Finite Group Databasebeta

← #14802177

Subgroups — #14802177

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622583C211yesmaximal, characteristic, complemented
2C2×#10622655C211yesmaximal, characteristic
3#13071641C211yesmaximal, characteristic, complemented
4#13070088C211yesmaximal, characteristic, complemented
5#13070025C211yesmaximal, characteristic, complemented
6#13070004C211yesmaximal, characteristic, complemented
7#13069933C211yesmaximal, characteristic, complemented
8#13069372C211yesmaximal, characteristic, complemented
9#13069233C211yesmaximal, characteristic, complemented
10#13068974C211yesmaximal, characteristic, complemented
11#13068939C211yesmaximal, characteristic
12#13068801C211yesmaximal, characteristic, complemented
13#13068618C211yesmaximal, characteristic, complemented
14#13068335C211yesmaximal, characteristic, complemented
15C11×#2501C211yesmaximal, characteristic
16C2×C11×#123—21no—
17C2×C11×#123—21no—
18C2×C11×#121C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C2×C4×Dic22C2211yescharacteristic
25C11×#399—21no—
26C11×#399—21no—
27C11×#390C2211yescharacteristic
28C11×#390C2211yescharacteristic
29C11×#384C2211yescharacteristic
30C11×#384C2211yescharacteristic
31C4×C11×C22⋊C4C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622655—24no—
37#10622583—24no—
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622558—21no—
45#10622557—21no—
46C4×C4⋊Dic11C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622541C2211yescharacteristic
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622265—21no—
52#10622262—21no—
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622162C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11C2311yescharacteristic
65C22×Dic22C2311yescharacteristic
66C11×#123—44no—
67C11×#123—44no—
68C11×#121—22no—
69C11×#121—22no—
70C2×C11×C4⋊C4—22no—
71C2×C11×C4⋊C4—22no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4D411yescharacteristic
86C2×C11×C22⋊C4D411yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91C2×#4324—22no—
92C2×#4324—22no—
93C2×#4324—41no—
94#66979—22no—
95#66979—41no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99#66977—22no—
100#66977D414yes—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—21no—
106C2×C4×Dic11—21no—
107C2×#4318—22no—
108C2×#4318—22no—
109C2×#4318—41no—
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C4×Dic22—22no—
115C4×Dic22—41no—
116C11×#95D411yescharacteristic
117C11×#95D411yescharacteristic
118#66896—22no—
119#66896—22no—
120#66896—41no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C22⋊(C11⋊C8)—22no—
126#66874—22no—
127#66874—22no—
128#66874—22no—
129#66871—22no—
130#66871—22no—
131#66871—22no—
132C4⋊(C11⋊C8)—22no—
133C4⋊(C11⋊C8)—41no—
134#25217—111nomaximal, Sylow
135C24×C11—21no—
136C24×C11C2×D411yescharacteristic
137C2×D4×C11—21no—
138C2×D4×C11—21no—
139C2×D4×C11—21no—
140C2×D4×C11—21no—
141C2×D4×C11—21no—
142C2×D4×C11—21no—
143C2×D4×C11—42no—
144C2×D4×C11—42no—
145C2×D4×C11—42no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2×D412yes—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11#4112yes—
163C22×C4×C11C2411yescharacteristic
164C22×Dic11—21no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C2×Dic22—21no—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22C2×D412yes—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—42no—
182C11×C4⋊C4—42no—
183C11×C4⋊C4—42no—
184C11×C4⋊C4—42no—
185C11×C22⋊C4—22no—
186C11×C22⋊C4—22no—
187C11×C22⋊C4—42no—
188C11×C22⋊C4—42no—
189C11×C22⋊C4—42no—
190C11×C22⋊C4—42no—
191C11×C22⋊C4—42no—
192C42×C11—21no—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—21no—
196C22⋊Dic11—24no—
197C22⋊Dic11—42no—
198#4324—44no—
199C4⋊Dic11—21no—
200C4⋊Dic11—21no—
201C4⋊Dic11—21no—
202C4⋊Dic11—21no—
203C4⋊Dic11C2×D412yes—
204C4⋊Dic11#4112yes—
205Dic11⋊C4—24no—
206Dic11⋊C4—42no—
207Dic11⋊C4—42no—
208C4×Dic11—42no—
209C4×Dic11—42no—
210C4×Dic11—42no—
211#4318—44no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217C2×C11⋊C8—21no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8#4112yes—
224C2×#484—111no—
225C2×#468—111no—
226#2501D1111yescharacteristic
227#2362—111no—
228#2083—111no—
229#2072—111no—
230#2067—111no—
231#2055—111no—
232#1947—111no—
233#1925—111no—
234#1880—111no—
235#1875—111no—
