Finite Group Databasebeta

← #14803878

Subgroups — #14803878

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622459C211yesmaximal, characteristic, complemented
2#13073608C211yesmaximal, characteristic, complemented
3#13073529C211yesmaximal, characteristic
4#13070039C212yesmaximal, complemented
5#13069799C212yesmaximal, complemented
6#13069577C211yesmaximal, characteristic, complemented
7#13069375C211yesmaximal, characteristic, complemented
8#13069044C212yesmaximal, complemented
9#13068645C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic, complemented
11C2×C8×D4×C11C211yesmaximal, characteristic, complemented
12C23×C8×C11C2212yes—
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66991—21no—
15C2×#66989—21no—
16C2×#66983C2212yes—
17C2×C4×D44C2211yescharacteristic
18C2×#66922C2211yescharacteristic
19C8×D4×C11—24no—
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8C2212yes—
22C2×C4×C8×C11C2211yescharacteristic
23#10622825C2212yes—
24#10622825C2212yes—
25#10622825C2212yes—
26C2×#66885C2212yes—
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66882C2212yes—
30C2×#66882C2212yes—
31#10622600—21no—
32#10622587—21no—
33#10622574—22no—
34#10622566—22no—
35#10622548C2211yescharacteristic
36C4×C4⋊Dic11C2211yescharacteristic
37#10622459—24no—
38#10622189C2212yes—
39#10622189C2212yes—
40#10622189C2212yes—
41#10622189C2211yescharacteristic
42#10622189C2211yescharacteristic
43C22×D4×C11D411yescharacteristic
44C23×C4×C11C2312yes—
45C22×C22⋊D11—22no—
46C22×D44C2311yescharacteristic
47C22×C4×D11—21no—
48C22×Dic22—21no—
49C22×C8×C11—24no—
50C22×C8×C11—24no—
51C22×C8×C11—42no—
52C22×C8×C11C2311yescharacteristic
53C22×C8×C11C2312yes—
54C22×C8×C11C2311yescharacteristic
55C4×D4×C11—22no—
56C4×D4×C11—22no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C22⋊C4D412yes—
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11—22no—
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63#66991—44no—
64#66989—44no—
65#66983—24no—
66#66983—42no—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2312yes—
77C2×C4×Dic11—21no—
78C4×D44—22no—
79C4×D44—22no—
80#66922—22no—
81#66922—22no—
82C11×C4⋊C8D414yescomplemented
83C11×C22⋊C8—24no—
84C4×C8×C11—22no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89#66885—22no—
90#66885—24no—
91#66885—22no—
92#66882—24no—
93#66882—42no—
94#25338—111nomaximal, Sylow
95C24×C11C2×D412yes—
96C23×D11—21no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11D814yes—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2411yescharacteristic
110C2×C22⋊D11—44no—
111C2×C22⋊D11—44no—
112C2×C22⋊D11—82no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—22no—
116C22×Dic11—21no—
117C22×Dic11—22no—
118C2×D44—21no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44#4112yes—
124C2×C4×D11—42no—
125C2×C4×D11—42no—
126C2×C4×D11—42no—
127C2×Dic22—42no—
128C2×Dic22—42no—
129C2×Dic22—42no—
130C2×C8×C11—21no—
131C2×C8×C11—21no—
132C2×C8×C11—22no—
133C2×C8×C11—21no—
134C2×C8×C11—22no—
135C2×C8×C11—21no—
136C2×C8×C11—21no—
137C2×C8×C11—48no—
138C2×C8×C11C2×D414yes—
139C2×C8×C11#4112yes—
140C11×C4⋊C4—22no—
141C11×C22⋊C4—24no—
142C42×C11C2×D412yes—
143C42×C11#4112yes—
144C22⋊Dic11—44no—
145C22⋊Dic11—44no—
146C22⋊Dic11—44no—
147(C2×D11)⋊C4—44no—
148(C2×D11)⋊C4—42no—
149C4⋊Dic11—21no—
150C4⋊Dic11—22no—
151C4⋊Dic11—21no—
152C4⋊Dic11—21no—
153C4⋊Dic11—22no—
154C4⋊Dic11—21no—
155C4⋊Dic11—22no—
156C4⋊Dic11—21no—
157C4⋊Dic11—22no—
158C4⋊Dic11—21no—
159C4⋊Dic11—42no—
160C4⋊Dic11—42no—
161C4⋊Dic11—81no—
162C4×Dic11—42no—
163C2×#474—111no—
164C2×C8×D4D1111yescharacteristic, complemented
165#2547—111no—
166#2537—111no—
167#2075—112no—
168#2033—112no—
169#1990—111no—
170#1947—111no—
171#1893—112no—
172#1808—112no—
173C4×#102—111no—
174C23×C11—22no—
