Finite Group Databasebeta

← #27205906

Subgroups — #27205906

Order 13184.

472 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 115 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#20268301C211yesmaximal, characteristic, complemented
2C2×#15692992C211yesmaximal, characteristic, complemented
3#20268127C211yesmaximal, characteristic, complemented
4#20268113C212yesmaximal, complemented
5#20268107C211yesmaximal, characteristic, complemented
6#20268024C212yesmaximal, complemented
7#20268019C212yesmaximal, complemented
8#20267942C211yesmaximal, characteristic, complemented
9#20267933C212yesmaximal, complemented
10C22⋊C8×D103C211yesmaximal, characteristic, complemented
11#447×C103C211yesmaximal, characteristic, complemented
12C2×#13110104C2211yescharacteristic, complemented
13C22×C22⋊D103—21no—
14C22×C4×D103C2211yescharacteristic
15C2×#13110093C2212yescomplemented
16C2×C8×D103C2212yescomplemented
17#15693003—21no—
18#15693001C2211yescharacteristic, complemented
19#15693000C2211yescharacteristic
20#15692992—21no—
21#15692992—21no—
22#15692992C2212yes—
23#15692992C2212yes—
24#15692992C2211yescharacteristic, complemented
25#15692989—21no—
26D4×Dic103—21no—
27(C22⋊D103)⋊C4—21no—
28#15692979C2211yescharacteristic, complemented
29C2×C4⋊Dic103C2211yescharacteristic
30C2×C22⋊Dic103—21no—
31#15692955C2212yescomplemented
32#15692952C2212yescomplemented
33#15692946C2212yescomplemented
34#15692942C2212yescomplemented
35#15692942C2212yescomplemented
36C22⋊(C103⋊C8)C2211yescharacteristic
37(C2×D103)⋊C8C2212yescomplemented
38C22×D4×C103C2211yescharacteristic
39C2×D8×C103C2212yescomplemented
40#121×C103C2211yescharacteristic
41#102×C103C2212yescomplemented
42C22⋊C8×C103C2211yescharacteristic
43C23×D103D411yescharacteristic
44#13110104—42no—
45C2×Dic206C2311yescharacteristic
46C2×C22⋊D103—22no—
47C2×C22⋊D103—22no—
48C2×C22⋊D103—21no—
49C2×C22⋊D103—21no—
50C2×C22⋊D103—44no—
51C22×Dic103—21no—
52C22×Dic103—21no—
53C22×Dic103D411yescharacteristic
54C2×C4×D103—42no—
55C2×C4×D103D411yescharacteristic
56C2×C4×D103D411yescharacteristic
57C2×C4×D103C2311yescharacteristic
58C2×C4×D103C2311yescharacteristic
59#13110093—42no—
60C2×C103⋊C8C2312yes—
61C8×D103—42no—
62C4⋊Dic103—21no—
63C4⋊Dic103—21no—
64C4⋊Dic103C2311yescharacteristic
65C4⋊Dic103C2312yes—
66Dic103⋊C4—21no—
67C22⋊Dic103—21no—
68C22⋊Dic103—22no—
69C22⋊Dic103—22no—
70C22⋊Dic103—21no—
71(C2×D103)⋊C4—21no—
72(C2×D103)⋊C4—21no—
73C4×Dic103—21no—
74C24×C103—21no—
75C2×D4×C103—21no—
76C2×D4×C103—21no—
77C2×D4×C103—42no—
78C2×D4×C103C2311yescharacteristic
79C2×D4×C103C2312yes—
80C22×C4×C103C2311yescharacteristic
81D8×C103—42no—
82C2×C8×C103C2312yes—
83C4⋊C4×C103C2311yescharacteristic
84C22⋊C4×C103—21no—
85C23×C103—21no—
86C23×C103—22no—
87C23×C103—42no—
