Finite Group Databasebeta

← #15683240

Subgroups — #15683240

Order 2944.

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

normal subgroups only

This group has 362 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
1#13093045C211yesmaximal, characteristic
2#13092894C211yesmaximal, characteristic
3#13092725C212yesmaximal, complemented
4#13092725C212yesmaximal, complemented
5#13092713C212yesmaximal, complemented
6#13092703C212yesmaximal, complemented
7#13092459C211yesmaximal, characteristic
8#13092455C211yesmaximal, characteristic
9#13092427C211yesmaximal, characteristic
10C2×#10624998C211yesmaximal, characteristic
11C23×#424C211yesmaximal, characteristic
12C22×Dic46C2211yescharacteristic
13C2×M16×C23C2211yescharacteristic
14C22×C8×C23C2211yescharacteristic
15C23×#117C2211yescharacteristic
16#10625097C2211yescharacteristic
17#10625097C2211yescharacteristic
18C2×C4⋊Dic23C2211yescharacteristic
19#10625061—21no—
20#10625059—21no—
21#10625058—21no—
22#10625058—21no—
23#10625049—22no—
24#10625048—22no—
25#10625041C2212yes—
26#10625040C2212yes—
27C4×Dic46C2212yes—
28C4×Dic46C2212yes—
29C23×C4⋊C8C2212yes—
30C23×C4⋊C8C2212yes—
31#10625000C2211yescharacteristic
32#10625000C2211yescharacteristic
33#10625000C2212yes—
34#10624999C2211yescharacteristic
35#10624999C2212yes—
36#10624999C2211yescharacteristic
37#10624998C2212yes—
38#10624998C2212yes—
39#10624998C2212yes—
40#10624998C2212yes—
41C22×C4×C23C2311yescharacteristic
42C22×Dic23—21no—
43C22×Dic23—21no—
44C2×Dic46—21no—
45C2×Dic46—22no—
46C2×Dic46—22no—
47C2×Dic46Q814yescomplemented
48C2×Dic46C2312yes—
49M16×C23—22no—
50C2×C8×C23—22no—
51C2×C8×C23C2311yescharacteristic
52C2×C8×C23C2311yescharacteristic
53C2×C8×C23C2312yes—
54C4⋊C4×C23D411yescharacteristic
55C4⋊C4×C23D411yescharacteristic
56C22⋊C4×C23D412yes—
57C42×C23C2312yes—
58C22⋊Dic23—21no—
59C22⋊Dic23—21no—
60C4⋊Dic23—22no—
61C4⋊Dic23—21no—
62C4⋊Dic23C2311yescharacteristic
63C4⋊Dic23C2311yescharacteristic
64C4⋊Dic23C2311yescharacteristic
65C4⋊Dic23C2312yes—
66C4⋊Dic23C2311yescharacteristic
67Dic23⋊C4—22no—
68Dic23⋊C4—22no—
69Dic23⋊C4—22no—
70Dic23⋊C4—22no—
71C4×Dic23—22no—
72C4×Dic23—22no—
73C4×Dic23—21no—
74C4×Dic23—21no—
75C23×C23C2×D411yescharacteristic
76C2×C4×C23C2×D412yes—
77C2×C4×C23C2×D412yes—
78C2×C4×C23C2×D411yescharacteristic
79C2×C4×C23C2×Q812yes—
80C2×C4×C23#4112yes—
81C2×C4×C23C2411yescharacteristic
82C2×Dic23—24no—
83C2×Dic23—22no—
84C2×Dic23—21no—
85C2×Dic23—21no—
86C2×Dic23—21no—
87C2×Dic23—21no—
88C2×Dic23—22no—
89C2×Dic23—81no—
90Dic46—24no—
91Dic46—22no—
92Dic46—82no—
93Dic46C2×Q814yes—
94C8×C23—21no—
95C8×C23—21no—
96C8×C23—22no—
97#3082—231nomaximal, Sylow
98C22×C23—21no—
99C22×C23—21no—
100C22×C23C22⋊Q812yes—
101C22×C23C22×D411yescharacteristic
102C4×C23—22no—
103C4×C23—22no—
104C4×C23C22⋊Q812yes—
105C4×C23C22×Q811yescharacteristic
106C4×C23C2×#4111yescharacteristic
107Dic23—24no—
108Dic23—41no—
109Dic23—42no—
110Dic23—41no—
