Finite Group Databasebeta

← #27193684

Subgroups — #27193684

Order 13184.

286 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 63 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#20268301C211yesmaximal, characteristic
2#20267753C211yesmaximal, characteristic, complemented
3#20267650C211yesmaximal, characteristic, complemented
4#20267529C211yesmaximal, characteristic, complemented
5#20267527C211yesmaximal, characteristic, complemented
6#20267525C211yesmaximal, characteristic, complemented
7#327×C103C211yesmaximal, characteristic, complemented
8C2×#13110104C411yescharacteristic, complemented
9C22×C4×D103C2211yescharacteristic
10C2×#13110088—21no—
11#15693003—21no—
12#15693001C411yescharacteristic, complemented
13#15693000C2211yescharacteristic
14#15692992C411yescharacteristic, complemented
15#15692989—21no—
16D4×Dic103—21no—
17(C22⋊D103)⋊C4—21no—
18#15692979C411yescharacteristic, complemented
19C2×Dic103⋊C4—21no—
20C2×(C2×D103)⋊C4—21no—
21C22⋊(C103⋊C8)C2211yescharacteristic
22(C2×D103)⋊C8—21no—
23C103⋊#95C2211yescharacteristic
24#121×C103C2211yescharacteristic
25C22⋊C8×C103C2211yescharacteristic
26#95×C103C2211yescharacteristic
27C23×D103D411yescharacteristic
28#13110104—42no—
29C2×Dic206C2×C411yescharacteristic
30C2×C22⋊D103—21no—
31C2×C22⋊D103—21no—
32C22×Dic103—21no—
33C22×Dic103—21no—
34C22×Dic103D411yescharacteristic
35C2×C4×D103—42no—
36C2×C4×D103C2×C411yescharacteristic
37C2×C4×D103C2×C411yescharacteristic
38C2×C4×D103D411yescharacteristic
39C2×C4×D103D411yescharacteristic
40#13110088—42no—
41C2×C103⋊C8—21no—
42C4⋊Dic103—21no—
43C4⋊Dic103C2×C411yescharacteristic
44Dic103⋊C4—21no—
45Dic103⋊C4—42no—
46C22⋊Dic103—21no—
47C22⋊Dic103—21no—
48(C2×D103)⋊C4—21no—
49(C2×D103)⋊C4—21no—
50(C2×D103)⋊C4—42no—
51C4×Dic103—21no—
52C2×D4×C103—21no—
53C2×D4×C103C2×C411yescharacteristic
54C22×C4×C103—21no—
55C22×C4×C103C2311yescharacteristic
56C2×C8×C103—21no—
57C4⋊C4×C103C2×C411yescharacteristic
58C22⋊C4×C103—21no—
59C23×C103—21no—
60C23×C103C2×D411yescharacteristic
61C22×D103—21no—
62C22×D103—21no—
63C22×D103—41no—
64C22×D103—41no—
65C22×D103C22⋊C411yescharacteristic
66C22×D103C22⋊C411yescharacteristic
67D4×C103—41no—
68D4×C103—41no—
69D4×C103—41no—
70C2×C4×C103—21no—
71C2×C4×C103—41no—
72C2×C4×C103—41no—
73C2×C4×C103—41no—
74C2×C4×C103—41no—
75C2×C4×C103C22×C411yescharacteristic
76C2×C4×C103C2×D411yescharacteristic
77C22⋊D103—42no—
78C22⋊D103—42no—
79C2×Dic103—22no—
80C2×Dic103—21no—
81C2×Dic103—21no—
82C2×Dic103—42no—
83C2×Dic103—41no—
84C2×Dic103—41no—
85C2×Dic103—41no—
86C2×Dic103C22⋊C411yescharacteristic
87C2×Dic103C22⋊C411yescharacteristic
88C4×D103—22no—
89C4×D103—22no—
90C4×D103—41no—
91C4×D103—41no—
92Dic206—41no—
93C8×C103—41no—
94C103⋊C8—41no—
95C22×C103—21no—
96C22×C103—21no—
97C22×C103—41no—
98C22×C103—41no—
99C22×C103—41no—
100C22×C103C2×C22⋊C411yescharacteristic
101C22×C103AGL(1,ℤ/8)11yescharacteristic
102C22×C103#13711yescharacteristic
103C2×D103—21no—
104C2×D103—21no—
105C2×D103—21no—
106C2×D103—21no—
107C2×D103—21no—
108C2×D103—21no—
109C2×D103—42no—
110C2×D103—42no—
111C4×C103—21no—
112C4×C103—21no—
113C4×C103—41no—
114C4×C103—81no—
115Dic103—21no—
116Dic103—41no—
117Dic103—41no—
118Dic103—81no—
119Dic103#9912yes—
120C2×C103—21no—
