Finite Group Databasebeta

← #14771468

Subgroups — #14771468

Order 2816.

866 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#107C211yesmaximal, characteristic
2#13071484C211yesmaximal, characteristic
3#13071481C211yesmaximal, characteristic
4#13069353C211yesmaximal, characteristic, complemented
5#13069351C211yesmaximal, characteristic, complemented
6#13069210C211yesmaximal, characteristic, complemented
7#13069209C211yesmaximal, characteristic, complemented
8#13069207C211yesmaximal, characteristic, complemented
9#13068701C211yesmaximal, characteristic
10#13068701C211yesmaximal, characteristic
11#13068640C211yesmaximal, characteristic
12#13068514C211yesmaximal, characteristic, complemented
13#13068512C211yesmaximal, characteristic, complemented
14#13068391C211yesmaximal, characteristic
15C11×#1921C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C2×#66945—21no—
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×C4⋊C4×D11C2211yescharacteristic
20C2×#66925—21no—
21C2×C11×#107C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×(C2×D11)⋊C8C2211yescharacteristic
25C2×#66882C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27#10622600C2211yescharacteristic
28#10622600C2211yescharacteristic
29#10622598C2211yescharacteristic
30#10622591—21no—
31C4⋊C4×Dic11C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33#10622586C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C4×(C2×D11)⋊C4C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40#10622546—21no—
41#10622541C2211yescharacteristic
42C2×#66867C2211yescharacteristic
43D11×#107C418yescomplemented
44#10622277—21no—
45#10622277—21no—
46#10622268—21no—
47#10622265—21no—
48C11×#340C2211yescharacteristic
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#336C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—21no—
62C22×C4×D11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C42×C11—21no—
71C2×C42×C11C2311yescharacteristic
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4D411yescharacteristic
75C2×(C2×D11)⋊C4D411yescharacteristic
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11—21no—
88C2×C4×Dic11C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C2×C8×D11—22no—
92C2×C8×D11—22no—
93C2×C8×D11C2×C414yes—
94#66945—44no—
95C4⋊C4×D11—22no—
96C4⋊C4×D11—22no—
97C4⋊C4×D11C2×C414yes—
98C4⋊C4×D11C2×C414yes—
99#66925—44no—
100C11×#107C2×C414yes—
101C11×#95—21no—
102C11×#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95D411yescharacteristic
112C11⋊#95D411yescharacteristic
113(C2×D11)⋊C8—22no—
114#66882C2×C414yes—
115#66879—22no—
116#66872—22no—
117#66872—22no—
118#66871C2×C414yes—
119#66871C2×C414yes—
120#66867—22no—
121#22617—111nomaximal, Sylow
122C23×D11C2×D411yescharacteristic
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2411yescharacteristic
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C22×Dic11C2×D411yescharacteristic
137C2×C4×D11—24no—
138C2×C4×D11—24no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×C4×D11—42no—
146C2×C4×D11—42no—
147C2×C4×D11C22×C412yes—
148C2×C4×D11#4112yes—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11C22×C412yes—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—42no—
162C11×C4⋊C4C22×C412yes—
163C11×C4⋊C4C22×C412yes—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—42no—
167(C2×D11)⋊C4—22no—
168(C2×D11)⋊C4—22no—
169(C2×D11)⋊C4—42no—
170(C2×D11)⋊C4—42no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—42no—
178C4⋊Dic11C22×C412yes—
179C4⋊Dic11C22×C412yes—
180Dic11⋊C4—24no—
181Dic11⋊C4—24no—
