Finite Group Databasebeta

← #15618563

Subgroups — #15618563

Order 2816.

2590 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D11C211yesmaximal, characteristic
2#13077655C212yesmaximal, complemented
3#13077646C218yesmaximal, complemented
4#13077645C211yesmaximal, characteristic, complemented
5#13077644C212yesmaximal, complemented
6#13077638C212yesmaximal, complemented
7#13077349C218yesmaximal, complemented
8#13077246C212yesmaximal, complemented
9C2×#10622339C212yesmaximal, complemented
10D11×#407C212yesmaximal, complemented
11C11×#2973C211yesmaximal, characteristic, complemented
12C22×D4×D11C411yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×D4×Dic11C411yescharacteristic
17C2×C4×C22⋊D11C2211yescharacteristic
18C2×C4×C22⋊D11C2211yescharacteristic
19C2×M16×D11C2214yescomplemented
20C22×#4313C2214yescomplemented
21C4×D4×D11C414yes—
22C4×D4×D11C414yes—
23C4×D4×D11C2214yes—
24C4×D4×D11C2214yes—
25C2×#66946C411yescharacteristic
26C2×C4⋊C4×D11C411yescharacteristic
27C2×(C22⋊D11)⋊C4C411yescharacteristic
28C2×(C22⋊D11)⋊C4C411yescharacteristic
29C2×C22⋊C4×D11C411yescharacteristic
30C2×C22⋊C4×D11C411yescharacteristic
31C2×C4×D44C2211yescharacteristic
32C2×C42×D11C2211yescharacteristic
33C11×#435C2218yescomplemented
34C11×#432C2212yescomplemented
35C11×#407C2212yescomplemented
36C2×C11×C22⋊C8C2212yescomplemented
37#10622820C2212yescomplemented
38C2×C22⋊(C11⋊C8)C2212yescomplemented
39#10622741C2218yescomplemented
40#10622739C2214yescomplemented
41C8×C22⋊D11C2218yescomplemented
42C2×(C2×D11)⋊C8C2214yescomplemented
43#10622624C2218yescomplemented
44#10622539C2212yescomplemented
45#10622450C2214yescomplemented
46#10622449C2218yescomplemented
47#10622446C2214yescomplemented
48#10622342C2218yescomplemented
49#10622339C2214yes—
50#10622339C2214yescomplemented
51#10622339C2214yescomplemented
52#10622339C2214yescomplemented
53#10622339C2214yescomplemented
54(C22⋊D11)⋊C8C2218yescomplemented
55D11×C22⋊C8C2214yescomplemented
56D11×C22⋊C8C2214yescomplemented
57#10622331C2214yescomplemented
58#10622320C2214yescomplemented
59#10622319C2218yescomplemented
60#10622318C2214yescomplemented
61C24×D11C2×C411yescharacteristic
62C24×D11C2×C411yescharacteristic
63C22×D4×C11C2×C411yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C22×C22⋊D11C2×C411yescharacteristic
68C23×Dic11C2×C411yescharacteristic
69C23×Dic11C2×C411yescharacteristic
70C2×D4×D11—28no—
71C2×D4×D11C2×C414yes—
72C2×D4×D11C2×C414yes—
73C22×D44C2×C411yescharacteristic
74C22×C4×D11—44no—
75C22×C4×D11—44no—
76C22×C4×D11C2×C411yescharacteristic
77C22×C4×D11C2×C411yescharacteristic
