Finite Group Databasebeta

← #13119306

Subgroups — #13119306

Order 1664.

708 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 708 conjugacy classes of subgroups — too many to draw. Only its 169 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×#88192C211yesmaximal, characteristic
2C2×C4⋊C4×D13C211yesmaximal, characteristic, complemented
3C2×#88137C214yesmaximal, complemented
4C13×#390C211yesmaximal, characteristic, complemented
5#11718882C211yesmaximal, characteristic, complemented
6#11718637C211yesmaximal, characteristic, complemented
7#11718610C214yesmaximal, complemented
8C4×#6103C211yesmaximal, characteristic, complemented
9#11718596C211yesmaximal, characteristic, complemented
10C22×D4×C13C2211yescharacteristic
11C22×C22⋊D13C2212yes—
12C22×C4×D13C2212yes—
13C22×C4×D13C2211yescharacteristic
14C2×C13×C4⋊C4C2211yescharacteristic
15C2×C13×C22⋊C4C2214yes—
16C2×C42×C13C2211yescharacteristic
17C2×C22⋊Dic13C2214yes—
18C2×C22⋊Dic13C2212yes—
19#88192—24no—
20C2×#6103C2212yes—
21C2×C4⋊Dic13C2214yes—
22C2×C4⋊Dic13C2211yescharacteristic
23C2×C4⋊Dic13C2211yescharacteristic
24C2×#6101C2214yes—
25C2×#6101C2212yes—
26C2×C4×Dic13C2211yescharacteristic
27C4⋊C4×D13—24no—
28#88137—216no—
29#88071C2212yes—
30C24×C13C2312yes—
31C23×D13C2311yescharacteristic
32C2×D4×C13—22no—
33C2×D4×C13—22no—
34C2×D4×C13—22no—
35C22×C4×C13C2312yes—
36C22×C4×C13C2312yes—
37C22×C4×C13C2311yescharacteristic
38C2×C22⋊D13—28no—
39C2×C22⋊D13—24no—
40C22×Dic13C2312yes—
41C22×Dic13C2312yes—
42C22×Dic13C2311yescharacteristic
43C22×Dic13C2312yes—
44C2×C4×D13—22no—
45C2×C4×D13—22no—
46C2×C4×D13—28no—
47C2×C4×D13—24no—
48C2×C4×D13D414yes—
49C13×C4⋊C4—22no—
50C13×C22⋊C4—28no—
51C42×C13—22no—
52C22⋊Dic13—28no—
53C22⋊Dic13—24no—
54#6103D418yescomplemented
55C4⋊Dic13—28no—
56C4⋊Dic13—22no—
57C4⋊Dic13—22no—
58#6101—28no—
59#6101—24no—
60C4×Dic13—22no—
61#2501—131nomaximal, Sylow
62C23×C13—24no—
63C23×C13—22no—
64C23×C13—22no—
65C23×C13—22no—
66C23×C13—24no—
67C23×C13C2411yescharacteristic
68C22×D13—21no—
69C22×D13—21no—
70C22×D13—22no—
71C22×D13C2×D414yes—
72C22×D13C2×D412yes—
73D4×C13—44no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13—24no—
77C2×C4×C13—22no—
78C2×C4×C13C2×D414yes—
79C2×C4×C13C2×D412yes—
80C2×C4×C13#4112yes—
81C2×C4×C13#4112yes—
82C22⋊D13—48no—
83C2×Dic13—22no—
84C2×Dic13—21no—
85C2×Dic13—21no—
86C2×Dic13—22no—
87C2×Dic13—22no—
88C2×Dic13—24no—
89C2×Dic13—24no—
90C2×Dic13—22no—
91C2×Dic13C2×D414yes—
92C2×Dic13C2×D412yes—
93C4×D13—28no—
94C4×D13—48no—
95C2×#123—134no—
96C2×#121—131no—
97C22×C4⋊C4—131no—
98#399—134no—
99#390—131no—
100#390D1311yescharacteristic, complemented
101#384—131no—
102#384—131no—
103C4×C22⋊C4—131no—
104C22×C13—42no—
105C22×C13—42no—
106C22×C13—42no—
107C22×C13—44no—
108C22×C13—44no—
109C22×C13C22×D411yescharacteristic
110C22×C13C22×D412yes—
111C22×C13C2×#4111yescharacteristic
112C22×C13C2×#4111yescharacteristic
113C22×C132−1+412yes—
114C2×D13—22no—
115C2×D13—22no—
116C2×D13—24no—
117C2×D13—24no—
118C2×D13#12714yes—
119C4×C13—24no—
120C4×C13—42no—
