Finite Group Databasebeta

← #13127365

Subgroups — #13127365

Order 1664.

336 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719437C211yesmaximal, characteristic
2#11719399C211yesmaximal, characteristic
3C13×#501C211yesmaximal, characteristic, complemented
4#11718752C211yesmaximal, 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#11718528C211yesmaximal, characteristic, complemented
12#11718528C211yesmaximal, characteristic, complemented
13#11718521C211yesmaximal, characteristic, complemented
14#11718377C211yesmaximal, characteristic, complemented
15#11718367C211yesmaximal, characteristic
16C13×C4⋊Q8C2211yescharacteristic
17C13×#125C2211yescharacteristic
18#88201—21no—
19Q8×Dic13—21no—
20C2×Dic52C2211yescharacteristic
21C2×#6094C2211yescharacteristic
22C2×C8×D13C2211yescharacteristic
23#88152—21no—
24#88152—21no—
25#88152—21no—
26#88151C2211yescharacteristic
27#88151C2211yescharacteristic
28#88151C2211yescharacteristic
29#88151C2211yescharacteristic
30#88148—21no—
31#88146—21no—
32#88146C2211yescharacteristic
33#88146C2211yescharacteristic
34#88146C2211yescharacteristic
35C4⋊C4×D13C2211yescharacteristic
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#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×D52D411yescharacteristic
61C2×C4×D13—21no—
62C2×C4×D13C2311yescharacteristic
63C2×C4×D13C2311yescharacteristic
64C2×Dic26C2311yescharacteristic
65C2×Dic26C2311yescharacteristic
66C2×C8×C13C2311yescharacteristic
67C2×C8×C13C2311yescharacteristic
68C13×C4⋊C4—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4C2311yescharacteristic
72C13×C4⋊C4C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C4⋊C4C2311yescharacteristic
75C42×C13C2311yescharacteristic
76#6103—21no—
77#6103—21no—
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—
95C4×Dic13—21no—
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C2×#1055C2311yescharacteristic
101C2×#1055C2311yescharacteristic
102Dic52—22no—
103#6094—22no—
104C8×D13—22no—
105#3349—131nomaximal, Sylow
106C22×D13C2×D411yescharacteristic
107C22×D13C2×D411yescharacteristic
108Q8×C13—42no—
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—41no—
123C4×D13—21no—
124C4×D13—21no—
125C4×D13—21no—
126C4×D13—21no—
127C4×D13—42no—
128Dic26—21no—
129Dic26—21no—
130Dic26—21no—
131Dic26—21no—
132C8×C13—21no—
133C8×C13#4112yes—
134#1055—21no—
135#1055—21no—
136#556—131no—
137#552—131no—
138#501D1311yescharacteristic, complemented
139#485—131no—
140#485—131no—
141#485—131no—
142#484—131no—
143#479—131no—
144#477—131no—
145#470—131no—
146#467—131no—
147#441—131no—
148#435—131no—
149#428—131no—
150#427—131no—
151C22×C13C22×D411yescharacteristic
152C2×D13—21no—
153C2×D13—21no—
154C2×D13—21no—
155C2×D13—21no—
156C2×D13—21no—
157C2×D13—21no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13C2×#4111yescharacteristic
165C4×C132−1+411yescharacteristic
166Dic13—21no—
167Dic13—21no—
168Dic13—41no—
169Dic13—41no—
170Dic13—41no—
171Dic13—41no—
172C2×Q16—131no—
173C2×M16—131no—
174C22×C8—131no—
175C4⋊Q8C2×D1311yescharacteristic
176#126—261no—
177#126—261no—
178#126—261no—
179#125—261no—
180#125C2×D1311yescharacteristic
181#124—261no—
182#123—261no—
183C22⋊Q8—131no—
184C22⋊Q8—131no—
185C22⋊Q8—131no—
186C22⋊Q8—131no—
