Finite Group Databasebeta

← #14676125

Subgroups — #14676125

Order 2816.

1426 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622541C211yesmaximal, characteristic
2C2×#10622586C211yesmaximal, characteristic
3C2×#10622263C212yesmaximal
4C2×C4⋊C4×Dic11C211yesmaximal, characteristic
5#13066874C212yesmaximal
6#13066871C212yesmaximal
7#13066845C211yesmaximal, characteristic
8#13066845C211yesmaximal, characteristic
9#13066841C212yesmaximal
10C4×C11⋊#95C211yesmaximal, characteristic
11C11×C4⋊#95C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×Dic11⋊C4C2212yes—
18C22×Dic11⋊C4C2212yes—
19C22×C4×Dic11C2211yescharacteristic
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2212yes—
22C2×C11×#95C2212yes—
23C2×C11×#95C2212yes—
24C2×C11⋊#95C2211yescharacteristic
25C2×C11⋊#95C2211yescharacteristic
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C4⋊C4×Dic11C418yescomplemented
36#10622586—24no—
37#10622541—24no—
38#10622263—28no—
39C23×C4×C11C2312yes—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×Dic11C2312yes—
45C23×Dic11C2311yescharacteristic
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4C2×C414yes—
56C2×C42×C11—22no—
57C2×C42×C11—22no—
58C2×C42×C11—22no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11C2×C414yes—
63C2×C4⋊Dic11D414yes—
64C2×C4⋊Dic11Q814yes—
65C2×Dic11⋊C4—24no—
66C2×Dic11⋊C4—24no—
67C2×Dic11⋊C4—24no—
68C2×Dic11⋊C4—24no—
69C2×Dic11⋊C4—42no—
70C2×Dic11⋊C4—42no—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—22no—
76C2×C4×Dic11—22no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11C2×C418yes—
79C2×C4×Dic11C2×C414yes—
80C11×#95—24no—
81C11×#95—24no—
82C11⋊#95—22no—
83C11⋊#95—24no—
84C11⋊#95—24no—
85C11⋊#95—24no—
86C11⋊#95—24no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89C11⋊#95—24no—
90C11⋊#95—42no—
91C11⋊#95C2×C418yes—
92C11⋊#95D414yes—
93#13918—111nomaximal, Sylow
94C24×C11C2411yescharacteristic
95C22×C4×C11—21no—
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—22no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11C22×C414yes—
121C22×C4×C11C22×C412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×Q812yes—
125C22×C4×C11#4112yes—
126C22×C4×C11#4112yes—
127C22×C4×C11#4112yes—
128C22×C4×C11#4112yes—
129C22×C4×C11#4112yes—
130C22×Dic11—22no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—22no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C22×Dic11—22no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—22no—
163C22×Dic11C22×C412yes—
164C22×Dic11C22×C414yes—
165C22×Dic11C22×C412yes—
166C22×Dic11C2×D412yes—
167C22×Dic11C2×D414yes—
168C22×Dic11C2×D412yes—
169C22×Dic11C2×Q814yes—
170C22×Dic11#4112yes—
171C22×Dic11#4112yes—
172C11×C4⋊C4—28no—
173C11×C4⋊C4—44no—
174C42×C11—44no—
175C4⋊Dic11—44no—
176C4⋊Dic11C4⋊C4116yes—
177Dic11⋊C4—48no—
178Dic11⋊C4—48no—
179C4×Dic11—216no—
180C4×Dic11—28no—
181C4×Dic11—44no—
182C2×#389—111no—
183C2×#389—111no—
184C2×#382—112no—
185C2×C4×C4⋊C4—111no—
186#1442—112no—
187#1442—112no—
188C4⋊#95—111no—
189C4⋊#95—111no—
190C4⋊#95D1111yescharacteristic
191#1434—112no—
192C4×#95—111no—
193C23×C11C23×C411yescharacteristic
194C23×C11C22×D411yescharacteristic
195C23×C11C22×D411yescharacteristic
196C23×C11C22×Q811yescharacteristic
197C23×C11C2×#4111yescharacteristic
198C23×C11C2×#4111yescharacteristic
199C23×C11C2×#4111yescharacteristic
200C23×C11C2×#4111yescharacteristic
201C23×C11C2×#4111yescharacteristic
202C23×C11C2×#4111yescharacteristic
203C23×C11C2×#4111yescharacteristic
204C23×C11H(5,𝔽2)11yescharacteristic
205C23×C112−1+411yescharacteristic
206C23×C112−1+411yescharacteristic
207C23×C112−1+411yescharacteristic
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—22no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—41no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—41no—
224C2×C4×C11—41no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—42no—
236C2×C4×C11C2×C4⋊C414yes—
237C2×C4×C11#11714yes—
238C2×C4×C11#11714yes—
239C2×C4×C11#12414yes—
240C2×C4×C11#12414yes—
241C2×C4×C11#12514yes—
