Finite Group Databasebeta

← #13119144

Subgroups — #13119144

Order 1664.

624 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 181 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×#88189C212yesmaximal
3C22×C4⋊Dic13C211yesmaximal, characteristic, complemented
4#11718873C212yesmaximal, complemented
5#11718873C211yesmaximal, characteristic, complemented
6#11718644C212yesmaximal, complemented
7#11718614C212yesmaximal, complemented
8#11718604C212yesmaximal, complemented
9#11718589C212yesmaximal, complemented
10C22×D4×C13C2211yescharacteristic
11C23×C4×C13C2211yescharacteristic
12C23×C4×C13C2211yescharacteristic
13C23×Dic13C2212yes—
14C4×D4×C13—24no—
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2211yescharacteristic
17C2×C13×C22⋊C4C2211yescharacteristic
18C2×C42×C13C2211yescharacteristic
19C2×C22⋊Dic13C2212yes—
20C2×C22⋊Dic13C2214yes—
21#88189—28no—
22C2×C4⋊Dic13—24no—
23C2×C4⋊Dic13C2212yes—
24C2×C4⋊Dic13C2212yes—
25C2×C4⋊Dic13C2212yes—
26C2×#6101C2214yes—
27#88071C2214yes—
28#88071C2214yes—
29#88071C2212yes—
30C24×C13C2311yescharacteristic
31C24×C13C2311yescharacteristic
32C2×D4×C13—22no—
33C2×D4×C13—22no—
34C2×D4×C13D414yes—
35C22×C4×C13—24no—
36C22×C4×C13—22no—
37C22×C4×C13—24no—
38C22×C4×C13D414yes—
39C22×C4×C13C2311yescharacteristic
40C22×C4×C13C2311yescharacteristic
41C22×C4×C13C2311yescharacteristic
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×Dic13—24no—
45C22×Dic13—24no—
46C22×Dic13—24no—
47C22×Dic13C2314yes—
48C22×Dic13C2314yes—
49C13×C4⋊C4—22no—
50C13×C22⋊C4—22no—
51C13×C22⋊C4—22no—
52C42×C13—22no—
53C22⋊Dic13—24no—
54C22⋊Dic13—28no—
55C4⋊Dic13—24no—
56C4⋊Dic13—24no—
57C4⋊Dic13—24no—
58#6101—28no—
59#2486—131nomaximal, Sylow
60C23×C13—22no—
61C23×C13—22no—
62C23×C13—21no—
63C23×C13—22no—
64C23×C13—21no—
65C23×C13—22no—
66C23×C13C2×D412yes—
67C23×C13C2×D412yes—
68C23×C13C2×D412yes—
69C23×C13#4112yes—
70C23×C13C2411yescharacteristic
71D4×C13—28no—
72C2×C4×C13—21no—
73C2×C4×C13—22no—
74C2×C4×C13—21no—
75C2×C4×C13—28no—
76C2×C4×C13—21no—
77C2×C4×C13—21no—
78C2×C4×C13—22no—
79C2×C4×C13—22no—
80C2×C4×C13—44no—
81C2×C4×C13C2×D412yes—
82C2×C4×C13C2×D412yes—
83C2×C4×C13C2×D412yes—
84C2×C4×C13#4114yes—
85C2×Dic13—24no—
86C2×Dic13—24no—
87C2×Dic13—24no—
88C2×Dic13—24no—
89C2×Dic13—24no—
90C2×Dic13—24no—
91C2×Dic13—48no—
92C2×#123—132no—
93C2×C4×D4D1311yescharacteristic
94C22×C4⋊C4—131no—
95#398—132no—
96#397—132no—
97#389—132no—
98#381—132no—
99#380—132no—
100#380—131no—
101C22×C13—22no—
102C22×C13—22no—
103C22×C13—24no—
104C22×C13—24no—
105C22×C13—22no—
106C22×C13—24no—
107C22×C13—41no—
108C22×C13—41no—
109C22×C13—42no—
110C22×C13#12114yes—
111C22×C13C22×D411yescharacteristic
112C22×C13C22×D411yescharacteristic
113C22×C13C2×#4111yescharacteristic
114C22×C13C2×#4112yes—
115C22×C132−1+412yes—
116C4×C13—22no—
117C4×C13—22no—
118C4×C13—41no—
119C4×C13—41no—
120C4×C13#12314yescomplemented
121Dic13—44no—
122Dic13—44no—
123C22×D4C2×D1311yescharacteristic
