Finite Group Databasebeta

← #13131659

Subgroups — #13131659

Order 1664.

362 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#11719411C211yesmaximal, characteristic
2#11719080C211yesmaximal, characteristic, complemented
3#11719078C211yesmaximal, characteristic, complemented
4#11719077C211yesmaximal, characteristic, complemented
5#11719076C211yesmaximal, characteristic, complemented
6#11719075C211yesmaximal, characteristic, complemented
7#11719072C211yesmaximal, characteristic, complemented
8#11719068C211yesmaximal, characteristic, complemented
9#11719066C211yesmaximal, characteristic, complemented
10#11719065C211yesmaximal, characteristic, complemented
11#11719064C211yesmaximal, characteristic, complemented
12#11719064C211yesmaximal, characteristic, complemented
13#11719062C211yesmaximal, characteristic, complemented
14#11719054C211yesmaximal, characteristic, complemented
15C4×#6118C211yesmaximal, characteristic, complemented
16C2×#6122C2211yescharacteristic
17C22×#1057C2211yescharacteristic
18C2×#6118C2211yescharacteristic
19C2×#6118C2211yescharacteristic
20C2×#6118C2211yescharacteristic
21C2×D13⋊C8C2211yescharacteristic
22C13×#126C411yescharacteristic
23#88150C411yescharacteristic
24#88148C411yescharacteristic
25#88147C2211yescharacteristic
26#88146C2211yescharacteristic
27#88143C411yescharacteristic
28#88141C2211yescharacteristic
29#88139C411yescharacteristic
30#88138C411yescharacteristic
31#88137C411yescharacteristic
32#88135C2211yescharacteristic
33#88135C2211yescharacteristic
34#88131C2211yescharacteristic
35#88130C411yescharacteristic
36C42×D13C2211yescharacteristic
37C22⋊#1057C2211yescharacteristic
38C22⋊#1057C2211yescharacteristic
39#88112C2211yescharacteristic
40#88112C2211yescharacteristic
41#88111C2211yescharacteristic
42#88111C2211yescharacteristic
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×C22⋊D13C2×C411yescharacteristic
60C2×C22⋊D13C2×C411yescharacteristic
61C22×Dic13C2311yescharacteristic
62C2×D52C2×C411yescharacteristic
63C2×C4×D13C2×C411yescharacteristic
64C2×C4×D13C2×C411yescharacteristic
65C2×C4×D13C2311yescharacteristic
66C2×C4×D13C2311yescharacteristic
67C2×Dic26C2×C411yescharacteristic
68#6122—22no—
69C2×#1057—22no—
70C2×#1057C2311yescharacteristic
71C2×#1057C2311yescharacteristic
72C2×#1057C2311yescharacteristic
73C2×#1057C2311yescharacteristic
74C2×#1057C2311yescharacteristic
75C2×#1057C2311yescharacteristic
76C2×#1057C2311yescharacteristic
77C2×#1057C2311yescharacteristic
78#6118—22no—
79#6118—22no—
80#6118—22no—
81D13⋊C8—22no—
82C13×C4⋊C4C2×C411yescharacteristic
83C13×C4⋊C4C2×C411yescharacteristic
84C13×C4⋊C4C2×C411yescharacteristic
85C13×C22⋊C4C2×C411yescharacteristic
86C13×C22⋊C4C2×C411yescharacteristic
87C13×C22⋊C4C2×C411yescharacteristic
88C42×C13C2×C411yescharacteristic
89C22⋊Dic13C2×C411yescharacteristic
90#6103C2×C411yescharacteristic
91#6103C2×C411yescharacteristic
92#6103C2×C411yescharacteristic
93#6103C2×C411yescharacteristic
94#6103C2×C411yescharacteristic
95#6103C2×C411yescharacteristic
96C4⋊Dic13C2×C411yescharacteristic
97#6101C2×C411yescharacteristic
98#6101C2×C411yescharacteristic
99#6101C2×C411yescharacteristic
100#6101C2×C411yescharacteristic
101#6101C2×C411yescharacteristic
102#6101C2×C411yescharacteristic
103C4×Dic13C2×C411yescharacteristic
104C4×Dic13C2311yescharacteristic
105C4×Dic13C2311yescharacteristic
106C4×Dic13C2311yescharacteristic
107C4×Dic13C2311yescharacteristic
108#2967—131nomaximal, Sylow
109C23×C13C22×C411yescharacteristic
110C22×D13C22×C411yescharacteristic
111C22×D13C22×C411yescharacteristic
112C2×C4×C13C22×C411yescharacteristic
113C2×C4×C13C22×C411yescharacteristic
114C2×C4×C13C22×C411yescharacteristic
115C2×C4×C13C22×C411yescharacteristic