121C2×C103—21no—
122C2×C103—81no—
123C2×C103C2×#9911yescharacteristic
124C2×C103#41711yescharacteristic
125C2×C103#42111yescharacteristic
126D103—41no—
127D103—41no—
128#1513—1031nomaximal, Sylow
129C103#151311yescharacteristic, complemented, Sylow
130#525—1031no—
131#407—1031no—
132#380—1031no—
133#328—1031no—
134#328—1031no—
135#327—1031no—
136#327D10311yescharacteristic, complemented
137C2×#41—1031no—
138C23×C4—1031no—
139C2×M16—2061no—
140#123—2061no—
141C22⋊Q8—1031no—
142C22⋊Q8—1031no—
143#121—1031no—
144#121C2×D10311yescharacteristic
145#120—2061no—
146C4×D4—2061no—
147C4×D4—2061no—
148#117—1031no—
149C2×C4⋊C4—2061no—
150C2×C22⋊C4—2061no—
151C22⋊C8—1031no—
152C22⋊C8—2061no—
153C22⋊C8C2×D10311yescharacteristic
154#95—1031no—
155#95C2×D10311yescharacteristic
156C24—1031no—
157#41—4122no—
158C2×Q8—1031no—
159C2×D4—21no—
160C2×D4—2061no—
161C2×D4—2061no—
162C2×D4C4×D10311yescharacteristic
163C22×C4—21no—
164C22×C4—1031no—
165C22×C4—1031no—
166C22×C4—1031no—
167C22×C4—1031no—
168C22×C4—1031no—
169C22×C4—4122no—
170C22×C4—2061no—
171C22×C4—2061no—
172C22×C4C22×D10311yescharacteristic
173M16—4122no—
174C2×C8—21no—
175C2×C8—2061no—
176C4⋊C4—1031no—
177C4⋊C4—4122no—
178C4⋊C4—2061no—
179C4⋊C4—2061no—
180C4⋊C4C4×D10311yescharacteristic
181C22⋊C4—21no—
182C22⋊C4—4122no—
183C22⋊C4—2061no—
184C22⋊C4—2061no—
185C22⋊C4—2061no—
186C22⋊C4—2061no—
187C42—2061no—
188C23—21no—
189C23—1031no—
190C23—1031no—
191C23—4121no—
192C23—4121no—
193C23—2061no—
194C23—2061no—
195C23D4×D10311yescharacteristic
196Q8—4121no—
197D4—41no—
198D4—41no—
199D4—41no—
200D4—4122no—
201D4—4122no—
202C2×C4—21no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—1031no—
208C2×C4—1031no—
209C2×C4—4121no—
210C2×C4—4121no—
211C2×C4—4121no—
212C2×C4—4121no—
213C2×C4—4121no—
214C2×C4—4122no—
215C2×C4—2062no—
216C2×C4—2062no—
217C2×C4—2062no—
218C2×C4—2061no—
219C2×C4—2061no—
220C2×C4C2×C4×D10311yescharacteristic
221C2×C4D4×D10311yescharacteristic
222C8—41no—
223C8—4121no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—4122no—
230C22—4122no—
231C22—2061no—
232C22—2061no—
233C22—2061no—
234C22—2061no—
235C22—2061no—
236C22—2061no—
237C22C22⋊C4×D10311yescharacteristic
238C22#1569304511yescharacteristic
239C22#1569305011yescharacteristic
240C4—21no—
241C4—21no—
242C4—41no—
243C4—81no—
244C4—8241no—
245C4—1032no—
246C4—4121no—
247C4—4121no—
248C4—2061no—
249C2—21no—
250C2—21no—
251C2—81no—
252C2—4121no—
253C2—4121no—
254C2#99×D10311yescharacteristic
255C2#2026778911yescharacteristic
256C2#2026780611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#327×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268301C2
cosocleC22×C4×C103C23
hypercenter#327D103
hypocenterC103#1513
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #20267753C2semidirect
3. #20267650C2semidirect
4. #20267529C2semidirect
5. #20267527C2semidirect
6. #20267525C2semidirect
7. #327×C103C2semidirect
8. C2×#13110104C4semidirect
12. #15693001C4semidirect
14. #15692992C4semidirect
18. #15692979C4semidirect
129. C103#1513semidirect
136. #327D103semidirect

Maximal subgroups

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

subgroupindex
#202683012
#202677532
#202676502
#202675292
#202675272
#202675252
#327×C1032
#1513103