Finite Group Databasebeta

← #14823618

Subgroups — #14823618

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×#10622684C211yesmaximal, characteristic
2C2×#10622631C211yesmaximal, characteristic, complemented
3#13072477C211yesmaximal, characteristic, complemented
4#13070004C211yesmaximal, characteristic, complemented
5#13069954C211yesmaximal, characteristic, complemented
6#13069933C211yesmaximal, characteristic, complemented
7#13069704C211yesmaximal, characteristic
8#13069469C211yesmaximal, characteristic, complemented
9#13069316C211yesmaximal, characteristic, complemented
10#13069305C211yesmaximal, characteristic, complemented
11#13069302C211yesmaximal, characteristic, complemented
12#13068974C211yesmaximal, characteristic, complemented
13#13068877C211yesmaximal, characteristic, complemented
14#13068485C211yesmaximal, characteristic, complemented
15C11×#2445C211yesmaximal, characteristic
16C2×C11×#127C2211yescharacteristic
17C2×C11×#123—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C2×#66923C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#394—21no—
24C11×#394—21no—
25C11×#390C2211yescharacteristic
26C11×#390C2211yescharacteristic
27C11×#390C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#386—21no—
30C4×C11×C4⋊C4C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37#10622684—24no—
38#10622631—24no—
39#10622593—21no—
40#10622585—21no—
41C2×#66874C2211yescharacteristic
42C2×#66874C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44C2×#66871C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622541C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×#66867C2211yescharacteristic
51C2×#66867C2211yescharacteristic
52C2×C4×C11⋊C8C2211yescharacteristic
53#10622271—21no—
54#10622265—21no—
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C22×Dic22C2311yescharacteristic
67C11×#127—22no—
68C11×#127—41no—
69C11×#123—44no—
70C4×D4×C11—22no—
71C4×D4×C11—41no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×#4324—22no—
88C2×#4324—22no—
89C2×#4324—22no—
90C2×#4324—22no—
91C2×#4324—22no—
92C2×#4324—41no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—21no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106#66923—22no—
107#66923—41no—
108C4×Dic22—22no—
109C4×Dic22—41no—
110C11×#95—21no—
111C11×#95D411yescharacteristic
112C11×#95D411yescharacteristic
113#66896—22no—
114#66896—22no—
115#66896—22no—
116#66896—22no—
117#66896—22no—
118#66896D414yes—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125#66874—22no—
126#66874—22no—
127#66872—41no—
128#66871—22no—
129C4⋊(C11⋊C8)—22no—
130#66867—22no—
131#66867—22no—
132C4×C11⋊C8—22no—
133#26841—111nomaximal, Sylow
134C24×C11—21no—
135C24×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—42no—
148C2×D4×C11—42no—
149C2×D4×C11—42no—
150C2×D4×C11—42no—
151C2×D4×C11—81no—
152C2×D4×C11—81no—
153C2×D4×C11C2×D412yes—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—81no—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2411yescharacteristic
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22#4112yes—
176C11×C4⋊C4—22no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—41no—
182C11×C4⋊C4—42no—
183C11×C22⋊C4—42no—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—42no—
187C11×C22⋊C4—81no—
188C11×C22⋊C4—81no—
189C11×C22⋊C4—81no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196#4324—28no—
197#4324—44no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11C2×D412yes—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209C4×Dic11—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#2453—111no—
225#2445D1111yescharacteristic
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×C11—22no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11—41no—
244C23×C11—41no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11C22×D411yescharacteristic
252D4×C11—22no—
253D4×C11—22no—
254D4×C11—41no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11—41no—
259D4×C11—41no—
260D4×C11—84no—
261D4×C11—84no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
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—21no—
276C2×C4×C11—21no—
277C2×C4×C11—21no—
278C2×C4×C11—21no—
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×C11—84no—
286C2×C4×C11AGL(1,ℤ/8)12yes—
287C2×C4×C11C22×D411yescharacteristic
288C2×C4×C11C2×#4111yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11H(5,𝔽2)11yescharacteristic
292C2×C4×C112−1+411yescharacteristic
293C2×Dic11—22no—
294C2×Dic11—22no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305Dic22—22no—
306Dic22—22no—
307Dic22—41no—
308Dic22—41no—
309C11⋊C8—22no—
310C11⋊C8—22no—
311C11⋊C8—22no—
312C11⋊C8—41no—
313C22×SD16—111no—
314C22×SD16—111no—
315C2×#127C2×D1111yescharacteristic
316C2×#125—111no—
317C2×#123—21no—
318C2×C4×Q8—111no—
319C2×C4×D4C2×D1111yescharacteristic
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—221no—
337#398—221no—
338#394—21no—
339#394—21no—
340#391—111no—
341#391—111no—
342#390C2×D1111yescharacteristic
343#390C2×D1111yescharacteristic
344#390C2×D1111yescharacteristic
345#389—111no—
346#389—111no—
347#389—221no—
348#389C2×D1111yescharacteristic
