Finite Group Databasebeta

← #13119145

Subgroups — #13119145

Order 1664.

624 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 173 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×C22⋊D13C211yesmaximal, characteristic
2C22×C4⋊Dic13C211yesmaximal, characteristic, complemented
3C2×#88140C212yesmaximal
4C13×#380C211yesmaximal, characteristic, complemented
5#11718648C212yesmaximal, complemented
6#11718646C212yesmaximal, complemented
7#11718604C212yesmaximal, complemented
8#11718335C212yesmaximal, complemented
9#11718322C212yesmaximal, complemented
10C23×C4×C13C2211yescharacteristic
11C22×C22⋊D13C2211yescharacteristic
12C23×Dic13C2212yes—
13C22×C4×D13C2211yescharacteristic
14C2×C13×C4⋊C4C2212yes—
15C2×C13×C22⋊C4C2212yes—
16C2×C22⋊Dic13C2211yescharacteristic
17C4×C22⋊D13—24no—
18C2×#6103C2214yes—
19C2×#6103C2211yescharacteristic
20C2×C4⋊Dic13—24no—
21C2×C4⋊Dic13C2214yes—
22C2×C4⋊Dic13C2212yes—
23C2×C4⋊Dic13C2212yes—
24C2×#6101C2211yescharacteristic
25C2×C4×Dic13C2211yescharacteristic
26#88140—28no—
27C13×#95C2212yes—
28#88071C2214yes—
29#88071C2214yes—
30C24×C13C2311yescharacteristic
31C23×D13C2311yescharacteristic
32C22×C4×C13—24no—
33C22×C4×C13D414yes—
34C22×C4×C13C2314yes—
35C22×C4×C13C2311yescharacteristic
36C22×C4×C13C2311yescharacteristic
37C2×C22⋊D13—22no—
38C2×C22⋊D13—22no—
39C2×C22⋊D13D414yes—
40C22×Dic13—24no—
41C22×Dic13—24no—
42C22×Dic13—24no—
43C22×Dic13C2311yescharacteristic
44C22×Dic13C2311yescharacteristic
45C22×Dic13C2314yes—
46C22×Dic13C2311yescharacteristic
47C2×C4×D13—22no—
48C2×C4×D13—24no—
49C13×C4⋊C4—24no—
50C13×C22⋊C4—24no—
51C22⋊Dic13—22no—
52#6103—28no—
53#6103—22no—
54C4⋊Dic13—24no—
55C4⋊Dic13—24no—
56C4⋊Dic13—28no—
57#6101—22no—
58C4×Dic13—22no—
59#2486—131nomaximal, Sylow
60C23×C13—22no—
61C23×C13—22no—
62C23×C13C2×D412yes—
63C23×C13C2×D412yes—
64C23×C13#4112yes—
65C23×C13C2411yescharacteristic
66C22×D13—21no—
67C22×D13—22no—
68C22×D13—21no—
69C22×D13—22no—
70C22×D13C2×D412yes—
71C2×C4×C13—22no—
72C2×C4×C13—28no—
73C2×C4×C13—24no—
74C2×C4×C13—24no—
75C2×C4×C13—24no—
76C2×C4×C13C2×D412yes—
77C2×C4×C13C2×D412yes—
78C2×C4×C13#4114yes—
79C22⋊D13—28no—
80C2×Dic13—21no—
81C2×Dic13—21no—
82C2×Dic13—21no—
83C2×Dic13—21no—
84C2×Dic13—24no—
85C2×Dic13—24no—
86C2×Dic13—22no—
87C2×Dic13—24no—
88C2×Dic13—22no—
89C2×Dic13—48no—
90C2×Dic13C2×D412yes—
91C4×D13—44no—
92C2×#123—132no—
93C2×C4×D4—131no—
94C22×C4⋊C4—131no—
95#398—132no—
96#397—132no—
97#389—132no—
98#381—132no—
99#380—132no—
100#380D1311yescharacteristic, complemented
101C22×C13—22no—
102C22×C13—22no—
103C22×C13—24no—
104C22×C13—24no—
105C22×C13#12114yes—
106C22×C13C22×D411yescharacteristic
107C22×C13C22×D411yescharacteristic
108C22×C13C2×#4112yes—
109C22×C13C2×#4111yescharacteristic
110C22×C132−1+412yes—
111C2×D13—22no—
112C2×D13—24no—
113C2×D13—41no—
114C2×D13—41no—
115C2×D13—42no—
116C4×C13—22no—
117C4×C13—44no—
118C4×C13#12314yescomplemented
