Finite Group Databasebeta

← #28400306

Subgroups — #28400306

Order 14464.

446 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299394C211yesmaximal, characteristic
2C2×#16813651C211yesmaximal, characteristic, complemented
3#137×D113C211yesmaximal, characteristic, complemented
4#20299363C211yesmaximal, characteristic, complemented
5#20298874C211yesmaximal, characteristic, complemented
6#20298873C211yesmaximal, characteristic, complemented
7#20298872C211yesmaximal, characteristic, complemented
8#20298871C211yesmaximal, characteristic, complemented
9#20298860C211yesmaximal, characteristic, complemented
10#20298859C211yesmaximal, characteristic, complemented
11#20298858C211yesmaximal, characteristic, complemented
12#20298645C211yesmaximal, characteristic, complemented
13#20298579C211yesmaximal, characteristic, complemented
14#101×D113C211yesmaximal, characteristic, complemented
15#471×C113C211yesmaximal, characteristic, complemented
16C2×#14268646C2211yescharacteristic
17#41×D113C2211yescharacteristic
18C2×Q8×D113C2211yescharacteristic
19#16813655C2211yescharacteristic
20#16813655C2211yescharacteristic
21#16813654—21no—
22#16813653C2211yescharacteristic
23#16813652C2211yescharacteristic
24#16813652C2211yescharacteristic
25#16813651—21no—
26#16813651—21no—
27#16813651—21no—
28#16813651—21no—
29#16813651—21no—
30#16813651—21no—
31#16813648C2211yescharacteristic
32#16813646—21no—
33#16813643—21no—
34#16813641—21no—
35C2×Dic452C2211yescharacteristic, complemented
36C2×#14268637C2211yescharacteristic, complemented
37Q16×D113—21no—
38C2×#14268635C2211yescharacteristic, complemented
39SD16×D113—21no—
40#16813630—21no—
41#16813630C2211yescharacteristic
42#16813629C2211yescharacteristic
43#16813628—21no—
44#16813628C2211yescharacteristic
45C2×#14268630—21no—
46C2×#14268630C2211yescharacteristic
47M16×D113—21no—
48M16×D113C2211yescharacteristic
49M16×D113C2211yescharacteristic
50M16×D113C2211yescharacteristic
51#16813558C2211yescharacteristic, complemented
52#16813557C2211yescharacteristic, complemented
53#16813557C2211yescharacteristic, complemented
54#16813541C2211yescharacteristic, complemented
55#16813540C2211yescharacteristic, complemented
56#16813540C2211yescharacteristic, complemented
57#16813540C2211yescharacteristic, complemented
58#16813540C2211yescharacteristic, complemented
59#16813539C2211yescharacteristic, 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#14268648D411yescharacteristic
68#14268647—21no—
69#14268647C2311yescharacteristic
70#14268646—21no—
71#14268646—21no—
72#14268646—21no—
73#14268646—21no—
74#14268646—21no—
75#14268646D411yescharacteristic
76C2×Dic226—21no—
77C2×Dic226C2311yescharacteristic
78C2×Dic226C2311yescharacteristic
79Q8×D113—21no—
80Q8×D113—21no—
81Q8×D113—21no—
82Q8×D113—21no—
83Q8×D113D411yescharacteristic
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—
92Dic452—21no—
93Dic452—21no—
94Dic452—21no—
95#14268637—21no—
96#14268637—21no—
97#14268637—21no—
98#14268637—21no—
99#14268637—21no—
100#14268636—21no—
101#14268636—21no—
102#14268635—21no—
103#14268635—21no—
104#14268635—21no—
105#14268635—21no—
106#14268635—21no—
107#14268634—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—
118#14268630D411yescharacteristic
119#14268630D411yescharacteristic
120#14268630D411yescharacteristic
121#14268630D411yescharacteristic
122C2×#11744751—21no—
123C2×#11744751C2311yescharacteristic
124C8×D113—21no—
125C8×D113—21no—
126C8×D113—21no—
