Finite Group Databasebeta

← #14823491

Subgroups — #14823491

Order 2816.

892 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622701C211yesmaximal, characteristic
2C2×#10622639C211yesmaximal, characteristic, complemented
3#13072381C211yesmaximal, characteristic
4#13070001C211yesmaximal, characteristic, complemented
5#13069941C211yesmaximal, characteristic, complemented
6#13069931C211yesmaximal, characteristic, complemented
7#13069703C211yesmaximal, characteristic
8#13069500C211yesmaximal, characteristic, complemented
9#13069312C211yesmaximal, characteristic, complemented
10#13069312C211yesmaximal, characteristic, complemented
11#13069295C211yesmaximal, characteristic, complemented
12#13068971C211yesmaximal, characteristic, complemented
13#13068862C211yesmaximal, characteristic, complemented
14#13068491C211yesmaximal, characteristic, complemented
15C11×#2451C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C2×#66947—21no—
21C2×#66927C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#398—21no—
24C11×#395—21no—
25C11×#391—21no—
26C11×#391C2211yescharacteristic
27C11×#391C2211yescharacteristic
28C11×#389C2211yescharacteristic
29C11×#389C2211yescharacteristic
30C11×#387—21no—
31C4×C11×C4⋊C4C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34#10622701—24no—
35#10622639—24no—
36#10622604—21no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66871C2211yescharacteristic
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×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C22×D44—21no—
64C22×D44—21no—
65C22×D44C2311yescharacteristic
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C11×C4⋊Q8—22no—
69C11×C4⋊Q8—41no—
70C4×Q8×C11—22no—
71C4×Q8×C11—41no—
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#66871—22no—
128#66871—41no—
129C4⋊(C11⋊C8)—22no—
130#66867—22no—
131#66867—22no—
132C4×C11⋊C8—22no—
133#26832—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—42no—
142C2×Q8×C11—42no—
143C2×Q8×C11—81no—
144C2×Q8×C11#4112yes—
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×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2411yescharacteristic
156C22×Dic11—21no—
157C22×Dic11—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—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44—42no—
170C2×D44—42no—
171C2×D44—42no—
172C2×D44—42no—
173C2×D44—81no—
174C2×D44—81no—
175C2×D44C2×D412yes—
176C2×C4×D11—42no—
177C2×C4×D11—42no—
178C2×C4×D11—81no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—22no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—42no—
187C11×C4⋊C4—42no—
188C11×C4⋊C4—81no—
189C11×C4⋊C4—81no—
190C11×C4⋊C4C2×D412yes—
191C42×C11—21no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C42×C11—21no—
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⋊C8C2×D412yes—
222C2×C11⋊C8#4112yes—
223C2×C11⋊C8#4112yes—
224C2×#486—111no—
225C2×#440—111no—
226#2451D1111yescharacteristic, complemented
227#2445—111no—
228#2067—111no—
229#2057—111no—
230#2055—111no—
231#2014—111no—
232#1973—111no—
233#1936—111no—
234#1936—111no—
235#1933—111no—
236#1880—111no—
237#1862—111no—
238#1771—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—41no—
257Q8×C11—41no—
258Q8×C11—84no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—21no—
266C2×C4×C11—21no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
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—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×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11AGL(1,ℤ/8)12yes—
288C2×C4×C11#13712yes—
289C2×C4×C11C22×D411yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11C2×#4111yescharacteristic
293C2×C4×C11H(5,𝔽2)11yescharacteristic
294C2×C4×C112−1+411yescharacteristic
