Finite Group Databasebeta

← #27205911

Subgroups — #27205911

Order 13184.

472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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#20268302C211yesmaximal, characteristic, complemented
2C2×#15692995C211yesmaximal, characteristic, complemented
3#20268127C211yesmaximal, characteristic, complemented
4#20268116C212yesmaximal, complemented
5#20268110C211yesmaximal, characteristic, complemented
6#20268027C212yesmaximal, complemented
7#20268020C212yesmaximal, complemented
8#20267944C211yesmaximal, characteristic, complemented
9#20267938C212yesmaximal, complemented
10#20267927C211yesmaximal, characteristic, complemented
11C2×C22⋊C8×C103C211yesmaximal, characteristic, complemented
12C2×#13110105C2211yescharacteristic, complemented
13C22×D412C2211yescharacteristic
14C22×C22⋊D103—21no—
15C2×#13110094C2212yescomplemented
16C2×D824C2212yescomplemented
17#15693004—21no—
18#15693000C2211yescharacteristic
19#15693000C2211yescharacteristic, complemented
20#15692995—21no—
21#15692995—21no—
22#15692995C2211yescharacteristic
23#15692995C2212yes—
24#15692995C2212yes—
25#15692995C2211yescharacteristic, complemented
26#15692990—21no—
27C4×C22⋊D103—21no—
28C4×C22⋊D103—21no—
29#15692980C2211yescharacteristic, complemented
30C2×C4⋊Dic103C2211yescharacteristic
31C2×(C2×D103)⋊C4—21no—
32#15692955C2212yescomplemented
33#15692953C2212yescomplemented
34#15692946C2212yescomplemented
35#15692943C2212yescomplemented
36#15692943C2212yescomplemented
37#15692943C2212yescomplemented
38C23×C4×C103C2211yescharacteristic
39C22×C8×C103C2212yescomplemented
40C22⋊C8×C103C2211yescharacteristic
41C22⋊C8×C103C2211yescharacteristic
42C22⋊C8×C103C2212yescomplemented
43C23×D103—21no—
44#13110105—42no—
45C2×Dic206C2311yescharacteristic
46C2×D412—21no—
47C2×D412—42no—
48C2×D412C2312yes—
49C2×D412C2311yescharacteristic
50C2×C22⋊D103—22no—
51C2×C22⋊D103—22no—
52C2×C22⋊D103—21no—
53C2×C22⋊D103—21no—
54C2×C22⋊D103—21no—
55C2×C22⋊D103—44no—
56C22×Dic103—21no—
57C2×C4×D103—21no—
58#13110094—42no—
59D824—42no—
60C4⋊Dic103—21no—
61C4⋊Dic103C2311yescharacteristic
62C4⋊Dic103C2311yescharacteristic
63C4⋊Dic103C2312yes—
64Dic103⋊C4—21no—
65Dic103⋊C4—21no—
66C22⋊Dic103—21no—
67C22⋊Dic103—21no—
68C22⋊Dic103—21no—
69(C2×D103)⋊C4—22no—
70(C2×D103)⋊C4—22no—
71(C2×D103)⋊C4—21no—
72(C2×D103)⋊C4—21no—
73C4×Dic103—21no—
74C24×C103D411yescharacteristic
75C22×C4×C103—42no—
76C22×C4×C103D411yescharacteristic
77C22×C4×C103D411yescharacteristic
78C22×C4×C103D411yescharacteristic
79C22×C4×C103C2311yescharacteristic
80C22×C4×C103C2311yescharacteristic
81C22×C4×C103C2311yescharacteristic
82C2×C8×C103—42no—
83C2×C8×C103C2312yes—
84C2×C8×C103C2312yes—
85C23×C103—22no—
86C23×C103—22no—
87C23×C103—41no—
88C23×C103C2×D411yescharacteristic
89C23×C103C2×D411yescharacteristic
90C23×C103C2×D411yescharacteristic
91C22×D103—21no—
92C22×D103—22no—
93C22×D103—42no—
94C22×D103—42no—
95C22×D103—42no—
96C2×C4×C103—22no—
97C2×C4×C103—22no—
98C2×C4×C103—22no—
99C2×C4×C103—41no—
100C2×C4×C103—41no—
101C2×C4×C103—41no—
102C2×C4×C103C2×D411yescharacteristic
103C2×C4×C103C2×D411yescharacteristic
104C2×C4×C103C2×D411yescharacteristic
105C2×C4×C103C2411yescharacteristic
106C22⋊D103—44no—
107C22⋊D103—42no—
108C22⋊D103—42no—
109C22⋊D103—42no—
110C22⋊D103—44no—
111C2×Dic103—21no—
112C2×Dic103—21no—
113C2×Dic103—22no—
114C2×Dic103—21no—
115C2×Dic103—42no—
116D412—22no—
117D412—22no—
118D412—22no—
119D412—42no—
120C4×D103—42no—
121Dic206—22no—
122C8×C103—22no—
123C8×C103—22no—
124C22×C103—21no—
125C22×C103—21no—
126C22×C103—21no—
127C22×C103—21no—
128C22×C103—21no—
129C22×C103—21no—
130C22×C103—21no—
131C22×C103—44no—
132C22×C103#13512yes—
133C22×C103AGL(1,ℤ/8)12yes—
134C22×C103C22×D411yescharacteristic
135C2×D103—41no—
136C2×D103—42no—
137C2×D103—41no—
138C2×D103—42no—
139C2×D103—42no—
140C2×D103—41no—
141C2×D103—84no—
142C4×C103—21no—
143C4×C103—21no—
144C4×C103—21no—
145C4×C103H(5,𝔽2)12yes—
146Dic103—41no—
147Dic103—41no—
