Finite Group Databasebeta

← #15686050

Subgroups — #15686050

Order 2944.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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#13093141C211yesmaximal, characteristic, complemented
2#13093124C211yesmaximal, characteristic, complemented
3#13092773C212yesmaximal, complemented
4#13092767C211yesmaximal, characteristic, complemented
5#13092722C212yesmaximal, complemented
6#13092708C211yesmaximal, characteristic, complemented
7#13092634C212yesmaximal
8#13092541C211yesmaximal, characteristic, complemented
9SD16×Dic23C212yesmaximal, complemented
10C4×#67272C211yesmaximal, characteristic
11C23×#461C211yesmaximal, characteristic, complemented
12C2×SD16×C23C2212yes—
13C23×C4⋊Q8C2211yescharacteristic
14C4×D4×C23C2211yescharacteristic
15#10625118C2212yes—
16Q8×Dic23C2212yes—
17D4×Dic23C2212yes—
18C2×#67272C2211yescharacteristic
19C2×C4⋊Dic23—21no—
20#10625095—21no—
21#10625069—22no—
22#10625068—21no—
23#10625063—21no—
24#10625061C2212yes—
25#10625049—22no—
26C4×D92C2211yescharacteristic
27#10625040C2211yescharacteristic
28C4×Dic46C2211yescharacteristic
29C23×C4⋊C8C2211yescharacteristic
30C23×#103C2212yes—
31#10625017C2212yes—
32#10625017C2212yes—
33#10625014C2211yescharacteristic
34#10625003C2212yes—
35#10624999C2212yes—
36Dic23⋊C8C2212yes—
37C8×Dic23C2212yes—
38#10624991C2211yescharacteristic
39#10624989C2211yescharacteristic
40C4×C23⋊C8C2211yescharacteristic
41C2×Q8×C23C2312yes—
42C2×D4×C23C2311yescharacteristic
43C22×C4×C23—21no—
44C22×Dic23—22no—
45C2×D92C2311yescharacteristic
46C2×C4×D23—21no—
47C2×Dic46—21no—
48C2×Dic46D411yescharacteristic
49SD16×C23—24no—
50C2×C8×C23C2312yes—
51C4⋊C4×C23—21no—
52C4⋊C4×C23—21no—
53C4⋊C4×C23C2311yescharacteristic
54C22⋊C4×C23—21no—
55C42×C23C2311yescharacteristic
56C22⋊Dic23—22no—
57#67272—22no—
58(C2×D23)⋊C4—21no—
59(C2×D23)⋊C4—22no—
60(C2×D23)⋊C4—22no—
61C4⋊Dic23—21no—
62C4⋊Dic23—22no—
63C4⋊Dic23—22no—
64C4⋊Dic23D411yescharacteristic
65C4⋊Dic23C2312yes—
66C4⋊Dic23C2311yescharacteristic
67Dic23⋊C4—22no—
68Dic23⋊C4D412yes—
69C4×Dic23—22no—
70C4×Dic23C2312yes—
71C2×C23⋊C8C2311yescharacteristic
72C2×C23⋊C8C2311yescharacteristic
73C23×C23—21no—
74C22×D23—21no—
75Q8×C23—22no—
76Q8×C23—22no—
77D4×C23—21no—
78D4×C23#4112yes—
79C2×C4×C23—22no—
80C2×C4×C23—21no—
81C2×C4×C23—42no—
82C2×C4×C23C2×D411yescharacteristic
83C2×C4×C23C2×D411yescharacteristic
84C2×C4×C23C2411yescharacteristic
85C2×Dic23—21no—
86C2×Dic23—22no—
87C2×Dic23—82no—
88C2×Dic23C2×D412yes—
89C2×Dic23C2×D412yes—
90D92—21no—
91D92—21no—
92C4×D23—42no—
93Dic46—22no—
94Dic46—81no—
95C8×C23—22no—
96C23⋊C8—21no—
97C23⋊C8—21no—
98#3360—231nomaximal, Sylow
99C22×C23—22no—
100C22×C23—41no—
101C22×C23—41no—
102C22×C23C22×D411yescharacteristic
103C2×D23—41no—
104C2×D23—41no—
105C2×D23—41no—
106C4×C23—21no—
107C4×C23—42no—
108C4×C23—41no—
109C4×C23#13512yes—
110C4×C23C2×#4111yescharacteristic
111C4×C232−1+411yescharacteristic
112Dic23—22no—
113Dic23—22no—
114Dic23—41no—
115Dic23—42no—
116#556—231no—
