Finite Group Databasebeta

← #14802037

Subgroups — #14802037

Order 2816.

904 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622648C211yesmaximal, characteristic, complemented
2#13073079C211yesmaximal, characteristic, complemented
3#13071658C211yesmaximal, characteristic, complemented
4#13070090C211yesmaximal, characteristic, complemented
5#13070032C211yesmaximal, characteristic, complemented
6#13069986C211yesmaximal, characteristic, complemented
7#13069924C211yesmaximal, characteristic, complemented
8#13069381C211yesmaximal, characteristic, complemented
9#13069239C211yesmaximal, characteristic, complemented
10#13068966C211yesmaximal, characteristic, complemented
11#13068939C211yesmaximal, characteristic, complemented
12#13068794C211yesmaximal, characteristic, complemented
13#13068614C211yesmaximal, characteristic, complemented
14#13068333C211yesmaximal, characteristic, complemented
15C2×C11×#466C211yesmaximal, characteristic
16C22×C11×D8C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×C11×#121C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C11×#466—24no—
24C2×C11×#107C2211yescharacteristic
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27#10622835—21no—
28#10622835—21no—
29#10622834—21no—
30#10622834C2211yescharacteristic
31#10622834C2211yescharacteristic
32#10622834C2211yescharacteristic
33#10622833—21no—
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C4×C22⋊Dic11C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40C2×Dic11⋊C8C2211yescharacteristic
41C2×Dic11⋊C8C2211yescharacteristic
42#10622648—24no—
43#10622598C2211yescharacteristic
44#10622590C2211yescharacteristic
45#10622589C2211yescharacteristic
46C4⋊C4×Dic11C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49#10622564—21no—
50#10622557—21no—
51#10622557—21no—
52C22⋊C4×Dic11—21no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622188C2211yescharacteristic
58#10622188C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11C2311yescharacteristic
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×Dic11—21no—
67C2×C11×D8—22no—
68C2×C11×D8—22no—
69C2×C11×D8—41no—
70C22×C8×C11—22no—
71C22×C8×C11—22no—
72C22×C8×C11—41no—
73C22×C8×C11C2311yescharacteristic
74C22×C8×C11C2311yescharacteristic
75C11×#121—22no—
76C11×#121—22no—
77C11×#121—22no—
78C11×#121D414yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11D411yescharacteristic
93C2×C22⋊Dic11D411yescharacteristic
94D4×Dic11—22no—
95D4×Dic11—41no—
96#66979—22no—
97#66979—22no—
98#66979—22no—
99#66979—41no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—21no—
106C2×Dic11⋊C4—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11C2311yescharacteristic
111C2×C4×Dic11C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C11×#107—22no—
115C11×#102—22no—
116C11×#102—22no—
117#66896—22no—
118#66896—22no—
119#66896—22no—
120#66896—41no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95D411yescharacteristic
126C11⋊#95D411yescharacteristic
127C22⋊(C11⋊C8)—22no—
128Dic11⋊C8—22no—
129Dic11⋊C8—41no—
130#66872—22no—
131#66871—22no—
132#25207—111nomaximal, Sylow
133C24×C11—21no—
134C24×C11—21no—
135C24×C11C2×D411yescharacteristic
136C2×D4×C11—24no—
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—42no—
149C2×D4×C11—81no—
150C2×D4×C11—81no—