349#387—221no—
350#386—21no—
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—81no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11#53211yescharacteristic
373C22×C11D4211yescharacteristic
374C22×C11#54811yescharacteristic
375C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
376C22×C11#57511yescharacteristic
377C22×C11#57711yescharacteristic
378C22×C11#57711yescharacteristic
379C4×C11—22no—
380C4×C11—41no—
381C4×C11—41no—
382C4×C11—41no—
383C4×C11—41no—
384C4×C11—41no—
385C4×C11—81no—
386C4×C11—81no—
387C4×C11#52511yescharacteristic
388C4×C11#54211yescharacteristic
389C4×C11#54711yescharacteristic
390C4×C11#55111yescharacteristic
391Dic11—42no—
392Dic11—42no—
393Dic11—81no—
394Dic11—81no—
395C22×Q8—111no—
396C22×D4—21no—
397C22×D4—21no—
398C22×D4C22×D1111yescharacteristic
399C22×D4C22×D1111yescharacteristic
400C23×C4—21no—
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—22no—
412#127—41no—
413#125—222no—
414#125—441no—
415#123—44no—
416C4×Q8—222no—
417C4×Q8—441no—
418C4×D4—22no—
419C4×D4—41no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—221no—
425C2×C4⋊C4—221no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4C22⋊D1111yescharacteristic
430C2×C4⋊C4C22⋊D1111yescharacteristic
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C42—221no—
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—221no—
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—161no—
469C2×C11#246111yescharacteristic
470C2×C11#317411yescharacteristic
471C2×C11#318011yescharacteristic
472C2×C11#327211yescharacteristic
473C2×C11#327511yescharacteristic
474C2×C11#336811yescharacteristic
475C2×C11#337111yescharacteristic
476C24—21no—
477C24—21no—
478C2×Q8—112no—
479C2×Q8—221no—
480C2×Q8—221no—
481C2×Q8—221no—
482C2×Q8—221no—
483C2×Q8—221no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—42no—
496C2×D4—42no—
497C2×D4—42no—
498C2×D4—42no—
499C2×D4—81no—
500C2×D4—81no—
501C2×D4D4×D1112yes—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—81no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
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—41no—
538C4⋊C4—42no—
539C4⋊C4—112no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—442no—
546C4⋊C4—442no—
547C4⋊C4—442no—
548C4⋊C4—442no—
549C4⋊C4—442no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—42no—
553C22⋊C4—42no—
554C22⋊C4—81no—
555C22⋊C4—81no—
556C22⋊C4—81no—
557C42—21no—
558C42—21no—
559C42—21no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—442no—
564C11#2684111yescharacteristic, complemented, Sylow
565C23—22no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23—41no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23C22×C22⋊D1111yescharacteristic
580Q8—222no—
581Q8—222no—
582Q8—441no—
583Q8—441no—
584D4—22no—
585D4—22no—
586D4—41no—
587D4—41no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—41no—
592D4—84no—
593D4—84no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
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—84no—
618C2×C4—222no—
619C2×C4—222no—
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—441no—
630C2×C4#6698512yes—
631C2×C4C2×D4×D1111yescharacteristic
632C2×C4#6703711yescharacteristic
633C2×C4#41×D1111yescharacteristic
634C2×C4#41×D1111yescharacteristic
635C2×C4#41×D1111yescharacteristic
636C2×C4#6704311yescharacteristic
637C8—222no—
638C8—222no—
639C8—222no—
640C8—441no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22C2×#6698511yescharacteristic
656C22D4×C22⋊D1111yescharacteristic
657C22#1062335311yescharacteristic
658C22#1062336211yescharacteristic
659C22#1062336311yescharacteristic
660C22#1062336711yescharacteristic
661C22#1062336711yescharacteristic
662C4—22no—
663C4—41no—
664C4—41no—
665C4—41no—
666C4—41no—
667C4—41no—
668C4—81no—
669C4—81no—
670C4—442no—
671C4—442no—
672C4—881no—
673C4—881no—
674C4#1062318611yescharacteristic
675C4#1062318711yescharacteristic
676C4#1062319011yescharacteristic
677C4#1062319311yescharacteristic
678C2—82no—
679C2—161no—
680C2#1307258211yescharacteristic
681C2#1307923811yescharacteristic
682C2#1307930811yescharacteristic
683C2#1308021211yescharacteristic
684C2#1308024311yescharacteristic
685C2#1308134111yescharacteristic
686C2#1308137811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2445C2
socleC23×C11C22×D4
prime radicalC2×C11×#127C22
hypercenter#2445D11
hypocenterC11#26841
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2445

Complements

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

NH ≅ G/Ntype
2. C2×#10622631C2semidirect
3. #13072477C2semidirect
4. #13070004C2semidirect
5. #13069954C2semidirect
6. #13069933C2semidirect
8. #13069469C2semidirect
9. #13069316C2semidirect
10. #13069305C2semidirect
11. #13069302C2semidirect
12. #13068974C2semidirect
13. #13068877C2semidirect
14. #13068485C2semidirect
564. C11#26841semidirect

Maximal subgroups

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

subgroupindex
C2×#106226842
C2×#106226312
#130724772
#130700042
#130699542
#130699332
#130697042
#130694692
#130693162
#130693052
#130693022
#130689742
#130688772
#130684852
C11×#24452
#2684111