175C23×C11—22no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11C2×D814yes—
181C23×C11C22×D411yescharacteristic
182C22×D11—22no—
183C22×D11—41no—
184C22×D11—41no—
185C22×D11—41no—
186C22×D11—41no—
187C22×D11—41no—
188C22×D11—41no—
189D4×C11—28no—
190C2×C4×C11—21no—
191C2×C4×C11—21no—
192C2×C4×C11—22no—
193C2×C4×C11—22no—
194C2×C4×C11—22no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11—42no—
199C2×C4×C11#12112yes—
200C2×C4×C11#12112yes—
201C2×C4×C11C2×D812yes—
202C2×C4×C11#13512yes—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11H(5,𝔽2)11yescharacteristic
208C2×C4×C112−1+411yescharacteristic
209C22⋊D11—88no—
210C2×Dic11—42no—
211C2×Dic11—41no—
212C2×Dic11—42no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—42no—
218C2×Dic11—42no—
219C2×Dic11—41no—
220C2×Dic11—42no—
221C2×Dic11—41no—
222C2×Dic11—42no—
223C2×Dic11—41no—
224C2×Dic11—41no—
225D44—22no—
226D44—22no—
227D44—41no—
228D44—41no—
229C4×D11—84no—
230Dic22—84no—
231C8×C11—22no—
232C8×C11—24no—
233C8×C11—41no—
234C23×C8C2×D1112yes—
235C2×C4⋊Q8—111no—
236C2×#124—221no—
237C2×#121—112no—
238C2×#121—221no—
239C2×C4×D4—111no—
240C2×C4×D4C2×D1111yescharacteristic
241#474—224no—
242C8×D4—24no—
243C2×#107—112no—
244C2×#107—112no—
245C2×C4⋊C8C2×D1111yescharacteristic
246C2×#102—111no—
247C2×#102—112no—
248C2×#102—111no—
249C2×C22⋊C8C2×D1112yes—
250C2×C4×C8C2×D1111yescharacteristic
251#397—222no—
252#394—222no—
253#391—221no—
254#384—111no—
255#380—112no—
256#380—112no—
257#380—112no—
258#380—221no—
259C4×C4⋊C4—111no—
260#340—111no—
261#340—112no—
262#340—111no—
263#340—112no—
264#340—112no—
265C22×C11—24no—
266C22×C11—24no—
267C22×C11—24no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11C2×#12111yescharacteristic
273C22×C11#54611yescharacteristic
274C22×C11#54711yescharacteristic
275C22×C11C22×D811yescharacteristic
276C22×C11C2×#13511yescharacteristic
277C22×C11#57711yescharacteristic
278C22×C11#57811yescharacteristic
279C2×D11—42no—
280C2×D11—42no—
281C2×D11—42no—
282C2×D11—81no—
283C2×D11—81no—
284C2×D11—81no—
285C2×D11—81no—
286C4×C11—22no—
287C4×C11—42no—
288C4×C11#46614yes—
289C4×C11#52911yescharacteristic
290C4×C11#54211yescharacteristic
291C4×C11#54611yescharacteristic
292C4×C11#54811yescharacteristic
293Dic11—81no—
294Dic11—81no—
295Dic11—82no—
296Dic11—82no—
297Dic11—81no—
298C22×Q8—221no—
299C22×D4—111no—
300C22×D4—222no—
301C22×D4D4411yescharacteristic
302C23×C4—221no—
303C23×C4C22×D1112yes—
304C22×C8—24no—
305C22×C8—24no—
306C22×C8—42no—
307C22×C8C22×D1111yescharacteristic
308C22×C8C22×D1111yescharacteristic
309C22×C8C22×D1112yes—
310C4⋊Q8—222no—
311C4⋊Q8—222no—
312#124—444no—
313#121—224no—
314#121—442no—
315#121—444no—
316C4×D4—22no—
317C4×D4—22no—
318C4×D4—222no—
319C4×D4—222no—
320C2×C4⋊C4—111no—
321C2×C4⋊C4—112no—
322C2×C4⋊C4—112no—
323C2×C4⋊C4—111no—
324C2×C4⋊C4—111no—
325C2×C4⋊C4—221no—
326C2×C4⋊C4—221no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4D4411yescharacteristic
329C2×C22⋊C4—222no—
330C2×C22⋊C4—222no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—221no—
333C2×C22⋊C4—222no—
334C2×C22⋊C4D4412yes—
335C2×C42—221no—
336C2×C42C22×D1111yescharacteristic
337#107—224no—
338#107—442no—
339C4⋊C8C22⋊D1114yescomplemented
340#102—222no—
341#102—222no—
342#102—224no—
343C22⋊C8—24no—
344C4×C8—22no—
345#95—221no—
346#95—222no—
347#95—222no—
348#95—222no—
349C2×C11—44no—
350C2×C11#242711yescharacteristic
351C2×C11C2×#46611yescharacteristic
352C2×C11#306311yescharacteristic
353C2×C11#329411yescharacteristic
354C2×C11#330211yescharacteristic
355C2×C11#333411yescharacteristic
356C2×C11#334011yescharacteristic
357D11—82no—
358C24—221no—
359C24C2×D4412yes—
360C2×Q8—442no—
361C2×Q8—442no—
362C2×Q8—442no—
363C2×D4—22no—
364C2×D4—22no—
365C2×D4—112no—
366C2×D4—221no—
