Finite Group Databasebeta

← #14762004

Subgroups — #14762004

Order 2816.

718 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#66932C211yesmaximal, characteristic
2#13069232C211yesmaximal, characteristic
3#13069219C211yesmaximal, characteristic
4#13069180C211yesmaximal, characteristic, complemented
5#13069179C211yesmaximal, characteristic, complemented
6#13069170C211yesmaximal, characteristic, complemented
7#13068758C211yesmaximal, characteristic, complemented
8#13068493C211yesmaximal, characteristic, complemented
9#13068489C211yesmaximal, characteristic, complemented
10#13068482C211yesmaximal, characteristic, complemented
11#13068395C211yesmaximal, characteristic
12#13068394C211yesmaximal, characteristic
13#13068390C211yesmaximal, characteristic
14#97×Dic11C211yesmaximal, characteristic, complemented
15C11×#1924C211yesmaximal, characteristic
16C23×C11⋊C8C2211yescharacteristic
17C2×#66932C411yescharacteristic
18C2×C11×C4⋊C8C2211yescharacteristic
19C2×C11×C22⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21C2×C11×#97C2211yescharacteristic
22C4×C11×C22⋊C4C2211yescharacteristic
23C4×C22⋊Dic11C2211yescharacteristic
24C4×C22⋊Dic11C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×#66879C2211yescharacteristic
27C2×#66879C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622564C411yescharacteristic
35#10622558C411yescharacteristic
36#10622557C411yescharacteristic
37C4×C4⋊Dic11C2211yescharacteristic
38C4×Dic11⋊C4C2211yescharacteristic
39C4×Dic11⋊C4C2211yescharacteristic
40C42×Dic11C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42C2×#66867C2211yescharacteristic
43#10622268C411yescharacteristic
44#10622266C411yescharacteristic
45#10622265C411yescharacteristic
46#10622264C411yescharacteristic
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
72C2×C4⋊Dic11C2×C411yescharacteristic
73C2×C4⋊Dic11C2×C411yescharacteristic
74C2×Dic11⋊C4C2×C411yescharacteristic
75C2×Dic11⋊C4C2×C411yescharacteristic
76C2×Dic11⋊C4C2×C411yescharacteristic
77C2×Dic11⋊C4C2×C411yescharacteristic
78C2×C4×Dic11C2×C411yescharacteristic
79C2×C4×Dic11C2×C411yescharacteristic
80C2×C4×Dic11C2×C411yescharacteristic
81C2×C4×Dic11C2×C411yescharacteristic
82C2×C4×Dic11C2311yescharacteristic
83C2×C4×Dic11C2311yescharacteristic
84C2×C4×Dic11C2311yescharacteristic
85C2×C4×Dic11C2311yescharacteristic
86C22×C11⋊C8—22no—
87C22×C11⋊C8—22no—
88C22×C11⋊C8—22no—
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93#66932—24no—
94C11×C4⋊C8—22no—
95C11×C22⋊C8—22no—
96C11×C22⋊C8—22no—
97C11×#97—22no—
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
108C11⋊#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110C22⋊(C11⋊C8)—22no—
111#66879—22no—
112#66879—22no—
113#66879—22no—
114Dic11⋊C8—22no—
115Dic11⋊C8—22no—
116C8×Dic11—22no—
117C8×Dic11—22no—
118C8×Dic11—22no—
119#66867—22no—
120#66867—22no—
121#21665—111nomaximal, Sylow
122C24×C11C22×C411yescharacteristic
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11C22×C411yescharacteristic
136C22×Dic11C22×C411yescharacteristic
137C22×Dic11C22×C411yescharacteristic
138C22×Dic11C22×C411yescharacteristic
139C22×Dic11C22×C411yescharacteristic
140C22×Dic11C22×C411yescharacteristic
141C22×Dic11C22×C411yescharacteristic
142C22×Dic11C22×C411yescharacteristic
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—21no—
153C2×C8×C11#4112yes—
154C2×C8×C11#4112yes—
155C11×C22⋊C4—22no—
156C11×C22⋊C4—41no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—21no—
161C22⋊Dic11—22no—
162C22⋊Dic11—22no—
163C22⋊Dic11—41no—
164C22⋊Dic11M1614yes—
165C4⋊Dic11—22no—
166C4⋊Dic11—41no—
167Dic11⋊C4—22no—
168Dic11⋊C4—22no—
169Dic11⋊C4—22no—
