Finite Group Databasebeta

← #14801993

Subgroups — #14801993

Order 2816.

940 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622475C211yesmaximal, characteristic, complemented
2C2×#10622477C211yesmaximal, characteristic
3#13073084C211yesmaximal, characteristic
4#13071623C211yesmaximal, characteristic, complemented
5#13070095C211yesmaximal, characteristic, complemented
6#13070025C211yesmaximal, characteristic, complemented
7#13069985C211yesmaximal, characteristic, complemented
8#13069934C211yesmaximal, characteristic, complemented
9#13069243C211yesmaximal, characteristic, complemented
10#13068972C211yesmaximal, characteristic, complemented
11#13068932C211yesmaximal, characteristic
12#13068792C211yesmaximal, characteristic, complemented
13#13068620C211yesmaximal, characteristic, complemented
14D11×#340C211yesmaximal, characteristic, complemented
15C11×#1948C211yesmaximal, characteristic, complemented
16C22×#4314C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×#66950C2211yescharacteristic
19C2×#66948C2211yescharacteristic
20C2×#66947—21no—
21C2×#66947—21no—
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C4⋊C4×D11C2211yescharacteristic
24C2×#66940C2211yescharacteristic
25C2×C11×#106C2211yescharacteristic
26C2×C11×#106C2211yescharacteristic
27C2×C11×C4⋊C8C2211yescharacteristic
28C11×#384C2211yescharacteristic
29C4×C11×C4⋊C4C2211yescharacteristic
30C2×#66885C2211yescharacteristic
31C2×(C2×D11)⋊C8C2211yescharacteristic
32C2×#66880C2211yescharacteristic
33C2×Dic11⋊C8C2211yescharacteristic
34#10622605—21no—
35#10622605—21no—
36#10622601C2211yescharacteristic
37#10622598C2211yescharacteristic
38#10622589C2211yescharacteristic
39C2×#66874C2211yescharacteristic
40C2×#66874C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66872C2211yescharacteristic
44#10622552C2211yescharacteristic
45C4×(C2×D11)⋊C4—21no—
46C4×(C2×D11)⋊C4C2211yescharacteristic
47#10622542C2211yescharacteristic
48#10622541—21no—
49#10622477—24no—
50#10622475—24no—
51#10622281—21no—
52#10622266—21no—
53C11×#340C2211yescharacteristic
54C11×#340C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622188C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622162C2211yescharacteristic
61C22×D44—21no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—21no—
64C22×C4×D11—21no—
65C22×C4×D11C2311yescharacteristic
66C22×Dic22C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C22×C8×C11C2311yescharacteristic
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4D411yescharacteristic
84C2×(C2×D11)⋊C4D411yescharacteristic
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C2×#4314—22no—
99C2×#4314—22no—
100C2×#4314—41no—
101C2×C8×D11—22no—
102C2×C8×D11—22no—
103C2×C8×D11—41no—
104#66950—22no—
105#66950D414yes—
106#66948—22no—
107#66948—22no—
108#66947—44no—
109#66947—44no—
110C4⋊C4×D11—22no—