119Dic13—22no—
120Dic13—44no—
121Dic13—41no—
122Dic13—41no—
123C22×D4—131no—
124C23×C4—132no—
125C23×C4—131no—
126C23×C4C2×D1311yescharacteristic
127#123—268no—
128C4×D4—264no—
129C2×C4⋊C4—132no—
130C2×C4⋊C4—132no—
131C2×C4⋊C4—131no—
132C2×C4⋊C4—134no—
133C2×C4⋊C4—264no—
134C2×C4⋊C4C2×D1312yes—
135C2×C22⋊C4—131no—
136C2×C22⋊C4—131no—
137C2×C22⋊C4—134no—
138C2×C22⋊C4C2×D1312yes—
139C2×C42—131no—
140#95—134no—
141#95—134no—
142#95C2×D1312yes—
143C2×C13—24no—
144C2×C13C2×#12111yescharacteristic
145C2×C13C2×#12311yescharacteristic
146C2×C13#53611yescharacteristic
147C2×C13#54712yes—
148C2×C13#55212yes—
149D13—42no—
150C24—131no—
151C24C22×D1311yescharacteristic
152C2×D4—134no—
153C2×D4—262no—
154C2×D4—262no—
155C22×C4—24no—
156C22×C4—131no—
157C22×C4—131no—
158C22×C4—131no—
159C22×C4—134no—
160C22×C4—264no—
161C22×C4—264no—
162C22×C4—264no—
163C22×C4—262no—
164C22×C4—264no—
165C22×C4D5214yes—
166C22×C4C22×D1314yes—
167C22×C4C22×D1311yescharacteristic
168C22×C4C22×D1311yescharacteristic
169C4⋊C4—24no—
170C4⋊C4—268no—
171C4⋊C4—264no—
172C4⋊C4—264no—
173C4⋊C4—262no—
174C22⋊C4—24no—
175C22⋊C4—268no—
176C22⋊C4—262no—
177C22⋊C4—262no—
178C42—262no—
179C13#248611yescharacteristic, complemented, Sylow
180C23—22no—
181C23—22no—
182C23—132no—
183C23—261no—
184C23—262no—
185C23—261no—
186C23—262no—
187C23C2×D5212yes—
188C23D4×D1312yes—
189C23#613112yes—
190C23C23×D1311yescharacteristic
191D4—268no—
192C2×C4—22no—
193C2×C4—28no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—132no—
198C2×C4—261no—
199C2×C4—261no—
200C2×C4—261no—
201C2×C4—261no—
202C2×C4—264no—
203C2×C4—264no—
204C2×C4—262no—
205C2×C4—264no—
206C2×C4—262no—
207C2×C4—528no—
208C2×C4—524no—
209C2×C4C2×D5212yes—
210C2×C4C2×D5212yes—
211C2×C4#612914yes—
212C22—22no—
213C22—22no—
214C22—24no—
215C22—24no—
216C22—262no—
217C22—264no—
218C22—521no—
219C22—521no—
220C22—522no—
221C22#8814914yes—
222C22C22×D5211yescharacteristic
223C22C2×D4×D1311yescharacteristic
224C22C2×#612912yes—
225C22C2×#613111yescharacteristic
226C22#8825712yes—
227C4—22no—
228C4—44no—
229C4—262no—
230C4—521no—
231C4—524no—
232C4—521no—
233C4#8814014yescomplemented
234C2—24no—
235C2—522no—
236C2C2×#8814011yescharacteristic
237C2C2×#8814911yescharacteristic
238C2#1171923111yescharacteristic
239C2#1171931612yes—
240C2#1171934712yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#380C2
prime radicalC22×C22⋊D13C22
hypercenter#380D13
hypocenterC13#2486
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic13C2semidirect
4. C13×#380C2semidirect
5. #11718648C2semidirect
6. #11718646C2semidirect
7. #11718604C2semidirect
8. #11718335C2semidirect
9. #11718322C2semidirect
100. #380D13semidirect
118. C4×C13#123semidirect
179. C13#2486semidirect
233. C4#88140semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D132
C22×C4⋊Dic132
C2×#881402
C13×#3802
#117186482
#117186462
#117186042
#117183352
#117183222
#248613