Finite Group Databasebeta

← #14853516

Subgroups — #14853516

Order 2816.

742 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076979C211yesmaximal, characteristic, complemented
2#13070183C212yesmaximal, complemented
3#13069852C212yesmaximal
4#13069316C212yesmaximal
5#13069309C212yesmaximal, complemented
6#13068621C211yesmaximal, characteristic, complemented
7#13068621C211yesmaximal, characteristic, complemented
8#13068616C211yesmaximal, characteristic
9#13068616C211yesmaximal, characteristic
10#13068469C211yesmaximal, characteristic, complemented
11C4×C11×#124C211yesmaximal, characteristic
12C2×C11×#124C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C2×#66923—21no—
16C11×#391C2211yescharacteristic
17C11×#390C2211yescharacteristic
18C11×#388—21no—
19C11×#388—21no—
20C11×#382C2211yescharacteristic
21C4×C11×C22⋊C4—21no—
22C4×C11×C22⋊C4—21no—
23C43×C11C2211yescharacteristic
24C2×#66899C2212yes—
25C2×#66899C2212yes—
26C2×#66896C2212yes—
27C2×#66896C2212yes—
28#10622549—21no—
29#10622548C2211yescharacteristic
30#10622548C2211yescharacteristic
31#10622541—21no—
32#10622541—21no—
33#10622541C2212yes—
34#10622541C2212yes—
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×#66867C2212yes—
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622162C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11C2311yescharacteristic
45C23×C4×C11—21no—
46C11×#124—22no—
47C11×#124—22no—
48C4×Q8×C11—22no—
49C4×Q8×C11—22no—
50C4×D4×C11—22no—
51C4×D4×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C22⋊C4—21no—
56C2×C11×C22⋊C4—21no—
57C2×C11×C22⋊C4—21no—
58C2×C11×C22⋊C4—21no—
59C2×C11×C22⋊C4—21no—
60C2×C42×C11—21no—
61C2×C42×C11D411yescharacteristic
62C2×C42×C11D411yescharacteristic
63C2×C42×C11D411yescharacteristic
64C2×C42×C11D411yescharacteristic
65C2×C42×C11C2311yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2312yes—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C22×C11⋊C8C2312yes—
77C22×C11⋊C8C2312yes—
78#66923—44no—
79C11×#95—21no—
80C11×#95—21no—
81C11×#95—21no—
82C11×#95—21no—
83#66899—24no—
84#66899—42no—
85#66896—24no—
86#66896—42no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C4⋊(C11⋊C8)—22no—
90C4⋊(C11⋊C8)—22no—
91#66867—42no—
92#29131—111nomaximal, Sylow
93C24×C11—21no—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11#4112yes—
100C2×D4×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11#4112yes—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11—42no—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C22×Dic11—22no—
120C22×Dic11—22no—
121C11×C4⋊C4—21no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—42no—
126C11×C22⋊C4—24no—
127C11×C22⋊C4—24no—
128C11×C22⋊C4—42no—
129C11×C22⋊C4—42no—
130C11×C22⋊C4—42no—
131C42×C11—22no—
132C42×C11—22no—
133C42×C11—21no—
134C42×C11—21no—
135C42×C11—21no—
136C42×C11—21no—
137C42×C11—41no—
138C42×C11—41no—
139C42×C11—42no—
140C42×C11#4112yes—
141C42×C11#4112yes—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—42no—
147C4⋊Dic11—42no—
148C4⋊Dic11—42no—
149C4⋊Dic11—42no—
150Dic11⋊C4—44no—
151Dic11⋊C4—44no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158#2859—111no—
159C4×#124D1111yescharacteristic
160#2101—112no—
161#2042—112no—
162#1936—112no—
163#1935—112no—
164#1803—111no—
165#1803—111no—
166#1802—111no—
167#1802—111no—
168#1767—111no—
169C23×C11—22no—
170C23×C11—41no—
