Finite Group Databasebeta

← #14823206

Subgroups — #14823206

Order 2816.

832 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622501C211yesmaximal, characteristic, complemented
2#13072960C211yesmaximal, characteristic, complemented
3#13071650C211yesmaximal, characteristic
4#13069996C211yesmaximal, characteristic, complemented
5#13069951C211yesmaximal, characteristic, complemented
6#13069804C211yesmaximal, characteristic
7#13069620C211yesmaximal, characteristic
8#13069498C211yesmaximal, characteristic, complemented
9#13069249C211yesmaximal, characteristic, complemented
10#13069246C211yesmaximal, characteristic, complemented
11#13069228C211yesmaximal, characteristic, complemented
12#13068950C211yesmaximal, characteristic, complemented
13#13068814C211yesmaximal, characteristic, complemented
14#13068515C211yesmaximal, characteristic, complemented
15C2×C11×#478C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×#66991C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C2×#66950C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C11×#478—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#106C2211yescharacteristic
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28#10622834C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30#10622826—21no—
31C4×C22⋊Dic11—21no—
32C2×(C2×D11)⋊C8C2211yescharacteristic
33C2×(C2×D11)⋊C8C2211yescharacteristic
34C2×#66881C2211yescharacteristic
35C2×#66880C2211yescharacteristic
36C2×#66880C2211yescharacteristic
37C2×#66879C2211yescharacteristic
38#10622606—21no—
39#10622603—21no—
40#10622600C2211yescharacteristic
41#10622599—21no—
42#10622590—21no—
43C4⋊C4×Dic11C2211yescharacteristic
44C4⋊C4×Dic11C2211yescharacteristic
45#10622587C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622570—21no—
50#10622557—21no—
51C4×(C2×D11)⋊C4C2211yescharacteristic
52#10622542C2211yescharacteristic
53#10622541C2211yescharacteristic
54#10622501—24no—
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C23×C4×C11—21no—
63C22×C22⋊D11—21no—
64C22×C4×D11C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C11×#125—22no—
69C11×#125—41no—
70C4×D4×C11—22no—
71C4×D4×C11—41no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82#66991—22no—
83#66991—22no—
84C2×#4324—22no—
85C2×#4324—22no—
86C2×#4324—41no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4D411yescharacteristic
91C2×(C2×D11)⋊C4D411yescharacteristic
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103#66950—22no—
104#66950—41no—
105#66945—22no—
106#66945—41no—
107C11×#107D414yescomplemented
108C11×#106—22no—
109C11×C4⋊C8—22no—
110C11×#102—22no—
111C11×#102—22no—
112#66896—22no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95D411yescharacteristic
122C11⋊#95D411yescharacteristic
123(C2×D11)⋊C8—22no—
124(C2×D11)⋊C8—22no—
125#66881—22no—
126#66880—22no—
127#66880—22no—
128#66879—22no—
129#66874—22no—
130#66872—22no—
131#66871—41no—
132#26813—111nomaximal, Sylow
133C24×C11—21no—
134C23×D11C2×D411yescharacteristic
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11#4112yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—81no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C2×C22⋊D11—24no—
151C2×C22⋊D11—81no—
152C2×C22⋊D11—81no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159C22×Dic11C2×D411yescharacteristic
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11C2×D412yes—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4C2×D412yes—
185C11×C4⋊C4C2×D412yes—
186C11×C22⋊C4—42no—
187C42×C11—21no—
188C42×C11—21no—
189C22⋊Dic11—24no—
190C22⋊Dic11—42no—
191C22⋊Dic11—81no—
192#4324—44no—
193(C2×D11)⋊C4—41no—
194(C2×D11)⋊C4—41no—
195(C2×D11)⋊C4—42no—
196(C2×D11)⋊C4—42no—
197(C2×D11)⋊C4—42no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—42no—
204C4⋊Dic11#4112yes—
205Dic11⋊C4—81no—
206C4×Dic11—21no—
207C4×Dic11—21no—
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×#485—111no—
218C2×#478D1111yescharacteristic, complemented
219#2489—111no—
220#2363—111no—
221#2066—111no—
222#2059—111no—
223#2034—111no—
