Finite Group Databasebeta

← #14814614

Subgroups — #14814614

Order 2816.

840 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13072045C211yesmaximal, characteristic
2#13070178C211yesmaximal, characteristic, complemented
3#13070042C211yesmaximal, characteristic, complemented
4#13070025C211yesmaximal, characteristic, complemented
5#13069812C211yesmaximal, characteristic, complemented
6#13069257C211yesmaximal, characteristic, complemented
7#13069194C211yesmaximal, characteristic, complemented
8#13069047C211yesmaximal, characteristic, complemented
9#13068923C211yesmaximal, characteristic, complemented
10#13068923C211yesmaximal, characteristic, complemented
11#13068914C211yesmaximal, characteristic
12#13068813C211yesmaximal, characteristic, complemented
13#13068702C211yesmaximal, characteristic, complemented
14#13068335C211yesmaximal, characteristic, complemented
15D4×C11×C4⋊C4C211yesmaximal, characteristic
16C2×C4×D4×C11—21no—
17C2×C4×D4×C11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24C11×#389—21no—
25C11×#385—21no—
26C11×#385—21no—
27C11×#384C2211yescharacteristic
28C11×#380C2211yescharacteristic
29C11×#380C2211yescharacteristic
30C4×C11×C4⋊C4C2211yescharacteristic
31#10622835—21no—
32#10622825C2211yescharacteristic
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36#10622585—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66872C2211yescharacteristic
42C2×#66871C2211yescharacteristic
43#10622565—21no—
44#10622558—21no—
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47#10622167C2211yescharacteristic
48#10622167C2211yescharacteristic
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11D411yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11—21no—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×Dic22C2311yescharacteristic
65C4×D4×C11—22no—
66C4×D4×C11—22no—
67C4×D4×C11—44no—
68C2×C11×C4⋊C4—22no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—41no—
75C2×C11×C4⋊C4—41no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4D411yescharacteristic
84C2×C11×C22⋊C4D411yescharacteristic
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91#66979—22no—
92#66979—41no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96#66977—22no—
97#66977—22no—
98#66977—22no—
99#66977—41no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×C4×Dic11—21no—
104C2×#4318—22no—
105C2×#4318—41no—
106C2×#4318—41no—
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C11×#95—21no—
112C11×#95—21no—
113C11×#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C22⋊(C11⋊C8)—22no—
119C22⋊(C11⋊C8)—41no—
120C22⋊(C11⋊C8)—41no—
121#66874—22no—
122#66874—41no—
123#66874—41no—
124#66874—41no—
125#66872—22no—
126#66871—41no—
127#26216—111nomaximal, Sylow
128C24×C11C2×D411yescharacteristic
129C24×C11C2×D411yescharacteristic
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
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×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—42no—
148C22×C4×C11—42no—
149C22×C4×C11—42no—
150C22×C4×C11—42no—
151C22×C4×C11—81no—
152C22×C4×C11—81no—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11#4112yes—
158C22×C4×C11#4112yes—
