Finite Group Databasebeta

← #27193679

Subgroups — #27193679

Order 13184.

222 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 61 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#20268322C211yesmaximal, characteristic
2#20267845C211yesmaximal, characteristic, complemented
3#20267655C211yesmaximal, characteristic, complemented
4#20267529C211yesmaximal, characteristic, complemented
5#20267527C211yesmaximal, characteristic, complemented
6#20267525C211yesmaximal, characteristic
7#327×C103C211yesmaximal, characteristic
8#15693014—21no—
9#15693012C411yescharacteristic, complemented
10#15693008C411yescharacteristic, complemented
11#15693002—21no—
12#15693000C2211yescharacteristic
13#15692986C411yescharacteristic, complemented
14D4×Dic103—21no—
15D4×Dic103C411yescharacteristic, complemented
16#15692977—21no—
17C2×Dic103⋊C4—21no—
18C2×C4×Dic103C2211yescharacteristic
19Dic103⋊C8—21no—
20C22⋊(C103⋊C8)C2211yescharacteristic
21#15692931—21no—
22C103⋊#95—21no—
23C103⋊#95C2211yescharacteristic
24#121×C103C2211yescharacteristic
25C22⋊C8×C103C2211yescharacteristic
26#95×C103C2211yescharacteristic
27C2×Dic206C2×C411yescharacteristic
28C22×Dic103—21no—
29C22×Dic103—21no—
30C22×Dic103D411yescharacteristic
31C22×Dic103D411yescharacteristic
32C2×C103⋊C8—21no—
33C4⋊Dic103—21no—
34C4⋊Dic103C2×C411yescharacteristic
35Dic103⋊C4—21no—
36Dic103⋊C4—21no—
37Dic103⋊C4—21no—
38Dic103⋊C4—42no—
39C22⋊Dic103—21no—
40C22⋊Dic103—21no—
41C22⋊Dic103—21no—
42C22⋊Dic103—21no—
43C4×Dic103—21no—
44C4×Dic103C2×C411yescharacteristic
45C4×Dic103C2×C411yescharacteristic
46C4×Dic103D411yescharacteristic
47C4×Dic103D411yescharacteristic
48C2×D4×C103—21no—
49C2×D4×C103C2×C411yescharacteristic
50C22×C4×C103—21no—
51C22×C4×C103C2311yescharacteristic
52C2×C8×C103—21no—
53C4⋊C4×C103C2×C411yescharacteristic
54C22⋊C4×C103—21no—
55C23×C103—21no—
56C23×C103C2×D411yescharacteristic
57D4×C103—41no—
58D4×C103—41no—
59D4×C103—41no—
60C2×C4×C103—21no—
61C2×C4×C103—41no—
62C2×C4×C103—41no—
63C2×C4×C103—41no—
64C2×C4×C103—41no—
65C2×C4×C103C22×C411yescharacteristic
66C2×C4×C103C2×D411yescharacteristic
67C2×Dic103—21no—
68C2×Dic103—21no—
69C2×Dic103—21no—
70C2×Dic103—21no—
71C2×Dic103—41no—
72C2×Dic103—42no—
73C2×Dic103—41no—
74C2×Dic103—41no—
75C2×Dic103—41no—
76C2×Dic103C22⋊C411yescharacteristic
77C2×Dic103C22⋊C411yescharacteristic
78C2×Dic103C22⋊C411yescharacteristic
79C2×Dic103C22⋊C411yescharacteristic
80Dic206—41no—
81C8×C103—41no—
82C103⋊C8—41no—
83C22×C103—21no—
84C22×C103—21no—
85C22×C103—41no—
86C22×C103—41no—
87C22×C103—41no—
88C22×C103C2×C22⋊C411yescharacteristic
89C22×C103AGL(1,ℤ/8)11yescharacteristic
90C22×C103#13711yescharacteristic
91C4×C103—21no—
92C4×C103—21no—
93C4×C103—41no—
94C4×C103—81no—
95Dic103—21no—
96Dic103—21no—
97Dic103—21no—
98Dic103—21no—
99Dic103—41no—
100Dic103—41no—
101Dic103—81no—
102C2×C103—21no—