121C4×C13#12314yescomplemented
122Dic13—22no—
123Dic13—24no—
124Dic13—42no—
125Dic13—42no—
126C22×D4—132no—
127C22×D4C2×D1311yescharacteristic
128C23×C4—131no—
129C23×C4—132no—
130#123—2616no—
131#121—264no—
132C2×C4⋊C4—132no—
133C2×C4⋊C4—131no—
134C2×C4⋊C4—131no—
135C2×C4⋊C4—134no—
136C2×C4⋊C4—134no—
137C2×C4⋊C4—264no—
138C2×C4⋊C4C2×D1311yescharacteristic
139C2×C22⋊C4—132no—
140C2×C22⋊C4—132no—
141C2×C22⋊C4—134no—
142C2×C22⋊C4C2×D1314yes—
143C2×C42—131no—
144C2×C42C2×D1311yescharacteristic
145#95—132no—
146C2×C13—82no—
147C2×C13C2×#12311yescharacteristic
148C2×C13C2×#12711yescharacteristic
149C2×C13#53611yescharacteristic
150C2×C13#54712yes—
151C2×C13#54712yes—
152D13—24no—
153C24—131no—
154C24C22×D1312yes—
155C2×D4—22no—
156C2×D4—22no—
157C2×D4—22no—
158C2×D4—264no—
159C2×D4—268no—
160C22×C4—131no—
161C22×C4—132no—
162C22×C4—134no—
163C22×C4—132no—
164C22×C4—132no—
165C22×C4—264no—
166C22×C4—268no—
167C22×C4—262no—
168C22×C4—262no—
169C22×C4C22×D1312yes—
170C22×C4C22×D1312yes—
171C22×C4C22×D1311yescharacteristic
172C4⋊C4—22no—
173C4⋊C4—264no—
174C4⋊C4—268no—
175C4⋊C4—262no—
176C4⋊C4—262no—
177C4⋊C4—268no—
178C22⋊C4—28no—
179C22⋊C4—138no—
180C22⋊C4—264no—
181C22⋊C4—268no—
182C42—22no—
183C42—262no—
184C13#250111yescharacteristic, complemented, Sylow
185C23—22no—
186C23—24no—
187C23—22no—
188C23—22no—
189C23—24no—
190C23—134no—
191C23—132no—
192C23—261no—
193C23—261no—
194C23—262no—
195C23C23×D1311yescharacteristic
196D4—44no—
197D4—528no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—22no—
202C2×C4—134no—
203C2×C4—132no—
204C2×C4—262no—
205C2×C4—261no—
206C2×C4—261no—
207C2×C4—262no—
208C2×C4—268no—
209C2×C4—264no—
210C2×C4—262no—
211C2×C4—262no—
212C2×C4—264no—
213C2×C4—528no—
214C2×C4#612712yes—
215C2×C4D4×D1314yes—
216C2×C4D4×D1312yes—
217C2×C4#612912yes—
218C22—42no—
219C22—44no—
220C22—44no—
221C22—42no—
222C22—42no—
223C22—134no—
224C22—262no—
225C22—264no—
226C22—264no—
227C22—262no—
228C22C2×#612711yescharacteristic
229C22C2×D4×D1311yescharacteristic
230C22C2×D4×D1312yes—
231C22C2×#612911yescharacteristic
232C22#8825712yes—
233C4—24no—
234C4—42no—
235C4—262no—
236C4—264no—
237C4—522no—
238C4—522no—
239C4#8813714yescomplemented
240C2—82no—
241C2—264no—
242C2C2×#8813711yescharacteristic
243C2#1171925612yes—
244C2#1171931612yes—
245C2#1171938011yescharacteristic
246C2D13×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#390C2
prime radicalC2×#88192C2
hypercenter#390D13
hypocenterC13#2501
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D13C2semidirect
3. C2×#88137C2semidirect
4. C13×#390C2semidirect
5. #11718882C2semidirect
6. #11718637C2semidirect
7. #11718610C2semidirect
8. C4×#6103C2semidirect
9. #11718596C2semidirect
54. #6103D4semidirect
100. #390D13semidirect
121. C4×C13#123semidirect
184. C13#2501semidirect
239. C4#88137semidirect

Maximal subgroups

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

subgroupindex
C2×#881922
C2×C4⋊C4×D132
C2×#881372
C13×#3902
#117188822
#117186372
#117186102
C4×#61032
#117185962
#250113