242C2×C4×C11#12514yes—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—22no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—24no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11—42no—
283C2×Dic11C2×C4⋊C418yes—
284C2×Dic11C4×D414yes—
285C22×C4⋊C4—111no—
286C22×C4⋊C4—111no—
287C22×C4⋊C4—112no—
288C22×C4⋊C4—112no—
289C22×C4⋊C4C2×D1111yescharacteristic
290C22×C4⋊C4C2×D1111yescharacteristic
291C22×C42—111no—
292C22×C42—112no—
293C22×C42—111no—
294C22×C42C2×D1111yescharacteristic
295#389—224no—
296#389—224no—
297#382—228no—
298C4×C4⋊C4—118no—
299C2×#95—111no—
300C2×#95—112no—
301C2×#95—111no—
302C2×#95—111no—
303C2×#95—111no—
304C2×#95—112no—
305C2×#95—112no—
306C2×#95—112no—
307C2×#95—112no—
308C2×#95—112no—
309C2×#95—112no—
310C2×#95C2×D1112yes—
311C2×#95C2×D1112yes—
312C22×C11C22×C4⋊C411yescharacteristic
313C22×C11C2×#11711yescharacteristic
314C22×C11C2×#11711yescharacteristic
315C22×C11C2×C4×D411yescharacteristic
316C22×C11C4×#4111yescharacteristic
317C22×C11#51911yescharacteristic
318C22×C11#52011yescharacteristic
319C22×C11C2×#12411yescharacteristic
320C22×C11C2×#12411yescharacteristic
321C22×C11C2×#12511yescharacteristic
322C22×C11C2×#12511yescharacteristic
323C22×C11#52911yescharacteristic
324C22×C11#52911yescharacteristic
325C22×C11#53211yescharacteristic
326C22×C11#53211yescharacteristic
327C22×C11#54111yescharacteristic
328C22×C11#54111yescharacteristic
329C22×C11#54211yescharacteristic
330C22×C11#54211yescharacteristic
331C22×C11D4211yescharacteristic
332C22×C11#54711yescharacteristic
333C22×C11#54711yescharacteristic
334C22×C11#54711yescharacteristic
335C22×C11#54811yescharacteristic
336C22×C11#54811yescharacteristic
337C22×C11D4×Q811yescharacteristic
338C22×C11#55211yescharacteristic
339C22×C11#55211yescharacteristic
340C22×C11#55211yescharacteristic
341C22×C11#55211yescharacteristic
342C22×C11#55411yescharacteristic
343C22×C11#55511yescharacteristic
344C22×C11#55511yescharacteristic
345C22×C11#55711yescharacteristic
346C22×C11#55711yescharacteristic
347C4×C11—42no—
348C4×C11—42no—
349C4×C11—44no—
350C4×C11—82no—
351C4×C11#38218yescomplemented
352Dic11—24no—
353Dic11—28no—
354Dic11—42no—
355Dic11—42no—
356Dic11—42no—
357Dic11—82no—
358C23×C4—112no—
359C23×C4—111no—
360C23×C4—111no—
361C23×C4—111no—
362C23×C4—111no—
363C23×C4—112no—
364C23×C4C22×D1112yes—
365C23×C4C22×D1112yes—
366C23×C4C22×D1111yescharacteristic
367C23×C4C22×D1111yescharacteristic
368C23×C4C22×D1111yescharacteristic
369C2×C4⋊C4—22no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—22no—
374C2×C4⋊C4—114no—
375C2×C4⋊C4—114no—
376C2×C4⋊C4—114no—
377C2×C4⋊C4—224no—
378C2×C4⋊C4—224no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—224no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—222no—
384C2×C4⋊C4—442no—
385C2×C4⋊C4—442no—
386C2×C4⋊C4C4×D1114yes—
387C2×C42—22no—
388C2×C42—22no—
389C2×C42—22no—
390C2×C42—118no—
391C2×C42—114no—
392C2×C42—224no—
393C2×C42—224no—
394C2×C42—222no—
395C2×C42—222no—
396C2×C42—222no—
397C2×C42—222no—
398C2×C42—222no—
399#95—24no—
400#95—24no—
401#95—118no—
402#95—114no—
403#95—222no—
404#95—222no—
405#95—224no—
406#95—224no—
407#95—224no—
408#95—224no—
409#95—224no—
410#95—222no—
411#95—442no—
412C2×C11C2×#38211yescharacteristic
413C2×C11#229311yescharacteristic
414C2×C11#232011yescharacteristic
415C2×C11#234411yescharacteristic
416C2×C11#234611yescharacteristic
417C2×C11D4×C4⋊C411yescharacteristic
418C2×C11#235111yescharacteristic
419C2×C11#248911yescharacteristic
420C2×C11#248911yescharacteristic
421C2×C11#249111yescharacteristic
422C2×C11#249111yescharacteristic
423C2×C11#250611yescharacteristic
424C2×C11#250611yescharacteristic
425C2×C11#250811yescharacteristic
426C2×C11#250811yescharacteristic
427C24C23×D1111yescharacteristic
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—114no—
454C22×C4—112no—
455C22×C4—112no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—112no—
459C22×C4—112no—
460C22×C4—112no—
461C22×C4—112no—
462C22×C4—221no—
463C22×C4—221no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—221no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—221no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—221no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4C2×C4×D1114yes—