224#2000—111no—
225#1973—111no—
226#1927—111no—
227#1926—111no—
228#1924—111no—
229#1877—111no—
230#1854—111no—
231#1776—111no—
232C23×C11—22no—
233C23×C11—41no—
234C23×C11—41no—
235C23×C11—41no—
236C23×C11—41no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11C22×D411yescharacteristic
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247D4×C11—22no—
248D4×C11—22no—
249D4×C11—41no—
250D4×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—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
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—84no—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×C4×C112−1+411yescharacteristic
273C22⋊D11—84no—
274C2×Dic11—22no—
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
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—
295C4×D11—41no—
296C4×D11—41no—
297C4×D11—41no—
298C4×D11—41no—
299Dic22—41no—
300Dic22—41no—
301Dic22—41no—
302Dic22—41no—
303C8×C11—22no—
304C8×C11—41no—
305C11⋊C8—22no—
306C11⋊C8—41no—
307C22×SD16—111no—
308C2×#125C2×D1111yescharacteristic
309C2×C22⋊Q8—111no—
310C2×#121—111no—
311C2×C4×D4C2×D1111yescharacteristic
312C2×#117—111no—
313#485—224no—
314#478—24no—
315C2×#107—111no—
316C2×#107C2×D1111yescharacteristic
317C2×#106—111no—
318C2×#106—111no—
319C2×#106C2×D1111yescharacteristic
320C2×C4⋊C8C2×D1111yescharacteristic
321C2×#103—111no—
322C2×#103—111no—
323C2×#103—111no—
324C2×#102—111no—
325C2×#102C2×D1111yescharacteristic
326C2×#102C2×D1111yescharacteristic
327C2×C22⋊C8—111no—
328C2×C22⋊C8—111no—
329C2×#97—111no—
330#400—221no—
331#397—221no—
332#391—111no—
333#391—111no—
334#390—111no—
335#390—221no—
336#389—111no—
337#388—221no—
338#388—221no—
339#386—221no—
340#382—221no—
341#380—111no—
342C4×C4⋊C4—111no—
343C4×C4⋊C4—111no—
344C4×C22⋊C4—111no—
345C4×C22⋊C4—221no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340—111no—
350#336—111no—
351#336—111no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—42no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11—81no—
359C22×C11#52511yescharacteristic
360C22×C11D4211yescharacteristic
361C22×C11#54711yescharacteristic
362C22×C11#57511yescharacteristic
363C22×C11#57511yescharacteristic
364C22×C11#57711yescharacteristic
365C22×C11#57711yescharacteristic
366C2×D11—41no—
367C2×D11—41no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C2×D11—41no—
373C4×C11—41no—
374C4×C11—42no—
375C4×C11—42no—
376C4×C11—41no—
377C4×C11—81no—
378C4×C11#53211yescharacteristic
379C4×C11#54211yescharacteristic
380C4×C11#54811yescharacteristic
381C4×C11#55111yescharacteristic
382Dic11—41no—
383Dic11—41no—
384Dic11—42no—
385Dic11—41no—
386Dic11—81no—
387Dic11—81no—
388Dic11—81no—
389C22×Q8—111no—
390C22×D4—221no—
391C22×D4C22×D1111yescharacteristic
392C23×C4—21no—
393C23×C4—111no—
394C2×SD16—222no—
395C2×SD16—222no—
396C2×SD16—441no—
397C22×C8—111no—
398C22×C8—111no—
399C22×C8C22×D1111yescharacteristic
400C22×C8C22×D1111yescharacteristic
401#125—22no—
402#125—41no—
403C22⋊Q8—222no—
404C22⋊Q8—441no—
405#121—222no—
406#121—222no—
407C4×D4—22no—
408C4×D4—41no—
409#117—222no—
410#117—441no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—221no—
417C2×C4⋊C4—221no—
418C2×C4⋊C4C22×D1111yescharacteristic
419C2×C4⋊C4C22×D1111yescharacteristic
420C2×C4⋊C4C22×D1111yescharacteristic
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—221no—
432C2×C42—221no—
433C2×C42—221no—
434C2×C42C22×D1111yescharacteristic
435#107—441no—
436#107C22⋊D1114yescomplemented
437#106—22no—
438#106—222no—
439#106—222no—
440C4⋊C8—22no—
441#103—222no—
442#103—222no—
443#103—222no—
444#102—22no—
445#102—22no—
446#102—222no—
447C22⋊C8—222no—
448C22⋊C8—222no—
449#97—222no—
450#95—111no—
451#95—111no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459#95—221no—
460C2×C11—82no—
461C2×C11#246111yescharacteristic
462C2×C11#311111yescharacteristic
463C2×C11#312311yescharacteristic
464C2×C11#326711yescharacteristic
465C2×C11#327111yescharacteristic
466C2×C11#334811yescharacteristic
467C2×C11#335111yescharacteristic
468D11—81no—
