Finite Group Databasebeta

← #13127551

Subgroups — #13127551

Order 1664.

372 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719432C211yesmaximal, characteristic, complemented
2#11719376C211yesmaximal, characteristic, complemented
3C13×#489C211yesmaximal, characteristic, complemented
4#11718752C211yesmaximal, characteristic, complemented
5#11718718C211yesmaximal, characteristic
6#11718479C211yesmaximal, characteristic, complemented
7#11718478C211yesmaximal, characteristic, complemented
8#11718455C211yesmaximal, characteristic, complemented
9#11718453C211yesmaximal, characteristic, complemented
10#11718448C211yesmaximal, characteristic
11#11718426C211yesmaximal, characteristic, complemented
12#11718420C211yesmaximal, characteristic, complemented
13#11718417C211yesmaximal, characteristic
14#11718371C211yesmaximal, characteristic, complemented
15#11718362C211yesmaximal, characteristic, complemented
16C2×Q8×D13—21no—
17C13×C4⋊Q8C2211yescharacteristic
18C13×#124C2211yescharacteristic
19#88200—21no—
20Q8×Dic13C2211yescharacteristic
21#88198C2211yescharacteristic
22C2×#6106C2211yescharacteristic
23#88190C2211yescharacteristic
24D4×Dic13C2211yescharacteristic
25C2×#6104C2211yescharacteristic
26C2×#6095C2211yescharacteristic
27#88150—21no—
28#88150—21no—
29#88147C2211yescharacteristic
30#88147C2211yescharacteristic
31#88142C2211yescharacteristic
32#88142C2211yescharacteristic
33#88133—21no—
34#88133—21no—
35#88132—21no—
36#88131—21no—
37C4×D52C2211yescharacteristic
38C4×Dic26C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×#103C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#102C2211yescharacteristic
43C13×#102C2211yescharacteristic
44C13×#97C2211yescharacteristic
45#88075C2211yescharacteristic
46#88072C2211yescharacteristic
47#88061C2211yescharacteristic
48#88058C2211yescharacteristic
49#88056C2211yescharacteristic
50#88055C2211yescharacteristic
51#88054C2211yescharacteristic
52#88054C2211yescharacteristic
53C8×Dic13C2211yescharacteristic
54#88050C2211yescharacteristic
55#88050C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×Dic13—21no—
63Q8×D13—44no—
64C2×D52C2311yescharacteristic
65C2×C4×D13—21no—
66C2×C4×D13—21no—
67C2×C4×D13—21no—
68C2×Dic26—21no—
69C2×Dic26—21no—
70C2×Dic26D411yescharacteristic
71C2×Dic26C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C13×C4⋊C4—21no—
75C13×C4⋊C4C2311yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C42×C13C2311yescharacteristic
80C22⋊Dic13—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83#6106—22no—
84#6104—22no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13D411yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92#6101—21no—
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#6095—22no—
106#3367—131nomaximal, Sylow
107C23×C13—21no—
108C22×D13—21no—
109Q8×C13—21no—
110Q8×C13—21no—
111Q8×C13—42no—
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
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—42no—
124C2×Dic13C2×D411yescharacteristic
125C2×Dic13C2×D411yescharacteristic
126C2×Dic13C2×D411yescharacteristic
127C2×Dic13C2×D411yescharacteristic
128D52—21no—
129D52#4112yes—
130C4×D13—42no—
131C4×D13—42no—
132C4×D13—42no—
133Dic26—22no—
134Dic26—21no—
135Dic26—21no—
136Dic26—42no—
137Dic26—42no—
138C8×C13—21no—
139C8×C13—21no—
140#1055—21no—
141#1055—21no—
142#556—131no—
143D4×Q8—131no—
144#489—131no—
145#489D1311yescharacteristic, complemented
146#487—131no—
147#477—131no—
148#477—131no—
149#474—131no—
150#463—131no—
151#463—131no—
152#461—131no—
153#446—131no—
154#440—131no—
155#440—131no—
156C4×D8—131no—
157C22×C13—41no—
158C22×C13—41no—
159C22×C13—41no—
160C22×C13C22×D411yescharacteristic
161C2×D13—22no—
162C2×D13—41no—