151C2×D4×C11—81no—
152C2×D4×C11—81no—
153C2×D4×C11C2×D412yes—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D412yes—
162C22×C4×C11#4112yes—
163C22×C4×C11C2411yescharacteristic
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—42no—
169C22×Dic11—42no—
170C22×Dic11—81no—
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175C11×D8—44no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—44no—
182C2×C8×C11#4112yes—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4C2×D412yes—
187C11×C22⋊C4—24no—
188C11×C22⋊C4—42no—
189C22⋊Dic11—22no—
190C22⋊Dic11—41no—
191C22⋊Dic11—42no—
192C22⋊Dic11—42no—
193C22⋊Dic11—42no—
194C22⋊Dic11—42no—
195C22⋊Dic11—42no—
196C22⋊Dic11—42no—
197C22⋊Dic11—81no—
198C22⋊Dic11—81no—
199C22⋊Dic11—81no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—81no—
208C4⋊Dic11#4112yes—
209Dic11⋊C4—81no—
210Dic11⋊C4—81no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—21no—
214C4×Dic11—21no—
215C4×Dic11—42no—
216C4×Dic11—42no—
217C4×Dic11—81no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224C2×#482—111no—
225C2×#466D1111yescharacteristic
226#2500—111no—
227#2363—111no—
228#2083—111no—
229#2073—111no—
230#2065—111no—
231#2054—111no—
232#1949—111no—
233#1925—111no—
234#1879—111no—
235#1875—111no—
236#1850—111no—
237#1802—111no—
238#1735—111no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—22no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11—41no—
253C23×C11—41no—
254C23×C11—41no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11#12112yes—
260C23×C11C22×D411yescharacteristic
261D4×C11—22no—
262D4×C11—22no—
263D4×C11—41no—
264D4×C11—41no—
265D4×C11—41no—
266D4×C11—41no—
267D4×C11—41no—
268D4×C11—41no—
269D4×C11—84no—
270D4×C11—84no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11#12112yes—
284C2×C4×C11C22×D411yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11C2×#4111yescharacteristic
287C2×C4×C11C2×#4111yescharacteristic
288C2×C4×C11H(5,𝔽2)11yescharacteristic
289C2×C4×C112−1+411yescharacteristic
290C2×Dic11—21no—
291C2×Dic11—21no—
292C2×Dic11—21no—
293C2×Dic11—22no—
294C2×Dic11—21no—
295C2×Dic11—21no—
296C2×Dic11—21no—
297C2×Dic11—21no—
298C2×Dic11—21no—
299C2×Dic11—21no—
300C2×Dic11—21no—
301C2×Dic11—21no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306C2×Dic11—41no—
307C2×Dic11—41no—
308C2×Dic11—41no—
309C2×Dic11—41no—
310C2×Dic11—41no—
311C2×Dic11—41no—
312C2×Dic11—41no—
313C2×Dic11—84no—
314C2×Dic11#13512yes—
315C8×C11—22no—
316C8×C11—41no—
317C11⋊C8—41no—
318C11⋊C8—41no—
319C22×D8C2×D1111yescharacteristic
320C23×C8C2×D1111yescharacteristic
321C2×#121C2×D1111yescharacteristic
322C2×#121C2×D1111yescharacteristic
323C2×C4×D4—111no—
324C2×#117—111no—
325C2×#117—111no—
326#482—224no—
327#466—24no—
328C2×#107—111no—
329C2×#107C2×D1111yescharacteristic
330C2×#106—111no—
331C2×C4⋊C8—111no—
332C2×C4⋊C8—111no—
333C2×#102—111no—
334C2×#102—111no—
335C2×#102—111no—
336C2×#102—111no—
337C2×#102C2×D1111yescharacteristic
338C2×#102C2×D1111yescharacteristic
339C2×C22⋊C8—111no—
340#394—221no—
341#394—221no—
342#390—111no—
343#390—111no—
344#390—111no—
345#390—221no—
346#389—111no—
347#388—221no—
348#388—221no—
349#388—221no—
350#386—221no—
351#384—111no—
352#382—111no—
353C4×C4⋊C4—111no—
354C4×C22⋊C4—111no—
355C4×C22⋊C4—221no—
