Finite Group Databasebeta

← #13127316

Subgroups — #13127316

Order 1664.

356 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719340C211yesmaximal, characteristic, complemented
2#11719319C211yesmaximal, characteristic
3C13×#468C211yesmaximal, characteristic, complemented
4#11718832C211yesmaximal, characteristic, complemented
5#11718825C211yesmaximal, characteristic, complemented
6#11718788C211yesmaximal, characteristic, complemented
7#11718782C211yesmaximal, characteristic, complemented
8#11718706C211yesmaximal, characteristic, complemented
9#11718694C211yesmaximal, characteristic, complemented
10D13×#107C211yesmaximal, characteristic, complemented
11#11718537C211yesmaximal, characteristic, complemented
12#11718470C211yesmaximal, characteristic, complemented
13#11718460C211yesmaximal, characteristic, complemented
14#11718438C211yesmaximal, characteristic, complemented
15#11718420C211yesmaximal, characteristic, complemented
16C2×C13×SD16C2211yescharacteristic
17C2×C13×M16C2211yescharacteristic
18C13×C22⋊Q8C2211yescharacteristic
19C13×#121C2211yescharacteristic
20#88200C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22#88192—21no—
23#88192C2211yescharacteristic
24#88189—21no—
25D4×Dic13C2211yescharacteristic
26C4×C22⋊D13C2211yescharacteristic
27#88180C2211yescharacteristic
28C2×C4⋊Dic13C2211yescharacteristic
29C2×C8×D13C2211yescharacteristic
30#88151—21no—
31C4⋊C4×D13C2211yescharacteristic
32C4⋊C4×D13C2211yescharacteristic
33#88144C2211yescharacteristic
34#88143—21no—
35#88142C2211yescharacteristic
36#88135—21no—
37#88135—21no—
38#88133—21no—
39#88132—21no—
40C13×#107C2211yescharacteristic
41C13×#103C2211yescharacteristic
42C13×#102C2211yescharacteristic
43#88075C2211yescharacteristic
44#88075C2211yescharacteristic
45#88072C2211yescharacteristic
46#88072C2211yescharacteristic
47C22⋊#1055C2211yescharacteristic
48#88060C2211yescharacteristic
49#88058C2211yescharacteristic
50#88058C2211yescharacteristic
51#88057C2211yescharacteristic
52#88057C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88048C2211yescharacteristic
56#88047C2211yescharacteristic
57#88047C2211yescharacteristic
58#88047C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×D4×C13—21no—
61C2×D4×C13C2311yescharacteristic
62C22×C4×C13C2311yescharacteristic
63C2×C22⋊D13—21no—
64C2×C22⋊D13D411yescharacteristic
65C22×Dic13—21no—
66C22×Dic13—21no—
67C2×C4×D13—21no—
68C2×C4×D13—21no—
69C2×C4×D13C2311yescharacteristic
70C2×Dic26—21no—
71C13×SD16—22no—
72C13×M16—22no—
73C2×C8×C13C2311yescharacteristic
74C2×C8×C13C2311yescharacteristic
75C13×C4⋊C4—21no—
76C13×C4⋊C4C2311yescharacteristic
77C13×C4⋊C4C2311yescharacteristic
78C13×C22⋊C4—21no—
79C13×C22⋊C4—21no—
80C22⋊Dic13—21no—
81C22⋊Dic13—21no—
82C22⋊Dic13—21no—
83C22⋊Dic13D411yescharacteristic
84#6103—21no—
85#6103D411yescharacteristic
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13—21no—
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91C4⋊Dic13C2311yescharacteristic
92C4⋊Dic13C2311yescharacteristic
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101D411yescharacteristic
99C4×Dic13—21no—
100C4×Dic13—21no—
101C4×Dic13C2311yescharacteristic
102C2×#1055C2311yescharacteristic
103C2×#1055C2311yescharacteristic
104C8×D13—22no—
105#3346—131nomaximal, Sylow
106C23×C13—21no—
107C23×C13C2×D411yescharacteristic
108C22×D13C2×D411yescharacteristic
109Q8×C13—21no—
110Q8×C13—21no—
111D4×C13—21no—
112D4×C13—21no—
113D4×C13—81no—
114C2×C4×C13—21no—
115C2×C4×C13—21no—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13C2×D411yescharacteristic
120C2×C4×C13C2411yescharacteristic
121C22⋊D13—22no—
122C22⋊D13—42no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—21no—
127C2×Dic13—81no—
128C2×Dic13—81no—
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C4×D13—21no—
133C4×D13—21no—
134C4×D13—81no—
135C4×D13—81no—
136Dic26—81no—
137C8×C13—21no—
138C8×C13#4112yes—
139#1055—21no—
140#1055—21no—
141#554—131no—
142#553—131no—
143#501—131no—
144#485—131no—
145#484—131no—
146#481—131no—
147#480—131no—
148#479—131no—
149#474—131no—
150#468D1311yescharacteristic, complemented
151#465—131no—
152#440—131no—
153#435—131no—
