Finite Group Databasebeta

← #13081677

Subgroups — #13081677

Order 1408.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623244C211yesmaximal, characteristic, complemented
2#10623202C211yesmaximal, characteristic, complemented
3C11×#496C211yesmaximal, characteristic
4#10622780C211yesmaximal, characteristic, complemented
5#10622779C211yesmaximal, characteristic, complemented
6#10622775C211yesmaximal, characteristic, complemented
7SD16×Dic11C211yesmaximal, characteristic, complemented
8#10622768C211yesmaximal, characteristic, complemented
9#10622766C211yesmaximal, characteristic, complemented
10#10622766C211yesmaximal, characteristic, complemented
11#10622765C211yesmaximal, characteristic, complemented
12#10622688C211yesmaximal, characteristic, complemented
13#10622667C211yesmaximal, characteristic, complemented
14#10622329C211yesmaximal, characteristic, complemented
15#10622314C211yesmaximal, characteristic, complemented
16C2×C11×SD16C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C2×C11×D8C2211yescharacteristic
19C2×C11×D8C2211yescharacteristic
20C11×#127C2211yescharacteristic
21C11×#124C2211yescharacteristic
22Q8×Dic11C2211yescharacteristic
23#66997C2211yescharacteristic
24C2×#4326C2211yescharacteristic
25#66989—21no—
26#66989C2211yescharacteristic
27#66989C2211yescharacteristic
28#66989C2211yescharacteristic
29#66988—21no—
30#66988—21no—
31D4×Dic11—21no—
32D4×Dic11C2211yescharacteristic
33D4×Dic11C2211yescharacteristic
34D4×Dic11C2211yescharacteristic
35C2×#4324C2211yescharacteristic
36C2×#4324C2211yescharacteristic
37C2×#4324C2211yescharacteristic
38C2×Dic44C2211yescharacteristic
39#66932—21no—
40#66932—21no—
41#66931—21no—
42#66930—21no—
43C4×Dic22C2211yescharacteristic
44C4×Dic22C2211yescharacteristic
45C4×Dic22C2211yescharacteristic
46C11×#97C2211yescharacteristic
47#66899C2211yescharacteristic
48#66896C2211yescharacteristic
49#66896C2211yescharacteristic
50#66896C2211yescharacteristic
51#66881C2211yescharacteristic
52#66880C2211yescharacteristic
53#66880C2211yescharacteristic
54#66879C2211yescharacteristic
55Dic11⋊C8C2211yescharacteristic
56Dic11⋊C8C2211yescharacteristic
57C8×Dic11C2211yescharacteristic
58C4⋊(C11⋊C8)C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×D4×C11—21no—
61C2×D4×C11—21no—
62C2×D4×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C22×Dic11—21no—
66C22×Dic11—21no—
67C22×Dic11—21no—
68C2×Dic22D411yescharacteristic
69C2×Dic22C2311yescharacteristic
70C2×Dic22C2311yescharacteristic
71C11×SD16—22no—
72C11×SD16—41no—
73C11×D8—22no—
74C11×D8—41no—
75C2×C8×C11C2311yescharacteristic
76C2×C8×C11C2311yescharacteristic
77C11×C22⋊C4—21no—
78C11×C22⋊C4—21no—
79C42×C11C2311yescharacteristic
80C22⋊Dic11—21no—
81C22⋊Dic11—21no—
82C22⋊Dic11—21no—
83C22⋊Dic11—21no—
84C22⋊Dic11—21no—
85C22⋊Dic11—21no—
86C22⋊Dic11—21no—
87C22⋊Dic11—21no—
88C22⋊Dic11—21no—
89#4326—41no—
90#4324—41no—
91#4324—41no—
92#4324—41no—
93C4⋊Dic11—21no—
94C4⋊Dic11D411yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101Dic11⋊C4D411yescharacteristic
102Dic11⋊C4D411yescharacteristic
103C4×Dic11—21no—
104C4×Dic11—21no—
105C4×Dic11—21no—
106C4×Dic11C2311yescharacteristic
107C4×Dic11C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109C2×C11⋊C8C2311yescharacteristic
110Dic44—22no—
111#3401—111nomaximal, Sylow
112C23×C11—21no—
113C23×C11—21no—
114C23×C11—21no—
115Q8×C11—21no—
116Q8×C11—21no—
117D4×C11—21no—
118D4×C11—21no—
119D4×C11—21no—
120D4×C11—21no—
121D4×C11—21no—
122D4×C11—21no—
123D4×C11—42no—
124D4×C11—81no—
125C2×C4×C11—21no—
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2×D411yescharacteristic
128C2×C4×C11C2411yescharacteristic
129C2×Dic11—21no—
130C2×Dic11—21no—
131C2×Dic11—21no—
132C2×Dic11—21no—
133C2×Dic11—42no—
134C2×Dic11—81no—
135C2×Dic11—81no—
136C2×Dic11C2×D411yescharacteristic
137C2×Dic11C2×D411yescharacteristic
138C2×Dic11C2×D411yescharacteristic
139C2×Dic11C2×D411yescharacteristic
140Dic22—21no—
141Dic22—21no—
142Dic22—21no—
143Dic22—21no—
144Dic22—41no—
145C8×C11—21no—
146C8×C11#4112yes—
147C11⋊C8—21no—
148C11⋊C8—21no—
149#559—111no—
150#556—111no—
151#497—111no—
152#496D1111yescharacteristic
153#495—111no—
154#464—111no—
155#464—111no—
