Finite Group Databasebeta

← #13080296

Subgroups — #13080296

Order 1408.

526 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66969C211yesmaximal, characteristic, complemented
2C2×D8×D11C211yesmaximal, characteristic, complemented
3#10623207C211yesmaximal, characteristic, complemented
4#10623085C211yesmaximal, characteristic, complemented
5C11×#463C211yesmaximal, characteristic, complemented
6#10622782C211yesmaximal, characteristic, complemented
7#10622771C211yesmaximal, characteristic, complemented
8#10622672C211yesmaximal, characteristic, complemented
9C4×#4323C211yesmaximal, characteristic, complemented
10#10622457C211yesmaximal, characteristic, complemented
11#10622447C211yesmaximal, characteristic, complemented
12#10622426C211yesmaximal, characteristic, complemented
13#10622424C211yesmaximal, characteristic, complemented
14#10622389C211yesmaximal, characteristic, complemented
15#10622388C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic, complemented
17C2×#4341C2211yescharacteristic, complemented
18C2×D4×D11C2211yescharacteristic
19C2×D4×D11C2211yescharacteristic
20C2×C11×SD16C2211yescharacteristic, complemented
21C2×C11×D8C2211yescharacteristic
22C11×#124C2211yescharacteristic, complemented
23C4×D4×C11C2211yescharacteristic, complemented
24#66999C2211yescharacteristic
25C2×#4326C2211yescharacteristic, complemented
26C2×#4325C2211yescharacteristic, complemented
27#66991C2211yescharacteristic, complemented
28C2×#4324C2211yescharacteristic, complemented
29C2×#4323C2211yescharacteristic
30C2×#4323C2211yescharacteristic
31#66983—21no—
32C2×(C2×D11)⋊C4—21no—
33#66969—24no—
34D8×D11—24no—
35C2×D88C2211yescharacteristic
36C2×#4314C2211yescharacteristic, complemented
37C2×C8×D11C2211yescharacteristic
38C2×C8×D11C2211yescharacteristic, complemented
39#66950C2211yescharacteristic
40#66948C2211yescharacteristic, complemented
41#66939—21no—
42#66937—21no—
43#66936—21no—
44#66935—21no—
45#66935—21no—
46C22⋊C4×D11—21no—
47#66928C2211yescharacteristic, complemented
48C4×D44C2211yescharacteristic
49C4×D44C2211yescharacteristic, complemented
50C11×C4⋊C8C2211yescharacteristic, complemented
51C11×#103C2211yescharacteristic, complemented
52C11×#102C2211yescharacteristic, complemented
53#66896C2211yescharacteristic, complemented
54#66885C2211yescharacteristic, complemented
55(C2×D11)⋊C8C2211yescharacteristic
56(C2×D11)⋊C8C2211yescharacteristic, complemented
57#66880C2211yescharacteristic, complemented
58#66873C2211yescharacteristic, complemented
59#66871C2211yescharacteristic, complemented
60C4×C11⋊C8C2211yescharacteristic, complemented
61C23×D11—21no—
62C23×D11—21no—
63C2×Q8×C11C2311yescharacteristic
64C2×D4×C11C2311yescharacteristic
65C2×D4×C11C2311yescharacteristic
66C22×C4×C11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11—21no—
71C22×Dic11—21no—
72#4343—22no—
73#4343—41no—
74#4341—22no—
75#4341—41no—
76D4×D11—22no—
77D4×D11—22no—
78D4×D11—41no—
79D4×D11—41no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44D411yescharacteristic
83C2×D44C2311yescharacteristic
84C2×D44C2311yescharacteristic
85C2×C4×D11—21no—
86C2×C4×D11—21no—
87C2×C4×D11C2311yescharacteristic
88C2×C4×D11C2311yescharacteristic
89C2×Dic22C2311yescharacteristic
90C11×SD16—22no—
91C11×D8—22no—
92C2×C8×C11C2311yescharacteristic
93C2×C8×C11C2311yescharacteristic
94C11×C4⋊C4C2311yescharacteristic
95C11×C22⋊C4—21no—
96C11×C22⋊C4—21no—
97C11×C22⋊C4—21no—
98C42×C11C2311yescharacteristic
99C22⋊Dic11—21no—
100#4326—22no—
101#4325—41no—
102#4324—41no—
103#4323—22no—
104#4323D414yescomplemented
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)⋊C4—21no—
111(C2×D11)⋊C4D411yescharacteristic
112(C2×D11)⋊C4D411yescharacteristic
113C4⋊Dic11—21no—
114C4⋊Dic11D411yescharacteristic
