Finite Group Databasebeta

← #14677302

Subgroups — #14677302

Order 2816.

1326 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622541C211yesmaximal, characteristic
2C2×#10622549C211yesmaximal, characteristic
3C2×C4×C4⋊Dic11C211yesmaximal, characteristic
4#13066877C212yesmaximal
5#13066874C212yesmaximal
6#13066847C212yesmaximal
7#13066846C211yesmaximal, characteristic
8#13066846C211yesmaximal, characteristic
9#13066846C211yesmaximal, characteristic
10#13066842C212yesmaximal
11C4×C11×#95C211yesmaximal, characteristic
12C22×C42×C11C2211yescharacteristic
13C22×C42×C11C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×C4⋊Dic11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2212yes—
21C2×C11×#95C2211yescharacteristic
22C2×C11×#95C2211yescharacteristic
23C2×C11×#95C2211yescharacteristic
24C2×C11×#95C2211yescharacteristic
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35#10622549C418yescomplemented
36C4×C4⋊Dic11—24no—
37#10622541—24no—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C2×C42×C11—22no—
50C2×C42×C11—22no—
51C2×C42×C11—22no—
52C2×C42×C11—22no—
53C2×C42×C11—22no—
54C2×C42×C11—22no—
55C2×C42×C11—22no—
56C2×C42×C11C2×C414yes—
57C2×C42×C11Q814yes—
58C2×C4⋊Dic11—22no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11C2×C414yes—
68C2×C4⋊Dic11C2×C414yes—
69C2×C4⋊Dic11D414yes—
70C2×Dic11⋊C4—24no—
71C2×Dic11⋊C4—24no—
72C2×Dic11⋊C4—42no—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—42no—
76C11×#95—22no—
77C11×#95—22no—
78C11×#95—22no—
79C11×#95—22no—
80C11⋊#95—24no—
81C11⋊#95—24no—
82C11⋊#95—24no—
83C11⋊#95—24no—
84C11⋊#95—42no—
85C11⋊#95—42no—
86C11⋊#95—42no—
87C11⋊#95—42no—
88C11⋊#95C2×C418yes—
89C11⋊#95C2×C418yes—
90#14030—111nomaximal, Sylow
91C24×C11C2411yescharacteristic
92C22×C4×C11—21no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C22×C412yes—
128C22×C4×C11C22×C412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×Q812yes—
131C22×C4×C11C2×Q812yes—
132C22×C4×C11C2×Q812yes—
133C22×C4×C11#4112yes—
134C22×C4×C11#4112yes—
135C22×C4×C11#4112yes—
136C22×C4×C11#4112yes—
137C22×C4×C11#4112yes—
138C22×C4×C11#4112yes—
139C22×C4×C11#4112yes—
140C22×C4×C11#4112yes—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—22no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11C22×C414yes—
167C22×Dic11C22×C414yes—
168C22×Dic11C2×D414yes—
169C42×C11—28no—
170C42×C11—28no—
171C42×C11—44no—
172C4⋊Dic11—28no—
173C4⋊Dic11—28no—
174C4⋊Dic11—28no—
175C4⋊Dic11—44no—
176Dic11⋊C4—48no—
177C4×Dic11—48no—
178C2×#389—111no—
179C2×#382—111no—
180C2×C4×C4⋊C4—111no—
181#1443—112no—
182#1442—112no—
183#1436—112no—
184C4⋊#95—111no—
185C4⋊#95—111no—
186C4⋊#95—111no—
187#1434—112no—
188C4×#95D1111yescharacteristic
189C23×C11C23×C411yescharacteristic
190C23×C11C22×D411yescharacteristic
191C23×C11C22×Q811yescharacteristic
192C23×C11C2×#4111yescharacteristic
193C23×C11C2×#4111yescharacteristic
194C23×C11C2×#4111yescharacteristic
195C23×C11C2×#4111yescharacteristic
196C23×C11C2×#4111yescharacteristic
197C23×C11C2×#4111yescharacteristic
198C23×C11C2×#4111yescharacteristic
199C23×C11C2×#4111yescharacteristic
200C23×C11H(5,𝔽2)11yescharacteristic
201C23×C11H(5,𝔽2)11yescharacteristic
202C23×C112−1+411yescharacteristic
203C23×C112−1+411yescharacteristic
204C2×C4×C11—22no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
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—22no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—41no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11#11714yes—
246C2×C4×C11C4×D414yes—
247C2×C4×C11C4×Q814yes—
248C2×C4×C11C22⋊Q814yes—
249C2×C4×C11#12314yes—
250C2×C4×C11#12514yes—
251C2×C4×C11#12514yes—
252C2×C4×C11#12614yes—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—42no—
263C2×Dic11—42no—
264C2×Dic11—42no—
265C2×Dic11—42no—
266C2×Dic11—42no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—42no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—42no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—42no—