103C2×C103—21no—
104C2×C103—81no—
105C2×C103#41011yescharacteristic
106C2×C103#41711yescharacteristic
107C2×C103#42111yescharacteristic
108#1512—1031nomaximal, Sylow
109C103#151211yescharacteristic, complemented, Sylow
110#529—1031no—
111#432—1031no—
112#382—1031no—
113#328—1031no—
114#328—1031no—
115#327—1031no—
116#327D10311yescharacteristic
117#126—2061no—
118#125—1031no—
119#124—1031no—
120#123—2061no—
121C22⋊Q8—1031no—
122#121C2×D10311yescharacteristic
123C4×Q8—1031no—
124C4×D4—1031no—
125C4×D4—2061no—
126#117—2061no—
127C2×C4⋊C4—2061no—
128C2×C42—1031no—
129C4⋊C8—2061no—
130C22⋊C8—1031no—
131C22⋊C8C2×D10311yescharacteristic
132#97—2061no—
133#95—1031no—
134#95—2061no—
135#95C2×D10311yescharacteristic
136C2×Q8—1031no—
137C2×D4—21no—
138C2×D4C4×D10311yescharacteristic
139C22×C4—21no—
140C22×C4—1031no—
141C22×C4—1031no—
142C22×C4—2061no—
143C22×C4—2061no—
144C22×C4C22×D10311yescharacteristic
145C2×C8—21no—
146C2×C8—2061no—
147C4⋊C4—1031no—
148C4⋊C4—4122no—
149C4⋊C4—2061no—
150C4⋊C4—2061no—
151C4⋊C4—2061no—
152C4⋊C4—2061no—
153C4⋊C4C4×D10311yescharacteristic
154C22⋊C4—21no—
155C22⋊C4—2061no—
156C22⋊C4—2061no—
157C22⋊C4—2061no—
158C22⋊C4—2061no—
159C42—1031no—
160C42—1031no—
161C42—1031no—
162C42—1031no—
163C42—2061no—
164C23—21no—
165C23D4×D10311yescharacteristic
166Q8—4121no—
167D4—41no—
168D4—41no—
169D4—41no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—1031no—
176C2×C4—1031no—
177C2×C4—1031no—
178C2×C4—1031no—
179C2×C4—4121no—
180C2×C4—4121no—
181C2×C4—4121no—
182C2×C4—4122no—
183C2×C4—4121no—
184C2×C4—2061no—
185C2×C4—2061no—
186C2×C4—2061no—
187C2×C4—2061no—
188C2×C4C2×C4×D10311yescharacteristic
189C2×C4D4×D10311yescharacteristic
190C8—41no—
191C8—4121no—
192C22—21no—
193C22—21no—
194C22—41no—
195C22—41no—
196C22—41no—
197C22C22⋊C4×D10311yescharacteristic
198C22#1569304511yescharacteristic
199C22#1569305011yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—81no—
204C4—8241no—
205C4—4121no—
206C4—4121no—
207C4—2061no—
208C4—2061no—
209C4—2061no—
210C4—2061no—
211C2—21no—
212C2—21no—
213C2—81no—
214C2#2026776311yescharacteristic
215C2#2026778911yescharacteristic
216C2#2026780611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D103
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#327×C103C2
socleC22×C103C2×C22⋊C4
prime radical#121×C103C22
cosocleC22×C4×C103C23
hypercenter#327D103
hypocenterC103#1512
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. #20267845C2semidirect
3. #20267655C2semidirect
4. #20267529C2semidirect
5. #20267527C2semidirect
9. #15693012C4semidirect
10. #15693008C4semidirect
13. #15692986C4semidirect
15. D4×Dic103C4semidirect
109. C103#1512semidirect

Maximal subgroups

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

subgroupindex
#202683222
#202678452
#202676552
#202675292
#202675272
#202675252
#327×C1032
#1512103