Finite Group Databasebeta

← #14811369

Subgroups — #14811369

Order 2816.

802 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072314C211yesmaximal, characteristic
2#13071484C211yesmaximal, characteristic
3#13070177C211yesmaximal, characteristic, complemented
4#13070107C211yesmaximal, characteristic, complemented
5#13070106C211yesmaximal, characteristic, complemented
6#13069569C211yesmaximal, characteristic, complemented
7#13069371C211yesmaximal, characteristic, complemented
8#13069189C211yesmaximal, characteristic, complemented
9#13069188C211yesmaximal, characteristic, complemented
10#13068802C211yesmaximal, characteristic
11#13068795C211yesmaximal, characteristic
12#13068701C211yesmaximal, characteristic
13#13068642C211yesmaximal, characteristic
14D11×#340C211yesmaximal, characteristic
15C11×#2057C211yesmaximal, characteristic, complemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×#66999—21no—
18C22×C8×D11C2211yescharacteristic
19C2×#66945—21no—
20C2×C4⋊C4×D11C2211yescharacteristic
21C2×C4⋊C4×D11C2211yescharacteristic
22C2×C11×#107C2211yescharacteristic
23C2×C11×#107C2211yescharacteristic
24C11×#389C2211yescharacteristic
25#10622842—21no—
26C2×(C2×D11)⋊C8C2211yescharacteristic
27C2×#66882C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29#10622602—21no—
30#10622600C2211yescharacteristic
31#10622600C2211yescharacteristic
32#10622598C2211yescharacteristic
33#10622598C2211yescharacteristic
34#10622597—21no—
35#10622591—21no—
36#10622589C2211yescharacteristic
37C4⋊C4×Dic11C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C4×(C2×D11)⋊C4C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622541C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43#10622277—21no—
44#10622268—21no—
45C11×#340C2211yescharacteristic
46C11×#340C2211yescharacteristic
47C11×#336C2211yescharacteristic
48#10622189C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622188C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×Q8×C11—21no—
60C22×C4×D11—21no—
61C22×C4×D11—21no—
62C22×C4×D11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8—41no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74#66999—44no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4D411yescharacteristic
78C2×(C2×D11)⋊C4D411yescharacteristic
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
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×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C2×C8×D11—22no—
96C2×C8×D11—22no—
97C2×C8×D11—41no—
98#66945—44no—
99C4⋊C4×D11—22no—
100C4⋊C4×D11—22no—
101C4⋊C4×D11—41no—
102C4⋊C4×D11Q814yescomplemented
103C11×#107—22no—
104C11×#107—41no—
105C11×#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95D411yescharacteristic
114C11⋊#95D411yescharacteristic
115(C2×D11)⋊C8—22no—
116#66882—22no—
117Dic11⋊C8—22no—
118#66871—41no—
119C4⋊(C11⋊C8)—41no—
120#25988—111nomaximal, Sylow
121C23×D11C2×D411yescharacteristic
122C2×Q8×C11—42no—
123C2×Q8×C11—42no—
124C2×Q8×C11—81no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11C2×D411yescharacteristic
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C2×C4×D11—24no—
140C2×C4×D11—21no—
141C2×C4×D11—21no—
142C2×C4×D11—21no—
143C2×C4×D11—21no—
144C2×C4×D11—42no—
145C2×C4×D11—42no—
146C2×C4×D11—42no—
147C2×C4×D11—42no—
148C2×C4×D11—81no—
149C2×C4×D11C2×Q812yes—
150C2×C4×D11#4112yes—
151C2×C8×C11—21no—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11#4112yes—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4C2×Q812yes—
166C11×C4⋊C4#4112yes—
167C42×C11—21no—
168C42×C11—21no—
169(C2×D11)⋊C4—22no—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4—42no—
172(C2×D11)⋊C4D814yes—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—42no—
181C4⋊Dic11—42no—
182C4⋊Dic11C2×Q812yes—
183Dic11⋊C4—24no—
