Finite Group Databasebeta

← #13127608

Subgroups — #13127608

Order 1664.

344 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719386C211yesmaximal, characteristic
2#11719274C211yesmaximal, characteristic, complemented
3C13×#464C211yesmaximal, characteristic, complemented
4#11718846C211yesmaximal, characteristic, complemented
5#11718845C211yesmaximal, characteristic, complemented
6#11718825C211yesmaximal, characteristic, complemented
7#11718824C211yesmaximal, characteristic
8#11718717C211yesmaximal, characteristic, complemented
9C4×#6106C211yesmaximal, characteristic, complemented
10#11718508C211yesmaximal, characteristic, complemented
11#11718492C211yesmaximal, characteristic, complemented
12#11718457C211yesmaximal, characteristic, complemented
13#11718456C211yesmaximal, characteristic, complemented
14#11718425C211yesmaximal, characteristic
15#11718422C211yesmaximal, characteristic, complemented
16C2×C13×Q16C2211yescharacteristic
17C2×C13×SD16C2211yescharacteristic
18C13×#124C2211yescharacteristic
19C4×Q8×C13C2211yescharacteristic
20#88201C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24C2×#6106C2211yescharacteristic
25#88194C2211yescharacteristic
26D4×Dic13C2211yescharacteristic
27#88144—21no—
28#88144C2211yescharacteristic
29#88142—21no—
30#88142C2211yescharacteristic
31#88140—21no—
32#88139—21no—
33#88137—21no—
34#88135—21no—
35C4×D52C2211yescharacteristic
36#88124—21no—
37#88124C2211yescharacteristic
38C4×Dic26—21no—
39C4×Dic26C2211yescharacteristic
40C13×C4⋊C8C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#102C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88055C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88054C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C22×Dic13—21no—
65C2×D52C2311yescharacteristic
66C2×C4×D13—21no—
67C2×Dic26—21no—
68C2×Dic26D411yescharacteristic
69C13×Q16—22no—
70C13×SD16—22no—
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4—21no—
74C13×C4⋊C4C2311yescharacteristic
75C13×C22⋊C4—21no—
76C13×C22⋊C4—21no—
77C42×C13—21no—
78C42×C13C2311yescharacteristic
79C22⋊Dic13—21no—
80#6106—22no—
81#6103—21no—
82#6103—21no—
83#6103—21no—
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13D411yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101D411yescharacteristic
97#6101D411yescharacteristic
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C4×Dic13C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3371—131nomaximal, Sylow
106C23×C13—21no—
107C22×D13—21no—
108Q8×C13—21no—
109Q8×C13—21no—
110Q8×C13—21no—
111Q8×C13#4112yes—
112D4×C13—21no—
113D4×C13—21no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2411yescharacteristic
120C22⋊D13—42no—
121C22⋊D13—81no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—81no—
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130D52—21no—
131D52—21no—
132C4×D13—81no—
133Dic26—41no—
134Dic26—42no—
135C8×C13—21no—
136C8×C13—21no—
137#1055—21no—
138#1055—21no—
139#559—131no—
140#557—131no—
141#490—131no—
142#489—131no—
143#488—131no—
144#479—131no—
145#478—131no—
146#476—131no—
147#464—131no—
148#464D1311yescharacteristic, complemented
149#460—131no—
150#446—131no—
151#441—131no—
152#440—131no—
153C4×SD16—131no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13—41no—
157C22×C13C22×D411yescharacteristic
158C2×D13—41no—
159C2×D13—41no—
160C2×D13—41no—
161C4×C13—22no—
162C4×C13—21no—
163C4×C13—21no—
164C4×C13—41no—
165C4×C13—41no—
166C4×C13C2×#4111yescharacteristic
167C4×C132−1+411yescharacteristic
168Dic13—21no—
169Dic13—21no—
170Dic13—21no—
171Dic13—21no—
