Finite Group Databasebeta

← #14826424

Subgroups — #14826424

Order 2816.

812 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073038C211yesmaximal, characteristic, complemented
2#13070019C211yesmaximal, characteristic, complemented
3#13070004C211yesmaximal, characteristic, complemented
4#13069795C211yesmaximal, characteristic
5#13069795C211yesmaximal, characteristic
6#13069374C211yesmaximal, characteristic, complemented
7#13069346C211yesmaximal, characteristic, complemented
8#13069224C211yesmaximal, characteristic, complemented
9#13069187C211yesmaximal, characteristic, complemented
10#13069184C211yesmaximal, characteristic, complemented
11#13068863C211yesmaximal, characteristic, complemented
12#13068804C211yesmaximal, characteristic, complemented
13#13068702C211yesmaximal, characteristic, complemented
14C4×#66896C211yesmaximal, characteristic, complemented
15C11×#2361C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11—21no—
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C2×#66932—21no—
21C11×#390C2211yescharacteristic
22C11×#389C2211yescharacteristic
23C11×#388—21no—
24C11×#386—21no—
25C11×#385—21no—
26C4×C11×C4⋊C4C2211yescharacteristic
27C4×C11×C22⋊C4C2211yescharacteristic
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622825C2211yescharacteristic
33#10622825C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35C2×C22⋊(C11⋊C8)C2211yescharacteristic
36C2×#66871C2211yescharacteristic
37C2×#66871C2211yescharacteristic
38C2×#66871C2211yescharacteristic
39C2×#66871C2211yescharacteristic
40#10622566—21no—
41#10622548C2211yescharacteristic
42C4×C4⋊Dic11C2211yescharacteristic
43#10622541C2211yescharacteristic
44#10622541C2211yescharacteristic
45C2×C4⋊(C11⋊C8)C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622272—21no—
48#10622266—21no—
49#10622167C2211yescharacteristic
50#10622167C2211yescharacteristic
51#10622167C2211yescharacteristic
52#10622167C2211yescharacteristic
53#10622167C2211yescharacteristic
54#10622167C2211yescharacteristic
55#10622167C2211yescharacteristic
56#10622167C2211yescharacteristic
57#10622162C2211yescharacteristic
58#10622162C2211yescharacteristic
59C22×D4×C11—21no—
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—21no—
62C23×C4×C11—21no—
63C23×C4×C11C2311yescharacteristic
64C11×#121—22no—
65C11×#121—22no—
66C4×D4×C11—22no—
67C4×D4×C11—41no—
68C4×D4×C11—44no—
69C2×C11×C4⋊C4—22no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—41no—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4D411yescharacteristic
81C2×C11×C22⋊C4D411yescharacteristic
82C2×C42×C11—21no—
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C22⋊Dic11—21no—
86C2×C22⋊Dic11—21no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11C2311yescharacteristic
90C2×C4⋊Dic11C2311yescharacteristic
91C2×C4⋊Dic11C2311yescharacteristic
92C2×C4⋊Dic11C2311yescharacteristic
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×C4×Dic11—21no—
96C22×C11⋊C8C2311yescharacteristic
97C22×C11⋊C8C2311yescharacteristic
98C22×C11⋊C8C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100#66932—44no—
101C11×#95—21no—
102C11×#95—21no—
103C11×#95D411yescharacteristic
104C11×#95D411yescharacteristic
