Finite Group Databasebeta

← #13127371

Subgroups — #13127371

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#11719289C211yesmaximal, characteristic
2#11719286C211yesmaximal, characteristic
3C13×#441C211yesmaximal, characteristic, complemented
4#11718850C211yesmaximal, characteristic, complemented
5#11718849C211yesmaximal, characteristic, complemented
6#11718683C211yesmaximal, characteristic, complemented
7#11718682C211yesmaximal, characteristic, complemented
8#11718522C211yesmaximal, characteristic, complemented
9#11718521C211yesmaximal, characteristic, complemented
10#11718476C211yesmaximal, characteristic, complemented
11#11718476C211yesmaximal, characteristic, complemented
12#11718475C211yesmaximal, characteristic, complemented
13#11718470C211yesmaximal, characteristic, complemented
14#11718367C211yesmaximal, characteristic
15#11718363C211yesmaximal, characteristic, complemented
16C2×C13×Q16C2211yescharacteristic
17C4×Q8×C13C2211yescharacteristic
18C4×Q8×C13C2211yescharacteristic
19#88200C2211yescharacteristic
20#88200C2211yescharacteristic
21#88200C2211yescharacteristic
22#88200C2211yescharacteristic
23C2×#6094C2211yescharacteristic
24C2×C8×D13C2211yescharacteristic
25#88152—21no—
26#88152—21no—
27#88148—21no—
28#88146C2211yescharacteristic
29#88146C2211yescharacteristic
30#88146C2211yescharacteristic
31C4⋊C4×D13C2211yescharacteristic
32#88143—21no—
33#88130—21no—
34#88129—21no—
35C4×D52C2211yescharacteristic
36#88126—21no—
37#88124C2211yescharacteristic
38#88123C2211yescharacteristic
39C4×Dic26—21no—
40C13×#106C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#103C2211yescharacteristic
43C13×#97C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88075C2211yescharacteristic
48#88060C2211yescharacteristic
49#88060C2211yescharacteristic
50#88058C2211yescharacteristic
51#88058C2211yescharacteristic
52#88057C2211yescharacteristic
53#88057C2211yescharacteristic
54#88048C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×D52D411yescharacteristic
62C2×C4×D13—21no—
63C2×C4×D13C2311yescharacteristic
64C2×C4×D13C2311yescharacteristic
65C2×Dic26—21no—
66C13×Q16—22no—
67C2×C8×C13C2311yescharacteristic
68C2×C8×C13C2311yescharacteristic
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4C2311yescharacteristic
72C13×C4⋊C4C2311yescharacteristic
73C42×C13—21no—
74C42×C13—21no—
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⋊Dic13D411yescharacteristic
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C2×#1055C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103#6094—22no—
104C8×D13—22no—
105#3349—131nomaximal, Sylow
106C22×D13C2×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×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2411yescharacteristic
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13C2×D411yescharacteristic
124C2×Dic13C2×D411yescharacteristic
125D52—41no—
126C4×D13—21no—
127C4×D13—21no—
128C4×D13—21no—
129C4×D13—21no—
130C4×D13—42no—
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#470—131no—
146#467—131no—
147#441D1311yescharacteristic, complemented
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×Q16C2×D1311yescharacteristic
173C2×M16—131no—
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⋊Q8—131no—
186C22⋊Q8—131no—
187C4×Q8—261no—
188C4×Q8C2×D1311yescharacteristic
189C4×Q8C2×D1311yescharacteristic
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#97C2×D1311yescharacteristic
215C2×C13#54711yescharacteristic
216C2×C13#57511yescharacteristic
217C2×C13#57811yescharacteristic
218D13—41no—
219D13—41no—
220C2×Q8—261no—
221C2×Q8C22×D1311yescharacteristic
222C2×Q8C22×D1311yescharacteristic
223C2×D4—131no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—261no—
227Q16—22no—
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—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—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—21no—
261C42—21no—
262C42—261no—
263C42—261no—
264C42—261no—
265C42C22×D1311yescharacteristic
266C13#334911yescharacteristic, complemented, Sylow
267C23—131no—
268C23—131no—
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—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#612712yes—
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×#612711yescharacteristic
317C4#8825711yescharacteristic
318C2—521no—
319C2—521no—
320C2#1171925611yescharacteristic
321C2#1171948211yescharacteristic
322C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#441C2
socleC22×C13C22×D4
prime radicalC2×D52D4
hypercenter#441D13
hypocenterC13#3349
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
3. C13×#441C2semidirect
4. #11718850C2semidirect
5. #11718849C2semidirect
6. #11718683C2semidirect
7. #11718682C2semidirect
8. #11718522C2semidirect
9. #11718521C2semidirect
10. #11718476C2semidirect
11. #11718476C2semidirect
12. #11718475C2semidirect
13. #11718470C2semidirect
15. #11718363C2semidirect
147. #441D13semidirect
266. C13#3349semidirect

Maximal subgroups

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

subgroupindex
#117192892
#117192862
C13×#4412
#117188502
#117188492
#117186832
#117186822
#117185222
#117185212
#117184762
#117184752
#117184702
#117183672
#117183632
#334913