Finite Group Databasebeta

← #14909113

Subgroups — #14909113

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079149C211yesmaximal, characteristic, complemented
2#13079106C211yesmaximal, characteristic
3#13070862C211yesmaximal, characteristic, complemented
4#13070860C211yesmaximal, characteristic, complemented
5#13070851C211yesmaximal, characteristic, complemented
6#13070847C211yesmaximal, characteristic, complemented
7#13070846C211yesmaximal, characteristic, complemented
8#13070845C211yesmaximal, characteristic, complemented
9#13070842C211yesmaximal, characteristic, complemented
10#13070334C211yesmaximal, characteristic, complemented
11#13070325C211yesmaximal, characteristic
12#13070320C211yesmaximal, characteristic
13D11×#358C211yesmaximal, characteristic, complemented
14#13070214C211yesmaximal, characteristic, complemented
15C11×#2243C211yesmaximal, characteristic, complemented
16C2×Q16×D11C2211yescharacteristic
17C2×#66968—21no—
18C2×#66965C2211yescharacteristic
19#10623260—21no—
20#10623206—21no—
21C11×#500C2211yescharacteristic
22C11×#495C2211yescharacteristic
23#10622794C2211yescharacteristic
24#10622780—21no—
25#10622768C2211yescharacteristic
26#10622693—21no—
27#10622673—21no—
28C2×#66862C2211yescharacteristic
29C2×C16×D11C2211yescharacteristic
30#10622494—21no—
31#10622493C2211yescharacteristic
32D11×#107C2211yescharacteristic
33#10622491C2211yescharacteristic
34#10622489—21no—
35#10622487C2211yescharacteristic
36#10622312C2211yescharacteristic
37#10622302C2211yescharacteristic
38#10622296C2211yescharacteristic
39C11×#358C2211yescharacteristic
40C11×#358C2211yescharacteristic
41C11×#357C2211yescharacteristic
42C11×#357C2211yescharacteristic
43C11×#346C2211yescharacteristic
44#10622202C2211yescharacteristic
45#10622202C2211yescharacteristic
46#10622200C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622141C2211yescharacteristic
49#10622141C2211yescharacteristic
50#10622141C2211yescharacteristic
51#10622141C2211yescharacteristic
52#10622140C2211yescharacteristic
53C16×Dic11C2211yescharacteristic
54#10622130C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622130C2211yescharacteristic
57#10622130C2211yescharacteristic
58C4×C11⋊C16C2211yescharacteristic
59C2×Q8×D11—21no—
60C2×#4341—21no—
61C2×C11×Q16C2311yescharacteristic
62C2×C11×SD16—21no—
63C2×C11×D8C2311yescharacteristic
64C11×C4⋊Q8—21no—
65C11×#124—21no—
66#66999—41no—
67#66997—21no—
68#66997—41no—
69C2×#4326—21no—
70C2×#4326—21no—
71#66989—21no—
72C2×#4324—21no—
73C2×#4324—21no—
74Q16×D11—22no—
75Q16×D11—22no—
76#66968—44no—
77#66965—22no—
78#66965—22no—
79C2×Dic44—21no—
80C2×Dic44C2311yescharacteristic
81C2×Dic44C2311yescharacteristic
82C2×#4313D411yescharacteristic
83C2×C8×D11C2311yescharacteristic
84#66949—41no—
85#66945—21no—
86C4⋊C4×D11—21no—
87#66943—21no—
88#66942—41no—
89#66941—21no—
90#66936—41no—
91#66936—41no—
92#66931—41no—
93#66931—41no—