111C4⋊C4×D11—22no—
112C4⋊C4×D11—22no—
113C4⋊C4×D11—41no—
114#66940—22no—
115#66940—41no—
116C11×#106—22no—
117C11×#106—22no—
118C11×C4⋊C8—22no—
119C11×#95—21no—
120C11⋊#95—21no—
121C11⋊#95—21no—
122C11⋊#95—21no—
123C11⋊#95D411yescharacteristic
124C11⋊#95D411yescharacteristic
125#66885—41no—
126(C2×D11)⋊C8—22no—
127#66880—22no—
128Dic11⋊C8—41no—
129#66874—22no—
130#66874—22no—
131#66873—22no—
132#66873—22no—
133#66872—22no—
134#25204—111nomaximal, Sylow
135C23×D11—21no—
136C23×D11C2×D411yescharacteristic
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11C2×D411yescharacteristic
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C2×D44—21no—
151C2×D44—21no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—21no—
156C2×D44—42no—
157C2×D44—42no—
158C2×D44—42no—
159C2×C4×D11—21no—
160C2×C4×D11—21no—
161C2×C4×D11—21no—
162C2×C4×D11—21no—
163C2×C4×D11—42no—
164C2×C4×D11—42no—
165C2×C4×D11—42no—
166C2×C4×D11—42no—
167C2×C4×D11—42no—
168C2×C4×D11—81no—
169C2×C4×D11C2×D412yes—
170C2×C4×D11#4112yes—
171C2×Dic22—21no—
172C2×Dic22—21no—
173C2×Dic22—21no—
174C2×Dic22—21no—
175C2×Dic22—21no—
176C2×Dic22C2×D412yes—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11#4112yes—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—21no—
185C11×C4⋊C4—21no—
186C11×C4⋊C4—21no—
187C11×C4⋊C4—21no—
188C11×C4⋊C4—21no—
189C11×C4⋊C4—42no—
190C11×C4⋊C4—42no—
191C11×C4⋊C4C2×D412yes—
192C11×C4⋊C4#4112yes—
193C42×C11—21no—
194C42×C11—21no—
195C42×C11—81no—
196(C2×D11)⋊C4—24no—
197(C2×D11)⋊C4—22no—
198(C2×D11)⋊C4—42no—
199(C2×D11)⋊C4—42no—
200(C2×D11)⋊C4—42no—
201(C2×D11)⋊C4—42no—
202(C2×D11)⋊C4—42no—
203(C2×D11)⋊C4SD1614yescomplemented
204C4⋊Dic11—24no—
205C4⋊Dic11—21no—
206C4⋊Dic11—21no—
207C4⋊Dic11—21no—
208C4⋊Dic11—21no—
209C4⋊Dic11—81no—
210Dic11⋊C4—42no—
211Dic11⋊C4—42no—
212Dic11⋊C4—42no—
213Dic11⋊C4—42no—
214Dic11⋊C4—42no—
215C4×Dic11—21no—
216C4×Dic11—21no—
217C4×Dic11—42no—
218C2×C11⋊C8—21no—
219C2×C11⋊C8—21no—
220C2×C11⋊C8—21no—
221C2×C11⋊C8—21no—
222C2×C11⋊C8—21no—
223C2×C11⋊C8—21no—
224#4314—44no—
225C8×D11—44no—
226C2×#483—111no—
227C2×#465—111no—
228#2501—111no—
229#2360—111no—
230#2084—111no—
231#2072—111no—
232#2065—111no—
233#2055—111no—
234#1948D1111yescharacteristic, complemented
235#1926—111no—
236#1880—111no—
237#1874—111no—
238#1850—111no—
239#1803—111no—
240C2×#340—111no—
241C23×C11C22×D411yescharacteristic
242C22×D11—21no—
243C22×D11—21no—
244C22×D11—21no—
245C22×D11—21no—
246C22×D11—41no—
247C22×D11—41no—
248C22×D11—41no—
249C22×D11—41no—
250C22×D11—41no—
251C22×D11—41no—
252C22×D11—41no—
253C22×D11#12112yes—
254C22×D11C2×SD1612yes—
255C22×D11AGL(1,ℤ/8)12yes—
256C2×C4×C11—21no—
257C2×C4×C11—21no—
258C2×C4×C11—22no—
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×C11C2×SD1612yes—
274C2×C4×C11C22×D411yescharacteristic
275C2×C4×C11C2×#4111yescharacteristic
