Finite Group Databasebeta

← #14769080

Subgroups — #14769080

Order 2816.

1540 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic
2C2×#10622301C211yesmaximal, characteristic, complemented
3C2×C8×D44C211yesmaximal, characteristic, complemented
4C2×#10622340C212yesmaximal, complemented
5#13069410C211yesmaximal, characteristic, complemented
6#13069410C211yesmaximal, characteristic, complemented
7#13068912C212yesmaximal, complemented
8#13068907C212yesmaximal, complemented
9#13068596C211yesmaximal, characteristic, complemented
10#13068527C212yesmaximal, complemented
11C4×C11×C22⋊C8C211yesmaximal, characteristic, complemented
12C22×#4339C2212yes—
13C22×C42×C11C2211yescharacteristic
14C2×#66983C411yescharacteristic
15C2×#66983C412yes—
16C2×#66983C411yescharacteristic
17C22×#4313C2212yes—
18C22×C8×D11C2212yes—
19#10623008—24no—
20#10623008—24no—
21C2×#66928C412yes—
22C2×#66927C411yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×C4×D44C2212yes—
25C2×C4×D44C2211yescharacteristic
26C2×#66922C411yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28C2×C11×C22⋊C8C2211yescharacteristic
29C2×C4×C8×C11C2211yescharacteristic
30C2×C4×C8×C11C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2212yes—
32C2×(C2×D11)⋊C8C2212yes—
33C2×(C2×D11)⋊C8C2212yes—
34C2×(C2×D11)⋊C8C2212yes—
35C2×(C2×D11)⋊C8C2212yes—
36C2×(C2×D11)⋊C8C2212yes—
37C2×(C2×D11)⋊C8C2212yes—
38C2×C4⋊(C11⋊C8)C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622340—28no—
41#10622301—24no—
42C8×D44—24no—
43C11×#336C2211yescharacteristic
44C11×#336C2211yescharacteristic
45#10622162C2212yes—
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2×C411yescharacteristic
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11C2×C412yes—
50C22×C22⋊D11C2×C412yes—
51C2×#4339—24no—
52C2×#4339—24no—
53C2×#4339—24no—
54C2×#4339—24no—
55C2×#4339—42no—
56C2×#4339—42no—
57C22×D44C2×C411yescharacteristic
58C22×D44C2×C412yes—
59C22×D44C2×C412yes—
60C22×D44C2×C411yescharacteristic
61C22×C4×D11C2312yes—
62C22×C4×D11C2312yes—
63C22×Dic22C2×C412yes—
64C22×C8×C11C2311yescharacteristic
65C22×C8×C11C2311yescharacteristic
66C22×C8×C11C2311yescharacteristic
67C22×C8×C11C2311yescharacteristic
68C2×C42×C11—22no—
69C2×C42×C11—22no—
70C2×C42×C11C2×C411yescharacteristic
71C2×C42×C11C2×C411yescharacteristic
72C2×C42×C11C2311yescharacteristic
73C2×C42×C11C2311yescharacteristic
74#66983—24no—
75#66983—28no—
76#66983—24no—
77C2×(C2×D11)⋊C4C2×C412yes—
78C2×(C2×D11)⋊C4C2×C412yes—
79C2×(C2×D11)⋊C4C2×C412yes—
80C2×(C2×D11)⋊C4C2×C412yes—
81C2×C4⋊Dic11C2×C412yes—
82C2×C4⋊Dic11C2×C411yescharacteristic
83C2×C4⋊Dic11C2×C411yescharacteristic
84C22×C11⋊C8C2312yes—
85C22×C11⋊C8C2312yes—
86C2×#4313—24no—
87C2×#4313—24no—
88C2×#4313—42no—
89C2×C8×D11—24no—
90C2×C8×D11—24no—
91C2×C8×D11—42no—
92#66928—28no—
93#66927—24no—
94C4×D44—24no—
95C4×D44—24no—
96C4×D44—22no—
97C4×D44—22no—
