Finite Group Databasebeta

← #14853510

Subgroups — #14853510

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
2C4×#66928C211yesmaximal, characteristic
3#13070185C212yesmaximal, complemented
4#13069858C212yesmaximal
5#13069313C212yesmaximal
6#13069306C212yesmaximal, complemented
7#13068622C211yesmaximal, characteristic, complemented
8#13068622C211yesmaximal, characteristic, complemented
9#13068617C211yesmaximal, characteristic
10#13068617C211yesmaximal, characteristic
11C11×#1767C211yesmaximal, characteristic, complemented
12C2×#66928C2211yescharacteristic
13C2×C4×D44C2211yescharacteristic
14C2×#66923—21no—
15C2×C4×Dic22C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×#97C2212yes—
19C43×C11C2211yescharacteristic
20C2×#66885C2212yes—
21C2×#66885C2212yes—
22C2×#66880C2212yes—
23C2×#66880C2212yes—
24#10622553—21no—
25#10622553—21no—
26#10622552C2211yescharacteristic
27C4×(C2×D11)⋊C4—21no—
28C4×(C2×D11)⋊C4—21no—
29#10622549—21no—
30#10622549C2211yescharacteristic
31#10622548C2211yescharacteristic
32#10622548C2211yescharacteristic
33#10622542C2211yescharacteristic
34#10622541—21no—
35#10622541—21no—
36#10622541C2212yes—
37#10622541C2212yes—
38C11×#336C2212yes—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622189C2212yes—
42#10622189C2212yes—
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×Dic22C2311yescharacteristic
46C22×C8×C11C2312yes—
47C22×C8×C11C2312yes—
48C2×C42×C11D411yescharacteristic
49C2×C42×C11D411yescharacteristic
50C2×C42×C11D411yescharacteristic
51C2×C42×C11D411yescharacteristic
52C2×C42×C11C2311yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11C2312yes—
65C2×C4⋊Dic11C2312yes—
66C2×C4⋊Dic11C2311yescharacteristic
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4—21no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—22no—
71C2×C4×Dic11—21no—
72#66928—22no—
73#66928—22no—
74C4×D44—22no—
75C4×D44—22no—
76#66923—44no—
77C4×Dic22—22no—
78C4×Dic22—22no—
79C11×C4⋊C8—22no—
80C11×C4⋊C8—22no—
81C11×#97—42no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—21no—
85C11⋊#95—21no—
86C11⋊#95—21no—
87C11⋊#95—21no—
88#66885—24no—
89#66885—42no—
90#66880—24no—
91#66880—42no—
92#29131—111nomaximal, Sylow
93C23×D11—21no—
94C22×C4×C11C2×D411yescharacteristic
95C22×C4×C11C2×D411yescharacteristic
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—21no—
104C22×Dic11—22no—
105C22×Dic11—22no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44#4112yes—
112C2×C4×D11—42no—
113C2×C4×D11—42no—
114C2×C4×D11—42no—
115C2×Dic22—21no—
116C2×Dic22—21no—
117C2×Dic22—21no—
118C2×Dic22—21no—
119C2×Dic22—21no—
120C2×Dic22#4112yes—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C42×C11—22no—
128C42×C11—22no—
129C42×C11—21no—
130C42×C11—21no—
131C42×C11—21no—
132C42×C11—21no—
133C42×C11—41no—
134C42×C11—41no—
135C42×C11#4112yes—
136C42×C11#4112yes—
137(C2×D11)⋊C4—24no—
138(C2×D11)⋊C4—24no—
139(C2×D11)⋊C4—42no—
140(C2×D11)⋊C4—42no—
141(C2×D11)⋊C4—42no—
142C4⋊Dic11—22no—
143C4⋊Dic11—22no—
144C4⋊Dic11—21no—
145C4⋊Dic11—21no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—42no—
151C4⋊Dic11—42no—
152C4⋊Dic11—42no—
153C4⋊Dic11—42no—
154Dic11⋊C4—44no—
155Dic11⋊C4—44no—
156Dic11⋊C4—42no—
157C4×Dic11—42no—
158#2859—111no—
159C4×#124—111no—
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#1767D1111yescharacteristic, complemented
