Finite Group Databasebeta

← #14761479

Subgroups — #14761479

Order 2816.

868 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622376C211yesmaximal, characteristic
2#13071353C211yesmaximal, characteristic, complemented
3#13070977C211yesmaximal, characteristic
4#13069572C211yesmaximal, characteristic, complemented
5#13069378C211yesmaximal, characteristic, complemented
6#13069193C211yesmaximal, characteristic, complemented
7#13069190C211yesmaximal, characteristic, complemented
8#13068879C211yesmaximal, characteristic
9#13068875C211yesmaximal, characteristic
10#13068614C211yesmaximal, characteristic
11#13068514C211yesmaximal, characteristic, complemented
12C4×#66881C211yesmaximal, characteristic, complemented
13#13068474C211yesmaximal, characteristic, complemented
14#13068441C211yesmaximal, characteristic
15C4×C11×#102C211yesmaximal, characteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×D4×Dic11C2211yescharacteristic
18C2×D4×Dic11C2211yescharacteristic
19C2×#66943C2211yescharacteristic
20C2×C11×#102C2211yescharacteristic
21C2×C11×#102C2211yescharacteristic
22C2×C4×C8×C11C2211yescharacteristic
23C4×C11×C4⋊C4C2211yescharacteristic
24C2×#66896C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26C4×C22⋊Dic11—21no—
27C2×C11⋊#95—21no—
28C2×#66881C2211yescharacteristic
29C2×#66881C2211yescharacteristic
30C2×Dic11⋊C8C2211yescharacteristic
31C2×Dic11⋊C8C2211yescharacteristic
32#10622598C2211yescharacteristic
33#10622589C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622586C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C22⋊C4×Dic11—21no—
40C22⋊C4×Dic11—21no—
41C4×C4⋊Dic11C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622546—21no—
44#10622545C2211yescharacteristic
45#10622541—21no—
46C2×#66867C2211yescharacteristic
47#10622376C418yescomplemented
48#10622267—21no—
49#10622260—21no—
50C11×#340C2211yescharacteristic
51C11×#340C2211yescharacteristic
52#10622189C2211yescharacteristic
53#10622189C2211yescharacteristic
54#10622188C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×Dic11—21no—
63C23×Dic11—21no—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C4×D4×C11—22no—
67C4×D4×C11Q814yes—
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76D4×Dic11—22no—
77D4×Dic11—22no—
78D4×Dic11—22no—
79D4×Dic11C2×C414yes—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C2×C4×Dic11—21no—
93C2×C4×Dic11—21no—
94C2×C4×Dic11C2311yescharacteristic
95C2×C4×Dic11C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98#66943—22no—
99#66943C2×C414yescomplemented
100C11×#102—22no—
101C11×#102C2×C414yes—
102C4×C8×C11—22no—
103C11×#95—21no—
104#66896—22no—
105#66896C2×C414yes—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95D411yescharacteristic
113C11⋊#95D411yescharacteristic
114C11⋊#95D411yescharacteristic
115C11⋊#95D411yescharacteristic
116#66881—22no—
117#66881C2×C414yescomplemented
118Dic11⋊C8—22no—
119Dic11⋊C8C2×C414yescomplemented
120#66872—22no—
121#66871C2×C414yescomplemented
122#66867—22no—
123#21619—111nomaximal, Sylow
124C24×C11—21no—
125C2×D4×C11—21no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11C22×C412yes—
129C2×D4×C11C2×Q812yes—
130C2×D4×C11#4112yes—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—24no—
134C22×C4×C11—21no—
135C22×C4×C11—81no—
136C22×C4×C11—81no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—81no—
147C22×Dic11—81no—
148C22×Dic11—81no—
149C22×Dic11—81no—
150C22×Dic11C2×D411yescharacteristic
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11—21no—
159C2×C8×C11C22×C412yes—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4C22×C412yes—
165C11×C4⋊C4C2×Q812yes—
166C11×C22⋊C4—24no—
167C42×C11—81no—
168C42×C11C2×Q812yes—
169C42×C11#4112yes—
170C22⋊Dic11—24no—
171C22⋊Dic11—24no—
172C4⋊Dic11—24no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—81no—
179C4⋊Dic11C22×C412yes—
180C4⋊Dic11C22×C412yes—
181C4⋊Dic11#4112yes—
182Dic11⋊C4—24no—
183Dic11⋊C4—81no—
184Dic11⋊C4—81no—