98C4×D44D414yes—
99C4×D44D414yes—
100#66922—24no—
101C11×C22⋊C8—22no—
102C11×C22⋊C8D414yescomplemented
103C4×C8×C11—22no—
104C4×C8×C11—22no—
105C22⋊(C11⋊C8)—24no—
106(C2×D11)⋊C8—24no—
107(C2×D11)⋊C8—24no—
108(C2×D11)⋊C8—24no—
109(C2×D11)⋊C8—24no—
110(C2×D11)⋊C8—42no—
111(C2×D11)⋊C8—42no—
112C4⋊(C11⋊C8)—22no—
113C4⋊(C11⋊C8)—22no—
114#22402—111nomaximal, Sylow
115C24×C11C22×C411yescharacteristic
116C23×D11C22×C412yes—
117C23×D11C22×C412yes—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—21no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—41no—
128C22×C4×C11C22×C411yescharacteristic
129C22×C4×C11C22×C411yescharacteristic
130C22×C4×C11C22×C411yescharacteristic
131C22×C4×C11C22×C411yescharacteristic
132C22×C4×C11C22×C411yescharacteristic
133C22×C4×C11C2×D412yes—
134C22×C4×C11#4112yes—
135C22×C4×C11C2411yescharacteristic
136C2×C22⋊D11—24no—
137C2×C22⋊D11—24no—
138C2×C22⋊D11—24no—
139C2×C22⋊D11—24no—
140C2×C22⋊D11—42no—
141C2×C22⋊D11—42no—
142C22×Dic11C22×C412yes—
143C22×Dic11C22×C412yes—
144#4339—48no—
145#4339—48no—
146#4339—48no—
147#4339—48no—
148C2×D44—24no—
149C2×D44—24no—
150C2×D44—22no—
151C2×D44—24no—
152C2×D44—22no—
153C2×D44—22no—
154C2×D44—24no—
155C2×D44—22no—
156C2×D44—22no—
157C2×D44—42no—
158C2×D44—42no—
159C2×D44C22⋊C414yes—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—22no—
163C2×C4×D11—22no—
164C2×C4×D11—22no—
165C2×C4×D11—22no—
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×C4×D11—22no—
169C2×C4×D11—22no—
170C2×C4×D11C2×D414yes—
171C2×C4×D11C2×D414yes—
172C2×Dic22—24no—
173C2×Dic22—24no—
174C2×Dic22—42no—
175C2×C8×C11—21no—
176C2×C8×C11—21no—
177C2×C8×C11—21no—
178C2×C8×C11—21no—
179C2×C8×C11—21no—
180C2×C8×C11—21no—
181C2×C8×C11—21no—
182C2×C8×C11—21no—
183C2×C8×C11—21no—
184C2×C8×C11—21no—
185C2×C8×C11C2×D412yes—
186C2×C8×C11C2×D412yes—
187C42×C11—22no—
188C42×C11—22no—
189C42×C11—21no—
190C42×C11—21no—
191C42×C11C2×D412yes—
192C42×C11C2×D412yes—
193(C2×D11)⋊C4—24no—
194(C2×D11)⋊C4—24no—
195(C2×D11)⋊C4—24no—
196(C2×D11)⋊C4C22⋊C418yes—
197C4⋊Dic11—24no—
198C4⋊Dic11—22no—
199C4⋊Dic11C22⋊C414yes—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—22no—
204C2×C11⋊C8—22no—
205C2×C11⋊C8—22no—
206#4313—48no—
207C8×D11—48no—
208C2×#532—111no—
209C2×#436—111no—
210C2×C8×D4—111no—
211C2×#408—112no—
212#1954—111no—
213#1954—111no—
214#1870—112no—
215#1869—112no—
216#1797—111no—
217#1780—112no—
218C4×C22⋊C8D1111yescharacteristic, complemented
219C23×C11—21no—
220C23×C11—21no—
221C23×C11—21no—
222C23×C11—21no—
223C23×C11—21no—
224C23×C11—21no—
225C23×C11C4×D412yes—
226C23×C11C23×C411yescharacteristic
227C22×D11—22no—
228C22×D11—22no—
229C22×D11—22no—
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—22no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11C2×C22⋊C414yes—
241C2×C4×C11—21no—
242C2×C4×C11—21no—
243C2×C4×C11—21no—
244C2×C4×C11—21no—
