Finite Group Databasebeta

← #13131663

Subgroups — #13131663

Order 1664.

372 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719354C211yesmaximal, characteristic
2#11719144C211yesmaximal, characteristic, complemented
3D4×#1057C211yesmaximal, characteristic, complemented
4C2×#88110C211yesmaximal, characteristic, complemented
5#11719119C211yesmaximal, characteristic, complemented
6#11719080C211yesmaximal, characteristic, complemented
7#11719078C211yesmaximal, characteristic, complemented
8#11719077C211yesmaximal, characteristic, complemented
9#11719072C211yesmaximal, characteristic, complemented
10#11719068C211yesmaximal, characteristic, complemented
11#11719065C211yesmaximal, characteristic, complemented
12#11719064C211yesmaximal, characteristic, complemented
13#11719064C211yesmaximal, characteristic, complemented
14#11719063C211yesmaximal, characteristic, complemented
15#11719062C211yesmaximal, characteristic, complemented
16C2×#6122C2211yescharacteristic
17C22×#1057C2211yescharacteristic
18C22×#1057C2211yescharacteristic
19C22×#1057C2211yescharacteristic
20C2×#6118C2211yescharacteristic
21C2×D13⋊C8C2211yescharacteristic
22C13×#123C411yescharacteristic
23#88193C411yescharacteristic
24D4×Dic13C2211yescharacteristic
25#88183C411yescharacteristic
26C2×C4×Dic13C2211yescharacteristic
27#88152C411yescharacteristic
28#88146C2211yescharacteristic
29#88143C411yescharacteristic
30#88141C2211yescharacteristic
31#88139C411yescharacteristic
32#88135C2211yescharacteristic
33#88135C2211yescharacteristic
34#88133C411yescharacteristic
35#88132C411yescharacteristic
36#88131C2211yescharacteristic
37C22⋊#1057C2211yescharacteristic
38C22⋊#1057C2211yescharacteristic
39C22⋊#1057C2211yescharacteristic
40C22⋊#1057C2211yescharacteristic
41#88112C2211yescharacteristic
42#88112C2211yescharacteristic
43#88111C2211yescharacteristic
44#88111C2211yescharacteristic
45#88110C2211yescharacteristic
46#88110C2211yescharacteristic
47#88110C2211yescharacteristic
48#88110C2211yescharacteristic
49#88110C2211yescharacteristic
50#88110C2211yescharacteristic
51C4⋊#1057C2211yescharacteristic
52C4⋊#1057C2211yescharacteristic
53C4⋊#1057C2211yescharacteristic
54C4⋊#1057C2211yescharacteristic
55C4×#1057C2211yescharacteristic
56C4×#1057C2211yescharacteristic
57C4×#1057C2211yescharacteristic
58C4×#1057C2211yescharacteristic
59C2×D4×C13C2×C411yescharacteristic
60C22×C4×C13C2×C411yescharacteristic
61C2×C22⋊D13C2×C411yescharacteristic
62C2×C22⋊D13C2×C411yescharacteristic
63C22×Dic13C2×C411yescharacteristic
64C22×Dic13C2311yescharacteristic
65C22×Dic13C2311yescharacteristic
66C2×C4×D13C2311yescharacteristic
67C2×Dic26C2×C411yescharacteristic
68#6122—22no—
69C2×#1057—22no—
70C2×#1057—22no—
71C2×#1057—22no—
72C2×#1057C2311yescharacteristic
73C2×#1057C2311yescharacteristic
74C2×#1057C2311yescharacteristic
75C2×#1057C2311yescharacteristic
76C2×#1057C2311yescharacteristic
77C2×#1057C2311yescharacteristic
78C2×#1057C2311yescharacteristic
79C2×#1057C2311yescharacteristic
80#6118—22no—
81D13⋊C8—22no—
82C13×C4⋊C4C2×C411yescharacteristic
