Finite Group Databasebeta

← #13125008

Subgroups — #13125008

Order 1664.

386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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
1C2×Q8×Dic13C211yesmaximal, characteristic, complemented
2#11719329C211yesmaximal, characteristic
3C13×#451C211yesmaximal, characteristic, complemented
4#11718888C211yesmaximal, characteristic
5#11718846C212yesmaximal, complemented
6#11718845C212yesmaximal, complemented
7#11718705C211yesmaximal, characteristic, complemented
8#11718478C212yesmaximal, complemented
9#11718460C212yesmaximal, complemented
10#11718396C211yesmaximal, characteristic
11#11718380C211yesmaximal, characteristic, complemented
12C22×Q8×C13C2211yescharacteristic
13C2×C13×Q16C2212yes—
14C13×C22⋊Q8C2211yescharacteristic
15#88201C2211yescharacteristic
16Q8×Dic13—21no—
17Q8×Dic13—21no—
18Q8×Dic13C2212yes—
19Q8×Dic13C2212yes—
20Q8×Dic13C2211yescharacteristic
21C2×#6106C2212yes—
22#88184C2211yescharacteristic
23C2×C4⋊Dic13—21no—
24C2×C4⋊Dic13C2211yescharacteristic
25C2×C4×Dic13—21no—
26C2×C4×Dic13C2211yescharacteristic
27#88152—21no—
28#88147C2211yescharacteristic
29#88146—21no—
30#88144C2211yescharacteristic
31#88140—21no—
32#88135—21no—
33C13×#103C2212yes—
34C13×C22⋊C8C2211yescharacteristic
35#88075C2212yes—
36#88075C2212yes—
37C22⋊#1055C2211yescharacteristic
38#88061C2212yes—
39#88057C2212yes—
40#88055C2212yes—
41#88054C2212yes—
42#88047C2212yes—
43C2×Q8×C13—24no—
44C2×Q8×C13—21no—
45C2×Q8×C13C2311yescharacteristic
46C2×Q8×C13C2312yes—
47C22×C4×C13—21no—
48C22×C4×C13C2311yescharacteristic
49C2×C22⋊D13—21no—
50C22×Dic13—21no—
51C22×Dic13D411yescharacteristic
52C22×Dic13D411yescharacteristic
53C2×D52C2311yescharacteristic
54C2×C4×D13—21no—
55C13×Q16—24no—
56C2×C8×C13C2312yes—
57C13×C4⋊C4—21no—
58C13×C4⋊C4C2311yescharacteristic
59C13×C22⋊C4—21no—
60#6106—24no—
61#6103—21no—
62#6103—21no—
63#6103—21no—
64#6103—21no—
65C4⋊Dic13—21no—
66C4⋊Dic13—21no—
67C4⋊Dic13—21no—
68C4⋊Dic13—22no—
69C4⋊Dic13—22no—
70C4⋊Dic13C2311yescharacteristic
71C4⋊Dic13C2312yes—
72#6101—21no—
73C4×Dic13—21no—
74C4×Dic13—22no—
75C4×Dic13—22no—
76C4×Dic13D411yescharacteristic
77C4×Dic13D411yescharacteristic
78C4×Dic13C2311yescharacteristic
79C4×Dic13C2311yescharacteristic
80C2×#1055C2312yes—
81#3117—131nomaximal, Sylow
82C23×C13C2×D411yescharacteristic
83C22×D13—21no—
84Q8×C13—24no—
85Q8×C13—22no—
86Q8×C13—22no—
87Q8×C13#4114yes—
88C2×C4×C13—24no—
89C2×C4×C13—22no—
90C2×C4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13C2×D411yescharacteristic
94C2×C4×C13C2411yescharacteristic
95C22⋊D13—42no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—21no—
99C2×Dic13—41no—
100C2×Dic13—42no—
101C2×Dic13C2×D411yescharacteristic
102C2×Dic13C2×D411yescharacteristic
103C2×Dic13C2×D411yescharacteristic
104C2×Dic13C2×D411yescharacteristic
105D52—22no—
106C4×D13—42no—
107C8×C13—22no—
108#1055—22no—
109#529—131no—
110C2×C4×Q8—131no—
111#484—131no—
112#481—131no—
113#479—132no—
114#464—132no—
115#451D1311yescharacteristic, complemented
116#448—131no—
117#441—132no—
118#440—132no—
119#432—131no—
120C22×C13—21no—
121C22×C13—21no—
