Finite Group Databasebeta

← #14771122

Subgroups — #14771122

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13077274C211yesmaximal, characteristic, complemented
2#13077065C211yesmaximal, characteristic
3#13069329C212yesmaximal, complemented
4#13069266C212yesmaximal, complemented
5#13068893C212yesmaximal, complemented
6#13068715C211yesmaximal, characteristic, complemented
7#13068654C211yesmaximal, characteristic, complemented
8#13068560C211yesmaximal, characteristic
9#13068463C212yesmaximal, complemented
10#13068392C211yesmaximal, characteristic, complemented
11C2×C11×#416C211yesmaximal, characteristic
12C22×C11×#41C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C2×C11×#117C2211yescharacteristic
15C2×#67001C2212yes—
16C11×#416C411yescharacteristic, complemented
17C11×#416C411yescharacteristic, complemented
18C11×#416C411yescharacteristic, complemented
19C11×#416C411yescharacteristic, complemented
20C11×#416C2211yescharacteristic
21C11×#416C2211yescharacteristic
22C11×#416C2211yescharacteristic
23C11×#416C2211yescharacteristic
24C2×C11×#103C411yescharacteristic, complemented
25C2×C11×#103C411yescharacteristic, complemented
26C2×C11×#102C411yescharacteristic, complemented
27C2×C11×#102C411yescharacteristic, complemented
28C2×#66901C2212yes—
29C2×#66901C2212yes—
30#10622847—22no—
31#10622847C2212yes—
32C4×C22⋊Dic11C2211yescharacteristic
33#10622820—21no—
34#10622820C2211yescharacteristic
35#10622820C2211yescharacteristic
36C2×C22⋊(C11⋊C8)—21no—
37C2×C22⋊(C11⋊C8)C2211yescharacteristic
38C2×#66883C2212yescomplemented
39C2×#66879C2212yescomplemented
40#10622613—22no—
41#10622612C2212yescomplemented
42#10622610C2212yescomplemented
43#10622539—21no—
44#10622538—21no—
45#10622190C2212yescomplemented
46#10622188C2212yescomplemented
47#10622170C2212yescomplemented
48#10622170C2212yescomplemented
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×C11×#41—24no—
52C2×C11×#41—42no—
53C2×C11×#41C2×C411yescharacteristic
54C2×C11×#41C2×C411yescharacteristic
55C2×C11×#41C2311yescharacteristic
56C2×C11×#41C2311yescharacteristic
57C22×Q8×C11C2×C411yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2×C411yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11C2311yescharacteristic
62C22×C8×C11—42no—
63C22×C8×C11C2×C411yescharacteristic
64C22×C8×C11C2×C411yescharacteristic
65C22×C8×C11C2×C411yescharacteristic
66C22×C8×C11C2×C411yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#117—21no—
70C11×#117—21no—
71C11×#117C2×C411yescharacteristic
72C11×#117C2×C411yescharacteristic
73C11×#117C2311yescharacteristic
74C11×#117C2311yescharacteristic
75C2×C11×C4⋊C4C2×C411yescharacteristic
76C2×C11×C4⋊C4C2×C411yescharacteristic
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—21no—
79C2×C22⋊Dic11—21no—
80#67001—24no—
81#67001—42no—
82C2×C4×Dic11C2312yes—
83C2×#4318—22no—
84C2×#4318C2312yes—
85C2×#4318C2312yes—
86C22×C11⋊C8—22no—
87C22×C11⋊C8C2312yes—
88C11×#103C2×C411yescharacteristic
89C11×#103C2×C411yescharacteristic
90C11×#103C2×C411yescharacteristic
91C11×#103C2×C411yescharacteristic
92C11×#103C2×C411yescharacteristic
93C11×#103C2×C411yescharacteristic
94C11×#103C2×C411yescharacteristic
95C11×#103C2×C411yescharacteristic
96C11×#102C2×C411yescharacteristic
97C11×#102C2×C411yescharacteristic
98C11×#102C2×C411yescharacteristic
99C11×#102C2×C411yescharacteristic
100C11×#102C2×C411yescharacteristic
101C11×#102C2×C411yescharacteristic
102C11×#102C2×C411yescharacteristic
103C11×#102C2×C411yescharacteristic
104#66901—24no—
105#66901—42no—
106C11⋊#95—21no—
107C22⋊(C11⋊C8)—21no—
108C22⋊(C11⋊C8)—21no—
109C22⋊(C11⋊C8)—21no—
110C22⋊(C11⋊C8)—21no—
111C22⋊(C11⋊C8)—22no—
112C22⋊(C11⋊C8)—22no—
113C22⋊(C11⋊C8)D411yescharacteristic