236#1851—111no—
237#1803—111no—
238#1736—111no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11—21no—
245C23×C11—41no—
246C23×C11—41no—
247C23×C11—41no—
248C23×C11—41no—
249C23×C11—41no—
250C23×C11—41no—
251C23×C11—41no—
252C23×C11#12112yes—
253C23×C11C22×D411yescharacteristic
254D4×C11—41no—
255D4×C11—41no—
256D4×C11—41no—
257D4×C11—41no—
258D4×C11—84no—
259C2×C4×C11—21no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—21no—
264C2×C4×C11—21no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—22no—
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—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—41no—
279C2×C4×C11—41no—
280C2×C4×C11—41no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—84no—
285C2×C4×C11#12112yes—
286C2×C4×C11AGL(1,ℤ/8)12yes—
287C2×C4×C11AGL(1,ℤ/8)12yes—
288C2×C4×C11C22×D411yescharacteristic
289C2×C4×C11C2×#4111yescharacteristic
290C2×C4×C11C2×#4111yescharacteristic
291C2×C4×C11C2×#4111yescharacteristic
292C2×C4×C11H(5,𝔽2)11yescharacteristic
293C2×C4×C112−1+411yescharacteristic
294C2×Dic11—22no—
295C2×Dic11—22no—
296C2×Dic11—22no—
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—
306Dic22—22no—
307Dic22—22no—
308Dic22—41no—
309Dic22—41no—
310C11⋊C8—22no—
311C11⋊C8—41no—
312C11⋊C8—41no—
313C11⋊C8—41no—
314C22×SD16—111no—
315C22×M16—111no—
316C2×#123—21no—
317C2×#123—21no—
318C2×C22⋊Q8—111no—
319C2×#121C2×D1111yescharacteristic
320C2×C4×Q8—111no—
321C2×#117—111no—
322C22×C4⋊C4C2×D1111yescharacteristic
323#484—224no—
324#468—224no—
325C2×#107—111no—
326C2×#107—111no—
327C2×#107—111no—
328C2×C4⋊C8—111no—
329C2×C4⋊C8—111no—
330C2×#103—111no—
331C2×#103—111no—
332C2×#103—111no—
333C2×#102—111no—
334C2×#102—111no—
335C2×#102—111no—
336C2×C22⋊C8—111no—
337#399—21no—
338#399—21no—
339#391—111no—
340#390C2×D1111yescharacteristic
341#390C2×D1111yescharacteristic
342#389—111no—
343#388—221no—
344#388—221no—
345#387—221no—
346#384C2×D1111yescharacteristic
347#384C2×D1111yescharacteristic
348C4×C4⋊C4—111no—
349C4×C4⋊C4—221no—
350C4×C22⋊C4C2×D1111yescharacteristic
351#340—111no—
352#340—111no—
353#340—111no—
354#340—111no—
355#340—111no—
356#340—111no—
357#336—111no—
358#336—111no—
359C22×C11—22no—
360C22×C11—22no—
361C22×C11—22no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11—41no—
366C22×C11—81no—
367C22×C11—81no—
368C22×C11—81no—
369C22×C11—81no—
370C22×C11—81no—
371C22×C11—81no—
372C22×C11—81no—
373C22×C11C2×#12111yescharacteristic
374C22×C11#54611yescharacteristic
375C22×C11#54711yescharacteristic
376C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
377C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
378C22×C11#57811yescharacteristic
379C22×C11#57811yescharacteristic
380C4×C11—22no—
381C4×C11—22no—
382C4×C11—22no—
383C4×C11—41no—
384C4×C11—41no—
385C4×C11—81no—
386C4×C11—81no—
387C4×C11—81no—
388C4×C11#52911yescharacteristic
389C4×C11#53911yescharacteristic
390C4×C11#54611yescharacteristic
391C4×C11#54711yescharacteristic
392Dic11—42no—
393Dic11—42no—
394Dic11—42no—
395Dic11—81no—
396C22×Q8—111no—
397C22×D4—21no—
398C22×D4C22×D1111yescharacteristic
399C23×C4—21no—
400C23×C4C22×D1111yescharacteristic
401C2×SD16—222no—
402C2×SD16—222no—
403C2×SD16—441no—
404C2×M16—222no—
405C2×M16—222no—
406C2×M16—441no—
407C22×C8—111no—
408C22×C8—111no—
409C22×C8—111no—
410C22×C8—111no—
411#123—44no—
412#123—44no—
413C22⋊Q8—114no—
414C22⋊Q8—222no—
415#121—22no—
416#121—22no—
417C4×Q8—222no—
418C4×Q8—441no—
419#117—222no—
420#117—441no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—111no—
429C2×C4⋊C4—111no—
430C2×C4⋊C4—111no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4C22×D1111yescharacteristic
435C2×C4⋊C4C22×D1111yescharacteristic
436C2×C4⋊C4C22×D1111yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—221no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4C22⋊D1111yescharacteristic
445C2×C22⋊C4C22⋊D1111yescharacteristic
446C2×C42—221no—
447C2×C42—221no—
448C2×C42—221no—
449C2×C42C22×D1111yescharacteristic
450C2×C42C22×D1111yescharacteristic
451#107—222no—
452#107—222no—
453#107—222no—
454C4⋊C8—222no—
455C4⋊C8—441no—
456#103—222no—
457#103—222no—
458#103—222no—
459#102—222no—
460#102—222no—
461#102—441no—
462C22⋊C8—222no—
463#95—221no—
464#95—221no—
465#95—221no—
466#95—221no—
467#95C22⋊D1111yescharacteristic
