Finite Group Databasebeta

← #14795104

Subgroups — #14795104

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622459C211yesmaximal, characteristic, complemented
2#13074437C211yesmaximal, characteristic, complemented
3#13071309C211yesmaximal, characteristic
4#13070044C211yesmaximal, characteristic, complemented
5#13070039C211yesmaximal, characteristic, complemented
6#13069806C211yesmaximal, characteristic
7#13069799C211yesmaximal, characteristic
8#13069563C211yesmaximal, characteristic, complemented
9#13069386C211yesmaximal, characteristic, complemented
10#13069359C211yesmaximal, characteristic, complemented
11#13069349C211yesmaximal, characteristic, complemented
12#13069313C211yesmaximal, characteristic, complemented
13#13069299C211yesmaximal, characteristic, complemented
14#13068627C211yesmaximal, characteristic, complemented
15C2×C11×#433C211yesmaximal, characteristic, complemented
16C2×C11×#117C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C11×#433—24no—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×#97C2211yescharacteristic
26C2×C4×C8×C11C2211yescharacteristic
27#10622825C2211yescharacteristic
28#10622825C2211yescharacteristic
29#10622825C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66882C2211yescharacteristic
36C2×#66882C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38#10622603—21no—
39#10622602—21no—
40#10622599—21no—
41#10622592—21no—
42#10622570—21no—
43#10622569—21no—
44#10622562—21no—
45#10622560—21no—
46#10622552C2211yescharacteristic
47#10622549C2211yescharacteristic
48C4×C4⋊Dic11C2211yescharacteristic
49#10622541C2211yescharacteristic
50#10622541C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622459—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×Dic22—21no—
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×#117—22no—
71C11×#117—22no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C22⋊C4D411yescharacteristic
75C2×C11×C22⋊C4D411yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81#66983—22no—
82#66983—22no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C4×D44—22no—
100C4×D44—22no—
101#66922—22no—
102#66922—22no—
103C11×C4⋊C8—22no—
104C11×C4⋊C8D414yescomplemented
105C11×C22⋊C8—22no—
106C11×C22⋊C8—22no—
107C11×#97—22no—
108C4×C8×C11—22no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118#66885—22no—
119#66885—22no—
120#66885—22no—
121#66885—22no—
122#66882—22no—
123#66882—22no—
124#66882—22no—
125#66881—22no—
126#24712—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C23×D11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C2×C22⋊D11—24no—
142C2×C22⋊D11—81no—
143C2×C22⋊D11—81no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44#4112yes—
157C2×C4×D11—42no—
158C2×C4×D11—81no—
159C2×C4×D11—81no—
160C2×Dic22—42no—
161C2×Dic22—81no—
162C2×Dic22—81no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11C2×D412yes—
174C2×C8×C11C2×D412yes—
175C11×C4⋊C4—22no—
176C11×C4⋊C4—22no—
177C11×C22⋊C4—22no—
178C11×C22⋊C4—22no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11C2×D412yes—
182C42×C11#4112yes—
183C22⋊Dic11—81no—
184C22⋊Dic11—81no—
185C22⋊Dic11—81no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—81no—
189(C2×D11)⋊C4—81no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—42no—
204C4⋊Dic11#4112yes—
205Dic11⋊C4—81no—
206Dic11⋊C4—81no—
207Dic11⋊C4—81no—
208C4×Dic11—81no—
209C2×#474—111no—
210C2×#433D1111yescharacteristic, complemented
211#2628—111no—
212#2324—111no—
213#2076—111no—
214#2075—111no—
215#2034—111no—
216#2033—111no—
217#1987—111no—
218#1949—111no—
219#1944—111no—
220#1942—111no—
221#1936—111no—
222#1934—111no—