184Dic11⋊C4—42no—
185Dic11⋊C4—42no—
186Dic11⋊C4—42no—
187Dic11⋊C4—81no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—42no—
191C4×Dic11—42no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C8×D11—44no—
199#2440—111no—
200#2344—111no—
201#2099—111no—
202#2086—111no—
203#2086—111no—
204#2057D1111yescharacteristic, complemented
205#1988—111no—
206#1947—111no—
207#1918—111no—
208#1918—111no—
209#1852—111no—
210#1850—111no—
211#1823—111no—
212#1808—111no—
213C2×#340—111no—
214C23×C11C22×D411yescharacteristic
215C22×D11—21no—
216C22×D11—21no—
217C22×D11—21no—
218C22×D11—21no—
219C22×D11C22⋊Q812yes—
220C22×D11C2×D812yes—
221C22×D11#13712yes—
222Q8×C11—84no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
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×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11C2×D812yes—
241C2×C4×C11C22×Q811yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11H(5,𝔽2)11yescharacteristic
246C2×C4×C112−1+411yescharacteristic
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—22no—
252C2×Dic11—21no—
253C2×Dic11—21no—
254C2×Dic11—21no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
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×Dic11C22⋊Q812yes—
267C2×Dic11C2×D812yes—
268C4×D11—22no—
269C4×D11—22no—
270C4×D11—22no—
271C4×D11—22no—
272C4×D11—48no—
273C4×D11—84no—
274C8×C11—22no—
275C8×C11—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C23×C8—111no—
279C2×C4⋊Q8C2×D1111yescharacteristic
280C2×C22⋊Q8—221no—
281C2×#117—221no—
282C22×C4⋊C4—111no—
283C22×C4⋊C4—111no—
284C2×#107—111no—
285C2×#107—111no—
286C2×#107C2×D1111yescharacteristic
287C2×#107C2×D1111yescharacteristic
288C2×C4⋊C8—111no—
289C2×C4⋊C8—111no—
290C2×C22⋊C8—111no—
291#398—221no—
292#395—221no—
293#389—111no—
294#389—111no—
295#389—111no—
296#389C2×D1111yescharacteristic
297#387—221no—
298#387—221no—
299#385—221no—
300#384—111no—
301#381—221no—
302#380—111no—
303#380—111no—
304C4×C4⋊C4—111no—
305C4×C4⋊C4—111no—
306C4×C22⋊C4—111no—
307#340—111no—
308#340—111no—
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340C2×D1111yescharacteristic
318#340C2×D1111yescharacteristic
319#336—111no—
320#336C2×D1111yescharacteristic
321C22×C11C2×C22⋊Q811yescharacteristic
322C22×C11#54611yescharacteristic
323C22×C11#54711yescharacteristic
324C22×C11C22×D811yescharacteristic
325C22×C11C2×#13711yescharacteristic
326C22×C11#57711yescharacteristic
327C22×C11#57811yescharacteristic
328C2×D11—22no—
329C2×D11—22no—
330C2×D11—22no—
331C2×D11—22no—
332C2×D11—22no—
333C2×D11—22no—
334C2×D11#47414yes—
335C4×C11—22no—
336C4×C11—42no—
337C4×C11—41no—
338C4×C11—42no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11#53311yescharacteristic
342C4×C11#54411yescharacteristic
343C4×C11#55111yescharacteristic
344C4×C11#55211yescharacteristic
345Dic11—22no—
346Dic11—22no—
347Dic11—41no—
348Dic11—42no—
349Dic11—81no—
350Dic11—81no—
351Dic11—81no—
352C22×Q8—21no—
353C23×C4—111no—
354C23×C4—221no—
355C23×C4—221no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—222no—
359C22×C8—222no—
360C22×C8—441no—
361C22×C8C22×D1111yescharacteristic
362C22×C8C22×D1111yescharacteristic
363C4⋊Q8—22no—
364C4⋊Q8—41no—
365C22⋊Q8—444no—
366#117—444no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—114no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—441no—
384C2×C4⋊C4C22×D1111yescharacteristic
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C22⋊C4—111no—
389C2×C22⋊C4—111no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C42—111no—
393C2×C42—221no—
394C2×C42—221no—
395C2×C42C22×D1111yescharacteristic
396#107—22no—
397#107—41no—
398#107—222no—
399#107—441no—
400C4⋊C8—222no—
401C4⋊C8—441no—
402C22⋊C8—222no—
403#95—21no—
404#95—111no—
