Finite Group Databasebeta

← #13115845

Subgroups — #13115845

Order 1664.

392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 91 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×#88200C211yesmaximal, characteristic
2C22×#6107C211yesmaximal, characteristic, complemented
3C2×#88151C211yesmaximal, characteristic
4C2×C13×#103C211yesmaximal, characteristic, complemented
5C2×#88060C211yesmaximal, characteristic
6C2×#88056C211yesmaximal, characteristic, complemented
7#11718121C211yesmaximal, characteristic, complemented
8C22×Q8×C13C2211yescharacteristic
9C22×C4×D13C2211yescharacteristic
10C22×Dic26C2211yescharacteristic
11C22×C8×C13C2211yescharacteristic
12C2×C13×C4⋊C4C2211yescharacteristic
13#88200—22no—
14#88200—22no—
15C2×#6107—22no—
16C2×#6107—22no—
17C2×#6107—22no—
18C2×#6103—21no—
19C2×#6103—21no—
20C2×C4⋊Dic13—21no—
21C2×C4⋊Dic13C2211yescharacteristic
22C2×#6101—21no—
23C22×#1055C2211yescharacteristic
24#88151—22no—
25#88151—22no—
26C13×#103—22no—
27#88060—22no—
28#88056—22no—
29C23×D13D411yescharacteristic
30C2×Q8×C13—21no—
31C2×Q8×C13—21no—
32C2×Q8×C13—21no—
33C2×Q8×C13—21no—
34C2×Q8×C13—21no—
35C2×Q8×C13D412yes—
36C22×C4×C13—21no—
37C22×C4×C13—21no—
38C22×C4×C13C2311yescharacteristic
39C22×Dic13—21no—
40C22×Dic13—21no—
41C22×Dic13D411yescharacteristic
42C2×C4×D13—21no—
43C2×C4×D13—21no—
44C2×C4×D13—21no—
45C2×C4×D13—21no—
46C2×C4×D13—21no—
47C2×C4×D13—21no—
48C2×Dic26—21no—
49C2×Dic26—21no—
50C2×Dic26—21no—
51C2×Dic26—21no—
52C2×Dic26—21no—
53C2×Dic26D412yes—
54C2×C8×C13—21no—
55C2×C8×C13—21no—
56C2×C8×C13—21no—
57C13×C4⋊C4—21no—
58C13×C4⋊C4D412yes—
59#6107—28no—
60#6103—24no—
61#6103—24no—
62C4⋊Dic13—24no—
63C4⋊Dic13—21no—
64C4⋊Dic13D412yes—
65#6101—24no—
66C2×#1055—21no—
67C2×#1055—21no—
68C2×#1055D412yes—
69#2001—131nomaximal, Sylow
70C23×C13C2×D411yescharacteristic
71C22×D13—21no—
72C22×D13—21no—
73C22×D13—21no—
74C22×D13—21no—
75C22×D13—21no—
76C22×D13—21no—
77C22×D13Q1612yescomplemented
78Q8×C13—22no—
79Q8×C13—22no—
80Q8×C13—41no—
81Q8×C13—41no—
82C2×C4×C13—22no—
83C2×C4×C13—22no—
84C2×C4×C13—41no—
85C2×C4×C13—41no—
86C2×C4×C13—41no—
87C2×C4×C13—41no—
88C2×C4×C13C2×D411yescharacteristic
89C2×C4×C13C2×D411yescharacteristic
90C2×C4×C13C2×D411yescharacteristic
91C2×C4×C13C2×D411yescharacteristic
92C2×C4×C13C2×D411yescharacteristic
93C2×C4×C13#4111yescharacteristic
94C2×Dic13—21no—
95C2×Dic13—22no—
96C2×Dic13—21no—
97C2×Dic13—22no—
98C2×Dic13—21no—
99C2×Dic13—41no—
100C2×Dic13—41no—
101C2×Dic13—41no—
102C2×Dic13—41no—
103C4×D13—41no—
104C4×D13—41no—
105C4×D13—41no—
106C4×D13—41no—
107Dic26—22no—
108Dic26—22no—
109Dic26—41no—
110Dic26—41no—
111C8×C13—41no—
112#1055—22no—
113C22×Q16—131no—
114C2×C22⋊Q8—131no—
115C2×C22⋊Q8—131no—
116C2×#103—131no—
117C2×#103D1311yescharacteristic, complemented
118C2×C22⋊C8—131no—
119#340—131no—
120C22×C13#12011yescharacteristic
121C22×C13#12011yescharacteristic
122C22×C13#12111yescharacteristic
123C22×C13C2×Q1611yescharacteristic
124C22×C13#13511yescharacteristic
125C22×C13#13711yescharacteristic
126C22×C13#13711yescharacteristic
127C2×D13—22no—
128C2×D13—22no—
129C2×D13—22no—
130C2×D13—41no—
131C2×D13—41no—
132C2×D13—41no—
133C2×D13—41no—
134C4×C13—42no—
135C4×C13—42no—
136C4×C13#12011yescharacteristic
137C4×C13#12111yescharacteristic
138C4×C13#12111yescharacteristic
139C4×C13#12711yescharacteristic
140Dic13—42no—
141Dic13—41no—
142Dic13—42no—
143C22×Q8—131no—
144C22×Q8C2×D1311yescharacteristic
145C23×C4—131no—