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C2×Dic22—21no—
165C2×Dic22—21no—
166C2×Dic22—21no—
167C2×Dic22—21no—
168C2×Dic22—21no—
169C2×Dic22—21no—
170C11×C4⋊C4—22no—
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—42no—
179C11×C4⋊C4—42no—
180C11×C4⋊C4—42no—
181C11×C4⋊C4—81no—
182C11×C4⋊C4#4112yes—
183C11×C22⋊C4—22no—
184C11×C22⋊C4—22no—
185C11×C22⋊C4—42no—
186C11×C22⋊C4—42no—
187C42×C11—21no—
188C42×C11—21no—
189C42×C11—42no—
190C22⋊Dic11—42no—
191C22⋊Dic11—42no—
192C22⋊Dic11—42no—
193C22⋊Dic11—42no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—21no—
197C4⋊Dic11—21no—
198C4⋊Dic11—21no—
199C4⋊Dic11#4112yes—
200Dic11⋊C4—42no—
201Dic11⋊C4—42no—
202Dic11⋊C4—42no—
203C4×Dic11—42no—
204#4318—44no—
205C2×C11⋊C8—21no—
206C2×C11⋊C8—21no—
207C2×C11⋊C8—21no—
208C2×C11⋊C8—21no—
209C2×C11⋊C8—21no—
210C2×C11⋊C8—21no—
211C2×C11⋊C8—21no—
212C2×C11⋊C8—21no—
213C2×C11⋊C8—21no—
214C2×C11⋊C8—21no—
215C2×C11⋊C8—21no—
216C2×C11⋊C8—21no—
217#2415—111no—
218D4×C4⋊C4D1111yescharacteristic
219#2100—111no—
220#2075—111no—
221#2072—111no—
222#2035—111no—
223#1928—111no—
224#1919—111no—
225#1894—111no—
226#1872—111no—
227#1872—111no—
228#1870—111no—
229#1854—111no—
230#1823—111no—
231#1736—111no—
232C23×C11—21no—
233C23×C11—21no—
234C23×C11—21no—
235C23×C11—21no—
236C23×C11—21no—
237C23×C11—21no—
238C23×C11—21no—
239C23×C11—21no—
240C23×C11—21no—
241C23×C11—21no—
242C23×C11—21no—
243C23×C11—21no—
244C23×C11#12312yes—
245C23×C11AGL(1,ℤ/8)12yes—
246C23×C11C22×D411yescharacteristic
247D4×C11—28no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—21no—
259C2×C4×C11—22no—
260C2×C4×C11—21no—
261C2×C4×C11—21no—
262C2×C4×C11—21no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—41no—
267C2×C4×C11—41no—
268C2×C4×C11—41no—
269C2×C4×C11—41no—
270C2×C4×C11—41no—
271C2×C4×C11—41no—
272C2×C4×C11—41no—
273C2×C4×C11—41no—
274C2×C4×C11—41no—
275C2×C4×C11—41no—
276C2×C4×C11—41no—
277C2×C4×C11—41no—
278C2×C4×C11—84no—
279C2×C4×C11—84no—
280C2×C4×C11#12312yes—
281C2×C4×C11#13712yes—
282C2×C4×C11C2×#4111yescharacteristic
283C2×C4×C11C2×#4111yescharacteristic
284C2×C4×C11C2×#4111yescharacteristic
285C2×C4×C11C2×#4111yescharacteristic
286C2×C4×C11H(5,𝔽2)11yescharacteristic
287C2×C4×C11H(5,𝔽2)11yescharacteristic
288C2×Dic11—22no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11—41no—
297C2×Dic11—41no—
298C2×Dic11—41no—
299C2×Dic11—41no—
300Dic22—41no—
301Dic22—41no—
302Dic22—41no—
303Dic22—41no—
304C11⋊C8—41no—
305C11⋊C8—41no—
306C11⋊C8—41no—
307C11⋊C8—41no—
308C22×M16—111no—
309C2×C22⋊Q8—111no—
310C2×C22⋊Q8—111no—
311C2×C4×D4—21no—
312C2×C4×D4C2×D1111yescharacteristic
313C2×#117—111no—
314C22×C4⋊C4C2×D1111yescharacteristic
315C22×C4⋊C4C2×D1111yescharacteristic
316C2×#107—111no—
317C2×#106—111no—
318C2×#103—111no—
319C2×#103—111no—
320C2×#103—111no—
321C2×#103—111no—
322C2×C22⋊C8—111no—
323C2×C22⋊C8—111no—
324C2×C22⋊C8—111no—
325#397—221no—
326#394—221no—
327#391—111no—
328#389—21no—
329#389—111no—
330#389—221no—
331#388—221no—
332#385—21no—
333#385—21no—
334#384C2×D1111yescharacteristic
335#380—111no—
336#380C2×D1111yescharacteristic
337#380C2×D1111yescharacteristic
338C4×C4⋊C4C2×D1111yescharacteristic
