Finite Group Databasebeta

← #14826994

Subgroups — #14826994

Order 2816.

708 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#13073191C211yesmaximal, characteristic
2#13070154C211yesmaximal, characteristic
3#13069938C211yesmaximal, characteristic
4#13069859C211yesmaximal, characteristic
5#13069716C211yesmaximal, characteristic
6#13069476C211yesmaximal, characteristic
7#13069257C211yesmaximal, characteristic
8#13069254C211yesmaximal, characteristic
9#13069208C211yesmaximal, characteristic
10#13069175C211yesmaximal, characteristic
11#13068957C211yesmaximal, characteristic
12#13068957C211yesmaximal, characteristic
13#13068621C211yesmaximal, characteristic
14C4×#66899C211yesmaximal, characteristic
15C11×#2365C211yesmaximal, characteristic
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C11×#391C2211yescharacteristic
22C11×#391C2211yescharacteristic
23C11×#389—21no—
24C11×#387—21no—
25C11×#387—21no—
26C4×C11×C4⋊C4—21no—
27C4×C11×C4⋊C4C2211yescharacteristic
28C4×C11×C4⋊C4C2211yescharacteristic
29C2×#66899C2211yescharacteristic
30C2×#66899C2211yescharacteristic
31C2×#66899C2211yescharacteristic
32C2×#66899C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35#10622599—21no—
36#10622594—21no—
37C2×#66874C2211yescharacteristic
38C2×#66874C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40C2×#66871C2211yescharacteristic
41#10622548C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622542C2211yescharacteristic
44#10622542C2211yescharacteristic
45#10622542C2211yescharacteristic
46#10622541C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622273—21no—
50#10622267—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622162C2211yescharacteristic
56#10622162C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×Q8×C11C2311yescharacteristic
60C22×Q8×C11C2311yescharacteristic
61C22×Dic22C2311yescharacteristic
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8—22no—
64C4×Q8×C11—22no—
65C4×Q8×C11—22no—
66C4×Q8×C11—41no—
67C4×Q8×C11—41no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4D411yescharacteristic
73C2×C11×C4⋊C4D411yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C42×C11—21no—
77C2×C42×C11—21no—
78C2×C42×C11—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C42×C11C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82C2×#4326—22no—
83C2×#4326—22no—
84C2×#4326—22no—
85C2×#4326—41no—
86C2×#4326—41no—
87C2×#4326—41no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×C4×Dic11—21no—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C11×#95—21no—
100C11×#95—21no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95—21no—
104C11×#95D411yescharacteristic
105C11×#95D411yescharacteristic
106#66899—22no—
107#66899—22no—
108#66899—22no—
109#66899—41no—
110#66899—41no—
111#66899—41no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C11⋊#95—21no—
115C11⋊#95—21no—
116C11⋊#95—21no—
117C11⋊#95—21no—
118C11⋊#95—21no—
119C11⋊#95—21no—
120#66874—22no—
121#66874—41no—
122#66871—22no—
123#66871—41no—
124C4⋊(C11⋊C8)—41no—
125C4×C11⋊C8—41no—
126#27068—111nomaximal, Sylow
127C2×Q8×C11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—21no—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—21no—
133C2×Q8×C11—21no—
134C2×Q8×C11—21no—
135C2×Q8×C11—21no—
136C2×Q8×C11—21no—
137C2×Q8×C11#4112yes—
138C2×Q8×C11#4112yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2411yescharacteristic
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22—21no—
158C2×Dic22—21no—
159C2×Dic22—21no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—21no—
165C11×C4⋊C4—41no—
166C11×C4⋊C4—42no—
167C11×C4⋊C4—42no—
168C11×C4⋊C4Q1614yescomplemented
169C11×C4⋊C4#4112yes—
170C42×C11—21no—
171C42×C11—21no—
172C42×C11—21no—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—42no—
177C42×C11—42no—
178C42×C11—42no—
