Finite Group Databasebeta

← #13127361

Subgroups — #13127361

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#11719346C211yesmaximal, characteristic
3C13×#470C211yesmaximal, characteristic, complemented
4#11718849C211yesmaximal, characteristic, complemented
5#11718845C211yesmaximal, characteristic, complemented
6#11718788C211yesmaximal, characteristic
7#11718782C211yesmaximal, characteristic, complemented
8#11718706C211yesmaximal, characteristic, complemented
9#11718705C211yesmaximal, characteristic, complemented
10#11718521C211yesmaximal, characteristic, complemented
11#11718517C211yesmaximal, characteristic, complemented
12#11718476C211yesmaximal, characteristic, complemented
13#11718475C211yesmaximal, characteristic, complemented
14#11718460C211yesmaximal, characteristic, complemented
15#11718455C211yesmaximal, characteristic, complemented
16C2×C13×Q16C2211yescharacteristic
17C2×C13×M16C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic
19C13×C22⋊Q8C2211yescharacteristic
20#88200C2211yescharacteristic
21#88200C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24C4×C22⋊D13C2211yescharacteristic
25#88180C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×C8×D13C2211yescharacteristic
28#88152—21no—
29#88152—21no—
30#88146C2211yescharacteristic
31#88146C2211yescharacteristic
32#88144—21no—
33#88144C2211yescharacteristic
34#88142C2211yescharacteristic
35#88141—21no—
36#88140—21no—
37#88139—21no—
38#88133—21no—
39#88131—21no—
40C13×#106C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#103C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47C22⋊#1055C2211yescharacteristic
48#88060C2211yescharacteristic
49#88058C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88057C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13D411yescharacteristic
63C22×Dic13—21no—
64C2×C4×D13C2311yescharacteristic
65C2×Dic26—21no—
66C13×Q16—22no—
67C13×M16—22no—
68C2×C8×C13C2311yescharacteristic
69C2×C8×C13C2311yescharacteristic
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C22⋊C4—21no—
75C13×C22⋊C4—21no—
76C22⋊Dic13—21no—
77C22⋊Dic13D411yescharacteristic
78#6103—21no—
79#6103—21no—
80#6103—21no—
81#6103—21no—
82#6103D411yescharacteristic
83C4⋊Dic13—21no—
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101D411yescharacteristic
96C4×Dic13—21no—
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C8×D13—22no—
105#3349—131nomaximal, Sylow
106C23×C13C2×D411yescharacteristic
107C22×D13C2×D411yescharacteristic
108Q8×C13—21no—
109Q8×C13—21no—
110Q8×C13—21no—
111Q8×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2411yescharacteristic
120C22⋊D13—41no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—42no—
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C4×D13—21no—
130C4×D13—21no—
131Dic26—42no—
132C8×C13—21no—
133C8×C13#4112yes—
134#1055—21no—
135#1055—21no—
136#556—131no—
137#552—131no—
138#501—131no—
139#485—131no—
140#485—131no—
141#485—131no—
142#484—131no—
143#479—131no—
144#477—131no—
145#470D1311yescharacteristic, complemented
146#467—131no—
147#441—131no—
148#435—131no—
149#428—131no—
150#427—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×Q16C2×D1311yescharacteristic
173C2×M16C2×D1311yescharacteristic
174C22×C8—131no—
175C4⋊Q8—131no—
176#126—261no—
177#126—261no—
178#126—261no—
179#125—131no—
180#125—261no—
181#124—261no—
182#123—261no—
183C22⋊Q8—131no—
184C22⋊Q8—131no—
185C22⋊Q8C2×D1311yescharacteristic
186C22⋊Q8C2×D1311yescharacteristic
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#107—131no—
200#107—131no—
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⋊C8—131no—
214#97—131no—
215C2×C13—41no—
216C2×C13#54711yescharacteristic
217C2×C13#57511yescharacteristic
218C2×C13#57811yescharacteristic
219D13—41no—
220C2×Q8—261no—
221C2×Q8C22×D1311yescharacteristic
222C2×Q8C22×D1311yescharacteristic
223C2×D4—131no—
224C22×C4—131no—
225C22×C4—261no—
226C22×C4C22×D1311yescharacteristic
227Q16—22no—
228M16—22no—
229C2×C8—131no—
230C2×C8—131no—
231C2×C8—262no—
232C2×C8C22×D1311yescharacteristic
233C2×C8C22×D1311yescharacteristic
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
251C22⋊C4—21no—
252C22⋊C4—21no—
253C22⋊C4—131no—
254C22⋊C4—131no—
255C22⋊C4—261no—
256C22⋊C4—261no—
257C22⋊C4—261no—
258C22⋊C4—261no—
259C22⋊C4—261no—
260C42—131no—
261C42—261no—
262C42—261no—
263C42—261no—
264C42—261no—
265C42—261no—
266C13#334911yescharacteristic, complemented, Sylow
267C23—131no—
268C23D4×D1311yescharacteristic
269Q8—21no—
270Q8—21no—
271Q8—21no—
272Q8—21no—
273Q8—522no—
274D4—521no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—131no—
282C2×C4—131no—
283C2×C4—131no—
284C2×C4—261no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—522no—
291C2×C4D4×D1311yescharacteristic
292C2×C4C23×D1311yescharacteristic
293C8—21no—
294C8—261no—
295C8—261no—
296C8#612912yes—
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—
316C4C2×#612911yescharacteristic
317C4#8825711yescharacteristic
318C2—41no—
319C2—521no—
320C2#1171931611yescharacteristic
321C2#1171948211yescharacteristic
322C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#470C2
socleC22×C13C22×D4
prime radicalC2×C22⋊D13D4
hypercenter#470D13
hypocenterC13#3349
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
3. C13×#470C2semidirect
4. #11718849C2semidirect
5. #11718845C2semidirect
7. #11718782C2semidirect
8. #11718706C2semidirect
9. #11718705C2semidirect
10. #11718521C2semidirect
11. #11718517C2semidirect
12. #11718476C2semidirect
13. #11718475C2semidirect
14. #11718460C2semidirect
15. #11718455C2semidirect
145. #470D13semidirect
266. C13#3349semidirect

Maximal subgroups

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

subgroupindex
#117193472
#117193462
C13×#4702
#117188492
#117188452
#117187882
#117187822
#117187062
#117187052
#117185212
#117185172
#117184762
#117184752
#117184602
#117184552
#334913