Finite Group Databasebeta

← #14719648

Subgroups — #14719648

Order 2816.

1738 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622820C211yesmaximal, characteristic, complemented
3#13066952C214yesmaximal, complemented
4#13066945C212yesmaximal, complemented
5#13066942C212yesmaximal, complemented
6#13066932C214yesmaximal, complemented
7C2×C11×#407C211yesmaximal, characteristic, complemented
8C24×C4×C11C2211yescharacteristic
9C23×C22⋊D11C411yescharacteristic
10C23×C4×D11C411yescharacteristic
11C22×C11×M16—21no—
12C22×C22⋊Dic11C411yescharacteristic
13C2×C4×C22⋊D11—21no—
14C2×C4×C22⋊D11—21no—
15C2×C4×C22⋊D11—21no—
16C2×C4×C22⋊D11—21no—
17C2×C4×C22⋊D11—21no—
18C2×C4×C22⋊D11—21no—
19C2×C4×C22⋊D11—21no—
20C2×C4×C22⋊D11—21no—
21C2×C4×C22⋊D11C412yes—
22C2×C4×C22⋊D11C412yes—
23C2×C4×C22⋊D11C2212yes—
24C2×C4×C22⋊D11C2212yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×C4×Dic11C411yescharacteristic
28C22×#4318—21no—
29C11×#407—21no—
30C11×#407—21no—
31C11×#407C2212yes—
32C11×#407C2212yescomplemented
33C2×C11×C22⋊C8—21no—
34C2×C11×C22⋊C8C2212yescomplemented
35#10622820—21no—
36#10622820—21no—
37#10622820C2212yes—
38#10622820C2212yescomplemented
39C2×C22⋊(C11⋊C8)—21no—
40C2×C22⋊(C11⋊C8)C2212yescomplemented
41#10622107C2218yescomplemented
42#10622106C2218yescomplemented
43C25×C11C2×C411yescharacteristic
44C24×D11C2×C411yescharacteristic
45C23×C4×C11—44no—
46C23×C4×C11C2×C411yescharacteristic
47C23×C4×C11C2×C411yescharacteristic
48C23×C4×C11C2×C411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11D411yescharacteristic
52C23×C4×C11D411yescharacteristic
53C23×C4×C11D411yescharacteristic
54C23×C4×C11D411yescharacteristic
55C23×C4×C11D411yescharacteristic
56C23×C4×C11D411yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C22×C22⋊D11—21no—
62C22×C22⋊D11—21no—
63C22×C22⋊D11—21no—
64C22×C22⋊D11—28no—
65C22×C22⋊D11C2×C412yes—
66C22×C22⋊D11C2×C412yes—
67C23×Dic11C2×C411yescharacteristic
68C23×Dic11C2×C411yescharacteristic
69C23×Dic11C2×C411yescharacteristic
70C22×C4×D11—21no—
71C22×C4×D11—21no—
72C22×C4×D11—21no—
73C22×C4×D11—21no—
74C22×C4×D11—44no—
75C22×C4×D11C2×C412yes—
76C22×C4×D11C2×C412yes—
77C2×C11×M16—22no—
78C2×C11×M16—22no—
79C2×C11×M16—44no—
80C22×C8×C11—22no—
81C2×C22⋊Dic11—21no—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—21no—
84C2×C22⋊Dic11—21no—
85C2×C22⋊Dic11C2×C412yes—
86C2×C22⋊Dic11C2×C412yes—
87C4×C22⋊D11—22no—
88C4×C22⋊D11—22no—
89C4×C22⋊D11—22no—
90C4×C22⋊D11—22no—
91C4×C22⋊D11—22no—
92C4×C22⋊D11—22no—
93C4×C22⋊D11—22no—
94C4×C22⋊D11—22no—
95C4×C22⋊D11—22no—
96C4×C22⋊D11—22no—
97C4×C22⋊D11—22no—
98C4×C22⋊D11—22no—
99C4×C22⋊D11—22no—
100C4×C22⋊D11—22no—
101C4×C22⋊D11—22no—