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301D44—22no—
302D44—22no—
303D44—41no—
304D44—41no—
305D44—41no—
306D44—41no—
307D44—41no—
308D44—41no—
309D44—84no—
310D44—84no—
311C4×D11—84no—
312C11⋊C8—22no—
313C11⋊C8—22no—
314C11⋊C8—22no—
315C11⋊C8—41no—
316C22×SD16—111no—
317C22×SD16—111no—
318C2×C4⋊Q8C2×D1111yescharacteristic
319C2×#127—111no—
320C2×#123—221no—
321C2×C4×Q8C2×D1111yescharacteristic
322C2×C4×D4—111no—
323#486—224no—
324#440—224no—
325C2×#107—111no—
326C2×#107—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×#97—111no—
337C2×#97—111no—
338C2×C4×C8—111no—
339#398—21no—
340#395—21no—
341#394—221no—
342#394—221no—
343#391—21no—
344#391C2×D1111yescharacteristic
345#391C2×D1111yescharacteristic
346#390—111no—
347#390—111no—
348#390—111no—
349#389—111no—
350#389C2×D1111yescharacteristic
351#389C2×D1111yescharacteristic
352#387—21no—
353#386—221no—
354C4×C4⋊C4C2×D1111yescharacteristic
355#340—111no—
356#340—111no—
357#340—111no—
358#340—111no—
359#336—111no—
360#336—111no—
361C22×C11#53211yescharacteristic
362C22×C11D4211yescharacteristic
363C22×C11#54811yescharacteristic
364C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
365C22×C11C2×#13711yescharacteristic
366C22×C11#57611yescharacteristic
367C22×C11#57711yescharacteristic
368C2×D11—42no—
369C2×D11—42no—
370C2×D11—42no—
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—
381C2×D11—81no—
382C4×C11—22no—
383C4×C11—22no—
384C4×C11—41no—
385C4×C11—41no—
386C4×C11—42no—
387C4×C11—41no—
388C4×C11—42no—
389C4×C11—41no—
390C4×C11—81no—
391C4×C11—81no—
392C4×C11#52511yescharacteristic
393C4×C11#54211yescharacteristic
394C4×C11#54711yescharacteristic
395C4×C11#55111yescharacteristic
396Dic11—81no—
397Dic11—81no—
398C22×Q8—21no—
399C22×Q8C22×D1111yescharacteristic
400C22×D4—111no—
401C22×D4—111no—
402C22×D4—221no—
403C22×D4—221no—
404C23×C4—221no—
405C2×SD16—222no—
406C2×SD16—222no—
407C2×SD16—222no—
408C2×SD16—222no—
409C2×SD16—222no—
410C2×SD16—441no—
411C22×C8—111no—
412C22×C8—111no—
413C22×C8—111no—
414C22×C8—111no—
415C4⋊Q8—22no—
416C4⋊Q8—41no—
417#127—222no—
418#127—441no—
419#123—444no—
420C4×Q8—22no—
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—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4C22⋊D1111yescharacteristic
432C2×C4⋊C4C22⋊D1111yescharacteristic
433C2×C4⋊C4C22×D1111yescharacteristic
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C22⋊C4—221no—
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×C42—21no—
444C2×C42C22×D1111yescharacteristic
445C2×C42C22×D1111yescharacteristic
446C2×C42C22×D1111yescharacteristic
447#107—222no—
448#107—441no—
449C4⋊C8—222no—
450#103—222no—
451#103—222no—
452#102—114no—
453#102—222no—
454#102—222no—
455#102—222no—
456#102—222no—
457#102—222no—
458#97—222no—
459#97—222no—
460C4×C8—222no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—221no—
468#95C22⋊D1111yescharacteristic
469#95C22⋊D1111yescharacteristic
470C2×C11#246111yescharacteristic
471C2×C11#317911yescharacteristic
472C2×C11#318211yescharacteristic
473C2×C11#326411yescharacteristic
474C2×C11#326611yescharacteristic
475C2×C11#336811yescharacteristic
476C2×C11#337511yescharacteristic
477D11—82no—
478D11—161no—
479C24—221no—
480C24—221no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—42no—
487C2×Q8—42no—
488C2×Q8—81no—
489C2×Q8#434312yes—
490C2×D4—112no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4—221no—
494C2×D4—221no—
495C2×D4—221no—
496C2×D4—221no—
497C2×D4—221no—
498C2×D4—221no—
499C2×D4—221no—
500C2×D4—221no—
501C2×D4—221no—
502C2×D4—442no—
503C2×D4—442no—
504C2×D4—442no—
505C2×D4—442no—
506C2×D4—881no—
507C2×D4—881no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—881no—
517C22×C4C2×C22⋊D1111yescharacteristic
