Finite Group Databasebeta

← #14900656

Subgroups — #14900656

Order 2816.

480 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13070199C211yesmaximal, characteristic, complemented
2#13070195C211yesmaximal, characteristic, complemented
3#13070194C211yesmaximal, characteristic, complemented
4#13070071C211yesmaximal, characteristic, complemented
5#13070066C211yesmaximal, characteristic, complemented
6#13069902C211yesmaximal, characteristic
7#13069321C211yesmaximal, characteristic, complemented
8#13069317C211yesmaximal, characteristic, complemented
9#13068978C211yesmaximal, characteristic
10#13068975C211yesmaximal, characteristic
11#13068855C211yesmaximal, characteristic, complemented
12#13068836C211yesmaximal, characteristic, complemented
13#13068834C211yesmaximal, characteristic, complemented
14#13068753C211yesmaximal, characteristic, complemented
15C11×#1861C211yesmaximal, characteristic, complemented
16C11×#568C2211yescharacteristic
17#10623353C2211yescharacteristic
18#10623276C2211yescharacteristic
19C11×#430C2211yescharacteristic
20C11×#423C2211yescharacteristic
21C11×#421C2211yescharacteristic
22C2×C11×#104C2211yescharacteristic
23#10622850C2211yescharacteristic
24#10622847C2211yescharacteristic
25#10622846C2211yescharacteristic
26#10622752C2211yescharacteristic
27#10622745C2211yescharacteristic
28#10622742C2211yescharacteristic
29#10622737C2211yescharacteristic
30#10622737C2211yescharacteristic
31#10622732C2211yescharacteristic
32#10622615C2211yescharacteristic
33#10622612C2211yescharacteristic
34C2×#66869C2211yescharacteristic
35#10622537C2211yescharacteristic
36C2×C4×C11⋊C8C2211yescharacteristic
37C11×#344C2211yescharacteristic
38C11×#339C2211yescharacteristic
39C11⋊#338C2211yescharacteristic
40#10622196C2211yescharacteristic
41#10622196C2211yescharacteristic
42#10622196C2211yescharacteristic
43#10622196C2211yescharacteristic
44#10622196C2211yescharacteristic
45#10622196C2211yescharacteristic
46#10622194C2211yescharacteristic
47#10622194C2211yescharacteristic
48#10622171C2211yescharacteristic
49#10622169C2211yescharacteristic
50#10622161C2211yescharacteristic
51C2×C11×#41C2311yescharacteristic
52C2×#4339C2311yescharacteristic
53C11×#131—41no—
54C11×#131—41no—
55C2×C11×M16—41no—
56C2×C11×M16C2311yescharacteristic
57C2×C11×M16C2311yescharacteristic
58C2×C11×M16C2311yescharacteristic
59C2×C11×M16C2311yescharacteristic
60C11×#117C2311yescharacteristic
61C2×C42×C11C2311yescharacteristic
62#67004—21no—
63#67003—41no—
64#67002—21no—
65#66995—21no—
66#66985—21no—
67#66979C2311yescharacteristic
68C2×#4318C2311yescharacteristic
69C2×#4318C2311yescharacteristic
70C2×#4318C2311yescharacteristic
71C2×#4318C2311yescharacteristic
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2311yescharacteristic
74#66960—41no—
75M16×D11—41no—
76#66954—41no—
77C11×#108—41no—
78C11×C4⋊C8—41no—
79C11×#104—21no—
80C11×#104—21no—
81C11×#104—41no—
82#66900—21no—
83#66899—21no—
84#66897—21no—
85#66896—21no—
86C22⋊(C11⋊C8)—41no—
87#66889—41no—
88#66888—21no—
89#66887—21no—
90#66886—41no—
91#66886—41no—
92(C2×D11)⋊C8—41no—
93Dic11⋊C8—41no—
94#66874—21no—
95#66873—21no—
96#66869—21no—
97#66869—21no—
98C4⋊(C11⋊C8)—41no—
99C4⋊(C11⋊C8)—41no—
100C4×C11⋊C8—21no—
101C4×C11⋊C8—21no—
102#32702—111nomaximal, Sylow
103C11×#41—21no—
104C11×#41—21no—
105C11×#41—21no—
106C11×#41—21no—
107C2×Q8×C11#4111yescharacteristic
108C2×D4×C11—21no—
109C2×D4×C11#4111yescharacteristic
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11C2411yescharacteristic
113C2×C22⋊D11—21no—
114#4339—21no—
115#4339—21no—
116#4339—21no—
117#4339—21no—
118C2×D44#4111yescharacteristic
