46—21no—
40C2×Dic46—21no—
41C2×Dic46—21no—
42C2×Dic46C2×C412yes—
43C2×Dic46D412yes—
44C2×Dic46D412yes—
45C2×C8×C23—21no—
46C2×C8×C23—21no—
47C2×C8×C23C2×C412yes—
48C4⋊C4×C23—21no—
49C4⋊C4×C23—21no—
50C4⋊C4×C23—21no—
51C4⋊C4×C23D412yes—
52(C2×D23)⋊C4—42no—
53(C2×D23)⋊C4—42no—
54Dic23⋊C4—24no—
55C4×Dic23—24no—
56C4×Dic23—21no—
57C4×Dic23—21no—
58C2×C23⋊C8—21no—
59C2×C23⋊C8—21no—
60C2×C23⋊C8—21no—
61#67263—28no—
62C23×C23C2×D411yescharacteristic
63C22×D23—22no—
64C22×D23—41no—
65C22×D23—41no—
66C22×D23—41no—
67C22×D23—41no—
68C22×D23—41no—
69C22×D23—41no—
70C2×C4×C23—22no—
71C2×C4×C23—41no—
72C2×C4×C23—41no—
73C2×C4×C23—41no—
74C2×C4×C23—41no—
75C2×C4×C23—41no—
76C2×C4×C23C22×C411yescharacteristic
77C2×C4×C23C2×D411yescharacteristic
78C2×C4×C23C2×D411yescharacteristic
79C2×C4×C23C2×D411yescharacteristic
80C2×C4×C23#4111yescharacteristic
81C2×C4×C23#4111yescharacteristic
82C2×Dic23—22no—
83C2×Dic23—21no—
84C2×Dic23—22no—
85C2×Dic23—22no—
86C2×Dic23—21no—
87C2×Dic23—21no—
88C2×Dic23—21no—
89C2×Dic23—21no—
90C2×Dic23SD1612yescomplemented
91D92—22no—
92D92—22no—
93D92—41no—
94D92—41no—
95Dic46—22no—
96Dic46—22no—
97Dic46—22no—
98Dic46C22⋊C414yescomplemented
99C8×C23—22no—
100C23⋊C8—41no—
101#1880—231nomaximal, Sylow
102C22×C23C4×D411yescharacteristic
103C22×C23#12011yescharacteristic
104C22×C23#12111yescharacteristic
105C22×C23C2×SD1611yescharacteristic
106C22×C23#13511yescharacteristic
107C22×C23AGL(1,ℤ/8)11yescharacteristic
108C22×C23#13711yescharacteristic
109C2×D23—42no—
110C2×D23—42no—
111C2×D23—42no—
112C2×D23—81no—
113C2×D23—81no—
114C2×D23—81no—
115C2×D23—81no—
116C4×C23—42no—
117C4×C23—81no—
118C4×C23C2×C22⋊C411yescharacteristic
119C4×C23C4×D411yescharacteristic
120C4×C23#12111yescharacteristic
121C4×C23#12311yescharacteristic
122Dic23—24no—
123Dic23—22no—
124Dic23—41no—
125C22×SD16—231no—
126C2×C4×Q8—231no—
127C2×#103—231no—
128C2×#102—231no—
129#390—231no—
130#340D2311yescharacteristic, complemented
131#336—231no—
132C2×C23#38611yescharacteristic
133C2×C23C4×SD1611yescharacteristic
134C2×C23#44011yescharacteristic
135C2×C23#44811yescharacteristic
136C2×C23#44911yescharacteristic
137C2×C23#46011yescharacteristic
138C2×C23#46411yescharacteristic
139D23—82no—
140C22×Q8—231no—
141C22×D4—231no—
142C2×SD16—234no—
143C2×SD16—462no—
144C2×SD16—462no—
145C22×C8—231no—
146C22×C8C2×D2311yescharacteristic
147C4×Q8—462no—
148C4×Q8—462no—
149C2×C4⋊C4—461no—
150C2×C4⋊C4C2×D2311yescharacteristic
151C2×C4⋊C4C2×D2311yescharacteristic
152C2×C22⋊C4—461no—
153C2×C22⋊C4—461no—
154C2×C42—231no—
155C2×C42—461no—
156#103—462no—
157#102—462no—
158C23#188011yescharacteristic, complemented, Sylow
159C24—461no—
160C2×Q8—232no—
161C2×Q8—232no—
