Finite Group Databasebeta

← #14821783

Subgroups — #14821783

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#13072414C211yesmaximal, characteristic
2#13070107C211yesmaximal, characteristic, complemented
3#13069857C211yesmaximal, characteristic
4#13069764C211yesmaximal, characteristic, complemented
5#13069759C211yesmaximal, characteristic
6#13069548C211yesmaximal, characteristic
7#13069312C211yesmaximal, characteristic
8#13069257C211yesmaximal, characteristic, complemented
9#13069236C211yesmaximal, characteristic
10#13069236C211yesmaximal, characteristic
11#13069208C211yesmaximal, characteristic, complemented
12#13069182C211yesmaximal, characteristic, complemented
13#13068869C211yesmaximal, characteristic, complemented
14#13068449C211yesmaximal, characteristic, complemented
15C11×#2370C211yesmaximal, characteristic, complemented
16C2×C11×#125C2211yescharacteristic
17C2×#66928C2211yescharacteristic
18C2×C4×Dic22C2211yescharacteristic
19C11×#389—21no—
20C11×#389C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C11×#387—21no—
23C11×#387—21no—
24C4×C11×C4⋊C4—21no—
25C4×C11×C4⋊C4C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29#10622605—21no—
30#10622603—21no—
31C2×#66874C2211yescharacteristic
32C2×#66874C2211yescharacteristic
33C2×#66874C2211yescharacteristic
34C2×#66874C2211yescharacteristic
35C2×#66873C2211yescharacteristic
36C2×#66873C2211yescharacteristic
37C2×#66873C2211yescharacteristic
38C2×#66873C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622552C2211yescharacteristic
42#10622552C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×#66867C2211yescharacteristic
47#10622288—21no—
48#10622282—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×Dic22C2311yescharacteristic
61C11×#125—22no—
62C11×#125—22no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C42×C11—21no—
74C2×C42×C11—21no—
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77C2×C42×C11C2311yescharacteristic
78C2×C42×C11C2311yescharacteristic
79C2×(C2×D11)⋊C4—21no—
80C2×(C2×D11)⋊C4—21no—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—21no—
89C2×C4×Dic11—21no—
90C22×C11⋊C8C2311yescharacteristic
91C22×C11⋊C8C2311yescharacteristic
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94#66928—22no—
95#66928—41no—
96C4×Dic22—22no—
97C4×Dic22—41no—
98C11×#95—21no—
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95D411yescharacteristic
104C11×#95D411yescharacteristic
105C11⋊#95—21no—
106C11⋊#95—21no—
107C11⋊#95—21no—
108#66874—22no—
109#66874—22no—
110#66874—22no—
111#66874—22no—
112#66873—22no—
113#66873—22no—
114#66873—22no—
115#66873—41no—
116#66871—22no—
117#66871—41no—
118C4⋊(C11⋊C8)—41no—
119#66867—41no—
120#26719—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×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11C2411yescharacteristic
133C22×Dic11—21no—
134C22×Dic11—21no—
135C22×Dic11—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44—21no—
140C2×D44—21no—
141C2×D44—21no—
142C2×Dic22—21no—
143C2×Dic22—21no—
144C2×Dic22—21no—
145C2×Dic22—21no—
146C2×Dic22—21no—
147C2×Dic22#4112yes—
148C11×C4⋊C4—24no—
149C11×C4⋊C4—24no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—21no—
152C11×C4⋊C4—21no—
153C11×C4⋊C4—21no—
154C11×C4⋊C4—21no—
155C11×C4⋊C4—41no—
156C11×C4⋊C4—41no—
157C11×C4⋊C4—42no—
158C11×C4⋊C4—81no—
159C11×C4⋊C4#4112yes—
160C11×C4⋊C4#4112yes—
161C11×C4⋊C4#4112yes—
162C42×C11—21no—
163C42×C11—21no—
164C42×C11—21no—
165C42×C11—21no—
166C42×C11—21no—
167C42×C11—21no—
168C42×C11—42no—
169C42×C11—81no—
170C42×C11—81no—