169C23×C11C22×D411yescharacteristic
170C22×D11—22no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—21no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—21no—
188C2×C4×C11—21no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11#12412yes—
192C2×C4×C11#12412yes—
193C2×C4×C11AGL(1,ℤ/8)12yes—
194C2×C4×C11#13712yes—
195C2×C4×C11C2×#4111yescharacteristic
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11H(5,𝔽2)11yescharacteristic
200C2×C4×C112−1+411yescharacteristic
201C2×Dic11—22no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—42no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216D44—22no—
217D44—22no—
218D44—41no—
219D44—41no—
220C4×D11—84no—
221Dic22—22no—
222Dic22—22no—
223Dic22—41no—
224Dic22—41no—
225C8×C11—42no—
226C8×C11—42no—
227C2×#125—221no—
228C2×#124—111no—
229C2×C4×Q8—111no—
230C2×C4×D4—111no—
231C2×C4⋊C8C2×D1111yescharacteristic
232C2×C4⋊C8C2×D1111yescharacteristic
233C2×#103—112no—
234C2×#103—112no—
235C2×#102—112no—
236C2×#102—112no—
237C2×#97C2×D1112yes—
238#391—111no—
239#390—111no—
240#389—112no—
241#389—112no—
242#389—221no—
243#389—221no—
244#388—221no—
245#388—221no—
246#384—111no—
247#384—111no—
248#382—111no—
249#382—221no—
250C4×C22⋊C4—221no—
251C4×C22⋊C4—221no—
252C43C2×D1111yescharacteristic
253#340—112no—
254#340—112no—
255#340—112no—
256#340—112no—
257#336C2×D1112yes—
258C22×C11#52511yescharacteristic
259C22×C11C2×#12411yescharacteristic
260C22×C11#53711yescharacteristic
261C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
262C22×C11C2×#13711yescharacteristic
263C22×C11#57511yescharacteristic
264C22×C11#57511yescharacteristic
265C2×D11—42no—
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C2×D11—81no—
272C4×C11—22no—
273C4×C11—41no—
274C4×C11—41no—
275C4×C11—41no—
276C4×C11—41no—
277C4×C11#48914yes—
278C4×C11#55211yescharacteristic
279C4×C11#55211yescharacteristic
280C4×C11#55311yescharacteristic
281C4×C11#55311yescharacteristic
282Dic11—42no—
283Dic11—82no—
284Dic11—81no—
285Dic11—81no—
286Dic11—82no—
287C22×Q8—111no—
288C22×D4—111no—
289C23×C4—221no—
290C22×C8C22×D1112yes—
291C22×C8C22×D1112yes—
292#125—444no—
293#124—222no—
294#124—222no—
295C4×Q8—222no—
296C4×Q8—222no—
297C4×D4—222no—
298C4×D4—222no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—112no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—221no—
310C2×C22⋊C4—221no—
311C2×C22⋊C4—221no—
312C2×C22⋊C4—221no—
313C2×C22⋊C4—221no—
314C2×C22⋊C4—221no—
315C2×C42—221no—
316C2×C42D4411yescharacteristic
317C2×C42D4411yescharacteristic
318C2×C42D4411yescharacteristic
319C2×C42D4411yescharacteristic
320C2×C42C22×D1111yescharacteristic
321C2×C42C22×D1111yescharacteristic
322C2×C42C22×D1111yescharacteristic
323C4⋊C8—22no—
324C4⋊C8—22no—
325#103—224no—
326#103—442no—
327#102—224no—
328#102—442no—
329#97—42no—
330#95—221no—
331#95—221no—
332#95—221no—
333#95—221no—
334#95—222no—
335#95—222no—
336C2×C11#256211yescharacteristic
337C2×C11#311511yescharacteristic
338C2×C11#311611yescharacteristic
339C2×C11C2×#48911yescharacteristic
340C2×C11#314211yescharacteristic
341C2×C11#325111yescharacteristic
342C2×C11#325211yescharacteristic
343D11—82no—
344C24—221no—
345C2×Q8—112no—
346C2×Q8—221no—
347C2×Q8—221no—
348C2×Q8—221no—
349C2×Q8—221no—
350C2×Q8—221no—
351C2×D4—112no—
352C2×D4—221no—