162C2×Q8—232no—
163C2×Q8—461no—
164C2×Q8—461no—
165C2×Q8—461no—
166C2×D4—232no—
167C2×D4—461no—
168C2×D4—461no—
169C2×D4—461no—
170C2×D4—461no—
171C2×D4—461no—
172C22×C4—21no—
173C22×C4—21no—
174C22×C4—231no—
175C22×C4—231no—
176C22×C4—461no—
177C22×C4C22×D2311yescharacteristic
178SD16—468no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—461no—
182C2×C8—461no—
183C2×C8—461no—
184C2×C8C4×D2312yes—
185C4⋊C4—21no—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—464no—
189C4⋊C4D9212yes—
190C22⋊C4—922no—
191C22⋊C4—922no—
192C42—464no—
193C42—461no—
194C42—461no—
195C23—462no—
196C23—921no—
197C23—921no—
198C23—921no—
199C23—921no—
200C23—921no—
201C23—921no—
202C23D4×D2311yescharacteristic
203Q8—234no—
204Q8—462no—
205Q8—462no—
206Q8—462no—
207D4—462no—
208D4—462no—
209D4—921no—
210D4—921no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—232no—
218C2×C4—461no—
219C2×C4—462no—
220C2×C4—462no—
221C2×C4—462no—
222C2×C4—461no—
223C2×C4—461no—
224C2×C4—461no—
225C2×C4—461no—
226C2×C4C2×C4×D2311yescharacteristic
227C2×C4C2×D9211yescharacteristic
228C2×C4#6728811yescharacteristic
229C2×C4D4×D2311yescharacteristic
230C2×C4D4×D2311yescharacteristic
231C2×C4#6729211yescharacteristic
232C8—22no—
233C8—921no—
234C22—922no—
235C22—922no—
236C22—922no—
237C22—1841no—
238C22—1841no—
239C22—1841no—
240C22—1841no—
241C22#1062505311yescharacteristic
242C22#1062505511yescharacteristic
243C22#1062506411yescharacteristic
244C22#1062508211yescharacteristic
245C22SD16×D2311yescharacteristic
246C22#1062508711yescharacteristic
247C22#1062508911yescharacteristic
248C4—42no—
249C4—81no—
250C4—464no—
251C4—462no—
252C4—921no—
253C4C4×D9211yescharacteristic
254C4C22⋊C4×D2311yescharacteristic
255C4#1062506511yescharacteristic
256C4#1062506611yescharacteristic
257C2—1842no—
258C2#1309229511yescharacteristic
259C2#1309250411yescharacteristic
260C2#1309251611yescharacteristic
261C2#1309255711yescharacteristic
262C2#1309256311yescharacteristic
263C2#1309261611yescharacteristic
264C2#1309264211yescharacteristic
subgroupG/H
centerC23D4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#340C2
socleC23×C23C2×D4
prime radicalC22×D92C22
cosocleC22×C4×C23C23
hypercenter#340D23
hypocenterC23#1880
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×#10625058C2semidirect
3. C2×#10624992C2semidirect
6. #13092171C2semidirect
7. C23×#340C2semidirect
21. C2×#67263C4semidirect
90. C2×Dic23SD16semidirect
98. Dic46C22⋊C4semidirect
130. #340D23semidirect
158. C23#1880semidirect

Maximal subgroups

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

subgroupindex
C22×#672632
C2×#106250582
C2×#106249922
C2×#106249912
#130923182
#130921712
C23×#3402
#188023