Finite Group Databasebeta

← #13081703

Subgroups — #13081703

Order 1408.

380 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623212C211yesmaximal, characteristic, complemented
2#10623116C211yesmaximal, characteristic, complemented
3C11×#464C211yesmaximal, characteristic, complemented
4#10622804C211yesmaximal, characteristic, complemented
5#10622798C211yesmaximal, characteristic, complemented
6#10622789C211yesmaximal, characteristic, complemented
7#10622778C211yesmaximal, characteristic, complemented
8#10622671C211yesmaximal, characteristic, complemented
9#10622639C211yesmaximal, characteristic, complemented
10#10622456C211yesmaximal, characteristic, complemented
11#10622441C211yesmaximal, characteristic, complemented
12#10622432C211yesmaximal, characteristic, complemented
13#10622430C211yesmaximal, characteristic, complemented
14#10622399C211yesmaximal, characteristic, complemented
15#10622369C211yesmaximal, characteristic, complemented
16C2×C11×Q16C2211yescharacteristic
17C2×C11×SD16C2211yescharacteristic
18C11×#124C2211yescharacteristic
19C4×Q8×C11C2211yescharacteristic
20#67000C2211yescharacteristic
21#67000C2211yescharacteristic
22#67000C2211yescharacteristic
23Q8×Dic11C2211yescharacteristic
24C2×#4325C2211yescharacteristic
25C2×#4325C2211yescharacteristic
26C2×#4325C2211yescharacteristic
27#66993C2211yescharacteristic
28D4×Dic11C2211yescharacteristic
29C2×#4323C2211yescharacteristic
30C2×#4323C2211yescharacteristic
31C2×D88C2211yescharacteristic
32C2×D88C2211yescharacteristic
33#66947—21no—
34#66947—21no—
35#66946C2211yescharacteristic
36#66946C2211yescharacteristic
37#66939—21no—
38#66938—21no—
39#66936—21no—
40(C22⋊D11)⋊C4—21no—
41#66928—21no—
42#66927C2211yescharacteristic
43C4×D44—21no—
44C4×D44C2211yescharacteristic
45C4×Dic22C2211yescharacteristic
46C11×C4⋊C8C2211yescharacteristic
47C11×#103C2211yescharacteristic
48C11×#102C2211yescharacteristic
49#66899C2211yescharacteristic
50#66885C2211yescharacteristic
51#66885C2211yescharacteristic
52#66879C2211yescharacteristic
53Dic11⋊C8C2211yescharacteristic
54Dic11⋊C8C2211yescharacteristic
55C8×Dic11C2211yescharacteristic
56#66873C2211yescharacteristic
57#66871C2211yescharacteristic
58#66867C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C2×Q8×C11C2311yescharacteristic
61C2×D4×C11C2311yescharacteristic
62C2×C22⋊D11—21no—
63C2×C22⋊D11—21no—
64C22×Dic11—21no—
65C2×D44—21no—
66C2×D44—21no—
67C2×D44C2311yescharacteristic
68C2×D44C2311yescharacteristic
69C2×D44C2311yescharacteristic
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11—21no—
73C2×Dic22D411yescharacteristic
74C11×Q16—41no—
75C11×SD16—41no—
76C2×C8×C11C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C11×C4⋊C4—21no—
79C11×C4⋊C4C2311yescharacteristic
80C11×C22⋊C4—21no—
81C11×C22⋊C4—21no—
82C42×C11—21no—
83C42×C11C2311yescharacteristic
84C22⋊Dic11—21no—
85#4325—22no—
86#4325—22no—
87#4325—41no—
88#4323—22no—
89#4323—41no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92(C2×D11)⋊C4—21no—
