Finite Group Databasebeta

← #14822443

Subgroups — #14822443

Order 2816.

712 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
1#13073143C211yesmaximal, characteristic, complemented
2#13070019C211yesmaximal, characteristic
3#13070004C211yesmaximal, characteristic
4#13069852C211yesmaximal, characteristic
5#13069852C211yesmaximal, characteristic
6#13069295C211yesmaximal, characteristic, complemented
7#13069254C211yesmaximal, characteristic, complemented
8#13069194C211yesmaximal, characteristic, complemented
9#13069187C211yesmaximal, characteristic, complemented
10#13069175C211yesmaximal, characteristic, complemented
11#13068884C211yesmaximal, characteristic, complemented
12#13068877C211yesmaximal, characteristic
13#13068621C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic
15C11×#2367C211yesmaximal, characteristic
16C2×C11×#124C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C11×#391C2211yescharacteristic
20C11×#390C2211yescharacteristic
21C11×#388—21no—
22C11×#388—21no—
23C11×#385—21no—
24C4×C11×C4⋊C4C2211yescharacteristic
25C4×C11×C4⋊C4C2211yescharacteristic
26C4×C11×C22⋊C4—21no—
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35#10622597—21no—
36#10622594—21no—
37C2×#66872C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39#10622548C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41#10622541C2211yescharacteristic
42#10622541C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622270—21no—
48#10622260—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C11×#124—22no—
63C11×#124—22no—
64C4×Q8×C11—22no—
65C4×Q8×C11—41no—
66C4×D4×C11—22no—
67C4×D4×C11—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4D411yescharacteristic
70C2×C11×C4⋊C4D411yescharacteristic
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C42×C11—21no—
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C42×C11C2311yescharacteristic
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×C4×Dic11—21no—
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95D411yescharacteristic
102C11×#95D411yescharacteristic
103#66899—22no—
104#66899—22no—
105#66899—22no—
106#66899—41no—
107#66896—22no—
108#66896—22no—
109#66896—22no—
110#66896—41no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116#66872—22no—
117#66871—22no—
118C4⋊(C11⋊C8)—41no—
119C4×C11⋊C8—41no—
120#26763—111nomaximal, Sylow
121C24×C11—21no—
122C2×Q8×C11—21no—
123C2×Q8×C11—21no—
124C2×Q8×C11—21no—
125C2×Q8×C11—21no—
126C2×Q8×C11—21no—
127C2×Q8×C11#4112yes—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—21no—
132C2×D4×C11—21no—
133C2×D4×C11#4112yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—42no—
138C22×C4×C11—42no—
139C22×C4×C11—81no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C11×C4⋊C4—22no—
152C11×C4⋊C4—22no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—21no—
156C11×C4⋊C4—42no—
157C11×C4⋊C4#4112yes—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—42no—
161C11×C22⋊C4—42no—
162C11×C22⋊C4—81no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—21no—
169C42×C11—42no—
170C42×C11—81no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11—21no—
177C4⋊Dic11—21no—
178C4⋊Dic11—81no—
179C4⋊Dic11—81no—
180C4⋊Dic11#4112yes—
181Dic11⋊C4—42no—
182Dic11⋊C4—81no—
183Dic11⋊C4—81no—
184Dic11⋊C4—81no—
185C4×Dic11—81no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8—21no—
188C2×C11⋊C8—21no—
189C2×C11⋊C8—21no—
190C2×C11⋊C8—21no—
191C2×C11⋊C8—21no—
192C2×C11⋊C8—21no—
193C2×C11⋊C8—21no—
194C2×C11⋊C8—21no—
195C2×C11⋊C8—21no—
196C2×C11⋊C8—21no—
197C2×C11⋊C8—21no—
198#2507—111no—
199#2367D1111yescharacteristic
200#2071—111no—
201#2067—111no—
202#2042—111no—
203#2042—111no—
204#1933—111no—
205#1928—111no—
206#1919—111no—
207#1918—111no—
208#1916—111no—
209#1865—111no—
210#1864—111no—
211#1803—111no—
212C4×#102—111no—
213C23×C11—22no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11—41no—
219C23×C11—41no—
220C23×C11C22×D411yescharacteristic
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—41no—
224Q8×C11—41no—
225D4×C11—22no—
226D4×C11—22no—
227D4×C11—41no—
228D4×C11—41no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—22no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—41no—
253C2×C4×C11—41no—
254C2×C4×C11—84no—
255C2×C4×C11#13512yes—
256C2×C4×C11#13712yes—
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C112−1+411yescharacteristic
263C2×Dic11—22no—
264C2×Dic11—41no—
265C2×Dic11—41no—
266C2×Dic11—41no—
267C2×Dic11—41no—
268C2×Dic11—41no—
269C2×Dic11—41no—
270C2×Dic11—41no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—41no—
274C2×Dic11—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C11⋊C8—41no—
278C11⋊C8—41no—
279C2×#124C2×D1111yescharacteristic
280C2×C4×Q8C2×D1111yescharacteristic
281C2×C4×D4C2×D1111yescharacteristic
282C2×#107—111no—
283C2×#106—111no—
284C2×C4⋊C8—111no—
285C2×#103—111no—
286C2×#103—111no—
287C2×#103—111no—
288C2×#103—111no—
289C2×#102—111no—
290C2×#102—111no—
291C2×#102—111no—
292C2×#102—111no—
293C2×C4×C8—111no—
294#398—221no—
295#398—221no—
296#391C2×D1111yescharacteristic
297#390C2×D1111yescharacteristic
298#389—111no—
299#389—111no—
300#389—111no—
301#389—111no—
302#389—221no—
303#388—21no—
304#388—21no—
305#387—221no—
306#385—21no—
307#384—111no—
308C4×C4⋊C4—111no—
309C4×C4⋊C4C2×D1111yescharacteristic
310C4×C4⋊C4C2×D1111yescharacteristic
