Finite Group Databasebeta

← #27205917

Subgroups — #27205917

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×#15692997C211yesmaximal, characteristic
2C22⋊Q8×D103C211yesmaximal, characteristic
3#20268127C211yesmaximal, characteristic, complemented
4#20268125C212yesmaximal, complemented
5#20268124C211yesmaximal, characteristic, complemented
6#20268031C212yesmaximal, complemented
7#20268029C212yesmaximal, complemented
8#20267947C211yesmaximal, characteristic, complemented
9#20267945C212yesmaximal, complemented
10C22⋊C8×D103C211yesmaximal, characteristic
11#451×C103C211yesmaximal, characteristic, complemented
12C2×Q8×D103C2211yescharacteristic
13C22×C4×D103C2211yescharacteristic
14C2×#13110095C2212yescomplemented
15C2×C8×D103C2212yes—
16#15693001C2211yescharacteristic
17#15693000C2211yescharacteristic
18#15692999—21no—
19#15692998—21no—
20#15692997—21no—
21#15692997—21no—
22#15692997C2212yes—
23#15692997C2211yescharacteristic
24#15692997C2212yes—
25C2×C4⋊Dic103C2211yescharacteristic
26C2×Dic103⋊C4—21no—
27C4⋊C4×D103—21no—
28C4⋊C4×D103C2211yescharacteristic
29C2×(C2×D103)⋊C4—21no—
30C22⋊C4×D103—21no—
31#15692955C2212yescomplemented
32#15692954C2212yescomplemented
33#15692946C2212yescomplemented
34#15692945C2212yescomplemented
35#15692945C2212yescomplemented
36C22⋊(C103⋊C8)C2211yescharacteristic
37(C2×D103)⋊C8C2212yes—
38C22×Q8×C103C2211yescharacteristic
39C2×Q16×C103C2212yescomplemented
40C22⋊Q8×C103C2211yescharacteristic
41#103×C103C2212yescomplemented
42C22⋊C8×C103C2211yescharacteristic
43C23×D103D411yescharacteristic
44C2×Dic206—21no—
45C2×Dic206C2311yescharacteristic
46Q8×D103—42no—
47C22×Dic103—21no—
48C22×Dic103D411yescharacteristic
49C2×C4×D103—21no—
50C2×C4×D103—21no—
51C2×C4×D103—42no—
52C2×C4×D103D411yescharacteristic
53C2×C4×D103D411yescharacteristic
54C2×C4×D103C2311yescharacteristic
55C2×C4×D103C2311yescharacteristic
56#13110095—42no—
57C2×C103⋊C8C2312yes—
58C8×D103—42no—
59C4⋊Dic103—21no—
60C4⋊Dic103—21no—
61C4⋊Dic103C2311yescharacteristic
62C4⋊Dic103C2312yes—
63Dic103⋊C4—21no—
64Dic103⋊C4—21no—
65Dic103⋊C4—21no—
66Dic103⋊C4—22no—
67Dic103⋊C4—22no—
68C22⋊Dic103—21no—
69(C2×D103)⋊C4—21no—
70(C2×D103)⋊C4—21no—
71(C2×D103)⋊C4—22no—
72(C2×D103)⋊C4—22no—
73C2×Q8×C103—21no—
74C2×Q8×C103—42no—
75C2×Q8×C103C2311yescharacteristic
76C2×Q8×C103C2312yes—
77C22×C4×C103—21no—
78C22×C4×C103C2311yescharacteristic
79Q16×C103—42no—
80C2×C8×C103C2312yes—
81C4⋊C4×C103—21no—
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—
91Q8×C103—22no—
92Q8×C103—22no—
93Q8×C103—42no—
94C2×C4×C103—22no—
95C2×C4×C103—21no—
96C2×C4×C103—21no—
97C2×C4×C103—22no—
98C2×C4×C103—42no—
99C2×C4×C103C2×D411yescharacteristic
100C2×C4×C103C2411yescharacteristic
101C2×Dic103—22no—
102C2×Dic103—21no—
103C2×Dic103—21no—
104C2×Dic103—41no—
105C2×Dic103—42no—
106C2×Dic103C2×D411yescharacteristic
107C2×Dic103C2×D411yescharacteristic
108C4×D103—22no—