245C2×C4×C11—21no—
246C2×C4×C11—21no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—21no—
252C2×C4×C11—21no—
253C2×C4×C11—21no—
254C2×C4×C11—44no—
255C2×C4×C11—44no—
256C2×C4×C11C2×C22⋊C412yes—
257C2×C4×C11C2×C22⋊C412yes—
258C2×C4×C11C4×D412yes—
259C2×C4×C11#13112yes—
260C2×C4×C11#13112yes—
261C2×C4×C11#13112yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D411yescharacteristic
264C2×C4×C11C22×D411yescharacteristic
265C2×C4×C11C2×#4111yescharacteristic
266C2×C4×C11H(5,𝔽2)11yescharacteristic
267C2×C4×C11H(5,𝔽2)11yescharacteristic
268C22⋊D11—48no—
269C22⋊D11—48no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11C2×C22⋊C414yes—
276D44—28no—
277D44—48no—
278D44—48no—
279D44—44no—
280C4×D11—24no—
281C4×D11—24no—
282C4×D11—24no—
283C4×D11—24no—
284C4×D11—42no—
285C4×D11—42no—
286C4×D11—42no—
287C4×D11—42no—
288Dic22—48no—
289C8×C11—22no—
290C8×C11—22no—
291C8×C11—41no—
292C8×C11—41no—
293C11⋊C8—42no—
294C11⋊C8—42no—
295C22×#41—112no—
296C22×M16—112no—
297C23×C8—112no—
298#532—224no—
299#532—224no—
300C2×C4⋊Q8—111no—
301C2×#127—111no—
302C2×#124—112no—
303C2×#121—112no—
304C2×#121—111no—
305C2×#121—111no—
306C2×C4×D4—111no—
307C2×C4×D4—112no—
308C2×C4×D4—111no—
309C22×C42C2×D1111yescharacteristic
310#436—224no—
311C8×D4—224no—
312C2×C4⋊C8—111no—
313C2×C4⋊C8—111no—
314#408—228no—
315C2×C22⋊C8—112no—
316C2×C22⋊C8—112no—
317C2×C22⋊C8—112no—
318C2×C22⋊C8—112no—
319C2×C22⋊C8—112no—
320C2×C22⋊C8—112no—
321C2×C22⋊C8—112no—
322C2×C22⋊C8C2×D1111yescharacteristic
323C2×C22⋊C8C2×D1111yescharacteristic
324C2×C4×C8C2×D1111yescharacteristic
325C2×C4×C8C2×D1111yescharacteristic
326#336—112no—
327#336C2×D1111yescharacteristic
328#336C2×D1111yescharacteristic
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—22no—
332C22×C11—41no—
333C22×C11—41no—
334C22×C11—41no—
335C22×C11—41no—
336C22×C11C22×C22⋊C411yescharacteristic
337C22×C11C2×C4×D411yescharacteristic
338C22×C11#51811yescharacteristic
339C22×C11C2×#13111yescharacteristic
340C22×C11C2×#13111yescharacteristic
341C22×C11C2×#13111yescharacteristic
342C22×C11#56811yescharacteristic
343C2×D11—24no—
344C2×D11—24no—
345C2×D11—24no—
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—42no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—42no—
355C2×D11—42no—
356C2×D11—42no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—22no—
360C4×C11—41no—
361C4×C11#40814yescomplemented
362C4×C11D4211yescharacteristic
363C4×C11D4211yescharacteristic
364C4×C11#54611yescharacteristic
365C4×C11#54611yescharacteristic
366Dic11—24no—
367Dic11—42no—
368C2×#41—224no—
369C2×#41—224no—
370C2×#41—224no—
371C2×#41—224no—
372C2×#41—442no—
373C2×#41—442no—
374C22×Q8—112no—
375C22×D4—112no—
376C22×D4—112no—
377C22×D4—111no—
378C22×D4—111no—
379C22×D4—112no—
380C22×D4—112no—
381C23×C4—112no—
382C23×C4—112no—
383C23×C4C4×D1111yescharacteristic
384C23×C4C4×D1111yescharacteristic
