Finite Group Databasebeta

← #13120687

Subgroups — #13120687

Order 1664.

628 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 628 conjugacy classes of subgroups — too many to draw. Only its 133 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, complemented
2C2×#88139C211yesmaximal, characteristic, complemented
3C13×#392C211yesmaximal, characteristic, complemented
4#11718884C212yesmaximal, complemented
5#11718884C211yesmaximal, characteristic, complemented
6#11718881C212yesmaximal, complemented
7#11718619C212yesmaximal, complemented
8#11718614C211yesmaximal, characteristic, complemented
9#11718608C212yesmaximal, complemented
10#11718335C211yesmaximal, characteristic, complemented
11#11718312C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C22×D4×C13C2212yes—
14C22×C22⋊D13C2211yescharacteristic
15C22×C22⋊D13C2212yes—
16C23×Dic13C2212yes—
17C22×Dic26C2211yescharacteristic
18C2×C13×C22⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2212yes—
20C2×C22⋊Dic13C2211yescharacteristic
21C2×C22⋊Dic13C2212yes—
22C2×C22⋊Dic13C2212yes—
23C2×C22⋊Dic13C2212yes—
24D4×Dic13—24no—
25C2×#6103C2211yescharacteristic
26C2×#6103C2211yescharacteristic
27C2×#6103C2212yes—
28C2×C4⋊Dic13C2211yescharacteristic
29C2×C4×Dic13C2211yescharacteristic
30#88139—24no—
31C13×#95C2211yescharacteristic
32#88071C2212yes—
33#88071C2211yescharacteristic
34#88071C2212yes—
35#88071C2212yes—
36#88071C2212yes—
37C24×C13C2311yescharacteristic
38C24×C13C2312yes—
39C23×D13C2311yescharacteristic
40C2×D4×C13—24no—
41C2×D4×C13—24no—
42C2×D4×C13—22no—
43C2×D4×C13—42no—
44C2×D4×C13—42no—
45C22×C4×C13C2312yes—
46C22×C4×C13C2311yescharacteristic
47C22×C4×C13C2311yescharacteristic
48C2×C22⋊D13—24no—
49C2×C22⋊D13—22no—
50C2×C22⋊D13—42no—
51C2×C22⋊D13—42no—
52C2×C22⋊D13—42no—
53C22×Dic13—24no—
54C22×Dic13—42no—
55C22×Dic13—42no—
56C22×Dic13C2312yes—
57C22×Dic13C2312yes—
58C22×Dic13C2311yescharacteristic
59C22×Dic13C2311yescharacteristic
60C22×Dic13C2311yescharacteristic
61C2×Dic26—22no—
62C2×Dic26—42no—
63C13×C22⋊C4—22no—
64C13×C22⋊C4—42no—
65C22⋊Dic13—22no—
66C22⋊Dic13—24no—
67C22⋊Dic13—42no—
68C22⋊Dic13—42no—
69#6103—22no—
70#6103—22no—
71#6103—42no—
72C4⋊Dic13—22no—
73C4×Dic13D414yescomplemented
74#2631—131nomaximal, Sylow
75C23×C13—22no—
76C23×C13—22no—
77C23×C13—22no—
78C23×C13—22no—
79C23×C13—22no—
80C23×C13—22no—
81C23×C13—21no—
82C23×C13—22no—
83C23×C13—21no—
84C23×C13—22no—
85C23×C13—21no—
86C23×C13#4114yes—
87C23×C13C2411yescharacteristic
88C22×D13—21no—
89C22×D13—22no—
90C22×D13—21no—
91C22×D13—22no—
92C22×D13—21no—
93D4×C13—28no—
94D4×C13—48no—
95C2×C4×C13—22no—
96C2×C4×C13—21no—
97C2×C4×C13—22no—
98C2×C4×C13—22no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13C2×D412yes—
102C22⋊D13—44no—
103C22⋊D13—48no—
104C2×Dic13—22no—
105C2×Dic13—21no—
106C2×Dic13—21no—
107C2×Dic13—22no—
108C2×Dic13—21no—
109C2×Dic13—22no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—22no—
114C2×Dic13—22no—
115C2×Dic13—48no—
116C2×Dic13C2×D412yes—
117C2×Dic13C2×D412yes—
118Dic26—44no—
119C2×#124—131no—
120C2×C4×D4—131no—
121#397—131no—
122#397—131no—
123#393—132no—
124#392—132no—
125#392—131no—
126#392D1311yescharacteristic, complemented
127#386—132no—
128#386—132no—
129#383—131no—
130C22×C13—24no—
131C22×C13—24no—
132C22×C13—24no—
133C22×C13—42no—
134C22×C13—42no—
135C22×C13—42no—
136C22×C13—42no—
137C22×C13—41no—
138C22×C13—41no—
139C22×C13—41no—
140C22×C13—42no—
141C22×C13—42no—
142C22×C13C22×D411yescharacteristic
143C22×C13C2×#4112yes—
144C22×C13H(5,𝔽2)11yescharacteristic
145C22×C13H(5,𝔽2)12yes—
