Finite Group Databasebeta

← #14765629

Subgroups — #14765629

Order 2816.

738 conjugacy classes of subgroups.

The subgroup lattice has 698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13078533C211yesmaximal, characteristic
2#13077312C211yesmaximal, characteristic
3D11×#424C211yesmaximal, characteristic, complemented
4#13069365C211yesmaximal, characteristic, complemented
5#13069363C211yesmaximal, characteristic, complemented
6#13069321C211yesmaximal, characteristic, complemented
7#13069318C211yesmaximal, characteristic, complemented
8#13069215C211yesmaximal, characteristic, complemented
9#13068917C211yesmaximal, characteristic
10#13068894C211yesmaximal, characteristic, complemented
11#13068890C211yesmaximal, characteristic, complemented
12#13068822C211yesmaximal, characteristic, complemented
13#13068714C211yesmaximal, characteristic, complemented
14#13068386C211yesmaximal, characteristic, complemented
15C11×#1922C211yesmaximal, characteristic, complemented
16C2×M16×D11C2211yescharacteristic
17C2×#66954C2211yescharacteristic
18C22×C8×D11C2211yescharacteristic
19#10623055C2211yescharacteristic
20D11×#117C2211yescharacteristic
21C11×#427C2211yescharacteristic
22C11×#424C2211yescharacteristic
23C11×#405C2211yescharacteristic
24C2×#66889C2211yescharacteristic
25#10622742C2211yescharacteristic
26#10622739C2211yescharacteristic
27C2×#66886C2211yescharacteristic
28#10622732C2211yescharacteristic
29#10622726C2211yescharacteristic
30C2×(C2×D11)⋊C8C2211yescharacteristic
31C2×#66883C2211yescharacteristic
32#10622715C2211yescharacteristic
33C2×C8×Dic11C2211yescharacteristic
34#10622615C2211yescharacteristic
35#10622612C2211yescharacteristic
36#10622612C2211yescharacteristic
37#10622611C2211yescharacteristic
38C4×(C2×D11)⋊C4C2211yescharacteristic
39C2×#66869C2211yescharacteristic
40C2×C4×C11⋊C8C2211yescharacteristic
41#10622501C411yescharacteristic, complemented
42#10622498C411yescharacteristic, complemented
43#10622497C411yescharacteristic, complemented
44#10622495C411yescharacteristic, complemented
45#10622480C411yescharacteristic, complemented
46#10622479C411yescharacteristic, complemented
47#10622476C411yescharacteristic, complemented
48#10622475C411yescharacteristic, complemented
49#10622452—21no—
50#10622452—21no—
51D11×C4⋊C8—21no—
52D11×C4⋊C8—21no—
53#10622319—21no—
54#10622319—21no—
55C8×D44—21no—
56C8×D44—21no—
57C11×#341C2211yescharacteristic
58C11×#339C2211yescharacteristic
59C11×#339C2211yescharacteristic
60C11×#336C2211yescharacteristic
61#10622196C2211yescharacteristic
62#10622193C2211yescharacteristic
63#10622188C2211yescharacteristic
64#10622170C2211yescharacteristic
65#10622170C2211yescharacteristic
66#10622161C2211yescharacteristic
67C2×#4339C2311yescharacteristic
68C22×C4×D11C2311yescharacteristic
69C2×C11×M16C2311yescharacteristic
70C2×C11×M16C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C11×#117C2311yescharacteristic
74C11×#117C2311yescharacteristic
75C2×C42×C11C2311yescharacteristic
76C2×(C2×D11)⋊C4—21no—
77#66979C2311yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C2×#4318C2311yescharacteristic
80C2×#4318C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83M16×D11—41no—
84M16×D11—41no—
85#66954—41no—
86#66954—41no—
87C2×#4313—21no—
88C2×#4313—21no—