185Dic11⋊C4—81no—
186C4×Dic11—21no—
187C4×Dic11—21no—
188C4×Dic11—81no—
189C4×Dic11—81no—
190C4×Dic11—81no—
191C4×Dic11—81no—
192C4×Dic11C22×C412yes—
193C4×Dic11#4112yes—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198C2×C11⋊C8—21no—
199C2×C11⋊C8C22×C412yes—
200C2×#478—111no—
201#2330—111no—
202#2275—111no—
203#1989—111no—
204#1948—111no—
205#1919—111no—
206#1918—111no—
207#1864—111no—
208#1864—111no—
209#1802—111no—
210#1776—111no—
211C4×#106—111no—
212#1768—111no—
213#1762—111no—
214C4×#102D1111yescharacteristic
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11—41no—
221C23×C11—41no—
222C23×C11C22×D411yescharacteristic
223D4×C11—22no—
224D4×C11—22no—
225D4×C11—22no—
226D4×C11C4×Q814yes—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—84no—
241C2×C4×C11C22⋊Q812yes—
242C2×C4×C11C22⋊Q812yes—
243C2×C4×C11C23×C411yescharacteristic
244C2×C4×C11C22×Q811yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—21no—
252C2×Dic11—21no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—21no—
256C2×Dic11—21no—
257C2×Dic11—22no—
258C2×Dic11—21no—
259C2×Dic11—21no—
260C2×Dic11—21no—
261C2×Dic11—21no—
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—84no—
272C2×Dic11—84no—
273C2×Dic11C4×D412yes—
274C2×Dic11C4×D412yes—
275C8×C11—22no—
276C8×C11—41no—
277C11⋊C8—22no—
278C11⋊C8—41no—
279C2×#125—111no—
280C2×C4×D4—111no—
281C2×C4×D4—111no—
282C2×C4×D4C2×D1111yescharacteristic
283#478—118no—
284C2×#107—111no—
285C2×#106—111no—
286C2×#106—111no—
287C2×#106—111no—
288C2×C4⋊C8—111no—
289C2×C4⋊C8—111no—
290C2×#102—111no—
291C2×#102—111no—
292C2×#102C2×D1111yescharacteristic
293C2×#102C2×D1111yescharacteristic
294C2×#97—111no—
295C2×C4×C8C2×D1111yescharacteristic
296#389—111no—
297#389—111no—
298#389—221no—
299#389—221no—
300#387—221no—
301#387—221no—
302#384—111no—
303C4×C4⋊C4—111no—
304C4×C4⋊C4—111no—
305C4×C4⋊C4—111no—
306C4×C4⋊C4—111no—
307C4×C4⋊C4C2×D1111yescharacteristic
308C4×C22⋊C4—221no—
309C4×C22⋊C4—221no—
310C4×C22⋊C4—221no—
311#376—111no—
312C2×#95—221no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340C2×D1111yescharacteristic
320#340C2×D1111yescharacteristic
321#336—111no—
322#336—111no—
323C22×C11—24no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—42no—
328C22×C11—42no—
329C22×C11—42no—
330C22×C11C2×C4×D411yescharacteristic
331C22×C11C2×C22⋊Q811yescharacteristic
332C22×C11#52511yescharacteristic
333C22×C11#57611yescharacteristic
334C22×C11#57711yescharacteristic
335C22×C11#57711yescharacteristic
336C22×C11#57711yescharacteristic
337C4×C11—22no—
338C4×C11—22no—
339C4×C11—42no—
340C4×C11—42no—
341C4×C11—81no—
342C4×C11C2×C4×Q811yescharacteristic
343C4×C11C4×#4111yescharacteristic
344C4×C11#52911yescharacteristic
345C4×C11#53311yescharacteristic
346Dic11—22no—
347Dic11—22no—
348Dic11—41no—
349Dic11—41no—
350Dic11—42no—
351Dic11—42no—
352Dic11—42no—
353Dic11—81no—
354C22×D4C22×D1111yescharacteristic
355C23×C4—21no—
356C23×C4—221no—
357C23×C4—221no—
358C22×C8—111no—
359C22×C8—111no—
360C22×C8C22×D1111yescharacteristic
361C22×C8C22×D1111yescharacteristic
362#125—114no—
363#125—222no—
364C4×D4—22no—
365C4×D4—114no—
366C4×D4—222no—
367C4×D4—222no—
368C4×D4—222no—
369C4×D4Dic2214yes—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C22⋊C4—21no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C42—21no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—221no—
390C2×C42—221no—
391C2×C42—221no—
392C2×C42—221no—
393C2×C42C22×D1111yescharacteristic
394#107—114no—
395#106—114no—
396#106—222no—
397#106—222no—
398C4⋊C8—114no—
399C4⋊C8—222no—
400#102—22no—
401#102—114no—
402#102—222no—
403#102C4×D1114yes—
404#97—222no—
405C4×C8—22no—
406#95—21no—
407#95—111no—
408#95—111no—
409#95—111no—
410#95—111no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417C2×C11—44no—
418C2×C11C4×C22⋊Q811yescharacteristic
419C2×C11#294611yescharacteristic
420C2×C11#295211yescharacteristic
421C2×C11#308111yescharacteristic
