Finite Group Databasebeta

← #13124692

Subgroups — #13124692

Order 1664.

376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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#11719209C211yesmaximal, characteristic
2#11719205C211yesmaximal, characteristic, complemented
3C2×C13×#107C211yesmaximal, characteristic, complemented
4#11718774C211yesmaximal, characteristic
5#11718763C211yesmaximal, characteristic, complemented
6#11718627C211yesmaximal, characteristic
7#11718625C211yesmaximal, characteristic, complemented
8#11718552C212yesmaximal, complemented
9#11718551C212yesmaximal, complemented
10#11718538C212yesmaximal, complemented
11#11718536C212yesmaximal, complemented
12C2×#6127C2211yescharacteristic
13C22×C8×C13C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16C4×C22⋊D13—22no—
17#88180C2211yescharacteristic
18#88180C2211yescharacteristic
19#88178—22no—
20C2×#6099C2211yescharacteristic
21#88147C2212yes—
22#88146—21no—
23C4⋊C4×D13—21no—
24#88144—21no—
25#88144C2212yes—
26#88142—21no—
27#88142C2212yes—
28#88141C2212yes—
29C13×#107C2212yes—
30C13×#107C2212yes—
31#88061C2211yescharacteristic
32#88061C2211yescharacteristic
33#88056C2211yescharacteristic
34#88056C2211yescharacteristic
35#88054C2212yes—
36#88054C2212yes—
37#88050C2212yes—
38#88049C2212yes—
39#88048C2212yes—
40#88047C2212yes—
41C22×C4×C13—21no—
42C22×C4×C13—21no—
43C22×C4×C13C2311yescharacteristic
44C2×C22⋊D13—21no—
45#6127—22no—
46#6127Q814yescomplemented
47C2×D52C2311yescharacteristic
48C2×C4×D13—21no—
49C2×C4×D13—22no—
50C2×Dic26—22no—
51C2×Dic26C2311yescharacteristic
52C2×C8×C13—22no—
53C2×C8×C13C2311yescharacteristic
54C2×C8×C13C2311yescharacteristic
55C13×C4⋊C4—21no—
56C13×C4⋊C4—21no—
57C13×C4⋊C4C2312yes—
58C13×C4⋊C4C2312yes—
59C22⋊Dic13—21no—
60C22⋊Dic13D412yes—
61#6103—22no—
62C4⋊Dic13—22no—
63C4⋊Dic13D411yescharacteristic
64C4⋊Dic13D411yescharacteristic
65C4⋊Dic13C2311yescharacteristic
66C4⋊Dic13C2311yescharacteristic
67#6101—22no—
68#6101—22no—
69#6101—22no—
70C4×Dic13—21no—
71C4×Dic13—22no—
72C4×Dic13C2312yes—
73#6099—22no—
74C2×#1055C2312yes—
75#3083—131nomaximal, Sylow
76C23×C13C2×D411yescharacteristic
77C22×D13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—81no—
81C2×C4×C13—81no—
82C2×C4×C13C2×D411yescharacteristic
83C2×C4×C13C2×Q812yes—
84C2×C4×C13#4112yes—
85C2×C4×C13C2411yescharacteristic
86C22⋊D13—24no—
87C2×Dic13—21no—
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13C2×D412yes—
91C2×Dic13C2×D412yes—
92D52—21no—
93D52C2×Q812yes—
94C4×D13—24no—
95C4×D13—82no—
96Dic26—21no—
97Dic26—82no—
98Dic26C2×Q812yes—
99C8×C13—21no—
100C8×C13—21no—
101#1055—22no—
102#544—131no—
103#520—131no—
104#479—132no—
105#478—132no—
106#477—132no—
107#474—132no—
108#428—131no—
109C2×#107D1311yescharacteristic, complemented
110#424—131no—
111#417—131no—
112#416—131no—
113C22×C13—21no—
114C22×C13—21no—
115C22×C13C22⋊Q812yes—
116C22×C13C22×D411yescharacteristic
117C2×D13—22no—
118C2×D13—41no—
119C2×D13—41no—
120C4×C13—42no—
121C4×C13—42no—
122C4×C13C22⋊Q812yes—
123C4×C13C22×Q811yescharacteristic
