Finite Group Databasebeta

← #14816630

Subgroups — #14816630

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×#10622676C211yesmaximal, characteristic, complemented
2C2×#10622608C211yesmaximal, characteristic
3#13071619C211yesmaximal, characteristic
4#13070155C211yesmaximal, characteristic, complemented
5#13070107C211yesmaximal, characteristic, complemented
6#13069994C211yesmaximal, characteristic, complemented
7#13069951C211yesmaximal, characteristic, complemented
8#13069372C211yesmaximal, characteristic, complemented
9#13069191C211yesmaximal, characteristic, complemented
10#13069047C211yesmaximal, characteristic
11#13068928C211yesmaximal, characteristic
12#13068869C211yesmaximal, characteristic, complemented
13#13068803C211yesmaximal, characteristic
14#13068801C211yesmaximal, characteristic
15C11×#2441C211yesmaximal, characteristic
16C2×C11×#125C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C2×#66977C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C11×#399—21no—
23C11×#396—21no—
24C11×#389—21no—
25C11×#389C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#387—21no—
28C11×#384C2211yescharacteristic
29C11×#380C2211yescharacteristic
30C4×C11×C22⋊C4C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32#10622676—24no—
33#10622608—24no—
34C2×#66874C2211yescharacteristic
35C2×#66874C2211yescharacteristic
36C2×#66874C2211yescharacteristic
37C2×#66874C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66872C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622559—21no—
45C22⋊C4×Dic11—21no—
46C4×C4⋊Dic11C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622268—21no—
52#10622260—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×Dic11—21no—
63C22×Dic22C2311yescharacteristic
64C11×#125—22no—
65C11×#125—41no—
66C11×#117—22no—
67C11×#117—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—41no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92#66977—22no—
93#66977Q814yes—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×C4×Dic11—21no—
98C2×C4×Dic11—21no—
99C2×#4318—22no—
100C2×#4318—22no—
101C2×#4318—22no—
102C22×C11⋊C8C2311yescharacteristic
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C4×Dic22—22no—
107C4×Dic22—41no—
108C11×#95—21no—
109C11×#95—21no—
110C11×#95—21no—
111C11×#95D411yescharacteristic
112C11×#95D411yescharacteristic
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C22⋊(C11⋊C8)—22no—
118#66874—22no—
119#66874—22no—
120#66874—22no—
121#66874—41no—
122#66872—22no—
123#66872D414yes—
124#66871—22no—
125#66871—22no—
126#66871—22no—
127#66871—41no—
128C4⋊(C11⋊C8)—22no—
129C4⋊(C11⋊C8)—22no—
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×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×Q812yes—
146C22×C4×C11#4112yes—
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—42no—
153C22×Dic11—42no—
154C22×Dic11—81no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C2×Dic22C2×Q812yes—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—21no—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—42no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—42no—
171C11×C4⋊C4—42no—
172C11×C4⋊C4—81no—
173C11×C4⋊C4—81no—
174C11×C4⋊C4C2×D412yes—
175C11×C22⋊C4—22no—
176C11×C22⋊C4—41no—
177C11×C22⋊C4—42no—
178C11×C22⋊C4—81no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—42no—
184C22⋊Dic11—24no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—42no—
190C4⋊Dic11C2×D412yes—
191C4⋊Dic11C2×Q812yes—
192Dic11⋊C4—24no—
193Dic11⋊C4—42no—
194Dic11⋊C4—81no—
195C4×Dic11—42no—
196C4×Dic11—81no—
197#4318—28no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8C2×D412yes—
209C2×C11⋊C8#4112yes—
210C2×#479—111no—
211C2×#428—111no—
212#2441D1111yescharacteristic
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—21no—
236C2×C4×C11—21no—
237C2×C4×C11—22no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—21no—
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—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
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×C11C22⋊Q812yes—
263C2×C4×C11#13712yes—
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C22×Q811yescharacteristic
266C2×C4×C11C2×#4111yescharacteristic
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11H(5,𝔽2)11yescharacteristic
269C2×C4×C112−1+411yescharacteristic
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
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—84no—
283Dic22—22no—
284Dic22—22no—
285Dic22—41no—
286Dic22—41no—
287C11⋊C8—22no—
288C11⋊C8—22no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C22×M16—111no—
292C2×#125C2×D1111yescharacteristic
293C2×C22⋊Q8—111no—
294C2×C4×Q8—111no—
295C2×#117C2×D1111yescharacteristic
296C22×C4⋊C4—111no—
297#479—224no—
298#428—224no—
299C2×#107—111no—
300C2×#107—111no—
301C2×#107—111no—
302C2×#107—111no—
303C2×#106—111no—
304C2×#106—111no—
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—21no—
313#396—21no—
314#391—111no—
315#389—21no—
316#389—111no—
317#389—221no—