223#1804—111no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11C22×D411yescharacteristic
232C22×D11—22no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C22×D11—41no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11#12112yes—
257C2×C4×C11#12112yes—
258C2×C4×C11C22×D411yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11C2×#4111yescharacteristic
262C2×C4×C112−1+411yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C22⋊D11—84no—
265C2×Dic11—22no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286D44—22no—
287D44—22no—
288D44—41no—
289D44—41no—
290C4×D11—84no—
291Dic22—84no—
292C8×C11—22no—
293C8×C11—22no—
294C8×C11—41no—
295C8×C11—41no—
296C2×C4⋊Q8—111no—
297C2×#121—111no—
298C2×C4×D4—111no—
299C2×#117C2×D1111yescharacteristic
300#474—224no—
301#433—24no—
302C2×#107—111no—
303C2×#107—111no—
304C2×#107—111no—
305C2×#106—111no—
306C2×C4⋊C8C2×D1111yescharacteristic
307C2×C4⋊C8C2×D1111yescharacteristic
308C2×#102—111no—
309C2×#102—111no—
310C2×#102—111no—
311C2×#102—111no—
312C2×C22⋊C8C2×D1111yescharacteristic
313C2×C22⋊C8C2×D1111yescharacteristic
314C2×#97C2×D1111yescharacteristic
315C2×C4×C8C2×D1111yescharacteristic
316#400—221no—
317#399—221no—
318#395—221no—
319#393—221no—
320#390—111no—
321#390—221no—
322#389—111no—
323#389—111no—
324#389—111no—
325#388—221no—
326#386—221no—
327#385—221no—
328#382—111no—
329#380—111no—
330#380—111no—
331#380—111no—
332C4×C4⋊C4—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#340—111no—
337#340—111no—
338#340—111no—
339#340—111no—
340#340—111no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11C2×#12111yescharacteristic
349C22×C11#52511yescharacteristic
350C22×C11#53611yescharacteristic
351C22×C11#57611yescharacteristic
352C22×C11#57611yescharacteristic
353C22×C11#57711yescharacteristic
354C22×C11#57811yescharacteristic
355C2×D11—42no—
356C2×D11—42no—
357C2×D11—42no—
358C2×D11—81no—
359C2×D11—81no—
360C2×D11—81no—
361C2×D11—81no—
362C4×C11—22no—
363C4×C11—22no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11#54711yescharacteristic
368C4×C11#54811yescharacteristic
369C4×C11#55211yescharacteristic
370C4×C11#55611yescharacteristic
371Dic11—42no—
372Dic11—81no—
373Dic11—81no—
374Dic11—81no—
375Dic11—81no—
376Dic11—81no—
377Dic11—81no—
378C22×Q8—221no—
379C22×D4—111no—
380C22×D4—221no—
381C23×C4—221no—
382C23×C4C22×D1111yescharacteristic
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385C22×C8C22×D1111yescharacteristic
386C22×C8C22×D1111yescharacteristic
387C4⋊Q8—222no—
388C4⋊Q8—222no—
389#121—222no—
390#121—222no—
391C4×D4—222no—
392C4×D4—222no—
393#117—22no—
394#117—22no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—221no—
403C2×C4⋊C4—221no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4D4411yescharacteristic
407C2×C4⋊C4D4411yescharacteristic
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4D4411yescharacteristic
416C2×C22⋊C4D4411yescharacteristic
417C2×C42—221no—
418C2×C42C22×D1111yescharacteristic
419C2×C42C22×D1111yescharacteristic
420#107—222no—
421#107—222no—
422#107—222no—
423#106—222no—
424C4⋊C8—22no—
425C4⋊C8C22⋊D1114yescomplemented
426#102—222no—
427#102—222no—
428#102—222no—
429#102—222no—
430C22⋊C8—22no—
431C22⋊C8—22no—
432#97—22no—
433C4×C8—22no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95—221no—
439#95—221no—
440#95—221no—
441#95—221no—
442#95—221no—
443C2×C11—81no—
444C2×C11#241511yescharacteristic
445C2×C11#305811yescharacteristic
446C2×C11#306311yescharacteristic
447C2×C11#311811yescharacteristic
448C2×C11#312411yescharacteristic
449C2×C11#324111yescharacteristic
450C2×C11#324311yescharacteristic
451D11—82no—
452C24—221no—
