Finite Group Databasebeta

← #27205790

Subgroups — #27205790

Order 13184.

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

normal subgroups only

This group has 386 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#20268392C212yesmaximal, complemented
2#20268192C211yesmaximal, characteristic, complemented
3#20268166C211yesmaximal, characteristic, complemented
4#20268154C212yesmaximal, complemented
5#20268043C212yesmaximal, complemented
6#20268028C211yesmaximal, characteristic, complemented
7#20268024C211yesmaximal, characteristic, complemented
8#20267901C212yesmaximal, complemented
9C4×D824C211yesmaximal, characteristic, complemented
10#20267745C211yesmaximal, characteristic, complemented
11C4×D8×C103C211yesmaximal, characteristic, complemented
12C2×D824C2211yescharacteristic
13C2×#13110090C2212yes—
14C2×#13110088C2211yescharacteristic
15C2×C8×D103C2211yescharacteristic
16#15693017C2212yes—
17#15693012C2212yes—
18#15693004—22no—
19#15693003—22no—
20#15692996C2212yes—
21#15692995—22no—
22#15692994—22no—
23#15692992C2212yes—
24C4×D412C2212yes—
25#15692978C2211yescharacteristic
26#15692955C2211yescharacteristic
27#15692952C2212yes—
28#15692943C2212yes—
29#15692942C2212yes—
30#15692941C2212yes—
31#15692932C2211yescharacteristic
32#15692931C2211yescharacteristic
33C8×Dic103C2211yescharacteristic
34C2×D8×C103C2211yescharacteristic
35C4×D4×C103C2212yes—
36#107×C103C2211yescharacteristic
37#102×C103C2212yes—
38C4×C8×C103C2211yescharacteristic
39C2×D412—22no—
40C2×D412C2312yes—
41C2×C22⋊D103—22no—
42C2×C22⋊D103—22no—
43C2×C22⋊D103—22no—
44C2×C4×D103—22no—
45C2×C4×D103C2311yescharacteristic
46D824—22no—
47#13110090—24no—
48#13110088—22no—
49C2×C103⋊C8C2311yescharacteristic
50C2×C103⋊C8C2311yescharacteristic
51C8×D103—22no—
52C4⋊Dic103—22no—
53C4⋊Dic103C2312yes—
54Dic103⋊C4—22no—
55Dic103⋊C4D411yescharacteristic
56Dic103⋊C4D411yescharacteristic
57C22⋊Dic103—22no—
58(C2×D103)⋊C4—22no—
59(C2×D103)⋊C4—22no—
60(C2×D103)⋊C4D411yescharacteristic
61(C2×D103)⋊C4D411yescharacteristic
62C4×Dic103C2311yescharacteristic
63C2×D4×C103C2312yes—
64C22×C4×C103—22no—
65D8×C103—22no—
66C2×C8×C103C2311yescharacteristic
67C2×C8×C103C2311yescharacteristic
68C4⋊C4×C103C2312yes—
69C22⋊C4×C103—22no—
70C42×C103C2311yescharacteristic
71C23×C103—22no—
72C22×D103—22no—
73C22×D103C2×D411yescharacteristic
74D4×C103—22no—
75D4×C103—22no—
76C2×C4×C103—22no—
77C2×C4×C103—82no—
78C2×C4×C103C2×D411yescharacteristic
79C2×C4×C103C2×D411yescharacteristic
80C2×C4×C103C2411yescharacteristic
81C22⋊D103—82no—
82C22⋊D103—82no—
83C22⋊D103—82no—
84C2×Dic103—22no—
85C2×Dic103C2×D411yescharacteristic
86C2×Dic103C2×D411yescharacteristic
87C2×Dic103C2×D411yescharacteristic
88D412—22no—
89D412—22no—
90D412—82no—
91C4×D103—21no—
92C4×D103—21no—
93C4×D103—82no—
94C8×C103—21no—
95C8×C103#4112yes—
96C103⋊C8—21no—
97C103⋊C8#4112yes—
98C22×C103—42no—
99C22×C103—42no—
100C22×C103—42no—
101C22×C103C22×D411yescharacteristic
102C2×D103—21no—
103C2×D103—21no—
104C2×D103—21no—
105C2×D103—42no—
106C2×D103—42no—
107C2×D103—42no—
108C4×C103—21no—
109C4×C103—21no—
110C4×C103—42no—
111C4×C103C2×#4111yescharacteristic
112C4×C103C2×#4111yescharacteristic
113Dic103—21no—
114Dic103—21no—
115Dic103—21no—
