Finite Group Databasebeta

← #14803943

Subgroups — #14803943

Order 2816.

850 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×#10622635C211yesmaximal, characteristic, complemented
2C2×C8×D44C211yesmaximal, characteristic
3#13073777C211yesmaximal, characteristic
4#13073521C211yesmaximal, characteristic
5#13070054C211yesmaximal, characteristic, complemented
6#13070043C211yesmaximal, characteristic, complemented
7#13069817C211yesmaximal, characteristic, complemented
8#13069810C211yesmaximal, characteristic, complemented
9#13069581C211yesmaximal, characteristic, complemented
10#13069384C211yesmaximal, characteristic, complemented
11#13069036C211yesmaximal, characteristic, complemented
12#13069036C211yesmaximal, characteristic, complemented
13#13068644C211yesmaximal, characteristic, complemented
14#13068640C211yesmaximal, characteristic, complemented
15C4×C11×#103C211yesmaximal, characteristic, complemented
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C2×#66999C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C22×C8×D11C2211yescharacteristic
21C2×C4×D44C2211yescharacteristic
22C2×#66923C2211yescharacteristic
23C2×C11×#103C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×(C2×D11)⋊C8C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31#10622635—24no—
32#10622604—21no—
33#10622600C2211yescharacteristic
34#10622600C2211yescharacteristic
35#10622600C2211yescharacteristic
36#10622600C2211yescharacteristic
37#10622600C2211yescharacteristic
38#10622600C2211yescharacteristic
39#10622596—21no—
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622553—21no—
45#10622553—21no—
46#10622553—21no—
47#10622553—21no—
48#10622549C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C8×D44—24no—
51#10622285—21no—
52#10622272—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C22×Q8×C11C2311yescharacteristic
62C22×D44D411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C4×Q8×C11—22no—
68C4×Q8×C11—22no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76#66999—22no—
77#66999—22no—
78#66999—41no—
79#66999—41no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4D411yescharacteristic
89C2×(C2×D11)⋊C4D411yescharacteristic
90C2×C4⋊Dic11D411yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×C8×D11—22no—
102C2×C8×D11—22no—
103C2×C8×D11—22no—
104C2×C8×D11—22no—
105C2×C8×D11—41no—
106C2×C8×D11—41no—
107C4×D44—22no—
108C4×D44—22no—
109#66923—22no—
110#66923—22no—
111C11×#103—22no—
112C11×#103—22no—
113C4×C8×C11—22no—
114C11×#95—21no—
115#66899—22no—
116#66899—22no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125(C2×D11)⋊C8—22no—
126(C2×D11)⋊C8—22no—
127#66872—22no—
128#66872—41no—
129#66871—22no—
130#66871—41no—
131C4⋊(C11⋊C8)D414yes—
132#25343—111nomaximal, Sylow
133C23×D11C2×D411yescharacteristic
134C23×D11C2×D411yescharacteristic
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×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—22no—
157C2×C4×D11—21no—
158C2×C4×D11—21no—
159C2×C4×D11—21no—
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×C4×D11—21no—
167C2×C4×D11—21no—
168C2×C4×D11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C2×C8×C11—21no—
174C2×C8×C11#4112yes—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—21no—
181C11×C4⋊C4—42no—
182C42×C11—42no—
183C42×C11—81no—
184C42×C11C2×D412yes—
185C42×C11#4112yes—
186(C2×D11)⋊C4—22no—
187(C2×D11)⋊C4—22no—
188(C2×D11)⋊C4—42no—
189(C2×D11)⋊C4—42no—
190(C2×D11)⋊C4—42no—
191(C2×D11)⋊C4—42no—
192(C2×D11)⋊C4—42no—
193(C2×D11)⋊C4—42no—
194(C2×D11)⋊C4—81no—
195(C2×D11)⋊C4—81no—
196C4⋊Dic11—22no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11—21no—
204C4⋊Dic11—21no—
205Dic11⋊C4—42no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208Dic11⋊C4—42no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8C2×D412yes—
214C2×C11⋊C8C2×D412yes—
215C8×D11—44no—
216C8×D11—44no—
217C2×#479—111no—
218C2×C8×D4—111no—
219#2562—111no—
220#2536—111no—
221#2077—111no—
222#2075—111no—
223#2036—111no—
224#2035—111no—
225#1991—111no—
226#1949—111no—
227#1892—111no—
228#1892—111no—
229#1808—111no—
230#1807—111no—