405#95—111no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413C2×C11#243811yescharacteristic
414C2×C11C2×#47411yescharacteristic
415C2×C11#308211yescharacteristic
416C2×C11#329411yescharacteristic
417C2×C11#331211yescharacteristic
418C2×C11#333411yescharacteristic
419C2×C11#334411yescharacteristic
420D11—24no—
421C24—111no—
422C2×Q8—42no—
423C2×Q8—42no—
424C2×Q8—81no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—112no—
432C22×C4—112no—
433C22×C4—111no—
434C22×C4—224no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—442no—
444C22×C4—442no—
445C22×C4—442no—
446C22×C4—442no—
447C22×C4—881no—
448C22×C4D4×D1111yescharacteristic
449C22×C4D4×D1111yescharacteristic
450C22×C4C23×D1111yescharacteristic
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—444no—
463C2×C8#434312yes—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—42no—
471C4⋊C4—42no—
472C4⋊C4—112no—
473C4⋊C4—224no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—442no—
482C4⋊C4—442no—
483C4⋊C4—442no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C4⋊C4—881no—
487C4⋊C4#434112yes—
488C4⋊C4Q8×D1112yes—
489C22⋊C4—114no—
490C22⋊C4—222no—
491C22⋊C4—442no—
492C22⋊C4—442no—
493C42—21no—
494C42—21no—
495C42—221no—
496C42—221no—
497C42—442no—
498C42—442no—
499C11#2598811yescharacteristic, complemented, Sylow
500C23—112no—
501C23—112no—
502C23—112no—
503C23—221no—
504C23—221no—
505C23—221no—
506C23—221no—
507C23C2×D4×D1111yescharacteristic
508Q8—84no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—112no—
527C2×C4—112no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—222no—
533C2×C4—222no—
534C2×C4—222no—
535C2×C4—222no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—221no—
539C2×C4—222no—
540C2×C4—448no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—884no—
553C2×C4D8×D1112yes—
554C2×C4C2×#434111yescharacteristic
555C2×C4#6703711yescharacteristic
556C2×C4C2×Q8×D1111yescharacteristic
557C2×C4C2×#434311yescharacteristic
558C2×C4#6704011yescharacteristic
559C2×C4#41×D1111yescharacteristic
560C8—22no—
561C8—41no—
562C8—441no—
563C8—441no—
564C22—114no—
565C22—222no—
566C22—222no—
567C22—222no—
568C22—222no—
569C22—222no—
570C22—222no—
571C22#1062312211yescharacteristic
572C22D11×C22⋊Q811yescharacteristic
573C22#1062325711yescharacteristic
574C22C2×D8×D1111yescharacteristic
575C22#1062329711yescharacteristic
576C22#1062330611yescharacteristic
577C22D11×#13711yescharacteristic
578C4—22no—
579C4—41no—
580C4—42no—
581C4—42no—
582C4—81no—
583C4—81no—
584C4—222no—
585C4—222no—
586C4—442no—
587C4—441no—
588C4—881no—
589C4—881no—
590C4—881no—
591C4#1062316811yescharacteristic
592C4#1062317011yescharacteristic
593C4#1062325911yescharacteristic
594C4#1062326011yescharacteristic
595C2—224no—
596C2#1307228511yescharacteristic
597C2D11×#47411yescharacteristic
598C2#1307845311yescharacteristic
599C2#1308042211yescharacteristic
600C2#1308066011yescharacteristic
601C2#1308096311yescharacteristic
602C2#1308107011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2057C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenter#2057D11
hypocenterC11#25988
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2057

Complements

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

NH ≅ G/Ntype
3. #13070177C2semidirect
4. #13070107C2semidirect
5. #13070106C2semidirect
6. #13069569C2semidirect
7. #13069371C2semidirect
8. #13069189C2semidirect
9. #13069188C2semidirect
15. C11×#2057C2semidirect
102. C4⋊C4×D11Q8semidirect
204. #2057D11semidirect
499. C11#25988semidirect

Maximal subgroups

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

subgroupindex
#130723142
#130714842
#130701772
#130701072
#130701062
#130695692
#130693712
#130691892
#130691882
#130688022
#130687952
#130687012
#130686422
D11×#3402
C11×#20572
#2598811