Finite Group Databasebeta

← #14771566

Subgroups — #14771566

Order 2816.

744 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071019C211yesmaximal, characteristic
2#13069331C211yesmaximal, characteristic, complemented
3#13069331C211yesmaximal, characteristic, complemented
4#13069178C211yesmaximal, characteristic, complemented
5#13069177C211yesmaximal, characteristic, complemented
6#13069171C211yesmaximal, characteristic, complemented
7#13069170C211yesmaximal, characteristic, complemented
8#13068598C211yesmaximal, characteristic
9#13068594C211yesmaximal, characteristic
10#13068482C211yesmaximal, characteristic, complemented
11#13068477C211yesmaximal, characteristic, complemented
12#13068384C211yesmaximal, characteristic
13#13068382C211yesmaximal, characteristic
14C22⋊C8×Dic11C211yesmaximal, characteristic
15C11×#1798C211yesmaximal, characteristic
16C2×C11×#117C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25C2×#66879C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×C8×Dic11C2211yescharacteristic
31C2×C8×Dic11C2211yescharacteristic
32C2×C8×Dic11C2211yescharacteristic
33#10622590C411yescharacteristic
34#10622590C411yescharacteristic
35#10622589C411yescharacteristic
36#10622589C411yescharacteristic
37#10622555C411yescharacteristic
38#10622555C411yescharacteristic
39#10622555C411yescharacteristic
40#10622555C411yescharacteristic
41C4×Dic11⋊C4C2211yescharacteristic
42C4×Dic11⋊C4C2211yescharacteristic
43C4×Dic11⋊C4C2211yescharacteristic
44C4×Dic11⋊C4C2211yescharacteristic
45C2×#66867C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
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
60C23×Dic11C2×C411yescharacteristic
61C23×Dic11C2×C411yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C11×#117—41no—
67C11×#117—41no—
68C2×C11×C4⋊C4C2×C411yescharacteristic
69C2×C11×C4⋊C4C2×C411yescharacteristic
70C2×C11×C22⋊C4C2×C411yescharacteristic
71C2×C11×C22⋊C4C2×C411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11C2×C411yescharacteristic
75C2×C22⋊Dic11C2×C411yescharacteristic
76#66979—41no—
77#66979—41no—
78C2×C4⋊Dic11C2×C411yescharacteristic
79C2×C4⋊Dic11C2×C411yescharacteristic
80C2×Dic11⋊C4C2×C411yescharacteristic
81C2×Dic11⋊C4C2×C411yescharacteristic
82C2×Dic11⋊C4C2×C411yescharacteristic
83C2×Dic11⋊C4C2×C411yescharacteristic
84C2×Dic11⋊C4C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2×C411yescharacteristic
87C2×Dic11⋊C4C2×C411yescharacteristic
88C2×C4×Dic11—22no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11C2×C411yescharacteristic
91C2×C4×Dic11C2×C411yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C11×C4⋊C8—41no—
101C11×C4⋊C8—41no—
102C11×C22⋊C8—22no—
103C11×C22⋊C8—22no—
104C11⋊#95C2×C411yescharacteristic
105C11⋊#95C2×C411yescharacteristic
106C11⋊#95C2×C411yescharacteristic
107C11⋊#95C2×C411yescharacteristic
108C11⋊#95C2×C411yescharacteristic
109C11⋊#95C2×C411yescharacteristic
110C11⋊#95C2×C411yescharacteristic
111C11⋊#95C2×C411yescharacteristic
112C22⋊(C11⋊C8)—22no—
113C22⋊(C11⋊C8)Q814yes—
114#66879—41no—
115Dic11⋊C8—22no—
116Dic11⋊C8—22no—
117Dic11⋊C8—41no—
118Dic11⋊C8—41no—
119C8×Dic11—22no—
120C8×Dic11—22no—
121C8×Dic11—41no—
122#66867—41no—
123C4×C11⋊C8—41no—
124#22626—111nomaximal, Sylow
125C24×C11C22×C411yescharacteristic
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C2×Q812yes—
136C22×C4×C11#4112yes—
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—41no—
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C22×Dic11C22×C411yescharacteristic
147C22×Dic11C22×C411yescharacteristic
148C22×Dic11C22×C411yescharacteristic
149C22×Dic11C22×C411yescharacteristic
150C22×Dic11C22×C411yescharacteristic
151C22×Dic11C22×C411yescharacteristic
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—21no—
160C2×C8×C11—21no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C11×C4⋊C4—41no—
165C11×C4⋊C4—41no—
166C11×C22⋊C4—41no—
167C11×C22⋊C4—41no—
168C42×C11—21no—
169C42×C11—21no—
170C42×C11—21no—