122C22×C13#13712yes—
123C22×C13C22×D411yescharacteristic
124C2×D13—41no—
125C2×D13—41no—
126C2×D13—41no—
127C4×C13—24no—
128C4×C13—21no—
129C4×C13—41no—
130C4×C13—41no—
131C4×C13C2×#4112yes—
132Dic13—21no—
133Dic13—21no—
134Dic13—21no—
135Dic13—21no—
136Dic13—41no—
137Dic13—42no—
138C22×Q8C2×D1311yescharacteristic
139C2×Q16C2×D1312yes—
140C2×SD16—132no—
141#126—261no—
142#125—131no—
143#124—131no—
144#123—261no—
145C22⋊Q8C2×D1311yescharacteristic
146#121—131no—
147C4×Q8—132no—
148C4×Q8—132no—
149C4×Q8—131no—
150C4×Q8—261no—
151C4×Q8—261no—
152C4×D4—131no—
153C4×D4—261no—
154#117—261no—
155C2×C4⋊C4—131no—
156C2×C4⋊C4—261no—
157C2×C42—131no—
158C2×C42—261no—
159#107—132no—
160#106—132no—
161C4⋊C8—132no—
162#103—132no—
163#103—132no—
164#103C2×D1312yes—
165#102—132no—
166C22⋊C8—131no—
167C22⋊C8C2×D1311yescharacteristic
168#97—132no—
169C2×C13—22no—
170C2×C13#52511yescharacteristic
171C2×C13C2×#13711yescharacteristic
172C2×C13#57511yescharacteristic
173D13—81no—
174C2×Q8—24no—
175C2×Q8—21no—
176C2×Q8C22×D1311yescharacteristic
177C2×Q8C22×D1312yes—
178C2×D4—131no—
179C2×D4—261no—
180C22×C4—21no—
181C22×C4—131no—
182C22×C4—131no—
183C22×C4—261no—
184C22×C4—261no—
185C22×C4C22×D1311yescharacteristic
186Q16—24no—
187SD16—264no—
188C2×C8—132no—
189C2×C8C22×D1312yes—
190C4⋊C4—21no—
191C4⋊C4—132no—
192C4⋊C4—131no—
193C4⋊C4—262no—
194C4⋊C4—262no—
195C4⋊C4—261no—
196C4⋊C4—261no—
197C4⋊C4—261no—
198C4⋊C4—261no—
199C4⋊C4C22×D1311yescharacteristic
200C22⋊C4—21no—
201C22⋊C4—261no—
202C22⋊C4—261no—
203C22⋊C4—261no—
204C22⋊C4—261no—
205C42—131no—
206C42—131no—
207C42—131no—
208C42—131no—
209C42—262no—
210C42—262no—
211C42—261no—
212C13#311711yescharacteristic, complemented, Sylow
213C23—261no—
214C23D4×D1311yescharacteristic
215Q8—24no—
216Q8—22no—
217Q8—22no—
218Q8#612914yes—
219D4—262no—
220D4—522no—
221C2×C4—24no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—131no—
227C2×C4—131no—
228C2×C4—131no—
229C2×C4—131no—
230C2×C4—262no—
231C2×C4—262no—
232C2×C4—261no—
233C2×C4—522no—
234C2×C4—521no—
235C2×C4—522no—
236C2×C4D4×D1311yescharacteristic
237C2×C4C23×D1311yescharacteristic
238C8—22no—
239C8—262no—
240C22—21no—
241C22—21no—
242C22—521no—
243C22—521no—
244C22—521no—
245C22#8817212yes—
246C22C2×D4×D1311yescharacteristic
247C4—24no—
248C4—21no—
249C4—41no—
250C4—41no—
251C4—261no—
252C4—261no—
253C4—261no—
254C4—261no—
255C4—521no—
256C4—522no—
257C4C2×#612912yes—
258C2—22no—
259C2—1041no—
260C2#1171929111yescharacteristic
261C2C2×#8817211yescharacteristic
262C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#451C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenter#451D13
hypocenterC13#3117
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
1. C2×Q8×Dic13C2semidirect
3. C13×#451C2semidirect
5. #11718846C2semidirect
6. #11718845C2semidirect
7. #11718705C2semidirect
8. #11718478C2semidirect
9. #11718460C2semidirect
11. #11718380C2semidirect
115. #451D13semidirect
212. C13#3117semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×Dic132
#117193292
C13×#4512
#117188882
#117188462
#117188452
#117187052
#117184782
#117184602
#117183962
#117183802
#311713