Finite Group Databasebeta

← #14764159

Subgroups — #14764159

Order 2816.

862 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×C4⋊C8C211yesmaximal, characteristic
2#13071020C211yesmaximal, characteristic
3#13071009C211yesmaximal, characteristic
4#13069386C211yesmaximal, characteristic, complemented
5#13069384C211yesmaximal, characteristic, complemented
6#13069382C211yesmaximal, characteristic, complemented
7#13069378C211yesmaximal, characteristic, complemented
8#13069376C211yesmaximal, characteristic, complemented
9#13069373C211yesmaximal, characteristic, complemented
10#13069371C211yesmaximal, characteristic, complemented
11#13068644C211yesmaximal, characteristic
12#13068642C211yesmaximal, characteristic
13#13068640C211yesmaximal, characteristic
14#13068638C211yesmaximal, characteristic
15C11×#1949C211yesmaximal, characteristic, complemented
16C22×C8×D11C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18C2×#66925—21no—
19C2×C42×D11C2211yescharacteristic
20C2×C11×#107C2211yescharacteristic
21C2×C11×#106C2211yescharacteristic
22C2×C11×C4⋊C8C2211yescharacteristic
23C11×#382C2211yescharacteristic
24C4×C11×C4⋊C4C2211yescharacteristic
25C2×#66882C2211yescharacteristic
26C2×#66881C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×Dic11⋊C8C2211yescharacteristic
29#10622600C2211yescharacteristic
30#10622600C2211yescharacteristic
31#10622600C2211yescharacteristic
32#10622600C2211yescharacteristic
33#10622589C2211yescharacteristic
34#10622589C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36C4⋊C4×Dic11C2211yescharacteristic
37C2×#66872C2211yescharacteristic
38C2×#66872C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622549C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43C4×Dic11⋊C4—21no—
44C2×C4⋊(C11⋊C8)C2211yescharacteristic
45D11×C4⋊C8C418yescomplemented
46#10622280—21no—
47#10622279—21no—
48#10622277—21no—
49#10622264—21no—
50#10622263—21no—
51#10622261—21no—
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54#10622189C2211yescharacteristic
55#10622189C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60C22×C4×D11D411yescharacteristic
61C22×C4×D11D411yescharacteristic
62C22×C4×D11C2311yescharacteristic
63C22×C8×C11C2311yescharacteristic
64C22×C8×C11C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C42×C11—21no—
70C2×C42×C11C2311yescharacteristic
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—21no—
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11—21no—
85C2×C4×Dic11—21no—
86C2×C4×Dic11D411yescharacteristic
87C2×C4×Dic11D411yescharacteristic
88C2×C4×Dic11C2311yescharacteristic
89C22×C11⋊C8C2311yescharacteristic
90C22×C11⋊C8C2311yescharacteristic
91C2×C8×D11—41no—
92C2×C8×D11—41no—
93C2×C8×D11—41no—
94C2×C8×D11—41no—
95C2×C8×D11C2×C414yes—
96C2×C8×D11C2×C414yes—
97#66925—44no—
98C42×D11C2×C414yes—
99C42×D11Q814yes—
100C11×#107—41no—
101C11×#106—41no—
102C11×C4⋊C8C2×C414yes—
103C11×#95—21no—
104C11×#95—21no—
105C11×#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115#66882—41no—
116#66881—41no—
117Dic11⋊C8C2×C414yes—
118Dic11⋊C8C2×C414yes—
119#66872—41no—
120#66872—41no—
121#66871—41no—
122#66871—41no—
123C4⋊(C11⋊C8)C2×C414yes—
124#21962—111nomaximal, Sylow
125C23×D11C2×D411yescharacteristic
126C22×C4×C11—21no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C22×Dic11—21no—
137C22×Dic11C2×D411yescharacteristic
138C22×Dic11C2×D411yescharacteristic
139C22×Dic11C2×D411yescharacteristic
140C2×C4×D11—22no—
141C2×C4×D11—22no—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—21no—
145C2×C4×D11—21no—
146C2×C4×D11—21no—
147C2×C4×D11—21no—
148C2×C4×D11C4⋊C414yes—
149C2×C4×D11C4⋊C414yes—
150C2×C4×D11C22×C412yes—
151C2×C4×D11C2×Q812yes—
152C2×C8×C11—21no—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11C22×C412yes—
157C2×C8×C11C22×C412yes—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—21no—
166C42×C11—42no—
167C42×C11C22×C412yes—
168C42×C11C2×Q812yes—
169(C2×D11)⋊C4—42no—
170(C2×D11)⋊C4—42no—
171(C2×D11)⋊C4—42no—
