Finite Group Databasebeta

← #14645596

Subgroups — #14645596

Order 2816.

900 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068934C211yesmaximal, characteristic
2#13068924C211yesmaximal, characteristic, complemented
3C2×#10622176C211yesmaximal, characteristic, complemented
4C2×#10622175C211yesmaximal, characteristic
5C2×#10622166C211yesmaximal, characteristic, complemented
6#13066869C211yesmaximal, characteristic, complemented
7C2×C11×#539C211yesmaximal, characteristic
8C11×#539—22no—
9C11×#539—22no—
10C11×#539—22no—
11C11×#539C414yescomplemented
12C2×C11×#126—21no—
13C2×C11×#125—21no—
14C2×C11×#123—21no—
15C2×C11×#123—21no—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C4×D4×C11—21no—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C2×#66899—21no—
23C2×#66896—21no—
24C2×C11⋊#95—21no—
25C2×C11⋊#95—21no—
26C2×C11⋊#95C2211yescharacteristic
27C2×C22⋊(C11⋊C8)C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29#10622176—22no—
30#10622175—22no—
31#10622167—21no—
32#10622167—21no—
33#10622166—22no—
34C22×Q8×C11D411yescharacteristic
35C22×D4×C11—21no—
36C22×D4×C11D411yescharacteristic
37C23×C4×C11—21no—
38C23×C4×C11D411yescharacteristic
39C23×C4×C11D411yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×Dic11—21no—
42C23×Dic11—21no—
43C11×#126—24no—
44C11×#126—24no—
45C11×#125—24no—
46C11×#125—24no—
47C11×#123—24no—
48C11×#123—24no—
49C11×#123—24no—
50C11×#123—24no—
51C11×C22⋊Q8—24no—
52C11×C22⋊Q8—24no—
53C11×C22⋊Q8—21no—
54C11×C22⋊Q8—21no—
55C11×C22⋊Q8C2×C412yes—
56C11×C22⋊Q8D412yes—
57C11×#121—21no—
58C11×#121—21no—
59C11×#121C2×C412yes—
60C11×#121D412yes—
61C4×D4×C11—24no—
62C4×D4×C11—24no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2×C412yes—
72C2×C11×C4⋊C4D412yes—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—42no—
84C22×C11⋊C8—21no—
85C22×C11⋊C8—21no—
86#66899—42no—
87#66896—42no—
88C11⋊#95—21no—
89C11⋊#95—21no—
90C11⋊#95—42no—
91C11⋊#95—42no—
92C22⋊(C11⋊C8)—21no—
93C22⋊(C11⋊C8)—21no—
94C22⋊(C11⋊C8)—21no—
95C22⋊(C11⋊C8)—21no—
96#8407—111nomaximal, Sylow
97C24×C11—21no—
98C24×C11C2×D411yescharacteristic
99C2×Q8×C11—21no—
100C2×Q8×C11—41no—
101C2×Q8×C11—41no—
102C2×Q8×C11C22⋊C412yes—
103C2×D4×C11—22no—
104C2×D4×C11—22no—
105C2×D4×C11—21no—
106C2×D4×C11—41no—
107C2×D4×C11—41no—
108C2×D4×C11—41no—
109C2×D4×C11—41no—
110C2×D4×C11—41no—
111C2×D4×C11—41no—
112C2×D4×C11C22⋊C412yes—
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—24no—
124C22×C4×C11—21no—
125C22×C4×C11—41no—
126C22×C4×C11—41no—
127C22×C4×C11—41no—
128C22×C4×C11—41no—
129C22×C4×C11—81no—
130C22×C4×C11—81no—
131C22×C4×C11C22⋊C412yes—
132C22×C4×C11C22⋊C412yes—
133C22×C4×C11C22×C411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—41no—
142C22×Dic11—41no—
143C22×Dic11—41no—
144C22×Dic11—41no—
145C22×Dic11—41no—
146C22×Dic11—41no—
147C22×Dic11—41no—
148C22×Dic11—41no—
149C22×Dic11—41no—
150C22×Dic11—41no—
151C22×Dic11—41no—
152C22×Dic11—41no—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—22no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4C22⋊C412yes—
165C11×C4⋊C4C22⋊C412yes—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C42×C11—24no—
174C4⋊Dic11—22no—
175C4⋊Dic11—22no—
176C4⋊Dic11—41no—
177C4⋊Dic11—41no—
178C2×C11⋊C8—41no—
179C2×C11⋊C8—41no—
180C2×C11⋊C8—41no—
181C2×C11⋊C8—41no—
182C2×C11⋊C8—41no—
183C2×C11⋊C8—41no—
184C2×#539D1111yescharacteristic
185#1874—111no—
186#1872—111no—
187C2×#328—111no—
188C2×#327—111no—
189C2×#324—111no—
190#1441—111no—
191C23×C11—21no—
192C23×C11—21no—
193C23×C11—21no—
194C23×C11—21no—
195C23×C11—22no—
196C23×C11—41no—
197C23×C11—41no—
198C23×C11—41no—
199C23×C11—41no—
200C23×C11—41no—
201C23×C11—41no—
202C23×C11C2×C22⋊C411yescharacteristic
203C23×C11#12011yescharacteristic
