Finite Group Databasebeta

← #14795200

Subgroups — #14795200

Order 2816.

746 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622633C211yesmaximal, characteristic, complemented
2C2×#10622613C211yesmaximal, characteristic
3#13074437C211yesmaximal, characteristic
4#13070053C211yesmaximal, characteristic
5#13070052C211yesmaximal, characteristic
6#13069816C211yesmaximal, characteristic
7#13069809C211yesmaximal, characteristic
8#13069564C211yesmaximal, characteristic, complemented
9#13069384C211yesmaximal, characteristic, complemented
10#13069351C211yesmaximal, characteristic, complemented
11#13069341C211yesmaximal, characteristic, complemented
12#13069309C211yesmaximal, characteristic, complemented
13#13069295C211yesmaximal, characteristic, complemented
14#13068631C211yesmaximal, characteristic, complemented
15C11×#2323C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×#66922C2211yescharacteristic
20C11×#391C2211yescharacteristic
21C11×#389—21no—
22C11×#389C2211yescharacteristic
23C11×#388—21no—
24C11×#388—21no—
25C11×#387—21no—
26C11×#380C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622825C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622633—24no—
37#10622613—24no—
38#10622599—21no—
39#10622592—21no—
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66872C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622562—21no—
45#10622560—21no—
46#10622549C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×Dic22—21no—
64C11×C22⋊Q8—22no—
65C11×C22⋊Q8—22no—
66C4×Q8×C11—22no—
67C4×Q8×C11—22no—
68C11×#117—22no—
69C11×#117—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99#66922—22no—
100#66922—22no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106#66899—22no—
107#66899—22no—
108#66899—22no—
109#66899—22no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C22⋊(C11⋊C8)—22no—
117C22⋊(C11⋊C8)—22no—
118#66872—22no—
119#66872—22no—
120#66872—22no—
121#66871—22no—
122C4⋊(C11⋊C8)—22no—
123C4⋊(C11⋊C8)D414yes—
124#66867—22no—
125C4×C11⋊C8—22no—
126#24718—111nomaximal, Sylow
127C24×C11C2×D411yescharacteristic
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11#4112yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C2×Dic22—42no—
155C2×Dic22—81no—
156C2×Dic22—81no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—42no—
166C11×C4⋊C4—81no—
167C11×C4⋊C4#4112yes—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—81no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—42no—
175C42×C11—81no—
176C42×C11C2×D412yes—
177C42×C11#4112yes—
178C22⋊Dic11—81no—
179C22⋊Dic11—81no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—42no—
189Dic11⋊C4—81no—
190Dic11⋊C4—81no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8C2×D412yes—
202C2×C11⋊C8C2×D412yes—
203C2×#475—111no—
204C2×#433—111no—
205#2628—111no—
206#2323D1111yescharacteristic
207#2077—111no—
208#2077—111no—
209#2036—111no—
210#2035—111no—
211#1987—111no—
212#1949—111no—
213#1943—111no—
214#1941—111no—
215#1935—111no—
216#1933—111no—
217#1805—111no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11C22×D411yescharacteristic
226Q8×C11—22no—
227Q8×C11—22no—
228Q8×C11—41no—
229Q8×C11—41no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
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—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11#12112yes—
260C2×C4×C11#12112yes—
261C2×C4×C11C22×D411yescharacteristic
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C112−1+411yescharacteristic
266C2×C4×C112−1+411yescharacteristic
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—
279Dic22—84no—
280C11⋊C8—22no—
281C11⋊C8—22no—
282C11⋊C8—41no—
283C11⋊C8—41no—
284C2×C4⋊Q8—111no—
285C2×C22⋊Q8C2×D1111yescharacteristic
286C2×C4×Q8C2×D1111yescharacteristic
287C2×#117C2×D1111yescharacteristic
288#475—224no—
289#433—224no—
290C2×#107—111no—
291C2×#106—111no—
292C2×#106—111no—
293C2×#106—111no—
294C2×C4⋊C8—111no—
295C2×C4⋊C8—111no—
296C2×#103—111no—
297C2×#103—111no—
298C2×#103—111no—
299C2×#103—111no—
300C2×C22⋊C8—111no—
301C2×C22⋊C8—111no—
302C2×#97—111no—
303C2×C4×C8—111no—
304#400—221no—
305#399—221no—
306#395—221no—
307#393—221no—
308#391C2×D1111yescharacteristic
309#389—21no—
310#389—111no—
311#389—111no—
312#389C2×D1111yescharacteristic
313#388—21no—
314#388—21no—
315#387—21no—
316#382—111no—
317#380—111no—
318#380—111no—
319#380C2×D1111yescharacteristic
320C4×C4⋊C4C2×D1111yescharacteristic
321#340—111no—
322#340—111no—
323#340—111no—
324#340—111no—
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11C2×#12111yescharacteristic
337C22×C11#52511yescharacteristic
338C22×C11#53611yescharacteristic
339C22×C11#57711yescharacteristic
340C22×C11#57711yescharacteristic
341C22×C11#57711yescharacteristic
342C22×C11#57811yescharacteristic
343C4×C11—22no—
344C4×C11—22no—
345C4×C11—42no—