367C2×D4—221no—
368C2×D4—221no—
369C2×D4—221no—
370C2×D4—221no—
371C2×D4—444no—
372C2×D4—444no—
373C2×D4—882no—
374C2×D4D8814yes—
375C22×C4—22no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—221no—
382C22×C4—221no—
383C22×C4—221no—
384C22×C4—222no—
385C22×C4—222no—
386C22×C4—442no—
387C22×C4—442no—
388C22×C4—442no—
389C22×C4C2×D4412yes—
390C22×C4C2×D4411yescharacteristic
391C22×C4C2×D4411yescharacteristic
392C22×C4C23×D1111yescharacteristic
393C2×C8—22no—
394C2×C8—22no—
395C2×C8—21no—
396C2×C8—21no—
397C2×C8—21no—
398C2×C8—21no—
399C2×C8—21no—
400C2×C8—48no—
401C2×C8#434112yes—
402C2×C8C2×C22⋊D1114yes—
403C4⋊C4—22no—
404C4⋊C4—221no—
405C4⋊C4—222no—
406C4⋊C4—221no—
407C4⋊C4—221no—
408C4⋊C4—222no—
409C4⋊C4—221no—
410C4⋊C4—222no—
411C4⋊C4—221no—
412C4⋊C4—222no—
413C4⋊C4—221no—
414C4⋊C4—442no—
415C4⋊C4—442no—
416C4⋊C4—881no—
417C22⋊C4—24no—
418C22⋊C4—444no—
419C22⋊C4—444no—
420C22⋊C4—444no—
421C22⋊C4—444no—
422C22⋊C4—442no—
423C42—442no—
424C42#433912yes—
425C42C2×C22⋊D1112yes—
426C11#2533811yescharacteristic, complemented, Sylow
427C23—22no—
428C23—22no—
429C23—22no—
430C23—22no—
431C23—22no—
432C23—22no—
433C23—222no—
434C23—441no—
435C23—441no—
436C23—441no—
437C23—441no—
438C23—441no—
439C23—441no—
440C23C2×D8814yes—
441C23C22×D4411yescharacteristic
442Q8—884no—
443D4—28no—
444D4—222no—
445D4—222no—
446D4—441no—
447D4—441no—
448D4—888no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—441no—
459C2×C4—441no—
460C2×C4—441no—
461C2×C4—442no—
462C2×C4—442no—
463C2×C4—441no—
464C2×C4—442no—
465C2×C4—442no—
466C2×C4—441no—
467C2×C4—441no—
468C2×C4—441no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4—441no—
472C2×C4—441no—
473C2×C4—884no—
474C2×C4C2×D8812yes—
475C2×C4#6695712yes—
476C2×C4#6698312yes—
477C2×C4#6698312yes—
478C2×C4C2×#433911yescharacteristic
479C2×C4C2×#434111yescharacteristic
480C2×C4#6703711yescharacteristic
481C2×C4#41×D1111yescharacteristic
482C2×C4#6704311yescharacteristic
483C2×C4C22×C22⋊D1111yescharacteristic
484C8—22no—
485C8—24no—
486C8—41no—
487C22—24no—
488C22—24no—
489C22—24no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—442no—
495C22—442no—
496C22—442no—
497C22—881no—
498C22—881no—
499C22—881no—
500C22—881no—
501C22#1062308511yescharacteristic
502C22#1062308611yescharacteristic
503C22C22×D8811yescharacteristic
504C22C2×#6695711yescharacteristic
505C22#1062328211yescharacteristic
506C22#1062328411yescharacteristic
507C22C2×#6698311yescharacteristic
508C4—22no—
509C4—42no—
510C4—882no—
511C4—881no—
512C4—881no—
513C4—881no—
514C4—882no—
515C4#1062272814yes—
516C4#1062308811yescharacteristic
517C4#1062309211yescharacteristic
518C4#1062333711yescharacteristic
519C4#1062336211yescharacteristic
520C2—44no—
521C2—882no—
522C2#1307218711yescharacteristic
523C2C2×#1062272811yescharacteristic
524C2#1307830711yescharacteristic
525C2#1308043011yescharacteristic
526C2#1308053411yescharacteristic
527C2#1308096411yescharacteristic
528C2#1308103011yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C8×D4×C11C2
socleC23×C11C22×D4
prime radical#13073529C2
hypercenterC2×C8×D4D11
hypocenterC11#25338
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10622459C2semidirect
2. #13073608C2semidirect
4. #13070039C2semidirect
5. #13069799C2semidirect
6. #13069577C2semidirect
7. #13069375C2semidirect
8. #13069044C2semidirect
9. #13068645C2semidirect
10. C4×#66885C2semidirect
11. C2×C8×D4×C11C2semidirect
82. C11×C4⋊C8D4semidirect
164. C2×C8×D4D11semidirect
339. C4⋊C8C22⋊D11semidirect
426. C11#25338semidirect

Maximal subgroups

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

subgroupindex
C2×#106224592
#130736082
#130735292
#130700392
#130697992
#130695772
#130693752
#130690442
#130686452
C4×#668852
C2×C8×D4×C112
#2533811