171C23×C11—41no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11C22×D411yescharacteristic
177Q8×C11—22no—
178Q8×C11—22no—
179Q8×C11—41no—
180Q8×C11—41no—
181D4×C11—22no—
182D4×C11—22no—
183D4×C11—41no—
184D4×C11—41no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—21no—
193C2×C4×C11—21no—
194C2×C4×C11—21no—
195C2×C4×C11—21no—
196C2×C4×C11—21no—
197C2×C4×C11—21no—
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×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—84no—
209C2×C4×C11#12412yes—
210C2×C4×C11#12412yes—
211C2×C4×C11AGL(1,ℤ/8)12yes—
212C2×C4×C11#13712yes—
213C2×C4×C11C2×#4111yescharacteristic
214C2×C4×C11C2×#4111yescharacteristic
215C2×C4×C11C2×#4111yescharacteristic
216C2×C4×C11C2×#4111yescharacteristic
217C2×C4×C11H(5,𝔽2)11yescharacteristic
218C2×C4×C112−1+411yescharacteristic
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11—42no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C11⋊C8—42no—
226C11⋊C8—42no—
227C2×#125—221no—
228C2×#124C2×D1111yescharacteristic
229C2×C4×Q8C2×D1111yescharacteristic
230C2×C4×D4C2×D1111yescharacteristic
231C2×C4⋊C8—111no—
232C2×C4⋊C8—111no—
233C2×#103—112no—
234C2×#103—112no—
235C2×#102—112no—
236C2×#102—112no—
237C2×#97—112no—
238#391C2×D1111yescharacteristic
239#390C2×D1111yescharacteristic
240#389—112no—
241#389—112no—
242#389—221no—
243#389—221no—
244#388—21no—
245#388—21no—
246#384—111no—
247#384—111no—
248#382—221no—
249#382C2×D1111yescharacteristic
250C4×C22⋊C4—21no—
251C4×C22⋊C4—21no—
252C43C2×D1111yescharacteristic
253#340—112no—
254#340—112no—
255#340—112no—
256#340—112no—
257#336—112no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11—42no—
261C22×C11—81no—
262C22×C11—81no—
263C22×C11—81no—
264C22×C11—81no—
265C22×C11#52511yescharacteristic
266C22×C11C2×#12411yescharacteristic
267C22×C11#53711yescharacteristic
268C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
269C22×C11C2×#13711yescharacteristic
270C22×C11#57511yescharacteristic
271C22×C11#57511yescharacteristic
272C4×C11—22no—
273C4×C11—42no—
274C4×C11—41no—
275C4×C11—41no—
276C4×C11—41no—
277C4×C11—41no—
278C4×C11—81no—
279C4×C11—81no—
280C4×C11#48914yes—
281C4×C11#55211yescharacteristic
282C4×C11#55211yescharacteristic
283C4×C11#55311yescharacteristic
284C4×C11#55311yescharacteristic
285Dic11—82no—
286Dic11—82no—
287C22×Q8C22×D1111yescharacteristic
288C22×D4C22×D1111yescharacteristic
289C23×C4—21no—
290C22×C8—112no—
291C22×C8—112no—
292#125—444no—
293#124—22no—
294#124—22no—
295C4×Q8—22no—
296C4×Q8—22no—
297C4×D4—22no—
298C4×D4—22no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—112no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4C22×D1111yescharacteristic
309C2×C4⋊C4C22×D1111yescharacteristic
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C42—21no—
316C2×C42C22⋊D1111yescharacteristic
317C2×C42C22⋊D1111yescharacteristic
318C2×C42C22⋊D1111yescharacteristic
319C2×C42C22⋊D1111yescharacteristic
320C2×C42C22×D1111yescharacteristic
321C2×C42C22×D1111yescharacteristic
322C2×C42C22×D1111yescharacteristic
323C4⋊C8—222no—
324C4⋊C8—222no—
325#103—224no—
326#103—442no—
327#102—224no—
328#102—442no—
329#97—442no—
330#95—21no—
331#95—21no—
332#95—21no—
333#95—21no—
334#95—222no—
335#95—222no—
336C2×C11—82no—
337C2×C11#256211yescharacteristic
338C2×C11#311511yescharacteristic
339C2×C11#311611yescharacteristic
340C2×C11C2×#48911yescharacteristic
