Finite Group Databasebeta

← #14690481

Subgroups — #14690481

Order 2816.

1934 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66997C211yesmaximal, characteristic
2C2×#10622269C211yesmaximal, characteristic
3C2×#10622592C211yesmaximal, characteristic
4C2×#10622842C211yesmaximal, characteristic
5C2×#10622585C211yesmaximal, characteristic
6C2×#10622589C212yesmaximal
7#13066880C212yesmaximal
8#13066879C212yesmaximal
9Dic11⋊#95C212yesmaximal
10#95×Dic11C211yesmaximal, characteristic
11C2×C11×#395C211yesmaximal, characteristic
12C23×Q8×C11C2211yescharacteristic
13C23×Dic22C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C2×#66997—28no—
17C2×#66997—24no—
18C22×C4⋊Dic11C2212yes—
19C22×Dic11⋊C4C2212yes—
20C22×Dic11⋊C4C2211yescharacteristic
21C22×Dic11⋊C4C2211yescharacteristic
22C22×Dic11⋊C4C2212yes—
23C22×Dic11⋊C4C2212yes—
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2212yes—
28C11×#395—24no—
29C2×C11×#95C2212yes—
30C2×C11×#95C2211yescharacteristic
31#10622842—24no—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39#10622592—24no—
40#10622589—28no—
41#10622585—24no—
42#10622269—24no—
43C22×Q8×C11—24no—
44C22×Q8×C11—22no—
45C22×Q8×C11—22no—
46C22×Q8×C11—22no—
47C22×Q8×C11—42no—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×Dic11C2311yescharacteristic
54C23×Dic11C2312yes—
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C22×Dic22—22no—
60C22×Dic22—24no—
61C22×Dic22—22no—
62C22×Dic22—22no—
63C22×Dic22—42no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4—22no—
67C2×C11×C4⋊C4—24no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—42no—
70#66997—232no—
71C2×C4⋊Dic11—24no—
72C2×C4⋊Dic11—24no—
73C2×C4⋊Dic11—42no—
74C2×Dic11⋊C4—24no—
75C2×Dic11⋊C4—24no—
76C2×Dic11⋊C4—24no—
77C2×Dic11⋊C4—24no—
78C2×Dic11⋊C4—24no—
79C2×Dic11⋊C4—22no—
80C2×Dic11⋊C4—22no—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—22no—
83C2×Dic11⋊C4—22no—
84C2×Dic11⋊C4—24no—
85C2×Dic11⋊C4—22no—
86C2×Dic11⋊C4—24no—
87C2×Dic11⋊C4—24no—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—42no—
91C2×Dic11⋊C4—42no—
92C2×Dic11⋊C4D418yes—
93C2×Dic11⋊C4Q814yescomplemented
94C2×C4×Dic11—24no—
95C2×C4×Dic11—24no—
96C2×C4×Dic11—24no—
97C2×C4×Dic11D414yes—
98C2×C4×Dic11Q818yescomplemented
99C11×#95—24no—
100C11×#95D414yes—
101C11⋊#95—24no—
102C11⋊#95—22no—
103C11⋊#95—22no—
104C11⋊#95—24no—
105C11⋊#95—24no—
106C11⋊#95D414yes—
107C11⋊#95Q818yescomplemented
108#15143—111nomaximal, Sylow
109C24×C11C2411yescharacteristic
110C2×Q8×C11—28no—
111C2×Q8×C11—48no—
112C2×Q8×C11—48no—
113C2×Q8×C11—44no—
114C2×Q8×C11—44no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—22no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11C2×D414yes—
139C22×C4×C11C2×D412yes—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D414yes—
143C22×C4×C11C2×Q812yes—
144C22×C4×C11C2×Q814yes—
145C22×C4×C11C2×Q814yes—
146C22×Dic11—22no—
147C22×Dic11—22no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—22no—
158C22×Dic11—21no—
159C22×Dic11—22no—
160C22×Dic11—21no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—21no—
