Finite Group Databasebeta

← #14675348

Subgroups — #14675348

Order 2816.

1778 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622585C212yesmaximal
2C2×C4×Dic11⋊C4C212yesmaximal
3C2×C4×Dic11⋊C4C211yesmaximal, characteristic
4C2×#10622262C211yesmaximal, characteristic
5#13066849C212yesmaximal
6#13066848C212yesmaximal
7Dic11⋊#95C211yesmaximal, characteristic
8#13066843C211yesmaximal, characteristic
9#13066840C211yesmaximal, characteristic
10#95×Dic11C211yesmaximal, characteristic
11C2×C4×C11×C4⋊C4C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2212yes—
13C22×C42×C11C2212yes—
14C22×C42×C11C2211yescharacteristic
15C22×Dic11⋊C4C2212yes—
16C22×Dic11⋊C4C2212yes—
17C22×Dic11⋊C4C2211yescharacteristic
18C22×Dic11⋊C4C2211yescharacteristic
19C22×C4×Dic11C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23C4×C11×C4⋊C4—24no—
24C2×C11×#95C2211yescharacteristic
25C2×C11×#95C2211yescharacteristic
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2211yescharacteristic
36#10622585C4116yescomplemented
37C4×Dic11⋊C4—28no—
38C4×Dic11⋊C4C418yescomplemented
39#10622262—24no—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2312yes—
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C2×C11×C4⋊C4—24no—
52C2×C11×C4⋊C4—24no—
53C2×C11×C4⋊C4C2×C418yes—
54C2×C42×C11—22no—
55C2×C42×C11—22no—
56C2×C42×C11—24no—
57C2×C42×C11—24no—
58C2×C42×C11—42no—
59C2×C42×C11C2×C414yes—
60C2×Dic11⋊C4—24no—
61C2×Dic11⋊C4—24no—
62C2×Dic11⋊C4—24no—
63C2×Dic11⋊C4—24no—
64C2×Dic11⋊C4C2×C418yes—
65C2×Dic11⋊C4C2×C418yes—
66C2×Dic11⋊C4C2×C414yes—
67C2×Dic11⋊C4C2×C418yes—
68C2×Dic11⋊C4C2×C414yes—
69C2×Dic11⋊C4D414yes—
70C2×Dic11⋊C4Q814yes—
71C2×C4×Dic11—22no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11—24no—
74C2×C4×Dic11—24no—
75C2×C4×Dic11—24no—
76C2×C4×Dic11—24no—
77C2×C4×Dic11—24no—
78C2×C4×Dic11—42no—
79C2×C4×Dic11C2×C414yes—
80C2×C4×Dic11C2×C414yes—
81C2×C4×Dic11C2×C418yes—
82C11×#95—22no—
83C11×#95D414yes—
84C11⋊#95—22no—
85C11⋊#95—24no—
86C11⋊#95—22no—
87C11⋊#95—24no—
88C11⋊#95—24no—
89C11⋊#95—42no—
90C11⋊#95C2×C414yes—
91C11⋊#95C2×C414yes—
92C11⋊#95C2×C418yes—
93C11⋊#95C2×C418yes—
94#13821—111nomaximal, Sylow
95C24×C11C2411yescharacteristic
96C22×C4×C11—22no—
97C22×C4×C11—21no—
98C22×C4×C11—21no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—21no—
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—22no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11C22×C414yes—
116C22×C4×C11C22×C412yes—
117C22×C4×C11C22×C414yes—
118C22×C4×C11C22×C412yes—
119C22×C4×C11C22×C412yes—
120C22×C4×C11C22×C414yes—
121C22×C4×C11C2×D412yes—
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D414yes—
124C22×C4×C11C2×Q812yes—
125C22×C4×C11#4112yes—
126C22×C4×C11#4114yes—
127C22×Dic11—21no—
128C22×Dic11—21no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—22no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11C22×C412yes—
