Finite Group Databasebeta

← #14822310

Subgroups — #14822310

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#13071680C211yesmaximal, characteristic
2#13070020C211yesmaximal, characteristic, complemented
3#13069987C211yesmaximal, characteristic, complemented
4#13069850C211yesmaximal, characteristic
5#13069850C211yesmaximal, characteristic
6#13069298C211yesmaximal, characteristic, complemented
7#13069243C211yesmaximal, characteristic, complemented
8#13069198C211yesmaximal, characteristic, complemented
9#13069198C211yesmaximal, characteristic, complemented
10#13069175C211yesmaximal, characteristic, complemented
11#13068876C211yesmaximal, characteristic, complemented
12#13068876C211yesmaximal, characteristic, complemented
13#13068613C211yesmaximal, characteristic, complemented
14C4×#66873C211yesmaximal, characteristic, complemented
15C11×#2507C211yesmaximal, characteristic, complemented
16C2×#66946—21no—
17C2×#66927C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C2×C4×D44C2211yescharacteristic
20C11×#398—21no—
21C11×#398—21no—
22C11×#389—21no—
23C11×#389C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#389C2211yescharacteristic
26C11×#389C2211yescharacteristic
27C11×#387—21no—
28C11×#384C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31#10622601—21no—
32C2×#66873C2211yescharacteristic
33C2×#66873C2211yescharacteristic
34C2×#66873C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66873C2211yescharacteristic
40C2×#66872C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42#10622552C2211yescharacteristic
43#10622552C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622278—21no—
48#10622278—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44—21no—
60C22×D44—21no—
61C22×D44C2311yescharacteristic
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4D411yescharacteristic
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4×Dic11—21no—
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94#66946—44no—
95#66927—22no—
96#66927—22no—
97C4×D44—22no—
98C4×D44—22no—
99C4×D44—41no—
100C4×D44—41no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11×#95D411yescharacteristic
107C11×#95D411yescharacteristic
108C11⋊#95—21no—
109#66873—22no—
110#66873—22no—
111#66873—22no—
112#66873—22no—
113#66873—22no—
114#66873—22no—
115#66873—41no—
116#66873—41no—
117#66872—22no—
118#66872—22no—
119C4⋊(C11⋊C8)—41no—
120C4×C11⋊C8—41no—
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×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2411yescharacteristic
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—
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—21no—
168C11×C4⋊C4—41no—
169C11×C4⋊C4—42no—
170C11×C4⋊C4—81no—
171C11×C4⋊C4—81no—
172C11×C4⋊C4—81no—
173C11×C4⋊C4—81no—
174C11×C4⋊C4—81no—
175C11×C4⋊C4SD1614yes—
176C11×C4⋊C4#4112yes—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C42×C11—21no—
181C42×C11—21no—
182C42×C11—21no—
183C42×C11—81no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—42no—
186(C2×D11)⋊C4—42no—
187(C2×D11)⋊C4—42no—
188(C2×D11)⋊C4—81no—
189(C2×D11)⋊C4—81no—
190C4⋊Dic11—21no—
191C4⋊Dic11—21no—
192C4⋊Dic11—21no—
193C4⋊Dic11#4112yes—
194C4×Dic11—42no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
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#2507D1111yescharacteristic, complemented
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#1920—111no—
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—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—22no—
247C2×C4×C11—21no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—41no—
254C2×C4×C11—41no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11C2×SD1612yes—
265C2×C4×C11C2×SD1612yes—
266C2×C4×C11C2×SD1612yes—
267C2×C4×C11C2×#4111yescharacteristic
268C2×C4×C11C2×#4111yescharacteristic
269C2×C4×C11C2×#4111yescharacteristic
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11H(5,𝔽2)11yescharacteristic
272C2×C4×C112−1+411yescharacteristic
273C2×Dic11—22no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
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—
291C11⋊C8—41no—
292C11⋊C8—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×#106—111no—
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—21no—
312#398—21no—
313#390—111no—
314#390—111no—
315#390—221no—
316#389—21no—
317#389C2×D1111yescharacteristic
318#389C2×D1111yescharacteristic
319#389C2×D1111yescharacteristic
320#389C2×D1111yescharacteristic
321#387—21no—
