Finite Group Databasebeta

← #13127579

Subgroups — #13127579

Order 1664.

338 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719427C211yesmaximal, characteristic, complemented
2#11719273C211yesmaximal, characteristic
3C13×#475C211yesmaximal, characteristic, complemented
4#11718750C211yesmaximal, characteristic
5#11718691C211yesmaximal, characteristic, complemented
6#11718531C211yesmaximal, characteristic
7#11718515C211yesmaximal, characteristic, complemented
8#11718514C211yesmaximal, characteristic, complemented
9#11718513C211yesmaximal, characteristic
10#11718506C211yesmaximal, characteristic
11#11718489C211yesmaximal, characteristic, complemented
12#11718459C211yesmaximal, characteristic
13#11718456C211yesmaximal, characteristic
14#11718454C211yesmaximal, characteristic, complemented
15#11718453C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C4×Q8×C13C2211yescharacteristic
18#88201C2211yescharacteristic
19#88198—21no—
20#88198—21no—
21#88198C2211yescharacteristic
22C2×#6107C2211yescharacteristic
23C2×Dic52C2211yescharacteristic
24C2×#6095C2211yescharacteristic
25#88152—21no—
26#88150—21no—
27#88147C2211yescharacteristic
28#88142—21no—
29#88142C2211yescharacteristic
30#88142C2211yescharacteristic
31#88141—21no—
32#88141C2211yescharacteristic
33#88141C2211yescharacteristic
34#88141C2211yescharacteristic
35#88130—21no—
36#88129C2211yescharacteristic
37#88126—21no—
38C4×Dic26C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×#106C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C13×C4⋊C8C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×#103C2211yescharacteristic
45#88075C2211yescharacteristic
46#88061C2211yescharacteristic
47#88056C2211yescharacteristic
48#88055C2211yescharacteristic
49#88054C2211yescharacteristic
50#88054C2211yescharacteristic
51C8×Dic13C2211yescharacteristic
52#88050C2211yescharacteristic
53#88050C2211yescharacteristic
54#88050C2211yescharacteristic
55#88049C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D52C2311yescharacteristic
62C2×C4×D13—21no—
63C2×Dic26—21no—
64C2×Dic26—21no—
65C2×Dic26D411yescharacteristic
66C2×Dic26C2311yescharacteristic
67C2×Dic26C2311yescharacteristic
68C2×C8×C13C2311yescharacteristic
69C2×C8×C13C2311yescharacteristic
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C42×C13—21no—
76C42×C13C2311yescharacteristic
77#6107—22no—
78#6103—21no—
79#6103—21no—
80#6103—21no—
81#6103—21no—
82#6103—21no—
83C4⋊Dic13D411yescharacteristic
84C4⋊Dic13C2311yescharacteristic
85#6101—21no—
86#6101—21no—
87#6101—21no—
88#6101—21no—
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101D411yescharacteristic
94#6101D411yescharacteristic
95C4×Dic13—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13C2311yescharacteristic
100C4×Dic13C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103Dic52—22no—
104#6095—22no—
105#3369—131nomaximal, Sylow
106C22×D13—21no—
107Q8×C13—21no—
108Q8×C13—21no—
109Q8×C13—81no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2411yescharacteristic
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13C2×D411yescharacteristic
121C2×Dic13C2×D411yescharacteristic
122C2×Dic13C2×D411yescharacteristic
123C2×Dic13C2×D411yescharacteristic
124D52—21no—
125D52—21no—
126C4×D13—42no—
127Dic26—21no—
128Dic26—22no—
129Dic26—21no—
130Dic26—21no—
131Dic26—81no—
132Dic26—81no—
133Dic26#4112yes—
134C8×C13—21no—
135C8×C13—21no—
136#1055—21no—
137#1055—21no—
138Q82—131no—
139#556—131no—
140#489—131no—
141#489—131no—
142#487—131no—
143#476—131no—
144#475—131no—
145#475D1311yescharacteristic, complemented
146#464—131no—
147#464—131no—
148#462—131no—
149#446—131no—
150#441—131no—
151#441—131no—
152C4×SD16—131no—