496C22×C4C2×C4×D1112yes—
497C22×C4#433912yes—
498C22×C4#433912yes—
499C22×C4D4×D1112yes—
500C22×C4D4×D1112yes—
501C22×C4#434112yes—
502C22×C4#434112yes—
503C22×C4#434112yes—
504C22×C4Q8×D1112yes—
505C4⋊C4—28no—
506C4⋊C4—44no—
507C4⋊C4—1116no—
508C4⋊C4—448no—
509C4⋊C4—448no—
510C4⋊C4—444no—
511C42—44no—
512C42—2216no—
513C42—228no—
514C42—444no—
515C11#1391811yescharacteristic, complemented, Sylow
516C23C22×C4×D1111yescharacteristic
517C23C2×#433911yescharacteristic
518C23C2×#433911yescharacteristic
519C23C2×D4×D1111yescharacteristic
520C23C2×D4×D1111yescharacteristic
521C23C2×#434111yescharacteristic
522C23C2×#434111yescharacteristic
523C23C2×#434111yescharacteristic
524C23C2×Q8×D1111yescharacteristic
525C23#6704011yescharacteristic
526C23#6704011yescharacteristic
527C23#41×D1111yescharacteristic
528C23#41×D1111yescharacteristic
529C23#6704211yescharacteristic
530C23#6704311yescharacteristic
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—42no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—118no—
560C2×C4—114no—
561C2×C4—224no—
562C2×C4—222no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—224no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—224no—
569C2×C4—222no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—222no—
574C2×C4—222no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—441no—
593C2×C4—441no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—442no—
599C2×C4—442no—
600C2×C4—442no—
601C2×C4#6692514yes—
602C2×C4#6693014yes—
603C2×C4#6693814yes—
604C2×C4#6693814yes—
605C2×C4#6694214yes—
606C2×C4#6694214yes—
607C2×C4C4⋊C4×D1114yes—
608C22C2×#6692511yescharacteristic
609C22C2×#6693011yescharacteristic
610C22C2×#6693811yescharacteristic
611C22C2×#6693811yescharacteristic
612C22C2×#6694211yescharacteristic
613C22C2×#6694211yescharacteristic
614C22C2×C4⋊C4×D1111yescharacteristic
615C22#1062303811yescharacteristic
616C22#1062304411yescharacteristic
617C22#1062306011yescharacteristic
618C22#1062306311yescharacteristic
619C22C4×#434111yescharacteristic
620C22C4×D4×D1111yescharacteristic
621C22#1062308211yescharacteristic
622C22#1062309411yescharacteristic
623C22#1062310311yescharacteristic
624C22#1062310511yescharacteristic
625C22#1062311211yescharacteristic
626C22#1062311211yescharacteristic
627C22#1062312711yescharacteristic
628C22#1062312911yescharacteristic
629C22#1062313111yescharacteristic
630C22#1062314011yescharacteristic
631C22#1062315611yescharacteristic
632C22#1062316211yescharacteristic
633C22#1062316411yescharacteristic
634C22#1062317411yescharacteristic
635C22#1062321111yescharacteristic
636C22#1062321311yescharacteristic
637C22#1062321611yescharacteristic
638C22#1062322111yescharacteristic
639C22#1062324711yescharacteristic
640C22#1062325211yescharacteristic
641C22#1062325811yescharacteristic
642C22#1062326211yescharacteristic
643C4—42no—
644C4—42no—
645C4—44no—
646C4—82no—
647C4—224no—
648C4—228no—
649C4—442no—
650C4—442no—
651C4—442no—
652C4—882no—
653C4#1062226318yescomplemented
654C2C2×#1062226311yescharacteristic
655C2#1307107811yescharacteristic
656C2#1307126111yescharacteristic
657C2#1307148111yescharacteristic
658C2#1307149711yescharacteristic
659C2#1307151711yescharacteristic
660C2#1307153511yescharacteristic
661C2#1307295311yescharacteristic
662C2#1307295511yescharacteristic
663C2#1307297511yescharacteristic
664C2#1307297711yescharacteristic
665C2#1307312811yescharacteristic
666C2#1307313011yescharacteristic
667C2#1307315011yescharacteristic
668C2#1307315211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, prime radical, cosocleC24×C11C24
hypercenterC4⋊#95D11
hypocenterC11#13918
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
35. C4⋊C4×Dic11C4semidirect
351. C4×C11#382semidirect
515. C11#13918semidirect
653. C4#10622263semidirect

Maximal subgroups

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

subgroupindex
C2×#106225412
C2×#106225862
C2×#106222632
C2×C4⋊C4×Dic112
#130668742
#130668712
#130668452
#130668412
C4×C11⋊#952
C11×C4⋊#952
#1391811