Finite Group Databasebeta

← #14810895

Subgroups — #14810895

Order 2816.

994 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622459C211yesmaximal, characteristic, complemented
2C2×#10622726C211yesmaximal, characteristic
3#13072307C211yesmaximal, characteristic, complemented
4#13071447C211yesmaximal, characteristic
5#13070163C211yesmaximal, characteristic, complemented
6#13070010C211yesmaximal, characteristic, complemented
7#13070010C211yesmaximal, characteristic, complemented
8#13069758C211yesmaximal, characteristic, complemented
9#13068880C211yesmaximal, characteristic, complemented
10#13068866C211yesmaximal, characteristic, complemented
11#13068817C211yesmaximal, characteristic, complemented
12#13068645C211yesmaximal, characteristic, complemented
13#13068627C211yesmaximal, characteristic, complemented
14#13068557C211yesmaximal, characteristic
15C11×#1850C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×C8×C11C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C4×C11×C22⋊C4C2211yescharacteristic
26#10622825C2211yescharacteristic
27#10622825C2211yescharacteristic
28#10622726—24no—
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×#66885C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66882C2211yescharacteristic
36C2×#66881C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×#66880C2211yescharacteristic
40C2×#66880C2211yescharacteristic
41#10622569—21no—
42#10622569—21no—
43#10622561—21no—
44#10622560—21no—
45#10622549C2211yescharacteristic
46#10622542C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622541C2211yescharacteristic
49#10622541C2211yescharacteristic
50#10622459—24no—
51#10622277—21no—
52D11×#95—21no—
53#10622268—21no—
54#10622259—21no—
55C11×#336C2211yescharacteristic
56C11×#336C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622189C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—21no—
63C2×#4339—22no—
64C2×#4339—22no—
65C2×#4339—22no—
66C2×#4339—41no—
67C2×#4339—41no—
68C2×#4339Q814yescomplemented
69C22×D44C2311yescharacteristic
70C22×C4×D11—21no—
71C22×C4×D11—21no—
72C22×C4×D11—21no—
73C22×Dic22—21no—
74C22×Dic22C2311yescharacteristic
75C22×C8×C11—22no—
76C22×C8×C11—22no—
77C22×C8×C11—41no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C2×C11×C22⋊C4D411yescharacteristic
83C2×C11×C22⋊C4D411yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91#66979—22no—
92#66979—41no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C4×D44—22no—
104C4×D44—22no—
105C4×D44—41no—
106C4×D44—41no—
107#66922—22no—
108#66922—41no—
109C11×C4⋊C8—22no—
110C11×C4⋊C8—41no—
111C11×C22⋊C8—22no—
112C11×#95D411yescharacteristic
113C11×#95D411yescharacteristic
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124#66885—22no—
125#66885—22no—
126#66885—22no—
127#66885D414yes—
128#66882—22no—
129#66882—22no—
130#66882—41no—
131#66881—41no—
132#66880—22no—
133#66880—22no—
134#66880—41no—
135#66880—41no—
136#25954—111nomaximal, Sylow
137C24×C11C2×D411yescharacteristic
138C23×D11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×Q812yes—
149C22×C4×C11#4112yes—
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—24no—
152C2×C22⋊D11—42no—
153C2×C22⋊D11—42no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161#4339—28no—
162#4339—44no—
163#4339—44no—
164#4339—44no—
165C2×D44—21no—
166C2×D44—21no—
167C2×D44—21no—
168C2×D44C2×D412yes—
