Finite Group Databasebeta

← #13127301

Subgroups — #13127301

Order 1664.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719319C211yesmaximal, characteristic, complemented
2#11719316C211yesmaximal, characteristic, complemented
3C13×#469C211yesmaximal, characteristic, complemented
4#11718818C211yesmaximal, characteristic, complemented
5#11718813C211yesmaximal, characteristic, complemented
6#11718788C211yesmaximal, characteristic, complemented
7#11718782C211yesmaximal, characteristic, complemented
8#11718696C211yesmaximal, characteristic, complemented
9#11718695C211yesmaximal, characteristic, complemented
10D13×#106C211yesmaximal, characteristic, complemented
11#11718517C211yesmaximal, characteristic, complemented
12#11718438C211yesmaximal, characteristic, complemented
13#11718435C211yesmaximal, characteristic, complemented
14#11718427C211yesmaximal, characteristic, complemented
15#11718422C211yesmaximal, characteristic, complemented
16C2×#6129—21no—
17C2×C13×D8C2211yescharacteristic
18C2×C13×M16C2211yescharacteristic
19C13×#121C2211yescharacteristic
20C13×#121C2211yescharacteristic
21#88192—21no—
22#88192C2211yescharacteristic
23#88192C2211yescharacteristic
24#88189—21no—
25#88189—21no—
26D4×Dic13C2211yescharacteristic
27D4×Dic13C2211yescharacteristic
28C4×C22⋊D13C2211yescharacteristic
29#88180C2211yescharacteristic
30C2×C4⋊Dic13C2211yescharacteristic
31C2×C8×D13C2211yescharacteristic
32C4⋊C4×D13C2211yescharacteristic
33C4⋊C4×D13C2211yescharacteristic
34#88144C2211yescharacteristic
35#88142C2211yescharacteristic
36#88137—21no—
37#88135—21no—
38#88133—21no—
39#88132—21no—
40C13×#106C2211yescharacteristic
41C13×#102C2211yescharacteristic
42C13×#102C2211yescharacteristic
43#88072C2211yescharacteristic
44#88072C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47C22⋊#1055C2211yescharacteristic
48#88060C2211yescharacteristic
49#88058C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88057C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88048C2211yescharacteristic
56#88048C2211yescharacteristic
57#88048C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×D4×C13—21no—
60C2×D4×C13—21no—
61C2×D4×C13C2311yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C22×C4×C13C2311yescharacteristic
64C2×C22⋊D13—21no—
65C2×C22⋊D13—21no—
66C2×C22⋊D13D411yescharacteristic
67C22×Dic13—21no—
68C22×Dic13—21no—
69C22×Dic13—21no—
70#6129—44no—
71C2×C4×D13—21no—
72C2×C4×D13—21no—
73C2×C4×D13C2311yescharacteristic
74C2×Dic26—21no—
75C13×D8—22no—
76C13×M16—22no—
77C2×C8×C13C2311yescharacteristic
78C2×C8×C13C2311yescharacteristic
79C13×C4⋊C4C2311yescharacteristic
80C13×C4⋊C4C2311yescharacteristic
81C13×C22⋊C4—21no—
82C13×C22⋊C4—21no—
83C22⋊Dic13—21no—
84C22⋊Dic13—21no—
85C22⋊Dic13—21no—
86C22⋊Dic13—21no—
87C22⋊Dic13—21no—
88C22⋊Dic13D411yescharacteristic
89#6103D411yescharacteristic
90C4⋊Dic13—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13C2311yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94C4⋊Dic13C2311yescharacteristic
95C4⋊Dic13C2311yescharacteristic
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101D411yescharacteristic
101C4×Dic13—21no—
102C4×Dic13C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C2×#1055C2311yescharacteristic
105C8×D13—22no—
106#3345—131nomaximal, Sylow
107C23×C13—21no—
108C23×C13—21no—
109C23×C13C2×D411yescharacteristic
110C22×D13C2×D411yescharacteristic
111D4×C13—21no—
112D4×C13—21no—
113D4×C13—21no—
114D4×C13—21no—
115D4×C13—42no—
116D4×C13—81no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13C2×D411yescharacteristic
122C2×C4×C13C2411yescharacteristic
123C22⋊D13—22no—
124C22⋊D13—42no—
125C22⋊D13—42no—
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—21no—
130C2×Dic13—42no—
131C2×Dic13—42no—
132C2×Dic13—81no—
133C2×Dic13C2×D411yescharacteristic
134C2×Dic13C2×D411yescharacteristic
135C2×Dic13C2×D411yescharacteristic
136C4×D13—21no—
137C4×D13—21no—
138C4×D13—42no—
139C4×D13—81no—
140Dic26—42no—
141C8×C13—21no—
142C8×C13#4112yescomplemented
143#1055—21no—
144#1055—21no—
145#553—131no—
146#547—131no—
147#501—131no—
148#482—131no—
149#481—131no—
150#481—131no—
151#480—131no—
152#478—131no—
153#476—131no—
154#469D1311yescharacteristic, complemented
155#466—131no—
156#442—131no—
157#435—131no—
158#428—131no—
159C2×#106—131no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—41no—
