Finite Group Databasebeta

← #13127290

Subgroups — #13127290

Order 1664.

344 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719435C211yesmaximal, characteristic
2#11719399C211yesmaximal, characteristic
3C13×#501C211yesmaximal, characteristic, complemented
4#11718755C211yesmaximal, characteristic, complemented
5#11718724C211yesmaximal, characteristic, complemented
6#11718549C211yesmaximal, characteristic, complemented
7#11718548C211yesmaximal, characteristic, complemented
8#11718545C211yesmaximal, characteristic, complemented
9#11718542C211yesmaximal, characteristic, complemented
10#11718529C211yesmaximal, characteristic, complemented
11#11718523C211yesmaximal, characteristic, complemented
12#11718523C211yesmaximal, characteristic, complemented
13D13×#106C211yesmaximal, characteristic, complemented
14#11718377C211yesmaximal, characteristic, complemented
15#11718367C211yesmaximal, characteristic
16C13×C4⋊Q8C2211yescharacteristic
17C13×#125C2211yescharacteristic
18#88200—21no—
19#88200—21no—
20C2×Dic52C2211yescharacteristic
21C2×#6094C2211yescharacteristic
22C2×C8×D13C2211yescharacteristic
23#88152—21no—
24#88151C2211yescharacteristic
25#88151C2211yescharacteristic
26#88151C2211yescharacteristic
27#88151C2211yescharacteristic
28#88148—21no—
29#88147—21no—
30#88146—21no—
31#88146C2211yescharacteristic
32C4⋊C4×D13C2211yescharacteristic
33C4⋊C4×D13C2211yescharacteristic
34C4⋊C4×D13C2211yescharacteristic
35#88144—21no—
36#88144—21no—
37C4×D52C2211yescharacteristic
38C4×Dic26C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×#107C2211yescharacteristic
41C13×#107C2211yescharacteristic
42C13×#106C2211yescharacteristic
43C13×#106C2211yescharacteristic
44C13×#97C2211yescharacteristic
45#88060C2211yescharacteristic
46#88060C2211yescharacteristic
47#88057C2211yescharacteristic
48#88056C2211yescharacteristic
49#88056C2211yescharacteristic
50#88050C2211yescharacteristic
51#88050C2211yescharacteristic
52#88050C2211yescharacteristic
53#88050C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×D52D411yescharacteristic
61C2×C4×D13—21no—
62C2×C4×D13—21no—
63C2×C4×D13—21no—
64C2×C4×D13C2311yescharacteristic
65C2×C4×D13C2311yescharacteristic
66C2×Dic26C2311yescharacteristic
67C2×Dic26C2311yescharacteristic
68C2×C8×C13C2311yescharacteristic
69C2×C8×C13C2311yescharacteristic
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C42×C13C2311yescharacteristic
78#6103—21no—
79#6103—21no—
80#6103—21no—
81#6103—21no—
82#6103—21no—
83#6103D411yescharacteristic
84#6103D411yescharacteristic
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13D411yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102Dic52—22no—
103#6094—22no—
104C8×D13—22no—
105#3344—131nomaximal, Sylow
106C22×D13C2×D411yescharacteristic
107C22×D13C2×D411yescharacteristic
108Q8×C13—81no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13C2×D411yescharacteristic
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2411yescharacteristic
116C2×Dic13—21no—
117C2×Dic13—21no—
118C2×Dic13—21no—
119C2×Dic13—21no—
120C2×Dic13C2×D411yescharacteristic
121C2×Dic13C2×D411yescharacteristic
122D52—22no—
123C4×D13—21no—
124C4×D13—21no—
125C4×D13—21no—
126C4×D13—21no—
127C4×D13—42no—
128C4×D13—81no—
129C4×D13—81no—
130Dic26—21no—
131Dic26—21no—
132Dic26—21no—
133Dic26—21no—
134C8×C13—21no—
135C8×C13#4112yes—
136#1055—21no—
137#1055—21no—
138#554—131no—
139#552—131no—
140#501D1311yescharacteristic, complemented
141#485—131no—
142#484—131no—
143#483—131no—
144#483—131no—
145#479—131no—
146#475—131no—
147#470—131no—
148#467—131no—
149#441—131no—
150#435—131no—
151#428—131no—
152C2×#106—131no—
153C22×C13C22×D411yescharacteristic
154C2×D13—21no—
155C2×D13—21no—
156C2×D13—21no—
157C2×D13—21no—
158C2×D13—21no—
159C2×D13#13712yes—
