Finite Group Databasebeta

← #27208279

Subgroups — #27208279

Order 13184.

364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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×#15693044C211yesmaximal, characteristic, complemented
2#135×D103C211yesmaximal, characteristic, complemented
3#20268233C212yesmaximal, complemented
4#20268232C211yesmaximal, characteristic, complemented
5#20268229C211yesmaximal, characteristic, complemented
6#20268228C212yesmaximal, complemented
7#20268226C211yesmaximal, characteristic, complemented
8#20268224C212yesmaximal, complemented
9#20268222C212yesmaximal, complemented
10M32×D103C211yesmaximal, characteristic, complemented
11#510×C103C211yesmaximal, characteristic, complemented
12C2×#13110106—21no—
13#41×D103—21no—
14#15693044—21no—
15#15693044—21no—
16#15693044C2212yes—
17#15693044C2211yescharacteristic, complemented
18#15693044C2212yescomplemented
19#15693043C2211yescharacteristic
20#15693042—21no—
21#15693041—21no—
22#15693040C2211yescharacteristic, complemented
23Q16×D103C2211yescharacteristic, complemented
24C2×#13110092—21no—
25SD16×D103—21no—
26C2×D824C2211yescharacteristic, complemented
27D8×D103C2211yescharacteristic, complemented
28C2×C8×D103C2211yescharacteristic
29#15692967C2212yescomplemented
30#15692966C2212yescomplemented
31#15692964C2212yescomplemented
32#15692964C2212yescomplemented
33D1648C2212yescomplemented
34#15692962C2212yescomplemented
35#15692961C2211yescharacteristic, complemented
36#15692960C2212yescomplemented
37C16×D103C2212yescomplemented
38#135×C103C2211yescharacteristic
39C2×Q16×C103C2211yescharacteristic, complemented
40Q32×C103C2212yescomplemented
41SD32×C103C2212yescomplemented
42M32×C103C2211yescharacteristic, complemented
43#13110106—21no—
44#13110106—22no—
45#13110106—22no—
46#13110106—41no—
47#13110106—41no—
48#13110105—21no—
49#13110105—41no—
50#13110104—21no—
51#13110104—41no—
52Q8×D103—21no—
53C2×D412—21no—
54C2×D412—41no—
55D4×D103—21no—
56D4×D103—41no—
57C2×C4×D103—41no—
58C2×C4×D103—41no—
59C2×C4×D103D411yescharacteristic
60Dic412C2311yescharacteristic
61#13110095—21no—
62#13110094—21no—
63#13110093—21no—
64#13110092—21no—
65#13110092—22no—
66#13110092—22no—
67D824—21no—
68D824C2312yes—
69D824C2311yescharacteristic
70#13110090—21no—
71C2×C103⋊C8D411yescharacteristic
72C8×D103D411yescharacteristic
73C8×D103D411yescharacteristic
74C8×D103C2311yescharacteristic
75C8×D103C2311yescharacteristic
76C103⋊C16C2312yes—
77#41×C103—21no—
78C2×Q8×C103—21no—
79Q16×C103—21no—
80Q16×C103C2312yes—
81Q16×C103C2311yescharacteristic
82SD16×C103—21no—
83D8×C103C2311yescharacteristic
84C2×C8×C103C2311yescharacteristic
85C16×C103C2312yes—
86C22×D103—41no—
87C22×D103—41no—
88C22×D103D811yescharacteristic
89Q8×C103—21no—
90Q8×C103—22no—
91Q8×C103—41no—
92D4×C103—21no—
93D4×C103—41no—
94C2×C4×C103—41no—
95C2×C4×C103—41no—
96C2×C4×C103C2×D411yescharacteristic
97C22⋊D103—41no—
98C22⋊D103—41no—
99C22⋊D103—41no—
100C2×Dic103—41no—
101C2×Dic103D811yescharacteristic
102D412—21no—
103D412—22no—
104D412—41no—
105D412—42no—
106D412—42no—
107D412—41no—
108C4×D103—41no—
109C4×D103—41no—
110C4×D103—41no—
111C4×D103—42no—
112C4×D103—42no—
113C4×D103D811yescharacteristic
114C4×D103D811yescharacteristic
115C4×D103C2×D411yescharacteristic
116C4×D103C2×D411yescharacteristic
117Dic206—21no—
118Dic206—41no—
119C8×C103C2×D411yescharacteristic
120C8×C103C2411yescharacteristic
121C103⋊C8C2×D411yescharacteristic
122C103⋊C8C2×D411yescharacteristic
123C22×C103—41no—
124C22×C103C2×D811yescharacteristic
125C2×D103—41no—
126C2×D103—42no—
127C2×D103—41no—
128C2×D103—82no—
129C2×D103—82no—
130C2×D103C2×D811yescharacteristic
131C2×D103C2×D811yescharacteristic
132C4×C103—41no—
133C4×C103—42no—
134C4×C103C2×D811yescharacteristic
135C4×C103C22×D411yescharacteristic
136Dic103—41no—
137Dic103C2×D811yescharacteristic
138Dic103C2×D811yescharacteristic
139C2×C103—21no—
140C2×C103—81no—
141C2×C103C22×D811yescharacteristic
142D103—21no—
143D103—21no—
144D103—82no—
145D103—81no—
146#3414—1031nomaximal, Sylow
