Finite Group Databasebeta

← #13078580

Subgroups — #13078580

Order 1408.

386 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623159C211yesmaximal, characteristic
2#10623054C211yesmaximal, characteristic
3C11×#485C211yesmaximal, characteristic, complemented
4#10622656C211yesmaximal, characteristic, complemented
5#10622609C211yesmaximal, characteristic, complemented
6#10622501C211yesmaximal, characteristic, complemented
7#10622493C211yesmaximal, characteristic, complemented
8#10622475C211yesmaximal, characteristic, complemented
9#10622474C211yesmaximal, characteristic, complemented
10#10622427C211yesmaximal, characteristic, complemented
11#10622422C211yesmaximal, characteristic, complemented
12#10622415C211yesmaximal, characteristic, complemented
13D11×#103C211yesmaximal, characteristic, complemented
14#10622340C211yesmaximal, characteristic
15#10622335C211yesmaximal, characteristic, complemented
16C2×Q8×D11C2211yescharacteristic
17C2×#4339C2211yescharacteristic
18C11×C22⋊Q8C2211yescharacteristic
19C11×#117C2211yescharacteristic
20#66999C2211yescharacteristic
21C2×C4⋊Dic11C2211yescharacteristic
22#66977C2211yescharacteristic
23C2×#4313C2211yescharacteristic
24C2×C8×D11C2211yescharacteristic
25#66950C2211yescharacteristic
26#66947—21no—
27#66945C2211yescharacteristic
28#66945C2211yescharacteristic
29#66945C2211yescharacteristic
30C4⋊C4×D11C2211yescharacteristic
31C4⋊C4×D11C2211yescharacteristic
32#66941—21no—
33#66938—21no—
34#66936—21no—
35(C22⋊D11)⋊C4—21no—
36(C22⋊D11)⋊C4—21no—
37C4×D44—21no—
38C4×Dic22—21no—
39C11×#107C2211yescharacteristic
40C11×#106C2211yescharacteristic
41C11×#103C2211yescharacteristic
42C11×#103C2211yescharacteristic
43C11×C22⋊C8C2211yescharacteristic
44#66899C2211yescharacteristic
45#66899C2211yescharacteristic
46C22⋊(C11⋊C8)C2211yescharacteristic
47(C2×D11)⋊C8C2211yescharacteristic
48(C2×D11)⋊C8C2211yescharacteristic
49#66882C2211yescharacteristic
50#66882C2211yescharacteristic
51#66880C2211yescharacteristic
52#66880C2211yescharacteristic
53#66874C2211yescharacteristic
54#66874C2211yescharacteristic
55#66872C2211yescharacteristic
56#66872C2211yescharacteristic
57#66872C2211yescharacteristic
58#66871C2211yescharacteristic
59C2×Q8×C11C2311yescharacteristic
60C22×C4×C11C2311yescharacteristic
61C2×C22⋊D11D411yescharacteristic
62C2×C22⋊D11D411yescharacteristic
63C22×Dic11—21no—
64Q8×D11—22no—
65Q8×D11—22no—
66#4339—22no—
67#4339—22no—
68C2×D44D411yescharacteristic
69C2×C4×D11—21no—
70C2×C4×D11—21no—
71C2×C4×D11—21no—
72C2×C4×D11C2311yescharacteristic
73C2×C4×D11C2311yescharacteristic
74C2×Dic22—21no—
75C2×Dic22D411yescharacteristic
76C2×Dic22C2311yescharacteristic
77C2×C8×C11C2311yescharacteristic
78C2×C8×C11C2311yescharacteristic
79C11×C4⋊C4—21no—
80C11×C4⋊C4C2311yescharacteristic
81C11×C4⋊C4C2311yescharacteristic
82C11×C4⋊C4C2311yescharacteristic
83C11×C22⋊C4—21no—