160C4×C13—21no—
161C4×C13—21no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13C2×#4111yescharacteristic
167C4×C132−1+411yescharacteristic
168Dic13—21no—
169Dic13—21no—
170Dic13—41no—
171Dic13—41no—
172Dic13—41no—
173Dic13—41no—
174C2×Q16—131no—
175C2×M16—131no—
176C22×C8—131no—
177C4⋊Q8C2×D1311yescharacteristic
178#126—261no—
179#125—261no—
180#125—261no—
181#125C2×D1311yescharacteristic
182#123—261no—
183C22⋊Q8—131no—
184C22⋊Q8—131no—
185C22⋊Q8—131no—
186C22⋊Q8—131no—
187C22⋊Q8—261no—
188C22⋊Q8—261no—
189C4×Q8—131no—
190C4×Q8—131no—
191C4×D4—131no—
192C4×D4—261no—
193#117—131no—
194#117—261no—
195C2×C4⋊C4—131no—
196C2×C4⋊C4—131no—
197C2×C4⋊C4—131no—
198#107—131no—
199#107C2×D1311yescharacteristic
200#107C2×D1311yescharacteristic
201#106—131no—
202#106—131no—
203#106—131no—
204#106—131no—
205#106C2×D1311yescharacteristic
206#106C2×D1311yescharacteristic
207C4⋊C8—131no—
208#103—131no—
209#103—131no—
210#103—131no—
211#103—131no—
212#103—131no—
213#103—131no—
214C22⋊C8—131no—
215C22⋊C8—131no—
216#97C2×D1311yescharacteristic
217C2×C13#54711yescharacteristic
218C2×C13C2×#13711yescharacteristic
219C2×C13#57711yescharacteristic
220D13—22no—
221D13—41no—
222C2×Q8—21no—
223C2×Q8—131no—
224C2×Q8—131no—
225C2×D4—131no—
226C22×C4—131no—
227C22×C4—131no—
228C22×C4—261no—
229C22×C4—261no—
230C22×C4—261no—
231Q16—262no—
232M16—262no—
233C2×C8—131no—
234C2×C8—131no—
235C2×C8—262no—
236C2×C8C22×D1311yescharacteristic
237C2×C8C22×D1311yescharacteristic
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—131no—
242C4⋊C4—131no—
243C4⋊C4—131no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4—261no—
247C4⋊C4—261no—
248C4⋊C4—261no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4C22×D1311yescharacteristic
254C4⋊C4C22×D1311yescharacteristic
255C4⋊C4C22×D1311yescharacteristic
256C4⋊C4C22×D1311yescharacteristic
257C22⋊C4—131no—
258C22⋊C4—131no—
259C22⋊C4—261no—
260C22⋊C4—261no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C42—261no—
265C42—261no—
266C42—261no—
267C42C22×D1311yescharacteristic
268C13#334411yescharacteristic, complemented, Sylow
269C23—131no—
270C23—131no—
271Q8—81no—
272Q8—261no—
273Q8—261no—
274Q8—261no—
275Q8—261no—
276D4—262no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—131no—
282C2×C4—131no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—522no—
292C2×C4—1041no—
293C2×C4—1041no—
294C2×C4D4×D1311yescharacteristic
295C2×C4D4×D1311yescharacteristic
296C2×C4C23×D1311yescharacteristic
297C8—21no—
298C8—261no—
299C8—261no—
300C8#613112yes—
301C22—132no—
302C22—261no—
303C22—261no—
304C22—261no—
305C22—261no—
306C22—261no—
307C22C2×D4×D1311yescharacteristic
308C4—21no—
309C4—21no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—41no—
314C4—261no—
315C4—261no—
316C4—521no—
317C4—521no—
318C4—521no—
319C4—521no—
320C4C2×#613111yescharacteristic
321C4#8825411yescharacteristic
322C2—262no—
323C2—521no—
324C2#1171943111yescharacteristic
325C2#1171948011yescharacteristic
326C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#501C2
socleC22×C13C22×D4
prime radicalC2×D52D4
hypercenter#501D13
hypocenterC13#3344
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
3. C13×#501C2semidirect
4. #11718755C2semidirect
5. #11718724C2semidirect
6. #11718549C2semidirect
7. #11718548C2semidirect
8. #11718545C2semidirect
9. #11718542C2semidirect
10. #11718529C2semidirect
11. #11718523C2semidirect
12. #11718523C2semidirect
13. D13×#106C2semidirect
14. #11718377C2semidirect
140. #501D13semidirect
268. C13#3344semidirect

Maximal subgroups

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

subgroupindex
#117194352
#117193992
C13×#5012
#117187552
#117187242
#117185492
#117185482
#117185452
#117185422
#117185292
#117185232
D13×#1062
#117183772
#117183672
#334413