346C4×C11—41no—
347C4×C11—42no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11—81no—
351C4×C11—81no—
352C4×C11#54711yescharacteristic
353C4×C11#54811yescharacteristic
354C4×C11#55211yescharacteristic
355C4×C11#55611yescharacteristic
356Dic11—81no—
357Dic11—81no—
358Dic11—81no—
359Dic11—81no—
360C22×Q8—221no—
361C22×Q8C22×D1111yescharacteristic
362C23×C4C22×D1111yescharacteristic
363C22×C8—111no—
364C22×C8—111no—
365C22×C8—111no—
366C22×C8—111no—
367C4⋊Q8—222no—
368C4⋊Q8—222no—
369C22⋊Q8—22no—
370C22⋊Q8—22no—
371C4×Q8—22no—
372C4×Q8—22no—
373#117—22no—
374#117—22no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4C22⋊D1111yescharacteristic
386C2×C4⋊C4C22⋊D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C4⋊C4C22×D1111yescharacteristic
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4C22⋊D1111yescharacteristic
395C2×C22⋊C4C22⋊D1111yescharacteristic
396C2×C42—21no—
397C2×C42—21no—
398C2×C42C22×D1111yescharacteristic
399C2×C42C22×D1111yescharacteristic
400#107—222no—
401#106—222no—
402#106—222no—
403#106—222no—
404C4⋊C8—114no—
405C4⋊C8—222no—
406#103—222no—
407#103—222no—
408#103—222no—
409#103—222no—
410C22⋊C8—222no—
411C22⋊C8—222no—
412#97—222no—
413C4×C8—222no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425C2×C11—81no—
426C2×C11#241511yescharacteristic
427C2×C11#305711yescharacteristic
428C2×C11#306311yescharacteristic
429C2×C11#312111yescharacteristic
430C2×C11#312511yescharacteristic
431C2×C11#324211yescharacteristic
432C2×C11#324411yescharacteristic
433C24C2×C22⋊D1111yescharacteristic
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—442no—
440C2×Q8—881no—
441C2×Q8—881no—
442C2×Q8#433912yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—221no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—221no—
457C22×C4C2×C22⋊D1111yescharacteristic
458C22×C4C2×C22⋊D1111yescharacteristic
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C23×D1111yescharacteristic
463C2×C8—112no—
464C2×C8—112no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C2×C8—221no—
473C2×C8—221no—
474C2×C8—221no—
475C4⋊C4—24no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—42no—
484C4⋊C4—81no—
485C4⋊C4—221no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—442no—
494C4⋊C4—881no—
495C4⋊C4—881no—
496C4⋊C4#433912yes—
497C22⋊C4—24no—
498C22⋊C4—22no—
499C22⋊C4—22no—
500C22⋊C4—81no—
501C22⋊C4—881no—
502C22⋊C4—881no—
503C42—21no—
504C42—21no—
505C42—42no—
506C42—81no—
507C42D4×D1112yes—
508C42#434112yes—
509C11#2471811yescharacteristic, complemented, Sylow
510C23—21no—
511C23—21no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23C22×C22⋊D1111yescharacteristic
518Q8—22no—
519Q8—22no—
520Q8—41no—
521Q8—41no—
522Q8—884no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4—441no—
558C2×C4—441no—
559C2×C4—441no—
560C2×C4—441no—
561C2×C4—441no—
562C2×C4—441no—
563C2×C4—441no—
564C2×C4#6699212yes—
565C2×C4#6699212yes—
566C2×C4C2×#433911yescharacteristic
567C2×C4C2×#433911yescharacteristic
568C2×C4C2×D4×D1111yescharacteristic
569C2×C4C2×#434111yescharacteristic
570C2×C4#6704311yescharacteristic
571C2×C4#6704311yescharacteristic
572C8—222no—
573C8—222no—
574C8—441no—
575C8—441no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22#1062332211yescharacteristic
584C22C2×#6699211yescharacteristic
585C22#1062335611yescharacteristic
586C22#1062336711yescharacteristic
587C22#1062336811yescharacteristic
588C22#1062336811yescharacteristic
589C22#1062336911yescharacteristic
590C4—22no—
591C4—22no—
592C4—41no—
593C4—42no—
594C4—41no—
595C4—42no—
596C4—41no—
597C4—81no—
598C4—81no—
599C4—881no—
600C4—881no—
601C4—881no—
602C4—881no—
603C4#1062307211yescharacteristic
604C4#1062307311yescharacteristic
605C4#1062308211yescharacteristic
606C4#1062308311yescharacteristic
607C2—81no—
608C2#1307204511yescharacteristic
609C2#1307825711yescharacteristic
610C2#1307830911yescharacteristic
611C2#1307884511yescharacteristic
612C2#1307889311yescharacteristic
613C2#1307987811yescharacteristic
614C2#1307990811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2323C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2323D11
hypocenterC11#24718
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2323

Complements

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

NH ≅ G/Ntype
1. C2×#10622633C2semidirect
8. #13069564C2semidirect
9. #13069384C2semidirect
10. #13069351C2semidirect
11. #13069341C2semidirect
12. #13069309C2semidirect
13. #13069295C2semidirect
14. #13068631C2semidirect
509. C11#24718semidirect

Maximal subgroups

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

subgroupindex
C2×#106226332
C2×#106226132
#130744372
#130700532
#130700522
#130698162
#130698092
#130695642
#130693842
#130693512
#130693412
#130693092
#130692952
#130686312
C11×#23232
#2471811