Finite Group Databasebeta

← #27205912

Subgroups — #27205912

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#20268304C211yesmaximal, characteristic, complemented
2C2×#15692992C211yesmaximal, characteristic, complemented
3#20268124C211yesmaximal, characteristic, complemented
4#20268114C212yesmaximal, complemented
5#20268110C211yesmaximal, characteristic, complemented
6#20268026C212yesmaximal, complemented
7#20268017C212yesmaximal, complemented
8#20267935C212yesmaximal, complemented
9#20267925C211yesmaximal, characteristic, complemented
10C22⋊C8×D103C211yesmaximal, characteristic, complemented
11#450×C103C211yesmaximal, characteristic, complemented
12C2×#13110106C2211yescharacteristic, complemented
13C22×C22⋊D103—21no—
14C22×C4×D103C2211yescharacteristic
15C2×#13110090C2212yescomplemented
16C2×C8×D103C2212yescomplemented
17#15693006—21no—
18#15692997C2211yescharacteristic, complemented
19#15692996C2211yescharacteristic, complemented
20#15692995C2211yescharacteristic
21#15692992—21no—
22#15692992—21no—
23#15692992C2212yes—
24#15692992C2212yes—
25#15692991—21no—
26#15692983—21no—
27(C22⋊D103)⋊C4—21no—
28#15692979C2211yescharacteristic, complemented
29C2×C4⋊Dic103C2211yescharacteristic
30C2×C22⋊Dic103—21no—
31#15692954C2212yescomplemented
32#15692953C2212yescomplemented
33#15692945C2212yescomplemented
34#15692943C2212yescomplemented
35#15692942C2212yescomplemented
36C22⋊(C103⋊C8)C2211yescharacteristic
37(C2×D103)⋊C8C2212yescomplemented
38C22×D4×C103C2211yescharacteristic
39C2×SD16×C103C2212yescomplemented
40C22⋊Q8×C103C2211yescharacteristic
41#102×C103C2212yescomplemented
42C22⋊C8×C103C2211yescharacteristic
43C23×D103D411yescharacteristic
44#13110106—42no—
45C2×D412—21no—
46C2×D412—21no—
47C2×D412C2311yescharacteristic
48C2×C22⋊D103—21no—
49C2×C22⋊D103—22no—
50C2×C22⋊D103—22no—
51C2×C22⋊D103—44no—
52C22×Dic103—21no—
53C22×Dic103D411yescharacteristic
54C2×C4×D103—21no—
55C2×C4×D103—42no—
56C2×C4×D103D411yescharacteristic
57C2×C4×D103D411yescharacteristic
58C2×C4×D103C2311yescharacteristic
59C2×C4×D103C2311yescharacteristic
60#13110090—42no—
61C2×C103⋊C8C2312yes—
62C8×D103—42no—
63C4⋊Dic103—21no—
64C4⋊Dic103C2311yescharacteristic
65C4⋊Dic103C2312yes—
66Dic103⋊C4—21no—
67C22⋊Dic103—22no—
68C22⋊Dic103—22no—
69(C2×D103)⋊C4—21no—
70(C2×D103)⋊C4—21no—
71(C2×D103)⋊C4—21no—
72(C2×D103)⋊C4—21no—
73C4×Dic103—21no—
74C24×C103—21no—
75C2×Q8×C103C2311yescharacteristic
76C2×D4×C103—21no—
77C2×D4×C103—42no—
78C2×D4×C103C2312yes—
79C22×C4×C103C2311yescharacteristic
80SD16×C103—42no—
81C2×C8×C103C2312yes—
82C4⋊C4×C103—21no—
83C4⋊C4×C103C2311yescharacteristic
84C22⋊C4×C103—21no—
85C23×C103—22no—
86C23×C103—42no—
87C23×C103—42no—
88C23×C103—42no—
89C23×C103C2×D411yescharacteristic
90C22×D103—22no—
91C22×D103—22no—
92C22×D103—21no—
93C22×D103—41no—
94C22×D103C2×D411yescharacteristic
95C22×D103C2×D411yescharacteristic
96Q8×C103—22no—
97D4×C103—22no—
98D4×C103—22no—
99D4×C103—42no—
100C2×C4×C103—22no—
101C2×C4×C103—21no—
102C2×C4×C103—21no—
103C2×C4×C103C2×D411yescharacteristic
104C2×C4×C103C2411yescharacteristic
105C22⋊D103—44no—
106C22⋊D103—42no—
107C22⋊D103—44no—
108C2×Dic103—21no—
109C2×Dic103—22no—
110C2×Dic103—41no—
111C2×Dic103—42no—
112C2×Dic103C2×D411yescharacteristic
113C2×Dic103C2×D411yescharacteristic
114D412—22no—
115D412—42no—
116D412—42no—
117C4×D103—22no—
118C4×D103—22no—
119C4×D103—41no—
120C4×D103—41no—
121C4×D103—42no—
122C8×C103—22no—
123C103⋊C8—22no—
124C22×C103—21no—
125C22×C103—21no—
126C22×C103—42no—
127C22×C103—42no—
128C22×C103—42no—
129C22×C103—84no—
130C22×C103#13512yes—
131C22×C103C22×D411yescharacteristic
132C2×D103—21no—
133C2×D103—21no—
134C2×D103—21no—
135C2×D103—21no—
136C2×D103—21no—
137C2×D103—44no—
138C2×D103—41no—
139C2×D103—41no—
140C2×D103—41no—
141C2×D103AGL(1,ℤ/8)12yes—
