Finite Group Databasebeta

← #27205388

Subgroups — #27205388

Order 13184.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#20268396C211yesmaximal, characteristic, complemented
2#20268265C211yesmaximal, characteristic, complemented
3#20268116C212yesmaximal, complemented
4#20268092C212yesmaximal, complemented
5#20267987C212yesmaximal, complemented
6#20267927C212yesmaximal, complemented
7#20267904C212yesmaximal, complemented
8C4×D824C212yesmaximal, complemented
9#433×C103C211yesmaximal, characteristic, complemented
10C22×D412C2211yescharacteristic
11C2×D824C2212yes—
12C2×D824C2212yes—
13#15693018C2211yescharacteristic, complemented
14#15693013C2211yescharacteristic, complemented
15#15693006—22no—
16#15692995C2212yes—
17#15692994—22no—
18C4×D412C2212yes—
19C4×D412C2212yes—
20C4×D412C2212yescomplemented
21#15692983—22no—
22#15692980C2211yescharacteristic
23C22⋊C4×D103—22no—
24#15692955C2212yescomplemented
25#15692953C2212yescomplemented
26#15692943C2212yes—
27#15692943C2212yes—
28#15692943C2212yescomplemented
29#15692943C2212yescomplemented
30#117×C103C2211yescharacteristic
31C4⋊C8×C103C2212yescomplemented
32C22⋊C8×C103C2212yes—
33#97×C103C2211yescharacteristic, complemented
34C4×C8×C103C2211yescharacteristic, complemented
35C23×D103—21no—
36C2×D412—21no—
37C2×D412—24no—
38C2×D412—22no—
39C2×D412C2312yes—
40C2×D412C2312yes—
41C2×C22⋊D103—22no—
42C2×C4×D103—22no—
43C2×C4×D103—22no—
44C2×C4×D103—22no—
45D824—24no—
46D824—24no—
47C4⋊Dic103C2312yes—
48C4⋊Dic103C2312yes—
49Dic103⋊C4—22no—
50C22⋊Dic103—21no—
51(C2×D103)⋊C4—22no—
52(C2×D103)⋊C4—22no—
53(C2×D103)⋊C4—22no—
54(C2×D103)⋊C4—22no—
55C4×Dic103—21no—
56C22×C4×C103C2311yescharacteristic
57C2×C8×C103C2312yes—
58C2×C8×C103C2312yes—
59C4⋊C4×C103D412yes—
60C22⋊C4×C103D412yes—
61C42×C103C2311yescharacteristic
62C42×C103C2311yescharacteristic
63C23×C103C2×D411yescharacteristic
64C22×D103—22no—
65C22×D103—24no—
66C22×D103—22no—
67C22×D103—82no—
68C2×C4×C103—22no—
69C2×C4×C103C2×D412yes—
70C2×C4×C103C2×D412yes—
71C2×C4×C103C2×D411yescharacteristic
72C2×C4×C103C2411yescharacteristic
73C22⋊D103—82no—
74C2×Dic103—22no—
75C2×Dic103—22no—
76D412—24no—
77D412—22no—
78D412—22no—
79D412—22no—
80D412—82no—
81D412#4114yes—
82C4×D103—82no—
83C4×D103—82no—
84C4×D103—82no—
85C8×C103—22no—
86C8×C103—22no—
87C22×C103—21no—
88C22×C103—22no—
89C22×C103C22×D411yescharacteristic
90C2×D103—24no—
91C2×D103—42no—
92C2×D103—42no—
93C2×D103—42no—
94C2×D103—42no—
95C2×D103—42no—
96C2×D103—84no—
97C4×C103—21no—
98C4×C103—22no—
99C4×C103—22no—
100C4×C103C2×#4112yes—
101Dic103—42no—
102Dic103—42no—
103C2×C103—41no—
104C2×C103#52511yescharacteristic
105C2×C103#57612yes—
106D103—44no—
107D103—82no—
108#3122—1031nomaximal, Sylow
109C103#312211yescharacteristic, complemented, Sylow
110#540—1031no—
111#518—1031no—
112#482—1032no—
113#478—1032no—
114#459—1032no—
115#447—1032no—
116#442—1032no—
117C4×D8—1032no—