276C2×C4×C11C2×#4111yescharacteristic
277C2×C4×C11C2×#4111yescharacteristic
278C2×C4×C11H(5,𝔽2)11yescharacteristic
279C2×C4×C112−1+411yescharacteristic
280C2×Dic11—21no—
281C2×Dic11—21no—
282C2×Dic11—21no—
283C2×Dic11—21no—
284C2×Dic11—22no—
285C2×Dic11—21no—
286C2×Dic11—21no—
287C2×Dic11—21no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—41no—
294C2×Dic11—41no—
295C2×Dic11—41no—
296C2×Dic11#12112yes—
297C2×Dic11C2×SD1612yes—
298D44—41no—
299D44—41no—
300D44—41no—
301D44—41no—
302D44—84no—
303C4×D11—22no—
304C4×D11—22no—
305C4×D11—22no—
306C4×D11—22no—
307C4×D11—84no—
308C4×D11—84no—
309Dic22—22no—
310Dic22—22no—
311Dic22—41no—
312Dic22—41no—
313C8×C11—22no—
314C8×C11—41no—
315C11⋊C8—41no—
316C11⋊C8—41no—
317C22×SD16—111no—
318C23×C8—111no—
319C2×#123—221no—
320C2×#123—221no—
321C2×C22⋊Q8—111no—
322C2×#121—111no—
323C2×C4×Q8—111no—
324C22×C4⋊C4—111no—
325C22×C4⋊C4—111no—
326#483—224no—
327#465—224no—
328C2×#106—111no—
329C2×#106C2×D1111yescharacteristic
330C2×#106C2×D1111yescharacteristic
331C2×C4⋊C8—111no—
332C2×C4⋊C8C2×D1111yescharacteristic
333C2×#103—111no—
334C2×#103—111no—
335C2×#103—111no—
336C2×#102—111no—
337C2×#102—111no—
338C2×#102—111no—
339C2×C22⋊C8—111no—
340#399—221no—
341#399—221no—
342#391—111no—
343#390—111no—
344#390—111no—
345#389—111no—
346#389—221no—
347#387—221no—
348#385—221no—
349#384—111no—
350#384C2×D1111yescharacteristic
351C4×C4⋊C4C2×D1111yescharacteristic
352C4×C22⋊C4—111no—
353C4×C22⋊C4—221no—
354#340—111no—
355#340—111no—
356#340—111no—
357#340—111no—
358#340C2×D1111yescharacteristic
359#340C2×D1111yescharacteristic
360#336—111no—
361#336—111no—
362C22×C11C2×#12111yescharacteristic
363C22×C11#54611yescharacteristic
364C22×C11#54711yescharacteristic
365C22×C11C22×SD1611yescharacteristic
366C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C11#57711yescharacteristic
368C22×C11#57811yescharacteristic
369C2×D11—22no—
370C2×D11—22no—
371C2×D11—22no—
372C2×D11—22no—
373C2×D11—22no—
374C2×D11—22no—
375C2×D11—81no—
376C2×D11—81no—
377C2×D11—81no—
378C2×D11—81no—
379C2×D11—81no—
380C2×D11—81no—
381C2×D11—81no—
382C2×D11#46014yes—
383C4×C11—22no—
384C4×C11—41no—
385C4×C11—42no—
386C4×C11—42no—
387C4×C11—81no—
388C4×C11—81no—
389C4×C11#52911yescharacteristic
390C4×C11#53911yescharacteristic
391C4×C11#54611yescharacteristic
392C4×C11#54711yescharacteristic
393Dic11—22no—
394Dic11—22no—
395Dic11—42no—
396Dic11—41no—
397Dic11—81no—
398Dic11—81no—
399C22×Q8—111no—
400C22×D4—111no—
401C22×D4—221no—
402C23×C4—111no—
403C23×C4—221no—
404C23×C4—221no—
405C2×SD16—222no—
406C2×SD16—222no—
407C2×SD16—441no—
408C22×C8—111no—
409C22×C8—111no—
410C22×C8—222no—
411C22×C8—222no—
412C22×C8—441no—
413C22×C8C22×D1111yescharacteristic
414C22×C8C22×D1111yescharacteristic
415#123—444no—
416#123—444no—
417C22⋊Q8—114no—
418C22⋊Q8—222no—
419#121—222no—
420#121—222no—
