Finite Group Databasebeta

← #13127297

Subgroups — #13127297

Order 1664.

344 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719347C211yesmaximal, characteristic
2#11719340C211yesmaximal, characteristic
3C13×#467C211yesmaximal, characteristic, complemented
4#11718850C211yesmaximal, characteristic, complemented
5#11718845C211yesmaximal, characteristic, complemented
6#11718772C211yesmaximal, characteristic
7C2×#88057C211yesmaximal, characteristic, complemented
8#11718705C211yesmaximal, characteristic, complemented
9#11718704C211yesmaximal, characteristic, complemented
10#11718542C211yesmaximal, characteristic, complemented
11#11718537C211yesmaximal, characteristic, complemented
12#11718476C211yesmaximal, characteristic, complemented
13#11718466C211yesmaximal, characteristic, complemented
14#11718460C211yesmaximal, characteristic, complemented
15#11718452C211yesmaximal, characteristic, complemented
16C2×C13×Q16C2211yescharacteristic
17C22×C8×C13C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic
19C13×C22⋊Q8C2211yescharacteristic
20#88200C2211yescharacteristic
21#88200C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24C4×C22⋊D13C2211yescharacteristic
25C2×C4⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27C2×#6094C2211yescharacteristic
28#88152—21no—
29#88151—21no—
30#88146C2211yescharacteristic
31C4⋊C4×D13C2211yescharacteristic
32#88144—21no—
33#88144C2211yescharacteristic
34#88143—21no—
35#88142C2211yescharacteristic
36#88140—21no—
37#88135—21no—
38#88132—21no—
39#88131—21no—
40C13×#107C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#103C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47C22⋊#1055C2211yescharacteristic
48#88060C2211yescharacteristic
49#88057C2211yescharacteristic
50#88057C2211yescharacteristic
51#88057C2211yescharacteristic
52#88057C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13D411yescharacteristic
63C22×Dic13—21no—
64C22×Dic13—21no—
65C2×C4×D13—21no—
66C2×C4×D13C2311yescharacteristic
67C2×Dic26—21no—
68C13×Q16—22no—
69C2×C8×C13—22no—
70C2×C8×C13C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4C2311yescharacteristic
75C13×C4⋊C4C2311yescharacteristic
76C13×C22⋊C4—21no—
77C13×C22⋊C4—21no—
78C22⋊Dic13D411yescharacteristic
79#6103—21no—
80#6103—21no—
81#6103—21no—
82#6103D411yescharacteristic
83C4⋊Dic13—21no—
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101D411yescharacteristic
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104#6094—22no—
105#3344—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—22no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—42no—
126C2×Dic13—81no—
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130C4×D13—21no—
131C4×D13—21no—
132C4×D13—81no—
133Dic26—81no—
134C8×C13—21no—
135C8×C13#4112yes—
136#1055—21no—
137#1055—21no—
138#554—131no—
139#552—131no—
140#501—131no—
141#485—131no—
142#484—131no—
143#483—131no—
144#483—131no—
145#479—131no—
146#475—131no—
147#470—131no—
148#467D1311yescharacteristic, complemented
149#441—131no—
150#435—131no—
151#428—131no—
152C2×#106—131no—
153C22×C13—21no—
154C22×C13—21no—
155C22×C13#13712yes—
156C22×C13C22×D411yescharacteristic
157C2×D13—21no—
158C2×D13—21no—
159C2×D13—21no—
160C4×C13—21no—
161C4×C13—41no—
162C4×C13—41no—
163C4×C13—41no—
164C4×C13—41no—
165C4×C13C2×#4111yescharacteristic
166C4×C132−1+411yescharacteristic
167Dic13—21no—
168Dic13—21no—
169Dic13—21no—
170Dic13—41no—
171Dic13—41no—
172Dic13—41no—
173Dic13—41no—
174C2×Q16C2×D1311yescharacteristic
