Finite Group Databasebeta

← #13078331

Subgroups — #13078331

Order 1408.

452 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623308C211yesmaximal, characteristic, complemented
2#10623304C211yesmaximal, characteristic, complemented
3C2×#66969C211yesmaximal, characteristic, complemented
4D11×#131C211yesmaximal, characteristic, complemented
5C11×#471C211yesmaximal, characteristic, complemented
6#10622817C211yesmaximal, characteristic, complemented
7#10622812C211yesmaximal, characteristic, complemented
8#10622790C211yesmaximal, characteristic, complemented
9#10622754C211yesmaximal, characteristic, complemented
10#10622511C211yesmaximal, characteristic, complemented
11D11×#108C211yesmaximal, characteristic, complemented
12#10622368C211yesmaximal, characteristic, complemented
13#10622364C211yesmaximal, characteristic, complemented
14#10622362C211yesmaximal, characteristic, complemented
15#10622358C211yesmaximal, characteristic, complemented
16#41×D11C2211yescharacteristic
17C2×#4343C2211yescharacteristic
18C2×#4341C2211yescharacteristic
19C11×#137C2211yescharacteristic
20C11×AGL(1,ℤ/8)C2211yescharacteristic
21C2×C11×SD16C2211yescharacteristic, complemented
22C11×#131C2211yescharacteristic
23#67004C2211yescharacteristic
24#67002C2211yescharacteristic
25#67001C2211yescharacteristic
26C2×#4326C2211yescharacteristic, complemented
27#66995C2211yescharacteristic
28#66985C2211yescharacteristic
29C2×#4323C2211yescharacteristic, complemented
30#66972—21no—
31#66971—21no—
32#66969—21no—
33#66969—21no—
34#66969—21no—
35#66969—21no—
36#66969—21no—
37#66969—21no—
38#66968—21no—
39#66967—21no—
40#66965—21no—
41#66964—21no—
42#66962C2211yescharacteristic
43#66961C2211yescharacteristic
44#66960—21no—
45#66960C2211yescharacteristic
46M16×D11—21no—
47M16×D11C2211yescharacteristic
48M16×D11C2211yescharacteristic
49M16×D11C2211yescharacteristic
50C2×#4314C2211yescharacteristic, complemented
51#66954—21no—
52#66954C2211yescharacteristic
53C2×C8×D11—21no—
54C2×C8×D11C2211yescharacteristic
55C11×#108C2211yescharacteristic, complemented
56C11×#101C2211yescharacteristic, complemented
57C11×#100C2211yescharacteristic, complemented
58#66900C2211yescharacteristic, complemented
59#66897C2211yescharacteristic, complemented
60#66888C2211yescharacteristic, complemented
61#66888C2211yescharacteristic, complemented
62#66887C2211yescharacteristic, complemented
63#66887C2211yescharacteristic, complemented
64#66886C2211yescharacteristic, complemented
65#66886C2211yescharacteristic, complemented
66#66883C2211yescharacteristic, complemented
67C11×#41C2311yescharacteristic
68C2×Q8×C11C2311yescharacteristic
69C2×D4×C11C2311yescharacteristic
70C2×C22⋊D11—21no—
71C22×Dic11—21no—
72#4343—21no—
73#4343—21no—
74#4343—21no—
75#4343—21no—
76#4343D411yescharacteristic