102C4×C22⋊D11—22no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4C2×C412yes—
108C2×(C2×D11)⋊C4C2312yes—
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×Dic11⋊C4C2×C412yes—
114C2×Dic11⋊C4C2312yes—
115C2×C4×Dic11—21no—
116C2×C4×Dic11—21no—
117C2×C4×Dic11—21no—
118C2×C4×Dic11—21no—
119C2×C4×Dic11C2×C412yes—
120C2×C4×Dic11C2×C412yes—
121C2×#4318—22no—
122C2×#4318—22no—
123C2×#4318—44no—
124C22×C11⋊C8—22no—
125C11×C22⋊C8—22no—
126C11×C22⋊C8—22no—
127C11×C22⋊C8—22no—
128C11×C22⋊C8C2314yes—
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)—22no—
131C22⋊(C11⋊C8)—22no—
132C22⋊(C11⋊C8)C2314yes—
133#17362—111nomaximal, Sylow
134C24×C11—24no—
135C24×C11—42no—
136C24×C11—42no—
137C24×C11C22⋊C411yescharacteristic
138C24×C11C22⋊C411yescharacteristic
139C24×C11C22⋊C411yescharacteristic
140C24×C11C22⋊C411yescharacteristic
141C24×C11C22×C411yescharacteristic
142C24×C11C22×C411yescharacteristic
143C24×C11C22×C411yescharacteristic
144C23×D11—21no—
145C23×D11—21no—
146C23×D11—24no—
147C23×D11—42no—
148C23×D11—42no—
149C23×D11C22×C412yes—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—24no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11—42no—
156C22×C4×C11—42no—
157C22×C4×C11—42no—
158C22×C4×C11—42no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11—42no—
162C22×C4×C11—42no—
163C22×C4×C11—42no—
164C22×C4×C11C22⋊C411yescharacteristic
165C22×C4×C11C22⋊C411yescharacteristic
166C22×C4×C11C22⋊C411yescharacteristic
167C22×C4×C11C22⋊C411yescharacteristic
168C22×C4×C11C22⋊C411yescharacteristic
169C22×C4×C11C22⋊C411yescharacteristic
170C22×C4×C11C22⋊C411yescharacteristic
171C22×C4×C11C22⋊C411yescharacteristic
172C22×C4×C11C22⋊C411yescharacteristic
173C22×C4×C11C22⋊C411yescharacteristic
174C22×C4×C11C22⋊C411yescharacteristic
175C22×C4×C11C22⋊C411yescharacteristic
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C22×C411yescharacteristic
178C22×C4×C11C22×C411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2411yescharacteristic
192C2×C22⋊D11—28no—
193C2×C22⋊D11—28no—
194C2×C22⋊D11—28no—
195C2×C22⋊D11—28no—
196C2×C22⋊D11—24no—
197C2×C22⋊D11—22no—
198C2×C22⋊D11—22no—
199C2×C22⋊D11—22no—
200C2×C22⋊D11—22no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11M1618yescomplemented
204C22×Dic11—24no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—42no—
212C22×Dic11—42no—
213C22×Dic11C22×C412yes—
214C22×Dic11C22×C412yes—
215C22×Dic11C22×C412yes—
216C2×C4×D11—22no—
217C2×C4×D11—22no—
218C2×C4×D11—22no—
219C2×C4×D11—22no—
220C2×C4×D11—44no—
221C2×C4×D11—44no—
222C2×C4×D11—44no—
223C2×C4×D11—44no—
224C2×C4×D11—44no—
225C2×C4×D11—44no—
226C11×M16—44no—
227C11×M16—44no—
228C2×C8×C11—24no—
229C2×C8×C11—44no—
