Finite Group Databasebeta

← #13120753

Subgroups — #13120753

Order 1664.

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

normal subgroups only

This group has 520 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
1C2×C4×D4×C13C211yesmaximal, characteristic
2C2×#88178C211yesmaximal, characteristic, complemented
3#11718883C212yesmaximal
4#11718872C211yesmaximal, characteristic, complemented
5#11718871C212yesmaximal, complemented
6#11718644C211yesmaximal, characteristic, complemented
7#11718640C211yesmaximal, characteristic, complemented
8#11718614C211yesmaximal, characteristic, complemented
9#11718613C212yesmaximal, complemented
10#11718608C211yesmaximal, characteristic, complemented
11#11718594C212yesmaximal, complemented
12C22×D4×C13C2211yescharacteristic
13C23×C4×C13C2211yescharacteristic
14C23×C4×C13C2211yescharacteristic
15C22×Dic26C2211yescharacteristic
16C4×D4×C13—24no—
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C22⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2211yescharacteristic
20C2×C42×C13C2211yescharacteristic
21C2×C22⋊Dic13C2212yes—
22C2×C22⋊Dic13C2212yes—
23C2×C22⋊Dic13C2212yes—
24C2×C22⋊Dic13C2212yes—
25C2×C4⋊Dic13C2211yescharacteristic
26#88178—24no—
27C2×#6101C2212yes—
28C2×#6101C2212yes—
29C2×#6101C2212yes—
30#88071C2212yes—
31#88071C2212yes—
32#88071C2212yes—
33#88071C2212yes—
34#88071C2211yescharacteristic
35#88071C2212yes—
36#88071C2211yescharacteristic
37C24×C13C2311yescharacteristic
38C24×C13C2311yescharacteristic
39C2×D4×C13—22no—
40C2×D4×C13—22no—
41C2×D4×C13—22no—
42C22×C4×C13—22no—
43C22×C4×C13—42no—
44C22×C4×C13—42no—
45C22×C4×C13D414yes—
46C22×C4×C13C2311yescharacteristic
47C22×C4×C13C2311yescharacteristic
48C22×C4×C13C2311yescharacteristic
49C22×C4×C13C2311yescharacteristic
50C22×C4×C13C2311yescharacteristic
51C22×Dic13C2312yes—
52C22×Dic13C2312yes—
53C22×Dic13C2312yes—
54C22×Dic13C2312yes—
55C2×Dic26—22no—
56C2×Dic26—42no—
57C13×C4⋊C4—22no—
58C13×C22⋊C4—22no—
59C13×C22⋊C4—22no—
60C42×C13—22no—
61C22⋊Dic13—24no—
62C22⋊Dic13—24no—
63C22⋊Dic13—42no—
64C22⋊Dic13—42no—
65C4⋊Dic13—22no—
66#6101—24no—
67#6101—24no—
68#6101—42no—
69#2638—131nomaximal, Sylow
70C23×C13—21no—
71C23×C13—21no—
72C23×C13—21no—
73C23×C13—21no—
74C23×C13—22no—
75C23×C13—22no—
76C23×C13—22no—
77C23×C13—22no—
78C23×C13C2×D412yes—
79C23×C13#4112yes—
80C23×C13C2411yescharacteristic
81D4×C13—28no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—22no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13—44no—
91C2×C4×C13—44no—
92C2×C4×C13C2×D412yes—
93C2×C4×C13C2×D412yes—
94C2×C4×C13#4112yes—
95C2×Dic13—22no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—22no—
104C2×Dic13—22no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107Dic26—44no—
108C2×C22⋊Q8—131no—
109C2×C4×D4D1311yescharacteristic
110#398—131no—
111#397—132no—
112#397—131no—
113#395—131no—
114#394—132no—
115#393—131no—
116#387—132no—
117#385—132no—
118#381—131no—
119C22×C13—22no—
120C22×C13—22no—
121C22×C13—22no—
122C22×C13—22no—
123C22×C13—24no—
124C22×C13—41no—
125C22×C13—41no—
126C22×C13—42no—
127C22×C13—42no—
128C22×C13—42no—
129C22×C13C22×D411yescharacteristic
130C22×C13C2×#4111yescharacteristic
131C22×C13C2×#4111yescharacteristic
132C22×C13H(5,𝔽2)12yes—
133C22×C132−1+412yes—
134C4×C13—22no—
135C4×C13—22no—
