Finite Group Databasebeta

← #14822327

Subgroups — #14822327

Order 2816.

804 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073165C211yesmaximal, characteristic, complemented
2#13071680C211yesmaximal, characteristic
3#13070031C211yesmaximal, characteristic, complemented
4#13069989C211yesmaximal, characteristic, complemented
5#13069851C211yesmaximal, characteristic
6#13069851C211yesmaximal, characteristic
7#13069299C211yesmaximal, characteristic, complemented
8#13069244C211yesmaximal, characteristic, complemented
9#13069209C211yesmaximal, characteristic, complemented
10#13069195C211yesmaximal, characteristic, complemented
11#13068866C211yesmaximal, characteristic, complemented
12#13068866C211yesmaximal, characteristic, complemented
13#13068627C211yesmaximal, characteristic, complemented
14C4×#66885C211yesmaximal, characteristic, complemented
15C11×#1916C211yesmaximal, characteristic, complemented
16C2×#66946—21no—
17C2×#66927C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C2×C11×C4⋊C8C2211yescharacteristic
21C2×C4×C8×C11C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33#10622601—21no—
34#10622595—21no—
35#10622585—21no—
36#10622552C2211yescharacteristic
37#10622552C2211yescharacteristic
38#10622549C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622278—21no—
46#10622278—21no—
47#10622271—21no—
48#10622265—21no—
49C11×#336C2211yescharacteristic
50C11×#336C2211yescharacteristic
51C11×#336C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C22×D44—21no—
60C22×D44—21no—
61C22×D44C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×(C2×D11)⋊C4—21no—
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92#66946—44no—
93#66927—22no—
94#66927—22no—
95C4×D44—22no—
96C4×D44—22no—
97C4×D44—41no—
98C4×D44—41no—
99C11×C4⋊C8—41no—
100C4×C8×C11—41no—
101C11×#95D411yescharacteristic
102C11×#95D411yescharacteristic
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111#66885—22no—
112#66885—22no—
113#66885—22no—
114#66885—22no—
115#66885—22no—
116#66885—22no—
117#66885—41no—
118#66885—41no—
119#66882—22no—
120#66881—22no—
121#26755—111nomaximal, Sylow
122C23×D11—21no—
123C23×D11—21no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C2×D44—24no—
138C2×D44—24no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44—21no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—21no—
149C2×D44—42no—
150C2×D44—42no—
151C2×D44—81no—
152C2×D44—81no—
153C2×D44#4112yes—
154C2×D44#4112yes—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11—42no—
158C2×C4×D11—42no—
159C2×C4×D11—81no—
160C2×C4×D11—81no—
161C2×C8×C11—21no—
162C2×C8×C11—21no—
163C2×C8×C11—21no—
164C2×C8×C11—21no—
165C2×C8×C11—21no—
166C2×C8×C11—21no—
167C2×C8×C11—21no—
168C2×C8×C11—21no—
169C2×C8×C11—21no—
170C2×C8×C11—21no—
171C2×C8×C11—21no—
172C2×C8×C11—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—42no—
183(C2×D11)⋊C4—42no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—81no—
186(C2×D11)⋊C4—81no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—21no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11#4112yes—
198C4⋊Dic11#4112yes—
199Dic11⋊C4—42no—
200Dic11⋊C4—42no—
201Dic11⋊C4—81no—
202Dic11⋊C4—81no—
203C4×Dic11—42no—
204C4×Dic11—81no—
205#2509—111no—
206#2366—111no—
207#2073—111no—
208#2065—111no—
209#2041—111no—
210#2041—111no—
211#1934—111no—
212#1926—111no—
213#1921—111no—
214#1919—111no—
215#1916D1111yescharacteristic, complemented
216#1862—111no—
217#1862—111no—
218#1804—111no—
219C4×#102—111no—
220C23×C11C22×D411yescharacteristic
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—41no—
224C22×D11—41no—
225C22×D11—41no—
