Finite Group Databasebeta

← #27193702

Subgroups — #27193702

Order 13184.

264 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 69 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#20268336C211yesmaximal, characteristic
2#20267841C211yesmaximal, characteristic, complemented
3#20267655C211yesmaximal, characteristic, complemented
4#20267526C211yesmaximal, characteristic, complemented
5#20267525C211yesmaximal, characteristic, complemented
6#20267524C211yesmaximal, characteristic, complemented
7#327×C103C211yesmaximal, characteristic, complemented
8C2×#13110104—21no—
9#15693020C411yescharacteristic, complemented
10#15693017C411yescharacteristic, complemented
11#15693007—21no—
12#15692995C2211yescharacteristic
13#15692993—21no—
14D4×Dic103C411yescharacteristic, complemented
15#15692983C411yescharacteristic, complemented
16(C22⋊D103)⋊C4—21no—
17C2×Dic103⋊C4—21no—
18C2×C4×Dic103C2211yescharacteristic
19Dic103⋊C8—21no—
20C22⋊(C103⋊C8)C2211yescharacteristic
21C8×Dic103—21no—
22C103⋊#95—21no—
23C103⋊#95C2211yescharacteristic
24#121×C103C2211yescharacteristic
25C22⋊C8×C103C2211yescharacteristic
26#95×C103C2211yescharacteristic
27#13110104—42no—
28#13110104—42no—
29C2×Dic206—21no—
30C2×D412C2×C411yescharacteristic
31C2×C22⋊D103—21no—
32C2×C22⋊D103—21no—
33C2×C22⋊D103—21no—
34C22×Dic103—21no—
35C22×Dic103—21no—
36C22×Dic103D411yescharacteristic
37C22×Dic103D411yescharacteristic
38C2×C4×D103—21no—
39C2×C103⋊C8—21no—
40C4⋊Dic103C2×C411yescharacteristic
41Dic103⋊C4—21no—
42Dic103⋊C4—42no—
43C22⋊Dic103—21no—
44(C2×D103)⋊C4—21no—
45(C2×D103)⋊C4—21no—
46C4×Dic103C2×C411yescharacteristic
47C4×Dic103C2×C411yescharacteristic
48C4×Dic103D411yescharacteristic
49C4×Dic103D411yescharacteristic
50C2×D4×C103—21no—
51C2×D4×C103C2×C411yescharacteristic
52C22×C4×C103—21no—
53C22×C4×C103C2311yescharacteristic
54C2×C8×C103—21no—
55C4⋊C4×C103C2×C411yescharacteristic
56C22⋊C4×C103—21no—
57C23×C103—21no—
58C23×C103C2×D411yescharacteristic
59C22×D103—21no—
60D4×C103—41no—
61D4×C103—41no—
62D4×C103—41no—
63C2×C4×C103—21no—
64C2×C4×C103—41no—
65C2×C4×C103—41no—
66C2×C4×C103—41no—
67C2×C4×C103—41no—
68C2×C4×C103C22×C411yescharacteristic
69C2×C4×C103C2×D411yescharacteristic
70C22⋊D103—42no—
71C22⋊D103—41no—
72C22⋊D103—41no—
73C22⋊D103—42no—
74C2×Dic103—21no—
75C2×Dic103—41no—
76C2×Dic103—42no—
77C2×Dic103—41no—
78C2×Dic103—41no—
79C2×Dic103—41no—
80C2×Dic103C22⋊C411yescharacteristic
81C2×Dic103C22⋊C411yescharacteristic
82C2×Dic103C22⋊C411yescharacteristic
83C2×Dic103C22⋊C411yescharacteristic
84C2×Dic103D812yes—
85C2×Dic103SD1612yes—
86D412—41no—
87C4×D103—42no—
88Dic206—42no—
89C8×C103—41no—
90C103⋊C8—41no—
91C22×C103—21no—
92C22×C103—21no—
93C22×C103—41no—
94C22×C103—41no—
95C22×C103—41no—
96C22×C103C2×C22⋊C411yescharacteristic
97C22×C103C2×D811yescharacteristic
98C22×C103C2×SD1611yescharacteristic
99C2×D103—41no—
100C2×D103—41no—
101C2×D103—41no—
102C4×C103—21no—
103C4×C103—21no—
104C4×C103—41no—
105C4×C103—81no—
106Dic103—21no—
107Dic103—21no—
108Dic103—41no—
109Dic103—81no—
110Dic103#10212yes—
111Dic103#10212yes—
