Finite Group Databasebeta

← #14759261

Subgroups — #14759261

Order 2816.

710 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
1#13069231C211yesmaximal, characteristic
2#13069231C211yesmaximal, characteristic
3#13069224C211yesmaximal, characteristic
4#13069224C211yesmaximal, characteristic
5#13069182C211yesmaximal, characteristic, complemented
6#13069182C211yesmaximal, characteristic, complemented
7#13069175C211yesmaximal, characteristic, complemented
8#13069175C211yesmaximal, characteristic, complemented
9#13068473C211yesmaximal, characteristic, complemented
10#13068473C211yesmaximal, characteristic, complemented
11#13068378C211yesmaximal, characteristic
12C4×C22⋊(C11⋊C8)C211yesmaximal, characteristic
13#13068368C211yesmaximal, characteristic, complemented
14#13068303C211yesmaximal, characteristic, complemented
15C11×#2283C211yesmaximal, characteristic
16C22×C42×C11C2211yescharacteristic
17C11×#383C411yescharacteristic
18C11×#383C411yescharacteristic
19C11×#382C411yescharacteristic
20C11×#382C411yescharacteristic
21C11×#381C411yescharacteristic
22C11×#381C411yescharacteristic
23C11×#380C411yescharacteristic
24C11×#380C411yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C22⋊C4C2211yescharacteristic
28C4×C11×C22⋊C4C2211yescharacteristic
29C11×#376C2211yescharacteristic
30C11×#376C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×C22⋊(C11⋊C8)C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×#66867C2211yescharacteristic
40C2×#66867C2211yescharacteristic
41C2×#66867C2211yescharacteristic
42C2×#66867C2211yescharacteristic
43C2×C4×C11⋊C8C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45C2×C4×C11⋊C8C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622162C2211yescharacteristic
48#10622162C2211yescharacteristic
49#10622162C2211yescharacteristic
50#10622162C2211yescharacteristic
51#10622162C2211yescharacteristic
52#10622162C2211yescharacteristic
53#10622162C2211yescharacteristic
54#10622162C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C23×C4×C11C2×C411yescharacteristic
60C23×C4×C11C2×C411yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C2×C11×C4⋊C4C2×C411yescharacteristic
63C2×C11×C4⋊C4C2×C411yescharacteristic
64C2×C11×C4⋊C4C2×C411yescharacteristic
65C2×C11×C4⋊C4C2×C411yescharacteristic
66C2×C11×C22⋊C4C2×C411yescharacteristic
67C2×C11×C22⋊C4C2×C411yescharacteristic
68C2×C11×C22⋊C4C2×C411yescharacteristic
69C2×C11×C22⋊C4C2×C411yescharacteristic
70C2×C42×C11—22no—
71C2×C42×C11—22no—
72C2×C42×C11C2×C411yescharacteristic
73C2×C42×C11C2×C411yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C22×C11⋊C8C2311yescharacteristic
84C22×C11⋊C8C2311yescharacteristic
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C11×#95C2×C411yescharacteristic
89C11×#95C2×C411yescharacteristic
90C11×#95C2×C411yescharacteristic
91C11×#95C2×C411yescharacteristic
92C11×#95C2×C411yescharacteristic
93C11×#95C2×C411yescharacteristic
94C11×#95C2×C411yescharacteristic
95C11×#95C2×C411yescharacteristic
96C11×#95C2×C411yescharacteristic
97C11×#95C2×C411yescharacteristic
98C11×#95C2×C411yescharacteristic
99C11×#95C2×C411yescharacteristic
100C11×#95C2×C411yescharacteristic
101C11×#95C2×C411yescharacteristic
102C11×#95C2×C411yescharacteristic
103C11×#95C2×C411yescharacteristic
104C22⋊(C11⋊C8)—22no—
105C22⋊(C11⋊C8)—22no—
106C22⋊(C11⋊C8)—22no—
107C22⋊(C11⋊C8)—22no—
108C4⋊(C11⋊C8)—22no—
109C4⋊(C11⋊C8)—22no—
110C4⋊(C11⋊C8)—22no—
111C4⋊(C11⋊C8)—22no—
112#66867—22no—
113#66867—22no—
114#66867—22no—
115#66867—22no—
116C4×C11⋊C8—22no—
117C4×C11⋊C8—22no—
118C4×C11⋊C8—22no—
119C4×C11⋊C8—22no—
120#21437—111nomaximal, Sylow
121C24×C11C22×C411yescharacteristic
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—41no—
133C22×C4×C11—41no—
134C22×C4×C11C22×C411yescharacteristic
135C22×C4×C11C22×C411yescharacteristic
136C22×C4×C11C22×C411yescharacteristic
137C22×C4×C11C22×C411yescharacteristic
138C22×C4×C11C22×C411yescharacteristic
139C22×C4×C11C22×C411yescharacteristic
140C22×C4×C11C22×C411yescharacteristic
141C22×C4×C11C22×C411yescharacteristic