115C4⋊Dic11C2311yescharacteristic
116Dic11⋊C4—21no—
117C2×C11⋊C8C2311yescharacteristic
118C2×C11⋊C8C2311yescharacteristic
119D88—22no—
120#4314—22no—
121C8×D11—22no—
122C8×D11—22no—
123#3280—111nomaximal, Sylow
124C23×C11—21no—
125C23×C11—21no—
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—42no—
131C22×D11—42no—
132C22×D11—81no—
133C22×D11—81no—
134C22×D11C2×D411yescharacteristic
135C22×D11C2×D411yescharacteristic
136Q8×C11—21no—
137Q8×C11—21no—
138D4×C11—21no—
139D4×C11—21no—
140D4×C11—21no—
141D4×C11C2×D412yes—
142C2×C4×C11—21no—
143C2×C4×C11—21no—
144C2×C4×C11—81no—
145C2×C4×C11C2×D411yescharacteristic
146C2×C4×C11C2×D411yescharacteristic
147C2×C4×C11C2411yescharacteristic
148C22⋊D11—42no—
149C22⋊D11—42no—
150C22⋊D11—42no—
151C22⋊D11—81no—
152C2×Dic11—21no—
153C2×Dic11—21no—
154C2×Dic11—42no—
155C2×Dic11C2×D411yescharacteristic
156C2×Dic11C2×D411yescharacteristic
157D44—22no—
158D44—21no—
159D44—21no—
160D44—21no—
161D44—42no—
162D44—81no—
163D44C2×D412yes—
164C4×D11—21no—
165C4×D11—21no—
166C4×D11—21no—
167C4×D11—21no—
168C4×D11—42no—
169C4×D11—81no—
170Dic22—21no—
171Dic22—21no—
172C8×C11—21no—
173C8×C11—21no—
174C11⋊C8—21no—
175C11⋊C8C2×D412yes—
176C2×#135—111no—
177C22×D8—111no—
178#546—111no—
179#546—111no—
180#495—111no—
181#467—111no—
182#466—111no—
183#463—111no—
184#463D1111yescharacteristic, complemented
185#450—111no—
186#450—111no—
187#449—111no—
188#449—111no—
189C4×D8—111no—
190C8×D4—111no—
191C22×C11—22no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11—41no—
195C22×C11—41no—
196C22×C11—41no—
197C22×C11C22×D411yescharacteristic
198C2×D11—21no—
199C2×D11—21no—
200C2×D11—22no—
201C2×D11—21no—
202C2×D11—21no—
203C2×D11—21no—
204C2×D11—41no—
205C2×D11—41no—
206C2×D11—41no—
207C2×D11—41no—
208C2×D11—41no—
209C2×D11—84no—
210C2×D11—84no—
211C2×D11#13512yescomplemented
212C4×C11—21no—
213C4×C11—21no—
214C4×C11—41no—
215C4×C11—41no—
216C4×C11C22×D411yescharacteristic
217C4×C11H(5,𝔽2)11yescharacteristic
218Dic11—21no—
219Dic11—21no—
220Dic11—41no—
221Dic11—41no—
222C2×#41—111no—
223C2×#41—111no—
224C22×D4—111no—
225C22×D4—111no—
226#135—224no—
227C2×Q16—111no—
228C2×SD16—111no—
229C2×SD16—111no—
230C2×SD16—111no—
231C2×SD16C2×D1111yescharacteristic, complemented
232C2×D8—111no—
233C2×D8—111no—
234C2×D8—111no—
235C2×D8—224no—
236C2×D8C2×D1111yescharacteristic
237C22×C8—111no—
238C22×C8—111no—
239#124—111no—
240#124C2×D1111yescharacteristic, complemented
241#123—221no—
242#123—221no—
243C22⋊Q8—111no—
244C22⋊Q8—111no—
245#121—111no—
246#121—111no—
247#121—221no—
248#121—221no—
249#120—221no—
250#120—221no—
251C4×D4—111no—
252C4×D4—111no—
253C4×D4C2×D1111yescharacteristic, complemented
254C2×C22⋊C4—221no—
255C2×C22⋊C4—221no—
256#107—111no—
257C4⋊C8C2×D1111yescharacteristic, complemented
258#103—111no—
259#103C2×D1111yescharacteristic, complemented
260#102—111no—
261#102—111no—
262#102—111no—
263#102C2×D1111yescharacteristic, complemented
264C22⋊C8—111no—
265C22⋊C8—111no—
266C4×C8—111no—
267C2×C11—42no—
268C2×C11—81no—
269C2×C11D4211yescharacteristic
270C2×C11C2×#13511yescharacteristic
271C2×C11#57611yescharacteristic
272D11—22no—
273D11—41no—
274D11—42no—
275D11—81no—
276C24—221no—
277C24—221no—
278#41—222no—
279#41—222no—
280#41—441no—
281#41—441no—
282C2×Q8—111no—
283C2×Q8C22×D1111yescharacteristic
284C2×D4—111no—
285C2×D4—111no—
286C2×D4—111no—
287C2×D4—221no—
288C2×D4—221no—
289C2×D4—221no—
290C2×D4—221no—
291C2×D4—222no—
292C2×D4—222no—
293C2×D4—221no—
294C2×D4—221no—
295C2×D4—441no—
296C2×D4—441no—
297C2×D4C22×D1111yescharacteristic
298C2×D4C22×D1111yescharacteristic
299C22×C4—21no—
300C22×C4—111no—
301C22×C4—111no—
302C22×C4—221no—
303C22×C4—221no—
304C22×C4—221no—
305Q16—222no—
306SD16—22no—
307SD16—222no—
