Finite Group Databasebeta

← #27205789

Subgroups — #27205789

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#20268394C212yesmaximal, complemented
2#20268191C211yesmaximal, characteristic, complemented
3#20268166C211yesmaximal, characteristic, complemented
4#20268154C212yesmaximal, complemented
5#20268044C211yesmaximal, characteristic, complemented
6#20268025C212yesmaximal, complemented
7#20267903C211yesmaximal, characteristic, complemented
8#20267902C211yesmaximal, characteristic, complemented
9#20267871C212yesmaximal, complemented
10#20267749C211yesmaximal, characteristic, complemented
11#469×C103C211yesmaximal, characteristic, complemented
12C2×D824C2211yescharacteristic
13C2×#13110090C2212yes—
14C22×C103⋊C8C2211yescharacteristic
15#15693017C2212yes—
16#15693012C2212yes—
17#15693005—22no—
18#15693003—22no—
19#15692995C2212yes—
20#15692993—22no—
21#15692992—22no—
22D4×Dic103C2212yes—
23#15692983C2212yes—
24#15692980C2211yescharacteristic
25#15692954C2212yes—
26#15692953C2211yescharacteristic
27#15692943C2212yes—
28#15692942C2212yes—
29#15692941C2212yes—
30#15692931C2211yescharacteristic
31#15692931C2211yescharacteristic
32C8×Dic103C2211yescharacteristic
33C8×Dic103C2211yescharacteristic
34C2×D8×C103C2211yescharacteristic
35C2×M16×C103C2211yescharacteristic
36#121×C103C2212yes—
37#106×C103C2211yescharacteristic
38#102×C103C2212yes—
39C2×D412C2312yes—
40C2×C22⋊D103—22no—
41C2×C22⋊D103—22no—
42C2×C22⋊D103—22no—
43C22×Dic103—22no—
44C2×C4×D103—22no—
45D824—22no—
46#13110090—24no—
47C2×C103⋊C8—22no—
48C2×C103⋊C8C2311yescharacteristic
49C2×C103⋊C8C2311yescharacteristic
50C4⋊Dic103—22no—
51C4⋊Dic103D412yes—
52C4⋊Dic103C2312yes—
53Dic103⋊C4—22no—
54C22⋊Dic103—22no—
55C22⋊Dic103D412yes—
56(C2×D103)⋊C4—22no—
57(C2×D103)⋊C4—22no—
58C4×Dic103C2311yescharacteristic
59C4×Dic103C2311yescharacteristic
60C2×D4×C103—22no—
61C2×D4×C103C2312yes—
62C22×C4×C103C2311yescharacteristic
63D8×C103—22no—
64M16×C103—22no—
65C2×C8×C103C2311yescharacteristic
66C2×C8×C103C2311yescharacteristic
67C4⋊C4×C103C2312yes—
68C22⋊C4×C103—22no—
69C23×C103—22no—
70C23×C103C2×D411yescharacteristic
71C22×D103—22no—
72D4×C103—22no—
73D4×C103—22no—
74D4×C103—82no—
75C2×C4×C103—21no—
76C2×C4×C103—21no—
77C2×C4×C103—22no—
78C2×C4×C103C2×D411yescharacteristic
79C2×C4×C103C2411yescharacteristic
80C22⋊D103—82no—
81C22⋊D103—82no—
82C22⋊D103—82no—
83C2×Dic103—22no—
84C2×Dic103—82no—
85C2×Dic103C2×D412yes—
86C2×Dic103C2×D412yes—
87D412—22no—
88D412—22no—
89C4×D103—82no—
90C8×C103—21no—
91C8×C103#4112yes—
92C103⋊C8—21no—
93C103⋊C8#4112yes—
94C22×C103—21no—
95C22×C103—22no—
96C22×C103—42no—
97C22×C103—42no—
98C22×C103—42no—
99C22×C103C22×D411yescharacteristic
100C2×D103—42no—
101C2×D103—42no—
102C2×D103—42no—
103C4×C103—21no—
104C4×C103—42no—
105C4×C103C2×#4111yescharacteristic
106C4×C103C2×#4111yescharacteristic
107Dic103—22no—
108Dic103—22no—
109Dic103—42no—
110C2×C103—41no—
111C2×C103—82no—
112C2×C103#53211yescharacteristic
