Finite Group Databasebeta

← #14779910

Subgroups — #14779910

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071875C211yesmaximal, characteristic
2#13069411C211yesmaximal, characteristic
3#13069338C211yesmaximal, characteristic, complemented
4#13069333C211yesmaximal, characteristic, complemented
5#13069232C211yesmaximal, characteristic, complemented
6#13069226C211yesmaximal, characteristic, complemented
7#13069225C211yesmaximal, characteristic, complemented
8#13069219C211yesmaximal, characteristic, complemented
9#13069171C211yesmaximal, characteristic, complemented
10#13069171C211yesmaximal, characteristic, complemented
11#13068794C211yesmaximal, characteristic, complemented
12#13068794C211yesmaximal, characteristic, complemented
13#13068598C211yesmaximal, characteristic, complemented
14#13068598C211yesmaximal, characteristic, complemented
15C11×#1869C211yesmaximal, characteristic
16C23×C8×C11C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×C11×C22⋊C8C2211yescharacteristic
20C2×C11×C22⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22#10622835C411yescharacteristic
23#10622835C411yescharacteristic
24C4×C22⋊Dic11C2211yescharacteristic
25C4×C22⋊Dic11C2211yescharacteristic
26C4×C22⋊Dic11C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×#66879C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37C2×Dic11⋊C8C2211yescharacteristic
38C2×C8×Dic11C2211yescharacteristic
39#10622599C411yescharacteristic
40#10622596C411yescharacteristic
41#10622566C411yescharacteristic
42#10622565C411yescharacteristic
43#10622565C411yescharacteristic
44#10622562C411yescharacteristic
45C4×Dic11⋊C4C2211yescharacteristic
46C4×Dic11⋊C4C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59C22×D4×C11C2×C411yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C8×C11—41no—
63C22×C8×C11—41no—
64C22×C8×C11—41no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C4×D4×C11—41no—
70C4×D4×C11—41no—
71C2×C11×C4⋊C4C2×C411yescharacteristic
72C2×C11×C22⋊C4C2×C411yescharacteristic
73C2×C11×C22⋊C4C2×C411yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11C2×C411yescharacteristic
76C2×C22⋊Dic11C2×C411yescharacteristic
77C2×C22⋊Dic11C2×C411yescharacteristic
78C2×C22⋊Dic11C2×C411yescharacteristic
79C2×C22⋊Dic11C2×C411yescharacteristic
80C2×C22⋊Dic11C2×C411yescharacteristic
81C2×C22⋊Dic11C2×C411yescharacteristic
82C2×C22⋊Dic11C2×C411yescharacteristic
83#66979—41no—
84#66979—41no—
85C2×C4⋊Dic11C2×C411yescharacteristic
86C2×C4⋊Dic11C2×C411yescharacteristic
87C2×Dic11⋊C4C2×C411yescharacteristic
88C2×Dic11⋊C4C2×C411yescharacteristic
89C2×Dic11⋊C4C2×C411yescharacteristic
90C2×Dic11⋊C4C2×C411yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C2×C4×Dic11C2311yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C11×C22⋊C8—41no—
100C11×C22⋊C8—41no—
101C11×C22⋊C8—41no—
102C11⋊#95C2×C411yescharacteristic
103C11⋊#95C2×C411yescharacteristic
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)—41no—
113C22⋊(C11⋊C8)—41no—
114C22⋊(C11⋊C8)—41no—
115C22⋊(C11⋊C8)—41no—
116#66879—41no—
117Dic11⋊C8—41no—
118Dic11⋊C8—41no—
119Dic11⋊C8—41no—
120Dic11⋊C8—41no—
121Dic11⋊C8—41no—
122Dic11⋊C8—41no—
123C8×Dic11—41no—
124C4⋊(C11⋊C8)—41no—
125C4×C11⋊C8—41no—
126#23319—111nomaximal, Sylow
127C24×C11C22×C411yescharacteristic
128C24×C11C22×C411yescharacteristic
129C2×D4×C11—22no—
130C2×D4×C11—22no—
131C2×D4×C11—41no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C22×C411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11C22×C411yescharacteristic
150C22×Dic11C22×C411yescharacteristic
151C22×Dic11C22×C411yescharacteristic
152C22×Dic11C22×C411yescharacteristic
153C22×Dic11C22×C411yescharacteristic
154C22×Dic11C22×C411yescharacteristic
155C22×Dic11C22×C411yescharacteristic
156C22×Dic11C22×C411yescharacteristic
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—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—44no—
170C11×C4⋊C4—41no—
171C11×C22⋊C4—41no—
172C11×C22⋊C4—41no—
173C42×C11—21no—
174C42×C11—21no—
175C22⋊Dic11—22no—
176C22⋊Dic11—22no—
177C22⋊Dic11—22no—
