Finite Group Databasebeta

← #27205762

Subgroups — #27205762

Order 13184.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#20268414C212yesmaximal, complemented
2#20268188C211yesmaximal, characteristic, complemented
3#20268176C211yesmaximal, characteristic, complemented
4#20268152C212yesmaximal, complemented
5#20268044C211yesmaximal, characteristic
6#20268022C212yesmaximal, complemented
7#20267902C211yesmaximal, characteristic, complemented
8#20267898C211yesmaximal, characteristic, complemented
9#20267876C212yesmaximal, complemented
10#20267749C211yesmaximal, characteristic, complemented
11#470×C103C211yesmaximal, characteristic, complemented
12C2×#13110092C2212yes—
13C2×D824C2211yescharacteristic
14C22×C103⋊C8C2211yescharacteristic
15#15693020C2212yes—
16#15693016—22no—
17#15693010C2212yes—
18#15693007—22no—
19#15693003—22no—
20#15693001—22no—
21#15692995C2212yes—
22Q8×Dic103C2212yes—
23#15692983C2212yes—
24#15692980C2211yescharacteristic
25#15692953C2211yescharacteristic
26#15692952C2212yes—
27#15692945C2212yes—
28#15692943C2212yes—
29#15692941C2212yes—
30#15692931C2211yescharacteristic
31#15692931C2211yescharacteristic
32C8×Dic103C2211yescharacteristic
33C8×Dic103C2211yescharacteristic
34C2×Q16×C103C2211yescharacteristic
35C2×M16×C103C2211yescharacteristic
36C22⋊Q8×C103C2212yes—
37#106×C103C2211yescharacteristic
38#103×C103C2212yes—
39C2×Dic206—22no—
40C2×D412C2312yes—
41C2×C22⋊D103—22no—
42C2×C4×D103—22no—
43#13110092—24no—
44D824—22no—
45C2×C103⋊C8—22no—
46C2×C103⋊C8C2311yescharacteristic
47C2×C103⋊C8C2311yescharacteristic
48C4⋊Dic103—22no—
49C4⋊Dic103D412yes—
50C4⋊Dic103C2312yes—
51Dic103⋊C4—22no—
52C22⋊Dic103D412yes—
53(C2×D103)⋊C4—22no—
54(C2×D103)⋊C4—22no—
55(C2×D103)⋊C4—22no—
56(C2×D103)⋊C4—22no—
57C4×Dic103—22no—
58C4×Dic103C2311yescharacteristic
59C4×Dic103C2311yescharacteristic
60C2×Q8×C103C2312yes—
61C22×C4×C103C2311yescharacteristic
62Q16×C103—22no—
63M16×C103—22no—
64C2×C8×C103C2311yescharacteristic
65C2×C8×C103C2311yescharacteristic
66C4⋊C4×C103—22no—
67C4⋊C4×C103C2312yes—
68C22⋊C4×C103—22no—
69C23×C103C2×D411yescharacteristic
70C22×D103—22no—
71Q8×C103—22no—
72Q8×C103—22no—
73C2×C4×C103—21no—
74C2×C4×C103—21no—
75C2×C4×C103—22no—
76C2×C4×C103—22no—
77C2×C4×C103C2×D411yescharacteristic
78C2×C4×C103C2411yescharacteristic
79C22⋊D103—82no—
80C2×Dic103—22no—
81C2×Dic103C2×D412yes—
82C2×Dic103C2×D412yes—
83D412—22no—
84D412—22no—
85C4×D103—82no—
86Dic206—82no—
87C8×C103—21no—
88C8×C103#4112yes—
89C103⋊C8—21no—
90C103⋊C8#4112yes—
91C22×C103—21no—
92C22×C103—22no—
93C22×C103C22×D411yescharacteristic
94C2×D103—42no—
95C2×D103—42no—
96C2×D103—42no—
97C4×C103—21no—
98C4×C103—42no—
99C4×C103—42no—
100C4×C103C2×#4111yescharacteristic
101C4×C103C2×#4111yescharacteristic
102Dic103—22no—
103Dic103—22no—
104Dic103—42no—
105C2×C103—41no—
106C2×C103#53211yescharacteristic
