Finite Group Databasebeta

← #14795077

Subgroups — #14795077

Order 2816.

912 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622620C211yesmaximal, characteristic, complemented
2C2×#10622539C211yesmaximal, characteristic, complemented
3#13076968C211yesmaximal, characteristic, complemented
4#13070047C212yesmaximal, complemented
5#13069802C212yesmaximal
6#13069568C211yesmaximal, characteristic, complemented
7#13069379C211yesmaximal, characteristic, complemented
8#13069356C212yesmaximal, complemented
9#13069316C212yesmaximal, complemented
10#13068616C211yesmaximal, characteristic, complemented
11C4×C11×#121C211yesmaximal, characteristic
12C2×C11×#121C2211yescharacteristic
13C2×C4×D4×C11—21no—
14C2×C4×D4×C11C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C2×#66977—21no—
17C2×#66922C2211yescharacteristic
18C11×#390C2211yescharacteristic
19C11×#389C2211yescharacteristic
20C11×#388—21no—
21C11×#386—21no—
22C11×#380C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C4×C11×C22⋊C4—21no—
25C2×#66896C2212yes—
26C2×#66896C2212yes—
27#10622825—21no—
28#10622825C2212yes—
29C2×C22⋊(C11⋊C8)C2212yes—
30#10622620—24no—
31C2×#66872C2212yes—
32C2×#66871C2212yes—
33#10622548C2211yescharacteristic
34#10622542—21no—
35#10622541—21no—
36#10622541C2212yes—
37#10622539—24no—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40C2×#66867C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44#10622167C2212yes—
45C22×D4×C11—21no—
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C22×Dic22—21no—
52C11×#121—22no—
53C11×#121—22no—
54C4×D4×C11—22no—
55C4×D4×C11—22no—
56C4×D4×C11—44no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2311yescharacteristic
60C2×C11×C4⋊C4C2311yescharacteristic
61C2×C11×C22⋊C4—21no—
62C2×C11×C22⋊C4—21no—
63C2×C11×C22⋊C4—21no—
64C2×C11×C22⋊C4—21no—
65C2×C11×C22⋊C4—21no—
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×C42×C11—21no—
69C2×C42×C11D411yescharacteristic
70C2×C42×C11D411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11—22no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2312yes—
78C2×C4⋊Dic11C2312yes—
79#66977—44no—
80C2×Dic11⋊C4—22no—
81C22×C11⋊C8C2312yes—
82C22×C11⋊C8C2312yes—
83#66922—22no—
84#66922—22no—
85C11×#95—21no—
86C11×#95—21no—
87C11×#95—21no—
88#66896—24no—
89#66896—24no—
90C11⋊#95—22no—
91C11⋊#95—22no—
92C22⋊(C11⋊C8)—24no—
93#66872—24no—
94#66871—24no—
95C4⋊(C11⋊C8)—22no—
96C4⋊(C11⋊C8)D414yescomplemented
97#66867—24no—
98#24709—111nomaximal, Sylow
99C24×C11—21no—
100C24×C11C2×D411yescharacteristic
101C2×D4×C11—24no—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11—21no—
106C2×D4×C11—21no—
107C2×D4×C11—42no—
108C2×D4×C11—42no—
109C2×D4×C11#4112yes—
110C22×C4×C11—22no—
111C22×C4×C11—21no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—41no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C22×Dic11—22no—
135C22×Dic11—22no—
136C2×Dic22—42no—
137C2×Dic22—42no—
138C2×Dic22—42no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—21no—
141C11×C4⋊C4—21no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—42no—
145C11×C4⋊C4#4112yes—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—42no—
148C11×C22⋊C4—42no—
149C11×C22⋊C4—42no—
150C11×C22⋊C4—42no—
151C42×C11—22no—
152C42×C11—22no—
153C42×C11—21no—
154C42×C11—21no—
155C42×C11—42no—
156C42×C11C2×D412yes—
157C42×C11#4112yes—
158C22⋊Dic11—44no—
159C4⋊Dic11—22no—
160C4⋊Dic11—22no—
161C4⋊Dic11—22no—
162C4⋊Dic11—22no—
163C4⋊Dic11—42no—
164C4⋊Dic11—42no—
165C4⋊Dic11—42no—
166Dic11⋊C4—44no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—22no—
170C2×C11⋊C8—22no—
171C2×C11⋊C8—22no—
172C2×C11⋊C8C2×D414yes—
173C2×#474—111no—
174C2×#432—111no—
175#2857—111no—
176C4×#121D1111yescharacteristic
177#2076—112no—
178#2034—112no—
179#1988—111no—
180#1948—111no—
181#1944—112no—
182#1936—112no—
183#1802—111no—
184C23×C11—21no—
