Finite Group Databasebeta

← #13124674

Subgroups — #13124674

Order 1664.

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

normal subgroups only

This group has 362 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#11719517C211yesmaximal, characteristic
2#11719205C211yesmaximal, characteristic
3C2×C13×#103C211yesmaximal, characteristic
4#11718886C211yesmaximal, characteristic
5#11718767C211yesmaximal, characteristic
6#11718763C211yesmaximal, characteristic
7#11718625C211yesmaximal, characteristic
8#11718460C212yesmaximal, complemented
9#11718457C212yesmaximal, complemented
10#11718455C212yesmaximal, complemented
11#11718452C212yesmaximal, complemented
12C22×Q8×C13C2211yescharacteristic
13C22×C8×C13C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15Q8×Dic13—21no—
16Q8×Dic13—21no—
17Q8×Dic13C2212yes—
18Q8×Dic13C2212yes—
19#88180—22no—
20#88180C2211yescharacteristic
21#88180C2211yescharacteristic
22#88180C2211yescharacteristic
23#88178—22no—
24C2×#6099C2211yescharacteristic
25#88144—21no—
26#88144C2212yes—
27#88142—21no—
28#88142C2212yes—
29C13×#103C2212yes—
30C13×#103C2212yes—
31#88075C2212yes—
32#88075C2212yes—
33#88058C2211yescharacteristic
34#88058C2211yescharacteristic
35#88057C2211yescharacteristic
36#88057C2211yescharacteristic
37#88054C2212yes—
38#88054C2212yes—
39#88048C2212yes—
40#88047C2212yes—
41C2×Q8×C13—21no—
42C2×Q8×C13—22no—
43C2×Q8×C13Q814yescomplemented
44C2×Q8×C13C2312yes—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13C2311yescharacteristic
48C2×Dic26—22no—
49C2×C8×C13—22no—
50C2×C8×C13C2311yescharacteristic
51C2×C8×C13C2311yescharacteristic
52C13×C4⋊C4—21no—
53C13×C4⋊C4C2312yes—
54C22⋊Dic13—21no—
55C22⋊Dic13—21no—
56C22⋊Dic13D412yes—
57C4⋊Dic13—22no—
58C4⋊Dic13—22no—
59C4⋊Dic13—22no—
60C4⋊Dic13D411yescharacteristic
61C4⋊Dic13D411yescharacteristic
62C4⋊Dic13C2311yescharacteristic
63C4⋊Dic13C2311yescharacteristic
64C4⋊Dic13C2311yescharacteristic
65C4⋊Dic13C2311yescharacteristic
66#6101—22no—
67#6101—22no—
68C4×Dic13—21no—
69C4×Dic13—21no—
70C4×Dic13—22no—
71C4×Dic13—22no—
72C4×Dic13C2312yes—
73#6099—22no—
74C2×#1055C2312yes—
75#3082—131nomaximal, Sylow
76C23×C13C2×D411yescharacteristic
77Q8×C13—24no—
78Q8×C13—22no—
79Q8×C13C2×Q814yes—
80C2×C4×C13—24no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13—81no—
84C2×C4×C13C2×D411yescharacteristic
85C2×C4×C13C2×Q812yes—
86C2×C4×C13#4112yes—
87C2×C4×C13C2411yescharacteristic
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13—21no—
91C2×Dic13—21no—
92C2×Dic13C2×D412yes—
93C2×Dic13C2×D412yes—
94Dic26—82no—
95C8×C13—21no—
96C8×C13—21no—
97#1055—22no—
98#544—131no—
99#519—131no—
100#479—132no—
101#479—132no—
102#477—132no—
103#475—132no—
104#428—131no—
105#427—131no—
106#424—131no—
107#419—131no—
108C2×#103D1311yescharacteristic
109C22×C13—21no—
110C22×C13—21no—
111C22×C13C22⋊Q812yes—
112C22×C13C22×D411yescharacteristic
113C4×C13—24no—
114C4×C13—42no—
