Finite Group Databasebeta

← #14759249

Subgroups — #14759249

Order 2816.

688 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
1#13071112C211yesmaximal, characteristic
2#13069226C211yesmaximal, characteristic
3#13069225C211yesmaximal, characteristic
4#13069224C211yesmaximal, characteristic
5#13069180C211yesmaximal, characteristic, complemented
6#13069177C211yesmaximal, characteristic, complemented
7#13069176C211yesmaximal, characteristic, complemented
8#13069171C211yesmaximal, characteristic, complemented
9#13068468C211yesmaximal, characteristic, complemented
10C4⋊C8×Dic11C211yesmaximal, characteristic, complemented
11#13068384C211yesmaximal, characteristic
12#13068384C211yesmaximal, characteristic
13#13068366C211yesmaximal, characteristic, complemented
14#13068304C211yesmaximal, characteristic, complemented
15C11×#1924C211yesmaximal, characteristic
16C2×#66979C2211yescharacteristic
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C22⋊C8C2211yescharacteristic
19C2×C11×C22⋊C8C2211yescharacteristic
20C2×C11×#97C2211yescharacteristic
21C4×C11×C22⋊C4C2211yescharacteristic
22C4×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25C2×#66879C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622558C411yescharacteristic
34#10622558C411yescharacteristic
35#10622557C411yescharacteristic
36#10622557C411yescharacteristic
37#10622545C2211yescharacteristic
38C4×Dic11⋊C4C2211yescharacteristic
39C4×Dic11⋊C4C2211yescharacteristic
40C42×Dic11C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4×C11⋊C8C2211yescharacteristic
43#10622267C411yescharacteristic
44#10622267C411yescharacteristic
45#10622266C411yescharacteristic
46#10622266C411yescharacteristic
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622188C2211yescharacteristic
50#10622188C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C8×C11C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C2×C11×C22⋊C4C2×C411yescharacteristic
65C2×C11×C22⋊C4C2×C411yescharacteristic
66C2×C42×C11C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68C2×C22⋊Dic11C2×C411yescharacteristic
69C2×C22⋊Dic11C2×C411yescharacteristic
70C2×C22⋊Dic11C2×C411yescharacteristic
71C2×C22⋊Dic11C2×C411yescharacteristic
72#66979—22no—
73#66979—22no—
74C2×C4⋊Dic11C2×C411yescharacteristic
75C2×C4⋊Dic11C2×C411yescharacteristic
76C2×Dic11⋊C4C2×C411yescharacteristic
77C2×Dic11⋊C4C2×C411yescharacteristic
78C2×Dic11⋊C4C2×C411yescharacteristic
79C2×Dic11⋊C4C2×C411yescharacteristic
80C2×C4×Dic11C2×C411yescharacteristic
81C2×C4×Dic11C2×C411yescharacteristic
82C2×C4×Dic11C2×C411yescharacteristic
83C2×C4×Dic11C2×C411yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C2×C4×Dic11C2311yescharacteristic
87C2×C4×Dic11C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C11×C4⋊C8—22no—
93C11×C22⋊C8—22no—
94C11×C22⋊C8—22no—
95C11×#97—22no—
96C11×#95C2×C411yescharacteristic
97C11×#95C2×C411yescharacteristic
98C11⋊#95C2×C411yescharacteristic
99C11⋊#95C2×C411yescharacteristic
100C11⋊#95C2×C411yescharacteristic
101C11⋊#95C2×C411yescharacteristic
102C11⋊#95C2×C411yescharacteristic
103C11⋊#95C2×C411yescharacteristic
104C11⋊#95C2×C411yescharacteristic
105C11⋊#95C2×C411yescharacteristic
106C11⋊#95C2×C411yescharacteristic
107C11⋊#95C2×C411yescharacteristic
108C22⋊(C11⋊C8)—22no—
109C22⋊(C11⋊C8)—22no—
110#66879—22no—
111#66879—22no—
112#66879—22no—
113Dic11⋊C8—22no—
114Dic11⋊C8—22no—
115C8×Dic11—22no—
116C8×Dic11—22no—
117C8×Dic11—22no—
118C4⋊(C11⋊C8)—22no—
119C4×C11⋊C8—22no—
120#21436—111nomaximal, Sylow
121C24×C11C22×C411yescharacteristic
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C2411yescharacteristic
134C22×Dic11C22×C411yescharacteristic
135C22×Dic11C22×C411yescharacteristic
136C22×Dic11C22×C411yescharacteristic
137C22×Dic11C22×C411yescharacteristic
138C22×Dic11C22×C411yescharacteristic
139C22×Dic11C22×C411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C411yescharacteristic