179#4326—44no—
180#4326—44no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—42no—
188C4⋊Dic11—81no—
189Dic11⋊C4—81no—
190C4×Dic11—81no—
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—
198C2×C11⋊C8—21no—
199C2×C11⋊C8—21no—
200C2×C11⋊C8—21no—
201C2×C11⋊C8—21no—
202C2×C11⋊C8#4112yes—
203#2511—111no—
204#2365D1111yescharacteristic
205#2095—111no—
206#2056—111no—
207#2043—111no—
208#2016—111no—
209#1969—111no—
210#1928—111no—
211#1928—111no—
212#1921—111no—
213#1916—111no—
214#1878—111no—
215#1878—111no—
216#1803—111no—
217C4×#103—111no—
218C23×C11C22×D411yescharacteristic
219Q8×C11—22no—
220Q8×C11—22no—
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—41no—
224Q8×C11—41no—
225Q8×C11—41no—
226Q8×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—21no—
234C2×C4×C11—22no—
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—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—41no—
253C2×C4×C11—41no—
254C2×C4×C11C2×Q1612yes—
255C2×C4×C11C2×Q1612yes—
256C2×C4×C11C2×Q1612yes—
257C2×C4×C11C2×#4111yescharacteristic
258C2×C4×C11C2×#4111yescharacteristic
259C2×C4×C11C2×#4111yescharacteristic
260C2×C4×C11C2×#4111yescharacteristic
261C2×C4×C11H(5,𝔽2)11yescharacteristic
262C2×C4×C11H(5,𝔽2)11yescharacteristic
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—
273C2×Dic11—41no—
274C2×Dic11—41no—
275Dic22—41no—
276Dic22—41no—
277Dic22—41no—
278Dic22—41no—
279C11⋊C8—22no—
280C11⋊C8—41no—
281C11⋊C8—41no—
282C11⋊C8—41no—
283C22×Q16—111no—
284C22×Q16—111no—
285C2×C4⋊Q8C2×D1111yescharacteristic
286C2×C4×Q8C2×D1111yescharacteristic
287C2×C4×Q8C2×D1111yescharacteristic
288C2×#107—111no—
289C2×#107—111no—
290C2×C4⋊C8—111no—
291C2×#103—111no—
292C2×#103—111no—
293C2×#103—111no—
294C2×#103—111no—
295C2×#103—111no—
296C2×#103—111no—
297C2×#103—111no—
298C2×#103—111no—
299C2×C4×C8—111no—
300#400—221no—
301#400—221no—
302#391—111no—
303#391—111no—
304#391—111no—
305#391C2×D1111yescharacteristic
306#391C2×D1111yescharacteristic
307#389—21no—
308#389—111no—
309#387—21no—
310#387—21no—
311#387—221no—
312#387—221no—
313#384—111no—
314C4×C4⋊C4—21no—
315C4×C4⋊C4—111no—
316C4×C4⋊C4C2×D1111yescharacteristic
317C4×C4⋊C4C2×D1111yescharacteristic
318#340—111no—
319#340—111no—
320#340—111no—
321#340—111no—
322#336—111no—
323#336—111no—
324#336—111no—
325#336—111no—
326C22×C11#52511yescharacteristic
327C22×C11#54611yescharacteristic
328C22×C11#55011yescharacteristic
329C22×C11C22×Q1611yescharacteristic
330C22×C11#57511yescharacteristic
331C22×C11#57711yescharacteristic
332C22×C11#57811yescharacteristic
333C4×C11—22no—
334C4×C11—22no—
335C4×C11—22no—
336C4×C11—41no—
337C4×C11—42no—
338C4×C11—42no—
339C4×C11—41no—
340C4×C11—41no—
341C4×C11—42no—
342C4×C11—81no—
343C4×C11#52911yescharacteristic
344C4×C11#53811yescharacteristic
345C4×C11#55111yescharacteristic
346C4×C11#55311yescharacteristic
347Dic11—81no—
348Dic11—81no—
349Dic11—81no—
350Dic11—81no—
351C22×Q8—111no—
352C22×Q8C22×D1111yescharacteristic
353C22×Q8C22×D1111yescharacteristic
354C2×Q16—222no—
355C2×Q16—222no—
356C2×Q16—222no—
357C2×Q16—441no—
358C2×Q16—441no—
359C2×Q16—441no—
360C22×C8—111no—
361C22×C8—111no—
362C22×C8—111no—
363C22×C8—111no—
364C4⋊Q8—22no—
365C4⋊Q8—22no—
366C4×Q8—22no—
367C4×Q8—22no—
368C4×Q8—41no—
369C4×Q8—41no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—111no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4C22⋊D1111yescharacteristic
381C2×C4⋊C4C22⋊D1111yescharacteristic
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—221no—
388C2×C42C22×D1111yescharacteristic
389C2×C42C22×D1111yescharacteristic
390C2×C42C22×D1111yescharacteristic
391#107—222no—
392#107—441no—
393C4⋊C8—441no—
394#103—222no—
395#103—222no—
396#103—222no—
397#103—222no—
398#103—441no—
399#103—441no—
400#103—441no—
401#103—441no—
402C4×C8—441no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—221no—
