Finite Group Databasebeta

← #14813708

Subgroups — #14813708

Order 2816.

854 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622427C211yesmaximal, characteristic, complemented
2C2×#10622474C211yesmaximal, characteristic, complemented
3#13072070C211yesmaximal, characteristic
4#13071567C211yesmaximal, characteristic
5#13070093C211yesmaximal, characteristic, complemented
6#13070050C211yesmaximal, characteristic, complemented
7#13069810C211yesmaximal, characteristic, complemented
8#13069254C211yesmaximal, characteristic, complemented
9#13069209C211yesmaximal, characteristic, complemented
10#13069046C211yesmaximal, characteristic, complemented
11#13068925C211yesmaximal, characteristic, complemented
12#13068912C211yesmaximal, characteristic
13#13068814C211yesmaximal, characteristic, complemented
14#13068807C211yesmaximal, characteristic, complemented
15C11×#2096C211yesmaximal, characteristic, complemented
16C2×#66999C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C22×#4313C2211yescharacteristic
19C2×#66945C2211yescharacteristic
20C2×#66945C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C2×C11×#106C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#103C2211yescharacteristic
27C11×#391C2211yescharacteristic
28C11×#384C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35#10622603—21no—
36#10622603—21no—
37#10622601—21no—
38#10622600C2211yescharacteristic
39#10622600C2211yescharacteristic
40#10622600C2211yescharacteristic
41C4⋊C4×Dic11—21no—
42C2×#66872C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45C4×C4⋊Dic11C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622474—24no—
48#10622427—24no—
49#10622289—21no—
50#10622280—21no—
51#10622278—21no—
52#10622270—21no—
53C11×#336C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44D411yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11C2311yescharacteristic
65C22×C4×D11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74#66999—22no—
75#66999—22no—
76#66999—22no—
77#66999—41no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4D411yescharacteristic
86C2×(C2×D11)⋊C4D411yescharacteristic
87C2×C4⋊Dic11D411yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×#4313—22no—
102C2×#4313—22no—
103C2×#4313—22no—
104#66945—22no—
105#66945—22no—
106#66945—41no—
107#66945—41no—
108C4⋊C4×D11—22no—
109C4⋊C4×D11—41no—
110C4×D44—22no—
111C4×D44—22no—
112C11×#106—22no—
113C11×#106—41no—
114C11×#103—22no—
115C11×#103—41no—
116C11×#95—21no—
117C11×#95—21no—
118#66899—22no—
119#66899—22no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125(C2×D11)⋊C8—22no—
126(C2×D11)⋊C8—22no—
127(C2×D11)⋊C8—22no—
128#66882D414yescomplemented
129#66872—22no—
130#66872—22no—
131#66871—22no—
132#26155—111nomaximal, Sylow
133C23×D11C2×D411yescharacteristic
134C23×D11C2×D411yescharacteristic
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—41no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—42no—
168C2×C4×D11—42no—
169C2×C4×D11—81no—
170C2×C4×D11#4112yes—
171C2×C4×D11#4112yes—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11C2×D412yes—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—42no—
185C11×C4⋊C4—81no—
186C42×C11—21no—
187C42×C11—21no—
188(C2×D11)⋊C4—22no—
189(C2×D11)⋊C4—22no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—81no—
195(C2×D11)⋊C4—81no—
196(C2×D11)⋊C4—81no—
197C4⋊Dic11—22no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11C2×D412yes—
205C4⋊Dic11C2×D412yes—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209Dic11⋊C4—81no—
210C4×Dic11—42no—
211C4×Dic11—42no—
212C4×Dic11—42no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8#4112yes—
219#4313—28no—
220C2×#485—111no—
221C2×#428—111no—
222#2417—111no—
223#2354—111no—
224#2096D1111yescharacteristic, complemented
225#2084—111no—
226#2077—111no—
227#2035—111no—
228#1928—111no—
229#1921—111no—
230#1894—111no—
231#1873—111no—
232#1870—111no—
