Finite Group Databasebeta

← #14900657

Subgroups — #14900657

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#13070198C211yesmaximal, characteristic, complemented
3#13070193C211yesmaximal, characteristic, complemented
4#13070070C211yesmaximal, characteristic, complemented
5#13070066C211yesmaximal, characteristic, complemented
6#13069900C211yesmaximal, characteristic
7#13069323C211yesmaximal, characteristic, complemented
8#13069322C211yesmaximal, characteristic, complemented
9#13068980C211yesmaximal, characteristic
10#13068856C211yesmaximal, characteristic, complemented
11#13068854C211yesmaximal, characteristic, complemented
12#13068836C211yesmaximal, characteristic, complemented
13#13068835C211yesmaximal, characteristic, complemented
14#13068752C211yesmaximal, characteristic, complemented
15C11×#1881C211yesmaximal, characteristic
16C11×#575C2211yescharacteristic
17C11×#568C2211yescharacteristic
18#10623350C2211yescharacteristic
19C11×#421C2211yescharacteristic
20C11×#416C2211yescharacteristic
21C11×#408C2211yescharacteristic
22#10622850C2211yescharacteristic
23#10622850C2211yescharacteristic
24#10622849C2211yescharacteristic
25C2×#66901C2211yescharacteristic
26C2×#66901C2211yescharacteristic
27#10622847C2211yescharacteristic
28#10622846C2211yescharacteristic
29#10622737C2211yescharacteristic
30#10622737C2211yescharacteristic
31#10622737C2211yescharacteristic
32#10622731C2211yescharacteristic
33#10622731C2211yescharacteristic
34#10622715C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622612C2211yescharacteristic
37C11×#344C2211yescharacteristic
38C11×#341C2211yescharacteristic
39C11⋊#338C2211yescharacteristic
40#10622197C2211yescharacteristic
41#10622196C2211yescharacteristic
42#10622196C2211yescharacteristic
43#10622196C2211yescharacteristic
44#10622194C2211yescharacteristic
45#10622193C2211yescharacteristic
46#10622190C2211yescharacteristic
47#10622190C2211yescharacteristic
48#10622171C2211yescharacteristic
49#10622170C2211yescharacteristic
50#10622169C2211yescharacteristic
51C2×C11×#41C2311yescharacteristic
52C2×C11×#41C2311yescharacteristic
53C11×#137—21no—
54C11×#137—21no—
55C11×AGL(1,ℤ/8)—21no—
56C11×AGL(1,ℤ/8)—21no—
57C11×#135—41no—
58C11×#131—41no—
59C11×#131—41no—
60C2×C11×M16—41no—
61C2×C11×M16C2311yescharacteristic
62C2×C11×M16C2311yescharacteristic
63C2×C11×M16C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×#117C2311yescharacteristic
66#67001—41no—
67#67001—41no—
68#66979C2311yescharacteristic
69C2×C4×Dic11C2311yescharacteristic
70C2×#4318—41no—
71C2×#4318C2311yescharacteristic
72C2×#4318C2311yescharacteristic
73C2×#4318C2311yescharacteristic
74C2×#4318C2311yescharacteristic
75C2×#4318C2311yescharacteristic
76C22×C11⋊C8C2311yescharacteristic
77C11×#104—41no—
78C11×#103—21no—
79C11×#102—21no—
80C11×C22⋊C8—41no—
81#66901—21no—
82#66901—21no—
83#66901—21no—
84#66901—21no—
85#66901—41no—
86#66900—21no—
87#66900—21no—
88#66899—21no—
89#66897—21no—
90#66897—21no—
91#66896—21no—
92C22⋊(C11⋊C8)—41no—
93#66886—41no—
94#66886—41no—
95#66886—41no—
96Dic11⋊C8—41no—
97Dic11⋊C8—41no—
98Dic11⋊C8—41no—
99C8×Dic11—21no—
100C8×Dic11—21no—
101C4⋊(C11⋊C8)—41no—
102#32702—111nomaximal, Sylow
103C11×#41—21no—
104C11×#41—21no—
105C11×#41—21no—
106C11×#41—21no—
107C11×#41—21no—
108C11×#41—21no—
