Finite Group Databasebeta

← #13126288

Subgroups — #13126288

Order 1664.

322 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719436C211yesmaximal, characteristic
2#11719288C211yesmaximal, characteristic
3C13×#462C211yesmaximal, characteristic, complemented
4#11718850C211yesmaximal, characteristic
5#11718849C211yesmaximal, characteristic
6#11718843C211yesmaximal, characteristic, complemented
7#11718843C211yesmaximal, characteristic, complemented
8#11718751C211yesmaximal, characteristic, complemented
9#11718683C211yesmaximal, characteristic, complemented
10#11718500C211yesmaximal, characteristic
11#11718490C211yesmaximal, characteristic, complemented
12#11718477C211yesmaximal, characteristic
13#11718474C211yesmaximal, characteristic
14#11718460C211yesmaximal, characteristic, complemented
15#11718457C211yesmaximal, characteristic, complemented
16C2×C13×Q16C2211yescharacteristic
17C2×C13×Q16C2211yescharacteristic
18C13×C4⋊Q8C2211yescharacteristic
19C4×Q8×C13C2211yescharacteristic
20#88200C2211yescharacteristic
21#88200C2211yescharacteristic
22#88200C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24Q8×Dic13C2211yescharacteristic
25#88198C2211yescharacteristic
26C2×#6107C2211yescharacteristic
27C2×#6107C2211yescharacteristic
28C2×#6094C2211yescharacteristic
29C2×C8×D13C2211yescharacteristic
30#88152—21no—
31#88152—21no—
32#88152—21no—
33#88151C2211yescharacteristic
34#88144C2211yescharacteristic
35#88143—21no—
36#88143—21no—
37#88143—21no—
38#88130—21no—
39#88126C2211yescharacteristic
40#88124—21no—
41#88124C2211yescharacteristic
42C4×Dic26C2211yescharacteristic
43C13×C4⋊C8C2211yescharacteristic
44C13×#103C2211yescharacteristic
45C13×#103C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48#88075C2211yescharacteristic
49#88075C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88056C2211yescharacteristic
53#88056C2211yescharacteristic
54#88054C2211yescharacteristic
55#88054C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×Q8×C13C2311yescharacteristic
62C2×C4×D13C2311yescharacteristic
63C2×Dic26C2311yescharacteristic
64C13×Q16—41no—
65C13×Q16—41no—
66C2×C8×C13C2311yescharacteristic
67C2×C8×C13C2311yescharacteristic
68C13×C4⋊C4—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4C2311yescharacteristic
72C42×C13—21no—
73C42×C13C2311yescharacteristic
74#6107—41no—
75#6107—41no—
76#6103—21no—
77#6103—21no—
78#6103—21no—
79#6103—21no—
80#6103D411yescharacteristic
81#6103D411yescharacteristic
82C4⋊Dic13—21no—
83C4⋊Dic13—21no—
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13C2311yescharacteristic
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89#6101—21no—
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101D411yescharacteristic
99#6101D411yescharacteristic
100C4×Dic13—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#6094—41no—
107C8×D13—41no—
108#3261—131nomaximal, Sylow
109C22×D13C2×D411yescharacteristic
110Q8×C13—21no—
111Q8×C13—21no—
112Q8×C13—21no—
113Q8×C13—21no—
114Q8×C13—21no—
115Q8×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13C2×D411yescharacteristic
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2411yescharacteristic
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130C4×D13—21no—
131C4×D13—21no—
132Dic26—21no—
133Dic26—21no—
134C8×C13—21no—
135C8×C13—21no—
136#1055—21no—
137#1055—21no—
138#541—131no—
139#541—131no—
140#479—131no—
141#479—131no—
142#479—131no—
143#479—131no—
144#470—131no—
145#470—131no—
146#467—131no—
147#467—131no—
148#462—131no—
149#462—131no—
150#462—131no—
