Finite Group Databasebeta

← #14817337

Subgroups — #14817337

Order 2816.

802 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#13072307C211yesmaximal, characteristic, complemented
2#13071652C211yesmaximal, characteristic
3#13070185C211yesmaximal, characteristic, complemented
4#13070114C211yesmaximal, characteristic, complemented
5#13069989C211yesmaximal, characteristic, complemented
6#13069753C211yesmaximal, characteristic, complemented
7#13069567C211yesmaximal, characteristic, complemented
8#13069209C211yesmaximal, characteristic, complemented
9#13069044C211yesmaximal, characteristic
10#13068936C211yesmaximal, characteristic
11#13068866C211yesmaximal, characteristic, complemented
12#13068817C211yesmaximal, characteristic, complemented
13#13068627C211yesmaximal, characteristic, complemented
14#13068333C211yesmaximal, characteristic, complemented
15C11×#1850C211yesmaximal, characteristic, complemented
16C23×C8×C11C2211yescharacteristic
17C2×#66983C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C2×#66979C2211yescharacteristic
20C2×C4×D44C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C4×C11×C22⋊C4C2211yescharacteristic
26#10622825C2211yescharacteristic
27C2×#66885C2211yescharacteristic
28C2×#66885C2211yescharacteristic
29C2×#66885C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×#66882C2211yescharacteristic
32C2×#66881C2211yescharacteristic
33#10622570—21no—
34#10622569—21no—
35#10622561—21no—
36#10622560—21no—
37#10622552C2211yescharacteristic
38#10622549C2211yescharacteristic
39C4×C4⋊Dic11C2211yescharacteristic
40#10622541C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622282—21no—
44#10622279—21no—
45#10622268—21no—
46#10622259—21no—
47C11×#336C2211yescharacteristic
48C11×#336C2211yescharacteristic
49#10622189C2211yescharacteristic
50#10622189C2211yescharacteristic
51#10622189C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622189C2211yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×D44C2311yescharacteristic
62C22×C4×D11—21no—
63C22×Dic22—21no—
64C22×C8×C11—22no—
65C22×C8×C11—41no—
66C22×C8×C11—41no—
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C2×C11×C22⋊C4D411yescharacteristic
72C2×C11×C22⋊C4D411yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78#66983—22no—
79#66983Q814yescomplemented
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84#66979—22no—
85#66979—22no—
86#66979—41no—
87#66979—41no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—21no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—21no—
101C2×C4×Dic11—21no—
102C4×D44—22no—
103C4×D44—41no—
104#66922—22no—
105#66922—41no—
106C11×C4⋊C8—41no—
107C11×C4⋊C8—41no—
108C11×C22⋊C8—22no—
109C11×#95D411yescharacteristic
110C11×#95D411yescharacteristic
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118#66885—22no—
119#66885—41no—
120#66885—41no—
121#66885—41no—
122#66882—22no—
123#66881—41no—
124#26409—111nomaximal, Sylow
125C24×C11C2×D411yescharacteristic
126C23×D11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×Q812yes—
137C22×C4×C11#4112yes—
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—24no—
140C2×C22⋊D11—81no—
141C2×C22⋊D11—81no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C2×D44—21no—
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44C2×Q812yes—
155C2×C4×D11—42no—
156C2×C4×D11—42no—
157C2×C4×D11—81no—
158C2×Dic22—42no—
159C2×Dic22—42no—
160C2×Dic22—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—
173C2×C8×C11—44no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—41no—
176C42×C11—21no—
177C42×C11—21no—
178C42×C11—21no—
179C42×C11—21no—
180C22⋊Dic11—42no—
181C22⋊Dic11—42no—
182C22⋊Dic11—81no—
183(C2×D11)⋊C4—24no—
184(C2×D11)⋊C4—42no—
185(C2×D11)⋊C4—42no—
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—21no—
198C4⋊Dic11—42no—
199C4⋊Dic11C2×Q812yes—
200C4⋊Dic11#4112yes—
201C4⋊Dic11#4112yes—
202Dic11⋊C4—42no—
203Dic11⋊C4—81no—
204Dic11⋊C4—81no—
205C4×Dic11—42no—
206C4×Dic11—42no—
207C4×Dic11—81no—
208#2439—111no—
209#2363—111no—
210#2101—111no—
211#2088—111no—
212#2065—111no—
213#2023—111no—