163C2×D13—41no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13C2×#4111yescharacteristic
170C4×C132−1+411yescharacteristic
171Dic13—21no—
172Dic13—21no—
173Dic13—21no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177Dic13AGL(1,ℤ/8)12yes—
178C22×Q8—261no—
179C2×SD16—131no—
180C2×SD16—131no—
181C2×D8—131no—
182C4⋊Q8—131no—
183C4⋊Q8—131no—
184C4⋊Q8—131no—
185C4⋊Q8C2×D1311yescharacteristic
186#126—261no—
187#126—261no—
188#124—131no—
189#124C2×D1311yescharacteristic
190C22⋊Q8—261no—
191C22⋊Q8—261no—
192C22⋊Q8—261no—
193C22⋊Q8—261no—
194C4×Q8—131no—
195C4×Q8—131no—
196C4×Q8—131no—
197C4×D4—131no—
198C4×D4—131no—
199C4×D4—131no—
200C4×D4—131no—
201#117—261no—
202#107—131no—
203#107—131no—
204#107—131no—
205C4⋊C8—131no—
206C4⋊C8—131no—
207C4⋊C8—131no—
208#103—131no—
209#103—131no—
210#103—131no—
211#103—131no—
212#103C2×D1311yescharacteristic
213#103C2×D1311yescharacteristic
214#102—131no—
215#102—131no—
216#102C2×D1311yescharacteristic
217#102C2×D1311yescharacteristic
218#97—131no—
219#97C2×D1311yescharacteristic
220C4×C8—131no—
221C2×C13—81no—
222C2×C13#54811yescharacteristic
223C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
224C2×C13#57811yescharacteristic
225D13—42no—
226C2×Q8—21no—
227C2×Q8—131no—
228C2×Q8—131no—
229C2×Q8—261no—
230C2×Q8—261no—
231C2×Q8—524no—
232C2×Q8C22×D1311yescharacteristic
233C2×D4—131no—
234C2×D4C22×D1311yescharacteristic
235C22×C4—261no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4—261no—
239SD16—262no—
240SD16—262no—
241D8—262no—
242C2×C8—131no—
243C2×C8—131no—
244C2×C8C22×D1311yescharacteristic
245C2×C8C22×D1311yescharacteristic
246C4⋊C4—21no—
247C4⋊C4—131no—
248C4⋊C4—131no—
249C4⋊C4—131no—
250C4⋊C4—131no—
251C4⋊C4—131no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4C22×D1311yescharacteristic
259C4⋊C4C22×D1311yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C42—131no—
269C42—131no—
270C42—261no—
271C42—261no—
272C42C22×D1311yescharacteristic
273C13#336711yescharacteristic, complemented, Sylow
274C23—21no—
275C23—261no—
276Q8—21no—
277Q8—21no—
278Q8—42no—
279Q8—262no—
280Q8—261no—
281Q8—261no—
282Q8—522no—
283Q8—522no—
284D4—21no—
285D4—21no—
286D4—132no—
287D4—261no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—131no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—131no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—522no—
299C2×C4—522no—
300C2×C4—522no—
301C2×C4—522no—
302C2×C4D4×D1311yescharacteristic
303C2×C4D4×D1311yescharacteristic
304C2×C4C23×D1311yescharacteristic
305C8—21no—
306C8—21no—
307C8—261no—
308C8—261no—
309C22—41no—
310C22—41no—
311C22—41no—
312C22—262no—
313C22—521no—
314C22—521no—
315C22C2×D4×D1311yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—132no—
322C4—261no—
323C4—261no—
324C4—261no—
325C4—521no—
326C4—521no—
327C4—521no—
328C4#41×D1311yescharacteristic
329C4#8825711yescharacteristic
330C2—81no—
331C2—522no—
332C2#1171938211yescharacteristic
333C2D13×AGL(1,ℤ/8)11yescharacteristic
334C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#489C2
socleC22×C13C22×D4
prime radicalC2×#6104C22
hypercenter#489D13
hypocenterC13#3367
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #11719432C2semidirect
2. #11719376C2semidirect
3. C13×#489C2semidirect
4. #11718752C2semidirect
6. #11718479C2semidirect
7. #11718478C2semidirect
8. #11718455C2semidirect
9. #11718453C2semidirect
11. #11718426C2semidirect
12. #11718420C2semidirect
14. #11718371C2semidirect
15. #11718362C2semidirect
145. #489D13semidirect
273. C13#3367semidirect

Maximal subgroups

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

subgroupindex
#117194322
#117193762
C13×#4892
#117187522
#117187182
#117184792
#117184782
#117184552
#117184532
#117184482
#117184262
#117184202
#117184172
#117183712
#117183622
#336713