Finite Group Databasebeta

← #13080158

Subgroups — #13080158

Order 1408.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66969C211yesmaximal, characteristic, complemented
2C2×#66967C211yesmaximal, characteristic, complemented
3#10623108C211yesmaximal, characteristic, complemented
4#10623085C211yesmaximal, characteristic, complemented
5C11×#440C211yesmaximal, characteristic, complemented
6#10622641C211yesmaximal, characteristic, complemented
7#10622628C211yesmaximal, characteristic, complemented
8#10622499C211yesmaximal, characteristic, complemented
9#10622496C211yesmaximal, characteristic, complemented
10#10622424C211yesmaximal, characteristic, complemented
11#10622423C211yesmaximal, characteristic, complemented
12#10622394C211yesmaximal, characteristic, complemented
13#10622386C211yesmaximal, characteristic, complemented
14#10622325C211yesmaximal, characteristic, complemented
15#10622319C211yesmaximal, characteristic, complemented
16C2×#4343C2211yescharacteristic
17C2×#4343C2211yescharacteristic, complemented
18C2×#4341C2211yescharacteristic
19C2×D4×D11C2211yescharacteristic
20C2×C11×SD16C2211yescharacteristic
21C4×Q8×C11C2211yescharacteristic, complemented
22C4×D4×C11C2211yescharacteristic
23C2×#4326C2211yescharacteristic, complemented
24C2×#4325C2211yescharacteristic
25C2×#4323C2211yescharacteristic
26C2×#4323C2211yescharacteristic
27#66983—21no—
28C2×(C2×D11)⋊C4—21no—
29#66969—24no—
30#66967—24no—
31C2×D88C2211yescharacteristic
32C2×D88C2211yescharacteristic
33C2×#4314C2211yescharacteristic, complemented
34C2×#4314C2211yescharacteristic, complemented
35C2×#4313C2211yescharacteristic
36C2×C8×D11C2211yescharacteristic, complemented
37#66950C2211yescharacteristic
38#66948—21no—
39#66948—21no—
40#66948C2211yescharacteristic
41#66948C2211yescharacteristic
42#66948C2211yescharacteristic, complemented
43#66939—21no—
44#66935—21no—
45#66928C2211yescharacteristic
46#66927—21no—
47#66927C2211yescharacteristic, complemented
48C4×D44—21no—
49C4×D44C2211yescharacteristic
50C11×#107C2211yescharacteristic, complemented
51C11×#103C2211yescharacteristic, complemented
52C11×#102C2211yescharacteristic
53C11×#97C2211yescharacteristic, complemented
54(C2×D11)⋊C8C2211yescharacteristic
55(C2×D11)⋊C8C2211yescharacteristic, complemented
56#66874C2211yescharacteristic, complemented
57#66873C2211yescharacteristic
58#66873C2211yescharacteristic, complemented
59#66873C2211yescharacteristic, complemented
60C4⋊(C11⋊C8)C2211yescharacteristic, complemented
61C23×D11—21no—
62C2×Q8×C11C2311yescharacteristic
63C2×D4×C11C2311yescharacteristic
64C22×C4×C11—21no—
65C2×C22⋊D11—21no—
66C2×C22⋊D11—21no—
67C22×Dic11—21no—
68#4343—22no—
69#4343—22no—
70#4343—41no—
71#4343—41no—
72#4341—22no—
73#4341—41no—
74D4×D11—22no—
75D4×D11—41no—
76C2×D44—21no—
77C2×D44—21no—
78C2×D44—21no—
79C2×D44—21no—
80C2×D44—21no—
81C2×D44—21no—
82C2×D44—21no—
83C2×D44D411yescharacteristic
84C2×D44C2311yescharacteristic
85C2×D44C2311yescharacteristic
86C2×D44C2311yescharacteristic
87C2×C4×D11—21no—
88C2×C4×D11—21no—
89C2×C4×D11C2311yescharacteristic
90C2×C4×D11C2311yescharacteristic
91C2×Dic22C2311yescharacteristic
92C11×SD16D414yescomplemented
93C2×C8×C11C2311yescharacteristic
94C2×C8×C11C2311yescharacteristic
95C11×C4⋊C4—21no—
96C11×C4⋊C4C2311yescharacteristic
97C11×C4⋊C4C2311yescharacteristic
98C11×C22⋊C4—21no—
99C42×C11—21no—
100C42×C11C2311yescharacteristic
101#4326—22no—
102#4325—22no—
103#4323—22no—
104#4323—22no—