118#433D10311yescharacteristic, complemented
119C22×D4—1031no—
120C2×D8—1032no—
121C2×D8—1032no—
122#127—1031no—
123#125—1031no—
124#123—2062no—
125#121—1032no—
126#121—2062no—
127C4×D4—1032no—
128C4×D4—1032no—
129C4×D4—1032no—
130C4×D4—2062no—
131#117—1031no—
132#117C2×D10311yescharacteristic
133C2×C22⋊C4—2062no—
134#107—1032no—
135#106—1032no—
136C4⋊C8C2×D10312yescomplemented
137#102—1032no—
138#102—1032no—
139#102—1032no—
140#102—1032no—
141C22⋊C8C2×D10312yes—
142#97C2×D10311yescharacteristic, complemented
143C4×C8C2×D10311yescharacteristic, complemented
144C24—2061no—
145C2×D4—1032no—
146C2×D4—1032no—
147C2×D4—2064no—
148C2×D4—2062no—
149C2×D4—2062no—
150C2×D4—2061no—
151C22×C4—2062no—
152C22×C4—2062no—
153C22×C4—2062no—
154C22×C4C22×D10311yescharacteristic
155D8—2064no—
156D8—2064no—
157C2×C8C22×D10312yes—
158C2×C8C22×D10312yes—
159C4⋊C4—1032no—
160C4⋊C4—1032no—
161C4⋊C4—2062no—
162C4⋊C4D41212yes—
163C22⋊C4—2061no—
164C22⋊C4—2062no—
165C22⋊C4—2062no—
166C22⋊C4—2062no—
167C22⋊C4—2062no—
168C22⋊C4D41212yes—
169C42—2061no—
170C42C22×D10311yescharacteristic
171C42C22×D10311yescharacteristic
172C23—8242no—
173C23—2064no—
174C23—2062no—
175C23—2062no—
176C23C2×D41211yescharacteristic
177D4—8242no—
178D4—8242no—
179D4—1034no—
180D4—2064no—
181D4—2062no—
182D4—2062no—
183D4—2062no—
184C2×C4—22no—
185C2×C4—8242no—
186C2×C4—8242no—
187C2×C4—8242no—
188C2×C4—2062no—
189C2×C4—2062no—
190C2×C4C2×D41211yescharacteristic
191C2×C4C2×D41212yes—
192C2×C4C2×D41212yes—
193C2×C4C23×D10311yescharacteristic
194C8—22no—
195C8—22no—
196C22—21no—
197C22—22no—
198C22—8244no—
199C22—4122no—
200C22—4122no—
201C22—4122no—
202C22—4122no—
203C22—4122no—
204C22—2064no—
205C22C22×D41211yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—4122no—
210C4—4122no—
211C4#41×D10312yes—
212C2—41no—
213C2—8242no—
214C2—4124no—
215C2#2026830311yescharacteristic
216C2#2026859612yes—
subgroupG/H
centerC22C22×D412
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#433×C103C2
socleC22×C103C22×D4
hypercenter#433D103
hypocenterC103#3122
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #20268396C2semidirect
2. #20268265C2semidirect
3. #20268116C2semidirect
4. #20268092C2semidirect
5. #20267987C2semidirect
6. #20267927C2semidirect
7. #20267904C2semidirect
8. C4×D824C2semidirect
9. #433×C103C2semidirect
13. #15693018C22semidirect
14. #15693013C22semidirect
20. C4×D412C22semidirect
24. #15692955C22semidirect
25. #15692953C22semidirect
28. #15692943C22semidirect
29. #15692943C22semidirect
31. C4⋊C8×C103C22semidirect
33. #97×C103C22semidirect
34. C4×C8×C103C22semidirect
109. C103#3122semidirect
118. #433D103semidirect
136. C4⋊C8C2×D103semidirect
142. #97C2×D103semidirect
143. C4×C8C2×D103semidirect

Maximal subgroups

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

subgroupindex
#202683962
#202682652
#202681162
#202680922
#202679872
#202679272
#202679042
C4×D8242
#433×C1032
#3122103