111Dic23—41no—
112Dic23—41no—
113#544—231no—
114#519—231no—
115#479—232no—
116#479—232no—
117#477—232no—
118#475—232no—
119#428—231no—
120#427—231no—
121#424D2311yescharacteristic
122#419—231no—
123C2×#103—231no—
124C2×C23—22no—
125C2×C23C2×C22⋊Q811yescharacteristic
126C2×C23#57711yescharacteristic
127C2×C23#57811yescharacteristic
128C22×Q8—231no—
129C2×M16C2×D2311yescharacteristic
130C22×C8C2×D2311yescharacteristic
131C4⋊Q8—232no—
132C4⋊Q8—461no—
133#125—232no—
134#125—461no—
135C22⋊Q8—462no—
136C4×Q8—232no—
137C4×Q8—232no—
138C4×Q8—461no—
139C4×Q8—461no—
140#117—231no—
141#117—231no—
142#117—462no—
143#117C2×D2311yescharacteristic
144C2×C4⋊C4—231no—
145#107—231no—
146#107—231no—
147#107—232no—
148#106—231no—
149#106—231no—
150#106—232no—
151C4⋊C8C2×D2312yes—
152C4⋊C8C2×D2312yes—
153#103—232no—
154#103—232no—
155#103—232no—
156#103—232no—
157C23#308211yescharacteristic, complemented, Sylow
158C2×Q8—234no—
159C2×Q8—232no—
160C2×Q8—461no—
161C2×Q8—462no—
162C2×Q8—462no—
163C22×C4—461no—
164C22×C4—461no—
165C22×C4C22×D2311yescharacteristic
166M16—22no—
167C2×C8—22no—
168C2×C8C22×D2311yescharacteristic
169C2×C8C22×D2312yes—
170C2×C8C22×D2311yescharacteristic
171C4⋊C4—232no—
172C4⋊C4—231no—
173C4⋊C4—231no—
174C4⋊C4—231no—
175C4⋊C4—231no—
176C4⋊C4—461no—
177C4⋊C4—462no—
178C4⋊C4—462no—
179C4⋊C4—462no—
180C4⋊C4—462no—
181C4⋊C4—462no—
182C4⋊C4D9211yescharacteristic
183C4⋊C4D9211yescharacteristic
184C22⋊C4—461no—
185C22⋊C4—461no—
186C22⋊C4D9212yes—
187C42—461no—
188C42—461no—
189C42—462no—
190C42—462no—
191C42C22×D2312yes—
192C23C2×D9211yescharacteristic
193Q8—234no—
194Q8—464no—
195Q8—462no—
196Q8—1842no—
197C2×C4—464no—
198C2×C4—462no—
199C2×C4—461no—
200C2×C4—461no—
201C2×C4—461no—
202C2×C4—461no—
203C2×C4—462no—
204C2×C4—1841no—
205C2×C4C2×D9212yes—
206C2×C4C2×D9212yes—
207C2×C4C2×D9211yescharacteristic
208C2×C4#6729012yes—
209C2×C4Q8×D2312yes—
210C2×C4C23×D2311yescharacteristic
211C8—21no—
212C8—21no—
213C8—22no—
214C22—21no—
215C22—21no—
216C22#1062506812yes—
217C22C22×D9211yescharacteristic
218C4—22no—
219C4—22no—
220C4—464no—
221C4—922no—
222C4—921no—
223C4—921no—
224C4—921no—
225C4—921no—
226C4#1062506812yes—
227C4C2×#6729011yescharacteristic
228C4C2×Q8×D2311yescharacteristic
229C2—22no—
230C2C2×#1062506811yescharacteristic
231C2#1309322911yescharacteristic
232C2#1309323411yescharacteristic
subgroupG/H
centerC22C22×D92
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC23×#424C2
socleC22×C23C22×D4
prime radicalC23×C23C2×D4
hypercenter#424D23
hypocenterC23#3082
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
3. #13092725C2semidirect
4. #13092725C2semidirect
5. #13092713C2semidirect
6. #13092703C2semidirect
47. C2×Dic46Q8semidirect
157. C23#3082semidirect

Maximal subgroups

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

subgroupindex
#130930452
#130928942
#130927252
#130927132
#130927032
#130924592
#130924552
#130924272
C2×#106249982
C23×#4242
#308223