Finite Group Databasebeta

← #13080321

Subgroups — #13080321

Order 1408.

504 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623360C211yesmaximal, characteristic, complemented
2C2×#67003C211yesmaximal, characteristic, complemented
3C2×SD16×D11C211yesmaximal, characteristic, complemented
4#10623164C211yesmaximal, characteristic, complemented
5C11×#452C211yesmaximal, characteristic, complemented
6#10622804C211yesmaximal, characteristic, complemented
7#10622799C211yesmaximal, characteristic, complemented
8#10622778C211yesmaximal, characteristic, complemented
9#10622661C211yesmaximal, characteristic, complemented
10#10622420C211yesmaximal, characteristic, complemented
11#10622411C211yesmaximal, characteristic, complemented
12#10622386C211yesmaximal, characteristic, complemented
13#10622371C211yesmaximal, characteristic, complemented
14#10622347C211yesmaximal, characteristic, complemented
15(C22⋊D11)⋊C8C211yesmaximal, characteristic, complemented
16C2×C11×#41C2211yescharacteristic
17C2×Q8×D11C2211yescharacteristic
18C2×D4×D11C2211yescharacteristic
19C2×#4339C2211yescharacteristic, complemented
20C2×C11×Q16C2211yescharacteristic, complemented
21C2×C11×SD16C2211yescharacteristic
22C11×C22⋊Q8C2211yescharacteristic, complemented
23#67003—24no—
24#67000C2211yescharacteristic
25#67000C2211yescharacteristic, complemented
26#66999C2211yescharacteristic
27C2×#4326C2211yescharacteristic, complemented
28C2×#4325C2211yescharacteristic
29C2×#4325C2211yescharacteristic, complemented
30#66992—21no—
31#66990—21no—
32D4×Dic11C2211yescharacteristic
33C2×#4324C2211yescharacteristic
34C2×#4323C2211yescharacteristic
35#66983C2211yescharacteristic
36#66982—21no—
37C4×C22⋊D11C2211yescharacteristic
38C2×(C2×D11)⋊C4—21no—
39C22×C11⋊C8C2211yescharacteristic, complemented
40SD16×D11—24no—
41C2×D88C2211yescharacteristic
42C2×#4314C2211yescharacteristic
43C2×C8×D11C2211yescharacteristic
44#66949—21no—
45#66948C2211yescharacteristic
46#66946—21no—
47#66940C2211yescharacteristic, complemented
48#66938—21no—
49#66937—21no—
50C11×#103C2211yescharacteristic, complemented
51C11×#102C2211yescharacteristic
52C11×C22⋊C8C2211yescharacteristic, complemented
53#66899C2211yescharacteristic, complemented
54#66885C2211yescharacteristic, complemented
55(C2×D11)⋊C8C2211yescharacteristic
56#66880C2211yescharacteristic, complemented
57Dic11⋊C8C2211yescharacteristic, complemented
58C8×Dic11C2211yescharacteristic, complemented
59#66873C2211yescharacteristic
60#66872C2211yescharacteristic, complemented
61C23×D11—21no—
62C11×#41—22no—
63C11×#41—41no—
64C2×Q8×C11C2311yescharacteristic
65C2×Q8×C11C2311yescharacteristic
66C2×D4×C11—21no—
67C2×D4×C11C2311yescharacteristic
68C22×C4×C11—21no—
69C22×C4×C11C2311yescharacteristic
70C2×C22⋊D11—21no—
71C2×C22⋊D11—21no—
72C2×C22⋊D11—21no—
73C2×C22⋊D11D411yescharacteristic
74C22×Dic11—21no—
75Q8×D11—22no—
76Q8×D11—41no—
77D4×D11—22no—
78D4×D11—41no—
79#4339—22no—
80#4339—41no—
81C2×D44—21no—
82C2×D44C2311yescharacteristic
83C2×D44C2311yescharacteristic
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11C2311yescharacteristic
87C2×Dic22—21no—
88C2×Dic22C2311yescharacteristic
89C11×Q16—41no—
90C11×SD16—22no—
91C2×C8×C11C2311yescharacteristic
92C2×C8×C11C2311yescharacteristic
93C11×C4⋊C4—21no—
94C11×C4⋊C4C2311yescharacteristic
95C11×C22⋊C4—21no—
96C22⋊Dic11—21no—
97C22⋊Dic11D411yescharacteristic
98#4326—22no—
99#4325—22no—
100#4325—22no—
101#4324D414yescomplemented
102#4323—22no—
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105(C2×D11)⋊C4—21no—
106(C2×D11)⋊C4—21no—
107(C2×D11)⋊C4—21no—
