Finite Group Databasebeta

← #14813598

Subgroups — #14813598

Order 2816.

904 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622335C211yesmaximal, characteristic, complemented
2C2×#10622734C211yesmaximal, characteristic, complemented
3#13072045C211yesmaximal, characteristic
4D4×C4⋊Dic11C211yesmaximal, characteristic
5#13070158C211yesmaximal, characteristic, complemented
6#13070089C211yesmaximal, characteristic, complemented
7#13070049C211yesmaximal, characteristic, complemented
8#13069820C211yesmaximal, characteristic, complemented
9#13069251C211yesmaximal, characteristic, complemented
10#13069188C211yesmaximal, characteristic, complemented
11#13069049C211yesmaximal, characteristic, complemented
12#13068921C211yesmaximal, characteristic, complemented
13#13068817C211yesmaximal, characteristic, complemented
14#13068811C211yesmaximal, characteristic, complemented
15C11×#1870C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×D4×Dic11—21no—
19C2×#66979C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C2×C11×C22⋊C8C2211yescharacteristic
27#10622835—21no—
28#10622825C2211yescharacteristic
29#10622825C2211yescharacteristic
30#10622825C2211yescharacteristic
31#10622734—24no—
32C2×#66882C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66881C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42#10622598—21no—
43#10622585—21no—
44#10622565—21no—
45#10622563—21no—
46#10622563—21no—
47#10622558—21no—
48#10622548C2211yescharacteristic
49C4×C4⋊Dic11C2211yescharacteristic
50#10622542C2211yescharacteristic
51#10622541C2211yescharacteristic
52#10622335—24no—
53C11×#336C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C22×D4×C11D411yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11—21no—
65C23×Dic11—21no—
66C22×Dic22C2311yescharacteristic
67C2×C11×M16—22no—
68C2×C11×M16—22no—
69C2×C11×M16—22no—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C4×D4×C11—22no—
75C4×D4×C11—22no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C22⋊C4D411yescharacteristic
78C2×C11×C22⋊C4D411yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86D4×Dic11—44no—
87#66979—22no—
88#66979—41no—
89C2×C4⋊Dic11—22no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—41no—
96C2×C4⋊Dic11—41no—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104#66977—22no—
105#66977—22no—
106#66977—22no—
107#66977—41no—
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C11×C22⋊C8—22no—
114C11×C22⋊C8—22no—
115C11×C22⋊C8—22no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123#66882—22no—
124#66882—22no—
125#66882D414yescomplemented
126#66881—22no—
127#66881—22no—
128#66881—41no—
129#66880—22no—
130#66880—22no—
131#66880—22no—
132#66880—41no—
133#26148—111nomaximal, Sylow
134C24×C11C2×D411yescharacteristic
135C24×C11C2×D411yescharacteristic
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—42no—
165C22×Dic11—42no—
166C22×Dic11—42no—
167C22×Dic11—42no—
168C22×Dic11—81no—
169C22×Dic11—81no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C11×M16—28no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11—21no—
186C2×C8×C11—21no—
187C2×C8×C11C2×D412yes—
188C2×C8×C11#4112yes—
189C11×C4⋊C4—22no—
190C11×C22⋊C4—22no—
191C11×C22⋊C4—22no—
192C42×C11—21no—
193C42×C11—21no—
194C22⋊Dic11—42no—
195C22⋊Dic11—42no—
196C22⋊Dic11—42no—
197C22⋊Dic11—42no—
198C22⋊Dic11—42no—
199C22⋊Dic11—42no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211C4⋊Dic11—21no—
212C4⋊Dic11—42no—
213C4⋊Dic11—42no—
214C4⋊Dic11—42no—
215C4⋊Dic11—81no—
216C4⋊Dic11C2×D412yes—
217C4⋊Dic11C2×D412yes—
218Dic11⋊C4—42no—
219Dic11⋊C4—42no—
220Dic11⋊C4—42no—
221C4×Dic11—42no—
222C4×Dic11—42no—
223C2×#484—111no—
224C2×#428—111no—
225#2415—111no—
226D4×C4⋊C4—111no—
227#2096—111no—
228#2083—111no—
229#2077—111no—
230#2036—111no—
231#1927—111no—
232#1918—111no—
