Finite Group Databasebeta

← #14764340

Subgroups — #14764340

Order 2816.

830 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622332C211yesmaximal, characteristic
2#13071019C211yesmaximal, characteristic
3#13071018C211yesmaximal, characteristic
4#13069378C211yesmaximal, characteristic, complemented
5#13069376C211yesmaximal, characteristic, complemented
6#13069373C211yesmaximal, characteristic, complemented
7#13069371C211yesmaximal, characteristic, complemented
8#13068817C211yesmaximal, characteristic
9#13068815C211yesmaximal, characteristic
10#13068813C211yesmaximal, characteristic
11#13068783C211yesmaximal, characteristic, complemented
12#13068781C211yesmaximal, characteristic, complemented
13#13068748C211yesmaximal, characteristic, complemented
14#13068748C211yesmaximal, characteristic, complemented
15C11×#1854C211yesmaximal, characteristic
16C2×C11×#117C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×C4×Dic11C2211yescharacteristic
19C2×#66930—21no—
20C2×C11×#107C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×C22⋊C8C2211yescharacteristic
23C11×#380C2211yescharacteristic
24#10622825C2211yescharacteristic
25C2×C22⋊(C11⋊C8)C2211yescharacteristic
26C2×#66882C2211yescharacteristic
27C2×#66881C2211yescharacteristic
28C2×#66879C2211yescharacteristic
29C2×#66879C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32#10622590C2211yescharacteristic
33#10622590C2211yescharacteristic
34#10622589C2211yescharacteristic
35#10622589C2211yescharacteristic
36#10622589C2211yescharacteristic
37#10622589C2211yescharacteristic
38C4⋊C4×Dic11C2211yescharacteristic
39C4⋊C4×Dic11C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43C2×#66871C2211yescharacteristic
44#10622555—21no—
45#10622555—21no—
46#10622555—21no—
47C4×Dic11⋊C4—21no—
48C4×Dic11⋊C4—21no—
49#10622332C418yescomplemented
50#10622263—21no—
51#10622262—21no—
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×Dic11D411yescharacteristic
62C23×Dic11D411yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×#117—41no—
66C11×#117—41no—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C42×C11—21no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76#66979—41no—
77#66979—41no—
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11C2×C414yes—
94C2×C4×Dic11D411yescharacteristic
95C2×C4×Dic11D411yescharacteristic
96C2×C4×Dic11Q814yes—
97C2×C4×Dic11C2311yescharacteristic
98C2×C4×Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66930—44no—
102C11×#107—41no—
103C11×#106—41no—
104C11×C22⋊C8C2×C414yes—
105C11×#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C22⋊(C11⋊C8)C2×C414yes—
114#66882—41no—
115#66881—41no—
116#66879C2×C414yes—
117#66879C2×C414yes—
118Dic11⋊C8C2×C414yes—
119Dic11⋊C8C2×C414yes—
120#66872—41no—
121#66872—41no—
122#66871—41no—
123#66871—41no—
124#21988—111nomaximal, Sylow
125C24×C11C2×D411yescharacteristic
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11C22×C412yes—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×Q812yes—
137C22×C4×C11C2411yescharacteristic
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—41no—
145C22×Dic11—41no—
146C22×Dic11C4⋊C414yes—
147C22×Dic11C4⋊C414yes—
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11C22×C412yes—
157C2×C8×C11C22×C412yes—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C11×C22⋊C4—42no—
167C11×C22⋊C4—42no—
168C42×C11—42no—
169C22⋊Dic11—42no—
170C22⋊Dic11—42no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179Dic11⋊C4—42no—
180Dic11⋊C4—42no—
181Dic11⋊C4—42no—
182Dic11⋊C4—42no—
183Dic11⋊C4—42no—
184Dic11⋊C4—42no—
185Dic11⋊C4—42no—
186Dic11⋊C4—42no—
187C4×Dic11—42no—
188C4×Dic11—42no—
