Finite Group Databasebeta

← #13125498

Subgroups — #13125498

Order 1664.

350 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#542C211yesmaximal, characteristic
2#11719223C211yesmaximal, characteristic, complemented
3#11718754C211yesmaximal, characteristic, complemented
4#11718741C211yesmaximal, characteristic, complemented
5#11718721C211yesmaximal, characteristic, complemented
6#11718717C211yesmaximal, characteristic, complemented
7#11718713C211yesmaximal, characteristic, complemented
8#11718712C211yesmaximal, characteristic, complemented
9#11718703C211yesmaximal, characteristic
10#11718702C211yesmaximal, characteristic
11#11718691C211yesmaximal, characteristic, complemented
12C4×#6107C211yesmaximal, characteristic, complemented
13#11718679C211yesmaximal, characteristic, complemented
14C4×#6105C211yesmaximal, characteristic, complemented
15#11718658C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C13×#126—21no—
18C13×#124—21no—
19C13×#124C2211yescharacteristic
20C13×#123—21no—
21C13×C22⋊Q8—21no—
22C13×C22⋊Q8C2211yescharacteristic
23C13×#121C2211yescharacteristic
24C4×Q8×C13C2211yescharacteristic
25C4×D4×C13C2211yescharacteristic
26C13×#117C2211yescharacteristic
27C2×#6107C2211yescharacteristic
28C2×#6107C2211yescharacteristic
29C2×#6105C2211yescharacteristic
30C2×#6105C2211yescharacteristic
31#88178C2211yescharacteristic
32#88178C2211yescharacteristic
33C2×#6099C2211yescharacteristic
34C22×#1055C2211yescharacteristic
35#88143—21no—
36#88143—21no—
37#88133—21no—
38#88133—21no—
39#88124C2211yescharacteristic
40#88123C2211yescharacteristic
41C4×Dic26C2211yescharacteristic
42C4×Dic26C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47#88050C2211yescharacteristic
48#88050C2211yescharacteristic
49#88050C2211yescharacteristic
50#88050C2211yescharacteristic
51#88048C2211yescharacteristic
52#88048C2211yescharacteristic
53#88047C2211yescharacteristic
54#88047C2211yescharacteristic
55#88043C2211yescharacteristic
56#88043C2211yescharacteristic
57C4×#1055C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13—21no—
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13—21no—
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13—21no—
64C22×C4×C13C2311yescharacteristic
65C2×Dic26C2311yescharacteristic
66C2×Dic26C2311yescharacteristic
67C13×C4⋊C4—21no—
68C13×C4⋊C4—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4D411yescharacteristic
71C13×C4⋊C4D411yescharacteristic
72C13×C4⋊C4C2311yescharacteristic
73C13×C4⋊C4C2311yescharacteristic
74C13×C22⋊C4—21no—
75C13×C22⋊C4—21no—
76C13×C22⋊C4—21no—
77C13×C22⋊C4—21no—
78C13×C22⋊C4—21no—
79C13×C22⋊C4D411yescharacteristic
80C13×C22⋊C4D411yescharacteristic
81C42×C13—21no—
82C42×C13C2311yescharacteristic
83C42×C13C2311yescharacteristic
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86#6107—22no—
87#6107—22no—
88#6105—22no—
89#6105—22no—
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13C2311yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100C4×Dic13—21no—
101C4×Dic13—21no—
102#6099—22no—
103C2×#1055—22no—
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#3178—131nomaximal, Sylow
109C23×C13—21no—
110C23×C13C2×D411yescharacteristic
111Q8×C13—21no—
112Q8×C13—21no—
113Q8×C13—81no—
114D4×C13—21no—
115D4×C13—21no—
116D4×C13—81no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—81no—
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2×D411yescharacteristic
128C2×C4×C13C2411yescharacteristic
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—21no—
133Dic26—21no—
134Dic26—21no—
135Dic26—21no—
136Dic26—21no—
137#1055—21no—
138#1055—21no—
139#1055#4112yes—
140#1055#4112yes—
141#542D1311yescharacteristic
142#541—131no—
143#501—131no—
144#497—131no—
145#488—131no—
146#487—131no—
147#470—131no—
148#468—131no—
149#467—131no—
150#465—131no—
151#441—131no—
152#440—131no—
153C4×Q16—131no—
154C4×SD16—131no—
155#405—131no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13C22×D411yescharacteristic