112C2×C103—21no—
113C2×C103—21no—
114C2×C103—81no—
115C2×C103#41011yescharacteristic
116C2×C103C2×#10211yescharacteristic
117C2×C103#42111yescharacteristic
118D103—81no—
119#1517—1031nomaximal, Sylow
120C103#151711yescharacteristic, complemented, Sylow
121#532—1031no—
122#431—1031no—
123#382—1031no—
124#327—1031no—
125#327—1031no—
126#327—1031no—
127#327D10311yescharacteristic, complemented
128C2×#41—2061no—
129C4⋊Q8—1031no—
130#127—1031no—
131#124—2061no—
132#121—1031no—
133#121—2061no—
134#121C2×D10311yescharacteristic
135C4×D4—1031no—
136C4×D4—1031no—
137C4×D4—2061no—
138C2×C4⋊C4—2061no—
139C2×C42—1031no—
140C4⋊C8—2061no—
141C22⋊C8—1031no—
142C22⋊C8C2×D10311yescharacteristic
143C4×C8—2061no—
144#95—1031no—
145#95—2061no—
146#95C2×D10311yescharacteristic
147#41—4122no—
148#41—4122no—
149C2×Q8—2061no—
150C2×D4—21no—
151C2×D4—1031no—
152C2×D4—2061no—
153C2×D4—2061no—
154C2×D4—2061no—
155C2×D4C4×D10311yescharacteristic
156C22×C4—21no—
157C22×C4—1031no—
158C22×C4—1031no—
159C22×C4—2061no—
160C22×C4—2061no—
161C22×C4—2061no—
162C22×C4C22×D10311yescharacteristic
163C2×C8—21no—
164C2×C8—2061no—
165C4⋊C4—1031no—
166C4⋊C4—4122no—
167C4⋊C4—2061no—
168C4⋊C4C4×D10311yescharacteristic
169C22⋊C4—21no—
170C22⋊C4—2061no—
171C22⋊C4—2061no—
172C22⋊C4—2061no—
173C42—1031no—
174C42—1031no—
175C42—1031no—
176C42—1031no—
177C23—21no—
178C23—2061no—
179C23D4×D10311yescharacteristic
180Q8—4122no—
181D4—41no—
182D4—41no—
183D4—41no—
184D4—4121no—
185D4—4122no—
186D4—4121no—
187D4—4121no—
188D4—4122no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—1031no—
195C2×C4—1031no—
196C2×C4—1032no—
197C2×C4—1032no—
198C2×C4—1031no—
199C2×C4—1031no—
200C2×C4—4122no—
201C2×C4—4121no—
202C2×C4—4121no—
203C2×C4—4121no—
204C2×C4—4122no—
205C2×C4—4121no—
206C2×C4—2061no—
207C2×C4C2×C4×D10311yescharacteristic
208C2×C4D4×D10311yescharacteristic
209C8—41no—
210C8—4121no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—4121no—
217C22—4121no—
218C22—4121no—
219C22C22⋊C4×D10311yescharacteristic
220C22D8×D10311yescharacteristic
221C22SD16×D10311yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—81no—
226C4—8241no—
227C4—1032no—
228C4—1032no—
229C4—4121no—
230C4—2061no—
231C4—2061no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—8241no—
236C2#2026776311yescharacteristic
237C2#102×D10311yescharacteristic
238C2#2026780611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#327×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268336C2
cosocleC22×C4×C103C23
hypercenter#327D103
hypocenterC103#1517
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. #20267841C2semidirect
3. #20267655C2semidirect
4. #20267526C2semidirect
5. #20267525C2semidirect
6. #20267524C2semidirect
7. #327×C103C2semidirect
9. #15693020C4semidirect
10. #15693017C4semidirect
14. D4×Dic103C4semidirect
15. #15692983C4semidirect
120. C103#1517semidirect
127. #327D103semidirect

Maximal subgroups

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

subgroupindex
#202683362
#202678412
#202676552
#202675262
#202675252
#202675242
#327×C1032
#1517103