311C4×C22⋊C4—21no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#336—111no—
319#336—111no—
320#336—111no—
321#336—111no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11—81no—
328C22×C11—81no—
329C22×C11#52511yescharacteristic
330C22×C11#54611yescharacteristic
331C22×C11#54811yescharacteristic
332C22×C11C2×#13511yescharacteristic
333C22×C11C2×#13711yescharacteristic
334C22×C11#57611yescharacteristic
335C22×C11#57711yescharacteristic
336C4×C11—22no—
337C4×C11—22no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—42no—
341C4×C11—41no—
342C4×C11—41no—
343C4×C11—42no—
344C4×C11—81no—
345C4×C11#52911yescharacteristic
346C4×C11#53911yescharacteristic
347C4×C11#55211yescharacteristic
348C4×C11#55311yescharacteristic
349Dic11—42no—
350Dic11—81no—
351Dic11—81no—
352Dic11—81no—
353C22×Q8C22×D1111yescharacteristic
354C22×D4C22×D1111yescharacteristic
355C23×C4—21no—
356C22×C8—111no—
357C22×C8—111no—
358C22×C8—111no—
359C22×C8—111no—
360#124—22no—
361#124—22no—
362C4×Q8—22no—
363C4×Q8—41no—
364C4×D4—22no—
365C4×D4—41no—
366C2×C4⋊C4—21no—
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⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4C22⋊D1111yescharacteristic
378C2×C4⋊C4C22⋊D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42—221no—
389C2×C42C22×D1111yescharacteristic
390C2×C42C22×D1111yescharacteristic
391C2×C42C22×D1111yescharacteristic
392#107—222no—
393#106—222no—
394C4⋊C8—441no—
395#103—222no—
396#103—222no—
397#103—222no—
398#103—441no—
399#102—222no—
400#102—222no—
401#102—222no—
402#102—441no—
403C4×C8—441no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—221no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95C22⋊D1111yescharacteristic
413#95C22⋊D1111yescharacteristic
414C2×C11—82no—
415C2×C11#246011yescharacteristic
416C2×C11#310711yescharacteristic
417C2×C11#311911yescharacteristic
418C2×C11#330111yescharacteristic
419C2×C11#331411yescharacteristic
420C2×C11#336111yescharacteristic
421C2×C11#336911yescharacteristic
422C24—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8#433912yes—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4#433912yes—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—81no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—221no—
444C22×C4—221no—
445C22×C4C2×C22⋊D1111yescharacteristic
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C2×C22⋊D1111yescharacteristic
450C22×C4C2×C22⋊D1111yescharacteristic
451C22×C4C23×D1111yescharacteristic
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C2×C8—221no—
459C2×C8—221no—
460C2×C8—221no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C4⋊C4—22no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—42no—
470C4⋊C4—112no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—442no—
479C4⋊C4—881no—
480C4⋊C4—881no—
481C4⋊C4—881no—
482C4⋊C4—881no—
483C4⋊C4—881no—
484C4⋊C4#434112yes—
485C22⋊C4—24no—
486C22⋊C4—24no—
487C22⋊C4—42no—
488C22⋊C4—42no—
489C22⋊C4—81no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—42no—
497C42—81no—
498C42—881no—
499C11#2676311yescharacteristic, complemented, Sylow
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23C22×C22⋊D1111yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—41no—
511Q8—41no—
512D4—22no—
513D4—22no—
514D4—41no—
515D4—41no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—84no—
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—441no—
553C2×C4—441no—
554C2×C4#6700312yes—
555C2×C4#6700412yes—
556C2×C4C2×#433911yescharacteristic
557C2×C4C2×#433911yescharacteristic
558C2×C4C2×#434111yescharacteristic
559C2×C4#6703711yescharacteristic
560C2×C4#41×D1111yescharacteristic
561C2×C4#6704311yescharacteristic
562C8—441no—
563C8—441no—
564C8—441no—
565C8—441no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22#1062332211yescharacteristic
574C22#1062333711yescharacteristic
575C22C2×#6700311yescharacteristic
576C22C2×#6700411yescharacteristic
577C22#1062336211yescharacteristic
578C22#1062336611yescharacteristic
579C22#1062336811yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—41no—
584C4—42no—
585C4—41no—
586C4—42no—
587C4—41no—
588C4—81no—
589C4—442no—
590C4—881no—
591C4—881no—
592C4—881no—
593C4#1062306911yescharacteristic
594C4#1062307111yescharacteristic
595C4#1062307211yescharacteristic
596C4#1062309511yescharacteristic
597C2—82no—
598C2#1307256211yescharacteristic
599C2#1307868711yescharacteristic
600C2#1307881511yescharacteristic
601C2#1308051811yescharacteristic
602C2#1308069711yescharacteristic
603C2#1308127211yescharacteristic
604C2#1308135211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2367C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2367D11
hypocenterC11#26763
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2367

Complements

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

NH ≅ G/Ntype
1. #13073143C2semidirect
6. #13069295C2semidirect
7. #13069254C2semidirect
8. #13069194C2semidirect
9. #13069187C2semidirect
10. #13069175C2semidirect
11. #13068884C2semidirect
13. #13068621C2semidirect
499. C11#26763semidirect

Maximal subgroups

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

subgroupindex
#130731432
#130700192
#130700042
#130698522
#130692952
#130692542
#130691942
#130691872
#130691752
#130688842
#130688772
#130686212
C4×#668962
C11×#23672
#2676311