Finite Group Databasebeta

← #14795074

Subgroups — #14795074

Order 2816.

912 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×#10622372C211yesmaximal, characteristic, complemented
2C2×#10622318C211yesmaximal, characteristic, complemented
3#13076967C211yesmaximal, characteristic, complemented
4#13071132C211yesmaximal, characteristic
5#13070048C211yesmaximal, characteristic, complemented
6#13070046C211yesmaximal, characteristic, complemented
7#13069804C211yesmaximal, characteristic
8#13069803C211yesmaximal, characteristic
9#13069566C211yesmaximal, characteristic, complemented
10#13069378C211yesmaximal, characteristic, complemented
11#13069359C211yesmaximal, characteristic, complemented
12#13069356C211yesmaximal, characteristic, complemented
13#13069316C211yesmaximal, characteristic, complemented
14#13068614C211yesmaximal, characteristic, complemented
15C11×#1936C211yesmaximal, characteristic, complemented
16C2×#66991C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×#66949—21no—
19C2×#66941C2211yescharacteristic
20C2×(C22⋊D11)⋊C4—21no—
21C2×C42×D11C2211yescharacteristic
22C2×C11×#102C2211yescharacteristic
23C2×C11×#102C2211yescharacteristic
24C2×C11×#97C2211yescharacteristic
25C11×#390C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C2×#66896C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622600C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622589C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40#10622585—21no—
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622569—21no—
44#10622558—21no—
45C22⋊C4×Dic11—21no—
46#10622541C2211yescharacteristic
47#10622541C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49#10622372—24no—
50#10622318—24no—
51#10622280—21no—
52#10622259—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×D4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C23×Dic11—21no—
64C22×C4×D11D411yescharacteristic
65C22×C4×D11D411yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×Dic22—21no—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11—21no—
79#66991—22no—
80#66991—22no—
81D4×Dic11—22no—
82D4×Dic11—22no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C2×C4×Dic11D411yescharacteristic
97C2×C4×Dic11D411yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66949—44no—
102#66941—22no—
103#66941—22no—
104(C22⋊D11)⋊C4—44no—
105C42×D11—22no—
106C42×D11—22no—
107C11×#102—22no—
108C11×#102—22no—
109C11×#97—22no—
110C11×#95—21no—
111#66896—22no—
112#66896—22no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119(C2×D11)⋊C8—22no—
120(C2×D11)⋊C8—22no—
121#66882—22no—
122#66881—22no—
123Dic11⋊C8—22no—
124Dic11⋊C8D414yescomplemented
125#66872—22no—
126#66871—22no—
127#66867—22no—
128#24709—111nomaximal, Sylow
129C24×C11—21no—
130C23×D11C2×D411yescharacteristic
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11—21no—
134C2×D4×C11—21no—
135C2×D4×C11—21no—
136C2×D4×C11#4112yes—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C2×C22⋊D11—24no—
144C2×C22⋊D11—42no—
145C2×C22⋊D11—42no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—42no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C2×C4×D11—22no—
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—22no—
160C2×C4×D11—22no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—21no—
164C2×C4×D11—21no—
165C2×C4×D11—21no—
166C2×C4×D11—21no—
167C2×C4×D11—41no—
168C2×Dic22—42no—
169C2×Dic22—42no—
170C2×Dic22—42no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11—21no—
175C2×C8×C11—21no—
176C2×C8×C11C2×D412yes—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—42no—
184C11×C22⋊C4—42no—
185C11×C22⋊C4—42no—
186C42×C11—21no—
187C42×C11—21no—
188C22⋊Dic11—24no—
189C22⋊Dic11—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11#4112yes—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203Dic11⋊C4—42no—
204Dic11⋊C4—42no—
205Dic11⋊C4—42no—
206C4×Dic11—22no—
207C4×Dic11—22no—
208C4×Dic11—42no—
209C4×Dic11C2×D412yes—
210C4×Dic11#4112yes—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8C2×D412yes—
217C2×#474—111no—