77Q8×D11D411yescharacteristic
78#4341—21no—
79#4341—21no—
80#4341—21no—
81#4341—21no—
82#4341—21no—
83#4341D411yescharacteristic
84D4×D11—21no—
85D4×D11D411yescharacteristic
86#4339—21no—
87#4339C2311yescharacteristic
88C2×D44—21no—
89C2×D44C2311yescharacteristic
90C2×C4×D11—21no—
91C2×C4×D11—21no—
92C2×C4×D11C2311yescharacteristic
93C2×Dic22C2311yescharacteristic
94C11×Q16—21no—
95C11×SD16—21no—
96C11×SD16—21no—
97C11×SD16—21no—
98C11×SD16—21no—
99C11×D8—21no—
100C11×M16—21no—
101C11×M16C2311yescharacteristic
102C11×M16C2311yescharacteristic
103C11×M16C2311yescharacteristic
104C2×C8×C11—21no—
105C2×C8×C11C2311yescharacteristic
106#4326—21no—
107#4326—21no—
108#4326—21no—
109#4326—21no—
110#4325—21no—
111#4325—21no—
112#4324—21no—
113#4324—21no—
114#4323—21no—
115#4323—21no—
116#4323—21no—
117#4323—21no—
118#4318—21no—
119#4318C2311yescharacteristic
120#4318C2311yescharacteristic
121#4318C2311yescharacteristic
122C2×C11⋊C8—21no—
123C2×C11⋊C8C2311yescharacteristic
124Dic44—21no—
125D88—21no—
126#4314—21no—
127#4314—21no—
128#4314—21no—
129#4314—21no—
130#4313—21no—
131#4313—21no—
132#4313—21no—
133#4313—21no—
134#4313—21no—
135C8×D11—21no—
136C8×D11—21no—
137C8×D11—21no—
138C8×D11—21no—
139C8×D11—21no—
140C8×D11D411yescharacteristic
141C8×D11D411yescharacteristic
142C8×D11D411yescharacteristic
143C8×D11D411yescharacteristic
144#3067—111nomaximal, Sylow
145C23×C11—21no—
146C22×D11—21no—
147C22×D11—21no—
148C22×D11#4111yescharacteristic
149Q8×C11—21no—
150Q8×C11—21no—
151Q8×C11C2×D411yescharacteristic
152D4×C11—21no—
153D4×C11—21no—
154D4×C11—21no—
155D4×C11C2×D411yescharacteristic
156C2×C4×C11—21no—
157C2×C4×C11—21no—
158C2×C4×C11C2411yescharacteristic
159C22⋊D11—21no—
160C22⋊D11—21no—
161C22⋊D11—21no—
162C22⋊D11—41no—
163C22⋊D11—41no—
164C2×Dic11—21no—
165C2×Dic11—21no—
166C2×Dic11—41no—
167C2×Dic11—41no—
168C2×Dic11#4111yescharacteristic
169D44—21no—
170D44—21no—
171D44—21no—
172D44—41no—
173D44—41no—
174D44C2×D411yescharacteristic
175C4×D11—21no—
176C4×D11—21no—
177C4×D11—21no—
178C4×D11—41no—
179C4×D11—41no—
180C4×D11C2×D411yescharacteristic
181C4×D11C2×D411yescharacteristic
182C4×D11C2×D411yescharacteristic
183C4×D11C2×D411yescharacteristic
184Dic22—21no—
185Dic22—21no—
186Dic22—21no—
187Dic22C2×D411yescharacteristic
188C8×C11—21no—
189C8×C11—21no—
190C8×C11—21no—
191C8×C11C2×D411yescharacteristic
192C8×C11C2×D411yescharacteristic
193C11⋊C8—21no—
194C11⋊C8—21no—
195C11⋊C8—21no—
196C11⋊C8C2×D411yescharacteristic
197C11⋊C8C2×D411yescharacteristic
198#575—111no—
199#575—111no—
200C2×#135—111no—
201C2×#131—111no—
202#473—111no—
203#473—111no—
204#472—111no—
205#472—111no—
206#471—111no—
207#471—111no—
208#471—111no—
209#471D1111yescharacteristic, complemented
210C2×#108—111no—
211#413—111no—
212#413—111no—
213C22×C11—21no—
