Finite Group Databasebeta

← #13119740

Subgroups — #13119740

Order 1664.

604 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 151 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×D4×Dic13C211yesmaximal, characteristic
2C2×#88141C211yesmaximal, characteristic, complemented
3C2×#88132C212yesmaximal, complemented
4C13×#394C211yesmaximal, characteristic
5#11718883C211yesmaximal, characteristic
6#11718644C211yesmaximal, characteristic, complemented
7#11718612C212yesmaximal, complemented
8#11718606C212yesmaximal, complemented
9#11718603C212yesmaximal, complemented
10#11718322C211yesmaximal, characteristic, complemented
11#11718311C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C23×Dic13C2212yes—
14C22×Dic26C2211yescharacteristic
15C2×C13×C4⋊C4C2211yescharacteristic
16C2×C13×C22⋊C4C2212yes—
17C2×C13×C22⋊C4C2212yes—
18C2×C22⋊Dic13C2212yes—
19C2×C22⋊Dic13C2212yes—
20C2×C22⋊Dic13C2212yes—
21D4×Dic13—24no—
22C2×C4⋊Dic13C2212yes—
23C2×C4⋊Dic13C2211yescharacteristic
24C2×#6101C2212yes—
25C2×#6101C2212yes—
26C2×#6101C2211yescharacteristic
27C2×#6101C2211yescharacteristic
28C2×C4×Dic13C2211yescharacteristic
29C2×C4×Dic13C2211yescharacteristic
30C2×C4×Dic13C2211yescharacteristic
31#88141—24no—
32#88132—28no—
33C13×#95C2211yescharacteristic
34#88071C2212yes—
35#88071C2211yescharacteristic
36#88071C2212yes—
37#88071C2212yes—
38C24×C13C2312yes—
39C2×D4×C13—24no—
40C2×D4×C13—22no—
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C22×Dic13—24no—
46C22×Dic13—24no—
47C22×Dic13—24no—
48C22×Dic13C2312yes—
49C22×Dic13C2311yescharacteristic
50C22×Dic13C2312yes—
51C22×Dic13C2311yescharacteristic
52C22×Dic13C2311yescharacteristic
53C22×Dic13C2311yescharacteristic
54C2×Dic26—22no—
55C2×Dic26—22no—
56C2×Dic26D414yescomplemented
57C13×C4⋊C4—22no—
58C13×C22⋊C4—24no—
59C13×C22⋊C4—24no—
60C22⋊Dic13—24no—
61C22⋊Dic13—24no—
62C22⋊Dic13—24no—
63C4⋊Dic13—22no—
64C4⋊Dic13—24no—
65#6101—24no—
66#6101—22no—
67#6101—24no—
68#6101—22no—
69C4×Dic13—22no—
70C4×Dic13—22no—
71C4×Dic13D414yes—
72#2536—131nomaximal, Sylow
73C23×C13—22no—
74C23×C13—22no—
75C23×C13—22no—
76C23×C13—22no—
77C23×C13—22no—
78C23×C13—22no—
79C23×C13#4114yes—
80C23×C13C2411yescharacteristic
81D4×C13—28no—
82C2×C4×C13—21no—
83C2×C4×C13—21no—
84C2×C4×C13—22no—
85C2×C4×C13—21no—
86C2×C4×C13—22no—
87C2×C4×C13—22no—
88C2×C4×C13—22no—
89C2×C4×C13—22no—
90C2×C4×C13C2×D412yes—
91C2×C4×C13C2×D412yes—
92C2×Dic13—21no—
93C2×Dic13—21no—
94C2×Dic13—22no—
95C2×Dic13—21no—
96C2×Dic13—22no—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—22no—
101C2×Dic13—22no—
102C2×Dic13—22no—
103C2×Dic13—48no—
104C2×Dic13C2×D412yes—
105C2×Dic13C2×D412yes—
106C2×Dic13C2×D412yes—
107C2×Dic13C2×D412yes—
108C2×Dic13#4112yes—
109Dic26—28no—
110C2×C22⋊Q8—132no—
111C2×C4×Q8—131no—
112C2×C4×D4—131no—
113#398—131no—
114#398—131no—
115#394—131no—
116#394D1311yescharacteristic
117#388—132no—
118#388—132no—
119#382—131no—
120#380—132no—
121C22×C13—24no—
122C22×C13—24no—
123C22×C13—24no—
124C22×C13—42no—
125C22×C13—42no—
126C22×C13—42no—
127C22×C13—42no—
128C22×C13C22×D411yescharacteristic
129C22×C13C22×D411yescharacteristic
130C22×C13C2×#4112yes—
131C22×C13C2×#4111yescharacteristic