142C2×C8×C11—21no—
143C2×C8×C11—21no—
144C2×C8×C11—21no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11#4112yes—
153C2×C8×C11#4112yes—
154C11×C22⋊C4—22no—
155C11×C22⋊C4—41no—
156C42×C11—21no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—21no—
160C22⋊Dic11—22no—
161C22⋊Dic11—22no—
162C22⋊Dic11—22no—
163C22⋊Dic11—41no—
164C4⋊Dic11—22no—
165C4⋊Dic11—22no—
166Dic11⋊C4—22no—
167Dic11⋊C4—22no—
168Dic11⋊C4—41no—
169Dic11⋊C4—41no—
170C4×Dic11—22no—
171C4×Dic11—22no—
172C4×Dic11—21no—
173C4×Dic11—21no—
174C4×Dic11—21no—
175C4×Dic11—21no—
176C4×Dic11—21no—
177C4×Dic11—21no—
178C4×Dic11—41no—
179C4×Dic11—41no—
180C4×Dic11#4112yes—
181C4×Dic11#4112yes—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8#4112yes—
193C2×C11⋊C8#4112yes—
194#2298—111no—
195#1924—111no—
196#1924D1111yescharacteristic
197#1923—111no—
198#1923—111no—
199#1917—111no—
200#1917—111no—
201#1916—111no—
202#1916—111no—
203#1767—111no—
204C4×C4⋊C8—111no—
205#1750—111no—
206#1750—111no—
207#1746—111no—
208#1726—111no—
209C23×C11—21no—
210C23×C11—21no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11C23×C411yescharacteristic
217C2×C4×C11—21no—
218C2×C4×C11—21no—
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—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11#13112yes—
236C2×C4×C11C2×#4111yescharacteristic
237C2×C4×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×Dic11—21no—
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—21no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11#11712yes—
264C2×Dic11#11712yes—
265C2×Dic11#13112yes—
266C8×C11—22no—
267C8×C11—22no—
268C8×C11—41no—
269C8×C11—41no—
270C11⋊C8—22no—
271C11⋊C8—22no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C2×#117—111no—
275C2×C4⋊C8—111no—
276C2×C4⋊C8—111no—
277C2×C4⋊C8—111no—
278C2×C4⋊C8C2×D1111yescharacteristic
279C2×C22⋊C8—111no—
280C2×C22⋊C8—111no—
281C2×C22⋊C8C2×D1111yescharacteristic
282C2×C22⋊C8C2×D1111yescharacteristic
283C2×#97—111no—
284C2×#97—111no—
285C2×#97—111no—
286C2×#97C2×D1111yescharacteristic
287C2×C4×C8—111no—
288C2×C4×C8—111no—
289C2×C4×C8—111no—
290C2×C4×C8—111no—
291#388—111no—
292#388—111no—
293#388—111no—
294#388—111no—
295#387—111no—
296#387—111no—
297#387—111no—
298#387—111no—
299C4×C4⋊C4—111no—
300C4×C4⋊C4—111no—
301C4×C22⋊C4—111no—
302C4×C22⋊C4C2×D1111yescharacteristic
303#376—111no—
304C43—111no—
305#336—111no—
306#336—111no—
307#336—111no—
308#336—111no—
309#336—111no—
310#336—111no—
311#336—111no—
312#336—111no—
313#336—111no—
314#336—111no—
315#336C2×D1111yescharacteristic
316#336C2×D1111yescharacteristic
317C22×C11—41no—
318C22×C11—41no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11C2×#11711yescharacteristic
325C22×C11C4×#4111yescharacteristic
326C22×C11C4×#4111yescharacteristic
327C22×C11C2×#13111yescharacteristic
328C22×C11C2×#13111yescharacteristic
329C22×C11#56811yescharacteristic
330C22×C11#56811yescharacteristic
331C4×C11—22no—
332C4×C11—41no—
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11#52911yescharacteristic
337C4×C11#52911yescharacteristic
338C4×C11#52911yescharacteristic
339C4×C11#52911yescharacteristic
340Dic11—22no—
341Dic11—22no—
342Dic11—22no—
343Dic11—41no—
344Dic11—41no—
345Dic11—41no—
346Dic11—41no—
347Dic11—41no—
348C23×C4C22×D1111yescharacteristic
349C22×C8—111no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8—111no—
353C22×C8C22×D1111yescharacteristic
354C22×C8C22×D1111yescharacteristic
355C22×C8C22×D1111yescharacteristic
356C22×C8C22×D1111yescharacteristic
357#117—222no—
358#117—222no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C22⋊C4—111no—
366C2×C22⋊C4—111no—
367C2×C22⋊C4—111no—
368C2×C22⋊C4—111no—
369C2×C22⋊C4C4×D1111yescharacteristic
370C2×C22⋊C4C4×D1111yescharacteristic
371C2×C42—111no—
372C2×C42—111no—
373C2×C42—111no—
374C2×C42—111no—
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—111no—
379C2×C42C22×D1111yescharacteristic