171C42×C11—21no—
172C22⋊Dic11—41no—
173C22⋊Dic11—41no—
174C4⋊Dic11—41no—
175C4⋊Dic11—41no—
176Dic11⋊C4—22no—
177Dic11⋊C4—22no—
178Dic11⋊C4—22no—
179Dic11⋊C4—22no—
180Dic11⋊C4—22no—
181Dic11⋊C4—22no—
182Dic11⋊C4—41no—
183Dic11⋊C4—41no—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C4×Dic11—21no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11#4112yes—
193C4×Dic11#4112yes—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8C2×Q812yes—
205C2×C11⋊C8C2×Q812yes—
206#2285—111no—
207#1939—111no—
208#1939—111no—
209#1917—111no—
210#1917—111no—
211#1916—111no—
212#1916—111no—
213#1798—111no—
214#1798D1111yescharacteristic
215#1797—111no—
216#1770—111no—
217C8×C4⋊C4—111no—
218#1750—111no—
219#1750—111no—
220C4×C22⋊C8—111no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11C4×Q812yes—
228C23×C11C23×C411yescharacteristic
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11C4×Q812yes—
248C2×C4×C11C22×Q811yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
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×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—44no—
274C2×Dic11—44no—
275C2×Dic11#11712yes—
276C2×Dic11#11712yes—
277C2×Dic11#13112yes—
278C2×Dic11#13112yes—
279C2×Dic11#13112yes—
280C8×C11—41no—
281C8×C11—41no—
282C8×C11—41no—
283C8×C11—41no—
284C11⋊C8—22no—
285C11⋊C8—22no—
286C11⋊C8—41no—
287C11⋊C8—41no—
288C2×#117—111no—
289C2×#117C2×D1111yescharacteristic
290C22×C42—111no—
291C2×C4⋊C8—111no—
292C2×C4⋊C8—111no—
293C2×C4⋊C8—111no—
294C2×C4⋊C8—111no—
295C2×C4⋊C8C2×D1111yescharacteristic
296C2×C4⋊C8C2×D1111yescharacteristic
297C2×C22⋊C8—111no—
298C2×C22⋊C8—111no—
299C2×C22⋊C8C2×D1111yescharacteristic
300C2×C22⋊C8C2×D1111yescharacteristic
301C2×#97—111no—
302C2×#97—111no—
303C2×C4×C8—111no—
304C2×C4×C8—111no—
305C2×C4×C8—111no—
306C2×C4×C8—111no—
307#384—111no—
308#384—111no—
309#382—111no—
310#382—111no—
311#380—111no—
312#380—111no—
313#380—111no—
314#380—111no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4—111no—
317C4×C4⋊C4—111no—
318C4×C4⋊C4—111no—
319#336—111no—
320#336—111no—
321#336—111no—
322#336—111no—
323#336—111no—
324#336—111no—
325#336—111no—
326#336—111no—
327#336—111no—
328#336—111no—
329#336C2×D1111yescharacteristic
330#336C2×D1111yescharacteristic
331C22×C11—22no—
332C22×C11—22no—
333C22×C11—22no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11—41no—
337C22×C11—41no—
338C22×C11C2×#11711yescharacteristic
339C22×C11C2×C4×Q811yescharacteristic
340C22×C11#51811yescharacteristic
341C22×C11C2×#13111yescharacteristic
342C22×C11C2×#13111yescharacteristic
343C22×C11C2×#13111yescharacteristic
344C22×C11#56811yescharacteristic
345C4×C11—22no—
346C4×C11—41no—
347C4×C11—41no—
348C4×C11—41no—
349C4×C11—41no—
350C4×C11#55311yescharacteristic
351C4×C11#55311yescharacteristic
352C4×C11#55411yescharacteristic
353C4×C11#55411yescharacteristic
354Dic11—22no—
355Dic11—22no—
356Dic11—41no—
357Dic11—41no—
358Dic11—41no—
359Dic11—41no—
360Dic11—41no—
361Dic11#43314yes—
362C23×C4—111no—
363C23×C4—111no—
364C23×C4C22×D1111yescharacteristic
365C22×C8—111no—
366C22×C8—111no—
367C22×C8—111no—
368C22×C8—111no—
369C22×C8C22×D1111yescharacteristic
370C22×C8C22×D1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1111yescharacteristic
373#117—41no—
374#117—41no—
375#117—441no—
376#117—441no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—111no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—111no—
383C2×C4⋊C4—111no—
384C2×C4⋊C4—111no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4C4×D1111yescharacteristic
388C2×C4⋊C4C4×D1111yescharacteristic
389C2×C22⋊C4—111no—
390C2×C22⋊C4—111no—
391C2×C22⋊C4C4×D1111yescharacteristic
392C2×C22⋊C4C4×D1111yescharacteristic
393C2×C42—111no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—111no—
398C2×C42—111no—
399C2×C42—222no—
400C2×C42—222no—
401C2×C42C22×D1111yescharacteristic
402C2×C42C22×D1111yescharacteristic
403C4⋊C8—41no—
404C4⋊C8—41no—
405C4⋊C8—222no—
406C4⋊C8—222no—