308SD16—441no—
309SD16—441no—
310D8—22no—
311D8—114no—
312D8—222no—
313D8—222no—
314C2×C8—111no—
315C2×C8—111no—
316C2×C8—222no—
317C2×C8—222no—
318C2×C8C22×D1111yescharacteristic
319C2×C8C22×D1111yescharacteristic
320C4⋊C4—111no—
321C4⋊C4—111no—
322C4⋊C4—221no—
323C4⋊C4—221no—
324C4⋊C4C22×D1111yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—111no—
329C22⋊C4—111no—
330C22⋊C4—221no—
331C22⋊C4—221no—
332C22⋊C4—221no—
333C22⋊C4—221no—
334C22⋊C4—221no—
335C22⋊C4—221no—
336C22⋊C4—221no—
337C42C22×D1111yescharacteristic
338C11#328011yescharacteristic, complemented, Sylow
339C23—21no—
340C23—21no—
341C23—111no—
342C23—111no—
343C23—221no—
344C23—221no—
345C23—442no—
346C23—442no—
347C23—442no—
348C23—442no—
349C23—881no—
350C23—881no—
351Q8—21no—
352Q8—21no—
353Q8—221no—
354Q8—221no—
355D4—21no—
356D4—21no—
357D4—21no—
358D4—112no—
359D4—222no—
360D4—221no—
361D4—221no—
362D4—221no—
363D4—442no—
364D4—442no—
365D4—442no—
366D4—442no—
367D4—881no—
368D4—881no—
369D4D4×D1112yes—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—81no—
373C2×C4—111no—
374C2×C4—111no—
375C2×C4—221no—
376C2×C4—221no—
377C2×C4—221no—
378C2×C4—221no—
379C2×C4—221no—
380C2×C4—221no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4—881no—
384C2×C4D4×D1111yescharacteristic
385C2×C4D4×D1111yescharacteristic
386C2×C4C23×D1111yescharacteristic
387C8—21no—
388C8—21no—
389C8—112no—
390C8—221no—
391C22—22no—
392C22—41no—
393C22—41no—
394C22—41no—
395C22—41no—
396C22—41no—
397C22—112no—
398C22—221no—
399C22—221no—
400C22—221no—
401C22—221no—
402C22—221no—
403C22—222no—
404C22—441no—
405C22—441no—
406C22—441no—
407C22—441no—
408C22—441no—
409C22—884no—
410C22—884no—
411C22C2×D4×D1111yescharacteristic
412C4—21no—
413C4—21no—
414C4—41no—
415C4—41no—
416C4—221no—
417C4—221no—
418C4—441no—
419C4—441no—
420C4C2×D4×D1111yescharacteristic
421C4#6704211yescharacteristic
422C2—42no—
423C2—81no—
424C2—222no—
425C2—441no—
426C2—442no—
427C2—881no—
428C2#1062314011yescharacteristic
429C2D11×#13511yescharacteristic
430C2#1062330511yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#463C2
socleC22×C11C22×D4
hypercenter#463D11
hypocenterC11#3280
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#66969C2semidirect
2. C2×D8×D11C2semidirect
3. #10623207C2semidirect
4. #10623085C2semidirect
5. C11×#463C2semidirect
6. #10622782C2semidirect
7. #10622771C2semidirect
8. #10622672C2semidirect
9. C4×#4323C2semidirect
10. #10622457C2semidirect
11. #10622447C2semidirect
12. #10622426C2semidirect
13. #10622424C2semidirect
14. #10622389C2semidirect
15. #10622388C2semidirect
16. C2×#4343C22semidirect
17. C2×#4341C22semidirect
20. C2×C11×SD16C22semidirect
22. C11×#124C22semidirect
23. C4×D4×C11C22semidirect
25. C2×#4326C22semidirect
26. C2×#4325C22semidirect
27. #66991C22semidirect
28. C2×#4324C22semidirect
36. C2×#4314C22semidirect
38. C2×C8×D11C22semidirect
40. #66948C22semidirect
47. #66928C22semidirect
49. C4×D44C22semidirect
50. C11×C4⋊C8C22semidirect
51. C11×#103C22semidirect
52. C11×#102C22semidirect
53. #66896C22semidirect
54. #66885C22semidirect
56. (C2×D11)⋊C8C22semidirect
57. #66880C22semidirect
58. #66873C22semidirect
59. #66871C22semidirect
60. C4×C11⋊C8C22semidirect
104. #4323D4semidirect
184. #463D11semidirect
211. C2×D11#135semidirect
231. C2×SD16C2×D11semidirect
240. #124C2×D11semidirect
253. C4×D4C2×D11semidirect
257. C4⋊C8C2×D11semidirect
259. #103C2×D11semidirect
263. #102C2×D11semidirect
338. C11#3280semidirect

Maximal subgroups

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

subgroupindex
C2×#669692
C2×D8×D112
#106232072
#106230852
C11×#4632
#106227822
#106227712
#106226722
C4×#43232
#106224572
#106224472
#106224262
#106224242
#106223892
#106223882
#328011