Finite Group Databasebeta

← #27193636

Subgroups — #27193636

Order 13184.

304 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 77 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#20268302C211yesmaximal, characteristic
2C4×C22⋊Dic103C211yesmaximal, characteristic, complemented
3#20267529C212yesmaximal, complemented
4#20267526C212yesmaximal, complemented
5C2×C22⋊C8×C103C211yesmaximal, characteristic, complemented
6C2×#13110105C411yescharacteristic, complemented
7#15693004—21no—
8#15693000C411yescharacteristic, complemented
9#15693000C2211yescharacteristic
10#15692995C411yescharacteristic, complemented
11#15692995C2211yescharacteristic
12#15692990—21no—
13C4×C22⋊D103—21no—
14C4×C22⋊D103—21no—
15#15692980C411yescharacteristic, complemented
16C2×C22⋊Dic103—21no—
17C2×C4×Dic103—21no—
18C103⋊#95C2212yes—
19C23×C4×C103C2211yescharacteristic
20C22×C8×C103—21no—
21C22⋊C8×C103—21no—
22C22⋊C8×C103C2212yes—
23#13110105—42no—
24C2×Dic206C2×C411yescharacteristic
25C2×D412C2×C411yescharacteristic
26C2×C22⋊D103—21no—
27C2×C22⋊D103—21no—
28C2×C22⋊D103—21no—
29C22×Dic103—22no—
30C2×C4×D103—21no—
31C4⋊Dic103C2×C411yescharacteristic
32C4⋊Dic103C2×C411yescharacteristic
33Dic103⋊C4—21no—
34Dic103⋊C4—21no—
35C22⋊Dic103—24no—
36C22⋊Dic103—21no—
37C22⋊Dic103—21no—
38C22⋊Dic103—21no—
39(C2×D103)⋊C4—21no—
40(C2×D103)⋊C4—21no—
41C4×Dic103—21no—
42C4×Dic103—42no—
43C24×C103D411yescharacteristic
44C22×C4×C103—42no—
45C22×C4×C103C2×C411yescharacteristic
46C22×C4×C103C2×C411yescharacteristic
47C22×C4×C103D411yescharacteristic
48C22×C4×C103D411yescharacteristic
49C22×C4×C103D411yescharacteristic
50C22×C4×C103C2311yescharacteristic
51C2×C8×C103—22no—
52C2×C8×C103—42no—
53C23×C103—22no—
54C23×C103—22no—
55C23×C103—41no—
56C23×C103C22⋊C411yescharacteristic
57C23×C103C22⋊C411yescharacteristic
58C23×C103C2×D411yescharacteristic
59C22×D103—21no—
60C2×C4×C103—22no—
61C2×C4×C103—22no—
62C2×C4×C103—22no—
63C2×C4×C103—41no—
64C2×C4×C103—41no—
65C2×C4×C103—41no—
66C2×C4×C103C22⋊C411yescharacteristic
67C2×C4×C103C22⋊C411yescharacteristic
68C2×C4×C103C22×C411yescharacteristic
69C2×C4×C103C2×D411yescharacteristic
70C22⋊D103—42no—
71C22⋊D103—42no—
72C22⋊D103—42no—
73C2×Dic103—24no—
74C2×Dic103—21no—
75C2×Dic103—21no—
76C2×Dic103—21no—
77C2×Dic103—42no—
78C2×Dic103—42no—
79D412—41no—
80C4×D103—42no—
81Dic206—41no—
82C8×C103—42no—
83C22×C103—21no—
84C22×C103—21no—
85C22×C103—21no—
86C22×C103—21no—
87C22×C103—21no—
88C22×C103—21no—
89C22×C103—21no—
90C22×C103—44no—
91C22×C103#10412yes—
92C22×C103C2×C22⋊C411yescharacteristic
93C22×C103#13512yes—
94C2×D103—41no—
95C2×D103—41no—
96C2×D103—41no—
97C4×C103—21no—
98C4×C103—21no—
99C4×C103—21no—
100C4×C103#9912yes—
101Dic103—44no—
102Dic103—41no—
103Dic103—41no—
104Dic103—41no—
105C2×C103—22no—
106C2×C103—22no—
107C2×C103—41no—
108C2×C103C2×#9911yescharacteristic
109C2×C103#41611yescharacteristic
110C2×C103C2×#10411yescharacteristic
111D103—81no—
