Finite Group Databasebeta

← #28400289

Subgroups — #28400289

Order 14464.

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#20299397C211yesmaximal, characteristic, complemented
2#20299394C211yesmaximal, characteristic, complemented
3C2×#16813643C211yesmaximal, characteristic, complemented
4#131×D113C211yesmaximal, characteristic, complemented
5#20298872C211yesmaximal, characteristic, complemented
6#20298871C211yesmaximal, characteristic, complemented
7#20298867C211yesmaximal, characteristic, complemented
8#20298866C211yesmaximal, characteristic, complemented
9#20298862C211yesmaximal, characteristic, complemented
10#20298861C211yesmaximal, characteristic, complemented
11#20298858C211yesmaximal, characteristic, complemented
12#108×D113C211yesmaximal, characteristic, complemented
13#20298581C211yesmaximal, characteristic, complemented
14#20298579C211yesmaximal, characteristic, complemented
15#471×C113C211yesmaximal, characteristic, complemented
16C2×#14268648C2211yescharacteristic
17C2×#14268646C2211yescharacteristic
18#41×D113C2211yescharacteristic
19#16813655C2211yescharacteristic
20#16813654—21no—
21#16813653C2211yescharacteristic
22#16813652C2211yescharacteristic
23#16813651—21no—
24#16813650C2211yescharacteristic
25#16813649—21no—
26#16813648C2211yescharacteristic
27#16813647C2211yescharacteristic
28#16813646—21no—
29#16813645—21no—
30#16813643—21no—
31#16813643—21no—
32#16813643—21no—
33#16813643—21no—
34#16813643—21no—
35#16813643—21no—
36#16813641—21no—
37C2×#14268637C2211yescharacteristic, complemented
38C2×#14268636C2211yescharacteristic, complemented
39C2×#14268632C2211yescharacteristic, complemented
40#16813630—21no—
41#16813630C2211yescharacteristic
42#16813629C2211yescharacteristic
43#16813628—21no—
44#16813628C2211yescharacteristic
45M16×D113—21no—
46M16×D113C2211yescharacteristic
47M16×D113C2211yescharacteristic
48M16×D113C2211yescharacteristic
49C2×C8×D113—21no—
50C2×C8×D113C2211yescharacteristic
51#16813558C2211yescharacteristic, complemented
52#16813557C2211yescharacteristic, complemented
53#16813557C2211yescharacteristic, complemented
54#16813541C2211yescharacteristic, complemented
55#16813540C2211yescharacteristic, complemented
56#16813540C2211yescharacteristic, complemented
57#16813539C2211yescharacteristic, complemented
58#16813538C2211yescharacteristic, complemented
59#16813538C2211yescharacteristic, complemented
60#137×C113C2211yescharacteristic
61AGL(1,ℤ/8)×C113C2211yescharacteristic
62C2×SD16×C113C2211yescharacteristic, complemented
63#131×C113C2211yescharacteristic
64#108×C113C2211yescharacteristic, complemented
65#101×C113C2211yescharacteristic, complemented
66#100×C113C2211yescharacteristic, complemented
67#14268648—21no—
68#14268648—21no—
69#14268648—21no—
70#14268648—21no—
71#14268648D411yescharacteristic
72#14268647—21no—
73#14268647C2311yescharacteristic
74#14268646—21no—
75#14268646—21no—
76#14268646—21no—
77#14268646—21no—
78#14268646—21no—
79#14268646D411yescharacteristic
80C2×Dic226C2311yescharacteristic
81Q8×D113D411yescharacteristic
82C2×D452—21no—
83C2×D452C2311yescharacteristic
84C2×C22⋊D113—21no—
85D4×D113—21no—
86D4×D113D411yescharacteristic
87C22×Dic113—21no—
88C2×C4×D113—21no—
89C2×C4×D113—21no—
90C2×C4×D113C2311yescharacteristic
91Dic452—21no—
92#14268637—21no—
93#14268637—21no—
94#14268637—21no—
95#14268637—21no—
96#14268636—21no—
97#14268636—21no—
98#14268636—21no—
99#14268636—21no—
100#14268635—21no—
101#14268635—21no—
102#14268634—21no—
103#14268634—21no—
104D904—21no—
105#14268632—21no—