187C4×Q8—131no—
188C4×Q8—131no—
189C4×Q8—261no—
190C4×D4—131no—
191#117—131no—
192#117—131no—
193#117—131no—
194#117—261no—
195C2×C4⋊C4—131no—
196#107—131no—
197#107—131no—
198#107—131no—
199#107C2×D1311yescharacteristic
200#107C2×D1311yescharacteristic
201#106—131no—
202#106—131no—
203#106C2×D1311yescharacteristic
204#106C2×D1311yescharacteristic
205C4⋊C8—131no—
206#103—131no—
207#103—131no—
208#103—131no—
209#103—131no—
210#103—131no—
211#103—131no—
212C22⋊C8—131no—
213C22⋊C8—131no—
214#97C2×D1311yescharacteristic
215C2×C13#54711yescharacteristic
216C2×C13#57511yescharacteristic
217C2×C13#57811yescharacteristic
218D13—41no—
219D13—41no—
220C2×Q8—21no—
221C2×Q8—131no—
222C2×Q8—131no—
223C2×D4—131no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—261no—
227Q16—262no—
228M16—262no—
229C2×C8—131no—
230C2×C8—131no—
231C2×C8—262no—
232C2×C8C22×D1311yescharacteristic
233C2×C8C22×D1311yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—21no—
236C4⋊C4—21no—
237C4⋊C4—131no—
238C4⋊C4—131no—
239C4⋊C4—131no—
240C4⋊C4—261no—
241C4⋊C4—261no—
242C4⋊C4—261no—
243C4⋊C4—261no—
244C4⋊C4—261no—
245C4⋊C4—261no—
246C4⋊C4—261no—
247C4⋊C4C22×D1311yescharacteristic
248C4⋊C4C22×D1311yescharacteristic
249C4⋊C4C22×D1311yescharacteristic
250C4⋊C4C22×D1311yescharacteristic
251C22⋊C4—131no—
252C22⋊C4—131no—
253C22⋊C4—261no—
254C22⋊C4—261no—
255C22⋊C4—261no—
256C22⋊C4—261no—
257C22⋊C4—261no—
258C22⋊C4—261no—
259C22⋊C4—261no—
260C42—261no—
261C42—261no—
262C42—261no—
263C42—261no—
264C42—261no—
265C42C22×D1311yescharacteristic
266C13#334911yescharacteristic, complemented, Sylow
267C23—131no—
268C23—131no—
269Q8—42no—
270Q8—261no—
271Q8—261no—
272Q8—261no—
273Q8—261no—
274D4—521no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—131no—
280C2×C4—131no—
281C2×C4—261no—
282C2×C4—261no—
283C2×C4—261no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—522no—
290C2×C4D4×D1311yescharacteristic
291C2×C4D4×D1311yescharacteristic
292C2×C4C23×D1311yescharacteristic
293C8—21no—
294C8—261no—
295C8—261no—
296C8#613112yes—
297C22—261no—
298C22—261no—
299C22—261no—
300C22—261no—
301C22—261no—
302C22—261no—
303C22C2×D4×D1311yescharacteristic
304C4—21no—
305C4—21no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—261no—
311C4—261no—
312C4—521no—
313C4—521no—
314C4—521no—
315C4—521no—
316C4C2×#613111yescharacteristic
317C4#8825411yescharacteristic
318C2—521no—
319C2—521no—
320C2#1171943111yescharacteristic
321C2#1171947811yescharacteristic
322C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#501C2
socleC22×C13C22×D4
prime radicalC2×D52D4
hypercenter#501D13
hypocenterC13#3349
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. #11718752C2semidirect
5. #11718724C2semidirect
6. #11718549C2semidirect
7. #11718548C2semidirect
8. #11718545C2semidirect
9. #11718542C2semidirect
10. #11718529C2semidirect
11. #11718528C2semidirect
12. #11718528C2semidirect
13. #11718521C2semidirect
14. #11718377C2semidirect
138. #501D13semidirect
266. C13#3349semidirect

Maximal subgroups

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

subgroupindex
#117194372
#117193992
C13×#5012
#117187522
#117187242
#117185492
#117185482
#117185452
#117185422
#117185292
#117185282
#117185212
#117183772
#117183672
#334913