Finite Group Databasebeta

← #14910681

Subgroups — #14910681

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081014C211yesmaximal, characteristic, complemented
2#13080357C211yesmaximal, characteristic, complemented
3#13070849C211yesmaximal, characteristic, complemented
4#13070823C211yesmaximal, characteristic, complemented
5#13070801C211yesmaximal, characteristic, complemented
6#13070782C211yesmaximal, characteristic, complemented
7#13070715C211yesmaximal, characteristic, complemented
8#13070702C211yesmaximal, characteristic, complemented
9#13070674C211yesmaximal, characteristic, complemented
10#13070542C211yesmaximal, characteristic, complemented
11#13070533C211yesmaximal, characteristic, complemented
12#13070465C211yesmaximal, characteristic, complemented
13C16×C22⋊D11C211yesmaximal, characteristic, complemented
14#13070322C211yesmaximal, characteristic, complemented
15C2×C11×#358C211yesmaximal, characteristic, complemented
16C22×C11×Q16C2211yescharacteristic
17#10623348—21no—
18C2×#66972C2211yescharacteristic
19#10623045—21no—
20C22×C11×C16C2211yescharacteristic
21C2×C11×#107C2211yescharacteristic
22#10622840—21no—
23#10622804C2211yescharacteristic
24#10622801C2211yescharacteristic
25#10622800—21no—
26#10622798—21no—
27Q16×Dic11C2211yescharacteristic
28C2×#66892C2211yescharacteristic
29C2×#66892C2211yescharacteristic
30#10622728C2211yescharacteristic
31#10622728C2211yescharacteristic
32C8×C22⋊D11C2211yescharacteristic
33#10622581—21no—
34C2×D176C2211yescharacteristic
35C2×C16×D11C2211yescharacteristic
36#10622504—21no—
37#10622498—21no—
38#10622496C2211yescharacteristic
39#10622493C2211yescharacteristic
40#10622491C2211yescharacteristic
41#10622485C2211yescharacteristic
42C11×#358C2211yescharacteristic
43C11×#358C2211yescharacteristic
44C11×#358C2211yescharacteristic
45C11×#358C2211yescharacteristic
46#10622202C2211yescharacteristic
47#10622202C2211yescharacteristic
48C22⋊(C11⋊C16)C2211yescharacteristic
49#10622147C2211yescharacteristic
50#10622147C2211yescharacteristic
51(C2×D11)⋊C16C2211yescharacteristic
52#10622142C2211yescharacteristic
53Dic11⋊C16C2211yescharacteristic
54C16×Dic11C2211yescharacteristic
55#10622129C2211yescharacteristic
56#10622129C2211yescharacteristic
57#10622128C2211yescharacteristic
58#10622128C2211yescharacteristic
59C22×Q8×C11—21no—
60C2×#4343—21no—
61C2×C11×Q16—22no—
62C2×C11×Q16—21no—
63C2×C11×Q16—41no—
64C2×C11×Q16C2311yescharacteristic
65C2×C11×Q16C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68#67000—21no—
69#67000—41no—
70#66999—21no—
71#66999—41no—
72Q8×Dic11—21no—
73C2×#4325—21no—
74C2×#4325—21no—
75#66983—21no—
76#66983—21no—
77#66983—41no—
78#66983—41no—
79C4×C22⋊D11—41no—
80C4×C22⋊D11—41no—
81C4×C22⋊D11D411yescharacteristic
82#66972—22no—
83#66972—41no—
84C2×D88C2311yescharacteristic
85C2×D88C2311yescharacteristic
86C2×C8×D11C2311yescharacteristic
87#66951—41no—
88#66948—21no—
89#66947—41no—
90#66946—21no—
91#66945—21no—
92#66943—21no—
93C2×C11×C16—41no—
94C2×C11×C16C2311yescharacteristic