185C23×C11—21no—
186C23×C11—21no—
187C23×C11—21no—
188C23×C11—21no—
189C23×C11—21no—
190C23×C11—22no—
191C23×C11—41no—
192C23×C11—41no—
193C23×C11—41no—
194C23×C11—41no—
195C23×C11—41no—
196C23×C11—41no—
197C23×C11#13712yes—
198C23×C11C22×D411yescharacteristic
199D4×C11—22no—
200D4×C11—22no—
201D4×C11—48no—
202D4×C11—41no—
203D4×C11—41no—
204C2×C4×C11—21no—
205C2×C4×C11—21no—
206C2×C4×C11—21no—
207C2×C4×C11—21no—
208C2×C4×C11—21no—
209C2×C4×C11—21no—
210C2×C4×C11—22no—
211C2×C4×C11—21no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—44no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—41no—
220C2×C4×C11—41no—
221C2×C4×C11—41no—
222C2×C4×C11—41no—
223C2×C4×C11—44no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—84no—
231C2×C4×C11#12112yes—
232C2×C4×C11#12112yes—
233C2×C4×C11AGL(1,ℤ/8)12yes—
234C2×C4×C11AGL(1,ℤ/8)12yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C2×Dic11—42no—
242C2×Dic11—42no—
243C2×Dic11—42no—
244C2×Dic11—42no—
245C2×Dic11—42no—
246C2×Dic11—42no—
247Dic22—84no—
248C11⋊C8—24no—
249C11⋊C8—42no—
250C2×C4⋊Q8—111no—
251C2×C22⋊Q8—221no—
252C2×#121C2×D1111yescharacteristic
253C2×C4×D4—21no—
254C2×C4×D4C2×D1111yescharacteristic
255C22×C42C2×D1111yescharacteristic
256#474—224no—
257#432—224no—
258C2×#107—112no—
259C2×#106—112no—
260C2×C4⋊C8—111no—
261C2×C4⋊C8—111no—
262C2×#102—112no—
263C2×#102—112no—
264C2×C22⋊C8—112no—
265C2×#97—112no—
266#391—221no—
267#390C2×D1111yescharacteristic
268#389—112no—
269#389—221no—
270#389C2×D1111yescharacteristic
271#388—21no—
272#386—21no—
273#384—111no—
274#380—112no—
275#380—221no—
276#380C2×D1111yescharacteristic
277C4×C4⋊C4C2×D1111yescharacteristic
278C4×C22⋊C4—21no—
279#340—112no—
280#340—112no—
281#340—112no—
282#340—112no—
283C22×C11—22no—
284C22×C11—22no—
285C22×C11—22no—
286C22×C11—41no—
287C22×C11—41no—
288C22×C11—41no—
289C22×C11—41no—
290C22×C11—42no—
291C22×C11—42no—
292C22×C11—42no—
293C22×C11—81no—
294C22×C11—81no—
295C22×C11—81no—
296C22×C11—81no—
297C22×C11C2×#12111yescharacteristic
298C22×C11#52511yescharacteristic
299C22×C11#53611yescharacteristic
300C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
301C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
302C22×C11C2×#13711yescharacteristic
303C22×C11#57511yescharacteristic
304C4×C11—22no—
305C4×C11—42no—
306C4×C11—41no—
307C4×C11—41no—
308C4×C11—41no—
309C4×C11—81no—
310C4×C11—81no—
311C4×C11#46914yes—
312C4×C11#54711yescharacteristic
313C4×C11#54811yescharacteristic
314C4×C11#55211yescharacteristic
315C4×C11#55611yescharacteristic
316Dic11—82no—
317Dic11—82no—
318C22×Q8—221no—
319C22×D4—21no—
320C22×D4C22×D1111yescharacteristic
321C23×C4—21no—
322C23×C4C22⋊D1111yescharacteristic
323C23×C4C22⋊D1111yescharacteristic
324C23×C4C22×D1111yescharacteristic
325C22×C8—112no—
326C22×C8—112no—
327C4⋊Q8—222no—
328C4⋊Q8—222no—
329C22⋊Q8—444no—
330#121—22no—
331#121—22no—
332C4×D4—22no—
333C4×D4—22no—
334C4×D4—44no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—112no—
337C2×C4⋊C4—112no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4—222no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4C22×D1111yescharacteristic
343C2×C4⋊C4C22×D1111yescharacteristic
344C2×C4⋊C4C22×D1111yescharacteristic
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—222no—
351C2×C42—22no—
352C2×C42—22no—
353C2×C42—21no—
354C2×C42C22⋊D1111yescharacteristic
355C2×C42C22⋊D1111yescharacteristic
356C2×C42C22×D1111yescharacteristic
357C2×C42C22×D1111yescharacteristic
358#107—224no—
359#106—224no—
360C4⋊C8—114no—
361C4⋊C8—222no—
362#102—224no—
363#102—224no—
364C22⋊C8—224no—
365#97—224no—
366#95—21no—
367#95—21no—
368#95—21no—
369#95—222no—
370#95—222no—
371C2×C11—42no—
372C2×C11—82no—
373C2×C11#241511yescharacteristic
374C2×C11C2×#46911yescharacteristic
375C2×C11#305611yescharacteristic
376C2×C11#311011yescharacteristic