124C23×C4—132no—
125C23×C4C2×D1311yescharacteristic
126C23×C4C2×D1311yescharacteristic
127#123—268no—
128C4×D4—24no—
129C2×C4⋊C4—132no—
130C2×C4⋊C4—132no—
131C2×C4⋊C4—134no—
132C2×C4⋊C4—132no—
133C2×C4⋊C4—264no—
134C2×C4⋊C4C2×D1311yescharacteristic
135C2×C22⋊C4—132no—
136C2×C22⋊C4—134no—
137C2×C22⋊C4C2×D1311yescharacteristic
138C2×C22⋊C4C2×D1311yescharacteristic
139C2×C42C2×D1311yescharacteristic
140#95—134no—
141#95—132no—
142#95—134no—
143C2×C13—24no—
144C2×C13—42no—
145C2×C13C2×#12111yescharacteristic
146C2×C13C2×#12311yescharacteristic
147C2×C13#53611yescharacteristic
148C2×C13#54712yes—
149C2×C13#55212yes—
150C24C22×D1311yescharacteristic
151C24C22×D1311yescharacteristic
152C2×D4—22no—
153C2×D4—22no—
154C2×D4D5214yes—
155C22×C4—24no—
156C22×C4—24no—
157C22×C4—22no—
158C22×C4—134no—
159C22×C4—134no—
160C22×C4—264no—
161C22×C4—264no—
162C22×C4—264no—
163C22×C4C22⋊D1314yes—
164C22×C4C22×D1311yescharacteristic
165C22×C4C22×D1311yescharacteristic
166C22×C4C22×D1311yescharacteristic
167C22×C4C22×D1311yescharacteristic
168C22×C4C22×D1311yescharacteristic
169C4⋊C4—22no—
170C4⋊C4—268no—
171C4⋊C4—264no—
172C4⋊C4—264no—
173C4⋊C4—264no—
174C22⋊C4—22no—
175C22⋊C4—22no—
176C22⋊C4—264no—
177C22⋊C4—268no—
178C42—22no—
179C13#248611yescharacteristic, complemented, Sylow
180C23—22no—
181C23—22no—
182C23—21no—
183C23—22no—
184C23—22no—
185C23—21no—
186C23C2×D5212yes—
187C23C2×D5212yes—
188C23#612712yes—
189C23C2×C22⋊D1312yes—
190C23C23×D1311yescharacteristic
191D4—28no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—28no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—44no—
201C2×C4—264no—
202C2×C4—264no—
203C2×C4—264no—
204C2×C4—264no—
205C2×C4—264no—
206C2×C4—264no—
207C2×C4—528no—
208C2×C4C2×D5212yes—
209C2×C4#612914yes—
210C2×C4C2×C22⋊D1312yes—
211C2×C4C2×C22⋊D1312yes—
212C22—22no—
213C22—24no—
214C22—24no—
215C22—22no—
216C22—22no—
217C22—24no—
218C22—41no—
219C22—42no—
220C22—41no—
221C22#8818414yes—
222C22C22×D5211yescharacteristic
223C22C2×#612711yescharacteristic
224C22C2×#612912yes—
225C22#8825712yes—
226C22C22×C22⋊D1311yescharacteristic
227C4—22no—
228C4—22no—
229C4—41no—
230C4—41no—
231C4—524no—
232C4—524no—
233C4#8818914yescomplemented
234C2—24no—
235C2—42no—
236C2#1171924612yes—
237C2#1171926012yes—
238C2C2×#8818411yescharacteristic
239C2C2×#8818911yescharacteristic
240C2#1171953011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C4×D4×C13C2
prime radicalC22×D4×C13C22
hypercenterC2×C4×D4D13
hypocenterC13#2486
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊Dic13C2semidirect
4. #11718873C2semidirect
5. #11718873C2semidirect
6. #11718644C2semidirect
7. #11718614C2semidirect
8. #11718604C2semidirect
9. #11718589C2semidirect
120. C4×C13#123semidirect
179. C13#2486semidirect
233. C4#88189semidirect

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×#881892
C22×C4⋊Dic132
#117188732
#117186442
#117186142
#117186042
#117185892
#248613