339#340—111no—
340#340—111no—
341#340—111no—
342#340—111no—
343#340—111no—
344#340—111no—
345#340—111no—
346#340—111no—
347#340—111no—
348#340—111no—
349#336—111no—
350#336—111no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—22no—
354C22×C11—22no—
355C22×C11—22no—
356C22×C11—22no—
357C22×C11—41no—
358C22×C11—41no—
359C22×C11—41no—
360C22×C11—41no—
361C22×C11—41no—
362C22×C11—41no—
363C22×C11—41no—
364C22×C11—41no—
365C22×C11C2×#12311yescharacteristic
366C22×C11#54611yescharacteristic
367C22×C11#54611yescharacteristic
368C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
369C22×C11C2×#13711yescharacteristic
370C22×C11#57711yescharacteristic
371C22×C11#57811yescharacteristic
372C4×C11—22no—
373C4×C11—22no—
374C4×C11—41no—
375C4×C11—41no—
376C4×C11—42no—
377C4×C11—81no—
378C4×C11—81no—
379C4×C11—81no—
380C4×C11#52911yescharacteristic
381C4×C11#53811yescharacteristic
382C4×C11#55311yescharacteristic
383C4×C11#55311yescharacteristic
384Dic11—42no—
385Dic11—81no—
386Dic11—81no—
387Dic11—81no—
388C22×Q8—111no—
389C22×D4C22⋊D1111yescharacteristic
390C23×C4—21no—
391C23×C4—21no—
392C23×C4C22×D1111yescharacteristic
393C23×C4C22×D1111yescharacteristic
394C2×M16—222no—
395C2×M16—441no—
396C2×M16—441no—
397C22×C8—111no—
398C22×C8—111no—
399C22×C8—111no—
400C22×C8—111no—
401C22⋊Q8—222no—
402C22⋊Q8—222no—
403C22⋊Q8—222no—
404C22⋊Q8—441no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—44no—
408#117—222no—
409#117—441no—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—22no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—41no—
417C2×C4⋊C4—41no—
418C2×C4⋊C4—111no—
419C2×C4⋊C4—111no—
420C2×C4⋊C4—111no—
421C2×C4⋊C4—221no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4—221no—
424C2×C4⋊C4C22⋊D1111yescharacteristic
425C2×C4⋊C4C22×D1111yescharacteristic
426C2×C4⋊C4C22×D1111yescharacteristic
427C2×C4⋊C4C22×D1111yescharacteristic
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C22⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—221no—
432C2×C22⋊C4—221no—
433C2×C22⋊C4—221no—
434C2×C22⋊C4—221no—
435C2×C22⋊C4C22⋊D1111yescharacteristic
436C2×C22⋊C4C22⋊D1111yescharacteristic
437C2×C42—21no—
438C2×C42—221no—
439C2×C42C22×D1111yescharacteristic
440#107—441no—
441#106—222no—
442#103—222no—
443#103—441no—
444#103—441no—
445#103—441no—
446C22⋊C8—222no—
447C22⋊C8—441no—
448C22⋊C8—441no—
449#95—21no—
450#95—21no—
451#95—21no—
452#95—221no—
453#95—221no—
454#95—221no—
455#95—221no—
456C2×C11—42no—
457C2×C11—42no—
458C2×C11#244411yescharacteristic
459C2×C11#309211yescharacteristic
460C2×C11#309711yescharacteristic
461C2×C11#330811yescharacteristic
462C2×C11#331011yescharacteristic
463C2×C11#332811yescharacteristic
464C2×C11#333111yescharacteristic
465C24C2×C22⋊D1111yescharacteristic
466C24C2×C22⋊D1111yescharacteristic
467C2×Q8—221no—
468C2×Q8—221no—
469C2×Q8—221no—
470C2×Q8—221no—
471C2×Q8—221no—
472C2×Q8—221no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—42no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—81no—
495C22×C4—81no—
496C22×C4—221no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4#433912yes—
501C22×C4#433912yes—
502C22×C4C2×C22⋊D1111yescharacteristic