95C2×C11×C16C2311yescharacteristic
96C11×#107—21no—
97C11×#107C2311yescharacteristic
98C11×#107C2311yescharacteristic
99#66899—21no—
100#66899—21no—
101C22⋊(C11⋊C8)D411yescharacteristic
102#66892—22no—
103#66892—41no—
104#66885—21no—
105#66885—21no—
106(C2×D11)⋊C8D411yescharacteristic
107#66882C2311yescharacteristic
108#66882C2311yescharacteristic
109Dic11⋊C8D411yescharacteristic
110C8×Dic11C2311yescharacteristic
111C2×C11⋊C16C2311yescharacteristic
112C2×C11⋊C16C2311yescharacteristic
113#66873—21no—
114#66873—21no—
115#66872—21no—
116#66872—21no—
117D176—41no—
118C16×D11—41no—
119#33868—111nomaximal, Sylow
120C2×Q8×C11—21no—
121C2×Q8×C11—21no—
122C2×Q8×C11—42no—
123C2×Q8×C11—41no—
124C2×Q8×C11—81no—
125C22×C4×C11—41no—
126C22×C4×C11—41no—
127C22×C4×C11C2×D411yescharacteristic
128C2×C22⋊D11—41no—
129C2×C22⋊D11—41no—
130C2×C22⋊D11D811yescharacteristic
131#4343—42no—
132#4343—81no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—41no—
136C2×D44—41no—
137C2×C4×D11—41no—
138C2×C4×D11—41no—
139C2×C4×D11C2×D411yescharacteristic
140C11×Q16—21no—
141C11×Q16—21no—
142C11×Q16—21no—
143C11×Q16—42no—
144C11×Q16#4112yes—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11C2×D411yescharacteristic
148C2×C8×C11C2411yescharacteristic
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—41no—
152C22⋊Dic11D811yescharacteristic
153#4325—42no—
154#4325—81no—
155(C2×D11)⋊C4—41no—
156(C2×D11)⋊C4—41no—
157(C2×D11)⋊C4—41no—
158(C2×D11)⋊C4—41no—
159(C2×D11)⋊C4—41no—
160(C2×D11)⋊C4—41no—
161(C2×D11)⋊C4—41no—
162(C2×D11)⋊C4—41no—
163(C2×D11)⋊C4D811yescharacteristic
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—41no—
167C4⋊Dic11—41no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170Dic11⋊C4D811yescharacteristic
171C4×Dic11—41no—
172C4×Dic11—41no—
173C4×Dic11C2×D411yescharacteristic
174C2×C11⋊C8C2×D411yescharacteristic
175C2×C11⋊C8C2×D411yescharacteristic
176D88—21no—
177D88—21no—
178D88—21no—
179D88—21no—
180C8×D11—21no—
181C8×D11—21no—
182C11×C16—21no—
183C11×C16—21no—
184C11⋊C16—21no—
185C11⋊C16—21no—
186#3339—111no—
187#3285—111no—
188#2242—111no—
189#2237—111no—
190#2233—111no—
191#2229—111no—
192#2217—111no—
193#2215—111no—
194#2210—111no—
195#2186—111no—
196#2185—111no—
197C4×SD32—111no—
198D4×C16—111no—
199#2138—111no—
200C2×#358D1111yescharacteristic, complemented
201C23×C11C2×D811yescharacteristic
202C22×D11—41no—
203C22×D11—41no—
204C22×D11C2×D811yescharacteristic
205Q8×C11—22no—
206Q8×C11—41no—
207Q8×C11—41no—
208Q8×C11—41no—
209Q8×C11—82no—
210C2×C4×C11—21no—
211C2×C4×C11—21no—
212C2×C4×C11—41no—
213C2×C4×C11—41no—
214C2×C4×C11—41no—
215C2×C4×C11—41no—
216C2×C4×C11—82no—
217C2×C4×C11—161no—
218C2×C4×C11C2×D811yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C22⋊D11—22no—
221C22⋊D11—82no—
222C22⋊D11—82no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225C2×Dic11C2×D811yescharacteristic
226C2×Dic11C2×D811yescharacteristic
227C2×Dic11C2×D811yescharacteristic
228D44—41no—
229D44—41no—
230D44—41no—