182Dic11⋊C4—42no—
183Dic11⋊C4—42no—
184C4×Dic11—21no—
185C4×Dic11—21no—
186C4×Dic11—42no—
187C4×Dic11—42no—
188C4×Dic11—42no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8C22×C412yes—
193C2×C11⋊C8#4112yes—
194C2×C11⋊C8#4112yes—
195C8×D11—28no—
196C22×#107—111no—
197#2344—111no—
198#2344—111no—
199#1943—111no—
200#1943—111no—
201#1921—111no—
202#1921—111no—
203#1921—111no—
204#1921D1111yescharacteristic, complemented
205#1823—111no—
206#1823—111no—
207#1807—111no—
208#1776—111no—
209#1776—111no—
210#1752—111no—
211C23×C11C22×D411yescharacteristic
212C22×D11—21no—
213C22×D11—21no—
214C22×D11—21no—
215C22×D11—21no—
216C22×D11C4×D412yes—
217C22×D11AGL(1,ℤ/8)12yes—
218C22×D11AGL(1,ℤ/8)12yes—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11C23×C411yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C112−1+411yescharacteristic
242C2×C4×C112−1+411yescharacteristic
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—22no—
246C2×Dic11—22no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11C4×D412yes—
264C4×D11—22no—
265C4×D11—22no—
266C4×D11—22no—
267C4×D11—22no—
268C4×D11—48no—
269C4×D11—48no—
270C8×C11—22no—
271C8×C11—41no—
272C11⋊C8—41no—
273C11⋊C8#11714yescomplemented
274C23×C8—111no—
275C2×#117—221no—
276C2×#117—221no—
277C22×C4⋊C4—111no—
278C22×C4⋊C4—111no—
279C2×#107—111no—
280C2×#107—111no—
281C2×#107—111no—
282C2×#107—118no—
283C2×#107C2×D1111yescharacteristic
284C2×#106—111no—
285C2×#106—111no—
286C2×C22⋊C8—111no—
287C2×#97—111no—
288C2×#97—111no—
289#389—111no—
290#389—111no—
291#389—111no—
292#389C2×D1111yescharacteristic
293#387—221no—
294#387—221no—
295#387—221no—
296#387—221no—
297#381—221no—
298#381—221no—
299#380—111no—
300#380—111no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4—111no—
303C4×C4⋊C4—111no—
304C4×C4⋊C4C2×D1111yescharacteristic
305C4×C22⋊C4—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340C2×D1111yescharacteristic
314#340C2×D1111yescharacteristic
315#340C2×D1111yescharacteristic
316#336—111no—
317#336C2×D1111yescharacteristic
318C22×C11C2×C4×D411yescharacteristic
319C22×C11#54711yescharacteristic
320C22×C11#54711yescharacteristic
321C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
322C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
323C22×C11#57811yescharacteristic
324C22×C11#57811yescharacteristic
325C2×D11—22no—
326C2×D11—22no—
327C2×D11—22no—
328C2×D11—22no—
329C2×D11—22no—
330C2×D11—22no—
331C2×D11#44214yes—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—42no—
335C4×C11—42no—
336C4×C11—81no—
337C4×C11—81no—
338C4×C11C2×#11711yescharacteristic
339C4×C11#51911yescharacteristic
340C4×C11#55211yescharacteristic
341C4×C11#55211yescharacteristic
342Dic11—22no—
343Dic11—41no—
344Dic11—41no—
345Dic11—42no—
346Dic11—42no—
347Dic11—81no—
348Dic11—81no—
349C23×C4—111no—
350C23×C4—221no—
351C23×C4—221no—
352C22×C8—111no—
353C22×C8—114no—
354C22×C8—111no—
355C22×C8—222no—
356C22×C8—222no—
357C22×C8C22×D1111yescharacteristic
358C22×C8C22×D1111yescharacteristic
359#117—444no—
360#117—444no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C22⋊C4—111no—
380C2×C22⋊C4—111no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C42—21no—
384C2×C42—111no—
385C2×C42—221no—
386C2×C42—221no—
387C2×C42—221no—
388C2×C42C22×D1111yescharacteristic
389#107—114no—
390#107—114no—
391#107—114no—
392#107C4×D1114yes—
393#106—222no—
394#106—222no—
395C22⋊C8—222no—
396#97—222no—
397#97—222no—
398#95—21no—
399#95—21no—
400#95—111no—
401#95—111no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410C2×C11#234411yescharacteristic
