Finite Group Databasebeta

← #14779947

Subgroups — #14779947

Order 2816.

680 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#13071877C211yesmaximal, characteristic
2#13069412C211yesmaximal, characteristic
3#13069337C211yesmaximal, characteristic, complemented
4#13069331C211yesmaximal, characteristic, complemented
5#13069231C211yesmaximal, characteristic, complemented
6#13069227C211yesmaximal, characteristic, complemented
7#13069221C211yesmaximal, characteristic, complemented
8#13069219C211yesmaximal, characteristic, complemented
9#13069183C211yesmaximal, characteristic, complemented
10#13069181C211yesmaximal, characteristic, complemented
11#13068913C211yesmaximal, characteristic
12#13068799C211yesmaximal, characteristic, complemented
13#13068599C211yesmaximal, characteristic, complemented
14#13068597C211yesmaximal, characteristic, complemented
15C11×#1851C211yesmaximal, characteristic, complemented
16C22×C11×M16C2211yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C2×#66925C2211yescharacteristic
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C11×C22⋊C8C2211yescharacteristic
22C4×C11×C22⋊C4C2211yescharacteristic
23C4×C22⋊Dic11C2211yescharacteristic
24C2×C22⋊(C11⋊C8)C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×(C2×D11)⋊C8C2211yescharacteristic
28C2×(C2×D11)⋊C8C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×#66879C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32C2×Dic11⋊C8C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×C8×Dic11C2211yescharacteristic
36#10622574C411yescharacteristic
37#10622572C411yescharacteristic
38#10622565C411yescharacteristic
39#10622562C411yescharacteristic
40C4×(C2×D11)⋊C4C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42C4×Dic11⋊C4C2211yescharacteristic
43C2×C4⋊(C11⋊C8)C2211yescharacteristic
44C2×#66867C2211yescharacteristic
45#10622288C411yescharacteristic
46#10622287C411yescharacteristic
47#10622271C411yescharacteristic
48#10622270C411yescharacteristic
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622188C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11C2×C411yescharacteristic
61C22×C4×D11C2311yescharacteristic
62C2×C11×M16—41no—
63C2×C11×M16—41no—
64C2×C11×M16—41no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C22⋊C4C2×C411yescharacteristic
70C2×C11×C22⋊C4C2×C411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C22⋊Dic11C2×C411yescharacteristic
74C2×C22⋊Dic11C2×C411yescharacteristic
75C2×C22⋊Dic11C2×C411yescharacteristic
76C4×C22⋊D11—41no—
77C4×C22⋊D11—41no—
78C2×(C2×D11)⋊C4C2×C411yescharacteristic
79C2×(C2×D11)⋊C4C2×C411yescharacteristic
80C2×(C2×D11)⋊C4C2×C411yescharacteristic
81C2×(C2×D11)⋊C4C2×C411yescharacteristic
82C2×(C2×D11)⋊C4C2×C411yescharacteristic
83C2×C4⋊Dic11C2×C411yescharacteristic
84C2×C4⋊Dic11C2×C411yescharacteristic
85C2×Dic11⋊C4C2×C411yescharacteristic
86C2×Dic11⋊C4C2×C411yescharacteristic
87C2×Dic11⋊C4C2×C411yescharacteristic
88C2×Dic11⋊C4C2×C411yescharacteristic
89C2×Dic11⋊C4C2×C411yescharacteristic
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66925—41no—
98#66925—41no—
99C11×C4⋊C8—41no—
100C11×C4⋊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—
114(C2×D11)⋊C8—41no—
115(C2×D11)⋊C8—41no—
116(C2×D11)⋊C8—41no—
117(C2×D11)⋊C8—41no—
118#66879—41no—
119Dic11⋊C8—41no—
120Dic11⋊C8—41no—
121Dic11⋊C8—41no—
122Dic11⋊C8—41no—
123C8×Dic11—41no—
124C4⋊(C11⋊C8)—41no—
125#66867—41no—
126#23321—111nomaximal, Sylow
127C24×C11C22×C411yescharacteristic
128C23×D11C22×C411yescharacteristic
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C2411yescharacteristic
141C2×C22⋊D11—41no—
142C2×C22⋊D11—41no—
143C2×C22⋊D11—41no—
144C22×Dic11C22×C411yescharacteristic
145C22×Dic11C22×C411yescharacteristic
146C22×Dic11C22×C411yescharacteristic
147C22×Dic11C22×C411yescharacteristic
