Finite Group Databasebeta

← #27205542

Subgroups — #27205542

Order 13184.

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

normal subgroups only

This group has 392 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#20268337C211yesmaximal, characteristic
2C2×#15693012C211yesmaximal, characteristic, complemented
3#20268158C212yesmaximal, complemented
4#20268154C212yesmaximal, complemented
5#20268147C212yesmaximal, complemented
6#20268144C212yesmaximal, complemented
7#20267793C211yesmaximal, characteristic, complemented
8#20267792C211yesmaximal, characteristic, complemented
9#20267790C211yesmaximal, characteristic, complemented
10M16×Dic103C211yesmaximal, characteristic, complemented
11#417×C103C211yesmaximal, characteristic, complemented
12C2×#13110105C2211yescharacteristic
13C2×#13110089C2211yescharacteristic
14#15693019C2211yescharacteristic
15#15693017C2211yescharacteristic
16#15693012—21no—
17#15693012—21no—
18#15693012C2212yes—
19#15693012C2212yes—
20#15693010C2211yescharacteristic
21#15693008C2211yescharacteristic
22#15692993—21no—
23#15692993—21no—
24C4×C22⋊D103—21no—
25C4×C22⋊D103—21no—
26C2×C4⋊Dic103—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×Dic206C2311yescharacteristic
46C2×D412C2311yescharacteristic
47C2×C22⋊D103—21no—
48C2×C22⋊D103—21no—
49C2×C22⋊D103—21no—
50C22×Dic103—21no—
51C22×Dic103D411yescharacteristic
52C22×Dic103D411yescharacteristic
53C2×C4×D103—21no—
54#13110089—22no—
55C2×C103⋊C8C2312yes—
56C4⋊Dic103—21no—
57C4⋊Dic103—22no—
58C4⋊Dic103—22no—
59C4⋊Dic103C2312yes—
60Dic103⋊C4—22no—
61Dic103⋊C4—22no—
62Dic103⋊C4—21no—
63Dic103⋊C4—21no—
64C22⋊Dic103—21no—
65C22⋊Dic103—21no—
66(C2×D103)⋊C4—21no—
67(C2×D103)⋊C4—21no—
68C4×Dic103D411yescharacteristic
69C4×Dic103D411yescharacteristic
70C4×Dic103C2311yescharacteristic
71C4×Dic103C2311yescharacteristic
72#41×C103—22no—
73#41×C103—22no—
74C2×Q8×C103C2311yescharacteristic
75C2×D4×C103—21no—
76C2×D4×C103C2311yescharacteristic
77C22×C4×C103—21no—
78C22×C4×C103—21no—
79C22×C4×C103C2311yescharacteristic
80M16×C103—22no—
81C2×C8×C103C2312yes—
82C4⋊C4×C103—21no—
83C4⋊C4×C103C2312yes—
84C23×C103—21no—
85C23×C103C2×D411yescharacteristic
86C22×D103—21no—
87Q8×C103—21no—
88Q8×C103—21no—
89D4×C103—21no—
90D4×C103—21no—
91D4×C103—42no—
92C2×C4×C103—22no—
93C2×C4×C103—21no—
94C2×C4×C103—42no—
95C2×C4×C103—42no—
96C2×C4×C103C2×D411yescharacteristic
97C2×C4×C103#4112yes—
98C2×C4×C103#4112yes—
99C2×C4×C103C2411yescharacteristic
100C22⋊D103—42no—
101C22⋊D103—42no—
102C22⋊D103—42no—
103C2×Dic103—21no—
104C2×Dic103—22no—
105C2×Dic103—41no—
106C2×Dic103—41no—
107C2×Dic103—42no—
108C2×Dic103C2×D411yescharacteristic
109C2×Dic103C2×D411yescharacteristic
110C2×Dic103C2×D411yescharacteristic
111C2×Dic103C2×D411yescharacteristic
112D412—21no—
113D412—21no—
114C4×D103—42no—
115Dic206—21no—
116Dic206—21no—
117C8×C103—22no—
118C103⋊C8—22no—
119C22×C103—21no—
120C22×C103—21no—
121C22×C103—41no—
122C22×C103—41no—
123C22×C103—41no—
124C22×C103#12412yes—
125C22×C103C22×D411yescharacteristic
126C2×D103—41no—
127C2×D103—41no—
128C2×D103—41no—
129C4×C103—41no—
130C4×C103—42no—
131C4×C103#12412yes—
132C4×C103C2×#4111yescharacteristic
133C4×C103C2×#4111yescharacteristic
134Dic103—21no—
135Dic103—21no—
136Dic103—21no—
137Dic103—21no—
138Dic103—41no—
139Dic103—42no—
140C2×C103—22no—
141C2×C103—81no—
142C2×C103C2×#12411yescharacteristic
143C2×C103#57511yescharacteristic
144C2×C103#57511yescharacteristic
145D103—81no—
146#3142—1031nomaximal, Sylow
