Finite Group Databasebeta

← #14853524

Subgroups — #14853524

Order 2816.

710 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076975C211yesmaximal, characteristic
2#13071185C211yesmaximal, characteristic
3#13070177C211yesmaximal, characteristic
4#13070176C211yesmaximal, characteristic
5#13069861C211yesmaximal, characteristic
6#13069860C211yesmaximal, characteristic
7#13069309C211yesmaximal, characteristic
8#13069306C211yesmaximal, characteristic
9#13069305C211yesmaximal, characteristic
10#13068620C211yesmaximal, characteristic
11#13068620C211yesmaximal, characteristic
12#13068619C211yesmaximal, characteristic
13#13068619C211yesmaximal, characteristic
14#13068470C211yesmaximal, characteristic
15C11×#1935C211yesmaximal, characteristic
16C2×Q8×Dic11C2211yescharacteristic
17C2×#66997C2211yescharacteristic
18C2×#66942—21no—
19C2×#66940C2211yescharacteristic
20C2×C11×#103C2211yescharacteristic
21C2×C11×#103C2211yescharacteristic
22C2×C11×#97C2211yescharacteristic
23C11×#391C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C2×#66899C2211yescharacteristic
26C2×#66899C2211yescharacteristic
27C2×#66880C2211yescharacteristic
28C2×#66880C2211yescharacteristic
29C2×Dic11⋊C8C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31#10622598C2211yescharacteristic
32#10622589C2211yescharacteristic
33#10622589C2211yescharacteristic
34#10622589C2211yescharacteristic
35#10622586C2211yescharacteristic
36#10622585—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C42×Dic11C2211yescharacteristic
40#10622542C2211yescharacteristic
41#10622541C2211yescharacteristic
42C2×#66867C2211yescharacteristic
43#10622263—21no—
44#10622262—21no—
45#10622262—21no—
46#10622260—21no—
47#10622260—21no—
48#10622260—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×Dic22C2311yescharacteristic
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C42×C11C2311yescharacteristic
68Q8×Dic11—22no—
69Q8×Dic11—22no—
70#66997—22no—
71#66997—22no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×Dic11⋊C4—21no—
78C2×Dic11⋊C4—21no—
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
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×C4×Dic11—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11D411yescharacteristic
91C2×C4×Dic11D411yescharacteristic
92C2×C4×Dic11D411yescharacteristic
93C2×C4×Dic11D411yescharacteristic
94C2×C4×Dic11C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98#66942—44no—
99#66940—22no—
100#66940—22no—
101C11×#103—22no—
102C11×#103—41no—
103C11×#97—41no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95—21no—
107#66899—22no—
108#66899—41no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114#66880—22no—
115#66880—41no—
116Dic11⋊C8—22no—
117Dic11⋊C8—22no—
118#66874—22no—
119#66874—41no—
120#66867—41no—
121#29132—111nomaximal, Sylow
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11#4112yes—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11C2×D411yescharacteristic
140C22×Dic11C2×D411yescharacteristic
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22—21no—
148C2×Dic22#4112yes—
149C2×C8×C11—21no—
150C2×C8×C11—21no—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—42no—
162C42×C11—21no—
163C42×C11—21no—
164C4⋊Dic11—21no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—21no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—42no—
171C4⋊Dic11—42no—
172Dic11⋊C4—24no—
173Dic11⋊C4—24no—
174Dic11⋊C4—42no—
175Dic11⋊C4—42no—
176Dic11⋊C4—42no—
177Dic11⋊C4—42no—
178Dic11⋊C4—42no—
