Finite Group Databasebeta

← #14812733

Subgroups — #14812733

Order 2816.

750 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073650C211yesmaximal, characteristic, complemented
2#13071561C211yesmaximal, characteristic
3#13070143C211yesmaximal, characteristic
4#13070141C211yesmaximal, characteristic
5#13070005C211yesmaximal, characteristic
6#13070001C211yesmaximal, characteristic
7#13069374C211yesmaximal, characteristic, complemented
8#13069373C211yesmaximal, characteristic, complemented
9#13069373C211yesmaximal, characteristic, complemented
10#13069333C211yesmaximal, characteristic, complemented
11#13069186C211yesmaximal, characteristic, complemented
12#13068774C211yesmaximal, characteristic, complemented
13#13068615C211yesmaximal, characteristic
14#13068430C211yesmaximal, characteristic
15C11×#1918C211yesmaximal, characteristic, complemented
16C2×#66946C2211yescharacteristic
17C2×#66942—21no—
18C2×#66925—21no—
19C2×C11×#107C2211yescharacteristic
20C11×#389C2211yescharacteristic
21C4×C11×C4⋊C4C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×#66885C2211yescharacteristic
24C2×#66882C2211yescharacteristic
25C2×#66882C2211yescharacteristic
26C2×Dic11⋊C8C2211yescharacteristic
27C2×Dic11⋊C8C2211yescharacteristic
28C2×C8×Dic11C2211yescharacteristic
29#10622601C2211yescharacteristic
30#10622596—21no—
31#10622589C2211yescharacteristic
32#10622589C2211yescharacteristic
33#10622589C2211yescharacteristic
34C4⋊C4×Dic11C2211yescharacteristic
35C4⋊C4×Dic11C2211yescharacteristic
36#10622586C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41C2×#66871C2211yescharacteristic
42#10622553—21no—
43#10622552C2211yescharacteristic
44#10622548C2211yescharacteristic
45C4×Dic11⋊C4C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47#10622282—21no—
48#10622280—21no—
49#10622270—21no—
50#10622260—21no—
51C11×#340C2211yescharacteristic
52C11×#340C2211yescharacteristic
53C11×#340C2211yescharacteristic
54C11×#336C2211yescharacteristic
55#10622188C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C8×C11C2311yescharacteristic
62C22×C8×C11C2311yescharacteristic
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4C2311yescharacteristic
65C2×C11×C4⋊C4C2311yescharacteristic
66C2×C11×C4⋊C4C2311yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C42×C11—21no—
69C2×C42×C11C2311yescharacteristic
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—21no—
73C2×(C2×D11)⋊C4—21no—
74C2×(C2×D11)⋊C4—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×C4⋊Dic11C2311yescharacteristic
80C2×Dic11⋊C4—21no—
81C2×Dic11⋊C4—21no—
82C2×Dic11⋊C4—21no—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4D411yescharacteristic
88C2×Dic11⋊C4D411yescharacteristic
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11C2311yescharacteristic
92C2×C4×Dic11C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95#66946—22no—
96#66946Q814yes—
97#66942—44no—
98#66925—44no—
99C11×#107—22no—
100C11×#95—21no—
101C11×#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104C11⋊#95—21no—
105C11⋊#95D411yescharacteristic
106C11⋊#95D411yescharacteristic
107#66885—22no—
108#66885—41no—
109#66882—22no—
110#66882—41no—
111Dic11⋊C8—22no—
112Dic11⋊C8—22no—
113C8×Dic11—22no—
114#66873—22no—
115#66873—41no—
116#66871—41no—
117#66871—41no—
118#66871—41no—
119C4⋊(C11⋊C8)—22no—
120#26086—111nomaximal, Sylow
121C23×D11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2411yescharacteristic
129C22×Dic11—21no—
130C22×Dic11—21no—
131C22×Dic11—21no—
132C22×Dic11C2×D411yescharacteristic
133C22×Dic11C2×D411yescharacteristic
134C22×Dic11C2×D411yescharacteristic
135C22×Dic11C2×D411yescharacteristic
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44C2×Q812yes—
142C2×C4×D11—24no—
143C2×C4×D11—42no—
144C2×C4×D11—42no—
145C2×C8×C11—21no—
146C2×C8×C11—21no—
147C2×C8×C11—21no—
148C2×C8×C11—21no—
149C2×C8×C11—21no—
150C2×C8×C11#4112yes—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—21no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—42no—
159C11×C4⋊C4C2×Q812yes—
160C42×C11—21no—
