Finite Group Databasebeta

← #14812953

Subgroups — #14812953

Order 2816.

672 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071587C211yesmaximal, characteristic
2#13070140C211yesmaximal, characteristic
3#13070140C211yesmaximal, characteristic
4#13070001C211yesmaximal, characteristic
5#13069987C211yesmaximal, characteristic
6#13069384C211yesmaximal, characteristic, complemented
7#13069382C211yesmaximal, characteristic, complemented
8#13069382C211yesmaximal, characteristic, complemented
9#13069340C211yesmaximal, characteristic, complemented
10#13069198C211yesmaximal, characteristic, complemented
11#13069184C211yesmaximal, characteristic, complemented
12#13068782C211yesmaximal, characteristic, complemented
13#13068613C211yesmaximal, characteristic
14#13068444C211yesmaximal, characteristic
15C11×#2571C211yesmaximal, characteristic, complemented
16C2×C4×D44C2211yescharacteristic
17C11×#400—21no—
18C11×#400—21no—
19C11×#389—21no—
20C11×#389C2211yescharacteristic
21C11×#389C2211yescharacteristic
22C11×#384C2211yescharacteristic
23C11×#382—21no—
24C11×#382C2211yescharacteristic
25C11×#382C2211yescharacteristic
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C4⋊C4C2211yescharacteristic
28#10622603—21no—
29#10622603—21no—
30C2×#66873C2211yescharacteristic
31C2×#66873C2211yescharacteristic
32C2×#66873C2211yescharacteristic
33C2×#66873C2211yescharacteristic
34C2×#66872C2211yescharacteristic
35C2×#66872C2211yescharacteristic
36C2×#66872C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622552C2211yescharacteristic
41#10622552C2211yescharacteristic
42#10622549C2211yescharacteristic
43C4×C4⋊Dic11C2211yescharacteristic
44C4×C4⋊Dic11C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4⋊(C11⋊C8)C2211yescharacteristic
47C2×C4⋊(C11⋊C8)C2211yescharacteristic
48C2×#66867C2211yescharacteristic
49#10622279—21no—
50#10622277—21no—
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4D411yescharacteristic
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2311yescharacteristic
69C2×C11×C4⋊C4C2311yescharacteristic
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C42×C11—21no—
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74C2×C42×C11C2311yescharacteristic
75C2×(C2×D11)⋊C4—21no—
76C2×(C2×D11)⋊C4—21no—
77C2×(C2×D11)⋊C4—21no—
78C2×(C2×D11)⋊C4—21no—
79C2×(C2×D11)⋊C4—21no—
80C2×C4⋊Dic11C2311yescharacteristic
81C2×C4⋊Dic11C2311yescharacteristic
82C2×C4⋊Dic11C2311yescharacteristic
83C2×C4×Dic11—21no—
84C2×C4×Dic11—21no—
85C22×C11⋊C8C2311yescharacteristic
86C22×C11⋊C8C2311yescharacteristic
87C22×C11⋊C8C2311yescharacteristic
88C22×C11⋊C8C2311yescharacteristic
89C4×D44—22no—
90C4×D44Q814yes—
91C11×#95—21no—
92C11×#95—21no—
93C11×#95—21no—
94C11×#95—21no—
95C11×#95—21no—
96C11×#95—21no—
97C11×#95—21no—
98C11×#95D411yescharacteristic
99C11×#95D411yescharacteristic
100C11⋊#95—21no—
101C11⋊#95—21no—
102C11⋊#95—21no—
103C11⋊#95—21no—
104#66873—22no—
105#66873—22no—
106#66873—41no—
107#66873—41no—
108#66872—22no—
109#66872—41no—
110#66872—41no—
111#66871—22no—
112#66871—41no—