469C24—21no—
470C24—111no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×Q8—221no—
474C2×Q8—221no—
475C2×Q8—221no—
476C2×Q8—221no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—224no—
483C2×D4—881no—
484C2×D4—881no—
485C2×D4#434312yes—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—42no—
490C22×C4—42no—
491C22×C4—81no—
492C22×C4—111no—
493C22×C4—111no—
494C22×C4—111no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4D4×D1111yescharacteristic
506C22×C4D4×D1111yescharacteristic
507C22×C4C23×D1111yescharacteristic
508SD16—444no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—112no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C2×C8C2×C22⋊D1112yes—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—42no—
526C4⋊C4—42no—
527C4⋊C4—112no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—442no—
534C4⋊C4—881no—
535C4⋊C4C2×C22⋊D1112yes—
536C4⋊C4C2×C22⋊D1112yes—
537C22⋊C4—42no—
538C22⋊C4—224no—
539C22⋊C4—441no—
540C22⋊C4—441no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—442no—
545C22⋊C4—881no—
546C42—21no—
547C42—21no—
548C42—221no—
549C42—221no—
550C42—442no—
551C42—442no—
552C42—881no—
553C11#2681311yescharacteristic, complemented, Sylow
554C23—22no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—221no—
562C23—221no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23—221no—
568C23C2×D4×D1111yescharacteristic
569Q8—441no—
570Q8—441no—
571Q8—441no—
572Q8—441no—
573D4—22no—
574D4—22no—
575D4—41no—
576D4—41no—
577D4—884no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—84no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—221no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—221no—
600C2×C4—222no—
601C2×C4—221no—
602C2×C4—221no—
603C2×C4—221no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
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#6703711yescharacteristic
620C2×C4C2×#434311yescharacteristic
621C2×C4#6704011yescharacteristic
622C2×C4#41×D1111yescharacteristic
623C2×C4#41×D1111yescharacteristic
624C2×C4C22×C22⋊D1111yescharacteristic
625C8—22no—
626C8—41no—
627C8—222no—
628C8—441no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—441no—
637C22—441no—
638C22—441no—
639C22—441no—
640C22—441no—
641C22—441no—
642C22—441no—
643C22#1062315811yescharacteristic
644C22#1062316211yescharacteristic
645C22#1062329911yescharacteristic
646C22#1062330111yescharacteristic
647C22#1062330411yescharacteristic
648C22#1062330611yescharacteristic
649C22D4×C22⋊D1111yescharacteristic
650C4—41no—
651C4—42no—
652C4—42no—
653C4—41no—
654C4—81no—
655C4—441no—
656C4—442no—
657C4—441no—
658C4—441no—
659C4—881no—
660C4—881no—
661C4—881no—
662C4#1062316811yescharacteristic
663C4#1062317111yescharacteristic
664C4#1062334811yescharacteristic
665C4#1062336311yescharacteristic
666C2—82no—
667C2—881no—
668C2#1307259011yescharacteristic
669C2#1307873011yescharacteristic
670C2#1307887011yescharacteristic
671C2#1308013511yescharacteristic
672C2#1308020111yescharacteristic
673C2#1308112811yescharacteristic
674C2#1308118311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#478C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenterC2×#478D11
hypocenterC11#26813
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#478

Complements

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

NH ≅ G/Ntype
1. C2×#10622501C2semidirect
2. #13072960C2semidirect
4. #13069996C2semidirect
5. #13069951C2semidirect
8. #13069498C2semidirect
9. #13069249C2semidirect
10. #13069246C2semidirect
11. #13069228C2semidirect
12. #13068950C2semidirect
13. #13068814C2semidirect
14. #13068515C2semidirect
15. C2×C11×#478C2semidirect
107. C11×#107D4semidirect
218. C2×#478D11semidirect
436. #107C22⋊D11semidirect
553. C11#26813semidirect

Maximal subgroups

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

subgroupindex
C2×#106225012
#130729602
#130716502
#130699962
#130699512
#130698042
#130696202
#130694982
#130692492
#130692462
#130692282
#130689502
#130688142
#130685152
C2×C11×#4782
#2681311