318#389C2×D1111yescharacteristic
319#389C2×D1111yescharacteristic
320#387—21no—
321#387—221no—
322#385—221no—
323#384C2×D1111yescharacteristic
324#380C2×D1111yescharacteristic
325C4×C4⋊C4—111no—
326C4×C22⋊C4—221no—
327C4×C22⋊C4C2×D1111yescharacteristic
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—22no—
352C4×C11—41no—
353C4×C11—41no—
354C4×C11—41no—
355C4×C11—42no—
356C4×C11—81no—
357C4×C11—81no—
358C4×C11—81no—
359C4×C11#52511yescharacteristic
360C4×C11#53911yescharacteristic
361C4×C11D4×Q811yescharacteristic
362C4×C11#55411yescharacteristic
363Dic11—42no—
364Dic11—42no—
365Dic11—42no—
366Dic11—81no—
367C22×Q8—111no—
368C23×C4—221no—
369C23×C4C22×D1111yescharacteristic
370C2×M16—222no—
371C2×M16—222no—
372C2×M16—222no—
373C22×C8—111no—
374C22×C8—111no—
375C22×C8—111no—
376C22×C8—111no—
377#125—22no—
378#125—41no—
379C22⋊Q8—114no—
380C22⋊Q8—222no—
381C4×Q8—222no—
382C4×Q8—441no—
383#117—22no—
384#117—41no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—441no—
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4C22⋊D1111yescharacteristic
408C2×C22⋊C4C22⋊D1111yescharacteristic
409C2×C42—21no—
410C2×C42—221no—
411C2×C42—221no—
412C2×C42C22×D1111yescharacteristic
413C2×C42C22×D1111yescharacteristic
414#107—222no—
415#107—222no—
416#107—222no—
417#107—441no—
418#106—114no—
419#106—222no—
420C4⋊C8—222no—
421C4⋊C8—222no—
422#103—222no—
423#103—222no—
424#103—222no—
425#103—441no—
426C22⋊C8—222no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95C22⋊D1111yescharacteristic
435#95C22⋊D1111yescharacteristic
436C2×C11—42no—
437C2×C11#244911yescharacteristic
438C2×C11#307811yescharacteristic
439C2×C11#308311yescharacteristic
440C2×C11#326811yescharacteristic
441C2×C11#327611yescharacteristic
442C2×C11#334611yescharacteristic
443C2×C11#335211yescharacteristic
444C24C2×C22⋊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—221no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—442no—
464C22×C4—442no—
465C22×C4—881no—
466C22×C4Q8×D1112yes—
467C22×C4#434312yes—
468C22×C4C2×C22⋊D1111yescharacteristic
469C22×C4C2×C22⋊D1111yescharacteristic
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C23×D1111yescharacteristic
474M16—228no—
475C2×C8—112no—
476C2×C8—112no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C2×C8—221no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—81no—
499C4⋊C4—81no—
500C4⋊C4—112no—
501C4⋊C4—112no—
502C4⋊C4—224no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—442no—
508C4⋊C4—442no—
509C4⋊C4—881no—
510C4⋊C4D4×D1112yes—
511C22⋊C4—22no—
512C22⋊C4—41no—
513C22⋊C4—42no—
514C22⋊C4—81no—
515C22⋊C4—224no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—42no—
521C42—442no—
522C42—881no—
523C11#2636211yescharacteristic, complemented, Sylow
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23#6699912yes—
531C23C22×C22⋊D1111yescharacteristic
532Q8—222no—
533Q8—222no—
534Q8—441no—
535Q8—441no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—441no—
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—884no—
578C2×C4#6699912yes—
579C2×C4#6700412yes—
580C2×C4C2×D4×D1111yescharacteristic
581C2×C4#6703711yescharacteristic
582C2×C4C2×Q8×D1111yescharacteristic
583C2×C4C2×#434311yescharacteristic
584C2×C4#41×D1111yescharacteristic
585C2×C4#6704311yescharacteristic
586C8—222no—
587C8—222no—
588C8—441no—
589C8—441no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22D4×C22⋊D1111yescharacteristic
598C22C2×#6699911yescharacteristic
599C22#1062335311yescharacteristic
600C22C2×#6700411yescharacteristic
601C22#1062335511yescharacteristic
602C22#1062336611yescharacteristic
603C22#1062336911yescharacteristic
604C4—22no—
605C4—22no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—42no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4—442no—
614C4—442no—
615C4—442no—
616C4—881no—
617C4#1062315811yescharacteristic
618C4#1062316311yescharacteristic
619C4#1062316711yescharacteristic
620C4#1062317611yescharacteristic
621C2—42no—
622C2#1307242111yescharacteristic
623C2#1307841711yescharacteristic
624C2#1307846311yescharacteristic
625C2#1308015711yescharacteristic
626C2#1308025811yescharacteristic
627C2#1308110111yescharacteristic
628C2#1308118511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2441C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2441D11
hypocenterC11#26362
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2441

Complements

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

NH ≅ G/Ntype
1. C2×#10622676C2semidirect
4. #13070155C2semidirect
5. #13070107C2semidirect
6. #13069994C2semidirect
7. #13069951C2semidirect
8. #13069372C2semidirect
9. #13069191C2semidirect
12. #13068869C2semidirect
523. C11#26362semidirect

Maximal subgroups

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

subgroupindex
C2×#106226762
C2×#106226082
#130716192
#130701552
#130701072
#130699942
#130699512
#130693722
#130691912
#130690472
#130689282
#130688692
#130688032
#130688012
C11×#24412
#2636211