88C23×C103—42no—
89C23×C103—42no—
90C23×C103C2×D411yescharacteristic
91C22×D103—22no—
92C22×D103—22no—
93C22×D103—41no—
94C22×D103C2×D411yescharacteristic
95C22×D103C2×D411yescharacteristic
96D4×C103—22no—
97D4×C103—22no—
98D4×C103—22no—
99D4×C103—42no—
100D4×C103—42no—
101C2×C4×C103—22no—
102C2×C4×C103—21no—
103C2×C4×C103C2×D411yescharacteristic
104C2×C4×C103C2411yescharacteristic
105C22⋊D103—44no—
106C22⋊D103—42no—
107C22⋊D103—42no—
108C22⋊D103—44no—
109C2×Dic103—21no—
110C2×Dic103—21no—
111C2×Dic103—22no—
112C2×Dic103—41no—
113C2×Dic103—42no—
114C2×Dic103—42no—
115C2×Dic103C2×D411yescharacteristic
116C2×Dic103C2×D411yescharacteristic
117C4×D103—22no—
118C4×D103—22no—
119C4×D103—41no—
120C4×D103—41no—
121Dic206—22no—
122C8×C103—22no—
123C103⋊C8—22no—
124C22×C103—21no—
125C22×C103—21no—
126C22×C103—41no—
127C22×C103—42no—
128C22×C103—41no—
129C22×C103—42no—
130C22×C103—42no—
131C22×C103—41no—
132C22×C103—84no—
133C22×C103#13512yes—
134C22×C103C22×D411yescharacteristic
135C2×D103—21no—
136C2×D103—21no—
137C2×D103—21no—
138C2×D103—21no—
139C2×D103—21no—
140C2×D103—44no—
141C2×D103AGL(1,ℤ/8)12yes—
142C4×C103—21no—
143C4×C103—41no—
144C4×C103H(5,𝔽2)12yes—
145Dic103—21no—
146Dic103—21no—
147Dic103—41no—
148Dic103—42no—
149Dic103—41no—
150C2×C103—22no—
151C2×C103—81no—
152C2×C103—82no—
153C2×C103#53411yescharacteristic
154C2×C103C2×#13511yescharacteristic
155C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
156D103—22no—
157D103—41no—
158#3188—1031nomaximal, Sylow
159C103#318811yescharacteristic, complemented, Sylow
160#525—1031no—
161C2×#121—1031no—
162#484—1031no—
163#482—1032no—
164#481—1031no—
165#466—1032no—
166#465—1032no—
167#450—1031no—
168#449—1032no—
169#447D10311yescharacteristic, complemented
170C2×C22⋊C8—1031no—
171C2×#41—1031no—
172C22×D4—2061no—
173C22×D4C2×D10311yescharacteristic
174C23×C4—1031no—
175C2×SD16—1032no—
176C2×D8C2×D10312yescomplemented
177C22×C8—1032no—
178#123—2061no—
179C22⋊Q8—1031no—
180C22⋊Q8—1031no—
181#121—1032no—
182#121—1032no—
183#121—1031no—
184#121—2061no—
185#121—2061no—
186#121C2×D10311yescharacteristic
187#120—2061no—
188C4×D4—2061no—
189C4×D4—2061no—
190#117—1031no—
191C2×C4⋊C4—1031no—
192C2×C22⋊C4—2061no—
193#107—1032no—
194#106—1032no—
195#103—1032no—
196#102—1032no—
197#102—1032no—
198#102C2×D10312yescomplemented
199C22⋊C8—1031no—
200C22⋊C8—1032no—
201C22⋊C8C2×D10311yescharacteristic
202C24—21no—
203C24—1031no—
204#41—4122no—
205C2×Q8—1031no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—42no—
209C2×D4—4124no—
210C2×D4—2061no—
211C2×D4—2061no—
212C2×D4—2062no—
213C2×D4—2062no—
214C2×D4C22×D10311yescharacteristic
215C2×D4C22×D10312yes—
216C22×C4—1031no—
217C22×C4—1031no—
218C22×C4—1031no—
219C22×C4—1031no—
220C22×C4—1031no—
221C22×C4—4122no—
