Finite Group Databasebeta

← #14802107

Subgroups — #14802107

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622387C211yesmaximal, characteristic
2C2×#10622784C211yesmaximal, characteristic
3#13073100C211yesmaximal, characteristic, complemented
4#13071637C211yesmaximal, characteristic
5#13070102C211yesmaximal, characteristic, complemented
6#13070029C211yesmaximal, characteristic, complemented
7#13070009C211yesmaximal, characteristic, complemented
8#13069386C211yesmaximal, characteristic, complemented
9#13069254C211yesmaximal, characteristic, complemented
10#13068952C211yesmaximal, characteristic, complemented
11#13068920C211yesmaximal, characteristic, complemented
12#13068792C211yesmaximal, characteristic, complemented
13#13068624C211yesmaximal, characteristic, complemented
14D11×#340C211yesmaximal, characteristic, complemented
15C11×#2055C211yesmaximal, characteristic, complemented
16C22×C11×SD16C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C2×#66991C2211yescharacteristic
19C2×D4×Dic11C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×(C22⋊D11)⋊C4—21no—
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C11×#103C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C11×#391C2211yescharacteristic
28C11×#390C2211yescharacteristic
29#10622843C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34#10622784—24no—
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×#66882C2211yescharacteristic
37C2×#66881C2211yescharacteristic
38C2×Dic11⋊C8C2211yescharacteristic
39#10622590C2211yescharacteristic
40#10622586C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622569—21no—
43#10622559—21no—
44#10622557—21no—
45C4×(C2×D11)⋊C4C2211yescharacteristic
46#10622549C2211yescharacteristic
47C4×C4⋊Dic11C2211yescharacteristic
48#10622387—24no—
49#10622277—21no—
50#10622277—21no—
51#10622271—21no—
52#10622271—21no—
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C22×C22⋊D11—21no—
64C23×Dic11—21no—
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C22×C4×D11C2311yescharacteristic
68C2×C11×SD16—22no—
69C2×C11×SD16—22no—
70C2×C11×SD16—41no—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80#66999—22no—
81#66999—22no—
82#66991—22no—
83#66991D414yes—
84D4×Dic11—22no—
85D4×Dic11—41no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4D411yescharacteristic
88C2×(C2×D11)⋊C4D411yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×C8×D11—22no—
102C2×C8×D11—22no—
103C2×C8×D11—41no—
104C4⋊C4×D11—22no—
105C4⋊C4×D11—22no—
106C4⋊C4×D11—22no—
107C4⋊C4×D11—41no—
108(C22⋊D11)⋊C4—44no—
109C11×C4⋊C8—22no—
110C11×#103—41no—
111C11×#102—22no—
112C11×#95—21no—
113C11×#95—21no—
114#66899—22no—
115#66899—22no—
116#66896—22no—
117#66896—22no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95D411yescharacteristic
127C11⋊#95D411yescharacteristic
128(C2×D11)⋊C8—22no—
129#66882—22no—
130#66881—22no—
131Dic11⋊C8—41no—
132#66871—22no—
133#25212—111nomaximal, Sylow
134C24×C11—21no—
135C23×D11C2×D411yescharacteristic
136C2×Q8×C11—21no—
137C2×Q8×C11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—21no—
140C2×Q8×C11—21no—
141C2×Q8×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11C2×D412yes—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2411yescharacteristic
154C2×C22⋊D11—24no—
155C2×C22⋊D11—42no—
156C2×C22⋊D11—42no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—42no—
162C22×Dic11—42no—
163C22×Dic11—81no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C4×D11—21no—
170C2×C4×D11—21no—
171C2×C4×D11—42no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—42no—
176C2×C4×D11—81no—
177C2×C4×D11C2×D412yes—
178C2×C4×D11#4112yes—
179C11×SD16—44no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11#4112yes—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—21no—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—81no—
192C42×C11—21no—
193C42×C11—21no—
194C22⋊Dic11—24no—
195C22⋊Dic11—42no—
196(C2×D11)⋊C4—22no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—42no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205C4⋊Dic11C2×D412yes—
206C4⋊Dic11#4112yes—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209Dic11⋊C4—42no—
210Dic11⋊C4—42no—
211C4×Dic11—21no—
212C4×Dic11—21no—
213C4×Dic11—42no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C8×D11—44no—
