Finite Group Databasebeta

← #13120593

Subgroups — #13120593

Order 1664.

612 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 612 conjugacy classes of subgroups — too many to draw. Only its 165 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×C13×#117C211yesmaximal, characteristic, complemented
2C2×#88184C211yesmaximal, characteristic
3C2×#88178C211yesmaximal, characteristic, complemented
4C2×#88129C211yesmaximal, characteristic, complemented
5#11718655C214yesmaximal, complemented
6#11718622C214yesmaximal, complemented
7#11718600C211yesmaximal, characteristic, complemented
8#11718596C211yesmaximal, characteristic, complemented
9#11718590C211yesmaximal, characteristic, complemented
10C23×C4×C13C2211yescharacteristic
11C22×C22⋊D13C2212yes—
12C22×D52C2211yescharacteristic
13C22×Dic26C2211yescharacteristic
14C13×#117—24no—
15C2×C13×C4⋊C4C2212yes—
16C2×C13×C22⋊C4C2212yes—
17C2×C42×C13C2211yescharacteristic
18C2×C42×C13C2211yescharacteristic
19C2×C22⋊Dic13C2212yes—
20#88184—24no—
21C2×#6103C2214yes—
22C2×#6103C2212yes—
23C2×#6103C2214yes—
24C2×C4⋊Dic13C2211yescharacteristic
25C2×C4⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2214yes—
27#88178—24no—
28C2×#6101C2212yes—
29#88129—24no—
30#88071C2214yes—
31C24×C13C2311yescharacteristic
32C23×D13C2312yes—
33C22×C4×C13—22no—
34C22×C4×C13—22no—
35C22×C4×C13D414yes—
36C22×C4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C22×C4×C13C2312yes—
39C22×C4×C13C2311yescharacteristic
40C2×C22⋊D13—24no—
41C2×C22⋊D13—44no—
42C22×Dic13C2312yes—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C2×D52—22no—
46C2×D52—22no—
47C2×D52—22no—
48C2×Dic26—22no—
49C2×Dic26—22no—
50C2×Dic26—22no—
51C13×C4⋊C4—24no—
52C13×C22⋊C4—24no—
53C42×C13—22no—
54C42×C13D414yescomplemented
55C22⋊Dic13—24no—
56#6103—28no—
57#6103—24no—
58#6103—44no—
59C4⋊Dic13—22no—
60C4⋊Dic13—22no—
61C4⋊Dic13—44no—
62#6101—24no—
63#2620—131nomaximal, Sylow
64C23×C13—21no—
65C23×C13—21no—
66C23×C13—22no—
67C23×C13—22no—
68C23×C13C2×D412yes—
69C23×C13C2411yescharacteristic
70C22×D13—22no—
71C22×D13—22no—
72C22×D13—22no—
73C22×D13—24no—
74C22×D13—24no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—22no—
78C2×C4×C13—22no—
79C2×C4×C13—28no—
80C2×C4×C13—22no—
81C2×C4×C13—22no—
82C2×C4×C13—22no—
83C2×C4×C13C2×D412yes—
84C2×C4×C13C2×D414yes—
85C2×C4×C13C2×D412yes—
86C2×C4×C13C2×D412yes—
87C2×C4×C13#4112yes—
88C22⋊D13—48no—
89C2×Dic13—22no—
90C2×Dic13—22no—
91C2×Dic13—22no—
92C2×Dic13—22no—
93C2×Dic13—22no—
94C2×Dic13—24no—
95C2×Dic13—24no—
96D52—44no—
97Dic26—44no—
98C2×#124—131no—
99C2×C22⋊Q8—131no—
100C2×#121—131no—
101C2×#117D1311yescharacteristic, complemented
102#396—134no—
103#394—134no—
104#391—131no—
105#390—131no—
106#384—131no—
107C22×C13—22no—
108C22×C13—22no—
109C22×C13—22no—
110C22×C13—42no—
111C22×C13—42no—
112C22×C13C22×D411yescharacteristic
113C22×C13C22×D411yescharacteristic
114C22×C13C2×#4111yescharacteristic
115C22×C13H(5,𝔽2)12yes—
116C22×C132−1+412yes—
117C2×D13—42no—
118C2×D13—42no—
119C2×D13—42no—
120C2×D13—44no—
121C2×D13—44no—
122C4×C13—22no—
123C4×C13—24no—