124C4×C13C2×#4111yescharacteristic
125Dic13—22no—
126Dic13—22no—
127Dic13—22no—
128Dic13—41no—
129Dic13—41no—
130C2×#41—131no—
131C2×M16—131no—
132C22×C8C2×D1311yescharacteristic
133C4⋊Q8—132no—
134C4⋊Q8—261no—
135#125—132no—
136#125—261no—
137C22⋊Q8—262no—
138C4×Q8—132no—
139C4×D4—132no—
140C4×D4—262no—
141#117—131no—
142#117—131no—
143#117—261no—
144C2×C4⋊C4—261no—
145C2×C4⋊C4C2×D1311yescharacteristic
146C2×C4⋊C4C2×D1311yescharacteristic
147#107—132no—
148#107C2×D1312yes—
149#107C2×D1312yes—
150#106—132no—
151C4⋊C8—132no—
152C4⋊C8—132no—
153#103—131no—
154#103—131no—
155#103—132no—
156#102—131no—
157#102—131no—
158#102—132no—
159C2×C13—22no—
160C2×C13C2×C22⋊Q811yescharacteristic
161C2×C13#57611yescharacteristic
162C2×C13#57811yescharacteristic
163D13—42no—
164#41—134no—
165#41—262no—
166C2×Q8—131no—
167C2×Q8—262no—
168C2×D4—131no—
169C2×D4—261no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—262no—
173C22×C4—261no—
174C22×C4C22×D1311yescharacteristic
175M16—262no—
176C2×C8—22no—
177C2×C8—132no—
178C2×C8C22×D1311yescharacteristic
179C2×C8C22×D1311yescharacteristic
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—131no—
183C4⋊C4—131no—
184C4⋊C4—131no—
185C4⋊C4—131no—
186C4⋊C4—262no—
187C4⋊C4—262no—
188C4⋊C4—262no—
189C4⋊C4—262no—
190C4⋊C4C22×D1312yes—
191C4⋊C4C22×D1312yes—
192C22⋊C4—132no—
193C22⋊C4—262no—
194C22⋊C4—261no—
195C42—132no—
196C42—262no—
197C42—261no—
198C13#308311yescharacteristic, complemented, Sylow
199C23—261no—
200C23D4×D1311yescharacteristic
201Q8—132no—
202Q8—261no—
203Q8—1042no—
204D4—132no—
205D4—264no—
206D4—261no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—81no—
210C2×C4—81no—
211C2×C4—132no—
212C2×C4—132no—
213C2×C4—261no—
214C2×C4—264no—
215C2×C4—261no—
216C2×C4—261no—
217C2×C4—1042no—
218C2×C4#612712yes—
219C2×C4D4×D1311yescharacteristic
220C2×C4Q8×D1312yes—
221C2×C4C23×D1311yescharacteristic
222C8—21no—
223C8—21no—
224C8—262no—
225C22—21no—
226C22—21no—
227C22—262no—
228C22—521no—
229C22—521no—
230C22#8815012yes—
231C22C2×D4×D1311yescharacteristic
232C4—42no—
233C4—42no—
234C4—262no—
235C4—262no—
236C4—262no—
237C4—521no—
238C4—521no—
239C4#8815012yes—
240C4C2×#612711yescharacteristic
241C4C2×Q8×D1311yescharacteristic
242C2—22no—
243C2—522no—
244C2C2×#8815011yescharacteristic
245C2#1171946211yescharacteristic
246C2#1171947111yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#107C2
socleC22×C13C22×D4
prime radicalC2×#6127C22
hypercenterC2×#107D13
hypocenterC13#3083
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. #11719205C2semidirect
3. C2×C13×#107C2semidirect
5. #11718763C2semidirect
7. #11718625C2semidirect
8. #11718552C2semidirect
9. #11718551C2semidirect
10. #11718538C2semidirect
11. #11718536C2semidirect
46. #6127Q8semidirect
109. C2×#107D13semidirect
198. C13#3083semidirect

Maximal subgroups

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

subgroupindex
#117192092
#117192052
C2×C13×#1072
#117187742
#117187632
#117186272
#117186252
#117185522
#117185512
#117185382
#117185362
#308313