Finite Group Databasebeta

← #14823162

Subgroups — #14823162

Order 2816.

818 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622350C211yesmaximal, characteristic
2C2×#10622409C211yesmaximal, characteristic, complemented
3#13072964C211yesmaximal, characteristic
4#13071647C211yesmaximal, characteristic, complemented
5#13069985C211yesmaximal, characteristic, complemented
6#13069953C211yesmaximal, characteristic, complemented
7#13069617C211yesmaximal, characteristic
8#13069494C211yesmaximal, characteristic, complemented
9#13069252C211yesmaximal, characteristic, complemented
10#13069241C211yesmaximal, characteristic, complemented
11#13069232C211yesmaximal, characteristic, complemented
12#13068969C211yesmaximal, characteristic, complemented
13#13068813C211yesmaximal, characteristic, complemented
14#13068516C211yesmaximal, characteristic, complemented
15C11×#2035C211yesmaximal, characteristic, complemented
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C22×#4325C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66943C2211yescharacteristic
22C2×C11×#106C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26C11×#380C2211yescharacteristic
27#10622843C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C4×C22⋊Dic11C2211yescharacteristic
30C2×C22⋊(C11⋊C8)C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66879C2211yescharacteristic
36C2×Dic11⋊C8C2211yescharacteristic
37#10622601C2211yescharacteristic
38#10622601C2211yescharacteristic
39#10622598C2211yescharacteristic
40#10622594—21no—
41C4⋊C4×Dic11—21no—
42C4⋊C4×Dic11C2211yescharacteristic
43C4⋊C4×Dic11C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66872C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47#10622574—21no—
48#10622570—21no—
49#10622564—21no—
50#10622564—21no—
51#10622409—24no—
52#10622350—24no—
53#10622288—21no—
54#10622283—21no—
55C11×#340C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C22×D44C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C11×C22⋊Q8—22no—
68C11×C22⋊Q8—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11D411yescharacteristic
77C2×C22⋊Dic11D411yescharacteristic
78Q8×Dic11—22no—
79Q8×Dic11—41no—
80C2×#4325—22no—
81C2×#4325—22no—
82C2×#4325—41no—
83#66983—22no—
84#66983—41no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90#66979—22no—
91#66979—41no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11C2311yescharacteristic
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107#66943—22no—
108#66943—41no—
109C11×#106—22no—
110C11×#103—22no—
111C11×#103—22no—
112C11×C22⋊C8—22no—
113C11×#95—21no—
114#66899—22no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95D411yescharacteristic
121C11⋊#95D411yescharacteristic
122C22⋊(C11⋊C8)—22no—
123#66885—22no—
124#66885—22no—
125#66882D414yes—
126#66881—22no—
127#66879—22no—
128Dic11⋊C8—22no—
129#66873—22no—
130#66872—22no—
131#66871—41no—
132#26811—111nomaximal, Sylow
133C24×C11C2×D411yescharacteristic
134C23×D11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11#4112yes—
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×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—42no—
154C2×C22⋊D11—42no—
155C2×C22⋊D11—81no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11C2×D411yescharacteristic
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C2×D44—21no—
164C2×D44—21no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11C2×D412yes—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4#4112yes—
182C11×C22⋊C4—24no—
183C11×C22⋊C4—81no—
184C22⋊Dic11—41no—
185C22⋊Dic11—41no—
186C22⋊Dic11—42no—
187#4325—44no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—81no—
191(C2×D11)⋊C4—81no—
192(C2×D11)⋊C4—81no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—42no—
198C4⋊Dic11—42no—
199C4⋊Dic11—42no—
200C4⋊Dic11C2×D412yes—
201C4⋊Dic11C2×D412yes—
202Dic11⋊C4—42no—
203C4×Dic11—21no—
204C4×Dic11—21no—
205C4×Dic11—21no—
206C4×Dic11—21no—
