Finite Group Databasebeta

← #13119834

Subgroups — #13119834

Order 1664.

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

normal subgroups only

This group has 676 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×#88194C211yesmaximal, characteristic
2C2×#88141C211yesmaximal, characteristic, complemented
3C2×#88139C212yesmaximal, complemented
4C13×#394C211yesmaximal, characteristic, complemented
5#11718883C211yesmaximal, characteristic, complemented
6#11718652C211yesmaximal, characteristic, complemented
7#11718618C212yesmaximal, complemented
8#11718618C212yesmaximal, complemented
9#11718618C212yesmaximal, complemented
10#11718333C211yesmaximal, characteristic, complemented
11#11718310C211yesmaximal, characteristic, complemented
12C22×D4×C13C2211yescharacteristic
13C22×C22⋊D13C2212yes—
14C22×C22⋊D13C2212yes—
15C22×D52C2211yescharacteristic
16C22×Dic26C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18C2×C13×C22⋊C4C2212yes—
19C2×C13×C22⋊C4C2212yes—
20C2×C22⋊Dic13C2212yes—
21C2×C22⋊Dic13C2212yes—
22#88194—24no—
23C2×#6103C2212yes—
24C2×#6103C2212yes—
25C2×#6103C2212yes—
26C2×#6103C2212yes—
27C2×#6101C2211yescharacteristic
28C2×#6101C2211yescharacteristic
29C2×#6101C2212yes—
30C2×C4×Dic13C2212yes—
31C2×C4×Dic13C2211yescharacteristic
32C2×C4×Dic13C2211yescharacteristic
33C2×C4×Dic13C2211yescharacteristic
34#88141—24no—
35#88139—28no—
36C13×#95C2211yescharacteristic
37#88071C2211yescharacteristic
38C24×C13C2312yes—
39C23×D13C2312yes—
40C2×D4×C13—22no—
41C2×D4×C13—42no—
42C22×C4×C13C2312yes—
43C22×C4×C13C2311yescharacteristic
44C22×C4×C13C2311yescharacteristic
45C22×C4×C13C2311yescharacteristic
46C2×C22⋊D13—24no—
47C2×C22⋊D13—24no—
48C2×C22⋊D13—24no—
49C2×C22⋊D13—24no—
50C2×C22⋊D13—24no—
51C2×C22⋊D13—24no—
52C22×Dic13C2312yes—
53C22×Dic13C2311yescharacteristic
54C22×Dic13C2311yescharacteristic
55C22×Dic13C2311yescharacteristic
56C22×Dic13C2311yescharacteristic
57C2×D52—22no—
58C2×D52—42no—
59C2×Dic26—22no—
60C2×Dic26—22no—
61C2×Dic26D414yescomplemented
62C13×C4⋊C4—22no—
63C13×C22⋊C4—24no—
64C13×C22⋊C4—42no—
65C22⋊Dic13—24no—
66C22⋊Dic13—42no—
67#6103—24no—
68#6103—24no—
69#6103—42no—
70#6103—42no—
71#6101—22no—
72#6101—22no—
73#6101—24no—
74C4×Dic13—24no—
75C4×Dic13—22no—
76C4×Dic13—22no—
77C4×Dic13D414yes—
78#2548—131nomaximal, Sylow
79C23×C13—22no—
80C23×C13—22no—
81C23×C13—22no—
82C23×C13—22no—
83C23×C13—22no—
84C23×C13—22no—
85C23×C13—22no—
86C23×C13C2411yescharacteristic
87C22×D13—22no—
88C22×D13—22no—
89C22×D13—22no—
90C22×D13—22no—
91C22×D13—22no—
92C22×D13—22no—
93C22×D13—22no—
94D4×C13—44no—
95C2×C4×C13—21no—
96C2×C4×C13—21no—
97C2×C4×C13—22no—
98C2×C4×C13—21no—
99C2×C4×C13—22no—
100C2×C4×C13—22no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13C2×D412yes—
104C2×C4×C13C2×D412yes—
105C22⋊D13—48no—
106C22⋊D13—48no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—21no—
110C2×Dic13—22no—
111C2×Dic13—22no—
112C2×Dic13—22no—
113C2×Dic13—22no—
114C2×Dic13C2×D412yes—
115C2×Dic13C2×D412yes—
116C2×Dic13C2×D412yes—
117C2×Dic13C2×D412yes—
118C2×Dic13#4112yes—
119C2×Dic13#4114yes—
120D52—44no—
121Dic26—28no—
122C2×#127—131no—
123C2×#124—132no—
124C2×C4×Q8—131no—
125#394—131no—
126#394—131no—
127#394—131no—
128#394D1311yescharacteristic, complemented
129#390—132no—
130#390—132no—
131#390—132no—
132C4×C4⋊C4—131no—
133C22×C13—42no—
134C22×C13—42no—
135C22×C13—42no—
136C22×C13—42no—
137C22×C13—42no—
138C22×C13—42no—
139C22×C13—42no—
140C22×C13C22×D411yescharacteristic
141C22×C13C22×D411yescharacteristic
142C22×C13C2×#4111yescharacteristic
143C22×C13C2×#4112yes—
144C22×C13H(5,𝔽2)12yes—
145C2×D13—42no—
146C2×D13—42no—
147C2×D13—42no—