231D44—41no—
232D44—82no—
233D44—161no—
234C4×D11—21no—
235C4×D11—21no—
236C4×D11—82no—
237C4×D11—161no—
238C8×C11—21no—
239C8×C11C2×#4111yescharacteristic
240C8×C11H(5,𝔽2)11yescharacteristic
241C11⋊C8—21no—
242C11⋊C8—21no—
243C2×#135—111no—
244C22×Q16C2×D1111yescharacteristic
245#553—221no—
246#548—221no—
247C2×SD32—111no—
248C2×SD32—111no—
249C2×D16—111no—
250C22×C16—111no—
251C22×C16C2×D1111yescharacteristic
252#499—111no—
253#495—111no—
254#482—221no—
255#481—221no—
256#478—221no—
257#467—111no—
258#466—111no—
259#466—111no—
260#466—111no—
261#464—221no—
262#452—221no—
263#448—221no—
264C4×Q16—111no—
265C4×D8—111no—
266C8×D4—111no—
267#427—111no—
268C2×#107C2×D1111yescharacteristic
269#367—111no—
270#367—111no—
271#366—111no—
272C4⋊C16—111no—
273#358—111no—
274#358—111no—
275#358C2×D1111yescharacteristic
276#358C2×D1111yescharacteristic
277#358C2×D1111yescharacteristic
278#358C2×D1111yescharacteristic
279#357—111no—
280#357—111no—
281#357—111no—
282#357—111no—
283C22⋊C16—111no—
284C22⋊C16—111no—
285C4×C16—111no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11#50812yes—
289C22×C11C22×D811yescharacteristic
290C2×D11—21no—
291C2×D11—21no—
292C2×D11—21no—
293C2×D11—81no—
294C2×D11—81no—
295C2×D11—81no—
296C2×D11—81no—
297C2×D11—81no—
298C2×D11—81no—
299C4×C11—21no—
300C4×C11—42no—
301C4×C11—81no—
302C4×C11—81no—
303C4×C11—81no—
304C4×C11#54611yescharacteristic
305C4×C11#57711yescharacteristic
306Dic11—21no—
307Dic11—21no—
308Dic11—21no—
309Dic11—81no—
310Dic11—81no—
311C2×#41—221no—
312C22×Q8—21no—
313#135—222no—
314#135—441no—
315C2×Q16—22no—
316C2×Q16—21no—
317C2×Q16—41no—
318C2×Q16C22×D1111yescharacteristic
319C2×Q16C22×D1111yescharacteristic
320C2×SD16—221no—
321C2×SD16—221no—
322C2×D8—111no—
323C2×D8—111no—
324C22×C8—111no—
325C22×C8C22×D1111yescharacteristic
326#126—441no—
327#125—221no—
328#124—221no—
329#124—441no—
330#123—441no—
331C22⋊Q8—221no—
332C22⋊Q8—441no—
333#121—221no—
334#121—221no—
335#121—221no—
336#121—441no—
337#121—441no—
338C4×Q8—221no—
339C4×D4—111no—
340C4×D4—221no—
341C4×D4—441no—
342C4×D4—441no—
343#117—221no—
344C2×C4⋊C4—21no—
345SD32—222no—
346SD32—441no—
347D16—441no—
348C2×C16—41no—
349C2×C16—111no—
350C2×C16—111no—
351C2×C16—441no—
352C2×C16C22×D1111yescharacteristic
353C2×C16C22×D1111yescharacteristic
354#107—21no—
355#107—111no—
356#107—111no—
357#107C22×D1111yescharacteristic
358#107C22×D1111yescharacteristic
359#106—221no—
360#106—221no—
361C4⋊C8—111no—
362#103—221no—
363#103—221no—
364#102—221no—
365#102—221no—
366#102—221no—
367#102—221no—
368C22⋊C8—111no—
369C22⋊C8—111no—
370C4×C8—111no—
371C2×C11—22no—
372C2×C11#329411yescharacteristic
373C2×C11C2×#50811yescharacteristic
374C2×C11#341611yescharacteristic
375D11—41no—
376D11—161no—
377D11—161no—
378#41—442no—
379#41—881no—
380C2×Q8—21no—
381C2×Q8—21no—
382C2×Q8—42no—
383C2×Q8—41no—
384C2×Q8—81no—
385C2×D4—111no—
386C2×D4—221no—
387C2×D4—221no—
388C2×D4—441no—
389C2×D4—441no—
390C2×D4—441no—
391C2×D4—441no—
392C22×C4—41no—
393C22×C4—41no—