93(C2×D11)⋊C4—21no—
94(C2×D11)⋊C4—21no—
95(C2×D11)⋊C4—21no—
96(C2×D11)⋊C4—21no—
97(C2×D11)⋊C4—21no—
98(C2×D11)⋊C4—21no—
99C4⋊Dic11—21no—
100C4⋊Dic11D411yescharacteristic
101C4⋊Dic11C2311yescharacteristic
102Dic11⋊C4D411yescharacteristic
103Dic11⋊C4D411yescharacteristic
104C4×Dic11—21no—
105C4×Dic11C2311yescharacteristic
106C4×Dic11C2311yescharacteristic
107C2×C11⋊C8C2311yescharacteristic
108C2×C11⋊C8C2311yescharacteristic
109D88—41no—
110D88—41no—
111#3403—111nomaximal, Sylow
112C23×C11—21no—
113C22×D11—21no—
114C22×D11—21no—
115C22×D11—21no—
116Q8×C11—21no—
117Q8×C11—21no—
118Q8×C11—21no—
119Q8×C11—21no—
120D4×C11—21no—
121D4×C11—21no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11—21no—
125C2×C4×C11C2×D411yescharacteristic
126C2×C4×C11C2×D411yescharacteristic
127C2×C4×C11C2411yescharacteristic
128C22⋊D11—42no—
129C22⋊D11—81no—
130C2×Dic11—21no—
131C2×Dic11—81no—
132C2×Dic11C2×D411yescharacteristic
133C2×Dic11C2×D411yescharacteristic
134C2×Dic11C2×D411yescharacteristic
135C2×Dic11C2×D411yescharacteristic
136D44—21no—
137D44—21no—
138D44—21no—
139D44—21no—
140D44—21no—
141D44—21no—
142D44—42no—
143D44—81no—
144C4×D11—81no—
145C4×D11—81no—
146C4×D11—81no—
147Dic22—41no—
148C8×C11—21no—
149C8×C11—21no—
150C11⋊C8—21no—
151C11⋊C8#4112yes—
152#559—111no—
153#559—111no—
154#496—111no—
155#496—111no—
156#495—111no—
157#464—111no—
158#464D1111yescharacteristic, complemented
159#463—111no—
160#463—111no—
161#459—111no—
162#459—111no—
163#446—111no—
164#440—111no—
165#440—111no—
166C4×D8—111no—
167C22×C11—41no—
168C22×C11—41no—
169C22×C11—41no—
170C22×C11C22×D411yescharacteristic
171C2×D11—41no—
172C2×D11—41no—
173C2×D11—41no—
174C2×D11—41no—
175C2×D11—41no—
176C2×D11—41no—
177C2×D11—41no—
178C2×D11—41no—
179C2×D11—41no—
180C4×C11—21no—
181C4×C11—21no—
182C4×C11—41no—
183C4×C11—41no—
184C4×C11—41no—
185C4×C11C2×#4111yescharacteristic
186C4×C11H(5,𝔽2)11yescharacteristic
187Dic11—21no—
188Dic11—21no—
189Dic11—21no—
190Dic11—21no—
191Dic11—41no—
192C2×Q16C2×D1111yescharacteristic
193C2×SD16—111no—
194C2×SD16—111no—
195C2×SD16—111no—
196C2×SD16C2×D1111yescharacteristic
197C2×D8—111no—
198C2×D8—111no—
199C2×D8—111no—
200C2×D8—111no—
201#127—111no—
202#127—111no—
203#124—111no—
204#124—111no—
205#124—111no—
206#124—221no—
207#124—221no—
208#124C2×D1111yescharacteristic
209#123—221no—
210#123—221no—
211#123—221no—
212#123—221no—
213C4×Q8—111no—
214C4×Q8—111no—
215C4×Q8C2×D1111yescharacteristic
216C4×D4—111no—
217C4×D4—111no—
218C4×D4—111no—
219C4×D4—111no—
220C4×D4—221no—
221C4×D4—221no—
222#107—111no—
223C4⋊C8—111no—
224C4⋊C8—111no—
225C4⋊C8C2×D1111yescharacteristic
226#103—111no—
227#103C2×D1111yescharacteristic
228#102—111no—
229#102—111no—
230#102—111no—
231#102C2×D1111yescharacteristic
232#97—111no—
233#97—111no—
234C4×C8—111no—
235C2×C11—81no—
236C2×C11#55011yescharacteristic
237C2×C11#57511yescharacteristic
238C2×C11#57611yescharacteristic
239D11—81no—
240D11—81no—
241D11—81no—
