Finite Group Databasebeta

← #14823641

Subgroups — #14823641

Order 2816.

882 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622702C211yesmaximal, characteristic, complemented
2C2×#10622627C211yesmaximal, characteristic
3#13072403C211yesmaximal, characteristic, complemented
4#13069994C211yesmaximal, characteristic, complemented
5#13069946C211yesmaximal, characteristic, complemented
6#13069926C211yesmaximal, characteristic
7#13069692C211yesmaximal, characteristic
8#13069469C211yesmaximal, characteristic, complemented
9#13069316C211yesmaximal, characteristic, complemented
10#13069305C211yesmaximal, characteristic, complemented
11#13069298C211yesmaximal, characteristic, complemented
12#13068950C211yesmaximal, characteristic, complemented
13#13068876C211yesmaximal, characteristic, complemented
14#13068485C211yesmaximal, characteristic, complemented
15C11×#2452C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C2×#66928C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#396—21no—
24C11×#393—21no—
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#385—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33#10622702—24no—
34#10622627—24no—
35#10622606—21no—
36#10622602—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66872C2211yescharacteristic
45#10622552C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622288—21no—
54#10622277—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×Dic22C2311yescharacteristic
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8—41no—
69C11×C22⋊Q8—44no—
70C4×D4×C11—22no—
71C4×D4×C11—41no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×#4324—22no—
89C2×#4324—22no—
90C2×#4324—41no—
91C2×#4323—22no—
92C2×#4323—22no—
93C2×#4323—22no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×Dic11⋊C4—21no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66928—22no—
107#66928—41no—
108C4×D44—22no—
109C4×D44—41no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95D411yescharacteristic
113C11×#95D411yescharacteristic
114#66896—22no—
115#66896—22no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121#66874—22no—
122#66874—22no—
123#66874—22no—
124#66873—22no—
125#66873—22no—
126#66873D414yes—
127#66872—22no—
128#66872—41no—
129C4⋊(C11⋊C8)—22no—
130#66867—22no—
131#66867—22no—
132C4×C11⋊C8—22no—
133#26842—111nomaximal, Sylow
134C24×C11—21no—
135C23×D11—21no—
136C2×Q8×C11—42no—
137C2×Q8×C11—42no—
138C2×Q8×C11—81no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11#4112yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—81no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2411yescharacteristic
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44C2×D412yes—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—81no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—41no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4—42no—
186C11×C4⋊C4C2×D412yes—
187C11×C22⋊C4—42no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—81no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
197C42×C11—21no—
198#4324—44no—
199#4323—28no—
200(C2×D11)⋊C4—42no—
201(C2×D11)⋊C4—42no—
202(C2×D11)⋊C4—42no—
203(C2×D11)⋊C4—42no—
204(C2×D11)⋊C4—81no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209Dic11⋊C4—81no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8C2×D412yes—
220C2×C11⋊C8#4112yes—
221C2×C11⋊C8#4112yes—
222C2×#489—111no—
223C2×#442—111no—
224#2452D1111yescharacteristic, complemented
225#2447—111no—
226#2066—111no—
227#2058—111no—
228#2054—111no—
229#2012—111no—
230#1968—111no—
231#1936—111no—
232#1935—111no—
233#1934—111no—
234#1877—111no—
235#1864—111no—
236#1770—111no—
237C23×C11—22no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11C22×D411yescharacteristic
