Finite Group Databasebeta

← #27205535

Subgroups — #27205535

Order 13184.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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#20268337C211yesmaximal, characteristic
2C2×#15693020C211yesmaximal, characteristic, complemented
3#20268152C212yesmaximal, complemented
4#20268149C212yesmaximal, complemented
5#20268140C212yesmaximal, complemented
6#20268136C212yesmaximal, complemented
7#20267793C211yesmaximal, characteristic, complemented
8#20267792C211yesmaximal, characteristic, complemented
9#20267790C211yesmaximal, characteristic, complemented
10M16×Dic103C211yesmaximal, characteristic, complemented
11#417×C103C211yesmaximal, characteristic, complemented
12C2×#13110105C2211yescharacteristic
13C22×Dic206—21no—
14C2×#13110089C2211yescharacteristic
15#15693020—21no—
16#15693020—21no—
17#15693020C2212yes—
18#15693020C2212yes—
19#15693019C2211yescharacteristic
20#15693017C2211yescharacteristic
21#15693010C2211yescharacteristic
22#15693008C2211yescharacteristic
23#15692993—21no—
24#15692993—21no—
25C4×C22⋊D103—21no—
26C4×C22⋊D103—21no—
27C2×C4⋊Dic103C2211yescharacteristic
28C2×Dic103⋊C4—21no—
29C2×C4×Dic103C2211yescharacteristic
30#15692946C2212yes—
31#15692945C2212yes—
32#15692944C2212yes—
33#15692943C2212yes—
34#15692942C2212yes—
35#15692941C2212yes—
36#15692931C2212yes—
37C8×Dic103C2212yes—
38C2×#41×C103C2211yescharacteristic
39C2×M16×C103C2211yescharacteristic
40C2×C4⋊C4×C103C2211yescharacteristic
41#103×C103C2212yes—
42#102×C103C2212yes—
43#13110105—22no—
44#13110105—22no—
45C2×Dic206—22no—
46C2×Dic206—22no—
47C2×Dic206—44no—
48C2×Dic206C2311yescharacteristic
49C2×D412C2311yescharacteristic
50C2×C22⋊D103—21no—
51C2×C22⋊D103—21no—
52C2×C22⋊D103—21no—
53C22×Dic103—21no—
54C22×Dic103D411yescharacteristic
55C22×Dic103D411yescharacteristic
56C2×C4×D103—21no—
57#13110089—22no—
58C2×C103⋊C8C2312yes—
59C4⋊Dic103—21no—
60C4⋊Dic103C2312yes—
61Dic103⋊C4—22no—
62Dic103⋊C4—22no—
63Dic103⋊C4—21no—
64Dic103⋊C4—21no—
65C22⋊Dic103—21no—
66C22⋊Dic103—21no—
67(C2×D103)⋊C4—21no—
68(C2×D103)⋊C4—21no—
69C4×Dic103D411yescharacteristic
70C4×Dic103D411yescharacteristic
71C4×Dic103C2311yescharacteristic
72C4×Dic103C2311yescharacteristic
73#41×C103—22no—
74#41×C103—22no—
75C2×Q8×C103C2311yescharacteristic
76C2×D4×C103—21no—
77C2×D4×C103C2311yescharacteristic
78C22×C4×C103—21no—
79C22×C4×C103—21no—
80C22×C4×C103C2311yescharacteristic
81M16×C103—22no—
82C2×C8×C103C2312yes—
83C4⋊C4×C103—21no—
84C4⋊C4×C103C2312yes—
85C23×C103—21no—
86C23×C103C2×D411yescharacteristic
87C22×D103—21no—
88Q8×C103—21no—
89Q8×C103—21no—
90D4×C103—21no—
91D4×C103—21no—
92D4×C103—42no—
93C2×C4×C103—22no—
94C2×C4×C103—21no—
95C2×C4×C103—42no—
96C2×C4×C103—42no—
97C2×C4×C103C2×D411yescharacteristic
98C2×C4×C103#4112yes—
99C2×C4×C103#4112yes—
100C2×C4×C103C2411yescharacteristic
101C22⋊D103—42no—
102C22⋊D103—42no—
103C22⋊D103—42no—
104C2×Dic103—22no—
105C2×Dic103—22no—
106C2×Dic103—21no—
107C2×Dic103—22no—
108C2×Dic103—42no—
109C2×Dic103C2×D411yescharacteristic
110C2×Dic103C2×D411yescharacteristic
111C2×Dic103C2×D411yescharacteristic
112C2×Dic103C2×D411yescharacteristic
113D412—21no—
114D412—21no—
115C4×D103—42no—
116Dic206—21no—
117Dic206—21no—
118Dic206—44no—
119Dic206—44no—
120C8×C103—22no—
121C103⋊C8—22no—
122C22×C103—21no—
123C22×C103—21no—
124C22×C103—41no—
125C22×C103—41no—
126C22×C103—41no—
127C22×C103#12412yes—
128C22×C103C22×D411yescharacteristic
129C2×D103—41no—
130C2×D103—41no—
131C2×D103—41no—
132C4×C103—41no—
133C4×C103—42no—
134C4×C103#12412yes—
135C4×C103C2×#4111yescharacteristic
136C4×C103C2×#4111yescharacteristic
137Dic103—21no—
138Dic103—21no—
139Dic103—41no—
140Dic103—42no—
141Dic103AGL(1,ℤ/8)12yes—
