Finite Group Databasebeta

← #13127276

Subgroups — #13127276

Order 1664.

376 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#552C211yesmaximal, characteristic, complemented
2#11719260C211yesmaximal, characteristic
3#11718727C211yesmaximal, characteristic, complemented
4#11718726C211yesmaximal, characteristic, complemented
5#11718710C211yesmaximal, characteristic, complemented
6#11718709C211yesmaximal, characteristic, complemented
7#11718705C211yesmaximal, characteristic, complemented
8#11718704C211yesmaximal, characteristic, complemented
9#11718687C211yesmaximal, characteristic, complemented
10#11718682C211yesmaximal, characteristic, complemented
11#11718672C211yesmaximal, characteristic, complemented
12#11718664C211yesmaximal, characteristic, complemented
13#11718656C211yesmaximal, characteristic, complemented
14#11718628C211yesmaximal, characteristic, complemented
15C2×#88047C211yesmaximal, characteristic, complemented
16C2×#6129—21no—
17C13×#126—21no—
18C13×#125—21no—
19C13×#125C2211yescharacteristic
20C13×#123—21no—
21C13×C22⋊Q8C2211yescharacteristic
22C13×C22⋊Q8C2211yescharacteristic
23C4×Q8×C13C2211yescharacteristic
24C4×D4×C13C2211yescharacteristic
25C13×#117—21no—
26C13×#117C2211yescharacteristic
27C2×C13×C4⋊C4C2211yescharacteristic
28C2×#6106C2211yescharacteristic
29#88184C2211yescharacteristic
30#88184C2211yescharacteristic
31C2×C4⋊Dic13C2211yescharacteristic
32C2×C4⋊Dic13C2211yescharacteristic
33C2×#6099C2211yescharacteristic
34C22×#1055C2211yescharacteristic
35#88151—21no—
36#88140—21no—
37#88140—21no—
38C4×D52C2211yescharacteristic
39#88123C2211yescharacteristic
40#88075C2211yescharacteristic
41#88075C2211yescharacteristic
42#88075C2211yescharacteristic
43C22⋊#1055C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88049C2211yescharacteristic
46#88049C2211yescharacteristic
47#88049C2211yescharacteristic
48#88048C2211yescharacteristic
49#88048C2211yescharacteristic
50#88048C2211yescharacteristic
51#88047C2211yescharacteristic
52#88047C2211yescharacteristic
53#88047C2211yescharacteristic
54#88047C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13D411yescharacteristic
61C22×C4×C13—21no—
62C22×C4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C22×Dic13—21no—
67C22×Dic13—21no—
68#6129—44no—
69C2×D52C2311yescharacteristic
70C2×C4×D13—21no—
71C2×Dic26—21no—
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4—21no—
76C13×C4⋊C4—21no—
77C13×C4⋊C4—21no—
78C13×C4⋊C4D411yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C4⋊C4C2311yescharacteristic
81C13×C4⋊C4C2311yescharacteristic
82C13×C22⋊C4—21no—
83C13×C22⋊C4—21no—
84C13×C22⋊C4—21no—
85C13×C22⋊C4D411yescharacteristic
86C13×C22⋊C4D411yescharacteristic
87C42×C13—21no—
88C42×C13—21no—
89C42×C13C2311yescharacteristic
90#6106—22no—
91#6103—21no—
92#6103—21no—
93#6103—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13—21no—
96C4⋊Dic13—21no—
97C4⋊Dic13C2311yescharacteristic
98C4⋊Dic13C2311yescharacteristic
99C4⋊Dic13C2311yescharacteristic
100#6099—22no—
101C2×#1055—22no—
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#3343—131nomaximal, Sylow
107C23×C13C2×D411yescharacteristic
108C23×C13C2×D411yescharacteristic
109C22×D13—21no—
110Q8×C13—21no—
111Q8×C13—21no—
112D4×C13—22no—
113C2×C4×C13—21no—
114C2×C4×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×C13—42no—
122C2×C4×C13C2×D411yescharacteristic
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2411yescharacteristic
127C22⋊D13—42no—
128C22⋊D13—42no—
129C2×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—21no—
132C2×Dic13—42no—
133C2×Dic13—42no—
134D52—21no—
135D52—21no—
136C4×D13—42no—
137Dic26—42no—
138#1055—21no—
139#1055—21no—
140#1055—21no—
141#1055#4112yescomplemented
142#552D1311yescharacteristic, complemented
143#547—131no—
144#501—131no—
145#484—131no—
146#483—131no—
147#482—131no—
148#480—131no—
149#478—131no—
150#477—131no—
151#468—131no—
152#465—131no—
153#440—131no—
154#435—131no—
155#428—131no—
156C2×#107—131no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13AGL(1,ℤ/8)12yes—