453C24C2×D4411yescharacteristic
454C2×Q8—442no—
455C2×Q8—881no—
456C2×Q8—881no—
457C2×D4—112no—
458C2×D4—224no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—221no—
462C2×D4—221no—
463C2×D4—221no—
464C2×D4—881no—
465C2×D4—881no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—442no—
480C22×C4—881no—
481C22×C4—881no—
482C22×C4C2×D4411yescharacteristic
483C22×C4C2×D4411yescharacteristic
484C22×C4C2×D4411yescharacteristic
485C22×C4C2×D4411yescharacteristic
486C22×C4C2×D4411yescharacteristic
487C22×C4C23×D1111yescharacteristic
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8C2×C22⋊D1112yes—
499C2×C8C2×C22⋊D1112yes—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—112no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4—221no—
516C4⋊C4—442no—
517C4⋊C4—881no—
518C4⋊C4—881no—
519C4⋊C4—881no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—224no—
523C22⋊C4—442no—
524C22⋊C4—881no—
525C22⋊C4—881no—
526C22⋊C4—881no—
527C22⋊C4—881no—
528C22⋊C4—881no—
529C42—21no—
530C42—21no—
531C42—881no—
532C42#433912yes—
533C42C2×C22⋊D1112yes—
534C11#2471211yescharacteristic, complemented, Sylow
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—222no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23—441no—
547C23—441no—
548C23—441no—
549C23C22×D4411yescharacteristic
550Q8—884no—
551D4—222no—
552D4—222no—
553D4—441no—
554D4—441no—
555D4—884no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—222no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—884no—
595C2×C4#6698312yes—
596C2×C4#6698312yes—
597C2×C4C2×#433911yescharacteristic
598C2×C4#41×D1111yescharacteristic
599C2×C4#41×D1111yescharacteristic
600C2×C4#6704311yescharacteristic
601C2×C4#6704311yescharacteristic
602C2×C4C22×C22⋊D1111yescharacteristic
603C8—22no—
604C8—22no—
605C8—41no—
606C8—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—442no—
615C22—442no—
616C22—442no—
617C22—881no—
618C22—881no—
619C22—881no—
620C22—881no—
621C22#1062305511yescharacteristic
622C22#1062305711yescharacteristic
623C22#1062328211yescharacteristic
624C22#1062328311yescharacteristic
625C22#1062328311yescharacteristic
626C22#1062328411yescharacteristic
627C22C2×#6698311yescharacteristic
628C4—22no—
629C4—22no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—442no—
634C4—881no—
635C4—881no—
636C4—881no—
637C4—881no—
638C4—881no—
639C4—881no—
640C4#1062306011yescharacteristic
641C4#1062306411yescharacteristic
642C4#1062335511yescharacteristic
643C4#1062336211yescharacteristic
644C2—81no—
645C2—882no—
646C2#1307203911yescharacteristic
647C2#1307826411yescharacteristic
648C2#1307830711yescharacteristic
649C2#1307880211yescharacteristic
650C2#1307888011yescharacteristic
651C2#1307987111yescharacteristic
652C2#1307990111yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#433C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#433D11
hypocenterC11#24712
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#10622459C2semidirect
2. #13074437C2semidirect
4. #13070044C2semidirect
5. #13070039C2semidirect
8. #13069563C2semidirect
9. #13069386C2semidirect
10. #13069359C2semidirect
11. #13069349C2semidirect
12. #13069313C2semidirect
13. #13069299C2semidirect
14. #13068627C2semidirect
15. C2×C11×#433C2semidirect
104. C11×C4⋊C8D4semidirect
210. C2×#433D11semidirect
425. C4⋊C8C22⋊D11semidirect
534. C11#24712semidirect

Maximal subgroups

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

subgroupindex
C2×#106224592
#130744372
#130713092
#130700442
#130700392
#130698062
#130697992
#130695632
#130693862
#130693592
#130693492
#130693132
#130692992
#130686272
C2×C11×#4332
#2471211