Finite Group Databasebeta

← #14910215

Subgroups — #14910215

Order 2816.

488 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13079256C211yesmaximal, characteristic, complemented
2#13079248C211yesmaximal, characteristic, complemented
3#13070762C211yesmaximal, characteristic, complemented
4#13070761C211yesmaximal, characteristic, complemented
5#13070757C211yesmaximal, characteristic, complemented
6#13070756C211yesmaximal, characteristic, complemented
7#13070722C211yesmaximal, characteristic, complemented
8#13070717C211yesmaximal, characteristic
9#13070712C211yesmaximal, characteristic, complemented
10#13070681C211yesmaximal, characteristic, complemented
11#13070676C211yesmaximal, characteristic, complemented
12#13070673C211yesmaximal, characteristic, complemented
13#13070670C211yesmaximal, characteristic, complemented
14#13070374C211yesmaximal, characteristic, complemented
15C11×#2217C211yesmaximal, characteristic, complemented
16#10623174—21no—
17#10623134—21no—
18C2×C11×SD32C2211yescharacteristic
19C22×C11×C16C2211yescharacteristic
20C11×#467C2211yescharacteristic
21C11×#466C2211yescharacteristic
22#10622804C2211yescharacteristic
23Q16×Dic11C2211yescharacteristic
24C2×#66893C2211yescharacteristic
25#10622768C2211yescharacteristic
26D8×Dic11C2211yescharacteristic
27C2×#66890C2211yescharacteristic
28#10622729C2211yescharacteristic
29#10622728C2211yescharacteristic
30#10622714C2211yescharacteristic
31C2×#66876C2211yescharacteristic
32#10622662—21no—
33#10622655—21no—
34C2×#66864C2211yescharacteristic
35#10622487C2211yescharacteristic
36#10622487C2211yescharacteristic
37#10622486C2211yescharacteristic
38#10622485C2211yescharacteristic
39#10622430—21no—
40#10622408—21no—
41#10622378—21no—
42#10622370—21no—
43C11×#367C2211yescharacteristic
44C11×#358C2211yescharacteristic
45C11×#357C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622200C2211yescharacteristic
48#10622147C2211yescharacteristic
49#10622143C2211yescharacteristic
50#10622141C2211yescharacteristic
51Dic11⋊C16C2211yescharacteristic
52Dic11⋊C16C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54Dic11⋊C16C2211yescharacteristic
55#10622130C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622128C2211yescharacteristic
59C2×C11×Q16C2311yescharacteristic
60C2×C11×D8C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C11×C22⋊Q8—21no—
63C11×#121—21no—
64#67000—21no—
65Q8×Dic11—21no—
66C2×#4325—21no—
67#66989—21no—
68#66989—41no—
69#66988—41no—
70D4×Dic11—21no—
71C2×#4324—21no—
72#66983—21no—
73#66979D411yescharacteristic
74#66977—21no—
75C2×#4318D411yescharacteristic
76C2×Dic44C2311yescharacteristic
77C2×D88C2311yescharacteristic
78#66951—41no—
79#66950—41no—
80#66946—21no—
81#66941—21no—
82#66941—21no—
83#66940—21no—
84#66938—41no—
85#66936—41no—
86#66932—41no—
87#66931—41no—
88C11×SD32—41no—
89C2×C11×C16—41no—
90C2×C11×C16C2311yescharacteristic
91C2×C11×C16C2311yescharacteristic
92C11×#107C2311yescharacteristic
93C11×#107C2311yescharacteristic
94C11×#103—21no—
95C11×#102—21no—
96#66899—21no—
97#66896—21no—
98#66893—41no—
99#66890—41no—
100#66885—21no—
101#66882C2311yescharacteristic
102#66882C2311yescharacteristic
103#66880—21no—
104#66879D411yescharacteristic
105#66879D411yescharacteristic
106C8×Dic11C2311yescharacteristic
107C8×Dic11C2311yescharacteristic
108#66876—41no—
109C2×C11⋊C16C2311yescharacteristic
110C2×C11⋊C16C2311yescharacteristic
111#66874—21no—
112#66873—21no—
113#66871—21no—
114#66871—21no—
115#66864—41no—
116#33829—111nomaximal, Sylow
117C2×Q8×C11—21no—
118C2×D4×C11—21no—
119C2×D4×C11—41no—
120C22×C4×C11C2×D411yescharacteristic
121C2×C22⋊D11—41no—
122C22×Dic11—41no—
123C2×D44—21no—
124C2×C4×D11—41no—
125C2×Dic22—21no—
126C2×Dic22—41no—
127C2×Dic22—41no—
128C11×Q16—21no—
129C11×Q16—21no—
