Finite Group Databasebeta

← #14771476

Subgroups — #14771476

Order 2816.

810 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#107C211yesmaximal, characteristic
2#13071492C211yesmaximal, characteristic
3#13071489C211yesmaximal, characteristic
4#13069353C211yesmaximal, characteristic, complemented
5#13069351C211yesmaximal, characteristic, complemented
6#13069189C211yesmaximal, characteristic, complemented
7#13069188C211yesmaximal, characteristic, complemented
8#13069186C211yesmaximal, characteristic, complemented
9#13068705C211yesmaximal, characteristic
10#13068705C211yesmaximal, characteristic
11#13068640C211yesmaximal, characteristic
12#13068514C211yesmaximal, characteristic, complemented
13#13068512C211yesmaximal, characteristic, complemented
14#13068391C211yesmaximal, characteristic
15C11×#1918C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C2×C4⋊C4×D11C2211yescharacteristic
18C2×C4⋊C4×D11C2211yescharacteristic
19C2×C11×#107C2211yescharacteristic
20C11×#389C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×(C2×D11)⋊C8C2211yescharacteristic
23C2×#66882C2211yescharacteristic
24C2×#66879C2211yescharacteristic
25#10622600—21no—
26#10622600C2211yescharacteristic
27#10622600C2211yescharacteristic
28#10622598C2211yescharacteristic
29#10622591—21no—
30C4⋊C4×Dic11C2211yescharacteristic
31C4⋊C4×Dic11C2211yescharacteristic
32#10622586C2211yescharacteristic
33C2×#66872C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35C2×#66871C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C4×(C2×D11)⋊C4—21no—
38C4×(C2×D11)⋊C4C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40#10622546—21no—
41#10622541C2211yescharacteristic
42C2×#66867C2211yescharacteristic
43D11×#107C418yescomplemented
44#10622280—21no—
45#10622279—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—
94C4⋊C4×D11—22no—
95C4⋊C4×D11—22no—
96C4⋊C4×D11C2×C414yes—
97C4⋊C4×D11C2×C414yes—
98C11×#107C2×C414yes—
99C11×#95—21no—
100C11×#95—21no—
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⋊#95D411yescharacteristic
110C11⋊#95D411yescharacteristic
111(C2×D11)⋊C8—22no—
112#66882C2×C414yes—
113#66879—22no—
114#66872—22no—
115#66872—22no—
116#66871C2×C414yes—
117#66871C2×C414yes—
118#66867—22no—
119#22618—111nomaximal, Sylow
120C23×D11C2×D411yescharacteristic
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2411yescharacteristic
128C22×Dic11—21no—
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C2×C4×D11—24no—
136C2×C4×D11—24no—
137C2×C4×D11—21no—
138C2×C4×D11—21no—
139C2×C4×D11—21no—
140C2×C4×D11—21no—
141C2×C4×D11—81no—
142C2×C4×D11—81no—
143C2×C4×D11—81no—
144C2×C4×D11—81no—
145C2×C4×D11C22×C412yes—
146C2×C4×D11#4112yes—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11C22×C412yes—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—81no—
160C11×C4⋊C4C22×C412yes—
161C11×C4⋊C4C22×C412yes—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—81no—
165(C2×D11)⋊C4—22no—
166(C2×D11)⋊C4—22no—
167(C2×D11)⋊C4—42no—
168(C2×D11)⋊C4—42no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—81no—
176C4⋊Dic11C22×C412yes—
177C4⋊Dic11C22×C412yes—
178Dic11⋊C4—24no—
179Dic11⋊C4—24no—
180Dic11⋊C4—81no—
181Dic11⋊C4—81no—
182C4×Dic11—21no—
183C4×Dic11—21no—
184C4×Dic11—81no—
185C4×Dic11—81no—
186C4×Dic11—81no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8C22×C412yes—
191C2×C11⋊C8#4112yes—
192C2×C11⋊C8#4112yes—
193C8×D11—28no—
194C22×#107—111no—
195#2345—111no—
196#2345—111no—
197#1943—111no—
198#1943—111no—