175C2×M16—131no—
176C22×C8C2×D1311yescharacteristic
177C4⋊Q8—131no—
178#126—261no—
179#125—131no—
180#125—261no—
181#125—261no—
182#123—261no—
183C22⋊Q8—131no—
184C22⋊Q8—131no—
185C22⋊Q8—261no—
186C22⋊Q8—261no—
187C22⋊Q8C2×D1311yescharacteristic
188C22⋊Q8C2×D1311yescharacteristic
189C4×Q8—131no—
190C4×Q8—131no—
191C4×D4—131no—
192C4×D4—261no—
193#117—131no—
194#117—261no—
195C2×C4⋊C4—131no—
196C2×C4⋊C4—131no—
197C2×C4⋊C4—131no—
198#107—131no—
199#107—131no—
200#107C2×D1311yescharacteristic
201#106—131no—
202#106—131no—
203#106—131no—
204#106—131no—
205#106—131no—
206#106—131no—
207C4⋊C8—131no—
208#103—131no—
209#103—131no—
210#103—131no—
211#103—131no—
212#103C2×D1311yescharacteristic
213#103C2×D1311yescharacteristic
214C22⋊C8—131no—
215C22⋊C8—131no—
216#97—131no—
217C2×C13—22no—
218C2×C13#54711yescharacteristic
219C2×C13C2×#13711yescharacteristic
220C2×C13#57711yescharacteristic
221D13—41no—
222C2×Q8—261no—
223C2×Q8C22×D1311yescharacteristic
224C2×Q8C22×D1311yescharacteristic
225C2×D4—131no—
226C22×C4—131no—
227C22×C4—261no—
228C22×C4—261no—
229C22×C4—261no—
230C22×C4C22×D1311yescharacteristic
231Q16—22no—
232M16—262no—
233C2×C8—22no—
234C2×C8—131no—
235C2×C8—131no—
236C2×C8C22×D1311yescharacteristic
237C2×C8C22×D1311yescharacteristic
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—131no—
241C4⋊C4—131no—
242C4⋊C4—131no—
243C4⋊C4—131no—
244C4⋊C4—131no—
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
256C4⋊C4C22×D1311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—131no—
260C22⋊C4—131no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C42—131no—
265C42—261no—
266C42—261no—
267C42—261no—
268C13#334411yescharacteristic, complemented, Sylow
269C23—131no—
270C23D4×D1311yescharacteristic
271Q8—21no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—1041no—
276D4—262no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—131no—
284C2×C4—131no—
285C2×C4—131no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—522no—
293C2×C4—1041no—
294C2×C4—1041no—
295C2×C4D4×D1311yescharacteristic
296C2×C4C23×D1311yescharacteristic
297C8—21no—
298C8—261no—
299C8—261no—
300C8#612912yes—
301C22—21no—
302C22—21no—
303C22—261no—
304C22—261no—
305C22—261no—
306C22#8817212yes—
307C22C2×D4×D1311yescharacteristic
308C4—21no—
309C4—41no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—261no—
314C4—261no—
315C4—261no—
316C4—521no—
317C4—521no—
318C4—521no—
319C4—521no—
320C4C2×#612911yescharacteristic
321C4#8825711yescharacteristic
322C2—22no—
323C2—521no—
324C2#1171931611yescharacteristic
325C2C2×#8817211yescharacteristic
326C2#1171947511yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#467C2
socleC22×C13C22×D4
prime radicalC2×C22⋊D13D4
hypercenter#467D13
hypocenterC13#3344
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #467

Complements

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

NH ≅ G/Ntype
3. C13×#467C2semidirect
4. #11718850C2semidirect
5. #11718845C2semidirect
7. C2×#88057C2semidirect
8. #11718705C2semidirect
9. #11718704C2semidirect
10. #11718542C2semidirect
11. #11718537C2semidirect
12. #11718476C2semidirect
13. #11718466C2semidirect
14. #11718460C2semidirect
15. #11718452C2semidirect
148. #467D13semidirect
268. C13#3344semidirect

Maximal subgroups

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

subgroupindex
#117193472
#117193402
C13×#4672
#117188502
#117188452
#117187722
C2×#880572
#117187052
#117187042
#117185422
#117185372
#117184762
#117184662
#117184602
#117184522
#334413