Finite Group Databasebeta

← #14719840

Subgroups — #14719840

Order 2816.

1450 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66982C211yesmaximal, characteristic
2C2×#10622820C211yesmaximal, characteristic, complemented
3#13066965C214yesmaximal, complemented
4#13066962C214yesmaximal, complemented
5#13066945C212yesmaximal, complemented
6#13066942C212yesmaximal, complemented
7C2×C11×#407C211yesmaximal, characteristic, complemented
8C24×C4×C11C2211yescharacteristic
9C23×C22⋊D11C411yescharacteristic
10C22×C11×M16—21no—
11C22×C22⋊Dic11C411yescharacteristic
12C2×#66982—21no—
13C2×#66982—21no—
14C2×#66982—21no—
15C2×#66982—21no—
16C2×#66982—21no—
17C2×#66982—21no—
18C2×#66982—21no—
19C2×#66982—21no—
20C2×#66982C412yes—
21C2×#66982C412yes—
22C2×#66982C2212yes—
23C2×#66982C2212yes—
24C22×(C2×D11)⋊C4C411yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×Dic11⋊C4C411yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
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—44no—
65C22×C22⋊D11C2×C412yes—
66C22×C22⋊D11C2×C412yes—
67C23×Dic11C2×C411yescharacteristic
68C23×Dic11C2×C411yescharacteristic
69C23×Dic11C2×C411yescharacteristic
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16—44no—
73C22×C8×C11—22no—
74C2×C22⋊Dic11—21no—
75C2×C22⋊Dic11—21no—
76C2×C22⋊Dic11—21no—
77C2×C22⋊Dic11—21no—
78C2×C22⋊Dic11C2×C412yes—
79C2×C22⋊Dic11C2×C412yes—
80#66982—22no—
81#66982—22no—
82#66982—22no—
83#66982—22no—
84#66982—22no—
85#66982—22no—
86#66982—22no—
87#66982—22no—
88#66982—22no—
89#66982—22no—
90#66982—22no—
91#66982—22no—
92#66982—22no—
93#66982—22no—
94#66982—22no—
95#66982—22no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4C2×C412yes—
105C2×(C2×D11)⋊C4C2×C412yes—
106C2×(C2×D11)⋊C4C2×C412yes—
107C2×(C2×D11)⋊C4C2312yes—
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×Dic11⋊C4—21no—
114C2×Dic11⋊C4—21no—
115C2×Dic11⋊C4—21no—
116C2×Dic11⋊C4C2×C412yes—
117C2×Dic11⋊C4C2×C412yes—
118C2×Dic11⋊C4C2×C412yes—
119C2×Dic11⋊C4C2312yes—
120C2×#4318—22no—
121C2×#4318—22no—
122C2×#4318—44no—
123C22×C11⋊C8—22no—
124C11×C22⋊C8—22no—
125C11×C22⋊C8—22no—
126C11×C22⋊C8—22no—
127C11×C22⋊C8C2314yes—
128C22⋊(C11⋊C8)—22no—
129C22⋊(C11⋊C8)—22no—
130C22⋊(C11⋊C8)—22no—
131C22⋊(C11⋊C8)C2314yes—
132#17392—111nomaximal, Sylow
133C24×C11—24no—
134C24×C11—42no—
135C24×C11—42no—
136C24×C11C22⋊C411yescharacteristic
137C24×C11C22⋊C411yescharacteristic
138C24×C11C22⋊C411yescharacteristic
139C24×C11C22⋊C411yescharacteristic
140C24×C11C22×C411yescharacteristic
141C24×C11C22×C411yescharacteristic
142C24×C11C22×C411yescharacteristic
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—42no—
146C23×D11—42no—
147C23×D11—42no—
148C23×D11C22×C412yes—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—42no—
152C22×C4×C11—42no—
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×C11C22⋊C411yescharacteristic
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×C11C2×D411yescharacteristic
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×C11C2411yescharacteristic
191C2×C22⋊D11—22no—
192C2×C22⋊D11—22no—
193C2×C22⋊D11—22no—
194C2×C22⋊D11—22no—
195C2×C22⋊D11—44no—
196C2×C22⋊D11—44no—
197C2×C22⋊D11—44no—
198C2×C22⋊D11—44no—
199C2×C22⋊D11—44no—
200C2×C22⋊D11—44no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—42no—
208C22×Dic11—42no—
209C22×Dic11—42no—
210C22×Dic11C22×C412yes—
211C22×Dic11C22×C412yes—
212C22×Dic11C22×C412yes—
213C11×M16—44no—