230C22⋊Dic11—22no—
231C22⋊Dic11—22no—
232C22⋊Dic11—22no—
233C22⋊Dic11—22no—
234(C2×D11)⋊C4—22no—
235(C2×D11)⋊C4—22no—
236(C2×D11)⋊C4—22no—
237(C2×D11)⋊C4—22no—
238Dic11⋊C4—22no—
239Dic11⋊C4—22no—
240Dic11⋊C4—22no—
241Dic11⋊C4—22no—
242C4×Dic11—22no—
243C4×Dic11—22no—
244C4×Dic11—22no—
245C4×Dic11—22no—
246#4318—44no—
247#4318—44no—
248C2×C11⋊C8—24no—
249C2×C11⋊C8—44no—
250C22×C4×D4—111no—
251C2×#407—111no—
252C2×#407D1111yescharacteristic, complemented
253#1465—114no—
254#1463—112no—
255#1462—112no—
256#1459—114no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—416no—
278C23×C11C2×C22⋊C411yescharacteristic
279C23×C11C2×C22⋊C411yescharacteristic
280C23×C11C2×C22⋊C411yescharacteristic
281C23×C11C2×C22⋊C411yescharacteristic
282C23×C11C2×C22⋊C411yescharacteristic
283C23×C11C2×C22⋊C411yescharacteristic
284C23×C11C2×M1614yes—
285C23×C11C23×C411yescharacteristic
286C22×D11—24no—
287C22×D11—24no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—42no—
291C22×D11—416no—
292C22×D11—42no—
293C22×D11—42no—
294C22×D11—42no—
295C22×D11—42no—
296C22×D11—42no—
297C22×D11C2×M1614yescomplemented
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11#9914yes—
326C2×C4×C11C2×C22⋊C411yescharacteristic
327C2×C4×C11C2×C22⋊C411yescharacteristic
328C2×C4×C11C2×C22⋊C411yescharacteristic
329C2×C4×C11C2×C22⋊C411yescharacteristic
330C2×C4×C11C2×C22⋊C411yescharacteristic
331C2×C4×C11C2×C22⋊C411yescharacteristic
332C2×C4×C11C22×D411yescharacteristic
333C2×C4×C11C22×D411yescharacteristic
334C22⋊D11—28no—
335C22⋊D11—28no—
336C22⋊D11—28no—
337C22⋊D11—28no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—22no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11C2×M1614yescomplemented
351C4×D11—44no—
352C4×D11—44no—
353C4×D11—44no—
354C4×D11—44no—
355C8×C11—44no—
356C11⋊C8—44no—
357C23×D4—111no—
358C24×C4—111no—
359C24×C4C2×D1111yescharacteristic
360C22×M16—21no—
361C22×M16—221no—
362C2×C4×D4—112no—
363C2×C4×D4—112no—
364C2×C4×D4—112no—
365C2×C4×D4—112no—
366C2×C4×D4—221no—
367C2×C4×D4—221no—
368C2×C4×D4—221no—
369C2×C4×D4—221no—
370C2×C4×D4—221no—
371C2×C4×D4—221no—
372C2×C4×D4—221no—
373C2×C4×D4—221no—
374C22×C4⋊C4—111no—
375C22×C22⋊C4—111no—
376C22×C22⋊C4—111no—
377C22×C42—111no—
378#407—21no—
379#407—21no—
380#407—112no—
381#407—112no—
382#407—221no—
383#407—221no—
384#407C2×D1112yes—
385#407C2×D1112yescomplemented
386C2×C22⋊C8—21no—
387C2×C22⋊C8—112no—
388C2×C22⋊C8—221no—
389C2×C22⋊C8C2×D1112yescomplemented
390#324—118no—
391#323—118no—
392C22×C11—28no—
393C22×C11—21no—
394C22×C11—21no—
395C22×C11—21no—
396C22×C11—21no—
397C22×C11—21no—
398C22×C11—21no—
399C22×C11—21no—
400C22×C11—21no—
401C22×C11—21no—
402C22×C11—21no—
