Finite Group Databasebeta

← #13127270

Subgroups — #13127270

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×#547C211yesmaximal, characteristic
2#11719246C211yesmaximal, characteristic, complemented
3#11718752C211yesmaximal, characteristic, complemented
4#11718741C211yesmaximal, characteristic, complemented
5#11718703C211yesmaximal, characteristic, complemented
6#11718702C211yesmaximal, characteristic, complemented
7#11718696C211yesmaximal, characteristic, complemented
8#11718694C211yesmaximal, characteristic, complemented
9#11718679C211yesmaximal, characteristic, complemented
10#11718672C211yesmaximal, characteristic, complemented
11#11718670C211yesmaximal, characteristic, complemented
12#11718632C211yesmaximal, characteristic, complemented
13#11718631C211yesmaximal, characteristic, complemented
14#11718625C211yesmaximal, characteristic, complemented
15C2×#88047C211yesmaximal, characteristic, complemented
16C2×C13×#41—21no—
17C13×C4⋊Q8C2211yescharacteristic
18C13×#123—21no—
19C13×#123—21no—
20C13×C22⋊Q8—21no—
21C13×#121C2211yescharacteristic
22C13×#121C2211yescharacteristic
23C4×D4×C13C2211yescharacteristic
24C4×D4×C13C2211yescharacteristic
25C2×C13×C4⋊C4C2211yescharacteristic
26C2×C13×C4⋊C4C2211yescharacteristic
27#88189—21no—
28C2×#6105C2211yescharacteristic
29#88180C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31#88178C2211yescharacteristic
32#88178C2211yescharacteristic
33C2×#6099C2211yescharacteristic
34C22×#1055C2211yescharacteristic
35#88143—21no—
36#88133—21no—
37#88131—21no—
38#88124C2211yescharacteristic
39C4×Dic26C2211yescharacteristic
40#88072C2211yescharacteristic
41#88072C2211yescharacteristic
42#88072C2211yescharacteristic
43C22⋊#1055C2211yescharacteristic
44C22⋊#1055C2211yescharacteristic
45#88050C2211yescharacteristic
46#88050C2211yescharacteristic
47#88050C2211yescharacteristic
48#88048C2211yescharacteristic
49#88048C2211yescharacteristic
50#88048C2211yescharacteristic
51#88047C2211yescharacteristic
52#88047C2211yescharacteristic
53#88047C2211yescharacteristic
54#88047C2211yescharacteristic
55#88047C2211yescharacteristic
56#88047C2211yescharacteristic
57C4⋊#1055C2211yescharacteristic
58#88043C2211yescharacteristic
59C13×#41—44no—
60C2×Q8×C13—21no—
61C2×D4×C13—21no—
62C2×D4×C13—21no—
63C2×D4×C13D411yescharacteristic
64C2×D4×C13C2311yescharacteristic
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—21no—
68C22×C4×C13C2311yescharacteristic
69C22×C4×C13C2311yescharacteristic
70C22×Dic13—21no—
71C2×Dic26C2311yescharacteristic
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4D411yescharacteristic
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C4⋊C4C2311yescharacteristic
79C13×C22⋊C4—21no—
80C13×C22⋊C4—21no—
81C13×C22⋊C4—21no—
82C13×C22⋊C4D411yescharacteristic
83C13×C22⋊C4D411yescharacteristic
84C42×C13C2311yescharacteristic
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88#6105—22no—
89C4⋊Dic13—21no—
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98C4×Dic13—21no—
99C4×Dic13—21no—
100#6099—22no—
101C2×#1055—22no—
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C2×#1055C2311yescharacteristic
106#3343—131nomaximal, Sylow
107C23×C13—21no—
108C23×C13C2×D411yescharacteristic
109C23×C13C2×D411yescharacteristic
110Q8×C13—42no—
111D4×C13—22no—
112D4×C13—21no—
113D4×C13—21no—
114D4×C13—42no—
115D4×C13—42no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—42no—
124C2×C4×C13—42no—
125C2×C4×C13—42no—
126C2×C4×C13C2×D411yescharacteristic
127C2×C4×C13C2×D411yescharacteristic