114C22⋊(C11⋊C8)D411yescharacteristic
115C22⋊(C11⋊C8)D412yes—
116#66883—42no—
117#66879—42no—
118C4⋊(C11⋊C8)—22no—
119C4⋊(C11⋊C8)—22no—
120#66867—22no—
121C4×C11⋊C8—22no—
122#22586—111nomaximal, Sylow
123C24×C11—21no—
124C24×C11#4111yescharacteristic
125C11×#41—22no—
126C11×#41—22no—
127C11×#41—22no—
128C11×#41—22no—
129C11×#41—22no—
130C11×#41—44no—
131C11×#41—41no—
132C11×#41—41no—
133C11×#41—44no—
134C11×#41#4114yes—
135C2×Q8×C11—21no—
136C2×Q8×C11—22no—
137C2×Q8×C11—41no—
138C2×Q8×C11C22×C411yescharacteristic
139C2×Q8×C11C22×C411yescharacteristic
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—21no—
143C2×D4×C11—21no—
144C2×D4×C11—21no—
145C2×D4×C11—21no—
146C2×D4×C11—41no—
147C2×D4×C11—44no—
148C2×D4×C11C22×C411yescharacteristic
149C2×D4×C11C22×C411yescharacteristic
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—44no—
160C22×C4×C11C22×C411yescharacteristic
161C22×C4×C11C22×C411yescharacteristic
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11#4111yescharacteristic
165C22×C4×C11C2411yescharacteristic
166C22×Dic11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—41no—
170C2×C8×C11—41no—
171C2×C8×C11—41no—
172C2×C8×C11—41no—
173C2×C8×C11C22×C411yescharacteristic
174C2×C8×C11C22×C411yescharacteristic
175C2×C8×C11C22×C411yescharacteristic
176C2×C8×C11C22×C411yescharacteristic
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4C22×C411yescharacteristic
180C11×C4⋊C4C22×C411yescharacteristic
181C11×C4⋊C4C22×C411yescharacteristic
182C11×C4⋊C4C22×C411yescharacteristic
183C11×C22⋊C4—21no—
184C11×C22⋊C4—21no—
185C11×C22⋊C4—21no—
186C11×C22⋊C4—21no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—21no—
190C42×C11—21no—
191C22⋊Dic11—42no—
192C4×Dic11—22no—
193C4×Dic11—22no—
194#4318—22no—
195#4318—22no—
196#4318—22no—
197#4318—22no—
198#4318—44no—
199C2×C11⋊C8—22no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—44no—
204C2×C11⋊C8C2×D412yes—
205C2×C11⋊C8C2×D412yes—
206#2924—111no—
207C2×#416D1111yescharacteristic
208#2880—111no—
209#1938—112no—
210#1929—112no—
211#1866—112no—
212#1826—111no—
213#1810—111no—
214#1789—111no—
215#1765—112no—
216#1752—111no—
217C23×C11—21no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—21no—
221C23×C11—41no—
222C23×C11—42no—
223C23×C11—42no—
224C23×C11—81no—
225C23×C11C4×D411yescharacteristic
226C23×C11C4×D411yescharacteristic
227C23×C11C2×#4111yescharacteristic
228Q8×C11—21no—
229Q8×C11—21no—
230Q8×C11—21no—
231Q8×C11—42no—
232Q8×C11#11712yes—
233D4×C11—24no—
234D4×C11—21no—
235D4×C11—21no—
236D4×C11—21no—
237D4×C11—42no—
238D4×C11—42no—
239D4×C11—42no—
240D4×C11—42no—
241D4×C11#11712yes—
242C2×C4×C11—21no—
243C2×C4×C11—22no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—21no—
256C2×C4×C11—42no—
257C2×C4×C11—42no—
258C2×C4×C11—42no—
259C2×C4×C11—42no—
260C2×C4×C11—42no—
261C2×C4×C11—81no—
262C2×C4×C11C4×D411yescharacteristic
263C2×C4×C11C4×D411yescharacteristic
264C2×C4×C11C23×C411yescharacteristic
265C2×C4×C11C22×D411yescharacteristic
266C2×C4×C11C2×#4112yes—
267C2×C4×C11H(5,𝔽2)12yes—
268C2×Dic11—42no—
269C2×Dic11—42no—
270C2×Dic11—42no—
271C8×C11—21no—
272C8×C11—21no—
273C8×C11—21no—
274C8×C11—21no—
275C11⋊C8—22no—
276C11⋊C8—22no—
277C11⋊C8—42no—
278C11⋊C8—42no—
279C22×#41C2×D1111yescharacteristic
280C2×#131—112no—
281C23×C8C2×D1111yescharacteristic
282C2×#117C2×D1111yescharacteristic
283#433—222no—
284#432—221no—
285#431—221no—
286C2×#108—112no—
287#424—112no—
288C2×#104—112no—
289C2×#104—112no—
290#416Dic1111yescharacteristic, complemented
291#416Dic1111yescharacteristic, complemented
292#416Dic1111yescharacteristic, complemented
293#416Dic1111yescharacteristic, complemented
294#416C2×D1111yescharacteristic
295#416C2×D1111yescharacteristic