207C4×Dic11—42no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C4×Dic11—81no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8#4112yes—
217C2×#482—111no—
218C2×#479—111no—
219#2490—111no—
220#2362—111no—
221#2065—111no—
222#2059—111no—
223#2035D1111yescharacteristic, complemented
224#2000—111no—
225#1973—111no—
226#1927—111no—
227#1926—111no—
228#1924—111no—
229#1880—111no—
230#1854—111no—
231#1776—111no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11C22×D411yescharacteristic
240C22×D11—41no—
241C22×D11—41no—
242C22×D11—41no—
243C22×D11—41no—
244C22×D11—41no—
245C22×D11—41no—
246C22×D11—41no—
247Q8×C11—22no—
248Q8×C11—22no—
249Q8×C11—41no—
250Q8×C11—41no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11C22×D411yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C22⋊D11—84no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298D44—41no—
299D44—41no—
300D44—41no—
301D44—41no—
302C8×C11—22no—
303C8×C11—41no—
304C11⋊C8—22no—
305C11⋊C8—41no—
306C22×SD16—111no—
307C2×#125—111no—
308C2×C22⋊Q8C2×D1111yescharacteristic
309C2×#121—111no—
310C2×C4×Q8—111no—
311C2×#117—111no—
312#482—224no—
313#479—224no—
314C2×#107—111no—
315C2×#107—111no—
316C2×#106—111no—
317C2×#106—111no—
318C2×#106C2×D1111yescharacteristic
319C2×C4⋊C8—111no—
320C2×#103—111no—
321C2×#103C2×D1111yescharacteristic
322C2×#103C2×D1111yescharacteristic
323C2×#102—111no—
324C2×#102—111no—
325C2×#102—111no—
326C2×C22⋊C8—111no—
327C2×C22⋊C8C2×D1111yescharacteristic
328C2×#97—111no—
329#397—221no—
330#394—221no—
331#391—111no—
332#390—111no—
333#390—111no—
334#390—221no—
335#389—111no—
336#388—221no—
337#388—221no—
338#388—221no—
339#387—221no—
340#380C2×D1111yescharacteristic
341C4×C4⋊C4—111no—
342C4×C4⋊C4—111no—
343C4×C4⋊C4—221no—
344C4×C22⋊C4—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340C2×D1111yescharacteristic
349#336—111no—
350#336—111no—
351C22×C11—41no—
352C22×C11—41no—
353C22×C11—41no—
354C22×C11—41no—
355C22×C11—41no—
356C22×C11—41no—
357C22×C11—41no—
358C22×C11#52511yescharacteristic
359C22×C11D4211yescharacteristic
360C22×C11#54711yescharacteristic
361C22×C11#57511yescharacteristic
362C22×C11#57511yescharacteristic
363C22×C11#57711yescharacteristic
364C22×C11#57711yescharacteristic
365C2×D11—81no—
366C2×D11—81no—
367C2×D11—81no—
368C2×D11—81no—
369C2×D11—81no—
370C2×D11—81no—
371C2×D11—81no—
372C4×C11—42no—
373C4×C11—41no—
374C4×C11—42no—
375C4×C11—81no—
376C4×C11—81no—
377C4×C11#53211yescharacteristic
378C4×C11#54211yescharacteristic
379C4×C11#54811yescharacteristic
380C4×C11#55111yescharacteristic
381Dic11—41no—
382Dic11—41no—
383Dic11—41no—
384Dic11—42no—
385Dic11—42no—
386Dic11—41no—
387Dic11—81no—
388C22×Q8C22×D1111yescharacteristic
389C22×D4—111no—
390C22×D4—221no—
391C23×C4C22×D1111yescharacteristic
392C2×SD16—222no—
393C2×SD16—222no—
394C2×SD16—441no—
395C22×C8—111no—
396C22×C8—111no—
397C22×C8C22×D1111yescharacteristic
398C22×C8C22×D1111yescharacteristic
399#125—222no—
400#125—441no—
401C22⋊Q8—22no—
402C22⋊Q8—22no—
403#121—222no—
404#121—441no—
405C4×Q8—222no—
406C4×Q8—441no—
407#117—222no—
408#117—441no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—111no—
413C2×C4⋊C4—221no—
414C2×C4⋊C4—221no—
415C2×C4⋊C4—221no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4C22×D1111yescharacteristic
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—111no—
423C2×C22⋊C4—111no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C42—111no—
431C2×C42—111no—
432C2×C42—221no—
433C2×C42—221no—
434C2×C42—221no—
435C2×C42—221no—
436#107—114no—
437#107—441no—
438#106—22no—
439#106—222no—
440#106—222no—
441C4⋊C8—222no—
442#103—22no—
443#103—22no—
444#103—222no—
445#102—222no—
446#102—222no—
447#102—222no—
448C22⋊C8—22no—
449C22⋊C8—222no—
450#97—222no—
451#95—21no—
452#95—111no—
453#95—111no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459C2×C11—81no—
460C2×C11#246111yescharacteristic
461C2×C11#311111yescharacteristic
462C2×C11#312611yescharacteristic
463C2×C11#326711yescharacteristic