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
115C2×C11⋊C8C2311yescharacteristic
116C2×C11⋊C8C2311yescharacteristic
117D88—22no—
118D88—41no—
119#4314—22no—
120#4314—41no—
121#4313—22no—
122C8×D11—22no—
123#3268—111nomaximal, Sylow
124C23×C11—21no—
125C22×D11—21no—
126C22×D11—21no—
127C22×D11—21no—
128C22×D11—42no—
129C22×D11—42no—
130C22×D11—81no—
131C22×D11C2×D411yescharacteristic
132C22×D11C2×D411yescharacteristic
133Q8×C11—21no—
134Q8×C11C2×D412yes—
135D4×C11—21no—
136D4×C11C2×D412yes—
137C2×C4×C11—21no—
138C2×C4×C11—21no—
139C2×C4×C11—21no—
140C2×C4×C11—81no—
141C2×C4×C11C2×D411yescharacteristic
142C2×C4×C11C2×D411yescharacteristic
143C2×C4×C11C2411yescharacteristic
144C22⋊D11—42no—
145C22⋊D11—42no—
146C2×Dic11—21no—
147C2×Dic11—42no—
148C2×Dic11C2×D411yescharacteristic
149C2×Dic11C2×D411yescharacteristic
150D44—21no—
151D44—21no—
152D44—21no—
153D44—21no—
154D44—21no—
155D44—21no—
156D44—41no—
157D44—42no—
158D44—42no—
159D44—42no—
160D44—81no—
161D44—81no—
162D44—81no—
163D44—81no—
164C4×D11—21no—
165C4×D11—21no—
166C4×D11—21no—
167C4×D11—21no—
168C4×D11—42no—
169C4×D11—42no—
170Dic22—21no—
171Dic22—21no—
172C8×C11—21no—
173C8×C11C2×D412yes—
174C11⋊C8—21no—
175C11⋊C8—21no—
176C2×AGL(1,ℤ/8)—111no—
177C2×#135—111no—
178#550—111no—
179#546—111no—
180#496—111no—
181#468—111no—
182#466—111no—
183#464—111no—
184#459—111no—
185#452—111no—
186#449—111no—
187#449—111no—
188#447—111no—
189#440D1111yescharacteristic, complemented
190#435—111no—
191C22×C11—22no—
192C22×C11—41no—
193C22×C11—41no—
194C22×C11C22×D411yescharacteristic
195C2×D11—21no—
196C2×D11—21no—
197C2×D11—21no—
198C2×D11—21no—
199C2×D11—21no—
200C2×D11—21no—
201C2×D11—41no—
202C2×D11—41no—
203C2×D11—41no—
204C2×D11—41no—
205C2×D11—41no—
206C2×D11—41no—
207C2×D11—41no—
208C2×D11—41no—
209C2×D11—41no—
210C2×D11—84no—
211C4×C11—22no—
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—
221C2×#41—111no—
222C2×#41—111no—
223C2×#41—111no—
224C22×D4—111no—
225AGL(1,ℤ/8)—224no—
226#135—224no—
227C2×Q16—111no—
228C2×SD16—111no—
229C2×SD16—111no—
230C2×SD16—111no—
231C2×SD16C2×D1111yescharacteristic
232C2×D8—111no—
233C2×D8—111no—
234C2×D8—111no—
235C2×D8—111no—
236C2×M16—111no—
237C22×C8—111no—
238#127—111no—
239#127—221no—
240#124—111no—
241#123—221no—
242C22⋊Q8—111no—
243#121—111no—
244#121—111no—
245#121—111no—
246#121—221no—
247#121—221no—
248#121—221no—
249#120—221no—
250C4×Q8C2×D1111yescharacteristic, complemented
251C4×D4—111no—
252C4×D4—221no—
253C4×D4C2×D1111yescharacteristic
254C2×C22⋊C4—221no—
255#107C2×D1111yescharacteristic, complemented
256C4⋊C8—111no—
257#103—111no—
258#103C2×D1111yescharacteristic, complemented
259#102—111no—
260#102—111no—
261#102—111no—
262#102C2×D1111yescharacteristic
263C22⋊C8—111no—
264C22⋊C8—111no—
265#97C2×D1111yescharacteristic, complemented
266C2×C11—42no—
267C2×C11D4211yescharacteristic
268C2×C11#57511yescharacteristic
269C2×C11#57611yescharacteristic
270D11—41no—
271D11—41no—
272D11—81no—
273D11—81no—
274D11—81no—
275C24—221no—
276#41—222no—
277#41—222no—
278#41—222no—
279#41—441no—
280#41—441no—
281#41—441no—
282C2×Q8—111no—
283C2×Q8C22×D1111yescharacteristic
284C2×D4—111no—
285C2×D4—111no—
286C2×D4—111no—
287C2×D4—111no—
288C2×D4—221no—
289C2×D4—221no—
290C2×D4—221no—
291C2×D4—221no—
292C2×D4—221no—
293C2×D4—221no—
294C2×D4—222no—
295C2×D4—221no—
296C2×D4—221no—
297C2×D4—221no—
298C2×D4—441no—
299C2×D4C22×D1111yescharacteristic
300C22×C4—21no—
301C22×C4—111no—
302C22×C4—111no—