179Dic11⋊C4—42no—
180Dic11⋊C4—42no—
181Dic11⋊C4—42no—
182Dic11⋊C4—42no—
183C4×Dic11—22no—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C4×Dic11—22no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—42no—
190C4×Dic11—42no—
191C4×Dic11#4112yes—
192C4×Dic11#4112yes—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199#2859—111no—
200C4×C4⋊Q8—111no—
201#2099—111no—
202#2099—111no—
203#2043—111no—
204#2043—111no—
205#1935—111no—
206#1935—111no—
207#1935—111no—
208#1935D1111yescharacteristic
209#1803—111no—
210#1803—111no—
211#1803—111no—
212#1803—111no—
213#1767—111no—
214C23×C11C22×D411yescharacteristic
215Q8×C11—22no—
216Q8×C11—22no—
217Q8×C11—41no—
218Q8×C11—41no—
219C2×C4×C11—22no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—41no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
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×C11C2×#4111yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11H(5,𝔽2)11yescharacteristic
242C2×C4×C112−1+411yescharacteristic
243C2×Dic11—21no—
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—22no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11#12412yes—
262C2×Dic11#12412yes—
263C2×Dic11AGL(1,ℤ/8)12yes—
264C2×Dic11#13712yes—
265C2×Dic11#13712yes—
266C2×Dic11#13712yes—
267Dic22—22no—
268Dic22—22no—
269Dic22—41no—
270Dic22—41no—
271C8×C11—41no—
272C8×C11—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C2×C4⋊Q8—111no—
276C2×#125—221no—
277C2×C4×Q8—111no—
278C2×C4×Q8—111no—
279C2×C4⋊C8—111no—
280C2×C4⋊C8—111no—
281C2×#103—111no—
282C2×#103—111no—
283C2×#103—111no—
284C2×#103—111no—
285C2×#103—111no—
286C2×#103—111no—
287C2×#103C2×D1111yescharacteristic
288C2×#103C2×D1111yescharacteristic
289C2×#97—111no—
290C2×#97C2×D1111yescharacteristic
291#391—111no—
292#391C2×D1111yescharacteristic
293#389—111no—
294#389—111no—
295#389—111no—
296#389—221no—
297#389—221no—
298#389—221no—
299#389—221no—
300#389C2×D1111yescharacteristic
301#384—111no—
302#384—111no—
303#384—111no—
304#382—221no—
305C4×C4⋊C4—221no—
306C4×C4⋊C4—221no—
307C43—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340C2×D1111yescharacteristic
315#340C2×D1111yescharacteristic
316#336—111no—
317#336—111no—
318C22×C11#52511yescharacteristic
319C22×C11C2×#12411yescharacteristic
320C22×C11#53711yescharacteristic
321C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
322C22×C11C2×#13711yescharacteristic
323C22×C11C2×#13711yescharacteristic
324C22×C11C2×#13711yescharacteristic
325C4×C11—42no—
326C4×C11—41no—
327C4×C11—41no—
328C4×C11—81no—
329C4×C11—81no—
330C4×C11—81no—
331C4×C11#55211yescharacteristic
332C4×C11#55211yescharacteristic
333C4×C11#55311yescharacteristic
334C4×C11#55311yescharacteristic
335Dic11—22no—
336Dic11—22no—
337Dic11—22no—
338Dic11—42no—
339Dic11—81no—
340Dic11—81no—
341Dic11—81no—
342Dic11#49114yes—
343C22×Q8—111no—
344C22×Q8C22×D1111yescharacteristic
345C22×C8—111no—
346C22×C8—111no—
347C22×C8C22×D1111yescharacteristic
348C22×C8C22×D1111yescharacteristic
349C4⋊Q8—222no—
350C4⋊Q8—222no—
351#125—444no—
352C4×Q8—222no—
353C4×Q8—222no—
354C4×Q8—222no—
355C4×Q8—222no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—111no—
358C2×C4⋊C4—111no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C42—111no—
377C2×C42—111no—
378C2×C42—111no—
379C2×C42—111no—
380C2×C42—111no—
381C2×C42—111no—
382C2×C42—221no—
383C2×C42—221no—
384C2×C42C22×D1111yescharacteristic
385C4⋊C8—222no—
386C4⋊C8—222no—
387#103—22no—
388#103—41no—
389#103—222no—
390#103—222no—
