Finite Group Databasebeta

← #28372948

Subgroups — #28372948

Order 13952.

420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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#20295539C211yesmaximal, characteristic
2C2×#16812657C211yesmaximal, characteristic, complemented
3#20295366C212yesmaximal, complemented
4#20295354C211yesmaximal, characteristic, complemented
5#20295353C212yesmaximal, complemented
6#20295344C211yesmaximal, characteristic, complemented
7#20295340C211yesmaximal, characteristic, complemented
8#20295063C212yesmaximal, complemented
9#20295021C212yesmaximal, complemented
10C22⋊C8×D109C211yesmaximal, characteristic, complemented
11#484×C109C211yesmaximal, characteristic, complemented
12C2×#13182030C2211yescharacteristic
13C22×C4×D109C2211yescharacteristic
14C2×C8×D109C2212yes—
15#16812684—21no—
16#16812675C2211yescharacteristic
17#16812674C2211yescharacteristic
18#16812673C2211yescharacteristic
19#16812669—21no—
20#16812661—21no—
21#16812659—21no—
22#16812657—21no—
23#16812657—21no—
24#16812657C2212yes—
25#16812657C2212yes—
26#16812657C2211yescharacteristic
27C2×C4⋊Dic109C2211yescharacteristic
28C2×#13182006—21no—
29C2×C4×Dic109—21no—
30#16812633C2212yescomplemented
31#16812630C2212yescomplemented
32#16812630C2212yescomplemented
33#16812623C2212yescomplemented
34#16812621C2212yescomplemented
35#16812619C2212yescomplemented
36C22⋊#11724784C2211yescharacteristic
37#16812611C2212yes—
38C22⋊Q8×C109C2211yescharacteristic
39C2×C4⋊C4×C109C2211yescharacteristic
40#107×C109C2212yescomplemented
41#103×C109C2212yescomplemented
42C22⋊C8×C109C2211yescharacteristic
43C23×D109D411yescharacteristic
44#13182030—24no—
45C2×D436—21no—
46C2×D436—21no—
47C2×D436C2311yescharacteristic
48C2×C22⋊D109—21no—
49C22×Dic109—21no—
50C22×Dic109D411yescharacteristic
51C2×C4×D109—24no—
52C2×C4×D109—21no—
53C2×C4×D109D411yescharacteristic
54C2×C4×D109D411yescharacteristic
55C2×C4×D109C2311yescharacteristic
56C2×C4×D109C2311yescharacteristic
57C2×#11724784C2312yes—
58C8×D109—24no—
59C4⋊Dic109—21no—
60C4⋊Dic109C2312yes—
61C4⋊Dic109C2311yescharacteristic
62#13182008—21no—
63#13182006—22no—
64#13182006—22no—
65#13182006—21no—
66#13182006—21no—
67#13182006—21no—
68#13182006—21no—
69C4×Dic109—22no—
70C4×Dic109—22no—
71C4×Dic109—21no—
72C2×Q8×C109C2311yescharacteristic
73C22×C4×C109—21no—
74C22×C4×C109C2311yescharacteristic
75C2×C8×C109C2312yes—
76C4⋊C4×C109—21no—
77C4⋊C4×C109—21no—
78C4⋊C4×C109C2312yes—
79C4⋊C4×C109C2311yescharacteristic
80C22⋊C4×C109—21no—
81C23×C109C2×D411yescharacteristic
82C22×D109—22no—
83C22×D109—22no—
84C22×D109—21no—
85C22×D109—41no—
86C22×D109C2×D411yescharacteristic
87C22×D109C2×D411yescharacteristic
88Q8×C109—22no—
89C2×C4×C109—22no—
90C2×C4×C109—21no—
91C2×C4×C109—21no—
92C2×C4×C109—22no—
93C2×C4×C109—42no—
94C2×C4×C109C2×D411yescharacteristic
95C2×C4×C109C2411yescharacteristic
96C22⋊D109—42no—
97C2×Dic109—22no—
98C2×Dic109—22no—
99C2×Dic109—21no—
100C2×Dic109—42no—
101C2×Dic109C2×D411yescharacteristic
102C2×Dic109C2×D411yescharacteristic
103D436—22no—
104D436—42no—
105D436—42no—
106C4×D109—22no—
107C4×D109—22no—
108C4×D109—22no—
109C4×D109—42no—
110C4×D109#4114yes—
111C8×C109—22no—
112#11724784—22no—
113C22×C109—21no—
114C22×C109—21no—
115C22×C109#13512yes—
116C22×C109C22×D411yescharacteristic
117C2×D109—21no—
118C2×D109—21no—
119C2×D109—21no—
120C2×D109—21no—
121C2×D109—21no—
122C2×D109—44no—
123C2×D109—41no—
124C2×D109—41no—
125C2×D109—41no—
126C2×D109#12312yes—
127C4×C109—21no—
128C4×C109—41no—
129C4×C109—41no—
130C4×C109—42no—
131C4×C109C2×#4112yes—
132Dic109—21no—
133Dic109—42no—
134Dic109—41no—
135Dic109#12312yes—
136C2×C109—22no—
137C2×C109C2×#12311yescharacteristic
138C2×C109C2×#13511yescharacteristic
139C2×C109#57511yescharacteristic