84C11×C22⋊C4—21no—
85C42×C11—21no—
86C22⋊Dic11—21no—
87(C2×D11)⋊C4—21no—
88(C2×D11)⋊C4—21no—
89(C2×D11)⋊C4—21no—
90(C2×D11)⋊C4—21no—
91(C2×D11)⋊C4—21no—
92C4⋊Dic11—21no—
93C4⋊Dic11—21no—
94C4⋊Dic11C2311yescharacteristic
95C4⋊Dic11C2311yescharacteristic
96C4⋊Dic11C2311yescharacteristic
97Dic11⋊C4—21no—
98Dic11⋊C4—21no—
99Dic11⋊C4—21no—
100Dic11⋊C4—21no—
101C4×Dic11—21no—
102C4×Dic11—21no—
103C4×Dic11—21no—
104C2×C11⋊C8C2311yescharacteristic
105C2×C11⋊C8C2311yescharacteristic
106#4313—22no—
107C8×D11—22no—
108#3097—111nomaximal, Sylow
109C23×C11C2×D411yescharacteristic
110C22×D11C2×D411yescharacteristic
111C22×D11C2×D411yescharacteristic
112Q8×C11—21no—
113Q8×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—21no—
119C2×C4×C11—21no—
120C2×C4×C11C2×D411yescharacteristic
121C2×C4×C11C2411yescharacteristic
122C22⋊D11—22no—
123C22⋊D11—22no—
124C2×Dic11—21no—
125C2×Dic11—21no—
126C2×Dic11—21no—
127C2×Dic11—21no—
128C2×Dic11—81no—
129C2×Dic11C2×D411yescharacteristic
130C2×Dic11C2×D411yescharacteristic
131D44—22no—
132C4×D11—21no—
133C4×D11—21no—
134C4×D11—42no—
135C4×D11—81no—
136C4×D11—81no—
137C4×D11#4112yes—
138C4×D11#4112yes—
139Dic22—22no—
140Dic22—21no—
141Dic22—21no—
142Dic22—42no—
143C8×C11—21no—
144C8×C11—21no—
145C11⋊C8—21no—
146C11⋊C8—21no—
147#536—111no—
148#520—111no—
149#485—111no—
150#485—111no—
151#485—111no—
152#485D1111yescharacteristic, complemented
153#484—111no—
154#484—111no—
155#483—111no—
156#483—111no—
157#428—111no—
158#427—111no—
159#419—111no—
160C2×#103—111no—
161#408—111no—
162C22×C11—21no—
163C22×C11—21no—
164C22×C11—21no—
165C22×C11C22×D411yescharacteristic
166C2×D11—21no—
167C2×D11—21no—
168C2×D11—21no—
169C2×D11—21no—
170C2×D11—21no—
171C2×D11#12312yes—
172C4×C11—21no—
173C4×C11—41no—
174C4×C11—41no—
175C4×C11—41no—
176C4×C11—41no—
177C4×C11C2×#4111yescharacteristic
178C4×C11C2×#4111yescharacteristic
179Dic11—21no—
180Dic11—41no—
181Dic11—41no—
182Dic11—41no—
183Dic11—41no—
184Dic11#12312yes—
185C2×#41—111no—
186C22×Q8—111no—
187C2×M16—111no—
188C22×C8—111no—
189C4⋊Q8—221no—
190#124—221no—
191#123—221no—
192#123—221no—
193C22⋊Q8—111no—
194C22⋊Q8—111no—
195C22⋊Q8—111no—
196C22⋊Q8C2×D1111yescharacteristic
197C4×Q8—221no—
198C4×D4—221no—
199C4×D4—221no—
200C4×D4—221no—
201#117—111no—
202#117—111no—
203#117—111no—
204#117C2×D1111yescharacteristic
205C2×C4⋊C4—111no—
206C2×C4⋊C4—111no—
207C2×C4⋊C4—111no—
208#107—111no—
209#107—111no—
210#107—111no—
211#107C2×D1111yescharacteristic
212#106—111no—
213#106—111no—
214#106—111no—
215#106C2×D1111yescharacteristic
216#103—111no—
217#103—111no—
218#103—111no—
219#103—111no—
220#103—111no—
221#103—111no—
222#103C2×D1111yescharacteristic
223#103C2×D1111yescharacteristic
224C22⋊C8—111no—
225C22⋊C8—111no—
226C22⋊C8—111no—
227C22⋊C8C2×D1111yescharacteristic
228C2×C11—41no—
229C2×C11C2×#12311yescharacteristic
230C2×C11#57711yescharacteristic