78C22×C4×D11C2×C411yescharacteristic
79C22×C4×D11C2×C411yescharacteristic
80C22×C4×D11C2×C411yescharacteristic
81C22×C4×D11C2×C411yescharacteristic
82C22×C4×D11C2×C412yes—
83C22×C4×D11C2×C412yes—
84C22×C4×D11C2×C412yes—
85C22×C4×D11C2×C412yes—
86C22×C4×D11C2311yescharacteristic
87C22×C4×D11C2312yes—
88C22×C4×D11C2312yes—
89C22×C4×D11C2312yes—
90C22×C4×D11C2312yes—
91C22×C4×D11C2311yescharacteristic
92C22×C4×D11C2311yescharacteristic
93C2×C11×M16C2314yescomplemented
94C22×C8×C11C2314yescomplemented
95C4×D4×C11C2×C414yes—
96C4×D4×C11C2314yes—
97C2×C11×C4⋊C4C2×C411yescharacteristic
98C2×C11×C22⋊C4C2×C411yescharacteristic
99C2×C11×C22⋊C4C2×C411yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C22⋊Dic11C2×C411yescharacteristic
102C2×C22⋊Dic11C2×C411yescharacteristic
103D4×Dic11C2×C414yes—
104D4×Dic11C2×C414yes—
105C4×C22⋊D11C2×C414yes—
106C4×C22⋊D11C2×C414yes—
107C4×C22⋊D11C2314yes—
108C4×C22⋊D11C2314yes—
109C2×(C2×D11)⋊C4C2×C411yescharacteristic
110C2×(C2×D11)⋊C4C2×C411yescharacteristic
111C2×(C2×D11)⋊C4C2×C411yescharacteristic
112C2×(C2×D11)⋊C4C2×C411yescharacteristic
113C2×C4⋊Dic11C2×C411yescharacteristic
114C2×Dic11⋊C4C2×C411yescharacteristic
115C2×Dic11⋊C4C2×C411yescharacteristic
116C2×C4×Dic11C2×C411yescharacteristic
117C2×C4×Dic11C2×C411yescharacteristic
118C2×C4×Dic11C2311yescharacteristic
119C2×#4318C2314yescomplemented
120C22×C11⋊C8C2314yescomplemented
121M16×D11—48no—
122C2×#4313—48no—
123C2×#4313C2318yes—
124C2×#4313C2318yescomplemented
125C2×C8×D11C2318yescomplemented
126#66946C2×C414yes—
127#66946C2×C414yes—
128C4⋊C4×D11C2×C414yes—
129C4⋊C4×D11C2×C414yes—
130(C22⋊D11)⋊C4C2×C414yes—
131(C22⋊D11)⋊C4C2×C414yes—
132(C22⋊D11)⋊C4C2×C414yes—
133(C22⋊D11)⋊C4C2×C414yes—
134C22⋊C4×D11C2×C414yes—
135C22⋊C4×D11C2×C414yes—
136C22⋊C4×D11C2×C414yes—
137C22⋊C4×D11C2×C414yes—
138C4×D44C2×C414yes—
139C4×D44C2314yes—
140C42×D11C2×C412yes—
141C42×D11C2×C412yes—
142C42×D11C2312yes—
143C42×D11C2312yes—
144C11×C4⋊C8C2314yescomplemented
145C11×C22⋊C8C2314yes—
146C11×C22⋊C8C2314yescomplemented
147C11×C22⋊C8C2314yescomplemented
148C11×#97C2314yescomplemented
149C22⋊(C11⋊C8)C2314yes—
150C22⋊(C11⋊C8)C2314yescomplemented
151C22⋊(C11⋊C8)C2314yescomplemented
152(C2×D11)⋊C8C2318yes—
153(C2×D11)⋊C8C2318yescomplemented
154(C2×D11)⋊C8C2318yescomplemented
155Dic11⋊C8C2318yescomplemented
156C8×Dic11C2318yescomplemented
157C4⋊(C11⋊C8)C2314yescomplemented
158#66867C2314yescomplemented
159#60230—111nomaximal, Sylow
160C24×C11C22×C411yescharacteristic
161C24×C11C22×C411yescharacteristic
162C23×D11—24no—
163C23×D11—24no—
