Finite Group Databasebeta

← #14813765

Subgroups — #14813765

Order 2816.

910 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622640C211yesmaximal, characteristic
2C2×C4×#4325C211yesmaximal, characteristic, complemented
3#13072381C211yesmaximal, characteristic
4#13070140C211yesmaximal, characteristic, complemented
5#13070117C211yesmaximal, characteristic, complemented
6#13070030C211yesmaximal, characteristic, complemented
7#13069850C211yesmaximal, characteristic
8#13069298C211yesmaximal, characteristic, complemented
9#13069175C211yesmaximal, characteristic, complemented
10#13068971C211yesmaximal, characteristic, complemented
11#13068971C211yesmaximal, characteristic, complemented
12#13068971C211yesmaximal, characteristic, complemented
13#13068870C211yesmaximal, characteristic, complemented
14#13068862C211yesmaximal, characteristic, complemented
15C11×#2351C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×#66947—21no—
22C2×#66927C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C11×#389—21no—
25C11×#389—21no—
26C11×#389C2211yescharacteristic
27C11×#389C2211yescharacteristic
28C11×#382—21no—
29C11×#382C2211yescharacteristic
30C4×C11×C4⋊C4—21no—
31C4×C11×C4⋊C4C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34#10622640—24no—
35C4×#4325—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×C4×C11⋊C8C2211yescharacteristic
51#10622285—21no—
52#10622278—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44—21no—
63C22×D44—21no—
64C22×D44C2311yescharacteristic
65C22×D44C2311yescharacteristic
66C22×C4×D11—21no—
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C4×Q8×C11—22no—
70C4×Q8×C11—22no—
71C4×Q8×C11—41no—
72C4×Q8×C11—41no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4D411yescharacteristic
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C42×C11—21no—
84C2×C42×C11—21no—
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×#4325—22no—
90C2×#4325—22no—
91C2×#4325—22no—
92C2×#4325—22no—
93C2×#4325—22no—
94C2×#4325D414yes—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×Dic11⋊C4—21no—
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66947—44no—
110#66927—22no—
111#66927—41no—
112C4×D44—22no—
113C4×D44—41no—
114C11×#95—21no—
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95D411yescharacteristic
119C11×#95D411yescharacteristic
120#66899—22no—
121#66899—22no—
122C11⋊#95—21no—
123#66873—22no—
124#66873—22no—
125#66873—22no—
126#66873—22no—
127#66873—22no—
128#66873—41no—
129#66872—22no—
130#66871—41no—
131C4⋊(C11⋊C8)—22no—
132C4×C11⋊C8—22no—
133#26159—111nomaximal, Sylow
134C23×D11—21no—
135C23×D11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11C2×D412yes—
140C2×Q8×C11#4112yes—
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—24no—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—22no—
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—42no—
186C11×C4⋊C4—42no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4#4112yes—
189C42×C11—24no—
190C42×C11—21no—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—42no—
197C42×C11—42no—
198#4325—28no—
199#4325—44no—
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—
205(C2×D11)⋊C4—81no—
206(C2×D11)⋊C4—81no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—21no—
210C4⋊Dic11—21no—
211Dic11⋊C4—42no—
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⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8C2×D412yes—
224C2×#460—111no—
225C2×C4×SD16—111no—
226#2445—111no—
227#2351D1111yescharacteristic, complemented
228#2092—111no—
229#2088—111no—
230#2073—111no—
231#2041—111no—
232#1934—111no—
233#1916—111no—
234#1880—111no—
235#1880—111no—
236#1880—111no—
237#1863—111no—
238#1862—111no—
239C23×C11C22×D411yescharacteristic
240C22×D11—22no—
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—
252C22×D11—41no—
253C22×D11—41no—
254Q8×C11—22no—