106#14268632—21no—
107#14268632—21no—
108#14268632—21no—
109#14268631—21no—
110#14268631C2311yescharacteristic
111#14268631C2311yescharacteristic
112#14268631C2311yescharacteristic
113#14268630—21no—
114#14268630—21no—
115#14268630—21no—
116#14268630—21no—
117#14268630—21no—
118C2×#11744751—21no—
119C2×#11744751C2311yescharacteristic
120C8×D113—21no—
121C8×D113—21no—
122C8×D113—21no—
123C8×D113—21no—
124C8×D113—21no—
125C8×D113D411yescharacteristic
126C8×D113D411yescharacteristic
127C8×D113D411yescharacteristic
128C8×D113D411yescharacteristic
129#41×C113C2311yescharacteristic
130C2×Q8×C113C2311yescharacteristic
131C2×D4×C113C2311yescharacteristic
132Q16×C113—21no—
133SD16×C113—21no—
134SD16×C113—21no—
135SD16×C113—21no—
136SD16×C113—21no—
137D8×C113—21no—
138M16×C113—21no—
139M16×C113C2311yescharacteristic
140M16×C113C2311yescharacteristic
141M16×C113C2311yescharacteristic
142C2×C8×C113—21no—
143C2×C8×C113C2311yescharacteristic
144C23×C113—21no—
145C22×D113—21no—
146C22×D113—21no—
147C22×D113#4111yescharacteristic
148Q8×C113—21no—
149Q8×C113—21no—
150Q8×C113C2×D411yescharacteristic
151D4×C113—21no—
152D4×C113—21no—
153D4×C113—21no—
154D4×C113C2×D411yescharacteristic
155C2×C4×C113—21no—
156C2×C4×C113—21no—
157C2×C4×C113C2411yescharacteristic
158C22⋊D113—21no—
159C22⋊D113—21no—
160C22⋊D113—21no—
161C22⋊D113—41no—
162C22⋊D113—41no—
163C2×Dic113—21no—
164C2×Dic113—21no—
165C2×Dic113—41no—
166C2×Dic113—41no—
167C2×Dic113#4111yescharacteristic
168D452—21no—
169D452—21no—
170D452—21no—
171D452—41no—
172D452—41no—
173D452C2×D411yescharacteristic
174C4×D113—21no—
175C4×D113—21no—
176C4×D113—21no—
177C4×D113—41no—
178C4×D113—41no—
179C4×D113C2×D411yescharacteristic
180C4×D113C2×D411yescharacteristic
181C4×D113C2×D411yescharacteristic
182C4×D113C2×D411yescharacteristic
183Dic226—21no—
184Dic226—21no—
185Dic226—21no—
186Dic226C2×D411yescharacteristic
187C8×C113—21no—
188C8×C113—21no—
189C8×C113—21no—
190C8×C113C2×D411yescharacteristic
191C8×C113C2×D411yescharacteristic
192#11744751—21no—
193#11744751—21no—
194#11744751—21no—
195#11744751C2×D411yescharacteristic
196#11744751C2×D411yescharacteristic
197C22×C113—21no—
198C22×C113—41no—
199C22×C113—81no—
200C22×C113C2×#4111yescharacteristic
201C2×D113—21no—
202C2×D113—41no—
203C2×D113—42no—
204C2×D113—41no—
205C2×D113—81no—
206C2×D113#12111yescharacteristic
207C2×D113#12111yescharacteristic
208C4×C113—21no—
209C4×C113—41no—
210C4×C113C22×D411yescharacteristic
211C4×C113C22×D411yescharacteristic
212Dic113—21no—
213Dic113—41no—
214Dic113#12111yescharacteristic
215Dic113#12111yescharacteristic
216C2×C113—21no—
217C2×C113—41no—
218C2×C113—81no—
219C2×C113C2×#12111yescharacteristic
220D113—21no—
221D113—21no—
222D113—41no—
223D113—81no—
224#3067—1131nomaximal, Sylow
225C113#306711yescharacteristic, complemented, Sylow
226#575—1131no—
227#575—1131no—
228C2×#135—1131no—
229C2×#131—1131no—
230#473—1131no—
231#473—1131no—
232#472—1131no—
233#472—1131no—
234#471—1131no—
235#471—1131no—
236#471—1131no—
237#471D11311yescharacteristic, complemented
238C2×#108—1131no—
239#413—1131no—
240#413—1131no—
241C2×#41—1131no—
242C2×#41—1131no—
243C2×#41—1131no—
244#137—1131no—
245#137—1131no—
246#137—1131no—
247#137—2261no—
248#137—2261no—
249#137C2×D11311yescharacteristic
250AGL(1,ℤ/8)—1131no—
251AGL(1,ℤ/8)—1131no—
252AGL(1,ℤ/8)—1131no—
253AGL(1,ℤ/8)—2261no—
254AGL(1,ℤ/8)—2261no—
255AGL(1,ℤ/8)C2×D11311yescharacteristic
256#135—2261no—
257#135—2261no—
258#135—2261no—
259#135—2261no—
260#135—2261no—
261#135—2261no—
262#135—2261no—