214#1988—111no—
215#1921—111no—
216#1893—111no—
217#1875—111no—
218#1862—111no—
219#1854—111no—
220#1850D1111yescharacteristic, complemented
221#1804—111no—
222#1735—111no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—21no—
227C23×C11—21no—
228C23×C11—21no—
229C23×C11C22⋊Q812yes—
230C23×C11C22×D411yescharacteristic
231C22×D11—22no—
232C22×D11—41no—
233C22×D11—41no—
234C22×D11—41no—
235C22×D11—41no—
236C22×D11—41no—
237C22×D11—41no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
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—21no—
254C2×C4×C11—21no—
255C2×C4×C11C22⋊Q812yes—
256C2×C4×C11#13512yes—
257C2×C4×C11C22×Q811yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
263C22⋊D11—84no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
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—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285D44—22no—
286D44—22no—
287D44—41no—
288D44—41no—
289C4×D11—84no—
290Dic22—84no—
291C8×C11—41no—
292C8×C11—41no—
293C8×C11—41no—
294C8×C11—41no—
295C23×C8C2×D1111yescharacteristic
296C2×C4⋊Q8—111no—
297C2×#121—111no—
298C2×C4×D4—111no—
299C2×#117—111no—
300C2×#117—111no—
301C2×#107—111no—
302C2×#106—111no—
303C2×C4⋊C8C2×D1111yescharacteristic
304C2×C4⋊C8C2×D1111yescharacteristic
305C2×#102—111no—
306C2×#102—111no—
307C2×#102—111no—
308C2×#102—111no—
309C2×C22⋊C8C2×D1111yescharacteristic
310#396—221no—
311#393—221no—
312#391—221no—
313#390—111no—
314#390—221no—
315#389—111no—
316#389—111no—
317#389—111no—
318#388—221no—
319#387—221no—
320#386—221no—
321#382—111no—
322#380—111no—
323C4×C4⋊C4—111no—
324C4×C22⋊C4—221no—
325C4×C22⋊C4C2×D1111yescharacteristic
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#340—111no—
334#340—111no—
335#340—111no—
336#336C2×D1111yescharacteristic
337#336C2×D1111yescharacteristic
338C22×C11—22no—
339C22×C11—22no—
340C22×C11—22no—
341C22×C11—41no—
342C22×C11—41no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11C2×C22⋊Q811yescharacteristic
346C22×C11#54611yescharacteristic
347C22×C11#54611yescharacteristic
348C22×C11C2×#13511yescharacteristic
349C22×C11#57511yescharacteristic
350C22×C11#57611yescharacteristic
351C22×C11#57711yescharacteristic
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—81no—
356C2×D11—81no—
357C2×D11—81no—
358C2×D11—81no—
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—41no—
362C4×C11—41no—
363C4×C11—41no—
364C4×C11#52911yescharacteristic
365C4×C11#53811yescharacteristic
366C4×C11#55411yescharacteristic
367C4×C11#55411yescharacteristic
368Dic11—42no—
369Dic11—42no—
370Dic11—42no—
371Dic11—81no—
372Dic11—81no—
373Dic11—81no—
374Dic11—81no—
375C22×Q8—221no—
376C22×D4—111no—
377C22×D4—221no—
378C23×C4—221no—
379C23×C4C22×D1111yescharacteristic
380C22×C8—22no—
381C22×C8—41no—
382C22×C8—41no—
383C22×C8C22×D1111yescharacteristic
384C22×C8C22×D1111yescharacteristic
385C22×C8C22×D1111yescharacteristic
386C22×C8C22×D1111yescharacteristic
387C4⋊Q8—222no—
388C4⋊Q8—441no—
389#121—114no—
390#121—222no—
391C4×D4—222no—
392C4×D4—441no—
393#117—222no—
394#117—222no—
395#117—441no—
396#117—441no—
397C2×C4⋊C4—111no—
398C2×C4⋊C4—111no—
399C2×C4⋊C4—111no—
400C2×C4⋊C4—111no—
401C2×C4⋊C4—111no—
402C2×C4⋊C4—111no—
403C2×C4⋊C4—111no—
404C2×C4⋊C4—221no—
405C2×C4⋊C4—221no—
406C2×C4⋊C4—221no—
407C2×C4⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C22⋊C4—221no—
410C2×C22⋊C4—221no—
411C2×C22⋊C4—221no—
412C2×C22⋊C4—221no—
413C2×C22⋊C4—221no—
414C2×C22⋊C4—221no—
415C2×C22⋊C4D4411yescharacteristic
416C2×C22⋊C4D4411yescharacteristic
417C2×C42—221no—
418C2×C42—221no—
419C2×C42—221no—
420C2×C42C22×D1111yescharacteristic
421C2×C42C22×D1111yescharacteristic
422#107—222no—
423#106—441no—
424C4⋊C8—41no—
425C4⋊C8—41no—
426#102—222no—
427#102—441no—
428#102—441no—
429#102—441no—
430C22⋊C8—22no—
431#95—221no—
432#95—221no—
433#95—221no—
434#95—221no—
435#95—221no—
436#95—221no—
437#95—221no—
438#95D4411yescharacteristic
439#95D4411yescharacteristic
440C2×C11—42no—
441C2×C11#245011yescharacteristic
442C2×C11#307611yescharacteristic
443C2×C11#308111yescharacteristic