231C2×C11#57811yescharacteristic
232D11—22no—
233D11—41no—
234#41—222no—
235#41—222no—
236C2×Q8—111no—
237C2×Q8—111no—
238C2×Q8—221no—
239C2×Q8—222no—
240C2×Q8—222no—
241C2×Q8C22×D1111yescharacteristic
242C2×D4—111no—
243C2×D4—111no—
244C2×D4—111no—
245C22×C4—111no—
246C22×C4—111no—
247C22×C4—221no—
248C22×C4—221no—
249C22×C4—221no—
250C22×C4—221no—
251C22×C4C22×D1111yescharacteristic
252M16—222no—
253C2×C8—111no—
254C2×C8—111no—
255C2×C8—222no—
256C2×C8C22×D1111yescharacteristic
257C2×C8C22×D1111yescharacteristic
258C4⋊C4—21no—
259C4⋊C4—111no—
260C4⋊C4—111no—
261C4⋊C4—111no—
262C4⋊C4—221no—
263C4⋊C4—221no—
264C4⋊C4—221no—
265C4⋊C4—221no—
266C4⋊C4—221no—
267C4⋊C4—221no—
268C4⋊C4C22×D1111yescharacteristic
269C4⋊C4C22×D1111yescharacteristic
270C4⋊C4C22×D1111yescharacteristic
271C22⋊C4—21no—
272C22⋊C4—21no—
273C22⋊C4—221no—
274C22⋊C4—221no—
275C22⋊C4—221no—
276C22⋊C4—221no—
277C22⋊C4—221no—
278C22⋊C4—221no—
279C42—21no—
280C42—221no—
281C42—221no—
282C42—221no—
283C11#309711yescharacteristic, complemented, Sylow
284C23—111no—
285C23—111no—
286C23D4×D1111yescharacteristic
287Q8—21no—
288Q8—21no—
289Q8—222no—
290Q8—221no—
291Q8—221no—
292Q8—442no—
293D4—222no—
294D4—222no—
295D4—222no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—111no—
303C2×C4—112no—
304C2×C4—112no—
305C2×C4—111no—
306C2×C4—221no—
307C2×C4—221no—
308C2×C4—221no—
309C2×C4—221no—
310C2×C4—221no—
311C2×C4—221no—
312C2×C4—442no—
313C2×C4—881no—
314C2×C4—881no—
315C2×C4—881no—
316C2×C4D4×D1111yescharacteristic
317C2×C4C23×D1111yescharacteristic
318C8—21no—
319C8—21no—
320C8—221no—
321C8—221no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—112no—
326C22—221no—
327C22—221no—
328C22—221no—
329C22—221no—
330C22—221no—
331C22C2×D4×D1111yescharacteristic
332C4—21no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—112no—
338C4—221no—
339C4—441no—
340C4—441no—
341C4—441no—
342C4—441no—
343C4#41×D1111yescharacteristic
344C4#41×D1111yescharacteristic
345C2—41no—
346C2—222no—
347C2—441no—
348C2D11×#12311yescharacteristic
349C2#1062330211yescharacteristic
350C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#485C2
socleC22×C11C22×D4
prime radicalC2×#4339C22
hypercenter#485D11
hypocenterC11#3097
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. C11×#485C2semidirect
4. #10622656C2semidirect
5. #10622609C2semidirect
6. #10622501C2semidirect
7. #10622493C2semidirect
8. #10622475C2semidirect
9. #10622474C2semidirect
10. #10622427C2semidirect
11. #10622422C2semidirect
12. #10622415C2semidirect
13. D11×#103C2semidirect
15. #10622335C2semidirect
152. #485D11semidirect
283. C11#3097semidirect

Maximal subgroups

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

subgroupindex
#106231592
#106230542
C11×#4852
#106226562
#106226092
#106225012
#106224932
#106224752
#106224742
#106224272
#106224222
#106224152
D11×#1032
#106223402
#106223352
#309711