385C23×C4C22×D1111yescharacteristic
386C2×M16—224no—
387C2×M16—224no—
388C2×M16—442no—
389C22×C8—112no—
390C22×C8—112no—
391C22×C8—224no—
392C22×C8—224no—
393C22×C8—442no—
394C22×C8C22×D1111yescharacteristic
395C22×C8C22×D1111yescharacteristic
396C22×C8C22×D1111yescharacteristic
397C22×C8C22×D1111yescharacteristic
398C4⋊Q8—224no—
399#127—224no—
400#124—228no—
401#121—228no—
402#121—224no—
403#121—224no—
404C4×D4—114no—
405C4×D4—114no—
406C4×D4—224no—
407C4×D4—224no—
408C4×D4—222no—
409C4×D4—222no—
410C2×C4⋊C4—111no—
411C2×C4⋊C4—112no—
412C2×C4⋊C4—111no—
413C2×C22⋊C4—112no—
414C2×C22⋊C4—112no—
415C2×C22⋊C4—112no—
416C2×C22⋊C4—112no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42C4×D1111yescharacteristic
420C2×C42C4×D1111yescharacteristic
421C2×C42C22×D1111yescharacteristic
422C2×C42C22×D1111yescharacteristic
423C4⋊C8—222no—
424C4⋊C8—222no—
425C22⋊C8—22no—
426C22⋊C8—224no—
427C22⋊C8—224no—
428C22⋊C8—224no—
429C22⋊C8—224no—
430C22⋊C8—224no—
431C22⋊C8—442no—
432C22⋊C8—442no—
433C22⋊C8D4414yescomplemented
434C4×C8—22no—
435C4×C8—22no—
436C2×C11—42no—
437C2×C11D4×C22⋊C411yescharacteristic
438C2×C11C2×#40811yescharacteristic
439C2×C11#288011yescharacteristic
440C2×C11#293111yescharacteristic
441C2×C11#293511yescharacteristic
442C2×C11#297911yescharacteristic
443C2×C11#298111yescharacteristic
444D11—44no—
445D11—82no—
446C24—112no—
447C24—112no—
448C24C2×C4×D1111yescharacteristic
449#41—448no—
450#41—448no—
451#41—448no—
452#41—448no—
453C2×Q8—224no—
454C2×Q8—224no—
455C2×Q8—442no—
456C2×D4—114no—
457C2×D4—224no—
458C2×D4—224no—
459C2×D4—224no—
460C2×D4—224no—
461C2×D4—224no—
462C2×D4—224no—
463C2×D4—224no—
464C2×D4—222no—
465C2×D4—222no—
466C2×D4—224no—
467C2×D4—222no—
468C2×D4—222no—
469C2×D4—222no—
470C2×D4—442no—
471C2×D4—442no—
472C2×D4—442no—
473C2×D4—442no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—41no—
484C22×C4—112no—
485C22×C4—114no—
486C22×C4—114no—
487C22×C4—112no—
488C22×C4—222no—
489C22×C4—222no—
490C22×C4—222no—
491C22×C4—222no—
492C22×C4—222no—
493C22×C4—222no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4C2×C4×D1111yescharacteristic
499C22×C4C2×C4×D1111yescharacteristic
500C22×C4C2×C4×D1111yescharacteristic
501C22×C4C2×C4×D1111yescharacteristic
502C22×C4C2×C4×D1111yescharacteristic
503C22×C4C2×D4412yes—
504C22×C4#433912yes—
505C22×C4C23×D1111yescharacteristic
506M16—448no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—222no—
518C2×C8—222no—
519C2×C8—222no—
520C2×C8—222no—
521C2×C8—222no—
522C2×C8—222no—
523C2×C8—448no—
524C2×C8C2×D4412yes—
525C2×C8C2×D4412yes—
526C4⋊C4—114no—
527C4⋊C4—224no—
528C4⋊C4—222no—
529C22⋊C4—118no—
530C22⋊C4—224no—
531C22⋊C4—224no—
532C22⋊C4—224no—
533C42—22no—
534C42—22no—
535C42—21no—
536C42—21no—
537C42D4×D1112yes—
538C42D4×D1112yes—
539C11#2240211yescharacteristic, complemented, Sylow