189C4×Dic11—42no—
190C4×Dic11C4⋊C414yes—
191C4×Dic11C4⋊C414yes—
192C4×Dic11C22×C412yes—
193C4×Dic11C22×C412yes—
194C4×Dic11C2×Q812yes—
195C4×Dic11C2×Q812yes—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8C22×C412yes—
201C2×C11⋊C8C22×C412yes—
202C2×#432—111no—
203#2285—111no—
204#2285—111no—
205#1948—111no—
206#1948—111no—
207#1947—111no—
208#1947—111no—
209#1854—111no—
210#1854—111no—
211#1854—111no—
212#1854D1111yescharacteristic
213#1847—111no—
214#1847—111no—
215#1836—111no—
216#1836—111no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11C2×C4⋊C412yes—
224C23×C11C22×D411yescharacteristic
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11C2×C4⋊C412yes—
244C2×C4×C11C23×C411yescharacteristic
245C2×C4×C11C22×Q811yescharacteristic
246C2×C4×C11H(5,𝔽2)11yescharacteristic
247C2×C4×C11H(5,𝔽2)11yescharacteristic
248C2×C4×C112−1+411yescharacteristic
249C2×C4×C112−1+411yescharacteristic
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—21no—
256C2×Dic11—28no—
257C2×Dic11—44no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11C2×C4⋊C412yes—
271C2×Dic11C2×C4⋊C412yes—
272C2×Dic11C2×C4⋊C412yes—
273C2×Dic11C2×C4⋊C412yes—
274C2×Dic11AGL(1,ℤ/8)12yes—
275C2×Dic11#13712yes—
276C8×C11—22no—
277C8×C11—22no—
278C11⋊C8—22no—
279C11⋊C8—22no—
280C2×#117—111no—
281C2×#117—221no—
282C2×#117C2×D1111yescharacteristic
283C22×C42—111no—
284#432—118no—
285C2×#107—111no—
286C2×#107—111no—
287C2×#107—111no—
288C2×#107C2×D1111yescharacteristic
289C2×#106—111no—
290C2×#106—111no—
291C2×#106—111no—
292C2×#106C2×D1111yescharacteristic
293C2×C4⋊C8—111no—
294C2×C4⋊C8—111no—
295C2×C22⋊C8—111no—
296C2×C22⋊C8C2×D1111yescharacteristic
297C2×#97—111no—
298C2×#97—111no—
299#384—111no—
300#384—111no—
301#384—111no—
302#384—111no—
303#382—111no—
304#382—111no—
305#382—221no—
306#380—111no—
307#380—221no—
308#380—221no—
309#380—221no—
310#380C2×D1111yescharacteristic
311C4×C4⋊C4—111no—
312C4×C4⋊C4—111no—
313C4×C4⋊C4—221no—
314C4×C4⋊C4—221no—
315C4×C4⋊C4—221no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340C2×D1111yescharacteristic
323#340C2×D1111yescharacteristic
324C22×C11—22no—
325C22×C11—22no—
326C22×C11—22no—
327C22×C11—41no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11C22×C4⋊C411yescharacteristic
332C22×C11#53511yescharacteristic
333C22×C11#53611yescharacteristic
334C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
335C22×C11C2×#13711yescharacteristic
336C22×C11#57511yescharacteristic
337C22×C11#57511yescharacteristic
338C4×C11—22no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11#52011yescharacteristic
344C4×C11#52011yescharacteristic
345C4×C11#54411yescharacteristic
346C4×C11#54411yescharacteristic
347Dic11—22no—
348Dic11—22no—
349Dic11—22no—
350Dic11—81no—
351Dic11—81no—
352Dic11—81no—
353Dic11—81no—
354Dic11#42814yes—
355C23×C4—111no—
356C23×C4—111no—
357C23×C4C22×D1111yescharacteristic
358C22×C8—111no—
359C22×C8—111no—
360C22×C8C22×D1111yescharacteristic
361C22×C8C22×D1111yescharacteristic
362#117—41no—
363#117—41no—
364#117—444no—
365#117—441no—
366#117—441no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—221no—
386C2×C22⋊C4—221no—
387C2×C42—21no—
388C2×C42—114no—
389C2×C42—111no—
390C2×C42—111no—
391C2×C42—114no—
392C2×C42—111no—
393C2×C42—111no—
394C2×C42—221no—
395C2×C42—221no—
396C2×C42—221no—
397#107—41no—
398#107—441no—
399#107—441no—
400#107—441no—
401#106—41no—
402#106—441no—
403#106—441no—
404#106—441no—
405C4⋊C8—114no—
406C4⋊C8—114no—
407C22⋊C8—114no—
408C22⋊C8C4×D1114yes—
409#97—114no—
410#97—114no—
411#95—21no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417#95—221no—
418#95—221no—
419C2×C11—42no—