226C22×D11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—41no—
231C22×D11—41no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11#13512yes—
252C2×C4×C11AGL(1,ℤ/8)12yes—
253C2×C4×C11C2×#4111yescharacteristic
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11H(5,𝔽2)11yescharacteristic
258C2×C4×C112−1+411yescharacteristic
259C2×Dic11—22no—
260C2×Dic11—22no—
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×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277D44—22no—
278D44—22no—
279D44—22no—
280D44—22no—
281D44—48no—
282D44—41no—
283D44—41no—
284D44—41no—
285D44—41no—
286D44—84no—
287C4×D11—84no—
288C4×D11—84no—
289C8×C11—41no—
290C8×C11—41no—
291C8×C11—41no—
292C8×C11—41no—
293C2×#127—111no—
294C2×C4×D4—111no—
295C2×C4×D4—111no—
296C2×C4×D4—221no—
297C2×#107—111no—
298C2×#106—111no—
299C2×C4⋊C8C2×D1111yescharacteristic
300C2×#102—111no—
301C2×#102—111no—
302C2×#102—111no—
303C2×#102—111no—
304C2×#102—111no—
305C2×#102—111no—
306C2×#102—111no—
307C2×#102—111no—
308C2×C4×C8C2×D1111yescharacteristic
309#400—221no—
310#400—221no—
311#390—111no—
312#390—111no—
313#390—221no—
314#389—111no—
315#389—111no—
316#389—111no—
317#389—111no—
318#389—221no—
319#387—221no—
320#386—221no—
321#386—221no—
322#382—111no—
323C4×C4⋊C4—111no—
324C4×C4⋊C4—111no—
325C4×C4⋊C4C2×D1111yescharacteristic
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#336C2×D1111yescharacteristic
333#336C2×D1111yescharacteristic
334#336C2×D1111yescharacteristic
335#336C2×D1111yescharacteristic
336C22×C11#52511yescharacteristic
337C22×C11#54611yescharacteristic
338C22×C11#54811yescharacteristic
339C22×C11C2×#13511yescharacteristic
340C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
341C22×C11#57611yescharacteristic
342C22×C11#57711yescharacteristic
343C2×D11—42no—
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—81no—
350C2×D11—81no—
351C2×D11—81no—
352C2×D11—81no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—41no—
360C4×C11—41no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11#52911yescharacteristic
364C4×C11#53911yescharacteristic
365C4×C11#55211yescharacteristic
366C4×C11#55311yescharacteristic
367Dic11—42no—
368Dic11—42no—
369Dic11—81no—
370Dic11—81no—
371Dic11—81no—
372Dic11—81no—
373C22×D4—111no—
374C22×D4—111no—
375C22×D4—221no—
376C22×D4—221no—
377C23×C4—221no—
378C23×C4—221no—
379C22×C8C22×D1111yescharacteristic
380C22×C8C22×D1111yescharacteristic
381C22×C8C22×D1111yescharacteristic
382C22×C8C22×D1111yescharacteristic
383#127—222no—
384#127—222no—
385C4×D4—222no—
386C4×D4—222no—
387C4×D4—441no—
388C4×D4—441no—
389C4×D4—444no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4D4411yescharacteristic
401C2×C4⋊C4D4411yescharacteristic
402C2×C22⋊C4—221no—
403C2×C22⋊C4—221no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C42—221no—
409C2×C42—221no—
410C2×C42C22×D1111yescharacteristic
411C2×C42C22×D1111yescharacteristic
412C2×C42C22×D1111yescharacteristic
413#107—222no—
414#106—222no—
415C4⋊C8—41no—
416#102—222no—
417#102—222no—
418#102—222no—
419#102—222no—
420#102—222no—
421#102—222no—
422#102—441no—
423#102—441no—
424C4×C8—41no—
425#95—221no—
426#95—221no—
427#95—221no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95D4411yescharacteristic
434#95D4411yescharacteristic
435C2×C11#246011yescharacteristic
436C2×C11#310511yescharacteristic
437C2×C11#311811yescharacteristic
438C2×C11#330411yescharacteristic
439C2×C11#331811yescharacteristic
440C2×C11#336111yescharacteristic
441C2×C11#336811yescharacteristic
442D11—82no—
443D11—82no—
444C24—221no—
445C24—221no—
446C2×D4—112no—
447C2×D4—112no—
448C2×D4—224no—
449C2×D4—224no—