231C4×#103D1111yescharacteristic, complemented
232C23×C11C22×D411yescharacteristic
233C22×D11—21no—
234C22×D11—21no—
235C22×D11—21no—
236C22×D11—21no—
237C22×D11—21no—
238C22×D11—21no—
239C22×D11—21no—
240C22×D11—21no—
241C22×D11—21no—
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11#13512yes—
246C22×D11#13512yes—
247Q8×C11—22no—
248Q8×C11—22no—
249Q8×C11—41no—
250Q8×C11—41no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—22no—
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#12112yes—
268C2×C4×C11#12112yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11H(5,𝔽2)11yescharacteristic
274C2×C4×C112−1+411yescharacteristic
275C2×Dic11—21no—
276C2×Dic11—21no—
277C2×Dic11—21no—
278C2×Dic11—21no—
279C2×Dic11—21no—
280C2×Dic11—21no—
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—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293D44—28no—
294C4×D11—41no—
295C4×D11—41no—
296C4×D11—41no—
297C4×D11—41no—
298C4×D11—41no—
299C4×D11—41no—
300C4×D11—41no—
301C4×D11—41no—
302C8×C11—22no—
303C8×C11—41no—
304C11⋊C8—22no—
305C11⋊C8—22no—
306C23×C8—111no—
307C23×C8—111no—
308C2×#125—111no—
309C2×C22⋊Q8—111no—
310C2×C22⋊Q8—111no—
311C2×C4×Q8C2×D1111yescharacteristic
312C2×C4×D4—111no—
313#479—224no—
314C8×D4—224no—
315C2×#107—111no—
316C2×#107—111no—
317C2×#106—111no—
318C2×#106—111no—
319C2×C4⋊C8—111no—
320C2×#103—111no—
321C2×#103—111no—
322C2×#103C2×D1111yescharacteristic
323C2×#103C2×D1111yescharacteristic
324C2×C22⋊C8—111no—
325C2×C22⋊C8—111no—
326C2×C4×C8C2×D1111yescharacteristic
327#400—221no—
328#398—221no—
329#394—221no—
330#394—221no—
331#388—221no—
332#388—221no—
333#388—221no—
334#388—221no—
335#382—111no—
336#380—111no—
337#380—111no—
338#380—111no—
339#380—111no—
340#380—111no—
341#380—111no—
342C4×C4⋊C4C2×D1111yescharacteristic
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×C11C2×#12111yescharacteristic
352C22×C11#54611yescharacteristic
353C22×C11#54711yescharacteristic
354C22×C11C2×#13511yescharacteristic
355C22×C11C2×#13511yescharacteristic
356C22×C11#57711yescharacteristic
357C22×C11#57811yescharacteristic
358C2×D11—22no—
359C2×D11—22no—
360C2×D11—22no—
361C2×D11—22no—
362C2×D11—22no—
363C2×D11—22no—
364C2×D11—41no—
365C2×D11—41no—
366C2×D11—41no—
367C2×D11—41no—
368C2×D11—41no—
369C2×D11—41no—
370C2×D11—41no—
371C2×D11—41no—
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—42no—
375C4×C11—81no—
376C4×C11—81no—
377C4×C11—81no—
378C4×C11#52911yescharacteristic
379C4×C11#54211yescharacteristic
380C4×C11#54611yescharacteristic
381C4×C11#54811yescharacteristic
382Dic11—41no—
383Dic11—41no—
384Dic11—81no—
385Dic11—81no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8C22×D1111yescharacteristic
389C22×D4—111no—
390C23×C4—111no—
391C23×C4—111no—
392C22×C8—111no—
393C22×C8—111no—
394C22×C8—222no—
395C22×C8—222no—
396C22×C8—222no—
397C22×C8—222no—
398C22×C8—441no—
399C22×C8—441no—
400C22×C8C22×D1111yescharacteristic
401C22×C8C22×D1111yescharacteristic
402#125—222no—
403#125—222no—
404C22⋊Q8—222no—
405C22⋊Q8—222no—
406C22⋊Q8—441no—
407C22⋊Q8—441no—
408C4×Q8—22no—
409C4×Q8—22no—
410C4×D4—222no—
411C4×D4—222no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—111no—
414C2×C4⋊C4—111no—
415C2×C4⋊C4—111no—
416C2×C4⋊C4—111no—
417C2×C4⋊C4—111no—
418C2×C4⋊C4—221no—
419C2×C4⋊C4—221no—
420C2×C4⋊C4—221no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4C22×D1111yescharacteristic
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C4⋊C4C22×D1111yescharacteristic
425C2×C22⋊C4—111no—
426C2×C22⋊C4—111no—
427C2×C22⋊C4—221no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C22⋊C4—221no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42C22×D1111yescharacteristic
438#107—222no—
439#107—441no—
440#106—222no—
441#106—441no—
442C4⋊C8—114no—
443#103—22no—
444#103—22no—
445#103—222no—
446#103—222no—
447C22⋊C8—222no—
448C22⋊C8—222no—
449C4×C8—22no—
450#95—21no—
451#95—221no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456#95—221no—
457#95—221no—
458#95—221no—
459C2×C11#242711yescharacteristic
460C2×C11#305011yescharacteristic
461C2×C11#306311yescharacteristic