245C22×D11—22no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252Q8×C11—84no—
253D4×C11—22no—
254D4×C11—22no—
255D4×C11—41no—
256D4×C11—41no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—22no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—84no—
284C2×C4×C11AGL(1,ℤ/8)12yes—
285C2×C4×C11C22×D411yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11H(5,𝔽2)11yescharacteristic
290C2×C4×C112−1+411yescharacteristic
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300D44—22no—
301D44—22no—
302D44—41no—
303D44—41no—
304C4×D11—84no—
305Dic22—41no—
306Dic22—41no—
307Dic22—41no—
308Dic22—41no—
309C11⋊C8—22no—
310C11⋊C8—22no—
311C11⋊C8—22no—
312C11⋊C8—41no—
313C22×SD16—111no—
314C22×D8—111no—
315C2×C4⋊Q8C2×D1111yescharacteristic
316C2×#124—111no—
317C2×C22⋊Q8—21no—
318C2×C4×D4—111no—
319C2×C4×D4C2×D1111yescharacteristic
320#489—224no—
321#442—224no—
322C2×#106—111no—
323C2×#106—111no—
324C2×C4⋊C8—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#103—111no—
328C2×#102—111no—
329C2×#102—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×#97—111no—
334C2×#97—111no—
335C2×C4×C8—111no—
336#397—221no—
337#397—221no—
338#396—21no—
339#393—21no—
340#391—111no—
341#391—111no—
342#390—111no—
343#390C2×D1111yescharacteristic
344#390C2×D1111yescharacteristic
345#389—111no—
346#389C2×D1111yescharacteristic
347#389C2×D1111yescharacteristic
348#385—21no—
349#385—221no—
350#381—221no—
351C4×C4⋊C4C2×D1111yescharacteristic
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#336—111no—
357#336—111no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11#53211yescharacteristic
366C22×C11D4211yescharacteristic
367C22×C11#54811yescharacteristic
368C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C11#57511yescharacteristic
370C22×C11#57711yescharacteristic
371C22×C11#57711yescharacteristic
372C2×D11—42no—
373C2×D11—42no—
374C2×D11—42no—
375C2×D11—81no—
376C2×D11—81no—
377C2×D11—81no—
378C2×D11—81no—
379C4×C11—22no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—41no—
383C4×C11—42no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11#52511yescharacteristic
389C4×C11#54211yescharacteristic
390C4×C11#54711yescharacteristic
391C4×C11#55111yescharacteristic
392Dic11—81no—
393Dic11—81no—
394Dic11—81no—
395C22×Q8—21no—
396C22×Q8—111no—
397C22×D4—111no—
398C22×D4C22×D1111yescharacteristic
399C23×C4—21no—
400C23×C4—221no—
401C2×SD16—222no—
402C2×SD16—222no—
403C2×SD16—441no—
404C2×D8—222no—
405C2×D8—222no—
406C2×D8—222no—
407C22×C8—111no—
408C22×C8—111no—
409C22×C8—111no—
410C22×C8—111no—
411C4⋊Q8—22no—
412C4⋊Q8—41no—
413#124—222no—
414#124—441no—
415C22⋊Q8—44no—
416C4×D4—22no—
417C4×D4—41no—
418C4×D4—222no—
419C4×D4—441no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4C22⋊D1111yescharacteristic
427C2×C4⋊C4C22⋊D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C42C22×D1111yescharacteristic
442C2×C42C22×D1111yescharacteristic
443C2×C42C22×D1111yescharacteristic
444#106—222no—
445#106—441no—
446C4⋊C8—222no—
447#103—222no—
448#103—222no—
449#103—222no—
450#102—114no—
451#102—222no—
452#102—222no—
453#102—222no—
454#102—222no—
455#97—222no—
456#97—222no—
457C4×C8—222no—
458#95—21no—
459#95—21no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95C22⋊D1111yescharacteristic
466#95C22⋊D1111yescharacteristic
467C2×C11—82no—
468C2×C11#246111yescharacteristic
469C2×C11#317311yescharacteristic
470C2×C11#318011yescharacteristic
471C2×C11#327211yescharacteristic
472C2×C11#327511yescharacteristic
473C2×C11#337311yescharacteristic
474C2×C11#337611yescharacteristic
475D11—82no—
476C24—21no—
477C24—221no—
478C2×Q8—42no—
479C2×Q8—42no—
480C2×Q8—81no—
481C2×Q8—221no—
482C2×Q8—221no—
483C2×Q8—221no—
484C2×Q8—221no—
485C2×Q8—221no—