171(C2×D11)⋊C4—42no—
172(C2×D11)⋊C4—42no—
173(C2×D11)⋊C4—42no—
174(C2×D11)⋊C4—42no—
175(C2×D11)⋊C4—81no—
176(C2×D11)⋊C4—81no—
177C4⋊Dic11—21no—
178C4⋊Dic11—21no—
179C4⋊Dic11—21no—
180C4⋊Dic11—21no—
181Dic11⋊C4—42no—
182Dic11⋊C4—81no—
183C4×Dic11—42no—
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#2448—111no—
197#2370D1111yescharacteristic, complemented
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×C11C22×D411yescharacteristic
212C22×D11—41no—
213C22×D11—41no—
214C22×D11—41no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—41no—
218C22×D11—41no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—22no—
222C2×C4×C11—22no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—22no—
228C2×C4×C11—21no—
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—21no—
236C2×C4×C11—21no—
237C2×C4×C11—21no—
238C2×C4×C11—21no—
239C2×C4×C11—21no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—41no—
248C2×C4×C11—41no—
249C2×C4×C11C2×#4111yescharacteristic
250C2×C4×C11C2×#4111yescharacteristic
251C2×C4×C11C2×#4111yescharacteristic
252C2×C4×C11C2×#4111yescharacteristic
253C2×C4×C11H(5,𝔽2)11yescharacteristic
254C2×C4×C112−1+411yescharacteristic
255C2×Dic11—22no—
256C2×Dic11—41no—
257C2×Dic11—41no—
258C2×Dic11—41no—
259C2×Dic11—41no—
260C2×Dic11—41no—
261C2×Dic11—41no—
262C2×Dic11—41no—
263C2×Dic11—41no—
264D44—41no—
265D44—41no—
266D44—41no—
267D44—41no—
268Dic22—22no—
269Dic22—22no—
270Dic22—41no—
271Dic22—41no—
272C11⋊C8—41no—
273C11⋊C8—41no—
274C11⋊C8—41no—
275C11⋊C8—41no—
276C2×#125C2×D1111yescharacteristic
277C2×#124—111no—
278C2×C4×Q8—111no—
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—221no—
292#397—221no—
293#391—111no—
294#390—111no—
295#390—111no—
296#389—21no—
297#389—111no—
298#389C2×D1111yescharacteristic
299#389C2×D1111yescharacteristic
300#388—221no—
301#388—221no—
302#387—21no—
303#387—21no—
304C4×C4⋊C4—21no—
305C4×C4⋊C4C2×D1111yescharacteristic
306C4×C4⋊C4C2×D1111yescharacteristic
307C4×C4⋊C4C2×D1111yescharacteristic
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#52511yescharacteristic
320C22×C11#54611yescharacteristic
321C22×C11#54811yescharacteristic
322C22×C11#57511yescharacteristic
323C22×C11#57511yescharacteristic
324C22×C11#57611yescharacteristic
325C22×C11#57811yescharacteristic
326C2×D11—81no—
327C2×D11—81no—
328C2×D11—81no—
329C2×D11—81no—
330C2×D11—81no—
331C2×D11—81no—
332C2×D11—81no—
333C4×C11—41no—
334C4×C11—42no—
335C4×C11—42no—
336C4×C11—41no—
337C4×C11—42no—
338C4×C11—41no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—41no—
342C4×C11—81no—
343C4×C11#52911yescharacteristic
344C4×C11#54211yescharacteristic
345C4×C11#55211yescharacteristic
346C4×C11#55911yescharacteristic
347Dic11—42no—
348Dic11—81no—
349Dic11—81no—
350C22×Q8—111no—
351C22×D4—111no—
352C22×C8—111no—
353C22×C8—111no—
354C22×C8—111no—
355C22×C8—111no—
356#125—22no—
357#125—22no—
358#124—222no—
359#124—441no—
360C4×Q8—222no—
361C4×Q8—441no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—111no—
367C2×C4⋊C4—111no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4C22⋊D1111yescharacteristic
371C2×C4⋊C4C22⋊D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C4⋊C4C22×D1111yescharacteristic
374C2×C4⋊C4C22×D1111yescharacteristic
375C2×C4⋊C4C22×D1111yescharacteristic
376C2×C22⋊C4—221no—
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—21no—
384C2×C42—21no—
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—21no—
405#95—21no—
406#95—221no—
407#95—221no—
408#95—221no—
409#95C22⋊D1111yescharacteristic