462C2×C11#330011yescharacteristic
463C2×C11#330111yescharacteristic
464C2×C11#333611yescharacteristic
465C2×C11#333711yescharacteristic
466D11—42no—
467D11—42no—
468C24—111no—
469C24—111no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8#433912yes—
476C2×D4—222no—
477C2×D4—222no—
478C2×D4—222no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—111no—
484C22×C4—111no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—221no—
488C22×C4—221no—
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—221no—
500C22×C4—221no—
501C22×C4D4×D1111yescharacteristic
502C22×C4D4×D1111yescharacteristic
503C22×C4C23×D1111yescharacteristic
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—112no—
510C2×C8—112no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—444no—
516C2×C8—444no—
517C2×C8#433912yes—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—42no—
525C4⋊C4—222no—
526C4⋊C4—221no—
527C4⋊C4—221no—
528C4⋊C4—221no—
529C4⋊C4—221no—
530C4⋊C4—221no—
531C4⋊C4—221no—
532C4⋊C4—221no—
533C4⋊C4—221no—
534C4⋊C4—442no—
535C4⋊C4—442no—
536C4⋊C4—442no—
537C4⋊C4—442no—
538C22⋊C4—222no—
539C22⋊C4—222no—
540C22⋊C4—442no—
541C22⋊C4—442no—
542C22⋊C4—442no—
543C22⋊C4—442no—
544C22⋊C4—442no—
545C22⋊C4—442no—
546C22⋊C4—881no—
547C22⋊C4—881no—
548C42—42no—
549C42—81no—
550C42#433912yes—
551C42D4×D1112yes—
552C11#2534311yescharacteristic, complemented, Sylow
553C23—112no—
554C23—112no—
555C23—221no—
556C23—221no—
557C23—221no—
558C23—221no—
559C23—221no—
560C23—221no—
561C23—221no—
562C23—221no—
563C23—221no—
564C23—221no—
565C23—221no—
566C23—221no—
567C23C2×D4×D1111yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572D4—228no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—41no—
579C2×C4—41no—
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—221no—
590C2×C4—221no—
591C2×C4—221no—
592C2×C4—221no—
593C2×C4—221no—
594C2×C4—221no—
595C2×C4—441no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—441no—
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#6693712yes—
616C2×C4#6693712yes—
617C2×C4C2×#433911yescharacteristic
618C2×C4C2×#433911yescharacteristic
619C2×C4C2×#433911yescharacteristic
620C2×C4C2×D4×D1111yescharacteristic
621C2×C4#6704211yescharacteristic
622C2×C4#6704311yescharacteristic
623C8—22no—
624C8—41no—
625C8—222no—
626C8—222no—
627C22—222no—
628C22—222no—
629C22—222no—
630C22—222no—
631C22—222no—
632C22—222no—
633C22—441no—
634C22—441no—
635C22—441no—
636C22—441no—
637C22—441no—
638C22—441no—
639C22—441no—
640C22—441no—
641C22C2×#6693711yescharacteristic
642C22#1062308111yescharacteristic
643C22#1062308211yescharacteristic
644C22#1062329311yescharacteristic
645C22#1062329711yescharacteristic
646C22D11×#13511yescharacteristic
647C22D11×#13511yescharacteristic
648C4—22no—
649C4—22no—
650C4—42no—
651C4—81no—
652C4—81no—
653C4—81no—
654C4—441no—
655C4—441no—
656C4—881no—
657C4—881no—
658C4—881no—
659C4—881no—
660C4#1062301011yescharacteristic
661C4#1062306511yescharacteristic
662C4#1062308111yescharacteristic
663C4#1062308311yescharacteristic
664C2—442no—
665C2—442no—
666C2#1307219311yescharacteristic
667C2#1307819611yescharacteristic
668C2#1307830511yescharacteristic
669C2#1308050811yescharacteristic
670C2#1308052311yescharacteristic
671C2#1308098611yescharacteristic
672C2#1308100011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC4×C11×#103C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC4×#103D11
hypocenterC11#25343
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
1. C2×#10622635C2semidirect
5. #13070054C2semidirect
6. #13070043C2semidirect
7. #13069817C2semidirect
8. #13069810C2semidirect
9. #13069581C2semidirect
10. #13069384C2semidirect
11. #13069036C2semidirect
12. #13069036C2semidirect
13. #13068644C2semidirect
14. #13068640C2semidirect
15. C4×C11×#103C2semidirect
231. C4×#103D11semidirect
552. C11#25343semidirect

Maximal subgroups

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

subgroupindex
C2×#106226352
C2×C8×D442
#130737772
#130735212
#130700542
#130700432
#130698172
#130698102
#130695812
#130693842
#130690362
#130686442
#130686402
C4×C11×#1032
#2534311