Finite Group Databasebeta

← #27203621

Subgroups — #27203621

Order 13184.

756 conjugacy classes of subgroups; only the 209 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 209 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
1C2×#15693067C211yesmaximal, characteristic
2#20268557C212yesmaximal, complemented
3#20267775C211yesmaximal, characteristic, complemented
4#20267774C214yesmaximal, complemented
5C2×#15692937C212yesmaximal, complemented
6#100×D103C214yesmaximal, complemented
7#413×C103C211yesmaximal, characteristic, complemented
8#15693067—24no—
9#15693067—24no—
10C2×#13110106C2212yes—
11C2×#13110105C412yes—
12C2×#13110105C2211yescharacteristic
13C22×D412C412yes—
14C22×D412C2211yescharacteristic
15C2×D4×D103C414yes—
16C2×D4×D103C2212yes—
17#15693029—24no—
18#15693027—24no—
19C2×#13110089C2212yescomplemented
20M16×D103C2218yescomplemented
21#15692940C2212yescomplemented
22#15692938C2212yescomplemented
23#15692937C2218yescomplemented
24C2×#41×C103C2211yescharacteristic
25C2×M16×C103C2212yescomplemented
26#101×C103C2212yescomplemented
27#100×C103C2212yescomplemented
28C23×D103C2×C412yes—
29C23×D103C2×C414yes—
30#13110106—28no—
31#13110105—24no—
32#13110105—24no—
33#13110105D414yes—
34#13110105D414yes—
35C2×Dic206C2×C411yescharacteristic
36C2×D412—22no—
37C2×D412—22no—
38C2×D412—24no—
39C2×D412—24no—
40C2×D412C2×C414yes—
41C2×D412C2×C412yes—
42C2×D412C2×C411yescharacteristic
43C2×D412C2312yes—
44C2×C22⋊D103C2×C414yes—
45C2×C22⋊D103C2×C412yes—
46D4×D103—216no—
47D4×D103—28no—
48C2×C4×D103C2×C414yes—
49C2×C4×D103C2312yes—
50#13110089—22no—
51#13110089C2314yes—
52#13110088—28no—
53C2×C103⋊C8—22no—
54C8×D103—28no—
55#41×C103—22no—
56#41×C103—22no—
57C2×Q8×C103C2311yescharacteristic
58C2×D4×C103C2×C412yes—
59C2×D4×C103C2311yescharacteristic
60C22×C4×C103C2×C412yes—
61C22×C4×C103C2311yescharacteristic
62M16×C103—22no—
63M16×C103C2314yes—
64C2×C8×C103—22no—
65C23×C103C22×C412yes—
66C23×C103C22×C411yescharacteristic
67C22×D103—24no—
68C22×D103—28no—
69C22×D103—84no—
70C22×D103—82no—
71C22×D103C22×C414yes—
72C22×D103C22×C412yes—
73Q8×C103—22no—
74D4×C103—24no—
75D4×C103—22no—
76C2×C4×C103—22no—
77C2×C4×C103—22no—
78C2×C4×C103C22×C412yes—
79C2×C4×C103C22×C411yescharacteristic
80C2×C4×C103C2×D412yes—
81C2×C4×C103C2×D412yes—
82C2×C4×C103C2411yescharacteristic
83C22⋊D103—28no—
84C22⋊D103C22⋊C418yes—
85C2×Dic103C22×C412yes—
86D412—28no—
87D412—22no—
88D412—22no—
89D412—24no—
90D412C22⋊C412yes—
91D412C22⋊C412yes—
92C4×D103—28no—
93C4×D103C2×D418yes—
94Dic206C22⋊C412yes—
95Dic206C22⋊C412yes—
96C8×C103—24no—
97C103⋊C8—24no—
98C22×C103—22no—
99C22×C103—41no—
100C22×C103—42no—
101C22×C103C2×C22⋊C412yes—
102C22×C103C23×C411yescharacteristic
103C2×D103—24no—
104C2×D103—42no—
105C2×D103—44no—
106C2×D103—88no—
107C2×D103—84no—
108C2×D103C2×C22⋊C414yes—
109C4×C103—22no—
110C4×C103C2×C22⋊C411yescharacteristic
111C4×C103C2×C22⋊C411yescharacteristic
112C4×C103C22×D412yes—
113Dic103C2×C22⋊C414yes—
114C2×C103—21no—
115C2×C103—22no—
116C2×C103—42no—
117C2×C103C22×C22⋊C411yescharacteristic
118D103—24no—
119D103—44no—
120#2888—1031nomaximal, Sylow
121C103#288811yescharacteristic, complemented, Sylow
122C2×H(5,𝔽2)—1031no—
123#568—1032no—
