Finite Group Databasebeta

← #13127915

Subgroups — #13127915

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#11719376C211yesmaximal, characteristic, complemented
2#11719273C211yesmaximal, characteristic, complemented
3C13×#464C211yesmaximal, characteristic, complemented
4#11718851C211yesmaximal, characteristic, complemented
5#11718843C211yesmaximal, characteristic, complemented
6#11718828C211yesmaximal, characteristic, complemented
7#11718826C211yesmaximal, characteristic
8#11718720C211yesmaximal, characteristic
9C4×#6107C211yesmaximal, characteristic, complemented
10#11718506C211yesmaximal, characteristic, complemented
11#11718492C211yesmaximal, characteristic, complemented
12#11718478C211yesmaximal, characteristic, complemented
13#11718454C211yesmaximal, characteristic, complemented
14#11718448C211yesmaximal, characteristic
15#11718418C211yesmaximal, characteristic, complemented
16C2×C13×Q16C2211yescharacteristic
17C2×C13×SD16C2211yescharacteristic
18C13×#124C2211yescharacteristic
19C4×Q8×C13C2211yescharacteristic
20#88201C2211yescharacteristic
21Q8×Dic13C2211yescharacteristic
22#88198C2211yescharacteristic
23#88198C2211yescharacteristic
24C2×#6107C2211yescharacteristic
25C2×#6107C2211yescharacteristic
26C2×#6106C2211yescharacteristic
27#88190C2211yescharacteristic
28D4×Dic13C2211yescharacteristic
29C2×#6105C2211yescharacteristic
30C2×#6104C2211yescharacteristic
31C2×Dic52C2211yescharacteristic
32C2×#6095C2211yescharacteristic
33#88152—21no—
34#88150—21no—
35#88147C2211yescharacteristic
36#88141C2211yescharacteristic
37#88133—21no—
38#88133—21no—
39#88132—21no—
40#88131—21no—
41#88130—21no—
42#88129C2211yescharacteristic
43#88126—21no—
44C4×Dic26C2211yescharacteristic
45C4×Dic26C2211yescharacteristic
46C13×C4⋊C8C2211yescharacteristic
47C13×#103C2211yescharacteristic
48C13×#102C2211yescharacteristic
49#88075C2211yescharacteristic
50#88061C2211yescharacteristic
51#88056C2211yescharacteristic
52#88055C2211yescharacteristic
53#88055C2211yescharacteristic
54#88054C2211yescharacteristic
55#88054C2211yescharacteristic
56#88050C2211yescharacteristic
57#88047C2211yescharacteristic
58C4×#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×D4×C13C2311yescharacteristic
62C22×Dic13—21no—
63C2×D52C2311yescharacteristic
64C2×C4×D13—21no—
65C2×Dic26D411yescharacteristic
66C2×Dic26C2311yescharacteristic
67C2×Dic26C2311yescharacteristic
68C13×Q16—41no—
69C13×SD16—41no—
70C2×C8×C13C2311yescharacteristic
71C2×C8×C13C2311yescharacteristic
72C13×C4⋊C4—21no—
73C13×C4⋊C4C2311yescharacteristic
74C13×C22⋊C4—21no—
75C13×C22⋊C4—21no—
76C42×C13—21no—
77C42×C13C2311yescharacteristic
78C22⋊Dic13—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81#6107—22no—
82#6107—41no—
83#6106—22no—
84#6105—22no—
85#6104—41no—
86#6103—21no—
87#6103—21no—
88#6103—21no—
89#6103—21no—
90#6103—21no—
91C4⋊Dic13—21no—
92C4⋊Dic13D411yescharacteristic
93C4⋊Dic13C2311yescharacteristic
94#6101—21no—
95#6101—21no—
96#6101—21no—
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
109Dic52—41no—
110#6095—41no—
111#3402—131nomaximal, Sylow
112C23×C13—21no—
113C22×D13—21no—
114Q8×C13—21no—
115Q8×C13—21no—
116Q8×C13—21no—
117Q8×C13—21no—
118D4×C13—21no—
119D4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13C2×D411yescharacteristic
124C2×C4×C13C2×D411yescharacteristic
125C2×C4×C13C2411yescharacteristic
126C2×Dic13—21no—
127C2×Dic13—21no—
128C2×Dic13—21no—
129C2×Dic13—42no—
130C2×Dic13C2×D411yescharacteristic
131C2×Dic13C2×D411yescharacteristic
132C2×Dic13C2×D411yescharacteristic
133C2×Dic13C2×D411yescharacteristic
134D52—21no—