233#1854—111no—
234#1853—111no—
235C23×C11C22×D411yescharacteristic
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11—21no—
249C22×D11#12312yes—
250Q8×C11—41no—
251Q8×C11—41no—
252Q8×C11—41no—
253Q8×C11—41no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11#13712yes—
272C2×C4×C11C22×D411yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11C2×#4111yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11H(5,𝔽2)11yescharacteristic
277C2×C4×C112−1+411yescharacteristic
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—21no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11#12312yes—
296D44—44no—
297C4×D11—22no—
298C4×D11—22no—
299C4×D11—22no—
300C4×D11—22no—
301C4×D11—41no—
302C4×D11—41no—
303C4×D11—41no—
304C4×D11—41no—
305C4×D11—84no—
306C8×C11—22no—
307C8×C11—41no—
308C11⋊C8—22no—
309C11⋊C8—41no—
310C22×M16—111no—
311C2×C22⋊Q8—111no—
312C2×C22⋊Q8—111no—
313C2×C4×D4—111no—
314C2×#117—111no—
315C2×#117—111no—
316C22×C4⋊C4—111no—
317#485—224no—
318#428—224no—
319C2×#107—111no—
320C2×#107—111no—
321C2×#106—111no—
322C2×#106—111no—
323C2×#106C2×D1111yescharacteristic
324C2×#106C2×D1111yescharacteristic
325C2×#103—111no—
326C2×#103—111no—
327C2×#103C2×D1111yescharacteristic
328C2×#103C2×D1111yescharacteristic
329C2×C22⋊C8—111no—
330C2×C22⋊C8—111no—
331C2×C22⋊C8—111no—
332#398—221no—
333#396—221no—
334#391C2×D1111yescharacteristic
335#390—221no—
336#389—111no—
337#388—221no—
338#388—221no—
339#386—221no—
340#384C2×D1111yescharacteristic
341#380—111no—
342#380—111no—
343#380—111no—
344#380—221no—
345C4×C4⋊C4—111no—
346C4×C4⋊C4—221no—
347#340—111no—
348#340—111no—
349#340—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#336—111no—
354#336C2×D1111yescharacteristic
355C22×C11C2×#12311yescharacteristic
356C22×C11D4211yescharacteristic
357C22×C11#54711yescharacteristic
358C22×C11C2×#13711yescharacteristic
359C22×C11#57511yescharacteristic
360C22×C11#57711yescharacteristic
361C22×C11#57711yescharacteristic
362C2×D11—22no—
363C2×D11—22no—
364C2×D11—22no—
365C2×D11—41no—
366C2×D11—41no—
367C2×D11—41no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—41no—
373C2×D11—41no—
374C2×D11—41no—
375C2×D11—41no—
376C4×C11—22no—
377C4×C11—41no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11—81no—
381C4×C11—81no—
382C4×C11#52511yescharacteristic
383C4×C11#53911yescharacteristic
384C4×C11#54811yescharacteristic
385C4×C11#55311yescharacteristic
386Dic11—22no—
387Dic11—41no—
388Dic11—42no—
389Dic11—42no—
390Dic11—81no—
391Dic11—81no—
392C22×Q8C22×D1111yescharacteristic
393C22×D4—111no—
394C23×C4—111no—
395C23×C4—111no—
396C23×C4—221no—
397C2×M16—222no—
398C2×M16—222no—
399C2×M16—222no—
400C22×C8—111no—
401C22×C8—111no—
402C22×C8C22×D1111yescharacteristic
403C22×C8C22×D1111yescharacteristic
404C22⋊Q8—222no—
405C22⋊Q8—222no—
406C22⋊Q8—222no—
407C22⋊Q8—441no—
408C4×D4—222no—
409C4×D4—222no—
410#117—222no—
411#117—222no—
412#117—441no—
413#117—441no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—222no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—441no—
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C22⋊C4—111no—
431C2×C22⋊C4—111no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4—221no—
436C2×C22⋊C4—221no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C42—221no—
440C2×C42—221no—
441C2×C42—221no—
442C2×C42C22×D1111yescharacteristic
443#107—114no—
444#107—222no—
445#106—22no—
446#106—41no—
447#106—222no—
448#106—222no—
449#103—22no—
450#103—41no—
451#103—222no—
452#103—222no—
453C22⋊C8—222no—
454C22⋊C8—222no—
455C22⋊C8—222no—
456#95—21no—
457#95—21no—
458#95—221no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463C2×C11#244311yescharacteristic
464C2×C11#309511yescharacteristic
465C2×C11#309911yescharacteristic
466C2×C11#326711yescharacteristic
467C2×C11#327811yescharacteristic
468C2×C11#334811yescharacteristic
469C2×C11#335611yescharacteristic
