Finite Group Databasebeta

← #14853544

Subgroups — #14853544

Order 2816.

690 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13074591C211yesmaximal, characteristic, complemented
2#13070178C211yesmaximal, characteristic, complemented
3#13070173C211yesmaximal, characteristic, complemented
4#13069852C211yesmaximal, characteristic
5#13069852C211yesmaximal, characteristic
6#13069316C211yesmaximal, characteristic
7#13069309C211yesmaximal, characteristic, complemented
8#13069302C211yesmaximal, characteristic
9#13069295C211yesmaximal, characteristic, complemented
10#13068631C211yesmaximal, characteristic, complemented
11#13068626C211yesmaximal, characteristic
12#13068621C211yesmaximal, characteristic, complemented
13#13068616C211yesmaximal, characteristic
14#13068473C211yesmaximal, characteristic, complemented
15C11×#2326C211yesmaximal, 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—
24C11×#385—21no—
25C11×#384C2211yescharacteristic
26C11×#376C2211yescharacteristic
27C2×#66899C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35#10622549C2211yescharacteristic
36#10622548C2211yescharacteristic
37#10622541C2211yescharacteristic
38#10622541C2211yescharacteristic
39#10622541C2211yescharacteristic
40#10622541C2211yescharacteristic
41C2×C4⋊(C11⋊C8)C2211yescharacteristic
42C2×C4⋊(C11⋊C8)C2211yescharacteristic
43C2×#66867C2211yescharacteristic
44C2×C4×C11⋊C8C2211yescharacteristic
45#10622273—21no—
46#10622273—21no—
47#10622270—21no—
48#10622270—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
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—22no—
66C4×D4×C11—22no—
67C4×D4×C11—22no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
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×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2311yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×C4⋊Dic11C2311yescharacteristic
88C2×Dic11⋊C4—21no—
89C2×Dic11⋊C4—21no—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C11×#95—21no—
97C11×#95—21no—
98C11×#95D411yescharacteristic
99C11×#95D411yescharacteristic
100C11×#95D411yescharacteristic
101C11×#95D411yescharacteristic
102#66899—22no—
103#66899—22no—
104#66899—41no—
105#66899—41no—
106#66896—22no—
107#66896—22no—
108#66896—41no—
109#66896—41no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C4⋊(C11⋊C8)—22no—
117C4⋊(C11⋊C8)—22no—
118#66867—41no—
119C4×C11⋊C8—41no—
120#29134—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—81no—
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—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—42no—
156C11×C4⋊C4—81no—
157C11×C4⋊C4—81no—
158C11×C22⋊C4—24no—
159C11×C22⋊C4—24no—
160C11×C22⋊C4—42no—
161C11×C22⋊C4—81no—
162C11×C22⋊C4—81no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—42no—
168C42×C11#4112yes—
169C42×C11#4112yes—
170C4⋊Dic11—21no—
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—
180Dic11⋊C4—81no—
181Dic11⋊C4—81no—
182Dic11⋊C4—81no—
183Dic11⋊C4—81no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
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—
196#2647—111no—
197#2326D1111yescharacteristic
198#2100—111no—
199#2099—111no—
200#2042—111no—
201#2042—111no—
202#1936—111no—
203#1935—111no—
204#1934—111no—
205#1933—111no—
206#1805—111no—
207#1804—111no—
208#1803—111no—
209#1802—111no—
210#1768—111no—
211C23×C11—22no—
212C23×C11—41no—
213C23×C11—41no—
214C23×C11—41no—
215C23×C11—41no—
216C23×C11—41no—
217C23×C11—41no—
218C23×C11C22×D411yescharacteristic
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—41no—
222Q8×C11—41no—
223D4×C11—22no—
224D4×C11—22no—
225D4×C11—41no—
226D4×C11—41no—
227C2×C4×C11—21no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—22no—
234C2×C4×C11—21no—
235C2×C4×C11—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11—41no—
250C2×C4×C11—41no—
251C2×C4×C11—41no—
252C2×C4×C11—84no—
253C2×C4×C11#12412yes—
254C2×C4×C11#12412yes—
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11H(5,𝔽2)11yescharacteristic
260C2×C4×C112−1+411yescharacteristic
261C2×Dic11—41no—
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—41no—
272C2×Dic11—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C11⋊C8—41no—
277C2×#124C2×D1111yescharacteristic
278C2×C4×Q8C2×D1111yescharacteristic
279C2×C4×D4C2×D1111yescharacteristic
280C2×C4⋊C8—111no—
281C2×C4⋊C8—111no—
282C2×#103—111no—
283C2×#103—111no—
284C2×#103—111no—
285C2×#103—111no—
286C2×#102—111no—
287C2×#102—111no—
288C2×#102—111no—
289C2×#102—111no—
290C2×#97—111no—
291C2×C4×C8—111no—
292#400—221no—
293#400—221no—
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#388—21no—
303#388—21no—
304#385—21no—
305#385—21no—
306#384—111no—
307#384C2×D1111yescharacteristic
308#382—111no—
309#376C2×D1111yescharacteristic
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#340—111no—
316#340—111no—
317#340—111no—
318#336—111no—
319#336—111no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11—81no—
327C22×C11#52511yescharacteristic
328C22×C11C2×#12411yescharacteristic