199#1918—111no—
200#1918—111no—
201#1918—111no—
202#1918D1111yescharacteristic, complemented
203#1824—111no—
204#1824—111no—
205#1807—111no—
206#1776—111no—
207#1776—111no—
208#1752—111no—
209C23×C11C22×D411yescharacteristic
210C22×D11—21no—
211C22×D11—21no—
212C22×D11—21no—
213C22×D11—21no—
214C22×D11C4×D412yes—
215C22×D11#13712yes—
216C22×D11#13712yes—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
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×C11C23×C411yescharacteristic
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C112−1+411yescharacteristic
240C2×C4×C112−1+411yescharacteristic
241C2×Dic11—21no—
242C2×Dic11—21no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—41no—
252C2×Dic11—41no—
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×Dic11C4×D412yes—
262C4×D11—22no—
263C4×D11—22no—
264C4×D11—22no—
265C4×D11—22no—
266C4×D11—84no—
267C4×D11—84no—
268C8×C11—22no—
269C8×C11—41no—
270C11⋊C8—41no—
271C11⋊C8#11714yes—
272C23×C8—111no—
273C22×C4⋊C4—111no—
274C22×C4⋊C4—111no—
275C2×#107—111no—
276C2×#107—111no—
277C2×#107—111no—
278C2×#107—118no—
279C2×#107C2×D1111yescharacteristic
280C2×#106—111no—
281C2×#106—111no—
282C2×C22⋊C8—111no—
283C2×#97—111no—
284C2×#97—111no—
285#389—111no—
286#389—111no—
287#389—111no—
288#389C2×D1111yescharacteristic
289#387—221no—
290#387—221no—
291#387—221no—
292#387—221no—
293#380—111no—
294#380—111no—
295#380—221no—
296#380—221no—
297C4×C4⋊C4—111no—
298C4×C4⋊C4—111no—
299C4×C4⋊C4—111no—
300C4×C4⋊C4C2×D1111yescharacteristic
301C4×C22⋊C4—111no—
302C4×C22⋊C4—221no—
303C4×C22⋊C4—221no—
304#340—111no—
305#340—111no—
306#340—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340C2×D1111yescharacteristic
312#340C2×D1111yescharacteristic
313#340C2×D1111yescharacteristic
314#336—111no—
315#336C2×D1111yescharacteristic
316C22×C11C2×C4×D411yescharacteristic
317C22×C11#54711yescharacteristic
318C22×C11#54711yescharacteristic
319C22×C11C2×#13711yescharacteristic
320C22×C11C2×#13711yescharacteristic
321C22×C11#57611yescharacteristic
322C22×C11#57611yescharacteristic
323C2×D11—22no—
324C2×D11—22no—
325C2×D11—22no—
326C2×D11—22no—
327C2×D11—22no—
328C2×D11—22no—
329C2×D11#44114yes—
330C4×C11—41no—
331C4×C11—41no—
332C4×C11—42no—
333C4×C11—42no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11C2×#11711yescharacteristic
337C4×C11#51911yescharacteristic
338C4×C11#55211yescharacteristic
339C4×C11#55211yescharacteristic
340Dic11—22no—
341Dic11—41no—
342Dic11—41no—
343Dic11—42no—
344Dic11—42no—
345Dic11—81no—
346Dic11—81no—
347C23×C4—111no—
348C23×C4—221no—
349C23×C4—221no—
350C22×C8—111no—
351C22×C8—114no—
352C22×C8—111no—
353C22×C8—222no—
354C22×C8—222no—
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357C2×C4⋊C4—21no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—114no—
361C2×C4⋊C4—114no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—222no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C22⋊C4—111no—
376C2×C22⋊C4—111no—
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C42—21no—
380C2×C42—111no—
381C2×C42—221no—
382C2×C42—221no—
383C2×C42—221no—
384C2×C42C22×D1111yescharacteristic
385#107—114no—
386#107—114no—
387#107—114no—
388#107C4×D1114yes—
389#106—222no—
390#106—222no—
391C22⋊C8—222no—
392#97—222no—
393#97—222no—
394#95—21no—
395#95—21no—
396#95—111no—
397#95—111no—
398#95—221no—
399#95—221no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406C2×C11#234411yescharacteristic
407C2×C11C2×#44111yescharacteristic