119C2×C4×D11—21no—
120C2×Dic22#4111yescharacteristic
121C11×M16—21no—
122C11×M16—21no—
123C11×M16—21no—
124C11×M16—21no—
125C11×M16—21no—
126C11×M16—21no—
127C11×M16—21no—
128C11×M16—21no—
129C11×M16—42no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—42no—
135C11×C4⋊C4—21no—
136C11×C22⋊C4—21no—
137C42×C11—21no—
138C42×C11—21no—
139C42×C11#4111yescharacteristic
140C42×C11#4111yescharacteristic
141C22⋊Dic11—21no—
142#4326—41no—
143#4325—41no—
144#4324—41no—
145#4323—41no—
146C4⋊Dic11—21no—
147C4×Dic11—21no—
148#4318—21no—
149#4318—21no—
150#4318—21no—
151#4318—21no—
152#4318—21no—
153#4318—21no—
154#4318—21no—
155#4318—21no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8—21no—
162C2×C11⋊C8—21no—
163C2×C11⋊C8—21no—
164C2×C11⋊C8—21no—
165C2×C11⋊C8—21no—
166#4313—42no—
167C8×D11—42no—
168#2103—111no—
169#2103—111no—
170#2102—111no—
171#2080—111no—
172#2080—111no—
173#2050—111no—
174#1937—111no—
175#1937—111no—
176#1881—111no—
177#1881—111no—
178#1861—111no—
179#1861D1111yescharacteristic, complemented
180#1858—111no—
181#1858—111no—
182#1837—111no—
183C23×C11—21no—
184C23×C112−1+411yescharacteristic
185C22×D11—21no—
186Q8×C11—21no—
187Q8×C11—21no—
188D4×C11—21no—
189D4×C11—21no—
190D4×C11—41no—
191D4×C11—41no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—42no—
196C2×C4×C11—41no—
197C2×C4×C11—41no—
198C2×C4×C11—41no—
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11C2×#4111yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11H(5,𝔽2)11yescharacteristic
203C2×C4×C11H(5,𝔽2)11yescharacteristic
204C2×C4×C11H(5,𝔽2)11yescharacteristic
205C22⋊D11—41no—
206C22⋊D11—41no—
207C2×Dic11—21no—
208C2×Dic11—41no—
209D44—21no—
210D44—21no—
211C4×D11—41no—
212C4×D11—41no—
213Dic22—21no—
214Dic22—21no—
215C8×C11—41no—
216C8×C11—41no—
217C8×C11—41no—
218C8×C11—41no—
219C11⋊C8—41no—
220C11⋊C8—41no—
221C11⋊C8—41no—
222C11⋊C8—41no—
223C11⋊C8—41no—
224C11⋊C8—41no—
225#575—111no—
226#568—111no—
227#568C2×D1111yescharacteristic
228#430—111no—
229#430—111no—
230#430C2×D1111yescharacteristic
231#424—111no—
232#424—111no—
233#423—111no—
234#423C2×D1111yescharacteristic
235#421—111no—
236#421C2×D1111yescharacteristic
237C2×#104—111no—
238C2×#104C2×D1111yescharacteristic
239#416—111no—
240#416—111no—
241#413—111no—
242#413—111no—
243#408—111no—
244#408—111no—
245C2×C4×C8—111no—
246#344—111no—
247#344—111no—
248#344—111no—
249#344C2×D1111yescharacteristic
250#341—111no—
251#341—111no—
252#341—111no—
253#341—111no—
254#341—111no—
255#341—111no—
256#339—111no—
257#339C2×D1111yescharacteristic
258#338—111no—
259H(3,ℤ/4)—111no—
260C22×C11—41no—
261C22×C11—41no—
262C22×C11—81no—
263C22×C11#53911yescharacteristic
264C22×C11#53911yescharacteristic
265C22×C11#53911yescharacteristic
266C2×D11—41no—
267C2×D11—81no—
268C4×C11—22no—
269C4×C11—41no—
270C4×C11—41no—
271C4×C11—81no—
272C4×C11#55111yescharacteristic
273C4×C11#55311yescharacteristic
274C4×C11#55311yescharacteristic
275C4×C11H(3,𝔽4)11yescharacteristic
276Dic11—41no—
277Dic11—81no—
278C2×#41—111no—
279C2×#41C22×D1111yescharacteristic
280#137—221no—
281#137—221no—
282AGL(1,ℤ/8)—221no—
283AGL(1,ℤ/8)—221no—
284#135—441no—
285#131—41no—
286#131—41no—
287#131—441no—
288#131—441no—
289C2×M16—41no—
290C2×M16—111no—
291C2×M16—111no—
292C2×M16—111no—
293C2×M16—111no—
294C2×M16—441no—
295C2×M16C22×D1111yescharacteristic
296C2×M16C22×D1111yescharacteristic
297C2×M16C22×D1111yescharacteristic
298C2×M16C22×D1111yescharacteristic
299C22×C8—111no—
300C22×C8—111no—
301#117—111no—
302#117C22×D1111yescharacteristic
303C2×C42C22×D1111yescharacteristic
304#108—41no—
305#108—441no—
306#108—441no—
307C4⋊C8—41no—
