Finite Group Databasebeta

← #15683568

Subgroups — #15683568

Order 2944.

386 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 129 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#13092951C211yesmaximal, characteristic
2#13092752C211yesmaximal, characteristic, complemented
3#13092735C211yesmaximal, characteristic
4#13092724C212yesmaximal, complemented
5#13092639C212yesmaximal, complemented
6#13092573C211yesmaximal, characteristic, complemented
7#13092556C211yesmaximal, characteristic
8#13092522C212yesmaximal, complemented
9#13092515C212yesmaximal, complemented
10#13092474C211yesmaximal, characteristic, complemented
11C2×C4×Q8×C23C211yesmaximal, characteristic, complemented
12C22×Q8×C23C2211yescharacteristic
13C4×Q8×C23—21no—
14C4×Q8×C23—21no—
15C4×Q8×C23C2212yes—
16C4×Q8×C23C2212yes—
17C2×C4⋊C4×C23—21no—
18C2×C4⋊C4×C23C2211yescharacteristic
19C2×C42×C23—21no—
20C2×C42×C23C2211yescharacteristic
21C2×#67275C2212yes—
22C2×#67274C2212yes—
23#10625101C2211yescharacteristic
24#10625100—21no—
25C4×C22⋊D23—21no—
26#10625095C2211yescharacteristic
27#10625047—21no—
28#10625046C2211yescharacteristic
29C4×D92C2211yescharacteristic
30#10625043—21no—
31#10625041C2211yescharacteristic
32C4×Dic46C2211yescharacteristic
33#10625017C2212yes—
34#10625017C2212yes—
35C22⋊(C23⋊C8)C2211yescharacteristic
36C22⋊(C23⋊C8)C2211yescharacteristic
37#10624992C2212yes—
38#10624991C2212yes—
39#10624990C2212yes—
40#10624989C2212yes—
41C4⋊(C23⋊C8)C2212yes—
42#10624985C2212yes—
43C2×Q8×C23—24no—
44C2×Q8×C23—21no—
45C2×Q8×C23C2312yes—
46C22×C4×C23—21no—
47C22×C4×C23—21no—
48C22×C4×C23D411yescharacteristic
49C22×C4×C23D411yescharacteristic
50C22×C4×C23C2311yescharacteristic
51C2×C22⋊D23—21no—
52C2×D92C2311yescharacteristic
53C2×C4×D23—21no—
54C2×Dic46C2311yescharacteristic
55C4⋊C4×C23—22no—
56C4⋊C4×C23—22no—
57C4⋊C4×C23—21no—
58C4⋊C4×C23C2312yes—
59C42×C23—22no—
60C42×C23—22no—
61C42×C23D411yescharacteristic
62C42×C23D411yescharacteristic
63C42×C23C2311yescharacteristic
64C42×C23C2311yescharacteristic
65C22⋊Dic23—21no—
66#67275—24no—
67#67274—24no—
68(C2×D23)⋊C4—21no—
69(C2×D23)⋊C4—21no—
70(C2×D23)⋊C4—21no—
71(C2×D23)⋊C4—21no—
72C4⋊Dic23C2311yescharacteristic
73C4⋊Dic23C2311yescharacteristic
74Dic23⋊C4—21no—
75Dic23⋊C4—21no—
76Dic23⋊C4—21no—
77Dic23⋊C4—21no—
78C4×Dic23—21no—
79C2×C23⋊C8C2312yes—
80C2×C23⋊C8C2312yes—
81C23×C23C2×D411yescharacteristic
82C22×D23—21no—
83Q8×C23—24no—
84Q8×C23—22no—
85Q8×C23#4114yes—
86C2×C4×C23—24no—
87C2×C4×C23—22no—
88C2×C4×C23—22no—
89C2×C4×C23—22no—
90C2×C4×C23—22no—
91C2×C4×C23—41no—
92C2×C4×C23—42no—
93C2×C4×C23C2×D411yescharacteristic
94C2×C4×C23C2×D411yescharacteristic
95C2×C4×C23C2×D411yescharacteristic
96C2×C4×C23C2×D411yescharacteristic
97C2×C4×C23C2×D411yescharacteristic
98C2×C4×C23C2411yescharacteristic
99C22⋊D23—42no—
100C2×Dic23—21no—
101C2×Dic23—21no—
102C2×Dic23—21no—
103D92—22no—
104C4×D23—42no—
105Dic46—22no—
106C23⋊C8—22no—
107C23⋊C8—22no—
108#3117—231nomaximal, Sylow
109C22×C23—21no—
110C22×C23—21no—
111C22×C23#13712yes—
112C22×C23C22×D411yescharacteristic
113C2×D23—41no—
114C2×D23—41no—
115C2×D23—41no—
116C4×C23—24no—
117C4×C23—21no—
118C4×C23—21no—
119C4×C23—21no—
120C4×C23—21no—
121C4×C23—21no—
122C4×C23—42no—
123C4×C23C2×#4112yes—
124Dic23—41no—
125Dic23—41no—
126Dic23—41no—
127#529—231no—
128C2×C4×Q8D2311yescharacteristic, complemented