296#416C2×D1111yescharacteristic
297#416C2×D1111yescharacteristic
298C2×#103Dic1111yescharacteristic, complemented
299C2×#103Dic1111yescharacteristic, complemented
300C2×#102Dic1111yescharacteristic, complemented
301C2×#102Dic1111yescharacteristic, complemented
302#408—112no—
303#408—222no—
304#407—111no—
305#407—111no—
306#407—221no—
307C2×C22⋊C8—111no—
308C2×C22⋊C8—221no—
309#405—112no—
310C2×#97—112no—
311C4×C22⋊C4—111no—
312#341—112no—
313#339—112no—
314#339—112no—
315#336—112no—
316C22×C11—21no—
317C22×C11—21no—
318C22×C11—21no—
319C22×C11—21no—
320C22×C11—21no—
321C22×C11—22no—
322C22×C11—21no—
323C22×C11—21no—
324C22×C11—44no—
325C22×C11—41no—
326C22×C11—41no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—84no—
331C22×C11#44412yes—
332C22×C11C2×C4×D411yescharacteristic
333C22×C11#55112yes—
334C4×C11—21no—
335C4×C11—21no—
336C4×C11—22no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11C2×#11711yescharacteristic
343C4×C11#51811yescharacteristic
344C4×C11#54612yes—
345Dic11—82no—
346C2×#41—21no—
347C2×#41—21no—
348C2×#41—24no—
349C2×#41—42no—
350C2×#41C2×Dic1111yescharacteristic
351C2×#41C2×Dic1111yescharacteristic
352C2×#41C22×D1111yescharacteristic
353C2×#41C22×D1111yescharacteristic
354C22×Q8C2×Dic1111yescharacteristic
355C22×D4—21no—
356C22×D4C2×Dic1111yescharacteristic
357C23×C4—21no—
358C23×C4C22×D1111yescharacteristic
359#131—224no—
360#131—442no—
361C2×M16—112no—
362C2×M16—112no—
363C2×M16—222no—
364C22×C8—42no—
365C22×C8—112no—
366C22×C8—222no—
367C22×C8C2×Dic1111yescharacteristic
368C22×C8C2×Dic1111yescharacteristic
369C22×C8C2×Dic1111yescharacteristic
370C22×C8C2×Dic1111yescharacteristic
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1111yescharacteristic
373#117—21no—
374#117—21no—
375#117C2×Dic1111yescharacteristic
376#117C2×Dic1111yescharacteristic
377#117C22×D1111yescharacteristic
378#117C22×D1111yescharacteristic
379C2×C4⋊C4C2×Dic1111yescharacteristic
380C2×C4⋊C4C2×Dic1111yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—221no—
383C2×C42—21no—
384C2×C42—112no—
385#108—442no—
386C4⋊C8—222no—
387C4⋊C8—222no—
388#104—224no—
389#104—442no—
390#103C2×Dic1111yescharacteristic
391#103C2×Dic1111yescharacteristic
392#103C2×Dic1111yescharacteristic
393#103C2×Dic1111yescharacteristic
394#103C2×Dic1111yescharacteristic
395#103C2×Dic1111yescharacteristic
396#103C2×Dic1111yescharacteristic
397#103C2×Dic1111yescharacteristic
398#102C2×Dic1111yescharacteristic
399#102C2×Dic1111yescharacteristic
400#102C2×Dic1111yescharacteristic
401#102C2×Dic1111yescharacteristic
402#102C2×Dic1111yescharacteristic
403#102C2×Dic1111yescharacteristic
404#102C2×Dic1111yescharacteristic
405#102C2×Dic1111yescharacteristic
406C22⋊C8—111no—
407C22⋊C8—111no—
408C22⋊C8—112no—
409C22⋊C8—222no—
410C22⋊C8—222no—
411C22⋊C8—221no—
412C22⋊C8—221no—
413C22⋊C8—221no—
414C22⋊C8—221no—
415#97—222no—
416#97—442no—
417C4×C8—222no—
418#95—221no—
419C2×C11—22no—
420C2×C11—22no—
421C2×C11—41no—
422C2×C11—42no—
423C2×C11—81no—
424C2×C11#234211yescharacteristic
425C2×C11C2×#44411yescharacteristic
426C2×C11#295711yescharacteristic
427C24—21no—
428C24#434111yescharacteristic
429#41—22no—
430#41—22no—
431#41—22no—
432#41—22no—
433#41—22no—
434#41—44no—
435#41—41no—
436#41—41no—
437#41—44no—
438#41#433914yes—
439C2×Q8—21no—
440C2×Q8—22no—
441C2×Q8—41no—
442C2×Q8C22×Dic1111yescharacteristic
443C2×Q8C22×Dic1111yescharacteristic
444C2×D4—21no—
445C2×D4—22no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—44no—
452C2×D4C22×Dic1111yescharacteristic
453C2×D4C22×Dic1111yescharacteristic
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—44no—
464C22×C4—222no—
465C22×C4D4×D1111yescharacteristic
466C22×C4D4×D1111yescharacteristic
