Finite Group Databasebeta

← #14765633

Subgroups — #14765633

Order 2816.

726 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078529C211yesmaximal, characteristic
2#13077306C211yesmaximal, characteristic
3C2×#10622612C211yesmaximal, characteristic, complemented
4#13069368C212yesmaximal, complemented
5#13069328C212yesmaximal, complemented
6#13069218C212yesmaximal, complemented
7#13068916C211yesmaximal, characteristic
8#13068892C212yesmaximal, complemented
9#13068820C211yesmaximal, characteristic, complemented
10#13068394C211yesmaximal, characteristic, complemented
11C11×#1826C211yesmaximal, characteristic, complemented
12C2×C11×#117C2211yescharacteristic
13#10623322C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C2×#66960C2211yescharacteristic
17C11×#407C2211yescharacteristic
18C4×C11×C22⋊C4C2211yescharacteristic
19C2×C22⋊(C11⋊C8)C2211yescharacteristic
20#10622742C2211yescharacteristic
21C2×#66886C2212yes—
22#10622735C2211yescharacteristic
23#10622732C2211yescharacteristic
24#10622616C412yescomplemented
25#10622615C2212yes—
26#10622612—21no—
27#10622612—21no—
28#10622612C2212yes—
29#10622612C2212yes—
30#10622611C2212yes—
31#10622609C412yescomplemented
32#10622584C411yescharacteristic, complemented
33#10622583C411yescharacteristic, complemented
34#10622581C411yescharacteristic, complemented
35#10622580C411yescharacteristic, complemented
36C2×#66869C2212yes—
37C2×C4⋊(C11⋊C8)—21no—
38C2×C4⋊(C11⋊C8)—21no—
39C2×#66867C2212yes—
40#10622343—21no—
41#10622343—21no—
42(C22⋊D11)⋊C8—21no—
43(C22⋊D11)⋊C8—21no—
44C11×#339C2212yes—
45C11×#339C2212yes—
46#10622196C2212yes—
47#10622162C2212yes—
48#10622161C2212yes—
49C23×C4×C11C2311yescharacteristic
50C2×#4339C2311yescharacteristic
51C2×C11×M16C2311yescharacteristic
52C2×C11×M16C2311yescharacteristic
53C11×#117—21no—
54C11×#117—21no—
55C11×#117C2×C412yes—
56C11×#117C2312yes—
57C2×C11×C4⋊C4C2×C411yescharacteristic
58C2×C11×C4⋊C4C2×C411yescharacteristic
59C2×C11×C22⋊C4—21no—
60C2×C11×C22⋊C4—21no—
61C2×C42×C11—21no—
62C2×C42×C11C2312yes—
63#67006—21no—
64#66983C2×C411yescharacteristic
65#66983C2×C411yescharacteristic
66#66982—21no—
67C4×C22⋊D11—21no—
68C4×C22⋊D11—21no—
69#66979C2311yescharacteristic
70#66977C2×C411yescharacteristic
71#66977C2×C411yescharacteristic
72C2×#4318—21no—
73C2×#4318—42no—
74C2×#4318C2312yes—
75C22×C11⋊C8—21no—
76C22×C11⋊C8—42no—
77C22×C11⋊C8D411yescharacteristic
78C22×C11⋊C8D411yescharacteristic
79C22×C11⋊C8D411yescharacteristic
80C22×C11⋊C8D411yescharacteristic
81C22×C11⋊C8C2312yes—
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84#66960—42no—
85C2×#4313—21no—
86C2×C8×D11—21no—
87C11×C22⋊C8—21no—
88C11×C22⋊C8—21no—
89C11×#95—21no—
90C22⋊(C11⋊C8)C2×C411yescharacteristic
91C22⋊(C11⋊C8)C2×C411yescharacteristic
92C22⋊(C11⋊C8)C2×C412yes—
93#66886—42no—
94(C2×D11)⋊C8—21no—
95(C2×D11)⋊C8—21no—
96#66879—21no—
97Dic11⋊C8—21no—
98Dic11⋊C8—21no—