422C2×C11#308411yescharacteristic
423C2×C11#311911yescharacteristic
424C2×C11#312311yescharacteristic
425C24—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4C2×Dic2212yes—
430C2×D4C2×C4×D1112yes—
431C2×D4#433912yes—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—24no—
435C22×C4—21no—
436C22×C4—81no—
437C22×C4—81no—
438C22×C4—111no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—224no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—224no—
447C22×C4—221no—
448C22×C4—881no—
449C22×C4—881no—
450C22×C4—881no—
451C22×C4—881no—
452C22×C4D4×D1111yescharacteristic
453C22×C4D4×D1111yescharacteristic
454C22×C4C23×D1111yescharacteristic
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—112no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8C2×C4×D1112yes—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—112no—
472C4⋊C4—112no—
473C4⋊C4—112no—
474C4⋊C4—224no—
475C4⋊C4—224no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—881no—
482C4⋊C4—881no—
483C4⋊C4—881no—
484C4⋊C4—881no—
485C4⋊C4C2×Dic2212yes—
486C4⋊C4C2×C4×D1112yes—
487C22⋊C4—24no—
488C22⋊C4—224no—
489C22⋊C4—224no—
490C42—81no—
491C42—112no—
492C42—112no—
493C42—221no—
494C42—221no—
495C42—881no—
496C42—881no—
497C42—881no—
498C42—881no—
499C42C2×Dic2212yes—
500C42#434112yes—
501C11#2161911yescharacteristic, complemented, Sylow
502C23—22no—
503C23—22no—
504C23—22no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23C2×D4×D1111yescharacteristic
510D4—22no—
511D4—22no—
512D4—22no—
513D4C4×Dic2214yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—84no—
528C2×C4—112no—
529C2×C4—112no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—221no—
537C2×C4—221no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—221no—
541C2×C4—221no—
542C2×C4—222no—
543C2×C4—441no—
544C2×C4—441no—
545C2×C4—441no—
546C2×C4—441no—
547C2×C4—441no—
548C2×C4—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4—884no—
553C2×C4—884no—
554C2×C4#6693112yes—
555C2×C4#6693112yes—
556C2×C4C22×Dic2211yescharacteristic
557C2×C4C22×C4×D1111yescharacteristic
558C2×C4C2×#433911yescharacteristic
559C2×C4C2×#434111yescharacteristic
560C2×C4#41×D1111yescharacteristic
561C2×C4#41×D1111yescharacteristic
562C8—22no—
563C8—41no—
564C8—222no—
565C8—441no—
566C22—24no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22C2×#6693111yescharacteristic
574C22C4×D4×D1111yescharacteristic
575C22#1062307811yescharacteristic
576C22#1062328811yescharacteristic
577C22#1062329311yescharacteristic
578C22#1062330111yescharacteristic
579C22#1062330111yescharacteristic
580C4—22no—
581C4—22no—
582C4—42no—
583C4—42no—
584C4—81no—
585C4—222no—
586C4—222no—
587C4—441no—
588C4—441no—
589C4—442no—
590C4—442no—
591C4—442no—
592C4—881no—
593C4C2×C4×Dic2211yescharacteristic
594C4#1062304811yescharacteristic
595C4C4×#434111yescharacteristic
596C4#1062306911yescharacteristic
597C2—44no—
598C2C4×#6693111yescharacteristic
599C2#1307744111yescharacteristic
600C2#1307749411yescharacteristic
601C2#1307844311yescharacteristic
602C2#1307847611yescharacteristic
603C2#1307881111yescharacteristic
604C2#1307886511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC4×C11×#102C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC4×#102D11
hypocenterC11#21619
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. #13071353C2semidirect
4. #13069572C2semidirect
5. #13069378C2semidirect
6. #13069193C2semidirect
7. #13069190C2semidirect
11. #13068514C2semidirect
12. C4×#66881C2semidirect
13. #13068474C2semidirect
47. #10622376C4semidirect
99. #66943C2×C4semidirect
117. #66881C2×C4semidirect
119. Dic11⋊C8C2×C4semidirect
121. #66871C2×C4semidirect
501. C11#21619semidirect

Maximal subgroups

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

subgroupindex
C2×#106223762
#130713532
#130709772
#130695722
#130693782
#130691932
#130691902
#130688792
#130688752
#130686142
#130685142
C4×#668812
#130684742
#130684412
C4×C11×#1022
#2161911