518C22×C4C2×C22⋊D1111yescharacteristic
519C22×C4C2×C22⋊D1111yescharacteristic
520C22×C4C2×C22⋊D1111yescharacteristic
521C22×C4C2×C22⋊D1111yescharacteristic
522C22×C4C2×C22⋊D1111yescharacteristic
523C22×C4C23×D1111yescharacteristic
524SD16—228no—
525SD16—444no—
526C2×C8—112no—
527C2×C8—112no—
528C2×C8—112no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—221no—
536C2×C8—221no—
537C2×C8—221no—
538C4⋊C4—22no—
539C4⋊C4—22no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—21no—
544C4⋊C4—21no—
545C4⋊C4—42no—
546C4⋊C4—42no—
547C4⋊C4—81no—
548C4⋊C4—81no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—442no—
554C4⋊C4D4×D1112yes—
555C22⋊C4—442no—
556C22⋊C4—442no—
557C22⋊C4—442no—
558C22⋊C4—442no—
559C22⋊C4—881no—
560C22⋊C4—881no—
561C22⋊C4—881no—
562C42—21no—
563C42—21no—
564C42—21no—
565C42—21no—
566C42—21no—
567C42—21no—
568C42—42no—
569C11#2683211yescharacteristic, complemented, Sylow
570C23—222no—
571C23—441no—
572C23—441no—
573C23—441no—
574C23—441no—
575C23—441no—
576C23—441no—
577C23—441no—
578C23—441no—
579C23—441no—
580C23—441no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23C22×C22⋊D1111yescharacteristic
585Q8—22no—
586Q8—22no—
587Q8—41no—
588Q8—41no—
589Q8—84no—
590D4—222no—
591D4—222no—
592D4—441no—
593D4—441no—
594D4—441no—
595D4—441no—
596D4—441no—
597D4—441no—
598D4—884no—
599D4—884no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—22no—
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—41no—
627C2×C4—41no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—884no—
635C2×C4#6699512yes—
636C2×C4#6700212yes—
637C2×C4C2×D4×D1111yescharacteristic
638C2×C4#6703711yescharacteristic
639C2×C4C2×#434311yescharacteristic
640C2×C4#6704011yescharacteristic
641C2×C4#41×D1111yescharacteristic
642C2×C4#41×D1111yescharacteristic
643C8—222no—
644C8—222no—
645C8—222no—
646C8—441no—
647C22—442no—
648C22—442no—
649C22—442no—
650C22—881no—
651C22—881no—
652C22—881no—
653C22—881no—
654C22—881no—
655C22—881no—
656C22—881no—
657C22—881no—
658C22—881no—
659C22—881no—
660C22—881no—
661C22D4×C22⋊D1111yescharacteristic
662C22C2×#6699511yescharacteristic
663C22#1062334811yescharacteristic
664C22C2×#6700211yescharacteristic
665C22#1062336311yescharacteristic
666C22#1062336611yescharacteristic
667C22#1062336811yescharacteristic
668C4—22no—
669C4—22no—
670C4—41no—
671C4—42no—
672C4—41no—
673C4—41no—
674C4—42no—
675C4—41no—
676C4—81no—
677C4—81no—
678C4—881no—
679C4—881no—
680C4#1062315811yescharacteristic
681C4#1062316211yescharacteristic
682C4#1062316811yescharacteristic
683C4#1062317111yescharacteristic
684C2—882no—
685C2—1761no—
686C2#1307259011yescharacteristic
687C2#1307929311yescharacteristic
688C2#1307933511yescharacteristic
689C2#1308009711yescharacteristic
690C2#1308012711yescharacteristic
691C2#1308134511yescharacteristic
692C2#1308143011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2451C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#2451D11
hypocenterC11#26832
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2451

Complements

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

NH ≅ G/Ntype
2. C2×#10622639C2semidirect
4. #13070001C2semidirect
5. #13069941C2semidirect
6. #13069931C2semidirect
8. #13069500C2semidirect
9. #13069312C2semidirect
10. #13069312C2semidirect
11. #13069295C2semidirect
12. #13068971C2semidirect
13. #13068862C2semidirect
14. #13068491C2semidirect
15. C11×#2451C2semidirect
226. #2451D11semidirect
569. C11#26832semidirect

Maximal subgroups

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

subgroupindex
C2×#106227012
C2×#106226392
#130723812
#130700012
#130699412
#130699312
#130697032
#130695002
#130693122
#130692952
#130689712
#130688622
#130684912
C11×#24512
#2683211