391#103—222no—
392#103—441no—
393#103—441no—
394#103—441no—
395#97—41no—
396#97—441no—
397#95—21no—
398#95—21no—
399#95—21no—
400#95—221no—
401#95—221no—
402#95—221no—
403#95—221no—
404#95—221no—
405C2×C11#256211yescharacteristic
406C2×C11#311211yescharacteristic
407C2×C11#311311yescharacteristic
408C2×C11C2×#49111yescharacteristic
409C2×C11#314111yescharacteristic
410C2×C11#325411yescharacteristic
411C2×C11#325511yescharacteristic
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—112no—
418C2×Q8—221no—
419C2×Q8—221no—
420C2×Q8—221no—
421C2×Q8—221no—
422C2×Q8—221no—
423C2×Q8#433912yes—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4D4×D1111yescharacteristic
437C22×C4D4×D1111yescharacteristic
438C22×C4C23×D1111yescharacteristic
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—221no—
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—42no—
458C4⋊C4—224no—
459C4⋊C4—224no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—442no—
467C4⋊C4—442no—
468C4⋊C4—442no—
469C4⋊C4—442no—
470C4⋊C4—442no—
471C4⋊C4—442no—
472C4⋊C4—442no—
473C4⋊C4—442no—
474C4⋊C4—442no—
475C4⋊C4—442no—
476C4⋊C4—442no—
477C42—21no—
478C42—21no—
479C42—112no—
480C42—112no—
481C42—222no—
482C42—222no—
483C42—222no—
484C42—222no—
485C42—221no—
486C42—221no—
487C42—442no—
488C42—442no—
489C11#2913211yescharacteristic, complemented, Sylow
490C23C2×D4×D1111yescharacteristic
491Q8—22no—
492Q8—22no—
493Q8—41no—
494Q8—41no—
495Q8—222no—
496Q8—222no—
497Q8—441no—
498Q8—441no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—112no—
518C2×C4—112no—
519C2×C4—112no—
520C2×C4—112no—
521C2×C4—112no—
522C2×C4—112no—
523C2×C4—221no—
524C2×C4—221no—
525C2×C4—221no—
526C2×C4—221no—
527C2×C4—221no—
528C2×C4—221no—
529C2×C4—222no—
530C2×C4—441no—
531C2×C4—441no—
532C2×C4—441no—
533C2×C4—441no—
534C2×C4—441no—
535C2×C4—441no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4C2×#433911yescharacteristic
542C2×C4#6703711yescharacteristic
543C2×C4#41×D1111yescharacteristic
544C2×C4#41×D1111yescharacteristic
545C2×C4#41×D1111yescharacteristic
546C2×C4#6704311yescharacteristic
547C8—41no—
548C8—41no—
549C8—441no—
550C8—441no—
551C22#1062307811yescharacteristic
552C22#1062312811yescharacteristic
553C22D11×#12411yescharacteristic
554C22D11×AGL(1,ℤ/8)11yescharacteristic
555C22D11×#13711yescharacteristic
556C22D11×#13711yescharacteristic
557C22D11×#13711yescharacteristic
558C4—42no—
559C4—41no—
560C4—41no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—114no—
565C4—222no—
566C4—222no—
567C4—222no—
568C4—442no—
569C4—881no—
570C4—881no—
571C4—881no—
572C4#1062306211yescharacteristic
573C4#1062307111yescharacteristic
574C4#1062319211yescharacteristic
575C4#1062323911yescharacteristic
576C2#1307378011yescharacteristic
577C2#1307873611yescharacteristic
578C2#1307874411yescharacteristic
579C2D11×#49111yescharacteristic
580C2#1307900811yescharacteristic
581C2#1307999811yescharacteristic
582C2#1308000611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1935C2
socle, prime radicalC23×C11C22×D4
hypercenter#1935D11
hypocenterC11#29132
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1935

Complements

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

NH ≅ G/Ntype
489. C11#29132semidirect

Maximal subgroups

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

subgroupindex
#130769752
#130711852
#130701772
#130701762
#130698612
#130698602
#130693092
#130693062
#130693052
#130686202
#130686192
#130684702
C11×#19352
#2913211