Finite Group Databasebeta

← #13127910

Subgroups — #13127910

Order 1664.

356 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719437C211yesmaximal, characteristic, complemented
2#11719273C211yesmaximal, characteristic, complemented
3C13×#462C211yesmaximal, characteristic, complemented
4#11718852C211yesmaximal, characteristic
5#11718851C211yesmaximal, characteristic, complemented
6#11718846C211yesmaximal, characteristic, complemented
7#11718843C211yesmaximal, characteristic, complemented
8#11718747C211yesmaximal, characteristic, complemented
9#11718687C211yesmaximal, characteristic, complemented
10#11718505C211yesmaximal, characteristic
11#11718489C211yesmaximal, characteristic, complemented
12#11718480C211yesmaximal, characteristic
13#11718478C211yesmaximal, characteristic, complemented
14#11718459C211yesmaximal, characteristic, complemented
15#11718451C211yesmaximal, characteristic, complemented
16C2×C13×Q16C2211yescharacteristic
17C2×C13×Q16C2211yescharacteristic
18C13×C4⋊Q8C2211yescharacteristic
19C4×Q8×C13C2211yescharacteristic
20#88201C2211yescharacteristic
21#88201C2211yescharacteristic
22#88201C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24Q8×Dic13C2211yescharacteristic
25#88198C2211yescharacteristic
26C2×#6107C2211yescharacteristic
27C2×#6107C2211yescharacteristic
28C2×#6106C2211yescharacteristic
29C2×#6106C2211yescharacteristic
30C2×#6106C2211yescharacteristic
31C2×D104C2211yescharacteristic
32C2×#6095C2211yescharacteristic
33#88152—21no—
34#88152—21no—
35#88152—21no—
36#88151—21no—
37#88150—21no—
38#88147C2211yescharacteristic
39#88146—21no—
40#88141C2211yescharacteristic
41#88130—21no—
42#88129C2211yescharacteristic
43C4×D52C2211yescharacteristic
44#88126—21no—
45C4×Dic26C2211yescharacteristic
46C13×C4⋊C8C2211yescharacteristic
47C13×#103C2211yescharacteristic
48C13×#103C2211yescharacteristic
49#88075C2211yescharacteristic
50#88061C2211yescharacteristic
51#88056C2211yescharacteristic
52#88055C2211yescharacteristic
53#88054C2211yescharacteristic
54#88054C2211yescharacteristic
55C8×Dic13C2211yescharacteristic
56#88049C2211yescharacteristic
57#88047C2211yescharacteristic
58#88043C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×Q8×C13C2311yescharacteristic
62C2×D52C2311yescharacteristic
63C2×D52C2311yescharacteristic
64C2×C4×D13—21no—
65C2×C4×D13—21no—
66C2×Dic26D411yescharacteristic
67C2×Dic26C2311yescharacteristic
68C13×Q16—41no—
69C13×Q16—41no—
70C2×C8×C13C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C13×C4⋊C4—21no—
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C4⋊C4C2311yescharacteristic
76C42×C13—21no—
77C42×C13C2311yescharacteristic
78#6107—22no—
79#6107—41no—
80#6106—22no—
81#6106—22no—
82#6106—41no—
83#6103—21no—
84#6103—21no—
85#6103—21no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91#6103—21no—
92#6103—21no—
93C4⋊Dic13—21no—
94C4⋊Dic13—21no—
95C4⋊Dic13D411yescharacteristic
96C4⋊Dic13C2311yescharacteristic
97#6101—21no—
98#6101—21no—
99#6101—21no—
100#6101D411yescharacteristic
101#6101D411yescharacteristic
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13—21no—
105C4×Dic13C2311yescharacteristic
106C4×Dic13C2311yescharacteristic
107C2×#1055C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109D104—41no—
110#6095—41no—
111#3402—131nomaximal, Sylow
112C22×D13—21no—
113C22×D13—21no—
114Q8×C13—21no—
115Q8×C13—21no—
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13—21no—
119Q8×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2×D411yescharacteristic
126C2×C4×C13C2411yescharacteristic
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13C2×D411yescharacteristic
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133D52—21no—
134D52—21no—
135D52—21no—
136D52—21no—
137C4×D13—42no—
138C4×D13—42no—
139Dic26—21no—
140Dic26—21no—
141Dic26—41no—
142C8×C13—21no—
143C8×C13—21no—
144#1055—21no—
145#1055#4112yes—
146#556—131no—
147#556—131no—
148#497—131no—
149#497—131no—
150#495—131no—
151#464—131no—
152#464—131no—
153#463—131no—
154#463—131no—
155#462—131no—
156#462D1311yescharacteristic, complemented
157#446—131no—