221C2×#480—111no—
222C2×#465—111no—
223#2503—111no—
224#2361—111no—
225#2085—111no—
226#2073—111no—
227#2068—111no—
228#2055D1111yescharacteristic, complemented
229#1949—111no—
230#1928—111no—
231#1877—111no—
232#1872—111no—
233#1850—111no—
234#1804—111no—
235C2×#340—111no—
236C23×C11—22no—
237C23×C11—41no—
238C23×C11—41no—
239C23×C11—41no—
240C23×C11—41no—
241C23×C11—41no—
242C23×C11—41no—
243C23×C11C22×D411yescharacteristic
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—21no—
247C22×D11—21no—
248C22×D11#12112yes—
249C22×D11#13512yes—
250C22×D11AGL(1,ℤ/8)12yes—
251Q8×C11—41no—
252Q8×C11—41no—
253Q8×C11—41no—
254Q8×C11—41no—
255D4×C11—22no—
256D4×C11—22no—
257D4×C11—41no—
258D4×C11—41no—
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—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C22⋊D11—48no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—22no—
284C2×Dic11—21no—
285C2×Dic11—21no—
286C2×Dic11—22no—
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—
298C2×Dic11—41no—
299C2×Dic11—41no—
300C2×Dic11—41no—
301C2×Dic11—84no—
302C2×Dic11#12112yes—
303C4×D11—22no—
304C4×D11—22no—
305C4×D11—22no—
306C4×D11—22no—
307C4×D11—84no—
308C4×D11—84no—
309C8×C11—22no—
310C8×C11—41no—
311C11⋊C8—41no—
312C11⋊C8—41no—
313C22×SD16C2×D1111yescharacteristic
314C23×C8—111no—
315C2×C22⋊Q8—111no—
316C2×#121—111no—
317C2×C4×D4—111no—
318C2×C4×D4—221no—
319C22×C4⋊C4—111no—
320C22×C4⋊C4—111no—
321#480—224no—
322#465—224no—
323C2×#107—111no—
324C2×#107—111no—
325C2×#106—111no—
326C2×C4⋊C8—111no—
327C2×C4⋊C8C2×D1111yescharacteristic
328C2×#103—111no—
329C2×#103—111no—
330C2×#103C2×D1111yescharacteristic
331C2×#102—111no—
332C2×#102—111no—
333C2×#102C2×D1111yescharacteristic
334C2×C22⋊C8—111no—
335#400—221no—
336#400—221no—
337#391—111no—
338#391C2×D1111yescharacteristic
339#390C2×D1111yescharacteristic
340#389—111no—
341#388—221no—
342#386—221no—
343#385—221no—
344#382—111no—
345#382—111no—
346#381—221no—
347#381—221no—
348C4×C4⋊C4—111no—
349C4×C22⋊C4—111no—
350#340—111no—
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340C2×D1111yescharacteristic
356#336—111no—
357#336—111no—
358C22×C11—42no—
359C22×C11—42no—
360C22×C11—42no—
361C22×C11—81no—
362C22×C11—81no—
363C22×C11—81no—
364C22×C11—81no—
365C22×C11C2×#12111yescharacteristic
366C22×C11#54611yescharacteristic
367C22×C11#54711yescharacteristic
368C22×C11C2×#13511yescharacteristic
369C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
370C22×C11#57711yescharacteristic
371C22×C11#57811yescharacteristic
372C2×D11—22no—
373C2×D11—22no—
374C2×D11—22no—
375C2×D11—22no—
376C2×D11—22no—
377C2×D11—22no—
378C2×D11#46314yes—
379C4×C11—41no—
380C4×C11—41no—
381C4×C11—81no—
382C4×C11—81no—
383C4×C11—81no—
384C4×C11#52911yescharacteristic
385C4×C11#53911yescharacteristic
386C4×C11#54611yescharacteristic
387C4×C11#54711yescharacteristic
388Dic11—22no—
389Dic11—42no—
390Dic11—41no—
391Dic11—42no—
392Dic11—41no—
393Dic11—81no—
394Dic11—81no—
395C22×Q8C22×D1111yescharacteristic
396C22×D4—221no—
397C22×D4C22×D1111yescharacteristic
398C23×C4—111no—
399C23×C4—221no—
400C23×C4—221no—
401C23×C4—221no—
402C2×SD16—22no—
403C2×SD16—22no—
404C2×SD16—41no—
405C22×C8—111no—
406C22×C8—111no—
407C22×C8—222no—
408C22×C8—222no—
409C22×C8—441no—
410C22×C8C22×D1111yescharacteristic
411C22×C8C22×D1111yescharacteristic
412C22⋊Q8—222no—
413C22⋊Q8—222no—
414#121—114no—
415#121—222no—
416C4×D4—222no—
417C4×D4—441no—
418C4×D4—444no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—222no—
424C2×C4⋊C4—222no—
425C2×C4⋊C4—222no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—441no—
431C2×C4⋊C4C22×D1111yescharacteristic
432C2×C4⋊C4C22×D1111yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—111no—
436C2×C22⋊C4—111no—
437C2×C22⋊C4—221no—
438C2×C22⋊C4—221no—
439C2×C22⋊C4—221no—
440C2×C42—111no—
441C2×C42—221no—
442C2×C42C22×D1111yescharacteristic
443#107—222no—
444#107—222no—
445#106—222no—
446C4⋊C8—22no—
447C4⋊C8—441no—
448#103—41no—
449#103—222no—
450#103—222no—
451#102—22no—
452#102—222no—
453#102—222no—
454C22⋊C8—222no—
455#95—21no—
456#95—21no—
457#95—111no—
458#95—111no—
459#95—221no—
460#95—221no—
461#95—221no—
462#95—221no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467C2×C11—82no—