169C2×D44C2×Q812yes—
170C2×D44#4112yes—
171C2×C4×D11—24no—
172C2×C4×D11—42no—
173C2×C4×D11—42no—
174C2×C4×D11—42no—
175C2×C4×D11—42no—
176C2×C4×D11—42no—
177C2×C4×D11—42no—
178C2×C4×D11—81no—
179C2×C4×D11—81no—
180C2×Dic22—21no—
181C2×Dic22—21no—
182C2×Dic22—21no—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22—42no—
186C2×Dic22—42no—
187C2×Dic22—81no—
188C2×Dic22C2×Q812yes—
189C2×C8×C11—21no—
190C2×C8×C11—21no—
191C2×C8×C11—21no—
192C2×C8×C11—21no—
193C2×C8×C11—21no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—44no—
201C2×C8×C11C2×D412yes—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—41no—
204C42×C11—21no—
205C42×C11—21no—
206C42×C11—21no—
207C42×C11—21no—
208C22⋊Dic11—42no—
209C22⋊Dic11—81no—
210C22⋊Dic11—81no—
211(C2×D11)⋊C4—42no—
212(C2×D11)⋊C4—42no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—42no—
225C4⋊Dic11C2×D412yes—
226Dic11⋊C4—42no—
227Dic11⋊C4—81no—
228C4×Dic11—42no—
229C2×#474—111no—
230C2×#416—111no—
231#2439—111no—
232#2339—111no—
233#2097—111no—
234#2068—111no—
235#2068—111no—
236#2024—111no—
237#1864—111no—
238#1862—111no—
239#1854—111no—
240#1850D1111yescharacteristic, complemented
241#1808—111no—
242#1804—111no—
243#1788—111no—
244C23×C11—21no—
245C23×C11—21no—
246C23×C11—21no—
247C23×C11—21no—
248C23×C11—21no—
249C23×C11—21no—
250C23×C11C22⋊Q812yes—
251C23×C11C22×D411yescharacteristic
252C22×D11—22no—
253C22×D11—22no—
254C22×D11—22no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11—41no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—21no—
268C2×C4×C11—21no—
269C2×C4×C11—21no—
270C2×C4×C11—21no—
271C2×C4×C11—21no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11C22⋊Q812yes—
277C2×C4×C11#13512yes—
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×Q811yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×C4×C11C2×#4111yescharacteristic
282C2×C4×C11H(5,𝔽2)11yescharacteristic
283C2×C4×C11H(5,𝔽2)11yescharacteristic
284C22⋊D11—48no—
285C2×Dic11—22no—
286C2×Dic11—22no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
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—41no—
302C2×Dic11—41no—
303C2×Dic11—41no—
304C2×Dic11—41no—
305C2×Dic11—41no—
306D44—22no—
307D44—22no—
308D44—22no—
309D44C22⋊Q814yes—
310C4×D11—48no—
311C4×D11—84no—
312C4×D11—84no—
313Dic22—22no—
314Dic22—22no—
315Dic22—41no—
316Dic22—41no—
317Dic22—84no—
318C8×C11—22no—
319C8×C11—41no—
320C8×C11—41no—
321C8×C11—41no—
322C22×#41—111no—
323C23×C8C2×D1111yescharacteristic
324C2×C4⋊Q8—111no—
325C2×C4×D4—111no—
326C2×C4×D4—111no—
327C2×#117—111no—
328#474—224no—
329C2×#107—111no—
330C2×#107—111no—
331C2×#107—111no—
332C2×#106—111no—
333C2×C4⋊C8C2×D1111yescharacteristic
334C2×C4⋊C8C2×D1111yescharacteristic
335#416—224no—
336C2×#103—111no—
337C2×#103—111no—
338C2×#103—111no—
339C2×#103—111no—
340C2×#102—111no—
341C2×#102—111no—
342C2×#102—111no—
343C2×#102—111no—
344C2×C22⋊C8C2×D1111yescharacteristic
345#396—221no—
346#393—221no—
347#391—111no—
348#391—111no—
349#391—221no—
350#389—111no—
351#389—111no—
352#387—221no—
353#386—221no—
354#386—221no—
355#382—111no—
356#381—221no—
357#380—111no—
358#380—111no—
359C4×C22⋊C4C2×D1111yescharacteristic
360C2×#95—221no—
361#340—111no—
362#340—111no—
363#340—111no—
364#340—111no—
365#336C2×D1111yescharacteristic
366#336C2×D1111yescharacteristic
367C22×C11—22no—
368C22×C11—22no—