109C11×#41—21no—
110C11×#41—21no—
111C2×Q8×C11#4111yescharacteristic
112C2×Q8×C11#4111yescharacteristic
113C2×D4×C11—21no—
114C2×D4×C11—21no—
115C2×D4×C11#4111yescharacteristic
116C2×D4×C11#4111yescharacteristic
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11C2411yescharacteristic
120C22×Dic11—21no—
121C11×Q16—41no—
122C11×SD16—41no—
123C11×SD16—41no—
124C11×D8—41no—
125C11×M16—21no—
126C11×M16—21no—
127C11×M16—21no—
128C11×M16—21no—
129C11×M16—21no—
130C11×M16—21no—
131C11×M16—42no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11—21no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—21no—
138C2×C8×C11—42no—
139C11×C4⋊C4—21no—
140C11×C22⋊C4—21no—
141C42×C11—21no—
142C22⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4×Dic11—21no—
145C4×Dic11—21no—
146C4×Dic11#4111yescharacteristic
147C4×Dic11#4111yescharacteristic
148#4318—21no—
149#4318—21no—
150#4318—21no—
151#4318—21no—
152#4318—21no—
153#4318—21no—
154#4318—21no—
155#4318—21no—
156#4318—21no—
157#4318—21no—
158#4318—42no—
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—
166C2×C11⋊C8—21no—
167C2×C11⋊C8—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#1881D1111yescharacteristic
178#1861—111no—
179#1861—111no—
180#1858—111no—
181#1858—111no—
182#1837—111no—
183C23×C11—21no—
184C23×C11—21no—
185C23×C112−1+411yescharacteristic
186Q8×C11—21no—
187Q8×C11—21no—
188Q8×C11—21no—
189Q8×C11—21no—
190D4×C11—21no—
191D4×C11—21no—
192D4×C11—21no—
193D4×C11—21no—
194D4×C11—41no—
195D4×C11—41no—
196D4×C11—41no—
197D4×C11—41no—
198C2×C4×C11—21no—
199C2×C4×C11—21no—
200C2×C4×C11—41no—
201C2×C4×C11—41no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11C2×#4111yescharacteristic
208C2×C4×C11H(5,𝔽2)11yescharacteristic
209C2×C4×C11H(5,𝔽2)11yescharacteristic
210C2×C4×C11H(5,𝔽2)11yescharacteristic
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—42no—
214C2×Dic11—41no—
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#575C2×D1111yescharacteristic
226#568—111no—
227#568C2×D1111yescharacteristic
228#430—111no—
229#430—111no—
230#430—111no—
231#424—111no—
232#424—111no—
233#423—111no—
234#423—111no—
235#421—111no—
236#421C2×D1111yescharacteristic
237C2×#104—111no—
238C2×#104—111no—
239#416—111no—
240#416C2×D1111yescharacteristic
241#413—111no—
242#413—111no—
243#408—111no—
244#408C2×D1111yescharacteristic
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#341C2×D1111yescharacteristic
256#339—111no—
257#339—111no—
258#338—111no—
259H(3,ℤ/4)—111no—
260C22×C11—41no—
261C22×C11—41no—
262C22×C11—41no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11#53911yescharacteristic
266C22×C11#53911yescharacteristic
267C22×C11#53911yescharacteristic
268C4×C11—41no—
269C4×C11—41no—
270C4×C11—81no—
271C4×C11#55111yescharacteristic
272C4×C11#55311yescharacteristic
273C4×C11#55311yescharacteristic
274C4×C11H(3,𝔽4)11yescharacteristic
275Dic11—22no—
276Dic11—41no—
277Dic11—81no—
278C2×#41C22×D1111yescharacteristic
279C2×#41C22×D1111yescharacteristic
280#137—21no—
281#137—21no—
282AGL(1,ℤ/8)—21no—
283AGL(1,ℤ/8)—21no—
284#135—41no—
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—111no—
295C2×M16—441no—
296C2×M16C22×D1111yescharacteristic
297C2×M16C22×D1111yescharacteristic
298C2×M16C22×D1111yescharacteristic
299C22×C8—111no—