94#66925D411yescharacteristic
95#66923—21no—
96#66922—21no—
97C2×C11×C16C2311yescharacteristic
98C2×C11×C16C2311yescharacteristic
99C11×#107—21no—
100C11×#107C2311yescharacteristic
101C11×#107C2311yescharacteristic
102C4×C8×C11C2311yescharacteristic
103#66882C2311yescharacteristic
104#66882C2311yescharacteristic
105#66881—21no—
106#66879D411yescharacteristic
107C8×Dic11C2311yescharacteristic
108C2×C11⋊C16C2311yescharacteristic
109C2×C11⋊C16C2311yescharacteristic
110#66872—21no—
111#66872—21no—
112#66871—21no—
113#66871—21no—
114#66867D411yescharacteristic
115#66862—22no—
116C16×D11—22no—
117#33703—111nomaximal, Sylow
118C2×Q8×C11—21no—
119C2×Q8×C11—41no—
120C2×D4×C11—21no—
121C2×C22⋊D11—41no—
122C22×Dic11—41no—
123Q8×D11—42no—
124Q8×D11—42no—
125#4341—42no—
126#4341—42no—
127C2×C4×D11—41no—
128C2×C4×D11—41no—
129C2×C4×D11C2×D411yescharacteristic
130C2×Dic22—21no—
131C2×Dic22—21no—
132C2×Dic22—41no—
133C2×Dic22—41no—
134C11×Q16—21no—
135C11×Q16—21no—
136C11×SD16—42no—
137C11×D8—21no—
138C11×D8—21no—
139C2×C8×C11C2×D411yescharacteristic
140C2×C8×C11C2411yescharacteristic
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—41no—
144C11×C22⋊C4—41no—
145C11×C22⋊C4—41no—
146C42×C11C2×D411yescharacteristic
147C22⋊Dic11—41no—
148C22⋊Dic11—41no—
149#4326—42no—
150#4326—42no—
151#4324—42no—
152#4324—42no—
153(C2×D11)⋊C4—41no—
154(C2×D11)⋊C4D811yescharacteristic
155(C2×D11)⋊C4D811yescharacteristic
156C4⋊Dic11—21no—
157C4⋊Dic11—21no—
158C4⋊Dic11—41no—
159C4⋊Dic11—41no—
160C4⋊Dic11—41no—
161Dic11⋊C4—41no—
162Dic11⋊C4—41no—
163Dic11⋊C4—41no—
164Dic11⋊C4—41no—
165Dic11⋊C4—41no—
166Dic11⋊C4—41no—
167Dic11⋊C4—41no—
168Dic11⋊C4D811yescharacteristic
169Dic11⋊C4D811yescharacteristic
170C4×Dic11—41no—
171C4×Dic11C2×D411yescharacteristic
172C2×C11⋊C8C2×D411yescharacteristic
173C2×C11⋊C8C2×D411yescharacteristic
174Dic44—21no—
175Dic44—21no—
176Dic44—21no—
177Dic44—21no—
178Dic44—42no—
179#4313SD1614yes—
180C8×D11#4112yes—
181C8×D11#4112yes—
182C11×C16—21no—
183C11×C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3164—111no—
187#3156—111no—
188#2245—111no—
189#2245—111no—
190#2243—111no—
191#2243D1111yescharacteristic, complemented
192#2242—111no—
193#2242—111no—
194#2241—111no—
195#2241—111no—
196#2141—111no—
197#2139—111no—
198#2138—111no—
199C2×#358—111no—
200#2108—111no—
201C23×C11—41no—
202C22×D11C2×D811yescharacteristic
203Q8×C11—41no—
204Q8×C11—41no—
205Q8×C11—161no—
206D4×C11—41no—
207D4×C11—41no—
208C2×C4×C11—41no—
209C2×C4×C11—41no—
210C2×C4×C11—41no—
211C2×C4×C11C2×D811yescharacteristic
212C2×C4×C11C2×D811yescharacteristic
213C2×C4×C11C22×D411yescharacteristic
214C22⋊D11—82no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—82no—
220C2×Dic11C2×D811yescharacteristic
221C2×Dic11C2×D811yescharacteristic
222C2×Dic11C2×D811yescharacteristic
223C4×D11—82no—
224C4×D11—161no—
225C4×D11#12412yes—
226C4×D11C2×SD1612yes—