154#428—131no—
155C2×#107—131no—
156C22×C13—21no—
157C22×C13—21no—
158C22×C13—21no—
159C22×C13—41no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13C22×D411yescharacteristic
163C2×D13—21no—
164C2×D13—21no—
165C2×D13#13712yes—
166C4×C13—21no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13—41no—
170C4×C13C2×#4111yescharacteristic
171C4×C132−1+411yescharacteristic
172Dic13—21no—
173Dic13—21no—
174Dic13—21no—
175Dic13—41no—
176Dic13—41no—
177Dic13—41no—
178Dic13—41no—
179C2×SD16C2×D1311yescharacteristic
180C2×M16C2×D1311yescharacteristic
181C22×C8—131no—
182C4⋊Q8—131no—
183#126—261no—
184#125—131no—
185#125—261no—
186#123—261no—
187C22⋊Q8—131no—
188C22⋊Q8—261no—
189C22⋊Q8—261no—
190C22⋊Q8C2×D1311yescharacteristic
191#121—131no—
192#121—261no—
193#121C2×D1311yescharacteristic
194C4×Q8—131no—
195C4×D4—131no—
196C4×D4—131no—
197C4×D4—261no—
198C4×D4—261no—
199#117—131no—
200C2×C4⋊C4—131no—
201C2×C4⋊C4—131no—
202C2×C4⋊C4—131no—
203#107—131no—
204#107—131no—
205#107—131no—
206#107—131no—
207#107—131no—
208#107C2×D1311yescharacteristic
209#106—131no—
210#106—131no—
211#106—131no—
212C4⋊C8—131no—
213#103—131no—
214#103—131no—
215#103C2×D1311yescharacteristic
216#102—131no—
217#102—131no—
218#102C2×D1311yescharacteristic
219C22⋊C8—131no—
220C22⋊C8—131no—
221#97—131no—
222C2×C13—41no—
223C2×C13—81no—
224C2×C13#54711yescharacteristic
225C2×C13C2×#13711yescharacteristic
226C2×C13#57611yescharacteristic
227D13—22no—
228C2×Q8—261no—
229C2×Q8C22×D1311yescharacteristic
230C2×D4—21no—
231C2×D4—131no—
232C2×D4—261no—
233C2×D4C22×D1311yescharacteristic
234C22×C4—131no—
235C22×C4—261no—
236C22×C4—261no—
237C22×C4—261no—
238C22×C4—261no—
239C22×C4C22×D1311yescharacteristic
240SD16—22no—
241M16—22no—
242C2×C8—131no—
243C2×C8—131no—
244C2×C8—262no—
245C2×C8C22×D1311yescharacteristic
246C2×C8C22×D1311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—131no—
249C4⋊C4—131no—
250C4⋊C4—131no—
251C4⋊C4—131no—
252C4⋊C4—131no—
253C4⋊C4—261no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4C22×D1311yescharacteristic
262C4⋊C4C22×D1311yescharacteristic
263C22⋊C4—21no—
264C22⋊C4—21no—
265C22⋊C4—131no—
266C22⋊C4—131no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C42—131no—
272C42—261no—
273C42—261no—
274C13#334611yescharacteristic, complemented, Sylow
275C23—21no—
276C23—131no—
277C23D4×D1311yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—1041no—
281D4—21no—
282D4—21no—
283D4—81no—
284D4—262no—
285D4—522no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—131no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—261no—
295C2×C4—261no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—1041no—
301C2×C4—1041no—
302C2×C4—1041no—
303C2×C4—1041no—
304C2×C4D4×D1311yescharacteristic
305C2×C4C23×D1311yescharacteristic
306C8—21no—
307C8—261no—
308C8—261no—
309C8#612912yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—132no—
317C22—261no—
318C22—261no—
319C22C2×D4×D1311yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—261no—
325C4—261no—
326C4—261no—
327C4—521no—
328C4—521no—
329C4—521no—
330C4—521no—
331C4C2×#612911yescharacteristic
332C4#8825711yescharacteristic
333C2—41no—
334C2—81no—
335C2—262no—
336C2#1171931611yescharacteristic
337C2#1171947911yescharacteristic
338C2D13×#13711yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#468C2
socleC22×C13C22×D4
prime radical#11719319C2
hypercenter#468D13
hypocenterC13#3346
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. #11719340C2semidirect
3. C13×#468C2semidirect
4. #11718832C2semidirect
5. #11718825C2semidirect
6. #11718788C2semidirect
7. #11718782C2semidirect
8. #11718706C2semidirect
9. #11718694C2semidirect
10. D13×#107C2semidirect
11. #11718537C2semidirect
12. #11718470C2semidirect
13. #11718460C2semidirect
14. #11718438C2semidirect
15. #11718420C2semidirect
150. #468D13semidirect
274. C13#3346semidirect

Maximal subgroups

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

subgroupindex
#117193402
#117193192
C13×#4682
#117188322
#117188252
#117187882
#117187822
#117187062
#117186942
D13×#1072
#117185372
#117184702
#117184602
#117184382
#117184202
#334613