Finite Group Databasebeta

← #15683049

Subgroups — #15683049

Order 2944.

460 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 141 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, complemented
2C2×#10625119C211yesmaximal, characteristic
3#13092988C211yesmaximal, characteristic
4#13092673C214yesmaximal, complemented
5#13092656C214yesmaximal, complemented
6#13092453C211yesmaximal, characteristic, complemented
7#13092426C211yesmaximal, characteristic, complemented
8#13092425C211yesmaximal, characteristic, complemented
9C23×#536C211yesmaximal, characteristic
10C2×#41×C23C2211yescharacteristic
11C22×Q8×C23C2211yescharacteristic
12C22×Dic46C2211yescharacteristic
13C23×C4⋊Q8—21no—
14C23×#124—21no—
15C23×#123—22no—
16C23×C22⋊Q8C2214yes—
17C23×#117C2211yescharacteristic
18#10625119—24no—
19#10625115—21no—
20C2×#67275—24no—
21C2×#67275C2212yes—
22C2×#67275C2212yes—
23#10625107—21no—
24#10625106—22no—
25#10625097C2211yescharacteristic
26#10625095C2214yes—
27C2×#67267C2212yes—
28C2×#67267C2211yescharacteristic
29C22×C23⋊C8C2212yes—
30C22×C23⋊C8C2211yescharacteristic
31#10625017C2214yes—
32#10624992C2214yes—
33#10624990C2212yes—
34#10624989C2212yes—
35#41×C23—22no—
36#41×C23—22no—
37C2×Q8×C23—21no—
38C2×Q8×C23—22no—
39C2×Q8×C23—22no—
40C2×Q8×C23D411yescharacteristic
41C2×Q8×C23C2312yes—
42C2×D4×C23D412yes—
43C2×D4×C23D411yescharacteristic
44C22×C4×C23—21no—
45C22×C4×C23C2312yes—
46C22×C4×C23C2311yescharacteristic
47C22×Dic23—21no—
48C2×Dic46—22no—
49C2×Dic46—22no—
50C2×Dic46—21no—
51C2×Dic46C2312yes—
52C4⋊C4×C23—24no—
53C4⋊C4×C23C2312yes—
54C22⋊C4×C23—21no—
55C22⋊C4×C23—24no—
56C42×C23—21no—
57C22⋊Dic23—24no—
58C22⋊Dic23—21no—
59#67275—24no—
60#67275—24no—
61C4⋊Dic23C2312yes—
62Dic23⋊C4—24no—
63C4×Dic23—21no—
64#67267—22no—
65#67267—24no—
66C2×C23⋊C8—24no—
67C2×C23⋊C8D414yes—
68C2×C23⋊C8C2312yes—
69C2×C23⋊C8C2311yescharacteristic
70C2×C23⋊C8C2311yescharacteristic
71C23×C23C2×D412yes—
72C23×C23C2×D411yescharacteristic
73Q8×C23—22no—
74Q8×C23—22no—
75Q8×C23—22no—
76Q8×C23—42no—
77D4×C23—24no—
78D4×C23—22no—
79C2×C4×C23—22no—
80C2×C4×C23—22no—
81C2×C4×C23—22no—
82C2×C4×C23—22no—
83C2×C4×C23—42no—
84C2×C4×C23C2×D412yes—
85C2×C4×C23C2×D412yes—
86C2×C4×C23C2×D411yescharacteristic
87C2×C4×C23#4112yes—
88C2×C4×C23C2411yescharacteristic
89C2×Dic23—22no—
90C2×Dic23—22no—
91C2×Dic23—42no—
92Dic46—22no—
93Dic46—22no—
94Dic46—42no—
95C23⋊C8—22no—
96C23⋊C8C2×D412yes—
97C23⋊C8C2×D412yes—
98#3059—231nomaximal, Sylow
99C22×C23—22no—
100C22×C23—22no—
101C22×C23—24no—
102C22×C23#12112yes—
103C22×C23C22×D411yescharacteristic
104C4×C23—22no—
105C4×C23—42no—
106C4×C23—42no—
107C4×C23#12112yes—
108C4×C23C22×D411yescharacteristic
109C4×C23C2×#4111yescharacteristic
110Dic23—42no—
111Dic23—42no—
112C22×Q16—231no—
113C2×#131—231no—
114#536—231no—
