Finite Group Databasebeta

← #14826619

Subgroups — #14826619

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073038C211yesmaximal, characteristic
2#13070024C211yesmaximal, characteristic, complemented
3#13070011C211yesmaximal, characteristic, complemented
4#13069816C211yesmaximal, characteristic
5#13069816C211yesmaximal, characteristic
6#13069374C211yesmaximal, characteristic, complemented
7#13069346C211yesmaximal, characteristic, complemented
8#13069224C211yesmaximal, characteristic
9#13069201C211yesmaximal, characteristic, complemented
10#13069184C211yesmaximal, characteristic, complemented
11#13068884C211yesmaximal, characteristic, complemented
12#13068815C211yesmaximal, characteristic
13#13068711C211yesmaximal, characteristic
14C4×#66899C211yesmaximal, characteristic, complemented
15C11×#2362C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C2×#66932—21no—
20C11×#391C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C11×#388—21no—
23C11×#388—21no—
24C11×#387—21no—
25C4×C11×C4⋊C4—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C22⋊C4C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32#10622825C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622566—21no—
41#10622548C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622272—21no—
48#10622266—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C11×C22⋊Q8—22no—
62C11×C22⋊Q8—22no—
63C4×Q8×C11—22no—
64C4×Q8×C11—41no—
65C11×#117—22no—
66C11×#117—41no—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4D411yescharacteristic
76C2×C11×C22⋊C4D411yescharacteristic
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×C4×Dic11—21no—
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97#66932—44no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95D411yescharacteristic
103C11×#95D411yescharacteristic
104#66899—22no—
105#66899—22no—
106#66899—22no—
107#66899—41no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C22⋊(C11⋊C8)—22no—
114C22⋊(C11⋊C8)—41no—
115#66872—22no—
116#66871—22no—
117#66871—22no—
118#66871—41no—
119C4⋊(C11⋊C8)—22no—
120C4×C11⋊C8—41no—
121#27043—111nomaximal, Sylow
122C24×C11C2×D411yescharacteristic
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11—21no—
128C2×Q8×C11#4112yes—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4#4112yes—
157C11×C4⋊C4#4112yes—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—22no—
160C11×C22⋊C4—22no—
161C11×C22⋊C4—42no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—42no—
167C42×C11—42no—
168C42×C11—42no—
169C22⋊Dic11—42no—
170C22⋊Dic11—42no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—42no—
180C4⋊Dic11—42no—
181Dic11⋊C4—42no—
182Dic11⋊C4—42no—
183C4×Dic11—42no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8#4112yes—
196#2496—111no—
197#2362D1111yescharacteristic
198#2072—111no—
199#2068—111no—
200#2036—111no—
201#2036—111no—
202#1947—111no—
203#1942—111no—
204#1923—111no—
205#1920—111no—
206#1918—111no—
207#1865—111no—
208#1854—111no—
209#1825—111no—
210C4×#103—111no—
211C23×C11—21no—
212C23×C11—21no—
213C23×C11—21no—
214C23×C11—21no—
215C23×C11—21no—
216C23×C11—21no—
217C23×C11—21no—
218C23×C11C22×D411yescharacteristic
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—41no—
222Q8×C11—41no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
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×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11#13512yes—
253C2×C4×C11AGL(1,ℤ/8)12yes—
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C112−1+411yescharacteristic
260C2×Dic11—41no—
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—
272C11⋊C8—22no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C2×#126—221no—
277C2×C22⋊Q8C2×D1111yescharacteristic
278C2×C4×Q8C2×D1111yescharacteristic
279C2×#117C2×D1111yescharacteristic
280C2×#107—111no—
281C2×#107—111no—
282C2×#107—111no—
283C2×#106—111no—
284C2×C4⋊C8—111no—
285C2×#103—111no—
286C2×#103—111no—
287C2×#103—111no—
288C2×#103—111no—
289C2×C22⋊C8—111no—
290C2×C22⋊C8—111no—
291C2×C4×C8—111no—
292#400—221no—
293#397—221no—
294#391C2×D1111yescharacteristic
295#389—111no—
296#389—111no—
297#389C2×D1111yescharacteristic
298#388—21no—
299#388—21no—
300#387—21no—
301#387—221no—
302#384—111no—
303#380—111no—
304#380—111no—
305C4×C4⋊C4—21no—
306C4×C4⋊C4—111no—
307C4×C4⋊C4C2×D1111yescharacteristic
308C4×C22⋊C4C2×D1111yescharacteristic
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#336—111no—
318#336—111no—
319C22×C11—41no—
320C22×C11—41no—
321C22×C11—41no—
322C22×C11—41no—
323C22×C11—41no—
324C22×C11—41no—
325C22×C11—41no—
326C22×C11#52511yescharacteristic
327C22×C11#54611yescharacteristic
328C22×C11#54711yescharacteristic
329C22×C11C2×#13511yescharacteristic