89C2×C8×D11—21no—
90C2×C8×D11—21no—
91C2×C8×D11—41no—
92C2×C8×D11—41no—
93C2×C8×D11D411yescharacteristic
94C2×C8×D11D411yescharacteristic
95C2×C8×D11D411yescharacteristic
96C2×C8×D11D411yescharacteristic
97#66950C2×C411yescharacteristic
98#66950C2×C411yescharacteristic
99#66948C2×C411yescharacteristic
100#66948C2×C411yescharacteristic
101#66945C2×C411yescharacteristic
102#66945C2×C411yescharacteristic
103C4⋊C4×D11C2×C411yescharacteristic
104C4⋊C4×D11C2×C411yescharacteristic
105#66939—21no—
106#66935—21no—
107C22⋊C4×D11—21no—
108#66930—21no—
109C4×D44—21no—
110C4×D44—21no—
111#66925—21no—
112C42×D11—21no—
113C11×#107C2×C411yescharacteristic
114C11×#107C2×C411yescharacteristic
115C11×#106C2×C411yescharacteristic
116C11×#106C2×C411yescharacteristic
117C11×C4⋊C8—21no—
118C11×C4⋊C8—21no—
119C11×#97—21no—
120C4×C8×C11—21no—
121C11⋊#95—21no—
122#66889—41no—
123#66886—41no—
124#66885C2×C411yescharacteristic
125#66885C2×C411yescharacteristic
126(C2×D11)⋊C8—21no—
127(C2×D11)⋊C8—21no—
128(C2×D11)⋊C8—21no—
129(C2×D11)⋊C8—21no—
130(C2×D11)⋊C8C2×C411yescharacteristic
131(C2×D11)⋊C8C2×C411yescharacteristic
132(C2×D11)⋊C8C2×C411yescharacteristic
133(C2×D11)⋊C8C2×C411yescharacteristic
134#66883—41no—
135#66880C2×C411yescharacteristic
136#66880C2×C411yescharacteristic
137Dic11⋊C8—21no—
138Dic11⋊C8—21no—
139Dic11⋊C8—21no—
140Dic11⋊C8—21no—
141C8×Dic11—41no—
142#66874C2×C411yescharacteristic
143#66874C2×C411yescharacteristic
144#66873C2×C411yescharacteristic
145#66873C2×C411yescharacteristic
146#66872C2×C411yescharacteristic
147#66872C2×C411yescharacteristic
148#66871C2×C411yescharacteristic
149#66871C2×C411yescharacteristic
150#66869—41no—
151C4⋊(C11⋊C8)—21no—
152C4⋊(C11⋊C8)—21no—
153C4⋊(C11⋊C8)—21no—
154C4⋊(C11⋊C8)—21no—
155C4×C11⋊C8—41no—
156#22095—111nomaximal, Sylow
157C23×D11#4111yescharacteristic
158C22×C4×C11—21no—
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—21no—
161C22×Dic11—21no—
162C22×Dic11#4111yescharacteristic
163#4339—21no—
164#4339—21no—
165#4339—21no—
166#4339—21no—
167C2×D44—21no—
168C2×D44—21no—
169C2×D44C22×C411yescharacteristic
170C2×C4×D11—21no—
171C2×C4×D11—21no—
172C2×C4×D11—21no—
173C2×C4×D11—21no—
174C2×C4×D11—21no—
175C2×C4×D11—21no—
176C2×C4×D11—21no—
177C2×C4×D11C22×C411yescharacteristic
178C2×C4×D11C22×C411yescharacteristic
179C2×C4×D11C2×D411yescharacteristic
180C2×C4×D11C2×D411yescharacteristic
181C2×Dic22C22×C411yescharacteristic
182C11×M16—21no—
183C11×M16—21no—
184C11×M16—21no—
185C11×M16—21no—
186C2×C8×C11—21no—
187C2×C8×C11—21no—
188C2×C8×C11—21no—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11C22×C411yescharacteristic
193C2×C8×C11C22×C411yescharacteristic
194C2×C8×C11C2×D411yescharacteristic
195C2×C8×C11C2×D411yescharacteristic
196C11×C4⋊C4C22×C411yescharacteristic
197C11×C4⋊C4C22×C411yescharacteristic
198C11×C4⋊C4C22×C411yescharacteristic
199C11×C4⋊C4C22×C411yescharacteristic
200C11×C22⋊C4—21no—
201C11×C22⋊C4—21no—
202C42×C11—21no—
203C42×C11—21no—
204C42×C11—21no—
205C42×C11—21no—
206C22⋊Dic11—21no—
207(C2×D11)⋊C4—24no—
208(C2×D11)⋊C4—21no—
209(C2×D11)⋊C4—21no—
210(C2×D11)⋊C4—21no—
211(C2×D11)⋊C4—21no—
212(C2×D11)⋊C4—21no—
213(C2×D11)⋊C4—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11C22×C411yescharacteristic
217C4⋊Dic11C22×C411yescharacteristic