279C2×Dic11—42no—
280C2×Dic11—42no—
281C22×C4⋊C4—111no—
282C22×C4⋊C4—111no—
283C22×C4⋊C4—111no—
284C22×C4⋊C4—111no—
285C22×C4⋊C4—112no—
286C22×C42—112no—
287C22×C42C2×D1111yescharacteristic
288C22×C42C2×D1111yescharacteristic
289C22×C42C2×D1111yescharacteristic
290#389—224no—
291#382—118no—
292C4×C4⋊C4—224no—
293C2×#95—112no—
294C2×#95—112no—
295C2×#95—112no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—112no—
301C2×#95—112no—
302C2×#95—112no—
303C2×#95C2×D1111yescharacteristic
304C2×#95C2×D1111yescharacteristic
305C2×#95C2×D1111yescharacteristic
306C2×#95C2×D1111yescharacteristic
307C22×C11C2×#11711yescharacteristic
308C22×C11C2×C4×D411yescharacteristic
309C22×C11C2×C4×Q811yescharacteristic
310C22×C11C4×#4111yescharacteristic
311C22×C11C4×#4111yescharacteristic
312C22×C11#52011yescharacteristic
313C22×C11#52011yescharacteristic
314C22×C11C2×C22⋊Q811yescharacteristic
315C22×C11C2×#12311yescharacteristic
316C22×C11C2×#12511yescharacteristic
317C22×C11C2×#12511yescharacteristic
318C22×C11C2×#12611yescharacteristic
319C22×C11#52911yescharacteristic
320C22×C11#52911yescharacteristic
321C22×C11#53311yescharacteristic
322C22×C11#54011yescharacteristic
323C22×C11#54111yescharacteristic
324C22×C11#54411yescharacteristic
325C22×C11#54411yescharacteristic
326C22×C11#54611yescharacteristic
327C22×C11#54611yescharacteristic
328C22×C11#54811yescharacteristic
329C22×C11#54811yescharacteristic
330C22×C11#55211yescharacteristic
331C22×C11#55211yescharacteristic
332C22×C11#55311yescharacteristic
333C22×C11#55311yescharacteristic
334C22×C11#55511yescharacteristic
335C22×C11#55511yescharacteristic
336C22×C11#55611yescharacteristic
337C22×C11#55611yescharacteristic
338C22×C11#55611yescharacteristic
339C22×C11#55611yescharacteristic
340C22×C11#55911yescharacteristic
341C22×C11#55911yescharacteristic
342C4×C11—24no—
343C4×C11—42no—
344C4×C11—42no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11—42no—
348C4×C11#38718yes—
349Dic11—44no—
350Dic11—44no—
351Dic11—44no—
352Dic11—82no—
353C23×C4—112no—
354C23×C4—112no—
355C23×C4—112no—
356C23×C4—112no—
357C23×C4C22×D1111yescharacteristic
358C23×C4C22×D1111yescharacteristic
359C23×C4C22×D1111yescharacteristic
360C23×C4C22×D1111yescharacteristic
361C23×C4C22×D1111yescharacteristic
362C23×C4C22×D1111yescharacteristic
363C23×C4C22×D1111yescharacteristic
364C2×C4⋊C4—114no—
365C2×C4⋊C4—114no—
366C2×C4⋊C4—114no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—222no—
369C2×C4⋊C4—222no—
370C2×C4⋊C4—222no—
371C2×C4⋊C4—222no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—442no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—22no—
383C2×C42—22no—
384C2×C42—22no—
385C2×C42—22no—
386C2×C42—224no—
387C2×C42—224no—
388C2×C42—442no—
389C2×C42Dic2214yes—
390C2×C42C4×D1114yes—
391#95—22no—
392#95—22no—
393#95—22no—
394#95—22no—
395#95—118no—
396#95—118no—
397#95—224no—
398#95—224no—
399#95—224no—
400#95—224no—
401#95—442no—
402#95—442no—
403#95—442no—
404#95—442no—
405C2×C11C2×#38711yescharacteristic
406C2×C11C4×#12511yescharacteristic
407C2×C11#233011yescharacteristic
408C2×C11#234611yescharacteristic
409C2×C11#234711yescharacteristic
410C2×C11#236711yescharacteristic
411C2×C11#236711yescharacteristic
412C2×C11#242011yescharacteristic
413C2×C11#242111yescharacteristic
414C2×C11#243911yescharacteristic
415C2×C11#244211yescharacteristic
416C2×C11#251311yescharacteristic
417C2×C11#251411yescharacteristic
418C2×C11#257011yescharacteristic
419C2×C11#257111yescharacteristic
420C24C23×D1111yescharacteristic
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—114no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—222no—
459C22×C4—222no—
460C22×C4—222no—
461C22×C4—222no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—222no—
466C22×C4—222no—
467C22×C4—222no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4C2×Dic2212yes—