410#95C22⋊D1111yescharacteristic
411C2×C11#245811yescharacteristic
412C2×C11#311111yescharacteristic
413C2×C11#312411yescharacteristic
414C2×C11#330911yescharacteristic
415C2×C11#332711yescharacteristic
416C2×C11#337011yescharacteristic
417C2×C11#337711yescharacteristic
418D11—161no—
419C24—221no—
420C2×Q8—112no—
421C2×Q8—221no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×Q8—221no—
425C2×Q8—221no—
426C2×D4—221no—
427C2×D4—221no—
428C2×D4—221no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—221no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
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—24no—
459C4⋊C4—24no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—42no—
468C4⋊C4—81no—
469C4⋊C4—221no—
470C4⋊C4—221no—
471C4⋊C4—221no—
472C4⋊C4—221no—
473C4⋊C4—442no—
474C4⋊C4—881no—
475C4⋊C4#433912yes—
476C4⋊C4#433912yes—
477C4⋊C4#434312yes—
478C22⋊C4—442no—
479C22⋊C4—442no—
480C22⋊C4—442no—
481C22⋊C4—442no—
482C22⋊C4—881no—
483C22⋊C4—881no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—42no—
491C42—81no—
492C42—81no—
493C42—442no—
494C11#2671911yescharacteristic, complemented, Sylow
495C23—441no—
496C23—441no—
497C23—441no—
498C23—441no—
499C23—441no—
500C23—441no—
501C23—441no—
502C23C22×C22⋊D1111yescharacteristic
503Q8—222no—
504Q8—222no—
505Q8—441no—
506Q8—441no—
507D4—441no—
508D4—441no—
509D4—441no—
510D4—441no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
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—21no—
531C2×C4—21no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—222no—
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×#433911yescharacteristic
551C2×C4C2×#433911yescharacteristic
552C2×C4C2×#434311yescharacteristic
553C2×C4#6704011yescharacteristic
554C2×C4#41×D1111yescharacteristic
555C2×C4#6704211yescharacteristic
556C8—441no—
557C8—441no—
558C8—441no—
559C8—441no—
560C22—881no—
561C22—881no—
562C22—881no—
563C22—881no—
564C22—881no—
565C22—881no—
566C22—881no—
567C22#1062332211yescharacteristic
568C22#1062334811yescharacteristic
569C22#1062335311yescharacteristic
570C22#1062335311yescharacteristic
571C22#1062336011yescharacteristic
572C22#1062336611yescharacteristic
573C22#1062336911yescharacteristic
574C4—42no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—42no—
581C4—41no—
582C4—42no—
583C4—81no—
584C4—442no—
585C4—881no—
586C4—881no—
587C4#1062311111yescharacteristic
588C4#1062311211yescharacteristic
589C4#1062311311yescharacteristic
590C4#1062311611yescharacteristic
591C2—1761no—
592C2#1307253211yescharacteristic
593C2#1307872511yescharacteristic
594C2#1307887811yescharacteristic
595C2#1308061611yescharacteristic
596C2#1308087811yescharacteristic
597C2#1308136911yescharacteristic
598C2#1308145811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2370C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2370D11
hypocenterC11#26719
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2370

Complements

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

NH ≅ G/Ntype
2. #13070107C2semidirect
4. #13069764C2semidirect
8. #13069257C2semidirect
11. #13069208C2semidirect
12. #13069182C2semidirect
13. #13068869C2semidirect
14. #13068449C2semidirect
15. C11×#2370C2semidirect
197. #2370D11semidirect
494. C11#26719semidirect

Maximal subgroups

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

subgroupindex
#130724142
#130701072
#130698572
#130697642
#130697592
#130695482
#130693122
#130692572
#130692362
#130692082
#130691822
#130688692
#130684492
C11×#23702
#2671911