Finite Group Databasebeta

← #13127864

Subgroups — #13127864

Order 1664.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719426C211yesmaximal, characteristic, complemented
2#11719376C211yesmaximal, characteristic
3C13×#497C211yesmaximal, characteristic
4#11718845C211yesmaximal, characteristic, complemented
5#11718843C211yesmaximal, characteristic, complemented
6#11718843C211yesmaximal, characteristic, complemented
7#11718842C211yesmaximal, characteristic, complemented
8#11718828C211yesmaximal, characteristic
9#11718827C211yesmaximal, characteristic
10#11718823C211yesmaximal, characteristic
11SD16×Dic13C211yesmaximal, characteristic
12#11718751C211yesmaximal, characteristic, complemented
13#11718715C211yesmaximal, characteristic
14#11718377C211yesmaximal, characteristic, complemented
15#11718362C211yesmaximal, characteristic, complemented
16C2×C13×Q16C2211yescharacteristic
17C2×C13×Q16C2211yescharacteristic
18C2×C13×SD16C2211yescharacteristic
19C2×C13×SD16C2211yescharacteristic
20C13×C4⋊Q8C2211yescharacteristic
21C13×#124C2211yescharacteristic
22Q8×Dic13C2211yescharacteristic
23Q8×Dic13C2211yescharacteristic
24Q8×Dic13C2211yescharacteristic
25#88198C2211yescharacteristic
26#88198C2211yescharacteristic
27#88198C2211yescharacteristic
28C2×#6107C2211yescharacteristic
29C2×#6107C2211yescharacteristic
30C2×#6107C2211yescharacteristic
31#88190C2211yescharacteristic
32D4×Dic13C2211yescharacteristic
33C2×#6105C2211yescharacteristic
34C2×Dic52C2211yescharacteristic
35#88144—21no—
36#88143—21no—
37#88143—21no—
38#88141—21no—
39#88133—21no—
40#88133—21no—
41#88132—21no—
42#88131—21no—
43C4×Dic26C2211yescharacteristic
44C4×Dic26C2211yescharacteristic
45C4×Dic26C2211yescharacteristic
46C13×#97C2211yescharacteristic
47#88075C2211yescharacteristic
48#88075C2211yescharacteristic
49#88075C2211yescharacteristic
50#88072C2211yescharacteristic
51#88057C2211yescharacteristic
52#88056C2211yescharacteristic
53#88056C2211yescharacteristic
54#88055C2211yescharacteristic
55#88054C2211yescharacteristic
56#88054C2211yescharacteristic
57C8×Dic13C2211yescharacteristic
58C4⋊#1055C2211yescharacteristic
59C2×Q8×C13C2311yescharacteristic
60C2×Q8×C13C2311yescharacteristic
61C2×Q8×C13C2311yescharacteristic
62C2×D4×C13C2311yescharacteristic
63C22×Dic13—21no—
64C2×Dic26D411yescharacteristic
65C2×Dic26C2311yescharacteristic
66C2×Dic26C2311yescharacteristic
67C13×Q16—22no—
68C13×Q16—41no—
69C13×SD16—22no—
70C13×SD16—41no—
71C2×C8×C13C2311yescharacteristic
72C2×C8×C13C2311yescharacteristic
73C13×C4⋊C4—21no—
74C13×C4⋊C4—21no—
75C13×C22⋊C4—21no—
76C13×C22⋊C4—21no—
77C42×C13C2311yescharacteristic
78C22⋊Dic13—21no—
79C22⋊Dic13—21no—
80C22⋊Dic13—21no—
81#6107—41no—
82#6107—41no—
83#6107—41no—
84#6105—41no—
85C4⋊Dic13—21no—
86C4⋊Dic13—21no—
87C4⋊Dic13—21no—
88C4⋊Dic13D411yescharacteristic
89C4⋊Dic13C2311yescharacteristic
90C4⋊Dic13C2311yescharacteristic
91#6101—21no—
92#6101—21no—
93#6101—21no—
94#6101—21no—
95#6101—21no—
96#6101—21no—
97#6101—21no—
98#6101—21no—
99#6101D411yescharacteristic
100#6101D411yescharacteristic
101C4×Dic13—21no—
102C4×Dic13—21no—
103C4×Dic13—21no—
104C4×Dic13—21no—
105C4×Dic13—21no—
106C4×Dic13C2311yescharacteristic
107C4×Dic13C2311yescharacteristic
108C2×#1055C2311yescharacteristic
109C2×#1055C2311yescharacteristic
110Dic52—22no—
111#3398—131nomaximal, Sylow
112C23×C13—21no—
113Q8×C13—21no—
114Q8×C13—21no—
115Q8×C13—21no—
116Q8×C13—21no—
117Q8×C13—21no—
118Q8×C13—21no—
119D4×C13—21no—
120D4×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×Dic13—21no—
130C2×Dic13—21no—
131C2×Dic13—42no—
132C2×Dic13C2×D411yescharacteristic
133C2×Dic13C2×D411yescharacteristic
134C2×Dic13C2×D411yescharacteristic
135C2×Dic13C2×D411yescharacteristic
136Dic26—22no—
137Dic26—21no—
138Dic26—21no—
139Dic26—21no—
140Dic26—21no—
141C8×C13—21no—
142C8×C13#4112yes—
143#1055—21no—
144#1055—21no—
145#557—131no—
146#556—131no—
147#497—131no—
148#497D1311yescharacteristic
149#494—131no—
150#464—131no—
151#464—131no—
152#462—131no—
153#462—131no—