353C2×D4—221no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—221no—
357C22×C4—221no—
358C22×C4—221no—
359C22×C4—221no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—442no—
363C22×C4—442no—
364C22×C4—442no—
365C22×C4C2×D4411yescharacteristic
366C22×C4C2×D4411yescharacteristic
367C22×C4C2×D4411yescharacteristic
368C22×C4C2×D4411yescharacteristic
369C22×C4C2×D4411yescharacteristic
370C22×C4C2×D4411yescharacteristic
371C22×C4C23×D1111yescharacteristic
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—221no—
382C4⋊C4—222no—
383C4⋊C4—222no—
384C4⋊C4—222no—
385C4⋊C4—222no—
386C4⋊C4—444no—
387C4⋊C4—444no—
388C4⋊C4—442no—
389C4⋊C4—442no—
390C4⋊C4—442no—
391C4⋊C4—442no—
392C4⋊C4—442no—
393C22⋊C4—224no—
394C22⋊C4—224no—
395C22⋊C4—442no—
396C22⋊C4—442no—
397C22⋊C4—442no—
398C42—22no—
399C42—22no—
400C42—21no—
401C42—21no—
402C42—21no—
403C42—21no—
404C42—41no—
405C42—41no—
406C42—442no—
407C42#433912yes—
408C42#433912yes—
409C11#2913111yescharacteristic, complemented, Sylow
410C23—222no—
411C23—441no—
412C23—441no—
413C23—441no—
414C23—441no—
415C23—441no—
416C23—441no—
417C23C22×D4411yescharacteristic
418Q8—222no—
419Q8—222no—
420Q8—441no—
421Q8—441no—
422D4—222no—
423D4—222no—
424D4—441no—
425D4—441no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
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—222no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—441no—
448C2×C4—441no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—884no—
456C2×C4#6692812yes—
457C2×C4#6692812yes—
458C2×C4#6696112yes—
459C2×C4#6696212yes—
460C2×C4C2×#433911yescharacteristic
461C2×C4C2×#433911yescharacteristic
462C2×C4#6703711yescharacteristic
463C2×C4#6704011yescharacteristic
464C2×C4#41×D1111yescharacteristic
465C2×C4#41×D1111yescharacteristic
466C8—42no—
467C8—42no—
468C22—442no—
469C22—442no—
470C22—442no—
471C22—881no—
472C22—881no—
473C22—881no—
474C22—881no—
475C22C2×#6692811yescharacteristic
476C22#1062304111yescharacteristic
477C22#1062305511yescharacteristic
478C22C2×#6696111yescharacteristic
479C22C2×#6696211yescharacteristic
480C22#1062327911yescharacteristic
481C22#1062327911yescharacteristic
482C4—22no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—442no—
488C4—881no—
489C4—882no—
490C4—881no—
491C4—882no—
492C4#1062232714yes—
493C4#1062308911yescharacteristic
494C4#1062308911yescharacteristic
495C4#1062311211yescharacteristic
496C4#1062311211yescharacteristic
497C2—882no—
498C2#1307377711yescharacteristic
499C2#1307876811yescharacteristic
500C2#1307877911yescharacteristic
501C2C2×#1062232711yescharacteristic
502C2#1307901711yescharacteristic
503C2#1307997911yescharacteristic
504C2#1307999011yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1767C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1767D11
hypocenterC11#29131
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C43 ◁ #1767

Complements

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

NH ≅ G/Ntype
1. #13076979C2semidirect
3. #13070185C2semidirect
6. #13069306C2semidirect
7. #13068622C2semidirect
8. #13068622C2semidirect
11. C11×#1767C2semidirect
168. #1767D11semidirect
409. C11#29131semidirect

Maximal subgroups

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

subgroupindex
#130769792
C4×#669282
#130701852
#130698582
#130693132
#130693062
#130686222
#130686172
C11×#17672
#2913111