308C4⋊C8—441no—
309C4⋊C8—441no—
310C4⋊C8—441no—
311#104—21no—
312#104—21no—
313#104—41no—
314#104—221no—
315#104—221no—
316#104—441no—
317#103—221no—
318#103—221no—
319#102—221no—
320#102—221no—
321#101—221no—
322#101—221no—
323#100—221no—
324#100—221no—
325C22⋊C8—441no—
326C22⋊C8—441no—
327C4×C8—221no—
328C4×C8—221no—
329C2×C11—21no—
330C2×C11—21no—
331C2×C11—21no—
332C2×C11—81no—
333C2×C11#278211yescharacteristic
334D11—81no—
335#41—21no—
336#41—21no—
337#41—21no—
338#41—21no—
339#41—221no—
340#41—221no—
341#41—221no—
342#41—221no—
343C2×Q8—111no—
344C2×Q8#434311yescharacteristic
345C2×D4—21no—
346C2×D4—111no—
347C2×D4—221no—
348C2×D4#434311yescharacteristic
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—221no—
352C22×C4C23×D1111yescharacteristic
353Q16—441no—
354SD16—441no—
355SD16—441no—
356D8—441no—
357M16—21no—
358M16—21no—
359M16—21no—
360M16—21no—
361M16—21no—
362M16—21no—
363M16—21no—
364M16—21no—
365M16—42no—
366M16—221no—
367M16—221no—
368M16—221no—
369M16—221no—
370M16—221no—
371M16—221no—
372M16—221no—
373M16—221no—
374M16—442no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—21no—
379C2×C8—42no—
380C2×C8—221no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8—221no—
384C2×C8—221no—
385C2×C8—221no—
386C2×C8—221no—
387C2×C8—221no—
388C2×C8—221no—
389C2×C8—221no—
390C2×C8—442no—
391C4⋊C4—21no—
392C4⋊C4—221no—
393C22⋊C4—21no—
394C22⋊C4—221no—
395C42—21no—
396C42—21no—
397C42—221no—
398C42#433911yescharacteristic
399C42#433911yescharacteristic
400C11#3270211yescharacteristic, complemented, Sylow
401C23—21no—
402C23—221no—
403C23#6704311yescharacteristic
404Q8—21no—
405Q8—21no—
406Q8—221no—
407Q8—221no—
408D4—21no—
409D4—21no—
410D4—41no—
411D4—41no—
412D4—221no—
413D4—221no—
414D4—441no—
415D4—441no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—221no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4C2×#433911yescharacteristic
428C2×C4#6703711yescharacteristic
429C2×C4#6703711yescharacteristic
430C2×C4#6703711yescharacteristic
431C2×C4C2×#434311yescharacteristic
432C2×C4#41×D1111yescharacteristic
433C8—41no—
434C8—41no—
435C8—41no—
436C8—41no—
437C8—441no—
438C8—441no—
439C8—441no—
440C8—441no—
441C8—441no—
442C8—441no—
443C22—41no—
444C22—41no—
445C22—81no—
446C22—441no—
447C22—881no—
448C22#1062309511yescharacteristic
449C22#1062317611yescharacteristic
450C22#1062319111yescharacteristic
451C4—22no—
452C4—41no—
453C4—41no—
454C4—81no—
455C4—441no—
456C4—881no—
457C4#1062304511yescharacteristic
458C4#1062308911yescharacteristic
459C4#1062312511yescharacteristic
460C4#1062316811yescharacteristic
461C2—21no—
462C2—21no—
463C2—21no—
464C2—81no—
465C2—881no—
466C2#1307628811yescharacteristic
subgroupG/H
centerC4#10623125
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1861C2
socleC2×C11#2782
prime radical#10623353C22
hypercenter#1861D11
hypocenterC11#32702
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1861

Complements

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

NH ≅ G/Ntype
1. #13070199C2semidirect
2. #13070195C2semidirect
3. #13070194C2semidirect
4. #13070071C2semidirect
5. #13070066C2semidirect
7. #13069321C2semidirect
8. #13069317C2semidirect
11. #13068855C2semidirect
12. #13068836C2semidirect
13. #13068834C2semidirect
14. #13068753C2semidirect
15. C11×#1861C2semidirect
179. #1861D11semidirect
400. C11#32702semidirect

Maximal subgroups

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

subgroupindex
#130701992
#130701952
#130701942
#130700712
#130700662
#130699022
#130693212
#130693172
#130689782
#130689752
#130688552
#130688362
#130688342
#130687532
C11×#18612
#3270211