99C8×Dic11—21no—
100#66874C2×C412yes—
101#66874C2×C412yes—
102#66873C2×C412yes—
103#66873C2×C412yes—
104#66872C2×C412yes—
105#66872C2×C412yes—
106#66871C2×C412yes—
107#66871C2×C412yes—
108#66869—42no—
109C4⋊(C11⋊C8)—22no—
110C4⋊(C11⋊C8)—22no—
111C4⋊(C11⋊C8)—22no—
112C4⋊(C11⋊C8)—22no—
113#66867—42no—
114#22096—111nomaximal, Sylow
115C24×C11#4111yescharacteristic
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11C22×C411yescharacteristic
122C22×C4×C11C22×C411yescharacteristic
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11#4111yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C2×C22⋊D11—21no—
128C2×C22⋊D11—21no—
129C2×C22⋊D11—21no—
130#4339—22no—
131#4339—22no—
132C2×D44C22×C411yescharacteristic
133C2×C4×D11—21no—
134C2×Dic22C22×C411yescharacteristic
135C11×M16—22no—
136C11×M16—22no—
137C2×C8×C11—21no—
138C2×C8×C11—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4C22×C412yes—
142C11×C4⋊C4C22×C412yes—
143C11×C22⋊C4—22no—
144C11×C22⋊C4—22no—
145C11×C22⋊C4—42no—
146C42×C11—22no—
147C42×C11—22no—
148C42×C11—22no—
149C42×C11—22no—
150C22⋊Dic11—21no—
151C22⋊Dic11—21no—
152C22⋊Dic11—21no—
153(C2×D11)⋊C4—21no—
154(C2×D11)⋊C4—21no—
155C4⋊Dic11C22×C411yescharacteristic
156C4⋊Dic11C22×C411yescharacteristic
157Dic11⋊C4—21no—
158Dic11⋊C4—21no—
159C4×Dic11—21no—
160#4318—22no—
161#4318—22no—
162#4318—42no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—41no—
169C2×C11⋊C8—41no—
170C2×C11⋊C8—41no—
171C2×C11⋊C8—41no—
172C2×C11⋊C8—42no—
173C2×C11⋊C8C22×C412yes—
174C2×C11⋊C8C22×C412yes—
175C2×C11⋊C8C2×D411yescharacteristic
176C2×C11⋊C8C2×D411yescharacteristic
177C2×C11⋊C8C2×D411yescharacteristic
178C2×C11⋊C8C2×D411yescharacteristic
179#4313—42no—
180C8×D11—42no—
181#3091—111no—
182#2929—111no—
183C2×#424—111no—
184#1946—112no—
185#1938—112no—
186#1922—112no—
187#1871—111no—
188#1866—112no—
189#1855—111no—
190#1826D1111yescharacteristic, complemented
191#1752—111no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—41no—
195C23×C11C4×D411yescharacteristic
196C23×C11C4×D411yescharacteristic
197C23×C11C2×#4111yescharacteristic
198C22×D11—21no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—21no—
203C2×C4×C11—21no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—42no—
213C2×C4×C11C4×D411yescharacteristic
214C2×C4×C11C4×D411yescharacteristic
215C2×C4×C11C23×C411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11H(5,𝔽2)12yes—
218C2×C4×C112−1+412yes—
219C22⋊D11—42no—
220C22⋊D11—42no—
221C22⋊D11—42no—
222C2×Dic11—21no—
223C2×Dic11—21no—
224C2×Dic11—21no—
225D44—22no—
226C4×D11—41no—
227C4×D11—41no—
228Dic22—22no—
229C8×C11—41no—
230C8×C11—41no—
231C11⋊C8—22no—
232C11⋊C8—22no—
233C11⋊C8—21no—
234C11⋊C8—21no—
235C11⋊C8—21no—
236C11⋊C8—21no—
237C11⋊C8—42no—
238C2×#131—111no—
239C22×M16—111no—
240C23×C8—111no—
241#525—111no—
242C2×#117C2×D1111yescharacteristic
243#485—112no—
244#484—111no—
245#483—111no—