255Q8×C11—22no—
256Q8×C11—22no—
257Q8×C11#12314yescomplemented
258C2×C4×C11—22no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—22no—
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—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×C11—41no—
286C2×C4×C11#13512yes—
287C2×C4×C11AGL(1,ℤ/8)12yes—
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11H(5,𝔽2)11yescharacteristic
293C2×C4×C112−1+411yescharacteristic
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—
304D44—41no—
305D44—41no—
306D44—41no—
307D44—41no—
308D44—84no—
309D44—84no—
310C4×D11—84no—
311C11⋊C8—22no—
312C11⋊C8—41no—
313C11⋊C8—41no—
314C11⋊C8—41no—
315C22×SD16—111no—
316C22×SD16—111no—
317C2×#127—111no—
318C2×#123—221no—
319C2×C4×Q8C2×D1111yescharacteristic
320C2×C4×Q8C2×D1111yescharacteristic
321C2×C4×Q8C2×D1111yescharacteristic
322C2×C4×D4—111no—
323#460—224no—
324C4×SD16—224no—
325C2×#107—111no—
326C2×#106—111no—
327C2×C4⋊C8—111no—
328C2×#103—111no—
329C2×#103—111no—
330C2×#102—111no—
331C2×#102—111no—
332C2×#102—111no—
333C2×#102—111no—
334C2×#102—111no—
335C2×#102—111no—
336C2×C4×C8—111no—
337#394—221no—
338#394—221no—
339#390—111no—
340#390—111no—
341#390—111no—
342#389—21no—
343#389—21no—
344#389—111no—
345#389C2×D1111yescharacteristic
346#389C2×D1111yescharacteristic
347#386—221no—
348#382—21no—
349#382C2×D1111yescharacteristic
350C4×C4⋊C4—21no—
351C4×C4⋊C4C2×D1111yescharacteristic
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#336—111no—
357#336—111no—
358#336—111no—
359#336—111no—
360C22×C11#52511yescharacteristic
361C22×C11D4211yescharacteristic
362C22×C11#54811yescharacteristic
363C22×C11C2×#13511yescharacteristic
364C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C11#57711yescharacteristic
366C22×C11#57711yescharacteristic
367C2×D11—42no—
368C2×D11—42no—
369C2×D11—42no—
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—
379C2×D11—81no—
380C2×D11—81no—
381C4×C11—24no—
382C4×C11—22no—
383C4×C11—22no—
384C4×C11—41no—
385C4×C11—42no—
386C4×C11—41no—
387C4×C11—41no—
388C4×C11—41no—
389C4×C11—81no—
390C4×C11—81no—
391C4×C11C2×#12311yescharacteristic
392C4×C11#53911yescharacteristic
393C4×C11#54711yescharacteristic
394C4×C11#55311yescharacteristic
395Dic11—81no—
396Dic11—81no—
397C22×Q8C22×D1111yescharacteristic
398C22×D4—111no—
399C22×D4—111no—
400C22×D4—221no—
401C22×D4—221no—
402C23×C4—221no—
403C2×SD16—114no—
404C2×SD16—222no—
405C2×SD16—222no—
406C2×SD16—222no—
407C2×SD16—222no—
408C2×SD16—222no—
409C22×C8—111no—
410C22×C8—111no—
411C22×C8—111no—
412C22×C8—111no—
413#127—222no—
414#127—441no—
415#123—444no—
416C4×Q8—22no—
417C4×Q8—22no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×Q8—41no—
421C4×Q8—41no—
422C4×D4—222no—
423C4×D4—441no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4C22⋊D1111yescharacteristic
433C2×C4⋊C4C22⋊D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
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⋊C4—221no—
444C2×C42—21no—
445C2×C42—21no—
446C2×C42—21no—
447C2×C42C22×D1111yescharacteristic
448C2×C42C22×D1111yescharacteristic
449C2×C42C22×D1111yescharacteristic
450#107—441no—
451#106—222no—
452C4⋊C8—222no—
453#103—222no—
454#103—222no—
455#102—222no—
456#102—222no—
457#102—222no—
458#102—222no—
459#102—222no—
460#102—441no—
461C4×C8—222no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—221no—
467#95C22⋊D1111yescharacteristic
468#95C22⋊D1111yescharacteristic
469C2×C11#244311yescharacteristic
470C2×C11#310611yescharacteristic
471C2×C11#312611yescharacteristic
472C2×C11#326511yescharacteristic
473C2×C11#328211yescharacteristic
474C2×C11#336511yescharacteristic
475C2×C11#336811yescharacteristic
476D11—82no—
477D11—161no—
478C24—221no—
479C24—221no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8#433912yes—
484C2×Q8D4×D1112yes—
485C2×Q8#434312yes—
486C2×D4—112no—