394C22×C4—111no—
395C22×C4—441no—
396C22×C4—441no—
397C22×C4D4×D1111yescharacteristic
398Q16—21no—
399Q16—21no—
400Q16—21no—
401Q16—42no—
402Q16#433912yes—
403SD16—442no—
404SD16—881no—
405D8—221no—
406D8—221no—
407D8—221no—
408D8—221no—
409C2×C8—21no—
410C2×C8—21no—
411C2×C8—111no—
412C2×C8—111no—
413C2×C8—221no—
414C2×C8—221no—
415C2×C8D4×D1111yescharacteristic
416C2×C8C23×D1111yescharacteristic
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—41no—
420C4⋊C4—111no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4—441no—
424C4⋊C4—441no—
425C4⋊C4—441no—
426C4⋊C4—441no—
427C22⋊C4—111no—
428C22⋊C4—111no—
429C22⋊C4—441no—
430C22⋊C4—441no—
431C22⋊C4—441no—
432C22⋊C4—441no—
433C22⋊C4—441no—
434C22⋊C4—441no—
435C22⋊C4—441no—
436C22⋊C4—441no—
437C42—111no—
438C42—441no—
439C42—441no—
440C16—21no—
441C16—21no—
442C16—221no—
443C16—221no—
444C11#3386811yescharacteristic, complemented, Sylow
445C23—111no—
446C23—441no—
447C23—441no—
448C23D8×D1111yescharacteristic
449Q8—22no—
450Q8—41no—
451Q8—41no—
452Q8—41no—
453Q8—82no—
454D4—222no—
455D4—441no—
456D4—441no—
457D4—441no—
458D4—441no—
459D4—882no—
460D4—882no—
461D4—882no—
462D4—1761no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—82no—
470C2×C4—111no—
471C2×C4—111no—
472C2×C4—111no—
473C2×C4—161no—
474C2×C4—221no—
475C2×C4—221no—
476C2×C4—441no—
477C2×C4—441no—
478C2×C4—882no—
479C2×C4—1761no—
480C2×C4D8×D1111yescharacteristic
481C2×C4C2×D4×D1111yescharacteristic
482C8—21no—
483C8—221no—
484C8—221no—
485C8C2×#433911yescharacteristic
486C8#6703711yescharacteristic
487C22—21no—
488C22—21no—
489C22—221no—
490C22—221no—
491C22—221no—
492C22—881no—
493C22—881no—
494C22—881no—
495C22—881no—
496C22—881no—
497C22—881no—
498C22#1062253212yes—
499C22C2×D8×D1111yescharacteristic
500C4—21no—
501C4—42no—
502C4—81no—
503C4—81no—
504C4—81no—
505C4—221no—
506C4—221no—
507C4—221no—
508C4—881no—
509C4—881no—
510C4#1062302111yescharacteristic
511C4#1062329311yescharacteristic
512C2—22no—
513C2—441no—
514C2—1761no—
515C2—1761no—
516C2#1308042511yescharacteristic
517C2C2×#1062253211yescharacteristic
518C2#1308175811yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC2×C11×#358C2
socleC22×C11C22×D8
hypercenterC2×#358D11
hypocenterC11#33868
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
1. #13081014C2semidirect
2. #13080357C2semidirect
3. #13070849C2semidirect
4. #13070823C2semidirect
5. #13070801C2semidirect
6. #13070782C2semidirect
7. #13070715C2semidirect
8. #13070702C2semidirect
9. #13070674C2semidirect
10. #13070542C2semidirect
11. #13070533C2semidirect
12. #13070465C2semidirect
13. C16×C22⋊D11C2semidirect
14. #13070322C2semidirect
15. C2×C11×#358C2semidirect
200. C2×#358D11semidirect
444. C11#33868semidirect

Maximal subgroups

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

subgroupindex
#130810142
#130803572
#130708492
#130708232
#130708012
#130707822
#130707152
#130707022
#130706742
#130705422
#130705332
#130704652
C16×C22⋊D112
#130703222
C2×C11×#3582
#3386811