464C2×C11#327111yescharacteristic
465C2×C11#335011yescharacteristic
466C2×C11#335111yescharacteristic
467D11—161no—
468C24—221no—
469C24D4×D1111yescharacteristic
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8#434112yes—
476C2×D4—221no—
477C2×D4—221no—
478C2×D4—221no—
479C2×D4—221no—
480C2×D4—221no—
481C2×D4—221no—
482C2×D4—442no—
483C2×D4—442no—
484C2×D4—881no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—111no—
496C22×C4—111no—
497C22×C4—111no—
498C22×C4—111no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4D4×D1111yescharacteristic
503C22×C4C23×D1111yescharacteristic
504SD16—444no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—112no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8D4×D1112yes—
517C4⋊C4—24no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—112no—
524C4⋊C4—112no—
525C4⋊C4—221no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—442no—
530C4⋊C4—442no—
531C4⋊C4—442no—
532C4⋊C4—442no—
533C4⋊C4#434112yes—
534C22⋊C4—24no—
535C22⋊C4—81no—
536C22⋊C4—442no—
537C22⋊C4—442no—
538C22⋊C4—441no—
539C22⋊C4—441no—
540C22⋊C4—442no—
541C22⋊C4—881no—
542C22⋊C4—881no—
543C22⋊C4—881no—
544C42—221no—
545C42—221no—
546C42—221no—
547C42—221no—
548C42—442no—
549C42—442no—
550C42—442no—
551C42—881no—
552C11#2681111yescharacteristic, complemented, Sylow
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—441no—
561C23—441no—
562C23—441no—
563C23—441no—
564C23—441no—
565C23—441no—
566C23—441no—
567C23C2×D4×D1111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572D4—441no—
573D4—441no—
574D4—441no—
575D4—441no—
576D4—884no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—221no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—221no—
609C2×C4—221no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4C2×D4×D1111yescharacteristic
618C2×C4C2×#434111yescharacteristic
619C2×C4C2×#434111yescharacteristic
620C2×C4#41×D1111yescharacteristic
621C2×C4#6704211yescharacteristic
622C2×C4#6704311yescharacteristic
623C8—22no—
624C8—41no—
625C8—222no—
626C8—441no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—41no—
631C22—41no—
632C22—41no—
633C22—41no—
634C22—881no—
635C22—881no—
636C22—881no—
637C22—881no—
638C22—881no—
639C22—881no—
640C22—881no—
641C22#1062311711yescharacteristic
642C22#1062314011yescharacteristic
643C22#1062318611yescharacteristic
644C22#1062329311yescharacteristic
645C22#1062329911yescharacteristic
646C22#1062330811yescharacteristic
647C22#1062330911yescharacteristic
648C4—41no—
649C4—42no—
650C4—42no—
651C4—81no—
652C4—81no—
653C4—441no—
654C4—441no—
655C4—442no—
656C4—442no—
657C4—441no—
658C4—441no—
659C4—881no—
660C4#1062312711yescharacteristic
661C4#1062312911yescharacteristic
662C4#1062318911yescharacteristic
663C4#1062321311yescharacteristic
664C2—81no—
665C2—1761no—
666C2#1307257611yescharacteristic
667C2#1307872611yescharacteristic
668C2#1307890111yescharacteristic
669C2#1308014811yescharacteristic
670C2#1308019811yescharacteristic
671C2#1308115911yescharacteristic
672C2#1308117911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2035C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#2035D11
hypocenterC11#26811
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2035

Complements

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

NH ≅ G/Ntype
2. C2×#10622409C2semidirect
4. #13071647C2semidirect
5. #13069985C2semidirect
6. #13069953C2semidirect
8. #13069494C2semidirect
9. #13069252C2semidirect
10. #13069241C2semidirect
11. #13069232C2semidirect
12. #13068969C2semidirect
13. #13068813C2semidirect
14. #13068516C2semidirect
15. C11×#2035C2semidirect
223. #2035D11semidirect
552. C11#26811semidirect

Maximal subgroups

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

subgroupindex
C2×#106223502
C2×#106224092
#130729642
#130716472
#130699852
#130699532
#130696172
#130694942
#130692522
#130692412
#130692322
#130689692
#130688132
#130685162
C11×#20352
#2681111