147C103#341411yescharacteristic, complemented, Sylow
148C2×#135—1031no—
149C2×#135—1031no—
150#510—1031no—
151#510—1032no—
152#510D10311yescharacteristic, complemented
153#509—1031no—
154#509—1032no—
155#509—1031no—
156#508—1032no—
157#508—1032no—
158C2×M32—1031no—
159C2×#41—2061no—
160C2×#41—2061no—
161#135—1032no—
162#135—1031no—
163#135—1032no—
164#135—1031no—
165#135—1031no—
166#135—2061no—
167#135—2061no—
168#135—2061no—
169#135—2061no—
170#135C2×D10311yescharacteristic
171C2×Q16—1031no—
172C2×Q16C2×D10311yescharacteristic, complemented
173C2×SD16—2061no—
174C2×SD16—2061no—
175C2×D8—1031no—
176C2×D8—1031no—
177C22×C8—1031no—
178Q32—1032no—
179Q32C2×D10312yescomplemented
180SD32—1032no—
181SD32—1032no—
182SD32—1032no—
183SD32C2×D10312yescomplemented
184D16—1032no—
185D16—1032no—
186M32—1031no—
187M32—1032no—
188M32C2×D10311yescharacteristic, complemented
189C2×C16—1032no—
190#41—21no—
191#41—4121no—
192#41—4121no—
193#41—4121no—
194#41—4121no—
195#41—2061no—
196#41—2062no—
197#41—2061no—
198#41—2062no—
199#41—2061no—
200C2×Q8—21no—
201C2×Q8—2061no—
202C2×D4—4121no—
203C2×D4—4121no—
204C2×D4—2061no—
205C2×D4—2061no—
206C22×C4—1031no—
207C22×C4—4121no—
208C22×C4—4121no—
209Q16—21no—
210Q16—1031no—
211Q16—2061no—
212Q16C22×D10311yescharacteristic
213Q16C22×D10312yes—
214SD16—21no—
215SD16—2061no—
216SD16—2062no—
217SD16—2061no—
218SD16—2062no—
219SD16—2061no—
220D8—1032no—
221D8—1031no—
222D8—2061no—
223D8—2061no—
224D8C22×D10311yescharacteristic
225C2×C8—1031no—
226C2×C8—1031no—
227C2×C8—1031no—
228C2×C8—1031no—
229C2×C8—1031no—
230C2×C8C22×D10311yescharacteristic
231C16—1032no—
232C16C22×D10312yes—
233C23—1031no—
234C23—4121no—
235C23—4121no—
236Q8—21no—
237Q8—22no—
238Q8—41no—
239Q8—4121no—
240Q8—2061no—
241D4—21no—
242D4—41no—
243D4—4121no—
244D4—4122no—
245D4—4122no—
246D4—4121no—
247D4—4121no—
248D4—4121no—
249D4—4121no—
250D4—2061no—
251D4—2062no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—1031no—
255C2×C4—1031no—
256C2×C4—1031no—
257C2×C4—1031no—
258C2×C4—1031no—
259C2×C4—4121no—
260C2×C4—4122no—
261C2×C4—4122no—
262C2×C4—4121no—
263C2×C4—4121no—
264C2×C4—4121no—
265C2×C4D4×D10311yescharacteristic
266C8—1031no—
267C8—1031no—
268C8D4×D10311yescharacteristic
269C8C23×D10311yescharacteristic
270C22—41no—
271C22—8242no—
272C22—8242no—
273C22—1031no—
274C22—1031no—
275C22—4121no—
276C22—4122no—
277C22—4121no—
278C22D8×D10311yescharacteristic
279C4—41no—
280C4—42no—
281C4—1031no—
282C4—1031no—
283C4—4121no—
284C4D8×D10311yescharacteristic
285C4C2×D4×D10311yescharacteristic
286C2—21no—
287C2—81no—
288C2—8242no—
289C2—8241no—
290C2—2061no—
291C2—2061no—
292C2C2×D8×D10311yescharacteristic
subgroupG/H
centerC2C2×D8×D103
commutator, cosocleC8×C103C24
FrattiniC8C23×D103
Fitting#510×C103C2
socleC2×C103C22×D8
hypercenter#510D103
hypocenterC103#3414
LCSG ▷ C8×C103 ▷ C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
1. C2×#15693044C2semidirect
2. #135×D103C2semidirect
3. #20268233C2semidirect
4. #20268232C2semidirect
5. #20268229C2semidirect
6. #20268228C2semidirect
7. #20268226C2semidirect
8. #20268224C2semidirect
9. #20268222C2semidirect
10. M32×D103C2semidirect
11. #510×C103C2semidirect
17. #15693044C22semidirect
18. #15693044C22semidirect
22. #15693040C22semidirect
23. Q16×D103C22semidirect
26. C2×D824C22semidirect
27. D8×D103C22semidirect
29. #15692967C22semidirect
30. #15692966C22semidirect
31. #15692964C22semidirect
32. #15692964C22semidirect
33. D1648C22semidirect
34. #15692962C22semidirect
35. #15692961C22semidirect
36. #15692960C22semidirect
37. C16×D103C22semidirect
39. C2×Q16×C103C22semidirect
40. Q32×C103C22semidirect
41. SD32×C103C22semidirect
42. M32×C103C22semidirect
147. C103#3414semidirect
152. #510D103semidirect
172. C2×Q16C2×D103semidirect
179. Q32C2×D103semidirect
183. SD32C2×D103semidirect
188. M32C2×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930442
#135×D1032
#202682332
#202682322
#202682292
#202682282
#202682262
#202682242
#202682222
M32×D1032
#510×C1032
#3414103