83C13×C4⋊C4C2×C411yescharacteristic
84C13×C22⋊C4C2×C411yescharacteristic
85C13×C22⋊C4C2×C411yescharacteristic
86C13×C22⋊C4C2×C411yescharacteristic
87C22⋊Dic13C2×C411yescharacteristic
88C22⋊Dic13C2×C411yescharacteristic
89C22⋊Dic13C2×C411yescharacteristic
90#6103C2×C411yescharacteristic
91#6103C2×C411yescharacteristic
92#6103C2×C411yescharacteristic
93#6103C2×C411yescharacteristic
94C4⋊Dic13C2×C411yescharacteristic
95C4⋊Dic13C2×C411yescharacteristic
96#6101C2×C411yescharacteristic
97#6101C2×C411yescharacteristic
98#6101C2×C411yescharacteristic
99#6101C2×C411yescharacteristic
100#6101C2×C411yescharacteristic
101#6101C2×C411yescharacteristic
102C4×Dic13C2×C411yescharacteristic
103C4×Dic13C2×C411yescharacteristic
104C4×Dic13C2311yescharacteristic
105C4×Dic13C2311yescharacteristic
106C4×Dic13C2311yescharacteristic
107C4×Dic13C2311yescharacteristic
108#2968—131nomaximal, Sylow
109C23×C13C22×C411yescharacteristic
110C23×C13C22×C411yescharacteristic
111C22×D13C22×C411yescharacteristic
112D4×C13—22no—
113C2×C4×C13—22no—
114C2×C4×C13C22×C411yescharacteristic
115C2×C4×C13C22×C411yescharacteristic
116C2×C4×C13C22×C411yescharacteristic
117C2×C4×C13C22×C411yescharacteristic
118C2×C4×C13C22×C411yescharacteristic
119C22⋊D13—22no—
120C22⋊D13—41no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—41no—
126C2×Dic13C22×C411yescharacteristic
127C2×Dic13C22×C411yescharacteristic
128C2×Dic13C22×C411yescharacteristic
129C2×Dic13C22×C411yescharacteristic
130C2×Dic13C22×C411yescharacteristic
131C2×Dic13C22×C411yescharacteristic
132C2×Dic13C2411yescharacteristic
133C4×D13—21no—
134C4×D13—21no—
135Dic26—41no—
136#1057—21no—
137#1057—21no—
138#1057—21no—
139#1057—21no—
140#1057—21no—
141#1057—21no—
142#1057#4112yes—
143#1057#4112yes—
144#529—131no—
145#446—131no—
146#446—131no—
147#435—131no—
148#435—131no—
149#435—131no—
150#435—131no—
151C8×D4—131no—
152C8×D4—131no—
153#433—131no—
154#433—131no—
155#431—131no—
156#405—131no—
157#405—131no—
158C2×#97—131no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13—21no—
163C22×C13—21no—
164C22×C13#13112yes—
165C22×C13C23×C411yescharacteristic
166C2×D13—21no—
167C2×D13—21no—
168C2×D13—21no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174Dic13—21no—
175Dic13—21no—
176Dic13—21no—
177Dic13—21no—
178Dic13—21no—
179Dic13—21no—
180Dic13C2×#4111yescharacteristic
181Dic13C2×#4111yescharacteristic
182C2×M16—131no—
183C2×M16—131no—
184C22×C8—131no—
185C22×C8—131no—
186C22×C8—131no—
187C22×C8—131no—
188#126—131no—
189#126—131no—
190#125—131no—
191#124—131no—
192#123—131no—
193#123#26111yescharacteristic
194C22⋊Q8—131no—
195#121—131no—
196C4×Q8—131no—
197C4×D4—131no—
198C4×D4—131no—
199C4×D4—131no—
200#117—131no—
201#117—131no—
202C2×C42—131no—
203C4⋊C8—131no—
204C4⋊C8—131no—
205C4⋊C8—131no—
206C4⋊C8—131no—
207C4⋊C8—131no—
208C4⋊C8—131no—
209C22⋊C8—131no—
210C22⋊C8—131no—
211C22⋊C8—131no—
212C22⋊C8—131no—
213C22⋊C8—131no—
214C22⋊C8—131no—
215#97—131no—
216#97—131no—
217#97—131no—
218#97—131no—
219#97—131no—
220#97—131no—
221C4×C8—131no—
222C4×C8—131no—
223C4×C8—131no—
224C4×C8—131no—