227Dic22—41no—
228Dic22—41no—
229Dic22—41no—
230Dic22—41no—
231Dic22—82no—
232Dic22—161no—
233C8×C11C2×SD1612yes—
234C8×C11C2×#4111yescharacteristic
235C8×C11C2×#4111yescharacteristic
236C11⋊C8#12412yes—
237C11⋊C8C2×SD1612yes—
238C2×#137—221no—
239C2×#135—111no—
240C22×Q16—111no—
241#544—221no—
242#536—221no—
243C2×M32—111no—
244C22×C16—111no—
245#501—221no—
246#501—221no—
247#500—111no—
248#500C2×D1111yescharacteristic
249#499—111no—
250#499—111no—
251#497—221no—
252#497—221no—
253#495—111no—
254#495C2×D1111yescharacteristic
255#494—111no—
256#494—111no—
257#428—221no—
258#427—111no—
259C2×#107—111no—
260#405—111no—
261#358—111no—
262#358—111no—
263#358—111no—
264#358—111no—
265#358—111no—
266#358—111no—
267#358—111no—
268#358—111no—
269#358—111no—
270#358—111no—
271#358C2×D1111yescharacteristic
272#358C2×D1111yescharacteristic
273#357—111no—
274#357—111no—
275#357C2×D1111yescharacteristic
276#357C2×D1111yescharacteristic
277#346—111no—
278#346C2×D1111yescharacteristic
279C4×C16—111no—
280C4×C16—111no—
281C22×C11—81no—
282C22×C11—81no—
283C22×C11—81no—
284C22×C11C22×D811yescharacteristic
285C2×D11—21no—
286C2×D11—21no—
287C2×D11#48612yes—
288C4×C11—21no—
289C4×C11—21no—
290C4×C11—81no—
291C4×C11—81no—
292C4×C11—81no—
293C4×C11C2×#12411yescharacteristic
294C4×C11C22×SD1611yescharacteristic
295Dic11—21no—
296Dic11—21no—
297Dic11—81no—
298Dic11—81no—
299Dic11—81no—
300Dic11—81no—
301Dic11#48612yes—
302C2×#41—221no—
303C22×Q8—221no—
304#137—444no—
305#135—222no—
306#135—222no—
307C2×Q16—111no—
308C2×Q16—111no—
309C2×Q16—222no—
310C2×Q16—222no—
311C2×Q16—221no—
312C2×Q16—221no—
313C2×Q16—221no—
314C2×Q16C22×D1111yescharacteristic
315C2×SD16—21no—
316C2×SD16—221no—
317C2×SD16—221no—
318C2×D8C22×D1111yescharacteristic
319C2×M16—111no—
320C22×C8—111no—
321C4⋊Q8—21no—
322C4⋊Q8—221no—
323C4⋊Q8—221no—
324C4⋊Q8—221no—
325C4⋊Q8—441no—
326#125—221no—
327#125—221no—
328#125—441no—
329#124—21no—
330#124—221no—
331#123—441no—
332#123—441no—
333C22⋊Q8—441no—
334C22⋊Q8—441no—
335C22⋊Q8—441no—
336C22⋊Q8—441no—
337#117—111no—
338#117—221no—
339C2×C4⋊C4—221no—
340M32—222no—
341C2×C16—111no—
342C2×C16—111no—
343C2×C16—222no—
344C2×C16C22×D1111yescharacteristic
345C2×C16C22×D1111yescharacteristic
346#107—21no—
347#107—111no—
348#107—111no—
349#107—221no—
350#107—221no—
351#107C22×D1111yescharacteristic
352#107C22×D1111yescharacteristic
353#106—221no—
354#106—221no—
355#106—221no—
356#97—111no—
357#97—111no—
358C4×C8—111no—
359C4×C8C22×D1111yescharacteristic
360C2×C11—161no—
361C2×C11C2×#48611yescharacteristic
362C2×C11#341611yescharacteristic
363C2×C11#341711yescharacteristic
364D11—22no—
365#41—442no—
366#41—442no—
367C2×Q8—21no—
368C2×Q8—41no—
369C2×Q8—221no—
370C2×Q8—221no—
371C2×Q8—441no—
372C2×Q8—441no—
373C2×Q8—442no—
374C2×Q8—442no—
375C2×D4—21no—
376C2×D4—441no—
377C22×C4—111no—
378C22×C4—441no—
379C22×C4—441no—
380C22×C4—441no—
381Q16—21no—