136C4×C13—22no—
137C4×C13—41no—
138C4×C13—41no—
139Dic13—42no—
140Dic13—42no—
141Dic13—42no—
142Dic13—42no—
143C22×Q8—131no—
144C22×D4C2×D1311yescharacteristic
145C23×C4C2×D1311yescharacteristic
146C23×C4C2×D1311yescharacteristic
147C22⋊Q8—264no—
148C4×D4—24no—
149C2×C4⋊C4—132no—
150C2×C4⋊C4—131no—
151C2×C4⋊C4—132no—
152C2×C4⋊C4—132no—
153C2×C4⋊C4C2×D1311yescharacteristic
154C2×C22⋊C4—132no—
155C2×C22⋊C4—132no—
156C2×C22⋊C4—132no—
157C2×C22⋊C4—132no—
158C2×C22⋊C4C2×D1311yescharacteristic
159C2×C22⋊C4C2×D1311yescharacteristic
160C2×C42C2×D1311yescharacteristic
161#95—132no—
162#95—131no—
163#95—131no—
164#95—132no—
165#95—132no—
166#95—132no—
167#95—132no—
168C2×C13—42no—
169C2×C13—42no—
170C2×C13#52511yescharacteristic
171C2×C13#53411yescharacteristic
172C2×C13#53611yescharacteristic
173C2×C13#53912yes—
174C2×C13#54212yes—
175C24C22×D1311yescharacteristic
176C24C22×D1311yescharacteristic
177C2×Q8—262no—
178C2×Q8—522no—
179C2×D4—22no—
180C2×D4—22no—
181C2×D4—22no—
182C22×C4—22no—
183C22×C4—42no—
184C22×C4—42no—
185C22×C4—132no—
186C22×C4—132no—
187C22×C4—132no—
188C22×C4—132no—
189C22×C4C22⋊D1314yes—
190C22×C4C22×D1311yescharacteristic
191C22×C4C22×D1311yescharacteristic
192C22×C4C22×D1311yescharacteristic
193C22×C4C22×D1311yescharacteristic
194C22×C4C22×D1311yescharacteristic
195C4⋊C4—22no—
196C4⋊C4—264no—
197C4⋊C4—264no—
198C4⋊C4—262no—
199C4⋊C4—522no—
200C22⋊C4—22no—
201C22⋊C4—22no—
202C22⋊C4—264no—
203C22⋊C4—264no—
204C22⋊C4—522no—
205C22⋊C4—522no—
206C42—22no—
207C13#263811yescharacteristic, complemented, Sylow
208C23—21no—
209C23—21no—
210C23—21no—
211C23—22no—
212C23—22no—
213C23—22no—
214C23—22no—
215C23—21no—
216C23#612712yes—
217C23C2×C22⋊D1312yes—
218C23C23×D1311yescharacteristic
219Q8—524no—
220D4—28no—
221C2×C4—21no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—44no—
230C2×C4—44no—
231C2×C4—262no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4—262no—
235C2×C4—262no—
236C2×C4—262no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—262no—
240C2×C4—262no—
241C2×C4—262no—
242C2×C4—262no—
243C2×C4#612712yes—
244C2×C4C2×C22⋊D1312yes—
245C2×C4C2×C22⋊D1312yes—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—24no—
250C22—22no—
251C22—41no—
252C22—42no—
253C22—42no—
254C22—42no—
255C22—41no—
256C22C2×#612711yescharacteristic
257C22C2×#612711yescharacteristic
258C22#8825112yes—
259C22#8825712yes—
260C22C22×C22⋊D1311yescharacteristic
261C4—22no—
262C4—22no—
263C4—22no—
264C4—41no—
265C4—41no—
266C4—522no—
267C4—522no—
268C4—522no—
269C4—522no—
270C2—42no—
271C2—42no—
272C2#1171926612yes—
273C2#1171926912yes—
274C2#1171949611yescharacteristic
275C2#1171950911yescharacteristic
276C2#1171953011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C4×D4×C13C2
prime radicalC22×D4×C13C22
hypercenterC2×C4×D4D13
hypocenterC13#2638
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#88178C2semidirect
4. #11718872C2semidirect
5. #11718871C2semidirect
6. #11718644C2semidirect
7. #11718640C2semidirect
8. #11718614C2semidirect
9. #11718613C2semidirect
10. #11718608C2semidirect
11. #11718594C2semidirect
207. C13#2638semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×C132
C2×#881782
#117188832
#117188722
#117188712
#117186442
#117186402
#117186142
#117186132
#117186082
#117185942
#263813