142C22×C4×C11C22×C411yescharacteristic
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C22×C411yescharacteristic
146C22×C4×C11C22×C411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C11×C4⋊C4—22no—
149C11×C4⋊C4—22no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4—41no—
152C11×C22⋊C4—22no—
153C11×C22⋊C4—22no—
154C11×C22⋊C4—41no—
155C11×C22⋊C4—41no—
156C42×C11—22no—
157C42×C11—22no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11#4112yes—
169C42×C11#4112yes—
170C2×C11⋊C8—21no—
171C2×C11⋊C8—21no—
172C2×C11⋊C8—21no—
173C2×C11⋊C8—21no—
174C2×C11⋊C8—21no—
175C2×C11⋊C8—21no—
176C2×C11⋊C8—21no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
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#4112yes—
191C2×C11⋊C8#4112yes—
192C2×C11⋊C8#4112yes—
193C2×C11⋊C8#4112yes—
194#2283D1111yescharacteristic
195#1924—111no—
196#1924—111no—
197#1923—111no—
198#1923—111no—
199#1917—111no—
200#1917—111no—
201#1916—111no—
202#1916—111no—
203#1768—111no—
204#1768—111no—
205#1749—111no—
206C4×C22⋊C8—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#13112yes—
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—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
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×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—44no—
254C2×C4×C11—44no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11#11712yes—
260C2×C4×C11#11712yes—
261C2×C4×C11#13112yes—
262C2×C4×C11C2×#4111yescharacteristic
263C2×C4×C11C2×#4111yescharacteristic
264C2×C4×C11C2×#4111yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C11⋊C8—22no—
269C11⋊C8—22no—
270C11⋊C8—22no—
271C11⋊C8—22no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C22×C42C2×D1111yescharacteristic
277C2×C4⋊C8—111no—
278C2×C4⋊C8—111no—
279C2×C4⋊C8—111no—
280C2×C4⋊C8—111no—
281C2×C22⋊C8—111no—
282C2×C22⋊C8—111no—
283C2×C22⋊C8—111no—
284C2×C22⋊C8—111no—
285C2×#97—111no—
286C2×#97—111no—
287C2×#97—111no—
288C2×#97—111no—
289C2×C4×C8—111no—
290C2×C4×C8—111no—
291C2×C4×C8—111no—
292C2×C4×C8—111no—
293#383Dic1111yescharacteristic
294#383Dic1111yescharacteristic
295#382Dic1111yescharacteristic
296#382Dic1111yescharacteristic
297#381Dic1111yescharacteristic
298#381Dic1111yescharacteristic
299#380Dic1111yescharacteristic
300#380Dic1111yescharacteristic
301C4×C4⋊C4C2×D1111yescharacteristic
302C4×C4⋊C4C2×D1111yescharacteristic
303C4×C22⋊C4C2×D1111yescharacteristic
304C4×C22⋊C4C2×D1111yescharacteristic
305#376C2×D1111yescharacteristic
306#376C2×D1111yescharacteristic
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#336—111no—
318#336—111no—
319C22×C11—22no—
320C22×C11—22no—
321C22×C11—22no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11C2×#11711yescharacteristic
327C22×C11C4×#4111yescharacteristic
328C22×C11C4×#4111yescharacteristic
329C22×C11C2×#13111yescharacteristic
330C22×C11C2×#13111yescharacteristic
331C22×C11#56811yescharacteristic
332C22×C11#56811yescharacteristic
333C4×C11—22no—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—41no—
344C4×C11—41no—
345C4×C11—41no—
346C4×C11#52911yescharacteristic
347C4×C11#52911yescharacteristic
348C4×C11#52911yescharacteristic
349C4×C11#52911yescharacteristic
350C23×C4C2×Dic1111yescharacteristic
351C23×C4C2×Dic1111yescharacteristic
352C23×C4C22×D1111yescharacteristic
353C22×C8—111no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8—111no—
360C22×C8—111no—
361C2×C4⋊C4C2×Dic1111yescharacteristic
362C2×C4⋊C4C2×Dic1111yescharacteristic
363C2×C4⋊C4C2×Dic1111yescharacteristic
364C2×C4⋊C4C2×Dic1111yescharacteristic
365C2×C22⋊C4C2×Dic1111yescharacteristic
366C2×C22⋊C4C2×Dic1111yescharacteristic
367C2×C22⋊C4C2×Dic1111yescharacteristic
368C2×C22⋊C4C2×Dic1111yescharacteristic
369C2×C42—22no—
370C2×C42—22no—
371C2×C42C2×Dic1111yescharacteristic
372C2×C42C2×Dic1111yescharacteristic
373C2×C42C22×D1111yescharacteristic
374C2×C42C22×D1111yescharacteristic
375C2×C42C22×D1111yescharacteristic
376C2×C42C22×D1111yescharacteristic
377C2×C42C22×D1111yescharacteristic
378C2×C42C22×D1111yescharacteristic
379C4⋊C8—222no—
380C4⋊C8—222no—