204C23×C11#12011yescharacteristic
205C23×C11#13511yescharacteristic
206C23×C11#13511yescharacteristic
207C23×C11AGL(1,ℤ/8)11yescharacteristic
208C23×C11#13711yescharacteristic
209Q8×C11—42no—
210Q8×C11—81no—
211D4×C11—42no—
212D4×C11—42no—
213D4×C11—42no—
214D4×C11—42no—
215D4×C11—42no—
216D4×C11—81no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
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—42no—
245C2×C4×C11—81no—
246C2×C4×C11—84no—
247C2×C4×C11C2×C22⋊C411yescharacteristic
248C2×C4×C11C2×C22⋊C411yescharacteristic
249C2×C4×C11#12011yescharacteristic
250C2×C4×C11#12011yescharacteristic
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—42no—
257C2×Dic11—81no—
258C2×Dic11—81no—
259C2×Dic11—81no—
260C2×Dic11—81no—
261C2×Dic11—81no—
262C2×Dic11—81no—
263C2×Dic11—81no—
264C2×Dic11—81no—
265C11⋊C8—81no—
266C11⋊C8—81no—
267#539—22no—
268#539—22no—
269#539—22no—
270#539Dic1114yescomplemented
271C2×#126—21no—
272C2×#125—21no—
273C2×#123—21no—
274C2×#123—21no—
275C2×C22⋊Q8—21no—
276C2×C22⋊Q8C2×D1111yescharacteristic
277C2×#121C2×D1111yescharacteristic
278C2×C4×D4—21no—
279C22×C4⋊C4—111no—
280C22×C4⋊C4C2×D1111yescharacteristic
281C2×#103—221no—
282C2×#102—221no—
283C2×C22⋊C8—111no—
284C2×C22⋊C8—111no—
285C2×#95—111no—
286C2×#95—221no—
287C2×#95—221no—
288#340—221no—
289#340—221no—
290#328—222no—
291#327—222no—
292#324—222no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—21no—
299C22×C11—21no—
300C22×C11—21no—
301C22×C11—21no—
302C22×C11—21no—
303C22×C11—21no—
304C22×C11—21no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—81no—
309C22×C11—81no—
310C22×C11—81no—
311C22×C11—81no—
312C22×C11#37911yescharacteristic
313C22×C11#41611yescharacteristic
314C22×C11#41711yescharacteristic
315C22×C11#44911yescharacteristic
316C22×C11#44911yescharacteristic
317C22×C11#45211yescharacteristic
318C22×C11#45211yescharacteristic
319C22×C11#45411yescharacteristic
320C22×C11#45611yescharacteristic
321C22×C11B(4,𝔽2)11yescharacteristic
322C22×C11#45811yescharacteristic
323C4×C11—21no—
324C4×C11—21no—
325C4×C11—21no—
326C4×C11—21no—
327C4×C11—42no—
328C4×C11—42no—
329C4×C11—42no—
330C4×C11—42no—
331C4×C11—42no—
332Dic11—82no—
333Dic11—82no—
334C22×Q8C22⋊D1111yescharacteristic
335C22×D4—21no—
336C22×D4C22⋊D1111yescharacteristic
337C23×C4—21no—
338C23×C4—221no—
339C23×C4—221no—
340C23×C4C22⋊D1111yescharacteristic
341C23×C4C22⋊D1111yescharacteristic
342C23×C4C22×D1111yescharacteristic
343C22×C8—221no—
344C22×C8—221no—
345#126—24no—
346#126—24no—
347#125—24no—
348#125—24no—
349#123—24no—
350#123—24no—
351#123—24no—
352#123—24no—
353C22⋊Q8—24no—
354C22⋊Q8—24no—
355C22⋊Q8—21no—
356C22⋊Q8—21no—
357C22⋊Q8C2×Dic1112yes—
358C22⋊Q8C22⋊D1112yes—
359#121—21no—
360#121—21no—
361#121C2×Dic1112yes—
362#121C22⋊D1112yes—
363C4×D4—24no—
364C4×D4—24no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—442no—
376C2×C4⋊C4C2×Dic1112yes—
377C2×C4⋊C4C22⋊D1112yes—
378C2×C4⋊C4C22⋊D1111yescharacteristic
379C2×C4⋊C4C22⋊D1111yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C42—21no—
386#103—442no—
387#102—442no—
388C22⋊C8—221no—
389C22⋊C8—221no—
390C22⋊C8—221no—
391C22⋊C8—221no—
392#95—221no—
393#95—221no—
394#95—442no—
395#95—442no—
396C2×C11—21no—
397C2×C11—21no—
398C2×C11—21no—
399C2×C11—21no—
400C2×C11—82no—
401C2×C11#159711yescharacteristic
402C2×C11#160311yescharacteristic
403C2×C11#160911yescharacteristic
404C2×C11#161511yescharacteristic
405C2×C11#178811yescharacteristic
406C2×C11#179011yescharacteristic
407C2×C11#179311yescharacteristic
408C24—21no—
409C24C2×C22⋊D1111yescharacteristic
410C2×Q8—21no—
411C2×Q8—41no—
412C2×Q8—41no—
413C2×Q8C22⋊Dic1112yes—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—21no—