116C2×C4×C13C22×C411yescharacteristic
117C2×C4×C13C22×C411yescharacteristic
118C22⋊D13—41no—
119C22⋊D13—41no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13C22×C411yescharacteristic
123C2×Dic13C22×C411yescharacteristic
124C2×Dic13C22×C411yescharacteristic
125C2×Dic13C22×C411yescharacteristic
126C2×Dic13C22×C411yescharacteristic
127C2×Dic13C2411yescharacteristic
128D52—41no—
129C4×D13—21no—
130C4×D13—21no—
131C4×D13—21no—
132C4×D13—21no—
133C4×D13—41no—
134C4×D13—41no—
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#436—131no—
148#436—131no—
149#435—131no—
150#435—131no—
151#435—131no—
152#435—131no—
153#433—131no—
154#433—131no—
155#432—131no—
156#405—131no—
157#405—131no—
158C4×M16—131no—
159C22×C13—21no—
160C22×C13—21no—
161C22×C13—21no—
162C22×C13C23×C411yescharacteristic
163C2×D13—21no—
164C2×D13—21no—
165C2×D13—21no—
166C2×D13—21no—
167C2×D13—21no—
168C2×D13—21no—
169C4×C13—21no—
170C4×C13—21no—
171C4×C13—21no—
172C4×C13—21no—
173C4×C13—21no—
174C4×C13—21no—
175Dic13—21no—
176Dic13—21no—
177Dic13—21no—
178Dic13—21no—
179Dic13—21no—
180Dic13C2×#4111yescharacteristic
181Dic13C2×#4111yescharacteristic
182C2×M16—131no—
183C2×M16—131no—
184C2×M16—131no—
185C2×M16—131no—
186C22×C8—131no—
187C22×C8—131no—
188#126—131no—
189#126#26111yescharacteristic
190#125—131no—
191#124—131no—
192#123—131no—
193#123—131no—
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—41no—
226C2×C13C4×#4111yescharacteristic
227C2×C13#56811yescharacteristic
228C2×C13#56811yescharacteristic
229D13—41no—
230D13—41no—
231C2×Q8—131no—
232C2×D4—131no—
233C2×D4—131no—
234C2×D4—131no—
235C22×C4—131no—
236C22×C4—131no—
237C22×C4—131no—
238C22×C4—131no—
239C22×C4—131no—
240M16—262no—
241M16—262no—
242M16—262no—
243M16—262no—
244C2×C8—131no—
245C2×C8—131no—
246C2×C8—131no—
247C2×C8—131no—
248C2×C8—131no—
249C2×C8—131no—
250C2×C8—131no—
251C2×C8—131no—
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⋊C4C2×#26111yescharacteristic
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—
279C42C2×#26111yescharacteristic
280C13#296711yescharacteristic, complemented, Sylow
281C23—131no—
282C23—131no—
283C23C22×#26111yescharacteristic
284Q8—521no—
285D4—521no—
286D4—521no—
287D4—521no—
288C2×C4—131no—
289C2×C4—131no—
290C2×C4—131no—
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—521no—
301C2×C4—521no—
302C2×C4C22×#26111yescharacteristic
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—261no—
320C22—261no—
321C22—261no—
322C22—261no—
323C22—261no—
324C22—261no—
325C22C23×#26111yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—131no—
333C4—131no—
334C4—261no—
335C4—261no—
336C4—261no—
337C4—261no—
338C4—261no—
339C2—41no—
340C2—521no—
341C2—521no—
342C2#1171962911yescharacteristic
343C2#1171962911yescharacteristic
344C2#41×#26111yescharacteristic
subgroupG/H
center, FrattiniC22C23×#261
commutator, socleC22×C13C23×C4
FittingC13×#126C4
prime radical#88138C4
cosocleC2×Dic13C24
hypercenter#126#261
hypocenterC13#2967
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #126

Complements

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

NH ≅ G/Ntype
2. #11719080C2semidirect
3. #11719078C2semidirect
4. #11719077C2semidirect
5. #11719076C2semidirect
6. #11719075C2semidirect
7. #11719072C2semidirect
8. #11719068C2semidirect
9. #11719066C2semidirect
10. #11719065C2semidirect
11. #11719064C2semidirect
12. #11719064C2semidirect
13. #11719062C2semidirect
14. #11719054C2semidirect
15. C4×#6118C2semidirect
280. C13#2967semidirect

Maximal subgroups

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

subgroupindex
#117194112
#117190802
#117190782
#117190772
#117190762
#117190752
#117190722
#117190682
#117190662
#117190652
#117190642
#117190622
#117190542
C4×#61182
#296713