112#1501—1031nomaximal, Sylow
113C103#150111yescharacteristic, complemented, Sylow
114#525—1031no—
115C2×C22⋊C8D10311yescharacteristic, complemented
116C4×C22⋊C4—1031no—
117#328—1032no—
118#327—1032no—
119C2×#41—1031no—
120C23×C4C2×D10311yescharacteristic
121C22×C8—21no—
122#123—2061no—
123C22⋊Q8—1031no—
124C22⋊Q8—1031no—
125#121—1031no—
126#121—1031no—
127#120—2061no—
128C4×D4—2061no—
129C4×D4—2061no—
130#117—1031no—
131C2×C22⋊C4—2061no—
132C2×C42—2061no—
133C22⋊C8—21no—
134C22⋊C8C2×D10312yes—
135#95—1032no—
136C24D41211yescharacteristic
137#41—4122no—
138C2×Q8—1031no—
139C2×D4—1031no—
140C2×D4—2061no—
141C2×D4—2061no—
142C2×D4—2061no—
143C22×C4—42no—
144C22×C4—2062no—
145C22×C4—2061no—
146C22×C4C4×D10311yescharacteristic
147C22×C4C4×D10311yescharacteristic
148C22×C4D41211yescharacteristic
149C22×C4C22⋊D10311yescharacteristic
150C22×C4C22⋊D10311yescharacteristic
151C22×C4C22×D10311yescharacteristic
152C2×C8—22no—
153C2×C8—42no—
154C4⋊C4—1031no—
155C4⋊C4—1031no—
156C4⋊C4—2061no—
157C4⋊C4—2061no—
158C22⋊C4—2064no—
159C22⋊C4—2061no—
160C22⋊C4—2061no—
161C22⋊C4—2061no—
162C22⋊C4—2061no—
163C22⋊C4—2061no—
164C42—4122no—
165C42—2061no—
166C23—22no—
167C23—22no—
168C23—41no—
169C23—2061no—
170C23(C2×D103)⋊C411yescharacteristic
171C23(C2×D103)⋊C411yescharacteristic
172C23C2×D41211yescharacteristic
173Q8—4121no—
174D4—4121no—
175D4—4122no—
176D4—4122no—
177D4—4122no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—4122no—
185C2×C4—4122no—
186C2×C4—4122no—
187C2×C4—2064no—
188C2×C4—2061no—
189C2×C4—2061no—
190C2×C4—2061no—
191C2×C4(C2×D103)⋊C411yescharacteristic
192C2×C4(C2×D103)⋊C411yescharacteristic
193C2×C4C2×C4×D10311yescharacteristic
194C2×C4C2×C22⋊D10311yescharacteristic
195C8—42no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—44no—
204C22—4121no—
205C22—4121no—
206C22—4121no—
207C22#1569294712yes—
208C22C2×(C2×D103)⋊C411yescharacteristic
209C22#1569304312yes—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—4124no—
214C4—4121no—
215C4—4121no—
216C4—4121no—
217C4#1569293512yes—
218C2—22no—
219C2—22no—
220C2—41no—
221C2—8241no—
222C2C2×#1569293511yescharacteristic
223C2#2026778811yescharacteristic
224C2C2×#1569294711yescharacteristic
subgroupG/H
centerC2×C4(C2×D103)⋊C4
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
FittingC2×C22⋊C8×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268302C2
cosocleC22×C4×C103C23
hypercenterC2×C22⋊C8D103
hypocenterC103#1501
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C4×C22⋊Dic103C2semidirect
3. #20267529C2semidirect
4. #20267526C2semidirect
5. C2×C22⋊C8×C103C2semidirect
6. C2×#13110105C4semidirect
8. #15693000C4semidirect
10. #15692995C4semidirect
15. #15692980C4semidirect
113. C103#1501semidirect
115. C2×C22⋊C8D103semidirect

Maximal subgroups

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

subgroupindex
#202683022
C4×C22⋊Dic1032
#202675292
#202675262
C2×C22⋊C8×C1032
#1501103