486C2×Q8—221no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—112no—
493C2×D4—221no—
494C2×D4—221no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4#434312yes—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—81no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—442no—
509C22×C4—442no—
510C22×C4—881no—
511C22×C4C2×C22⋊D1111yescharacteristic
512C22×C4C2×C22⋊D1111yescharacteristic
513C22×C4C2×C22⋊D1111yescharacteristic
514C22×C4C2×C22⋊D1111yescharacteristic
515C22×C4C2×C22⋊D1111yescharacteristic
516C22×C4C2×C22⋊D1111yescharacteristic
517C22×C4C23×D1111yescharacteristic
518SD16—444no—
519D8—228no—
520C2×C8—112no—
521C2×C8—112no—
522C2×C8—112no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C4⋊C4—22no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—41no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—881no—
547C4⋊C4D4×D1112yes—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—81no—
553C22⋊C4—442no—
554C22⋊C4—442no—
555C22⋊C4—442no—
556C22⋊C4—442no—
557C22⋊C4—881no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C11#2684211yescharacteristic, complemented, Sylow
565C23—22no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—222no—
573C23—441no—
574C23—441no—
575C23—441no—
576C23—441no—
577C23—441no—
578C23—441no—
579C23C22×C22⋊D1111yescharacteristic
580Q8—84no—
581Q8—441no—
582Q8—441no—
583Q8—441no—
584Q8—441no—
585D4—22no—
586D4—22no—
587D4—41no—
588D4—41no—
589D4—222no—
590D4—222no—
591D4—441no—
592D4—441no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—84no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—884no—
630C2×C4#6698512yes—
631C2×C4C2×D4×D1111yescharacteristic
632C2×C4#6703711yescharacteristic
633C2×C4C2×#434311yescharacteristic
634C2×C4#6704011yescharacteristic
635C2×C4#41×D1111yescharacteristic
636C2×C4#41×D1111yescharacteristic
637C8—222no—
638C8—222no—
639C8—222no—
640C8—441no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—442no—
649C22—442no—
650C22—442no—
651C22—881no—
652C22—881no—
653C22—881no—
654C22—881no—
655C22C2×#6698511yescharacteristic
656C22D4×C22⋊D1111yescharacteristic
657C22#1062334811yescharacteristic
658C22#1062335311yescharacteristic
659C22#1062336311yescharacteristic
660C22#1062336711yescharacteristic
661C22#1062336811yescharacteristic
662C4—22no—
663C4—41no—
664C4—41no—
665C4—42no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—81no—
670C4—81no—
671C4—881no—
672C4—881no—
673C4—881no—
674C4#1062315811yescharacteristic
675C4#1062316211yescharacteristic
676C4#1062316811yescharacteristic
677C4#1062317111yescharacteristic
678C2—82no—
679C2—882no—
680C2#1307259011yescharacteristic
681C2#1307922711yescharacteristic
682C2#1307930811yescharacteristic
683C2#1308021211yescharacteristic
684C2#1308024811yescharacteristic
685C2#1308140811yescharacteristic
686C2#1308144311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2452C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenter#2452D11
hypocenterC11#26842
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2452

Complements

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

NH ≅ G/Ntype
1. C2×#10622702C2semidirect
3. #13072403C2semidirect
4. #13069994C2semidirect
5. #13069946C2semidirect
8. #13069469C2semidirect
9. #13069316C2semidirect
10. #13069305C2semidirect
11. #13069298C2semidirect
12. #13068950C2semidirect
13. #13068876C2semidirect
14. #13068485C2semidirect
15. C11×#2452C2semidirect
224. #2452D11semidirect
564. C11#26842semidirect

Maximal subgroups

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

subgroupindex
C2×#106227022
C2×#106226272
#130724032
#130699942
#130699462
#130699262
#130696922
#130694692
#130693162
#130693052
#130692982
#130689502
#130688762
#130684852
C11×#24522
#2684211