Finite Group Databasebeta

← #13127398

Subgroups — #13127398

Order 1664.

348 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#11719270C211yesmaximal, characteristic
2#11719246C211yesmaximal, characteristic, complemented
3C13×#436C211yesmaximal, characteristic, complemented
4#11718795C211yesmaximal, characteristic, complemented
5#11718795C211yesmaximal, characteristic, complemented
6#11718782C211yesmaximal, characteristic, complemented
7#11718782C211yesmaximal, characteristic, complemented
8#11718508C211yesmaximal, characteristic, complemented
9#11718490C211yesmaximal, characteristic, complemented
10#11718398C211yesmaximal, characteristic, complemented
11#11718396C211yesmaximal, characteristic, complemented
12#11718384C211yesmaximal, characteristic, complemented
13#11718382C211yesmaximal, characteristic, complemented
14C4×#6095C211yesmaximal, characteristic, complemented
15#11718344C211yesmaximal, characteristic, complemented
16C2×C13×M16C2211yescharacteristic
17C2×C13×M16C2211yescharacteristic
18C4×D4×C13C2211yescharacteristic
19#88193—21no—
20#88189—21no—
21#88184C2211yescharacteristic
22#88184C2211yescharacteristic
23#88180C2211yescharacteristic
24#88180C2211yescharacteristic
25C2×C4⋊Dic13C2211yescharacteristic
26C2×C4⋊Dic13C2211yescharacteristic
27#88178C2211yescharacteristic
28#88178C2211yescharacteristic
29C2×#6095C2211yescharacteristic
30#88152—21no—
31#88143—21no—
32#88137—21no—
33#88135—21no—
34#88133—21no—
35#88131—21no—
36C4×D52C2211yescharacteristic
37#88124C2211yescharacteristic
38#88124C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40C13×C4⋊C8C2211yescharacteristic
41C13×C22⋊C8C2211yescharacteristic
42C13×C22⋊C8C2211yescharacteristic
43C4×C8×C13C2211yescharacteristic
44#88061C2211yescharacteristic
45#88061C2211yescharacteristic
46#88061C2211yescharacteristic
47#88058C2211yescharacteristic
48#88058C2211yescharacteristic
49#88058C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88057C2211yescharacteristic
53#88057C2211yescharacteristic
54#88057C2211yescharacteristic
55#88057C2211yescharacteristic
56#88056C2211yescharacteristic
57#88056C2211yescharacteristic
58#88056C2211yescharacteristic
59C2×D4×C13D411yescharacteristic
60C22×C4×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×C22⋊D13—21no—
64C22×Dic13—21no—
65C22×Dic13—21no—
66C2×D52C2311yescharacteristic
67C2×C4×D13—21no—
68C2×Dic26C2311yescharacteristic
69C13×M16—22no—
70C13×M16—22no—
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C2×C8×C13C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C13×C4⋊C4D411yescharacteristic
76C13×C22⋊C4D411yescharacteristic
77C13×C22⋊C4D411yescharacteristic
78C42×C13C2311yescharacteristic
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13C2311yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101—21no—
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104#6095—22no—
105#3351—131nomaximal, Sylow
106C23×C13C2×D411yescharacteristic
107C23×C13C2×D411yescharacteristic
108C22×D13—21no—
109D4×C13—41no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13C2×D411yescharacteristic
115C2×C4×C13C2×D411yescharacteristic
116C2×C4×C13C2×D411yescharacteristic
117C2×C4×C13C2×D411yescharacteristic
118C2×C4×C13C2411yescharacteristic
119C22⋊D13—42no—
120C22⋊D13—81no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—42no—
129C2×Dic13—81no—
130D52—21no—
131D52—21no—
132C4×D13—81no—
133Dic26—21no—
134Dic26—21no—
135C8×C13—21no—
136C8×C13—21no—
137C8×C13—21no—
138C8×C13#4112yes—
139#553—131no—
140#552—131no—
141#499—131no—
142#485—131no—
143#483—131no—
144#482—131no—
145#481—131no—
146#479—131no—
147#478—131no—
148#468—131no—
149#468—131no—
150C4×SD16—131no—
151#436D1311yescharacteristic, complemented
152#428—131no—
153#428—131no—
154C22×C13—21no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13C22×D411yescharacteristic
161C2×D13—41no—
162C2×D13—41no—
163C2×D13—41no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13C2×#4111yescharacteristic
169C4×C132−1+411yescharacteristic
170Dic13—41no—
171Dic13—41no—
172Dic13—41no—
