Finite Group Databasebeta

← #14816655

Subgroups — #14816655

Order 2816.

860 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622379C211yesmaximal, characteristic, complemented
2C2×#10622734C211yesmaximal, characteristic, complemented
3#13072341C211yesmaximal, characteristic, complemented
4#13071658C211yesmaximal, characteristic
5#13070139C211yesmaximal, characteristic, complemented
6#13070116C211yesmaximal, characteristic, complemented
7#13069988C211yesmaximal, characteristic, complemented
8#13069953C211yesmaximal, characteristic, complemented
9#13069387C211yesmaximal, characteristic, complemented
10#13069186C211yesmaximal, characteristic, complemented
11#13068934C211yesmaximal, characteristic
12#13068865C211yesmaximal, characteristic, complemented
13#13068813C211yesmaximal, characteristic, complemented
14#13068799C211yesmaximal, characteristic, complemented
15C11×#1895C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×#121C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C2×#66943C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C11×#380C2211yescharacteristic
25#10622834—21no—
26#10622834C2211yescharacteristic
27#10622833—21no—
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C4×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32#10622734—24no—
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622598C2211yescharacteristic
41#10622590C2211yescharacteristic
42C4⋊C4×Dic11C2211yescharacteristic
43#10622586C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45C2×#66871C2211yescharacteristic
46#10622564—21no—
47#10622563—21no—
48#10622555—21no—
49C22⋊C4×Dic11—21no—
50#10622379—24no—
51#10622274—21no—
52#10622273—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C23×Dic11—21no—
66C2×C11×M16—22no—
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C11×#121—22no—
72C11×#121Q814yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11D411yescharacteristic
83C2×C22⋊Dic11D411yescharacteristic
84D4×Dic11—22no—
85D4×Dic11—41no—
86#66979—22no—
87#66979—41no—
88C2×C4⋊Dic11—22no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—41no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11C2311yescharacteristic
103C2×C4×Dic11C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66943—22no—
107#66943—41no—
108C11×#102—22no—
109C11×#102—22no—
110C11×#95—21no—
111#66896—22no—
112#66896—41no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121C22⋊(C11⋊C8)—22no—
122#66882—22no—
123#66882D414yescomplemented
124#66881—22no—
125#66881—22no—
126Dic11⋊C8—22no—
127Dic11⋊C8—22no—
128#66872—22no—
129#66871—41no—
130#26363—111nomaximal, Sylow
131C24×C11—21no—
132C24×C11C2×D411yescharacteristic
133C2×D4×C11—24no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—81no—
140C2×D4×C11—81no—
141C2×D4×C11C2×Q812yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×Q812yes—
151C22×C4×C11#4112yes—
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—42no—
158C22×Dic11—42no—
159C22×Dic11—42no—
160C22×Dic11—42no—
161C22×Dic11—81no—
162C22×Dic11—81no—
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C11×M16—28no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11C2×D412yes—
173C2×C8×C11#4112yes—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4C2×Q812yes—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—42no—
182C22⋊Dic11—41no—
183C22⋊Dic11—41no—
184C22⋊Dic11—42no—
185C22⋊Dic11—42no—
186C22⋊Dic11—42no—
187C22⋊Dic11—81no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—42no—
195C4⋊Dic11—42no—
196C4⋊Dic11—81no—
197C4⋊Dic11—81no—
198C4⋊Dic11C2×D412yes—
199C4⋊Dic11C2×D412yes—
200Dic11⋊C4—42no—
201Dic11⋊C4—81no—
202C4×Dic11—21no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—42no—
207C4×Dic11—81no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×#478—111no—