148C2×D13—42no—
149C2×D13—42no—
150C2×D13—42no—
151C2×D13—42no—
152C4×C13—22no—
153C4×C13—22no—
154C4×C13—41no—
155C4×C13—42no—
156Dic13—22no—
157Dic13—41no—
158Dic13—42no—
159Dic13#12114yes—
160Dic13#12414yescomplemented
161C22×Q8—131no—
162C22×D4—132no—
163C22×D4—132no—
164C22×D4—131no—
165C22×D4C2×D1311yescharacteristic
166#127—264no—
167#124—268no—
168C4×Q8—264no—
169C2×C4⋊C4—131no—
170C2×C4⋊C4—131no—
171C2×C4⋊C4—132no—
172C2×C4⋊C4C2×D1311yescharacteristic
173C2×C22⋊C4—132no—
174C2×C22⋊C4—132no—
175C2×C22⋊C4—132no—
176C2×C22⋊C4—132no—
177C2×C22⋊C4—132no—
178C2×C22⋊C4—132no—
179C2×C22⋊C4C2×D1312yes—
180C2×C22⋊C4C2×D1312yes—
181C2×C42—131no—
182C2×C42—131no—
183C2×C42—131no—
184C2×C42—132no—
185#95—131no—
186#95C2×D1311yescharacteristic
187C2×C13—82no—
188C2×C13C2×#12111yescharacteristic
189C2×C13C2×#12411yescharacteristic
190C2×C13#53511yescharacteristic
191C2×C13#55012yes—
192C2×C13#55912yes—
193D13—82no—
194C24—132no—
195C24C22×D1312yes—
196C2×Q8—134no—
197C2×Q8—262no—
198C2×Q8—262no—
199C2×D4—22no—
200C2×D4—42no—
201C2×D4—264no—
202C2×D4—264no—
203C2×D4—264no—
204C2×D4—264no—
205C2×D4—264no—
206C2×D4—264no—
207C2×D4—262no—
208C2×D4—522no—
209C22×C4—131no—
210C22×C4—131no—
211C22×C4—131no—
212C22×C4—132no—
213C22×C4—131no—
214C22×C4C22×D1312yes—
215C22×C4C22×D1311yescharacteristic
216C22×C4C22×D1311yescharacteristic
217C22×C4C22×D1311yescharacteristic
218C4⋊C4—22no—
219C4⋊C4—262no—
220C4⋊C4—264no—
221C4⋊C4—262no—
222C22⋊C4—24no—
223C22⋊C4—42no—
224C22⋊C4—264no—
225C22⋊C4—264no—
226C22⋊C4—264no—
227C22⋊C4—522no—
228C22⋊C4—522no—
229C22⋊C4—522no—
230C42—134no—
231C42—262no—
232C42—262no—
233C42—264no—
234C13#254811yescharacteristic, complemented, Sylow
235C23—22no—
236C23—22no—
237C23—22no—
238C23—22no—
239C23—22no—
240C23—22no—
241C23—22no—
242C23—262no—
243C23—262no—
244C23—262no—
245C23—262no—
246C23—262no—
247C23—262no—
248C23—262no—
249C23C23×D1311yescharacteristic
250Q8—268no—
251D4—44no—
252D4—524no—
253D4—528no—
254D4—528no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—21no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—22no—
263C2×C4—132no—
264C2×C4—132no—
265C2×C4—132no—
266C2×C4—134no—
267C2×C4—132no—
268C2×C4—132no—
269C2×C4—261no—
270C2×C4—261no—
271C2×C4—262no—
272C2×C4—261no—
273C2×C4—262no—
274C2×C4—262no—
275C2×C4—262no—
276C2×C4D4×D1312yes—
277C2×C4D4×D1312yes—
278C22—42no—
279C22—42no—
280C22—42no—
281C22—42no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—522no—
286C22—522no—
287C22—522no—
288C22—522no—
289C22—522no—
290C22—522no—
291C22—522no—
292C22C2×D4×D1311yescharacteristic
293C22C2×D4×D1311yescharacteristic
294C22#8825112yes—
295C22#41×D1312yes—
296C22#41×D1311yescharacteristic
297C4—22no—
298C4—22no—
299C4—41no—
300C4—42no—
301C4—134no—
302C4—134no—
303C4—262no—
304C4—521no—
305C4—522no—
306C2—82no—
307C2—1042no—
308C2#1171929711yescharacteristic
309C2#1171930412yes—
310C2D13×#12111yescharacteristic
311C2#1171936912yes—
312C2D13×#12411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#394C2
prime radicalC2×#88194C2
hypercenter#394D13
hypocenterC13#2548
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×#88139C2semidirect
4. C13×#394C2semidirect
5. #11718883C2semidirect
6. #11718652C2semidirect
7. #11718618C2semidirect
8. #11718618C2semidirect
9. #11718618C2semidirect
10. #11718333C2semidirect
11. #11718310C2semidirect
61. C2×Dic26D4semidirect
128. #394D13semidirect
160. Dic13#124semidirect
234. C13#2548semidirect

Maximal subgroups

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

subgroupindex
C2×#881942
C2×#881412
C2×#881392
C13×#3942
#117188832
#117186522
#117186182
#117183332
#117183102
#254813