417C2×D4—41no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4C22⋊Dic1112yes—
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—24no—
435C22×C4—21no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—81no—
441C22×C4—81no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—441no—
445C22×C4—441no—
446C22×C4—441no—
447C22×C4—441no—
448C22×C4—441no—
449C22×C4—441no—
450C22×C4—441no—
451C22×C4—441no—
452C22×C4—441no—
453C22×C4—441no—
454C22×C4—441no—
455C22×C4—441no—
456C22×C4C22⋊Dic1112yes—
457C22×C4C22⋊Dic1112yes—
458C22×C4C22×Dic1111yescharacteristic
459C22×C4C2×C22⋊D1111yescharacteristic
460C22×C4C2×C22⋊D1111yescharacteristic
461C22×C4C2×C22⋊D1111yescharacteristic
462C22×C4C2×C22⋊D1111yescharacteristic
463C22×C4C2×C22⋊D1111yescharacteristic
464C2×C8—441no—
465C2×C8—441no—
466C2×C8—441no—
467C2×C8—441no—
468C2×C8—441no—
469C2×C8—441no—
470C4⋊C4—24no—
471C4⋊C4—24no—
472C4⋊C4—24no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—222no—
482C4⋊C4—222no—
483C4⋊C4—441no—
484C4⋊C4—441no—
485C4⋊C4C22⋊Dic1112yes—
486C4⋊C4C22⋊Dic1112yes—
487C22⋊C4—24no—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—22no—
491C22⋊C4—22no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C42—24no—
495C11#840711yescharacteristic, complemented, Sylow
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23#6700211yescharacteristic
508C23#6700311yescharacteristic
509C23#6700311yescharacteristic
510C23#6700411yescharacteristic
511C23C2×C22⋊Dic1111yescharacteristic
512C23#6700611yescharacteristic
513C23#6700611yescharacteristic
514Q8—42no—
515Q8—81no—
516D4—42no—
517D4—42no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—81no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—81no—
551C2×C4—84no—
552C2×C4—442no—
553C2×C4—442no—
554C2×C4—442no—
555C2×C4—442no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—881no—
559C2×C4—881no—
560C2×C4—881no—
561C2×C4—881no—
562C2×C4—881no—
563C2×C4—881no—
564C2×C4—881no—
565C2×C4—881no—
566C2×C4C2×C22⋊Dic1111yescharacteristic
567C2×C4C2×C22⋊Dic1111yescharacteristic
568C2×C4#6700611yescharacteristic
569C2×C4#6700611yescharacteristic
570C8—881no—
571C8—881no—
572C22—21no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—42no—
585C22—42no—
586C22—42no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22#1062284511yescharacteristic
592C22#1062284611yescharacteristic
593C22#1062285111yescharacteristic
594C22#1062285111yescharacteristic
595C22#1062285211yescharacteristic
596C22#1062285211yescharacteristic
597C22#1062285611yescharacteristic
598C22#1062285711yescharacteristic
599C22#1062285811yescharacteristic
600C22#1062285911yescharacteristic
601C22#1062286011yescharacteristic
602C4—21no—
603C4—21no—
604C4—21no—
605C4—21no—
606C4—42no—
607C4—42no—
608C4—42no—
609C4—42no—
610C4—42no—
611C4—882no—
612C4—882no—
613C2—21no—
614C2—21no—
615C2—21no—
616C2—21no—
617C2—82no—
618C2#1306754511yescharacteristic
619C2#1306757911yescharacteristic
620C2#1306761311yescharacteristic
621C2#1306764711yescharacteristic
622C2#1306855611yescharacteristic
623C2#1306856411yescharacteristic
624C2#1306857511yescharacteristic
subgroupG/H
centerC23#67006
commutatorC22×C4×C11C22×C4
FrattiniC23×C4C22×D11
FittingC2×C11×#539C2
socleC23×C11#120
prime radicalC2×C11×#121C22
cosocleC23×C4×C11C23
hypercenterC2×#539D11
hypocenterC11#8407
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
2. #13068924C2semidirect
3. C2×#10622176C2semidirect
5. C2×#10622166C2semidirect
6. #13066869C2semidirect
11. C11×#539C4semidirect
270. #539Dic11semidirect
495. C11#8407semidirect

Maximal subgroups

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

subgroupindex
#130689342
#130689242
C2×#106221762
C2×#106221752
C2×#106221662
#130668692
C2×C11×#5392
#840711