161C42×C11—21no—
162C42×C11—42no—
163(C2×D11)⋊C4—24no—
164(C2×D11)⋊C4—42no—
165(C2×D11)⋊C4—42no—
166(C2×D11)⋊C4—81no—
167(C2×D11)⋊C4—81no—
168C4⋊Dic11—21no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—42no—
175C4⋊Dic11—81no—
176Dic11⋊C4—22no—
177Dic11⋊C4—42no—
178Dic11⋊C4—42no—
179Dic11⋊C4—42no—
180Dic11⋊C4—42no—
181Dic11⋊C4—81no—
182Dic11⋊C4—81no—
183Dic11⋊C4—81no—
184Dic11⋊C4D814yes—
185C4×Dic11—21no—
186C4×Dic11—21no—
187C4×Dic11—42no—
188C4×Dic11—42no—
189C4×Dic11C2×Q812yes—
190C4×Dic11#4112yes—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8#4112yes—
197#2552—111no—
198#2354—111no—
199#2093—111no—
200#2093—111no—
201#2067—111no—
202#2067—111no—
203#1947—111no—
204#1947—111no—
205#1947—111no—
206#1939—111no—
207#1918—111no—
208#1918D1111yescharacteristic, complemented
209#1845—111no—
210#1802—111no—
211C4×#102—111no—
212C23×C11C22×D411yescharacteristic
213C22×D11—22no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C22×D11—41no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—22no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—41no—
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×C11C2×D812yes—
238C2×C4×C11C22×Q811yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×C4×C11C2×#4111yescharacteristic
242C2×C4×C11H(5,𝔽2)11yescharacteristic
243C2×C4×C112−1+411yescharacteristic
244C2×Dic11—21no—
245C2×Dic11—21no—
246C2×Dic11—21no—
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×Dic11C22⋊Q812yes—
261C2×Dic11C22⋊Q812yes—
262C2×Dic11C2×D812yes—
263C2×Dic11C2×D812yes—
264C2×Dic11#13712yes—
265D44—22no—
266D44—22no—
267D44—41no—
268D44—41no—
269C4×D11—48no—
270C8×C11—22no—
271C8×C11—41no—
272C11⋊C8—22no—
273C11⋊C8—41no—
274C2×#125—221no—
275C2×C4×D4—111no—
276C2×#117—221no—
277C2×#107—111no—
278C2×#107—111no—
279C2×#107—111no—
280C2×#107—111no—
281C2×#107—111no—
282C2×#107C2×D1111yescharacteristic
283C2×C4⋊C8—111no—
284C2×C4⋊C8—111no—
285C2×C4⋊C8—111no—
286C2×#102—111no—
287C2×#102—111no—
288C2×#102—111no—
289C2×#102—111no—
290C2×C4×C8—111no—
291#398—221no—
292#398—221no—
293#390—111no—
294#390—111no—
295#389—111no—
296#389—221no—
297#389C2×D1111yescharacteristic
298#388—221no—
299#388—221no—
300#384—111no—
301#384—111no—
302#384—111no—
303#384—111no—
304#380—221no—
305C4×C4⋊C4—111no—
306C4×C4⋊C4—111no—
307C4×C4⋊C4—111no—
308C4×C4⋊C4C2×D1111yescharacteristic
309#340—111no—
310#340—111no—
311#340—111no—
312#340C2×D1111yescharacteristic
313#340C2×D1111yescharacteristic
314#340C2×D1111yescharacteristic
315#336—111no—
316#336C2×D1111yescharacteristic
317C22×C11C2×C22⋊Q811yescharacteristic
318C22×C11#54711yescharacteristic
319C22×C11#55011yescharacteristic
320C22×C11C22×D811yescharacteristic
321C22×C11C2×#13711yescharacteristic
322C22×C11#57611yescharacteristic
323C22×C11#57811yescharacteristic
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C4×C11—22no—
332C4×C11—41no—
333C4×C11—42no—
334C4×C11—81no—
335C4×C11—81no—
336C4×C11—81no—
337C4×C11#53311yescharacteristic
338C4×C11#54411yescharacteristic
339C4×C11#55211yescharacteristic
340C4×C11#55311yescharacteristic
341Dic11—22no—
342Dic11—22no—
343Dic11—41no—
344Dic11—81no—
345Dic11—81no—
346Dic11—81no—
347Dic11#47414yes—
348C22×D4—111no—
349C23×C4—221no—
350C22×C8—111no—
351C22×C8—111no—
352C22×C8C22×D1111yescharacteristic
353C22×C8C22×D1111yescharacteristic
354#125—444no—
355C4×D4—114no—
356C4×D4—222no—
357#117—444no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—111no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4—221no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C22⋊C4—221no—
378C2×C22⋊C4—221no—
379C2×C22⋊C4—221no—
380C2×C22⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C42—21no—
383C2×C42—111no—
384C2×C42—111no—
385C2×C42—221no—
386C2×C42—221no—
387C2×C42C22×D1111yescharacteristic
388#107—22no—
389#107—222no—
390#107—441no—
391#107—441no—
392#107—441no—
393#107—441no—
394C4⋊C8—222no—
395C4⋊C8—222no—
396C4⋊C8—222no—
397#102—222no—
398#102—222no—
399#102—441no—
400#102—441no—
401C4×C8—222no—
402#95—21no—