113C2×C103#57612yes—
114D103—82no—
115#3176—1031nomaximal, Sylow
116C103#317611yescharacteristic, complemented, Sylow
117#540—1032no—
118#499—1031no—
119#493—1031no—
120#490—1032no—
121#469—1031no—
122#469D10311yescharacteristic, complemented
123#466—1032no—
124#442—1031no—
125#442—1031no—
126C4×D8—1032no—
127#405—1031no—
128C2×D8—1032no—
129C2×D8—1031no—
130C2×D8C2×D10311yescharacteristic
131C2×M16C2×D10311yescharacteristic
132C22×C8—1031no—
133#127—1032no—
134#125—1032no—
135#123—2062no—
136#123—2062no—
137#121—1032no—
138#121—2062no—
139#121—2062no—
140#121C2×D10312yes—
141C4×D4—1032no—
142C4×D4—1032no—
143#117—1031no—
144#107—1032no—
145#106—1031no—
146#106C2×D10311yescharacteristic
147#102—1032no—
148#102—1032no—
149#102—1032no—
150#102C2×D10312yes—
151#97—1031no—
152#97—1031no—
153C4×C8—1031no—
154C4×C8—1031no—
155C2×D4—22no—
156C2×D4—1032no—
157C2×D4—2062no—
158C2×D4—2062no—
159C2×D4—2062no—
160C2×D4C22×D10312yes—
161C22×C4—2062no—
162C22×C4—2062no—
163C22×C4C22×D10311yescharacteristic
164D8—22no—
165D8—2064no—
166D8—2062no—
167M16—22no—
168C2×C8—1031no—
169C2×C8—1031no—
170C2×C8—2062no—
171C2×C8C22×D10311yescharacteristic
172C2×C8C22×D10311yescharacteristic
173C4⋊C4—1032no—
174C4⋊C4—1032no—
175C4⋊C4—2062no—
176C4⋊C4—2062no—
177C4⋊C4C22×D10312yes—
178C22⋊C4—22no—
179C22⋊C4—1032no—
180C22⋊C4—2062no—
181C22⋊C4—2062no—
182C22⋊C4—2062no—
183C42—1031no—
184C42—1031no—
185C23—22no—
186C23—2062no—
187C23D4×D10311yescharacteristic
188D4—22no—
189D4—22no—
190D4—82no—
191D4—8242no—
192D4—8242no—
193D4—8242no—
194D4—2062no—
195D4—2062no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—22no—
199C2×C4—8242no—
200C2×C4—8242no—
201C2×C4—1032no—
202C2×C4—1032no—
203C2×C4—2062no—
204C2×C4D4×D10311yescharacteristic
205C2×C4C23×D10311yescharacteristic
206C8—21no—
207C8—1032no—
208C8—2061no—
209C8#1311010412yes—
210C22—21no—
211C22—22no—
212C22—42no—
213C22—42no—
214C22—42no—
215C22—4122no—
216C22—4122no—
217C22—4122no—
218C22C2×D4×D10311yescharacteristic
219C4—21no—
220C4—42no—
221C4—4122no—
222C4—2062no—
223C4—2062no—
224C4#41×D10311yescharacteristic
225C4C2×#1311010411yescharacteristic
226C2—41no—
227C2—82no—
228C2—8242no—
229C2#2026833611yescharacteristic
230C2#2026859512yes—
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#469×C103C2
socleC22×C103C22×D4
hypercenter#469D103
hypocenterC103#3176
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #20268394C2semidirect
2. #20268191C2semidirect
3. #20268166C2semidirect
4. #20268154C2semidirect
5. #20268044C2semidirect
6. #20268025C2semidirect
7. #20267903C2semidirect
8. #20267902C2semidirect
9. #20267871C2semidirect
10. #20267749C2semidirect
11. #469×C103C2semidirect
116. C103#3176semidirect
122. #469D103semidirect

Maximal subgroups

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

subgroupindex
#202683942
#202681912
#202681662
#202681542
#202680442
#202680252
#202679032
#202679022
#202678712
#202677492
#469×C1032
#3176103