356#340—111no—
357#340—111no—
358#340—111no—
359#340—111no—
360#340—111no—
361#340—111no—
362#336—111no—
363#336—111no—
364C22×C11—22no—
365C22×C11—22no—
366C22×C11—22no—
367C22×C11—41no—
368C22×C11—41no—
369C22×C11—41no—
370C22×C11—41no—
371C22×C11—42no—
372C22×C11—42no—
373C22×C11—42no—
374C22×C11—81no—
375C22×C11—81no—
376C22×C11—81no—
377C22×C11—81no—
378C22×C11—81no—
379C22×C11—81no—
380C22×C11—81no—
381C22×C11—81no—
382C22×C11—81no—
383C22×C11—81no—
384C22×C11—81no—
385C22×C11C2×#12111yescharacteristic
386C22×C11#54611yescharacteristic
387C22×C11#54711yescharacteristic
388C22×C11C2×#13511yescharacteristic
389C22×C11#57511yescharacteristic
390C22×C11#57611yescharacteristic
391C22×C11#57611yescharacteristic
392C4×C11—22no—
393C4×C11—42no—
394C4×C11—81no—
395C4×C11#52911yescharacteristic
396C4×C11#53911yescharacteristic
397C4×C11#54611yescharacteristic
398C4×C11#54711yescharacteristic
399Dic11—22no—
400Dic11—41no—
401Dic11—41no—
402Dic11—42no—
403Dic11—41no—
404Dic11—81no—
405Dic11—81no—
406Dic11—81no—
407C22×D4—21no—
408C22×D4—21no—
409C22×D4C22×D1111yescharacteristic
410C22×D4C22×D1111yescharacteristic
411C23×C4—221no—
412C23×C4C22×D1111yescharacteristic
413C2×D8—22no—
414C2×D8—22no—
415C2×D8—41no—
416C22×C8—22no—
417C22×C8—22no—
418C22×C8—41no—
419C22×C8—111no—
420C22×C8—111no—
421C22×C8C22×D1111yescharacteristic
422C22×C8C22×D1111yescharacteristic
423#121—22no—
424#121—22no—
425#121—22no—
426#121C22⋊D1114yes—
427C4×D4—222no—
428C4×D4—441no—
429#117—222no—
430#117—222no—
431#117—222no—
432#117—441no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—111no—
436C2×C4⋊C4—111no—
437C2×C4⋊C4—221no—
438C2×C4⋊C4—221no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—111no—
445C2×C22⋊C4—111no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C22⋊C4—221no—
451C2×C22⋊C4—221no—
452C2×C22⋊C4—221no—
453C2×C22⋊C4—221no—
454C2×C22⋊C4—221no—
455C2×C42—111no—
456C2×C42—111no—
457C2×C42—221no—
458C2×C42—221no—
459C2×C42—221no—
460#107—22no—
461#107—222no—
462#106—222no—
463C4⋊C8—222no—
464C4⋊C8—441no—
465#102—22no—
466#102—22no—
467#102—222no—
468#102—222no—
469#102—222no—
470#102—441no—
471C22⋊C8—222no—
472#95—111no—
473#95—111no—
474#95—221no—
475#95—221no—
476#95—221no—
477#95—221no—
478C2×C11—42no—
479C2×C11—82no—
480C2×C11—161no—
481C2×C11#242511yescharacteristic
482C2×C11#303511yescharacteristic
483C2×C11#304111yescharacteristic
484C2×C11#329711yescharacteristic
485C2×C11#330911yescharacteristic
486C2×C11#334111yescharacteristic
487C2×C11#334711yescharacteristic
488C24—21no—
489C24—21no—
490C24D4×D1111yescharacteristic
491C2×D4—24no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—42no—
504C2×D4—81no—
505C2×D4—81no—
506C2×D4—81no—
507C2×D4—81no—
508C2×D4C2×C22⋊D1112yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—111no—
516C22×C4—111no—
517C22×C4—111no—
518C22×C4—111no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—442no—
524C22×C4—442no—
525C22×C4—881no—
526C22×C4D4×D1111yescharacteristic
527C22×C4#434112yes—
528C22×C4C2×C22⋊D1112yes—
529C22×C4C23×D1111yescharacteristic
530D8—44no—
531C2×C8—21no—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—44no—
537C2×C8—221no—
538C2×C8—221no—
539C2×C8—221no—
540C2×C8—221no—
541C2×C8—221no—
542C2×C8—221no—
