Finite Group Databasebeta

← #14816634

Subgroups — #14816634

Order 2816.

812 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622470C211yesmaximal, characteristic, complemented
2#13072323C211yesmaximal, characteristic
3#13071621C211yesmaximal, characteristic
4#13070151C211yesmaximal, characteristic, complemented
5#13070105C211yesmaximal, characteristic, complemented
6#13069992C211yesmaximal, characteristic, complemented
7#13069956C211yesmaximal, characteristic, complemented
8#13069371C211yesmaximal, characteristic, complemented
9#13069196C211yesmaximal, characteristic, complemented
10#13069049C211yesmaximal, characteristic
11#13068928C211yesmaximal, characteristic
12#13068867C211yesmaximal, characteristic, complemented
13#13068804C211yesmaximal, characteristic
14#13068799C211yesmaximal, characteristic
15C2×C11×#428C211yesmaximal, characteristic
16C22×C11×M16C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C2×#66943C2211yescharacteristic
21C2×#66940C2211yescharacteristic
22C11×#428—24no—
23C2×C11×#107C2211yescharacteristic
24C2×C11×#107C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic
27#10622825C2211yescharacteristic
28#10622823—21no—
29C4×C22⋊Dic11—21no—
30C4×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×#66880C2211yescharacteristic
34C2×Dic11⋊C8C2211yescharacteristic
35C2×Dic11⋊C8C2211yescharacteristic
36#10622598C2211yescharacteristic
37#10622591—21no—
38#10622589C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40#10622587C2211yescharacteristic
41#10622586C2211yescharacteristic
42#10622586C2211yescharacteristic
43#10622585—21no—
44C2×#66874C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66871C2211yescharacteristic
47C2×#66871C2211yescharacteristic
48#10622562—21no—
49#10622561—21no—
50#10622546—21no—
51#10622541—21no—
52#10622470—24no—
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C22×Dic22C2311yescharacteristic
64C2×C11×M16—22no—
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C11×#117—22no—
70C11×#117—41no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—41no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C42×C11—21no—
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11D411yescharacteristic
83C2×C22⋊Dic11D411yescharacteristic
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89#66977—22no—
90#66977Q814yes—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11C2311yescharacteristic
101C2×C4×Dic11C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104#66943—22no—
105#66943—41no—
106#66940—22no—
107#66940—41no—
108C11×#107—22no—
109C11×#107—22no—
110C11×#106—22no—
111C11×#106D414yes—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95D411yescharacteristic
120C11⋊#95D411yescharacteristic
121C22⋊(C11⋊C8)—22no—
122#66880—22no—
123#66880—22no—
124Dic11⋊C8—22no—
125Dic11⋊C8—22no—
126#66874—22no—
127#66874—41no—
128#66871—22no—
129#66871—41no—
130#26362—111nomaximal, Sylow
131C24×C11C2×D411yescharacteristic
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—42no—
141C22×C4×C11—42no—
142C22×C4×C11—81no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×Q812yes—
145C22×C4×C11#4112yes—
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C22×Dic11C2×D411yescharacteristic
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22C2×Q812yes—
161C11×M16—28no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11C2×D412yes—
167C2×C8×C11#4112yes—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—42no—
175C11×C4⋊C4C2×D412yes—
176C11×C4⋊C4C2×D412yes—
177C11×C22⋊C4—42no—
178C42×C11—42no—
179C22⋊Dic11—22no—
180C22⋊Dic11—24no—
181C22⋊Dic11—41no—
182C22⋊Dic11—81no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—42no—
