Finite Group Databasebeta

← #13127404

Subgroups — #13127404

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#11719347C211yesmaximal, characteristic
2#11719234C211yesmaximal, characteristic
3C13×#485C211yesmaximal, characteristic, complemented
4#11718713C211yesmaximal, characteristic, complemented
5#11718656C211yesmaximal, characteristic, complemented
6#11718549C211yesmaximal, characteristic, complemented
7#11718539C211yesmaximal, characteristic, complemented
8#11718522C211yesmaximal, characteristic, complemented
9#11718518C211yesmaximal, characteristic, complemented
10#11718477C211yesmaximal, characteristic, complemented
11#11718470C211yesmaximal, characteristic, complemented
12#11718457C211yesmaximal, characteristic, complemented
13#11718451C211yesmaximal, characteristic, complemented
14#11718390C211yesmaximal, characteristic
15#11718383C211yesmaximal, characteristic, complemented
16C13×C22⋊Q8C2211yescharacteristic
17C13×#117C2211yescharacteristic
18#88200C2211yescharacteristic
19Q8×Dic13C2211yescharacteristic
20C2×#6107C2211yescharacteristic
21C4×C22⋊D13C2211yescharacteristic
22C2×C4⋊Dic13C2211yescharacteristic
23#88178C2211yescharacteristic
24C2×#6099C2211yescharacteristic
25C2×#6094C2211yescharacteristic
26#88152—21no—
27#88151C2211yescharacteristic
28#88146C2211yescharacteristic
29C4⋊C4×D13C2211yescharacteristic
30#88144—21no—
31#88144C2211yescharacteristic
32#88144C2211yescharacteristic
33#88141C2211yescharacteristic
34#88140—21no—
35#88137—21no—
36#88133—21no—
37#88131—21no—
38#88126—21no—
39#88124—21no—
40C13×#107C2211yescharacteristic
41C13×#106C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#103C2211yescharacteristic
44C13×C22⋊C8C2211yescharacteristic
45#88075C2211yescharacteristic
46#88060C2211yescharacteristic
47#88058C2211yescharacteristic
48#88058C2211yescharacteristic
49#88056C2211yescharacteristic
50#88056C2211yescharacteristic
51#88054C2211yescharacteristic
52C8×Dic13C2211yescharacteristic
53#88050C2211yescharacteristic
54#88048C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C2×C22⋊D13D411yescharacteristic
62C22×Dic13—21no—
63C2×C4×D13—21no—
64C2×C4×D13C2311yescharacteristic
65C2×Dic26C2311yescharacteristic
66C2×C8×C13C2311yescharacteristic
67C2×C8×C13C2311yescharacteristic
68C13×C4⋊C4—21no—
69C13×C4⋊C4C2311yescharacteristic
70C13×C4⋊C4C2311yescharacteristic
71C13×C4⋊C4C2311yescharacteristic
72C13×C22⋊C4—21no—
73C13×C22⋊C4—21no—
74C42×C13—21no—
75C22⋊Dic13—21no—
76C22⋊Dic13D411yescharacteristic
77#6107—22no—
78#6103—21no—
79#6103—21no—
80#6103—21no—
81#6103D411yescharacteristic
82C4⋊Dic13—21no—
83C4⋊Dic13—21no—
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101D411yescharacteristic
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13C2311yescharacteristic
101#6099—22no—
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104#6094—22no—
105#3352—131nomaximal, Sylow
106C23×C13C2×D411yescharacteristic
107C22×D13C2×D411yescharacteristic
108Q8×C13—21no—
109Q8×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2411yescharacteristic
118C22⋊D13—41no—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—42no—
124C2×Dic13C2×D411yescharacteristic
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127C4×D13—21no—
128C4×D13—21no—
129C4×D13—42no—
130Dic26—21no—
131Dic26—21no—
132C8×C13—21no—
133C8×C13—21no—
134#1055—21no—
135#1055#4112yes—
136#552—131no—
137#552—131no—
138#499—131no—
139#485—131no—
140#485D1311yescharacteristic, complemented
141#484—131no—
142#484—131no—
143#479—131no—
144#479—131no—
145#470—131no—
146#470—131no—
147C4×Q16—131no—
148#436—131no—
149#428—131no—
150#428—131no—
151C22×C13—21no—
152C22×C13—21no—
153C22×C13—21no—