130C11×D8—21no—
131C11×D8—21no—
132C2×C8×C11—21no—
133C2×C8×C11—21no—
134C2×C8×C11C2×D411yescharacteristic
135C2×C8×C11C2411yescharacteristic
136C11×C4⋊C4—21no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—41no—
139C11×C22⋊C4—41no—
140C11×C22⋊C4—41no—
141C22⋊Dic11—41no—
142C22⋊Dic11—41no—
143C22⋊Dic11—41no—
144C22⋊Dic11—41no—
145C22⋊Dic11D811yescharacteristic
146C22⋊Dic11D811yescharacteristic
147#4325—42no—
148#4324—42no—
149(C2×D11)⋊C4—41no—
150(C2×D11)⋊C4—41no—
151(C2×D11)⋊C4—41no—
152(C2×D11)⋊C4—41no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11—41no—
156C4⋊Dic11D811yescharacteristic
157C4⋊Dic11D811yescharacteristic
158Dic11⋊C4—41no—
159Dic11⋊C4—41no—
160Dic11⋊C4—41no—
161Dic11⋊C4—41no—
162C4×Dic11—41no—
163C4×Dic11—41no—
164C4×Dic11C2×D411yescharacteristic
165C4×Dic11C2×D411yescharacteristic
166#4318—41no—
167C2×C11⋊C8C2×D411yescharacteristic
168C2×C11⋊C8C2×D411yescharacteristic
169Dic44—21no—
170Dic44—21no—
171D88—21no—
172D88—21no—
173C11×C16—21no—
174C11×C16—21no—
175C11⋊C16—21no—
176C11⋊C16—21no—
177#3175—111no—
178#3175—111no—
179#2226—111no—
180#2226—111no—
181#2225—111no—
182#2225—111no—
183#2219—111no—
184#2218—111no—
185#2217—111no—
186#2217D1111yescharacteristic, complemented
187#2211—111no—
188#2211—111no—
189#2210—111no—
190#2210—111no—
191#2151—111no—
192C23×C11—41no—
193C23×C11C2×D811yescharacteristic
194C22×D11—41no—
195Q8×C11—41no—
196Q8×C11—41no—
197D4×C11—41no—
198D4×C11—41no—
199D4×C11—161no—
200C2×C4×C11—21no—
201C2×C4×C11—21no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—41no—
205C2×C4×C11C2×D811yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C22⋊D11—161no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—161no—
212C2×Dic11C2×D811yescharacteristic
213C2×Dic11C2×D811yescharacteristic
214C2×Dic11C2×D811yescharacteristic
215C2×Dic11C2×D811yescharacteristic
216D44—41no—
217D44—41no—
218C4×D11—161no—
219Dic22—41no—
220Dic22—41no—
221Dic22—161no—
222Dic22—161no—
223C8×C11—21no—
224C8×C11H(5,𝔽2)11yescharacteristic
225C8×C112−1+411yescharacteristic
226C11⋊C8—21no—
227C11⋊C8—21no—
228#542—221no—
229#542—221no—
230C2×Q32—111no—
231C2×SD32—111no—
232C2×SD32C2×D1111yescharacteristic
233C2×D16—111no—
234C2×M32—111no—
235C22×C16C2×D1111yescharacteristic
236#500—111no—
237#500—111no—
238#495—111no—
239#495—111no—
240#489—221no—
241#489—221no—
242#468—221no—
243#468—221no—
244#467—111no—
245#467C2×D1111yescharacteristic
246#466—111no—
247#466C2×D1111yescharacteristic
248#440—221no—
249#440—221no—
250C4×Q16—111no—
251C4×Q16—111no—
252C4×D8—111no—
253C4×D8—111no—
254#405—111no—
255#367—111no—
256#367—111no—
257#367—111no—
258#367C2×D1111yescharacteristic
259C4⋊C16—111no—
260C4⋊C16—111no—
261C4⋊C16—111no—
262C4⋊C16—111no—
263#358—111no—
264#358—111no—
265#358—111no—
266#358C2×D1111yescharacteristic
267#357—111no—
268#357—111no—
269#357—111no—
270#357C2×D1111yescharacteristic
271C22×C11—21no—
272C22×C11—21no—
273C22×C11—21no—
274C22×C11—81no—
275C22×C11—81no—
276C22×C11—81no—
277C22×C11C22×D811yescharacteristic
278C2×D11—81no—
279C2×D11—81no—
280C2×D11—81no—
281C4×C11—21no—
282C4×C11—81no—
283C4×C11—81no—
284C4×C11—81no—
285C4×C11#53711yescharacteristic
286C4×C11#57511yescharacteristic
287Dic11—21no—
288Dic11—21no—
289Dic11—21no—
290Dic11—21no—
291Dic11—81no—
292Dic11—81no—
293Dic11—81no—
294C2×Q16—111no—
295C2×Q16C22×D1111yescharacteristic
296C2×SD16—221no—
297C2×SD16—221no—
298C2×D8—111no—
299C2×D8C22×D1111yescharacteristic
300C2×M16—111no—
301C22×C8C22×D1111yescharacteristic
302C4⋊Q8—221no—
303C4⋊Q8—221no—
304#126—441no—
305#126—441no—
306#124—221no—
307#124—221no—
308#124—441no—
309#124—441no—
310#123—441no—
311#123—441no—
312C22⋊Q8—21no—
313C22⋊Q8—221no—
314C22⋊Q8—441no—
315C22⋊Q8—441no—
316#121—21no—
317#121—221no—
318C4×Q8—221no—
319C4×Q8—221no—
