Finite Group Databasebeta

← #14821828

Subgroups — #14821828

Order 2816.

848 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072990C211yesmaximal, characteristic, complemented
2#13069933C211yesmaximal, characteristic, complemented
3#13069802C211yesmaximal, characteristic
4#13069752C211yesmaximal, characteristic, complemented
5#13069619C211yesmaximal, characteristic
6#13069564C211yesmaximal, characteristic, complemented
7#13069291C211yesmaximal, characteristic, complemented
8#13069250C211yesmaximal, characteristic, complemented
9#13069224C211yesmaximal, characteristic, complemented
10#13069191C211yesmaximal, characteristic, complemented
11#13068950C211yesmaximal, characteristic, complemented
12#13068923C211yesmaximal, characteristic, complemented
13#13068702C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C11×#2361C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C11×#390C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#388—21no—
26C11×#386—21no—
27C11×#385—21no—
28C4×C11×C4⋊C4C2211yescharacteristic
29C4×C11×C22⋊C4C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40#10622564—21no—
41#10622560—21no—
42C4×C4⋊Dic11C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622542C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622273—21no—
48#10622259—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C22×Dic22—21no—
65C22×Dic22C2311yescharacteristic
66C11×#121—22no—
67C11×#121—22no—
68C4×D4×C11—22no—
69C4×D4×C11—41no—
70C4×D4×C11—44no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—41no—
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⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C11×C22⋊C4D411yescharacteristic
84C2×C42×C11—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×#4324—22no—
90C2×#4324—41no—
91C2×#4324—41no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96#66977—22no—
97#66977—41no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66922—22no—
105#66922—41no—
106C11×#95—21no—
107C11×#95—21no—
108C11×#95D411yescharacteristic
109C11×#95D411yescharacteristic
110#66896—22no—
111#66896—22no—
112#66896—41no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C22⋊(C11⋊C8)—41no—
120C22⋊(C11⋊C8)—41no—
121#66874—22no—
122#66874—22no—
123#66874—41no—
124#66872—22no—
125C4⋊(C11⋊C8)—41no—
126C4×C11⋊C8—41no—
127#26722—111nomaximal, Sylow
128C24×C11—21no—
129C24×C11C2×D411yescharacteristic
130C2×D4×C11—24no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—42no—
137C2×D4×C11—42no—
138C2×D4×C11#4112yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
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—42no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—42no—
152C22×C4×C11—81no—
153C22×C4×C11—81no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—42no—
171C2×Dic22—42no—
172C2×Dic22—81no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—42no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4#4112yes—
180C11×C4⋊C4#4112yes—
181C11×C22⋊C4—24no—
182C11×C22⋊C4—41no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—81no—
186C11×C22⋊C4SD1614yescomplemented
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—42no—
192C22⋊Dic11—42no—
193C22⋊Dic11—81no—
194#4324—44no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—42no—
201C4⋊Dic11#4112yes—
202Dic11⋊C4—42no—
203C4×Dic11—81no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
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×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216#2492—111no—
217#2361D1111yescharacteristic
218#2055—111no—
219#2034—111no—
220#2023—111no—
221#2000—111no—
222#1987—111no—
223#1933—111no—
224#1927—111no—
225#1923—111no—
226#1919—111no—
227#1877—111no—
228#1872—111no—
229#1823—111no—
230C4×#102—111no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—22no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11C2×SD1612yes—
245C23×C11C22×D411yescharacteristic
246D4×C11—22no—
247D4×C11—22no—
248D4×C11—48no—
249D4×C11—41no—
250D4×C11—41no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—22no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—22no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—84no—
278C2×C4×C11—84no—
279C2×C4×C11C2×SD1612yes—
280C2×C4×C11C2×SD1612yes—
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11H(5,𝔽2)11yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×Dic11—22no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299Dic22—41no—
300Dic22—41no—
301Dic22—41no—
302Dic22—41no—
303Dic22—84no—
304C11⋊C8—41no—
305C11⋊C8—41no—
306C11⋊C8—41no—
307C11⋊C8—41no—
308C22×SD16—111no—
309C2×C4⋊Q8—111no—
310C2×C22⋊Q8—111no—
311C2×#121C2×D1111yescharacteristic
312C2×C4×D4—21no—
313C2×C4×D4C2×D1111yescharacteristic
314C22×C4⋊C4C2×D1111yescharacteristic
315C2×#106—111no—
316C2×C4⋊C8—111no—
317C2×#103—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102—111no—
323C2×C22⋊C8—111no—
324C2×C22⋊C8—111no—
325C2×C4×C8—111no—
326#400—221no—
327#393—221no—
328#391—111no—
329#391—111no—
330#391—221no—
331#390C2×D1111yescharacteristic
332#389C2×D1111yescharacteristic
333#388—21no—
334#388—221no—
335#386—21no—
336#385—21no—
337#380—111no—
338C4×C4⋊C4—111no—
339C4×C4⋊C4C2×D1111yescharacteristic
340C4×C22⋊C4C2×D1111yescharacteristic
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#336—111no—
350#336—111no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11#52511yescharacteristic
366C22×C11#54611yescharacteristic