127C8×D113—21no—
128C8×D113—21no—
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#4111yescharacteristic
147Q8×C113—21no—
148Q8×C113—21no—
149Q8×C113C2×D411yescharacteristic
150D4×C113—21no—
151D4×C113—21no—
152D4×C113—21no—
153D4×C113C2×D411yescharacteristic
154C2×C4×C113—21no—
155C2×C4×C113—21no—
156C2×C4×C113C2411yescharacteristic
157C22⋊D113—21no—
158C22⋊D113—21no—
159C22⋊D113—21no—
160C22⋊D113—41no—
161C22⋊D113—41no—
162C2×Dic113—21no—
163C2×Dic113—21no—
164C2×Dic113—21no—
165C2×Dic113—41no—
166C2×Dic113—41no—
167C2×Dic113#4111yescharacteristic
168D452—21no—
169D452C2×D411yescharacteristic
170C4×D113—21no—
171C4×D113—21no—
172C4×D113—21no—
173C4×D113—41no—
174C4×D113—41no—
175C4×D113C2×D411yescharacteristic
176C4×D113C2×D411yescharacteristic
177C4×D113C2×D411yescharacteristic
178C4×D113C2×D411yescharacteristic
179Dic226—21no—
180Dic226—21no—
181Dic226—21no—
182Dic226—21no—
183Dic226—21no—
184Dic226—41no—
185Dic226—41no—
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—81no—
204C2×D113#12111yescharacteristic
205C2×D113#12111yescharacteristic
206C4×C113—21no—
207C4×C113—41no—
208C4×C113C22×D411yescharacteristic
209C4×C113C22×D411yescharacteristic
210Dic113—21no—
211Dic113—41no—
212Dic113—41no—
213Dic113#12111yescharacteristic
214Dic113#12111yescharacteristic
215C2×C113—21no—
216C2×C113—41no—
217C2×C113—81no—
218C2×C113C2×#12111yescharacteristic
219D113—21no—
220D113—21no—
221D113—41no—
222#3069—1131nomaximal, Sylow
223C113#306911yescharacteristic, complemented, Sylow
224#575—1131no—
225C2×#137—1131no—
226C2×#137—1131no—
227#568—1131no—
228#473—1131no—
229#473—1131no—
230#473—1131no—
231#473—1131no—
232#471—1131no—
233#471—1131no—
234#471—1131no—
235#471D11311yescharacteristic, complemented
236#430—1131no—
237#413—1131no—
238C2×#101—1131no—
239C2×#41—1131no—
240C2×#41—1131no—
241C22×Q8—1131no—
242#137—1131no—
243#137—1131no—
244#137—1131no—
245#137—1131no—
246#137—1131no—
247#137—2261no—
248#137—2261no—
249#137—2261no—
250#137—2261no—
251#137—2261no—
252#137—2261no—
253#137—2261no—
254#137C2×D11311yescharacteristic
255AGL(1,ℤ/8)—1131no—
256AGL(1,ℤ/8)—2261no—
257AGL(1,ℤ/8)C2×D11311yescharacteristic
258#135—2261no—
259#135—2261no—
260C2×Q16—1131no—
261C2×Q16—1131no—
262C2×Q16—2261no—
263C2×SD16—1131no—
264C2×SD16—2261no—
265C2×SD16C2×D11311yescharacteristic, complemented
266#131—1131no—
267#131—1131no—
268#131—1131no—
269#131—2261no—
270#131—2261no—
271#131C2×D11311yescharacteristic
272C2×M16—1131no—
273C2×M16—1131no—
274C2×M16—1131no—
275C2×M16—1131no—
276C2×M16—2261no—
277C2×M16—2261no—
278#108—1131no—
279#108—1131no—
280#108—1131no—
281#108C2×D11311yescharacteristic, complemented
282#101—1131no—
283#101—1131no—
284#101—1131no—
285#101—1131no—
286#101—1131no—
287#101C2×D11311yescharacteristic, complemented
288#100—1131no—
289#100C2×D11311yescharacteristic, complemented
290#41—1131no—
291#41—1131no—
292#41—1131no—
293#41—2261no—
294#41—2261no—
295#41—2261no—
296#41—2261no—
297#41—2261no—
298#41—2261no—
299#41C22×D11311yescharacteristic
300C2×Q8—1131no—
301C2×Q8—1131no—
302C2×Q8—1131no—
303C2×Q8—2261no—
304C2×Q8—2261no—
305C2×Q8—2261no—
306C2×Q8—2261no—
307C2×Q8—2261no—
308C2×Q8C22×D11311yescharacteristic
309C2×D4—1131no—
310C2×D4—2261no—
311C2×D4—2261no—
312C2×D4C22×D11311yescharacteristic
313C22×C4—1131no—
314C22×C4—2261no—
315C22×C4—2261no—
316C22×C4—2261no—
317Q16—21no—
318Q16—2261no—
319Q16—2261no—
320Q16—2261no—
321Q16—2261no—
322Q16—2261no—
323Q16—2261no—