218C2×#432—111no—
219#2857—111no—
220C4×#121—111no—
221#2076—111no—
222#2076—111no—
223#2034—111no—
224#2034—111no—
225#1988—111no—
226#1948—111no—
227#1944—111no—
228#1944—111no—
229#1936—111no—
230#1936D1111yescharacteristic, complemented
231#1802—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#13712yes—
247D4×C11—22no—
248D4×C11—22no—
249D4×C11—41no—
250D4×C11—41no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—21no—
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×C11C22×D411yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C112−1+411yescharacteristic
271C2×C4×C112−1+411yescharacteristic
272C22⋊D11—48no—
273C2×Dic11—21no—
274C2×Dic11—21no—
275C2×Dic11—21no—
276C2×Dic11—22no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—84no—
291C2×Dic11#12112yes—
292C2×Dic11#12112yes—
293C2×Dic11AGL(1,ℤ/8)12yes—
294C2×Dic11AGL(1,ℤ/8)12yes—
295C4×D11—44no—
296C4×D11—41no—
297C4×D11—41no—
298C4×D11—41no—
299C4×D11—41no—
300C4×D11—44no—
301Dic22—84no—
302C8×C11—22no—
303C8×C11—41no—
304C11⋊C8—22no—
305C11⋊C8—41no—
306C2×C4⋊Q8—111no—
307C2×C22⋊Q8—221no—
308C2×#121—111no—
309C2×C4×D4—111no—
310C2×C4×D4—221no—
311C22×C42—111no—
312#474—224no—
313#432—224no—
314C2×#107—111no—
315C2×#107—111no—
316C2×#106—111no—
317C2×#106—111no—
318C2×C4⋊C8—111no—
319C2×C4⋊C8—111no—
320C2×#102—111no—
321C2×#102—111no—
322C2×#102C2×D1111yescharacteristic
323C2×#102C2×D1111yescharacteristic
324C2×C22⋊C8—111no—
325C2×C22⋊C8—111no—
326C2×#97—111no—
327C2×#97C2×D1111yescharacteristic
328#391—221no—
329#390C2×D1111yescharacteristic
330#389—111no—
331#389—111no—
332#389—221no—
333#389C2×D1111yescharacteristic
334#388—221no—
335#386—221no—
336#384—111no—
337#380—111no—
338#380—111no—
339#380—111no—
340#380—221no—
341C4×C4⋊C4—111no—
342C4×C22⋊C4—221no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#340C2×D1111yescharacteristic
350#340C2×D1111yescharacteristic
351C22×C11—42no—
352C22×C11—42no—
353C22×C11—42no—
354C22×C11—81no—
355C22×C11—81no—
356C22×C11—81no—
357C22×C11—81no—
358C22×C11C2×#12111yescharacteristic
359C22×C11#52511yescharacteristic
360C22×C11#53611yescharacteristic
361C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
362C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
363C22×C11C2×#13711yescharacteristic
364C22×C11#57511yescharacteristic
365C2×D11—22no—
366C2×D11—22no—
367C2×D11—22no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C4×C11—41no—
373C4×C11—41no—
374C4×C11—81no—
375C4×C11—81no—
376C4×C11—81no—
377C4×C11#54711yescharacteristic
378C4×C11#54811yescharacteristic
379C4×C11#55211yescharacteristic
380C4×C11#55611yescharacteristic
381Dic11—22no—
382Dic11—42no—
383Dic11—41no—
384Dic11—81no—
385Dic11—81no—
386Dic11—81no—
387Dic11#46914yes—
388C22×Q8—221no—
389C22×D4—221no—
390C22×D4C22×D1111yescharacteristic
391C23×C4—111no—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—221no—
395C22×C8—111no—
396C22×C8—111no—
397C22×C8C22×D1111yescharacteristic
398C22×C8C22×D1111yescharacteristic
399C4⋊Q8—222no—
400C4⋊Q8—222no—
401C22⋊Q8—444no—
402#121—222no—
403#121—222no—
404C4×D4—222no—
405C4×D4—222no—
406C4×D4—444no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—111no—
409C2×C4⋊C4—111no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—111no—
412C2×C4⋊C4—221no—
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—221no—
423C2×C22⋊C4—221no—
424C2×C22⋊C4—221no—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—221no—
427C2×C42—111no—
428C2×C42—111no—
429C2×C42—111no—
430C2×C42—222no—
431C2×C42—222no—
432C2×C42—221no—
433C2×C42C22×D1111yescharacteristic
434#107—222no—
435#107—222no—
436#106—222no—
437#106—222no—
438C4⋊C8—114no—
439C4⋊C8—222no—
440#102—22no—
441#102—22no—
442#102—222no—
443#102—222no—
444C22⋊C8—222no—
445C22⋊C8—222no—
446#97—22no—
447#97—222no—
448#95—21no—
449#95—221no—
450#95—221no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455C2×C11—82no—
456C2×C11#241511yescharacteristic
457C2×C11C2×#46911yescharacteristic
458C2×C11#305611yescharacteristic
459C2×C11#311011yescharacteristic
460C2×C11#311511yescharacteristic
