Finite Group Databasebeta

← #27204971

Subgroups — #27204971

Order 13184.

398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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#20268422C211yesmaximal, characteristic, complemented
2#20268266C211yesmaximal, characteristic
3#20268093C212yesmaximal, complemented
4#20268089C212yesmaximal, complemented
5#20268079C212yesmaximal, complemented
6#20268069C212yesmaximal, complemented
7#20267831C211yesmaximal, characteristic, complemented
8#20267829C211yesmaximal, characteristic, complemented
9#20267817C211yesmaximal, characteristic, complemented
10#20267796C211yesmaximal, characteristic
11C2×#102×C103C211yesmaximal, characteristic
12C2×#13110089C2211yescharacteristic
13#15693020—21no—
14#15693020C2212yescomplemented
15#15693012—21no—
16#15693012C2212yescomplemented
17#15693000—22no—
18D4×Dic103—21no—
19D4×Dic103—21no—
20D4×Dic103C2212yes—
21D4×Dic103C2212yes—
22#15692980C2211yescharacteristic
23#15692980C2211yescharacteristic
24#15692980C2211yescharacteristic
25C2×C22⋊Dic103—22no—
26#15692955C2211yescharacteristic, complemented
27#15692955C2211yescharacteristic, complemented
28#15692954C2212yescomplemented
29#15692953C2211yescharacteristic, complemented
30#15692953C2211yescharacteristic, complemented
31#15692952C2212yescomplemented
32Dic103⋊C8C2212yescomplemented
33Dic103⋊C8C2212yescomplemented
34#15692942C2212yes—
35#15692942C2212yes—
36C22×D4×C103C2211yescharacteristic
37C22×C8×C103C2211yescharacteristic
38C2×C4⋊C4×C103C2211yescharacteristic
39#102×C103C2212yes—
40#102×C103C2212yes—
41C2×Dic206—22no—
42C22×Dic103—22no—
43C22×Dic103—22no—
44#13110089—22no—
45C2×C103⋊C8C2312yes—
46C4⋊Dic103—22no—
47C4⋊Dic103D411yescharacteristic
48C4⋊Dic103D411yescharacteristic
49C4⋊Dic103C2311yescharacteristic
50C4⋊Dic103C2311yescharacteristic
51C4⋊Dic103C2311yescharacteristic
52C4⋊Dic103C2311yescharacteristic
53Dic103⋊C4—22no—
54Dic103⋊C4—22no—
55C22⋊Dic103—21no—
56C22⋊Dic103—21no—
57C22⋊Dic103—22no—
58C22⋊Dic103—22no—
59C22⋊Dic103D412yes—
60C4×Dic103—21no—
61C4×Dic103—21no—
62C4×Dic103C2312yes—
63C24×C103—21no—
64C2×D4×C103—21no—
65C2×D4×C103—22no—
66C2×D4×C103Q814yescomplemented
67C2×D4×C103C2312yes—
68C22×C4×C103—21no—
69C22×C4×C103C2311yescharacteristic
70C2×C8×C103—22no—
71C2×C8×C103C2311yescharacteristic
72C2×C8×C103C2311yescharacteristic
73C4⋊C4×C103—21no—
74C4⋊C4×C103C2312yes—
75C23×C103—22no—
76C23×C103—24no—
77C23×C103—81no—
78C23×C103—81no—
79C23×C103C2×D411yescharacteristic
80D4×C103—24no—
81D4×C103—22no—
82D4×C103C2×Q814yes—
83C2×C4×C103—22no—
84C2×C4×C103—81no—
85C2×C4×C103C2×D411yescharacteristic
86C2×C4×C103C2×Q812yes—
87C2×C4×C103#4112yes—
88C2×C4×C103C2411yescharacteristic
89C2×Dic103—21no—
90C2×Dic103—21no—
91C2×Dic103—21no—
92C2×Dic103—21no—
93C2×Dic103—82no—
94C2×Dic103—82no—
95C2×Dic103C2×D412yes—
96C2×Dic103C2×D412yes—
97Dic206—82no—
98C8×C103—21no—
99C8×C103—21no—
100C103⋊C8—22no—
101C22×C103—21no—
102C22×C103—21no—
103C22×C103—24no—
104C22×C103—42no—
105C22×C103—42no—
106C22×C103—84no—
107C22×C103C22⋊Q812yes—
108C22×C103C22×D411yescharacteristic
109C4×C103—42no—
110C4×C103C22⋊Q812yes—
111C4×C103C22×Q811yescharacteristic
112C4×C103C2×#4111yescharacteristic
113Dic103—22no—
114Dic103—22no—
115Dic103—41no—
116Dic103—41no—
117Dic103—41no—
118Dic103—41no—
119C2×C103—22no—
120C2×C103—44no—
121C2×C103C2×C22⋊Q811yescharacteristic
122C2×C103#57611yescharacteristic
