Finite Group Databasebeta

← #14853519

Subgroups — #14853519

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#13076977C211yesmaximal, characteristic, complemented
2C4×#67000C211yesmaximal, characteristic
3#13070186C212yesmaximal, complemented
4#13069853C212yesmaximal
5#13069314C212yesmaximal
6#13069308C212yesmaximal, complemented
7#13068621C211yesmaximal, characteristic, complemented
8#13068617C211yesmaximal, characteristic
9#13068613C211yesmaximal, characteristic
10#13068471C211yesmaximal, characteristic, complemented
11C11×#1803C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#67000C2211yescharacteristic
14C2×#66943—21no—
15C2×C4×D44C2211yescharacteristic
16C2×C11×C4⋊C8C2211yescharacteristic
17C2×C11×#103C2212yes—
18C11×#384C2211yescharacteristic
19#10622843C2211yescharacteristic
20C2×#66899C2212yes—
21C2×#66885C2212yes—
22C2×#66879C2212yes—
23#10622603—21no—
24#10622603—21no—
25#10622601C2211yescharacteristic
26#10622598—21no—
27#10622598C2212yes—
28#10622590—21no—
29#10622590C2211yescharacteristic
30#10622586—21no—
31#10622586C2212yes—
32C2×#66873C2212yes—
33C4×(C2×D11)⋊C4—21no—
34C4×(C2×D11)⋊C4—21no—
35#10622548C2211yescharacteristic
36C42×Dic11C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C11×#340C2212yes—
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C22×Q8×C11C2311yescharacteristic
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×C8×C11C2312yes—
47C4×Q8×C11—22no—
48C4×Q8×C11—22no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C11×C4⋊C4C2312yes—
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56#67000—22no—
57#67000—22no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—21no—
62C2×(C2×D11)⋊C4—21no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4—22no—
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11D411yescharacteristic
72C2×C4×Dic11D411yescharacteristic
73C2×C4×Dic11C2311yescharacteristic
74C2×C4×Dic11C2311yescharacteristic
75C22×C11⋊C8C2312yes—
76#66943—44no—
77C4×D44—22no—
78C4×D44—22no—
79C11×C4⋊C8—22no—
80C11×#103—24no—
81#66899—42no—
82C11⋊#95—21no—
83C11⋊#95—21no—
84C11⋊#95—21no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88#66885—42no—
89#66879—42no—
90#66873—24no—
91C4⋊(C11⋊C8)—22no—
92#29131—111nomaximal, Sylow
93C23×D11—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—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—21no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2411yescharacteristic
106C22×Dic11—21no—
107C22×Dic11—22no—
108C22×Dic11C2×D411yescharacteristic
109C22×Dic11C2×D411yescharacteristic
110C22×Dic11C2×D411yescharacteristic
111C22×Dic11C2×D411yescharacteristic
112C2×D44—21no—
113C2×D44—21no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44#4112yes—
118C2×C4×D11—42no—
119C2×C4×D11—42no—
120C2×C4×D11—42no—
121C2×C8×C11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—42no—
131C42×C11—42no—
132C42×C11#4112yes—
133C42×C11#4112yes—
134(C2×D11)⋊C4—24no—
135(C2×D11)⋊C4—24no—
136(C2×D11)⋊C4—42no—
137(C2×D11)⋊C4—42no—
138(C2×D11)⋊C4—42no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11—22no—
142C4⋊Dic11—22no—
143C4⋊Dic11—42no—
144C4⋊Dic11—44no—
145C4⋊Dic11—42no—
146Dic11⋊C4—44no—
147C4×Dic11—22no—
148C4×Dic11—22no—
149C4×Dic11—21no—
150C4×Dic11—21no—
151C4×Dic11—21no—
152C4×Dic11—21no—
153C4×Dic11—41no—
154C4×Dic11—41no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8—22no—
158#2859—111no—
159C4×#124—111no—
160#2101—112no—
161#2042—112no—
162#1936—112no—
163#1935—112no—
164#1803—111no—
165#1803D1111yescharacteristic, complemented
166#1802—111no—
167#1802—111no—
168#1767—111no—
169C23×C11C22×D411yescharacteristic
170C22×D11—22no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177Q8×C11—22no—
178Q8×C11—22no—
179Q8×C11—41no—
180Q8×C11—41no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—22no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—42no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11#12412yes—
193C2×C4×C11#12412yes—
194C2×C4×C11AGL(1,ℤ/8)12yes—
195C2×C4×C11#13712yes—
196C2×C4×C11C2×#4111yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11H(5,𝔽2)11yescharacteristic
201C2×C4×C112−1+411yescharacteristic
202C2×Dic11—21no—
203C2×Dic11—21no—
204C2×Dic11—21no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—21no—
209C2×Dic11—21no—
210C2×Dic11—21no—
211C2×Dic11—21no—
212C2×Dic11—21no—
213C2×Dic11—21no—
214C2×Dic11—41no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220D44—22no—
221D44—22no—
222D44—41no—
223D44—41no—
224C4×D11—84no—
225C8×C11—42no—
226C11⋊C8—42no—
227C2×#125—221no—
228C2×#124—111no—
229C2×C4×Q8C2×D1111yescharacteristic
230C2×C4×D4—111no—
231C2×C4⋊C8—111no—
232C2×C4⋊C8C2×D1111yescharacteristic
233C2×#103—112no—
234C2×#103C2×D1112yes—
235C2×#102—112no—
236C2×#102—112no—
237C2×#97—112no—
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#384C2×D1111yescharacteristic
248#382—111no—
249#382—221no—