367C22×C11#54611yescharacteristic
368C22×C11C22×SD1611yescharacteristic
369C22×C11#57511yescharacteristic
370C22×C11#57611yescharacteristic
371C22×C11#57811yescharacteristic
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—42no—
375C4×C11—41no—
376C4×C11—42no—
377C4×C11—41no—
378C4×C11—41no—
379C4×C11—81no—
380C4×C11#52911yescharacteristic
381C4×C11#53811yescharacteristic
382C4×C11#55511yescharacteristic
383C4×C11#55911yescharacteristic
384Dic11—42no—
385Dic11—81no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8—111no—
389C22×Q8—221no—
390C22×D4—21no—
391C22×D4C22×D1111yescharacteristic
392C23×C4—21no—
393C23×C4—21no—
394C23×C4C22×D1111yescharacteristic
395C2×SD16—222no—
396C2×SD16—441no—
397C2×SD16—441no—
398C22×C8—111no—
399C22×C8—111no—
400C22×C8—111no—
401C22×C8—111no—
402C4⋊Q8—222no—
403C4⋊Q8—441no—
404C22⋊Q8—222no—
405C22⋊Q8—441no—
406#121—22no—
407#121—22no—
408C4×D4—22no—
409C4×D4—41no—
410C4×D4—44no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—41no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4C22×D1111yescharacteristic
421C2×C4⋊C4C22×D1111yescharacteristic
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C22⋊C4—21no—
426C2×C22⋊C4—21no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4C22⋊D1111yescharacteristic
430C2×C22⋊C4C22⋊D1111yescharacteristic
431C2×C42—21no—
432C2×C42—221no—
433C2×C42C22×D1111yescharacteristic
434C2×C42C22×D1111yescharacteristic
435#106—222no—
436C4⋊C8—441no—
437#103—222no—
438#103—222no—
439#103—441no—
440#102—222no—
441#102—222no—
442#102—441no—
443C22⋊C8—441no—
444C22⋊C8—441no—
445C4×C8—441no—
446#95—21no—
447#95—21no—
448#95—221no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95C22⋊D1111yescharacteristic
455#95C22⋊D1111yescharacteristic
456C2×C11—42no—
457C2×C11—82no—
458C2×C11#245911yescharacteristic
459C2×C11#310111yescharacteristic
460C2×C11#312411yescharacteristic
461C2×C11#329511yescharacteristic
462C2×C11#329811yescharacteristic
463C2×C11#331311yescharacteristic
464C2×C11#332211yescharacteristic
465C24—21no—
466C24C2×C22⋊D1111yescharacteristic
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—442no—
474C2×Q8—442no—
475C2×Q8—881no—
476C2×D4—24no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—42no—
483C2×D4—42no—
484C2×D4#433912yes—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—81no—
499C22×C4—81no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1111yescharacteristic
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C23×D1111yescharacteristic
510SD16—444no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—42no—
528C4⋊C4—42no—
529C4⋊C4—112no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—442no—
536C4⋊C4—442no—
537C4⋊C4#433912yes—
538C4⋊C4#434112yes—
539C22⋊C4—24no—
540C22⋊C4—41no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—81no—
544C22⋊C4—442no—
545C22⋊C4—881no—
546C22⋊C4#432414yescomplemented
547C42—21no—
548C42—21no—
549C42—21no—
550C42—21no—
551C42—42no—
552C42—881no—
553C11#2672211yescharacteristic, complemented, Sylow
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—22no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23C2×#432412yes—
568C23C22×C22⋊D1111yescharacteristic
569Q8—441no—
570Q8—441no—
571Q8—441no—
572Q8—441no—
573Q8—884no—
574D4—22no—
575D4—22no—
576D4—48no—
577D4—41no—
578D4—41no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—84no—
606C2×C4—84no—
607C2×C4—222no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4C2×#432412yes—
620C2×C4C2×#432412yes—
621C2×C4C2×#433911yescharacteristic
622C2×C4C2×#433911yescharacteristic
623C2×C4C2×#434111yescharacteristic
624C2×C4#6703711yescharacteristic
625C2×C4#41×D1111yescharacteristic
626C2×C4#6704211yescharacteristic
627C8—441no—
628C8—441no—
629C8—441no—
630C8—441no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22#1062332211yescharacteristic
646C22C22×#432411yescharacteristic
647C22#1062333711yescharacteristic
648C22#1062335311yescharacteristic
649C22#1062336011yescharacteristic
650C22#1062336611yescharacteristic
651C22#1062336911yescharacteristic
652C4—22no—
653C4—22no—
654C4—42no—
655C4—41no—
656C4—42no—
657C4—41no—
658C4—41no—
659C4—81no—
660C4—442no—
661C4—881no—
662C4—881no—
663C4—881no—
664C4#1062306911yescharacteristic
665C4#1062309011yescharacteristic
666C4#1062309111yescharacteristic
667C4#1062309411yescharacteristic
668C2—42no—
669C2—82no—
670C2#1307254711yescharacteristic
671C2#1307862411yescharacteristic
672C2#1307887811yescharacteristic
673C2#1308044011yescharacteristic
674C2#1308047511yescharacteristic
675C2#1308068211yescharacteristic
676C2#1308081111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2361C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2361D11
hypocenterC11#26722
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
1. #13072990C2semidirect
2. #13069933C2semidirect
4. #13069752C2semidirect
6. #13069564C2semidirect
7. #13069291C2semidirect
8. #13069250C2semidirect
9. #13069224C2semidirect
10. #13069191C2semidirect
11. #13068950C2semidirect
12. #13068923C2semidirect
13. #13068702C2semidirect
14. C4×#66896C2semidirect
186. C11×C22⋊C4SD16semidirect
546. C22⋊C4#4324semidirect
553. C11#26722semidirect

Maximal subgroups

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

subgroupindex
#130729902
#130699332
#130698022
#130697522
#130696192
#130695642
#130692912
#130692502
#130692242
#130691912
#130689502
#130689232
#130687022
C4×#668962
C11×#23612
#2672211