117#554—231no—
118#488—232no—
119#487—231no—
120#479—232no—
121#476—231no—
122#463—232no—
123#461D2311yescharacteristic, complemented
124C8×Q8—231no—
125C4×SD16—232no—
126C4×D8—231no—
127C2×C23—42no—
128C2×C23#54811yescharacteristic
129C2×C23C2×#13511yescharacteristic
130C2×C23#57711yescharacteristic
131D23—81no—
132C2×SD16C2×D2312yes—
133C2×D8—231no—
134C4⋊Q8—231no—
135C4⋊Q8C2×D2311yescharacteristic
136#126—462no—
137#125—232no—
138#124—232no—
139C22⋊Q8—462no—
140C22⋊Q8—461no—
141C22⋊Q8—461no—
142C4×Q8—231no—
143C4×Q8—232no—
144C4×D4—232no—
145C4×D4—231no—
146C4×D4C2×D2311yescharacteristic
147#117—461no—
148C2×C4⋊C4—461no—
149#107—231no—
150#106—232no—
151C4⋊C8—232no—
152C4⋊C8C2×D2311yescharacteristic
153#103—232no—
154#103—232no—
155#103C2×D2312yes—
156#102—231no—
157#102—232no—
158#102—231no—
159C4×C8—232no—
160C4×C8—231no—
161C23#336011yescharacteristic, complemented, Sylow
162C2×Q8—231no—
163C2×Q8—461no—
164C2×Q8C22×D2312yes—
165C2×D4—231no—
166C2×D4C22×D2311yescharacteristic
167C22×C4—21no—
168C22×C4—462no—
169C22×C4—461no—
170SD16—24no—
171D8—462no—
172C2×C8—231no—
173C2×C8—231no—
174C2×C8C22×D2312yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—231no—
178C4⋊C4—232no—
179C4⋊C4—232no—
180C4⋊C4—231no—
181C4⋊C4—462no—
182C4⋊C4—462no—
183C4⋊C4—462no—
184C4⋊C4—461no—
185C4⋊C4C22×D2311yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—462no—
188C22⋊C4—462no—
189C22⋊C4—462no—
190C22⋊C4—461no—
191C42—232no—
192C42—462no—
193C42C22×D2311yescharacteristic
194C23—21no—
195C23—461no—
196Q8—22no—
197Q8—22no—
198Q8—462no—
199Q8—1841no—
200D4—21no—
201D4—461no—
202D4—461no—
203D4#6729012yes—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—232no—
208C2×C4—232no—
209C2×C4—461no—
210C2×C4—462no—
211C2×C4—922no—
212C2×C4—1842no—
213C2×C4D4×D2311yescharacteristic
214C2×C4D4×D2311yescharacteristic
215C2×C4C23×D2311yescharacteristic
216C8—22no—
217C8—461no—
218C8—461no—
219C22—22no—
220C22—41no—
221C22—41no—
222C22—921no—
223C22—921no—
224C22—921no—
225C22C2×D4×D2311yescharacteristic
226C4—21no—
227C4—41no—
228C4—42no—
229C4—462no—
230C4—462no—
231C4—921no—
232C4—922no—
233C4#1062508712yes—
234C4C2×#6729011yescharacteristic
235C4#1062516111yescharacteristic
236C2—42no—
237C2—1841no—
238C2#1309307311yescharacteristic
239C2C2×#1062508711yescharacteristic
240C2#1309322611yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#461C2
socleC22×C23C22×D4
prime radicalC2×#67272C22
hypercenter#461D23
hypocenterC23#3360
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #13093141C2semidirect
2. #13093124C2semidirect
3. #13092773C2semidirect
4. #13092767C2semidirect
5. #13092722C2semidirect
6. #13092708C2semidirect
8. #13092541C2semidirect
9. SD16×Dic23C2semidirect
11. C23×#461C2semidirect
123. #461D23semidirect
161. C23#3360semidirect

Maximal subgroups

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

subgroupindex
#130931412
#130931242
#130927732
#130927672
#130927222
#130927082
#130926342
#130925412
SD16×Dic232
C4×#672722
C23×#4612
#336023