380C2×C42C22×D1111yescharacteristic
381C4⋊C8—22no—
382C4⋊C8—222no—
383C4⋊C8—222no—
384C4⋊C8—222no—
385C22⋊C8—22no—
386C22⋊C8—22no—
387C22⋊C8—222no—
388C22⋊C8—222no—
389#97—22no—
390#97—222no—
391#97—222no—
392#97—222no—
393C4×C8—222no—
394C4×C8—222no—
395C4×C8—222no—
396C4×C8—222no—
397#95—111no—
398#95—111no—
399#95—111no—
400#95—111no—
401#95—111no—
402#95—111no—
403#95—111no—
404#95—111no—
405#95—111no—
406#95—111no—
407#95C4×D1111yescharacteristic
408#95C4×D1111yescharacteristic
409C2×C11—81no—
410C2×C11#229811yescharacteristic
411C2×C11#292511yescharacteristic
412C2×C11#292511yescharacteristic
413C2×C11#296611yescharacteristic
414C2×C11#296711yescharacteristic
415C2×C11#296811yescharacteristic
416C2×C11#296911yescharacteristic
417C24C2×C4×D1111yescharacteristic
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—111no—
425C22×C4—111no—
426C22×C4—111no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4C2×C4×D1111yescharacteristic
433C22×C4C2×C4×D1111yescharacteristic
434C22×C4C2×C4×D1111yescharacteristic
435C22×C4C2×C4×D1111yescharacteristic
436C22×C4C2×C4×D1111yescharacteristic
437C22×C4C23×D1111yescharacteristic
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—112no—
449C2×C8—112no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8#434112yes—
461C2×C8#434112yes—
462C4⋊C4—222no—
463C4⋊C4—222no—
464C4⋊C4—222no—
465C4⋊C4—222no—
466C4⋊C4—441no—
467C4⋊C4—441no—
468C22⋊C4—22no—
469C22⋊C4—41no—
470C22⋊C4—222no—
471C22⋊C4—222no—
472C22⋊C4—222no—
473C22⋊C4—441no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—112no—
479C42—112no—
480C42—222no—
481C42—222no—
482C42—221no—
483C42—221no—
484C42—221no—
485C42—221no—
486C42—221no—
487C42—221no—
488C42—441no—
489C42—441no—
490C11#2143611yescharacteristic, complemented, Sylow
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23C22×C4×D1111yescharacteristic
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—112no—
518C2×C4—112no—
519C2×C4—112no—
520C2×C4—221no—
521C2×C4—221no—
522C2×C4—221no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4#6696012yes—
542C2×C4C2×#434111yescharacteristic
543C2×C4C2×#434111yescharacteristic
544C2×C4#41×D1111yescharacteristic
545C2×C4#41×D1111yescharacteristic
546C2×C4#41×D1111yescharacteristic
547C2×C4#41×D1111yescharacteristic
548C8—22no—
549C8—22no—
550C8—41no—
551C8—41no—
552C8—222no—
553C8—222no—
554C8—441no—
555C8—441no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22D11×#11711yescharacteristic
564C22C4×#434111yescharacteristic
565C22C4×#434111yescharacteristic
566C22C2×#6696011yescharacteristic
567C22#1062327611yescharacteristic
568C22D11×#13111yescharacteristic
569C22#1062328111yescharacteristic
570C4—22no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—222no—
576C4—222no—
577C4—222no—
578C4—441no—
579C4—441no—
580C4—441no—
581C4—441no—
582C4—441no—
583C4#1062313111yescharacteristic
584C4#1062318011yescharacteristic
585C4#1062321111yescharacteristic
586C4#1062323711yescharacteristic
587C2—81no—
588C2#1307111011yescharacteristic
589C2#1307727911yescharacteristic
590C2#1307728311yescharacteristic
591C2#1307758611yescharacteristic
592C2#1307759511yescharacteristic
593C2#1307760711yescharacteristic
594C2#1307762311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1924C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1924D11
hypocenterC11#21436
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
5. #13069180C2semidirect
6. #13069177C2semidirect
7. #13069176C2semidirect
8. #13069171C2semidirect
9. #13068468C2semidirect
10. C4⋊C8×Dic11C2semidirect
13. #13068366C2semidirect
14. #13068304C2semidirect
490. C11#21436semidirect

Maximal subgroups

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

subgroupindex
#130711122
#130692262
#130692252
#130692242
#130691802
#130691772
#130691762
#130691712
#130684682
C4⋊C8×Dic112
#130683842
#130683662
#130683042
C11×#19242
#2143611