142Dic103#13712yes—
143C2×C103—22no—
144C2×C103—81no—
145C2×C103C2×#12411yescharacteristic
146C2×C103C2×AGL(1,ℤ/8)11yescharacteristic
147C2×C103C2×#13711yescharacteristic
148D103—81no—
149#3141—1031nomaximal, Sylow
150C103#314111yescharacteristic, complemented, Sylow
151#532—1031no—
152C2×C4⋊Q8—1031no—
153#489—1032no—
154#489—1032no—
155#487—1032no—
156#486—1032no—
157#417—1031no—
158#417—1031no—
159#417—1031no—
160#417D10311yescharacteristic, complemented
161C4×M16—1031no—
162C2×#41—1031no—
163C2×#41C2×D10311yescharacteristic
164C22×Q8—2061no—
165C2×M16—1031no—
166C2×M16C2×D10311yescharacteristic
167C4⋊Q8—1032no—
168C4⋊Q8—1032no—
169C4⋊Q8—1031no—
170C4⋊Q8—2061no—
171C4⋊Q8—2061no—
172#127—1031no—
173#124—1031no—
174#124—1031no—
175#121—2061no—
176#121—2061no—
177C4×D4—2061no—
178C4×D4—2061no—
179C2×C4⋊C4—1031no—
180C2×C4⋊C4—2061no—
181C2×C4⋊C4C2×D10311yescharacteristic
182C2×C42—1031no—
183#103—1032no—
184#103—1032no—
185#103—1032no—
186#103C2×D10312yes—
187#102—1032no—
188#102—1032no—
189#102—1032no—
190#102C2×D10312yes—
191#97—1032no—
192C4×C8—1032no—
193#41—22no—
194#41—22no—
195#41—2062no—
196#41—2062no—
197C2×Q8—1031no—
198C2×Q8—4124no—
199C2×Q8—2062no—
200C2×Q8—2062no—
201C2×Q8C22×D10311yescharacteristic
202C2×D4—21no—
203C2×D4—1031no—
204C2×D4—2061no—
205C2×D4—2061no—
206C2×D4—2061no—
207C2×D4C22×D10311yescharacteristic
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—1031no—
211C22×C4—1031no—
212C22×C4—2061no—
213C22×C4—2061no—
214C22×C4C22×D10311yescharacteristic
215M16—22no—
216M16—2062no—
217C2×C8—1032no—
218C2×C8C22×D10312yes—
219C4⋊C4—21no—
220C4⋊C4—1032no—
221C4⋊C4—2062no—
222C4⋊C4—2062no—
223C4⋊C4—2061no—
224C4⋊C4—2061no—
225C4⋊C4—2061no—
226C4⋊C4C22×D10312yes—
227C22⋊C4—2061no—
228C22⋊C4—2061no—
229C22⋊C4—2061no—
230C22⋊C4—2061no—
231C42—1031no—
232C42—1031no—
233C42—1031no—
234C42—1031no—
235C23—21no—
236C23—2061no—
237C23D4×D10311yescharacteristic
238Q8—21no—
239Q8—21no—
240Q8—4124no—
241Q8—4124no—
242Q8—2061no—
243Q8—2061no—
244D4—21no—
245D4—21no—
246D4—42no—
247D4—4122no—
248D4—4122no—
249D4—4122no—
250D4—2061no—
251D4—2061no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—1031no—
257C2×C4—1031no—
258C2×C4—1031no—
259C2×C4—1031no—
260C2×C4—4122no—
261C2×C4—4122no—
262C2×C4—2062no—
263C2×C4—2062no—
264C2×C4—2061no—
265C2×C4—2062no—
266C2×C4D4×D10311yescharacteristic
267C2×C4#1311010412yes—
268C2×C4#1311010512yes—
269C2×C4C23×D10311yescharacteristic
270C8—22no—
271C8—2062no—
272C22—21no—
273C22—21no—
274C22—41no—
275C22—41no—
276C22—41no—
277C22—4121no—
278C22—4121no—
279C22—4121no—
280C22#1569300712yes—
281C22C2×D4×D10311yescharacteristic
282C4—41no—
283C4—42no—
284C4—1032no—
285C4—1032no—
286C4—4121no—
287C4—4122no—
288C4—2061no—
289C4—2061no—
290C4#1569300712yes—
291C4C2×#1311010411yescharacteristic
292C4C2×#1311010511yescharacteristic
293C2—22no—
294C2—81no—
295C2—8241no—
296C2C2×#1569300711yescharacteristic
297C2AGL(1,ℤ/8)×D10311yescharacteristic
298C2#137×D10311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#417×C103C2
socleC22×C103C22×D4
prime radical#20268337C2
hypercenter#417D103
hypocenterC103#3141
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#15693020C2semidirect
3. #20268152C2semidirect
4. #20268149C2semidirect
5. #20268140C2semidirect
6. #20268136C2semidirect
7. #20267793C2semidirect
8. #20267792C2semidirect
9. #20267790C2semidirect
10. M16×Dic103C2semidirect
11. #417×C103C2semidirect
150. C103#3141semidirect
160. #417D103semidirect

Maximal subgroups

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

subgroupindex
#202683372
C2×#156930202
#202681522
#202681492
#202681402
#202681362
#202677932
#202677922
#202677902
M16×Dic1032
#417×C1032
#3141103