377C2×C11#311511yescharacteristic
378C2×C11#323511yescharacteristic
379C2×C11#323911yescharacteristic
380C24—21no—
381C24C2×C22⋊D1111yescharacteristic
382C2×Q8—442no—
383C2×Q8—442no—
384C2×Q8—442no—
385C2×D4—24no—
386C2×D4—21no—
387C2×D4—21no—
388C2×D4—21no—
389C2×D4—21no—
390C2×D4—21no—
391C2×D4—42no—
392C2×D4—42no—
393C2×D4#433912yes—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—41no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—222no—
413C22×C4—222no—
414C22×C4C2×C22⋊D1111yescharacteristic
415C22×C4C2×C22⋊D1111yescharacteristic
416C22×C4C2×C22⋊D1111yescharacteristic
417C22×C4C2×C22⋊D1111yescharacteristic
418C22×C4C2×C22⋊D1111yescharacteristic
419C22×C4C23×D1111yescharacteristic
420C2×C8—114no—
421C2×C8—222no—
422C2×C8—222no—
423C2×C8—222no—
424C2×C8—222no—
425C2×C8—222no—
426C4⋊C4—21no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—42no—
432C4⋊C4—222no—
433C4⋊C4—222no—
434C4⋊C4—222no—
435C4⋊C4—222no—
436C4⋊C4—444no—
437C4⋊C4—442no—
438C4⋊C4—442no—
439C4⋊C4—442no—
440C4⋊C4#433912yes—
441C22⋊C4—24no—
442C22⋊C4—42no—
443C22⋊C4—42no—
444C22⋊C4—42no—
445C22⋊C4—42no—
446C22⋊C4—444no—
447C42—22no—
448C42—22no—
449C42—21no—
450C42—21no—
451C42—42no—
452C42D4×D1112yes—
453C42#434112yes—
454C11#2470911yescharacteristic, complemented, Sylow
455C23—21no—
456C23—21no—
457C23—21no—
458C23—21no—
459C23—21no—
460C23—21no—
461C23—22no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23#6700412yes—
469C23C22×C22⋊D1111yescharacteristic
470Q8—884no—
471D4—22no—
472D4—22no—
473D4—48no—
474D4—41no—
475D4—41no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—44no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—44no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—84no—
503C2×C4—442no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4—442no—
508C2×C4—442no—
509C2×C4#6698512yes—
510C2×C4#6699212yes—
511C2×C4#6699212yes—
512C2×C4#6700212yes—
513C2×C4C2×#433911yescharacteristic
514C2×C4C2×#433911yescharacteristic
515C2×C4C2×D4×D1111yescharacteristic
516C2×C4C2×#434111yescharacteristic
517C2×C4#6704311yescharacteristic
518C2×C4#6704311yescharacteristic
519C8—224no—
520C8—442no—
521C22—22no—
522C22—22no—
523C22—22no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—42no—
529C22—42no—
530C22—42no—
531C22—81no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22#1062332211yescharacteristic
536C22C2×#6698511yescharacteristic
537C22C2×#6699211yescharacteristic
538C22C2×#6700211yescharacteristic
539C22#1062335311yescharacteristic
540C22C2×#6700411yescharacteristic
541C22#1062335611yescharacteristic
542C4—22no—
543C4—41no—
544C4—42no—
545C4—41no—
546C4—41no—
547C4—81no—
548C4—81no—
549C4—882no—
550C4—882no—
551C4#1062265214yes—
552C4#1062307211yescharacteristic
553C4#1062307311yescharacteristic
554C4#1062308211yescharacteristic
555C4#1062308311yescharacteristic
556C2—42no—
557C2—82no—
558C2#1307204511yescharacteristic
559C2C2×#1062265211yescharacteristic
560C2#1307824811yescharacteristic
561C2#1307871511yescharacteristic
562C2#1307876711yescharacteristic
563C2#1307981011yescharacteristic
564C2#1307984311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#121C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenterC4×#121D11
hypocenterC11#24709
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10622620C2semidirect
2. C2×#10622539C2semidirect
3. #13076968C2semidirect
4. #13070047C2semidirect
6. #13069568C2semidirect
7. #13069379C2semidirect
8. #13069356C2semidirect
9. #13069316C2semidirect
10. #13068616C2semidirect
96. C4⋊(C11⋊C8)D4semidirect
454. C11#24709semidirect

Maximal subgroups

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

subgroupindex
C2×#106226202
C2×#106225392
#130769682
#130700472
#130698022
#130695682
#130693792
#130693562
#130693162
#130686162
C4×C11×#1212
#2470911