263#135—2261no—
264C2×Q16—1131no—
265C2×SD16—1131no—
266C2×SD16C2×D11311yescharacteristic, complemented
267C2×D8—1131no—
268#131—1131no—
269#131—1131no—
270#131—1131no—
271#131—2261no—
272#131—2261no—
273#131C2×D11311yescharacteristic
274C2×M16—1131no—
275C2×M16—1131no—
276C2×M16—1131no—
277C2×M16—2261no—
278C22×C8—1131no—
279C22×C8—2261no—
280#108—1131no—
281#108—1131no—
282#108—1131no—
283#108C2×D11311yescharacteristic, complemented
284#101—1131no—
285#101—1131no—
286#101—1131no—
287#101C2×D11311yescharacteristic, complemented
288#100—1131no—
289#100—1131no—
290#100—1131no—
291#100C2×D11311yescharacteristic, complemented
292#41—1131no—
293#41—1131no—
294#41—1131no—
295#41—2261no—
296#41—2261no—
297#41—2261no—
298#41—2261no—
299#41—2261no—
300#41—2261no—
301#41—2261no—
302#41—2261no—
303#41—2261no—
304#41—2261no—
305#41C22×D11311yescharacteristic
306C2×Q8—1131no—
307C2×Q8—1131no—
308C2×Q8C22×D11311yescharacteristic
309C2×D4—1131no—
310C2×D4—1131no—
311C2×D4—2261no—
312C2×D4—2261no—
313C2×D4—2261no—
314C2×D4C22×D11311yescharacteristic
315C22×C4—1131no—
316C22×C4—2261no—
317C22×C4—2261no—
318C22×C4—2261no—
319Q16—21no—
320Q16—2261no—
321Q16—2261no—
322Q16—2261no—
323Q16—2261no—
324Q16—2261no—
325SD16—21no—
326SD16—21no—
327SD16—21no—
328SD16—21no—
329SD16—2261no—
330SD16—2261no—
331SD16—2261no—
332SD16—2261no—
333SD16—2261no—
334SD16—2261no—
335SD16—2261no—
336SD16—2261no—
337D8—21no—
338D8—2261no—
339D8—2261no—
340D8—2261no—
341D8—2261no—
342D8—2261no—
343M16—21no—
344M16—1131no—
345M16—1131no—
346M16—1131no—
347M16—2261no—
348M16—2261no—
349M16—2261no—
350M16—2261no—
351M16—2261no—
352M16—2261no—
353M16C22×D11311yescharacteristic
354M16C22×D11311yescharacteristic
355M16C22×D11311yescharacteristic
356C2×C8—21no—
357C2×C8—1131no—
358C2×C8—1131no—
359C2×C8—1131no—
360C2×C8—1131no—
361C2×C8—1131no—
362C2×C8—2261no—
363C2×C8—2261no—
364C2×C8—2261no—
365C2×C8—2261no—
366C2×C8—2261no—
367C2×C8—2261no—
368C2×C8C22×D11311yescharacteristic
369C23—21no—
370C23—1131no—
371C23—2261no—
372C23—2261no—
373Q8—21no—
374Q8—21no—
375Q8—1131no—
376Q8—2261no—
377Q8—2261no—
378Q8—2261no—
379Q8D4×D11311yescharacteristic
380D4—21no—
381D4—21no—
382D4—21no—
383D4—1131no—
384D4—4521no—
385D4—4521no—
386D4—4521no—
387D4—4521no—
388D4—2261no—
389D4—2261no—
390D4—2261no—
391D4—2261no—
392D4—2261no—
393D4—2261no—
394D4D4×D11311yescharacteristic
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—1131no—
398C2×C4—1131no—
399C2×C4—1131no—
400C2×C4—1131no—
401C2×C4—1131no—
402C2×C4—4521no—
403C2×C4—4521no—
404C2×C4—4521no—
405C2×C4—4521no—
406C2×C4—2261no—
407C2×C4—2261no—
408C2×C4—2261no—
409C2×C4—2261no—
410C2×C4—2261no—
411C2×C4C23×D11311yescharacteristic
412C8—21no—
413C8—21no—
414C8—21no—
415C8—1131no—
416C8—1131no—
417C8—2261no—
418C8—2261no—
419C8—2261no—
420C8D4×D11311yescharacteristic
421C8D4×D11311yescharacteristic
422C22—21no—
423C22—41no—
424C22—81no—
425C22—1131no—
426C22—1131no—
427C22—9041no—
428C22—4521no—
429C22—4522no—
430C22—4521no—
431C22—2261no—
432C22#41×D11311yescharacteristic
433C4—21no—
434C4—41no—
435C4—1131no—
436C4—1131no—
437C4—4521no—
438C4—2261no—
439C4C2×D4×D11311yescharacteristic
440C4C2×D4×D11311yescharacteristic
441C2—21no—
442C2—41no—
443C2—81no—
444C2—9041no—
445C2—4521no—
446C2—2261no—
447C2—2261no—
448C2#121×D11311yescharacteristic
subgroupG/H
centerC2#121×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#471×C113C2
socleC2×C113C2×#121
hypercenter#471D113
hypocenterC113#3067
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ #471