148C22×Dic11C22×C411yescharacteristic
149C22×Dic11C22×C411yescharacteristic
150C22×Dic11C22×C411yescharacteristic
151C2×C4×D11—21no—
152C2×C4×D11—21no—
153C2×C4×D11—21no—
154C2×C4×D11—21no—
155C2×C4×D11—21no—
156C2×C4×D11—21no—
157C11×M16—44no—
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—21no—
170C11×C22⋊C4—41no—
171C11×C22⋊C4—41no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C22⋊Dic11—22no—
177C22⋊Dic11—41no—
178C22⋊Dic11—41no—
179(C2×D11)⋊C4—22no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4—41no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4—41no—
184C4⋊Dic11—41no—
185C4⋊Dic11—41no—
186Dic11⋊C4—22no—
187Dic11⋊C4—41no—
188Dic11⋊C4—41no—
189Dic11⋊C4—41no—
190Dic11⋊C4—41no—
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#1955—111no—
211#1940—111no—
212#1939—111no—
213#1924—111no—
214#1924—111no—
215#1923—111no—
216#1923—111no—
217#1917—111no—
218#1917—111no—
219#1870—111no—
220#1851—111no—
221#1851D1111yescharacteristic, complemented
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×C11C23×C411yescharacteristic
232C22×D11—21no—
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—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×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C11H(5,𝔽2)11yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C112−1+411yescharacteristic
263C2×C4×C112−1+411yescharacteristic
264C22⋊D11—44no—
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—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#13112yes—
286C4×D11—41no—
287C4×D11—41no—
288C4×D11—41no—
289C4×D11—41no—
290C8×C11—41no—
291C8×C11—41no—
292C8×C11—41no—
293C8×C11—41no—
294C11⋊C8—41no—
295C11⋊C8—41no—
296C11⋊C8—41no—
297C11⋊C8—41no—
298C22×M16C2×D1111yescharacteristic
299C2×C4×D4—111no—
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⋊C8C2×D1111yescharacteristic
307C2×C4⋊C8C2×D1111yescharacteristic
308C2×C22⋊C8—111no—
309C2×C22⋊C8—111no—
310C2×C22⋊C8—111no—
311C2×C22⋊C8—111no—
312C2×C22⋊C8—111no—
313C2×C22⋊C8—111no—
314C2×C22⋊C8C2×D1111yescharacteristic
315C2×#97—111no—
316C2×#97—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⋊C4C2×D1111yescharacteristic
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—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—41no—
346C22×C11—41no—
347C22×C11—41no—
348C22×C11#51811yescharacteristic
349C22×C11#52011yescharacteristic
350C22×C11#52011yescharacteristic
351C22×C11C2×#13111yescharacteristic
352C22×C11#56811yescharacteristic
353C22×C11#56811yescharacteristic
354C22×C11#56811yescharacteristic
355C2×D11—41no—
356C2×D11—41no—
357C2×D11—41no—
358C2×D11—41no—
359C2×D11—41no—
360C2×D11—41no—
361C2×D11—41no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—41no—
367C4×C11#56011yescharacteristic
368C4×C11#56211yescharacteristic
369C4×C11#56211yescharacteristic
370C4×C11#56311yescharacteristic
371Dic11—22no—
372Dic11—41no—
373Dic11—41no—
374Dic11—41no—
375Dic11—41no—
376Dic11—41no—
377Dic11—41no—
378C22×D4—111no—
379C23×C4—111no—
380C23×C4C22×D1111yescharacteristic
381C2×M16—41no—
382C2×M16—41no—
383C2×M16—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—441no—
393C4×D4—441no—
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⋊C4—111no—
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×C42C22×D1111yescharacteristic
417C2×C42C22×D1111yescharacteristic
418C4⋊C8—41no—
419C4⋊C8—41no—
420C4⋊C8—441no—
421C4⋊C8—441no—
422C4⋊C8—441no—
423C4⋊C8—441no—
424C4⋊C8—441no—
425C22⋊C8—41no—
426C22⋊C8—441no—
427C22⋊C8—441no—
428C22⋊C8—441no—
429C22⋊C8—441no—
430C22⋊C8—441no—
431C22⋊C8—441no—
432#97—441no—
433#97—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#95C4×D1111yescharacteristic
444#95C4×D1111yescharacteristic
445C2×C11—81no—
446C2×C11#237611yescharacteristic
447C2×C11#297811yescharacteristic
