Finite Group Databasebeta

← #27205918

Subgroups — #27205918

Order 13184.

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

normal subgroups only

This group has 416 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
1C2×#15693001C211yesmaximal, characteristic
2C22⋊Q8×D103C211yesmaximal, characteristic
3#20268128C212yesmaximal, complemented
4#20268126C211yesmaximal, characteristic, complemented
5#20268033C212yesmaximal, complemented
6#20268031C212yesmaximal, complemented
7#20267949C211yesmaximal, characteristic, complemented
8#20267948C212yesmaximal, complemented
9#20267946C211yesmaximal, characteristic, complemented
10C22⋊C8×D103C211yesmaximal, characteristic
11#484×C103C211yesmaximal, characteristic, complemented
12C22×Dic206C2211yescharacteristic
13C2×Q8×D103C2211yescharacteristic
14C22×C4×D103C2211yescharacteristic
15C2×Dic412C2212yescomplemented
16C2×#13110095C2212yescomplemented
17C2×C8×D103C2212yes—
18#15693001—21no—
19#15693001—21no—
20#15693001C2211yescharacteristic
21#15693001C2212yes—
22#15693001C2212yes—
23#15693000C2211yescharacteristic
24#15692999—21no—
25#15692998—21no—
26#15692997C2211yescharacteristic
27C2×C4⋊Dic103—21no—
28C4⋊C4×D103—21no—
29C4⋊C4×D103C2211yescharacteristic
30C2×(C2×D103)⋊C4—21no—
31C22⋊C4×D103—21no—
32#15692954C2212yescomplemented
33#15692946C2212yescomplemented
34#15692944C2212yescomplemented
35#15692944C2212yescomplemented
36C22⋊(C103⋊C8)C2211yescharacteristic
37(C2×D103)⋊C8C2212yes—
38C22⋊Q8×C103C2211yescharacteristic
39C2×C4⋊C4×C103C2211yescharacteristic
40#107×C103C2212yescomplemented
41#103×C103C2212yescomplemented
42C22⋊C8×C103C2211yescharacteristic
43C23×D103D411yescharacteristic
44C2×Dic206—21no—
45C2×Dic206—21no—
46C2×Dic206—42no—
47C2×Dic206C2311yescharacteristic
48C2×Dic206C2312yes—
49Q8×D103—42no—
50C22×Dic103—21no—
51C22×Dic103D411yescharacteristic
52C2×C4×D103—21no—
53C2×C4×D103—21no—
54C2×C4×D103—42no—
55C2×C4×D103D411yescharacteristic
56C2×C4×D103D411yescharacteristic
57C2×C4×D103C2311yescharacteristic
58C2×C4×D103C2311yescharacteristic
59Dic412—42no—
60#13110095—42no—
61C2×C103⋊C8C2312yes—
62C8×D103—42no—
63C4⋊Dic103—21no—
64C4⋊Dic103—22no—
65C4⋊Dic103—22no—
66C4⋊Dic103C2311yescharacteristic
67Dic103⋊C4—21no—
68Dic103⋊C4—21no—
69Dic103⋊C4—21no—
70C22⋊Dic103—21no—
71(C2×D103)⋊C4—21no—
72(C2×D103)⋊C4—21no—
73(C2×D103)⋊C4—22no—
74(C2×D103)⋊C4—22no—
75C2×Q8×C103C2311yescharacteristic
76C22×C4×C103—21no—
77C22×C4×C103C2311yescharacteristic
78C2×C8×C103C2312yes—
79C4⋊C4×C103—21no—
80C4⋊C4×C103—21no—
81C4⋊C4×C103C2312yes—
82C4⋊C4×C103C2311yescharacteristic
83C22⋊C4×C103—21no—
84C23×C103C2×D411yescharacteristic
85C22×D103—41no—
86C22×D103—41no—
87C22×D103Q1614yescomplemented
88C22×D103C2×D411yescharacteristic
89C22×D103C2×D411yescharacteristic
90Q8×C103—22no—
91C2×C4×C103—22no—
92C2×C4×C103—21no—
93C2×C4×C103—21no—
94C2×C4×C103—22no—
95C2×C4×C103—42no—
96C2×C4×C103C2×D411yescharacteristic
97C2×C4×C103C2411yescharacteristic
98C2×Dic103—22no—
99C2×Dic103—21no—
100C2×Dic103—21no—
101C2×Dic103—41no—
102C2×Dic103—42no—
103C2×Dic103C2×D411yescharacteristic
104C2×Dic103C2×D411yescharacteristic
105C4×D103—22no—
106C4×D103—22no—
107C4×D103—41no—
108C4×D103—41no—
109C4×D103—42no—
110C4×D103—42no—
111Dic206—22no—
112Dic206—22no—
113Dic206—22no—
114Dic206—42no—
115Dic206—42no—
116C8×C103—22no—
117C103⋊C8—22no—
118C22×C103—21no—
119C22×C103—21no—
120C22×C103C2×Q1612yes—
121C22×C103C22×D411yescharacteristic
122C2×D103—21no—
123C2×D103—21no—
124C2×D103—21no—
125C2×D103—21no—
126C2×D103—44no—
127C2×D103C2×Q1612yes—
128C2×D103C2×Q1612yes—
129C4×C103—21no—
130C4×C103—41no—
131C4×C103—41no—
132C4×C103—42no—
133C4×C103H(5,𝔽2)12yes—
134Dic103—21no—
135Dic103—21no—
136Dic103—41no—
137Dic103—42no—
138Dic103—41no—
139C2×C103—22no—
140C2×C103#53411yescharacteristic
