Finite Group Databasebeta

← #13120577

Subgroups — #13120577

Order 1664.

632 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 143 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×#88137C212yesmaximal, complemented
4C13×#394C211yesmaximal, characteristic, complemented
5#11718883C211yesmaximal, characteristic, complemented
6#11718644C211yesmaximal, characteristic, complemented
7#11718617C212yesmaximal, complemented
8#11718609C212yesmaximal, complemented
9#11718609C212yesmaximal, complemented
10#11718328C211yesmaximal, characteristic, complemented
11#11718322C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C22×C22⋊D13C2212yes—
14C22×C4×D13C2211yescharacteristic
15C22×C4×D13C2211yescharacteristic
16C22×C4×D13C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C22⋊C4C2212yes—
19C2×C13×C22⋊C4C2212yes—
20C2×C22⋊Dic13C2212yes—
21C2×C22⋊Dic13C2212yes—
22C2×C22⋊Dic13C2212yes—
23#88192—24no—
24C2×#6103C2212yes—
25C2×C4⋊Dic13C2212yes—
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C4⋊Dic13C2211yescharacteristic
28C2×#6101C2212yes—
29C2×#6101C2211yescharacteristic
30C2×#6101C2211yescharacteristic
31C2×#6101C2212yes—
32C4⋊C4×D13—24no—
33#88137—28no—
34C13×#95C2211yescharacteristic
35#88071C2212yes—
36#88071C2211yescharacteristic
37#88071C2212yes—
38C24×C13C2312yes—
39C23×D13C2311yescharacteristic
40C2×D4×C13—22no—
41C2×D4×C13—42no—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2312yes—
44C22×C4×C13C2311yescharacteristic
45C22×C4×C13C2311yescharacteristic
46C2×C22⋊D13—24no—
47C2×C22⋊D13—24no—
48C2×C22⋊D13—24no—
49C22×Dic13C2312yes—
50C22×Dic13C2312yes—
51C22×Dic13C2311yescharacteristic
52C22×Dic13C2311yescharacteristic
53C22×Dic13C2311yescharacteristic
54C2×C4×D13—22no—
55C2×C4×D13—22no—
56C2×C4×D13—22no—
57C2×C4×D13—42no—
58C2×C4×D13—42no—
59C2×C4×D13D414yes—
60C2×C4×D13D414yescomplemented
61C13×C4⋊C4—22no—
62C13×C22⋊C4—24no—
63C13×C22⋊C4—42no—
64C22⋊Dic13—24no—
65C22⋊Dic13—24no—
66C22⋊Dic13—42no—
67#6103—24no—
68C4⋊Dic13—22no—
69C4⋊Dic13—24no—
70C4⋊Dic13—22no—
71#6101—24no—
72#6101—22no—
73#6101—22no—
74#6101—42no—
75#2618—131nomaximal, Sylow
76C23×C13—22no—
77C23×C13—22no—
78C23×C13—22no—
79C23×C13—22no—
80C23×C13—22no—
81C23×C13—22no—
82C23×C13—22no—
83C23×C13C2411yescharacteristic
84C22×D13—22no—
85C22×D13—22no—
86C22×D13C2×D412yes—
87C22×D13C2×D412yes—
88C22×D13#4112yes—
89D4×C13—44no—
90C2×C4×C13—21no—
91C2×C4×C13—21no—
92C2×C4×C13—22no—
93C2×C4×C13—21no—
94C2×C4×C13—22no—
95C2×C4×C13—22no—
96C2×C4×C13—22no—
97C2×C4×C13—22no—
98C2×C4×C13C2×D412yes—
99C2×C4×C13C2×D412yes—
100C22⋊D13—48no—
101C2×Dic13—21no—
102C2×Dic13—21no—
103C2×Dic13—22no—
104C2×Dic13—21no—
105C2×Dic13—22no—
106C2×Dic13—22no—
107C2×Dic13—22no—
108C2×Dic13—22no—
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13C2×D412yes—
113C2×Dic13C2×D412yes—
114C4×D13—28no—
115C4×D13—44no—
116C4×D13—44no—
117C2×#123—132no—
118C2×#121—131no—
119C22×C4⋊C4—131no—
120#398—131no—
121#398—131no—
122#396—132no—
123#396—132no—
124#394—131no—
125#394D1311yescharacteristic, complemented
126#386—132no—
127#380—131no—
128C22×C13—42no—
129C22×C13—42no—
130C22×C13—42no—
131C22×C13—42no—
132C22×C13—42no—
133C22×C13—42no—
134C22×C13—42no—
135C22×C13C22×D411yescharacteristic
136C22×C13C22×D411yescharacteristic
137C22×C13C2×#4111yescharacteristic
138C22×C13H(5,𝔽2)12yes—
139C22×C132−1+412yes—
140C2×D13—22no—
141C2×D13—22no—
