Finite Group Databasebeta

← #15618404

Subgroups — #15618404

Order 2816.

1960 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623010C211yesmaximal, characteristic
2#13077620C214yesmaximal, complemented
3#13077610C214yesmaximal, complemented
4#13077601C214yesmaximal, complemented
5#13077591C214yesmaximal, complemented
6M16×Dic22C212yesmaximal, complemented
7M16×D44C212yesmaximal, complemented
8M16×C22⋊D11C214yesmaximal, complemented
9#13077252C212yesmaximal, complemented
10#13077249C211yesmaximal, characteristic, complemented
11#13077033C212yesmaximal, complemented
12C2×C4×C11×M16C211yesmaximal, characteristic, complemented
13C22×C11×M16C2212yes—
14C22×C42×C11C2211yescharacteristic
15C2×#66983C411yescharacteristic
16C2×#66982C412yes—
17C2×C4×C22⋊D11C2212yes—
18C2×#66977C411yescharacteristic
19C2×M16×D11C2214yes—
20#10623010C412yes—
21#10623010C412yes—
22#10623010C412yes—
23#10623010C412yes—
24#10623010C2212yes—
25#10623010C2212yes—
26#10623010C2212yes—
27#10623010C2212yes—
28C2×#66929C412yes—
29C2×#66928C411yescharacteristic
30C2×C4×D44C2211yescharacteristic
31C2×#66925C2212yes—
32C2×#66923C411yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C4×C11×M16C2211yescharacteristic
35C4×C11×M16C2211yescharacteristic
36C4×C11×M16C2212yes—
37C4×C11×M16C2212yescomplemented
38C4×C11×M16C2212yescomplemented
39C2×C11×#97C2212yescomplemented
40C2×C4×C8×C11C2212yescomplemented
41#10622820C2212yes—
42#10622741C2218yescomplemented
43#10622740C2218yescomplemented
44#10622739C2214yes—
45#10622731C2214yes—
46M16×Dic11C2214yes—
47#10622724C2218yescomplemented
48C8×C22⋊D11C2218yescomplemented
49#10622539C2212yescomplemented
50#10622539C2212yescomplemented
51#10622538C2212yescomplemented
52#10622538C2212yescomplemented
53#10622537C2212yes—
54C4×#4318C2212yes—
55#10622322C2218yescomplemented
56#10622321C2218yescomplemented
57#10622319C2218yescomplemented
58#10622314C2218yescomplemented
59#10622303C2218yescomplemented
60#10622302C2218yescomplemented
61#10622301C2214yescomplemented
62C8×D44C2214yescomplemented
63#10622292C2214yescomplemented
64C8×Dic22C2214yescomplemented
65C23×C4×C11C2×C411yescharacteristic
66C23×C4×C11C2×C411yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11C2×C412yes—
69C22×D44C2×C411yescharacteristic
70C22×C4×D11C2312yes—
71C22×Dic22C2×C411yescharacteristic
72C2×C11×M16—28no—
73C2×C11×M16C2312yes—
74C2×C11×M16C2314yes—
75C2×C11×M16C2312yes—
76C22×C8×C11C2314yes—
77C2×C42×C11C2×C411yescharacteristic
78C2×C42×C11C2×C411yescharacteristic
79C2×C42×C11C2×C411yescharacteristic
80C2×C42×C11C2×C411yescharacteristic
81C2×C42×C11C2×C411yescharacteristic
82C2×C42×C11C2×C411yescharacteristic
83C2×C42×C11C2311yescharacteristic