141C2×C103C22×Q1611yescharacteristic
142C2×C103#57511yescharacteristic
143D103—22no—
144D103—22no—
145#3189—1031nomaximal, Sylow
146C103#318911yescharacteristic, complemented, Sylow
147C2×C22⋊Q8—1031no—
148C2×C22⋊Q8—1031no—
149#484—1031no—
150#484—1032no—
151#484D10311yescharacteristic, complemented
152#467—1032no—
153#467—1032no—
154#451—1031no—
155#451—1032no—
156#451—1031no—
157C2×C22⋊C8—1031no—
158C22×Q8—1031no—
159C22×Q8—1031no—
160C23×C4—1031no—
161C2×Q16—1032no—
162C2×Q16—1032no—
163C22×C8—1032no—
164C22⋊Q8—1031no—
165C22⋊Q8—1031no—
166C22⋊Q8—1032no—
167C22⋊Q8—1031no—
168C22⋊Q8—1032no—
169C22⋊Q8—2061no—
170C22⋊Q8—2061no—
171C22⋊Q8—2061no—
172C22⋊Q8—2061no—
173C22⋊Q8C2×D10311yescharacteristic
174C2×C4⋊C4—1031no—
175C2×C4⋊C4—2061no—
176C2×C4⋊C4—2061no—
177C2×C4⋊C4C2×D10311yescharacteristic
178C2×C22⋊C4—2061no—
179C2×C22⋊C4—2061no—
180#107—1032no—
181#107C2×D10312yescomplemented
182#103—1032no—
183#103—1032no—
184#103—1032no—
185#103C2×D10312yescomplemented
186C22⋊C8—1031no—
187C22⋊C8—1032no—
188C22⋊C8C2×D10311yescharacteristic
189C24—1031no—
190C2×Q8—1031no—
191C2×Q8—1032no—
192C2×Q8—4122no—
193C2×Q8—4122no—
194C2×Q8—2061no—
195C2×Q8—2061no—
196C2×Q8C22×D10311yescharacteristic
197C22×C4—21no—
198C22×C4—1031no—
199C22×C4—1031no—
200C22×C4—1031no—
201C22×C4—1031no—
202C22×C4—1031no—
203C22×C4—4122no—
204C22×C4—2061no—
205C22×C4—2061no—
206C22×C4—2061no—
207C22×C4C22×D10311yescharacteristic
208Q16—4122no—
209Q16—4122no—
210C2×C8—1032no—
211C2×C8—4122no—
212C2×C8C22×D10312yes—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—1031no—
216C4⋊C4—2061no—
217C4⋊C4—2061no—
218C4⋊C4—2061no—
219C4⋊C4—2062no—
220C4⋊C4—2062no—
221C4⋊C4—2061no—
222C4⋊C4C22×D10311yescharacteristic
223C4⋊C4C22×D10312yes—
224C22⋊C4—21no—
225C22⋊C4—2061no—
226C22⋊C4—2061no—
227C22⋊C4—2062no—
228C22⋊C4—2062no—
229C22⋊C4—2061no—
230C23—1034no—
231C23—1031no—
232C23—1031no—
233C23—4121no—
234C23—4121no—
235C23D4×D10311yescharacteristic
236Q8—22no—
237Q8—4122no—
238Q8—4122no—
239Q8—2062no—
240Q8—2062no—
241Q8—2062no—
242C2×C4—22no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—1031no—
248C2×C4—1031no—
249C2×C4—4121no—
250C2×C4—4121no—
251C2×C4—4122no—
252C2×C4—4122no—
253C2×C4—4122no—
254C2×C4—4121no—
255C2×C4—2061no—
256C2×C4—2062no—
257C2×C4—2061no—
258C2×C4—2062no—
259C2×C4—2062no—
260C2×C4D4×D10311yescharacteristic
261C2×C4C23×D10311yescharacteristic
262C8—22no—
263C8—2062no—
264C22—21no—
265C22—21no—
266C22—1032no—
267C22—1032no—
268C22—4124no—
269C22—2061no—
270C22—2061no—
271C22—2061no—
272C22—2061no—
273C22Q16×D10312yes—
274C22C2×D4×D10311yescharacteristic
275C4—21no—
276C4—42no—
277C4—41no—
278C4—41no—
279C4—4121no—
280C4—4121no—
281C4—4122no—
282C4—2061no—
283C4—2061no—
284C4#1569306712yes—
285C2—22no—
286C2—2062no—
287C2—2062no—
288C2#2026835211yescharacteristic
289C2C2×Q16×D10311yescharacteristic
290C2#2026858711yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#484×C103C2
socleC22×C103C22×D4
prime radicalC23×D103D4
hypercenter#484D103
hypocenterC103#3189
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
3. #20268128C2semidirect
4. #20268126C2semidirect
5. #20268033C2semidirect
6. #20268031C2semidirect
7. #20267949C2semidirect
8. #20267948C2semidirect
9. #20267946C2semidirect
11. #484×C103C2semidirect
15. C2×Dic412C22semidirect
16. C2×#13110095C22semidirect
32. #15692954C22semidirect
33. #15692946C22semidirect
34. #15692944C22semidirect
35. #15692944C22semidirect
40. #107×C103C22semidirect
41. #103×C103C22semidirect
87. C22×D103Q16semidirect
146. C103#3189semidirect
151. #484D103semidirect
181. #107C2×D103semidirect
185. #103C2×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930012
C22⋊Q8×D1032
#202681282
#202681262
#202680332
#202680312
#202679492
#202679482
#202679462
C22⋊C8×D1032
#484×C1032
#3189103