409#95—221no—
410#95—221no—
411#95—221no—
412#95—221no—
413#95—221no—
414#95—221no—
415#95—221no—
416#95C22⋊D1111yescharacteristic
417#95C22⋊D1111yescharacteristic
418C2×C11#246711yescharacteristic
419C2×C11#310411yescharacteristic
420C2×C11#312111yescharacteristic
421C2×C11#329911yescharacteristic
422C2×C11#331511yescharacteristic
423C2×C11#339511yescharacteristic
424C2×C11#340111yescharacteristic
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—221no—
436C2×Q8—221no—
437C2×Q8—221no—
438C2×Q8—221no—
439C2×Q8—221no—
440C2×Q8—221no—
441C2×Q8#433912yes—
442C2×Q8#433912yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—221no—
448C22×C4—221no—
449C22×C4—221no—
450C22×C4—221no—
451C22×C4C2×C22⋊D1111yescharacteristic
452C22×C4C2×C22⋊D1111yescharacteristic
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C2×C22⋊D1111yescharacteristic
456C22×C4C2×C22⋊D1111yescharacteristic
457C22×C4C23×D1111yescharacteristic
458Q16—444no—
459Q16—444no—
460C2×C8—112no—
461C2×C8—221no—
462C2×C8—221no—
463C2×C8—221no—
464C2×C8—221no—
465C2×C8—221no—
466C2×C8—221no—
467C2×C8—221no—
468C2×C8—221no—
469C2×C8—221no—
470C2×C8—221no—
471C2×C8—221no—
472C4⋊C4—24no—
473C4⋊C4—24no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—221no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—221no—
484C4⋊C4—221no—
485C4⋊C4—221no—
486C4⋊C4—442no—
487C4⋊C4—881no—
488C4⋊C4—881no—
489C4⋊C4#432614yescomplemented
490C4⋊C4#434112yes—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—42no—
498C42—42no—
499C42—42no—
500C42—881no—
501C11#2706811yescharacteristic, complemented, Sylow
502C23C22×C22⋊D1111yescharacteristic
503Q8—22no—
504Q8—22no—
505Q8—22no—
506Q8—22no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—441no—
512Q8—441no—
513Q8—441no—
514Q8—441no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—22no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
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—41no—
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—441no—
551C2×C4—441no—
552C2×C4—441no—
553C2×C4—441no—
554C2×C4C2×#432612yes—
555C2×C4C2×#432612yes—
556C2×C4C2×#432612yes—
557C2×C4C2×#433911yescharacteristic
558C2×C4C2×#433911yescharacteristic
559C2×C4C2×#434111yescharacteristic
560C2×C4#6703711yescharacteristic
561C2×C4#41×D1111yescharacteristic
562C2×C4#6704211yescharacteristic
563C8—222no—
564C8—441no—
565C8—441no—
566C8—441no—
567C22#1062332211yescharacteristic
568C22#1062333711yescharacteristic
569C22C22×#432611yescharacteristic
570C22#1062335311yescharacteristic
571C22#1062336511yescharacteristic
572C22#1062336811yescharacteristic
573C22#1062336911yescharacteristic
574C4—22no—
575C4—22no—
576C4—22no—
577C4—42no—
578C4—42no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—42no—
583C4—81no—
584C4—881no—
585C4—881no—
586C4—881no—
587C4—881no—
588C4#1062306911yescharacteristic
589C4#1062308711yescharacteristic
590C4#1062309111yescharacteristic
591C4#1062309611yescharacteristic
592C2#1307266111yescharacteristic
593C2#1307865511yescharacteristic
594C2#1307884511yescharacteristic
595C2#1308049211yescharacteristic
596C2#1308071211yescharacteristic
597C2#1308161911yescharacteristic
598C2#1308168211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2365C2
socle, prime radicalC23×C11C22×D4
hypercenter#2365D11
hypocenterC11#27068
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2365

Complements

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

NH ≅ G/Ntype
168. C11×C4⋊C4Q16semidirect
489. C4⋊C4#4326semidirect
501. C11#27068semidirect

Maximal subgroups

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

subgroupindex
#130731912
#130701542
#130699382
#130698592
#130697162
#130694762
#130692572
#130692542
#130692082
#130691752
#130689572
#130686212
C4×#668992
C11×#23652
#2706811