164C23×D11—42no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—42no—
168C23×D11C22×C411yescharacteristic
169C23×D11C22×C412yes—
170C23×D11C22×C412yes—
171C23×D11C22×C412yes—
172C23×D11C22×C412yes—
173C23×D11C22×C411yescharacteristic
174C23×D11C22×C411yescharacteristic
175C2×D4×C11—24no—
176C2×D4×C11C22×C414yes—
177C22×C4×C11—42no—
178C22×C4×C11—42no—
179C22×C4×C11C22×C411yescharacteristic
180C22×C4×C11C22×C411yescharacteristic
181C22×C4×C11C22×C411yescharacteristic
182C22×C4×C11C22×C411yescharacteristic
183C22×C4×C11C22×C412yes—
184C22×C4×C11C22×C412yes—
185C22×C4×C11C2411yescharacteristic
186C22×C4×C11C2412yes—
187C22×C4×C11C2412yes—
188C2×C22⋊D11—24no—
189C2×C22⋊D11M1618yescomplemented
190C2×C22⋊D11C22×C414yes—
191C2×C22⋊D11C22×C414yes—
192C22×Dic11—42no—
193C22×Dic11—42no—
194C22×Dic11C22×C412yes—
195C22×Dic11C22×C412yes—
196C22×Dic11C22×C411yescharacteristic
197C22×Dic11C22×C412yes—
198C22×Dic11C22×C412yes—
199C22×Dic11C22×C411yescharacteristic
200C22×Dic11C22×C411yescharacteristic
201C22×Dic11C22×C411yescharacteristic
202C22×Dic11C22×C411yescharacteristic
203D4×D11—216no—
204D4×D11—216no—
205C2×D44—24no—
206C2×D44C22×C414yes—
207C2×C4×D11—24no—
208C2×C4×D11—28no—
209C2×C4×D11—28no—
210C2×C4×D11—24no—
211C2×C4×D11—44no—
212C2×C4×D11—44no—
213C2×C4×D11—42no—
214C2×C4×D11—42no—
215C2×C4×D11—42no—
216C2×C4×D11—42no—
217C2×C4×D11—44no—
218C2×C4×D11—44no—
219C2×C4×D11—42no—
220C2×C4×D11—44no—
221C2×C4×D11—44no—
222C2×C4×D11—42no—
223C2×C4×D11—42no—
224C2×C4×D11C22×C411yescharacteristic
225C2×C4×D11C22×C411yescharacteristic
226C2×C4×D11C22×C412yes—
227C2×C4×D11C22×C412yes—
228C2×C4×D11C22×C412yes—
229C2×C4×D11C22×C412yes—
230C2×C4×D11C22×C412yes—
231C2×C4×D11C22×C412yes—
232C2×C4×D11C22×C412yes—
233C2×C4×D11C22×C412yes—
234C2×C4×D11C22×C412yes—
235C2×C4×D11C22×C412yes—
236C2×C4×D11C22×C412yes—
237C2×C4×D11C22×C412yes—
238C2×C4×D11C22×C412yes—
239C2×C4×D11C22×C412yes—
240C2×C4×D11C2411yescharacteristic
241C2×C4×D11C2412yes—
242C2×C4×D11C2412yes—
243C2×C4×D11C2411yescharacteristic
244C11×M16—44no—
245C2×C8×C11—44no—
246C2×C8×C11C2418yes—
247C11×C4⋊C4C22×C414yes—
248C11×C22⋊C4C22×C414yes—
249C11×C22⋊C4C22×C414yes—
250C42×C11C22×C412yes—
251C42×C11C2412yes—
252C22⋊Dic11C22×C414yes—
253C22⋊Dic11C22×C414yes—
254(C2×D11)⋊C4C22×C414yes—
255(C2×D11)⋊C4C22×C414yes—
256(C2×D11)⋊C4C22×C414yes—
257(C2×D11)⋊C4C22×C414yes—
258C4⋊Dic11C22×C414yes—
259Dic11⋊C4C22×C414yes—
260Dic11⋊C4C22×C414yes—
261C4×Dic11C22×C412yes—
262C4×Dic11C22×C412yes—
263C4×Dic11C22×C412yes—
264C4×Dic11C22×C412yes—
265C4×Dic11C22×C412yes—
266C4×Dic11C2412yes—
