Finite Group Databasebeta

← #13127571

Subgroups — #13127571

Order 1664.

338 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#11719376C211yesmaximal, characteristic
2Q8×Dic26C211yesmaximal, characteristic, complemented
3C13×#464C211yesmaximal, characteristic
4#11718845C211yesmaximal, characteristic, complemented
5#11718843C211yesmaximal, characteristic, complemented
6#11718827C211yesmaximal, characteristic
7SD16×Dic13C211yesmaximal, characteristic
8#11718716C211yesmaximal, characteristic
9#11718691C211yesmaximal, characteristic, complemented
10#11718512C211yesmaximal, characteristic, complemented
11#11718489C211yesmaximal, characteristic, complemented
12#11718453C211yesmaximal, characteristic, complemented
13#11718452C211yesmaximal, characteristic, complemented
14#11718426C211yesmaximal, characteristic
15#11718422C211yesmaximal, characteristic
16C2×C13×Q16C2211yescharacteristic
17C2×C13×SD16C2211yescharacteristic
18C13×#124C2211yescharacteristic
19C4×Q8×C13C2211yescharacteristic
20Q8×Dic13C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23#88198C2211yescharacteristic
24C2×#6107C2211yescharacteristic
25#88190C2211yescharacteristic
26D4×Dic13C2211yescharacteristic
27#88142—21no—
28#88142—21no—
29#88142C2211yescharacteristic
30#88142C2211yescharacteristic
31#88133—21no—
32#88133—21no—
33#88132—21no—
34#88131—21no—
35#88123—21no—
36#88123C2211yescharacteristic
37C4×Dic26—21no—
38C4×Dic26C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×C4⋊C8C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#102C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88072C2211yescharacteristic
47#88072C2211yescharacteristic
48#88057C2211yescharacteristic
49#88057C2211yescharacteristic
50#88056C2211yescharacteristic
51#88056C2211yescharacteristic
52#88055C2211yescharacteristic
53#88054C2211yescharacteristic
54#88054C2211yescharacteristic
55C8×Dic13C2211yescharacteristic
56#88050C2211yescharacteristic
57#88048C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×Dic13—21no—
63C2×Dic26—21no—
64C2×Dic26—21no—
65C2×Dic26—21no—
66C2×Dic26D411yescharacteristic
67C2×Dic26C2311yescharacteristic
68C13×Q16—22no—
69C13×SD16—22no—
70C2×C8×C13C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C13×C4⋊C4—21no—
73C13×C4⋊C4C2311yescharacteristic
74C13×C22⋊C4—21no—
75C13×C22⋊C4—21no—
76C42×C13—21no—
77C42×C13C2311yescharacteristic
78C22⋊Dic13—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81#6107—22no—
82C4⋊Dic13—21no—
83C4⋊Dic13—21no—
84C4⋊Dic13—21no—
85C4⋊Dic13—21no—
86C4⋊Dic13D411yescharacteristic
87C4⋊Dic13C2311yescharacteristic
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90#6101—21no—
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101D411yescharacteristic
96#6101D411yescharacteristic
97C4×Dic13—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C4×Dic13C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3369—131nomaximal, Sylow
106C23×C13—21no—
107Q8×C13—21no—
108Q8×C13—21no—
109Q8×C13—21no—
110Q8×C13#4112yes—
111D4×C13—21no—
112D4×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×Dic13—42no—
124C2×Dic13C2×D411yescharacteristic
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128Dic26—22no—
129Dic26—21no—
130Dic26—21no—
131Dic26—81no—
132Dic26—81no—
133Dic26—81no—
134C8×C13—21no—
135C8×C13—21no—
136#1055—21no—
137#1055—21no—
138Q82—131no—
139#556—131no—
140#489—131no—
141#489—131no—
142#487—131no—
143#476—131no—
144#475—131no—
145#475—131no—
146#464—131no—
147#464D1311yescharacteristic
148#462—131no—
149#446—131no—
150#441—131no—
151#441—131no—
152C4×SD16—131no—
153C22×C13—41no—