158#440—131no—
159#440—131no—
160C4×Q16—131no—
161C22×C13C22×D411yescharacteristic
162C2×D13—41no—
163C2×D13—41no—
164C2×D13—41no—
165C2×D13—41no—
166C2×D13—41no—
167C2×D13—41no—
168C4×C13—21no—
169C4×C13—21no—
170C4×C13—41no—
171C4×C13—41no—
172C4×C13—41no—
173C4×C13—41no—
174C4×C13C2×#4111yescharacteristic
175C4×C13H(5,𝔽2)11yescharacteristic
176Dic13—21no—
177Dic13—21no—
178Dic13—21no—
179Dic13—21no—
180Dic13—41no—
181Dic13—41no—
182C2×Q16—131no—
183C2×Q16—131no—
184C2×Q16C2×D1311yescharacteristic
185C2×Q16C2×D1311yescharacteristic
186C2×SD16—131no—
187C2×SD16—131no—
188C2×SD16—131no—
189C2×SD16—131no—
190C2×D8—131no—
191C4⋊Q8—131no—
192C4⋊Q8C2×D1311yescharacteristic
193#126—261no—
194#126—261no—
195#126—261no—
196#126—261no—
197#124—131no—
198#124—131no—
199#124—131no—
200#124—131no—
201C22⋊Q8—261no—
202C22⋊Q8—261no—
203C4×Q8—131no—
204C4×Q8—131no—
205C4×Q8—131no—
206C4×Q8—131no—
207C4×Q8C2×D1311yescharacteristic
208C4×D4—131no—
209C4×D4—131no—
210#117—261no—
211#117—261no—
212#107—131no—
213C4⋊C8—131no—
214C4⋊C8—131no—
215C4⋊C8C2×D1311yescharacteristic
216#103—131no—
217#103—131no—
218#103C2×D1311yescharacteristic
219#103C2×D1311yescharacteristic
220#102—131no—
221#102—131no—
222#97—131no—
223#97—131no—
224C4×C8—131no—
225C2×C13#55011yescharacteristic
226C2×C13#57511yescharacteristic
227C2×C13#57811yescharacteristic
228D13—81no—
229D13—81no—
230C2×Q8—131no—
231C2×Q8—131no—
232C2×Q8C22×D1311yescharacteristic
233C2×Q8C22×D1311yescharacteristic
234C2×Q8C22×D1311yescharacteristic
235C2×D4—131no—
236C2×D4—131no—
237C22×C4—261no—
238C22×C4—261no—
239Q16—41no—
240Q16—41no—
241Q16—262no—
242Q16—521no—
243SD16—262no—
244SD16—262no—
245SD16—521no—
246SD16—521no—
247D8—521no—
248C2×C8—131no—
249C2×C8—131no—
250C2×C8C22×D1311yescharacteristic
251C2×C8C22×D1311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—131no—
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—131no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4C22×D1311yescharacteristic
265C22⋊C4—261no—
266C22⋊C4—261no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C22⋊C4—261no—
271C22⋊C4—261no—
272C22⋊C4—261no—
273C22⋊C4—261no—
274C22⋊C4—261no—
275C42—21no—
276C42—131no—
277C42—131no—
278C42—261no—
279C42—261no—
280C42—261no—
281C42C22×D1311yescharacteristic
282C13#340211yescharacteristic, complemented, Sylow
283C23—261no—
284C23—261no—
285Q8—21no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—21no—
290Q8—21no—
291Q8—261no—
292Q8—261no—
293Q8—521no—
294D4—261no—
295D4—261no—
296D4—261no—
297D4—261no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—131no—
303C2×C4—131no—
304C2×C4—131no—
305C2×C4—131no—
306C2×C4—261no—
307C2×C4—261no—
308C2×C4—522no—
309C2×C4—522no—
310C2×C4D4×D1311yescharacteristic
311C2×C4D4×D1311yescharacteristic
312C2×C4C23×D1311yescharacteristic
313C8—21no—
314C8—21no—
315C8—132no—
316C8—261no—
317C22—521no—
318C22—521no—
319C22—521no—
320C22—521no—
321C22—521no—
322C22—521no—
323C22C2×D4×D1311yescharacteristic
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—261no—
331C4—261no—
332C4—261no—
333C4—261no—
334C4—521no—
335C4—521no—
336C4#8825111yescharacteristic
337C4#41×D1311yescharacteristic
338C2—1041no—
339C2—1041no—
340C2#1171930411yescharacteristic
341C2#1171947111yescharacteristic
342C2#1171948211yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#462C2
socleC22×C13C22×D4
prime radicalC2×D104C22
hypercenter#462D13
hypocenterC13#3402
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
1. #11719437C2semidirect
2. #11719273C2semidirect
3. C13×#462C2semidirect
5. #11718851C2semidirect
6. #11718846C2semidirect
7. #11718843C2semidirect
8. #11718747C2semidirect
9. #11718687C2semidirect
11. #11718489C2semidirect
13. #11718478C2semidirect
14. #11718459C2semidirect
15. #11718451C2semidirect
156. #462D13semidirect
282. C13#3402semidirect

Maximal subgroups

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

subgroupindex
#117194372
#117192732
C13×#4622
#117188522
#117188512
#117188462
#117188432
#117187472
#117186872
#117185052
#117184892
#117184802
#117184782
#117184592
#117184512
#340213