267#4318—44no—
268C2×C11⋊C8—44no—
269C2×C11⋊C8C2418yes—
270#4313—216no—
271#4313—48no—
272C8×D11—48no—
273C22×C4×D4—111no—
274#2975—112no—
275#2974—118no—
276#2973—112no—
277#2973—111no—
278#2973D1111yescharacteristic, complemented
279#2972—112no—
280D4×M16—118no—
281#2920—112no—
282C2×#407—112no—
283C2×#407—112no—
284C23×C11—22no—
285C23×C11—41no—
286C23×C11—41no—
287C23×C11—41no—
288C23×C11—41no—
289C23×C11C2×M1614yescomplemented
290C23×C11C23×C412yes—
291C23×C11C23×C412yes—
292C23×C11C23×C411yescharacteristic
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—24no—
298C22×D11—24no—
299C22×D11—24no—
300C22×D11—24no—
301C22×D11—24no—
302C22×D11—24no—
303C22×D11—24no—
304C22×D11—24no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—41no—
308C22×D11—41no—
309C22×D11—42no—
310C22×D11—42no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—416no—
314C22×D11—416no—
315C22×D11C2×M1614yescomplemented
316C22×D11C23×C412yes—
317C22×D11C23×C411yescharacteristic
318C22×D11C23×C412yes—
319C22×D11C23×C411yescharacteristic
320D4×C11—28no—
321C2×C4×C11—22no—
322C2×C4×C11—24no—
323C2×C4×C11—24no—
324C2×C4×C11—22no—
325C2×C4×C11—42no—
326C2×C4×C11—42no—
327C2×C4×C11—41no—
328C2×C4×C11—41no—
329C2×C4×C11—41no—
330C2×C4×C11C23×C412yes—
331C2×C4×C11C23×C412yes—
332C2×C4×C11C23×C411yescharacteristic
333C2×C4×C11C23×C412yes—
334C2×C4×C11C23×C412yes—
335C2×C4×C11C2511yescharacteristic
336C22⋊D11—28no—
337C22⋊D11C2×M16116yescomplemented
338C2×Dic11—22no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11C2×M1614yescomplemented
347C2×Dic11C23×C411yescharacteristic
348C2×Dic11C23×C412yes—
349C2×Dic11C23×C412yes—
350C2×Dic11C23×C412yes—
351C2×Dic11C23×C411yescharacteristic
352C2×Dic11C23×C412yes—
353D44—28no—
354C4×D11—22no—
355C4×D11—24no—
356C4×D11—24no—
357C4×D11—24no—
358C4×D11—24no—
359C4×D11—24no—
360C4×D11—22no—
361C4×D11—22no—
362C4×D11—24no—
363C4×D11—24no—
364C4×D11—24no—
365C4×D11—24no—
366C4×D11—42no—
367C4×D11—42no—
368C4×D11—42no—
369C4×D11—42no—
370C4×D11—42no—
371C4×D11—42no—
372C4×D11—42no—
373C4×D11H(5,𝔽2)14yes—
374C8×C11—28no—
375C11⋊C8—28no—
376C23×D4—111no—
377C24×C4—111no—
378C24×C4—111no—
379C22×M16—114no—
380C22×M16—114no—
381C2×C4×D4—111no—
382C2×C4×D4—111no—
383C2×C4×D4—111no—
384C2×C4×D4—114no—
385C2×C4×D4—114no—
386C2×C4×D4—114no—
387C2×C4×D4—114no—
388C2×C4×D4—111no—
389C2×C4×D4—111no—
390C2×C4×D4—111no—
391C2×C4×D4—111no—
392C2×C4×D4C2×D1111yescharacteristic
393C22×C4⋊C4—111no—
394C22×C22⋊C4—111no—
395C22×C22⋊C4—111no—
396C22×C42—111no—
397#436—118no—
398#436—118no—
399#435—118no—
400#435—118no—