543C2×C8#434112yes—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—112no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—221no—
551C4⋊C4—221no—
552C4⋊C4—221no—
553C4⋊C4—221no—
554C4⋊C4—221no—
555C4⋊C4—881no—
556C4⋊C4—881no—
557C4⋊C4—881no—
558C4⋊C4C2×C22⋊D1112yes—
559C22⋊C4—24no—
560C22⋊C4—42no—
561C22⋊C4—222no—
562C22⋊C4—442no—
563C22⋊C4—441no—
564C22⋊C4—442no—
565C22⋊C4—442no—
566C22⋊C4—442no—
567C22⋊C4—442no—
568C22⋊C4—442no—
569C22⋊C4—881no—
570C22⋊C4—881no—
571C22⋊C4—881no—
572C42—221no—
573C42—221no—
574C42—221no—
575C42—221no—
576C42—442no—
577C42—442no—
578C42—881no—
579C11#2520711yescharacteristic, complemented, Sylow
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—22no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23#6699212yes—
601C23C2×D4×D1111yescharacteristic
602D4—22no—
603D4—22no—
604D4—41no—
605D4—41no—
606D4—41no—
607D4—41no—
608D4—41no—
609D4—41no—
610D4—84no—
611D4—84no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—112no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—221no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—222no—
635C2×C4—221no—
636C2×C4—221no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—441no—
646C2×C4—441no—
647C2×C4—441no—
648C2×C4—884no—
649C2×C4#6699212yes—
650C2×C4C2×#434111yescharacteristic
651C2×C4C2×#434111yescharacteristic
652C2×C4#6703711yescharacteristic
653C2×C4#41×D1111yescharacteristic
654C2×C4#6704311yescharacteristic
655C2×C4C22×C22⋊D1111yescharacteristic
656C8—22no—
657C8—41no—
658C8—441no—
659C8—441no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22#1062314111yescharacteristic
682C22#1062314211yescharacteristic
683C22#1062328811yescharacteristic
684C22#1062328811yescharacteristic
685C22D11×#13511yescharacteristic
686C22#1062329911yescharacteristic
687C22C2×#6699211yescharacteristic
688C4—22no—
689C4—42no—
690C4—81no—
691C4—222no—
692C4—441no—
693C4—441no—
694C4—442no—
695C4—441no—
696C4—881no—
697C4—881no—
698C4—881no—
699C4#1062313111yescharacteristic
700C4#1062313311yescharacteristic
701C4#1062333711yescharacteristic
702C4#1062335511yescharacteristic
703C2—42no—
704C2—82no—
705C2—161no—
706C2#1307217311yescharacteristic
707C2#1307806711yescharacteristic
708C2#1307811611yescharacteristic
709C2#1308046111yescharacteristic
710C2#1308062811yescharacteristic
711C2#1308103511yescharacteristic
712C2#1308112211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#466C2
socleC23×C11C22×D4
hypercenterC2×#466D11
hypocenterC11#25207
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#466

Complements

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

NH ≅ G/Ntype
1. C2×#10622648C2semidirect
2. #13073079C2semidirect
3. #13071658C2semidirect
4. #13070090C2semidirect
5. #13070032C2semidirect
6. #13069986C2semidirect
7. #13069924C2semidirect
8. #13069381C2semidirect
9. #13069239C2semidirect
10. #13068966C2semidirect
11. #13068939C2semidirect
12. #13068794C2semidirect
13. #13068614C2semidirect
14. #13068333C2semidirect
579. C11#25207semidirect

Maximal subgroups

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

subgroupindex
C2×#106226482
#130730792
#130716582
#130700902
#130700322
#130699862
#130699242
#130693812
#130692392
#130689662
#130689392
#130687942
#130686142
#130683332
C2×C11×#4662
#2520711