147C103#314211yescharacteristic, complemented, Sylow
148#532—1031no—
149C2×#125—1031no—
150#491—1032no—
151#490—1032no—
152#488—1032no—
153#488—1032no—
154#417—1031no—
155#417—1031no—
156#417—1031no—
157#417D10311yescharacteristic, complemented
158C4×M16—1031no—
159C2×#41—1031no—
160C2×#41C2×D10311yescharacteristic
161C2×M16—1031no—
162C2×M16C2×D10311yescharacteristic
163C4⋊Q8—1031no—
164#127—1031no—
165#125—1032no—
166#125—1032no—
167#125—2061no—
168#125—2061no—
169#124—1031no—
170#124—1031no—
171#121—2061no—
172#121—2061no—
173C4×D4—2061no—
174C4×D4—2061no—
175C2×C4⋊C4—1031no—
176C2×C4⋊C4—2061no—
177C2×C4⋊C4—2061no—
178C2×C4⋊C4C2×D10311yescharacteristic
179C2×C42—1031no—
180#103—1032no—
181#103—1032no—
182#103—1032no—
183#103C2×D10312yes—
184#102—1032no—
185#102—1032no—
186#102—1032no—
187#102C2×D10312yes—
188#97—1032no—
189C4×C8—1032no—
190#41—22no—
191#41—22no—
192#41—2062no—
193#41—2062no—
194C2×Q8—1031no—
195C2×Q8C22×D10311yescharacteristic
196C2×D4—21no—
197C2×D4—1031no—
198C2×D4—2061no—
199C2×D4—2061no—
200C2×D4—2061no—
201C2×D4C22×D10311yescharacteristic
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—1031no—
205C22×C4—1031no—
206C22×C4—2061no—
207C22×C4—2061no—
208C22×C4C22×D10311yescharacteristic
209M16—22no—
210M16—2062no—
211C2×C8—1032no—
212C2×C8C22×D10312yes—
213C4⋊C4—21no—
214C4⋊C4—1032no—
215C4⋊C4—2062no—
216C4⋊C4—2062no—
217C4⋊C4—2061no—
218C4⋊C4—2061no—
219C4⋊C4—2062no—
220C4⋊C4—2062no—
221C4⋊C4—2061no—
222C4⋊C4C22×D10312yes—
223C22⋊C4—2061no—
224C22⋊C4—2061no—
225C22⋊C4—2061no—
226C22⋊C4—2061no—
227C42—1031no—
228C42—1031no—
229C42—1031no—
230C42—1031no—
231C23—21no—
232C23—2061no—
233C23D4×D10311yescharacteristic
234Q8—21no—
235Q8—21no—
236Q8—2061no—
237Q8—2061no—
238D4—21no—
239D4—21no—
240D4—42no—
241D4—4122no—
242D4—4122no—
243D4—4122no—
244D4—2061no—
245D4—2061no—
246C2×C4—21no—
247C2×C4—22no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—1031no—
251C2×C4—1031no—
252C2×C4—1031no—
253C2×C4—1031no—
254C2×C4—4122no—
255C2×C4—4122no—
256C2×C4—4121no—
257C2×C4—4121no—
258C2×C4—2061no—
259C2×C4—2062no—
260C2×C4D4×D10311yescharacteristic
261C2×C4#1311010412yes—
262C2×C4#1311010512yes—
263C2×C4C23×D10311yescharacteristic
264C8—22no—
265C8—2062no—
266C22—21no—
267C22—21no—
268C22—41no—
269C22—41no—
270C22—41no—
271C22—4121no—
272C22—4121no—
273C22—4121no—
274C22#1569300712yes—
275C22C2×D4×D10311yescharacteristic
276C4—41no—
277C4—42no—
278C4—4121no—
279C4—4122no—
280C4—2061no—
281C4—2061no—
282C4—2061no—
283C4—2061no—
284C4#1569300712yes—
285C4C2×#1311010411yescharacteristic
286C4C2×#1311010511yescharacteristic
287C2—22no—
288C2—81no—
289C2—8241no—
290C2C2×#1569300711yescharacteristic
291C2#2026858711yescharacteristic
292C2#2026859011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#417×C103C2
socleC22×C103C22×D4
prime radical#20268337C2
hypercenter#417D103
hypocenterC103#3142
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×#15693012C2semidirect
3. #20268158C2semidirect
4. #20268154C2semidirect
5. #20268147C2semidirect
6. #20268144C2semidirect
7. #20267793C2semidirect
8. #20267792C2semidirect
9. #20267790C2semidirect
10. M16×Dic103C2semidirect
11. #417×C103C2semidirect
147. C103#3142semidirect
157. #417D103semidirect

Maximal subgroups

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

subgroupindex
#202683372
C2×#156930122
#202681582
#202681542
#202681472
#202681442
#202677932
#202677922
#202677902
M16×Dic1032
#417×C1032
#3142103