142C2×D13—24no—
143C2×D13—24no—
144C2×D13#12114yes—
145C4×C13—22no—
146C4×C13—22no—
147C4×C13—41no—
148C4×C13—42no—
149Dic13—22no—
150Dic13—22no—
151Dic13—42no—
152Dic13—41no—
153Dic13—42no—
154C22×D4—132no—
155C22×D4C2×D1311yescharacteristic
156C23×C4—131no—
157C23×C4—131no—
158C23×C4—131no—
159#123—268no—
160#121—264no—
161C2×C4⋊C4—131no—
162C2×C4⋊C4—131no—
163C2×C4⋊C4—131no—
164C2×C4⋊C4—131no—
165C2×C4⋊C4—132no—
166C2×C4⋊C4—132no—
167C2×C4⋊C4—132no—
168C2×C4⋊C4—264no—
169C2×C4⋊C4C2×D1311yescharacteristic
170C2×C22⋊C4—132no—
171C2×C22⋊C4—132no—
172C2×C22⋊C4—132no—
173C2×C22⋊C4—132no—
174C2×C22⋊C4C2×D1312yes—
175C2×C22⋊C4C2×D1312yes—
176#95—131no—
177#95—132no—
178#95—132no—
179#95C2×D1311yescharacteristic
180C2×C13—82no—
181C2×C13C2×#12111yescharacteristic
182C2×C13#53411yescharacteristic
183C2×C13#53611yescharacteristic
184C2×C13#53712yes—
185C2×C13#53912yes—
186D13—24no—
187C24—131no—
188C24C22×D1312yes—
189C2×D4—22no—
190C2×D4—42no—
191C2×D4—264no—
192C2×D4—264no—
193C2×D4—264no—
194C22×C4—131no—
195C22×C4—131no—
196C22×C4—134no—
197C22×C4—134no—
198C22×C4—132no—
199C22×C4—131no—
200C22×C4—132no—
201C22×C4—262no—
202C22×C4—262no—
203C22×C4—262no—
204C22×C4—522no—
205C22×C4—522no—
206C22×C4C22×D1311yescharacteristic
207C22×C4C22×D1312yes—
208C22×C4C22×D1311yescharacteristic
209C22×C4C22×D1311yescharacteristic
210C4⋊C4—22no—
211C4⋊C4—262no—
212C4⋊C4—262no—
213C4⋊C4—264no—
214C4⋊C4—262no—
215C4⋊C4—262no—
216C4⋊C4—264no—
217C4⋊C4—522no—
218C22⋊C4—24no—
219C22⋊C4—42no—
220C22⋊C4—264no—
221C22⋊C4—264no—
222C22⋊C4—264no—
223C22⋊C4—522no—
224C13#261811yescharacteristic, complemented, Sylow
225C23—22no—
226C23—22no—
227C23—22no—
228C23—22no—
229C23—22no—
230C23—22no—
231C23—22no—
232C23—132no—
233C23—132no—
234C23—132no—
235C23—262no—
236C23—262no—
237C23C23×D1311yescharacteristic
238D4—44no—
239D4—528no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—132no—
249C2×C4—132no—
250C2×C4—268no—
251C2×C4—261no—
252C2×C4—262no—
253C2×C4—261no—
254C2×C4—262no—
255C2×C4—262no—
256C2×C4—261no—
257C2×C4—262no—
258C2×C4—262no—
259C2×C4—262no—
260C2×C4—262no—
261C2×C4—262no—
262C2×C4—524no—
263C2×C4—524no—
264C2×C4D4×D1312yes—
265C2×C4D4×D1312yes—
266C22—42no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—42no—
271C22—42no—
272C22—42no—
273C22—134no—
274C22—262no—
275C22—264no—
276C22—264no—
277C22—262no—
278C22C2×D4×D1311yescharacteristic
279C22C2×D4×D1311yescharacteristic
280C22#8825112yes—
281C22#41×D1311yescharacteristic
282C22#8825712yes—
283C4—22no—
284C4—22no—
285C4—41no—
286C4—42no—
287C4—262no—
288C4—262no—
289C4—521no—
290C4—522no—
291C4—522no—
292C2—82no—
293C2—264no—
294C2#1171929411yescharacteristic
295C2D13×#12111yescharacteristic
296C2#1171931312yes—
297C2#1171936512yes—
298C2#1171938011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radicalC2×#88192C2
hypercenter#394D13
hypocenterC13#2618
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×D13C2semidirect
3. C2×#88137C2semidirect
4. C13×#394C2semidirect
5. #11718883C2semidirect
6. #11718644C2semidirect
7. #11718617C2semidirect
8. #11718609C2semidirect
9. #11718609C2semidirect
10. #11718328C2semidirect
11. #11718322C2semidirect
60. C2×C4×D13D4semidirect
125. #394D13semidirect
224. C13#2618semidirect

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×#3942
#117188832
#117186442
#117186172
#117186092
#117183282
#117183222
#261813