246#482—112no—
247#481—111no—
248#480—111no—
249#435—221no—
250#435—221no—
251C8×D4—221no—
252C8×D4—221no—
253C2×#108—112no—
254#427—112no—
255#424—111no—
256#424—112no—
257#424—112no—
258#424—221no—
259#424—221no—
260C2×C4⋊C8—221no—
261C2×C4⋊C8—221no—
262C2×#104—112no—
263#416—112no—
264#408—111no—
265#407C2×D1111yescharacteristic
266C2×C22⋊C8—111no—
267#405—111no—
268C2×#97—112no—
269C4×C22⋊C4C2×D1111yescharacteristic
270#341—112no—
271#339—112no—
272#339C2×D1112yes—
273#339C2×D1112yes—
274#336—112no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—21no—
279C22×C11—21no—
280C22×C11—21no—
281C22×C11—21no—
282C22×C11—44no—
283C22×C11#44412yes—
284C22×C11C2×C4×D411yescharacteristic
285C22×C11#53912yes—
286C2×D11—41no—
287C2×D11—41no—
288C2×D11—41no—
289C4×C11—21no—
290C4×C11—21no—
291C4×C11—42no—
292C4×C11—42no—
293C4×C11—82no—
294C4×C11#52012yes—
295C4×C11#53411yescharacteristic
296C4×C11#53611yescharacteristic
297Dic11—41no—
298Dic11—41no—
299Dic11—41no—
300C2×#41—111no—
301C23×C4C22×D1111yescharacteristic
302#131—442no—
303C2×M16—112no—
304C2×M16—221no—
305C2×M16—221no—
306C2×M16—442no—
307C2×M16C22×D1111yescharacteristic
308C2×M16C22×D1111yescharacteristic
309C22×C8—111no—
310C22×C8—111no—
311C22×C8—112no—
312C22×C8—111no—
313C22×C8—111no—
314C22×C8—111no—
315C22×C8—111no—
316C22×C8—221no—
317C22×C8—221no—
318C22×C8—442no—
319#123—221no—
320C22⋊Q8—111no—
321C22⋊Q8—111no—
322#121—111no—
323#121—111no—
324#120—221no—
325C4×D4—221no—
326C4×D4—221no—
327#117—21no—
328#117—21no—
329#117—111no—
330#117C4×D1112yes—
331#117C22×D1112yes—
332C2×C4⋊C4C4×D1111yescharacteristic
333C2×C4⋊C4C4×D1111yescharacteristic
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C42—21no—
337C2×C42C22×D1112yes—
338#108—442no—
339#107—112no—
340#107—112no—
341#106—112no—
342#106—112no—
343C4⋊C8—222no—
344C4⋊C8—222no—
345C4⋊C8—222no—
346C4⋊C8—222no—
347C4⋊C8—221no—
348C4⋊C8—221no—
349#104—442no—
350#103—112no—
351#103—112no—
352#102—112no—
353#102—112no—
354C22⋊C8—21no—
355C22⋊C8—21no—
356C22⋊C8—111no—
357C22⋊C8—111no—
358C22⋊C8—112no—
359C22⋊C8—221no—
360C22⋊C8—221no—
361#97—221no—
362#97—442no—
363C4×C8—221no—
364#95—21no—
365C2×C11—22no—
366C2×C11—22no—
367C2×C11—41no—
368C2×C11#232211yescharacteristic
369C2×C11C2×#44411yescharacteristic
370C2×C11#295511yescharacteristic
371D11—81no—
372C24#434111yescharacteristic
373#41—222no—
374#41—222no—
375C2×Q8—111no—
376C2×D4—111no—
377C2×D4—221no—
378C2×D4—221no—
379C2×D4—221no—
380C22×C4—22no—
381C22×C4—22no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—22no—
385C22×C4—221no—
386C22×C4C2×C4×D1111yescharacteristic
387C22×C4C2×C4×D1111yescharacteristic
388C22×C4D4×D1111yescharacteristic
389C22×C4D4×D1111yescharacteristic
390C22×C4#434111yescharacteristic
391C22×C4C23×D1111yescharacteristic
392M16—22no—
393M16—22no—
394M16—222no—
395M16—222no—
396M16—442no—