156#463—111no—
157#463—111no—
158#461—111no—
159#460—111no—
160#446—111no—
161#442—111no—
162#441—111no—
163C4×SD16—111no—
164C22×C11—41no—
165C22×C11—41no—
166C22×C11—41no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11—41no—
171C22×C11—41no—
172C22×C11—41no—
173C22×C11C22×D411yescharacteristic
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—41no—
177C4×C11C2×#4111yescharacteristic
178C4×C11H(5,𝔽2)11yescharacteristic
179Dic11—21no—
180Dic11—21no—
181Dic11—21no—
182Dic11—21no—
183Dic11—41no—
184Dic11—41no—
185Dic11—41no—
186Dic11—41no—
187C2×Q16—111no—
188C2×Q16—111no—
189C2×SD16—111no—
190C2×SD16—111no—
191C2×SD16—111no—
192C2×SD16C2×D1111yescharacteristic
193C2×SD16C2×D1111yescharacteristic
194C2×D8C2×D1111yescharacteristic
195C2×D8C2×D1111yescharacteristic
196C4⋊Q8—111no—
197#127C2×D1111yescharacteristic
198#126—221no—
199#126—221no—
200#124—111no—
201#124—111no—
202#124—111no—
203#124—221no—
204#124C2×D1111yescharacteristic
205#123—221no—
206#123—221no—
207C22⋊Q8—221no—
208C4×Q8—111no—
209C4×Q8—111no—
210C4×Q8—111no—
211C4×Q8—111no—
212C4×D4—111no—
213C4×D4—111no—
214C4×D4—111no—
215C4×D4—221no—
216#117—221no—
217#106—111no—
218C4⋊C8—111no—
219C4⋊C8—111no—
220C4⋊C8—111no—
221#103—111no—
222#103—111no—
223#103—111no—
224#102—111no—
225#102—111no—
226#102—111no—
227#97—111no—
228#97C2×D1111yescharacteristic
229C4×C8—111no—
230C2×C11—81no—
231C2×C11—81no—
232C2×C11—81no—
233C2×C11#55011yescharacteristic
234C2×C11#57511yescharacteristic
235C2×C11#57711yescharacteristic
236C2×Q8—111no—
237C2×Q8—111no—
238C2×Q8—111no—
239C2×Q8C22×D1111yescharacteristic
240C2×D4—21no—
241C2×D4—21no—
242C2×D4C22×D1111yescharacteristic
243C2×D4C22×D1111yescharacteristic
244C2×D4C22×D1111yescharacteristic
245C22×C4—221no—
246C22×C4—221no—
247C22×C4—221no—
248Q16—222no—
249Q16—441no—
250SD16—22no—
251SD16—41no—
252SD16—441no—
253SD16—441no—
254SD16—441no—
255D8—22no—
256D8—41no—
257C2×C8—111no—
258C2×C8—111no—
259C2×C8C22×D1111yescharacteristic
260C2×C8C22×D1111yescharacteristic
261C4⋊C4—111no—
262C4⋊C4—111no—
263C4⋊C4—111no—
264C4⋊C4—111no—
265C4⋊C4—111no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4—221no—
269C4⋊C4—221no—
270C4⋊C4—221no—
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C42—111no—
283C42—111no—
284C42—221no—
285C42—221no—
286C42—221no—
287C42C22×D1111yescharacteristic
288C11#340111yescharacteristic, complemented, Sylow
289C23—21no—
290C23—21no—
291C23—21no—
292Q8—21no—
293Q8—21no—
294Q8—221no—
295Q8—221no—
296Q8—221no—
297Q8—221no—
298Q8—441no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—21no—
305D4—42no—
306D4—81no—
307C2×C4—21no—
308C2×C4—111no—
309C2×C4—111no—
310C2×C4—111no—
311C2×C4—111no—
312C2×C4—221no—
313C2×C4—221no—
314C2×C4—221no—
315C2×C4—221no—
316C2×C4—442no—
317C2×C4—881no—
318C2×C4—881no—
319C2×C4D4×D1111yescharacteristic
320C2×C4D4×D1111yescharacteristic
321C2×C4C23×D1111yescharacteristic
322C8—21no—
323C8—221no—
324C8—221no—
325C8#434112yes—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22C2×D4×D1111yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—221no—
340C4—221no—
341C4—221no—
342C4—221no—
343C4—441no—
344C4—441no—
345C4—441no—
346C4—441no—
347C4C2×#434111yescharacteristic
348C4#6703711yescharacteristic
349C2—81no—
350C2—81no—
351C2—81no—
352C2#1062324911yescharacteristic
353C2#1062330411yescharacteristic
354C2#1062330611yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC11×#496C2
socleC22×C11C22×D4
hypercenter#496D11
hypocenterC11#3401
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #10623244C2semidirect
2. #10623202C2semidirect
4. #10622780C2semidirect
5. #10622779C2semidirect
6. #10622775C2semidirect
7. SD16×Dic11C2semidirect
8. #10622768C2semidirect
9. #10622766C2semidirect
10. #10622766C2semidirect
11. #10622765C2semidirect
12. #10622688C2semidirect
13. #10622667C2semidirect
14. #10622329C2semidirect
15. #10622314C2semidirect
288. C11#3401semidirect

Maximal subgroups

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

subgroupindex
#106232442
#106232022
C11×#4962
#106227802
#106227792
#106227752
SD16×Dic112
#106227682
#106227662
#106227652
#106226882
#106226672
#106223292
#106223142
#340111