163C22×C13C22×D411yescharacteristic
164C2×D13—41no—
165C2×D13—41no—
166C2×D13—41no—
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13—41no—
175C4×C13C2×#4111yescharacteristic
176C4×C132−1+411yescharacteristic
177Dic13—41no—
178Dic13—41no—
179Dic13—41no—
180C2×#41—261no—
181C2×SD16—131no—
182C2×M16—131no—
183C22×C8—131no—
184C4⋊Q8—131no—
185#126—21no—
186#125—21no—
187#125C2×D1311yescharacteristic
188#123—21no—
189#123—261no—
190#123—261no—
191C22⋊Q8—261no—
192C22⋊Q8C2×D1311yescharacteristic
193C22⋊Q8C2×D1311yescharacteristic
194#121—131no—
195#121—131no—
196C4×Q8C2×D1311yescharacteristic
197C4×D4—131no—
198C4×D4C2×D1311yescharacteristic
199#117—21no—
200#117C2×D1311yescharacteristic
201C2×C4⋊C4—131no—
202C2×C4⋊C4—131no—
203C2×C4⋊C4C2×D1311yescharacteristic
204#107—131no—
205#107—131no—
206#107—131no—
207#107—131no—
208#107—131no—
209#107—131no—
210#106—131no—
211#106—131no—
212#106—131no—
213C4⋊C8—131no—
214#103—131no—
215#103—131no—
216#103—131no—
217#102—131no—
218#102—131no—
219#102—131no—
220C22⋊C8—131no—
221C22⋊C8—131no—
222#97—131no—
223C2×C13—22no—
224C2×C13—41no—
225C2×C13#54711yescharacteristic
226C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
227C2×C13#57811yescharacteristic
228D13—81no—
229#41—524no—
230C2×Q8—261no—
231C2×Q8C22×D1311yescharacteristic
232C2×D4—131no—
233C2×D4—261no—
234C2×D4—261no—
235C2×D4C22⋊D1311yescharacteristic
236C22×C4—21no—
237C22×C4—261no—
238C22×C4—261no—
239C22×C4—261no—
240C22×C4C22×D1311yescharacteristic
241C22×C4C22×D1311yescharacteristic
242SD16—262no—
243M16—262no—
244C2×C8—131no—
245C2×C8—131no—
246C2×C8—131no—
247C2×C8—131no—
248C2×C8—262no—
249C4⋊C4—21no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—131no—
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4C22⋊D1311yescharacteristic
262C4⋊C4C22×D1311yescharacteristic
263C4⋊C4C22×D1311yescharacteristic
264C4⋊C4C22×D1311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4C22⋊D1311yescharacteristic
272C22⋊C4C22⋊D1311yescharacteristic
273C42—21no—
274C42—21no—
275C42C22×D1311yescharacteristic
276C13#334311yescharacteristic, complemented, Sylow
277C23—261no—
278C23C2×C22⋊D1311yescharacteristic
279C23C2×C22⋊D1311yescharacteristic
280Q8—21no—
281Q8—21no—
282Q8—522no—
283D4—22no—
284D4—261no—
285D4—261no—
286D4—522no—
287D4—522no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—42no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—522no—
301C2×C4—522no—
302C2×C4—522no—
303C2×C4C2×C22⋊D1311yescharacteristic
304C2×C4C2×C22⋊D1311yescharacteristic
305C2×C4C2×C22⋊D1311yescharacteristic
306C2×C4C2×C22⋊D1311yescharacteristic
307C2×C4C23×D1311yescharacteristic
308C8—132no—
309C8—261no—
310C8—261no—
311C8—261no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—521no—
318C22—521no—
319C22—521no—
320C22#8820312yes—
321C22C22×C22⋊D1311yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—521no—
331C4—521no—
332C4—521no—
333C4#41×D1311yescharacteristic
334C4#8825711yescharacteristic
335C2—22no—
336C2—41no—
337C2—1041no—
338C2C2×#8820311yescharacteristic
339C2#1171952911yescharacteristic
340C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#552C2
socleC22×C13C22×D4
prime radical#11719260C2
hypercenter#552D13
hypocenterC13#3343
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
1. C13×#552C2semidirect
3. #11718727C2semidirect
4. #11718726C2semidirect
5. #11718710C2semidirect
6. #11718709C2semidirect
7. #11718705C2semidirect
8. #11718704C2semidirect
9. #11718687C2semidirect
10. #11718682C2semidirect
11. #11718672C2semidirect
12. #11718664C2semidirect
13. #11718656C2semidirect
14. #11718628C2semidirect
15. C2×#88047C2semidirect
141. #1055#41semidirect
142. #552D13semidirect
276. C13#3343semidirect

Maximal subgroups

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

subgroupindex
C13×#5522
#117192602
#117187272
#117187262
#117187102
#117187092
#117187052
#117187042
#117186872
#117186822
#117186722
#117186642
#117186562
#117186282
C2×#880472
#334313