Finite Group Databasebeta

← #14822313

Subgroups — #14822313

Order 2816.

812 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073146C211yesmaximal, characteristic, complemented
2#13071680C211yesmaximal, characteristic
3#13070023C211yesmaximal, characteristic, complemented
4#13069985C211yesmaximal, characteristic, complemented
5#13069851C211yesmaximal, characteristic
6#13069850C211yesmaximal, characteristic
7#13069300C211yesmaximal, characteristic, complemented
8#13069242C211yesmaximal, characteristic, complemented
9#13069201C211yesmaximal, characteristic, complemented
10#13069172C211yesmaximal, characteristic, complemented
11#13068878C211yesmaximal, characteristic, complemented
12#13068878C211yesmaximal, characteristic, complemented
13#13068615C211yesmaximal, characteristic, complemented
14#13068430C211yesmaximal, characteristic, complemented
15C11×#1920C211yesmaximal, characteristic, complemented
16C2×#66946C2211yescharacteristic
17C2×#66946C2211yescharacteristic
18C2×#66927C2211yescharacteristic
19C2×C4×D44—21no—
20C2×C11×#106C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66885C2211yescharacteristic
25C2×#66885C2211yescharacteristic
26C2×#66885C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29#10622601C2211yescharacteristic
30#10622601C2211yescharacteristic
31#10622598C2211yescharacteristic
32#10622598C2211yescharacteristic
33#10622597—21no—
34#10622589C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622586—21no—
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42#10622552—21no—
43C4×C4⋊Dic11C2211yescharacteristic
44#10622541C2211yescharacteristic
45#10622278—21no—
46#10622278—21no—
47#10622274—21no—
48#10622267—21no—
49C11×#340C2211yescharacteristic
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52C11×#336C2211yescharacteristic
53#10622188C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44—21no—
60C22×D44—21no—
61C22×D44C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C42×C11—21no—
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⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11D411yescharacteristic
83C2×C4⋊Dic11D411yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11C2311yescharacteristic
91C2×C4×Dic11C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94#66946—22no—
95#66946—22no—
96#66946—41no—
97#66946—41no—
98#66927—22no—
99#66927—22no—
100C4×D44—44no—
101C11×#106—22no—
102C11×#95—21no—
103C11×#95—21no—
104C11⋊#95—21no—
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95D411yescharacteristic
109C11⋊#95D411yescharacteristic
110#66885—22no—
111#66885—22no—
112#66885—41no—
113#66885—41no—
114Dic11⋊C8—41no—
115C8×Dic11—41no—
116#66873—22no—
117#66873—22no—
118#66873—22no—
119#66873—22no—
120#66872—22no—
121#26754—111nomaximal, Sylow
122C23×D11—21no—
123C23×D11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C22×Dic11C2×D411yescharacteristic
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—
167C11×C4⋊C4—21no—
168C11×C4⋊C4—21no—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—21no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—81no—
174C11×C4⋊C4#4112yes—
175C11×C4⋊C4#4112yes—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—42no—
179(C2×D11)⋊C4—42no—
180(C2×D11)⋊C4—42no—
181(C2×D11)⋊C4—42no—
182(C2×D11)⋊C4—42no—
183(C2×D11)⋊C4—81no—
184(C2×D11)⋊C4—81no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—21no—
189C4⋊Dic11—41no—
190C4⋊Dic11—42no—
191C4⋊Dic11—81no—
192C4⋊Dic11SD1614yes—
193Dic11⋊C4—81no—
194Dic11⋊C4—81no—
195Dic11⋊C4—81no—
196C4×Dic11—21no—
197C4×Dic11—21no—
198C4×Dic11—21no—
199C4×Dic11—21no—
200C4×Dic11—81no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8—21no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207#2507—111no—
208#2366—111no—
209#2071—111no—
210#2065—111no—
211#2041—111no—
212#2041—111no—
213#1934—111no—
214#1926—111no—
215#1920—111no—
216#1920D1111yescharacteristic, complemented
