Finite Group Databasebeta

← #13119829

Subgroups — #13119829

Order 1664.

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

normal subgroups only

This group has 604 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×#124C211yesmaximal, characteristic
2C2×#88198C211yesmaximal, characteristic, complemented
3C2×#88190C211yesmaximal, characteristic
4C2×D4×Dic13C211yesmaximal, characteristic
5#11718891C211yesmaximal, characteristic, complemented
6#11718613C214yesmaximal, complemented
7#11718603C214yesmaximal, complemented
8C4×#6101C211yesmaximal, characteristic, complemented
9#11718590C211yesmaximal, characteristic, complemented
10C22×Q8×C13C2211yescharacteristic
11C22×D4×C13C2211yescharacteristic
12C23×Dic13C2212yes—
13C22×Dic26C2211yescharacteristic
14C13×#124—24no—
15C2×C13×C22⋊C4C2214yes—
16C2×C42×C13C2211yescharacteristic
17C2×C22⋊Dic13C2212yes—
18C2×C22⋊Dic13C2214yes—
19#88198—24no—
20#88190—24no—
21D4×Dic13—24no—
22C2×C4⋊Dic13C2211yescharacteristic
23C2×#6101C2212yes—
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×C4×Dic13C2211yescharacteristic
27C2×C4×Dic13C2211yescharacteristic
28#88071C2214yes—
29#88071C2212yes—
30#88071C2214yes—
31C24×C13C2312yes—
32C2×Q8×C13—22no—
33C2×Q8×C13—22no—
34C2×Q8×C13—22no—
35C2×D4×C13—22no—
36C2×D4×C13—22no—
37C2×D4×C13D414yes—
38C22×C4×C13C2312yes—
39C22×C4×C13C2312yes—
40C22×C4×C13C2311yescharacteristic
41C22×Dic13—24no—
42C22×Dic13—28no—
43C22×Dic13C2312yes—
44C22×Dic13C2312yes—
45C22×Dic13C2312yes—
46C22×Dic13C2311yescharacteristic
47C22×Dic13C2311yescharacteristic
48C2×Dic26—22no—
49C2×Dic26—22no—
50C2×Dic26—22no—
51C13×C22⋊C4—28no—
52C42×C13—22no—
53C22⋊Dic13—28no—
54C22⋊Dic13—24no—
55C4⋊Dic13—22no—
56#6101—24no—
57#6101—24no—
58#6101—24no—
59C4×Dic13—22no—
60C4×Dic13D414yes—
61#2547—131nomaximal, Sylow
62C23×C13—22no—
63C23×C13—24no—
64C23×C13—22no—
65C23×C13—24no—
66C23×C13C2×D414yes—
67C23×C13C2411yescharacteristic
68Q8×C13—44no—
69D4×C13—28no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13—22no—
76C2×C4×C13C2×D412yes—
77C2×C4×C13C2×D412yes—
78C2×C4×C13#4112yes—
79C2×Dic13—22no—
80C2×Dic13—22no—
81C2×Dic13—22no—
82C2×Dic13—22no—
83C2×Dic13—22no—
84C2×Dic13—22no—
85C2×Dic13—22no—
86C2×Dic13—24no—
87C2×Dic13—22no—
88C2×Dic13—48no—
89C2×Dic13C2×D412yes—
90C2×Dic13C2×D412yes—
91C2×Dic13#4114yes—
92Dic26—44no—
93C2×C4⋊Q8—131no—
94C2×#124—131no—
95C2×#124D1311yescharacteristic
96C2×C4×D4—131no—
97#397—134no—
98#391—131no—
99#391—131no—
100#380—134no—
101C4×C4⋊C4—131no—
102C22×C13—24no—
103C22×C13—28no—
104C22×C13—42no—
105C22×C13—42no—
106C22×C13—44no—
107C22×C13C22×D411yescharacteristic
108C22×C13C22×D411yescharacteristic
109C22×C13C2×#4111yescharacteristic
110C22×C13C2×#4112yes—
111C22×C132−1+412yes—
112C4×C13—42no—
113C4×C13—42no—