218Dic11⋊C4—21no—
219Dic11⋊C4—21no—
220C4×Dic11—21no—
221C4×Dic11—21no—
222C4×Dic11—21no—
223C4×Dic11—21no—
224C4×Dic11—21no—
225#4318—21no—
226#4318—21no—
227#4318—21no—
228#4318—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8C22×C411yescharacteristic
236C2×C11⋊C8C22×C411yescharacteristic
237C2×C11⋊C8C2×D411yescharacteristic
238C2×C11⋊C8C2×D411yescharacteristic
239#4313—42no—
240#4313—42no—
241C8×D11—41no—
242C8×D11—41no—
243C8×D11—41no—
244C8×D11—41no—
245C8×D11—42no—
246C8×D11—42no—
247#3091—111no—
248#2929—111no—
249C2×#424—111no—
250#1945—111no—
251#1945—111no—
252#1937—111no—
253#1937—111no—
254#1922—111no—
255#1922D1111yescharacteristic, complemented
256#1871—111no—
257#1866—111no—
258#1866—111no—
259#1855—111no—
260#1826—111no—
261C8×C22⋊C4—111no—
262C23×C11C2×#4111yescharacteristic
263C22×D11—21no—
264C22×D11—21no—
265C22×D11—22no—
266C22×D11—21no—
267C22×D11—41no—
268C22×D11C4×D411yescharacteristic
269C22×D11C4×D411yescharacteristic
270C2×C4×C11—22no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11C23×C411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11H(5,𝔽2)11yescharacteristic
280C2×C4×C11H(5,𝔽2)11yescharacteristic
281C2×C4×C112−1+411yescharacteristic
282C2×C4×C112−1+411yescharacteristic
283C22⋊D11—41no—
284C22⋊D11—41no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—22no—
288C2×Dic11—21no—
289C2×Dic11—21no—
290C2×Dic11—21no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11C4×D411yescharacteristic
294C2×Dic11C4×D411yescharacteristic
295D44—21no—
296D44—21no—
297D44—42no—
298D44—42no—
299C4×D11—21no—
300C4×D11—21no—
301C4×D11—21no—
302C4×D11—21no—
303C4×D11—21no—
304C4×D11—21no—
305C4×D11—21no—
306C4×D11—21no—
307C4×D11—42no—
308C4×D11—42no—
309C4×D11—41no—
310C4×D11—41no—
311Dic22—21no—
312Dic22—21no—
313C8×C11—21no—
314C8×C11—21no—
315C8×C11—21no—
316C8×C11—21no—
317C8×C11—41no—
318C8×C11—41no—
319C11⋊C8—21no—
320C11⋊C8—21no—
321C11⋊C8—21no—
322C11⋊C8—21no—
323C11⋊C8—41no—
324C11⋊C8—41no—
325C2×#131—111no—
326C22×M16—111no—
327C23×C8—111no—
328#525—111no—
329C2×#117—111no—
330#485—111no—
331#485—111no—
332#484—111no—
333#483—111no—
334#482—111no—
335#482—111no—
336#481—111no—
337#480—111no—
338#435—221no—
339#435—221no—
340C8×D4—221no—
341C8×D4—221no—
342C2×#108—111no—
343C2×#108—111no—
344#427—111no—
345#427C2×D1111yescharacteristic
346#424—111no—
347#424—111no—
348#424—111no—
349#424—111no—
350#424—221no—
351#424—221no—
352#424C2×D1111yescharacteristic
353C2×C4⋊C8—221no—
354C2×C4⋊C8—221no—
355C2×#104—111no—
356C2×#104—111no—
357#416—111no—
358#416—111no—
359#408—111no—
360#407—111no—
361C2×C22⋊C8—111no—
362#405C2×D1111yescharacteristic
363C2×C4×C8—111no—
364C2×C4×C8—111no—
365C4×C22⋊C4—111no—
366#341—111no—
367#341C2×D1111yescharacteristic
368#339—111no—
369#339—111no—
370#339—111no—
371#339—111no—
372#339C2×D1111yescharacteristic
373#339C2×D1111yescharacteristic
374#336—111no—
375#336C2×D1111yescharacteristic
376C22×C11—21no—
377C22×C11—21no—
378C22×C11C2×C4×D411yescharacteristic
379C22×C11#53911yescharacteristic
380C22×C11#53911yescharacteristic
381C2×D11—21no—
382C2×D11—21no—
383C2×D11—21no—
384C2×D11—21no—
385C2×D11—21no—
386C2×D11—42no—
387C2×D11—42no—
388C2×D11—41no—
389C2×D11—41no—
390C2×D11—41no—
391C2×D11#44312yes—
392C4×C11—42no—