233#1894—111no—
234#1872—111no—
235#1870D1111yescharacteristic
236#1854—111no—
237#1853—111no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11#12312yes—
251C23×C11#13712yes—
252C23×C11C22×D411yescharacteristic
253D4×C11—28no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
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—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11#12312yes—
273C2×C4×C11AGL(1,ℤ/8)12yes—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
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—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—84no—
305C2×Dic11—84no—
306Dic22—41no—
307Dic22—41no—
308Dic22—41no—
309Dic22—41no—
310C8×C11—22no—
311C8×C11—22no—
312C8×C11—41no—
313C8×C11—41no—
314C22×M16C2×D1111yescharacteristic
315C2×C22⋊Q8—111no—
316C2×C22⋊Q8—111no—
317C2×C4×D4—221no—
318C2×C4×D4C2×D1111yescharacteristic
319C2×#117—111no—
320C22×C4⋊C4—111no—
321C22×C4⋊C4—111no—
322#484—224no—
323#428—224no—
324C2×#107—111no—
325C2×#107—111no—
326C2×#107—111no—
327C2×#106—111no—
328C2×#106—111no—
329C2×#106—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#103—111no—
333C2×#103—111no—
334C2×C22⋊C8C2×D1111yescharacteristic
335C2×C22⋊C8C2×D1111yescharacteristic
336C2×C22⋊C8C2×D1111yescharacteristic
337#397—221no—
338#394—221no—
339#391—111no—
340#389—111no—
341#389—221no—
342#389—221no—
343#388—221no—
344#385—221no—
345#385—221no—
346#384—111no—
347#380—111no—
348#380—111no—
349#380—111no—
350C4×C4⋊C4—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340—111no—
357#336C2×D1111yescharacteristic
358#336C2×D1111yescharacteristic
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—22no—
363C22×C11—22no—
364C22×C11—22no—
365C22×C11—41no—
366C22×C11—41no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11C2×#12311yescharacteristic
374C22×C11D4211yescharacteristic
375C22×C11#54711yescharacteristic
376C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C11C2×#13711yescharacteristic
378C22×C11#57711yescharacteristic
379C22×C11#57811yescharacteristic
380C4×C11—22no—
381C4×C11—22no—
382C4×C11—41no—
383C4×C11—41no—
384C4×C11#52511yescharacteristic
385C4×C11#53911yescharacteristic
386C4×C11#54811yescharacteristic
387C4×C11#55311yescharacteristic
388Dic11—42no—
389Dic11—42no—
390Dic11—81no—
391Dic11—81no—
392Dic11—81no—
393Dic11—81no—
394Dic11—81no—
395Dic11—81no—
396C22×Q8—111no—
397C22×D4D4411yescharacteristic
398C23×C4—221no—
399C23×C4—221no—
400C23×C4C22×D1111yescharacteristic
401C23×C4C22×D1111yescharacteristic
402C2×M16—22no—
403C2×M16—22no—
404C2×M16—22no—
405C22×C8C22×D1111yescharacteristic
406C22×C8C22×D1111yescharacteristic
407C22×C8C22×D1111yescharacteristic
408C22×C8C22×D1111yescharacteristic
409C22⋊Q8—222no—
410C22⋊Q8—222no—
411C22⋊Q8—222no—
412C22⋊Q8—441no—
413C4×D4—22no—
414C4×D4—22no—
415C4×D4—444no—
416#117—222no—
417#117—441no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—111no—
424C2×C4⋊C4—111no—
425C2×C4⋊C4—222no—
426C2×C4⋊C4—222no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—441no—
435C2×C4⋊C4—441no—
436C2×C4⋊C4D4411yescharacteristic
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C22⋊C4—221no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4D4411yescharacteristic
444C2×C22⋊C4D4411yescharacteristic
445C2×C42—221no—
446C2×C42—221no—
447C2×C42C22×D1111yescharacteristic
448#107—114no—
449#107—222no—
450#107—222no—
451#106—222no—
452#106—222no—
453#106—441no—
454#103—222no—
455#103—222no—
456#103—222no—
457#103—441no—
458C22⋊C8—22no—
459C22⋊C8—22no—
460C22⋊C8—22no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95—221no—
468C2×C11—42no—
469C2×C11—42no—
470C2×C11#244311yescharacteristic
471C2×C11#309211yescharacteristic
472C2×C11#309711yescharacteristic
473C2×C11#327011yescharacteristic
474C2×C11#327211yescharacteristic