163C4×C13—21no—
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—21no—
167C4×C13—21no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13—41no—
171C4×C13C2×#4111yescharacteristic
172C4×C13C2×#4111yescharacteristic
173Dic13—41no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177C2×Q16—131no—
178C2×Q16—131no—
179C2×SD16—131no—
180C2×SD16—131no—
181C2×M16—131no—
182C22×C8—131no—
183C4⋊Q8—131no—
184C4⋊Q8C2×D1311yescharacteristic
185#126—21no—
186#126—261no—
187#126—261no—
188#125—131no—
189#125—261no—
190#125—261no—
191#124—21no—
192#124C2×D1311yescharacteristic
193#123—21no—
194C22⋊Q8—21no—
195C22⋊Q8—131no—
196C22⋊Q8—131no—
197C22⋊Q8C2×D1311yescharacteristic
198#121C2×D1311yescharacteristic
199C4×Q8—131no—
200C4×Q8—131no—
201C4×Q8C2×D1311yescharacteristic
202C4×D4C2×D1311yescharacteristic
203#117C2×D1311yescharacteristic
204#107—131no—
205#107—131no—
206#106—131no—
207#106—131no—
208#103—131no—
209#103—131no—
210#103—131no—
211#103—131no—
212#103—131no—
213#103—131no—
214#102—131no—
215#102—131no—
216#97—131no—
217#97—131no—
218C4×C8—131no—
219C4×C8—131no—
220C2×C13—41no—
221C2×C13—81no—
222C2×C13#53211yescharacteristic
223C2×C13#57711yescharacteristic
224C2×C13#57811yescharacteristic
225C2×Q8—21no—
226C2×Q8—131no—
227C2×Q8—131no—
228C2×Q8C22×D1311yescharacteristic
229C2×D4—21no—
230C2×D4C22×D1311yescharacteristic
231C22×C4—21no—
232C22×C4C22×D1311yescharacteristic
233Q16—262no—
234Q16—262no—
235SD16—262no—
236SD16—262no—
237M16—262no—
238C2×C8—131no—
239C2×C8—131no—
240C2×C8—131no—
241C2×C8—131no—
242C2×C8—262no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
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⋊C4—261no—
256C4⋊C4C22⋊D1311yescharacteristic
257C4⋊C4C22⋊D1311yescharacteristic
258C4⋊C4C22×D1311yescharacteristic
259C4⋊C4C22×D1311yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4C22⋊D1311yescharacteristic
268C22⋊C4C22⋊D1311yescharacteristic
269C42—21no—
270C42—261no—
271C42—261no—
272C42C22×D1311yescharacteristic
273C42C22×D1311yescharacteristic
274C13#317811yescharacteristic, complemented, Sylow
275C23—21no—
276C23C2×C22⋊D1311yescharacteristic
277Q8—21no—
278Q8—21no—
279Q8—81no—
280Q8—261no—
281Q8—261no—
282Q8—261no—
283Q8—261no—
284D4—21no—
285D4—21no—
286D4—81no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—81no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4C2×C22⋊D1311yescharacteristic
298C2×C4C2×C22⋊D1311yescharacteristic
299C2×C4C2×C22⋊D1311yescharacteristic
300C2×C4C2×C22⋊D1311yescharacteristic
301C2×C4C2×C22⋊D1311yescharacteristic
302C2×C4C23×D1311yescharacteristic
303C8—132no—
304C8—132no—
305C8—261no—
306C8—261no—
307C22—21no—
308C22—21no—
309C22—21no—
310C22—41no—
311C22—41no—
312C22—41no—
313C22C22×C22⋊D1311yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—521no—
323C4—521no—
324C4—521no—
325C4—521no—
326C4#41×D1311yescharacteristic
327C4#41×D1311yescharacteristic
328C2—41no—
329C2—81no—
330C2#1171953711yescharacteristic
331C2#1171954111yescharacteristic
332C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#542C2
socleC22×C13C22×D4
prime radicalC13×#121C22
hypercenter#542D13
hypocenterC13#3178
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #542

Complements

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

NH ≅ G/Ntype
2. #11719223C2semidirect
3. #11718754C2semidirect
4. #11718741C2semidirect
5. #11718721C2semidirect
6. #11718717C2semidirect
7. #11718713C2semidirect
8. #11718712C2semidirect
11. #11718691C2semidirect
12. C4×#6107C2semidirect
13. #11718679C2semidirect
14. C4×#6105C2semidirect
15. #11718658C2semidirect
274. C13#3178semidirect

Maximal subgroups

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

subgroupindex
C13×#5422
#117192232
#117187542
#117187412
#117187212
#117187172
#117187132
#117187122
#117187032
#117187022
#117186912
C4×#61072
#117186792
C4×#61052
#117186582
#317813