105#66896—22no—
106#66896—22no—
107#66896—22no—
108#66896—41no—
109C11⋊#95—21no—
110C11⋊#95—21no—
111C11⋊#95—21no—
112C11⋊#95—21no—
113C11⋊#95—21no—
114C22⋊(C11⋊C8)—22no—
115C22⋊(C11⋊C8)—41no—
116#66871—22no—
117#66871—22no—
118#66871—22no—
119#66871—41no—
120C4⋊(C11⋊C8)—22no—
121C4×C11⋊C8—41no—
122#27030—111nomaximal, Sylow
123C24×C11—21no—
124C24×C11C2×D411yescharacteristic
125C2×D4×C11—24no—
126C2×D4×C11—21no—
127C2×D4×C11—21no—
128C2×D4×C11—21no—
129C2×D4×C11—21no—
130C2×D4×C11—21no—
131C2×D4×C11—42no—
132C2×D4×C11—42no—
133C2×D4×C11#4112yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—42no—
144C22×C4×C11—42no—
145C22×C4×C11—42no—
146C22×C4×C11—42no—
147C22×C4×C11—81no—
148C22×C4×C11—81no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—42no—
165C11×C4⋊C4#4112yes—
166C11×C4⋊C4#4112yes—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—41no—
169C11×C22⋊C4—42no—
170C11×C22⋊C4—42no—
171C11×C22⋊C4—81no—
172C11×C22⋊C4D814yes—
173C42×C11—21no—
174C42×C11—21no—
175C42×C11—21no—
176C42×C11—21no—
177C42×C11—42no—
178C22⋊Dic11—42no—
179C22⋊Dic11—42no—
180C4⋊Dic11—21no—
181C4⋊Dic11—21no—
182C4⋊Dic11—21no—
183C4⋊Dic11—21no—
184C4⋊Dic11—21no—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11—21no—
188C4⋊Dic11—42no—
189C4⋊Dic11—42no—
190Dic11⋊C4—42no—
191Dic11⋊C4—42no—
192C4×Dic11—42no—
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—21no—
203C2×C11⋊C8—21no—
204C2×C11⋊C8#4112yes—
205#2496—111no—
206#2361D1111yescharacteristic
207#2071—111no—
208#2067—111no—
209#2033—111no—
210#2033—111no—
211#1947—111no—
212#1942—111no—
213#1923—111no—
214#1918—111no—
215#1918—111no—
216#1862—111no—
217#1852—111no—
218#1823—111no—
219C4×#102—111no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11—21no—
226C23×C11—22no—
227C23×C11—41no—
228C23×C11—41no—
229C23×C11—41no—
230C23×C11—41no—
231C23×C11—41no—
232C23×C11—41no—
233C23×C11C2×D812yes—
234C23×C11C22×D411yescharacteristic
235D4×C11—22no—
236D4×C11—22no—
237D4×C11—48no—
238D4×C11—41no—
239D4×C11—41no—
240C2×C4×C11—21no—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—22no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—21no—
249C2×C4×C11—21no—
250C2×C4×C11—21no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—21no—
255C2×C4×C11—41no—
256C2×C4×C11—41no—
257C2×C4×C11—41no—
258C2×C4×C11—41no—
259C2×C4×C11—41no—
260C2×C4×C11—41no—
261C2×C4×C11—41no—
262C2×C4×C11—41no—
263C2×C4×C11—41no—
264C2×C4×C11—41no—
265C2×C4×C11—41no—
266C2×C4×C11—84no—
267C2×C4×C11—84no—
268C2×C4×C11C2×D812yes—
269C2×C4×C11C2×D812yes—
270C2×C4×C11C2×#4111yescharacteristic
271C2×C4×C11C2×#4111yescharacteristic
272C2×C4×C11C2×#4111yescharacteristic
273C2×C4×C11C2×#4111yescharacteristic
274C2×C4×C11H(5,𝔽2)11yescharacteristic
275C2×C4×C112−1+411yescharacteristic
276C2×Dic11—41no—
277C2×Dic11—41no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C11⋊C8—22no—
289C11⋊C8—41no—
290C11⋊C8—41no—
291C11⋊C8—41no—
292C2×#126—221no—
293C2×#121C2×D1111yescharacteristic
294C2×C4×D4—21no—
295C2×C4×D4C2×D1111yescharacteristic
296C22×C4⋊C4C2×D1111yescharacteristic
297C2×#107—111no—
298C2×#107—111no—
299C2×#107—111no—
300C2×#107—111no—
301C2×C4⋊C8—111no—
302C2×#102—111no—