403C22×C11—21no—
404C22×C11—21no—
405C22×C11—21no—
406C22×C11—21no—
407C22×C11—21no—
408C22×C11—21no—
409C22×C11—44no—
410C22×C11—44no—
411C22×C11—44no—
412C22×C11—44no—
413C22×C11—44no—
414C22×C11—44no—
415C22×C11#40712yes—
416C22×C11#40712yes—
417C22×C11C2×#9912yes—
418C22×C11#41312yes—
419C22×C11C22×C22⋊C411yescharacteristic
420C22×C11C22×M1612yes—
421C2×D11—24no—
422C2×D11—44no—
423C2×D11—48no—
424C2×D11—48no—
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—44no—
428C4×C11—21no—
429C4×C11—21no—
430C4×C11—21no—
431C4×C11—21no—
432C4×C11—21no—
433C4×C11—21no—
434C4×C11C2×#9912yes—
435C4×C11C2×#9912yes—
436Dic11—24no—
437Dic11—42no—
438Dic11—42no—
439C25—111no—
440C25C4×D1111yescharacteristic
441C22×D4—112no—
442C22×D4—112no—
443C22×D4—228no—
444C22×D4—221no—
445C22×D4—221no—
446C22×D4—221no—
447C22×D4—221no—
448C23×C4—44no—
449C23×C4—111no—
450C23×C4—111no—
451C23×C4—111no—
452C23×C4—112no—
453C23×C4—112no—
454C23×C4—221no—
455C23×C4—221no—
456C23×C4—221no—
457C23×C4—221no—
458C23×C4—444no—
459C23×C4C4×D1111yescharacteristic
460C23×C4C4×D1111yescharacteristic
461C23×C4C4×D1111yescharacteristic
462C23×C4D4411yescharacteristic
463C23×C4D4411yescharacteristic
464C23×C4D4411yescharacteristic
465C23×C4D4411yescharacteristic
466C23×C4C22⋊D1111yescharacteristic
467C23×C4C22⋊D1111yescharacteristic
468C23×C4C22⋊D1111yescharacteristic
469C23×C4C22⋊D1111yescharacteristic
470C23×C4C22×D1111yescharacteristic
471C23×C4C22×D1111yescharacteristic
472C23×C4C22×D1111yescharacteristic
473C2×M16—22no—
474C2×M16—22no—
475C2×M16—44no—
476C2×M16—222no—
477C2×M16—222no—
478C2×M16—444no—
479C22×C8—22no—
480C22×C8—222no—
481C4×D4—222no—
482C4×D4—222no—
483C4×D4—222no—
484C4×D4—222no—
485C4×D4—222no—
486C4×D4—222no—
487C4×D4—222no—
488C4×D4—222no—
489C4×D4—222no—
490C4×D4—222no—
491C4×D4—222no—
492C4×D4—222no—
493C4×D4—222no—
494C4×D4—222no—
495C4×D4—222no—
496C4×D4—222no—
497C2×C4⋊C4—112no—
498C2×C4⋊C4—112no—
499C2×C4⋊C4—221no—
500C2×C4⋊C4—221no—
501C2×C4⋊C4—221no—
502C2×C4⋊C4—221no—
503C2×C22⋊C4—112no—
504C2×C22⋊C4—112no—
505C2×C22⋊C4—112no—
506C2×C22⋊C4—112no—
507C2×C22⋊C4—221no—
508C2×C22⋊C4—221no—
509C2×C22⋊C4—221no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C42—112no—
516C2×C42—112no—
517C2×C42—221no—
518C2×C42—221no—
519C2×C42—221no—
520C2×C42—221no—
521C22⋊C8—22no—
522C22⋊C8—22no—
523C22⋊C8—22no—
524C22⋊C8—114no—
525C22⋊C8—222no—
526C22⋊C8—222no—
527C22⋊C8—222no—
528C22⋊C8C22×D1114yes—
529C2×C11—22no—
530C2×C11—22no—
531C2×C11—22no—
532C2×C11—22no—
533C2×C11—22no—
534C2×C11—41no—
535C2×C11—41no—
536C2×C11C2×#40711yescharacteristic
537C2×C11C22×#9911yescharacteristic
538C2×C11C2×#41311yescharacteristic
539D11—44no—
