Finite Group Databasebeta

← #13078291

Subgroups — #13078291

Order 1408.

504 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66967C211yesmaximal, characteristic, complemented
2C2×#66960C211yesmaximal, characteristic, complemented
3#10623160C211yesmaximal, characteristic, complemented
4#10623138C211yesmaximal, characteristic, complemented
5C11×#468C211yesmaximal, characteristic, complemented
6#10622784C211yesmaximal, characteristic, complemented
7#10622748C211yesmaximal, characteristic, complemented
8#10622661C211yesmaximal, characteristic, complemented
9#10622651C211yesmaximal, characteristic, complemented
10#10622496C211yesmaximal, characteristic, complemented
11#10622494C211yesmaximal, characteristic, complemented
12#10622425C211yesmaximal, characteristic, complemented
13#10622417C211yesmaximal, characteristic, complemented
14#10622395C211yesmaximal, characteristic, complemented
15D11×#102C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×D4×D11C2211yescharacteristic
18C2×#4339C2211yescharacteristic
19C2×C11×SD16C2211yescharacteristic
20C2×C11×M16C2211yescharacteristic, complemented
21C11×C22⋊Q8C2211yescharacteristic, complemented
22C11×#121C2211yescharacteristic
23#66999C2211yescharacteristic, complemented
24C2×#4325C2211yescharacteristic
25#66993—21no—
26#66991C2211yescharacteristic
27#66990—21no—
28C2×#4323C2211yescharacteristic
29#66983C2211yescharacteristic
30#66983C2211yescharacteristic, complemented
31C22×C11⋊C8C2211yescharacteristic, complemented
32#66967—24no—
33#66960—24no—
34C2×D88C2211yescharacteristic
35C2×#4313C2211yescharacteristic
36C2×#4313C2211yescharacteristic, complemented
37C2×C8×D11C2211yescharacteristic
38C2×C8×D11C2211yescharacteristic, complemented
39#66949—21no—
40#66948—21no—
41#66948C2211yescharacteristic
42#66948C2211yescharacteristic, complemented
43#66945C2211yescharacteristic
44C4⋊C4×D11C2211yescharacteristic
45#66938—21no—
46#66937—21no—
47#66937—21no—
48#66935—21no—
49C11×#107C2211yescharacteristic, complemented
50C11×#103C2211yescharacteristic, complemented
51C11×#102C2211yescharacteristic
52#66899C2211yescharacteristic, complemented
53#66896C2211yescharacteristic
54#66885C2211yescharacteristic
55#66885C2211yescharacteristic, complemented
56#66881C2211yescharacteristic, complemented
57#66873C2211yescharacteristic
58#66873C2211yescharacteristic, complemented
59#66872C2211yescharacteristic, complemented
60#66871C2211yescharacteristic, complemented
61C23×D11—21no—
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11—21no—
64C2×D4×C11C2311yescharacteristic
65C22×C4×C11C2311yescharacteristic
66C2×C22⋊D11—21no—
67C2×C22⋊D11—21no—
68C2×C22⋊D11—21no—
69C2×C22⋊D11—21no—
70C2×C22⋊D11D411yescharacteristic
71C2×C22⋊D11D411yescharacteristic
72#4343—22no—
73#4343—22no—
74D4×D11—22no—
75D4×D11—22no—
76#4339—22no—
77#4339—22no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44D411yescharacteristic
82C2×D44C2311yescharacteristic
83C2×D44C2311yescharacteristic
84C2×C4×D11—21no—
85C2×C4×D11—21no—
86C2×C4×D11C2311yescharacteristic
87C2×C4×D11C2311yescharacteristic
88C2×Dic22D411yescharacteristic
89C11×SD16—22no—
90C11×M16—22no—
91C2×C8×C11C2311yescharacteristic
92C2×C8×C11C2311yescharacteristic
93C11×C4⋊C4—21no—
94C11×C4⋊C4C2311yescharacteristic
95C11×C4⋊C4C2311yescharacteristic
96C11×C22⋊C4—21no—
97C11×C22⋊C4—21no—
98C22⋊Dic11—21no—
99#4325—22no—
100#4323—22no—
101(C2×D11)⋊C4—21no—
102(C2×D11)⋊C4—21no—
103(C2×D11)⋊C4—21no—