166C22×Dic11—22no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11C2×D414yes—
171C22×Dic11C2×D412yes—
172C22×Dic11C2×D414yes—
173C22×Dic11C2×D414yes—
174C22×Dic11C2×D412yes—
175C22×Dic11C2×Q812yes—
176C22×Dic11C2×Q814yes—
177C22×Dic11C2×Q814yes—
178C22×Dic11C2×Q814yes—
179C22×Dic11C2×Q814yes—
180C22×Dic11C2×Q812yes—
181C22×Dic11#4112yes—
182C2×Dic22—28no—
183C2×Dic22—48no—
184C2×Dic22—48no—
185C2×Dic22—44no—
186C2×Dic22—44no—
187C11×C4⋊C4—48no—
188C11×C4⋊C4—44no—
189C4⋊Dic11—48no—
190Dic11⋊C4—216no—
191Dic11⋊C4—216no—
192Dic11⋊C4—28no—
193Dic11⋊C4—48no—
194Dic11⋊C4—48no—
195Dic11⋊C4—44no—
196Dic11⋊C4—44no—
197C4×Dic11—28no—
198C4×Dic11—216no—
199C22×C4⋊Q8—111no—
200C2×#395—111no—
201C2×#395—111no—
202C2×#395—111no—
203C2×#395D1111yescharacteristic
204C2×#389—111no—
205C2×#384—112no—
206#1444—112no—
207#1444—112no—
208C4⋊#95—112no—
209C4×#95—111no—
210C23×C11C22×D411yescharacteristic
211C23×C11C22×D412yes—
212C23×C11C22×D411yescharacteristic
213C23×C11C22×D411yescharacteristic
214C23×C11C22×Q812yes—
215C23×C11C22×Q811yescharacteristic
216C23×C11C22×Q812yes—
217C23×C11C2×#4111yescharacteristic
218C23×C11H(5,𝔽2)12yes—
219C23×C112−1+411yescharacteristic
220C23×C112−1+411yescharacteristic
221Q8×C11—416no—
222C2×C4×C11—22no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—41no—
242C2×C4×C11—42no—
243C2×C4×C11—42no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11#12714yes—
252C2×C4×C11C4⋊Q818yescomplemented
253C2×Dic11—22no—
254C2×Dic11—24no—
255C2×Dic11—22no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—24no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—22no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—41no—
270C2×Dic11—42no—
271C2×Dic11—42no—
272C2×Dic11—41no—
273C2×Dic11—42no—
274C2×Dic11—42no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—42no—
281C2×Dic11—42no—
282C2×Dic11#12014yes—
283C2×Dic11C22⋊Q818yes—
284C2×Dic11C22⋊Q814yes—
285C2×Dic11C4⋊Q814yes—
286C2×Dic11C4⋊Q814yes—
287C2×Dic11C4⋊Q818yes—
288C2×Dic11C4⋊Q818yescomplemented
289Dic22—416no—
290C23×Q8—111no—
291C23×Q8C2×D1111yescharacteristic
292C2×C4⋊Q8—224no—
293C2×C4⋊Q8—228no—
294C22×C4⋊C4—112no—
295C22×C4⋊C4—111no—
296C22×C4⋊C4—111no—
297C22×C4⋊C4—112no—
298C22×C4⋊C4—111no—
299C22×C4⋊C4—112no—
300C22×C4⋊C4—112no—
301C22×C4⋊C4—112no—
302C22×C4⋊C4C2×D1111yescharacteristic
303C22×C4⋊C4C2×D1112yes—
304C22×C42—111no—
305C22×C42—112no—
306#395—24no—
307#395—224no—
308#395—224no—
309#395—224no—
310#389—224no—
311#384—228no—
312C2×#95—111no—
313C2×#95—112no—
314C2×#95—112no—
315C2×#95—112no—
316C2×#95—112no—
317C2×#95—111no—
318C2×#95—111no—
319C2×#95C2×D1112yes—
320C2×#95C2×D1111yescharacteristic
321C22×C11C2×#12011yescharacteristic
322C22×C11C2×C22⋊Q811yescharacteristic
323C22×C11C2×C22⋊Q812yes—
324C22×C11C2×#12711yescharacteristic
325C22×C11C2×C4⋊Q811yescharacteristic
326C22×C11C2×C4⋊Q811yescharacteristic
327C22×C11C2×C4⋊Q812yes—
328C22×C11C2×C4⋊Q812yes—
329C22×C11C2×C4⋊Q812yes—
330C22×C11#53511yescharacteristic
331C22×C11#53611yescharacteristic
332C22×C11#54412yes—
333C22×C11#54412yes—
334C22×C11D4212yes—
335C22×C11D4212yes—