114C4×C13#12114yes—
115Dic13—22no—
116Dic13—42no—
117Dic13—42no—
118Dic13—42no—
119Dic13#12414yescomplemented
120C22×Q8—131no—
121C22×Q8C2×D1311yescharacteristic
122C22×D4C2×D1311yescharacteristic
123C23×C4—132no—
124C4⋊Q8—264no—
125#124—24no—
126#124—264no—
127C4×D4—264no—
128C2×C4⋊C4—131no—
129C2×C4⋊C4—132no—
130C2×C4⋊C4—132no—
131C2×C4⋊C4—132no—
132C2×C22⋊C4—132no—
133C2×C22⋊C4—134no—
134C2×C22⋊C4C2×D1314yes—
135C2×C42—131no—
136C2×C42—131no—
137C2×C42C2×D1311yescharacteristic
138#95—132no—
139#95—134no—
140#95—134no—
141C2×C13—44no—
142C2×C13C2×#12111yescharacteristic
143C2×C13C2×#12411yescharacteristic
144C2×C13#53611yescharacteristic
145C2×C13#54712yes—
146C2×C13#55612yes—
147C24C22×D1312yes—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—22no—
151C2×Q8—262no—
152C2×Q8—262no—
153C2×Q8—262no—
154C2×D4—22no—
155C2×D4—22no—
156C2×D4C22⋊D1314yes—
157C22×C4—131no—
158C22×C4—131no—
159C22×C4—132no—
160C22×C4—132no—
161C22×C4—132no—
162C22×C4—264no—
163C22×C4—268no—
164C22×C4C22×D1312yes—
165C22×C4C22×D1312yes—
166C22×C4C22×D1311yescharacteristic
167C4⋊C4—264no—
168C4⋊C4—264no—
169C4⋊C4—264no—
170C4⋊C4—262no—
171C22⋊C4—28no—
172C22⋊C4—264no—
173C22⋊C4—268no—
174C42—22no—
175C42—134no—
176C42—262no—
177C13#254711yescharacteristic, complemented, Sylow
178C23—22no—
179C23—22no—
180C23—24no—
181C23—24no—
182C23C2×C22⋊D1314yes—
183C23C23×D1311yescharacteristic
184Q8—44no—
185Q8—524no—
186D4—28no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—132no—
194C2×C4—134no—
195C2×C4—132no—
196C2×C4—262no—
197C2×C4—262no—
198C2×C4—262no—
199C2×C4—262no—
200C2×C4—262no—
201C2×C4—264no—
202C2×C4—262no—
203C2×C4—262no—
204C2×C4—262no—
205C2×C4—528no—
206C2×C4D4×D1312yes—
207C2×C4#612912yes—
208C2×C4C2×C22⋊D1312yes—
209C22—24no—
210C22—28no—
211C22—44no—
212C22—42no—
213C22—42no—
214C22C2×D4×D1311yescharacteristic
215C22C2×#612911yescharacteristic
216C22#41×D1312yes—
217C22#8825712yes—
218C22C22×C22⋊D1311yescharacteristic
219C4—42no—
220C4—42no—
221C4—134no—
222C4—262no—
223C4—522no—
224C4—522no—
225C4—522no—
226C4#8819314yes—
227C2—44no—
228C2#1171937612yes—
229C2D13×#12411yescharacteristic
230C2#1171938011yescharacteristic
231C2C2×#8819311yescharacteristic
232C2#1171952912yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC2×C13×#124C2
prime radicalC22×D4×C13C22
hypercenterC2×#124D13
hypocenterC13#2547
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. C2×#88198C2semidirect
5. #11718891C2semidirect
6. #11718613C2semidirect
7. #11718603C2semidirect
8. C4×#6101C2semidirect
9. #11718590C2semidirect
119. Dic13#124semidirect
177. C13#2547semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#1242
C2×#881982
C2×#881902
C2×D4×Dic132
#117188912
#117186132
#117186032
C4×#61012
#117185902
#254713