Finite Group Databasebeta

← #14826549

Subgroups — #14826549

Order 2816.

734 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073023C211yesmaximal, characteristic, complemented
2#13071654C211yesmaximal, characteristic
3#13070033C211yesmaximal, characteristic, complemented
4#13070005C211yesmaximal, characteristic, complemented
5#13069806C211yesmaximal, characteristic
6#13069798C211yesmaximal, characteristic
7#13069383C211yesmaximal, characteristic, complemented
8#13069348C211yesmaximal, characteristic, complemented
9#13069219C211yesmaximal, characteristic, complemented
10#13069200C211yesmaximal, characteristic, complemented
11#13069199C211yesmaximal, characteristic, complemented
12#13068878C211yesmaximal, characteristic, complemented
13#13068815C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1825C211yesmaximal, characteristic, complemented
16C2×C11×#117C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×#66946C2211yescharacteristic
19C2×C11×C22⋊C8C2211yescharacteristic
20C11×#380C2211yescharacteristic
21#10622825C2211yescharacteristic
22C4×C22⋊Dic11C2211yescharacteristic
23C2×C22⋊(C11⋊C8)C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66881C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29#10622601C2211yescharacteristic
30#10622598C2211yescharacteristic
31#10622590C2211yescharacteristic
32C4⋊C4×Dic11C2211yescharacteristic
33C4⋊C4×Dic11C2211yescharacteristic
34#10622586C2211yescharacteristic
35#10622586C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622570—21no—
42#10622569—21no—
43#10622566—21no—
44#10622558—21no—
45#10622553—21no—
46C4×(C2×D11)⋊C4—21no—
47#10622273—21no—
48#10622264—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C11×#117—22no—
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⋊Dic11D411yescharacteristic
76C2×C22⋊Dic11D411yescharacteristic
77#66983—22no—
78#66983—22no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95#66946—22no—
96#66946—41no—
97C11×C22⋊C8—41no—
98C11×#95—21no—
99C11⋊#95—21no—
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95D411yescharacteristic
108C11⋊#95D411yescharacteristic
109C22⋊(C11⋊C8)—22no—
110#66885—22no—
111#66885—41no—
112#66881—22no—
113Dic11⋊C8—22no—
114C8×Dic11—41no—
115#66873—22no—
116#66873—22no—
117#66872—22no—
118#66871—22no—
119#66871—41no—
120#27038—111nomaximal, Sylow
121C24×C11C2×D411yescharacteristic
122C23×D11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
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×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
135C2×C22⋊D11—24no—
136C2×C22⋊D11—81no—
137C2×C22⋊D11—81no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11C2×D411yescharacteristic
142C22×Dic11C2×D411yescharacteristic
143C22×Dic11C2×D411yescharacteristic
144C22×Dic11C2×D411yescharacteristic
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—21no—
150C2×D44#4112yes—
151C2×C4×D11—42no—
152C2×C4×D11—42no—
153C2×C4×D11—81no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11—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×C4⋊C4—21no—
167C11×C4⋊C4#4112yes—
168C11×C22⋊C4—42no—
169C11×C22⋊C4—81no—
170C42×C11—42no—
171C22⋊Dic11—22no—
172C22⋊Dic11—41no—
173C22⋊Dic11—42no—
174(C2×D11)⋊C4—24no—
175(C2×D11)⋊C4—42no—
176(C2×D11)⋊C4—42no—
177(C2×D11)⋊C4—81no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—81no—
184C4⋊Dic11#4112yes—
185Dic11⋊C4—81no—
186Dic11⋊C4—81no—
187C4×Dic11—21no—
188C4×Dic11—21no—
189C4×Dic11—21no—
190C4×Dic11—21no—
191C4×Dic11—42no—
192C4×Dic11—81no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8#4112yes—
199#2495—111no—
200#2363—111no—
201#2073—111no—
202#2067—111no—
203#2034—111no—
204#2033—111no—
205#1949—111no—
206#1942—111no—
207#1923—111no—
208#1920—111no—
209#1920—111no—
210#1864—111no—
211#1854—111no—
212#1825D1111yescharacteristic, complemented