320C4×D4—221no—
321C4×D4—221no—
322#117—111no—
323Q32—441no—
324SD32—41no—
325SD32—441no—
326D16—441no—
327M32—441no—
328C2×C16—41no—
329C2×C16—111no—
330C2×C16—111no—
331C2×C16C22×D1111yescharacteristic
332C2×C16C22×D1111yescharacteristic
333#107—111no—
334#107—111no—
335#107—221no—
336#107—221no—
337#107C22×D1111yescharacteristic
338#107C22×D1111yescharacteristic
339#103—21no—
340#103—221no—
341#103—221no—
342#103—221no—
343#102—21no—
344#102—221no—
345#102—221no—
346#102—221no—
347#97—111no—
348#97—111no—
349C4×C8—111no—
350C4×C8—111no—
351C2×C11—41no—
352C2×C11—161no—
353C2×C11#324511yescharacteristic
354C2×C11#341611yescharacteristic
355C2×C11#341611yescharacteristic
356D11—161no—
357C2×Q8—21no—
358C2×Q8—221no—
359C2×Q8—441no—
360C2×Q8—441no—
361C2×D4—21no—
362C2×D4—41no—
363C2×D4—221no—
364C2×D4—441no—
365C22×C4—441no—
366C22×C4—441no—
367C22×C4D4×D1111yescharacteristic
368Q16—21no—
369Q16—21no—
370Q16—221no—
371Q16—221no—
372SD16—442no—
373SD16—442no—
374D8—21no—
375D8—21no—
376D8—221no—
377D8—221no—
378M16—441no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8—111no—
382C2×C8—111no—
383C2×C8D4×D1111yescharacteristic
384C2×C8C23×D1111yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—41no—
388C4⋊C4—111no—
389C4⋊C4—111no—
390C4⋊C4—221no—
391C4⋊C4—221no—
392C4⋊C4—441no—
393C4⋊C4—441no—
394C4⋊C4—441no—
395C4⋊C4—441no—
396C4⋊C4—441no—
397C22⋊C4—41no—
398C22⋊C4—41no—
399C22⋊C4—111no—
400C22⋊C4—111no—
401C22⋊C4—441no—
402C22⋊C4—441no—
403C22⋊C4—441no—
404C22⋊C4—441no—
405C22⋊C4—441no—
406C22⋊C4—441no—
407C22⋊C4—441no—
408C22⋊C4—441no—
409C42—111no—
410C42—111no—
411C42—441no—
412C42—441no—
413C16—21no—
414C16—21no—
415C16—221no—
416C16—221no—
417C11#3382911yescharacteristic, complemented, Sylow
418C23—41no—
419C23—441no—
420C23D8×D1111yescharacteristic
421Q8—41no—
422Q8—41no—
423Q8—441no—
424Q8—441no—
425Q8—1761no—
426Q8—1761no—
427D4—41no—
428D4—41no—
429D4—161no—
430D4—441no—
431D4—441no—
432D4—1761no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—111no—
439C2×C4—111no—
440C2×C4—111no—
441C2×C4—111no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—1761no—
446C2×C4—1761no—
447C2×C4D8×D1111yescharacteristic
448C2×C4C2×D4×D1111yescharacteristic
449C8—21no—
450C8—221no—
451C8—221no—
452C8#6703711yescharacteristic
453C8#6704311yescharacteristic
454C22—21no—
455C22—21no—
456C22—21no—
457C22—81no—
458C22—81no—
459C22—81no—
460C22—881no—
461C22—881no—
462C22—881no—
463C22C2×D8×D1111yescharacteristic
464C4—21no—
465C4—81no—
466C4—81no—
467C4—81no—
468C4—221no—
469C4—221no—
470C4—221no—
471C4—221no—
472C4—881no—
473C4—881no—
474C4—881no—
475C4#1062312811yescharacteristic
476C4#1062329911yescharacteristic
477C2—41no—
478C2—161no—
479C2—1761no—
480C2#1307992211yescharacteristic
481C2#1308175811yescharacteristic
482C2#1308175911yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2217C2
socleC22×C11C22×D8
prime radical#13070717C2
hypercenter#2217D11
hypocenterC11#33829
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #2217

Complements

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

NH ≅ G/Ntype
1. #13079256C2semidirect
2. #13079248C2semidirect
3. #13070762C2semidirect
4. #13070761C2semidirect
5. #13070757C2semidirect
6. #13070756C2semidirect
7. #13070722C2semidirect
9. #13070712C2semidirect
10. #13070681C2semidirect
11. #13070676C2semidirect
12. #13070673C2semidirect
13. #13070670C2semidirect
14. #13070374C2semidirect
15. C11×#2217C2semidirect
186. #2217D11semidirect
417. C11#33829semidirect

Maximal subgroups

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

subgroupindex
#130792562
#130792482
#130707622
#130707612
#130707572
#130707562
#130707222
#130707172
#130707122
#130706812
#130706762
#130706732
#130706702
#130703742
C11×#22172
#3382911