Finite Group Databasebeta

← #27193637

Subgroups — #27193637

Order 13184.

284 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 71 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#20267642C211yesmaximal, 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×Dic103—21no—
19C2×C4×Dic103C2211yescharacteristic
20Dic103⋊C8—21no—
21C22⋊(C103⋊C8)C2211yescharacteristic
22C8×Dic103—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—24no—
42Dic103⋊C4—21no—
43C22⋊Dic103—21no—
44(C2×D103)⋊C4—21no—
45(C2×D103)⋊C4—21no—
46C4×Dic103—42no—
47C4×Dic103C2×C411yescharacteristic
48C4×Dic103C2×C411yescharacteristic
49C4×Dic103D411yescharacteristic
50C4×Dic103D411yescharacteristic
51C2×D4×C103—21no—
52C2×D4×C103C2×C411yescharacteristic
53C22×C4×C103—21no—
54C22×C4×C103C2311yescharacteristic
55C2×C8×C103—21no—
56C4⋊C4×C103C2×C411yescharacteristic
57C22⋊C4×C103—21no—
58C23×C103—21no—
59C23×C103C2×D411yescharacteristic
60C22×D103—21no—
61D4×C103—41no—
62D4×C103—41no—
63D4×C103—41no—
64C2×C4×C103—22no—
65C2×C4×C103—21no—
66C2×C4×C103—41no—
67C2×C4×C103—41no—
68C2×C4×C103—41no—
69C2×C4×C103C22×C411yescharacteristic
70C2×C4×C103C2×D411yescharacteristic
71C22⋊D103—41no—
72C22⋊D103—41no—
73C22⋊D103—42no—
74C22⋊D103—42no—
75C2×Dic103—22no—
76C2×Dic103—22no—
77C2×Dic103—21no—
78C2×Dic103—41no—
79C2×Dic103—41no—
80C2×Dic103—42no—
81C2×Dic103C22⋊C411yescharacteristic
82C2×Dic103C22⋊C411yescharacteristic
83C2×Dic103C22⋊C411yescharacteristic
84C2×Dic103C22⋊C411yescharacteristic
85C2×Dic103D812yes—
86C2×Dic103SD1612yes—
87D412—41no—
88C4×D103—42no—
89Dic206—42no—
90C8×C103—41no—
91C103⋊C8—41no—
92C22×C103—21no—
93C22×C103—21no—
94C22×C103—41no—
95C22×C103—41no—
96C22×C103—41no—
97C22×C103C2×C22⋊C411yescharacteristic
98C22×C103C2×D811yescharacteristic
99C22×C103C2×SD1611yescharacteristic
100C2×D103—41no—
101C2×D103—41no—
102C2×D103—41no—
103C4×C103—21no—
104C4×C103—21no—
105C4×C103—42no—
106C4×C103—41no—
107Dic103—21no—
108Dic103—42no—
109Dic103—41no—
110Dic103#10212yes—
111Dic103#10212yes—
112Dic103#10412yes—
113C2×C103—21no—
114C2×C103—21no—
115C2×C103—81no—
116C2×C103#41011yescharacteristic
117C2×C103C2×#10211yescharacteristic
118C2×C103C2×#10411yescharacteristic
119D103—81no—
120#1502—1031nomaximal, Sylow
121C103#150211yescharacteristic, complemented, Sylow
122#532—1031no—
123#431—1031no—
124C4×C4⋊C4—1031no—
125#327—1031no—
126#327—1031no—
127#327—1031no—
128#327D10311yescharacteristic, complemented
129C2×#41—2061no—
130C4⋊Q8—1031no—
131#127—1031no—
132#124—2061no—
133#121—1031no—
134#121—2061no—
135#121C2×D10311yescharacteristic
136C4×D4—1031no—
137C4×D4—1031no—
138C4×D4—2061no—
139C2×C4⋊C4—2061no—
140C2×C42—1031no—
141C2×C42—2061no—
142C4⋊C8—2061no—
143C22⋊C8—1031no—
144C22⋊C8C2×D10311yescharacteristic
145C4×C8—2061no—
146#95—1031no—
147#95C2×D10311yescharacteristic
148#41—4122no—
149#41—4122no—
150C2×Q8—2061no—
151C2×D4—21no—
152C2×D4—1031no—
153C2×D4—2061no—
154C2×D4—2061no—
155C2×D4—2061no—
156C2×D4C4×D10311yescharacteristic
157C22×C4—21no—
158C22×C4—1031no—
159C22×C4—1031no—
160C22×C4—2061no—
161C22×C4—2061no—
162C22×C4—2061no—
163C22×C4C22×D10311yescharacteristic
164C2×C8—21no—
165C2×C8—2061no—
166C4⋊C4—1031no—
167C4⋊C4—2061no—
168C4⋊C4—2064no—
169C4⋊C4C4×D10311yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—2061no—
172C22⋊C4—2061no—
173C22⋊C4—2061no—
174C42—1031no—
175C42—1031no—
176C42—1031no—
177C42—1031no—
178C42—4122no—
179C23—21no—
180C23—2061no—
181C23D4×D10311yescharacteristic
182Q8—4122no—
183D4—41no—
184D4—41no—
185D4—41no—
186D4—4121no—
187D4—4122no—
188D4—4122no—
189D4—4121no—
190D4—4121no—
191C2×C4—22no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—1031no—
197C2×C4—1031no—
198C2×C4—1031no—
199C2×C4—1032no—
200C2×C4—1032no—
201C2×C4—1031no—
202C2×C4—4122no—
203C2×C4—4122no—
204C2×C4—4121no—
205C2×C4—4121no—
206C2×C4—2062no—
207C2×C4—2062no—
208C2×C4—2061no—
209C2×C4C2×C4×D10311yescharacteristic
210C2×C4D4×D10311yescharacteristic
211C8—41no—
212C8—4121no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22—4121no—
219C22—4121no—
220C22—4121no—
221C22C22⋊C4×D10311yescharacteristic
222C22D8×D10311yescharacteristic
223C22SD16×D10311yescharacteristic
224C4—21no—
225C4—21no—
226C4—42no—
227C4—41no—
228C4—1032no—
229C4—1032no—
230C4—1032no—
231C4—4122no—
232C4—4121no—
233C4—2061no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—8241no—
238C2#2026776311yescharacteristic
239C2#102×D10311yescharacteristic
240C2#104×D10311yescharacteristic
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#1502
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. #20267642C2semidirect
4. #20267526C2semidirect
5. #20267525C2semidirect
6. #20267524C2semidirect
7. #327×C103C2semidirect
9. #15693020C4semidirect
10. #15693017C4semidirect
14. D4×Dic103C4semidirect
15. #15692983C4semidirect
121. C103#1502semidirect
128. #327D103semidirect

Maximal subgroups

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

subgroupindex
#202683362
#202678412
#202676422
#202675262
#202675252
#202675242
#327×C1032
#1502103