Finite Group Databasebeta

← #13127754

Subgroups — #13127754

Order 1664.

360 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719432C211yesmaximal, characteristic
2#11719390C211yesmaximal, characteristic, complemented
3C13×#501C211yesmaximal, characteristic, complemented
4#11718752C211yesmaximal, characteristic, complemented
5#11718727C211yesmaximal, characteristic
6#11718551C211yesmaximal, characteristic
7#11718550C211yesmaximal, characteristic
8#11718536C211yesmaximal, characteristic, complemented
9#11718535C211yesmaximal, characteristic, complemented
10#11718532C211yesmaximal, characteristic
11#11718517C211yesmaximal, characteristic, complemented
12#11718515C211yesmaximal, characteristic, complemented
13#11718513C211yesmaximal, characteristic
14#11718371C211yesmaximal, characteristic
15#11718362C211yesmaximal, characteristic, complemented
16C2×Q8×D13—21no—
17C13×C4⋊Q8C2211yescharacteristic
18C13×#125C2211yescharacteristic
19#88200—21no—
20C2×#6095C2211yescharacteristic
21#88150—21no—
22#88150—21no—
23#88147C2211yescharacteristic
24#88147C2211yescharacteristic
25#88144C2211yescharacteristic
26#88143—21no—
27#88143—21no—
28#88142—21no—
29#88142C2211yescharacteristic
30#88142C2211yescharacteristic
31#88142C2211yescharacteristic
32#88141—21no—
33#88141C2211yescharacteristic
34#88141C2211yescharacteristic
35C4×D52C2211yescharacteristic
36C4×Dic26C2211yescharacteristic
37C4×Dic26C2211yescharacteristic
38C13×#107C2211yescharacteristic
39C13×#107C2211yescharacteristic
40C13×#106C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C13×#97C2211yescharacteristic
43#88061C2211yescharacteristic
44#88058C2211yescharacteristic
45#88056C2211yescharacteristic
46#88055C2211yescharacteristic
47#88054C2211yescharacteristic
48#88054C2211yescharacteristic
49C8×Dic13C2211yescharacteristic
50#88050C2211yescharacteristic
51#88050C2211yescharacteristic
52#88049C2211yescharacteristic
53#88049C2211yescharacteristic
54#88048C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60Q8×D13—44no—
61C2×D52C2311yescharacteristic
62C2×C4×D13—21no—
63C2×C4×D13—21no—
64C2×C4×D13—21no—
65C2×Dic26—21no—
66C2×Dic26—21no—
67C2×Dic26—21no—
68C2×Dic26D411yescharacteristic
69C2×Dic26C2311yescharacteristic
70C2×C8×C13C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C42×C13C2311yescharacteristic
80#6103—21no—
81#6103—21no—
82#6103—21no—
83C4⋊Dic13—21no—
84C4⋊Dic13D411yescharacteristic
85C4⋊Dic13C2311yescharacteristic
86C4⋊Dic13C2311yescharacteristic
87#6101—21no—
88#6101—21no—
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101D411yescharacteristic
95#6101D411yescharacteristic
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13C2311yescharacteristic
100C4×Dic13C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103#6095Q814yescomplemented
104#3386—131nomaximal, Sylow
105C22×D13—21no—
106Q8×C13—42no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13C2×D411yescharacteristic
112C2×C4×C13C2×D411yescharacteristic
113C2×C4×C13C2411yescharacteristic
114C2×Dic13—21no—
115C2×Dic13—21no—
116C2×Dic13—21no—
117C2×Dic13C2×D411yescharacteristic
118C2×Dic13C2×D411yescharacteristic
119C2×Dic13C2×D411yescharacteristic
120C2×Dic13C2×D411yescharacteristic
121D52—21no—
122D52C2×Q812yes—
123C4×D13—42no—
124C4×D13—42no—
125C4×D13—42no—
126Dic26—21no—
127Dic26—22no—
128Dic26—42no—
129Dic26—42no—
130Dic26—42no—
131Dic26C2×Q812yescomplemented
132C8×C13—21no—
133C8×C13C2×Q812yescomplemented
134#1055—21no—
135#1055—21no—
136#557—131no—
137D4×Q8—131no—
138#501—131no—
139#501D1311yescharacteristic, complemented
140#500—131no—
141#478—131no—
142#478—131no—
143#477—131no—
144#477—131no—
145#475—131no—
146#474—131no—
147#446—131no—
148#440—131no—