146C22×C13H(5,𝔽2)11yescharacteristic
147C2×D13—41no—
148C2×D13—41no—
149C2×D13—41no—
150C2×D13—42no—
151C2×D13—42no—
152C4×C13—22no—
153C4×C13—41no—
154C4×C13—42no—
155Dic13—22no—
156Dic13—22no—
157Dic13—41no—
158Dic13—42no—
159Dic13—42no—
160C22×Q8—131no—
161C22×D4—131no—
162C22×D4—132no—
163C22×D4C2×D1311yescharacteristic
164C22×D4C2×D1312yes—
165C23×C4—132no—
166#124—264no—
167C4×D4—264no—
168C2×C4⋊C4—131no—
169C2×C22⋊C4—132no—
170C2×C22⋊C4—131no—
171C2×C22⋊C4—131no—
172C2×C22⋊C4—131no—
173C2×C22⋊C4—132no—
174C2×C22⋊C4—132no—
175C2×C22⋊C4—132no—
176C2×C22⋊C4C2×D1311yescharacteristic
177C2×C22⋊C4C2×D1312yes—
178C2×C42—131no—
179#95—132no—
180#95—132no—
181#95—131no—
182#95—132no—
183#95—132no—
184#95C2×D1311yescharacteristic
185C2×C13—44no—
186C2×C13—81no—
187C2×C13#52511yescharacteristic
188C2×C13#53511yescharacteristic
189C2×C13#53511yescharacteristic
190C2×C13#53812yes—
191C2×C13#53812yes—
192D13—81no—
193C24—131no—
194C24C22×D1311yescharacteristic
195C24C22×D1312yes—
196C2×Q8—262no—
197C2×Q8—522no—
198C2×D4—24no—
199C2×D4—24no—
200C2×D4—22no—
201C2×D4—42no—
202C2×D4—42no—
203C2×D4—262no—
204C2×D4—264no—
205C2×D4—522no—
206C2×D4—522no—
207C2×D4—522no—
208C22×C4—131no—
209C22×C4—131no—
210C22×C4—132no—
211C22×C4—131no—
212C22×C4—132no—
213C22×C4—264no—
214C22×C4—522no—
215C22×C4—522no—
216C22×C4C22×D1312yes—
217C22×C4C22×D1311yescharacteristic
218C22×C4C22×D1311yescharacteristic
219C4⋊C4—262no—
220C22⋊C4—22no—
221C22⋊C4—42no—
222C22⋊C4—262no—
223C22⋊C4—264no—
224C22⋊C4—262no—
225C22⋊C4—262no—
226C22⋊C4—522no—
227C22⋊C4—522no—
228C22⋊C4—522no—
229C42—134no—
230C13#263111yescharacteristic, complemented, Sylow
231C23—22no—
232C23—22no—
233C23—22no—
234C23—22no—
235C23—22no—
236C23—22no—
237C23—21no—
238C23—22no—
239C23—21no—
240C23—22no—
241C23—21no—
242C23—261no—
243C23—262no—
244C23—261no—
245C23—262no—
246C23—261no—
247C23#612914yes—
248C23C23×D1311yescharacteristic
249Q8—524no—
250D4—28no—
251D4—48no—
252D4—524no—
253D4—528no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—132no—
261C2×C4—132no—
262C2×C4—261no—
263C2×C4—262no—
264C2×C4—261no—
265C2×C4—261no—
266C2×C4—262no—
267C2×C4—262no—
268C2×C4—262no—
269C2×C4—262no—
270C2×C4—262no—
271C2×C4—262no—
272C2×C4—262no—
273C2×C4—528no—
274C2×C4D4×D1312yes—
275C22—24no—
276C22—24no—
277C22—24no—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—41no—
283C22—42no—
284C22—41no—
285C22—42no—
286C22—41no—
287C22—521no—
288C22—522no—
289C22—521no—
290C22—522no—
291C22—521no—
292C22C2×D4×D1311yescharacteristic
293C22C2×#612912yes—
294C22#8825111yescharacteristic
295C22#8825112yes—
296C22#8825611yescharacteristic
297C4—22no—
298C4—42no—
299C4—41no—
300C4—262no—
301C4—262no—
302C4—522no—
303C4—522no—
304C4—521no—
305C2—44no—
306C2—81no—
307C2—1041no—
308C2#1171929111yescharacteristic
309C2#1171929812yes—
310C2#1171931211yescharacteristic
311C2#1171932212yes—
312C2#1171942011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#392C2
hypercenter#392D13
hypocenterC13#2631
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic13C2semidirect
2. C2×#88139C2semidirect
3. C13×#392C2semidirect
4. #11718884C2semidirect
5. #11718884C2semidirect
6. #11718881C2semidirect
7. #11718619C2semidirect
8. #11718614C2semidirect
9. #11718608C2semidirect
10. #11718335C2semidirect
11. #11718312C2semidirect
73. C4×Dic13D4semidirect
126. #392D13semidirect
230. C13#2631semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic132
C2×#881392
C13×#3922
#117188842
#117188812
#117186192
#117186142
#117186082
#117183352
#117183122
#263113