113#66871—41no—
114C4⋊(C11⋊C8)—22no—
115C4⋊(C11⋊C8)—22no—
116C4⋊(C11⋊C8)—22no—
117#66867—22no—
118#26103—111nomaximal, Sylow
119C23×D11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2411yescharacteristic
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C2×D44—21no—
135C2×D44—21no—
136C2×D44—21no—
137C2×D44—21no—
138C2×D44—21no—
139C2×D44C2×Q812yes—
140C2×C4×D11—24no—
141C2×C4×D11—81no—
142C2×C4×D11—81no—
143C11×C4⋊C4—21no—
144C11×C4⋊C4—21no—
145C11×C4⋊C4—21no—
146C11×C4⋊C4—21no—
147C11×C4⋊C4—21no—
148C11×C4⋊C4—21no—
149C11×C4⋊C4—21no—
150C11×C4⋊C4—21no—
151C11×C4⋊C4—41no—
152C11×C4⋊C4—41no—
153C11×C4⋊C4—42no—
154C11×C4⋊C4—81no—
155C11×C4⋊C4—81no—
156C11×C4⋊C4—81no—
157C42×C11—21no—
158C42×C11—21no—
159C42×C11—21no—
160C42×C11—21no—
161C42×C11—42no—
162C42×C11C2×Q812yes—
163C42×C11#4112yes—
164(C2×D11)⋊C4—24no—
165(C2×D11)⋊C4—42no—
166(C2×D11)⋊C4—42no—
167(C2×D11)⋊C4—81no—
168(C2×D11)⋊C4—81no—
169C4⋊Dic11—21no—
170C4⋊Dic11—21no—
171C4⋊Dic11—21no—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11C2×Q812yes—
175C4×Dic11—81no—
176C4×Dic11—81no—
177C2×C11⋊C8—21no—
178C2×C11⋊C8—21no—
179C2×C11⋊C8—21no—
180C2×C11⋊C8—21no—
181C2×C11⋊C8—21no—
182C2×C11⋊C8—21no—
183C2×C11⋊C8—21no—
184C2×C11⋊C8—21no—
185C2×C11⋊C8—21no—
186C2×C11⋊C8—21no—
187C2×C11⋊C8#4112yes—
188C2×C11⋊C8#4112yes—
189#2571D1111yescharacteristic, complemented
190#2357—111no—
191#2092—111no—
192#2092—111no—
193#2067—111no—
194#2065—111no—
195#1949—111no—
196#1949—111no—
197#1949—111no—
198#1940—111no—
199#1920—111no—
200#1918—111no—
201#1847—111no—
202#1802—111no—
203#1762—111no—
204C23×C11C22×D411yescharacteristic
205C22×D11—22no—
206C22×D11—41no—
207C22×D11—41no—
208C22×D11—41no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11—41no—
212C2×C4×C11—21no—
213C2×C4×C11—21no—
214C2×C4×C11—21no—
215C2×C4×C11—21no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—21no—
219C2×C4×C11—21no—
220C2×C4×C11—21no—
221C2×C4×C11—21no—
222C2×C4×C11—21no—
223C2×C4×C11—21no—
224C2×C4×C11—21no—
225C2×C4×C11—21no—
226C2×C4×C11—21no—
227C2×C4×C11—21no—
228C2×C4×C11—41no—
229C2×C4×C11—41no—
230C2×C4×C11—41no—
231C2×C4×C11—41no—
232C2×C4×C11—41no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11C22⋊Q812yes—
241C2×C4×C11C22⋊Q812yes—
242C2×C4×C11C22×Q811yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×C4×C11H(5,𝔽2)11yescharacteristic
247C2×C4×C112−1+411yescharacteristic
248C2×Dic11—22no—
249C2×Dic11—41no—
250C2×Dic11—41no—
251C2×Dic11—41no—
252C2×Dic11—41no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—41no—
256C2×Dic11—41no—
257D44—22no—
258D44—22no—
259D44—41no—
260D44—41no—
261C4×D11—84no—
262C11⋊C8—22no—
263C11⋊C8—22no—
264C11⋊C8—41no—
265C11⋊C8—41no—
266C2×C4×D4—111no—
267C2×#107—111no—
268C2×#107—111no—
269C2×#107—111no—
270C2×#106—111no—
271C2×#106—111no—
272C2×#106—111no—
273C2×C4⋊C8—111no—
274C2×C4⋊C8—111no—
275C2×C4⋊C8—111no—
276C2×#102—111no—
277C2×#102—111no—
278C2×#102—111no—
279C2×#102—111no—
280C2×#97—111no—
281#400—21no—
282#400—21no—
283#390—111no—
284#390—111no—
285#389—21no—