154C22×C13—41no—
155C22×C13—41no—
156C22×C13C22×D411yescharacteristic
157C4×C13—22no—
158C4×C13—21no—
159C4×C13—21no—
160C4×C13—41no—
161C4×C13—41no—
162C4×C13C2×#4111yescharacteristic
163C4×C132−1+411yescharacteristic
164Dic13—21no—
165Dic13—21no—
166Dic13—21no—
167Dic13—41no—
168Dic13—41no—
169Dic13—41no—
170Dic13—41no—
171Dic13#13712yes—
172C2×Q16—131no—
173C2×Q16C2×D1311yescharacteristic
174C2×SD16C2×D1311yescharacteristic
175C4⋊Q8—131no—
176C4⋊Q8—131no—
177C4⋊Q8—131no—
178C4⋊Q8—131no—
179C4⋊Q8—261no—
180C4⋊Q8—261no—
181C4⋊Q8—261no—
182#126—261no—
183#126—261no—
184#124—131no—
185#124C2×D1311yescharacteristic
186C22⋊Q8—261no—
187C4×Q8—131no—
188C4×Q8—131no—
189C4×Q8—131no—
190C4×Q8—131no—
191C4×Q8—131no—
192C4×Q8—261no—
193C4×Q8C2×D1311yescharacteristic
194C4×D4—131no—
195#117—261no—
196#106—131no—
197#106—131no—
198#106—131no—
199C4⋊C8—131no—
200C4⋊C8—131no—
201C4⋊C8C2×D1311yescharacteristic
202#103—131no—
203#103—131no—
204#103—131no—
205#103—131no—
206#103—131no—
207#103—131no—
208#103C2×D1311yescharacteristic
209#102—131no—
210#102—131no—
211#102C2×D1311yescharacteristic
212#97—131no—
213#97—131no—
214C4×C8—131no—
215C2×C13—81no—
216C2×C13#54811yescharacteristic
217C2×C13C2×#13711yescharacteristic
218C2×C13#57711yescharacteristic
219C2×Q8—131no—
220C2×Q8—131no—
221C2×Q8—261no—
222C2×Q8—261no—
223C2×Q8—261no—
224C2×Q8C22×D1311yescharacteristic
225C2×Q8C22×D1311yescharacteristic
226C2×D4C22×D1311yescharacteristic
227C22×C4—261no—
228Q16—22no—
229Q16—262no—
230SD16—22no—
231C2×C8—131no—
232C2×C8—131no—
233C2×C8C22×D1311yescharacteristic
234C2×C8C22×D1311yescharacteristic
235C4⋊C4—21no—
236C4⋊C4—131no—
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⋊C4C22×D1311yescharacteristic
252C22⋊C4—21no—
253C22⋊C4—21no—
254C22⋊C4—261no—
255C22⋊C4—261no—
256C22⋊C4—261no—
257C42—21no—
258C42—131no—
259C42—131no—
260C42—261no—
261C42—261no—
262C42—261no—
263C42—261no—
264C42C22×D1311yescharacteristic
265C13#336911yescharacteristic, complemented, Sylow
266C23—21no—
267Q8—21no—
268Q8—21no—
269Q8—21no—
270Q8—262no—
271Q8—261no—
272Q8—261no—
273Q8—1041no—
274Q8—1041no—
275Q8—1041no—
276Q8#612912yes—
277D4—21no—
278D4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—131no—
283C2×C4—131no—
284C2×C4—131no—
285C2×C4—131no—
286C2×C4—261no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—522no—
291C2×C4D4×D1311yescharacteristic
292C2×C4D4×D1311yescharacteristic
293C2×C4C23×D1311yescharacteristic
294C8—21no—
295C8—21no—
296C8—261no—
297C8—261no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22C2×D4×D1311yescharacteristic
302C4—21no—
303C4—21no—
304C4—22no—
305C4—41no—
306C4—41no—
307C4—132no—
308C4—261no—
309C4—261no—
310C4—261no—
311C4—521no—
312C4—521no—
313C4—521no—
314C4—521no—
315C4C2×#612911yescharacteristic
316C4#8825711yescharacteristic
317C2—81no—
318C2#1171930311yescharacteristic
319C2#1171947511yescharacteristic
320C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#464C2
socleC22×C13C22×D4
prime radicalC2×D4×C13C23
hypercenter#464D13
hypocenterC13#3369
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. Q8×Dic26C2semidirect
4. #11718845C2semidirect
5. #11718843C2semidirect
9. #11718691C2semidirect
10. #11718512C2semidirect
11. #11718489C2semidirect
12. #11718453C2semidirect
13. #11718452C2semidirect
265. C13#3369semidirect

Maximal subgroups

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

subgroupindex
#117193762
Q8×Dic262
C13×#4642
#117188452
#117188432
#117188272
SD16×Dic132
#117187162
#117186912
#117185122
#117184892
#117184532
#117184522
#117184262
#117184222
#336913