140D109—22no—
141D109—41no—
142D109—81no—
143#3091—1091nomaximal, Sylow
144C109#309111yescharacteristic, complemented, Sylow
145#525—1091no—
146C2×#117—1091no—
147#485—1092no—
148#484D10911yescharacteristic, complemented
149#483—1091no—
150#482—1092no—
151#481—1091no—
152#480—1091no—
153#427—1092no—
154#416—1092no—
155C2×C22⋊C8—1091no—
156C2×#41—1091no—
157C23×C4—1091no—
158C22×C8—1092no—
159#123—2181no—
160C22⋊Q8—1091no—
161C22⋊Q8C2×D10911yescharacteristic
162#121—1091no—
163#121—1091no—
164#120—2181no—
165C4×D4—2181no—
166C4×D4—2181no—
167#117—1092no—
168#117—1092no—
169#117—1091no—
170#117—2181no—
171#117—2181no—
172C2×C4⋊C4—1091no—
173C2×C4⋊C4C2×D10911yescharacteristic
174C2×C22⋊C4—2181no—
175C2×C42—2181no—
176#107—1092no—
177#107C2×D10912yescomplemented
178#106—1092no—
179#106—1092no—
180#103—1092no—
181#103C2×D10912yescomplemented
182#102—1092no—
183#102—1092no—
184C22⋊C8—1091no—
185C22⋊C8—1092no—
186C22⋊C8C2×D10911yescharacteristic
187C24—1091no—
188#41—2184no—
189C2×Q8C22×D10911yescharacteristic
190C2×D4—1091no—
191C2×D4—2181no—
192C2×D4—2181no—
193C2×D4—2181no—
194C22×C4—21no—
195C22×C4—1091no—
196C22×C4—1091no—
197C22×C4—1091no—
198C22×C4—1091no—
199C22×C4—1091no—
200C22×C4—2181no—
201C22×C4—2184no—
202C22×C4—2181no—
203C22×C4C22×D10911yescharacteristic
204C2×C8—1092no—
205C2×C8—2184no—
206C2×C8C22×D10912yes—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—1092no—
210C4⋊C4—1091no—
211C4⋊C4—2181no—
212C4⋊C4—2181no—
213C4⋊C4C22×D10912yes—
214C4⋊C4C22×D10911yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—2181no—
217C22⋊C4—2182no—
218C22⋊C4—2182no—
219C22⋊C4—2181no—
220C22⋊C4—2181no—
221C22⋊C4—2181no—
222C42—2182no—
223C42—2182no—
224C42—2181no—
225C23—1091no—
226C23—1091no—
227C23—4361no—
228C23—2182no—
229C23—2181no—
230C23—2182no—
231C23D4×D10911yescharacteristic
232Q8—22no—
233D4—4362no—
234D4—4362no—
235D4—4362no—
236D4—2182no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—1091no—
243C2×C4—1094no—
244C2×C4—1091no—
245C2×C4—4362no—
246C2×C4—4362no—
247C2×C4—2182no—
248C2×C4—2182no—
249C2×C4—2182no—
250C2×C4—2182no—
251C2×C4—2181no—
252C2×C4—2182no—
253C2×C4D4×D10911yescharacteristic
254C2×C4C23×D10911yescharacteristic
255C8—22no—
256C8—2182no—
257C22—21no—
258C22—21no—
259C22—1092no—
260C22—4364no—
261C22—4361no—
262C22—4361no—
263C22—4361no—
264C22—2181no—
265C22—2181no—
266C22—2181no—
267C22—2181no—
268C22—2181no—
269C22#1681272212yes—
270C22C2×D4×D10911yescharacteristic
271C4—21no—
272C4—41no—
273C4—42no—
274C4—41no—
275C4—1092no—
276C4—4362no—
277C4—4361no—
278C4—2181no—
279C4#41×D10912yes—
280C2—22no—
281C2—8721no—
282C2—4361no—
283C2—2182no—
284C2#123×D10911yescharacteristic
285C2C2×#1681272211yescharacteristic
286C2#2029582211yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#484×C109C2
socleC22×C109C22×D4
prime radical#20295539C2
hypercenter#484D109
hypocenterC109#3091
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×#16812657C2semidirect
3. #20295366C2semidirect
4. #20295354C2semidirect
5. #20295353C2semidirect
6. #20295344C2semidirect
7. #20295340C2semidirect
8. #20295063C2semidirect
9. #20295021C2semidirect
10. C22⋊C8×D109C2semidirect
11. #484×C109C2semidirect
30. #16812633C22semidirect
31. #16812630C22semidirect
32. #16812630C22semidirect
33. #16812623C22semidirect
34. #16812621C22semidirect
35. #16812619C22semidirect
40. #107×C109C22semidirect
41. #103×C109C22semidirect
144. C109#3091semidirect
148. #484D109semidirect
177. #107C2×D109semidirect
181. #103C2×D109semidirect

Maximal subgroups

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

subgroupindex
#202955392
C2×#168126572
#202953662
#202953542
#202953532
#202953442
#202953402
#202950632
#202950212
C22⋊C8×D1092
#484×C1092
#3091109