Finite Group Databasebeta

← #13127656

Subgroups — #13127656

Order 1664.

346 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#11719437C211yesmaximal, characteristic, complemented
2#11719244C211yesmaximal, characteristic, complemented
3C13×#461C211yesmaximal, characteristic, complemented
4#11718826C211yesmaximal, characteristic
5#11718826C211yesmaximal, characteristic
6#11718825C211yesmaximal, characteristic, complemented
7SD16×Dic13C211yesmaximal, characteristic, complemented
8#11718743C211yesmaximal, characteristic, complemented
9#11718675C211yesmaximal, characteristic
10#11718508C211yesmaximal, characteristic, complemented
11#11718489C211yesmaximal, characteristic, complemented
12#11718461C211yesmaximal, characteristic, complemented
13#11718457C211yesmaximal, characteristic, complemented
14#11718456C211yesmaximal, characteristic, complemented
15#11718452C211yesmaximal, characteristic, complemented
16C2×C13×SD16C2211yescharacteristic
17C2×C13×SD16C2211yescharacteristic
18C13×C4⋊Q8C2211yescharacteristic
19C4×D4×C13C2211yescharacteristic
20#88201C2211yescharacteristic
21#88201C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24D4×Dic13C2211yescharacteristic
25D4×Dic13C2211yescharacteristic
26C2×#6104C2211yescharacteristic
27#88178—21no—
28C2×#6101—21no—
29#88152—21no—
30#88152—21no—
31#88151—21no—
32#88146—21no—
33#88144C2211yescharacteristic
34#88142C2211yescharacteristic
35#88132—21no—
36#88132—21no—
37C4×D52C2211yescharacteristic
38#88124C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×C4⋊C8C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#103C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88072C2211yescharacteristic
48#88061C2211yescharacteristic
49#88061C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88055C2211yescharacteristic
53#88054C2211yescharacteristic
54#88054C2211yescharacteristic
55C8×Dic13C2211yescharacteristic
56#88049C2211yescharacteristic
57#88048C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13—21no—
63C22×Dic13—21no—
64C22×Dic13—21no—
65C2×D52C2311yescharacteristic
66C2×C4×D13—21no—
67C2×Dic26—21no—
68C2×Dic26D411yescharacteristic
69C13×SD16—22no—
70C13×SD16—22no—
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4C2311yescharacteristic
76C13×C22⋊C4—21no—
77C42×C13C2311yescharacteristic
78C22⋊Dic13—21no—
79C22⋊Dic13—21no—
80#6104—22no—
81#6103—21no—
82#6103—21no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13D411yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101D411yescharacteristic
98#6101D411yescharacteristic
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C4×Dic13C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105#3376—131nomaximal, Sylow
106C23×C13—21no—
107C22×D13—21no—
108Q8×C13—21no—
109Q8×C13—21no—
110Q8×C13—21no—
111Q8×C13—21no—
112D4×C13—21no—
113D4×C13#4112yes—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—81no—
118C2×C4×C13C2×D411yescharacteristic
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2411yescharacteristic
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—42no—
125C2×Dic13—81no—
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128C2×Dic13C2×D411yescharacteristic
129C2×Dic13C2×D411yescharacteristic
130D52—21no—
131D52—21no—
132C4×D13—42no—
133Dic26—41no—
134Dic26—81no—
135C8×C13—21no—
136C8×C13—21no—
137#1055—21no—
138#1055—21no—
139#556—131no—
140#554—131no—
141#491—131no—
142#489—131no—
143#488—131no—
144#479—131no—
145#478—131no—
146#475—131no—
147#463—131no—
148#463—131no—
149#461D1311yescharacteristic, complemented
