Finite Group Databasebeta

← #14826949

Subgroups — #14826949

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073213C211yesmaximal, characteristic, complemented
2#13070137C211yesmaximal, characteristic, complemented
3#13069926C211yesmaximal, characteristic, complemented
4#13069847C211yesmaximal, characteristic, complemented
5#13069687C211yesmaximal, characteristic
6#13069481C211yesmaximal, characteristic, complemented
7#13069243C211yesmaximal, characteristic, complemented
8#13069240C211yesmaximal, characteristic, complemented
9#13069208C211yesmaximal, characteristic, complemented
10#13069175C211yesmaximal, characteristic, complemented
11#13068964C211yesmaximal, characteristic, complemented
12#13068964C211yesmaximal, characteristic, complemented
13#13068626C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C11×#2366C211yesmaximal, characteristic, complemented
16C2×C11×#127C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C22×#4323C2211yescharacteristic
22C11×#390—21no—
23C11×#390C2211yescharacteristic
24C11×#390C2211yescharacteristic
25C11×#386—21no—
26C11×#386—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35#10622606—21no—
36#10622603—21no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622552C2211yescharacteristic
42#10622552C2211yescharacteristic
43#10622552C2211yescharacteristic
44#10622549C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622541C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622288—21no—
50#10622282—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C22×D44C2311yescharacteristic
66C11×#127—22no—
67C11×#127—22no—
68C4×D4×C11—22no—
69C4×D4×C11—22no—
70C4×D4×C11—41no—
71C4×D4×C11—41no—
72C4×D4×C11—44no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C42×C11—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×#4323—22no—
88C2×#4323—22no—
89C2×#4323—22no—
90C2×#4323—41no—
91C2×#4323—41no—
92C2×#4323—41no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C11×#95—21no—
109C11×#95D411yescharacteristic
110C11×#95D411yescharacteristic
111#66896—22no—
112#66896—22no—
113#66896—22no—
114#66896—41no—
115#66896—41no—
116#66896—41no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121#66873—22no—
122#66873—41no—
123#66872—41no—
124#66871—22no—
125C4⋊(C11⋊C8)—41no—
126C4×C11⋊C8—41no—
127#27065—111nomaximal, Sylow
128C24×C11—21no—
129C24×C11—21no—
130C23×D11—21no—
131C2×D4×C11—24no—
132C2×D4×C11—24no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—42no—
144C2×D4×C11—42no—
145C2×D4×C11—81no—
146C2×D4×C11—81no—
147C2×D4×C11#4112yes—
148C2×D4×C11#4112yes—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—81no—
156C22×C4×C11—81no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2411yescharacteristic
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—21no—
170C2×D44—21no—
171C2×D44—21no—
172C2×D44—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4#4112yes—
179C11×C22⋊C4—42no—
180C11×C22⋊C4—42no—
181C11×C22⋊C4—42no—
182C11×C22⋊C4—42no—
183C11×C22⋊C4—81no—
184C11×C22⋊C4—81no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—42no—
192#4323—44no—
193#4323—44no—
194(C2×D11)⋊C4—42no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—81no—
197(C2×D11)⋊C4—81no—
198(C2×D11)⋊C4—81no—
199(C2×D11)⋊C4—81no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206Dic11⋊C4—81no—
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×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8#4112yes—
220#2513—111no—
221#2366D1111yescharacteristic, complemented
222#2092—111no—
223#2054—111no—
224#2041—111no—
225#2011—111no—
226#1970—111no—
227#1926—111no—
228#1926—111no—
229#1921—111no—
230#1916—111no—
231#1879—111no—
232#1879—111no—
233#1804—111no—
234C4×#102—111no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11C22×D411yescharacteristic
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11—41no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257D4×C11—22no—
258D4×C11—22no—
259D4×C11—22no—