151#462D1311yescharacteristic, complemented
152#424—131no—
153C22×C13C22×D411yescharacteristic
154C2×D13—21no—
155C2×D13—21no—
156C2×D13—21no—
157C4×C13—21no—
158C4×C13—21no—
159C4×C13—41no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13H(5,𝔽2)11yescharacteristic
164C4×C132−1+411yescharacteristic
165Dic13—21no—
166Dic13—21no—
167Dic13—21no—
168Dic13—41no—
169Dic13—41no—
170Dic13—41no—
171Dic13—41no—
172C2×Q16—131no—
173C2×Q16—131no—
174C2×Q16C2×D1311yescharacteristic
175C2×Q16C2×D1311yescharacteristic
176C2×M16—131no—
177C22×C8—131no—
178C4⋊Q8—131no—
179C4⋊Q8C2×D1311yescharacteristic
180#126—261no—
181#126—261no—
182#126—261no—
183#126—261no—
184#125—131no—
185#125—131no—
186#125—261no—
187#125—261no—
188#125—261no—
189#125—261no—
190C22⋊Q8—131no—
191C22⋊Q8—131no—
192C22⋊Q8—131no—
193C22⋊Q8—131no—
194C4×Q8—131no—
195C4×Q8—131no—
196C4×Q8—131no—
197C4×Q8C2×D1311yescharacteristic
198#117—131no—
199#107—131no—
200#107—131no—
201#106—131no—
202#106—131no—
203C4⋊C8—131no—
204C4⋊C8—131no—
205C4⋊C8—131no—
206C4⋊C8C2×D1311yescharacteristic
207#103—131no—
208#103—131no—
209#103—131no—
210#103—131no—
211#103—131no—
212#103—131no—
213#103C2×D1311yescharacteristic
214#103C2×D1311yescharacteristic
215C2×C13#53711yescharacteristic
216C2×C13#57811yescharacteristic
217C2×C13#57811yescharacteristic
218D13—41no—
219C2×Q8—131no—
220C2×Q8C22×D1311yescharacteristic
221C2×Q8C22×D1311yescharacteristic
222C2×Q8C22×D1311yescharacteristic
223C22×C4—131no—
224Q16—41no—
225Q16—41no—
226Q16—521no—
227Q16—521no—
228M16—521no—
229C2×C8—131no—
230C2×C8—131no—
231C2×C8—521no—
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—131no—
241C4⋊C4—131no—
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⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4C22×D1311yescharacteristic
256C22⋊C4—131no—
257C22⋊C4—131no—
258C22⋊C4—261no—
259C22⋊C4—261no—
260C22⋊C4—261no—
261C22⋊C4—261no—
262C42—21no—
263C42—131no—
264C42—261no—
265C42—261no—
266C42—261no—
267C42C22×D1311yescharacteristic
268C13#326111yescharacteristic, complemented, Sylow
269C23—131no—
270Q8—21no—
271Q8—21no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—261no—
277Q8—261no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—131no—
283C2×C4—131no—
284C2×C4—131no—
285C2×C4—261no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4D4×D1311yescharacteristic
292C2×C4D4×D1311yescharacteristic
293C2×C4C23×D1311yescharacteristic
294C8—21no—
295C8—21no—
296C8—261no—
297C8—261no—
298C22—261no—
299C22—261no—
300C22—261no—
301C22C2×D4×D1311yescharacteristic
302C4—21no—
303C4—21no—
304C4—41no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—261no—
309C4—261no—
310C4—261no—
311C4—521no—
312C4—521no—
313C4—521no—
314C4—521no—
315C4#8825111yescharacteristic
316C4#8825711yescharacteristic
317C2—521no—
318C2#1171931311yescharacteristic
319C2#1171947111yescharacteristic
320C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#462C2
socleC22×C13C22×D4
prime radicalC22×D13C2×D4
hypercenter#462D13
hypocenterC13#3261
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. C13×#462C2semidirect
6. #11718843C2semidirect
7. #11718843C2semidirect
8. #11718751C2semidirect
9. #11718683C2semidirect
11. #11718490C2semidirect
14. #11718460C2semidirect
15. #11718457C2semidirect
151. #462D13semidirect
268. C13#3261semidirect

Maximal subgroups

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

subgroupindex
#117194362
#117192882
C13×#4622
#117188502
#117188492
#117188432
#117187512
#117186832
#117185002
#117184902
#117184772
#117184742
#117184602
#117184572
#326113