129#484—231no—
130#481—231no—
131#479—232no—
132#464—232no—
133#451—231no—
134#448—231no—
135#441—232no—
136#440—232no—
137#432—231no—
138C2×C23—22no—
139C2×C23#52511yescharacteristic
140C2×C23C2×#13711yescharacteristic
141C2×C23#57511yescharacteristic
142D23—81no—
143C22×Q8C2×D2311yescharacteristic
144C2×Q16—232no—
145C2×SD16—232no—
146#126—461no—
147#125—231no—
148#124—231no—
149#123—461no—
150C22⋊Q8—231no—
151#121—231no—
152C4×Q8—21no—
153C4×Q8—21no—
154C4×Q8—231no—
155C4×Q8C2×D2312yes—
156C4×Q8C2×D2312yes—
157C4×D4—231no—
158C4×D4—461no—
159#117—461no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4C2×D2311yescharacteristic
162C2×C42—21no—
163C2×C42C2×D2311yescharacteristic
164#107—232no—
165#106—232no—
166C4⋊C8—232no—
167#103—232no—
168#103—232no—
169#103—232no—
170#102—232no—
171C22⋊C8—231no—
172C22⋊C8—231no—
173#97—232no—
174C23#311711yescharacteristic, complemented, Sylow
175C2×Q8—24no—
176C2×Q8—21no—
177C2×Q8—231no—
178C2×Q8C22×D2312yes—
179C2×D4—231no—
180C2×D4—461no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—461no—
184C22×C4C22⋊D2311yescharacteristic
185C22×C4C22⋊D2311yescharacteristic
186C22×C4C22×D2311yescharacteristic
187Q16—464no—
188SD16—464no—
189C2×C8—232no—
190C2×C8—232no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—21no—
194C4⋊C4—231no—
195C4⋊C4—231no—
196C4⋊C4—461no—
197C4⋊C4—461no—
198C4⋊C4—461no—
199C4⋊C4—461no—
200C4⋊C4C22×D2312yes—
201C22⋊C4—461no—
202C22⋊C4—461no—
203C22⋊C4—461no—
204C22⋊C4—461no—
205C22⋊C4—461no—
206C42—22no—
207C42—22no—
208C42—461no—
209C42C22⋊D2311yescharacteristic
210C42C22⋊D2311yescharacteristic
211C42C22×D2311yescharacteristic
212C42C22×D2311yescharacteristic
213C23—461no—
214C23C2×C22⋊D2311yescharacteristic
215Q8—24no—
216Q8—22no—
217Q8—462no—
218Q8#6728814yes—
219D4—462no—
220D4—922no—
221C2×C4—24no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—461no—
229C2×C4—461no—
230C2×C4—461no—
231C2×C4—922no—
232C2×C4C2×C22⋊D2311yescharacteristic
233C2×C4C2×C22⋊D2311yescharacteristic
234C2×C4C2×C22⋊D2311yescharacteristic
235C2×C4C2×C22⋊D2311yescharacteristic
236C2×C4C2×C22⋊D2311yescharacteristic
237C2×C4C23×D2311yescharacteristic
238C8—462no—
239C8—462no—
240C22—21no—
241C22—21no—
242C22—921no—
243C22—921no—
244C22—921no—
245C22#1062511312yes—
246C22C22×C22⋊D2311yescharacteristic
247C4—24no—
248C4—21no—
249C4—21no—
250C4—21no—
251C4—21no—
252C4—21no—
253C4—42no—
254C4—921no—
255C4—921no—
256C4—921no—
257C4C2×#6728812yes—
258C2—22no—
259C2—1841no—
260C2#1309292811yescharacteristic
261C2C2×#1062511311yescharacteristic
262C2#1309321511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D23
commutator, cosocleC2×C4×C23C24
FrattiniC2×C4C23×D23
FittingC2×C4×Q8×C23C2
socleC22×C23C22×D4
prime radical#10625101C22
hypercenterC2×C4×Q8D23
hypocenterC23#3117
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #13092752C2semidirect
4. #13092724C2semidirect
5. #13092639C2semidirect
6. #13092573C2semidirect
8. #13092522C2semidirect
9. #13092515C2semidirect
10. #13092474C2semidirect
11. C2×C4×Q8×C23C2semidirect
128. C2×C4×Q8D23semidirect
174. C23#3117semidirect

Maximal subgroups

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

subgroupindex
#130929512
#130927522
#130927352
#130927242
#130926392
#130925732
#130925562
#130925222
#130925152
#130924742
C2×C4×Q8×C232
#311723