341C2×C11#314211yescharacteristic
342C2×C11#325111yescharacteristic
343C2×C11#325211yescharacteristic
344C24—21no—
345C2×Q8—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8#433912yes—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4#433912yes—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—42no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4C2×C22⋊D1111yescharacteristic
366C22×C4C2×C22⋊D1111yescharacteristic
367C22×C4C2×C22⋊D1111yescharacteristic
368C22×C4C2×C22⋊D1111yescharacteristic
369C22×C4C2×C22⋊D1111yescharacteristic
370C22×C4C2×C22⋊D1111yescharacteristic
371C22×C4C23×D1111yescharacteristic
372C2×C8—222no—
373C2×C8—222no—
374C2×C8—222no—
375C2×C8—222no—
376C2×C8—222no—
377C2×C8—222no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—42no—
383C4⋊C4—222no—
384C4⋊C4—222no—
385C4⋊C4—222no—
386C4⋊C4—222no—
387C4⋊C4—444no—
388C4⋊C4—444no—
389C4⋊C4—442no—
390C4⋊C4—442no—
391C4⋊C4—442no—
392C4⋊C4—442no—
393C22⋊C4—24no—
394C22⋊C4—24no—
395C22⋊C4—42no—
396C22⋊C4—42no—
397C22⋊C4—42no—
398C42—22no—
399C42—22no—
400C42—21no—
401C42—21no—
402C42—21no—
403C42—21no—
404C42—41no—
405C42—41no—
406C42—42no—
407C42#434112yes—
408C42#434112yes—
409C11#2913111yescharacteristic, complemented, Sylow
410C23—22no—
411C23—41no—
412C23—41no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23C22×C22⋊D1111yescharacteristic
418Q8—22no—
419Q8—22no—
420Q8—41no—
421Q8—41no—
422D4—22no—
423D4—22no—
424D4—41no—
425D4—41no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—84no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4#6698912yes—
457C2×C4#6698912yes—
458C2×C4#6700212yes—
459C2×C4#6700412yes—
460C2×C4C2×#433911yescharacteristic
461C2×C4C2×#433911yescharacteristic
462C2×C4C2×#434111yescharacteristic
463C2×C4C2×#434111yescharacteristic
464C2×C4#6704211yescharacteristic
465C2×C4#6704311yescharacteristic
466C8—442no—
467C8—442no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22#1062332211yescharacteristic
476C22C2×#6698911yescharacteristic
477C22C2×#6700211yescharacteristic
478C22#1062335311yescharacteristic
479C22#1062335311yescharacteristic
480C22C2×#6700411yescharacteristic
481C22#1062336411yescharacteristic
482C4—22no—
483C4—42no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—81no—
489C4—81no—
490C4—882no—
491C4—882no—
492C4#1062266814yes—
493C4#1062307211yescharacteristic
494C4#1062307211yescharacteristic
495C4#1062309611yescharacteristic
496C4#1062309611yescharacteristic
497C2—82no—
498C2#1307378211yescharacteristic
499C2#1307876711yescharacteristic
500C2#1307877811yescharacteristic
501C2C2×#1062266811yescharacteristic
502C2#1307901611yescharacteristic
503C2#1307997811yescharacteristic
504C2#1307998911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#124C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC4×#124D11
hypocenterC11#29131
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ C4×#124

Complements

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

NH ≅ G/Ntype
1. #13076979C2semidirect
2. #13070183C2semidirect
5. #13069309C2semidirect
6. #13068621C2semidirect
7. #13068621C2semidirect
10. #13068469C2semidirect
409. C11#29131semidirect

Maximal subgroups

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

subgroupindex
#130769792
#130701832
#130698522
#130693162
#130693092
#130686212
#130686162
#130684692
C4×C11×#1242
#2913111