336C22×C11#54711yescharacteristic
337C22×C11#54711yescharacteristic
338C22×C11D4×Q812yes—
339C22×C11D4×Q811yescharacteristic
340C22×C11D4×Q812yes—
341C22×C11D4×Q811yescharacteristic
342C22×C11#55412yes—
343C22×C11Q8212yes—
344C4×C11—24no—
345C4×C11—28no—
346C4×C11—44no—
347C4×C11—42no—
348C4×C11—81no—
349Dic11—24no—
350Dic11—28no—
351Dic11—44no—
352Dic11—42no—
353Dic11—81no—
354Dic11#39518yescomplemented
355C22×Q8—24no—
356C22×Q8—22no—
357C22×Q8—22no—
358C22×Q8—22no—
359C22×Q8—42no—
360C22×Q8—224no—
361C22×Q8—222no—
362C22×Q8—222no—
363C22×Q8—222no—
364C22×Q8—442no—
365C23×C4—111no—
366C23×C4—112no—
367C23×C4—111no—
368C23×C4—112no—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4C22×D1111yescharacteristic
372C23×C4C22×D1112yes—
373C23×C4C22×D1111yescharacteristic
374C23×C4C22×D1111yescharacteristic
375C23×C4C22×D1112yes—
376C4⋊Q8—2232no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—22no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—118no—
384C2×C4⋊C4—114no—
385C2×C4⋊C4—224no—
386C2×C4⋊C4—224no—
387C2×C4⋊C4—224no—
388C2×C4⋊C4—224no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—224no—
392C2×C4⋊C4—224no—
393C2×C4⋊C4—224no—
394C2×C4⋊C4—224no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—224no—
397C2×C4⋊C4—224no—
398C2×C4⋊C4—224no—
399C2×C4⋊C4—222no—
400C2×C4⋊C4—222no—
401C2×C4⋊C4—222no—
402C2×C4⋊C4—224no—
403C2×C4⋊C4—442no—
404C2×C4⋊C4—442no—
405C2×C4⋊C4—442no—
406C2×C42—114no—
407C2×C42—118no—
408C2×C42—224no—
409C2×C42—224no—
410C2×C42—224no—
411#95—24no—
412#95—114no—
413#95—118no—
414#95—222no—
415#95—222no—
416#95—224no—
417#95—224no—
418#95—224no—
419#95C22⋊D1114yes—
420C2×C11C2×#39511yescharacteristic
421C2×C11#243311yescharacteristic
422C2×C11#243411yescharacteristic
423C2×C11#244012yes—
424C2×C11#244012yes—
425C2×C11#254211yescharacteristic
426C2×C11#255112yes—
427C2×C11#255112yes—
428C2×C11#256711yescharacteristic
429C2×C11#266011yescharacteristic
430C2×C11#286811yescharacteristic
431C24C23×D1111yescharacteristic
432C2×Q8—28no—
433C2×Q8—48no—
434C2×Q8—48no—
435C2×Q8—44no—
436C2×Q8—44no—
437C2×Q8—228no—
438C2×Q8—448no—
439C2×Q8—448no—
440C2×Q8—444no—
441C2×Q8—444no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—112no—
466C22×C4—114no—
467C22×C4—114no—
468C22×C4—112no—
469C22×C4—112no—
470C22×C4—114no—
471C22×C4—112no—
472C22×C4—114no—
473C22×C4—114no—
474C22×C4—114no—
475C22×C4—114no—
476C22×C4—112no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—222no—
480C22×C4—221no—
481C22×C4—222no—
482C22×C4—222no—
483C22×C4—221no—
484C22×C4—221no—
485C22×C4—221no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—222no—
496C22×C4—221no—
497C22×C4—222no—
498C22×C4—221no—
499C22×C4—222no—
500C22×C4—221no—
501C22×C4D4×D1114yes—
502C22×C4D4×D1112yes—
503C22×C4D4×D1112yes—
504C22×C4Q8×D1112yes—
505C22×C4Q8×D1114yes—
506C22×C4Q8×D1114yes—
507C22×C4C2×C22⋊D1112yes—
508C22×C4C2×C22⋊D1114yes—
509C4⋊C4—48no—
510C4⋊C4—44no—
511C4⋊C4—2216no—
512C4⋊C4—228no—
513C4⋊C4—2216no—
514C4⋊C4—448no—
515C4⋊C4—448no—
516C4⋊C4—444no—
517C4⋊C4—448no—
518C4⋊C4—444no—
519C42—228no—
520C42—2216no—