303C22×C4—221no—
304C22×C4—221no—
305C22×C4—221no—
306Q16—222no—
307SD16—222no—
308SD16—222no—
309SD16—441no—
310SD16D4414yescomplemented
311D8—222no—
312D8—222no—
313D8—222no—
314D8—441no—
315M16—222no—
316C2×C8—111no—
317C2×C8—111no—
318C2×C8—222no—
319C2×C8C22×D1111yescharacteristic
320C2×C8C22×D1111yescharacteristic
321C4⋊C4—21no—
322C4⋊C4—111no—
323C4⋊C4—221no—
324C4⋊C4C22×D1111yescharacteristic
325C4⋊C4C22×D1111yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—111no—
328C22⋊C4—111no—
329C22⋊C4—221no—
330C22⋊C4—221no—
331C22⋊C4—221no—
332C22⋊C4—221no—
333C22⋊C4—221no—
334C22⋊C4—221no—
335C42—21no—
336C42C22×D1111yescharacteristic
337C11#326811yescharacteristic, complemented, Sylow
338C23—21no—
339C23—111no—
340C23—111no—
341C23—221no—
342C23—221no—
343C23—221no—
344C23—442no—
345C23—442no—
346C23—881no—
347Q8—21no—
348Q8—221no—
349Q8—221no—
350Q8C2×D4412yes—
351D4—21no—
352D4—221no—
353D4—221no—
354D4—221no—
355D4—221no—
356D4—221no—
357D4—221no—
358D4—441no—
359D4—442no—
360D4—442no—
361D4—442no—
362D4—442no—
363D4—442no—
364D4—881no—
365D4—881no—
366D4—881no—
367D4—881no—
368D4C2×D4412yes—
369C2×C4—21no—
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—442no—
381C2×C4—442no—
382C2×C4—442no—
383C2×C4D4×D1111yescharacteristic
384C2×C4D4×D1111yescharacteristic
385C2×C4C23×D1111yescharacteristic
386C8—21no—
387C8—221no—
388C8—221no—
389C8C2×D4412yes—
390C22—22no—
391C22—41no—
392C22—41no—
393C22—221no—
394C22—221no—
395C22—221no—
396C22—221no—
397C22—221no—
398C22—221no—
399C22—441no—
400C22—441no—
401C22—441no—
402C22—441no—
403C22—441no—
404C22—441no—
405C22—441no—
406C22—441no—
407C22—441no—
408C22—884no—
409C22C2×D4×D1111yescharacteristic
410C4—21no—
411C4—21no—
412C4—22no—
413C4—41no—
414C4—41no—
415C4—221no—
416C4—221no—
417C4—441no—
418C4C22×D4411yescharacteristic
419C4#6704211yescharacteristic
420C2—42no—
421C2—441no—
422C2—441no—
423C2—881no—
424C2—881no—
425C2—881no—
426C2D4×D4411yescharacteristic
427C2#1062330511yescharacteristic
428C2#1062330811yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#440C2
socleC22×C11C22×D4
hypercenter#440D11
hypocenterC11#3268
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. C2×#66969C2semidirect
2. C2×#66967C2semidirect
3. #10623108C2semidirect
4. #10623085C2semidirect
5. C11×#440C2semidirect
6. #10622641C2semidirect
7. #10622628C2semidirect
8. #10622499C2semidirect
9. #10622496C2semidirect
10. #10622424C2semidirect
11. #10622423C2semidirect
12. #10622394C2semidirect
13. #10622386C2semidirect
14. #10622325C2semidirect
15. #10622319C2semidirect
17. C2×#4343C22semidirect
21. C4×Q8×C11C22semidirect
23. C2×#4326C22semidirect
33. C2×#4314C22semidirect
34. C2×#4314C22semidirect
36. C2×C8×D11C22semidirect
42. #66948C22semidirect
47. #66927C22semidirect
50. C11×#107C22semidirect
51. C11×#103C22semidirect
53. C11×#97C22semidirect
55. (C2×D11)⋊C8C22semidirect
56. #66874C22semidirect
58. #66873C22semidirect
59. #66873C22semidirect
60. C4⋊(C11⋊C8)C22semidirect
92. C11×SD16D4semidirect
189. #440D11semidirect
250. C4×Q8C2×D11semidirect
255. #107C2×D11semidirect
258. #103C2×D11semidirect
265. #97C2×D11semidirect
310. SD16D44semidirect
337. C11#3268semidirect

Maximal subgroups

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

subgroupindex
C2×#669692
C2×#669672
#106231082
#106230852
C11×#4402
#106226412
#106226282
#106224992
#106224962
#106224242
#106224232
#106223942
#106223862
#106223252
#106223192
#326811