214C11×M16—44no—
215C2×C8×C11—24no—
216C2×C8×C11—44no—
217C22⋊Dic11—22no—
218C22⋊Dic11—22no—
219C22⋊Dic11—22no—
220C22⋊Dic11—22no—
221(C2×D11)⋊C4—22no—
222(C2×D11)⋊C4—22no—
223(C2×D11)⋊C4—22no—
224(C2×D11)⋊C4—22no—
225(C2×D11)⋊C4—22no—
226(C2×D11)⋊C4—22no—
227(C2×D11)⋊C4—22no—
228(C2×D11)⋊C4—22no—
229Dic11⋊C4—22no—
230Dic11⋊C4—22no—
231Dic11⋊C4—22no—
232Dic11⋊C4—22no—
233Dic11⋊C4—22no—
234Dic11⋊C4—22no—
235Dic11⋊C4—22no—
236Dic11⋊C4—22no—
237#4318—44no—
238#4318—44no—
239C2×C11⋊C8—24no—
240C2×C11⋊C8—44no—
241C22×#123—111no—
242C2×#407—111no—
243C2×#407D1111yescharacteristic, complemented
244#1468—114no—
245#1468—114no—
246#1463—112no—
247#1462—112no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—22no—
252C23×C11—22no—
253C23×C11—22no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—416no—
269C23×C11#9914yes—
270C23×C11C2×C22⋊C411yescharacteristic
271C23×C11C2×C22⋊C411yescharacteristic
272C23×C11C2×C22⋊C411yescharacteristic
273C23×C11C2×C22⋊C411yescharacteristic
274C23×C11C2×C22⋊C411yescharacteristic
275C23×C11C2×C22⋊C411yescharacteristic
276C23×C11C23×C411yescharacteristic
277C22×D11—22no—
278C22×D11—24no—
279C22×D11—42no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—42no—
283C22×D11—42no—
284C22×D11—42no—
285C22×D11—42no—
286C22×D11—42no—
287C22×D11—88no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11C2×C22⋊C411yescharacteristic
317C2×C4×C11C2×C22⋊C411yescharacteristic
318C2×C4×C11C2×C22⋊C411yescharacteristic
319C2×C4×C11C2×C22⋊C411yescharacteristic
320C2×C4×C11C2×C22⋊C411yescharacteristic
321C2×C4×C11C2×C22⋊C411yescharacteristic
322C2×C4×C11C22×D411yescharacteristic
323C2×C4×C11C22×D411yescharacteristic
324C22⋊D11—44no—
325C22⋊D11—44no—
326C22⋊D11—44no—
327C22⋊D11—44no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—24no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C8×C11—44no—
341C11⋊C8—44no—
342C23×D4—111no—
343C24×C4C2×D1111yescharacteristic
344C22×M16—21no—
345C22×M16—221no—
346C2×#123—112no—
347C2×#123—112no—
348C2×#123—112no—
349C2×#123—112no—
350C2×#123—221no—
351C2×#123—221no—
352C2×#123—221no—
353C2×#123—221no—
354C2×#123—221no—
355C2×#123—221no—
356C2×#123—221no—
357C2×#123—221no—
358C22×C4⋊C4—111no—
359C22×C4⋊C4—111no—
360C22×C22⋊C4—111no—
361C22×C22⋊C4—111no—
362C22×C22⋊C4—111no—
363#407—21no—
364#407—21no—
365#407—112no—
366#407—112no—
367#407—221no—
368#407—221no—
369#407C2×D1112yes—
370#407C2×D1112yescomplemented
371C2×C22⋊C8—21no—
372C2×C22⋊C8—112no—
373C2×C22⋊C8—221no—
374C2×C22⋊C8C2×D1112yescomplemented
375#324—118no—
376#323—118no—
377C22×C11—28no—
378C22×C11—21no—
379C22×C11—21no—
380C22×C11—21no—
381C22×C11—21no—
382C22×C11—21no—
383C22×C11—21no—
384C22×C11—21no—
385C22×C11—21no—
386C22×C11—21no—
387C22×C11—21no—
388C22×C11—21no—
389C22×C11—21no—
390C22×C11—21no—
391C22×C11—21no—
392C22×C11—21no—
393C22×C11—21no—
394C22×C11—44no—
395C22×C11—44no—
396C22×C11—44no—
397C22×C11—44no—
398C22×C11—44no—
399C22×C11—44no—
400C22×C11C2×#9912yes—
401C22×C11C2×#9912yes—
402C22×C11C2×#9912yes—
403C22×C11#41312yes—
404C22×C11C22×C22⋊C411yescharacteristic
405C22×C11#56812yes—
406C2×D11—42no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—84no—
410C2×D11—84no—
411C2×D11—84no—
412C4×C11—21no—
413C4×C11—21no—
414C4×C11—21no—
415C4×C11—21no—
416C4×C11—21no—
417C4×C11—21no—
418C4×C11—21no—
419C4×C11—21no—
420Dic11—42no—
421Dic11—42no—
422Dic11—42no—
423C25—111no—
424C25C4×D1111yescharacteristic