250C4×C22⋊C4—221no—
251C4×C22⋊C4—221no—
252C43—111no—
253#340—112no—
254#340—112no—
255#340—112no—
256#340C2×D1112yes—
257#336—112no—
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—42no—
274C4×C11—82no—
275C4×C11—81no—
276C4×C11#48914yes—
277C4×C11#55211yescharacteristic
278C4×C11#55211yescharacteristic
279C4×C11#55311yescharacteristic
280C4×C11#55311yescharacteristic
281Dic11—41no—
282Dic11—41no—
283Dic11—41no—
284Dic11—41no—
285Dic11—81no—
286Dic11—82no—
287C22×Q8C22×D1111yescharacteristic
288C22×D4—111no—
289C23×C4—221no—
290C22×C8—112no—
291C22×C8C22×D1112yes—
292#125—444no—
293#124—222no—
294#124—222no—
295C4×Q8—22no—
296C4×Q8—22no—
297C4×D4—222no—
298C4×D4—222no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—112no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4C22×D1111yescharacteristic
309C2×C4⋊C4C22×D1112yes—
310C2×C22⋊C4—221no—
311C2×C22⋊C4—221no—
312C2×C22⋊C4—221no—
313C2×C22⋊C4—221no—
314C2×C22⋊C4—221no—
315C2×C42—21no—
316C2×C42—111no—
317C2×C42—111no—
318C2×C42—111no—
319C2×C42—111no—
320C2×C42—111no—
321C2×C42—111no—
322C2×C42C22×D1111yescharacteristic
323C4⋊C8—22no—
324C4⋊C8—222no—
325#103—24no—
326#103—442no—
327#102—224no—
328#102—442no—
329#97—442no—
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—21no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—21no—
350C2×Q8#434112yes—
351C2×D4—112no—
352C2×D4—221no—
353C2×D4—221no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—221no—
357C22×C4—21no—
358C22×C4—21no—
359C22×C4—22no—
360C22×C4—111no—
361C22×C4—111no—
362C22×C4—111no—
363C22×C4—111no—
364C22×C4—221no—
365C22×C4—222no—
366C22×C4—442no—
367C22×C4—442no—
368C22×C4—442no—
369C22×C4D4×D1111yescharacteristic
370C22×C4D4×D1111yescharacteristic
371C22×C4C23×D1111yescharacteristic
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—22no—
375C2×C8—222no—
376C2×C8—222no—
377C2×C8—222no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—42no—
383C4⋊C4—42no—
384C4⋊C4—42no—
385C4⋊C4—221no—
386C4⋊C4—221no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C4⋊C4—442no—
390C4⋊C4—444no—
391C4⋊C4—444no—
392C4⋊C4—442no—
393C22⋊C4—224no—
394C22⋊C4—224no—
395C22⋊C4—442no—
396C22⋊C4—442no—
397C22⋊C4—442no—
398C42—42no—
399C42—222no—
400C42—222no—
401C42—221no—
402C42—221no—
403C42—221no—
404C42—221no—
405C42—441no—
406C42—441no—
407C42#433912yes—
408C42#434112yes—
409C11#2913111yescharacteristic, complemented, Sylow
410C23—222no—
411C23—441no—
412C23—441no—
413C23—441no—
414C23—441no—
415C23—441no—
416C23—441no—
417C23C2×D4×D1111yescharacteristic
418Q8—22no—
419Q8—22no—
420Q8—41no—
421Q8—41no—
422D4—222no—
423D4—222no—
424D4—441no—
425D4—441no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—22no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—221no—
438C2×C4—221no—
439C2×C4—221no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—221no—
444C2×C4—221no—
445C2×C4—221no—
446C2×C4—221no—
447C2×C4—221no—
448C2×C4—221no—
449C2×C4—441no—
450C2×C4—442no—
451C2×C4—441no—
452C2×C4—441no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—884no—
456C2×C4#6693812yes—
457C2×C4#6693812yes—
458C2×C4#6696712yes—
459C2×C4#6697112yes—
460C2×C4C2×#433911yescharacteristic
461C2×C4C2×#434111yescharacteristic
462C2×C4C2×#434111yescharacteristic
463C2×C4#6704011yescharacteristic
464C2×C4#41×D1111yescharacteristic
465C2×C4#6704211yescharacteristic
466C8—42no—
467C8—442no—
468C22—442no—
469C22—442no—
470C22—442no—
471C22—881no—
472C22—881no—
473C22—881no—
474C22—881no—
475C22C2×#6693811yescharacteristic
476C22#1062313711yescharacteristic
477C22#1062316011yescharacteristic
478C22C2×#6696711yescharacteristic
479C22C2×#6697111yescharacteristic
480C22#1062330411yescharacteristic
481C22#1062330811yescharacteristic
482C4—22no—
483C4—42no—
484C4—81no—
485C4—82no—
486C4—441no—
487C4—441no—
488C4—441no—
489C4—441no—
490C4—881no—
491C4—882no—
492C4#1062240814yes—
493C4#1062304411yescharacteristic
494C4#1062306111yescharacteristic
495C4#1062314911yescharacteristic
496C4#1062317011yescharacteristic
497C2—882no—
498C2#1307377911yescharacteristic
499C2#1307876611yescharacteristic
500C2#1307877711yescharacteristic
501C2C2×#1062240811yescharacteristic
502C2#1307901411yescharacteristic
503C2#1307998111yescharacteristic
504C2#1307999211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1803C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1803D11
hypocenterC11#29131
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
1. #13076977C2semidirect
3. #13070186C2semidirect
6. #13069308C2semidirect
7. #13068621C2semidirect
10. #13068471C2semidirect
11. C11×#1803C2semidirect
165. #1803D11semidirect
409. C11#29131semidirect

Maximal subgroups

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

subgroupindex
#130769772
C4×#670002
#130701862
#130698532
#130693142
#130693082
#130686212
#130686172
#130686132
#130684712
C11×#18032
#2913111