Finite Group Databasebeta

← #14821785

Subgroups — #14821785

Order 2816.

680 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071710C211yesmaximal, characteristic, complemented
2#13070107C211yesmaximal, characteristic, complemented
3#13069852C211yesmaximal, characteristic
4#13069767C211yesmaximal, characteristic, complemented
5#13069762C211yesmaximal, characteristic
6#13069549C211yesmaximal, characteristic
7#13069316C211yesmaximal, characteristic
8#13069254C211yesmaximal, characteristic, complemented
9#13069233C211yesmaximal, characteristic
10#13069233C211yesmaximal, characteristic
11#13069205C211yesmaximal, characteristic, complemented
12#13069182C211yesmaximal, characteristic, complemented
13#13068870C211yesmaximal, characteristic, complemented
14#13068446C211yesmaximal, characteristic, complemented
15C11×#2448C211yesmaximal, characteristic
16C2×C11×#124C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#66923C2211yescharacteristic
19C11×#399—21no—
20C11×#397—21no—
21C11×#391C2211yescharacteristic
22C11×#390C2211yescharacteristic
23C11×#390C2211yescharacteristic
24C11×#389C2211yescharacteristic
25C11×#388—21no—
26C11×#388—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C2×#66899C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic
34C2×#66896C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36#10622591—21no—
37#10622585—21no—
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C4×C4⋊Dic11C2211yescharacteristic
41C4×C4⋊Dic11C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47#10622265—21no—
48#10622262—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
61C11×#124—22no—
62C11×#124—41no—
63C4×Q8×C11—22no—
64C4×Q8×C11—41no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4—21no—
67C2×C11×C4⋊C4D411yescharacteristic
68C2×C11×C4⋊C4D411yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C22⋊C4—21no—
72C2×C11×C22⋊C4—21no—
73C2×C11×C22⋊C4—21no—
74C2×C11×C22⋊C4—21no—
75C2×C11×C22⋊C4—21no—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11—21no—
78C2×C42×C11C2311yescharacteristic
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4⋊Dic11C2311yescharacteristic
84C2×C4⋊Dic11C2311yescharacteristic
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—21no—
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96#66923—22no—
97#66923—22no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95D411yescharacteristic
102C11×#95D411yescharacteristic
103#66899—22no—
104#66899—22no—
105#66899—22no—
106#66899—22no—
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#66871—22no—
117#66871—41no—
118C4⋊(C11⋊C8)—41no—
119#66867—41no—
120#26719—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—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2411yescharacteristic
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—41no—
153C11×C4⋊C4—41no—
154C11×C4⋊C4—42no—
155C11×C4⋊C4—81no—
156C11×C22⋊C4—42no—
157C11×C22⋊C4—42no—
158C11×C22⋊C4—42no—
159C11×C22⋊C4—42no—
160C11×C22⋊C4—81no—
161C11×C22⋊C4—81no—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—42no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11#4112yes—
175C4⋊Dic11#4112yes—
176C4⋊Dic11#4112yes—
177Dic11⋊C4—24no—
178Dic11⋊C4—24no—
179Dic11⋊C4—42no—
180Dic11⋊C4—81no—
181C4×Dic11—42no—
182C4×Dic11—81no—
183C4×Dic11—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#2448D1111yescharacteristic
197#2370—111no—
198#2086—111no—
199#2042—111no—
200#2026—111no—
201#2025—111no—
202#1983—111no—
203#1936—111no—
204#1928—111no—
205#1925—111no—
206#1925—111no—
207#1921—111no—
208#1917—111no—
209#1863—111no—
210#1763—111no—
211C23×C11—41no—
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—41no—
224D4×C11—41no—
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—21no—
245C2×C4×C11—21no—
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—41no—
253C2×C4×C11—41no—
254C2×C4×C11C2×#4111yescharacteristic
255C2×C4×C11C2×#4111yescharacteristic
256C2×C4×C11C2×#4111yescharacteristic
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11H(5,𝔽2)11yescharacteristic
259C2×C4×C112−1+411yescharacteristic
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—22no—
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—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C2×#125—111no—
277C2×#124C2×D1111yescharacteristic
278C2×C4×Q8C2×D1111yescharacteristic
279C2×#107—111no—
280C2×#107—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—
291#399—21no—
292#397—21no—
293#391C2×D1111yescharacteristic
294#390C2×D1111yescharacteristic
295#390C2×D1111yescharacteristic
296#389—111no—
297#389—111no—
298#389—221no—
299#389C2×D1111yescharacteristic
300#388—21no—
301#388—21no—
302#387—221no—
303#387—221no—
304C4×C4⋊C4—111no—
305C4×C4⋊C4—111no—
306C4×C4⋊C4—111no—
307C4×C4⋊C4—221no—
308C4×C4⋊C4C2×D1111yescharacteristic
309#340—111no—
310#340—111no—
311#340—111no—
312#340—111no—
313#340—111no—
314#340—111no—
315#336—111no—
316#336—111no—
317#336—111no—
318#336—111no—
319C22×C11—81no—
320C22×C11—81no—
321C22×C11—81no—
322C22×C11—81no—
323C22×C11—81no—
324C22×C11—81no—
325C22×C11—81no—
326C22×C11#52511yescharacteristic