286#389C2×D1111yescharacteristic
287#389C2×D1111yescharacteristic
288#388—221no—
289#388—221no—
290#384C2×D1111yescharacteristic
291#382—21no—
292#382—111no—
293#382C2×D1111yescharacteristic
294#382C2×D1111yescharacteristic
295#381—221no—
296C4×C4⋊C4—111no—
297C4×C4⋊C4—111no—
298C4×C4⋊C4C2×D1111yescharacteristic
299C4×C4⋊C4C2×D1111yescharacteristic
300C4×C22⋊C4—221no—
301#340—111no—
302#340—111no—
303#340—111no—
304#340—111no—
305#340—111no—
306#340—111no—
307#336—111no—
308#336—111no—
309C22×C11C2×C22⋊Q811yescharacteristic
310C22×C11#54711yescharacteristic
311C22×C11#55011yescharacteristic
312C22×C11#57511yescharacteristic
313C22×C11#57511yescharacteristic
314C22×C11#57611yescharacteristic
315C22×C11#57711yescharacteristic
316C2×D11—42no—
317C2×D11—42no—
318C2×D11—42no—
319C2×D11—81no—
320C2×D11—81no—
321C2×D11—81no—
322C2×D11—81no—
323C4×C11—22no—
324C4×C11—22no—
325C4×C11—41no—
326C4×C11—41no—
327C4×C11—41no—
328C4×C11—41no—
329C4×C11—81no—
330C4×C11—81no—
331C4×C11—81no—
332C4×C11—81no—
333C4×C11#53311yescharacteristic
334C4×C11#54411yescharacteristic
335C4×C11#55211yescharacteristic
336C4×C11#55311yescharacteristic
337Dic11—42no—
338Dic11—81no—
339Dic11—81no—
340C22×D4—111no—
341C23×C4—221no—
342C22×C8—111no—
343C22×C8—111no—
344C22×C8—111no—
345C22×C8—111no—
346C4×D4—114no—
347C4×D4—222no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—111no—
353C2×C4⋊C4—111no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4C22⋊D1111yescharacteristic
356C2×C4⋊C4C22⋊D1111yescharacteristic
357C2×C4⋊C4C22×D1111yescharacteristic
358C2×C4⋊C4C22×D1111yescharacteristic
359C2×C4⋊C4C22×D1111yescharacteristic
360C2×C4⋊C4C22×D1111yescharacteristic
361C2×C22⋊C4—221no—
362C2×C22⋊C4—221no—
363C2×C22⋊C4—221no—
364C2×C22⋊C4—221no—
365C2×C22⋊C4—221no—
366C2×C42—21no—
367C2×C42—221no—
368C2×C42—221no—
369C2×C42C22×D1111yescharacteristic
370C2×C42C22×D1111yescharacteristic
371C2×C42C22×D1111yescharacteristic
372#107—222no—
373#107—441no—
374#107—441no—
375#106—222no—
376#106—441no—
377#106—441no—
378C4⋊C8—222no—
379C4⋊C8—222no—
380C4⋊C8—222no—
381#102—222no—
382#102—222no—
383#102—441no—
384#102—441no—
385#97—222no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—221no—
394#95—221no—
395#95—221no—
396#95—221no—
397#95C22⋊D1111yescharacteristic
398#95C22⋊D1111yescharacteristic
399C2×C11#244111yescharacteristic
400C2×C11#308011yescharacteristic
401C2×C11#308111yescharacteristic
402C2×C11#334711yescharacteristic
403C2×C11#335011yescharacteristic
404C2×C11#340111yescharacteristic
405C2×C11#340311yescharacteristic
406D11—82no—
407C24—221no—
408C2×D4—112no—
409C2×D4—221no—
410C2×D4—221no—
411C2×D4—221no—
412C2×D4—221no—
413C2×D4—221no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—221no—
419C22×C4—224no—
420C22×C4—221no—
421C22×C4—221no—
422C22×C4—881no—
423C22×C4—881no—
424C22×C4C2×C22⋊D1111yescharacteristic
425C22×C4C2×C22⋊D1111yescharacteristic
426C22×C4C2×C22⋊D1111yescharacteristic
427C22×C4C2×C22⋊D1111yescharacteristic
428C22×C4C2×C22⋊D1111yescharacteristic
429C22×C4C2×C22⋊D1111yescharacteristic
