Finite Group Databasebeta

← #27193698

Subgroups — #27193698

Order 13184.

284 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 73 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
2C2×C22⋊(C103⋊C8)C211yesmaximal, characteristic, complemented
3#20267527C212yesmaximal, complemented
4#20267524C212yesmaximal, complemented
5#381×C103C211yesmaximal, characteristic, complemented
6C2×#13110105C411yescharacteristic, complemented
7C22×C103⋊C8—21no—
8#15693004—21no—
9#15693000C411yescharacteristic, complemented
10#15693000C2211yescharacteristic
11#15692995C411yescharacteristic, complemented
12#15692995C2211yescharacteristic
13#15692990—21no—
14C4×C22⋊D103—21no—
15C4×C22⋊D103—21no—
16#15692980C411yescharacteristic, complemented
17C22⋊(C103⋊C8)—21no—
18C22⋊(C103⋊C8)C2212yes—
19C23×C4×C103C2211yescharacteristic
20C2×C22⋊C4×C103—21no—
21#95×C103—21no—
22#95×C103C2212yes—
23#13110105—42no—
24C2×Dic206C2×C411yescharacteristic
25C2×D412C2×C411yescharacteristic
26C2×C22⋊D103—21no—
27C2×C22⋊D103—21no—
28C2×C22⋊D103—21no—
29C2×C4×D103—21no—
30C2×C103⋊C8—22no—
31C2×C103⋊C8—42no—
32C4⋊Dic103C2×C411yescharacteristic
33C4⋊Dic103C2×C411yescharacteristic
34Dic103⋊C4—21no—
35Dic103⋊C4—21no—
36C22⋊Dic103—21no—
37C22⋊Dic103—21no—
38C22⋊Dic103—21no—
39(C2×D103)⋊C4—21no—
40(C2×D103)⋊C4—21no—
41C4×Dic103—21no—
42C24×C103D411yescharacteristic
43C22×C4×C103—22no—
44C22×C4×C103—42no—
45C22×C4×C103C2×C411yescharacteristic
46C22×C4×C103C2×C411yescharacteristic
47C22×C4×C103D411yescharacteristic
48C22×C4×C103D411yescharacteristic
49C22×C4×C103D411yescharacteristic
50C22×C4×C103C2311yescharacteristic
51C22⋊C4×C103—42no—
52C23×C103—22no—
53C23×C103—22no—
54C23×C103—41no—
55C23×C103C22⋊C411yescharacteristic
56C23×C103C22⋊C411yescharacteristic
57C23×C103C2×D411yescharacteristic
58C22×D103—21no—
59C2×C4×C103—22no—
60C2×C4×C103—22no—
61C2×C4×C103—41no—
62C2×C4×C103—41no—
63C2×C4×C103—41no—
64C2×C4×C103—41no—
65C2×C4×C103—42no—
66C2×C4×C103—42no—
67C2×C4×C103—42no—
68C2×C4×C103C22⋊C411yescharacteristic
69C2×C4×C103C22⋊C411yescharacteristic
70C2×C4×C103C22×C411yescharacteristic
71C2×C4×C103C2×D411yescharacteristic
72C22⋊D103—42no—
73C22⋊D103—42no—
74C22⋊D103—42no—
75C2×Dic103—21no—
76C2×Dic103—21no—
77C2×Dic103—21no—
78D412—41no—
79C4×D103—42no—
80Dic206—41no—
81C103⋊C8—42no—
82C22×C103—21no—
83C22×C103—21no—
84C22×C103—21no—
85C22×C103—21no—
86C22×C103—21no—
87C22×C103—21no—
88C22×C103—21no—
89C22×C103—44no—
90C22×C103#9912yes—
91C22×C103C2×C22⋊C411yescharacteristic
92C22×C103#13512yes—
93C2×D103—41no—
94C2×D103—41no—
95C2×D103—41no—
96C4×C103—21no—
97C4×C103—21no—
98C4×C103—21no—
99C4×C103—21no—
100C4×C103—82no—
101Dic103—41no—
102Dic103—41no—
103Dic103—41no—
104C2×C103—22no—
105C2×C103—22no—
106C2×C103—41no—
107C2×C103C2×#9911yescharacteristic
108C2×C103#41611yescharacteristic
109C2×C103#42111yescharacteristic
110D103—81no—