421C4×Q8—222no—
422C4×Q8—441no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—111no—
426C2×C4⋊C4—111no—
427C2×C4⋊C4—222no—
428C2×C4⋊C4—222no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—222no—
431C2×C4⋊C4—221no—
432C2×C4⋊C4—221no—
433C2×C4⋊C4—221no—
434C2×C4⋊C4—221no—
435C2×C4⋊C4—221no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4—441no—
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C4⋊C4C22×D1111yescharacteristic
440C2×C4⋊C4C22×D1111yescharacteristic
441C2×C4⋊C4C22×D1111yescharacteristic
442C2×C22⋊C4—111no—
443C2×C22⋊C4—111no—
444C2×C22⋊C4—221no—
445C2×C22⋊C4—221no—
446C2×C22⋊C4—221no—
447C2×C22⋊C4—221no—
448C2×C22⋊C4—221no—
449C2×C22⋊C4—221no—
450C2×C42—21no—
451C2×C42—111no—
452C2×C42—221no—
453C2×C42C22×D1111yescharacteristic
454#106—22no—
455#106—22no—
456#106—222no—
457C4⋊C8—22no—
458C4⋊C8—441no—
459#103—222no—
460#103—222no—
461#103—222no—
462#102—222no—
463#102—222no—
464#102—441no—
465C22⋊C8—222no—
466#95—21no—
467#95—111no—
468#95—111no—
469#95—221no—
470#95—221no—
471#95—221no—
472C2×C11#242511yescharacteristic
473C2×C11C2×#46011yescharacteristic
474C2×C11#304611yescharacteristic
475C2×C11#329811yescharacteristic
476C2×C11#330611yescharacteristic
477C2×C11#333511yescharacteristic
478C2×C11#334311yescharacteristic
479D11—24no—
480D11—161no—
481C24—111no—
482C24—221no—
483C2×Q8—112no—
484C2×Q8—221no—
485C2×Q8—221no—
486C2×Q8—221no—
487C2×Q8—221no—
488C2×Q8—221no—
489C2×D4—221no—
490C2×D4—221no—
491C2×D4—221no—
492C2×D4—221no—
493C2×D4—221no—
494C2×D4—221no—
495C2×D4—442no—
496C2×D4—442no—
497C2×D4—442no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—111no—
503C22×C4—111no—
504C22×C4—112no—
505C22×C4—112no—
506C22×C4—111no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—442no—
515C22×C4—442no—
516C22×C4—442no—
517C22×C4—442no—
518C22×C4—442no—
519C22×C4—881no—
520C22×C4D4×D1111yescharacteristic
521C22×C4D4×D1111yescharacteristic
522C22×C4C23×D1111yescharacteristic
523SD16—444no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—21no—
529C2×C8—221no—
530C2×C8—221no—
531C2×C8—221no—
532C2×C8—221no—
533C2×C8—221no—
534C2×C8—221no—
535C2×C8—444no—
536C2×C8#433912yes—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—21no—
543C4⋊C4—42no—
544C4⋊C4—42no—
545C4⋊C4—224no—
546C4⋊C4—221no—
547C4⋊C4—221no—
548C4⋊C4—221no—
549C4⋊C4—221no—
550C4⋊C4—442no—
551C4⋊C4—442no—
552C4⋊C4—442no—
553C4⋊C4—442no—
554C4⋊C4—442no—
555C4⋊C4—881no—
556C4⋊C4D4×D1112yes—
557C4⋊C4#434312yes—
558C22⋊C4—114no—
559C22⋊C4—222no—
560C22⋊C4—224no—
561C22⋊C4—442no—
562C22⋊C4—442no—
563C22⋊C4—442no—
564C22⋊C4—442no—
565C22⋊C4—442no—
566C42—21no—
567C42—21no—
568C42—81no—
569C42—221no—
570C42—221no—
571C42—442no—
572C11#2520411yescharacteristic, complemented, Sylow
573C23—112no—
574C23—112no—
575C23—112no—
576C23—221no—
577C23—221no—
578C23—221no—