214C22×C11—41no—
215C22×C11—81no—
216C22×C11C2×#4111yescharacteristic
217C2×D11—21no—
218C2×D11—41no—
219C2×D11—42no—
220C2×D11—41no—
221C2×D11—81no—
222C2×D11#12111yescharacteristic
223C2×D11#12111yescharacteristic
224C4×C11—21no—
225C4×C11—41no—
226C4×C11C22×D411yescharacteristic
227C4×C11C22×D411yescharacteristic
228Dic11—21no—
229Dic11—41no—
230Dic11#12111yescharacteristic
231Dic11#12111yescharacteristic
232C2×#41—111no—
233C2×#41—111no—
234C2×#41—111no—
235#137—111no—
236#137—111no—
237#137—111no—
238#137—221no—
239#137—221no—
240#137C2×D1111yescharacteristic
241AGL(1,ℤ/8)—111no—
242AGL(1,ℤ/8)—111no—
243AGL(1,ℤ/8)—111no—
244AGL(1,ℤ/8)—221no—
245AGL(1,ℤ/8)—221no—
246AGL(1,ℤ/8)C2×D1111yescharacteristic
247#135—221no—
248#135—221no—
249#135—221no—
250#135—221no—
251#135—221no—
252#135—221no—
253#135—221no—
254#135—221no—
255C2×Q16—111no—
256C2×SD16—111no—
257C2×SD16C2×D1111yescharacteristic, complemented
258C2×D8—111no—
259#131—111no—
260#131—111no—
261#131—111no—
262#131—221no—
263#131—221no—
264#131C2×D1111yescharacteristic
265C2×M16—111no—
266C2×M16—111no—
267C2×M16—111no—
268C2×M16—221no—
269C22×C8—111no—
270C22×C8—221no—
271#108—111no—
272#108—111no—
273#108—111no—
274#108C2×D1111yescharacteristic, complemented
275#101—111no—
276#101—111no—
277#101—111no—
278#101C2×D1111yescharacteristic, complemented
279#100—111no—
280#100—111no—
281#100—111no—
282#100C2×D1111yescharacteristic, complemented
283C2×C11—21no—
284C2×C11—41no—
285C2×C11—81no—
286C2×C11C2×#12111yescharacteristic
287D11—21no—
288D11—21no—
289D11—41no—
290D11—81no—
291#41—111no—
292#41—111no—
293#41—111no—
294#41—221no—
295#41—221no—
296#41—221no—
297#41—221no—
298#41—221no—
299#41—221no—
300#41—221no—
301#41—221no—
302#41—221no—
303#41—221no—
304#41C22×D1111yescharacteristic
305C2×Q8—111no—
306C2×Q8—111no—
307C2×Q8C22×D1111yescharacteristic
308C2×D4—111no—
309C2×D4—111no—
310C2×D4—221no—
311C2×D4—221no—
312C2×D4—221no—
313C2×D4C22×D1111yescharacteristic
314C22×C4—111no—
315C22×C4—221no—
316C22×C4—221no—
317C22×C4—221no—
318Q16—21no—
319Q16—221no—
320Q16—221no—
321Q16—221no—
322Q16—221no—
323Q16—221no—
324SD16—21no—
325SD16—21no—
326SD16—21no—
327SD16—21no—
328SD16—221no—
329SD16—221no—
330SD16—221no—
331SD16—221no—
332SD16—221no—
333SD16—221no—
334SD16—221no—
335SD16—221no—
336D8—21no—
337D8—221no—
338D8—221no—
339D8—221no—
340D8—221no—
341D8—221no—
342M16—21no—
343M16—111no—
344M16—111no—
345M16—111no—
346M16—221no—
347M16—221no—
348M16—221no—
349M16—221no—
350M16—221no—
351M16—221no—
352M16C22×D1111yescharacteristic
353M16C22×D1111yescharacteristic
354M16C22×D1111yescharacteristic
355C2×C8—21no—
356C2×C8—111no—
357C2×C8—111no—
358C2×C8—111no—
359C2×C8—111no—
360C2×C8—111no—
361C2×C8—221no—
362C2×C8—221no—
363C2×C8—221no—
364C2×C8—221no—
365C2×C8—221no—