104(C2×D11)⋊C4—21no—
105(C2×D11)⋊C4—21no—
106(C2×D11)⋊C4—21no—
107C4⋊Dic11C2311yescharacteristic
108C4⋊Dic11C2311yescharacteristic
109Dic11⋊C4—21no—
110Dic11⋊C4—21no—
111C4×Dic11—21no—
112C2×C11⋊C8—22no—
113C2×C11⋊C8C2311yescharacteristic
114C2×C11⋊C8C2311yescharacteristic
115D88—22no—
116#4313—22no—
117#4313D414yescomplemented
118C8×D11—22no—
119C8×D11—22no—
120#3062—111nomaximal, Sylow
121C23×C11—21no—
122C23×C11C2×D411yescharacteristic
123C22×D11—21no—
124C22×D11—21no—
125C22×D11—42no—
126C22×D11—81no—
127C22×D11—81no—
128C22×D11C2×D411yescharacteristic
129C22×D11C2×D411yescharacteristic
130Q8×C11—21no—
131Q8×C11—21no—
132D4×C11—21no—
133D4×C11—21no—
134D4×C11—81no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11C2×D411yescharacteristic
141C2×C4×C11C2411yescharacteristic
142C22⋊D11—22no—
143C22⋊D11—22no—
144C22⋊D11—42no—
145C22⋊D11—81no—
146C22⋊D11—81no—
147C22⋊D11—81no—
148C2×Dic11—21no—
149C2×Dic11—21no—
150C2×Dic11C2×D411yescharacteristic
151C2×Dic11C2×D411yescharacteristic
152D44—22no—
153D44—21no—
154D44—21no—
155D44—21no—
156D44—21no—
157D44—42no—
158D44—81no—
159D44—81no—
160C4×D11—21no—
161C4×D11—21no—
162C4×D11—42no—
163C4×D11—81no—
164C4×D11C2×D412yes—
165C4×D11#4112yes—
166Dic22—22no—
167C8×C11—21no—
168C8×C11C2×D412yes—
169C11⋊C8—21no—
170C11⋊C8C2×D412yes—
171C2×AGL(1,ℤ/8)—111no—
172C2×#131—111no—
173#537—111no—
174#535—111no—
175#469—111no—
176#469—111no—
177#468—111no—
178#468D1111yescharacteristic, complemented
179#466—111no—
180#466—111no—
181#465—111no—
182#465—111no—
183#428—111no—
184#416—111no—
185C2×#102—111no—
186C22×C11—21no—
187C22×C11—21no—
188C22×C11—21no—
189C22×C11—41no—
190C22×C11—41no—
191C22×C11—41no—
192C22×C11C22×D411yescharacteristic
193C2×D11—21no—
194C2×D11—21no—
195C2×D11—21no—
196C2×D11—21no—
197C2×D11—21no—
198C2×D11—41no—
199C2×D11—41no—
200C2×D11—41no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—84no—
205C2×D11#12112yes—
206C4×C11—21no—
207C4×C11—41no—
208C4×C11—41no—
209C4×C11—41no—
210C4×C11C22×D411yescharacteristic
211C4×C11C2×#4111yescharacteristic
212Dic11—21no—
213Dic11—41no—
214Dic11—41no—
215Dic11#12112yes—
216C2×#41—111no—
217C2×#41—111no—
218C22×D4—111no—
219AGL(1,ℤ/8)—224no—
220C2×SD16—111no—
221C2×SD16C2×D1111yescharacteristic
222C2×D8—111no—
223C2×D8—111no—
224#131—224no—
225C2×M16—111no—
226C2×M16—111no—
227C2×M16C2×D1111yescharacteristic, complemented
228C22×C8—111no—
229C22×C8—111no—
230C22×C8—111no—
231#127—221no—
232#124—221no—
233C22⋊Q8—111no—
234C22⋊Q8—221no—
235C22⋊Q8C2×D1111yescharacteristic, complemented
236#121—111no—
237#121—111no—
238#121—111no—
239#121—111no—
240#121—111no—
241#121—221no—
242#121—221no—
243#121—221no—
244#121C2×D1111yescharacteristic
245#120—221no—
246#120—221no—
247#117—111no—
248C2×C4⋊C4—111no—
249#107—111no—
250#107C2×D1111yescharacteristic, complemented
251#106—111no—
252#106—111no—
253#103—111no—
254#103C2×D1111yescharacteristic, complemented
255#102—111no—
256#102—111no—
257#102—111no—
258#102—111no—
259#102—111no—
260#102C2×D1111yescharacteristic
261C2×C11—41no—
262C2×C11—81no—
263C2×C11C2×#12111yescharacteristic
264C2×C11#57611yescharacteristic
265C2×C11#57711yescharacteristic
266D11—22no—
267D11—41no—
268D11—81no—
269D11—81no—
270C24—221no—
271#41—222no—
272#41—222no—
273#41—222no—
274#41—222no—
275C2×Q8—111no—
276C2×Q8C22×D1111yescharacteristic
277C2×D4—21no—
278C2×D4—111no—
279C2×D4—111no—
280C2×D4—111no—
281C2×D4—111no—
282C2×D4—111no—
283C2×D4—221no—