382Q16—21no—
383Q16—221no—
384Q16—221no—
385Q16—221no—
386Q16—221no—
387Q16—442no—
388Q16—442no—
389Q16—442no—
390SD16—42no—
391SD16—442no—
392SD16—442no—
393D8—21no—
394D8—21no—
395M16—114no—
396C2×C8—111no—
397C2×C8—111no—
398C2×C8—112no—
399C2×C8—112no—
400C2×C8D4×D1111yescharacteristic
401C2×C8C23×D1111yescharacteristic
402C4⋊C4—21no—
403C4⋊C4—21no—
404C4⋊C4—41no—
405C4⋊C4—111no—
406C4⋊C4—111no—
407C4⋊C4—221no—
408C4⋊C4—221no—
409C4⋊C4—441no—
410C4⋊C4—441no—
411C4⋊C4—441no—
412C4⋊C4—441no—
413C4⋊C4—441no—
414C4⋊C4—441no—
415C4⋊C4—441no—
416C4⋊C4—441no—
417C4⋊C4—441no—
418C4⋊C4—441no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—111no—
422C22⋊C4—111no—
423C22⋊C4—441no—
424C22⋊C4—441no—
425C22⋊C4—441no—
426C42—111no—
427C42—441no—
428C42D4×D1111yescharacteristic
429C16—21no—
430C16—21no—
431C16—221no—
432C16—221no—
433C11#3370311yescharacteristic, complemented, Sylow
434C23—41no—
435C23—111no—
436Q8—41no—
437Q8—41no—
438Q8—161no—
439Q8—441no—
440Q8—441no—
441Q8—441no—
442Q8—441no—
443Q8—882no—
444Q8—1761no—
445D4—41no—
446D4—41no—
447D4—882no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—111no—
452C2×C4—112no—
453C2×C4—112no—
454C2×C4—111no—
455C2×C4—111no—
456C2×C4—441no—
457C2×C4—441no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—882no—
461C2×C4—882no—
462C2×C4—1761no—
463C2×C4D8×D1111yescharacteristic
464C2×C4D8×D1111yescharacteristic
465C2×C4C2×D4×D1111yescharacteristic
466C8—112no—
467C8—112no—
468C8SD16×D1112yes—
469C8#41×D1111yescharacteristic
470C8#41×D1111yescharacteristic
471C22—81no—
472C22—81no—
473C22—81no—
474C22—112no—
475C22—221no—
476C22—221no—
477C22C2×D8×D1111yescharacteristic
478C4—21no—
479C4—21no—
480C4—81no—
481C4—81no—
482C4—81no—
483C4—112no—
484C4—221no—
485C4—221no—
486C4—881no—
487C4—881no—
488C4—881no—
489C4—881no—
490C4D11×#12411yescharacteristic
491C4C2×SD16×D1111yescharacteristic
492C2—161no—
493C2—222no—
494C2D11×#48611yescharacteristic
495C2#1308176211yescharacteristic
496C2#1308176811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2243C2
socleC22×C11C22×D8
prime radicalC2×#66965C22
hypercenter#2243D11
hypocenterC11#33703
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2243

Complements

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

NH ≅ G/Ntype
1. #13079149C2semidirect
3. #13070862C2semidirect
4. #13070860C2semidirect
5. #13070851C2semidirect
6. #13070847C2semidirect
7. #13070846C2semidirect
8. #13070845C2semidirect
9. #13070842C2semidirect
10. #13070334C2semidirect
13. D11×#358C2semidirect
14. #13070214C2semidirect
15. C11×#2243C2semidirect
191. #2243D11semidirect
433. C11#33703semidirect

Maximal subgroups

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

subgroupindex
#130791492
#130791062
#130708622
#130708602
#130708512
#130708472
#130708462
#130708452
#130708422
#130703342
#130703252
#130703202
D11×#3582
#130702142
C11×#22432
#3370311