189C4⋊Dic11—42no—
190C4⋊Dic11C2×Q812yes—
191Dic11⋊C4—24no—
192Dic11⋊C4—42no—
193Dic11⋊C4—42no—
194Dic11⋊C4—42no—
195Dic11⋊C4—81no—
196Dic11⋊C4—81no—
197Dic11⋊C4—81no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—21no—
201C4×Dic11—21no—
202C4×Dic11—42no—
203C4×Dic11—81no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×#479—111no—
211C2×#428D1111yescharacteristic
212#2441—111no—
213#2360—111no—
214#2095—111no—
215#2086—111no—
216#2066—111no—
217#2059—111no—
218#1947—111no—
219#1919—111no—
220#1894—111no—
221#1873—111no—
222#1863—111no—
223#1852—111no—
224#1851—111no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11—21no—
230C23×C11—21no—
231C23×C11C22⋊Q812yes—
232C23×C11C22×D411yescharacteristic
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—84no—
252C2×C4×C11C22⋊Q812yes—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C22×Q811yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C2×C4×C112−1+411yescharacteristic
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—21no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11#13712yes—
283Dic22—22no—
284Dic22—22no—
285Dic22—41no—
286Dic22—41no—
287C8×C11—22no—
288C8×C11—22no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C22×M16C2×D1111yescharacteristic
292C2×#125—111no—
293C2×C22⋊Q8—111no—
294C2×C4×Q8—111no—
295C2×#117C2×D1111yescharacteristic
296C22×C4⋊C4C2×D1111yescharacteristic
297#479—224no—
298#428—24no—
299C2×#107—111no—
300C2×#107—111no—
301C2×#107C2×D1111yescharacteristic
302C2×#107C2×D1111yescharacteristic
303C2×#106C2×D1111yescharacteristic
304C2×#106C2×D1111yescharacteristic
305C2×C4⋊C8—111no—
306C2×C4⋊C8—111no—
307C2×#103—111no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#103—111no—
311C2×C22⋊C8—111no—
312#399—221no—
313#396—221no—
314#391—111no—
315#389—111no—
316#389—111no—
317#389—111no—
318#389—221no—
319#389—221no—
320#387—221no—
321#387—221no—
322#385—221no—
323#384—111no—
324#380—111no—
325C4×C4⋊C4—111no—
326C4×C22⋊C4—111no—
327C4×C22⋊C4—221no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#336—111no—
335#336—111no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—22no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11C2×C22⋊Q811yescharacteristic
344C22×C11D4211yescharacteristic
345C22×C11#54711yescharacteristic
346C22×C11C2×#13711yescharacteristic
347C22×C11#57511yescharacteristic
348C22×C11#57611yescharacteristic
349C22×C11#57811yescharacteristic
350C4×C11—22no—
351C4×C11—42no—
352C4×C11—42no—
353C4×C11—81no—
354C4×C11—81no—
355C4×C11#52511yescharacteristic
356C4×C11#53911yescharacteristic
357C4×C11D4×Q811yescharacteristic
358C4×C11#55411yescharacteristic
359Dic11—22no—
360Dic11—42no—
361Dic11—41no—
362Dic11—42no—
363Dic11—41no—
364Dic11—41no—
365Dic11—81no—
366Dic11—81no—
367C22×Q8—111no—
368C23×C4—21no—
369C23×C4C22×D1111yescharacteristic
370C2×M16—22no—
371C2×M16—22no—
372C2×M16—22no—
373C22×C8—111no—
374C22×C8—111no—
375C22×C8C22×D1111yescharacteristic
376C22×C8C22×D1111yescharacteristic
377#125—222no—
378#125—441no—
379C22⋊Q8—114no—
380C22⋊Q8—222no—
381C4×Q8—222no—
382C4×Q8—441no—
383#117—22no—
384#117—41no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—41no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—221no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—111no—
406C2×C22⋊C4—111no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C42—21no—
410C2×C42—111no—
411C2×C42—111no—
412C2×C42—221no—
413C2×C42—221no—
414#107—22no—
415#107—22no—
416#107—222no—
417#107—441no—
418#106—22no—
419#106C22⋊D1114yes—
420C4⋊C8—222no—
421C4⋊C8—222no—
422#103—222no—
423#103—222no—