393C4×C11—41no—
394C4×C11—41no—
395C4×C11—41no—
396C4×C11—41no—
397C4×C11#52011yescharacteristic
398C4×C11#52011yescharacteristic
399C4×C11#53411yescharacteristic
400C4×C11#53611yescharacteristic
401Dic11—21no—
402Dic11—21no—
403Dic11—42no—
404Dic11—41no—
405Dic11—41no—
406Dic11—41no—
407C2×#41—111no—
408C23×C4—111no—
409#131—441no—
410#131—441no—
411C2×M16—111no—
412C2×M16—111no—
413C2×M16—221no—
414C2×M16—221no—
415C2×M16—441no—
416C2×M16—441no—
417C2×M16C22×D1111yescharacteristic
418C2×M16C22×D1111yescharacteristic
419C22×C8—111no—
420C22×C8—111no—
421C22×C8—111no—
422C22×C8—111no—
423C22×C8—111no—
424C22×C8—111no—
425C22×C8—221no—
426C22×C8—221no—
427C22×C8—441no—
428C22×C8—441no—
429C22×C8C22×D1111yescharacteristic
430C22×C8C22×D1111yescharacteristic
431#123—221no—
432C22⋊Q8—111no—
433C22⋊Q8—111no—
434#121—111no—
435#121—111no—
436#120—221no—
437C4×D4—221no—
438C4×D4—221no—
439#117—111no—
440#117—111no—
441#117—111no—
442#117—221no—
443#117—221no—
444#117C22×D1111yescharacteristic
445#117C22×D1111yescharacteristic
446C2×C4⋊C4—111no—
447C2×C4⋊C4—111no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C42—111no—
451C2×C42—221no—
452C2×C42C22×D1111yescharacteristic
453#108—441no—
454#108—441no—
455#107—111no—
456#107—111no—
457#107C4×D1111yescharacteristic
458#107C4×D1111yescharacteristic
459#106—111no—
460#106—111no—
461#106C4×D1111yescharacteristic
462#106C4×D1111yescharacteristic
463C4⋊C8—21no—
464C4⋊C8—21no—
465C4⋊C8—221no—
466C4⋊C8—221no—
467C4⋊C8—221no—
468C4⋊C8—221no—
469C4⋊C8—221no—
470C4⋊C8—221no—
471C4⋊C8—221no—
472C4⋊C8—221no—
473#104—441no—
474#104—441no—
475#103—111no—
476#103—111no—
477#103—111no—
478#103—111no—
479#102—111no—
480#102—111no—
481#102—111no—
482#102—111no—
483C22⋊C8—111no—
484C22⋊C8—111no—
485C22⋊C8—111no—
486C22⋊C8—111no—
487C22⋊C8—221no—
488C22⋊C8—221no—
489C22⋊C8—221no—
490C22⋊C8—221no—
491#97—21no—
492C4×C8—21no—
493C4×C8—441no—
494C4×C8—441no—
495#95—221no—
496C2×C11—21no—
497C2×C11—21no—
498C2×C11#232211yescharacteristic
499C2×C11C2×#44311yescharacteristic
500C2×C11#295511yescharacteristic
501D11—22no—
502D11—41no—
503D11—81no—
504C24—111no—
505#41—221no—
506#41—221no—
507#41—221no—
508#41—221no—
509C2×Q8—111no—
510C2×D4—111no—
511C2×D4—221no—
512C2×D4—221no—
513C2×D4—221no—
514C22×C4—21no—
515C22×C4—111no—
516C22×C4—111no—
517C22×C4—111no—
518C22×C4—111no—
519C22×C4—111no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—221no—
525C22×C4—221no—
526C22×C4—221no—
527C22×C4—221no—
528C22×C4C23×D1111yescharacteristic
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—221no—
534M16—221no—
535M16—221no—
536M16—221no—
537M16—442no—
538M16—442no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—111no—
546C2×C8—111no—
547C2×C8—111no—
548C2×C8—111no—
549C2×C8—221no—
550C2×C8—221no—
551C2×C8—221no—
552C2×C8—221no—
553C2×C8—221no—
554C2×C8—221no—
555C2×C8—441no—
556C2×C8—441no—
557C2×C8—441no—
558C2×C8—441no—
559C2×C8—442no—
560C2×C8—442no—
561C2×C8C2×C4×D1111yescharacteristic
562C2×C8C2×C4×D1111yescharacteristic
563C2×C8D4×D1111yescharacteristic
564C2×C8D4×D1111yescharacteristic
565C4⋊C4—111no—
566C4⋊C4—111no—
567C4⋊C4—221no—
568C4⋊C4—221no—
569C4⋊C4—221no—
570C4⋊C4—221no—
571C4⋊C4C2×C4×D1111yescharacteristic
572C4⋊C4C2×C4×D1111yescharacteristic