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C23×D1111yescharacteristic
507M16—444no—
508C2×C8—221no—
509C2×C8—221no—
510C2×C8—221no—
511C2×C8—221no—
512C2×C8—221no—
513C2×C8—221no—
514C2×C8—221no—
515C2×C8—221no—
516C2×C8—221no—
517C2×C8—221no—
518C2×C8—221no—
519C2×C8—221no—
520C4⋊C4—22no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C4⋊C4—81no—
532C4⋊C4—112no—
533C4⋊C4—221no—
534C4⋊C4—221no—
535C4⋊C4—221no—
536C4⋊C4—221no—
537C4⋊C4—221no—
538C4⋊C4—442no—
539C4⋊C4—442no—
540C4⋊C4—442no—
541C4⋊C4#434112yes—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—442no—
547C22⋊C4—442no—
548C22⋊C4—442no—
549C22⋊C4—442no—
550C42—21no—
551C42—21no—
552C42—42no—
553C42—442no—
554C11#2621611yescharacteristic, complemented, Sylow
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23#6698212yes—
568C23#6698512yes—
569C23C22×C22⋊D1111yescharacteristic
570Q8—441no—
571Q8—441no—
572Q8—441no—
573Q8—441no—
574D4—28no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—84no—
606C2×C4—84no—
607C2×C4—222no—
608C2×C4—441no—
609C2×C4—441no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—441no—
613C2×C4—441no—
614C2×C4—441no—
615C2×C4—441no—
616C2×C4—441no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4#6698212yes—
620C2×C4#6699512yes—
621C2×C4C2×#433911yescharacteristic
622C2×C4C2×#433911yescharacteristic
623C2×C4C2×#434111yescharacteristic
624C2×C4#6703711yescharacteristic
625C2×C4#41×D1111yescharacteristic
626C2×C4#6704211yescharacteristic
627C8—441no—
628C8—441no—
629C8—441no—
630C8—441no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22C2×#6698211yescharacteristic
646C22C2×#6698511yescharacteristic
647C22#1062333711yescharacteristic
648C22C2×#6699511yescharacteristic
649C22#1062336011yescharacteristic
650C22#1062336711yescharacteristic
651C22#1062336911yescharacteristic
652C4—22no—
653C4—22no—
654C4—41no—
655C4—42no—
656C4—41no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—442no—
661C4—881no—
662C4—881no—
663C4—881no—
664C4#1062306911yescharacteristic
665C4#1062307111yescharacteristic
666C4#1062309111yescharacteristic
667C4#1062309611yescharacteristic
668C2—42no—
669C2—42no—
670C2#1307236011yescharacteristic
671C2#1307853911yescharacteristic
672C2#1307858511yescharacteristic
673C2#1308060111yescharacteristic
674C2#1308063711yescharacteristic
675C2#1308089911yescharacteristic
676C2#1308092611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingD4×C11×C4⋊C4C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenterD4×C4⋊C4D11
hypocenterC11#26216
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #13070178C2semidirect
3. #13070042C2semidirect
4. #13070025C2semidirect
5. #13069812C2semidirect
6. #13069257C2semidirect
7. #13069194C2semidirect
8. #13069047C2semidirect
9. #13068923C2semidirect
10. #13068923C2semidirect
12. #13068813C2semidirect
13. #13068702C2semidirect
14. #13068335C2semidirect
554. C11#26216semidirect

Maximal subgroups

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

subgroupindex
#130720452
#130701782
#130700422
#130700252
#130698122
#130692572
#130691942
#130690472
#130689232
#130689142
#130688132
#130687022
#130683352
D4×C11×C4⋊C42
#2621611