397M16—442no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—112no—
401C2×C8—112no—
402C2×C8—111no—
403C2×C8—111no—
404C2×C8—111no—
405C2×C8—111no—
406C2×C8—222no—
407C2×C8—222no—
408C2×C8—222no—
409C2×C8—222no—
410C2×C8—222no—
411C2×C8—442no—
412C2×C8—441no—
413C2×C8—441no—
414C2×C8—441no—
415C2×C8—441no—
416C2×C8—442no—
417C4⋊C4—21no—
418C4⋊C4—21no—
419C4⋊C4—111no—
420C4⋊C4—111no—
421C4⋊C4—221no—
422C4⋊C4—221no—
423C4⋊C4C2×C4×D1112yes—
424C4⋊C4C2×C4×D1112yes—
425C22⋊C4—22no—
426C22⋊C4—22no—
427C22⋊C4—42no—
428C22⋊C4—221no—
429C22⋊C4—221no—
430C22⋊C4—221no—
431C22⋊C4—221no—
432C22⋊C4—221no—
433C42—22no—
434C42—22no—
435C42—22no—
436C42—22no—
437C42—221no—
438C11#2209611yescharacteristic, complemented, Sylow
439C23—22no—
440C23—22no—
441C23—41no—
442C23—221no—
443C23(C22⋊D11)⋊C411yescharacteristic
444C23(C22⋊D11)⋊C411yescharacteristic
445C23C2×#434111yescharacteristic
446Q8—222no—
447D4—222no—
448D4—442no—
449D4—442no—
450D4—442no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—42no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—221no—
466C2×C4—221no—
467C2×C4—221no—
468C2×C4—441no—
469C2×C4—441no—
470C2×C4(C22⋊D11)⋊C411yescharacteristic
471C2×C4(C22⋊D11)⋊C411yescharacteristic
472C2×C4C22×C4×D1111yescharacteristic
473C2×C4C2×D4×D1111yescharacteristic
474C2×C4#6704212yes—
475C2×C4#6704312yes—
476C8—41no—
477C8—41no—
478C8—222no—
479C8—222no—
480C8—221no—
481C8—221no—
482C8—221no—
483C8—221no—
484C8—442no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—44no—
493C22—441no—
494C22—441no—
495C22—441no—
496C22#1062243612yes—
497C22C2×(C22⋊D11)⋊C411yescharacteristic
498C22#1062319612yes—
499C4—21no—
500C4—21no—
501C4—42no—
502C4—42no—
503C4—82no—
504C4—441no—
505C4—441no—
506C4—441no—
507C4#1062305412yes—
508C4#1062317911yescharacteristic
509C4#1062318411yescharacteristic
510C2—22no—
511C2—22no—
512C2—41no—
513C2—881no—
514C2#1307128211yescharacteristic
515C2C2×#1062243611yescharacteristic
516C2#1307751511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1826C2
socleC22×C11C2×C4×D4
prime radical#10623322C22
cosocleC22×C4×C11C24
hypercenter#1826D11
hypocenterC11#22096
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1826

Complements

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

NH ≅ G/Ntype
3. C2×#10622612C2semidirect
4. #13069368C2semidirect
5. #13069328C2semidirect
6. #13069218C2semidirect
8. #13068892C2semidirect
9. #13068820C2semidirect
10. #13068394C2semidirect
11. C11×#1826C2semidirect
24. #10622616C4semidirect
31. #10622609C4semidirect
32. #10622584C4semidirect
33. #10622583C4semidirect
34. #10622581C4semidirect
35. #10622580C4semidirect
190. #1826D11semidirect
438. C11#22096semidirect

Maximal subgroups

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

subgroupindex
#130785292
#130773062
C2×#106226122
#130693682
#130693282
#130692182
#130689162
#130688922
#130688202
#130683942
C11×#18262
#2209611