470D11—42no—
471D11—81no—
472C24—111no—
473C24—111no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×D4—222no—
481C2×D4—222no—
482C2×D4—441no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—111no—
488C22×C4—112no—
489C22×C4—112no—
490C22×C4—111no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—442no—
506C22×C4—442no—
507C22×C4—881no—
508C22×C4D4×D1111yescharacteristic
509C22×C4D4×D1111yescharacteristic
510C22×C4C23×D1111yescharacteristic
511M16—228no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—112no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8D4×D1112yes—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—42no—
531C4⋊C4—81no—
532C4⋊C4—112no—
533C4⋊C4—112no—
534C4⋊C4—222no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—442no—
542C4⋊C4—442no—
543C4⋊C4—442no—
544C4⋊C4—881no—
545C22⋊C4—222no—
546C22⋊C4—222no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C22⋊C4—442no—
551C22⋊C4—881no—
552C22⋊C4—881no—
553C22⋊C4—881no—
554C42—21no—
555C42—21no—
556C42—442no—
557C42—442no—
558C42—442no—
559C11#2615511yescharacteristic, complemented, Sylow
560C23—112no—
561C23—221no—
562C23—221no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23—221no—
569C23—221no—
570C23—221no—
571C23—221no—
572C23—221no—
573C23—221no—
574C23C2×D4×D1111yescharacteristic
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579D4—444no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—112no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—222no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—221no—
606C2×C4—222no—
607C2×C4—221no—
608C2×C4—221no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—884no—
624C2×C4#6696812yes—
625C2×C4C2×D4×D1111yescharacteristic
626C2×C4#6703711yescharacteristic
627C2×C4#6704011yescharacteristic
628C2×C4#41×D1111yescharacteristic
629C2×C4#41×D1111yescharacteristic
630C2×C4#41×D1111yescharacteristic
631C8—22no—
632C8—41no—
633C8—222no—
634C8—441no—
635C22—222no—
636C22—222no—
637C22—222no—
638C22—441no—
639C22—441no—
640C22—441no—
641C22—441no—
642C22—441no—
643C22—441no—
644C22—441no—
645C22—441no—
646C22—441no—
647C22—441no—
648C22—441no—
649C22#1062316211yescharacteristic
650C22D11×#12311yescharacteristic
651C22#1062324811yescharacteristic
652C22C2×#6696811yescharacteristic
653C22#1062329311yescharacteristic
654C22#1062330811yescharacteristic
655C22#1062330911yescharacteristic
656C4—22no—
657C4—41no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4—222no—
663C4—442no—
664C4—442no—
665C4—441no—
666C4—881no—
667C4—881no—
668C4#1062316411yescharacteristic
669C4#1062316911yescharacteristic
670C4#1062318711yescharacteristic
671C4#1062319211yescharacteristic
672C2—442no—
673C2—881no—
674C2#1307235411yescharacteristic
675C2#1307855911yescharacteristic
676C2#1307860011yescharacteristic
677C2#1308014011yescharacteristic
678C2#1308028111yescharacteristic
679C2#1308113811yescharacteristic
680C2#1308122811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2096C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenter#2096D11
hypocenterC11#26155
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2096

Complements

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

NH ≅ G/Ntype
1. C2×#10622427C2semidirect
2. C2×#10622474C2semidirect
5. #13070093C2semidirect
6. #13070050C2semidirect
7. #13069810C2semidirect
8. #13069254C2semidirect
9. #13069209C2semidirect
10. #13069046C2semidirect
11. #13068925C2semidirect
13. #13068814C2semidirect
14. #13068807C2semidirect
15. C11×#2096C2semidirect
128. #66882D4semidirect
224. #2096D11semidirect
559. C11#26155semidirect

Maximal subgroups

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

subgroupindex
C2×#106224272
C2×#106224742
#130720702
#130715672
#130700932
#130700502
#130698102
#130692542
#130692092
#130690462
#130689252
#130689122
#130688142
#130688072
C11×#20962
#2615511