170Dic11⋊C4—41no—
171C4×Dic11—22no—
172C4×Dic11—22no—
173C4×Dic11—21no—
174C4×Dic11—21no—
175C4×Dic11—21no—
176C4×Dic11—21no—
177C4×Dic11—21no—
178C4×Dic11—21no—
179C4×Dic11—21no—
180C4×Dic11—21no—
181C4×Dic11—41no—
182C4×Dic11—41no—
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—44no—
192C2×C11⋊C8#4112yes—
193C2×C11⋊C8#4112yes—
194C2×C11⋊C8#4112yes—
195C2×C11⋊C8#4112yes—
196C4×#126—111no—
197#1924—111no—
198#1924D1111yescharacteristic
199#1923—111no—
200#1917—111no—
201#1917—111no—
202#1916—111no—
203#1839—111no—
204#1771—111no—
205#1771—111no—
206#1770—111no—
207#1752—111no—
208#1752—111no—
209C8×C22⋊C4—111no—
210C4×#97—111no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11C2×M1612yes—
218C23×C11C23×C411yescharacteristic
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—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
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—21no—
264C2×Dic11—21no—
265C2×Dic11C2×M1612yes—
266C2×Dic11C2×M1612yes—
267C2×Dic11#13112yes—
268C8×C11—22no—
269C8×C11—22no—
270C8×C11—41no—
271C8×C11—41no—
272C11⋊C8—22no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8#12614yescomplemented
276C23×C8—111no—
277C2×#126—111no—
278C2×C4⋊C8—111no—
279C2×C4⋊C8—111no—
280C2×C4⋊C8C2×D1111yescharacteristic
281C2×C22⋊C8—111no—
282C2×C22⋊C8C2×D1111yescharacteristic
283C2×C22⋊C8C2×D1111yescharacteristic
284C2×#97—111no—
285C2×#97—111no—
286C2×#97—111no—
287C2×#97—111no—
288C2×#97—111no—
289C2×#97C2×D1111yescharacteristic
290C2×C4×C8—111no—
291C2×C4×C8—111no—
292C2×C4×C8—111no—
293#388—111no—
294#388—111no—
295#388—111no—
296#387—111no—
297#387—111no—
298#387—111no—
299#383—111no—
300C4×C4⋊C4—111no—
301C4×C4⋊C4—111no—
302C4×C4⋊C4—111no—
303C4×C22⋊C4—111no—
304C4×C22⋊C4—111no—
305C4×C22⋊C4C2×D1111yescharacteristic
306C43—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#336—111no—
316#336—111no—
317#336C2×D1111yescharacteristic
318#336C2×D1111yescharacteristic
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11C4×#4111yescharacteristic
327C22×C11C4×#4111yescharacteristic
328C22×C11C4×#4111yescharacteristic
329C22×C11C22×M1611yescharacteristic
330C22×C11C2×#13111yescharacteristic
331C22×C11#56811yescharacteristic
332C22×C11#56811yescharacteristic
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—41no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11C2×#12611yescharacteristic
339C4×C11#52911yescharacteristic
340C4×C11#52911yescharacteristic
341C4×C11#52911yescharacteristic
342Dic11—22no—
343Dic11—22no—
344Dic11—22no—
345Dic11—41no—
346Dic11—41no—
347Dic11—41no—
348Dic11—41no—
349Dic11—41no—
350C23×C4C22×D1111yescharacteristic
351C22×C8—111no—
352C22×C8—111no—
353C22×C8—111no—
354C22×C8—111no—
355C22×C8—222no—
356C22×C8—222no—
357C22×C8—222no—
358C22×C8C22×D1111yescharacteristic
359C22×C8C22×D1111yescharacteristic
360C22×C8C22×D1111yescharacteristic
361C22×C8C22×D1111yescharacteristic
362#126—224no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C22⋊C4—111no—
370C2×C22⋊C4—111no—
371C2×C22⋊C4—111no—
372C2×C22⋊C4—111no—
373C2×C22⋊C4C4×D1111yescharacteristic
374C2×C22⋊C4C4×D1111yescharacteristic
375C2×C42—111no—
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—111no—
382C2×C42—111no—
383C2×C42C22×D1111yescharacteristic
384C2×C42C22×D1111yescharacteristic
385C4⋊C8—22no—
386C4⋊C8—222no—
387C4⋊C8—222no—
388C22⋊C8—22no—
389C22⋊C8—22no—
390C22⋊C8—222no—
391#97—22no—
392#97—222no—
393#97—222no—
394#97—222no—
395#97—222no—
396#97—222no—
397C4×C8—222no—
398C4×C8—222no—
399C4×C8—222no—
400#95—111no—
401#95—111no—
402#95—111no—
403#95—111no—
404#95—111no—
405#95—111no—
406#95—111no—
407#95—111no—
408#95—111no—
