Finite Group Databasebeta

← #13125665

Subgroups — #13125665

Order 1664.

414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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
1#11719311C211yesmaximal, characteristic
2C2×#88151C211yesmaximal, characteristic, complemented
3C13×#481C211yesmaximal, characteristic, complemented
4#11718701C211yesmaximal, characteristic, complemented
5#11718631C211yesmaximal, characteristic, complemented
6#11718529C212yesmaximal, complemented
7#11718528C212yesmaximal, complemented
8#11718444C212yesmaximal, complemented
9#11718441C212yesmaximal, complemented
10#11718400C211yesmaximal, characteristic, complemented
11#11718387C211yesmaximal, characteristic, complemented
12C2×#6129C2211yescharacteristic
13C22×C4×D13C2211yescharacteristic
14C22×Dic26C2211yescharacteristic
15C13×#121C2211yescharacteristic
16C2×C13×C4⋊C4C2211yescharacteristic
17#88192C2211yescharacteristic
18#88191—21no—
19D4×Dic13—21no—
20C2×#6105C2212yescomplemented
21C2×#6103—21no—
22C2×C4⋊Dic13—21no—
23#88178C2211yescharacteristic
24C2×Dic52C2212yescomplemented
25C2×#6094C2212yes—
26#88151—21no—
27#88151—21no—
28#88151C2212yes—
29#88151C2212yes—
30#88151C2211yescharacteristic
31#88146C2211yescharacteristic
32#88137—21no—
33#88135—21no—
34C13×#106C2212yescomplemented
35C13×#102C2212yescomplemented
36C13×C22⋊C8C2211yescharacteristic
37C22⋊#1055C2211yescharacteristic
38#88060C2212yes—
39#88056C2212yescomplemented
40#88050C2212yescomplemented
41#88050C2212yescomplemented
42#88047C2212yescomplemented
43C23×D13D411yescharacteristic
44C2×D4×C13—21no—
45C2×D4×C13C2311yescharacteristic
46C22×C4×C13—21no—
47C22×C4×C13C2311yescharacteristic
48C2×C22⋊D13—21no—
49C2×C22⋊D13—21no—
50C22×Dic13—21no—
51C22×Dic13—21no—
52C22×Dic13D411yescharacteristic
53#6129—42no—
54C2×C4×D13—42no—
55C2×C4×D13D411yescharacteristic
56C2×C4×D13D411yescharacteristic
57C2×C4×D13C2311yescharacteristic
58C2×C4×D13C2311yescharacteristic
59C2×Dic26—21no—
60C2×Dic26—42no—
61C2×Dic26C2312yes—
62C2×Dic26C2311yescharacteristic
63C2×C8×C13C2312yes—
64C13×C4⋊C4—21no—
65C13×C4⋊C4C2312yes—
66C13×C4⋊C4C2311yescharacteristic
67C13×C22⋊C4—21no—
68C22⋊Dic13—21no—
69C22⋊Dic13—21no—
70#6105—42no—
71#6103—21no—
72#6103—21no—
73#6103—22no—
74#6103—22no—
75C4⋊Dic13—21no—
76C4⋊Dic13—22no—
77C4⋊Dic13—22no—
78C4⋊Dic13C2311yescharacteristic
79#6101—21no—
80C4×Dic13—21no—
81C2×#1055C2312yes—
82Dic52—42no—
83#6094—42no—
84#3196—131nomaximal, Sylow
85C23×C13—21no—
86C23×C13C2×D411yescharacteristic
87C22×D13—22no—
88C22×D13—41no—
89C22×D13—41no—
90C22×D13C2×D411yescharacteristic
91C22×D13C2×D411yescharacteristic
92D4×C13—22no—
93D4×C13—42no—
94C2×C4×C13—22no—
95C2×C4×C13—21no—
96C2×C4×C13—22no—
97C2×C4×C13—42no—
98C2×C4×C13C2×D411yescharacteristic
99C2×C4×C13C2411yescharacteristic
100C22⋊D13—42no—
101C22⋊D13—42no—
102C2×Dic13—21no—
103C2×Dic13—21no—
104C2×Dic13—22no—
105C2×Dic13—41no—
106C2×Dic13—42no—
107C2×Dic13—42no—
108C2×Dic13C2×D411yescharacteristic
109C2×Dic13C2×D411yescharacteristic
110C4×D13—22no—
111C4×D13—22no—
112C4×D13—41no—
113C4×D13—41no—
114Dic26—22no—
115Dic26—22no—
116Dic26—22no—
117Dic26—42no—
118C8×C13—22no—
119#1055—22no—
120#525—131no—
121C2×C22⋊Q8—131no—
122#485—132no—
123#484—131no—
124#481D1311yescharacteristic, complemented
125#470—132no—
126#468—132no—
127#452—132no—
128#451—131no—
129#448—131no—
130#407—131no—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13—41no—
134C22×C13—41no—
135C22×C13—41no—
136C22×C13#13712yes—
137C22×C13C22×D411yescharacteristic
138C2×D13—21no—
139C2×D13—21no—
140C2×D13—21no—
141C2×D13—21no—
142C2×D13—21no—
143C2×D13—21no—
144C2×D13—44no—
145C4×C13—21no—
146C4×C13—41no—
147C4×C13—42no—