124C4×C13—42no—
125C4×C13#12114yes—
126Dic13—42no—
127Dic13—42no—
128Dic13—42no—
129C22×Q8—131no—
130C22×D4—132no—
131C22×D4—131no—
132C23×C4C2×D1311yescharacteristic
133#124—264no—
134C22⋊Q8—264no—
135#121—264no—
136#117—24no—
137C2×C4⋊C4—131no—
138C2×C4⋊C4—132no—
139C2×C4⋊C4—131no—
140C2×C4⋊C4—134no—
141C2×C4⋊C4C2×D1312yes—
142C2×C22⋊C4—132no—
143C2×C22⋊C4—132no—
144C2×C22⋊C4—134no—
145C2×C22⋊C4—134no—
146C2×C22⋊C4C2×D1312yes—
147C2×C42C2×D1311yescharacteristic
148C2×C42C2×D1311yescharacteristic
149#95—134no—
150C2×C13—42no—
151C2×C13C2×#12111yescharacteristic
152C2×C13#53511yescharacteristic
153C2×C13#53611yescharacteristic
154C2×C13#53712yes—
155C2×C13#54212yes—
156D13—82no—
157C24—132no—
158C24C22×D1311yescharacteristic
159C2×Q8—262no—
160C2×Q8—262no—
161C2×Q8—262no—
162C2×D4—264no—
163C2×D4—262no—
164C2×D4—262no—
165C2×D4—262no—
166C2×D4—524no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—132no—
170C22×C4—132no—
171C22×C4—132no—
172C22×C4D5214yes—
173C22×C4C22×D1312yes—
174C22×C4C22×D1311yescharacteristic
175C22×C4C22×D1312yes—
176C22×C4C22×D1311yescharacteristic
177C4⋊C4—24no—
178C4⋊C4—262no—
179C4⋊C4—264no—
180C4⋊C4—262no—
181C4⋊C4—524no—
182C22⋊C4—24no—
183C22⋊C4—264no—
184C22⋊C4—264no—
185C22⋊C4—268no—
186C22⋊C4—524no—
187C42—22no—
188C42C22⋊D1314yescomplemented
189C13#262011yescharacteristic, complemented, Sylow
190C23—21no—
191C23—22no—
192C23—22no—
193C23—21no—
194C23—262no—
195C23—262no—
196C23—264no—
197C23—264no—
198C23—262no—
199C23C2×D5212yes—
200C23C23×D1311yescharacteristic
201Q8—524no—
202D4—528no—
203D4—524no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—28no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—262no—
213C2×C4—262no—
214C2×C4—262no—
215C2×C4—262no—
216C2×C4—264no—
217C2×C4—264no—
218C2×C4—262no—
219C2×C4C2×D5212yes—
220C2×C4C2×D5212yes—
221C2×C4#612712yes—
222C2×C4C2×C22⋊D1314yes—
223C2×C4C2×C22⋊D1312yes—
224C22—22no—
225C22—22no—
226C22—22no—
227C22—42no—
228C22—42no—
229C22—522no—
230C22—522no—
231C22—524no—
232C22—522no—
233C22—524no—
234C22C22×D5211yescharacteristic
235C22C2×#612711yescharacteristic
236C22#8825612yes—
237C22#8825712yes—
238C22C22×C22⋊D1311yescharacteristic
239C4—22no—
240C4—24no—
241C4—42no—
242C4—522no—
243C4—522no—
244C4—522no—
245C4#8818414yes—
246C2—42no—
247C2—1042no—
248C2#1171923011yescharacteristic
249C2#1171923111yescharacteristic
250C2#1171923912yes—
251C2C2×#8818411yescharacteristic
252C2#1171953812yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#117C2
prime radicalC2×#88184C2
hypercenterC2×#117D13
hypocenterC13#2620
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C13×#117C2semidirect
3. C2×#88178C2semidirect
4. C2×#88129C2semidirect
5. #11718655C2semidirect
6. #11718622C2semidirect
7. #11718600C2semidirect
8. #11718596C2semidirect
9. #11718590C2semidirect
54. C42×C13D4semidirect
101. C2×#117D13semidirect
188. C42C22⋊D13semidirect
189. C13#2620semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1172
C2×#881842
C2×#881782
C2×#881292
#117186552
#117186222
#117186002
#117185962
#117185902
#262013