401#435—118no—
402#435C2×D1118yescomplemented
403C8×D4—118no—
404C8×D4—118no—
405#432—112no—
406#432—114no—
407#432C2×D1112yescomplemented
408#431—114no—
409#431—114no—
410#423—114no—
411#407—112no—
412#407—114no—
413#407—114no—
414#407—114no—
415#407—114no—
416#407—114no—
417#407—114no—
418#407C2×D1112yescomplemented
419C2×C22⋊C8—112no—
420C2×C22⋊C8—114no—
421C2×C22⋊C8—114no—
422C2×C22⋊C8—114no—
423C2×C22⋊C8C2×D1112yescomplemented
424C4×M16—114no—
425C22×C11—21no—
426C22×C11—22no—
427C22×C11—21no—
428C22×C11—22no—
429C22×C11—22no—
430C22×C11—22no—
431C22×C11—22no—
432C22×C11—44no—
433C22×C11—44no—
434C22×C11C22×M1612yes—
435C22×C11C22×M1614yes—
436C22×C11C24×C411yescharacteristic
437C2×D11—28no—
438C2×D11—21no—
439C2×D11—22no—
440C2×D11—21no—
441C2×D11—21no—
442C2×D11—21no—
443C2×D11—22no—
444C2×D11—22no—
445C2×D11—22no—
446C2×D11—22no—
447C2×D11—44no—
448C2×D11—48no—
449C2×D11—48no—
450C2×D11—48no—
451C2×D11—48no—
452C2×D11—44no—
453C2×D11#51812yes—
454C2×D11C22×M1614yes—
455C2×D11#56812yes—
456C4×C11—21no—
457C4×C11—22no—
458C4×C11—22no—
459C4×C11—22no—
460C4×C11—22no—
461C4×C11C2×H(5,𝔽2)12yes—
462Dic11—21no—
463Dic11—22no—
464Dic11—22no—
465Dic11—22no—
466Dic11#51812yes—
467Dic11C22×M1614yes—
468C25—111no—
469C25—111no—
470C22×D4—111no—
471C22×D4—111no—
472C22×D4—114no—
473C22×D4—114no—
474C22×D4—111no—
475C22×D4—228no—
476C22×D4C4×D1111yescharacteristic
477C23×C4—111no—
478C23×C4—111no—
479C23×C4—111no—
480C23×C4—112no—
481C23×C4—112no—
482C23×C4—111no—
483C23×C4—111no—
484C23×C4—111no—
485C23×C4—111no—
486C23×C4—111no—
487C23×C4—111no—
488C23×C4—112no—
489C23×C4—112no—
490C23×C4—112no—
491C23×C4—112no—
492C23×C4—111no—
493C23×C4—112no—
494C23×C4—112no—
495C23×C4—111no—
496C23×C4—444no—
497C23×C4—444no—
498C23×C4C22×D1111yescharacteristic
499C23×C4C22×D1111yescharacteristic
500C2×M16—114no—
501C2×M16—118no—
502C2×M16—118no—
503C2×M16—448no—
504C2×M16—448no—
505C2×M16C22×D1114yescomplemented
506C22×C8—114no—
507C22×C8—118no—
508C22×C8C22×D1114yescomplemented
509C4×D4—114no—
510C4×D4—114no—
511C4×D4—114no—
512C4×D4—114no—
513C4×D4—114no—
514C4×D4—114no—
515C4×D4—114no—
516C4×D4—114no—
517C4×D4—114no—
518C4×D4—114no—
519C4×D4—114no—
520C4×D4—114no—
521C4×D4—114no—
522C4×D4—114no—
523C4×D4C4×D1114yes—
524C4×D4C22×D1114yes—
525C2×C4⋊C4—111no—
526C2×C4⋊C4—111no—
527C2×C4⋊C4—111no—
528C2×C4⋊C4—114no—
529C2×C4⋊C4—114no—
530C2×C4⋊C4C4×D1111yescharacteristic
531C2×C22⋊C4—111no—
532C2×C22⋊C4—111no—
533C2×C22⋊C4—111no—
534C2×C22⋊C4—111no—
535C2×C22⋊C4—111no—
536C2×C22⋊C4—111no—
537C2×C22⋊C4—114no—
538C2×C22⋊C4—114no—