215C2×#428—111no—
216#2442—111no—
217#2363—111no—
218#2092—111no—
219#2088—111no—
220#2065—111no—
221#2059—111no—
222#1949—111no—
223#1918—111no—
224#1895D1111yescharacteristic
225#1874—111no—
226#1862—111no—
227#1854—111no—
228#1851—111no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—22no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11C22⋊Q812yes—
243C23×C11C22×D411yescharacteristic
244D4×C11—22no—
245D4×C11—22no—
246D4×C11—41no—
247D4×C11—41no—
248D4×C11—84no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11C22⋊Q812yes—
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C22×Q811yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11H(5,𝔽2)11yescharacteristic
270C2×C4×C112−1+411yescharacteristic
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—84no—
296C2×Dic11—84no—
297C8×C11—22no—
298C8×C11—22no—
299C11⋊C8—41no—
300C11⋊C8—41no—
301C22×M16C2×D1111yescharacteristic
302C2×#125—111no—
303C2×#121C2×D1111yescharacteristic
304C2×C4×D4—111no—
305C2×#117—111no—
306C22×C4⋊C4—111no—
307#478—224no—
308#428—224no—
309C2×#107—111no—
310C2×#107—111no—
311C2×#107—111no—
312C2×#106—111no—
313C2×#106—111no—
314C2×#106—111no—
315C2×C4⋊C8—111no—
316C2×C4⋊C8—111no—
317C2×#102—111no—
318C2×#102—111no—
319C2×#102C2×D1111yescharacteristic
320C2×#102C2×D1111yescharacteristic
321C2×C22⋊C8—111no—
322#400—221no—
323#398—221no—
324#390—111no—
325#390—221no—
326#389—111no—
327#389—111no—
328#389—111no—
329#388—221no—
330#386—221no—
331#385—221no—
332#382—111no—
333#380—221no—
334#380C2×D1111yescharacteristic
335C4×C4⋊C4—111no—
336C4×C22⋊C4—111no—
337C4×C22⋊C4—221no—
338#340—111no—
339#340—111no—
340#340—111no—
341#340—111no—
342#340C2×D1111yescharacteristic
343#340C2×D1111yescharacteristic
344#336—111no—
345#336—111no—
346C22×C11—22no—
347C22×C11—22no—
348C22×C11—22no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—42no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11—81no—
360C22×C11C2×C22⋊Q811yescharacteristic
361C22×C11D4211yescharacteristic
362C22×C11#54711yescharacteristic
363C22×C11#57511yescharacteristic
364C22×C11#57511yescharacteristic
365C22×C11#57611yescharacteristic
366C22×C11#57711yescharacteristic
367C4×C11—22no—
368C4×C11—42no—
369C4×C11—81no—
370C4×C11—81no—
371C4×C11#52511yescharacteristic
372C4×C11#53911yescharacteristic
373C4×C11D4×Q811yescharacteristic
374C4×C11#55411yescharacteristic
375Dic11—41no—
376Dic11—41no—
377Dic11—41no—
378Dic11—41no—
379Dic11—42no—
380Dic11—42no—
381Dic11—81no—
382Dic11—81no—
383C22×D4—21no—
384C22×D4C22×D1111yescharacteristic
385C23×C4—221no—
386C23×C4—221no—
387C23×C4C22×D1111yescharacteristic
388C2×M16—22no—
389C2×M16—22no—
390C2×M16—22no—
391C22×C8—111no—
392C22×C8—111no—
393C22×C8C22×D1111yescharacteristic
394C22×C8C22×D1111yescharacteristic
395#125—222no—
396#125—441no—
397#121—22no—
398#121Dic2214yes—
399C4×D4—222no—
400C4×D4—441no—
401#117—222no—
402#117—441no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—111no—
405C2×C4⋊C4—111no—
406C2×C4⋊C4—111no—
407C2×C4⋊C4—222no—
408C2×C4⋊C4—221no—
409C2×C4⋊C4—221no—
410C2×C4⋊C4—221no—
411C2×C4⋊C4—221no—
412C2×C4⋊C4—221no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—441no—
415C2×C4⋊C4C22×D1111yescharacteristic
416C2×C4⋊C4C22×D1111yescharacteristic
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—111no—
421C2×C22⋊C4—111no—
422C2×C22⋊C4—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C42—111no—
427C2×C42—111no—
428C2×C42—221no—
429C2×C42—221no—
430#107—114no—
431#107—222no—
432#107—441no—
433#106—222no—
434#106—222no—
435#106—222no—
436C4⋊C8—222no—
437C4⋊C8—222no—
438#102—22no—
439#102—22no—
440#102—222no—
441#102—441no—
442C22⋊C8—222no—
443#95—21no—
444#95—111no—
445#95—111no—
446#95—221no—
447#95—221no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452C2×C11—42no—