213C4×#102—111no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11—21no—
219C23×C11—21no—
220C23×C11—21no—
221C23×C11C22×D411yescharacteristic
222C22×D11—22no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C2×C4×C11—21no—
230C2×C4×C11—22no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
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×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11C2×#4111yescharacteristic
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11H(5,𝔽2)11yescharacteristic
253C2×C4×C112−1+411yescharacteristic
254C22⋊D11—84no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—22no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11#13512yes—
276D44—22no—
277D44—22no—
278D44—41no—
279D44—41no—
280C4×D11—84no—
281C8×C11—41no—
282C8×C11—41no—
283C11⋊C8—22no—
284C11⋊C8—41no—
285C2×#121—111no—
286C2×C4×D4—111no—
287C2×#117C2×D1111yescharacteristic
288C2×#107—111no—
289C2×#107—111no—
290C2×#106—111no—
291C2×#106—111no—
292C2×C4⋊C8—111no—
293C2×#102—111no—
294C2×#102—111no—
295C2×#102—111no—
296C2×#102—111no—
297C2×C22⋊C8—111no—
298C2×C22⋊C8C2×D1111yescharacteristic
299C2×C4×C8—111no—
300#400—221no—
301#397—221no—
302#390—111no—
303#390—221no—
304#389—111no—
305#389—111no—
306#389—111no—
307#388—221no—
308#388—221no—
309#386—221no—
310#383—221no—
311#382—111no—
312#380—111no—
313#380C2×D1111yescharacteristic
314C4×C4⋊C4—111no—
315C4×C4⋊C4—111no—
316C4×C22⋊C4—111no—
317C4×C22⋊C4—221no—
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#340C2×D1111yescharacteristic
323#340C2×D1111yescharacteristic
324#340C2×D1111yescharacteristic
325#340C2×D1111yescharacteristic
326#336—111no—
327#336—111no—
328C22×C11—41no—
329C22×C11—41no—
330C22×C11—41no—
331C22×C11—41no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11#52511yescharacteristic
336C22×C11#54611yescharacteristic
337C22×C11#54711yescharacteristic
338C22×C11C2×#13511yescharacteristic
339C22×C11#57511yescharacteristic
340C22×C11#57611yescharacteristic
341C22×C11#57711yescharacteristic
342C2×D11—42no—
343C2×D11—42no—
344C2×D11—42no—
345C2×D11—81no—
346C2×D11—81no—
347C2×D11—81no—
348C2×D11—81no—
349C4×C11—41no—
350C4×C11—42no—
351C4×C11—81no—
352C4×C11—81no—
353C4×C11—81no—
354C4×C11#52911yescharacteristic
355C4×C11#53911yescharacteristic
356C4×C11#55311yescharacteristic
357C4×C11#55611yescharacteristic
358Dic11—22no—
359Dic11—41no—
360Dic11—41no—
361Dic11—42no—
362Dic11—41no—
363Dic11—81no—
364Dic11—81no—
365C22×D4—111no—
366C22×D4—221no—
367C23×C4—221no—
368C23×C4C22×D1111yescharacteristic
369C22×C8—111no—
370C22×C8—111no—
371C22×C8C22×D1111yescharacteristic
372C22×C8C22×D1111yescharacteristic
373#121—222no—
374#121—222no—
375C4×D4—222no—
376C4×D4—441no—
377#117—22no—
378#117—41no—
379C2×C4⋊C4—111no—
380C2×C4⋊C4—111no—
381C2×C4⋊C4—111no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4C22×D1111yescharacteristic
386C2×C4⋊C4C22×D1111yescharacteristic
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—111no—
392C2×C22⋊C4—111no—
393C2×C22⋊C4—221no—
394C2×C22⋊C4—221no—
395C2×C22⋊C4—221no—
396C2×C22⋊C4—221no—
397C2×C22⋊C4—221no—
398C2×C42—21no—
399C2×C42—111no—
400C2×C42—111no—
401C2×C42—221no—
402C2×C42—221no—
403#107—222no—
404#107—441no—
405#106—222no—
406#106—222no—
407C4⋊C8—222no—
408#102—222no—
409#102—222no—
410#102—222no—
411#102—441no—
412C22⋊C8—41no—
413C22⋊C8—222no—
414C4×C8—441no—
415#95—21no—
416#95—111no—
417#95—111no—
418#95—221no—
419#95—221no—
420#95—221no—
421#95—221no—
422#95—221no—
423#95—221no—
424#95—221no—
425#95—221no—
426C2×C11—81no—
427C2×C11#246611yescharacteristic
428C2×C11#310211yescharacteristic
429C2×C11#311811yescharacteristic
430C2×C11#329611yescharacteristic
431C2×C11#330911yescharacteristic
432C2×C11#334111yescharacteristic
433C2×C11#335111yescharacteristic
434D11—82no—
435C24—221no—
436C24D4×D1111yescharacteristic