222C22×C4—2061no—
223C22×C4—2061no—
224C22×C4C22×D10311yescharacteristic
225SD16—4122no—
226D8—42no—
227C2×C8—1032no—
228C2×C8—4122no—
229C2×C8C22×D10312yes—
230C4⋊C4—1031no—
231C4⋊C4—1032no—
232C4⋊C4—2061no—
233C4⋊C4—2061no—
234C4⋊C4—2061no—
235C4⋊C4C22×D10311yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—2061no—
238C22⋊C4—2061no—
239C22⋊C4—2062no—
240C22⋊C4—2062no—
241C22⋊C4—2061no—
242C22⋊C4—2061no—
243C42—2061no—
244C23—21no—
245C23—22no—
246C23—42no—
247C23—42no—
248C23—42no—
249C23—1031no—
250C23—1031no—
251C23—4121no—
252C23—2062no—
253C23—2062no—
254C23D4×D10311yescharacteristic
255Q8—2062no—
256D4—22no—
257D4—22no—
258D4—22no—
259D4—42no—
260D4—42no—
261D4—4124no—
262D4—4122no—
263D4—4124no—
264D4—4122no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—1031no—
268C2×C4—1031no—
269C2×C4—4121no—
270C2×C4—4121no—
271C2×C4—4122no—
272C2×C4—4122no—
273C2×C4—4121no—
274C2×C4—2061no—
275C2×C4—2062no—
276C2×C4—2061no—
277C2×C4—2062no—
278C2×C4—2062no—
279C2×C4D4×D10311yescharacteristic
280C2×C4C23×D10311yescharacteristic
281C8—22no—
282C8—2062no—
283C22—21no—
284C22—21no—
285C22—41no—
286C22—42no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—42no—
291C22—84no—
292C22—1032no—
293C22—4124no—
294C22—2061no—
295C22—2061no—
296C22—2061no—
297C22—2061no—
298C22—2061no—
299C22#1569304012yes—
300C22C2×D4×D10311yescharacteristic
301C4—21no—
302C4—41no—
303C4—4122no—
304C4—4121no—
305C4—4121no—
306C4—2061no—
307C4—2061no—
308C4#1569306612yes—
309C2—22no—
310C2—82no—
311C2—81no—
312C2—4121no—
313C2—2062no—
314C2#2026835111yescharacteristic
315C2C2×#1569304011yescharacteristic
316C2AGL(1,ℤ/8)×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#447×C103C2
socleC22×C103C22×D4
hypercenter#447D103
hypocenterC103#3188
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #20268301C2semidirect
2. C2×#15692992C2semidirect
3. #20268127C2semidirect
4. #20268113C2semidirect
5. #20268107C2semidirect
6. #20268024C2semidirect
7. #20268019C2semidirect
8. #20267942C2semidirect
9. #20267933C2semidirect
10. C22⋊C8×D103C2semidirect
11. #447×C103C2semidirect
12. C2×#13110104C22semidirect
15. C2×#13110093C22semidirect
16. C2×C8×D103C22semidirect
18. #15693001C22semidirect
24. #15692992C22semidirect
28. #15692979C22semidirect
31. #15692955C22semidirect
32. #15692952C22semidirect
33. #15692946C22semidirect
34. #15692942C22semidirect
35. #15692942C22semidirect
37. (C2×D103)⋊C8C22semidirect
39. C2×D8×C103C22semidirect
41. #102×C103C22semidirect
159. C103#3188semidirect
169. #447D103semidirect
176. C2×D8C2×D103semidirect
198. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683012
C2×#156929922
#202681272
#202681132
#202681072
#202680242
#202680192
#202679422
#202679332
C22⋊C8×D1032
#447×C1032
#3188103