111#1516—1031nomaximal, Sylow
112C103#151611yescharacteristic, complemented, Sylow
113#525—1031no—
114C2×C22⋊C8—1031no—
115#381D10311yescharacteristic, complemented
116#328—1032no—
117#327—1032no—
118C2×#41—1031no—
119C23×C4C2×D10311yescharacteristic
120C22×C8—2061no—
121#123—2061no—
122C22⋊Q8—1031no—
123C22⋊Q8—1031no—
124#121—1031no—
125#121—1031no—
126#120—2061no—
127C4×D4—2061no—
128C4×D4—2061no—
129#117—1031no—
130C2×C22⋊C4—21no—
131C22⋊C8—1032no—
132C22⋊C8—2061no—
133#95—21no—
134#95C2×D10312yes—
135C24C22⋊D10311yescharacteristic
136#41—4122no—
137C2×Q8—1031no—
138C2×D4—1031no—
139C2×D4—2061no—
140C2×D4—2061no—
141C2×D4—2061no—
142C22×C4—22no—
143C22×C4—42no—
144C22×C4—2061no—
145C22×C4C4×D10311yescharacteristic
146C22×C4C4×D10311yescharacteristic
147C22×C4D41211yescharacteristic
148C22×C4D41211yescharacteristic
149C22×C4C22⋊D10311yescharacteristic
150C22×C4C22×D10311yescharacteristic
151C2×C8—4122no—
152C2×C8—2062no—
153C4⋊C4—1031no—
154C4⋊C4—1031no—
155C4⋊C4—2061no—
156C4⋊C4—2061no—
157C22⋊C4—42no—
158C22⋊C4—2061no—
159C22⋊C4—2061no—
160C22⋊C4—2061no—
161C22⋊C4—2061no—
162C22⋊C4—2061no—
163C42—2061no—
164C23—22no—
165C23—22no—
166C23—41no—
167C23—2061no—
168C23(C2×D103)⋊C411yescharacteristic
169C23(C2×D103)⋊C411yescharacteristic
170C23C2×C22⋊D10311yescharacteristic
171Q8—4121no—
172D4—4121no—
173D4—4122no—
174D4—4122no—
175D4—4122no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—4122no—
186C2×C4—2061no—
187C2×C4—2061no—
188C2×C4—2061no—
189C2×C4(C2×D103)⋊C411yescharacteristic
190C2×C4(C2×D103)⋊C411yescharacteristic
191C2×C4C2×C4×D10311yescharacteristic
192C2×C4C2×D41211yescharacteristic
193C8—4122no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—4121no—
203C22—4121no—
204C22—4121no—
205C22#1569293512yes—
206C22C2×(C2×D103)⋊C411yescharacteristic
207C22#1569304112yes—
208C4—21no—
209C4—21no—
210C4—21no—
211C4—21no—
212C4—82no—
213C4—4121no—
214C4—4121no—
215C4—4121no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—8241no—
220C2C2×#1569293511yescharacteristic
221C2#2026778511yescharacteristic
222C2#2026780911yescharacteristic
subgroupG/H
centerC22C2×(C2×D103)⋊C4
commutatorC2×C4×C103C22×C4
FrattiniC22×C4C22×D103
Fitting#381×C103C2
socleC22×C103C2×C22⋊C4
prime radical#20268302C2
cosocleC22×C4×C103C23
hypercenter#381D103
hypocenterC103#1516
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C103
UCSC1 ◁ C22 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊(C103⋊C8)C2semidirect
3. #20267527C2semidirect
4. #20267524C2semidirect
5. #381×C103C2semidirect
6. C2×#13110105C4semidirect
9. #15693000C4semidirect
11. #15692995C4semidirect
16. #15692980C4semidirect
112. C103#1516semidirect
115. #381D103semidirect

Maximal subgroups

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

subgroupindex
#202683022
C2×C22⋊(C103⋊C8)2
#202675272
#202675242
#381×C1032
#1516103