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—221no—
497C2×D4—221no—
498C2×D4—442no—
499C2×D4—442no—
500C2×D4—442no—
501C2×D4—442no—
502C2×D4—881no—
503C2×D4—881no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—442no—
511C22×C4—442no—
512C22×C4—881no—
513C22×C4C2×C22⋊D1111yescharacteristic
514C22×C4C2×C22⋊D1111yescharacteristic
515C22×C4C2×C22⋊D1111yescharacteristic
516C22×C4C2×C22⋊D1111yescharacteristic
517C22×C4C2×C22⋊D1111yescharacteristic
518C22×C4C2×C22⋊D1111yescharacteristic
519C22×C4C23×D1111yescharacteristic
520SD16—228no—
521SD16—444no—
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—
532C2×C8—221no—
533C2×C8—221no—
534C4⋊C4—24no—
535C4⋊C4—22no—
536C4⋊C4—22no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—42no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—42no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—442no—
551C4⋊C4#433912yes—
552C22⋊C4—442no—
553C22⋊C4—442no—
554C22⋊C4—442no—
555C22⋊C4—442no—
556C22⋊C4—881no—
557C22⋊C4—881no—
558C22⋊C4—881no—
559C42—24no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—42no—
567C42—42no—
568C11#2615911yescharacteristic, complemented, Sylow
569C23—222no—
570C23—441no—
571C23—441no—
572C23—441no—
573C23—441no—
574C23—441no—
575C23—441no—
576C23—441no—
577C23—441no—
578C23—441no—
579C23—441no—
580C23—441no—
581C23—441no—
582C23—441no—
583C23C22×C22⋊D1111yescharacteristic
584Q8—22no—
585Q8—22no—
586Q8—22no—
587Q8#6694714yescomplemented
588D4—222no—
589D4—222no—
590D4—441no—
591D4—441no—
592D4—441no—
593D4—441no—
594D4—441no—
595D4—441no—
596D4—884no—
597D4—884no—
598C2×C4—22no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—884no—
633C2×C4#6700212yes—
634C2×C4#6700312yes—
635C2×C4C2×#433911yescharacteristic
636C2×C4C2×#433911yescharacteristic
637C2×C4C2×D4×D1111yescharacteristic
638C2×C4#6703711yescharacteristic
639C2×C4C2×#434311yescharacteristic
640C2×C4#6704011yescharacteristic
641C8—222no—
642C8—441no—
643C8—441no—
644C8—441no—
645C22—442no—
646C22—442no—
647C22—442no—
648C22—881no—
649C22—881no—
650C22—881no—
651C22—881no—
652C22—881no—
653C22—881no—
654C22—881no—
655C22—881no—
656C22—881no—
657C22—881no—
658C22—881no—
659C22#1062332211yescharacteristic
660C22D4×C22⋊D1111yescharacteristic
661C22#1062334811yescharacteristic
662C22C2×#6700211yescharacteristic
663C22C2×#6700311yescharacteristic
664C22#1062336811yescharacteristic
665C22#1062336811yescharacteristic
666C4—22no—
667C4—22no—
668C4—24no—
669C4—41no—
670C4—41no—
671C4—41no—
672C4—41no—
673C4—42no—
674C4—81no—
675C4—81no—
676C4—881no—
677C4—881no—
678C4C2×#6694711yescharacteristic
679C4#1062303811yescharacteristic
680C4#1062304511yescharacteristic
681C4#1062304611yescharacteristic
682C2—882no—
683C2—1761no—
684C2#1307235111yescharacteristic
685C2#1307867611yescharacteristic
686C2#1307890711yescharacteristic
687C2#1308011211yescharacteristic
688C2#1308032411yescharacteristic
689C2#1308131211yescharacteristic
690C2#1308134511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2351C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#2351D11
hypocenterC11#26159
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2351

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4325C2semidirect
4. #13070140C2semidirect
5. #13070117C2semidirect
6. #13070030C2semidirect
8. #13069298C2semidirect
9. #13069175C2semidirect
10. #13068971C2semidirect
11. #13068971C2semidirect
12. #13068971C2semidirect
13. #13068870C2semidirect
14. #13068862C2semidirect
15. C11×#2351C2semidirect
227. #2351D11semidirect
257. Q8×C11#123semidirect
568. C11#26159semidirect
587. Q8#66947semidirect

Maximal subgroups

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

subgroupindex
C2×#106226402
C2×C4×#43252
#130723812
#130701402
#130701172
#130700302
#130698502
#130692982
#130691752
#130689712
#130688702
#130688622
C11×#23512
#2615911