115C4×C13C22⋊Q812yes—
116C4×C13C22×Q811yescharacteristic
117C4×C13C2×#4111yescharacteristic
118Dic13—22no—
119Dic13—22no—
120Dic13—41no—
121Dic13—41no—
122Dic13—41no—
123Dic13—41no—
124C22×Q8C2×D1311yescharacteristic
125C2×M16—131no—
126C22×C8C2×D1311yescharacteristic
127C4⋊Q8—132no—
128C4⋊Q8—261no—
129#125—132no—
130#125—261no—
131C22⋊Q8—262no—
132C4×Q8—132no—
133C4×Q8—132no—
134C4×Q8—261no—
135C4×Q8—261no—
136#117—131no—
137#117—131no—
138#117—131no—
139#117—262no—
140C2×C4⋊C4C2×D1311yescharacteristic
141#107—131no—
142#107—131no—
143#107—132no—
144#106—131no—
145#106—131no—
146#106—132no—
147C4⋊C8—132no—
148C4⋊C8—132no—
149#103—132no—
150#103—132no—
151#103C2×D1312yes—
152#103C2×D1312yes—
153C2×C13—22no—
154C2×C13C2×C22⋊Q811yescharacteristic
155C2×C13#57711yescharacteristic
156C2×C13#57811yescharacteristic
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—262no—
160C2×Q8Dic2614yescomplemented
161C2×Q8C22×D1312yes—
162C22×C4—21no—
163C22×C4—21no—
164C22×C4C22×D1311yescharacteristic
165M16—262no—
166C2×C8—22no—
167C2×C8—132no—
168C2×C8C22×D1311yescharacteristic
169C2×C8C22×D1311yescharacteristic
170C4⋊C4—21no—
171C4⋊C4—131no—
172C4⋊C4—131no—
173C4⋊C4—131no—
174C4⋊C4—131no—
175C4⋊C4—131no—
176C4⋊C4—131no—
177C4⋊C4—262no—
178C4⋊C4—262no—
179C4⋊C4—262no—
180C4⋊C4—262no—
181C4⋊C4—262no—
182C4⋊C4C22×D1312yes—
183C22⋊C4—132no—
184C22⋊C4—261no—
185C22⋊C4—261no—
186C42—132no—
187C42—262no—
188C42—262no—
189C42—261no—
190C42—261no—
191C13#308211yescharacteristic, complemented, Sylow
192C23D4×D1311yescharacteristic
193Q8—24no—
194Q8—22no—
195Q8—1042no—
196Q8C2×Dic2614yes—
197C2×C4—24no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—81no—
201C2×C4—132no—
202C2×C4—132no—
203C2×C4—261no—
204C2×C4—261no—
205C2×C4—261no—
206C2×C4—261no—
207C2×C4C2×Dic2612yes—
208C2×C4D4×D1311yescharacteristic
209C2×C4#612912yes—
210C2×C4C23×D1311yescharacteristic
211C8—21no—
212C8—21no—
213C8—262no—
214C22—21no—
215C22—21no—
216C22#8813212yes—
217C22C2×D4×D1311yescharacteristic
218C4—24no—
219C4—42no—
220C4—262no—
221C4—262no—
222C4—521no—
223C4—521no—
224C4—521no—
225C4—521no—
226C4#8813212yes—
227C4C22×Dic2611yescharacteristic
228C4C2×#612911yescharacteristic
229C2—22no—
230C2C2×#8813211yescharacteristic
231C2#1171946711yescharacteristic
232C2#1171947111yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC2×C13×#103C2
socleC22×C13C22×D4
prime radicalC23×C13C2×D4
hypercenterC2×#103D13
hypocenterC13#3082
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
8. #11718460C2semidirect
9. #11718457C2semidirect
10. #11718455C2semidirect
11. #11718452C2semidirect
43. C2×Q8×C13Q8semidirect
160. C2×Q8Dic26semidirect
191. C13#3082semidirect

Maximal subgroups

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

subgroupindex
#117195172
#117192052
C2×C13×#1032
#117188862
#117187672
#117187632
#117186252
#117184602
#117184572
#117184552
#117184522
#308213