178C22⋊Dic11—22no—
179C22⋊Dic11—41no—
180C22⋊Dic11—41no—
181C22⋊Dic11—41no—
182C22⋊Dic11—41no—
183C4⋊Dic11—41no—
184C4⋊Dic11—41no—
185Dic11⋊C4—22no—
186Dic11⋊C4—22no—
187Dic11⋊C4—22no—
188Dic11⋊C4—41no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—21no—
192C4×Dic11—21no—
193C4×Dic11—21no—
194C4×Dic11—21no—
195C4×Dic11—21no—
196C4×Dic11—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⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209#2395—111no—
210#1954—111no—
211#1940—111no—
212#1939—111no—
213#1924—111no—
214#1924—111no—
215#1923—111no—
216#1923—111no—
217#1916—111no—
218#1916—111no—
219#1869D1111yescharacteristic
220#1850—111no—
221#1850—111no—
222#1798—111no—
223#1798—111no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11—21no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11#13112yes—
238C23×C11C23×C411yescharacteristic
239D4×C11—44no—
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×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11#13112yes—
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C2×C4×C11H(5,𝔽2)11yescharacteristic
264C2×C4×C112−1+411yescharacteristic
265C2×C4×C112−1+411yescharacteristic
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—21no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11#13112yes—
290C8×C11—41no—
291C8×C11—41no—
292C8×C11—41no—
293C8×C11—41no—
294C11⋊C8—41no—
295C11⋊C8—41no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C23×C8C2×D1111yescharacteristic
299C2×C4×D4C2×D1111yescharacteristic
300C2×#117—111no—
301C2×C4⋊C8—111no—
302C2×C4⋊C8—111no—
303C2×C4⋊C8—111no—
304C2×C4⋊C8—111no—
305C2×C4⋊C8—111no—
306C2×C4⋊C8—111no—
307C2×C4⋊C8—111no—
308C2×C22⋊C8—111no—
309C2×C22⋊C8—111no—
310C2×C22⋊C8—111no—
311C2×C22⋊C8—111no—
312C2×C22⋊C8C2×D1111yescharacteristic
313C2×C22⋊C8C2×D1111yescharacteristic
314C2×C22⋊C8C2×D1111yescharacteristic
315C2×#97—111no—
316C2×C4×C8—111no—
317C2×C4×C8—111no—
318#400—111no—
319#399—111no—
320#398—111no—
321#397—111no—
322#397—111no—
323#397—111no—
324#394—111no—
325#394—111no—
326C4×C4⋊C4—111no—
327C4×C4⋊C4—111no—
328C4×C22⋊C4—111no—
329C4×C22⋊C4—111no—
330C4×C22⋊C4—111no—
331#336—111no—
332#336—111no—
333#336—111no—
334#336—111no—
335#336—111no—
336#336—111no—
337#336—111no—
338#336—111no—
339#336C2×D1111yescharacteristic
340#336C2×D1111yescharacteristic
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11—41no—
349C22×C11—41no—
350C22×C11—41no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11#51811yescharacteristic
356C22×C11#52011yescharacteristic
357C22×C11#52011yescharacteristic
358C22×C11C2×#13111yescharacteristic
359C22×C11C2×#13111yescharacteristic
360C22×C11C2×#13111yescharacteristic
361C22×C11#56811yescharacteristic
362C4×C11—22no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11#56011yescharacteristic
367C4×C11#56211yescharacteristic
368C4×C11#56211yescharacteristic
369C4×C11#56311yescharacteristic
370Dic11—22no—
371Dic11—41no—
372Dic11—41no—
373Dic11—41no—
374Dic11—41no—
375Dic11—41no—
376Dic11—41no—
377Dic11—41no—
378C22×D4C4×D1111yescharacteristic
379C23×C4C22×D1111yescharacteristic
380C23×C4C22×D1111yescharacteristic
381C22×C8—41no—
382C22×C8—41no—
383C22×C8—41no—
384C22×C8—111no—
385C22×C8—111no—
386C22×C8—111no—
387C22×C8—111no—
388C22×C8C22×D1111yescharacteristic
389C22×C8C22×D1111yescharacteristic
390C22×C8C22×D1111yescharacteristic
391C22×C8C22×D1111yescharacteristic
392C4×D4—41no—
393C4×D4—41no—
394#117—441no—
395#117—441no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4C4×D1111yescharacteristic
403C2×C22⋊C4—111no—
404C2×C22⋊C4—111no—
405C2×C22⋊C4—111no—
406C2×C22⋊C4—111no—
407C2×C22⋊C4—111no—
408C2×C22⋊C4—111no—
409C2×C22⋊C4—111no—
410C2×C22⋊C4—111no—
411C2×C22⋊C4C4×D1111yescharacteristic
412C2×C22⋊C4C4×D1111yescharacteristic
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—111no—
416C2×C42—111no—
417C2×C42C22×D1111yescharacteristic
418C4⋊C8—441no—
419C4⋊C8—441no—
420C4⋊C8—441no—
421C4⋊C8—441no—
422C4⋊C8—441no—
423C4⋊C8—441no—
424C4⋊C8—441no—
425C22⋊C8—41no—