573C4⋊C4C2×C4×D1111yescharacteristic
574C4⋊C4C2×C4×D1111yescharacteristic
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4—221no—
578C22⋊C4—221no—
579C22⋊C4—221no—
580C22⋊C4—221no—
581C22⋊C4—221no—
582C22⋊C4—221no—
583C22⋊C4—224no—
584C22⋊C4—221no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—221no—
590C42—221no—
591C42—221no—
592C42—221no—
593C42—221no—
594C11#2209511yescharacteristic, complemented, Sylow
595C23—111no—
596C23—111no—
597C23—222no—
598C23—221no—
599C23—221no—
600C23—221no—
601C23—441no—
602C23#41×D1111yescharacteristic
603Q8—221no—
604Q8—221no—
605D4—221no—
606D4—221no—
607D4—442no—
608D4—442no—
609D4—441no—
610D4—441no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—111no—
619C2×C4—111no—
620C2×C4—221no—
621C2×C4—221no—
622C2×C4—221no—
623C2×C4—221no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—221no—
627C2×C4—221no—
628C2×C4—221no—
629C2×C4—221no—
630C2×C4—222no—
631C2×C4—221no—
632C2×C4—221no—
633C2×C4—221no—
634C2×C4—442no—
635C2×C4—442no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4C22×C4×D1111yescharacteristic
641C2×C4C2×D4×D1111yescharacteristic
642C2×C4#6704011yescharacteristic
643C2×C4#6704211yescharacteristic
644C2×C4#6704211yescharacteristic
645C2×C4#6704311yescharacteristic
646C8—21no—
647C8—21no—
648C8—21no—
649C8—21no—
650C8—41no—
651C8—41no—
652C8—221no—
653C8—221no—
654C8—221no—
655C8—221no—
656C8—441no—
657C8—441no—
658C22—21no—
659C22—21no—
660C22—112no—
661C22—221no—
662C22—221no—
663C22—221no—
664C22—221no—
665C22—221no—
666C22—442no—
667C22—442no—
668C22—441no—
669C22—441no—
670C22—441no—
671C22C4×D4×D1111yescharacteristic
672C22#1062322311yescharacteristic
673C22#1062323811yescharacteristic
674C4—42no—
675C4—41no—
676C4—41no—
677C4—41no—
678C4—41no—
679C4—221no—
680C4—221no—
681C4—442no—
682C4—441no—
683C4—441no—
684C4—441no—
685C4#1062305411yescharacteristic
686C4#1062310511yescharacteristic
687C4#1062315911yescharacteristic
688C4#1062318411yescharacteristic
689C2—21no—
690C2—21no—
691C2—222no—
692C2—441no—
693C2—881no—
694C2#1307128911yescharacteristic
695C2D11×#44311yescharacteristic
696C2#1307751611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1922C2
socleC22×C11C2×C4×D4
prime radical#10623055C22
cosocleC22×C4×C11C24
hypercenter#1922D11
hypocenterC11#22095
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1922

Complements

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

NH ≅ G/Ntype
3. D11×#424C2semidirect
4. #13069365C2semidirect
5. #13069363C2semidirect
6. #13069321C2semidirect
7. #13069318C2semidirect
8. #13069215C2semidirect
10. #13068894C2semidirect
11. #13068890C2semidirect
12. #13068822C2semidirect
13. #13068714C2semidirect
14. #13068386C2semidirect
15. C11×#1922C2semidirect
41. #10622501C4semidirect
42. #10622498C4semidirect
43. #10622497C4semidirect
44. #10622495C4semidirect
45. #10622480C4semidirect
46. #10622479C4semidirect
47. #10622476C4semidirect
48. #10622475C4semidirect
255. #1922D11semidirect
594. C11#22095semidirect

Maximal subgroups

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

subgroupindex
#130785332
#130773122
D11×#4242
#130693652
#130693632
#130693212
#130693182
#130692152
#130689172
#130688942
#130688902
#130688222
#130687142
#130683862
C11×#19222
#2209511