381C4⋊C8—222no—
382C4⋊C8—222no—
383C22⋊C8—222no—
384C22⋊C8—222no—
385C22⋊C8—222no—
386C22⋊C8—222no—
387#97—222no—
388#97—222no—
389#97—222no—
390#97—222no—
391C4×C8—222no—
392C4×C8—222no—
393C4×C8—222no—
394C4×C8—222no—
395#95C2×Dic1111yescharacteristic
396#95C2×Dic1111yescharacteristic
397#95C2×Dic1111yescharacteristic
398#95C2×Dic1111yescharacteristic
399#95C2×Dic1111yescharacteristic
400#95C2×Dic1111yescharacteristic
401#95C2×Dic1111yescharacteristic
402#95C2×Dic1111yescharacteristic
403#95C2×Dic1111yescharacteristic
404#95C2×Dic1111yescharacteristic
405#95C2×Dic1111yescharacteristic
406#95C2×Dic1111yescharacteristic
407#95C2×Dic1111yescharacteristic
408#95C2×Dic1111yescharacteristic
409#95C2×Dic1111yescharacteristic
410#95C2×Dic1111yescharacteristic
411C2×C11—42no—
412C2×C11#229811yescharacteristic
413C2×C11#292411yescharacteristic
414C2×C11#292411yescharacteristic
415C2×C11#296611yescharacteristic
416C2×C11#296711yescharacteristic
417C2×C11#296811yescharacteristic
418C2×C11#296911yescharacteristic
419C24C22×Dic1111yescharacteristic
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4C22×Dic1111yescharacteristic
433C22×C4C22×Dic1111yescharacteristic
434C22×C4C22×Dic1111yescharacteristic
435C22×C4C22×Dic1111yescharacteristic
436C22×C4C22×Dic1111yescharacteristic
437C22×C4C22×Dic1111yescharacteristic
438C22×C4C22×Dic1111yescharacteristic
439C22×C4C22×Dic1111yescharacteristic
440C22×C4C22×Dic1111yescharacteristic
441C22×C4C22×Dic1111yescharacteristic
442C22×C4C22×Dic1111yescharacteristic
443C22×C4C22×Dic1111yescharacteristic
444C22×C4C22×Dic1111yescharacteristic
445C22×C4C23×D1111yescharacteristic
446C2×C8—112no—
447C2×C8—112no—
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—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C42—22no—
479C42—22no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42#433912yes—
491C42#433912yes—
492C11#2143711yescharacteristic, complemented, Sylow
493C23—21no—
494C23—21no—
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23#6700112yes—
500C23C23×Dic1111yescharacteristic
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—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—44no—
538C2×C4—44no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4#6697912yes—
544C2×C4#6697912yes—
545C2×C4#6700112yes—
546C2×C4C2×#433911yescharacteristic
547C2×C4C2×#433911yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C2×C4#41×D1111yescharacteristic
550C2×C4#41×D1111yescharacteristic
551C2×C4#41×D1111yescharacteristic
552C8—222no—
553C8—222no—
554C8—222no—
555C8—222no—
556C8—441no—
557C8—441no—
558C8—441no—
559C8—441no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22C2×#6697911yescharacteristic
568C22C2×#6700111yescharacteristic
569C22C2×#6700111yescharacteristic
570C22#1062335011yescharacteristic
571C22#1062335011yescharacteristic
572C22#41×Dic1111yescharacteristic
573C22#41×Dic1111yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4#1062305911yescharacteristic
588C4#1062305911yescharacteristic
589C4#1062305911yescharacteristic
590C4#1062305911yescharacteristic
591C2—42no—
592C2#1307111411yescharacteristic
593C2#1307727411yescharacteristic
594C2#1307727411yescharacteristic
595C2#1307759211yescharacteristic
596C2#1307760311yescharacteristic
597C2#1307761211yescharacteristic
598C2#1307762111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC11×#2283C2
prime radicalC24×C11C22×C4
cosocleC22×C4×C11C24
hypercenter#2283D11
hypocenterC11#21437
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2283

Complements

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

NH ≅ G/Ntype
5. #13069182C2semidirect
6. #13069182C2semidirect
7. #13069175C2semidirect
8. #13069175C2semidirect
9. #13068473C2semidirect
10. #13068473C2semidirect
13. #13068368C2semidirect
14. #13068303C2semidirect
492. C11#21437semidirect

Maximal subgroups

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

subgroupindex
#130692312
#130692242
#130691822
#130691752
#130684732
#130683782
C4×C22⋊(C11⋊C8)2
#130683682
#130683032
C11×#22832
#2143711