Finite Group Databasebeta

← #27193668

Subgroups — #27193668

Order 13184.

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

normal subgroups only

This group has 242 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#20268327C211yesmaximal, characteristic
2#20267845C211yesmaximal, characteristic, complemented
3#20267642C211yesmaximal, characteristic, complemented
4#20267528C211yesmaximal, characteristic, complemented
5#20267526C211yesmaximal, characteristic
6#20267524C211yesmaximal, characteristic
7#328×C103C211yesmaximal, characteristic, complemented
8#15693016—21no—
9#15693012C411yescharacteristic, complemented
10#15693010C411yescharacteristic, complemented
11#15693005—21no—
12#15692995C2211yescharacteristic
13Q8×Dic103C411yescharacteristic, complemented
14#15692983C411yescharacteristic, complemented
15(C22⋊D103)⋊C4—21no—
16#15692979—21no—
17C2×Dic103⋊C4—21no—
18C2×C4×Dic103—21no—
19C2×C4×Dic103C2211yescharacteristic
20Dic103⋊C8—21no—
21C22⋊(C103⋊C8)C2211yescharacteristic
22#15692931—21no—
23C103⋊#95C2211yescharacteristic
24C22⋊Q8×C103C2211yescharacteristic
25C22⋊C8×C103C2211yescharacteristic
26#95×C103C2211yescharacteristic
27C2×D412C2×C411yescharacteristic
28C2×C22⋊D103—21no—
29C22×Dic103—21no—
30C22×Dic103D411yescharacteristic
31C22×Dic103D411yescharacteristic
32C2×C4×D103—21no—
33C2×C103⋊C8—21no—
34C4⋊Dic103—21no—
35C4⋊Dic103—21no—
36C4⋊Dic103C2×C411yescharacteristic
37Dic103⋊C4—24no—
38Dic103⋊C4—21no—
39(C2×D103)⋊C4—21no—
40(C2×D103)⋊C4—21no—
41(C2×D103)⋊C4—21no—
42(C2×D103)⋊C4—21no—
43C4×Dic103—21no—
44C4×Dic103—42no—
45C4×Dic103C2×C411yescharacteristic
46C4×Dic103C2×C411yescharacteristic
47C4×Dic103D411yescharacteristic
48C4×Dic103D411yescharacteristic
49C2×Q8×C103C2×C411yescharacteristic
50C22×C4×C103—21no—
51C22×C4×C103C2311yescharacteristic
52C2×C8×C103—21no—
53C4⋊C4×C103—21no—
54C4⋊C4×C103C2×C411yescharacteristic
55C22⋊C4×C103—21no—
56C23×C103C2×D411yescharacteristic
57C22×D103—21no—
58Q8×C103—41no—
59C2×C4×C103—22no—
60C2×C4×C103—21no—
61C2×C4×C103—21no—
62C2×C4×C103—41no—
63C2×C4×C103—41no—
64C2×C4×C103—41no—
65C2×C4×C103C22×C411yescharacteristic
66C2×C4×C103C2×D411yescharacteristic
67C22⋊D103—41no—
68C22⋊D103—41no—
69C2×Dic103—21no—
70C2×Dic103—21no—
71C2×Dic103—22no—
72C2×Dic103—22no—
73C2×Dic103—21no—
74C2×Dic103—41no—
75C2×Dic103—41no—
76C2×Dic103C22⋊C411yescharacteristic
77C2×Dic103C22⋊C411yescharacteristic
78C2×Dic103C22⋊C411yescharacteristic
79C2×Dic103C22⋊C411yescharacteristic
80D412—41no—
81C4×D103—42no—
82C8×C103—41no—
83C103⋊C8—41no—
84C22×C103—21no—
85C22×C103—21no—
86C22×C103C2×C22⋊C411yescharacteristic
87C22×C103AGL(1,ℤ/8)11yescharacteristic
88C22×C103#13711yescharacteristic
89C2×D103—41no—
90C2×D103—41no—
91C2×D103—41no—
92C4×C103—21no—
93C4×C103—21no—
94C4×C103—42no—
95C4×C103—41no—
96C4×C103—41no—
97Dic103—21no—
98Dic103—21no—
99Dic103—21no—
100Dic103—42no—
101Dic103—41no—