172Dic13—41no—
173Dic13—41no—
174Dic13—41no—
175C2×Q16C2×D1311yescharacteristic
176C2×SD16—131no—
177C2×SD16C2×D1311yescharacteristic
178C4⋊Q8—131no—
179C4⋊Q8—261no—
180#127—131no—
181#125—131no—
182#125—131no—
183#125—261no—
184#125—261no—
185#124—131no—
186#124—261no—
187#124C2×D1311yescharacteristic
188#123—261no—
189#123—261no—
190C4×Q8—131no—
191C4×Q8—131no—
192C4×Q8—131no—
193C4×Q8—131no—
194C4×Q8—261no—
195C4×Q8C2×D1311yescharacteristic
196C4×D4—131no—
197C4×D4—131no—
198C4×D4—261no—
199#107—131no—
200#106—131no—
201#106—131no—
202C4⋊C8—131no—
203C4⋊C8—131no—
204C4⋊C8C2×D1311yescharacteristic
205#103—131no—
206#103—131no—
207#103—131no—
208#103C2×D1311yescharacteristic
209#102—131no—
210#102—131no—
211#102—131no—
212#102—131no—
213#102—131no—
214#102C2×D1311yescharacteristic
215#97—131no—
216#97—131no—
217C4×C8—131no—
218C2×C13—81no—
219C2×C13#54811yescharacteristic
220C2×C13#57511yescharacteristic
221C2×C13#57711yescharacteristic
222D13—81no—
223C2×Q8—131no—
224C2×Q8—261no—
225C2×Q8C22×D1311yescharacteristic
226C2×Q8C22×D1311yescharacteristic
227C2×D4—131no—
228C2×D4—261no—
229C2×D4—261no—
230C2×D4C22×D1311yescharacteristic
231C22×C4—261no—
232C22×C4—261no—
233Q16—22no—
234SD16—22no—
235SD16—262no—
236C2×C8—131no—
237C2×C8—131no—
238C2×C8C22×D1311yescharacteristic
239C2×C8C22×D1311yescharacteristic
240C4⋊C4—21no—
241C4⋊C4—131no—
242C4⋊C4—131no—
243C4⋊C4—131no—
244C4⋊C4—131no—
245C4⋊C4—131no—
246C4⋊C4—131no—
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—21no—
257C22⋊C4—21no—
258C22⋊C4—261no—
259C22⋊C4—261no—
260C22⋊C4—261no—
261C22⋊C4—261no—
262C42—21no—
263C42—131no—
264C42—131no—
265C42—261no—
266C42—261no—
267C42—261no—
268C42C22×D1311yescharacteristic
269C13#337111yescharacteristic, complemented, Sylow
270C23—21no—
271C23—261no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—521no—
276Q8—522no—
277Q8#612912yes—
278D4—21no—
279D4—21no—
280D4—261no—
281D4—261no—
282D4—522no—
283D4—1041no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—131no—
288C2×C4—131no—
289C2×C4—131no—
290C2×C4—131no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—1041no—
295C2×C4—1041no—
296C2×C4D4×D1311yescharacteristic
297C2×C4D4×D1311yescharacteristic
298C2×C4C23×D1311yescharacteristic
299C8—21no—
300C8—21no—
301C8—261no—
302C8—261no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—521no—
307C22—521no—
308C22—521no—
309C22C2×D4×D1311yescharacteristic
310C4—21no—
311C4—21no—
312C4—22no—
313C4—41no—
314C4—41no—
315C4—261no—
316C4—261no—
317C4—261no—
318C4—261no—
319C4—521no—
320C4—521no—
321C4—521no—
322C4C2×#612911yescharacteristic
323C4#8825711yescharacteristic
324C2—81no—
325C2—1041no—
326C2#1171930311yescharacteristic
327C2#1171947311yescharacteristic
328C2#1171948311yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#464C2
socleC22×C13C22×D4
prime radical#88194C22
hypercenter#464D13
hypocenterC13#3371
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
2. #11719274C2semidirect
3. C13×#464C2semidirect
4. #11718846C2semidirect
5. #11718845C2semidirect
6. #11718825C2semidirect
8. #11718717C2semidirect
9. C4×#6106C2semidirect
10. #11718508C2semidirect
11. #11718492C2semidirect
12. #11718457C2semidirect
13. #11718456C2semidirect
15. #11718422C2semidirect
148. #464D13semidirect
269. C13#3371semidirect

Maximal subgroups

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

subgroupindex
#117193862
#117192742
C13×#4642
#117188462
#117188452
#117188252
#117188242
#117187172
C4×#61062
#117185082
#117184922
#117184572
#117184562
#117184252
#117184222
#337113