303C2×#102—111no—
304C2×#102—111no—
305C2×#102—111no—
306C2×C22⋊C8—111no—
307C2×C22⋊C8—111no—
308C2×C4×C8—111no—
309#400—221no—
310#397—221no—
311#390C2×D1111yescharacteristic
312#389—111no—
313#389—111no—
314#389C2×D1111yescharacteristic
315#388—21no—
316#387—221no—
317#386—21no—
318#385—21no—
319#384—111no—
320#380—111no—
321#380—111no—
322C4×C4⋊C4—111no—
323C4×C4⋊C4C2×D1111yescharacteristic
324C4×C22⋊C4C2×D1111yescharacteristic
325#340—111no—
326#340—111no—
327#340—111no—
328#340—111no—
329#340—111no—
330#340—111no—
331#340—111no—
332#340—111no—
333#336—111no—
334#336—111no—
335C22×C11—22no—
336C22×C11—22no—
337C22×C11—22no—
338C22×C11—41no—
339C22×C11—41no—
340C22×C11—41no—
341C22×C11—41no—
342C22×C11—42no—
343C22×C11—42no—
344C22×C11—42no—
345C22×C11—81no—
346C22×C11—81no—
347C22×C11—81no—
348C22×C11—81no—
349C22×C11#52511yescharacteristic
350C22×C11#54611yescharacteristic
351C22×C11#54711yescharacteristic
352C22×C11C22×D811yescharacteristic
353C22×C11#57511yescharacteristic
354C22×C11#57711yescharacteristic
355C22×C11#57811yescharacteristic
356C4×C11—22no—
357C4×C11—22no—
358C4×C11—41no—
359C4×C11—42no—
360C4×C11—41no—
361C4×C11—42no—
362C4×C11—41no—
363C4×C11—81no—
364C4×C11#52911yescharacteristic
365C4×C11#53911yescharacteristic
366C4×C11#55311yescharacteristic
367C4×C11#55611yescharacteristic
368Dic11—81no—
369Dic11—81no—
370Dic11—81no—
371Dic11—81no—
372C22×D4—21no—
373C22×D4C22×D1111yescharacteristic
374C23×C4—21no—
375C23×C4—21no—
376C23×C4C22×D1111yescharacteristic
377C22×C8—111no—
378C22×C8—111no—
379C22×C8—111no—
380C22×C8—111no—
381#126—444no—
382#121—22no—
383#121—22no—
384C4×D4—22no—
385C4×D4—41no—
386C4×D4—44no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—41no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C4⋊C4C22×D1111yescharacteristic
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4C22⋊D1111yescharacteristic
409C2×C22⋊C4C22⋊D1111yescharacteristic
410C2×C42—21no—
411C2×C42—221no—
412C2×C42C22×D1111yescharacteristic
413C2×C42C22×D1111yescharacteristic
414#107—222no—
415#107—222no—
416#107—222no—
417#107—441no—
418C4⋊C8—222no—
419#102—222no—
420#102—222no—
421#102—222no—
422#102—441no—
423C22⋊C8—222no—
424C22⋊C8—441no—
425C4×C8—441no—
426#95—21no—
427#95—21no—
428#95—221no—
429#95—221no—
430#95—221no—
431#95—221no—
432#95—221no—
433#95C22⋊D1111yescharacteristic
434#95C22⋊D1111yescharacteristic
435C2×C11—42no—
436C2×C11—82no—
437C2×C11#246611yescharacteristic
438C2×C11#310011yescharacteristic
439C2×C11#312011yescharacteristic
440C2×C11#329411yescharacteristic
441C2×C11#331311yescharacteristic
442C2×C11#333411yescharacteristic
443C2×C11#335111yescharacteristic
444C24—21no—
445C24C2×C22⋊D1111yescharacteristic
446C2×D4—24no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4#433912yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—81no—
469C22×C4—81no—
470C22×C4—221no—
471C22×C4—221no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4C2×C22⋊D1111yescharacteristic
475C22×C4C2×C22⋊D1111yescharacteristic
476C22×C4C2×C22⋊D1111yescharacteristic
477C22×C4C2×C22⋊D1111yescharacteristic
478C22×C4C2×C22⋊D1111yescharacteristic
479C22×C4C23×D1111yescharacteristic
480C2×C8—112no—