426C22⋊C8—41no—
427C22⋊C8—41no—
428C22⋊C8—441no—
429C22⋊C8—441no—
430C22⋊C8—441no—
431C22⋊C8—441no—
432#97—441no—
433C4×C8—441no—
434C4×C8—441no—
435#95—111no—
436#95—111no—
437#95—111no—
438#95—111no—
439#95—111no—
440#95—111no—
441#95—111no—
442#95—111no—
443#95—111no—
444#95—111no—
445C2×C11—42no—
446C2×C11—81no—
447C2×C11#237611yescharacteristic
448C2×C11#297711yescharacteristic
449C2×C11#298111yescharacteristic
450C2×C11#299211yescharacteristic
451C2×C11#299311yescharacteristic
452C2×C11#299411yescharacteristic
453C2×C11#299411yescharacteristic
454C24C2×C4×D1111yescharacteristic
455C24C2×C4×D1111yescharacteristic
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—41no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—111no—
475C22×C4—111no—
476C22×C4—111no—
477C22×C4—111no—
478C22×C4—111no—
479C22×C4C2×C4×D1111yescharacteristic
480C22×C4C2×C4×D1111yescharacteristic
481C22×C4C2×C4×D1111yescharacteristic
482C22×C4C2×C4×D1111yescharacteristic
483C22×C4C23×D1111yescharacteristic
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—44no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8—221no—
500C2×C8—221no—
501C2×C8—221no—
502C2×C8—221no—
503C2×C8—221no—
504C2×C8—221no—
505C2×C8—221no—
506C2×C8—221no—
507C2×C8—221no—
508C2×C8—221no—
509C4⋊C4—41no—
510C4⋊C4—222no—
511C4⋊C4—222no—
512C4⋊C4—222no—
513C4⋊C4—441no—
514C4⋊C4—441no—
515C4⋊C4—441no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—222no—
521C22⋊C4—222no—
522C22⋊C4—441no—
523C22⋊C4—441no—
524C22⋊C4—441no—
525C22⋊C4—441no—
526C42—21no—
527C42—21no—
528C42—221no—
529C42—221no—
530C42—221no—
531C42—221no—
532C42—221no—
533C42—221no—
534C42—221no—
535C42—221no—
536C11#2331911yescharacteristic, complemented, Sylow
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23#6696012yes—
551C23C22×C4×D1111yescharacteristic
552D4—44no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—112no—
573C2×C4—221no—
574C2×C4—221no—
575C2×C4—221no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—221no—
587C2×C4—221no—
588C2×C4—221no—
589C2×C4—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4#6695412yes—
597C2×C4#6703711yescharacteristic
598C2×C4#6703711yescharacteristic
599C2×C4#6703711yescharacteristic
600C2×C4#6703711yescharacteristic
601C2×C4#6704311yescharacteristic
602C2×C4#6704311yescharacteristic
603C8—41no—
604C8—41no—
605C8—41no—
606C8—41no—
607C8—441no—
608C8—441no—
609C8—441no—
610C8—441no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22#1062301711yescharacteristic
626C22#1062307711yescharacteristic
627C22#1062307711yescharacteristic
628C22C2×#6695411yescharacteristic
629C22C2×#6696011yescharacteristic
630C22D11×#13111yescharacteristic
631C22#1062328111yescharacteristic
632C4—22no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—222no—
637C4—441no—
638C4—441no—
639C4—441no—
640C4—441no—
641C4—441no—
642C4—441no—
643C4—441no—
644C4#1062312611yescharacteristic
645C4#1062315211yescharacteristic
646C4#1062315211yescharacteristic
647C4#1062318211yescharacteristic
648C2—42no—
649C2—81no—
650C2#1307175911yescharacteristic
651C2#1307767011yescharacteristic
652C2#1307768911yescharacteristic
653C2#1307775611yescharacteristic
654C2#1307776611yescharacteristic
655C2#1307776911yescharacteristic
656C2#1307777111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1869C2
prime radicalC22×D4×C11C2×C4
cosocleC22×C4×C11C24
hypercenter#1869D11
hypocenterC11#23319
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
3. #13069338C2semidirect
4. #13069333C2semidirect
5. #13069232C2semidirect
6. #13069226C2semidirect
7. #13069225C2semidirect
8. #13069219C2semidirect
9. #13069171C2semidirect
10. #13069171C2semidirect
11. #13068794C2semidirect
12. #13068794C2semidirect
13. #13068598C2semidirect
14. #13068598C2semidirect
536. C11#23319semidirect

Maximal subgroups

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

subgroupindex
#130718752
#130694112
#130693382
#130693332
#130692322
#130692262
#130692252
#130692192
#130691712
#130687942
#130685982
C11×#18692
#2331911