461C2×C11#323511yescharacteristic
462C2×C11#323911yescharacteristic
463D11—42no—
464C24—21no—
465C24—111no—
466C2×Q8—442no—
467C2×Q8—442no—
468C2×Q8—442no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—224no—
475C2×D4—442no—
476C2×D4—442no—
477C2×D4#433912yes—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—111no—
482C22×C4—111no—
483C22×C4—111no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—222no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—221no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—441no—
500C22×C4—442no—
501C22×C4—442no—
502C22×C4—442no—
503C22×C4D4×D1111yescharacteristic
504C22×C4D4×D1111yescharacteristic
505C22×C4C23×D1111yescharacteristic
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—112no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8D4×D1112yes—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—42no—
525C4⋊C4—112no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—442no—
534C4⋊C4—442no—
535C4⋊C4—442no—
536C4⋊C4—442no—
537C4⋊C4—442no—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—224no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—442no—
545C42—21no—
546C42—21no—
547C42—112no—
548C42—112no—
549C42—222no—
550C42—222no—
551C42—442no—
552C11#2470911yescharacteristic, complemented, Sylow
553C23—22no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—112no—
561C23—221no—
562C23—221no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23C2×D4×D1111yescharacteristic
568Q8—884no—
569D4—22no—
570D4—22no—
571D4—41no—
572D4—41no—
573D4—448no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—112no—
590C2×C4—112no—
591C2×C4—112no—
592C2×C4—112no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—221no—
596C2×C4—222no—
597C2×C4—221no—
598C2×C4—221no—
599C2×C4—444no—
600C2×C4—444no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—441no—
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—884no—
617C2×C4C2×#433911yescharacteristic
618C2×C4C2×D4×D1111yescharacteristic
619C2×C4#41×D1111yescharacteristic
620C2×C4#41×D1111yescharacteristic
621C2×C4#6704311yescharacteristic
622C2×C4#6704311yescharacteristic
623C8—22no—
624C8—41no—
625C8—222no—
626C8—441no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—81no—
631C22—81no—
632C22—81no—
633C22—81no—
634C22—222no—
635C22—222no—
636C22—222no—
637C22—441no—
638C22—441no—
639C22—441no—
640C22—441no—
641C22#1062307811yescharacteristic
642C22D11×#12111yescharacteristic
643C22#1062320611yescharacteristic
644C22D11×AGL(1,ℤ/8)11yescharacteristic
645C22D11×AGL(1,ℤ/8)11yescharacteristic
646C22#1062330411yescharacteristic
647C22D11×#13711yescharacteristic
648C4—41no—
649C4—41no—
650C4—81no—
651C4—81no—
652C4—81no—
653C4—114no—
654C4—222no—
655C4—441no—
656C4—442no—
657C4—881no—
658C4—881no—
659C4—881no—
660C4#1062306211yescharacteristic
661C4#1062308311yescharacteristic
662C4#1062318611yescharacteristic
663C4#1062323311yescharacteristic
664C2—82no—
665C2—442no—
666C2#1307204211yescharacteristic
667C2D11×#46911yescharacteristic
668C2#1307824111yescharacteristic
669C2#1307871311yescharacteristic
670C2#1307876311yescharacteristic
671C2#1307980911yescharacteristic
672C2#1307984211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1936C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenter#1936D11
hypocenterC11#24709
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
1. C2×#10622372C2semidirect
2. C2×#10622318C2semidirect
3. #13076967C2semidirect
5. #13070048C2semidirect
6. #13070046C2semidirect
9. #13069566C2semidirect
10. #13069378C2semidirect
11. #13069359C2semidirect
12. #13069356C2semidirect
13. #13069316C2semidirect
14. #13068614C2semidirect
15. C11×#1936C2semidirect
124. Dic11⋊C8D4semidirect
230. #1936D11semidirect
552. C11#24709semidirect

Maximal subgroups

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

subgroupindex
C2×#106223722
C2×#106223182
#130769672
#130711322
#130700482
#130700462
#130698042
#130698032
#130695662
#130693782
#130693592
#130693562
#130693162
#130686142
C11×#19362
#2470911