420C2×C11#231711yescharacteristic
421C2×C11C2×#42811yescharacteristic
422C2×C11#291111yescharacteristic
423C2×C11#321411yescharacteristic
424C2×C11#321611yescharacteristic
425C2×C11#323511yescharacteristic
426C2×C11#323711yescharacteristic
427C24D4×D1111yescharacteristic
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—111no—
437C22×C4—114no—
438C22×C4—111no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—114no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—441no—
449C22×C4—441no—
450C22×C4C2×C4×D1112yes—
451C22×C4D4×D1111yescharacteristic
452C22×C4Q8×D1112yes—
453C22×C4C23×D1111yescharacteristic
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—112no—
459C2×C8—112no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8C2×C4×D1112yes—
465C2×C8C2×C4×D1112yes—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—442no—
483C4⋊C4—442no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C4⋊C4—442no—
487C4⋊C4—442no—
488C4⋊C4—442no—
489C4⋊C4—442no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—442no—
493C22⋊C4—442no—
494C42—42no—
495C42—114no—
496C42—114no—
497C42—112no—
498C42—112no—
499C42—112no—
500C42—112no—
501C42—442no—
502C42—442no—
503C42—442no—
504C11#2198811yescharacteristic, complemented, Sylow
505C23—21no—
506C23—21no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23C4⋊C4×D1112yes—
512C23C2×D4×D1111yescharacteristic
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—112no—
532C2×C4—112no—
533C2×C4—112no—
534C2×C4—112no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—228no—
538C2×C4—221no—
539C2×C4—221no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—221no—
543C2×C4—221no—
544C2×C4—444no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4—441no—
555C2×C4—441no—
556C2×C4—441no—
557C2×C4C4⋊C4×D1112yes—
558C2×C4C22×C4×D1111yescharacteristic
559C2×C4#6703711yescharacteristic
560C2×C4#6703711yescharacteristic
561C2×C4C2×Q8×D1111yescharacteristic
562C2×C4#6704311yescharacteristic
563C2×C4#6704311yescharacteristic
564C8—22no—
565C8—22no—
566C8—222no—
567C8—222no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22C2×C4⋊C4×D1111yescharacteristic
576C22#1062312311yescharacteristic
577C22#1062317911yescharacteristic
578C22#1062329911yescharacteristic
579C22#1062329911yescharacteristic
580C22D11×AGL(1,ℤ/8)11yescharacteristic
581C22D11×#13711yescharacteristic
582C4—22no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4—114no—
588C4—222no—
589C4—222no—
590C4—222no—
591C4—881no—
592C4—881no—
593C4—881no—
594C4—881no—
595C4#1062307711yescharacteristic
596C4#1062307711yescharacteristic
597C4#1062315411yescharacteristic
598C4#1062315411yescharacteristic
599C2—42no—
600C2#1307123511yescharacteristic
601C2D11×#42811yescharacteristic
602C2#1307720411yescharacteristic
603C2#1307960811yescharacteristic
604C2#1307962411yescharacteristic
605C2#1307981111yescharacteristic
606C2#1307982711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1854C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
cosocleC22×C4×C11C24
hypercenter#1854D11
hypocenterC11#21988
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
4. #13069378C2semidirect
5. #13069376C2semidirect
6. #13069373C2semidirect
7. #13069371C2semidirect
11. #13068783C2semidirect
12. #13068781C2semidirect
13. #13068748C2semidirect
14. #13068748C2semidirect
49. #10622332C4semidirect
504. C11#21988semidirect

Maximal subgroups

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

subgroupindex
C2×#106223322
#130710192
#130710182
#130693782
#130693762
#130693732
#130693712
#130688172
#130688152
#130688132
#130687832
#130687812
#130687482
C11×#18542
#2198811