151C22×Dic11C22×C414yes—
152C22×Dic11C22×C414yes—
153C22×Dic11C22×C412yes—
154C22×Dic11C22×C414yes—
155C22×Dic11C22×C412yes—
156C22×Dic11C22×C412yes—
157C22×Dic11C22×C414yes—
158C22×Dic11C2×D412yes—
159C22×Dic11C2×D412yes—
160C22×Dic11C2×Q812yes—
161C22×Dic11C2×Q812yes—
162C22×Dic11#4114yes—
163C11×C4⋊C4—216no—
164C42×C11—28no—
165C42×C11—48no—
166Dic11⋊C4—216no—
167Dic11⋊C4—216no—
168Dic11⋊C4C42116yescomplemented
169Dic11⋊C4C4⋊C4116yescomplemented
170C4×Dic11—28no—
171C4×Dic11—216no—
172C4×Dic11—28no—
173C4×Dic11—48no—
174C2×#389—112no—
175C2×C4×C4⋊C4—111no—
176C2×C4×C4⋊C4—112no—
177C2×C4×C4⋊C4—111no—
178C2×C4×C4⋊C4D1111yescharacteristic
179#1436—112no—
180#1436—112no—
181C4⋊#95—111no—
182#1434—111no—
183#1434—111no—
184C4×#95—111no—
185C23×C11C23×C411yescharacteristic
186C23×C11C23×C412yes—
187C23×C11C22×D411yescharacteristic
188C23×C11C22×D411yescharacteristic
189C23×C11C22×Q811yescharacteristic
190C23×C11C2×#4111yescharacteristic
191C23×C11C2×#4112yes—
192C23×C11C2×#4112yes—
193C23×C11H(5,𝔽2)11yescharacteristic
194C23×C112−1+411yescharacteristic
195C23×C112−1+412yes—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—22no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—22no—
208C2×C4×C11—22no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—22no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11C2×C4214yes—
224C2×C4×C11C2×C4⋊C414yes—
225C2×C4×C11C4×D414yes—
226C2×C4×C11C4×D418yes—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—22no—
231C2×Dic11—24no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11C2×C4214yes—
257C2×Dic11C2×C4214yes—
258C2×Dic11C2×C4⋊C414yes—
259C2×Dic11C2×C4⋊C414yes—
260C2×Dic11#11714yes—
261C2×Dic11C4×D418yes—
262C2×Dic11C4×Q818yes—
263C22×C4⋊C4—111no—
264C22×C4⋊C4—111no—
265C22×C4⋊C4—112no—
266C22×C4⋊C4—112no—
267C22×C4⋊C4C2×D1112yes—
268C22×C42—111no—
269C22×C42—112no—
270C22×C42—111no—
271C22×C42—112no—
272C22×C42C2×D1112yes—
273C22×C42C2×D1111yescharacteristic
274#389—1116no—
275C4×C4⋊C4—24no—
276C4×C4⋊C4—118no—
277C4×C4⋊C4—228no—
278C4×C4⋊C4—224no—
279C2×#95—112no—
280C2×#95—112no—
281C2×#95—111no—
282C2×#95—111no—
283C2×#95—111no—
284C2×#95—112no—
285C2×#95—111no—
286C2×#95—112no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95C2×D1111yescharacteristic
290C2×#95C2×D1111yescharacteristic
291C22×C11C22×C4211yescharacteristic
292C22×C11C22×C4⋊C411yescharacteristic
293C22×C11C2×#11711yescharacteristic
294C22×C11C2×C4×D411yescharacteristic
295C22×C11C2×C4×D412yes—
296C22×C11C2×C4×D412yes—
297C22×C11C2×C4×Q812yes—
298C22×C11C4×#4111yescharacteristic
299C22×C11C4×#4112yes—
300C22×C11#51911yescharacteristic
301C22×C11#51912yes—
302C22×C11#52011yescharacteristic
303C22×C11#52012yes—
304C22×C11D4211yescharacteristic
305C22×C11#54711yescharacteristic
306C22×C11#54712yes—