467C22×C4#434111yescharacteristic
468C22×C4C22×Dic1111yescharacteristic
469C22×C4C22×Dic1111yescharacteristic
470C22×C4C23×D1111yescharacteristic
471M16—222no—
472M16—222no—
473M16—222no—
474M16—222no—
475M16—444no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—112no—
483C2×C8—112no—
484C2×C8—222no—
485C2×C8—222no—
486C2×C8—222no—
487C2×C8—222no—
488C2×C8—444no—
489C2×C8C22×Dic1111yescharacteristic
490C2×C8C22×Dic1111yescharacteristic
491C2×C8C22×Dic1111yescharacteristic
492C2×C8C22×Dic1111yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4C22×Dic1111yescharacteristic
496C4⋊C4C22×Dic1111yescharacteristic
497C4⋊C4C22×Dic1111yescharacteristic
498C4⋊C4C22×Dic1111yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—442no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—222no—
509C42—222no—
510C11#2258611yescharacteristic, complemented, Sylow
511C23—22no—
512C23—22no—
513C23—21no—
514C23—21no—
515C23—41no—
516C23—42no—
517C23—42no—
518C23—81no—
519C23D4×Dic1111yescharacteristic
520C23D4×Dic1111yescharacteristic
521C23C2×#434111yescharacteristic
522Q8—21no—
523Q8—21no—
524Q8—21no—
525Q8—42no—
526Q8#6697912yes—
527D4—24no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—42no—
533D4—42no—
534D4—42no—
535D4#6697912yes—
536C2×C4—22no—
537C2×C4—21no—
538C2×C4—24no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—42no—
551C2×C4—42no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—81no—
556C2×C4—442no—
557C2×C4—442no—
558C2×C4—442no—
559C2×C4D4×Dic1111yescharacteristic
560C2×C4D4×Dic1111yescharacteristic
561C2×C4C2×#433912yes—
562C2×C4C2×D4×D1111yescharacteristic
563C2×C4#6703712yes—
564C2×C4C23×Dic1111yescharacteristic
565C8—21no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—222no—
570C8—222no—
571C8—442no—
572C8—442no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—21no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—22no—
581C22—44no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—84no—
588C22#1062281012yes—
589C22#1062302612yes—
590C22C2×D4×Dic1111yescharacteristic
591C4—21no—
592C4—21no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—882no—
600C4#1062302112yes—
601C4C2×#6697911yescharacteristic
602C4#1062332911yescharacteristic
603C2—22no—
604C2—22no—
605C2—41no—
606C2—42no—
607C2—81no—
608C2#1307146511yescharacteristic
609C2C2×#1062281011yescharacteristic
610C2#1307753311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#416C2
socleC22×C11C2×C4×D4
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC2×#416D11
hypocenterC11#22586
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. #13077274C2semidirect
3. #13069329C2semidirect
4. #13069266C2semidirect
5. #13068893C2semidirect
6. #13068715C2semidirect
7. #13068654C2semidirect
9. #13068463C2semidirect
10. #13068392C2semidirect
16. C11×#416C4semidirect
17. C11×#416C4semidirect
18. C11×#416C4semidirect
19. C11×#416C4semidirect
24. C2×C11×#103C4semidirect
25. C2×C11×#103C4semidirect
26. C2×C11×#102C4semidirect
27. C2×C11×#102C4semidirect
38. C2×#66883C22semidirect
39. C2×#66879C22semidirect
41. #10622612C22semidirect
42. #10622610C22semidirect
45. #10622190C22semidirect
46. #10622188C22semidirect
47. #10622170C22semidirect
48. #10622170C22semidirect
290. #416Dic11semidirect
291. #416Dic11semidirect
292. #416Dic11semidirect
293. #416Dic11semidirect
298. C2×#103Dic11semidirect
299. C2×#103Dic11semidirect
300. C2×#102Dic11semidirect
301. C2×#102Dic11semidirect
510. C11#22586semidirect

Maximal subgroups

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

subgroupindex
#130772742
#130770652
#130693292
#130692662
#130688932
#130687152
#130686542
#130685602
#130684632
#130683922
C2×C11×#4162
#2258611