Finite Group Databasebeta

← #27196807

Subgroups — #27196807

Order 13184.

258 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 65 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#20268337C211yesmaximal, characteristic
2#20267765C211yesmaximal, characteristic, complemented
3#20267585C212yesmaximal, complemented
4#20267583C212yesmaximal, complemented
5#410×C103C211yesmaximal, characteristic, complemented
6C2×#13110105C411yescharacteristic, complemented
7#15693019C411yescharacteristic, complemented
8#15693017C2211yescharacteristic
9#15693010C411yescharacteristic, complemented
10#15693008C2211yescharacteristic
11#15692993—21no—
12#15692993—21no—
13C4×C22⋊D103—21no—
14C4×C22⋊D103—21no—
15#15692980—21no—
16C2×C4×Dic103C411yescharacteristic, complemented
17#15692936—21no—
18#15692936C2212yes—
19C2×#41×C103C2211yescharacteristic
20#117×C103—21no—
21#99×C103—21no—
22#99×C103C2212yes—
23#13110105—41no—
24#13110105—41no—
25C2×Dic206C2×C411yescharacteristic
26C2×D412C2×C411yescharacteristic
27C2×C22⋊D103—21no—
28C2×C22⋊D103—21no—
29C2×C22⋊D103—21no—
30C22×Dic103—21no—
31C2×C4×D103—21no—
32C4⋊Dic103—41no—
33Dic103⋊C4—21no—
34Dic103⋊C4—21no—
35C22⋊Dic103—21no—
36C22⋊Dic103—21no—
37C22⋊Dic103—22no—
38(C2×D103)⋊C4—21no—
39(C2×D103)⋊C4—21no—
40C4×Dic103—21no—
41C4×Dic103—41no—
42C4×Dic103C2×C411yescharacteristic
43C4×Dic103C2×C411yescharacteristic
44#41×C103—41no—
45#41×C103—41no—
46C2×Q8×C103C2×C411yescharacteristic
47C2×D4×C103D411yescharacteristic
48C2×D4×C103D411yescharacteristic
49C2×D4×C103C2311yescharacteristic
50C22×C4×C103C2×C411yescharacteristic
51C22×C4×C103D411yescharacteristic
52C22×C4×C103D411yescharacteristic
53C4⋊C4×C103—41no—
54C22⋊C4×C103—22no—
55C42×C103—41no—
56C23×C103C22⋊C411yescharacteristic
57C23×C103C2×D411yescharacteristic
58C23×C103C2×D411yescharacteristic
59C22×D103—21no—
60Q8×C103—41no—
61D4×C103—41no—
62D4×C103—41no—
63D4×C103—41no—
64C2×C4×C103—21no—
65C2×C4×C103—21no—
66C2×C4×C103—21no—
67C2×C4×C103—21no—
68C2×C4×C103—21no—
69C2×C4×C103—21no—
70C2×C4×C103—42no—
71C2×C4×C103C22⋊C411yescharacteristic
72C2×C4×C103C22⋊C411yescharacteristic
73C2×C4×C103C22⋊C411yescharacteristic
74C2×C4×C103C22×C411yescharacteristic
75C22⋊D103—42no—
76C22⋊D103—42no—
77C22⋊D103—42no—
78C2×Dic103—21no—
79C2×Dic103—21no—
80C2×Dic103—21no—
81C2×Dic103—42no—
82C2×Dic103—42no—
83D412—41no—
84C4×D103—41no—
85C4×D103—41no—
86Dic206—41no—
87C22×C103—21no—
88C22×C103—21no—
89C22×C103—21no—
90C22×C103—41no—
91C22×C103—41no—
92C22×C103—41no—
93C22×C103C2×C22⋊C411yescharacteristic
94C2×D103—41no—
95C2×D103—41no—
96C2×D103—41no—
97C4×C103—21no—
98C4×C103—21no—
99C4×C103—21no—
100C4×C103—82no—
101C4×C103#9911yescharacteristic
102C4×C103#9911yescharacteristic
103Dic103—22no—
104Dic103—41no—
105Dic103—41no—
106Dic103—82no—
107C2×C103—21no—
108C2×C103—41no—
109C2×C103—41no—
110C2×C103—41no—