327C22×C11#54611yescharacteristic
328C22×C11#54811yescharacteristic
329C22×C11#57511yescharacteristic
330C22×C11#57511yescharacteristic
331C22×C11#57611yescharacteristic
332C22×C11#57811yescharacteristic
333C4×C11—41no—
334C4×C11—41no—
335C4×C11—42no—
336C4×C11—41no—
337C4×C11—41no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—81no—
341C4×C11—81no—
342C4×C11#52911yescharacteristic
343C4×C11#54211yescharacteristic
344C4×C11#55211yescharacteristic
345C4×C11#55911yescharacteristic
346Dic11—42no—
347Dic11—42no—
348Dic11—42no—
349Dic11—81no—
350C22×Q8C22×D1111yescharacteristic
351C22×D4C22×D1111yescharacteristic
352C22×C8—111no—
353C22×C8—111no—
354C22×C8—111no—
355C22×C8—111no—
356#125—222no—
357#125—222no—
358#124—22no—
359#124—41no—
360C4×Q8—22no—
361C4×Q8—41no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4C22⋊D1111yescharacteristic
373C2×C4⋊C4C22⋊D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C42—21no—
383C2×C42—221no—
384C2×C42—221no—
385C2×C42—221no—
386C2×C42C22×D1111yescharacteristic
387C2×C42C22×D1111yescharacteristic
388C2×C42C22×D1111yescharacteristic
389#107—222no—
390#107—441no—
391C4⋊C8—441no—
392#103—222no—
393#103—222no—
394#103—222no—
395#103—222no—
396#102—222no—
397#102—222no—
398#102—222no—
399#102—441no—
400#97—441no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—221no—
405#95—221no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95C22⋊D1111yescharacteristic
410#95C22⋊D1111yescharacteristic
411C2×C11—161no—
412C2×C11#245811yescharacteristic
413C2×C11#311111yescharacteristic
414C2×C11#312411yescharacteristic
415C2×C11#330911yescharacteristic
416C2×C11#332711yescharacteristic
417C2×C11#337011yescharacteristic
418C2×C11#337711yescharacteristic
419C24—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8#434112yes—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—221no—
438C22×C4—221no—
439C22×C4C2×C22⋊D1111yescharacteristic
440C22×C4C2×C22⋊D1111yescharacteristic
441C22×C4C2×C22⋊D1111yescharacteristic
442C22×C4C2×C22⋊D1111yescharacteristic
443C22×C4C2×C22⋊D1111yescharacteristic
444C22×C4C2×C22⋊D1111yescharacteristic
445C22×C4C23×D1111yescharacteristic
446C2×C8—221no—
447C2×C8—221no—
448C2×C8—221no—
449C2×C8—221no—
450C2×C8—221no—
451C2×C8—221no—
452C2×C8—221no—
453C2×C8—221no—
454C2×C8—221no—
455C2×C8—221no—
456C2×C8—221no—
457C2×C8—221no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—42no—
465C4⋊C4—81no—
466C4⋊C4—112no—
467C4⋊C4—112no—
468C4⋊C4—112no—
469C4⋊C4—224no—
470C4⋊C4—224no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—221no—
474C4⋊C4—221no—
475C4⋊C4—221no—
476C4⋊C4—442no—
477C4⋊C4—881no—
478C22⋊C4—42no—
479C22⋊C4—42no—
480C22⋊C4—42no—
481C22⋊C4—42no—
482C22⋊C4—81no—
483C22⋊C4—81no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—42no—
491C42—442no—
492C42—881no—
493C42—881no—
494C11#2671911yescharacteristic, complemented, Sylow
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23C22×C22⋊D1111yescharacteristic
503Q8—22no—
504Q8—22no—
505Q8—41no—
506Q8—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
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—21no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—222no—
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×C4C2×#434111yescharacteristic
551C2×C4#6703711yescharacteristic
552C2×C4#41×D1111yescharacteristic
553C2×C4#41×D1111yescharacteristic
554C2×C4#41×D1111yescharacteristic
555C2×C4#6704311yescharacteristic
556C8—441no—
557C8—441no—
558C8—441no—
559C8—441no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22#1062333711yescharacteristic
568C22#1062335311yescharacteristic
569C22#1062335311yescharacteristic
570C22#1062335911yescharacteristic
571C22#1062336211yescharacteristic
572C22#1062336611yescharacteristic
573C22#1062336911yescharacteristic
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—42no—
580C4—41no—
581C4—81no—
582C4—81no—
583C4—442no—
584C4—442no—
585C4—442no—
586C4—881no—
587C4#1062318011yescharacteristic
588C4#1062318111yescharacteristic
589C4#1062319311yescharacteristic
590C4#1062319511yescharacteristic
591C2—161no—
592C2#1307253411yescharacteristic
593C2#1307871911yescharacteristic
594C2#1307887211yescharacteristic
595C2#1308062211yescharacteristic
596C2#1308088411yescharacteristic
597C2#1308136311yescharacteristic
598C2#1308145211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2448C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenter#2448D11
hypocenterC11#26719
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2448

Complements

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

NH ≅ G/Ntype
1. #13071710C2semidirect
2. #13070107C2semidirect
4. #13069767C2semidirect
8. #13069254C2semidirect
11. #13069205C2semidirect
12. #13069182C2semidirect
13. #13068870C2semidirect
14. #13068446C2semidirect
494. C11#26719semidirect

Maximal subgroups

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

subgroupindex
#130717102
#130701072
#130698522
#130697672
#130697622
#130695492
#130693162
#130692542
#130692332
#130692052
#130691822
#130688702
#130684462
C11×#24482
#2671911