109C4×D103—22no—
110C4×D103—41no—
111C4×D103—41no—
112C4×D103—42no—
113C4×D103—42no—
114Dic206—22no—
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—42no—
132C4×C103—41no—
133C4×C103H(5,𝔽2)12yes—
134Dic103—21no—
135Dic103—21no—
136Dic103—41no—
137Dic103—41no—
138Dic103—42no—
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#484—1031no—
152#467—1032no—
153#467—1032no—
154#451—1031no—
155#451—1032no—
156#451D10311yescharacteristic, complemented
157C2×C22⋊C8—1031no—
158C22×Q8—1031no—
159C22×Q8C2×D10311yescharacteristic
160C23×C4—1031no—
161C2×Q16—1032no—
162C2×Q16C2×D10312yescomplemented
163C22×C8—1032no—
164C22⋊Q8—1032no—
165C22⋊Q8—1031no—
166C22⋊Q8—1032no—
167C22⋊Q8—1031no—
168C22⋊Q8—1031no—
169C22⋊Q8—2061no—
170C22⋊Q8—2061no—
171C22⋊Q8—2061no—
172C22⋊Q8—2061no—
173C22⋊Q8C2×D10311yescharacteristic
174C2×C4⋊C4—1031no—
175C2×C4⋊C4—1031no—
176C2×C4⋊C4—2061no—
177C2×C4⋊C4—2061no—
178C2×C22⋊C4—2061no—
179C2×C22⋊C4—2061no—
180#107—1032no—
181#107—1032no—
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—21no—
191C2×Q8—42no—
192C2×Q8—1031no—
193C2×Q8—4122no—
194C2×Q8—2061no—
195C2×Q8C22×D10311yescharacteristic
196C2×Q8C22×D10312yes—
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—42no—
209Q16—4122no—
210C2×C8—1032no—
211C2×C8—4122no—
212C2×C8C22×D10312yes—
213C4⋊C4—21no—
214C4⋊C4—1031no—
215C4⋊C4—1032no—
216C4⋊C4—2061no—
217C4⋊C4—2061no—
218C4⋊C4—2062no—
219C4⋊C4—2062no—
220C4⋊C4—2061no—
221C4⋊C4—2061no—
222C4⋊C4—2061no—
223C4⋊C4C22×D10311yescharacteristic
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—22no—
238Q8—22no—
239Q8—42no—
240Q8—4122no—
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—2062no—
256C2×C4—2061no—
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—41no—
277C4—42no—
278C4—41no—
279C4—4121no—
280C4—4122no—
281C4—4121no—
282C4—2061no—
283C4—2061no—
284C4#1569306612yes—
285C2—22no—
286C2—2062no—
287C2—2062no—
288C2#2026835111yescharacteristic
289C2C2×Q16×D10311yescharacteristic
290C2#2026859011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#451×C103C2
socleC22×C103C22×D4
prime radicalC23×D103D4
hypercenter#451D103
hypocenterC103#3189
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #20268127C2semidirect
4. #20268125C2semidirect
5. #20268124C2semidirect
6. #20268031C2semidirect
7. #20268029C2semidirect
8. #20267947C2semidirect
9. #20267945C2semidirect
11. #451×C103C2semidirect
14. C2×#13110095C22semidirect
31. #15692955C22semidirect
32. #15692954C22semidirect
33. #15692946C22semidirect
34. #15692945C22semidirect
35. #15692945C22semidirect
39. C2×Q16×C103C22semidirect
41. #103×C103C22semidirect
87. C22×D103Q16semidirect
146. C103#3189semidirect
156. #451D103semidirect
162. C2×Q16C2×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×#156929972
C22⋊Q8×D1032
#202681272
#202681252
#202681242
#202680312
#202680292
#202679472
#202679452
C22⋊C8×D1032
#451×C1032
#3189103