425C22×D4—112no—
426C22×D4—112no—
427C22×D4—221no—
428C22×D4—221no—
429C22×D4—221no—
430C22×D4—221no—
431C22×D4—444no—
432C23×C4—44no—
433C23×C4—111no—
434C23×C4—111no—
435C23×C4—111no—
436C23×C4C4×D1111yescharacteristic
437C23×C4C4×D1111yescharacteristic
438C23×C4C4×D1111yescharacteristic
439C23×C4D4411yescharacteristic
440C23×C4D4411yescharacteristic
441C23×C4D4411yescharacteristic
442C23×C4D4411yescharacteristic
443C23×C4C22⋊D1111yescharacteristic
444C23×C4C22⋊D1111yescharacteristic
445C23×C4C22⋊D1111yescharacteristic
446C23×C4C22⋊D1111yescharacteristic
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C2×M16—22no—
451C2×M16—22no—
452C2×M16—44no—
453C2×M16—222no—
454C2×M16—222no—
455C2×M16—444no—
456C22×C8—22no—
457C22×C8—222no—
458#123—222no—
459#123—222no—
460#123—222no—
461#123—222no—
462#123—222no—
463#123—222no—
464#123—222no—
465#123—222no—
466#123—222no—
467#123—222no—
468#123—222no—
469#123—222no—
470#123—222no—
471#123—222no—
472#123—222no—
473#123—222no—
474C2×C4⋊C4—112no—
475C2×C4⋊C4—112no—
476C2×C4⋊C4—112no—
477C2×C4⋊C4—112no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4—221no—
480C2×C4⋊C4—221no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4—221no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—221no—
485C2×C4⋊C4—221no—
486C2×C22⋊C4—112no—
487C2×C22⋊C4—112no—
488C2×C22⋊C4—112no—
489C2×C22⋊C4—112no—
490C2×C22⋊C4—112no—
491C2×C22⋊C4—112no—
492C2×C22⋊C4—221no—
493C2×C22⋊C4—221no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4—221no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4—221no—
502C2×C22⋊C4—221no—
503C2×C22⋊C4—221no—
504C22⋊C8—22no—
505C22⋊C8—22no—
506C22⋊C8—22no—
507C22⋊C8—114no—
508C22⋊C8—222no—
509C22⋊C8—222no—
510C22⋊C8—222no—
511C22⋊C8C22×D1114yes—
512C2×C11—22no—
513C2×C11—22no—
514C2×C11—22no—
515C2×C11—22no—
516C2×C11—22no—
517C2×C11—41no—
518C2×C11—41no—
519C2×C11#287911yescharacteristic
520C2×C11C22×#9911yescharacteristic
521C2×C11C2×#41311yescharacteristic
522D11—82no—
523C24—24no—
524C24—42no—
525C24—42no—
526C24—112no—
527C24—221no—
528C24—221no—
529C24—442no—
530C24—442no—
531C24—442no—
532C24(C2×D11)⋊C411yescharacteristic
533C24(C2×D11)⋊C411yescharacteristic
534C24(C2×D11)⋊C411yescharacteristic
535C24(C2×D11)⋊C411yescharacteristic
536C24C2×C4×D1111yescharacteristic
537C24C2×C4×D1111yescharacteristic
538C24C2×C4×D1111yescharacteristic
539C2×D4—222no—
540C2×D4—222no—
541C2×D4—222no—
542C2×D4—222no—
543C2×D4—444no—
544C2×D4—444no—
545C2×D4—444no—
546C2×D4—444no—
547C2×D4—444no—
548C2×D4—444no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—42no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—112no—
564C22×C4—112no—
565C22×C4—112no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—442no—
573C22×C4—442no—
574C22×C4—442no—
575C22×C4(C2×D11)⋊C411yescharacteristic
576C22×C4(C2×D11)⋊C411yescharacteristic
577C22×C4(C2×D11)⋊C411yescharacteristic
578C22×C4(C2×D11)⋊C411yescharacteristic
579C22×C4(C2×D11)⋊C411yescharacteristic
580C22×C4(C2×D11)⋊C411yescharacteristic
581C22×C4(C2×D11)⋊C411yescharacteristic
582C22×C4(C2×D11)⋊C411yescharacteristic
583C22×C4(C2×D11)⋊C411yescharacteristic
584C22×C4(C2×D11)⋊C411yescharacteristic
585C22×C4(C2×D11)⋊C411yescharacteristic
586C22×C4(C2×D11)⋊C411yescharacteristic
587C22×C4C2×C4×D1111yescharacteristic
588C22×C4C2×C4×D1111yescharacteristic
589C22×C4C2×C4×D1111yescharacteristic
590C22×C4C2×D4411yescharacteristic