450C2×D4—221no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4—221no—
455C2×D4—221no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—442no—
461C2×D4—442no—
462C2×D4—881no—
463C2×D4—881no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—442no—
471C22×C4—442no—
472C22×C4—442no—
473C22×C4—442no—
474C22×C4—881no—
475C22×C4—881no—
476C22×C4C2×D4411yescharacteristic
477C22×C4C2×D4411yescharacteristic
478C22×C4C2×D4411yescharacteristic
479C22×C4C2×D4411yescharacteristic
480C22×C4C2×D4411yescharacteristic
481C22×C4C2×D4411yescharacteristic
482C22×C4C23×D1111yescharacteristic
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—112no—
498C4⋊C4—112no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—442no—
510C4⋊C4—442no—
511C4⋊C4—881no—
512C4⋊C4—881no—
513C22⋊C4—442no—
514C22⋊C4—442no—
515C22⋊C4—442no—
516C22⋊C4—442no—
517C22⋊C4—881no—
518C22⋊C4—881no—
519C42—21no—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—21no—
525C42—442no—
526C42—881no—
527C11#2675511yescharacteristic, complemented, Sylow
528C23—222no—
529C23—222no—
530C23—441no—
531C23—441no—
532C23—441no—
533C23—441no—
534C23—441no—
535C23—441no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23—441no—
541C23—441no—
542C23C22×D4411yescharacteristic
543D4—222no—
544D4—222no—
545D4—222no—
546D4—222no—
547D4—448no—
548D4—441no—
549D4—441no—
550D4—441no—
551D4—441no—
552D4—884no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—222no—
570C2×C4—222no—
571C2×C4—441no—
572C2×C4—441no—
573C2×C4—441no—
574C2×C4—441no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—884no—
588C2×C4—884no—
589C2×C4#6695712yes—
590C2×C4#6696112yes—
591C2×C4#6703711yescharacteristic
592C2×C4#6704011yescharacteristic
593C2×C4#41×D1111yescharacteristic
594C2×C4#41×D1111yescharacteristic
595C2×C4#41×D1111yescharacteristic
596C2×C4#41×D1111yescharacteristic
597C8—41no—
598C8—41no—
599C8—41no—
600C8—41no—
601C22—442no—
602C22—442no—
603C22—442no—
604C22—442no—
605C22—442no—
606C22—442no—
607C22—881no—
608C22—881no—
609C22—881no—
610C22—881no—
611C22—881no—
612C22—881no—
613C22—881no—
614C22—881no—
615C22#1062305511yescharacteristic
616C22#1062308511yescharacteristic
617C22#1062310711yescharacteristic
618C22C2×#6695711yescharacteristic
619C22C2×#6696111yescharacteristic
620C22#1062328211yescharacteristic
621C22#1062328311yescharacteristic
622C4—22no—
623C4—22no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—442no—
629C4—442no—
630C4—881no—
631C4—881no—
632C4—881no—
633C4—881no—
634C4#1062316911yescharacteristic
635C4#1062319211yescharacteristic
636C4#1062322411yescharacteristic
637C4#1062323711yescharacteristic
638C2—882no—
639C2—882no—
640C2#1307256611yescharacteristic
641C2#1307866511yescharacteristic
642C2#1307880211yescharacteristic
643C2#1308055611yescharacteristic
644C2#1308075911yescharacteristic
645C2#1308127811yescharacteristic
646C2#1308134711yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1916C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#1916D11
hypocenterC11#26755
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
1. #13073165C2semidirect
3. #13070031C2semidirect
4. #13069989C2semidirect
7. #13069299C2semidirect
8. #13069244C2semidirect
9. #13069209C2semidirect
10. #13069195C2semidirect
11. #13068866C2semidirect
12. #13068866C2semidirect
13. #13068627C2semidirect
14. C4×#66885C2semidirect
15. C11×#1916C2semidirect
215. #1916D11semidirect
527. C11#26755semidirect

Maximal subgroups

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

subgroupindex
#130731652
#130716802
#130700312
#130699892
#130698512
#130692992
#130692442
#130692092
#130691952
#130688662
#130686272
C4×#668852
C11×#19162
#2675511