307C22×C11#54812yes—
308C22×C11D4×Q811yescharacteristic
309C22×C11#55212yes—
310C22×C11#55312yes—
311C22×C11#55411yescharacteristic
312C22×C11#55612yes—
313C22×C11#55712yes—
314C4×C11—24no—
315C4×C11—24no—
316C4×C11—28no—
317C4×C11—24no—
318C4×C11—44no—
319Dic11—24no—
320Dic11—24no—
321Dic11—42no—
322Dic11—44no—
323Dic11—44no—
324Dic11C4×C4⋊C418yescomplemented
325C23×C4—111no—
326C23×C4—111no—
327C23×C4—111no—
328C23×C4—112no—
329C23×C4—112no—
330C23×C4—111no—
331C23×C4C22×D1112yes—
332C23×C4C22×D1111yescharacteristic
333C23×C4C22×D1112yes—
334C23×C4C22×D1111yescharacteristic
335C23×C4C22×D1111yescharacteristic
336C2×C4⋊C4—24no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—114no—
339C2×C4⋊C4—114no—
340C2×C4⋊C4—118no—
341C2×C4⋊C4—114no—
342C2×C4⋊C4—114no—
343C2×C4⋊C4—118no—
344C2×C4⋊C4—118no—
345C2×C4⋊C4—224no—
346C2×C4⋊C4—224no—
347C2×C4⋊C4—224no—
348C2×C4⋊C4—224no—
349C2×C4⋊C4C4×D1118yes—
350C2×C42—22no—
351C2×C42—22no—
352C2×C42—24no—
353C2×C42—24no—
354C2×C42—42no—
355C2×C42—114no—
356C2×C42—114no—
357C2×C42—118no—
358C2×C42—224no—
359C2×C42—224no—
360C2×C42—224no—
361C2×C42—222no—
362C2×C42—222no—
363C2×C42—224no—
364C2×C42—224no—
365C2×C42—442no—
366C2×C42C4×D1114yes—
367#95—22no—
368#95—114no—
369#95—114no—
370#95—118no—
371#95—118no—
372#95—224no—
373#95—222no—
374#95—224no—
375#95—224no—
376#95—222no—
377#95—442no—
378#95C22⋊D1114yes—
379C2×C11C2×C4×C4⋊C411yescharacteristic
380C2×C11C42×D411yescharacteristic
381C2×C11#227611yescharacteristic
382C2×C11#234411yescharacteristic
383C2×C11#234711yescharacteristic
384C2×C11D4×C4⋊C411yescharacteristic
385C2×C11#235111yescharacteristic
386C2×C11#236112yes—
387C2×C11#236212yes—
388C2×C11#236512yes—
389C2×C11#237012yes—
390C24C23×D1111yescharacteristic
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—112no—
411C22×C4—114no—
412C22×C4—112no—
413C22×C4—112no—
414C22×C4—114no—
415C22×C4—112no—
416C22×C4—112no—
417C22×C4—114no—
418C22×C4—112no—
419C22×C4—112no—
420C22×C4—112no—
421C22×C4—114no—
422C22×C4—114no—
423C22×C4—221no—
424C22×C4—221no—
425C22×C4—222no—
426C22×C4—221no—
427C22×C4—221no—
428C22×C4—221no—
429C22×C4—221no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—221no—
437C22×C4—222no—
438C22×C4—221no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—222no—
445C22×C4—222no—
446C22×C4C2×C4×D1114yes—
447C22×C4C2×C4×D1112yes—
448C22×C4C2×C4×D1114yes—
449C22×C4C2×C4×D1112yes—
450C22×C4C2×C4×D1112yes—
451C22×C4C2×C4×D1114yes—
452C22×C4#433912yes—
453C22×C4#433914yes—
454C22×C4D4×D1112yes—
455C22×C4Q8×D1112yes—
456C22×C4C2×C22⋊D1112yes—
457C22×C4C2×C22⋊D1114yes—
458C4⋊C4—216no—
459C4⋊C4—1116no—
460C4⋊C4—1116no—
461C4⋊C4—2216no—
462C4⋊C4—2216no—
463C42—28no—
464C42—48no—
465C42—228no—
466C42—2216no—
467C42—228no—
468C42—448no—
469C11#1382111yescharacteristic, complemented, Sylow