284C2×D4—221no—
285C2×D4—221no—
286C2×D4—222no—
287C2×D4—222no—
288C2×D4—221no—
289C2×D4—221no—
290C2×D4—221no—
291C2×D4—221no—
292C2×D4C22×D1111yescharacteristic
293C22×C4—111no—
294C22×C4—111no—
295C22×C4—221no—
296C22×C4—221no—
297C22×C4C22×D1111yescharacteristic
298SD16—22no—
299SD16—222no—
300D8—222no—
301D8—222no—
302M16—22no—
303M16—114no—
304M16—222no—
305C2×C8—111no—
306C2×C8—111no—
307C2×C8—222no—
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
318C4⋊C4C22×D1111yescharacteristic
319C22⋊C4—21no—
320C22⋊C4—21no—
321C22⋊C4—221no—
322C22⋊C4—221no—
323C22⋊C4—221no—
324C22⋊C4—221no—
325C22⋊C4—221no—
326C22⋊C4—221no—
327C22⋊C4—221no—
328C42—221no—
329C11#306211yescharacteristic, complemented, Sylow
330C23—21no—
331C23—111no—
332C23—111no—
333C23—221no—
334C23—221no—
335C23—442no—
336C23—881no—
337C23—881no—
338C23D4×D1111yescharacteristic
339Q8—21no—
340Q8—21no—
341Q8—222no—
342D4—21no—
343D4—21no—
344D4—81no—
345D4—222no—
346D4—222no—
347D4—222no—
348D4—221no—
349D4—221no—
350D4—221no—
351D4—221no—
352D4—442no—
353D4—442no—
354D4—881no—
355D4—881no—
356D4—881no—
357D4—881no—
358D4—881no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—111no—
365C2×C4—112no—
366C2×C4—112no—
367C2×C4—111no—
368C2×C4—221no—
369C2×C4—221no—
370C2×C4—221no—
371C2×C4—221no—
372C2×C4—442no—
373C2×C4—881no—
374C2×C4D4×D1111yescharacteristic
375C2×C4C23×D1111yescharacteristic
376C8—21no—
377C8—112no—
378C8—221no—
379C8D4×D1112yes—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—112no—
387C22—221no—
388C22—221no—
389C22—221no—
390C22—221no—
391C22—221no—
392C22—441no—
393C22—441no—
394C22—441no—
395C22—441no—
396C22—441no—
397C22—441no—
398C22—884no—
399C22C2×D4×D1111yescharacteristic
400C4—21no—
401C4—41no—
402C4—41no—
403C4—41no—
404C4—112no—
405C4—221no—
406C4—441no—
407C4—441no—
408C4C2×D4×D1111yescharacteristic
409C4#41×D1111yescharacteristic
410C2—41no—
411C2—81no—
412C2—222no—
413C2—441no—
414C2—881no—
415C2—881no—
416C2D11×#12111yescharacteristic
417C2#1062330511yescharacteristic
418C2#1062330911yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#468C2
socleC22×C11C22×D4
hypercenter#468D11
hypocenterC11#3062
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
1. C2×#66967C2semidirect
2. C2×#66960C2semidirect
3. #10623160C2semidirect
4. #10623138C2semidirect
5. C11×#468C2semidirect
6. #10622784C2semidirect
7. #10622748C2semidirect
8. #10622661C2semidirect
9. #10622651C2semidirect
10. #10622496C2semidirect
11. #10622494C2semidirect
12. #10622425C2semidirect
13. #10622417C2semidirect
14. #10622395C2semidirect
15. D11×#102C2semidirect
20. C2×C11×M16C22semidirect
21. C11×C22⋊Q8C22semidirect
23. #66999C22semidirect
30. #66983C22semidirect
31. C22×C11⋊C8C22semidirect
36. C2×#4313C22semidirect
38. C2×C8×D11C22semidirect
42. #66948C22semidirect
49. C11×#107C22semidirect
50. C11×#103C22semidirect
52. #66899C22semidirect
55. #66885C22semidirect
56. #66881C22semidirect
58. #66873C22semidirect
59. #66872C22semidirect
60. #66871C22semidirect
117. #4313D4semidirect
178. #468D11semidirect
227. C2×M16C2×D11semidirect
235. C22⋊Q8C2×D11semidirect
250. #107C2×D11semidirect
254. #103C2×D11semidirect
329. C11#3062semidirect

Maximal subgroups

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

subgroupindex
C2×#669672
C2×#669602
#106231602
#106231382
C11×#4682
#106227842
#106227482
#106226612
#106226512
#106224962
#106224942
#106224252
#106224172
#106223952
D11×#1022
#306211