115#536D2311yescharacteristic
116#470—234no—
117#467—234no—
118#427—231no—
119#419—231no—
120#419—231no—
121C2×C23—22no—
122C2×C23—42no—
123C2×C23C2×#12111yescharacteristic
124C2×C23#57812yes—
125C2×#41C2×D2311yescharacteristic
126C22×Q8—231no—
127C22×Q8C2×D2311yescharacteristic
128C2×Q16—232no—
129C2×Q16—232no—
130C2×Q16—464no—
131#131—464no—
132C2×M16—231no—
133C2×M16—232no—
134C22×C8—231no—
135C22×C8—232no—
136C4⋊Q8—21no—
137C4⋊Q8—461no—
138#124—21no—
139#124—461no—
140#123—22no—
141#123—462no—
142C22⋊Q8—234no—
143C22⋊Q8C2×D2314yes—
144#117—231no—
145#117C2×D2311yescharacteristic
146#107—232no—
147#106—232no—
148#103—234no—
149#103—234no—
150C23#305911yescharacteristic, complemented, Sylow
151#41—22no—
152#41—22no—
153C2×Q8—21no—
154C2×Q8—22no—
155C2×Q8—22no—
156C2×Q8—232no—
157C2×Q8—461no—
158C2×Q8—462no—
159C2×Q8—462no—
160C2×Q8C22⋊D2311yescharacteristic
161C2×Q8C22×D2312yes—
162C2×D4C22⋊D2312yes—
163C2×D4C22⋊D2311yescharacteristic
164C22×C4—21no—
165C22×C4—461no—
166C22×C4C22×D2312yes—
167C22×C4C22×D2311yescharacteristic
168Q16—464no—
169Q16—464no—
170M16—464no—
171M16—462no—
172C2×C8—234no—
173C2×C8—231no—
174C2×C8—231no—
175C2×C8—232no—
176C2×C8—464no—
177C4⋊C4—24no—
178C4⋊C4—232no—
179C4⋊C4—464no—
180C4⋊C4C22×D2312yes—
181C22⋊C4—21no—
182C22⋊C4—24no—
183C22⋊C4—461no—
184C22⋊C4—464no—
185C42—21no—
186C42—461no—
187C23C2×C22⋊D2312yes—
188C23C2×C22⋊D2311yescharacteristic
189Q8—22no—
190Q8—22no—
191Q8—22no—
192Q8—42no—
193Q8—462no—
194Q8—462no—
195Q8—922no—
196D4—24no—
197D4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—42no—
203C2×C4—462no—
204C2×C4—462no—
205C2×C4—922no—
206C2×C4D4×D2312yes—
207C2×C4#6729012yes—
208C2×C4C2×C22⋊D2312yes—
209C2×C4C2×C22⋊D2311yescharacteristic
210C2×C4C23×D2311yescharacteristic
211C8—232no—
212C8—232no—
213C8—462no—
214C22—22no—
215C22—22no—
216C22—24no—
217C22#1062511012yes—
218C22C22×C22⋊D2311yescharacteristic
219C4—22no—
220C4—42no—
221C4—42no—
222C4—922no—
223C4—922no—
224C4#1062511012yes—
225C4C2×D4×D2311yescharacteristic
226C4C2×#6729011yescharacteristic
227C2—22no—
228C2—42no—
229C2C2×#1062511011yescharacteristic
230C2#1309323212yes—
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#536C2
socleC22×C23C22×D4
prime radicalC2×#41×C23C22
hypercenter#536D23
hypocenterC23#3059
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×#41 ◁ #536

Complements

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

NH ≅ G/Ntype
1. C22×#67275C2semidirect
4. #13092673C2semidirect
5. #13092656C2semidirect
6. #13092453C2semidirect
7. #13092426C2semidirect
8. #13092425C2semidirect
150. C23#3059semidirect

Maximal subgroups

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

subgroupindex
C22×#672752
C2×#106251192
#130929882
#130926732
#130926562
#130924532
#130924262
#130924252
C23×#5362
#305923