153C22×C13C22×D411yescharacteristic
154C2×D13—41no—
155C2×D13—41no—
156C2×D13—41no—
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13C2×#4111yescharacteristic
164C4×C132−1+411yescharacteristic
165Dic13—22no—
166Dic13—21no—
167Dic13—21no—
168Dic13—21no—
169Dic13—41no—
170Dic13—41no—
171Dic13#13712yes—
172C2×Q16—131no—
173C2×Q16—131no—
174C2×SD16—131no—
175C4⋊Q8—131no—
176C4⋊Q8—131no—
177C4⋊Q8—131no—
178C4⋊Q8—261no—
179C4⋊Q8—261no—
180C4⋊Q8—261no—
181C4⋊Q8C2×D1311yescharacteristic
182#126—261no—
183#126—261no—
184#124—131no—
185#124—131no—
186C22⋊Q8—261no—
187C4×Q8—131no—
188C4×Q8—131no—
189C4×Q8—131no—
190C4×Q8—131no—
191C4×Q8—131no—
192C4×Q8—261no—
193C4×Q8C2×D1311yescharacteristic
194C4×D4—131no—
195#117—261no—
196#106—131no—
197#106C2×D1311yescharacteristic
198#106C2×D1311yescharacteristic
199C4⋊C8—131no—
200C4⋊C8—131no—
201C4⋊C8C2×D1311yescharacteristic
202#103—131no—
203#103—131no—
204#103—131no—
205#103—131no—
206#103—131no—
207#103C2×D1311yescharacteristic
208#103C2×D1311yescharacteristic
209#102—131no—
210#102—131no—
211#102—131no—
212#97—131no—
213#97—131no—
214C4×C8—131no—
215C2×C13#54811yescharacteristic
216C2×C13C2×#13711yescharacteristic
217C2×C13#57711yescharacteristic
218D13—81no—
219C2×Q8—21no—
220C2×Q8—131no—
221C2×Q8—131no—
222C2×Q8—131no—
223C2×Q8—261no—
224C2×Q8—261no—
225C2×Q8C22×D1311yescharacteristic
226C2×D4—131no—
227C22×C4—261no—
228Q16—262no—
229Q16—262no—
230SD16—262no—
231C2×C8—131no—
232C2×C8—131no—
233C2×C8C22×D1311yescharacteristic
234C2×C8C22×D1311yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—131no—
238C4⋊C4—131no—
239C4⋊C4—131no—
240C4⋊C4—131no—
241C4⋊C4—261no—
242C4⋊C4—261no—
243C4⋊C4—261no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4—261no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4C22×D1311yescharacteristic
250C4⋊C4C22×D1311yescharacteristic
251C4⋊C4C22×D1311yescharacteristic
252C22⋊C4—261no—
253C22⋊C4—261no—
254C22⋊C4—261no—
255C22⋊C4—261no—
256C22⋊C4—261no—
257C42—21no—
258C42—131no—
259C42—131no—
260C42—261no—
261C42—261no—
262C42—261no—
263C42—261no—
264C42C22×D1311yescharacteristic
265C13#336911yescharacteristic, complemented, Sylow
266C23—261no—
267Q8—21no—
268Q8—21no—
269Q8—81no—
270Q8—132no—
271Q8—262no—
272Q8—261no—
273Q8—261no—
274Q8—261no—
275Q8—1041no—
276Q8—1041no—
277D4—261no—
278D4—261no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—131no—
284C2×C4—131no—
285C2×C4—131no—
286C2×C4—131no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—522no—
291C2×C4D4×D1311yescharacteristic
292C2×C4D4×D1311yescharacteristic
293C2×C4C23×D1311yescharacteristic
294C8—21no—
295C8—21no—
296C8—261no—
297C8—261no—
298C22—521no—
299C22—521no—
300C22—521no—
301C22C2×D4×D1311yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—132no—
309C4—261no—
310C4—261no—
311C4—261no—
312C4—262no—
313C4—521no—
314C4—521no—
315C4#8825411yescharacteristic
316C4#41×D1311yescharacteristic
317C2—1041no—
318C2#1171933811yescharacteristic
319C2#1171946711yescharacteristic
320C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#475C2
socleC22×C13C22×D4
prime radicalC2×D52C23
hypercenter#475D13
hypocenterC13#3369
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
1. #11719427C2semidirect
3. C13×#475C2semidirect
5. #11718691C2semidirect
7. #11718515C2semidirect
8. #11718514C2semidirect
11. #11718489C2semidirect
14. #11718454C2semidirect
15. #11718453C2semidirect
145. #475D13semidirect
265. C13#3369semidirect

Maximal subgroups

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

subgroupindex
#117194272
#117192732
C13×#4752
#117187502
#117186912
#117185312
#117185152
#117185142
#117185132
#117185062
#117184892
#117184592
#117184562
#117184542
#117184532
#336913