108(C2×D11)⋊C4—21no—
109(C2×D11)⋊C4—21no—
110(C2×D11)⋊C4D411yescharacteristic
111C4⋊Dic11C2311yescharacteristic
112Dic11⋊C4—21no—
113Dic11⋊C4—21no—
114Dic11⋊C4D411yescharacteristic
115C4×Dic11—21no—
116C4×Dic11C2311yescharacteristic
117C2×C11⋊C8—22no—
118C2×C11⋊C8C2311yescharacteristic
119C2×C11⋊C8C2311yescharacteristic
120D88—41no—
121#4314—22no—
122C8×D11—22no—
123#3282—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11C2×D411yescharacteristic
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—81no—
131C22×D11C2×D411yescharacteristic
132Q8×C11—21no—
133Q8×C11—21no—
134Q8×C11—21no—
135Q8×C11—21no—
136D4×C11—21no—
137D4×C11—42no—
138D4×C11C2×D412yes—
139C2×C4×C11—21no—
140C2×C4×C11—21no—
141C2×C4×C11—21no—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—42no—
145C2×C4×C11C2×D411yescharacteristic
146C2×C4×C11C2411yescharacteristic
147C22⋊D11—22no—
148C22⋊D11—42no—
149C22⋊D11—42no—
150C22⋊D11—81no—
151C2×Dic11—21no—
152C2×Dic11—21no—
153C2×Dic11—81no—
154C2×Dic11C2×D411yescharacteristic
155C2×Dic11C2×D411yescharacteristic
156C2×Dic11C2×D411yescharacteristic
157D44—21no—
158D44—21no—
159D44—21no—
160D44—21no—
161D44—42no—
162C4×D11—21no—
163C4×D11—21no—
164C4×D11—42no—
165C4×D11—42no—
166Dic22—21no—
167Dic22—42no—
168Dic22C2×D412yes—
169C8×C11—21no—
170C8×C11—21no—
171C11⋊C8—21no—
172C11⋊C8C2×D412yes—
173C2×#135—111no—
174C22×SD16—111no—
175#548—111no—
176#546—111no—
177#495—111no—
178#465—111no—
179#465—111no—
180#464—111no—
181#463—111no—
182#452D1111yescharacteristic, complemented
183#451—111no—
184#449—111no—
185#447—111no—
186C4×SD16—111no—
187C8×D4—111no—
188C22×C11—21no—
189C22×C11—22no—
190C22×C11—21no—
191C22×C11—21no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11C22×D411yescharacteristic
195C2×D11—21no—
196C2×D11—21no—
197C2×D11—41no—
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—41no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—84no—
204C2×D11#13512yescomplemented
205C4×C11—21no—
206C4×C11—41no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11C22×D411yescharacteristic
210C4×C11H(5,𝔽2)11yescharacteristic
211Dic11—22no—
212Dic11—21no—
213Dic11—21no—
214Dic11—21no—
215Dic11—41no—
216C2×#41—111no—
217C2×#41C2×D1111yescharacteristic
218C22×Q8—111no—
219C22×D4—111no—
220#135—224no—
221C2×Q16—111no—
222C2×Q16C2×D1111yescharacteristic, complemented
223C2×SD16—111no—
224C2×SD16—111no—
225C2×SD16—111no—
226C2×SD16—111no—
227C2×SD16—224no—
228C2×SD16C2×D1111yescharacteristic
229C2×D8—111no—
230C2×D8—111no—
231C22×C8—111no—
232C22×C8—111no—
233#124—111no—
234#124—111no—
235#124—221no—
236#123—221no—
237C22⋊Q8—111no—
238C22⋊Q8—221no—
239C22⋊Q8C2×D1111yescharacteristic, complemented
240#121—111no—
241#121—111no—
242#121—221no—
243#121—221no—
244#120—221no—
245C4×Q8—111no—
246C4×D4—111no—
247C4×D4—111no—
248C4×D4—221no—
249C2×C22⋊C4—221no—
250#106—111no—
251C4⋊C8—111no—
252#103—111no—
253#103—111no—
254#103C2×D1111yescharacteristic, complemented
255#102—111no—
256#102—111no—
257#102C2×D1111yescharacteristic
258C22⋊C8—111no—
259C22⋊C8C2×D1111yescharacteristic, complemented
260C4×C8—111no—
261C2×C11—42no—
262C2×C11—41no—
263C2×C11D4211yescharacteristic
264C2×C11C2×#13511yescharacteristic
265C2×C11#57711yescharacteristic
266D11—22no—
267D11—81no—
268D11—81no—
269C24—221no—
270#41—22no—
271#41—41no—
272#41—222no—
273#41—441no—
274C2×Q8—111no—
275C2×Q8—221no—
276C2×Q8—222no—
277C2×Q8—441no—
278C2×Q8C22×D1111yescharacteristic
279C2×Q8C22×D1111yescharacteristic
280C2×D4—21no—
281C2×D4—111no—
282C2×D4—111no—
283C2×D4—111no—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—222no—