579C23—221no—
580C23—441no—
581C23—441no—
582C23—441no—
583C23—441no—
584C23—441no—
585C23—441no—
586C23—441no—
587C23C2×D4×D1111yescharacteristic
588Q8—222no—
589Q8—222no—
590Q8—441no—
591Q8—441no—
592D4—441no—
593D4—441no—
594D4—441no—
595D4—441no—
596D4—884no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—112no—
615C2×C4—112no—
616C2×C4—221no—
617C2×C4—221no—
618C2×C4—221no—
619C2×C4—221no—
620C2×C4—222no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—222no—
624C2×C4—221no—
625C2×C4—221no—
626C2×C4—222no—
627C2×C4—221no—
628C2×C4—441no—
629C2×C4—441no—
630C2×C4—441no—
631C2×C4—441no—
632C2×C4—441no—
633C2×C4—441no—
634C2×C4—441no—
635C2×C4—441no—
636C2×C4—884no—
637C2×C4—884no—
638C2×C4SD16×D1112yes—
639C2×C4C2×#433911yescharacteristic
640C2×C4C2×D4×D1111yescharacteristic
641C2×C4C2×#434311yescharacteristic
642C2×C4#6704011yescharacteristic
643C2×C4#41×D1111yescharacteristic
644C2×C4#6704211yescharacteristic
645C8—22no—
646C8—41no—
647C8—441no—
648C8—441no—
649C22—114no—
650C22—222no—
651C22—222no—
652C22—222no—
653C22—222no—
654C22—222no—
655C22—222no—
656C22—881no—
657C22—881no—
658C22—881no—
659C22—881no—
660C22—881no—
661C22—881no—
662C22—881no—
663C22#1062303811yescharacteristic
664C22D11×#12111yescharacteristic
665C22#1062316111yescharacteristic
666C22C2×SD16×D1111yescharacteristic
667C22#1062329311yescharacteristic
668C22D11×AGL(1,ℤ/8)11yescharacteristic
669C22#1062331011yescharacteristic
670C4—22no—
671C4—42no—
672C4—41no—
673C4—42no—
674C4—81no—
675C4—81no—
676C4—222no—
677C4—222no—
678C4—442no—
679C4—441no—
680C4—881no—
681C4—881no—
682C4#1062308111yescharacteristic
683C4#1062311111yescharacteristic
684C4#1062322311yescharacteristic
685C4#1062325711yescharacteristic
686C2—224no—
687C2—1761no—
688C2#1307217411yescharacteristic
689C2D11×#46011yescharacteristic
690C2#1307816111yescharacteristic
691C2#1308047811yescharacteristic
692C2#1308057411yescharacteristic
693C2#1308096911yescharacteristic
694C2#1308105711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1948C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenter#1948D11
hypocenterC11#25204
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
1. C2×#10622475C2semidirect
4. #13071623C2semidirect
5. #13070095C2semidirect
6. #13070025C2semidirect
7. #13069985C2semidirect
8. #13069934C2semidirect
9. #13069243C2semidirect
10. #13068972C2semidirect
12. #13068792C2semidirect
13. #13068620C2semidirect
14. D11×#340C2semidirect
15. C11×#1948C2semidirect
203. (C2×D11)⋊C4SD16semidirect
234. #1948D11semidirect
572. C11#25204semidirect

Maximal subgroups

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

subgroupindex
C2×#106224752
C2×#106224772
#130730842
#130716232
#130700952
#130700252
#130699852
#130699342
#130692432
#130689722
#130689322
#130687922
#130686202
D11×#3402
C11×#19482
#2520411