Finite Group Databasebeta

← #14823626

Subgroups — #14823626

Order 2816.

876 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×#10622680C211yesmaximal, characteristic
2C2×#10622639C211yesmaximal, characteristic, complemented
3#13072381C211yesmaximal, characteristic
4#13070001C211yesmaximal, characteristic, complemented
5#13069951C211yesmaximal, characteristic, complemented
6#13069931C211yesmaximal, characteristic, complemented
7#13069703C211yesmaximal, characteristic
8#13069473C211yesmaximal, characteristic, complemented
9#13069312C211yesmaximal, characteristic, complemented
10#13069309C211yesmaximal, characteristic, complemented
11#13069298C211yesmaximal, characteristic, complemented
12#13068971C211yesmaximal, characteristic, complemented
13#13068876C211yesmaximal, characteristic, complemented
14#13068485C211yesmaximal, characteristic, complemented
15C11×#2453C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×#66947—21no—
21C2×#66927C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#400—21no—
24C11×#398—21no—
25C11×#391C2211yescharacteristic
26C11×#391C2211yescharacteristic
27C11×#389—21no—
28C11×#389C2211yescharacteristic
29C11×#389C2211yescharacteristic
30C11×#387—21no—
31C4×C11×C4⋊C4C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34#10622680—24no—
35#10622639—24no—
36#10622604—21no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622552C2211yescharacteristic
46#10622552C2211yescharacteristic
47#10622552C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622285—21no—
54#10622278—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44—21no—
63C22×D44—21no—
64C22×D44C2311yescharacteristic
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C11×#125—22no—
68C11×#125—41no—
69C4×Q8×C11—22no—
70C4×Q8×C11—41no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×#4325—22no—
86C2×#4325—22no—
87C2×#4325—22no—
88C2×#4325—22no—
89C2×#4325—22no—
90C2×#4325—41no—
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105#66947—44no—
106#66927—22no—
107#66927—41no—
108C4×D44—22no—
109C4×D44—41no—
110C11×#95—21no—
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95D411yescharacteristic
117C11×#95D411yescharacteristic
118#66899—22no—
119#66899—22no—
120C11⋊#95—21no—
121#66873—22no—
122#66873—22no—
123#66873—22no—
124#66873—22no—
125#66873—22no—
126#66873D414yes—
127#66872—41no—
128#66871—22no—
129C4⋊(C11⋊C8)—22no—
130#66867—22no—
131#66867—22no—
132C4×C11⋊C8—22no—
133#26841—111nomaximal, Sylow
134C23×D11—21no—
135C23×D11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11#4112yes—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—21no—
155C2×D44—21no—
156C2×D44—21no—
157C2×D44—21no—
158C2×D44—21no—
159C2×D44—21no—
160C2×D44—21no—
161C2×D44—21no—
162C2×D44—21no—
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—42no—
167C2×D44—42no—
168C2×D44—42no—
169C2×D44—42no—
170C2×D44—81no—
171C2×D44—81no—
172C2×D44C2×D412yes—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—81no—
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⋊C4—42no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4C2×D412yes—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—42no—
196#4325—28no—
197#4325—44no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—42no—
201(C2×D11)⋊C4—42no—
202(C2×D11)⋊C4—81no—
203(C2×D11)⋊C4—81no—
204(C2×D11)⋊C4—81no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209Dic11⋊C4—42no—
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×#490—111no—
223C2×#440—111no—
224#2453D1111yescharacteristic, complemented
225#2445—111no—
226#2067—111no—
227#2059—111no—
228#2055—111no—
