Finite Group Databasebeta

← #13126100

Subgroups — #13126100

Order 1664.

308 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719330C211yesmaximal, characteristic
2#11719205C211yesmaximal, characteristic
3C13×#483C211yesmaximal, characteristic
4#11718706C211yesmaximal, characteristic
5#11718631C211yesmaximal, characteristic
6#11718519C211yesmaximal, characteristic, complemented
7#11718518C211yesmaximal, characteristic, complemented
8#11718517C211yesmaximal, characteristic, complemented
9#11718515C211yesmaximal, characteristic, complemented
10#11718460C211yesmaximal, characteristic, complemented
11#11718458C211yesmaximal, characteristic, complemented
12#11718455C211yesmaximal, characteristic, complemented
13#11718453C211yesmaximal, characteristic, complemented
14#11718384C211yesmaximal, characteristic
15#11718381C211yesmaximal, characteristic
16C13×C22⋊Q8C2211yescharacteristic
17C2×C13×C4⋊C4C2211yescharacteristic
18Q8×Dic13C2211yescharacteristic
19#88198C2211yescharacteristic
20#88180C2211yescharacteristic
21#88180C2211yescharacteristic
22#88178—21no—
23#88178—21no—
24#88178C2211yescharacteristic
25#88144—21no—
26#88144—21no—
27#88144C2211yescharacteristic
28#88144C2211yescharacteristic
29#88144C2211yescharacteristic
30#88143—21no—
31#88142—21no—
32#88142C2211yescharacteristic
33#88142C2211yescharacteristic
34#88141C2211yescharacteristic
35#88133—21no—
36#88133—21no—
37C13×#106C2211yescharacteristic
38C13×#106C2211yescharacteristic
39C13×#103C2211yescharacteristic
40C13×#103C2211yescharacteristic
41C13×C22⋊C8C2211yescharacteristic
42#88075C2211yescharacteristic
43#88075C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88058C2211yescharacteristic
46#88057C2211yescharacteristic
47#88056C2211yescharacteristic
48#88056C2211yescharacteristic
49#88055C2211yescharacteristic
50#88054C2211yescharacteristic
51#88054C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C22×C4×C13—21no—
61C22×C4×C13C2311yescharacteristic
62C2×Dic26—21no—
63C2×Dic26—21no—
64C2×Dic26C2311yescharacteristic
65C2×C8×C13C2311yescharacteristic
66C2×C8×C13C2311yescharacteristic
67C13×C4⋊C4—21no—
68C13×C4⋊C4—21no—
69C13×C4⋊C4C2311yescharacteristic
70C13×C4⋊C4C2311yescharacteristic
71C13×C4⋊C4C2311yescharacteristic
72C13×C22⋊C4—21no—
73C22⋊Dic13—21no—
74C22⋊Dic13—21no—
75C22⋊Dic13D411yescharacteristic
76C22⋊Dic13D411yescharacteristic
77C4⋊Dic13—21no—
78C4⋊Dic13—21no—
79C4⋊Dic13—21no—
80C4⋊Dic13—21no—
81C4⋊Dic13D411yescharacteristic
82C4⋊Dic13D411yescharacteristic
83C4⋊Dic13C2311yescharacteristic
84C4⋊Dic13C2311yescharacteristic
85C4⋊Dic13C2311yescharacteristic
86#6101—21no—
87#6101—21no—
88#6101—21no—
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95C4×Dic13—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13C2311yescharacteristic
99C4×Dic13C2311yescharacteristic
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102#3242—131nomaximal, Sylow
103C23×C13C2×D411yescharacteristic
104Q8×C13—21no—
105Q8×C13—21no—
106C2×C4×C13—21no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—81no—
113C2×C4×C13C2×D411yescharacteristic
114C2×C4×C13C2411yescharacteristic
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13C2×D411yescharacteristic
120C2×Dic13C2×D411yescharacteristic
121C2×Dic13C2×D411yescharacteristic
122C2×Dic13C2×D411yescharacteristic
123Dic26—21no—
124Dic26—21no—
125Dic26—81no—
126Dic26—81no—
127C8×C13—21no—
128C8×C13—21no—
129#1055—21no—
130#1055—21no—
131#544—131no—
132#541—131no—
133#501—131no—
134#499—131no—
135#491—131no—
136#487—131no—
137#485—131no—
138#485—131no—
139#484—131no—
140#483D1311yescharacteristic
141#479—131no—
142#479—131no—
143#477—131no—
144#475—131no—