437C2×D4—112no—
438C2×D4—224no—
439C2×D4—221no—
440C2×D4—221no—
441C2×D4—221no—
442C2×D4—221no—
443C2×D4—221no—
444C2×D4—881no—
445C2×D4—881no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—111no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—221no—
461C22×C4—221no—
462C22×C4—221no—
463C22×C4—442no—
464C22×C4—442no—
465C22×C4—881no—
466C22×C4D4×D1111yescharacteristic
467C22×C4C23×D1111yescharacteristic
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—112no—
475C2×C8—221no—
476C2×C8—221no—
477C2×C8—221no—
478C2×C8—221no—
479C2×C8—221no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—112no—
488C4⋊C4—221no—
489C4⋊C4—221no—
490C4⋊C4—221no—
491C4⋊C4—221no—
492C4⋊C4—221no—
493C4⋊C4—881no—
494C4⋊C4—881no—
495C4⋊C4—881no—
496C4⋊C4#433912yes—
497C22⋊C4—42no—
498C22⋊C4—81no—
499C22⋊C4—224no—
500C22⋊C4—222no—
501C22⋊C4—442no—
502C22⋊C4—442no—
503C22⋊C4—441no—
504C22⋊C4—442no—
505C22⋊C4—881no—
506C42—42no—
507C42—221no—
508C42—221no—
509C42—221no—
510C42—221no—
511C42—442no—
512C42—881no—
513C11#2703811yescharacteristic, complemented, Sylow
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—222no—
522C23—441no—
523C23—441no—
524C23—441no—
525C23—441no—
526C23—441no—
527C23—441no—
528C23C2×D4×D1111yescharacteristic
529D4—222no—
530D4—222no—
531D4—441no—
532D4—441no—
533D4—884no—
534C2×C4—21no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—112no—
554C2×C4—221no—
555C2×C4—221no—
556C2×C4—221no—
557C2×C4—221no—
558C2×C4—221no—
559C2×C4—221no—
560C2×C4—221no—
561C2×C4—221no—
562C2×C4—221no—
563C2×C4—221no—
564C2×C4—221no—
565C2×C4—222no—
566C2×C4—441no—
567C2×C4—441no—
568C2×C4—441no—
569C2×C4—441no—
570C2×C4—441no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—884no—
575C2×C4C2×#433911yescharacteristic
576C2×C4#6703711yescharacteristic
577C2×C4#41×D1111yescharacteristic
578C2×C4#41×D1111yescharacteristic
579C2×C4#41×D1111yescharacteristic
580C2×C4#6704311yescharacteristic
581C8—41no—
582C8—41no—
583C8—222no—
584C8—441no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—442no—
593C22—442no—
594C22—442no—
595C22—881no—
596C22—881no—
597C22—881no—
598C22—881no—
599C22#1062302111yescharacteristic
600C22#1062318611yescharacteristic
601C22#1062318711yescharacteristic
602C22D11×#13511yescharacteristic
603C22#1062330111yescharacteristic
604C22#1062330511yescharacteristic
605C22#1062330811yescharacteristic
606C4—41no—
607C4—42no—
608C4—81no—
609C4—81no—
610C4—81no—
611C4—222no—
612C4—442no—
613C4—441no—
614C4—441no—
615C4—441no—
616C4—881no—
617C4—881no—
618C4#1062305911yescharacteristic
619C4#1062306411yescharacteristic
620C4#1062319111yescharacteristic
621C4#1062319211yescharacteristic
622C2—81no—
623C2—882no—
624C2#1307265111yescharacteristic
625C2#1307863711yescharacteristic
626C2#1307879511yescharacteristic
627C2#1308045211yescharacteristic
628C2#1308062311yescharacteristic
629C2#1308103311yescharacteristic
630C2#1308117411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1825C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1825D11
hypocenterC11#27038
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1825

Complements

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

NH ≅ G/Ntype
1. #13073023C2semidirect
3. #13070033C2semidirect
4. #13070005C2semidirect
7. #13069383C2semidirect
8. #13069348C2semidirect
9. #13069219C2semidirect
10. #13069200C2semidirect
11. #13069199C2semidirect
12. #13068878C2semidirect
13. #13068815C2semidirect
14. #13068430C2semidirect
15. C11×#1825C2semidirect
212. #1825D11semidirect
513. C11#27038semidirect

Maximal subgroups

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

subgroupindex
#130730232
#130716542
#130700332
#130700052
#130698062
#130697982
#130693832
#130693482
#130692192
#130692002
#130691992
#130688782
#130688152
#130684302
C11×#18252
#2703811