539C2×C22⋊C4—114no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4C4×D1111yescharacteristic
542C2×C22⋊C4C4×D1111yescharacteristic
543C2×C42—111no—
544C2×C42—111no—
545C2×C42—111no—
546C2×C42—112no—
547C2×C42—112no—
548C2×C42—112no—
549C2×C42—112no—
550C2×C42C22×D1111yescharacteristic
551C4⋊C8—118no—
552C4⋊C8—114no—
553C4⋊C8C22×D1114yescomplemented
554C22⋊C8—114no—
555C22⋊C8—114no—
556C22⋊C8—114no—
557C22⋊C8—118no—
558C22⋊C8—118no—
559C22⋊C8—118no—
560C22⋊C8C22×D1114yes—
561C22⋊C8C22×D1114yescomplemented
562C22⋊C8C22×D1114yescomplemented
563#97—114no—
564#97C22×D1114yescomplemented
565C4×C8—118no—
566C2×C11—22no—
567C2×C11—24no—
568C2×C11—42no—
569C2×C11C2×#51811yescharacteristic
570C2×C11C23×M1611yescharacteristic
571C2×C11C2×#56811yescharacteristic
572D11—22no—
573D11—22no—
574D11—24no—
575D11—42no—
576C24—111no—
577C24—111no—
578C24—112no—
579C24—112no—
580C24—112no—
581C24—112no—
582C24—111no—
583C24—224no—
584C24—224no—
585C24—442no—
586C24—442no—
587C24—442no—
588C24—442no—
589C24C2×C4×D1111yescharacteristic
590C24C2×C4×D1111yescharacteristic
591C2×D4—24no—
592C2×D4—118no—
593C2×D4—114no—
594C2×D4—114no—
595C2×D4—114no—
596C2×D4—224no—
597C2×D4—224no—
598C2×D4—2216no—
599C2×D4—2216no—
600C2×D4C2×C4×D1114yes—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4—111no—
604C22×C4—111no—
605C22×C4—111no—
606C22×C4—112no—
607C22×C4—112no—
608C22×C4—111no—
609C22×C4—111no—
610C22×C4—111no—
611C22×C4—112no—
612C22×C4—112no—
613C22×C4—112no—
614C22×C4—112no—
615C22×C4—112no—
616C22×C4—111no—
617C22×C4—111no—
618C22×C4—112no—
619C22×C4—112no—
620C22×C4—112no—
621C22×C4—112no—
622C22×C4—111no—
623C22×C4—112no—
624C22×C4—112no—
625C22×C4—112no—
626C22×C4—112no—
627C22×C4—112no—
628C22×C4—112no—
629C22×C4—112no—
630C22×C4—112no—
631C22×C4—112no—
632C22×C4—228no—
633C22×C4—228no—
634C22×C4—224no—
635C22×C4—224no—
636C22×C4—444no—
637C22×C4—444no—
638C22×C4—442no—
639C22×C4—442no—
640C22×C4—444no—
641C22×C4—444no—
642C22×C4—442no—
643C22×C4—442no—
644C22×C4—444no—
645C22×C4—444no—
646C22×C4—442no—
647C22×C4—442no—
648C22×C4—442no—
649C22×C4—442no—
650C22×C4—442no—
651C22×C4C2×C4×D1111yescharacteristic
652C22×C4C2×C4×D1111yescharacteristic
653C22×C4C2×C4×D1111yescharacteristic
654C22×C4C2×C4×D1111yescharacteristic
655C22×C4C2×C4×D1112yes—
656C22×C4C2×C4×D1112yes—
657C22×C4C23×D1111yescharacteristic
658C22×C4C23×D1112yes—
659C22×C4C23×D1112yes—
660M16—44no—
661M16—2216no—
662M16—448no—
663M16—444no—
664C2×C8—44no—
665C2×C8—118no—
666C2×C8—448no—
667C2×C8—444no—
668C2×C8C23×D1118yes—
669C4⋊C4—114no—
670C4⋊C4—114no—