260D4×C11—22no—
261D4×C11—48no—
262D4×C11—41no—
263D4×C11—41no—
264D4×C11—41no—
265D4×C11—41no—
266D4×C11—84no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—22no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
279C2×C4×C11—21no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—84no—
290C2×C4×C11—84no—
291C2×C4×C11#13512yes—
292C2×C4×C11AGL(1,ℤ/8)12yes—
293C2×C4×C11C2×#4111yescharacteristic
294C2×C4×C11C2×#4111yescharacteristic
295C2×C4×C11C2×#4111yescharacteristic
296C2×C4×C11C2×#4111yescharacteristic
297C2×C4×C11H(5,𝔽2)11yescharacteristic
298C2×C4×C11H(5,𝔽2)11yescharacteristic
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308D44—41no—
309D44—41no—
310D44—41no—
311D44—41no—
312C11⋊C8—22no—
313C11⋊C8—41no—
314C11⋊C8—41no—
315C11⋊C8—41no—
316C22×D8—111no—
317C22×D8—111no—
318C2×#127C2×D1111yescharacteristic
319C2×C4×D4—21no—
320C2×C4×D4C2×D1111yescharacteristic
321C2×C4×D4C2×D1111yescharacteristic
322C2×#107—111no—
323C2×#106—111no—
324C2×C4⋊C8—111no—
325C2×#102—111no—
326C2×#102—111no—
327C2×#102—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×C4×C8—111no—
334#397—221no—
335#397—221no—
336#390—21no—
337#390—111no—
338#390—111no—
339#390—111no—
340#390C2×D1111yescharacteristic
341#390C2×D1111yescharacteristic
342#389—111no—
343#388—221no—
344#388—221no—
345#386—21no—
346#386—21no—
347#382—111no—
348C4×C4⋊C4—111no—
349C4×C4⋊C4C2×D1111yescharacteristic
350C4×C4⋊C4C2×D1111yescharacteristic
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#336—111no—
356#336—111no—
357#336—111no—
358#336—111no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—42no—
362C22×C11—42no—
363C22×C11—42no—
364C22×C11—42no—
365C22×C11—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11#52511yescharacteristic
374C22×C11#54611yescharacteristic
375C22×C11#55011yescharacteristic
376C22×C11C2×#13511yescharacteristic
377C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C11#57611yescharacteristic
379C22×C11#57611yescharacteristic
380C2×D11—81no—
381C2×D11—81no—
382C2×D11—81no—
383C2×D11—81no—
384C2×D11—81no—
385C2×D11—81no—
386C2×D11—81no—
387C4×C11—22no—
388C4×C11—22no—
389C4×C11—41no—
390C4×C11—41no—
391C4×C11—41no—
392C4×C11—41no—
393C4×C11—42no—
394C4×C11—81no—
395C4×C11#52911yescharacteristic
396C4×C11#53811yescharacteristic
397C4×C11#55111yescharacteristic
398C4×C11#55311yescharacteristic
399Dic11—81no—
400Dic11—81no—
401Dic11—81no—
402C22×D4—21no—
403C22×D4—21no—
404C22×D4—111no—
405C22×D4C22×D1111yescharacteristic
406C22×D4C22×D1111yescharacteristic
407C23×C4—21no—
408C23×C4—21no—
409C2×D8—222no—
410C2×D8—222no—
411C2×D8—222no—
412C2×D8—441no—
413C2×D8—441no—
414C2×D8—441no—
415C22×C8—111no—
416C22×C8—111no—
417C22×C8—111no—
418C22×C8—111no—
419#127—22no—
420#127—22no—
421C4×D4—22no—
422C4×D4—22no—
423C4×D4—41no—
424C4×D4—41no—
425C4×D4—44no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—111no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4C22⋊D1111yescharacteristic
431C2×C4⋊C4C22⋊D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C42—21no—
447C2×C42—221no—
448C2×C42C22×D1111yescharacteristic
449C2×C42C22×D1111yescharacteristic
450C2×C42C22×D1111yescharacteristic
451#107—222no—
452#106—441no—
453C4⋊C8—441no—
454#102—222no—
455#102—222no—
456#102—222no—
457#102—222no—
458#102—441no—
459#102—441no—
460#102—441no—
461#102—441no—
462C4×C8—441no—
463#95—21no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468#95C22⋊D1111yescharacteristic
469#95C22⋊D1111yescharacteristic
470C2×C11—82no—
471C2×C11—82no—
472C2×C11#246711yescharacteristic
473C2×C11#310511yescharacteristic
474C2×C11#312211yescharacteristic
475C2×C11#330511yescharacteristic
476C2×C11#331811yescharacteristic
477C2×C11#339611yescharacteristic
478C2×C11#339911yescharacteristic
479D11—161no—
480C24—21no—
481C24—21no—
482C24—221no—
483C2×D4—24no—
484C2×D4—24no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—81no—
498C2×D4—81no—
499C2×D4—221no—
500C2×D4—221no—
501C2×D4—221no—