154C22×C13C22×D411yescharacteristic
155C2×D13—21no—
156C2×D13—21no—
157C2×D13—21no—
158C4×C13—21no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13C2×#4111yescharacteristic
164C4×C132−1+411yescharacteristic
165Dic13—21no—
166Dic13—21no—
167Dic13—21no—
168Dic13—41no—
169Dic13—41no—
170Dic13—41no—
171Dic13—41no—
172C2×Q16—131no—
173C2×M16—131no—
174C2×M16—131no—
175#126—261no—
176#126—261no—
177#125—131no—
178#125—131no—
179#125—261no—
180#125—261no—
181#123—261no—
182#123—261no—
183C22⋊Q8—131no—
184C22⋊Q8—131no—
185C22⋊Q8—131no—
186C22⋊Q8C2×D1311yescharacteristic
187C4×Q8—131no—
188C4×Q8—131no—
189C4×D4—131no—
190#117—131no—
191#117—261no—
192#117—261no—
193#117C2×D1311yescharacteristic
194C2×C4⋊C4—131no—
195C2×C4⋊C4—131no—
196#107—131no—
197#107—131no—
198#107—131no—
199#107—131no—
200#107C2×D1311yescharacteristic
201#106—131no—
202#106—131no—
203#106—131no—
204#106C2×D1311yescharacteristic
205C4⋊C8—131no—
206#103—131no—
207#103—131no—
208#103—131no—
209#103—131no—
210#103C2×D1311yescharacteristic
211#103C2×D1311yescharacteristic
212C22⋊C8—131no—
213C22⋊C8C2×D1311yescharacteristic
214C4×C8—131no—
215C2×C13—41no—
216C2×C13#54711yescharacteristic
217C2×C13#57511yescharacteristic
218C2×C13#57811yescharacteristic
219D13—41no—
220C2×Q8—131no—
221C2×Q8C22×D1311yescharacteristic
222C2×D4—131no—
223C22×C4—131no—
224C22×C4—261no—
225C22×C4—261no—
226C22×C4C22×D1311yescharacteristic
227Q16—262no—
228M16—262no—
229M16—262no—
230C2×C8—131no—
231C2×C8—131no—
232C2×C8C22×D1311yescharacteristic
233C2×C8C22×D1311yescharacteristic
234C4⋊C4—21no—
235C4⋊C4—131no—
236C4⋊C4—131no—
237C4⋊C4—131no—
238C4⋊C4—131no—
239C4⋊C4—261no—
240C4⋊C4—261no—
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⋊C4—261no—
250C4⋊C4C22×D1311yescharacteristic
251C4⋊C4C22×D1311yescharacteristic
252C4⋊C4C22×D1311yescharacteristic
253C22⋊C4—21no—
254C22⋊C4—21no—
255C22⋊C4—131no—
256C22⋊C4—131no—
257C22⋊C4—261no—
258C22⋊C4—261no—
259C22⋊C4—261no—
260C22⋊C4—261no—
261C42—21no—
262C42—131no—
263C42—261no—
264C42—261no—
265C42—261no—
266C13#335211yescharacteristic, complemented, Sylow
267C23—131no—
268C23D4×D1311yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—261no—
272Q8—261no—
273D4—521no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—131no—
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—522no—
290C2×C4—522no—
291C2×C4D4×D1311yescharacteristic
292C2×C4C23×D1311yescharacteristic
293C8—21no—
294C8—21no—
295C8—132no—
296C8—261no—
297C22—21no—
298C22—21no—
299C22—21no—
300C22—261no—
301C22—261no—
302C22—261no—
303C22C2×D4×D1311yescharacteristic
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—261no—
310C4—261no—
311C4—261no—
312C4—521no—
313C4—521no—
314C4—521no—
315C4—521no—
316C4#41×D1311yescharacteristic
317C4#8825711yescharacteristic
318C2—41no—
319C2—521no—
320C2#1171936011yescharacteristic
321C2#1171947611yescharacteristic
322C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#485C2
socleC22×C13C22×D4
prime radicalC2×C22⋊D13D4
hypercenter#485D13
hypocenterC13#3352
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. C13×#485C2semidirect
4. #11718713C2semidirect
5. #11718656C2semidirect
6. #11718549C2semidirect
7. #11718539C2semidirect
8. #11718522C2semidirect
9. #11718518C2semidirect
10. #11718477C2semidirect
11. #11718470C2semidirect
12. #11718457C2semidirect
13. #11718451C2semidirect
15. #11718383C2semidirect
140. #485D13semidirect
266. C13#3352semidirect

Maximal subgroups

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

subgroupindex
#117193472
#117192342
C13×#4852
#117187132
#117186562
#117185492
#117185392
#117185222
#117185182
#117184772
#117184702
#117184572
#117184512
#117183902
#117183832
#335213