671C4⋊C4—114no—
672C4⋊C4C2×C4×D1114yes—
673C22⋊C4—114no—
674C22⋊C4—114no—
675C22⋊C4—114no—
676C22⋊C4—114no—
677C22⋊C4—114no—
678C22⋊C4—114no—
679C22⋊C4C2×C4×D1114yes—
680C22⋊C4C2×C4×D1114yes—
681C42—112no—
682C42—112no—
683C42—112no—
684C42—112no—
685C42—112no—
686C42—112no—
687C42C2×C4×D1112yes—
688C42C23×D1112yes—
689C11#6023011yescharacteristic, complemented, Sylow
690C23—22no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23—41no—
695C23—112no—
696C23—111no—
697C23—111no—
698C23—114no—
699C23—112no—
700C23—222no—
701C23—222no—
702C23—224no—
703C23—224no—
704C23—224no—
705C23—224no—
706C23—224no—
707C23—224no—
708C23—222no—
709C23—224no—
710C23—224no—
711C23—222no—
712C23—441no—
713C23—441no—
714C23—442no—
715C23—442no—
716C23—441no—
717C23—441no—
718C23—442no—
719C23—442no—
720C23—4416no—
721C23—4416no—
722C23M16×D1114yescomplemented
723C23C22×C4×D1112yes—
724C23C22×C4×D1112yes—
725C23C22×C4×D1111yescharacteristic
726D4—28no—
727D4—1116no—
728D4—228no—
729D4—228no—
730C2×C4—22no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—22no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—114no—
740C2×C4—112no—
741C2×C4—111no—
742C2×C4—114no—
743C2×C4—112no—
744C2×C4—111no—
745C2×C4—112no—
746C2×C4—112no—
747C2×C4—222no—
748C2×C4—224no—
749C2×C4—224no—
750C2×C4—224no—
751C2×C4—224no—
752C2×C4—222no—
753C2×C4—224no—
754C2×C4—224no—
755C2×C4—224no—
756C2×C4—222no—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—224no—
760C2×C4—224no—
761C2×C4—222no—
762C2×C4—442no—
763C2×C4—442no—
764C2×C4—442no—
765C2×C4—442no—
766C2×C4—442no—
767C2×C4—442no—
768C2×C4—442no—
769C2×C4—442no—
770C2×C4—442no—
771C2×C4—441no—
772C2×C4—441no—
773C2×C4—441no—
774C2×C4C22×C4×D1111yescharacteristic
775C2×C4C22×C4×D1112yes—
776C2×C4C22×C4×D1112yes—
777C2×C4C22×C4×D1112yes—
778C2×C4C22×C4×D1112yes—
779C2×C4C24×D1111yescharacteristic
780C8—28no—
781C8—228no—
782C22—21no—
783C22—22no—
784C22—21no—
785C22—22no—
786C22—22no—
787C22—22no—
788C22—22no—
789C22—44no—
790C22—44no—
791C22—114no—
792C22—112no—
793C22—112no—
794C22—228no—
795C22—221no—
796C22—221no—
797C22—221no—
798C22—222no—
799C22—221no—
800C22—222no—
801C22—222no—
802C22—222no—
803C22—222no—
804C22—444no—
805C22—448no—
806C22—448no—
807C22—444no—
808C22—448no—
809C22—448no—
810C22C2×M16×D1112yes—
811C22C2×M16×D1114yes—
812C22C23×C4×D1111yescharacteristic
813C4—22no—
814C4—22no—
815C4—21no—
816C4—22no—
817C4—22no—
818C4—114no—
819C4—112no—
820C4—222no—
821C4—221no—
822C4—222no—
823C4—222no—
824C4D11×H(5,𝔽2)12yes—
825C2—22no—
826C2—24no—
827C2—42no—
828C2—222no—