403#95—21no—
404#95—111no—
405#95—111no—
406#95—221no—
407#95—221no—
408#95—221no—
409C2×C11#244111yescharacteristic
410C2×C11C2×#47411yescharacteristic
411C2×C11#308311yescharacteristic
412C2×C11#333411yescharacteristic
413C2×C11#335711yescharacteristic
414C2×C11#339111yescharacteristic
415C2×C11#339811yescharacteristic
416D11—82no—
417C24—221no—
418C2×D4—112no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—221no—
422C2×D4—221no—
423C2×D4—221no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—111no—
429C22×C4—111no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—224no—
433C22×C4—221no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—442no—
437C22×C4—442no—
438C22×C4D4×D1111yescharacteristic
439C22×C4D4×D1111yescharacteristic
440C22×C4C23×D1111yescharacteristic
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—112no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8#433912yes—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—42no—
461C4⋊C4—114no—
462C4⋊C4—222no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C4⋊C4—221no—
468C4⋊C4—221no—
469C4⋊C4—442no—
470C4⋊C4—442no—
471C4⋊C4—442no—
472C4⋊C4—442no—
473C4⋊C4—442no—
474C4⋊C4—881no—
475C4⋊C4—881no—
476C4⋊C4—881no—
477C4⋊C4—881no—
478C4⋊C4Q8×D1112yes—
479C22⋊C4—224no—
480C22⋊C4—442no—
481C22⋊C4—442no—
482C22⋊C4—881no—
483C22⋊C4—881no—
484C42—21no—
485C42—21no—
486C42—42no—
487C42—112no—
488C42—112no—
489C42—221no—
490C42—221no—
491C42—442no—
492C42—442no—
493C11#2608611yescharacteristic, complemented, Sylow
494C23—222no—
495C23—441no—
496C23—441no—
497C23—441no—
498C23—441no—
499C23—441no—
500C23—441no—
501C23C2×D4×D1111yescharacteristic
502D4—222no—
503D4—222no—
504D4—441no—
505D4—441no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—41no—
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—112no—
524C2×C4—112no—
525C2×C4—112no—
526C2×C4—112no—
527C2×C4—112no—
528C2×C4—221no—
529C2×C4—221no—
530C2×C4—221no—
531C2×C4—221no—
532C2×C4—221no—
533C2×C4—221no—
534C2×C4—221no—
535C2×C4—448no—
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×C4D8×D1112yes—
546C2×C4C2×#433911yescharacteristic
547C2×C4C2×Q8×D1111yescharacteristic
548C2×C4#41×D1111yescharacteristic
549C2×C4#41×D1111yescharacteristic
550C2×C4#6704211yescharacteristic
551C2×C4#6704311yescharacteristic
552C8—22no—
553C8—41no—
554C8—222no—
555C8—441no—
556C22—442no—
557C22—442no—
558C22—442no—
559C22—881no—
560C22—881no—
561C22—881no—
562C22—881no—
563C22#1062308411yescharacteristic
564C22D11×C22⋊Q811yescharacteristic
565C22#1062318611yescharacteristic
566C22C2×D8×D1111yescharacteristic
567C22#1062330011yescharacteristic
568C22D11×#13711yescharacteristic
569C22#1062331011yescharacteristic
570C4—22no—
571C4—42no—
572C4—41no—
573C4—81no—
574C4—81no—
575C4—81no—
576C4—114no—
577C4—222no—
578C4—222no—
579C4—441no—
580C4—881no—
581C4—881no—
582C4—881no—
583C4#1062306211yescharacteristic
584C4#1062310911yescharacteristic
585C4#1062322011yescharacteristic
586C4#1062324011yescharacteristic
587C2—882no—
588C2#1307232811yescharacteristic
589C2D11×#47411yescharacteristic
590C2#1307847011yescharacteristic
591C2#1308095811yescharacteristic
592C2#1308124011yescharacteristic
593C2#1308159011yescharacteristic
594C2#1308164811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1918C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1918D11
hypocenterC11#26086
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1918

Complements

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

NH ≅ G/Ntype
1. #13073650C2semidirect
7. #13069374C2semidirect
8. #13069373C2semidirect
9. #13069373C2semidirect
10. #13069333C2semidirect
11. #13069186C2semidirect
12. #13068774C2semidirect
15. C11×#1918C2semidirect
208. #1918D11semidirect
493. C11#26086semidirect

Maximal subgroups

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

subgroupindex
#130736502
#130715612
#130701432
#130701412
#130700052
#130700012
#130693742
#130693732
#130693332
#130691862
#130687742
#130686152
#130684302
C11×#19182
#2608611