107C2×C103#57712yes—
108D103—82no—
109#3173—1031nomaximal, Sylow
110C103#317311yescharacteristic, complemented, Sylow
111#542—1032no—
112#498—1031no—
113#495—1031no—
114#489—1032no—
115#470D10311yescharacteristic, complemented
116#469—1031no—
117#465—1032no—
118#442—1031no—
119#441—1031no—
120C4×SD16—1032no—
121#405—1031no—
122C2×Q16C2×D10311yescharacteristic
123C2×SD16—1032no—
124C2×D8—1031no—
125C2×M16C2×D10311yescharacteristic
126C22×C8—1031no—
127C4⋊Q8—1032no—
128#126—2062no—
129#124—1032no—
130#124—2062no—
131#123—2062no—
132C22⋊Q8—2062no—
133C22⋊Q8C2×D10312yes—
134#121—1032no—
135C4×Q8—1032no—
136C4×D4—1032no—
137#117—1031no—
138#106—1031no—
139#106—1032no—
140#106C2×D10311yescharacteristic
141#103—1032no—
142#103C2×D10312yes—
143#102—1032no—
144#102—1032no—
145#97—1031no—
146#97—1031no—
147C4×C8—1031no—
148C4×C8—1031no—
149C2×Q8—2062no—
150C2×Q8C22×D10312yes—
151C2×D4—1032no—
152C2×D4—2062no—
153C22×C4—2062no—
154C22×C4C22×D10311yescharacteristic
155Q16—22no—
156SD16—2064no—
157D8—2062no—
158M16—22no—
159C2×C8—1031no—
160C2×C8—1031no—
161C2×C8—2062no—
162C2×C8C22×D10311yescharacteristic
163C2×C8C22×D10311yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—1032no—
166C4⋊C4—1032no—
167C4⋊C4—2062no—
168C4⋊C4—2062no—
169C4⋊C4C22×D10312yes—
170C22⋊C4—22no—
171C22⋊C4—1032no—
172C22⋊C4—2062no—
173C22⋊C4—2062no—
174C22⋊C4—2062no—
175C22⋊C4—2062no—
176C42—1031no—
177C42—1031no—
178C42—2062no—
179C23—2062no—
180C23D4×D10311yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—8242no—
184D4—8242no—
185D4—2062no—
186D4—2062no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—8242no—
192C2×C4—1032no—
193C2×C4—1032no—
194C2×C4—2062no—
195C2×C4D4×D10311yescharacteristic
196C2×C4C23×D10311yescharacteristic
197C8—21no—
198C8—1032no—
199C8—2061no—
200C8#1311010412yes—
201C22—21no—
202C22—22no—
203C22—4122no—
204C22—4122no—
205C22—4122no—
206C22C2×D4×D10311yescharacteristic
207C4—21no—
208C4—42no—
209C4—42no—
210C4—4122no—
211C4—2062no—
212C4—2062no—
213C4#41×D10311yescharacteristic
214C4C2×#1311010411yescharacteristic
215C2—41no—
216C2—8242no—
217C2#2026833611yescharacteristic
218C2#2026860012yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#470×C103C2
socleC22×C103C22×D4
prime radical#20268044C2
hypercenter#470D103
hypocenterC103#3173
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #20268414C2semidirect
2. #20268188C2semidirect
3. #20268176C2semidirect
4. #20268152C2semidirect
6. #20268022C2semidirect
7. #20267902C2semidirect
8. #20267898C2semidirect
9. #20267876C2semidirect
10. #20267749C2semidirect
11. #470×C103C2semidirect
110. C103#3173semidirect
115. #470D103semidirect

Maximal subgroups

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

subgroupindex
#202684142
#202681882
#202681762
#202681522
#202680442
#202680222
#202679022
#202678982
#202678762
#202677492
#470×C1032
#3173103