540C24—24no—
541C24—42no—
542C24—42no—
543C24—112no—
544C24—224no—
545C24—221no—
546C24—221no—
547C24—442no—
548C24—442no—
549C24(C2×D11)⋊C411yescharacteristic
550C24(C2×D11)⋊C411yescharacteristic
551C24(C2×D11)⋊C411yescharacteristic
552C24(C2×D11)⋊C411yescharacteristic
553C24C2×C4×D1111yescharacteristic
554C24C2×C4×D1111yescharacteristic
555C24C2×C4×D1111yescharacteristic
556C2×D4—118no—
557C2×D4—224no—
558C2×D4—224no—
559C2×D4—228no—
560C2×D4—228no—
561C2×D4—228no—
562C2×D4—228no—
563C2×D4—224no—
564C2×D4—222no—
565C2×D4—222no—
566C2×D4—222no—
567C2×D4—222no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—112no—
583C22×C4—112no—
584C22×C4—112no—
585C22×C4—224no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—222no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—444no—
597C22×C4—444no—
598C22×C4—444no—
599C22×C4—444no—
600C22×C4—444no—
601C22×C4—444no—
602C22×C4—442no—
603C22×C4—442no—
604C22×C4(C2×D11)⋊C411yescharacteristic
605C22×C4(C2×D11)⋊C411yescharacteristic
606C22×C4(C2×D11)⋊C411yescharacteristic
607C22×C4(C2×D11)⋊C411yescharacteristic
608C22×C4(C2×D11)⋊C411yescharacteristic
609C22×C4(C2×D11)⋊C411yescharacteristic
610C22×C4(C2×D11)⋊C411yescharacteristic
611C22×C4(C2×D11)⋊C411yescharacteristic
612C22×C4(C2×D11)⋊C411yescharacteristic
613C22×C4(C2×D11)⋊C411yescharacteristic
614C22×C4(C2×D11)⋊C411yescharacteristic
615C22×C4(C2×D11)⋊C411yescharacteristic
616C22×C4C2×C4×D1111yescharacteristic
617C22×C4C2×C4×D1111yescharacteristic
618C22×C4C2×C4×D1111yescharacteristic
619C22×C4C2×D4411yescharacteristic
620C22×C4C2×D4411yescharacteristic
621C22×C4C2×D4411yescharacteristic
622C22×C4C2×D4411yescharacteristic
623C22×C4C2×D4411yescharacteristic
624C22×C4C2×D4411yescharacteristic
625C22×C4C2×C22⋊D1111yescharacteristic
626C22×C4C2×C22⋊D1111yescharacteristic
627C22×C4C2×C22⋊D1111yescharacteristic
628C22×C4C2×C22⋊D1111yescharacteristic
629C22×C4C2×C22⋊D1111yescharacteristic
630C22×C4C2×C22⋊D1111yescharacteristic
631C22×C4C23×D1111yescharacteristic
632M16—44no—
633M16—44no—
634M16—444no—
635M16—444no—
636C2×C8—24no—
637C2×C8—44no—
638C2×C8—224no—
639C2×C8—444no—
640C4⋊C4—222no—
641C4⋊C4—222no—
642C4⋊C4—222no—
643C4⋊C4—222no—
644C22⋊C4—222no—
645C22⋊C4—222no—
646C22⋊C4—222no—
647C22⋊C4—222no—
648C22⋊C4—222no—
649C22⋊C4—222no—
650C22⋊C4—222no—
651C22⋊C4—222no—
652C42—222no—
653C42—222no—
654C42—222no—
655C42—222no—
656C11#1736211yescharacteristic, complemented, Sylow
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—416no—
678C23—114no—
679C23—224no—
680C23—224no—
681C23—222no—
682C23—222no—
683C23—442no—
684C23—442no—
685C23—442no—
686C23—4416no—
687C23—442no—
688C23—442no—
689C23—442no—