150#446—131no—
151#442—131no—
152#440—131no—
153C4×SD16—131no—
154C22×C13—22no—
155C22×C13—41no—
156C22×C13—41no—
157C22×C13C22×D411yescharacteristic
158C2×D13—41no—
159C2×D13—41no—
160C2×D13—41no—
161C4×C13—21no—
162C4×C13—21no—
163C4×C13—41no—
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×SD16C2×D1311yescharacteristic
176C2×SD16C2×D1311yescharacteristic
177C2×D8—131no—
178C4⋊Q8—131no—
179C4⋊Q8C2×D1311yescharacteristic
180#126—261no—
181#126—261no—
182#125—131no—
183#125—131no—
184#124—131no—
185#124—131no—
186C22⋊Q8—261no—
187C22⋊Q8—261no—
188C22⋊Q8—261no—
189C22⋊Q8—261no—
190C4×Q8—131no—
191C4×Q8—131no—
192C4×Q8—131no—
193C4×D4—131no—
194C4×D4—131no—
195C4×D4—131no—
196C4×D4C2×D1311yescharacteristic
197#117—261no—
198C2×C4⋊C4—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#103—131no—
209#103C2×D1311yescharacteristic
210#103C2×D1311yescharacteristic
211#102—131no—
212#102—131no—
213#102—131no—
214#102—131no—
215#97—131no—
216#97—131no—
217C4×C8—131no—
218C2×C13—42no—
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×D4C22×D1311yescharacteristic
229C22×C4—21no—
230C22×C4—261no—
231C22×C4—261no—
232C22×C4—261no—
233SD16—22no—
234SD16—22no—
235D8—262no—
236C2×C8—131no—
237C2×C8—131no—
238C2×C8C22×D1311yescharacteristic
239C2×C8C22×D1311yescharacteristic
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—131no—
243C4⋊C4—131no—
244C4⋊C4—131no—
245C4⋊C4—131no—
246C4⋊C4—131no—
247C4⋊C4—131no—
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—261no—
258C22⋊C4—261no—
259C22⋊C4—261no—
260C22⋊C4—261no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C42—131no—
265C42—131no—
266C42—261no—
267C42—261no—
268C42C22×D1311yescharacteristic
269C13#337611yescharacteristic, complemented, Sylow
270C23—21no—
271C23—261no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—521no—
277Q8—1041no—
278D4—21no—
279D4—261no—
280D4—261no—
281D4#612912yes—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—81no—
286C2×C4—131no—
287C2×C4—131no—
288C2×C4—131no—
289C2×C4—131no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—522no—
294C2×C4—522no—
295C2×C4—1041no—
296C2×C4D4×D1311yescharacteristic
297C2×C4D4×D1311yescharacteristic
298C2×C4C23×D1311yescharacteristic
299C8—21no—
300C8—21no—
301C8—261no—
302C8—261no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—521no—
307C22—521no—
308C22—521no—
309C22C2×D4×D1311yescharacteristic
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—261no—
316C4—261no—
317C4—261no—
318C4—261no—
319C4—521no—
320C4—521no—
321C4—521no—
322C4C2×#612911yescharacteristic
323C4#8825711yescharacteristic
324C2—42no—
325C2—1041no—
326C2#1171930311yescharacteristic
327C2#1171946711yescharacteristic
328C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#461C2
socleC22×C13C22×D4
prime radicalC2×#6104C22
hypercenter#461D13
hypocenterC13#3376
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #11719437C2semidirect
2. #11719244C2semidirect
3. C13×#461C2semidirect
6. #11718825C2semidirect
7. SD16×Dic13C2semidirect
8. #11718743C2semidirect
10. #11718508C2semidirect
11. #11718489C2semidirect
12. #11718461C2semidirect
13. #11718457C2semidirect
14. #11718456C2semidirect
15. #11718452C2semidirect
149. #461D13semidirect
269. C13#3376semidirect

Maximal subgroups

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

subgroupindex
#117194372
#117192442
C13×#4612
#117188262
#117188252
SD16×Dic132
#117187432
#117186752
#117185082
#117184892
#117184612
#117184572
#117184562
#117184522
#337613