Finite Group Databasebeta

← #15683086

Subgroups — #15683086

Order 2944.

472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#10625113C211yesmaximal, characteristic, complemented
2C2×#10625072C211yesmaximal, characteristic, complemented
3#13092998C211yesmaximal, characteristic
4#13092991C211yesmaximal, characteristic, complemented
5#13092674C212yesmaximal, complemented
6#13092666C212yesmaximal, complemented
7#13092657C212yesmaximal, complemented
8#13092649C212yesmaximal, complemented
9#13092457C211yesmaximal, characteristic, complemented
10#13092414C211yesmaximal, characteristic, complemented
11C2×C23×#103C211yesmaximal, characteristic, complemented
12C22×Q8×C23C2211yescharacteristic
13C2×#67288C2211yescharacteristic
14C2×#67288C2211yescharacteristic
15C22×C8×C23C2211yescharacteristic
16C2×C4⋊C4×C23C2211yescharacteristic
17#10625118—21no—
18#10625117C2212yes—
19#10625117C2212yes—
20#10625115—21no—
21C2×#67275C2212yes—
22#10625113—24no—
23C2×#67274C2212yes—
24#10625101—22no—
25#10625100—22no—
26#10625097C2211yescharacteristic
27C2×#67267C2211yescharacteristic
28#10625072—24no—
29C2×#67262C2212yes—
30C2×C8×D23C2212yes—
31#10625068—21no—
32#10625068C2212yes—
33#10625066—21no—
34#10625066C2212yes—
35C23×#103C2212yes—
36C23×#103C2212yes—
37#10625003C2211yescharacteristic
38#10625003C2211yescharacteristic
39#10624998C2211yescharacteristic
40#10624998C2211yescharacteristic
41#10624990C2212yes—
42#10624989C2212yes—
43C2×Q8×C23—21no—
44C2×Q8×C23—22no—
45C2×Q8×C23—22no—
46C2×Q8×C23C2312yes—
47C22×C4×C23—21no—
48C22×C4×C23—21no—
49C22×C4×C23C2311yescharacteristic
50C2×C22⋊D23—21no—
51C2×C22⋊D23D412yes—
52#67288—22no—
53#67288—22no—
54#67288—22no—
55#67288—22no—
56C2×D92—22no—
57C2×D92D411yescharacteristic
58C2×D92C2311yescharacteristic
59C2×C4×D23—21no—
60C2×C4×D23C2312yes—
61C2×Dic46D411yescharacteristic
62C2×Dic46C2311yescharacteristic
63C2×C8×C23—22no—
64C2×C8×C23C2311yescharacteristic
65C2×C8×C23C2311yescharacteristic
66C4⋊C4×C23—21no—
67C4⋊C4×C23C2312yes—
68C22⋊Dic23—21no—
69#67275—24no—
70#67274—24no—
71(C2×D23)⋊C4—22no—
72(C2×D23)⋊C4—22no—
73(C2×D23)⋊C4—22no—
74(C2×D23)⋊C4—22no—
75C4⋊Dic23—22no—
76C4⋊Dic23C2311yescharacteristic
77C4⋊Dic23C2311yescharacteristic
78Dic23⋊C4—22no—
79Dic23⋊C4—22no—
80C4×Dic23—21no—
81#67267D414yescomplemented
82C2×C23⋊C8C2312yes—
83#67262—24no—
84C8×D23—24no—
85C23×C23C2×D411yescharacteristic
86C22×D23—21no—
87C22×D23C2×D412yes—
88Q8×C23—22no—
89Q8×C23—22no—
90Q8×C23—42no—
91C2×C4×C23—22no—
92C2×C4×C23—22no—
93C2×C4×C23—42no—
94C2×C4×C23—81no—
95C2×C4×C23C2×D411yescharacteristic
96C2×C4×C23C2×D412yes—
97C2×C4×C23#4112yes—
98C2×C4×C23C2411yescharacteristic
99C22⋊D23—24no—
100C22⋊D23—42no—
101C2×Dic23—21no—
102C2×Dic23—21no—
103C2×Dic23—21no—
104C2×Dic23C2×D412yes—
105D92—22no—
106D92—21no—
107D92—21no—
108D92—82no—
109C4×D23—22no—
110C4×D23—22no—
111C4×D23—42no—
112Dic46—22no—
113Dic46—21no—
114Dic46—21no—
115C8×C23—21no—
116C8×C23—21no—
117C23⋊C8C2×D414yes—
118#3063—231nomaximal, Sylow
119C22×C23—21no—
120C22×C23—21no—
121C22×C23#12112yes—
122C22×C23C22×D411yescharacteristic
123C2×D23—22no—
124C2×D23—22no—
125C2×D23—22no—
126C2×D23—41no—
127C2×D23—41no—
128C2×D23—41no—
129C4×C23—42no—
130C4×C23—42no—
131C4×C23#12112yes—
132C4×C23C22×D411yescharacteristic
133C4×C23C2×#4111yescharacteristic
134Dic23—22no—
135Dic23—41no—
136Dic23—41no—
137Dic23—41no—
138C2×#137—231no—
139C2×#131—231no—
140#537—231no—
141#536—231no—
142#470—232no—