475C2×C11#334411yescharacteristic
476C2×C11#335311yescharacteristic
477C24C2×D4411yescharacteristic
478C24C2×D4411yescharacteristic
479C2×Q8—221no—
480C2×Q8—221no—
481C2×Q8—221no—
482C2×Q8—221no—
483C2×Q8—221no—
484C2×Q8—221no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—442no—
507C22×C4—442no—
508C22×C4—442no—
509C22×C4—442no—
510C22×C4—881no—
511C22×C4—881no—
512C22×C4C2×D4411yescharacteristic
513C22×C4C2×D4411yescharacteristic
514C22×C4C2×D4411yescharacteristic
515C22×C4C2×D4411yescharacteristic
516C22×C4#434112yes—
517C22×C4#434112yes—
518C22×C4C23×D1111yescharacteristic
519M16—28no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8D4×D1112yes—
531C2×C8#434112yes—
532C4⋊C4—22no—
533C4⋊C4—112no—
534C4⋊C4—112no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—221no—
539C4⋊C4—221no—
540C4⋊C4—221no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—442no—
548C4⋊C4—442no—
549C4⋊C4—442no—
550C4⋊C4—442no—
551C4⋊C4—442no—
552C4⋊C4—442no—
553C4⋊C4—881no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—442no—
557C22⋊C4—442no—
558C22⋊C4—442no—
559C22⋊C4—442no—
560C22⋊C4—442no—
561C22⋊C4—442no—
562C42—21no—
563C42—21no—
564C42—442no—
565C42—442no—
566C11#2614811yescharacteristic, complemented, Sylow
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23#6693912yes—
580C23#6696212yes—
581C23C22×D4411yescharacteristic
582Q8—441no—
583Q8—441no—
584Q8—441no—
585Q8—441no—
586D4—28no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—441no—
608C2×C4—441no—
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—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—884no—
630C2×C4—884no—
631C2×C4#6693912yes—
632C2×C4#6696112yes—
633C2×C4C2×D4×D1111yescharacteristic
634C2×C4C2×#434111yescharacteristic
635C2×C4C2×#434111yescharacteristic
636C2×C4C2×#434111yescharacteristic
637C2×C4#6704211yescharacteristic
638C2×C4#6704311yescharacteristic
639C8—22no—
640C8—22no—
641C8—41no—
642C8—41no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—22no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—41no—
654C22—41no—
655C22—41no—
656C22—41no—
657C22C2×#6693911yescharacteristic
658C22D4×D4411yescharacteristic
659C22#1062308611yescharacteristic
660C22C2×#6696111yescharacteristic
661C22C2×#6696211yescharacteristic
662C22#1062328211yescharacteristic
663C22#1062328411yescharacteristic
664C4—22no—
665C4—22no—
666C4—41no—
667C4—41no—
668C4—442no—
669C4—442no—
670C4—881no—
671C4—881no—
672C4—881no—
673C4—881no—
674C4—881no—
675C4—881no—
676C4#1062311711yescharacteristic
677C4#1062312911yescharacteristic
678C4#1062314911yescharacteristic
679C4#1062319611yescharacteristic
680C2—42no—
681C2—42no—
682C2#1307234911yescharacteristic
683C2#1307854111yescharacteristic
684C2#1307858611yescharacteristic
685C2#1308019111yescharacteristic
686C2#1308021811yescharacteristic
687C2#1308107311yescharacteristic
688C2#1308120111yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1870C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#1870D11
hypocenterC11#26148
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #1870

Complements

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

NH ≅ G/Ntype
1. C2×#10622335C2semidirect
2. C2×#10622734C2semidirect
5. #13070158C2semidirect
6. #13070089C2semidirect
7. #13070049C2semidirect
8. #13069820C2semidirect
9. #13069251C2semidirect
10. #13069188C2semidirect
11. #13069049C2semidirect
12. #13068921C2semidirect
13. #13068817C2semidirect
14. #13068811C2semidirect
125. #66882D4semidirect
566. C11#26148semidirect

Maximal subgroups

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

subgroupindex
C2×#106223352
C2×#106227342
#130720452
D4×C4⋊Dic112
#130701582
#130700892
#130700492
#130698202
#130692512
#130691882
#130690492
#130689212
#130688172
#130688112
C11×#18702
#2614811