225C2×C13—22no—
226C2×C13—41no—
227C2×C13C4×#4111yescharacteristic
228C2×C13C2×#13111yescharacteristic
229C2×C13#56811yescharacteristic
230D13—41no—
231C2×Q8—131no—
232C2×D4—131no—
233C2×D4—131no—
234C2×D4C2×#26111yescharacteristic
235C22×C4—131no—
236C22×C4—131no—
237C22×C4—131no—
238C22×C4—131no—
239C22×C4C2×#26111yescharacteristic
240M16—262no—
241M16—262no—
242C2×C8—131no—
243C2×C8—131no—
244C2×C8—131no—
245C2×C8—131no—
246C2×C8—131no—
247C2×C8—131no—
248C2×C8—131no—
249C2×C8—131no—
250C2×C8—262no—
251C2×C8—262no—
252C2×C8—262no—
253C2×C8—262no—
254C4⋊C4—131no—
255C4⋊C4—131no—
256C4⋊C4—131no—
257C4⋊C4—131no—
258C4⋊C4—131no—
259C4⋊C4—131no—
260C4⋊C4—131no—
261C4⋊C4—131no—
262C4⋊C4C2×#26111yescharacteristic
263C4⋊C4C2×#26111yescharacteristic
264C22⋊C4—131no—
265C22⋊C4—131no—
266C22⋊C4—131no—
267C22⋊C4—131no—
268C22⋊C4—131no—
269C22⋊C4—131no—
270C22⋊C4—131no—
271C22⋊C4C2×#26111yescharacteristic
272C22⋊C4C2×#26111yescharacteristic
273C22⋊C4C2×#26111yescharacteristic
274C42—131no—
275C42—131no—
276C42—131no—
277C42—131no—
278C42—131no—
279C42—131no—
280C13#296811yescharacteristic, complemented, Sylow
281C23—131no—
282C23C22×#26111yescharacteristic
283C23C22×#26111yescharacteristic
284Q8—521no—
285D4—22no—
286D4—262no—
287D4—521no—
288C2×C4—22no—
289C2×C4—131no—
290C2×C4—131no—
291C2×C4—131no—
292C2×C4—131no—
293C2×C4—131no—
294C2×C4—131no—
295C2×C4—131no—
296C2×C4—261no—
297C2×C4—261no—
298C2×C4—261no—
299C2×C4—261no—
300C2×C4—261no—
301C2×C4—261no—
302C2×C4—521no—
303C2×C4C22×#26111yescharacteristic
304C2×C4C22×#26111yescharacteristic
305C2×C4C22×#26111yescharacteristic
306C2×C4C22×#26111yescharacteristic
307C2×C4C22×#26111yescharacteristic
308C8—132no—
309C8—132no—
310C8—261no—
311C8—261no—
312C8—261no—
313C8—261no—
314C8—261no—
315C8—261no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—261no—
322C22—261no—
323C22—261no—
324C22#8823812yes—
325C22C23×#26111yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—131no—
332C4—131no—
333C4—261no—
334C4—261no—
335C4—261no—
336C4—261no—
337C4—261no—
338C4—261no—
339C2—22no—
340C2—41no—
341C2—521no—
342C2C2×#8823811yescharacteristic
343C2#1171962911yescharacteristic
344C2#41×#26111yescharacteristic
subgroupG/H
center, FrattiniC22C23×#261
commutator, socleC22×C13C23×C4
FittingC13×#123C4
prime radical#88193C4
cosocleC2×Dic13C24
hypercenter#123#261
hypocenterC13#2968
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
2. #11719144C2semidirect
3. D4×#1057C2semidirect
4. C2×#88110C2semidirect
5. #11719119C2semidirect
6. #11719080C2semidirect
7. #11719078C2semidirect
8. #11719077C2semidirect
9. #11719072C2semidirect
10. #11719068C2semidirect
11. #11719065C2semidirect
12. #11719064C2semidirect
13. #11719064C2semidirect
14. #11719063C2semidirect
15. #11719062C2semidirect
280. C13#2968semidirect

Maximal subgroups

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

subgroupindex
#117193542
#117191442
D4×#10572
C2×#881102
#117191192
#117190802
#117190782
#117190772
#117190722
#117190682
#117190652
#117190642
#117190632
#117190622
#296813