143#468—232no—
144#467—232no—
145#465—232no—
146#428—231no—
147#416—231no—
148C2×#103D2311yescharacteristic, complemented
149C2×C23—22no—
150C2×C23C2×#12111yescharacteristic
151C2×C23#57711yescharacteristic
152C2×C23#57811yescharacteristic
153D23—42no—
154D23—81no—
155C2×#41—231no—
156C2×#41—231no—
157C22×Q8C2×D2311yescharacteristic
158#137—464no—
159C2×Q16—232no—
160C2×SD16—232no—
161#131—464no—
162C2×M16—231no—
163C2×M16—232no—
164C22×C8—232no—
165C22×C8C2×D2311yescharacteristic
166C4⋊Q8—461no—
167#124—461no—
168#123—462no—
169C22⋊Q8—232no—
170C22⋊Q8—232no—
171C22⋊Q8—232no—
172C22⋊Q8—461no—
173#121—232no—
174#121—461no—
175#121—462no—
176#117—231no—
177C2×C4⋊C4C2×D2311yescharacteristic
178#107—232no—
179#106—232no—
180#103—231no—
181#103—231no—
182#103C2×D2312yes—
183#103C2×D2312yes—
184#102—231no—
185#102—231no—
186C23#306311yescharacteristic, complemented, Sylow
187#41—462no—
188#41—462no—
189#41—462no—
190#41—462no—
191C2×Q8—21no—
192C2×Q8—22no—
193C2×Q8—22no—
194C2×Q8—231no—
195C2×Q8—231no—
196C2×Q8C22×D2312yes—
197C2×D4—232no—
198C2×D4—231no—
199C2×D4—231no—
200C2×D4—462no—
201C2×D4—461no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—232no—
205C22×C4—461no—
206C22×C4C22×D2311yescharacteristic
207Q16—464no—
208SD16—464no—
209M16—234no—
210M16—464no—
211C2×C8—22no—
212C2×C8—232no—
213C2×C8—464no—
214C2×C8C22×D2311yescharacteristic
215C2×C8C22×D2311yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—231no—
218C4⋊C4—231no—
219C4⋊C4—462no—
220C4⋊C4—462no—
221C4⋊C4—462no—
222C4⋊C4C22×D2312yes—
223C22⋊C4—462no—
224C22⋊C4—462no—
225C22⋊C4—462no—
226C22⋊C4—462no—
227C22⋊C4—461no—
228C42—461no—
229C23—232no—
230C23—461no—
231C23D4×D2311yescharacteristic
232Q8—22no—
233Q8—22no—
234Q8—42no—
235Q8—462no—
236Q8—461no—
237Q8—461no—
238D4—464no—
239D4—462no—
240D4—461no—
241D4—461no—
242D4—922no—
243D4—1842no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—81no—
248C2×C4—232no—
249C2×C4—462no—
250C2×C4—462no—
251C2×C4—461no—
252C2×C4—461no—
253C2×C4—461no—
254C2×C4—922no—
255C2×C4#6728812yes—
256C2×C4D4×D2311yescharacteristic
257C2×C4D4×D2312yes—
258C2×C4C23×D2311yescharacteristic
259C8—21no—
260C8—21no—
261C8—234no—
262C22—21no—
263C22—21no—
264C22—462no—
265C22—462no—
266C22—462no—
267C22—921no—
268C22—921no—
269C22—921no—
270C22#1062505512yes—
271C22C2×D4×D2311yescharacteristic
272C4—42no—
273C4—42no—
274C4—462no—
275C4—921no—
276C4—921no—
277C4—921no—
278C4#1062505512yes—
279C4C2×#6728811yescharacteristic
280C4C2×D4×D2311yescharacteristic
281C2—22no—
282C2—922no—
283C2—1841no—
284C2C2×#1062505511yescharacteristic
285C2#1309322311yescharacteristic
286C2#1309323011yescharacteristic
subgroupG/H
centerC22C2×D4×D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C23×#103C2
socleC22×C23C22×D4
prime radical#13092998C2
hypercenterC2×#103D23
hypocenterC23#3063
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. C2×#10625113C2semidirect
2. C2×#10625072C2semidirect
4. #13092991C2semidirect
5. #13092674C2semidirect
6. #13092666C2semidirect
7. #13092657C2semidirect
8. #13092649C2semidirect
9. #13092457C2semidirect
10. #13092414C2semidirect
11. C2×C23×#103C2semidirect
81. #67267D4semidirect
148. C2×#103D23semidirect
186. C23#3063semidirect

Maximal subgroups

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

subgroupindex
C2×#106251132
C2×#106250722
#130929982
#130929912
#130926742
#130926662
#130926572
#130926492
#130924572
#130924142
C2×C23×#1032
#306323