369C22×C11—22no—
370C22×C11—41no—
371C22×C11—41no—
372C22×C11—41no—
373C22×C11—41no—
374C22×C11C2×C22⋊Q811yescharacteristic
375C22×C11D4211yescharacteristic
376C22×C11#54611yescharacteristic
377C22×C11C2×#13511yescharacteristic
378C22×C11#57511yescharacteristic
379C22×C11#57611yescharacteristic
380C22×C11#57811yescharacteristic
381C2×D11—24no—
382C2×D11—42no—
383C2×D11—42no—
384C2×D11—42no—
385C2×D11—42no—
386C2×D11—42no—
387C2×D11—42no—
388C4×C11—22no—
389C4×C11—22no—
390C4×C11—41no—
391C4×C11—41no—
392C4×C11—41no—
393C4×C11C2×C22⋊Q811yescharacteristic
394C4×C11#54311yescharacteristic
395C4×C11#54611yescharacteristic
396C4×C11#55111yescharacteristic
397Dic11—42no—
398Dic11—42no—
399Dic11—81no—
400Dic11—81no—
401Dic11—81no—
402Dic11—81no—
403Dic11—81no—
404C2×#41—114no—
405C2×#41—222no—
406C2×#41—222no—
407C2×#41—222no—
408C2×#41—441no—
409C2×#41—441no—
410C22×Q8—111no—
411C22×Q8—221no—
412C22×D4—111no—
413C22×D4—221no—
414C23×C4—221no—
415C23×C4—221no—
416C23×C4—221no—
417C23×C4C22×D1111yescharacteristic
418C22×C8—22no—
419C22×C8—22no—
420C22×C8—41no—
421C22×C8C22×D1111yescharacteristic
422C22×C8C22×D1111yescharacteristic
423C22×C8C22×D1111yescharacteristic
424C22×C8C22×D1111yescharacteristic
425C4⋊Q8—222no—
426C4⋊Q8—441no—
427C4×D4—222no—
428C4×D4—222no—
429C4×D4—441no—
430C4×D4—441no—
431#117—222no—
432#117—441no—
433C2×C4⋊C4—111no—
434C2×C4⋊C4—111no—
435C2×C4⋊C4—111no—
436C2×C4⋊C4—111no—
437C2×C4⋊C4—111no—
438C2×C4⋊C4—111no—
439C2×C4⋊C4—221no—
440C2×C4⋊C4—221no—
441C2×C4⋊C4—221no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4D4411yescharacteristic
448C2×C22⋊C4D4411yescharacteristic
449C2×C42—221no—
450C2×C42C22×D1111yescharacteristic
451C2×C42C22×D1111yescharacteristic
452#107—222no—
453#107—222no—
454#107—441no—
455#106—441no—
456C4⋊C8—22no—
457C4⋊C8—41no—
458#103—222no—
459#103—222no—
460#103—441no—
461#103—441no—
462#102—114no—
463#102—222no—
464#102—222no—
465#102—222no—
466C22⋊C8—22no—
467#95—221no—
468#95—221no—
469#95—221no—
470#95—221no—
471#95—221no—
472#95—221no—
473#95—221no—
474#95—221no—
475#95—221no—
476#95—221no—
477#95D4411yescharacteristic
478#95D4411yescharacteristic
479C2×C11—42no—
480C2×C11#243711yescharacteristic
481C2×C11#307611yescharacteristic
482C2×C11#308311yescharacteristic
483C2×C11#326911yescharacteristic
484C2×C11#328011yescharacteristic
485C2×C11#330211yescharacteristic
486C2×C11#331911yescharacteristic
487D11—44no—
488C24—221no—
489C24C2×D4411yescharacteristic
490#41—228no—
491#41—444no—
492#41—444no—
493#41—444no—
494C2×Q8—112no—
495C2×Q8—221no—
496C2×Q8—221no—
497C2×Q8—221no—
498C2×Q8—221no—
499C2×Q8—221no—
500C2×Q8—442no—
501C2×Q8—442no—
502C2×Q8—881no—
503C2×D4—112no—
504C2×D4—112no—
505C2×D4—112no—
506C2×D4—224no—
507C2×D4—221no—
508C2×D4—221no—
509C2×D4—221no—
510C2×D4—442no—
511C2×D4—442no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—224no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—221no—
522C22×C4—221no—
523C22×C4—221no—
524C22×C4—442no—
525C22×C4—442no—
526C22×C4—442no—
527C22×C4—442no—
528C22×C4—442no—
529C22×C4—442no—
530C22×C4—881no—
531C22×C4—881no—
532C22×C4C2×D4411yescharacteristic
533C22×C4C2×D4411yescharacteristic
534C22×C4C2×D4411yescharacteristic
535C22×C4C2×D4411yescharacteristic
536C22×C4C2×D4411yescharacteristic
537C22×C4#434112yes—
538C22×C4Q8×D1112yes—
539C22×C4C23×D1111yescharacteristic