409#95—111no—
410#95C4×D1111yescharacteristic
411#95C4×D1111yescharacteristic
412C2×C11—42no—
413C2×C11C4×#12611yescharacteristic
414C2×C11#296511yescharacteristic
415C2×C11#296711yescharacteristic
416C2×C11#296811yescharacteristic
417C2×C11#296911yescharacteristic
418C2×C11#297011yescharacteristic
419C2×C11#297011yescharacteristic
420C24C2×C4×D1111yescharacteristic
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—111no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—111no—
434C22×C4—111no—
435C22×C4C2×C4×D1111yescharacteristic
436C22×C4C2×C4×D1111yescharacteristic
437C22×C4C2×C4×D1111yescharacteristic
438C22×C4C2×C4×D1111yescharacteristic
439C22×C4C2×C4×D1111yescharacteristic
440C22×C4C23×D1111yescharacteristic
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—112no—
452C2×C8—112no—
453C2×C8—112no—
454C2×C8—112no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—444no—
464C2×C8#434112yes—
465C2×C8#434112yes—
466C4⋊C4—222no—
467C4⋊C4—222no—
468C4⋊C4—222no—
469C4⋊C4—222no—
470C4⋊C4—441no—
471C4⋊C4—441no—
472C22⋊C4—22no—
473C22⋊C4—41no—
474C22⋊C4—114no—
475C22⋊C4—222no—
476C22⋊C4—222no—
477C22⋊C4—441no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—222no—
483C42—222no—
484C42—221no—
485C42—221no—
486C42—221no—
487C42—221no—
488C42—221no—
489C42—221no—
490C42—221no—
491C42—221no—
492C42—441no—
493C42—441no—
494C11#2166511yescharacteristic, complemented, Sylow
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23M16×D1112yes—
502C23C22×C4×D1111yescharacteristic
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—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—112no—
523C2×C4—112no—
524C2×C4—112no—
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—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—221no—
545C2×C4—221no—
546C2×C4C2×#434111yescharacteristic
547C2×C4C2×#434111yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C2×C4#41×D1111yescharacteristic
550C2×C4#41×D1111yescharacteristic
551C2×C4#41×D1111yescharacteristic
552C8—22no—
553C8—22no—
554C8—41no—
555C8—41no—
556C8—114no—
557C8—222no—
558C8—441no—
559C8—441no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22#1062305311yescharacteristic
568C22C4×#434111yescharacteristic
569C22C4×#434111yescharacteristic
570C22C2×M16×D1111yescharacteristic
571C22#1062327611yescharacteristic
572C22D11×#13111yescharacteristic
573C22#1062328111yescharacteristic
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—222no—
580C4—222no—
581C4—222no—
582C4—441no—
583C4—441no—
584C4—441no—
585C4—441no—
586C4—441no—
587C4#1062313111yescharacteristic
588C4#1062318011yescharacteristic
589C4#1062321111yescharacteristic
590C4D11×#12611yescharacteristic
591C2—42no—
592C2#1307117011yescharacteristic
593C2#1307757611yescharacteristic
594C2#1307760211yescharacteristic
595C2#1307760711yescharacteristic
596C2#1307761811yescharacteristic
597C2#1307762511yescharacteristic
598C2#1307762611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1924C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1924D11
hypocenterC11#21665
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
4. #13069180C2semidirect
5. #13069179C2semidirect
6. #13069170C2semidirect
7. #13068758C2semidirect
8. #13068493C2semidirect
9. #13068489C2semidirect
10. #13068482C2semidirect
14. #97×Dic11C2semidirect
275. C11⋊C8#126semidirect
494. C11#21665semidirect

Maximal subgroups

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

subgroupindex
C4×#669322
#130692322
#130692192
#130691802
#130691792
#130691702
#130687582
#130684932
#130684892
#130684822
#130683952
#130683942
#130683902
#97×Dic112
C11×#19242
#2166511