111C2×C103C2×#9911yescharacteristic
112D103—81no—
113#2126—1031nomaximal, Sylow
114C103#212611yescharacteristic, complemented, Sylow
115#532—1031no—
116#410—1031no—
117#410D10311yescharacteristic, complemented
118#354—1032no—
119#353—1032no—
120C2×#41—1031no—
121C2×#41C2×D10311yescharacteristic
122C4⋊Q8—1031no—
123#127—1031no—
124#124—1031no—
125#124—1031no—
126#121—2061no—
127#121—2061no—
128C4×D4—2061no—
129C4×D4—2061no—
130#117—21no—
131#117—2061no—
132C2×C42—1031no—
133#99—21no—
134#99—1032no—
135#99—2061no—
136#99C2×D10312yes—
137#41—41no—
138#41—41no—
139#41—4121no—
140#41—4121no—
141C2×Q8—1031no—
142C2×Q8C4×D10311yescharacteristic
143C2×D4—1031no—
144C2×D4—2061no—
145C2×D4—2061no—
146C2×D4—2061no—
147C2×D4D41211yescharacteristic
148C2×D4C22⋊D10311yescharacteristic
149C2×D4C22×D10311yescharacteristic
150C22×C4—2061no—
151C22×C4—2061no—
152C22×C4C4×D10311yescharacteristic
153C22×C4D41211yescharacteristic
154C22×C4C22⋊D10311yescharacteristic
155C4⋊C4—41no—
156C4⋊C4—4121no—
157C4⋊C4—2061no—
158C4⋊C4—2061no—
159C22⋊C4—22no—
160C22⋊C4—2062no—
161C22⋊C4—2061no—
162C22⋊C4—2061no—
163C22⋊C4—2061no—
164C22⋊C4—2061no—
165C42—41no—
166C42—1031no—
167C42—1031no—
168C42—4121no—
169C42—2061no—
170C23—2061no—
171C23(C2×D103)⋊C411yescharacteristic
172C23C2×C22⋊D10311yescharacteristic
173C23C2×D41211yescharacteristic
174Q8—41no—
175Q8—4121no—
176D4—41no—
177D4—41no—
178D4—41no—
179D4—4121no—
180D4—4122no—
181D4—4122no—
182D4—4122no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—4122no—
191C2×C4—4122no—
192C2×C4—4121no—
193C2×C4—4121no—
194C2×C4—2061no—
195C2×C4—2061no—
196C2×C4—2061no—
197C2×C4(C2×D103)⋊C411yescharacteristic
198C2×C4(C2×D103)⋊C411yescharacteristic
199C2×C4(C2×D103)⋊C411yescharacteristic
200C2×C4C2×C4×D10311yescharacteristic
201C22—21no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—4121no—
208C22—4121no—
209C22—4121no—
210C22C2×(C2×D103)⋊C411yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—82no—
215C4—8242no—
216C4—4121no—
217C4—4121no—
218C4—2062no—
219C4#1569293511yescharacteristic
220C4#1569293511yescharacteristic
221C2—21no—
222C2—41no—
223C2—41no—
224C2—41no—
225C2—8241no—
226C2C2×#1569293511yescharacteristic
subgroupG/H
centerC4#15692935
commutatorC2×C4×C103C22×C4
FrattiniC2×D4C22×D103
Fitting#410×C103C2
socleC2×C103C2×#99
prime radical#20268337C2
cosocleC2×D4×C103C23
hypercenter#410D103
hypocenterC103#2126
LCSG ▷ C2×C4×C103 ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #20267765C2semidirect
3. #20267585C2semidirect
4. #20267583C2semidirect
5. #410×C103C2semidirect
6. C2×#13110105C4semidirect
7. #15693019C4semidirect
9. #15693010C4semidirect
16. C2×C4×Dic103C4semidirect
114. C103#2126semidirect
117. #410D103semidirect

Maximal subgroups

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

subgroupindex
#202683372
#202677652
#202675852
#202675832
#410×C1032
#2126103