690C23M16×D1114yes—
691C23C2×(C2×D11)⋊C411yescharacteristic
692C23C2×(C2×D11)⋊C411yescharacteristic
693C23C2×(C2×D11)⋊C411yescharacteristic
694C23C2×(C2×D11)⋊C411yescharacteristic
695C23C2×(C2×D11)⋊C411yescharacteristic
696C23C2×(C2×D11)⋊C411yescharacteristic
697C23C22×C4×D1111yescharacteristic
698D4—228no—
699D4—228no—
700D4—228no—
701D4—228no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—114no—
730C2×C4—224no—
731C2×C4—224no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—444no—
737C2×C4—444no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4—444no—
743C2×C4—444no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4#6687014yes—
747C2×C4C2×(C2×D11)⋊C411yescharacteristic
748C2×C4C2×(C2×D11)⋊C411yescharacteristic
749C2×C4C2×(C2×D11)⋊C411yescharacteristic
750C2×C4C2×(C2×D11)⋊C411yescharacteristic
751C2×C4C2×(C2×D11)⋊C411yescharacteristic
752C2×C4C2×(C2×D11)⋊C411yescharacteristic
753C2×C4C22×D4411yescharacteristic
754C2×C4C22×C22⋊D1111yescharacteristic
755C8—44no—
756C8—444no—
757C22—28no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—21no—
769C22—21no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22—44no—
779C22—44no—
780C22—224no—
781C22—444no—
782C22—448no—
783C22—444no—
784C22—448no—
785C22—442no—
786C22—442no—
787C22C2×#6687012yes—
788C22#1062273912yes—
789C22#1062273912yes—
790C22#1062274512yes—
791C22C2×M16×D1112yes—
792C22C22×(C2×D11)⋊C411yescharacteristic
793C4—21no—
794C4—21no—
795C4—21no—
796C4—21no—
797C4—21no—
798C4—21no—
799C4—224no—
800C4—442no—
801C4—442no—
802C4C2×#6687012yes—
803C4C2×#6687012yes—
804C2—22no—
805C2—22no—
806C2—22no—
807C2—22no—
808C2—22no—
809C2—41no—
810C2—41no—
811C2—444no—
812C2C2×#1062273911yescharacteristic
813C2C22×#6687011yescharacteristic
814C2C2×#1062274511yescharacteristic
subgroupG/H
centerC2×C4C2×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#407C2
socleC22×C11C22×C22⋊C4
prime radicalC23×C22⋊D11C4
cosocleC22×C4×C11C24
hypercenterC2×#407D11
hypocenterC11#17362
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#10622820C2semidirect
3. #13066952C2semidirect
4. #13066945C2semidirect
5. #13066942C2semidirect
6. #13066932C2semidirect
7. C2×C11×#407C2semidirect
32. C11×#407C22semidirect
34. C2×C11×C22⋊C8C22semidirect
38. #10622820C22semidirect
40. C2×C22⋊(C11⋊C8)C22semidirect
41. #10622107C22semidirect
42. #10622106C22semidirect
203. C2×C22⋊D11M16semidirect
252. C2×#407D11semidirect
297. C22×D11C2×M16semidirect
350. C2×Dic11C2×M16semidirect
385. #407C2×D11semidirect
389. C2×C22⋊C8C2×D11semidirect
656. C11#17362semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106228202
#130669522
#130669452
#130669422
#130669322
C2×C11×#4072
#1736211