172(C2×D11)⋊C4—42no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181Dic11⋊C4—42no—
182Dic11⋊C4—42no—
183Dic11⋊C4—42no—
184Dic11⋊C4—42no—
185C4×Dic11—42no—
186C4×Dic11—42no—
187C4×Dic11—42no—
188C4×Dic11C4⋊C414yes—
189C4×Dic11C4⋊C414yes—
190C4×Dic11C22×C412yes—
191C4×Dic11C2×Q812yes—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8C22×C412yes—
197C2×C11⋊C8C22×C412yes—
198C8×D11—44no—
199C8×D11—44no—
200C22×C4⋊C8—111no—
201#2285—111no—
202#2283—111no—
203#1949—111no—
204#1949—111no—
205#1949—111no—
206#1949D1111yescharacteristic, complemented
207#1948—111no—
208#1948—111no—
209#1947—111no—
210#1947—111no—
211#1808—111no—
212#1808—111no—
213#1807—111no—
214#1807—111no—
215C23×C11C22×D411yescharacteristic
216C22×D11—21no—
217C22×D11—21no—
218C22×D11—21no—
219C22×D11—21no—
220C22×D11C2×C4⋊C412yes—
221C22×D11AGL(1,ℤ/8)12yes—
222C22×D11#13712yes—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—41no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
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×C11C2×C4⋊C412yes—
240C2×C4×C11C2×C4⋊C412yes—
241C2×C4×C11C23×C411yescharacteristic
242C2×C4×C11C22×Q811yescharacteristic
243C2×C4×C11H(5,𝔽2)11yescharacteristic
244C2×C4×C11H(5,𝔽2)11yescharacteristic
245C2×C4×C112−1+411yescharacteristic
246C2×C4×C112−1+411yescharacteristic
247C2×Dic11—21no—
248C2×Dic11—21no—
249C2×Dic11—21no—
250C2×Dic11—21no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11C2×C4⋊C412yes—
264C2×Dic11C2×C4⋊C412yes—
265C2×Dic11C2×C4⋊C412yes—
266C2×Dic11#13512yes—
267C2×Dic11#13512yes—
268C4×D11—28no—
269C4×D11—22no—
270C4×D11—22no—
271C4×D11—22no—
272C4×D11—22no—
273C4×D11—28no—
274C8×C11—22no—
275C8×C11—22no—
276C11⋊C8—22no—
277C11⋊C8—22no—
278C23×C8—111no—
279C23×C8—111no—
280C2×#117—221no—
281C22×C42—111no—
282C2×#107—111no—
283C2×#107—111no—
284C2×#107—111no—
285C2×#107C2×D1111yescharacteristic
286C2×#106—111no—
287C2×#106—111no—
288C2×#106—111no—
289C2×#106C2×D1111yescharacteristic
290C2×C4⋊C8—111no—
291C2×C4⋊C8—111no—
292C2×C4⋊C8—111no—
293C2×C4⋊C8—118no—
294C2×C4⋊C8C2×D1111yescharacteristic
295#384—111no—
296#384—111no—
297#383—221no—
298#382—111no—
299#382—221no—
300#382C2×D1111yescharacteristic
301#381—221no—
302#380—111no—
303#380—111no—
304#380—111no—
305#380—111no—
306#380—221no—
307C4×C4⋊C4—111no—
308C4×C4⋊C4—111no—
309C4×C4⋊C4—111no—
310C4×C4⋊C4—221no—
311C4×C4⋊C4C2×D1111yescharacteristic
312C4×C22⋊C4—221no—
313#376—221no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#340—111no—
319#340—111no—
320#340C2×D1111yescharacteristic
321#340C2×D1111yescharacteristic
322C22×C11C22×C4⋊C411yescharacteristic
323C22×C11#53711yescharacteristic
324C22×C11#53711yescharacteristic
325C22×C11C2×#13511yescharacteristic
326C22×C11C2×#13511yescharacteristic
327C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
328C22×C11C2×#13711yescharacteristic
329C2×D11—22no—
330C2×D11—22no—
331C2×D11—22no—
332C2×D11—22no—
333C2×D11—22no—
334C2×D11—22no—
335C2×D11#42814yes—
336C4×C11—22no—
337C4×C11—22no—
338C4×C11—81no—
339C4×C11—81no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11#51811yescharacteristic
343C4×C11#51911yescharacteristic
344C4×C11#54411yescharacteristic
345C4×C11#54411yescharacteristic
346Dic11—22no—
347Dic11—22no—
348Dic11—81no—
349Dic11—81no—
350Dic11—81no—
351Dic11—81no—
352Dic11#42714yes—
353C23×C4—111no—
354C23×C4—111no—
355C23×C4—111no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—114no—
359C22×C8—114no—
360C22×C8—441no—
361C22×C8—441no—
362C22×C8—441no—
363C22×C8—441no—
364C22×C8C22×D1111yescharacteristic
365C22×C8C22×D1111yescharacteristic
366#117—444no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—111no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1111yescharacteristic
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C42—21no—
384C2×C42—111no—
385C2×C42—111no—
386C2×C42—111no—
387C2×C42—114no—
388C2×C42—114no—
389C2×C42—221no—
390C2×C42—221no—
391C2×C42—221no—
392C2×C42C22×D1111yescharacteristic
393#107—41no—
394#107—441no—
395#107—441no—
396#107—441no—