Complements

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

NH ≅ G/Ntype
1. #20299397C2semidirect
2. #20299394C2semidirect
3. C2×#16813643C2semidirect
4. #131×D113C2semidirect
5. #20298872C2semidirect
6. #20298871C2semidirect
7. #20298867C2semidirect
8. #20298866C2semidirect
9. #20298862C2semidirect
10. #20298861C2semidirect
11. #20298858C2semidirect
12. #108×D113C2semidirect
13. #20298581C2semidirect
14. #20298579C2semidirect
15. #471×C113C2semidirect
37. C2×#14268637C22semidirect
38. C2×#14268636C22semidirect
39. C2×#14268632C22semidirect
51. #16813558C22semidirect
52. #16813557C22semidirect
53. #16813557C22semidirect
54. #16813541C22semidirect
55. #16813540C22semidirect
56. #16813540C22semidirect
57. #16813539C22semidirect
58. #16813538C22semidirect
59. #16813538C22semidirect
62. C2×SD16×C113C22semidirect
64. #108×C113C22semidirect
65. #101×C113C22semidirect
66. #100×C113C22semidirect
225. C113#3067semidirect
237. #471D113semidirect
266. C2×SD16C2×D113semidirect
283. #108C2×D113semidirect
287. #101C2×D113semidirect
291. #100C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993972
#202993942
C2×#168136432
#131×D1132
#202988722
#202988712
#202988672
#202988662
#202988622
#202988612
#202988582
#108×D1132
#202985812
#202985792
#471×C1132
#3067113