330C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
331C22×C11#57811yescharacteristic
332C22×C11#57811yescharacteristic
333C4×C11—22no—
334C4×C11—22no—
335C4×C11—41no—
336C4×C11—42no—
337C4×C11—41no—
338C4×C11—42no—
339C4×C11—41no—
340C4×C11—42no—
341C4×C11—81no—
342C4×C11#52911yescharacteristic
343C4×C11#53911yescharacteristic
344C4×C11#55311yescharacteristic
345C4×C11#55611yescharacteristic
346Dic11—81no—
347Dic11—81no—
348Dic11—81no—
349Dic11—81no—
350C22×Q8C22×D1111yescharacteristic
351C23×C4C22×D1111yescharacteristic
352C22×C8—111no—
353C22×C8—111no—
354C22×C8—111no—
355C22×C8—111no—
356#126—444no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C4×Q8—22no—
360C4×Q8—41no—
361#117—22no—
362#117—41no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4C22⋊D1111yescharacteristic
382C2×C22⋊C4C22⋊D1111yescharacteristic
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—221no—
387C2×C42C22×D1111yescharacteristic
388C2×C42C22×D1111yescharacteristic
389#107—222no—
390#107—222no—
391#107—441no—
392#106—222no—
393C4⋊C8—222no—
394#103—222no—
395#103—222no—
396#103—222no—
397#103—441no—
398C22⋊C8—222no—
399C22⋊C8—441no—
400C4×C8—441no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95C22⋊D1111yescharacteristic
411#95C22⋊D1111yescharacteristic
412C2×C11—81no—
413C2×C11#246611yescharacteristic
414C2×C11#310611yescharacteristic
415C2×C11#312711yescharacteristic
416C2×C11#330211yescharacteristic
417C2×C11#330811yescharacteristic
418C2×C11#333611yescharacteristic
419C2×C11#335311yescharacteristic
420C24C2×C22⋊D1111yescharacteristic
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8#433912yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C2×C22⋊D1111yescharacteristic
444C22×C4C2×C22⋊D1111yescharacteristic
445C22×C4C2×C22⋊D1111yescharacteristic
446C22×C4C23×D1111yescharacteristic
447C2×C8—112no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C4⋊C4—24no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—42no—
465C4⋊C4—42no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—442no—
475C4⋊C4—442no—
476C4⋊C4—442no—
477C4⋊C4—442no—
478C4⋊C4#433912yes—
479C4⋊C4#434112yes—
480C22⋊C4—24no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—42no—
484C22⋊C4—442no—
485C22⋊C4—442no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—42no—
491C42—42no—
492C42—42no—
493C42—442no—
494C11#2704311yescharacteristic, complemented, Sylow
495C23—21no—
496C23—21no—
497C23—21no—
498C23—21no—
499C23—21no—
500C23—21no—
501C23—21no—
502C23C22×C22⋊D1111yescharacteristic
503Q8—22no—
504Q8—22no—
505Q8—41no—
506Q8—41no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—441no—
537C2×C4—441no—
538C2×C4—441no—
539C2×C4—441no—
540C2×C4—441no—
541C2×C4—441no—
542C2×C4—441no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4#6700212yes—
549C2×C4#6700312yes—
550C2×C4C2×#433911yescharacteristic
551C2×C4C2×#433911yescharacteristic
552C2×C4C2×#434111yescharacteristic
553C2×C4#6703711yescharacteristic
554C2×C4#41×D1111yescharacteristic
555C2×C4#6704311yescharacteristic
556C8—222no—
557C8—441no—
558C8—441no—
559C8—441no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22#1062332211yescharacteristic
568C22#1062333711yescharacteristic
569C22C2×#6700211yescharacteristic
570C22C2×#6700311yescharacteristic
571C22#1062335511yescharacteristic
572C22#1062336911yescharacteristic
573C22#1062336911yescharacteristic
574C4—22no—
575C4—22no—
576C4—41no—
577C4—42no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4—42no—
582C4—81no—
583C4—881no—
584C4—881no—
585C4—881no—
586C4—881no—
587C4#1062306911yescharacteristic
588C4#1062307311yescharacteristic
589C4#1062308911yescharacteristic
590C4#1062309511yescharacteristic
591C2—81no—
592C2#1307264611yescharacteristic
593C2#1307867611yescharacteristic
594C2#1307891611yescharacteristic
595C2#1308053311yescharacteristic
596C2#1308060711yescharacteristic
597C2#1308097811yescharacteristic
598C2#1308119411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2362C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenter#2362D11
hypocenterC11#27043
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2362

Complements

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

NH ≅ G/Ntype
2. #13070024C2semidirect
3. #13070011C2semidirect
6. #13069374C2semidirect
7. #13069346C2semidirect
9. #13069201C2semidirect
10. #13069184C2semidirect
11. #13068884C2semidirect
14. C4×#66899C2semidirect
494. C11#27043semidirect

Maximal subgroups

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

subgroupindex
#130730382
#130700242
#130700112
#130698162
#130693742
#130693462
#130692242
#130692012
#130691842
#130688842
#130688152
#130687112
C4×#668992
C11×#23622
#2704311