397#106—41no—
398#106—441no—
399#106—441no—
400#106—441no—
401C4⋊C8—114no—
402C4⋊C8—114no—
403C4⋊C8—114no—
404C4⋊C8C4×D1114yes—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95—221no—
417C2×C11#231611yescharacteristic
418C2×C11C2×#42711yescharacteristic
419C2×C11C2×#42811yescharacteristic
420C2×C11#324711yescharacteristic
421C2×C11#324711yescharacteristic
422C2×C11#324811yescharacteristic
423C2×C11#324811yescharacteristic
424D11—24no—
425C24—111no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—114no—
434C22×C4—114no—
435C22×C4—112no—
436C22×C4—112no—
437C22×C4—222no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4—221no—
446C22×C4—221no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4D4×D1111yescharacteristic
450C22×C4D4×D1111yescharacteristic
451C22×C4C23×D1111yescharacteristic
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—112no—
457C2×C8—112no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—444no—
463C2×C8—444no—
464C2×C8C2×C4×D1112yes—
465C2×C8C2×C4×D1112yes—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—221no—
479C4⋊C4—221no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—442no—
483C4⋊C4—442no—
484C4⋊C4—442no—
485C4⋊C4—442no—
486C22⋊C4—442no—
487C22⋊C4—442no—
488C22⋊C4—442no—
489C22⋊C4—442no—
490C42—42no—
491C42—114no—
492C42—114no—
493C42—112no—
494C42—112no—
495C42—442no—
496C42—442no—
497C42—442no—
498C42C2×C4×D1112yes—
499C42Q8×D1112yes—
500C11#2196211yescharacteristic, complemented, Sylow
501C23—112no—
502C23—112no—
503C23—112no—
504C23—221no—
505C23—221no—
506C23—221no—
507C23—221no—
508C23C2×D4×D1111yescharacteristic
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—112no—
526C2×C4—112no—
527C2×C4—112no—
528C2×C4—112no—
529C2×C4—112no—
530C2×C4—228no—
531C2×C4—228no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—221no—
536C2×C4—222no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—222no—
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—441no—
549C2×C4—441no—
550C2×C4—441no—
551C2×C4—441no—
552C2×C4C4⋊C4×D1112yes—
553C2×C4C4⋊C4×D1112yes—
554C2×C4C22×C4×D1111yescharacteristic
555C2×C4#6703711yescharacteristic
556C2×C4C2×Q8×D1111yescharacteristic
557C2×C4#6704011yescharacteristic
558C2×C4#6704211yescharacteristic
559C2×C4#6704311yescharacteristic
560C8—22no—
561C8—22no—
562C8—222no—
563C8—222no—
564C22—114no—
565C22—222no—
566C22—222no—
567C22—222no—
568C22—222no—
569C22—222no—
570C22—222no—
571C22C2×C4⋊C4×D1111yescharacteristic
572C22#1062313911yescharacteristic
573C22#1062316011yescharacteristic
574C22D11×#13511yescharacteristic
575C22D11×#13511yescharacteristic
576C22D11×AGL(1,ℤ/8)11yescharacteristic
577C22D11×#13711yescharacteristic
578C4—22no—
579C4—22no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—114no—
585C4—222no—
586C4—222no—
587C4—881no—
588C4—881no—
589C4—881no—
590C4—881no—
591C4#1062307611yescharacteristic
592C4#1062310311yescharacteristic
593C4#1062322011yescharacteristic
594C4#1062326011yescharacteristic
595C2—224no—
596C2#1307123111yescharacteristic
597C2D11×#42711yescharacteristic
598C2D11×#42811yescharacteristic
599C2#1307993911yescharacteristic
600C2#1307994111yescharacteristic
601C2#1307995011yescharacteristic
602C2#1307995211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1949C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1949D11
hypocenterC11#21962
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1949

Complements

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

NH ≅ G/Ntype
4. #13069386C2semidirect
5. #13069384C2semidirect
6. #13069382C2semidirect
7. #13069378C2semidirect
8. #13069376C2semidirect
9. #13069373C2semidirect
10. #13069371C2semidirect
15. C11×#1949C2semidirect
45. D11×C4⋊C8C4semidirect
206. #1949D11semidirect
500. C11#21962semidirect

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊C82
#130710202
#130710092
#130693862
#130693842
#130693822
#130693782
#130693762
#130693732
#130693712
#130686442
#130686422
#130686402
#130686382
C11×#19492
#2196211