164C22×C13—41no—
165C22×C13—41no—
166C22×C13—41no—
167C22×C13—41no—
168C22×C13—41no—
169C22×C13C22×D411yescharacteristic
170C2×D13—21no—
171C2×D13—21no—
172C2×D13AGL(1,ℤ/8)12yes—
173C4×C13—21no—
174C4×C13—41no—
175C4×C13—41no—
176C4×C13C2×#4111yescharacteristic
177C4×C132−1+411yescharacteristic
178Dic13—21no—
179Dic13—21no—
180Dic13—21no—
181Dic13—41no—
182Dic13—41no—
183Dic13—41no—
184Dic13—41no—
185C2×#41—261no—
186C2×D8C2×D1311yescharacteristic
187C2×M16C2×D1311yescharacteristic
188C22×C8—131no—
189C4⋊Q8—131no—
190#126—261no—
191#125—131no—
192#123—261no—
193#123—261no—
194#123—261no—
195C22⋊Q8—261no—
196#121—131no—
197#121—131no—
198#121—261no—
199#121C2×D1311yescharacteristic
200#121C2×D1311yescharacteristic
201C4×D4—131no—
202C4×D4—131no—
203C4×D4—131no—
204C4×D4—261no—
205#117—131no—
206C2×C4⋊C4—131no—
207C2×C4⋊C4—131no—
208C2×C4⋊C4—131no—
209#107—131no—
210#107—131no—
211#107—131no—
212#106—131no—
213#106—131no—
214#106—131no—
215#106—131no—
216#106—131no—
217#106C2×D1311yescharacteristic
218C4⋊C8—131no—
219#102—131no—
220#102—131no—
221#102—131no—
222#102—131no—
223#102C2×D1311yescharacteristic
224#102C2×D1311yescharacteristic
225C22⋊C8—131no—
226C22⋊C8—131no—
227#97—131no—
228C2×C13—41no—
229C2×C13—81no—
230C2×C13—81no—
231C2×C13#54711yescharacteristic
232C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
233C2×C13#57711yescharacteristic
234D13—22no—
235#41—524no—
236C2×Q8—261no—
237C2×D4—21no—
238C2×D4—21no—
239C2×D4—131no—
240C2×D4—261no—
241C2×D4—261no—
242C2×D4C22×D1311yescharacteristic
243C2×D4C22×D1311yescharacteristic
244C22×C4—131no—
245C22×C4—261no—
246C22×C4—261no—
247C22×C4—261no—
248C22×C4—261no—
249C22×C4—261no—
250C22×C4C22×D1311yescharacteristic
251D8—22no—
252M16—22no—
253C2×C8—131no—
254C2×C8—131no—
255C2×C8—262no—
256C2×C8C22×D1311yescharacteristic
257C2×C8C22×D1311yescharacteristic
258C4⋊C4—131no—
259C4⋊C4—131no—
260C4⋊C4—131no—
261C4⋊C4—131no—
262C4⋊C4—131no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C4⋊C4—261no—
266C4⋊C4—261no—
267C4⋊C4—261no—
268C4⋊C4—261no—
269C4⋊C4C22×D1311yescharacteristic
270C4⋊C4C22×D1311yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—131no—
274C22⋊C4—131no—
275C22⋊C4—261no—
276C22⋊C4—261no—
277C22⋊C4—261no—
278C22⋊C4—261no—
279C22⋊C4—261no—
280C42—131no—
281C42—261no—
282C13#334511yescharacteristic, complemented, Sylow
283C23—21no—
284C23—21no—
285C23—131no—
286C23D4×D1311yescharacteristic
287Q8—522no—
288D4—21no—
289D4—21no—
290D4—21no—
291D4—21no—
292D4—42no—
293D4—81no—
294D4—262no—
295D4—522no—
296D4—522no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—131no—
304C2×C4—261no—
305C2×C4—261no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—261no—
309C2×C4—261no—
310C2×C4—522no—
311C2×C4—522no—
312C2×C4—522no—
313C2×C4—1041no—
314C2×C4—1041no—
315C2×C4D4×D1311yescharacteristic
316C2×C4C23×D1311yescharacteristic
317C8—21no—
318C8—261no—
319C8—261no—
320C8#612912yescomplemented
321C22—21no—
322C22—21no—
323C22—21no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—132no—
331C22—261no—
332C22—261no—
333C22C2×D4×D1311yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4—261no—
338C4—261no—
339C4—261no—
340C4—521no—
341C4—521no—
342C4—521no—
343C4—521no—
344C4C2×#612911yescharacteristic
345C4#8825711yescharacteristic
346C2—41no—
347C2—81no—
348C2—81no—
349C2—262no—
350C2#1171931611yescharacteristic
351C2D13×AGL(1,ℤ/8)11yescharacteristic
352C2#1171948011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#469C2
socleC22×C13C22×D4
hypercenter#469D13
hypocenterC13#3345
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #11719319C2semidirect
2. #11719316C2semidirect
3. C13×#469C2semidirect
4. #11718818C2semidirect
5. #11718813C2semidirect
6. #11718788C2semidirect
7. #11718782C2semidirect
8. #11718696C2semidirect
9. #11718695C2semidirect
10. D13×#106C2semidirect
11. #11718517C2semidirect
12. #11718438C2semidirect
13. #11718435C2semidirect
14. #11718427C2semidirect
15. #11718422C2semidirect
142. C8×C13#41semidirect
154. #469D13semidirect
282. C13#3345semidirect
320. C8#6129semidirect

Maximal subgroups

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

subgroupindex
#117193192
#117193162
C13×#4692
#117188182
#117188132
#117187882
#117187822
#117186962
#117186952
D13×#1062
#117185172
#117184382
#117184352
#117184272
#117184222
#334513