322#386—221no—
323#386—221no—
324#384C2×D1111yescharacteristic
325C4×C4⋊C4—111no—
326C4×C4⋊C4C2×D1111yescharacteristic
327C4×C4⋊C4C2×D1111yescharacteristic
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#336—111no—
335#336—111no—
336#336—111no—
337#336—111no—
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—22no—
361C4×C11—22no—
362C4×C11—42no—
363C4×C11—41no—
364C4×C11—41no—
365C4×C11—41no—
366C4×C11—81no—
367C4×C11—81no—
368C4×C11—81no—
369C4×C11#52911yescharacteristic
370C4×C11#53911yescharacteristic
371C4×C11#55211yescharacteristic
372C4×C11#55311yescharacteristic
373Dic11—42no—
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×C8—111no—
384C22×C8—111no—
385#127—222no—
386#127—222no—
387C4×D4—222no—
388C4×D4—222no—
389C4×D4—441no—
390C4×D4—441no—
391C4×D4—444no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4C22⋊D1111yescharacteristic
401C2×C4⋊C4C22⋊D1111yescharacteristic
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—221no—
414C2×C42C22×D1111yescharacteristic
415C2×C42C22×D1111yescharacteristic
416C2×C42C22×D1111yescharacteristic
417#106—222no—
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—21no—
432#95—21no—
433#95—21no—
434#95—221no—
435#95C22⋊D1111yescharacteristic
436#95C22⋊D1111yescharacteristic
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—221no—
471C22×C4—221no—
472C22×C4—442no—
473C22×C4—442no—
474C22×C4—442no—
475C22×C4—442no—
476C22×C4—881no—
477C22×C4—881no—
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C2×C22⋊D1111yescharacteristic
480C22×C4C2×C22⋊D1111yescharacteristic
481C22×C4C2×C22⋊D1111yescharacteristic
482C22×C4C2×C22⋊D1111yescharacteristic
483C22×C4C2×C22⋊D1111yescharacteristic
484C22×C4C23×D1111yescharacteristic
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
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—21no—
504C4⋊C4—41no—
505C4⋊C4—42no—
506C4⋊C4—81no—
507C4⋊C4—81no—
508C4⋊C4—81no—
509C4⋊C4—81no—
510C4⋊C4—81no—
511C4⋊C4—112no—
512C4⋊C4—221no—
513C4⋊C4—221no—
514C4⋊C4—221no—
515C4⋊C4#432514yes—
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—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—81no—
530C42—442no—
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—
546C23C22×C22⋊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—21no—
562C2×C4—21no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—222no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—884no—
591C2×C4—884no—
592C2×C4C2×#432512yes—
593C2×C4C2×#432512yes—
594C2×C4C2×#432512yes—
595C2×C4C2×#434311yescharacteristic
596C2×C4#6704011yescharacteristic
597C2×C4#41×D1111yescharacteristic
598C2×C4#41×D1111yescharacteristic
599C2×C4#41×D1111yescharacteristic
600C2×C4#6704211yescharacteristic
601C8—441no—
602C8—441no—
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—
619C22C22×#432511yescharacteristic
620C22#1062334811yescharacteristic
621C22#1062335311yescharacteristic
622C22#1062335911yescharacteristic
623C22#1062336011yescharacteristic
624C22#1062336611yescharacteristic
625C22#1062336611yescharacteristic
626C4—22no—
627C4—22no—
628C4—22no—
629C4—42no—
630C4—41no—
631C4—41no—
632C4—41no—
633C4—81no—
634C4—81no—
635C4—81no—
636C4—442no—
637C4—881no—
638C4#1062322211yescharacteristic
639C4#1062322311yescharacteristic
640C4#1062322411yescharacteristic
641C4#1062322611yescharacteristic
642C2—882no—
643C2—882no—
644C2#1307256411yescharacteristic
645C2#1307862011yescharacteristic
646C2#1307885411yescharacteristic
647C2#1308043411yescharacteristic
648C2#1308061611yescharacteristic
649C2#1308128711yescharacteristic
650C2#1308136911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2507C2
socleC23×C11C22×D4
prime radicalC2×#66927C22
hypercenter#2507D11
hypocenterC11#26754
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2507

Complements

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

NH ≅ G/Ntype
2. #13070020C2semidirect
3. #13069987C2semidirect
6. #13069298C2semidirect
7. #13069243C2semidirect
8. #13069198C2semidirect
9. #13069198C2semidirect
10. #13069175C2semidirect
11. #13068876C2semidirect
12. #13068876C2semidirect
13. #13068613C2semidirect
14. C4×#66873C2semidirect
15. C11×#2507C2semidirect
207. #2507D11semidirect
531. C11#26754semidirect

Maximal subgroups

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

subgroupindex
#130716802
#130700202
#130699872
#130698502
#130692982
#130692432
#130691982
#130691752
#130688762
#130686132
C4×#668732
C11×#25072
#2675411