468#95C22⋊D1111yescharacteristic
469C2×C11—42no—
470C2×C11—161no—
471C2×C11#242511yescharacteristic
472C2×C11#303811yescharacteristic
473C2×C11#304411yescharacteristic
474C2×C11#330811yescharacteristic
475C2×C11#333011yescharacteristic
476C2×C11#334311yescharacteristic
477C2×C11#335311yescharacteristic
478C24—21no—
479C24C2×C22⋊D1111yescharacteristic
480C2×Q8—112no—
481C2×Q8—221no—
482C2×Q8—221no—
483C2×Q8—221no—
484C2×Q8—221no—
485C2×Q8—221no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—42no—
493C2×D4—42no—
494C2×D4—42no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—42no—
503C22×C4—42no—
504C22×C4—42no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4D4×D1112yes—
510C22×C4#434112yes—
511C22×C4C2×C22⋊D1111yescharacteristic
512C22×C4C2×C22⋊D1111yescharacteristic
513C22×C4C2×C22⋊D1111yescharacteristic
514C22×C4C2×C22⋊D1111yescharacteristic
515C22×C4C2×C22⋊D1111yescharacteristic
516C22×C4C23×D1111yescharacteristic
517SD16—444no—
518M16—444no—
519C2×C8—112no—
520C2×C8—221no—
521C2×C8—221no—
522C2×C8—221no—
523C2×C8—221no—
524C2×C8—221no—
525C2×C8—221no—
526C2×C8—221no—
527C2×C8—221no—
528C2×C8—221no—
529C2×C8—221no—
530C2×C8—221no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—112no—
543C4⋊C4—112no—
544C4⋊C4—224no—
545C4⋊C4—221no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—442no—
550C4⋊C4—442no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—42no—
554C22⋊C4—42no—
555C22⋊C4—42no—
556C22⋊C4—42no—
557C22⋊C4—42no—
558C22⋊C4—224no—
559C22⋊C4—442no—
560C42—21no—
561C42—21no—
562C42—21no—
563C42—21no—
564C42—442no—
565C42—442no—
566C42—442no—
567C11#2521711yescharacteristic, complemented, Sylow
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—41no—
575C23—41no—
576C23—41no—
577C23—41no—
578C23—41no—
579C23—41no—
580C23—41no—
581C23#6699112yes—
582C23C22×C22⋊D1111yescharacteristic
583Q8—222no—
584Q8—222no—
585Q8—441no—
586Q8—441no—
587D4—41no—
588D4—41no—
589D4—41no—
590D4—41no—
591D4—84no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—84no—
618C2×C4—222no—
619C2×C4—222no—
620C2×C4—222no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4#6698512yes—
631C2×C4#6698512yes—
632C2×C4#6699112yes—
633C2×C4C2×D4×D1111yescharacteristic
634C2×C4C2×#434111yescharacteristic
635C2×C4#41×D1111yescharacteristic
636C2×C4#41×D1111yescharacteristic
637C2×C4#6704211yescharacteristic
638C2×C4#6704311yescharacteristic
639C8—222no—
640C8—441no—
641C8—441no—
642C8—441no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—81no—
651C22—81no—
652C22—81no—
653C22—81no—
654C22—81no—
655C22—81no—
656C22—81no—
657C22C2×#6698511yescharacteristic
658C22C2×#6698511yescharacteristic
659C22C2×#6699111yescharacteristic
660C22#1062335511yescharacteristic
661C22#1062336011yescharacteristic
662C22#1062336911yescharacteristic
663C22#1062336911yescharacteristic
664C4—22no—
665C4—22no—
666C4—22no—
667C4—41no—
668C4—41no—
669C4—81no—
670C4—81no—
671C4—81no—
672C4—442no—
673C4—442no—
674C4—442no—
675C4—881no—
676C4#1062318011yescharacteristic
677C4#1062318511yescharacteristic
678C4#1062318611yescharacteristic
679C4#1062319611yescharacteristic
680C2—42no—
681C2—161no—
682C2#1307216311yescharacteristic
683C2#1307809211yescharacteristic
684C2#1307814211yescharacteristic
685C2#1308060111yescharacteristic
686C2#1308091511yescharacteristic
687C2#1308105011yescharacteristic
688C2#1308120011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2501C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2501D11
hypocenterC11#25217
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2501

Complements

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

NH ≅ G/Ntype
1. C2×#10622583C2semidirect
3. #13071641C2semidirect
4. #13070088C2semidirect
5. #13070025C2semidirect
6. #13070004C2semidirect
7. #13069933C2semidirect
8. #13069372C2semidirect
9. #13069233C2semidirect
10. #13068974C2semidirect
12. #13068801C2semidirect
13. #13068618C2semidirect
14. #13068335C2semidirect
567. C11#25217semidirect

Maximal subgroups

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

subgroupindex
C2×#106225832
C2×#106226552
#130716412
#130700882
#130700252
#130700042
#130699332
#130693722
#130692332
#130689742
#130689392
#130688012
#130686182
#130683352
C11×#25012
#2521711