521C11#1514311yescharacteristic, complemented, Sylow
522C23C2×D4×D1111yescharacteristic
523C23C2×D4×D1111yescharacteristic
524C23C2×D4×D1112yes—
525C23#6703712yes—
526C23C2×Q8×D1111yescharacteristic
527C23C2×Q8×D1112yes—
528C23C2×Q8×D1112yes—
529C23#6704011yescharacteristic
530C23#41×D1111yescharacteristic
531C23#6704311yescharacteristic
532C23C22×C22⋊D1111yescharacteristic
533Q8—416no—
534Q8—4416no—
535C2×C4—24no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—22no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—24no—
546C2×C4—22no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—42no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—41no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—114no—
565C2×C4—118no—
566C2×C4—114no—
567C2×C4—118no—
568C2×C4—114no—
569C2×C4—114no—
570C2×C4—118no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—222no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—222no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—222no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—442no—
588C2×C4—441no—
589C2×C4—442no—
590C2×C4—441no—
591C2×C4—442no—
592C2×C4—442no—
593C2×C4—441no—
594C2×C4—441no—
595C2×C4—442no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—442no—
599C2×C4—441no—
600C2×C4#6699314yes—
601C2×C4#6699718yescomplemented
602C22D11×#12011yescharacteristic
603C22#1062312112yes—
604C22#1062312311yescharacteristic
605C22#1062315412yes—
606C22D11×C22⋊Q811yescharacteristic
607C22D11×C22⋊Q812yes—
608C22#1062315911yescharacteristic
609C22#1062316211yescharacteristic
610C22#1062316312yes—
611C22#1062316311yescharacteristic
612C22#1062316712yes—
613C22#1062325312yes—
614C22D11×C4⋊Q811yescharacteristic
615C22D11×C4⋊Q811yescharacteristic
616C22D11×C4⋊Q812yes—
617C22D11×C4⋊Q812yes—
618C22#1062325812yes—
619C22#1062326012yes—
620C22D4×C22⋊D1112yes—
621C22C2×#6699311yescharacteristic
622C22C2×#6699712yes—
623C22Q8×C22⋊D1111yescharacteristic
624C22#1062335511yescharacteristic
625C4—24no—
626C4—28no—
627C4—44no—
628C4—42no—
629C4—81no—
630C4—118no—
631C4—224no—
632C4—228no—
633C4—444no—
634C4—442no—
635C4—881no—
636C2D11×#39511yescharacteristic
637C2#1307225111yescharacteristic
638C2#1307225511yescharacteristic
639C2#1307231112yes—
640C2#1307231512yes—
641C2#1307356611yescharacteristic
642C2#1307364112yes—
643C2#1307364312yes—
644C2#1307382011yescharacteristic
645C2#1307473411yescharacteristic
646C2#1307701211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, prime radical, cosocleC24×C11C24
FittingC2×C11×#395C2
hypercenterC2×#395D11
hypocenterC11#15143
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
93. C2×Dic11⋊C4Q8semidirect
98. C2×C4×Dic11Q8semidirect
107. C11⋊#95Q8semidirect
252. C2×C4×C11C4⋊Q8semidirect
288. C2×Dic11C4⋊Q8semidirect
354. Dic11#395semidirect
521. C11#15143semidirect
601. C2×C4#66997semidirect

Maximal subgroups

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

subgroupindex
C22×#669972
C2×#106222692
C2×#106225922
C2×#106228422
C2×#106225852
C2×#106225892
#130668802
#130668792
Dic11⋊#952
#95×Dic112
C2×C11×#3952
#1514311