242C2×Q8—111no—
243C2×Q8C22×D1111yescharacteristic
244C2×Q8C22×D1111yescharacteristic
245C2×D4—111no—
246C2×D4—111no—
247C2×D4—111no—
248C2×D4—221no—
249C2×D4—221no—
250C2×D4—221no—
251C2×D4—221no—
252C2×D4C22×D1111yescharacteristic
253C22×C4—221no—
254C22×C4—221no—
255C22×C4—221no—
256C22×C4—221no—
257Q16—41no—
258SD16—41no—
259SD16—222no—
260SD16—222no—
261SD16—441no—
262D8—222no—
263D8—441no—
264D8—441no—
265D8—441no—
266C2×C8—111no—
267C2×C8—111no—
268C2×C8C22×D1111yescharacteristic
269C2×C8C22×D1111yescharacteristic
270C4⋊C4—21no—
271C4⋊C4—111no—
272C4⋊C4—111no—
273C4⋊C4—111no—
274C4⋊C4—111no—
275C4⋊C4—221no—
276C4⋊C4C22×D1111yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—221no—
280C22⋊C4—221no—
281C22⋊C4—221no—
282C22⋊C4—221no—
283C22⋊C4—221no—
284C22⋊C4—221no—
285C22⋊C4—221no—
286C22⋊C4—221no—
287C22⋊C4—221no—
288C22⋊C4—221no—
289C42—21no—
290C42—111no—
291C42—111no—
292C42—221no—
293C42C22×D1111yescharacteristic
294C11#340311yescharacteristic, complemented, Sylow
295C23—21no—
296C23—221no—
297C23—221no—
298C23—221no—
299Q8—21no—
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—441no—
304D4—21no—
305D4—21no—
306D4—221no—
307D4—221no—
308D4—221no—
309D4—221no—
310D4—221no—
311D4—221no—
312D4—442no—
313D4—442no—
314D4—881no—
315D4—881no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—111no—
320C2×C4—111no—
321C2×C4—111no—
322C2×C4—111no—
323C2×C4—221no—
324C2×C4—881no—
325C2×C4—881no—
326C2×C4—881no—
327C2×C4—881no—
328C2×C4D4×D1111yescharacteristic
329C2×C4D4×D1111yescharacteristic
330C2×C4C23×D1111yescharacteristic
331C8—21no—
332C8—21no—
333C8—112no—
334C8—221no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—441no—
339C22—441no—
340C22—441no—
341C22—441no—
342C22—441no—
343C22—441no—
344C22—441no—
345C22—441no—
346C22—441no—
347C22C2×D4×D1111yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—221no—
354C4—221no—
355C4—221no—
356C4—221no—
357C4—441no—
358C4#6703711yescharacteristic
359C4#41×D1111yescharacteristic
360C2—81no—
361C2—881no—
362C2—881no—
363C2—881no—
364C2#1062313011yescharacteristic
365C2#1062330011yescharacteristic
366C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#464C2
socleC22×C11C22×D4
hypercenter#464D11
hypocenterC11#3403
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #10623212C2semidirect
2. #10623116C2semidirect
3. C11×#464C2semidirect
4. #10622804C2semidirect
5. #10622798C2semidirect
6. #10622789C2semidirect
7. #10622778C2semidirect
8. #10622671C2semidirect
9. #10622639C2semidirect
10. #10622456C2semidirect
11. #10622441C2semidirect
12. #10622432C2semidirect
13. #10622430C2semidirect
14. #10622399C2semidirect
15. #10622369C2semidirect
158. #464D11semidirect
294. C11#3403semidirect

Maximal subgroups

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

subgroupindex
#106232122
#106231162
C11×#4642
#106228042
#106227982
#106227892
#106227782
#106226712
#106226392
#106224562
#106224412
#106224322
#106224302
#106223992
#106223692
#340311