591C22×C4C2×D4411yescharacteristic
592C22×C4C2×D4411yescharacteristic
593C22×C4C2×D4411yescharacteristic
594C22×C4C2×D4411yescharacteristic
595C22×C4C2×D4411yescharacteristic
596C22×C4C2×C22⋊D1111yescharacteristic
597C22×C4C2×C22⋊D1111yescharacteristic
598C22×C4C2×C22⋊D1111yescharacteristic
599C22×C4C2×C22⋊D1111yescharacteristic
600C22×C4C2×C22⋊D1111yescharacteristic
601C22×C4C2×C22⋊D1111yescharacteristic
602C22×C4C23×D1111yescharacteristic
603M16—44no—
604M16—44no—
605M16—444no—
606M16—444no—
607C2×C8—24no—
608C2×C8—44no—
609C2×C8—224no—
610C2×C8—444no—
611C4⋊C4—222no—
612C4⋊C4—222no—
613C4⋊C4—222no—
614C4⋊C4—222no—
615C4⋊C4—222no—
616C4⋊C4—222no—
617C4⋊C4—222no—
618C4⋊C4—222no—
619C22⋊C4—222no—
620C22⋊C4—222no—
621C22⋊C4—222no—
622C22⋊C4—222no—
623C22⋊C4—222no—
624C22⋊C4—222no—
625C22⋊C4—222no—
626C22⋊C4—222no—
627C22⋊C4—222no—
628C22⋊C4—222no—
629C22⋊C4—222no—
630C22⋊C4—222no—
631C11#1739211yescharacteristic, complemented, Sylow
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—416no—
653C23—222no—
654C23—224no—
655C23—442no—
656C23—442no—
657C23—442no—
658C23—442no—
659C23—442no—
660C23—442no—
661C23—442no—
662C23—442no—
663C23—888no—
664C23#6687014yes—
665C23C2×(C2×D11)⋊C411yescharacteristic
666C23C2×(C2×D11)⋊C411yescharacteristic
667C23C2×(C2×D11)⋊C411yescharacteristic
668C23C2×(C2×D11)⋊C411yescharacteristic
669C23C2×(C2×D11)⋊C411yescharacteristic
670C23C2×(C2×D11)⋊C411yescharacteristic
671C23C22×C4×D1111yescharacteristic
672D4—444no—
673D4—444no—
674D4—444no—
675D4—444no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—224no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—442no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4C2×(C2×D11)⋊C411yescharacteristic
717C2×C4C2×(C2×D11)⋊C411yescharacteristic
718C2×C4C2×(C2×D11)⋊C411yescharacteristic
719C2×C4C2×(C2×D11)⋊C411yescharacteristic
720C2×C4C2×(C2×D11)⋊C411yescharacteristic
721C2×C4C2×(C2×D11)⋊C411yescharacteristic
722C2×C4C22×D4411yescharacteristic
723C2×C4C22×C22⋊D1111yescharacteristic
724C8—44no—
725C8—444no—
726C22—28no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—442no—
750C22—442no—
751C22—442no—
752C22—884no—
753C22—884no—
754C22—884no—
755C22C2×#6687012yes—
756C22C2×#6687012yes—
757C22C2×#6687012yes—
758C22#1062274512yes—
759C22#1062327612yes—
760C22C22×(C2×D11)⋊C411yescharacteristic
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—21no—
767C4—21no—
768C4—21no—
769C4—442no—
770C4—442no—
771C4—442no—
772C2—22no—
773C2—22no—
774C2—22no—
775C2—22no—
776C2—22no—
777C2—41no—
778C2—41no—
779C2—882no—
780C2#1307706011yescharacteristic
781C2C22×#6687011yescharacteristic
782C2C2×#1062274511yescharacteristic
subgroupG/H
centerC22C22×(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#17392
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#10622820C2semidirect
3. #13066965C2semidirect
4. #13066962C2semidirect
5. #13066945C2semidirect
6. #13066942C2semidirect
7. C2×C11×#407C2semidirect
32. C11×#407C22semidirect
34. C2×C11×C22⋊C8C22semidirect
38. #10622820C22semidirect
40. C2×C22⋊(C11⋊C8)C22semidirect
41. #10622107C22semidirect
42. #10622106C22semidirect
243. C2×#407D11semidirect
370. #407C2×D11semidirect
374. C2×C22⋊C8C2×D11semidirect
631. C11#17392semidirect

Maximal subgroups

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

subgroupindex
C22×#669822
C2×#106228202
#130669652
#130669622
#130669452
#130669422
C2×C11×#4072
#1739211