468C2×C11#242511yescharacteristic
469C2×C11C2×#46311yescharacteristic
470C2×C11#304611yescharacteristic
471C2×C11#330011yescharacteristic
472C2×C11#331011yescharacteristic
473C2×C11#333711yescharacteristic
474C2×C11#334311yescharacteristic
475D11—24no—
476C24—21no—
477C24—111no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—224no—
490C2×D4—442no—
491C2×D4—442no—
492C2×D4D4×D1112yes—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—111no—
497C22×C4—112no—
498C22×C4—112no—
499C22×C4—111no—
500C22×C4—111no—
501C22×C4—221no—
502C22×C4—221no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—442no—
510C22×C4—442no—
511C22×C4—442no—
512C22×C4—442no—
513C22×C4—442no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—881no—
517C22×C4—881no—
518C22×C4D4×D1111yescharacteristic
519C22×C4D4×D1111yescharacteristic
520C22×C4C23×D1111yescharacteristic
521SD16—44no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—444no—
534C2×C8#434112yes—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—112no—
540C4⋊C4—112no—
541C4⋊C4—221no—
542C4⋊C4—221no—
543C4⋊C4—221no—
544C4⋊C4—221no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—442no—
548C4⋊C4—442no—
549C4⋊C4—442no—
550C4⋊C4—442no—
551C22⋊C4—42no—
552C22⋊C4—81no—
553C22⋊C4—222no—
554C22⋊C4—222no—
555C22⋊C4—224no—
556C22⋊C4—442no—
557C22⋊C4—442no—
558C42—21no—
559C42—21no—
560C42—221no—
561C42—221no—
562C42—442no—
563C11#2521211yescharacteristic, complemented, Sylow
564C23—22no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—112no—
572C23—112no—
573C23—112no—
574C23—221no—
575C23—221no—
576C23—221no—
577C23—221no—
578C23C2×D4×D1111yescharacteristic
579Q8—41no—
580Q8—41no—
581Q8—41no—
582Q8—41no—
583D4—22no—
584D4—22no—
585D4—41no—
586D4—41no—
587D4—448no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—112no—
604C2×C4—221no—
605C2×C4—221no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—221no—
611C2×C4—221no—
612C2×C4—221no—
613C2×C4—221no—
614C2×C4—222no—
615C2×C4—221no—
616C2×C4—221no—
617C2×C4—222no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—884no—
629C2×C4—884no—
630C2×C4—884no—
631C2×C4C2×D4×D1111yescharacteristic
632C2×C4C2×#434111yescharacteristic
633C2×C4#6703711yescharacteristic
634C2×C4#41×D1111yescharacteristic
635C2×C4#41×D1111yescharacteristic
636C2×C4#6704311yescharacteristic
637C8—22no—
638C8—41no—
639C8—441no—
640C8—441no—
641C22—42no—
642C22—42no—
643C22—42no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—114no—
649C22—222no—
650C22—222no—
651C22—222no—
652C22—222no—
653C22—222no—
654C22—222no—
655C22D11×#12111yescharacteristic
656C22#1062314211yescharacteristic
657C22#1062314311yescharacteristic
658C22#1062329311yescharacteristic
659C22D11×#13511yescharacteristic
660C22D11×AGL(1,ℤ/8)11yescharacteristic
661C22#1062331011yescharacteristic
662C4—41no—
663C4—41no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—222no—
668C4—442no—
669C4—441no—
670C4—442no—
671C4—441no—
672C4—881no—
673C4—881no—
674C4#1062312211yescharacteristic
675C4#1062318611yescharacteristic
676C4#1062319111yescharacteristic
677C4#1062321111yescharacteristic
678C2—82no—
679C2—224no—
680C2#1307216811yescharacteristic
681C2D11×#46311yescharacteristic
682C2#1307816111yescharacteristic
683C2#1308051011yescharacteristic
684C2#1308064411yescharacteristic
685C2#1308099011yescharacteristic
686C2#1308105111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2055C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#2055D11
hypocenterC11#25212
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2055

Complements

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

NH ≅ G/Ntype
3. #13073100C2semidirect
5. #13070102C2semidirect
6. #13070029C2semidirect
7. #13070009C2semidirect
8. #13069386C2semidirect
9. #13069254C2semidirect
10. #13068952C2semidirect
11. #13068920C2semidirect
12. #13068792C2semidirect
13. #13068624C2semidirect
14. D11×#340C2semidirect
15. C11×#2055C2semidirect
228. #2055D11semidirect
563. C11#25212semidirect

Maximal subgroups

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

subgroupindex
C2×#106223872
C2×#106227842
#130731002
#130716372
#130701022
#130700292
#130700092
#130693862
#130692542
#130689522
#130689202
#130687922
#130686242
D11×#3402
C11×#20552
#2521211