408C2×C11#294811yescharacteristic
409C2×C11#334611yescharacteristic
410C2×C11#334611yescharacteristic
411C2×C11#334611yescharacteristic
412C2×C11#334611yescharacteristic
413D11—24no—
414C24—111no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—111no—
420C22×C4—112no—
421C22×C4—112no—
422C22×C4—111no—
423C22×C4—111no—
424C22×C4—224no—
425C22×C4—224no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—221no—
431C22×C4—221no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—881no—
435C22×C4—881no—
436C22×C4—881no—
437C22×C4—881no—
438C22×C4D4×D1111yescharacteristic
439C22×C4D4×D1111yescharacteristic
440C22×C4C23×D1111yescharacteristic
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—112no—
447C2×C8—112no—
448C2×C8—112no—
449C2×C8—228no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8C2×C4×D1112yes—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—81no—
461C4⋊C4—112no—
462C4⋊C4—112no—
463C4⋊C4—224no—
464C4⋊C4—224no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—881no—
472C4⋊C4—881no—
473C4⋊C4—881no—
474C4⋊C4C2×C4×D1112yes—
475C4⋊C4C2×C4×D1112yes—
476C22⋊C4—222no—
477C22⋊C4—222no—
478C22⋊C4—442no—
479C22⋊C4—442no—
480C42—21no—
481C42—21no—
482C42—81no—
483C42—221no—
484C42—221no—
485C42—881no—
486C42—881no—
487C42—881no—
488C11#2261811yescharacteristic, complemented, Sylow
489C23—112no—
490C23—112no—
491C23—112no—
492C23—221no—
493C23—221no—
494C23—221no—
495C23—221no—
496C23C2×D4×D1111yescharacteristic
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—112no—
516C2×C4—221no—
517C2×C4—221no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—884no—
541C2×C4—884no—
542C2×C4C22×C4×D1111yescharacteristic
543C2×C4#6704011yescharacteristic
544C2×C4#41×D1111yescharacteristic
545C2×C4#41×D1111yescharacteristic
546C2×C4#41×D1111yescharacteristic
547C2×C4#6704311yescharacteristic
548C8—22no—
549C8—41no—
550C8—114no—
551C8—441no—
552C22—114no—
553C22—222no—
554C22—222no—
555C22—222no—
556C22—222no—
557C22—222no—
558C22—222no—
559C22C4×D4×D1111yescharacteristic
560C22#1062316211yescharacteristic
561C22#1062318611yescharacteristic
562C22#1062328811yescharacteristic
563C22#1062330011yescharacteristic
564C22D11×#13711yescharacteristic
565C22D11×#13711yescharacteristic
566C4—41no—
567C4—41no—
568C4—42no—
569C4—42no—
570C4—81no—
571C4—81no—
572C4—222no—
573C4—441no—
574C4—441no—
575C4—442no—
576C4—442no—
577C4—881no—
578C4—881no—
579C4D11×#11711yescharacteristic
580C4#1062310311yescharacteristic
581C4#1062322411yescharacteristic
582C4#1062323911yescharacteristic
583C2—224no—
584C2#1307148211yescharacteristic
585C2D11×#44111yescharacteristic
586C2#1307746311yescharacteristic
587C2#1308109411yescharacteristic
588C2#1308109811yescharacteristic
589C2#1308110411yescharacteristic
590C2#1308110811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1918C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1918D11
hypocenterC11#22618
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
4. #13069353C2semidirect
5. #13069351C2semidirect
6. #13069189C2semidirect
7. #13069188C2semidirect
8. #13069186C2semidirect
12. #13068514C2semidirect
13. #13068512C2semidirect
15. C11×#1918C2semidirect
43. D11×#107C4semidirect
202. #1918D11semidirect
488. C11#22618semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1072
#130714922
#130714892
#130693532
#130693512
#130691892
#130691882
#130691862
#130687052
#130686402
#130685142
#130685122
#130683912
C11×#19182
#2261811