146C2×Q16—262no—
147C2×Q16—262no—
148C2×Q16—262no—
149C22×C8—131no—
150C22×C8C2×D1311yescharacteristic
151C22⋊Q8—262no—
152C22⋊Q8—262no—
153C22⋊Q8—262no—
154C22⋊Q8—262no—
155C2×C4⋊C4—131no—
156C2×C4⋊C4—261no—
157C2×C4⋊C4—261no—
158C2×C4⋊C4C2×D1311yescharacteristic
159C2×C22⋊C4—261no—
160C2×C22⋊C4—261no—
161#103—22no—
162#103—262no—
163C22⋊C8—262no—
164C2×C13#39211yescharacteristic
165C2×C13#45111yescharacteristic
166C2×C13#45111yescharacteristic
167C2×C13#45211yescharacteristic
168C2×C13#45211yescharacteristic
169C2×C13#46711yescharacteristic
170C2×C13#47011yescharacteristic
171D13—42no—
172C24—131no—
173C2×Q8—21no—
174C2×Q8—21no—
175C2×Q8—21no—
176C2×Q8—21no—
177C2×Q8—21no—
178C2×Q8—132no—
179C2×Q8—261no—
180C2×Q8—261no—
181C2×Q8—261no—
182C2×Q8—261no—
183C2×Q8—261no—
184C2×Q8D5212yes—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—131no—
188C22×C4—261no—
189C22×C4—261no—
190C22×C4—261no—
191C22×C4—261no—
192C22×C4—261no—
193C22×C4—261no—
194C22×C4—261no—
195C22×C4—261no—
196C22×C4C22×D1311yescharacteristic
197Q16—268no—
198C2×C8—21no—
199C2×C8—21no—
200C2×C8—21no—
201C2×C8—132no—
202C2×C8—261no—
203C2×C8—261no—
204C4⋊C4—21no—
205C4⋊C4—132no—
206C4⋊C4—264no—
207C4⋊C4—264no—
208C4⋊C4—261no—
209C4⋊C4C22⋊D1312yes—
210C22⋊C4—264no—
211C22⋊C4—264no—
212C13#200111yescharacteristic, complemented, Sylow
213C23—132no—
214C23—261no—
215C23—261no—
216C23—261no—
217C23—261no—
218C23—261no—
219C23—261no—
220C23D4×D1311yescharacteristic
221Q8—22no—
222Q8—22no—
223Q8—41no—
224Q8—41no—
225Q8—262no—
226Q8—262no—
227Q8—521no—
228Q8—521no—
229C2×C4—22no—
230C2×C4—22no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—262no—
236C2×C4—261no—
237C2×C4—261no—
238C2×C4—262no—
239C2×C4—261no—
240C2×C4—521no—
241C2×C4—521no—
242C2×C4—521no—
243C2×C4—521no—
244C2×C4—521no—
245C2×C4—521no—
246C2×C4—521no—
247C2×C4—521no—
248C2×C4C2×D5211yescharacteristic
249C2×C4#612711yescharacteristic
250C2×C4D4×D1311yescharacteristic
251C2×C4D4×D1311yescharacteristic
252C2×C4D4×D1311yescharacteristic
253C2×C4C2×C22⋊D1311yescharacteristic
254C8—41no—
255C8—262no—
256C22—262no—
257C22—262no—
258C22—262no—
259C22—521no—
260C22—521no—
261C22—521no—
262C22—521no—
263C22#8813611yescharacteristic
264C22#8813811yescharacteristic
265C22#8816911yescharacteristic
266C22#8817011yescharacteristic
267C22Q16×D1311yescharacteristic
268C22#8817211yescharacteristic
269C22#8819111yescharacteristic
270C4—42no—
271C4—42no—
272C4—522no—
273C4—521no—
274C4—522no—
275C4#8813611yescharacteristic
276C4#8813811yescharacteristic
277C4#8818411yescharacteristic
278C4#8819411yescharacteristic
279C2—522no—
280C2#1171846911yescharacteristic
281C2#1171847111yescharacteristic
282C2#1171847411yescharacteristic
283C2#1171847711yescharacteristic
284C2#1171862111yescharacteristic
285C2#1171883411yescharacteristic
286C2#1171884711yescharacteristic
subgroupG/H
centerC23D4×D13
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC2×C13×#103C2
socleC23×C13C2×D4
prime radicalC23×D13D4
hypercenterC2×#103D13
hypocenterC13#2001
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C22×#6107C2semidirect
4. C2×C13×#103C2semidirect
6. C2×#88056C2semidirect
7. #11718121C2semidirect
77. C22×D13Q16semidirect
117. C2×#103D13semidirect
212. C13#2001semidirect

Maximal subgroups

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

subgroupindex
C2×#882002
C22×#61072
C2×#881512
C2×C13×#1032
C2×#880602
C2×#880562
#117181212
#200113