430C22×C4C23×D1111yescharacteristic
431C2×C8—112no—
432C2×C8—112no—
433C2×C8—221no—
434C2×C8—221no—
435C2×C8—221no—
436C2×C8—221no—
437C2×C8—221no—
438C2×C8—221no—
439C2×C8—221no—
440C2×C8—221no—
441C2×C8—221no—
442C2×C8—221no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—42no—
454C4⋊C4—81no—
455C4⋊C4—81no—
456C4⋊C4—81no—
457C4⋊C4—112no—
458C4⋊C4—221no—
459C4⋊C4—221no—
460C4⋊C4—221no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C22⋊C4—224no—
464C22⋊C4—442no—
465C22⋊C4—442no—
466C22⋊C4—881no—
467C22⋊C4—881no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—42no—
473C42—881no—
474C42—881no—
475C42Q8×D1112yes—
476C42#434312yes—
477C11#2610311yescharacteristic, complemented, Sylow
478C23—222no—
479C23—441no—
480C23—441no—
481C23—441no—
482C23—441no—
483C23—441no—
484C23—441no—
485C23C22×C22⋊D1111yescharacteristic
486D4—222no—
487D4—222no—
488D4—441no—
489D4—441no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—222no—
519C2×C4—441no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—441no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—884no—
528C2×C4#6699912yes—
529C2×C4#6699912yes—
530C2×C4C2×Q8×D1111yescharacteristic
531C2×C4C2×#434311yescharacteristic
532C2×C4#41×D1111yescharacteristic
533C2×C4#41×D1111yescharacteristic
534C2×C4#6704211yescharacteristic
535C2×C4#6704311yescharacteristic
536C8—222no—
537C8—222no—
538C8—441no—
539C8—441no—
540C22—442no—
541C22—442no—
542C22—442no—
543C22—881no—
544C22—881no—
545C22—881no—
546C22—881no—
547C22C2×#6699911yescharacteristic
548C22#1062335311yescharacteristic
549C22#1062335311yescharacteristic
550C22#1062335511yescharacteristic
551C22#1062336511yescharacteristic
552C22#1062336611yescharacteristic
553C22#1062336811yescharacteristic
554C4—22no—
555C4—22no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—442no—
565C4—881no—
566C4—881no—
567C4#1062321911yescharacteristic
568C4#1062322011yescharacteristic
569C4#1062322511yescharacteristic
570C4#1062322611yescharacteristic
571C2—882no—
572C2#1307232511yescharacteristic
573C2#1307843411yescharacteristic
574C2#1307844111yescharacteristic
575C2#1308111611yescharacteristic
576C2#1308116111yescharacteristic
577C2#1308168211yescharacteristic
578C2#1308170011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2571C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2571D11
hypocenterC11#26103
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2571

Complements

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

NH ≅ G/Ntype
6. #13069384C2semidirect
7. #13069382C2semidirect
8. #13069382C2semidirect
9. #13069340C2semidirect
10. #13069198C2semidirect
11. #13069184C2semidirect
12. #13068782C2semidirect
15. C11×#2571C2semidirect
189. #2571D11semidirect
477. C11#26103semidirect

Maximal subgroups

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

subgroupindex
#130715872
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#130700012
#130699872
#130693842
#130693822
#130693402
#130691982
#130691842
#130687822
#130686132
#130684442
C11×#25712
#2610311