329C22×C11#53711yescharacteristic
330C22×C11#57611yescharacteristic
331C22×C11#57711yescharacteristic
332C22×C11#57711yescharacteristic
333C22×C11#57811yescharacteristic
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—42no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—81no—
342C4×C11—81no—
343C4×C11#55211yescharacteristic
344C4×C11#55211yescharacteristic
345C4×C11#55311yescharacteristic
346C4×C11#55311yescharacteristic
347Dic11—81no—
348Dic11—81no—
349Dic11—81no—
350Dic11—81no—
351C22×Q8C22×D1111yescharacteristic
352C22×D4C22×D1111yescharacteristic
353C23×C4—21no—
354C22×C8—111no—
355C22×C8—111no—
356C22×C8—111no—
357C22×C8—111no—
358#124—22no—
359#124—22no—
360C4×Q8—22no—
361C4×Q8—22no—
362C4×D4—22no—
363C4×D4—22no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
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×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C42—21no—
385C2×C42C22×D1111yescharacteristic
386C2×C42C22×D1111yescharacteristic
387C2×C42C22×D1111yescharacteristic
388C4⋊C8—222no—
389C4⋊C8—222no—
390#103—222no—
391#103—222no—
392#103—441no—
393#103—441no—
394#102—222no—
395#102—222no—
396#102—441no—
397#102—441no—
398#97—441no—
399C4×C8—441no—
400#95—21no—
401#95—21no—
402#95—221no—
403#95—221no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95C22⋊D1111yescharacteristic
409#95C22⋊D1111yescharacteristic
410#95C22⋊D1111yescharacteristic
411#95C22⋊D1111yescharacteristic
412C2×C11—82no—
413C2×C11#256211yescharacteristic
414C2×C11#311911yescharacteristic
415C2×C11#312011yescharacteristic
416C2×C11#313611yescharacteristic
417C2×C11#313711yescharacteristic
418C2×C11#326211yescharacteristic
419C2×C11#326311yescharacteristic
420C24—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8#433912yes—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4#433912yes—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—42no—
437C22×C4—81no—
438C22×C4—81no—
439C22×C4—221no—
440C22×C4—221no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4C2×C22⋊D1111yescharacteristic
444C22×C4C2×C22⋊D1111yescharacteristic
445C22×C4C2×C22⋊D1111yescharacteristic
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C23×D1111yescharacteristic
450C2×C8—221no—
451C2×C8—221no—
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—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—42no—
467C4⋊C4—81no—
468C4⋊C4—81no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—221no—
477C4⋊C4—881no—
478C4⋊C4—881no—
479C4⋊C4—881no—
480C4⋊C4—881no—
481C4⋊C4—881no—
482C4⋊C4—881no—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—42no—
486C22⋊C4—81no—
487C22⋊C4—81no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—42no—
493C42#434112yes—
494C42#434112yes—
495C11#2913411yescharacteristic, complemented, Sylow
496C23—22no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23C22×C22⋊D1111yescharacteristic
504Q8—22no—
505Q8—22no—
506Q8—41no—
507Q8—41no—
508D4—22no—
509D4—22no—
510D4—41no—
511D4—41no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—84no—
538C2×C4—441no—
539C2×C4—441no—
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#6698912yes—
551C2×C4#6698912yes—
552C2×C4C2×#433911yescharacteristic
553C2×C4C2×#433911yescharacteristic
554C2×C4C2×#434111yescharacteristic
555C2×C4C2×#434111yescharacteristic
556C2×C4#6704211yescharacteristic
557C2×C4#6704311yescharacteristic
558C8—441no—
559C8—441no—
560C8—441no—
561C8—441no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22#1062332211yescharacteristic
570C22C2×#6698911yescharacteristic
571C22#1062336411yescharacteristic
572C22#1062336611yescharacteristic
573C22#1062336711yescharacteristic
574C22#1062336811yescharacteristic
575C22#1062336911yescharacteristic
576C4—22no—
577C4—22no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—81no—
584C4—81no—
585C4—881no—
586C4—881no—
587C4—881no—
588C4—881no—
589C4#1062307211yescharacteristic
590C4#1062307211yescharacteristic
591C4#1062309611yescharacteristic
592C4#1062309611yescharacteristic
593C2—82no—
594C2#1307378211yescharacteristic
595C2#1307881511yescharacteristic
596C2#1307883011yescharacteristic
597C2#1307897011yescharacteristic
598C2#1307898111yescharacteristic
599C2#1308007211yescharacteristic
600C2#1308008111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2326C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2326D11
hypocenterC11#29134
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376 ◁ #2326

Complements

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

NH ≅ G/Ntype
1. #13074591C2semidirect
2. #13070178C2semidirect
3. #13070173C2semidirect
7. #13069309C2semidirect
9. #13069295C2semidirect
10. #13068631C2semidirect
12. #13068621C2semidirect
14. #13068473C2semidirect
495. C11#29134semidirect

Maximal subgroups

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

subgroupindex
#130745912
#130701782
#130701732
#130698522
#130693162
#130693092
#130693022
#130692952
#130686312
#130686262
#130686212
#130686162
#130684732
C11×#23262
#2913411