481C2×C8—221no—
482C2×C8—221no—
483C2×C8—221no—
484C2×C8—221no—
485C2×C8—221no—
486C2×C8—221no—
487C2×C8—221no—
488C2×C8—221no—
489C2×C8—221no—
490C2×C8—221no—
491C2×C8—221no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—42no—
497C4⋊C4—42no—
498C4⋊C4—221no—
499C4⋊C4—221no—
500C4⋊C4—221no—
501C4⋊C4—221no—
502C4⋊C4—221no—
503C4⋊C4—221no—
504C4⋊C4—221no—
505C4⋊C4—221no—
506C4⋊C4—442no—
507C4⋊C4—442no—
508C4⋊C4—442no—
509C4⋊C4—442no—
510C4⋊C4#433912yes—
511C4⋊C4#434112yes—
512C22⋊C4—24no—
513C22⋊C4—41no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—81no—
517C22⋊C4—442no—
518C22⋊C4—442no—
519C22⋊C4#432314yes—
520C42—21no—
521C42—21no—
522C42—21no—
523C42—21no—
524C42—42no—
525C42—442no—
526C11#2703011yescharacteristic, complemented, Sylow
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—22no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23C2×#432312yes—
541C23C22×C22⋊D1111yescharacteristic
542D4—22no—
543D4—22no—
544D4—48no—
545D4—41no—
546D4—41no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—84no—
574C2×C4—84no—
575C2×C4—441no—
576C2×C4—441no—
577C2×C4—441no—
578C2×C4—441no—
579C2×C4—441no—
580C2×C4—441no—
581C2×C4—441no—
582C2×C4—441no—
583C2×C4—441no—
584C2×C4—441no—
585C2×C4—441no—
586C2×C4—441no—
587C2×C4C2×#432312yes—
588C2×C4C2×#432312yes—
589C2×C4C2×#433911yescharacteristic
590C2×C4C2×#433911yescharacteristic
591C2×C4C2×#434111yescharacteristic
592C2×C4#6703711yescharacteristic
593C2×C4#41×D1111yescharacteristic
594C2×C4#6704311yescharacteristic
595C8—222no—
596C8—441no—
597C8—441no—
598C8—441no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22#1062332211yescharacteristic
614C22C22×#432311yescharacteristic
615C22#1062333711yescharacteristic
616C22#1062335311yescharacteristic
617C22#1062335511yescharacteristic
618C22#1062336711yescharacteristic
619C22#1062336911yescharacteristic
620C4—22no—
621C4—22no—
622C4—41no—
623C4—41no—
624C4—42no—
625C4—41no—
626C4—42no—
627C4—81no—
628C4—881no—
629C4—881no—
630C4—881no—
631C4—881no—
632C4#1062306911yescharacteristic
633C4#1062307311yescharacteristic
634C4#1062308911yescharacteristic
635C4#1062309511yescharacteristic
636C2—42no—
637C2—82no—
638C2#1307264611yescharacteristic
639C2#1307861611yescharacteristic
640C2#1307883011yescharacteristic
641C2#1308042911yescharacteristic
642C2#1308068211yescharacteristic
643C2#1308095911yescharacteristic
644C2#1308117011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2361C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2361D11
hypocenterC11#27030
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
1. #13073038C2semidirect
2. #13070019C2semidirect
3. #13070004C2semidirect
6. #13069374C2semidirect
7. #13069346C2semidirect
8. #13069224C2semidirect
9. #13069187C2semidirect
10. #13069184C2semidirect
11. #13068863C2semidirect
12. #13068804C2semidirect
13. #13068702C2semidirect
14. C4×#66896C2semidirect
526. C11#27030semidirect

Maximal subgroups

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

subgroupindex
#130730382
#130700192
#130700042
#130697952
#130693742
#130693462
#130692242
#130691872
#130691842
#130688632
#130688042
#130687022
C4×#668962
C11×#23612
#2703011