217#1916—111no—
218#1864—111no—
219#1864—111no—
220#1802—111no—
221C4×#102—111no—
222C23×C11C22×D411yescharacteristic
223C22×D11—22no—
224C22×D11—22no—
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—
235C22×D11—41no—
236C22×D11—41no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11C2×SD1612yes—
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C112−1+411yescharacteristic
261C2×Dic11—21no—
262C2×Dic11—21no—
263C2×Dic11—21no—
264C2×Dic11—21no—
265C2×Dic11—21no—
266C2×Dic11—21no—
267C2×Dic11—21no—
268C2×Dic11—21no—
269C2×Dic11—21no—
270C2×Dic11—21no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11C2×SD1612yes—
278C2×Dic11C2×SD1612yes—
279D44—22no—
280D44—22no—
281D44—22no—
282D44—22no—
283D44—48no—
284D44—41no—
285D44—41no—
286D44—41no—
287D44—41no—
288D44—84no—
289C4×D11—84no—
290C4×D11—84no—
291C8×C11—41no—
292C8×C11—41no—
293C11⋊C8—41no—
294C11⋊C8—41no—
295C2×#127—111no—
296C2×C4×D4—111no—
297C2×C4×D4—111no—
298C2×C4×D4—221no—
299C2×#106—111no—
300C2×#106C2×D1111yescharacteristic
301C2×C4⋊C8—111no—
302C2×#102—111no—
303C2×#102—111no—
304C2×#102—111no—
305C2×#102—111no—
306C2×#102—111no—
307C2×#102—111no—
308C2×#102—111no—
309C2×#102—111no—
310C2×C4×C8—111no—
311#398—221no—
312#398—221no—
313#390—111no—
314#390—111no—
315#390—221no—
316#389—111no—
317#389—111no—
318#389—111no—
319#389—221no—
320#389C2×D1111yescharacteristic
321#387—221no—
322#386—221no—
323#386—221no—
324#384—111no—
325C4×C4⋊C4—111no—
326C4×C4⋊C4—111no—
327C4×C4⋊C4C2×D1111yescharacteristic
328#340—111no—
329#340—111no—
330#340—111no—
331#340C2×D1111yescharacteristic
332#340C2×D1111yescharacteristic
333#340C2×D1111yescharacteristic
334#336—111no—
335#336—111no—
336#336—111no—
337#336C2×D1111yescharacteristic
338C22×C11#52511yescharacteristic
339C22×C11#54611yescharacteristic
340C22×C11#54811yescharacteristic
341C22×C11C22×SD1611yescharacteristic
342C22×C11#57511yescharacteristic
343C22×C11#57611yescharacteristic
344C22×C11#57611yescharacteristic
345C2×D11—42no—
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—81no—
352C2×D11—81no—
353C2×D11—81no—
354C2×D11—81no—
355C2×D11—81no—
356C2×D11—81no—
357C2×D11—81no—
358C2×D11—81no—
359C4×C11—22no—
360C4×C11—42no—
361C4×C11—41no—
362C4×C11—42no—
363C4×C11—81no—
364C4×C11—81no—
365C4×C11#52911yescharacteristic
366C4×C11#53911yescharacteristic
367C4×C11#55211yescharacteristic
368C4×C11#55311yescharacteristic
369Dic11—22no—
370Dic11—22no—
371Dic11—41no—
372Dic11—41no—
373Dic11—81no—
374Dic11—81no—
375C22×D4—111no—
376C22×D4—111no—
377C22×D4—221no—
378C22×D4—221no—
379C23×C4—221no—
380C23×C4—221no—
381C22×C8—111no—
382C22×C8—111no—
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385#127—222no—
386#127—222no—
387C4×D4—222no—
388C4×D4—222no—
389C4×D4—444no—
390C4×D4—441no—
391C4×D4—441no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—111no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C4⋊C4C22×D1111yescharacteristic
404C2×C4⋊C4C22×D1111yescharacteristic
405C2×C4⋊C4C22×D1111yescharacteristic
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C42—21no—
413C2×C42—111no—
414C2×C42—111no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417#106—22no—
418#106—222no—
419C4⋊C8—441no—
420#102—222no—
421#102—222no—
422#102—222no—
423#102—222no—
424#102—222no—
425#102—222no—
426#102—441no—
427#102—441no—
428C4×C8—441no—
429#95—21no—
430#95—21no—
431#95—111no—
432#95—111no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437C2×C11#246011yescharacteristic
438C2×C11#310111yescharacteristic
439C2×C11#312211yescharacteristic
440C2×C11#329511yescharacteristic
441C2×C11#330911yescharacteristic
442C2×C11#336211yescharacteristic
443C2×C11#337011yescharacteristic
444D11—82no—
445D11—82no—
446C24—221no—
447C24—221no—
448C2×D4—112no—
449C2×D4—112no—
450C2×D4—224no—
451C2×D4—224no—
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—221no—
461C2×D4—221no—
462C2×D4—442no—