128C2×C4×C13C2×D411yescharacteristic
129C2×C4×C13C2×D411yescharacteristic
130C2×C4×C13C2411yescharacteristic
131C2×Dic13—21no—
132C2×Dic13—21no—
133C2×Dic13—21no—
134C2×Dic13—21no—
135C2×Dic13—42no—
136Dic26—21no—
137Dic26—21no—
138#1055—21no—
139#1055—21no—
140#1055—21no—
141#1055#4112yescomplemented
142#552—131no—
143#547D1311yescharacteristic
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×C13—41no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13AGL(1,ℤ/8)12yes—
166C22×C13C22×D411yescharacteristic
167C4×C13—21no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13C2×#4111yescharacteristic
175C4×C132−1+411yescharacteristic
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179Dic13—41no—
180C2×#41—21no—
181C2×SD16—131no—
182C2×M16—131no—
183C22×C8—131no—
184C4⋊Q8C2×D1311yescharacteristic
185#126—261no—
186#125—131no—
187#125—261no—
188#123—21no—
189#123—21no—
190#123—261no—
191C22⋊Q8—21no—
192C22⋊Q8—131no—
193C22⋊Q8—131no—
194#121C2×D1311yescharacteristic
195#121C2×D1311yescharacteristic
196C4×Q8—131no—
197C4×D4C2×D1311yescharacteristic
198C4×D4C2×D1311yescharacteristic
199#117—131no—
200#117—261no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4C2×D1311yescharacteristic
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—81no—
226C2×C13#54711yescharacteristic
227C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
228C2×C13#57811yescharacteristic
229#41—44no—
230C2×Q8—21no—
231C2×Q8—131no—
232C2×D4—21no—
233C2×D4—21no—
234C2×D4C22⋊D1311yescharacteristic
235C2×D4C22×D1311yescharacteristic
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
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—131no—
253C4⋊C4—131no—
254C4⋊C4—131no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
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—261no—
274C42—261no—
275C42C22×D1311yescharacteristic
276C13#334311yescharacteristic, complemented, Sylow
277C23—21no—
278C23C2×C22⋊D1311yescharacteristic
279C23C2×C22⋊D1311yescharacteristic
280Q8—42no—
281Q8—261no—
282Q8—261no—
283D4—22no—
284D4—21no—
285D4—21no—
286D4—42no—
287D4—42no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—42no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
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—41no—
318C22—41no—
319C22—41no—
320C22#8818612yes—
321C22C22×C22⋊D1311yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—521no—
330C4—521no—
331C4—521no—
332C4—521no—
333C4#41×D1311yescharacteristic
334C4#8825711yescharacteristic
335C2—22no—
336C2—41no—
337C2—81no—
338C2C2×#8818611yescharacteristic
339C2#1171952911yescharacteristic
340C2#1171954311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
Fitting, prime radicalC13×#547C2
socleC22×C13C22×D4
hypercenter#547D13
hypocenterC13#3343
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
2. #11719246C2semidirect
3. #11718752C2semidirect
4. #11718741C2semidirect
5. #11718703C2semidirect
6. #11718702C2semidirect
7. #11718696C2semidirect
8. #11718694C2semidirect
9. #11718679C2semidirect
10. #11718672C2semidirect
11. #11718670C2semidirect
12. #11718632C2semidirect
13. #11718631C2semidirect
14. #11718625C2semidirect
15. C2×#88047C2semidirect
141. #1055#41semidirect
276. C13#3343semidirect

Maximal subgroups

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

subgroupindex
C13×#5472
#117192462
#117187522
#117187412
#117187032
#117187022
#117186962
#117186942
#117186792
#117186722
#117186702
#117186322
#117186312
#117186252
C2×#880472
#334313