444C2×C11#329711yescharacteristic
445C2×C11#330411yescharacteristic
446C2×C11#331911yescharacteristic
447C2×C11#332111yescharacteristic
448D11—82no—
449C24—221no—
450C24C2×D4411yescharacteristic
451C2×Q8—442no—
452C2×Q8—442no—
453C2×Q8—881no—
454C2×D4—112no—
455C2×D4—224no—
456C2×D4—221no—
457C2×D4—221no—
458C2×D4—221no—
459C2×D4—221no—
460C2×D4—221no—
461C2×D4—881no—
462C2×D4—881no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—221no—
468C22×C4—221no—
469C22×C4—221no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—442no—
475C22×C4—442no—
476C22×C4—881no—
477C22×C4C2×D4411yescharacteristic
478C22×C4C2×D4411yescharacteristic
479C22×C4C2×D4411yescharacteristic
480C22×C4C2×D4411yescharacteristic
481C22×C4C2×D4411yescharacteristic
482C22×C4#434112yes—
483C22×C4Q8×D1112yes—
484C22×C4C23×D1111yescharacteristic
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—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—44no—
498C4⋊C4—112no—
499C4⋊C4—112no—
500C4⋊C4—112no—
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—221no—
510C4⋊C4—221no—
511C4⋊C4—221no—
512C4⋊C4—442no—
513C4⋊C4—442no—
514C4⋊C4—881no—
515C4⋊C4—881no—
516C22⋊C4—22no—
517C22⋊C4—41no—
518C22⋊C4—224no—
519C22⋊C4—442no—
520C22⋊C4—442no—
521C22⋊C4—442no—
522C22⋊C4—442no—
523C22⋊C4—881no—
524C22⋊C4—881no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—442no—
530C42—442no—
531C42—881no—
532C11#2640911yescharacteristic, complemented, Sylow
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—222no—
540C23—441no—
541C23—441no—
542C23—441no—
543C23—441no—
544C23—441no—
545C23—441no—
546C23#6695012yes—
547C23C22×D4411yescharacteristic
548Q8—884no—
549D4—222no—
550D4—222no—
551D4—441no—
552D4—441no—
553D4—884no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
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—441no—
588C2×C4—441no—
589C2×C4—441no—
590C2×C4—441no—
591C2×C4—441no—
592C2×C4—884no—
593C2×C4#6695012yes—
594C2×C4#6695712yes—
595C2×C4C2×#434111yescharacteristic
596C2×C4#6703711yescharacteristic
597C2×C4#6703711yescharacteristic
598C2×C4C2×Q8×D1111yescharacteristic
599C2×C4#41×D1111yescharacteristic
600C2×C4#41×D1111yescharacteristic
601C8—41no—
602C8—41no—
603C8—41no—
604C8—41no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—442no—
613C22—442no—
614C22—442no—
615C22—881no—
616C22—881no—
617C22—881no—
618C22—881no—
619C22C2×#6695011yescharacteristic
620C22#1062308511yescharacteristic
621C22#1062308511yescharacteristic
622C22C2×#6695711yescharacteristic
623C22#1062327911yescharacteristic
624C22#1062328211yescharacteristic
625C22#1062328311yescharacteristic
626C4—22no—
627C4—22no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—442no—
632C4—442no—
633C4—442no—
634C4—881no—
635C4—881no—
636C4—881no—
637C4—881no—
638C4#1062312411yescharacteristic
639C4#1062316711yescharacteristic
640C4#1062316711yescharacteristic
641C4#1062318011yescharacteristic
642C2—42no—
643C2—882no—
644C2#1307243811yescharacteristic
645C2#1307840611yescharacteristic
646C2#1307844811yescharacteristic
647C2#1308046811yescharacteristic
648C2#1308055611yescharacteristic
649C2#1308077411yescharacteristic
650C2#1308080411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1850C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1850D11
hypocenterC11#26409
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1850

Complements

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

NH ≅ G/Ntype
1. #13072307C2semidirect
3. #13070185C2semidirect
4. #13070114C2semidirect
5. #13069989C2semidirect
6. #13069753C2semidirect
7. #13069567C2semidirect
8. #13069209C2semidirect
11. #13068866C2semidirect
12. #13068817C2semidirect
13. #13068627C2semidirect
14. #13068333C2semidirect
15. C11×#1850C2semidirect
79. #66983Q8semidirect
220. #1850D11semidirect
532. C11#26409semidirect

Maximal subgroups

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

subgroupindex
#130723072
#130716522
#130701852
#130701142
#130699892
#130697532
#130695672
#130692092
#130690442
#130689362
#130688662
#130688172
#130686272
#130683332
C11×#18502
#2640911