Finite Group Databasebeta

← #13125506

Subgroups — #13125506

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×#541C211yesmaximal, characteristic, complemented
2#11719239C211yesmaximal, characteristic
3#11718747C211yesmaximal, characteristic, complemented
4#11718742C211yesmaximal, characteristic, complemented
5#11718729C211yesmaximal, characteristic, complemented
6#11718726C211yesmaximal, characteristic, complemented
7#11718713C211yesmaximal, characteristic, complemented
8#11718712C211yesmaximal, characteristic, complemented
9#11718710C211yesmaximal, characteristic
10#11718709C211yesmaximal, characteristic
11#11718691C211yesmaximal, characteristic, complemented
12C4×#6107C211yesmaximal, characteristic, complemented
13#11718687C211yesmaximal, characteristic, complemented
14C4×#6106C211yesmaximal, characteristic, complemented
15#11718658C211yesmaximal, characteristic, complemented
16C13×C4⋊Q8C2211yescharacteristic
17C13×#126—21no—
18C13×#126—21no—
19C13×#125—21no—
20C13×#125—21no—
21C13×#125C2211yescharacteristic
22C13×C22⋊Q8C2211yescharacteristic
23C13×C22⋊Q8C2211yescharacteristic
24C4×Q8×C13C2211yescharacteristic
25C4×Q8×C13C2211yescharacteristic
26C13×#117C2211yescharacteristic
27C2×#6107C2211yescharacteristic
28C2×#6107C2211yescharacteristic
29C2×#6106C2211yescharacteristic
30C2×#6106C2211yescharacteristic
31#88184C2211yescharacteristic
32#88178C2211yescharacteristic
33C2×#6099C2211yescharacteristic
34C22×#1055C2211yescharacteristic
35#88152—21no—
36#88150—21no—
37#88139—21no—
38#88137—21no—
39#88129C2211yescharacteristic
40C4×D52C2211yescharacteristic
41#88123C2211yescharacteristic
42C4×Dic26C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88075C2211yescharacteristic
46#88075C2211yescharacteristic
47#88050C2211yescharacteristic
48#88050C2211yescharacteristic
49#88049C2211yescharacteristic
50#88049C2211yescharacteristic
51#88048C2211yescharacteristic
52#88048C2211yescharacteristic
53#88047C2211yescharacteristic
54#88047C2211yescharacteristic
55#88043C2211yescharacteristic
56#88043C2211yescharacteristic
57C4×#1055C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C22×C4×C13C2311yescharacteristic
62C2×C22⋊D13—21no—
63C2×D52C2311yescharacteristic
64C2×C4×D13—21no—
65C2×Dic26—21no—
66C2×Dic26C2311yescharacteristic
67C13×C4⋊C4—21no—
68C13×C4⋊C4—21no—
69C13×C4⋊C4—21no—
70C13×C4⋊C4—21no—
71C13×C4⋊C4—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4D411yescharacteristic
76C13×C4⋊C4D411yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C13×C22⋊C4D411yescharacteristic
82C13×C22⋊C4D411yescharacteristic
83C42×C13—21no—
84C42×C13—21no—
85C42×C13C2311yescharacteristic
86C42×C13C2311yescharacteristic
87C22⋊Dic13—21no—
88#6107—22no—
89#6107—22no—
90#6106—22no—
91#6106—22no—
92#6103—21no—
93#6103—21no—
94#6103—21no—
95#6103—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99#6101—21no—
100#6101—21no—
101C4×Dic13—21no—
102#6099—22no—
103C2×#1055—22no—
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106C2×#1055C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108#3178—131nomaximal, Sylow
109C23×C13C2×D411yescharacteristic
110C22×D13—21no—
111Q8×C13—21no—
112Q8×C13—21no—
113Q8×C13—21no—
114Q8×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2411yescharacteristic
127C22⋊D13—81no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131D52—21no—
132D52—21no—
133C4×D13—81no—
134Dic26—21no—
135Dic26—21no—
136Dic26—81no—
137#1055—21no—
138#1055—21no—
139#1055#4112yes—
140#1055#4112yes—
141#542—131no—
142#541D1311yescharacteristic, complemented
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×C13C22×D411yescharacteristic
160C2×D13—41no—
161C2×D13—41no—
162C2×D13—41no—
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×C13—41no—
172C4×C13C2×#4111yescharacteristic
173C4×C13C2×#4111yescharacteristic
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—21no—
187#126—261no—
188#125—21no—
189#125—21no—
190#125C2×D1311yescharacteristic
191#124—131no—
192#124—261no—
193#123—261no—
194C22⋊Q8—131no—
195C22⋊Q8—261no—
196C22⋊Q8C2×D1311yescharacteristic
197C22⋊Q8C2×D1311yescharacteristic
198#121—131no—
199C4×Q8—131no—
200C4×Q8C2×D1311yescharacteristic
201C4×Q8C2×D1311yescharacteristic
202C4×D4—131no—
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#53211yescharacteristic
222C2×C13#57711yescharacteristic
223C2×C13#57811yescharacteristic
224D13—81no—
225C2×Q8—131no—
226C2×Q8—261no—
227C2×Q8C22×D1311yescharacteristic
228C2×Q8C22×D1311yescharacteristic
229C2×D4—131no—
230C2×D4—261no—
231C22×C4—261no—
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—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—131no—
252C4⋊C4—131no—
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—261no—
263C22⋊C4—261no—
264C22⋊C4—261no—
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4C22⋊D1311yescharacteristic
268C22⋊C4C22⋊D1311yescharacteristic
269C42—21no—
270C42—21no—
271C42—261no—
272C42C22×D1311yescharacteristic
273C42C22×D1311yescharacteristic
274C13#317811yescharacteristic, complemented, Sylow
275C23—261no—
276C23C2×C22⋊D1311yescharacteristic
277Q8—21no—
278Q8—21no—
279Q8—21no—
280Q8—21no—
281Q8—261no—
282Q8—261no—
283Q8—1041no—
284D4—261no—
285D4—261no—
286D4—1041no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—261no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—1041no—
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—521no—
311C22—521no—
312C22—521no—
313C22C22×C22⋊D1311yescharacteristic
314C4—21no—
315C4—21no—
316C4—21no—
317C4—21no—
318C4—21no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—521no—
324C4—521no—
325C4—521no—
326C4#41×D1311yescharacteristic
327C4#41×D1311yescharacteristic
328C2—41no—
329C2—1041no—
330C2#1171953711yescharacteristic
331C2#1171954211yescharacteristic
332C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#541C2
socleC22×C13C22×D4
prime radical#88184C22
hypercenter#541D13
hypocenterC13#3178
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
1. C13×#541C2semidirect
3. #11718747C2semidirect
4. #11718742C2semidirect
5. #11718729C2semidirect
6. #11718726C2semidirect
7. #11718713C2semidirect
8. #11718712C2semidirect
11. #11718691C2semidirect
12. C4×#6107C2semidirect
13. #11718687C2semidirect
14. C4×#6106C2semidirect
15. #11718658C2semidirect
142. #541D13semidirect
274. C13#3178semidirect

Maximal subgroups

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

subgroupindex
C13×#5412
#117192392
#117187472
#117187422
#117187292
#117187262
#117187132
#117187122
#117187102
#117187092
#117186912
C4×#61072
#117186872
C4×#61062
#117186582
#317813