484C22×C4C2×Dic2212yes—
485C22×C4C2×Dic2212yes—
486C22×C4C2×C4×D1112yes—
487C22×C4C2×C4×D1112yes—
488C22×C4C2×C4×D1112yes—
489C22×C4#433912yes—
490C22×C4#433912yes—
491C22×C4#433912yes—
492C22×C4#433912yes—
493C22×C4#433912yes—
494C22×C4D4×D1112yes—
495C22×C4#434112yes—
496C22×C4#434112yes—
497C22×C4#434312yes—
498C4⋊C4—228no—
499C4⋊C4—228no—
500C4⋊C4—228no—
501C4⋊C4—448no—
502C4⋊C4—444no—
503C42—28no—
504C42—28no—
505C42—44no—
506C42—448no—
507C11#1403011yescharacteristic, complemented, Sylow
508C23C22×Dic2211yescharacteristic
509C23C22×C4×D1111yescharacteristic
510C23C2×#433911yescharacteristic
511C23C2×#433911yescharacteristic
512C23C2×#433911yescharacteristic
513C23C2×#433911yescharacteristic
514C23C2×#433911yescharacteristic
515C23C2×D4×D1111yescharacteristic
516C23C2×#434111yescharacteristic
517C23C2×#434111yescharacteristic
518C23C2×#434311yescharacteristic
519C23#6704211yescharacteristic
520C23#6704211yescharacteristic
521C23#6704311yescharacteristic
522C23#6704311yescharacteristic
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—442no—
574C2×C4—442no—
575C2×C4—442no—
576C2×C4—442no—
577C2×C4—442no—
578C2×C4—442no—
579C2×C4—442no—
580C2×C4—442no—
581C2×C4—442no—
582C2×C4—442no—
583C2×C4—442no—
584C2×C4—442no—
585C2×C4—442no—
586C2×C4—442no—
587C2×C4—442no—
588C2×C4—442no—
589C2×C4—442no—
590C2×C4—442no—
591C2×C4—442no—
592C2×C4C4×Dic2214yes—
593C2×C4#6692314yes—
594C2×C4#6693014yes—
595C2×C4#6693114yes—
596C2×C4#6693614yes—
597C2×C4#6694314yes—
598C2×C4#6694614yes—
599C2×C4#6695114yes—
600C22C2×C4×Dic2211yescharacteristic
601C22C2×#6692311yescharacteristic
602C22#1062300111yescharacteristic
603C22C4×#433911yescharacteristic
604C22C4×#433911yescharacteristic
605C22#1062301011yescharacteristic
606C22#1062301011yescharacteristic
607C22C2×#6693011yescharacteristic
608C22C2×#6693111yescharacteristic
609C22C2×#6693611yescharacteristic
610C22C2×#6694311yescharacteristic
611C22C2×#6694611yescharacteristic
612C22C2×#6695111yescharacteristic
613C22#1062304911yescharacteristic
614C22#1062305011yescharacteristic
615C22#1062305011yescharacteristic
616C22#1062305411yescharacteristic
617C22#1062305411yescharacteristic
618C22#1062306611yescharacteristic
619C22#1062307211yescharacteristic
620C22#1062307211yescharacteristic
621C22#1062307311yescharacteristic
622C22#1062307311yescharacteristic
623C22#1062308111yescharacteristic
624C22#1062308111yescharacteristic
625C22#1062308311yescharacteristic
626C22#1062308311yescharacteristic
627C22#1062309411yescharacteristic
628C22#1062309411yescharacteristic
629C22#1062309611yescharacteristic
630C22#1062309611yescharacteristic
631C22#1062311511yescharacteristic
632C22#1062311511yescharacteristic
633C22#1062311611yescharacteristic
634C22#1062311611yescharacteristic
635C4—24no—
636C4—42no—
637C4—42no—
638C4—42no—
639C4—42no—
640C4—42no—
641C4—444no—
642C4—444no—
643C4—444no—
644C4—882no—
645C4#1062226718yes—
646C2C2×#1062226711yescharacteristic
647C2C4×#6692311yescharacteristic
648C2#1307135711yescharacteristic
649C2#1307149911yescharacteristic
650C2#1307150711yescharacteristic
651C2#1307168511yescharacteristic
652C2#1307168511yescharacteristic
653C2#1307210811yescharacteristic
654C2#1307211911yescharacteristic
655C2#1307230711yescharacteristic
656C2#1307234011yescharacteristic
657C2#1307321311yescharacteristic
658C2#1307322411yescharacteristic
659C2#1307385011yescharacteristic
660C2#1307385511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC4×C11×#95C2
socle, prime radical, cosocleC24×C11C24
hypercenterC4×#95D11
hypocenterC11#14030
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
35. #10622549C4semidirect
507. C11#14030semidirect

Maximal subgroups

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

subgroupindex
C2×#106225412
C2×#106225492
C2×C4×C4⋊Dic112
#130668772
#130668742
#130668472
#130668462
#130668422
C4×C11×#952
#1403011