148C4×C13H(5,𝔽2)12yes—
149Dic13—21no—
150Dic13—21no—
151Dic13—42no—
152Dic13—41no—
153Dic13—41no—
154C2×#41—131no—
155C22×Q8—131no—
156C23×C4—131no—
157C2×Q16—132no—
158C2×SD16—132no—
159C2×M16—132no—
160#123—261no—
161C22⋊Q8—131no—
162C22⋊Q8—132no—
163C22⋊Q8—132no—
164C22⋊Q8—131no—
165C22⋊Q8—261no—
166C22⋊Q8—261no—
167#121—131no—
168#121C2×D1311yescharacteristic
169#120—261no—
170C4×D4—261no—
171C4×D4—261no—
172#117—131no—
173C2×C4⋊C4—261no—
174C2×C4⋊C4C2×D1311yescharacteristic
175C2×C22⋊C4—261no—
176#107—132no—
177#106C2×D1312yescomplemented
178#103—132no—
179#103—132no—
180#103—132no—
181#102C2×D1312yescomplemented
182C22⋊C8—131no—
183C22⋊C8—132no—
184C22⋊C8C2×D1311yescharacteristic
185C2×C13—22no—
186C2×C13—81no—
187C2×C13#53411yescharacteristic
188C2×C13C2×#13711yescharacteristic
189C2×C13#57511yescharacteristic
190D13—41no—
191D13—41no—
192C24—131no—
193#41—522no—
194C2×Q8—132no—
195C2×Q8—131no—
196C2×Q8—261no—
197C2×Q8—522no—
198C2×D4—21no—
199C2×D4—261no—
200C2×D4—261no—
201C2×D4C22×D1311yescharacteristic
202C22×C4—21no—
203C22×C4—131no—
204C22×C4—131no—
205C22×C4—131no—
206C22×C4—131no—
207C22×C4—131no—
208C22×C4—261no—
209C22×C4—261no—
210C22×C4—522no—
211C22×C4C22×D1311yescharacteristic
212Q16—522no—
213SD16—522no—
214M16—522no—
215C2×C8—132no—
216C2×C8C22×D1312yes—
217C4⋊C4—21no—
218C4⋊C4—131no—
219C4⋊C4—262no—
220C4⋊C4—262no—
221C4⋊C4—261no—
222C4⋊C4—261no—
223C4⋊C4C22×D1312yes—
224C4⋊C4C22×D1311yescharacteristic
225C22⋊C4—21no—
226C22⋊C4—262no—
227C22⋊C4—262no—
228C22⋊C4—261no—
229C22⋊C4—261no—
230C22⋊C4—261no—
231C22⋊C4—261no—
232C42—261no—
233C13#319611yescharacteristic, complemented, Sylow
234C23—21no—
235C23—131no—
236C23—131no—
237C23—262no—
238C23—521no—
239C23—521no—
240C23D4×D1311yescharacteristic
241Q8—262no—
242Q8—262no—
243Q8—262no—
244Q8—522no—
245D4—22no—
246D4—42no—
247D4—522no—
248D4—522no—
249C2×C4—22no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—42no—
253C2×C4—131no—
254C2×C4—131no—
255C2×C4—262no—
256C2×C4—262no—
257C2×C4—261no—
258C2×C4—261no—
259C2×C4—262no—
260C2×C4—521no—
261C2×C4—521no—
262C2×C4—521no—
263C2×C4—522no—
264C2×C4—522no—
265C2×C4D4×D1311yescharacteristic
266C2×C4C23×D1311yescharacteristic
267C8—22no—
268C8—262no—
269C22—21no—
270C22—21no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—261no—
275C22—261no—
276C22—261no—
277C22—261no—
278C22—261no—
279C22—261no—
280C22—524no—
281C22#8816912yes—
282C22C2×D4×D1311yescharacteristic
283C4—21no—
284C4—41no—
285C4—42no—
286C4—261no—
287C4—261no—
288C4—521no—
289C4—521no—
290C4—522no—
291C4#8825612yes—
292C2—22no—
293C2—81no—
294C2—521no—
295C2—521no—
296C2#1171935811yescharacteristic
297C2C2×#8816911yescharacteristic
298C2#1171947811yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#481C2
socleC22×C13C22×D4
prime radical#11719311C2
hypercenter#481D13
hypocenterC13#3196
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#88151C2semidirect
3. C13×#481C2semidirect
4. #11718701C2semidirect
5. #11718631C2semidirect
6. #11718529C2semidirect
7. #11718528C2semidirect
8. #11718444C2semidirect
9. #11718441C2semidirect
10. #11718400C2semidirect
11. #11718387C2semidirect
20. C2×#6105C22semidirect
24. C2×Dic52C22semidirect
34. C13×#106C22semidirect
35. C13×#102C22semidirect
39. #88056C22semidirect
40. #88050C22semidirect
41. #88050C22semidirect
42. #88047C22semidirect
124. #481D13semidirect
177. #106C2×D13semidirect
181. #102C2×D13semidirect
233. C13#3196semidirect

Maximal subgroups

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

subgroupindex
#117193112
C2×#881512
C13×#4812
#117187012
#117186312
#117185292
#117185282
#117184442
#117184412
#117184002
#117183872
#319613