411C2×C11C2×#44211yescharacteristic
412C2×C11#295011yescharacteristic
413C2×C11#334311yescharacteristic
414C2×C11#334311yescharacteristic
415C2×C11#334311yescharacteristic
416C2×C11#334311yescharacteristic
417D11—24no—
418C24—111no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—111no—
424C22×C4—112no—
425C22×C4—112no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—442no—
439C22×C4—442no—
440C22×C4—442no—
441C22×C4—442no—
442C22×C4D4×D1111yescharacteristic
443C22×C4D4×D1111yescharacteristic
444C22×C4C23×D1111yescharacteristic
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—112no—
451C2×C8—112no—
452C2×C8—112no—
453C2×C8—228no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8C2×C4×D1112yes—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—42no—
465C4⋊C4—112no—
466C4⋊C4—112no—
467C4⋊C4—224no—
468C4⋊C4—224no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—442no—
476C4⋊C4—442no—
477C4⋊C4—442no—
478C4⋊C4C2×C4×D1112yes—
479C4⋊C4C2×C4×D1112yes—
480C22⋊C4—222no—
481C22⋊C4—222no—
482C22⋊C4—442no—
483C22⋊C4—442no—
484C42—21no—
485C42—21no—
486C42—42no—
487C42—221no—
488C42—221no—
489C42—442no—
490C42—442no—
491C42—442no—
492C11#2261711yescharacteristic, complemented, Sylow
493C23—112no—
494C23—112no—
495C23—112no—
496C23—221no—
497C23—221no—
498C23—221no—
499C23—221no—
500C23C2×D4×D1111yescharacteristic
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—112no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—448no—
535C2×C4—448no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4C22×C4×D1111yescharacteristic
547C2×C4#6704011yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C2×C4#41×D1111yescharacteristic
550C2×C4#41×D1111yescharacteristic
551C2×C4#6704311yescharacteristic
552C8—22no—
553C8—41no—
554C8—114no—
555C8—441no—
556C22—114no—
557C22—222no—
558C22—222no—
559C22—222no—
560C22—222no—
561C22—222no—
562C22—222no—
563C22C4×D4×D1111yescharacteristic
564C22#1062316211yescharacteristic
565C22#1062318611yescharacteristic
566C22#1062329711yescharacteristic
567C22#1062330211yescharacteristic
568C22D11×AGL(1,ℤ/8)11yescharacteristic
569C22D11×AGL(1,ℤ/8)11yescharacteristic
570C4—42no—
571C4—42no—
572C4—41no—
573C4—41no—
574C4—81no—
575C4—81no—
576C4—222no—
577C4—442no—
578C4—442no—
579C4—441no—
580C4—441no—
581C4—881no—
582C4—881no—
583C4D11×#11711yescharacteristic
584C4#1062310311yescharacteristic
585C4#1062322411yescharacteristic
586C4#1062323911yescharacteristic
587C2—224no—
588C2#1307148211yescharacteristic
589C2D11×#44211yescharacteristic
590C2#1307747911yescharacteristic
591C2#1308104911yescharacteristic
592C2#1308105311yescharacteristic
593C2#1308105911yescharacteristic
594C2#1308106311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1921C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1921D11
hypocenterC11#22617
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1921

Complements

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

NH ≅ G/Ntype
4. #13069353C2semidirect
5. #13069351C2semidirect
6. #13069210C2semidirect
7. #13069209C2semidirect
8. #13069207C2semidirect
12. #13068514C2semidirect
13. #13068512C2semidirect
15. C11×#1921C2semidirect
43. D11×#107C4semidirect
204. #1921D11semidirect
273. C11⋊C8#117semidirect
492. C11#22617semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1072
#130714842
#130714812
#130693532
#130693512
#130692102
#130692092
#130692072
#130687012
#130686402
#130685142
#130685122
#130683912
C11×#19212
#2261711