829C2—222no—
830C2—224no—
831C2—442no—
832C2D11×#51811yescharacteristic
833C2C22×M16×D1111yescharacteristic
834C2D11×#56811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2973C2
prime radicalC22×D4×D11C4
cosocleC2×C4×C11C25
hypercenter#2973D11
hypocenterC11#60230
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #13077655C2semidirect
3. #13077646C2semidirect
4. #13077645C2semidirect
5. #13077644C2semidirect
6. #13077638C2semidirect
7. #13077349C2semidirect
8. #13077246C2semidirect
9. C2×#10622339C2semidirect
10. D11×#407C2semidirect
11. C11×#2973C2semidirect
19. C2×M16×D11C22semidirect
20. C22×#4313C22semidirect
33. C11×#435C22semidirect
34. C11×#432C22semidirect
35. C11×#407C22semidirect
36. C2×C11×C22⋊C8C22semidirect
37. #10622820C22semidirect
38. C2×C22⋊(C11⋊C8)C22semidirect
39. #10622741C22semidirect
40. #10622739C22semidirect
41. C8×C22⋊D11C22semidirect
42. C2×(C2×D11)⋊C8C22semidirect
43. #10622624C22semidirect
44. #10622539C22semidirect
45. #10622450C22semidirect
46. #10622449C22semidirect
47. #10622446C22semidirect
48. #10622342C22semidirect
50. #10622339C22semidirect
51. #10622339C22semidirect
52. #10622339C22semidirect
53. #10622339C22semidirect
54. (C22⋊D11)⋊C8C22semidirect
55. D11×C22⋊C8C22semidirect
56. D11×C22⋊C8C22semidirect
57. #10622331C22semidirect
58. #10622320C22semidirect
59. #10622319C22semidirect
60. #10622318C22semidirect
93. C2×C11×M16C23semidirect
94. C22×C8×C11C23semidirect
119. C2×#4318C23semidirect
120. C22×C11⋊C8C23semidirect
124. C2×#4313C23semidirect
125. C2×C8×D11C23semidirect
144. C11×C4⋊C8C23semidirect
146. C11×C22⋊C8C23semidirect
147. C11×C22⋊C8C23semidirect
148. C11×#97C23semidirect
150. C22⋊(C11⋊C8)C23semidirect
151. C22⋊(C11⋊C8)C23semidirect
153. (C2×D11)⋊C8C23semidirect
154. (C2×D11)⋊C8C23semidirect
155. Dic11⋊C8C23semidirect
156. C8×Dic11C23semidirect
157. C4⋊(C11⋊C8)C23semidirect
158. #66867C23semidirect
189. C2×C22⋊D11M16semidirect
278. #2973D11semidirect
289. C23×C11C2×M16semidirect
315. C22×D11C2×M16semidirect
337. C22⋊D11C2×M16semidirect
346. C2×Dic11C2×M16semidirect
402. #435C2×D11semidirect
407. #432C2×D11semidirect
418. #407C2×D11semidirect
423. C2×C22⋊C8C2×D11semidirect
505. C2×M16C22×D11semidirect
508. C22×C8C22×D11semidirect
553. C4⋊C8C22×D11semidirect
561. C22⋊C8C22×D11semidirect
562. C22⋊C8C22×D11semidirect
564. #97C22×D11semidirect
689. C11#60230semidirect
722. C23M16×D11semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D4×D112
#130776552
#130776462
#130776452
#130776442
#130776382
#130773492
#130772462
C2×#106223392
D11×#4072
C11×#29732
#6023011