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—114no—
547C23—222no—
548C23—222no—
549C23—222no—
550C23—222no—
551C23—222no—
552C23—222no—
553C23—222no—
554C23—222no—
555C23—222no—
556C23—222no—
557C23—222no—
558C23—222no—
559C23—222no—
560C23C4×D4412yes—
561C23C22×C4×D1111yescharacteristic
562Q8—448no—
563D4—228no—
564D4—448no—
565D4—448no—
566D4—448no—
567D4—448no—
568D4—444no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—114no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—442no—
595C2×C4—442no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4C4×D4412yes—
599C2×C4C22⋊C4×D1112yes—
600C2×C4C22⋊C4×D1112yes—
601C2×C4#6695412yes—
602C2×C4#6695412yes—
603C2×C4#6696012yes—
604C2×C4C22×D4411yescharacteristic
605C2×C4C2×#433911yescharacteristic
606C2×C4C2×D4×D1111yescharacteristic
607C2×C4C2×D4×D1111yescharacteristic
608C2×C4#6704211yescharacteristic
609C2×C4#6704211yescharacteristic
610C8—22no—
611C8—22no—
612C8—41no—
613C8—41no—
614C8—442no—
615C8—442no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—224no—
624C22—224no—
625C22—224no—
626C22—442no—
627C22—442no—
628C22—442no—
629C22—442no—
630C22—442no—
631C22—442no—
632C22—442no—
633C22—442no—
634C22—442no—
635C22—442no—
636C22—442no—
637C22C2×C4×D4411yescharacteristic
638C22C2×C22⋊C4×D1111yescharacteristic
639C22#1062305211yescharacteristic
640C22C2×#6695411yescharacteristic
641C22C2×#6695411yescharacteristic
642C22C2×#6696011yescharacteristic
643C22#1062327611yescharacteristic
644C4—22no—
645C4—22no—
646C4—22no—
647C4—41no—
648C4—224no—
649C4—442no—
650C4#1062234014yescomplemented
651C4D4×D4411yescharacteristic
652C4D4×D4411yescharacteristic
653C4#1062308111yescharacteristic
654C4#1062308111yescharacteristic
655C2—42no—
656C2—444no—
657C2—882no—
658C2C22⋊C4×D4411yescharacteristic
659C2C2×#1062234011yescharacteristic
660C2#1307706211yescharacteristic
661C2#1307732911yescharacteristic
662C2#1307736211yescharacteristic
663C2#1307768211yescharacteristic
664C2#1307769111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D11
commutator, socleC23×C11C23×C4
FittingC4×C11×C22⋊C8C2
prime radicalC2×#10623008C2
cosocleC22×C4×C11C24
hypercenterC4×C22⋊C8D11
hypocenterC11#22402
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#10622301C2semidirect
3. C2×C8×D44C2semidirect
4. C2×#10622340C2semidirect
5. #13069410C2semidirect
6. #13069410C2semidirect
7. #13068912C2semidirect
8. #13068907C2semidirect
9. #13068596C2semidirect
10. #13068527C2semidirect
11. C4×C11×C22⋊C8C2semidirect
102. C11×C22⋊C8D4semidirect
218. C4×C22⋊C8D11semidirect
361. C4×C11#408semidirect
433. C22⋊C8D44semidirect
539. C11#22402semidirect
650. C4#10622340semidirect

Maximal subgroups

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

subgroupindex
C2×#106230082
C2×#106223012
C2×C8×D442
C2×#106223402
#130694102
#130689122
#130689072
#130685962
#130685272
C4×C11×C22⋊C82
#2240211