154#462—131no—
155#461—131no—
156#446—131no—
157#441—131no—
158#441—131no—
159C4×SD16—131no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13—41no—
163C22×C13C22×D411yescharacteristic
164C4×C13—21no—
165C4×C13—21no—
166C4×C13—41no—
167C4×C13—41no—
168C4×C13—41no—
169C4×C13C2×#4111yescharacteristic
170C4×C13H(5,𝔽2)11yescharacteristic
171Dic13—21no—
172Dic13—21no—
173Dic13—21no—
174Dic13—41no—
175Dic13—41no—
176Dic13—41no—
177Dic13—41no—
178Dic13#13712yes—
179C2×Q16—131no—
180C2×Q16—131no—
181C2×Q16—131no—
182C2×Q16—131no—
183C2×Q16C2×D1311yescharacteristic
184C2×Q16C2×D1311yescharacteristic
185C2×SD16—131no—
186C2×SD16C2×D1311yescharacteristic
187C2×SD16C2×D1311yescharacteristic
188C4⋊Q8—131no—
189C4⋊Q8—131no—
190C4⋊Q8—131no—
191C4⋊Q8C2×D1311yescharacteristic
192#126—261no—
193#126—261no—
194#125—261no—
195#125—261no—
196#125—261no—
197#124—131no—
198#124C2×D1311yescharacteristic
199C22⋊Q8—261no—
200C4×Q8—131no—
201C4×Q8—131no—
202C4×Q8—131no—
203C4×Q8—131no—
204C4×Q8—131no—
205C4×Q8—131no—
206C4×Q8—261no—
207C4×D4—131no—
208#117—261no—
209#106—131no—
210C4⋊C8—131no—
211C4⋊C8—131no—
212C4⋊C8—131no—
213#103—131no—
214#103—131no—
215#103—131no—
216#103—131no—
217#103—131no—
218#102—131no—
219#97—131no—
220#97C2×D1311yescharacteristic
221C4×C8—131no—
222C2×C13—81no—
223C2×C13#55011yescharacteristic
224C2×C13C2×#13711yescharacteristic
225C2×C13#57811yescharacteristic
226C2×Q8—131no—
227C2×Q8—131no—
228C2×Q8—131no—
229C2×Q8C22×D1311yescharacteristic
230C2×Q8C22×D1311yescharacteristic
231C2×Q8C22×D1311yescharacteristic
232C2×D4C22×D1311yescharacteristic
233C22×C4—261no—
234Q16—22no—
235Q16—41no—
236Q16—262no—
237Q16—521no—
238Q16—521no—
239Q16—521no—
240SD16—22no—
241SD16—41no—
242SD16—521no—
243C2×C8—131no—
244C2×C8—131no—
245C2×C8C22×D1311yescharacteristic
246C2×C8C22×D1311yescharacteristic
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—131no—
250C4⋊C4—131no—
251C4⋊C4—131no—
252C4⋊C4—131no—
253C4⋊C4—131no—
254C4⋊C4—261no—
255C4⋊C4—261no—
256C4⋊C4—261no—
257C4⋊C4—261no—
258C4⋊C4—261no—
259C4⋊C4—261no—
260C4⋊C4—261no—
261C4⋊C4—261no—
262C4⋊C4—261no—
263C4⋊C4—261no—
264C4⋊C4—261no—
265C22⋊C4—21no—
266C22⋊C4—21no—
267C22⋊C4—261no—
268C22⋊C4—261no—
269C22⋊C4—261no—
270C42—131no—
271C42—131no—
272C42—261no—
273C42—261no—
274C42—261no—
275C42—261no—
276C42—261no—
277C42C22×D1311yescharacteristic
278C13#339811yescharacteristic, complemented, Sylow
279C23—21no—
280Q8—21no—
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—21no—
285Q8—21no—
286Q8—262no—
287Q8—261no—
288Q8—261no—
289Q8—261no—
290Q8—261no—
291D4—21no—
292D4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—131no—
297C2×C4—131no—
298C2×C4—131no—
299C2×C4—131no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—261no—
303C2×C4—261no—
304C2×C4—522no—
305C2×C4D4×D1311yescharacteristic
306C2×C4D4×D1311yescharacteristic
307C2×C4C23×D1311yescharacteristic
308C8—21no—
309C8—261no—
310C8—261no—
311C8#612912yes—
312C22—41no—
313C22—41no—
314C22—41no—
315C22C2×D4×D1311yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—132no—
322C4—261no—
323C4—261no—
324C4—261no—
325C4—521no—
326C4—521no—
327C4—521no—
328C4—521no—
329C4C2×#612911yescharacteristic
330C4#8825111yescharacteristic
331C2—81no—
332C2#1171942311yescharacteristic
333C2D13×#13711yescharacteristic
334C2#1171948411yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#497C2
socleC22×C13C22×D4
prime radicalC2×D4×C13C23
hypercenter#497D13
hypocenterC13#3398
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #11719426C2semidirect
4. #11718845C2semidirect
5. #11718843C2semidirect
6. #11718843C2semidirect
7. #11718842C2semidirect
12. #11718751C2semidirect
14. #11718377C2semidirect
15. #11718362C2semidirect
278. C13#3398semidirect

Maximal subgroups

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

subgroupindex
#117194262
#117193762
C13×#4972
#117188452
#117188432
#117188422
#117188282
#117188272
#117188232
SD16×Dic132
#117187512
#117187152
#117183772
#117183622
#339813