135D52—21no—
136C4×D13—42no—
137Dic26—21no—
138Dic26—21no—
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#464D1311yescharacteristic, complemented
153#463—131no—
154#463—131no—
155#462—131no—
156#462—131no—
157#446—131no—
158#440—131no—
159#440—131no—
160C4×Q16—131no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13—41no—
164C22×C13C22×D411yescharacteristic
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×C13C2×#4111yescharacteristic
174C4×C13H(5,𝔽2)11yescharacteristic
175Dic13—21no—
176Dic13—21no—
177Dic13—21no—
178Dic13—21no—
179Dic13—41no—
180Dic13—41no—
181Dic13—41no—
182C2×Q16—131no—
183C2×Q16—131no—
184C2×Q16—131no—
185C2×Q16C2×D1311yescharacteristic
186C2×SD16—131no—
187C2×SD16—131no—
188C2×SD16—131no—
189C2×SD16C2×D1311yescharacteristic
190C2×D8—131no—
191C4⋊Q8—131no—
192C4⋊Q8—131no—
193#126—261no—
194#126—261no—
195#126—261no—
196#126—261no—
197#124—131no—
198#124—131no—
199#124—131no—
200#124C2×D1311yescharacteristic
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#103—131no—
219#103C2×D1311yescharacteristic
220#102—131no—
221#102C2×D1311yescharacteristic
222#97—131no—
223#97—131no—
224C4×C8—131no—
225C2×C13—81no—
226C2×C13#55011yescharacteristic
227C2×C13#57511yescharacteristic
228C2×C13#57811yescharacteristic
229D13—81no—
230C2×Q8—131no—
231C2×Q8—131no—
232C2×Q8—131no—
233C2×Q8C22×D1311yescharacteristic
234C2×Q8C22×D1311yescharacteristic
235C2×D4—131no—
236C2×D4C22×D1311yescharacteristic
237C22×C4—261no—
238C22×C4—261no—
239Q16—41no—
240Q16—262no—
241Q16—521no—
242Q16—521no—
243SD16—41no—
244SD16—262no—
245SD16—262no—
246SD16—521no—
247D8—521no—
248C2×C8—131no—
249C2×C8—131no—
250C2×C8C22×D1311yescharacteristic
251C2×C8C22×D1311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—131no—
254C4⋊C4—131no—
255C4⋊C4—131no—
256C4⋊C4—131no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4C22×D1311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—21no—
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—21no—
284C23—261no—
285Q8—21no—
286Q8—21no—
287Q8—21no—
288Q8—21no—
289Q8—261no—
290Q8—261no—
291Q8—261no—
292Q8—261no—
293Q8—521no—
294D4—21no—
295D4—21no—
296D4—261no—
297D4—261no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—131no—
302C2×C4—131no—
303C2×C4—131no—
304C2×C4—131no—
305C2×C4—261no—
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—41no—
318C22—41no—
319C22—41no—
320C22—521no—
321C22—521no—
322C22—521no—
323C22C2×D4×D1311yescharacteristic
324C4—21no—
325C4—21no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—261no—
330C4—261no—
331C4—261no—
332C4—261no—
333C4—521no—
334C4—521no—
335C4—521no—
336C4#8825111yescharacteristic
337C4#41×D1311yescharacteristic
338C2—81no—
339C2—1041no—
340C2#1171930411yescharacteristic
341C2#1171947311yescharacteristic
342C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#464C2
socleC22×C13C22×D4
prime radicalC2×#6104C22
hypercenter#464D13
hypocenterC13#3402
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #11719376C2semidirect
2. #11719273C2semidirect
3. C13×#464C2semidirect
4. #11718851C2semidirect
5. #11718843C2semidirect
6. #11718828C2semidirect
9. C4×#6107C2semidirect
10. #11718506C2semidirect
11. #11718492C2semidirect
12. #11718478C2semidirect
13. #11718454C2semidirect
15. #11718418C2semidirect
152. #464D13semidirect
282. C13#3402semidirect

Maximal subgroups

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

subgroupindex
#117193762
#117192732
C13×#4642
#117188512
#117188432
#117188282
#117188262
#117187202
C4×#61072
#117185062
#117184922
#117184782
#117184542
#117184482
#117184182
#340213