287C2×D4—221no—
288C2×D4—221no—
289C2×D4—441no—
290C2×D4C22×D1111yescharacteristic
291C22×C4—21no—
292C22×C4—111no—
293C22×C4—221no—
294C22×C4—221no—
295C22×C4—221no—
296C22×C4C22×D1111yescharacteristic
297Q16—41no—
298Q16—222no—
299SD16—22no—
300SD16—114no—
301SD16—222no—
302SD16—222no—
303SD16—222no—
304D8—222no—
305D8—441no—
306C2×C8—111no—
307C2×C8—111no—
308C2×C8—222no—
309C2×C8—222no—
310C2×C8C22×D1111yescharacteristic
311C2×C8C22×D1111yescharacteristic
312C4⋊C4—21no—
313C4⋊C4—111no—
314C4⋊C4—111no—
315C4⋊C4—221no—
316C4⋊C4—221no—
317C4⋊C4C22×D1111yescharacteristic
318C22⋊C4—21no—
319C22⋊C4—111no—
320C22⋊C4—111no—
321C22⋊C4—221no—
322C22⋊C4—221no—
323C22⋊C4—221no—
324C22⋊C4—221no—
325C22⋊C4—221no—
326C22⋊C4—221no—
327C22⋊C4—221no—
328C22⋊C4—221no—
329C42—111no—
330C42—221no—
331C11#328211yescharacteristic, complemented, Sylow
332C23—21no—
333C23—111no—
334C23—221no—
335C23—221no—
336C23—442no—
337C23—442no—
338C23—881no—
339C23D4×D1111yescharacteristic
340Q8—21no—
341Q8—21no—
342Q8—21no—
343Q8—21no—
344Q8—112no—
345Q8—221no—
346Q8—442no—
347D4—21no—
348D4—42no—
349D4—222no—
350D4—221no—
351D4—221no—
352D4—221no—
353D4—221no—
354D4—442no—
355D4—442no—
356D4—442no—
357D4—881no—
358D4D4×D1112yes—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—42no—
365C2×C4—111no—
366C2×C4—111no—
367C2×C4—111no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—442no—
373C2×C4—442no—
374C2×C4—881no—
375C2×C4D4×D1111yescharacteristic
376C2×C4C23×D1111yescharacteristic
377C8—21no—
378C8—21no—
379C8—112no—
380C8—221no—
381C22—21no—
382C22—21no—
383C22—21no—
384C22—22no—
385C22—41no—
386C22—41no—
387C22—112no—
388C22—221no—
389C22—221no—
390C22—441no—
391C22—441no—
392C22—441no—
393C22—441no—
394C22—441no—
395C22—441no—
396C22—884no—
397C22C2×D4×D1111yescharacteristic
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—221no—
403C4—221no—
404C4—221no—
405C4—222no—
406C4—441no—
407C4C2×D4×D1111yescharacteristic
408C4#6703711yescharacteristic
409C2—41no—
410C2—42no—
411C2—222no—
412C2—881no—
413C2—881no—
414C2#1062312111yescharacteristic
415C2D11×#13511yescharacteristic
416C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#452C2
socleC22×C11C22×D4
hypercenter#452D11
hypocenterC11#3282
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. #10623360C2semidirect
2. C2×#67003C2semidirect
3. C2×SD16×D11C2semidirect
4. #10623164C2semidirect
5. C11×#452C2semidirect
6. #10622804C2semidirect
7. #10622799C2semidirect
8. #10622778C2semidirect
9. #10622661C2semidirect
10. #10622420C2semidirect
11. #10622411C2semidirect
12. #10622386C2semidirect
13. #10622371C2semidirect
14. #10622347C2semidirect
15. (C22⋊D11)⋊C8C2semidirect
19. C2×#4339C22semidirect
20. C2×C11×Q16C22semidirect
22. C11×C22⋊Q8C22semidirect
25. #67000C22semidirect
27. C2×#4326C22semidirect
29. C2×#4325C22semidirect
39. C22×C11⋊C8C22semidirect
47. #66940C22semidirect
50. C11×#103C22semidirect
52. C11×C22⋊C8C22semidirect
53. #66899C22semidirect
54. #66885C22semidirect
56. #66880C22semidirect
57. Dic11⋊C8C22semidirect
58. C8×Dic11C22semidirect
60. #66872C22semidirect
101. #4324D4semidirect
182. #452D11semidirect
204. C2×D11#135semidirect
222. C2×Q16C2×D11semidirect
239. C22⋊Q8C2×D11semidirect
254. #103C2×D11semidirect
259. C22⋊C8C2×D11semidirect
331. C11#3282semidirect

Maximal subgroups

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

subgroupindex
#106233602
C2×#670032
C2×SD16×D112
#106231642
C11×#4522
#106228042
#106227992
#106227782
#106226612
#106224202
#106224112
#106223862
#106223712
#106223472
(C22⋊D11)⋊C82
#328211