142C4×C103—21no—
143C4×C103—41no—
144C4×C103—41no—
145C4×C103H(5,𝔽2)12yes—
146Dic103—21no—
147Dic103—21no—
148Dic103—41no—
149Dic103—42no—
150C2×C103—22no—
151C2×C103—82no—
152C2×C103#53411yescharacteristic
153C2×C103C2×#13511yescharacteristic
154C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
155D103—22no—
156D103—41no—
157D103—81no—
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#450D10311yescharacteristic, complemented
168#449—1032no—
169#447—1031no—
170C2×C22⋊C8—1031no—
171C2×#41—1031no—
172C22×D4—2061no—
173C22×D4C2×D10311yescharacteristic
174C23×C4—1031no—
175C2×SD16C2×D10312yescomplemented
176C2×D8—1032no—
177C22×C8—1032no—
178#123—2061no—
179C22⋊Q8—1031no—
180C22⋊Q8C2×D10311yescharacteristic
181#121—1032no—
182#121—1032no—
183#121—1031no—
184#121—1031no—
185#121—2061no—
186#121—2061no—
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×Q8C22×D10311yescharacteristic
206C2×D4—21no—
207C2×D4—42no—
208C2×D4—1031no—
209C2×D4—4124no—
210C2×D4—2061no—
211C2×D4—2061no—
212C2×D4—2062no—
213C2×D4—2062no—
214C2×D4—2061no—
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—42no—
226D8—4122no—
227C2×C8—1032no—
228C2×C8—4122no—
229C2×C8C22×D10312yes—
230C4⋊C4—21no—
231C4⋊C4—1031no—
232C4⋊C4—1032no—
233C4⋊C4—2061no—
234C4⋊C4—2061no—
235C4⋊C4C22×D10311yescharacteristic
236C22⋊C4—21no—
237C22⋊C4—2061no—
238C22⋊C4—2061no—
239C22⋊C4—2061no—
240C22⋊C4—2062no—
241C22⋊C4—2062no—
242C22⋊C4—2061no—
243C42—2061no—
244C23—22no—
245C23—42no—
246C23—42no—
247C23—42no—
248C23—1031no—
249C23—1031no—
250C23—4121no—
251C23—2062no—
252C23—2061no—
253C23—2062no—
254C23D4×D10311yescharacteristic
255Q8—22no—
256D4—22no—
257D4—22no—
258D4—42no—
259D4—4122no—
260D4—4122no—
261D4—4124no—
262D4—4124no—
263D4—4122no—
264D4—2062no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—1031no—
269C2×C4—1031no—
270C2×C4—4121no—
271C2×C4—4121no—
272C2×C4—4122no—
273C2×C4—4122no—
274C2×C4—4121no—
275C2×C4—2061no—
276C2×C4—2062no—
277C2×C4—2062no—
278C2×C4—2062no—
279C2×C4D4×D10311yescharacteristic
280C2×C4C23×D10311yescharacteristic
281C8—22no—
282C8—2062no—
283C22—21no—
284C22—21no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22—84no—
289C22—1032no—
290C22—4124no—
291C22—4121no—
292C22—4121no—
293C22—4121no—
294C22—2061no—
295C22—2061no—
296C22—2061no—
297C22—2061no—
298C22—2061no—
299C22#1569304212yes—
300C22C2×D4×D10311yescharacteristic
301C4—21no—
302C4—41no—
303C4—41no—
304C4—4121no—
305C4—4122no—
306C4—2061no—
307C4—2061no—
308C4#1569306612yes—
309C2—22no—
310C2—82no—
311C2—8241no—
312C2—4121no—
313C2—2062no—
314C2#2026835111yescharacteristic
315C2C2×#1569304211yescharacteristic
316C2AGL(1,ℤ/8)×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#450×C103C2
socleC22×C103C22×D4
hypercenter#450D103
hypocenterC103#3188
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #20268304C2semidirect
2. C2×#15692992C2semidirect
3. #20268124C2semidirect
4. #20268114C2semidirect
5. #20268110C2semidirect
6. #20268026C2semidirect
7. #20268017C2semidirect
8. #20267935C2semidirect
9. #20267925C2semidirect
10. C22⋊C8×D103C2semidirect
11. #450×C103C2semidirect
12. C2×#13110106C22semidirect
15. C2×#13110090C22semidirect
16. C2×C8×D103C22semidirect
18. #15692997C22semidirect
19. #15692996C22semidirect
28. #15692979C22semidirect
31. #15692954C22semidirect
32. #15692953C22semidirect
33. #15692945C22semidirect
34. #15692943C22semidirect
35. #15692942C22semidirect
37. (C2×D103)⋊C8C22semidirect
39. C2×SD16×C103C22semidirect
41. #102×C103C22semidirect
159. C103#3188semidirect
167. #450D103semidirect
175. C2×SD16C2×D103semidirect
198. #102C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683042
C2×#156929922
#202681242
#202681142
#202681102
#202680262
#202680172
#202679352
#202679252
C22⋊C8×D1032
#450×C1032
#3188103