470C23C22×C4×D1111yescharacteristic
471C23C22×C4×D1112yes—
472C23C2×#433911yescharacteristic
473C23C2×#433912yes—
474C23C2×D4×D1111yescharacteristic
475C23#6703711yescharacteristic
476C23C2×Q8×D1111yescharacteristic
477C23#6704011yescharacteristic
478C23#41×D1112yes—
479C23#6704312yes—
480C23C22×C22⋊D1111yescharacteristic
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—22no—
499C2×C4—24no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—114no—
509C2×C4—114no—
510C2×C4—114no—
511C2×C4—118no—
512C2×C4—118no—
513C2×C4—114no—
514C2×C4—114no—
515C2×C4—224no—
516C2×C4—222no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—222no—
520C2×C4—222no—
521C2×C4—222no—
522C2×C4—224no—
523C2×C4—222no—
524C2×C4—222no—
525C2×C4—224no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—224no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—224no—
534C2×C4—442no—
535C2×C4—442no—
536C2×C4—442no—
537C2×C4—442no—
538C2×C4—442no—
539C2×C4—442no—
540C2×C4—442no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—442no—
544C2×C4C42×D1114yes—
545C2×C4C4⋊C4×D1114yes—
546C2×C4C4×C22⋊D1114yes—
547C2×C4C4×C22⋊D1118yes—
548C22C2×C42×D1111yescharacteristic
549C22C4×#433912yes—
550C22C4×#433911yescharacteristic
551C22C2×C4⋊C4×D1111yescharacteristic
552C22#1062303511yescharacteristic
553C22#1062303811yescharacteristic
554C22#1062304211yescharacteristic
555C22#1062304711yescharacteristic
556C22D11×#11711yescharacteristic
557C22#1062306212yes—
558C22#1062307112yes—
559C22C4×D4×D1112yes—
560C22#1062307712yes—
561C22#1062308312yes—
562C22#1062309812yes—
563C22#1062309912yes—
564C22C4×Q8×D1112yes—
565C22#1062310312yes—
566C22C2×C4×C22⋊D1112yes—
567C22C2×C4×C22⋊D1111yescharacteristic
568C22D4×C22⋊D1111yescharacteristic
569C22Q8×C22⋊D1111yescharacteristic
570C22#1062335512yes—
571C4—28no—
572C4—24no—
573C4—24no—
574C4—24no—
575C4—44no—
576C4—118no—
577C4—224no—
578C4—224no—
579C4—444no—
580C4—444no—
581C4—442no—
582C2C4×C4⋊C4×D1111yescharacteristic
583C2C42×C22⋊D1111yescharacteristic
584C2#1307098011yescharacteristic
585C2#1307148611yescharacteristic
586C2#1307151011yescharacteristic
587C2C4⋊C4×C22⋊D1111yescharacteristic
588C2#1307153611yescharacteristic
589C2#1307163312yes—
590C2#1307164412yes—
591C2#1307167012yes—
592C2#1307171312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC2×C4×C11×C4⋊C4C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#13821
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
36. #10622585C4semidirect
38. C4×Dic11⋊C4C4semidirect
168. Dic11⋊C4C42semidirect
169. Dic11⋊C4C4⋊C4semidirect
324. Dic11C4×C4⋊C4semidirect
469. C11#13821semidirect

Maximal subgroups

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

subgroupindex
C2×#106225852
C2×C4×Dic11⋊C42
C2×#106222622
#130668492
#130668482
Dic11⋊#952
#130668432
#130668402
#95×Dic112
C2×C4×C11×C4⋊C42
#1382111