300C22×C8C22×D1111yescharacteristic
301#117—111no—
302#117C22×D1111yescharacteristic
303C2×C42—111no—
304#108—441no—
305#108—441no—
306#108—441no—
307C4⋊C8—441no—
308C4⋊C8—441no—
309C4⋊C8—441no—
310C4⋊C8—441no—
311#104—41no—
312#104—221no—
313#104—221no—
314#104—221no—
315#104—221no—
316#104—441no—
317#103—21no—
318#103—221no—
319#102—21no—
320#102—221no—
321#101—221no—
322#101—221no—
323#100—221no—
324#100—221no—
325C22⋊C8—41no—
326C22⋊C8—441no—
327C4×C8—221no—
328C4×C8—221no—
329C2×C11—21no—
330C2×C11—21no—
331C2×C11—21no—
332C2×C11—81no—
333C2×C11—81no—
334C2×C11#278211yescharacteristic
335#41—21no—
336#41—21no—
337#41—21no—
338#41—21no—
339#41—21no—
340#41—21no—
341#41—21no—
342#41—21no—
343C2×Q8#433911yescharacteristic
344C2×Q8#434111yescharacteristic
345C2×D4—21no—
346C2×D4—21no—
347C2×D4#433911yescharacteristic
348C2×D4#434111yescharacteristic
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—221no—
352C22×C4C23×D1111yescharacteristic
353Q16—41no—
354SD16—41no—
355SD16—41no—
356D8—41no—
357M16—21no—
358M16—21no—
359M16—21no—
360M16—21no—
361M16—21no—
362M16—21no—
363M16—42no—
364M16—221no—
365M16—221no—
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—21no—
380C2×C8—21no—
381C2×C8—42no—
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—111no—
397C42—111no—
398C42—221no—
399C42—221no—
400C11#3270211yescharacteristic, complemented, Sylow
401C23—21no—
402C23—21no—
403C23#6704311yescharacteristic
404Q8—21no—
405Q8—21no—
406Q8—21no—
407Q8—21no—
408D4—21no—
409D4—21no—
410D4—21no—
411D4—21no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—41no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—221no—
424C2×C4—221no—
425C2×C4—442no—
426C2×C4—441no—
427C2×C4C2×#433911yescharacteristic
428C2×C4C2×#434111yescharacteristic
429C2×C4#6703711yescharacteristic
430C2×C4#6703711yescharacteristic
431C2×C4#6703711yescharacteristic
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—41no—
446C22—81no—
447C22—81no—
448C22#1062309511yescharacteristic
449C22#1062313311yescharacteristic
450C22#1062319111yescharacteristic
451C4—41no—
452C4—41no—
453C4—81no—
454C4—222no—
455C4—441no—
456C4—881no—
457C4#1062302611yescharacteristic
458C4#1062307111yescharacteristic
459C4#1062312511yescharacteristic
460C4#1062313211yescharacteristic
461C2—21no—
462C2—21no—
463C2—21no—
464C2—81no—
465C2—81no—
466C2#1307628911yescharacteristic
subgroupG/H
centerC4#10623125
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1881C2
socleC2×C11#2782
prime radicalC11×#575C22
hypercenter#1881D11
hypocenterC11#32702
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #1881

Complements

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

NH ≅ G/Ntype
1. #13070199C2semidirect
2. #13070198C2semidirect
3. #13070193C2semidirect
4. #13070070C2semidirect
5. #13070066C2semidirect
7. #13069323C2semidirect
8. #13069322C2semidirect
10. #13068856C2semidirect
11. #13068854C2semidirect
12. #13068836C2semidirect
13. #13068835C2semidirect
14. #13068752C2semidirect
400. C11#32702semidirect

Maximal subgroups

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

subgroupindex
#130701992
#130701982
#130701932
#130700702
#130700662
#130699002
#130693232
#130693222
#130689802
#130688562
#130688542
#130688362
#130688352
#130687522
C11×#18812
#3270211