407C4⋊C8—441no—
408C4⋊C8—441no—
409C22⋊C8—22no—
410C22⋊C8—22no—
411C22⋊C8—114no—
412C22⋊C8—222no—
413#97—441no—
414#97—441no—
415C4×C8—222no—
416C4×C8—222no—
417C4×C8—441no—
418C4×C8—441no—
419#95—111no—
420#95—111no—
421#95—111no—
422#95—111no—
423#95—111no—
424#95—111no—
425#95—111no—
426#95—111no—
427C2×C11—42no—
428C2×C11#234511yescharacteristic
429C2×C11C2×#43311yescharacteristic
430C2×C11#292411yescharacteristic
431C2×C11#296011yescharacteristic
432C2×C11#296211yescharacteristic
433C2×C11#297911yescharacteristic
434C2×C11#298111yescharacteristic
435C24C2×C4×D1111yescharacteristic
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—111no—
447C22×C4—111no—
448C22×C4—222no—
449C22×C4—222no—
450C22×C4—222no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—441no—
454C22×C4C2×C4×D1111yescharacteristic
455C22×C4C2×C4×D1111yescharacteristic
456C22×C4C2×C4×D1111yescharacteristic
457C22×C4C2×C4×D1111yescharacteristic
458C22×C4C2×C4×D1111yescharacteristic
459C22×C4#434112yes—
460C22×C4Q8×D1112yes—
461C22×C4C23×D1111yescharacteristic
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—112no—
475C2×C8—112no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—222no—
489C4⋊C4—222no—
490C4⋊C4—222no—
491C4⋊C4—222no—
492C4⋊C4—222no—
493C4⋊C4—222no—
494C4⋊C4—441no—
495C4⋊C4—441no—
496C4⋊C4—441no—
497C4⋊C4—441no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—441no—
501C22⋊C4—441no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—112no—
507C42—112no—
508C42—222no—
509C42—222no—
510C42—221no—
511C42—221no—
512C42—221no—
513C42—221no—
514C42—221no—
515C42—221no—
516C11#2262611yescharacteristic, complemented, Sylow
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23#6694012yes—
524C23C22×C4×D1111yescharacteristic
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—112no—
544C2×C4—112no—
545C2×C4—112no—
546C2×C4—112no—
547C2×C4—112no—
548C2×C4—221no—
549C2×C4—221no—
550C2×C4—221no—
551C2×C4—221no—
552C2×C4—221no—
553C2×C4—221no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—444no—
568C2×C4—444no—
569C2×C4#6694012yes—
570C2×C4C2×#434111yescharacteristic
571C2×C4#6703711yescharacteristic
572C2×C4#6703711yescharacteristic
573C2×C4C2×Q8×D1111yescharacteristic
574C2×C4#41×D1111yescharacteristic
575C2×C4#41×D1111yescharacteristic
576C8—41no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—222no—
581C8—222no—
582C8—441no—
583C8—441no—
584C22—22no—
585C22—22no—
586C22—22no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22#1062301711yescharacteristic
592C22C2×#6694011yescharacteristic
593C22D11×#11711yescharacteristic
594C22D11×#13111yescharacteristic
595C22D11×#13111yescharacteristic
596C22D11×#13111yescharacteristic
597C22#1062328111yescharacteristic
598C4—22no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—114no—
604C4—222no—
605C4—222no—
606C4—441no—
607C4—441no—
608C4—441no—
609C4—441no—
610C4—441no—
611C4#1062313211yescharacteristic
612C4#1062313211yescharacteristic
613C4#1062316711yescharacteristic
614C4#1062316711yescharacteristic
615C2—42no—
616C2#1307148811yescharacteristic
617C2D11×#43311yescharacteristic
618C2#1307727211yescharacteristic
619C2#1307754911yescharacteristic
620C2#1307756211yescharacteristic
621C2#1307768011yescharacteristic
622C2#1307768911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1798C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#1798D11
hypocenterC11#22626
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. #13069331C2semidirect
3. #13069331C2semidirect
4. #13069178C2semidirect
5. #13069177C2semidirect
6. #13069171C2semidirect
7. #13069170C2semidirect
10. #13068482C2semidirect
11. #13068477C2semidirect
516. C11#22626semidirect

Maximal subgroups

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

subgroupindex
#130710192
#130693312
#130691782
#130691772
#130691712
#130691702
#130685982
#130685942
#130684822
#130684772
#130683842
#130683822
C22⋊C8×Dic112
C11×#17982
#2262611