149#440—131no—
150C4×SD16—131no—
151C22×C13C22×D411yescharacteristic
152C2×D13—22no—
153C2×D13—41no—
154C2×D13—41no—
155C4×C13—21no—
156C4×C13—21no—
157C4×C13—41no—
158C4×C13—41no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13C22×Q811yescharacteristic
162C4×C132−1+411yescharacteristic
163Dic13—22no—
164Dic13—21no—
165Dic13—21no—
166Dic13—21no—
167Dic13—41no—
168Dic13—41no—
169Dic13AGL(1,ℤ/8)12yes—
170C22×Q8—261no—
171C2×SD16—131no—
172C4⋊Q8—131no—
173C4⋊Q8—131no—
174C4⋊Q8—131no—
175C4⋊Q8—261no—
176C4⋊Q8C2×D1311yescharacteristic
177#125—131no—
178#125—261no—
179#125—261no—
180#125C2×D1311yescharacteristic
181C22⋊Q8—261no—
182C22⋊Q8—261no—
183C22⋊Q8—261no—
184C4×Q8—131no—
185C4×Q8—131no—
186C4×Q8—131no—
187C4×Q8—131no—
188C4×Q8—261no—
189C4×D4—131no—
190C4×D4—131no—
191C4×D4—131no—
192#107—131no—
193#107—131no—
194#107—131no—
195#107—131no—
196#107C2×D1311yescharacteristic
197#107C2×D1311yescharacteristic
198#106—131no—
199#106C2×D1311yescharacteristic
200#106C2×D1311yescharacteristic
201C4⋊C8—131no—
202C4⋊C8—131no—
203C4⋊C8—131no—
204#103—131no—
205#103—131no—
206#103—131no—
207#102—131no—
208#102—131no—
209#102—131no—
210#97—131no—
211#97C2×D1311yescharacteristic
212C4×C8—131no—
213C2×C13D4×Q811yescharacteristic
214C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C13#57811yescharacteristic
216D13—42no—
217C2×Q8—21no—
218C2×Q8—131no—
219C2×Q8—131no—
220C2×Q8—261no—
221C2×Q8—261no—
222C2×Q8—261no—
223C2×Q8—524no—
224C2×D4—131no—
225C22×C4—261no—
226C22×C4—261no—
227C22×C4—261no—
228SD16—134no—
229C2×C8—131no—
230C2×C8—131no—
231C2×C8C22×D1311yescharacteristic
232C2×C8C22×D1311yescharacteristic
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—131no—
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
252C4⋊C4C22×D1311yescharacteristic
253C22⋊C4—261no—
254C22⋊C4—261no—
255C22⋊C4—261no—
256C42—131no—
257C42—131no—
258C42—261no—
259C42—261no—
260C42—261no—
261C42C22×D1311yescharacteristic
262C13#338611yescharacteristic, complemented, Sylow
263C23—261no—
264Q8—42no—
265Q8—132no—
266Q8—262no—
267Q8—261no—
268Q8—522no—
269Q8—522no—
270Q8—522no—
271D4—132no—
272D4—261no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—131no—
278C2×C4—131no—
279C2×C4—131no—
280C2×C4—131no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—522no—
285C2×C4—522no—
286C2×C4—522no—
287C2×C4D4×D1311yescharacteristic
288C2×C4D4×D1311yescharacteristic
289C2×C4C23×D1311yescharacteristic
290C8—21no—
291C8—261no—
292C8—261no—
293C8Q8×D1312yescomplemented
294C22—262no—
295C22—521no—
296C22—521no—
297C22C2×D4×D1311yescharacteristic
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—132no—
305C4—262no—
306C4—261no—
307C4—261no—
308C4—261no—
309C4—521no—
310C4—521no—
311C4C2×Q8×D1311yescharacteristic
312C4#8825411yescharacteristic
313C2—522no—
314C2#1171943211yescharacteristic
315C2D13×AGL(1,ℤ/8)11yescharacteristic
316C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#501C2
socleC22×C13C22×D4
prime radicalC2×D52C23
hypercenter#501D13
hypocenterC13#3386
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
2. #11719390C2semidirect
3. C13×#501C2semidirect
4. #11718752C2semidirect
8. #11718536C2semidirect
9. #11718535C2semidirect
11. #11718517C2semidirect
12. #11718515C2semidirect
15. #11718362C2semidirect
103. #6095Q8semidirect
131. Dic26C2×Q8semidirect
133. C8×C13C2×Q8semidirect
139. #501D13semidirect
262. C13#3386semidirect
293. C8Q8×D13semidirect

Maximal subgroups

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

subgroupindex
#117194322
#117193902
C13×#5012
#117187522
#117187272
#117185512
#117185502
#117185362
#117185352
#117185322
#117185172
#117185152
#117185132
#117183712
#117183622
#338613