173Dic13—41no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177C2×SD16—131no—
178C2×M16C2×D1311yescharacteristic
179C2×M16C2×D1311yescharacteristic
180#126—261no—
181#126—261no—
182#125—131no—
183#125—131no—
184#125—261no—
185#123—261no—
186#123—261no—
187C22⋊Q8—131no—
188C22⋊Q8—131no—
189#121—131no—
190#121—131no—
191#121—261no—
192C4×Q8—131no—
193C4×D4—131no—
194C4×D4—261no—
195C4×D4C2×D1311yescharacteristic
196#117—131no—
197#117—131no—
198#117—261no—
199C2×C4⋊C4—131no—
200C2×C4⋊C4—131no—
201#107—131no—
202#107—131no—
203#107—131no—
204#107—131no—
205#106—131no—
206#106—131no—
207#106—131no—
208#106—131no—
209#106—131no—
210C4⋊C8C2×D1311yescharacteristic
211#103—131no—
212#103—131no—
213#103—131no—
214#102—131no—
215#102—131no—
216#102—131no—
217C22⋊C8C2×D1311yescharacteristic
218C22⋊C8C2×D1311yescharacteristic
219C4×C8C2×D1311yescharacteristic
220C2×C13—41no—
221C2×C13—41no—
222C2×C13#54711yescharacteristic
223C2×C13#57511yescharacteristic
224C2×C13#57711yescharacteristic
225D13—81no—
226C2×Q8—131no—
227C2×D4—131no—
228C2×D4—261no—
229C2×D4—261no—
230C2×D4D5211yescharacteristic
231C22×C4—261no—
232C22×C4—261no—
233C22×C4—261no—
234C22×C4C22×D1311yescharacteristic
235C22×C4C22×D1311yescharacteristic
236SD16—262no—
237M16—22no—
238M16—22no—
239C2×C8C22×D1311yescharacteristic
240C2×C8C22×D1311yescharacteristic
241C2×C8C22×D1311yescharacteristic
242C2×C8C22×D1311yescharacteristic
243C4⋊C4—131no—
244C4⋊C4—131no—
245C4⋊C4—131no—
246C4⋊C4—131no—
247C4⋊C4—131no—
248C4⋊C4—131no—
249C4⋊C4—261no—
250C4⋊C4—261no—
251C4⋊C4—261no—
252C4⋊C4—261no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4D5211yescharacteristic
259C22⋊C4—261no—
260C22⋊C4—261no—
261C22⋊C4—261no—
262C22⋊C4—261no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4D5211yescharacteristic
267C22⋊C4D5211yescharacteristic
268C42—261no—
269C42—261no—
270C42—261no—
271C42C22×D1311yescharacteristic
272C13#335111yescharacteristic, complemented, Sylow
273C23—261no—
274C23C2×D5211yescharacteristic
275C23C2×D5211yescharacteristic
276Q8—261no—
277Q8—261no—
278D4—41no—
279D4—261no—
280D4—261no—
281D4—522no—
282D4—1041no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—261no—
288C2×C4—261no—
289C2×C4—261no—
290C2×C4—261no—
291C2×C4—261no—
292C2×C4—261no—
293C2×C4—261no—
294C2×C4—522no—
295C2×C4—1041no—
296C2×C4—1041no—
297C2×C4C2×D5211yescharacteristic
298C2×C4C2×D5211yescharacteristic
299C2×C4C2×D5211yescharacteristic
300C2×C4C2×D5211yescharacteristic
301C2×C4C23×D1311yescharacteristic
302C8—21no—
303C8—21no—
304C8—21no—
305C8#612912yes—
306C22—21no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—21no—
311C22—21no—
312C22—521no—
313C22—521no—
314C22—521no—
315C22C22×D5211yescharacteristic
316C4—21no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—521no—
321C4—521no—
322C4—521no—
323C4—521no—
324C4—521no—
325C4—521no—
326C4—521no—
327C4C2×#612911yescharacteristic
328C4#8825711yescharacteristic
329C2—41no—
330C2—41no—
331C2—1041no—
332C2#1171926011yescharacteristic
333C2#1171945311yescharacteristic
334C2#1171945611yescharacteristic
subgroupG/H
centerC22C22×D52
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#436C2
socleC22×C13C22×D4
prime radical#11719270C2
hypercenter#436D13
hypocenterC13#3351
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #436

Complements

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

NH ≅ G/Ntype
2. #11719246C2semidirect
3. C13×#436C2semidirect
4. #11718795C2semidirect
5. #11718795C2semidirect
6. #11718782C2semidirect
7. #11718782C2semidirect
8. #11718508C2semidirect
9. #11718490C2semidirect
10. #11718398C2semidirect
11. #11718396C2semidirect
12. #11718384C2semidirect
13. #11718382C2semidirect
14. C4×#6095C2semidirect
15. #11718344C2semidirect
151. #436D13semidirect
272. C13#3351semidirect

Maximal subgroups

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

subgroupindex
#117192702
#117192462
C13×#4362
#117187952
#117187822
#117185082
#117184902
#117183982
#117183962
#117183842
#117183822
C4×#60952
#117183442
#335113