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—44no—
552C2×C8D4×D1112yes—
553C4⋊C4—112no—
554C4⋊C4—221no—
555C4⋊C4—221no—
556C4⋊C4—221no—
557C4⋊C4—221no—
558C4⋊C4—221no—
559C4⋊C4—221no—
560C4⋊C4—221no—
561C4⋊C4—221no—
562C4⋊C4—221no—
563C4⋊C4—221no—
564C4⋊C4—221no—
565C4⋊C4—442no—
566C4⋊C4—442no—
567C4⋊C4—881no—
568C22⋊C4—22no—
569C22⋊C4—41no—
570C22⋊C4—442no—
571C22⋊C4—442no—
572C22⋊C4—442no—
573C22⋊C4—881no—
574C22⋊C4—881no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—442no—
580C11#2595411yescharacteristic, complemented, Sylow
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—222no—
588C23—222no—
589C23—222no—
590C23—441no—
591C23—441no—
592C23—441no—
593C23—441no—
594C23#6695012yes—
595C23C22×D4411yescharacteristic
596Q8—222no—
597Q8—222no—
598Q8—441no—
599Q8—441no—
600Q8—884no—
601D4—114no—
602D4—222no—
603D4—222no—
604D4—222no—
605D4—448no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—222no—
624C2×C4—222no—
625C2×C4—448no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—441no—
637C2×C4—441no—
638C2×C4—441no—
639C2×C4—441no—
640C2×C4—441no—
641C2×C4—441no—
642C2×C4—441no—
643C2×C4—441no—
644C2×C4—441no—
645C2×C4—884no—
646C2×C4—884no—
647C2×C4#6695012yes—
648C2×C4#6695712yes—
649C2×C4C2×D4×D1111yescharacteristic
650C2×C4C2×#434111yescharacteristic
651C2×C4#6703711yescharacteristic
652C2×C4C2×Q8×D1111yescharacteristic
653C2×C4#41×D1111yescharacteristic
654C2×C4#6704211yescharacteristic
655C8—22no—
656C8—41no—
657C8—41no—
658C8—41no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—41no—
663C22—41no—
664C22—41no—
665C22—41no—
666C22—224no—
667C22—442no—
668C22—442no—
669C22—442no—
670C22—442no—
671C22—442no—
672C22—442no—
673C22C2×#6695011yescharacteristic
674C22D4×D4411yescharacteristic
675C22#1062308511yescharacteristic
676C22C2×#6695711yescharacteristic
677C22#1062327911yescharacteristic
678C22#1062328311yescharacteristic
679C22#1062328411yescharacteristic
680C4—22no—
681C4—22no—
682C4—41no—
683C4—41no—
684C4—41no—
685C4—442no—
686C4—442no—
687C4—881no—
688C4—881no—
689C4—881no—
690C4—881no—
691C4—881no—
692C4#1062312211yescharacteristic
693C4D11×C22⋊Q811yescharacteristic
694C4#1062316511yescharacteristic
695C4#1062318911yescharacteristic
696C2—42no—
697C2—444no—
698C2#1307228011yescharacteristic
699C2#1307840611yescharacteristic
700C2#1307846911yescharacteristic
701C2#1308017611yescharacteristic
702C2#1308030311yescharacteristic
703C2#1308053411yescharacteristic
704C2#1308077411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1850C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
hypercenter#1850D11
hypocenterC11#25954
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. C2×#10622459C2semidirect
3. #13072307C2semidirect
5. #13070163C2semidirect
6. #13070010C2semidirect
7. #13070010C2semidirect
8. #13069758C2semidirect
9. #13068880C2semidirect
10. #13068866C2semidirect
11. #13068817C2semidirect
12. #13068645C2semidirect
13. #13068627C2semidirect
15. C11×#1850C2semidirect
68. C2×#4339Q8semidirect
240. #1850D11semidirect
580. C11#25954semidirect

Maximal subgroups

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

subgroupindex
C2×#106224592
C2×#106227262
#130723072
#130714472
#130701632
#130700102
#130697582
#130688802
#130688662
#130688172
#130686452
#130686272
#130685572
C11×#18502
#2595411