424#103—222no—
425#103—441no—
426C22⋊C8—222no—
427#95—111no—
428#95—111no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436C2×C11—42no—
437C2×C11#244911yescharacteristic
438C2×C11#307811yescharacteristic
439C2×C11#308311yescharacteristic
440C2×C11#326811yescharacteristic
441C2×C11#327611yescharacteristic
442C2×C11#334611yescharacteristic
443C2×C11#335211yescharacteristic
444C24D4×D1111yescharacteristic
445C2×Q8—112no—
446C2×Q8—221no—
447C2×Q8—221no—
448C2×Q8—221no—
449C2×Q8—221no—
450C2×Q8—221no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—81no—
462C22×C4—111no—
463C22×C4—111no—
464C22×C4—111no—
465C22×C4—111no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4#433912yes—
471C22×C4D4×D1111yescharacteristic
472C22×C4Q8×D1112yes—
473C22×C4C23×D1111yescharacteristic
474M16—28no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8#433912yes—
486C2×C8C2×C22⋊D1112yes—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—42no—
494C4⋊C4—112no—
495C4⋊C4—224no—
496C4⋊C4—221no—
497C4⋊C4—221no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—442no—
502C4⋊C4—442no—
503C4⋊C4—442no—
504C4⋊C4—442no—
505C4⋊C4—442no—
506C4⋊C4—881no—
507C4⋊C4—881no—
508C4⋊C4—881no—
509C4⋊C4C2×C22⋊D1112yes—
510C4⋊C4C2×C22⋊D1112yes—
511C22⋊C4—42no—
512C22⋊C4—222no—
513C22⋊C4—224no—
514C22⋊C4—441no—
515C22⋊C4—881no—
516C42—42no—
517C42—221no—
518C42—221no—
519C42—221no—
520C42—221no—
521C42—442no—
522C42—881no—
523C11#2636211yescharacteristic, complemented, Sylow
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23#6694912yes—
531C23C2×D4×D1111yescharacteristic
532Q8—222no—
533Q8—222no—
534Q8—441no—
535Q8—441no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—84no—
555C2×C4—112no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—222no—
560C2×C4—222no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4#6694912yes—
580C2×C4C2×#433911yescharacteristic
581C2×C4C2×#433911yescharacteristic
582C2×C4#6703711yescharacteristic
583C2×C4C2×Q8×D1111yescharacteristic
584C2×C4#6704011yescharacteristic
585C2×C4C22×C22⋊D1111yescharacteristic
586C8—22no—
587C8—22no—
588C8—441no—
589C8—441no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22#1062303811yescharacteristic
598C22C2×#6694911yescharacteristic
599C22#1062330411yescharacteristic
600C22#1062330511yescharacteristic
601C22D11×#13711yescharacteristic
602C22#1062331011yescharacteristic
603C22D4×C22⋊D1111yescharacteristic
604C4—22no—
605C4—42no—
606C4—42no—
607C4—81no—
608C4—81no—
609C4—222no—
610C4—442no—
611C4—441no—
612C4—441no—
613C4—441no—
614C4—442no—
615C4—881no—
616C4—881no—
617C4#1062304211yescharacteristic
618C4#1062304611yescharacteristic
619C4#1062332211yescharacteristic
620C4Q8×C22⋊D1111yescharacteristic
621C2—42no—
622C2#1307242511yescharacteristic
623C2#1307842011yescharacteristic
624C2#1307846611yescharacteristic
625C2#1308015011yescharacteristic
626C2#1308025611yescharacteristic
627C2#1308110211yescharacteristic
628C2#1308118711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#428C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#428D11
hypocenterC11#26362
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#10622470C2semidirect
4. #13070151C2semidirect
5. #13070105C2semidirect
6. #13069992C2semidirect
7. #13069956C2semidirect
8. #13069371C2semidirect
9. #13069196C2semidirect
12. #13068867C2semidirect
523. C11#26362semidirect

Maximal subgroups

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

subgroupindex
C2×#106224702
#130723232
#130716212
#130701512
#130701052
#130699922
#130699562
#130693712
#130691962
#130690492
#130689282
#130688672
#130688042
#130687992
C2×C11×#4282
#2636211