324Q16—2261no—
325Q16—2261no—
326Q16—2261no—
327SD16—21no—
328SD16—21no—
329SD16—21no—
330SD16—21no—
331SD16—2261no—
332SD16—2261no—
333SD16—2261no—
334SD16—2261no—
335SD16—2261no—
336SD16—2261no—
337SD16—2261no—
338SD16—2261no—
339D8—21no—
340D8—2261no—
341M16—21no—
342M16—1131no—
343M16—1131no—
344M16—1131no—
345M16—1131no—
346M16—1131no—
347M16—1131no—
348M16—1131no—
349M16—2261no—
350M16—2261no—
351M16—2261no—
352M16—2261no—
353M16—2261no—
354M16—2261no—
355M16C22×D11311yescharacteristic
356M16C22×D11311yescharacteristic
357M16C22×D11311yescharacteristic
358C2×C8—21no—
359C2×C8—1131no—
360C2×C8—2261no—
361C2×C8—2261no—
362C2×C8—2261no—
363C2×C8—2261no—
364C2×C8—2261no—
365C2×C8—2261no—
366C2×C8C22×D11311yescharacteristic
367C23—21no—
368C23—1131no—
369C23—2261no—
370Q8—21no—
371Q8—21no—
372Q8—1131no—
373Q8—4521no—
374Q8—4521no—
375Q8—2261no—
376Q8—2261no—
377Q8—2261no—
378Q8—2261no—
379Q8—2261no—
380Q8D4×D11311yescharacteristic
381D4—21no—
382D4—21no—
383D4—21no—
384D4—1131no—
385D4—4521no—
386D4—4521no—
387D4—2261no—
388D4—2261no—
389D4—2261no—
390D4—2261no—
391D4D4×D11311yescharacteristic
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—1131no—
395C2×C4—1131no—
396C2×C4—1131no—
397C2×C4—1131no—
398C2×C4—1131no—
399C2×C4—4521no—
400C2×C4—4521no—
401C2×C4—4521no—
402C2×C4—4521no—
403C2×C4—2261no—
404C2×C4—2261no—
405C2×C4—2261no—
406C2×C4—2261no—
407C2×C4—2261no—
408C2×C4—2261no—
409C2×C4C23×D11311yescharacteristic
410C8—21no—
411C8—21no—
412C8—21no—
413C8—1131no—
414C8—1131no—
415C8—2261no—
416C8—2261no—
417C8—2261no—
418C8D4×D11311yescharacteristic
419C8D4×D11311yescharacteristic
420C22—21no—
421C22—41no—
422C22—81no—
423C22—1131no—
424C22—1131no—
425C22—9041no—
426C22—4521no—
427C22—2261no—
428C22#41×D11311yescharacteristic
429C4—21no—
430C4—41no—
431C4—1131no—
432C4—1131no—
433C4—4521no—
434C4—4521no—
435C4—2261no—
436C4C2×D4×D11311yescharacteristic
437C4C2×D4×D11311yescharacteristic
438C2—21no—
439C2—41no—
440C2—81no—
441C2—4521no—
442C2—2261no—
443C2—2261no—
444C2#121×D11311yescharacteristic
subgroupG/H
centerC2#121×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#471×C113C2
socleC2×C113C2×#121
prime radical#20299394C2
hypercenter#471D113
hypocenterC113#3069
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
2. C2×#16813651C2semidirect
3. #137×D113C2semidirect
4. #20299363C2semidirect
5. #20298874C2semidirect
6. #20298873C2semidirect
7. #20298872C2semidirect
8. #20298871C2semidirect
9. #20298860C2semidirect
10. #20298859C2semidirect
11. #20298858C2semidirect
12. #20298645C2semidirect
13. #20298579C2semidirect
14. #101×D113C2semidirect
15. #471×C113C2semidirect
35. C2×Dic452C22semidirect
36. C2×#14268637C22semidirect
38. C2×#14268635C22semidirect
51. #16813558C22semidirect
52. #16813557C22semidirect
53. #16813557C22semidirect
54. #16813541C22semidirect
55. #16813540C22semidirect
56. #16813540C22semidirect
57. #16813540C22semidirect
58. #16813540C22semidirect
59. #16813539C22semidirect
62. C2×SD16×C113C22semidirect
64. #108×C113C22semidirect
65. #101×C113C22semidirect
66. #100×C113C22semidirect
223. C113#3069semidirect
235. #471D113semidirect
265. C2×SD16C2×D113semidirect
281. #108C2×D113semidirect
287. #101C2×D113semidirect
289. #100C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993942
C2×#168136512
#137×D1132
#202993632
#202988742
#202988732
#202988722
#202988712
#202988602
#202988592
#202988582
#202986452
#202985792
#101×D1132
#471×C1132
#3069113