463C2×D4—442no—
464C2×D4—881no—
465C2×D4—881no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—111no—
471C22×C4—111no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—442no—
477C22×C4—442no—
478C22×C4—442no—
479C22×C4—442no—
480C22×C4—881no—
481C22×C4—881no—
482C22×C4D4×D1111yescharacteristic
483C22×C4D4×D1111yescharacteristic
484C22×C4C23×D1111yescharacteristic
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—221no—
492C2×C8—221no—
493C2×C8—221no—
494C2×C8—221no—
495C2×C8—221no—
496C2×C8—221no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—81no—
504C4⋊C4—114no—
505C4⋊C4—221no—
506C4⋊C4—221no—
507C4⋊C4—221no—
508C4⋊C4—221no—
509C4⋊C4—441no—
510C4⋊C4—442no—
511C4⋊C4—881no—
512C4⋊C4—881no—
513C4⋊C4—881no—
514C4⋊C4—881no—
515C4⋊C4#433912yes—
516C4⋊C4#434312yes—
517C22⋊C4—442no—
518C22⋊C4—442no—
519C22⋊C4—442no—
520C22⋊C4—442no—
521C22⋊C4—881no—
522C22⋊C4—881no—
523C42—21no—
524C42—21no—
525C42—42no—
526C42—221no—
527C42—221no—
528C42—221no—
529C42—221no—
530C42—881no—
531C11#2675411yescharacteristic, complemented, Sylow
532C23—222no—
533C23—222no—
534C23—441no—
535C23—441no—
536C23—441no—
537C23—441no—
538C23—441no—
539C23—441no—
540C23—441no—
541C23—441no—
542C23—441no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23C2×D4×D1111yescharacteristic
547D4—222no—
548D4—222no—
549D4—222no—
550D4—222no—
551D4—448no—
552D4—441no—
553D4—441no—
554D4—441no—
555D4—441no—
556D4—884no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—112no—
575C2×C4—112no—
576C2×C4—221no—
577C2×C4—221no—
578C2×C4—221no—
579C2×C4—221no—
580C2×C4—221no—
581C2×C4—221no—
582C2×C4—221no—
583C2×C4—221no—
584C2×C4—221no—
585C2×C4—221no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—884no—
593C2×C4—884no—
594C2×C4SD16×D1112yes—
595C2×C4C2×#433911yescharacteristic
596C2×C4C2×#434311yescharacteristic
597C2×C4#41×D1111yescharacteristic
598C2×C4#41×D1111yescharacteristic
599C2×C4#6704211yescharacteristic
600C2×C4#6704311yescharacteristic
601C8—41no—
602C8—41no—
603C8—441no—
604C8—441no—
605C22—442no—
606C22—442no—
607C22—442no—
608C22—442no—
609C22—442no—
610C22—442no—
611C22—881no—
612C22—881no—
613C22—881no—
614C22—881no—
615C22—881no—
616C22—881no—
617C22—881no—
618C22—881no—
619C22#1062308311yescharacteristic
620C22#1062316111yescharacteristic
621C22#1062318711yescharacteristic
622C22C2×SD16×D1111yescharacteristic
623C22#1062330011yescharacteristic
624C22#1062330511yescharacteristic
625C22#1062330811yescharacteristic
626C4—22no—
627C4—42no—
628C4—41no—
629C4—42no—
630C4—81no—
631C4—81no—
632C4—222no—
633C4—222no—
634C4—441no—
635C4—441no—
636C4—881no—
637C4—881no—
638C4#1062306111yescharacteristic
639C4#1062311111yescharacteristic
640C4#1062322511yescharacteristic
641C4#1062323811yescharacteristic
642C2—882no—
643C2—882no—
644C2#1307256711yescharacteristic
645C2#1307862111yescharacteristic
646C2#1307885511yescharacteristic
647C2#1308043711yescharacteristic
648C2#1308061911yescharacteristic
649C2#1308128511yescharacteristic
650C2#1308137011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1920C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#1920D11
hypocenterC11#26754
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1920

Complements

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

NH ≅ G/Ntype
1. #13073146C2semidirect
3. #13070023C2semidirect
4. #13069985C2semidirect
7. #13069300C2semidirect
8. #13069242C2semidirect
9. #13069201C2semidirect
10. #13069172C2semidirect
11. #13068878C2semidirect
12. #13068878C2semidirect
13. #13068615C2semidirect
14. #13068430C2semidirect
15. C11×#1920C2semidirect
216. #1920D11semidirect
531. C11#26754semidirect

Maximal subgroups

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

subgroupindex
#130731462
#130716802
#130700232
#130699852
#130698512
#130698502
#130693002
#130692422
#130692012
#130691722
#130688782
#130686152
#130684302
C11×#19202
#2675411