102Dic103#10412yes—
103C2×C103—21no—
104C2×C103—21no—
105C2×C103#41011yescharacteristic
106C2×C103#41711yescharacteristic
107C2×C103C2×#10411yescharacteristic
108D103—81no—
109#1509—1031nomaximal, Sylow
110C103#150911yescharacteristic, complemented, Sylow
111#529—1031no—
112#432—1031no—
113C4×C4⋊C4—1031no—
114#328—1031no—
115#328D10311yescharacteristic, complemented
116#327—1031no—
117#327—1031no—
118#126—2061no—
119#125—1031no—
120#124—1031no—
121#123—2061no—
122C22⋊Q8C2×D10311yescharacteristic
123#121—1031no—
124C4×Q8—1031no—
125C4×D4—1031no—
126C4×D4—2061no—
127#117—2061no—
128C2×C4⋊C4—2061no—
129C2×C42—1031no—
130C2×C42—2061no—
131C4⋊C8—2061no—
132C22⋊C8—1031no—
133C22⋊C8C2×D10311yescharacteristic
134#97—2061no—
135#95—1031no—
136#95C2×D10311yescharacteristic
137C2×Q8C4×D10311yescharacteristic
138C2×D4—1031no—
139C2×D4—2061no—
140C22×C4—21no—
141C22×C4—1031no—
142C22×C4—1031no—
143C22×C4—2061no—
144C22×C4—2061no—
145C22×C4C22×D10311yescharacteristic
146C2×C8—21no—
147C2×C8—2061no—
148C4⋊C4—21no—
149C4⋊C4—1031no—
150C4⋊C4—2061no—
151C4⋊C4—2061no—
152C4⋊C4—2061no—
153C4⋊C4—2064no—
154C4⋊C4C4×D10311yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—2061no—
157C22⋊C4—2061no—
158C22⋊C4—2061no—
159C22⋊C4—2061no—
160C42—1031no—
161C42—1031no—
162C42—1031no—
163C42—1031no—
164C42—4122no—
165C42—2061no—
166C23—2061no—
167C23D4×D10311yescharacteristic
168Q8—41no—
169D4—4121no—
170D4—4121no—
171D4—4121no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—1031no—
179C2×C4—1031no—
180C2×C4—1031no—
181C2×C4—1031no—
182C2×C4—4122no—
183C2×C4—4121no—
184C2×C4—4121no—
185C2×C4—2062no—
186C2×C4—2062no—
187C2×C4—2061no—
188C2×C4—2061no—
189C2×C4—2061no—
190C2×C4C2×C4×D10311yescharacteristic
191C2×C4D4×D10311yescharacteristic
192C8—41no—
193C8—4121no—
194C22—21no—
195C22—21no—
196C22—4121no—
197C22—4121no—
198C22—4121no—
199C22C22⋊C4×D10311yescharacteristic
200C22#1569304811yescharacteristic
201C22#1569305311yescharacteristic
202C4—21no—
203C4—21no—
204C4—42no—
205C4—41no—
206C4—41no—
207C4—1032no—
208C4—4122no—
209C4—4121no—
210C4—2061no—
211C4—2061no—
212C4—2061no—
213C2—21no—
214C2—21no—
215C2—8241no—
216C2#2026776311yescharacteristic
217C2#2026779111yescharacteristic
218C2#104×D10311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#328×C103C2
socleC22×C103C2×C22⋊C4
prime radical#15692995C22
cosocleC22×C4×C103C23
hypercenter#328D103
hypocenterC103#1509
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #20267845C2semidirect
3. #20267642C2semidirect
4. #20267528C2semidirect
7. #328×C103C2semidirect
9. #15693012C4semidirect
10. #15693010C4semidirect
13. Q8×Dic103C4semidirect
14. #15692983C4semidirect
110. C103#1509semidirect
115. #328D103semidirect

Maximal subgroups

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

subgroupindex
#202683272
#202678452
#202676422
#202675282
#202675262
#202675242
#328×C1032
#1509103