229#2014—111no—
230#1968—111no—
231#1936—111no—
232#1935—111no—
233#1934—111no—
234#1880—111no—
235#1864—111no—
236#1770—111no—
237C23×C11C22×D411yescharacteristic
238C22×D11—22no—
239C22×D11—41no—
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—41no—
255Q8×C11—41no—
256C2×C4×C11—21no—
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—22no—
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—41no—
284C2×C4×C11—41no—
285C2×C4×C11AGL(1,ℤ/8)12yes—
286C2×C4×C11C22×D411yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11H(5,𝔽2)11yescharacteristic
291C2×C4×C112−1+411yescharacteristic
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298D44—22no—
299D44—22no—
300D44—41no—
301D44—41no—
302D44—41no—
303D44—41no—
304D44—41no—
305D44—41no—
306D44—84no—
307D44—84no—
308C4×D11—84no—
309C11⋊C8—22no—
310C11⋊C8—22no—
311C11⋊C8—22no—
312C11⋊C8—41no—
313C22×SD16—111no—
314C22×SD16—111no—
315C2×#127—111no—
316C2×#125C2×D1111yescharacteristic
317C2×#123—221no—
318C2×C4×Q8C2×D1111yescharacteristic
319C2×C4×D4—111no—
320#490—224no—
321#440—224no—
322C2×#107—111no—
323C2×#106—111no—
324C2×C4⋊C8—111no—
325C2×#103—111no—
326C2×#103—111no—
327C2×#102—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#400—21no—
337#398—21no—
338#394—221no—
339#394—221no—
340#391C2×D1111yescharacteristic
341#391C2×D1111yescharacteristic
342#390—111no—
343#390—111no—
344#390—111no—
345#389—21no—
346#389—111no—
347#389C2×D1111yescharacteristic
348#389C2×D1111yescharacteristic
349#387—21no—
350#386—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#53211yescharacteristic
359C22×C11D4211yescharacteristic
360C22×C11#54811yescharacteristic
361C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
362C22×C11#57511yescharacteristic
363C22×C11#57711yescharacteristic
364C22×C11#57711yescharacteristic
365C2×D11—42no—
366C2×D11—42no—
367C2×D11—42no—
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—81no—
371C2×D11—81no—
372C2×D11—81no—
373C2×D11—81no—
374C2×D11—81no—
375C2×D11—81no—
376C2×D11—81no—
377C2×D11—81no—
378C2×D11—81no—
379C4×C11—22no—
380C4×C11—41no—
381C4×C11—42no—
382C4×C11—41no—
383C4×C11—41no—
384C4×C11—42no—
385C4×C11—41no—
386C4×C11—41no—
387C4×C11—81no—
388C4×C11—81no—
389C4×C11#52511yescharacteristic
390C4×C11#54211yescharacteristic
391C4×C11#54711yescharacteristic
392C4×C11#55111yescharacteristic
393Dic11—81no—
394Dic11—81no—
395C22×Q8C22×D1111yescharacteristic
396C22×D4—111no—
397C22×D4—111no—
398C22×D4—221no—
399C22×D4—221no—
400C23×C4—221no—
401C2×SD16—222no—
402C2×SD16—222no—
403C2×SD16—222no—
404C2×SD16—222no—
405C2×SD16—222no—
406C2×SD16—441no—
407C22×C8—111no—
408C22×C8—111no—
409C22×C8—111no—
410C22×C8—111no—
411#127—222no—
412#127—441no—
413#125—22no—
414#125—41no—
415#123—444no—
416C4×Q8—22no—
417C4×Q8—41no—
418C4×D4—222no—
419C4×D4—441no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4C22⋊D1111yescharacteristic
429C2×C4⋊C4C22⋊D1111yescharacteristic
430C2×C4⋊C4C22×D1111yescharacteristic
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
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×C22⋊C4—221no—
440C2×C42—21no—
441C2×C42C22×D1111yescharacteristic
442C2×C42C22×D1111yescharacteristic
443C2×C42C22×D1111yescharacteristic
444#107—222no—
445#106—441no—
446C4⋊C8—222no—
447#103—222no—
448#103—222no—
449#102—114no—
450#102—222no—
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—21no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—221no—
465#95C22⋊D1111yescharacteristic
466#95C22⋊D1111yescharacteristic
467C2×C11#246111yescharacteristic
468C2×C11#317411yescharacteristic
469C2×C11#318011yescharacteristic