448C2×C11#298111yescharacteristic
449C2×C11#299211yescharacteristic
450C2×C11#299311yescharacteristic
451C2×C11#299511yescharacteristic
452C2×C11#299511yescharacteristic
453D11—81no—
454C24—111no—
455C24C2×C4×D1111yescharacteristic
456C2×D4—441no—
457C2×D4—441no—
458C2×D4—441no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—111no—
466C22×C4—111no—
467C22×C4—111no—
468C22×C4—111no—
469C22×C4—111no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4C2×C4×D1111yescharacteristic
479C22×C4C2×C4×D1111yescharacteristic
480C22×C4C2×C4×D1111yescharacteristic
481C22×C4C2×C4×D1111yescharacteristic
482C22×C4C2×C4×D1111yescharacteristic
483C22×C4C23×D1111yescharacteristic
484M16—44no—
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—21no—
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—222no—
510C4⋊C4—441no—
511C4⋊C4—441no—
512C4⋊C4—441no—
513C4⋊C4—441no—
514C4⋊C4—441no—
515C4⋊C4—441no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—222no—
519C22⋊C4—222no—
520C22⋊C4—441no—
521C22⋊C4—441no—
522C22⋊C4—441no—
523C22⋊C4—441no—
524C22⋊C4—441no—
525C22⋊C4—441no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—221no—
531C42—221no—
532C42—221no—
533C42—221no—
534C42—221no—
535C42—221no—
536C11#2332111yescharacteristic, complemented, Sylow
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—221no—
545C23—221no—
546C23—221no—
547C23—221no—
548C23—221no—
549C23—221no—
550C23—221no—
551C23C22×C4×D1111yescharacteristic
552D4—444no—
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—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
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—441no—
594C2×C4—441no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4#6703711yescharacteristic
598C2×C4#6703711yescharacteristic
599C2×C4#6703711yescharacteristic
600C2×C4#6704011yescharacteristic
601C2×C4#6704211yescharacteristic
602C2×C4#6704311yescharacteristic
603C8—41no—
604C8—41no—
605C8—41no—
606C8—41no—
607C8—441no—
608C8—441no—
609C8—441no—
610C8—441no—
611C22—41no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—441no—
619C22—441no—
620C22—441no—
621C22—441no—
622C22—441no—
623C22—441no—
624C22—441no—
625C22#1062303511yescharacteristic
626C22#1062307611yescharacteristic
627C22#1062307711yescharacteristic
628C22#1062327611yescharacteristic
629C22#1062327611yescharacteristic
630C22D11×#13111yescharacteristic
631C22#1062328111yescharacteristic
632C4—41no—
633C4—41no—
634C4—41no—
635C4—41no—
636C4—41no—
637C4—222no—
638C4—441no—
639C4—441no—
640C4—441no—
641C4—441no—
642C4—441no—
643C4—441no—
644C4#1062312611yescharacteristic
645C4#1062317711yescharacteristic
646C4#1062317811yescharacteristic
647C4#1062319811yescharacteristic
648C2—81no—
649C2—881no—
650C2#1307176511yescharacteristic
651C2#1307767311yescharacteristic
652C2#1307768811yescharacteristic
653C2#1307775311yescharacteristic
654C2#1307775811yescharacteristic
655C2#1307778011yescharacteristic
656C2#1307778311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#1851C2
prime radicalC22×C22⋊D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1851D11
hypocenterC11#23321
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
3. #13069337C2semidirect
4. #13069331C2semidirect
5. #13069231C2semidirect
6. #13069227C2semidirect
7. #13069221C2semidirect
8. #13069219C2semidirect
9. #13069183C2semidirect
10. #13069181C2semidirect
12. #13068799C2semidirect
13. #13068599C2semidirect
14. #13068597C2semidirect
15. C11×#1851C2semidirect
221. #1851D11semidirect
536. C11#23321semidirect

Maximal subgroups

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

subgroupindex
#130718772
#130694122
#130693372
#130693312
#130692312
#130692272
#130692212
#130692192
#130691832
#130691812
#130689132
#130687992
#130685992
#130685972
C11×#18512
#2332111