366C2×C8—221no—
367C2×C8C22×D1111yescharacteristic
368C11#306711yescharacteristic, complemented, Sylow
369C23—21no—
370C23—111no—
371C23—221no—
372C23—221no—
373Q8—21no—
374Q8—21no—
375Q8—111no—
376Q8—221no—
377Q8—221no—
378Q8—221no—
379Q8D4×D1111yescharacteristic
380D4—21no—
381D4—21no—
382D4—21no—
383D4—111no—
384D4—221no—
385D4—221no—
386D4—221no—
387D4—221no—
388D4—221no—
389D4—221no—
390D4—441no—
391D4—441no—
392D4—441no—
393D4—441no—
394D4D4×D1111yescharacteristic
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—111no—
398C2×C4—111no—
399C2×C4—111no—
400C2×C4—111no—
401C2×C4—111no—
402C2×C4—221no—
403C2×C4—221no—
404C2×C4—221no—
405C2×C4—221no—
406C2×C4—221no—
407C2×C4—441no—
408C2×C4—441no—
409C2×C4—441no—
410C2×C4—441no—
411C2×C4C23×D1111yescharacteristic
412C8—21no—
413C8—21no—
414C8—21no—
415C8—111no—
416C8—111no—
417C8—221no—
418C8—221no—
419C8—221no—
420C8D4×D1111yescharacteristic
421C8D4×D1111yescharacteristic
422C22—21no—
423C22—41no—
424C22—81no—
425C22—111no—
426C22—111no—
427C22—221no—
428C22—441no—
429C22—442no—
430C22—441no—
431C22—881no—
432C22#41×D1111yescharacteristic
433C4—21no—
434C4—41no—
435C4—111no—
436C4—111no—
437C4—221no—
438C4—441no—
439C4C2×D4×D1111yescharacteristic
440C4C2×D4×D1111yescharacteristic
441C2—21no—
442C2—41no—
443C2—81no—
444C2—221no—
445C2—221no—
446C2—441no—
447C2—881no—
448C2D11×#12111yescharacteristic
subgroupG/H
centerC2D11×#121
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#471C2
socleC2×C11C2×#121
hypercenter#471D11
hypocenterC11#3067
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #10623308C2semidirect
2. #10623304C2semidirect
3. C2×#66969C2semidirect
4. D11×#131C2semidirect
5. C11×#471C2semidirect
6. #10622817C2semidirect
7. #10622812C2semidirect
8. #10622790C2semidirect
9. #10622754C2semidirect
10. #10622511C2semidirect
11. D11×#108C2semidirect
12. #10622368C2semidirect
13. #10622364C2semidirect
14. #10622362C2semidirect
15. #10622358C2semidirect
21. C2×C11×SD16C22semidirect
26. C2×#4326C22semidirect
29. C2×#4323C22semidirect
50. C2×#4314C22semidirect
55. C11×#108C22semidirect
56. C11×#101C22semidirect
57. C11×#100C22semidirect
58. #66900C22semidirect
59. #66897C22semidirect
60. #66888C22semidirect
61. #66888C22semidirect
62. #66887C22semidirect
63. #66887C22semidirect
64. #66886C22semidirect
65. #66886C22semidirect
66. #66883C22semidirect
209. #471D11semidirect
257. C2×SD16C2×D11semidirect
274. #108C2×D11semidirect
278. #101C2×D11semidirect
282. #100C2×D11semidirect
368. C11#3067semidirect

Maximal subgroups

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

subgroupindex
#106233082
#106233042
C2×#669692
D11×#1312
C11×#4712
#106228172
#106228122
#106227902
#106227542
#106225112
D11×#1082
#106223682
#106223642
#106223622
#106223582
#306711