116Dic103—42no—
117C2×C103—82no—
118C2×C103#53211yescharacteristic
119C2×C103#57611yescharacteristic
120C2×C103#57611yescharacteristic
121D103—41no—
122D103—82no—
123#3176—1031nomaximal, Sylow
124C103#317611yescharacteristic, complemented, Sylow
125#540—1032no—
126#499—1031no—
127#493—1031no—
128#490—1032no—
129#469—1032no—
130#466—1031no—
131#466—1031no—
132#442—1032no—
133C4×D8—1031no—
134C4×D8D10311yescharacteristic, complemented
135#405—1031no—
136C2×D8—1032no—
137C2×D8—1031no—
138C2×D8C2×D10311yescharacteristic
139C2×M16—1031no—
140C22×C8—1031no—
141#127—1032no—
142#125—1032no—
143#123—2062no—
144#123—2062no—
145#121—1032no—
146#121—1032no—
147#121—2062no—
148#121—2062no—
149C4×D4—1032no—
150C4×D4C2×D10312yes—
151#117—1031no—
152#107—1031no—
153#107C2×D10311yescharacteristic
154#106—1032no—
155#102—1032no—
156#102—1032no—
157#102—1032no—
158#102C2×D10312yes—
159#97—1031no—
160#97—1031no—
161C4×C8—1031no—
162C4×C8C2×D10311yescharacteristic
163C2×D4—1032no—
164C2×D4—2062no—
165C2×D4—2062no—
166C2×D4—2062no—
167C2×D4—2062no—
168C2×D4C22×D10312yes—
169C22×C4—22no—
170C22×C4—1031no—
171C22×C4—2062no—
172D8—22no—
173D8—2064no—
174D8—2062no—
175M16—2062no—
176C2×C8—1031no—
177C2×C8—1031no—
178C2×C8—2062no—
179C2×C8C22×D10311yescharacteristic
180C2×C8C22×D10311yescharacteristic
181C4⋊C4—1031no—
182C4⋊C4—1031no—
183C4⋊C4—1032no—
184C4⋊C4—2062no—
185C4⋊C4—2062no—
186C4⋊C4C22×D10312yes—
187C22⋊C4—22no—
188C22⋊C4—1031no—
189C22⋊C4—1031no—
190C22⋊C4—2062no—
191C22⋊C4—2062no—
192C22⋊C4—2062no—
193C42—1031no—
194C42C22×D10311yescharacteristic
195C23—22no—
196C23—1031no—
197C23—2062no—
198D4—22no—
199D4—22no—
200D4—8242no—
201D4—8242no—
202D4—8242no—
203D4—8242no—
204D4—2062no—
205D4—2062no—
206C2×C4—22no—
207C2×C4—82no—
208C2×C4—8242no—
209C2×C4—1031no—
210C2×C4—1031no—
211C2×C4—1031no—
212C2×C4—2062no—
213C2×C4—2061no—
214C2×C4—2061no—
215C2×C4D4×D10311yescharacteristic
216C2×C4D4×D10311yescharacteristic
217C2×C4C23×D10311yescharacteristic
218C8—21no—
219C8—1032no—
220C8—2061no—
221C8#1311010512yes—
222C22—42no—
223C22—42no—
224C22—42no—
225C22—4122no—
226C22—4122no—
227C22—4122no—
228C22—2061no—
229C22—2061no—
230C22—2061no—
231C22C2×D4×D10311yescharacteristic
232C4—21no—
233C4—21no—
234C4—42no—
235C4—4122no—
236C4—2061no—
237C4—2061no—
238C4—2061no—
239C4#41×D10311yescharacteristic
240C4C2×#1311010511yescharacteristic
241C2—82no—
242C2—8242no—
243C2—4121no—
244C2#2026833811yescharacteristic
245C2#2026859211yescharacteristic
246C2#2026859311yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC4×D8×C103C2
socleC22×C103C22×D4
hypercenterC4×D8D103
hypocenterC103#3176
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #20268392C2semidirect
2. #20268192C2semidirect
3. #20268166C2semidirect
4. #20268154C2semidirect
5. #20268043C2semidirect
6. #20268028C2semidirect
7. #20268024C2semidirect
8. #20267901C2semidirect
9. C4×D824C2semidirect
10. #20267745C2semidirect
11. C4×D8×C103C2semidirect
124. C103#3176semidirect
134. C4×D8D103semidirect

Maximal subgroups

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

subgroupindex
#202683922
#202681922
#202681662
#202681542
#202680432
#202680282
#202680242
#202679012
C4×D8242
#202677452
C4×D8×C1032
#3176103