470C2×C11#327211yescharacteristic
471C2×C11#327511yescharacteristic
472C2×C11#336811yescharacteristic
473C2×C11#337111yescharacteristic
474D11—82no—
475D11—161no—
476C24—221no—
477C24—221no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8#434312yes—
484C2×D4—112no—
485C2×D4—221no—
486C2×D4—221no—
487C2×D4—221no—
488C2×D4—221no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4—221no—
494C2×D4—221no—
495C2×D4—221no—
496C2×D4—442no—
497C2×D4—442no—
498C2×D4—442no—
499C2×D4—442no—
500C2×D4—881no—
501C2×D4—881no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
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—228no—
519SD16—444no—
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—42no—
543C4⋊C4—42no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—442no—
549C4⋊C4D4×D1112yes—
550C22⋊C4—442no—
551C22⋊C4—442no—
552C22⋊C4—442no—
553C22⋊C4—442no—
554C22⋊C4—881no—
555C22⋊C4—881no—
556C22⋊C4—881no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—42no—
564C11#2684111yescharacteristic, complemented, Sylow
565C23—222no—
566C23—441no—
567C23—441no—
568C23—441no—
569C23—441no—
570C23—441no—
571C23—441no—
572C23—441no—
573C23—441no—
574C23—441no—
575C23—441no—
576C23—441no—
577C23—441no—
578C23—441no—
579C23C22×C22⋊D1111yescharacteristic
580Q8—22no—
581Q8—22no—
582Q8—41no—
583Q8—41no—
584D4—222no—
585D4—222no—
586D4—441no—
587D4—441no—
588D4—441no—
589D4—441no—
590D4—441no—
591D4—441no—
592D4—884no—
593D4—884no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
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—21no—
612C2×C4—21no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—884no—
630C2×C4#6700212yes—
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—442no—
642C22—442no—
643C22—442no—
644C22—881no—
645C22—881no—
646C22—881no—
647C22—881no—
648C22—881no—
649C22—881no—
650C22—881no—
651C22—881no—
652C22—881no—
653C22—881no—
654C22—881no—
655C22D4×C22⋊D1111yescharacteristic
656C22#1062334811yescharacteristic
657C22C2×#6700211yescharacteristic
658C22#1062335311yescharacteristic
659C22#1062336311yescharacteristic
660C22#1062336811yescharacteristic
661C22#1062336811yescharacteristic
662C4—22no—
663C4—41no—
664C4—41no—
665C4—42no—
666C4—41no—
667C4—41no—
668C4—41no—
669C4—42no—
670C4—81no—
671C4—81no—
672C4—881no—
673C4—881no—
674C4#1062315811yescharacteristic
675C4#1062316211yescharacteristic
676C4#1062316811yescharacteristic
677C4#1062317111yescharacteristic
678C2—882no—
679C2—1761no—
680C2#1307259011yescharacteristic
681C2#1307924511yescharacteristic
682C2#1307931511yescharacteristic
683C2#1308021611yescharacteristic
684C2#1308024811yescharacteristic
685C2#1308134511yescharacteristic
686C2#1308138411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2453C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#2453D11
hypocenterC11#26841
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2453

Complements

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

NH ≅ G/Ntype
2. C2×#10622639C2semidirect
4. #13070001C2semidirect
5. #13069951C2semidirect
6. #13069931C2semidirect
8. #13069473C2semidirect
9. #13069312C2semidirect
10. #13069309C2semidirect
11. #13069298C2semidirect
12. #13068971C2semidirect
13. #13068876C2semidirect
14. #13068485C2semidirect
15. C11×#2453C2semidirect
224. #2453D11semidirect
564. C11#26841semidirect

Maximal subgroups

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

subgroupindex
C2×#106226802
C2×#106226392
#130723812
#130700012
#130699512
#130699312
#130697032
#130694732
#130693122
#130693092
#130692982
#130689712
#130688762
#130684852
C11×#24532
#2684111