453C2×C11—82no—
454C2×C11#244911yescharacteristic
455C2×C11#308011yescharacteristic
456C2×C11#308111yescharacteristic
457C2×C11#327111yescharacteristic
458C2×C11#327311yescharacteristic
459C2×C11#334811yescharacteristic
460C2×C11#335511yescharacteristic
461C24—21no—
462C24D4×D1111yescharacteristic
463C2×D4—24no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—81no—
470C2×D4—81no—
471C2×D4C2×Dic2212yes—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—111no—
480C22×C4—111no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—442no—
488C22×C4—442no—
489C22×C4—442no—
490C22×C4—442no—
491C22×C4—881no—
492C22×C4—881no—
493C22×C4C2×Dic2212yes—
494C22×C4D4×D1111yescharacteristic
495C22×C4#434112yes—
496C22×C4C23×D1111yescharacteristic
497M16—28no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8D4×D1112yes—
509C2×C8#434112yes—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—112no—
516C4⋊C4—112no—
517C4⋊C4—221no—
518C4⋊C4—221no—
519C4⋊C4—221no—
520C4⋊C4—221no—
521C4⋊C4—221no—
522C4⋊C4—221no—
523C4⋊C4—442no—
524C4⋊C4—442no—
525C4⋊C4—442no—
526C4⋊C4—881no—
527C4⋊C4—881no—
528C4⋊C4—881no—
529C4⋊C4C2×Dic2212yes—
530C22⋊C4—24no—
531C22⋊C4—42no—
532C22⋊C4—441no—
533C22⋊C4—441no—
534C22⋊C4—442no—
535C22⋊C4—442no—
536C22⋊C4—442no—
537C22⋊C4—881no—
538C42—221no—
539C42—221no—
540C42—221no—
541C42—221no—
542C42—442no—
543C42—881no—
544C11#2636311yescharacteristic, complemented, Sylow
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23#6693112yes—
559C23C2×D4×D1111yescharacteristic
560D4—22no—
561D4—22no—
562D4—41no—
563D4—41no—
564D4—84no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
604C2×C4—884no—
605C2×C4—884no—
606C2×C4#6693112yes—
607C2×C4C22×Dic2211yescharacteristic
608C2×C4C2×D4×D1111yescharacteristic
609C2×C4C2×#434111yescharacteristic
610C2×C4C2×#434111yescharacteristic
611C2×C4#6704211yescharacteristic
612C2×C4#6704311yescharacteristic
613C8—22no—
614C8—22no—
615C8—441no—
616C8—441no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—81no—
628C22—81no—
629C22—81no—
630C22—81no—
631C22C2×#6693111yescharacteristic
632C22#1062314011yescharacteristic
633C22#1062314211yescharacteristic
634C22#1062330411yescharacteristic
635C22#1062330511yescharacteristic
636C22#1062330611yescharacteristic
637C22#1062330811yescharacteristic
638C4—22no—
639C4—42no—
640C4—81no—
641C4—81no—
642C4—441no—
643C4—441no—
644C4—441no—
645C4—441no—
646C4—442no—
647C4—442no—
648C4—881no—
649C4—881no—
650C4D4×Dic2211yescharacteristic
651C4#1062307411yescharacteristic
652C4#1062311711yescharacteristic
653C4#1062319611yescharacteristic
654C2—42no—
655C2—82no—
656C2#1307243111yescharacteristic
657C2#1307843611yescharacteristic
658C2#1307844911yescharacteristic
659C2#1308020811yescharacteristic
660C2#1308022411yescharacteristic
661C2#1308112611yescharacteristic
662C2#1308121711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1895C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#1895D11
hypocenterC11#26363
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1895

Complements

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

NH ≅ G/Ntype
1. C2×#10622379C2semidirect
2. C2×#10622734C2semidirect
3. #13072341C2semidirect
5. #13070139C2semidirect
6. #13070116C2semidirect
7. #13069988C2semidirect
8. #13069953C2semidirect
9. #13069387C2semidirect
10. #13069186C2semidirect
12. #13068865C2semidirect
13. #13068813C2semidirect
14. #13068799C2semidirect
123. #66882D4semidirect
544. C11#26363semidirect

Maximal subgroups

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

subgroupindex
C2×#106223792
C2×#106227342
#130723412
#130716582
#130701392
#130701162
#130699882
#130699532
#130693872
#130691862
#130689342
#130688652
#130688132
#130687992
C11×#18952
#2636311