123C2×C103#57711yescharacteristic
124#3081—1031nomaximal, Sylow
125C103#308111yescharacteristic, complemented, Sylow
126#544—1031no—
127#518—1031no—
128#478—1032no—
129#478—1032no—
130#476—1032no—
131#474—1032no—
132#428—1031no—
133#427—1031no—
134#424—1031no—
135#418—1031no—
136C2×#102D10311yescharacteristic
137C22×D4C2×D10311yescharacteristic
138C2×M16—1031no—
139C22×C8C2×D10311yescharacteristic
140C4⋊Q8—1032no—
141C4⋊Q8—2061no—
142#125—1032no—
143#125—2061no—
144C22⋊Q8—2062no—
145C4×D4—1032no—
146C4×D4—1032no—
147C4×D4—2061no—
148C4×D4—2061no—
149#117—1031no—
150#117—1031no—
151#117—1031no—
152C2×C4⋊C4C2×D10311yescharacteristic
153C2×C22⋊C4—2062no—
154#107—1031no—
155#107—1031no—
156#107—1032no—
157#106—1031no—
158#106—1031no—
159#106—1032no—
160C4⋊C8—1032no—
161C4⋊C8—1032no—
162#102—1032no—
163#102—1032no—
164#102C2×D10312yes—
165#102C2×D10312yes—
166C24—21no—
167C2×Q8—2062no—
168C2×D4—21no—
169C2×D4—22no—
170C2×D4Dic20614yescomplemented
171C2×D4C22×D10312yes—
172C22×C4—21no—
173C22×C4—2062no—
174C22×C4—2062no—
175C22×C4C22×D10311yescharacteristic
176M16—2062no—
177C2×C8—22no—
178C2×C8—1032no—
179C2×C8C22×D10311yescharacteristic
180C2×C8C22×D10311yescharacteristic
181C4⋊C4—21no—
182C4⋊C4—1031no—
183C4⋊C4—1031no—
184C4⋊C4—1031no—
185C4⋊C4—1031no—
186C4⋊C4—1031no—
187C4⋊C4—1031no—
188C4⋊C4—2062no—
189C4⋊C4—2062no—
190C4⋊C4—2062no—
191C4⋊C4C22×D10312yes—
192C22⋊C4—1032no—
193C22⋊C4—2062no—
194C22⋊C4—2062no—
195C22⋊C4—2061no—
196C22⋊C4—2061no—
197C42—1032no—
198C42—2061no—
199C42—2061no—
200C23—22no—
201C23—24no—
202C23—81no—
203C23—81no—
204C23D4×D10311yescharacteristic
205Q8—8242no—
206D4—22no—
207D4—24no—
208D4C2×Dic20614yes—
209C2×C4—22no—
210C2×C4—81no—
211C2×C4—8242no—
212C2×C4—8242no—
213C2×C4—1032no—
214C2×C4—1032no—
215C2×C4—2061no—
216C2×C4—2061no—
217C2×C4—2061no—
218C2×C4—2061no—
219C2×C4D4×D10311yescharacteristic
220C2×C4C2×Dic20612yes—
221C2×C4#1311010412yes—
222C2×C4C23×D10311yescharacteristic
223C8—21no—
224C8—21no—
225C8—2062no—
226C22—21no—
227C22—21no—
228C22—24no—
229C22—42no—
230C22—42no—
231C22—84no—
232C22#1569299812yes—
233C22C2×D4×D10311yescharacteristic
234C4—42no—
235C4—4121no—
236C4—4121no—
237C4—4121no—
238C4—4121no—
239C4—2062no—
240C4—2062no—
241C4#1569299812yes—
242C4C22×Dic20611yescharacteristic
243C4C2×#1311010411yescharacteristic
244C2—22no—
245C2—44no—
246C2C2×#1569299811yescharacteristic
247C2#2026859211yescharacteristic
248C2#2026859711yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#102×C103C2
socleC22×C103C22×D4
prime radicalC22×D4×C103C22
hypercenterC2×#102D103
hypocenterC103#3081
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #20268422C2semidirect
3. #20268093C2semidirect
4. #20268089C2semidirect
5. #20268079C2semidirect
6. #20268069C2semidirect
7. #20267831C2semidirect
8. #20267829C2semidirect
9. #20267817C2semidirect
14. #15693020C22semidirect
16. #15693012C22semidirect
26. #15692955C22semidirect
27. #15692955C22semidirect
28. #15692954C22semidirect
29. #15692953C22semidirect
30. #15692953C22semidirect
31. #15692952C22semidirect
32. Dic103⋊C8C22semidirect
33. Dic103⋊C8C22semidirect
66. C2×D4×C103Q8semidirect
125. C103#3081semidirect
170. C2×D4Dic206semidirect

Maximal subgroups

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

subgroupindex
#202684222
#202682662
#202680932
#202680892
#202680792
#202680692
#202678312
#202678292
#202678172
#202677962
C2×#102×C1032
#3081103