124#413—1031no—
125#413—1034no—
126#413D10311yescharacteristic, complemented
127C2×#100—1032no—
128C2×#100—1034no—
129H(5,𝔽2)—2064no—
130H(5,𝔽2)—2064no—
131C2×#41—1032no—
132C2×#41—1032no—
133C2×#41—1031no—
134C2×#41C2×D10311yescharacteristic
135C22×D4—1034no—
136C22×D4—1032no—
137C22×D4—1032no—
138C22×D4—1031no—
139#131—2064no—
140#131—2064no—
141C2×M16—1032no—
142C2×M16—1038no—
143C2×M16C2×D10312yescomplemented
144#101—1032no—
145#101C2×D10312yescomplemented
146#100—1032no—
147#100—1038no—
148#100C2×D10312yescomplemented
149C24—1034no—
150C24—1032no—
151#41—22no—
152#41—22no—
153#41—1034no—
154#41—1034no—
155#41—2064no—
156#41—2064no—
157#41—2068no—
158C2×Q8—1031no—
159C2×Q8C22×D10311yescharacteristic
160C2×D4—1032no—
161C2×D4—1034no—
162C2×D4—1031no—
163C2×D4—1034no—
164C2×D4—1032no—
165C2×D4—1032no—
166C2×D4—2064no—
167C2×D4—2064no—
168C2×D4—2068no—
169C2×D4—20616no—
170C2×D4—2062no—
171C2×D4—2062no—
172C2×D4C4×D10312yes—
173C2×D4C22×D10311yescharacteristic
174C22×C4—1032no—
175C22×C4—1034no—
176C22×C4C4×D10312yes—
177C22×C4C22×D10311yescharacteristic
178M16—22no—
179M16—1034no—
180M16—2068no—
181M16—2062no—
182M16C22×D10314yes—
183C2×C8—22no—
184C2×C8—2068no—
185C2×C8—2062no—
186C23—8242no—
187C23—8244no—
188C23—1032no—
189C23—1034no—
190C23—2068no—
191C23—2064no—
192C23C2×C4×D10312yes—
193C23C2×C4×D10311yescharacteristic
194Q8—22no—
195Q8—1032no—
196Q8—1032no—
197D4—24no—
198D4—22no—
199D4—1038no—
200D4—1032no—
201D4—1032no—
202D4—2068no—
203D4—2068no—
204D4—2064no—
205D4—2062no—
206D4—2062no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—1032no—
210C2×C4—1038no—
211C2×C4—2068no—
212C2×C4C2×C4×D10312yes—
213C2×C4C2×C4×D10311yescharacteristic
214C2×C4D4×D10312yes—
215C2×C4D4×D10312yes—
216C2×C4C23×D10311yescharacteristic
217C8—24no—
218C8—2064no—
219C22—22no—
220C22—41no—
221C22—42no—
222C22—8244no—
223C22—8248no—
224C22—1034no—
225C22—4124no—
226C22—4122no—
227C22—2064no—
228C22C22⋊C4×D10312yes—
229C22C22×C4×D10311yescharacteristic
230C4—22no—
231C4—1034no—
232C4C22⋊C4×D10311yescharacteristic
233C4C22⋊C4×D10311yescharacteristic
234C4C2×D4×D10312yes—
235C2—21no—
236C2—22no—
237C2—42no—
238C2—4124no—
239C2—2064no—
240C2C2×C22⋊C4×D10311yescharacteristic
subgroupG/H
centerC2C2×C22⋊C4×D103
commutatorC22×C103C23×C4
FrattiniC2×C4C23×D103
Fitting#413×C103C2
socleC2×C103C22×C22⋊C4
prime radicalC2×#15693067C2
cosocleC2×C4×C103C24
hypercenter#413D103
hypocenterC103#2888
LCSG ▷ C22×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C2 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #20268557C2semidirect
3. #20267775C2semidirect
4. #20267774C2semidirect
5. C2×#15692937C2semidirect
6. #100×D103C2semidirect
7. #413×C103C2semidirect
19. C2×#13110089C22semidirect
20. M16×D103C22semidirect
21. #15692940C22semidirect
22. #15692938C22semidirect
23. #15692937C22semidirect
25. C2×M16×C103C22semidirect
26. #101×C103C22semidirect
27. #100×C103C22semidirect
121. C103#2888semidirect
126. #413D103semidirect
143. C2×M16C2×D103semidirect
145. #101C2×D103semidirect
148. #100C2×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156930672
#202685572
#202677752
#202677742
C2×#156929372
#100×D1032
#413×C1032
#2888103