132C22×C132−1+412yes—
133C4×C13—22no—
134C4×C13—22no—
135C4×C13—41no—
136C4×C13—42no—
137Dic13—22no—
138Dic13—22no—
139Dic13—42no—
140Dic13—41no—
141Dic13—42no—
142Dic13#12114yes—
143C22×Q8—131no—
144C22×D4C2×D1311yescharacteristic
145C23×C4—132no—
146C22⋊Q8—268no—
147C4×Q8—264no—
148C4×D4—264no—
149C2×C4⋊C4—131no—
150C2×C4⋊C4—131no—
151C2×C4⋊C4—131no—
152C2×C4⋊C4—132no—
153C2×C4⋊C4—132no—
154C2×C4⋊C4—132no—
155C2×C4⋊C4C2×D1311yescharacteristic
156C2×C22⋊C4—132no—
157C2×C22⋊C4—132no—
158C2×C22⋊C4—132no—
159C2×C22⋊C4C2×D1312yes—
160C2×C22⋊C4C2×D1312yes—
161C2×C42—131no—
162C2×C42—131no—
163C2×C42—131no—
164#95—132no—
165#95—132no—
166#95—132no—
167#95—131no—
168#95C2×D1311yescharacteristic
169C2×C13—44no—
170C2×C13C2×#12111yescharacteristic
171C2×C13#52511yescharacteristic
172C2×C13#53611yescharacteristic
173C2×C13#54812yes—
174C2×C13#55212yes—
175C24C22×D1312yes—
176C2×Q8—134no—
177C2×Q8—262no—
178C2×Q8—262no—
179C2×D4—24no—
180C2×D4—22no—
181C22×C4—131no—
182C22×C4—131no—
183C22×C4—131no—
184C22×C4—132no—
185C22×C4—131no—
186C22×C4—132no—
187C22×C4—264no—
188C22×C4—264no—
189C22×C4—264no—
190C22×C4C22×D1312yes—
191C22×C4C22×D1311yescharacteristic
192C22×C4C22×D1311yescharacteristic
193C22×C4C22×D1311yescharacteristic
194C4⋊C4—22no—
195C4⋊C4—262no—
196C4⋊C4—264no—
197C4⋊C4—264no—
198C4⋊C4—262no—
199C4⋊C4—262no—
200C4⋊C4—264no—
201C22⋊C4—24no—
202C22⋊C4—24no—
203C22⋊C4—264no—
204C22⋊C4—264no—
205C22⋊C4—264no—
206C42—134no—
207C42—262no—
208C42—262no—
209C13#253611yescharacteristic, complemented, Sylow
210C23—22no—
211C23—22no—
212C23—22no—
213C23—22no—
214C23—22no—
215C23—22no—
216C23#612914yes—
217C23C23×D1311yescharacteristic
218Q8—268no—
219D4—28no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—132no—
229C2×C4—132no—
230C2×C4—132no—
231C2×C4—132no—
232C2×C4—132no—
233C2×C4—261no—
234C2×C4—261no—
235C2×C4—262no—
236C2×C4—261no—
237C2×C4—262no—
238C2×C4—262no—
239C2×C4—262no—
240C2×C4—262no—
241C2×C4—262no—
242C2×C4—262no—
243C2×C4—262no—
244C2×C4—528no—
245C2×C4D4×D1312yes—
246C2×C4D4×D1312yes—
247C22—24no—
248C22—24no—
249C22—24no—
250C22—42no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22C2×D4×D1311yescharacteristic
255C22C2×D4×D1311yescharacteristic
256C22C2×#612912yes—
257C22#41×D1311yescharacteristic
258C22#8825712yes—
259C4—22no—
260C4—22no—
261C4—41no—
262C4—42no—
263C4—134no—
264C4—262no—
265C4—262no—
266C4—521no—
267C4—522no—
268C4—522no—
269C2—44no—
270C2#1171929111yescharacteristic
271C2#1171930312yes—
272C2D13×#12111yescharacteristic
273C2#1171935512yes—
274C2#1171938011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radicalC22×D4×C13C22
hypercenter#394D13
hypocenterC13#2536
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#88141C2semidirect
3. C2×#88132C2semidirect
6. #11718644C2semidirect
7. #11718612C2semidirect
8. #11718606C2semidirect
9. #11718603C2semidirect
10. #11718322C2semidirect
11. #11718311C2semidirect
56. C2×Dic26D4semidirect
209. C13#2536semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic132
C2×#881412
C2×#881322
C13×#3942
#117188832
#117186442
#117186122
#117186062
#117186032
#117183222
#117183112
#253613