145#433—131no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13C22×D411yescharacteristic
150C4×C13—21no—
151C4×C13—41no—
152C4×C13—41no—
153C4×C13—41no—
154C4×C13—41no—
155C4×C132−1+411yescharacteristic
156C4×C132−1+411yescharacteristic
157Dic13—21no—
158Dic13—21no—
159Dic13—21no—
160Dic13—21no—
161Dic13—41no—
162Dic13—41no—
163Dic13—41no—
164Dic13—41no—
165C4⋊Q8—131no—
166C4⋊Q8—131no—
167C4⋊Q8—131no—
168C4⋊Q8—261no—
169#126—261no—
170#126—261no—
171#125—131no—
172#125—131no—
173#125—131no—
174#125—261no—
175#125—261no—
176#125—261no—
177C22⋊Q8—131no—
178C22⋊Q8—261no—
179C22⋊Q8—261no—
180C22⋊Q8C2×D1311yescharacteristic
181C4×Q8—131no—
182C4×Q8—131no—
183#117—131no—
184#117—131no—
185C2×C4⋊C4C2×D1311yescharacteristic
186#107—131no—
187#107—131no—
188#107—131no—
189#107—131no—
190#106—131no—
191#106—131no—
192#106C2×D1311yescharacteristic
193#106C2×D1311yescharacteristic
194C4⋊C8—131no—
195C4⋊C8—131no—
196#103—131no—
197#103—131no—
198#103—131no—
199#103—131no—
200#103—131no—
201#103—131no—
202#103C2×D1311yescharacteristic
203#103C2×D1311yescharacteristic
204C22⋊C8—131no—
205C22⋊C8C2×D1311yescharacteristic
206#97—131no—
207C4×C8—131no—
208C2×C13—41no—
209C2×C13#53611yescharacteristic
210C2×C13#57711yescharacteristic
211C2×C13#57811yescharacteristic
212C2×Q8—131no—
213C2×Q8—261no—
214C2×Q8—261no—
215C2×Q8C22×D1311yescharacteristic
216C22×C4—21no—
217C22×C4C22×D1311yescharacteristic
218C2×C8—131no—
219C2×C8—131no—
220C2×C8C22×D1311yescharacteristic
221C2×C8C22×D1311yescharacteristic
222C4⋊C4—21no—
223C4⋊C4—21no—
224C4⋊C4—131no—
225C4⋊C4—131no—
226C4⋊C4—131no—
227C4⋊C4—131no—
228C4⋊C4—131no—
229C4⋊C4—261no—
230C4⋊C4—261no—
231C4⋊C4—261no—
232C4⋊C4—261no—
233C4⋊C4—261no—
234C4⋊C4—261no—
235C4⋊C4—261no—
236C4⋊C4—261no—
237C4⋊C4—261no—
238C4⋊C4—261no—
239C4⋊C4—261no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4C22×D1311yescharacteristic
243C4⋊C4C22×D1311yescharacteristic
244C4⋊C4C22×D1311yescharacteristic
245C22⋊C4—21no—
246C22⋊C4—131no—
247C22⋊C4—131no—
248C22⋊C4—261no—
249C22⋊C4—261no—
250C42—131no—
251C42—131no—
252C42—261no—
253C42—261no—
254C42—261no—
255C13#324211yescharacteristic, complemented, Sylow
256C23D4×D1311yescharacteristic
257Q8—21no—
258Q8—21no—
259Q8—261no—
260Q8—261no—
261Q8—1041no—
262Q8—1041no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—81no—
270C2×C4—131no—
271C2×C4—131no—
272C2×C4—131no—
273C2×C4—131no—
274C2×C4—261no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4D4×D1311yescharacteristic
279C2×C4C23×D1311yescharacteristic
280C8—21no—
281C8—21no—
282C8—261no—
283C8—261no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22C2×D4×D1311yescharacteristic
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—261no—
294C4—261no—
295C4—261no—
296C4—261no—
297C4—521no—
298C4—521no—
299C4—521no—
300C4—521no—
301C4#8825711yescharacteristic
302C4#8825711yescharacteristic
303C2—41no—
304C2#1171935311yescharacteristic
305C2#1171946711yescharacteristic
306C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#483C2
socleC22×C13C22×D4
prime radicalC23×C13C2×D4
hypercenter#483D13
hypocenterC13#3242
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
6. #11718519C2semidirect
7. #11718518C2semidirect
8. #11718517C2semidirect
9. #11718515C2semidirect
10. #11718460C2semidirect
11. #11718458C2semidirect
12. #11718455C2semidirect
13. #11718453C2semidirect
255. C13#3242semidirect

Maximal subgroups

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

subgroupindex
#117193302
#117192052
C13×#4832
#117187062
#117186312
#117185192
#117185182
#117185172
#117185152
#117184602
#117184582
#117184552
#117184532
#117183842
#117183812
#324213