148Dic103—42no—
149Dic103—41no—
150C2×C103—22no—
151C2×C103—22no—
152C2×C103—41no—
153C2×C103#53411yescharacteristic
154C2×C103C2×#13511yescharacteristic
155C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
156D103—81no—
157D103—82no—
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#447—1031no—
170C2×C22⋊C8D10311yescharacteristic, complemented
171C2×#41—1031no—
172C22×D4—1031no—
173C22×D4—2061no—
174C23×C4C2×D10311yescharacteristic
175C2×SD16—1032no—
176C2×D8—1032no—
177C22×C8C2×D10312yescomplemented
178#123—2061no—
179C22⋊Q8—1031no—
180C22⋊Q8—1031no—
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#102—1032no—
199C22⋊C8C2×D10311yescharacteristic
200C22⋊C8C2×D10311yescharacteristic
201C22⋊C8C2×D10312yescomplemented
202C24—2061no—
203C24D41211yescharacteristic
204#41—4122no—
205C2×Q8—1031no—
206C2×D4—1031no—
207C2×D4—1032no—
208C2×D4—4122no—
209C2×D4—4124no—
210C2×D4—2061no—
211C2×D4—2061no—
212C2×D4—2061no—
213C2×D4—2062no—
214C2×D4—2062no—
215C2×D4—2061no—
216C22×C4—42no—
217C22×C4—2061no—
218C22×C4—2061no—
219C22×C4D41211yescharacteristic
220C22×C4D41211yescharacteristic
221C22×C4D41211yescharacteristic
222C22×C4C22×D10311yescharacteristic
223C22×C4C22×D10311yescharacteristic
224C22×C4C22×D10311yescharacteristic
225SD16—4122no—
226D8—4122no—
227C2×C8—42no—
228C2×C8C22×D10312yes—
229C2×C8C22×D10312yes—
230C4⋊C4—1031no—
231C4⋊C4—1031no—
232C4⋊C4—1032no—
233C4⋊C4—2061no—
234C4⋊C4—2061no—
235C4⋊C4—2061no—
236C22⋊C4—2061no—
237C22⋊C4—2061no—
238C22⋊C4—2061no—
239C22⋊C4—2062no—
240C22⋊C4—2062no—
241C22⋊C4—2061no—
242C22⋊C4—2061no—
243C42—2061no—
244C23—22no—
245C23—22no—
246C23—41no—
247C23—4122no—
248C23—4122no—
249C23—4122no—
250C23—2061no—
251C23—2062no—
252C23C2×D41211yescharacteristic
253C23C2×D41211yescharacteristic
254C23C2×D41211yescharacteristic
255Q8—2062no—
256D4—4122no—
257D4—4124no—
258D4—4122no—
259D4—4122no—
260D4—4124no—
261D4—4122no—
262D4—2062no—
263D4—2062no—
264D4—2062no—
265C2×C4—22no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—4122no—
272C2×C4—4122no—
273C2×C4—2061no—
274C2×C4—2061no—
275C2×C4—2062no—
276C2×C4—2061no—
277C2×C4C2×D41211yescharacteristic
278C2×C4C2×D41211yescharacteristic
279C2×C4C2×D41211yescharacteristic
280C2×C4C23×D10311yescharacteristic
281C8—22no—
282C8—22no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—44no—
291C22—8244no—
292C22—4121no—
293C22—4122no—
294C22—4122no—
295C22—4121no—
296C22—4121no—
297C22—4122no—
298C22#1569304312yes—
299C22#1569304912yes—
300C22C22×D41211yescharacteristic
301C4—21no—
302C4—21no—
303C4—21no—
304C4—4121no—
305C4—4122no—
306C4—4121no—
307C4—4121no—
308C4#1569306612yes—
309C2—22no—
310C2—22no—
311C2—41no—
312C2—8242no—
313C2—8241no—
314C2#2026835311yescharacteristic
315C2C2×#1569304311yescharacteristic
316C2C2×#1569304911yescharacteristic
subgroupG/H
centerC22C22×D412
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×C22⋊C8×C103C2
socleC22×C103C22×D4
hypercenterC2×C22⋊C8D103
hypocenterC103#3188
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. #20268302C2semidirect
2. C2×#15692995C2semidirect
3. #20268127C2semidirect
4. #20268116C2semidirect
5. #20268110C2semidirect
6. #20268027C2semidirect
7. #20268020C2semidirect
8. #20267944C2semidirect
9. #20267938C2semidirect
10. #20267927C2semidirect
11. C2×C22⋊C8×C103C2semidirect
12. C2×#13110105C22semidirect
15. C2×#13110094C22semidirect
16. C2×D824C22semidirect
19. #15693000C22semidirect
25. #15692995C22semidirect
29. #15692980C22semidirect
32. #15692955C22semidirect
33. #15692953C22semidirect
34. #15692946C22semidirect
35. #15692943C22semidirect
36. #15692943C22semidirect
37. #15692943C22semidirect
39. C22×C8×C103C22semidirect
42. C22⋊C8×C103C22semidirect
159. C103#3188semidirect
170. C2×C22⋊C8D103semidirect
177. C22×C8C2×D103semidirect
201. C22⋊C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683022
C2×#156929952
#202681272
#202681162
#202681102
#202680272
#202680202
#202679442
#202679382
#202679272
C2×C22⋊C8×C1032
#3188103