502C2×D4—221no—
503C2×D4—221no—
504C2×D4—221no—
505C2×D4#433912yes—
506C2×D4#433912yes—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4—81no—
514C22×C4—81no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4C2×C22⋊D1111yescharacteristic
519C22×C4C2×C22⋊D1111yescharacteristic
520C22×C4C2×C22⋊D1111yescharacteristic
521C22×C4C2×C22⋊D1111yescharacteristic
522C22×C4C2×C22⋊D1111yescharacteristic
523C22×C4C2×C22⋊D1111yescharacteristic
524C22×C4C23×D1111yescharacteristic
525D8—444no—
526D8—444no—
527C2×C8—112no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C2×C8—221no—
539C4⋊C4—22no—
540C4⋊C4—22no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—881no—
551C4⋊C4#434112yes—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—81no—
557C22⋊C4—81no—
558C22⋊C4—442no—
559C22⋊C4—442no—
560C22⋊C4—881no—
561C22⋊C4—881no—
562C22⋊C4—881no—
563C22⋊C4—881no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—42no—
571C42—881no—
572C11#2706511yescharacteristic, complemented, Sylow
573C23—22no—
574C23—22no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23—41no—
582C23—41no—
583C23—41no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—441no—
588C23—441no—
589C23—441no—
590C23—441no—
591C23—441no—
592C23—441no—
593C23—441no—
594C23C22×C22⋊D1111yescharacteristic
595D4—22no—
596D4—22no—
597D4—22no—
598D4—22no—
599D4—48no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—84no—
605D4—441no—
606D4—441no—
607D4—441no—
608D4—441no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—22no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—84no—
632C2×C4—84no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4#6698512yes—
643C2×C4#6700312yes—
644C2×C4C2×#433911yescharacteristic
645C2×C4C2×#433911yescharacteristic
646C2×C4C2×#434111yescharacteristic
647C2×C4#6703711yescharacteristic
648C2×C4#41×D1111yescharacteristic
649C2×C4#6704211yescharacteristic
650C8—222no—
651C8—441no—
652C8—441no—
653C8—441no—
654C22—42no—
655C22—42no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22—81no—
661C22—81no—
662C22—81no—
663C22—81no—
664C22—81no—
665C22—81no—
666C22—81no—
667C22—81no—
668C22—881no—
669C22—881no—
670C22—881no—
671C22—881no—
672C22—881no—
673C22—881no—
674C22—881no—
675C22#1062332211yescharacteristic
676C22C2×#6698511yescharacteristic
677C22#1062333711yescharacteristic
678C22C2×#6700311yescharacteristic
679C22#1062336511yescharacteristic
680C22#1062336611yescharacteristic
681C22#1062336611yescharacteristic
682C4—22no—
683C4—22no—
684C4—41no—
685C4—41no—
686C4—42no—
687C4—41no—
688C4—41no—
689C4—81no—
690C4—881no—
691C4—881no—
692C4—881no—
693C4#1062306911yescharacteristic
694C4#1062308711yescharacteristic
695C4#1062309111yescharacteristic
696C4#1062309611yescharacteristic
697C2—82no—
698C2—82no—
699C2—1761no—
700C2#1307266111yescharacteristic
701C2#1307866311yescharacteristic
702C2#1307885911yescharacteristic
703C2#1308056611yescharacteristic
704C2#1308075711yescharacteristic
705C2#1308162411yescharacteristic
706C2#1308165811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2366C2
socleC23×C11C22×D4
prime radical#13069687C2
hypercenter#2366D11
hypocenterC11#27065
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2366

Complements

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

NH ≅ G/Ntype
1. #13073213C2semidirect
2. #13070137C2semidirect
3. #13069926C2semidirect
4. #13069847C2semidirect
6. #13069481C2semidirect
7. #13069243C2semidirect
8. #13069240C2semidirect
9. #13069208C2semidirect
10. #13069175C2semidirect
11. #13068964C2semidirect
12. #13068964C2semidirect
13. #13068626C2semidirect
14. C4×#66896C2semidirect
15. C11×#2366C2semidirect
221. #2366D11semidirect
572. C11#27065semidirect

Maximal subgroups

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

subgroupindex
#130732132
#130701372
#130699262
#130698472
#130696872
#130694812
#130692432
#130692402
#130692082
#130691752
#130689642
#130686262
C4×#668962
C11×#23662
#2706511