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2311yescharacteristic
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11C2×C412yes—
90#66983C2×C412yes—
91#66983C2×C412yes—
92#66983C2×C412yes—
93#66983C2×C412yes—
94#66982C2×C414yes—
95#66982C2×C414yes—
96#66982C2×C414yes—
97#66982C2×C414yes—
98C4×C22⋊D11C2×C414yes—
99C4×C22⋊D11C2×C414yes—
100C4×C22⋊D11C2314yes—
101C4×C22⋊D11C2314yes—
102C2×(C2×D11)⋊C4C2×C412yes—
103C2×(C2×D11)⋊C4C2×C412yes—
104C2×(C2×D11)⋊C4C2×C412yes—
105C2×(C2×D11)⋊C4C2×C412yes—
106C2×C4⋊Dic11C2×C411yescharacteristic
107C2×C4⋊Dic11C2×C411yescharacteristic
108#66977C2×C412yes—
109#66977C2×C412yes—
110#66977C2×C412yes—
111#66977C2×C412yes—
112C2×Dic11⋊C4C2×C412yes—
113C2×Dic11⋊C4C2×C412yes—
114C2×Dic11⋊C4C2×C412yes—
115C2×Dic11⋊C4C2×C412yes—
116C2×C4×Dic11C2312yes—
117C2×#4318C2314yes—
118M16×D11—216no—
119C2×#4313C2318yes—
120C2×C8×D11C2318yes—
121#66929C2×C414yes—
122#66929C2×C414yes—
123#66929C2×C414yes—
124#66929C2×C414yes—
125#66928C2×C412yes—
126#66928C2×C412yes—
127#66928C2×C412yes—
128#66928C2×C412yes—
129C4×D44C2×C412yes—
130C4×D44C2×C412yes—
131C4×D44C2312yes—
132C4×D44C2312yes—
133#66925C2×C414yes—
134#66925C2×C414yes—
135#66925C2314yes—
136#66925C2314yes—
137#66923C2×C412yes—
138#66923C2×C412yes—
139#66923C2×C412yes—
140#66923C2×C412yes—
141C4×Dic22C2×C412yes—
142C4×Dic22C2×C412yes—
143C4×Dic22C2312yes—
144C4×Dic22C2312yes—
145C11×#97C2314yes—
146C11×#97C2312yes—
147C11×#97C2312yes—
148C4×C8×C11C2314yes—
149C4×C8×C11C2312yes—
150C4×C8×C11C2312yes—
151C22⋊(C11⋊C8)C2314yes—
152C22⋊(C11⋊C8)C2314yes—
153(C2×D11)⋊C8C2318yes—
154(C2×D11)⋊C8C2318yes—
155#66879C2318yes—
156Dic11⋊C8C2318yes—
157Dic11⋊C8C2318yes—
158C8×Dic11C2318yes—
159C4⋊(C11⋊C8)C2314yes—
160C4⋊(C11⋊C8)C2314yes—
161#66867C2314yes—
162C4×C11⋊C8C2314yes—
163#60214—111nomaximal, Sylow
164C24×C11C22×C411yescharacteristic
165C23×D11C22×C412yes—
166C22×C4×C11—24no—
167C22×C4×C11—42no—
168C22×C4×C11—42no—
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×C11C22×C411yescharacteristic
180C22×C4×C11C22×C411yescharacteristic
181C22×C4×C11C22×C411yescharacteristic
182C22×C4×C11C22×C411yescharacteristic
183C22×C4×C11C22×C411yescharacteristic
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C2×C22⋊D11—44no—
188C2×C22⋊D11C22×C414yes—
189C2×C22⋊D11C22×C414yes—
190C22×Dic11C22×C412yes—
191C22×Dic11C22×C412yes—
192C22×Dic11C22×C412yes—
193C2×D44—42no—
194C2×D44C22×C412yes—
195C2×D44C22×C412yes—
196C2×C4×D11—28no—
197C2×C4×D11C22×C414yes—
198C2×C4×D11C2414yes—
199C2×Dic22—42no—
200C2×Dic22C22×C412yes—
201C2×Dic22C22×C412yes—
202C11×M16—28no—
203C11×M16—24no—
204C11×M16#4118yes—
205C2×C8×C11—28no—
206C2×C8×C11C2414yes—
207C2×C8×C11C2414yes—
208C42×C11C22×C411yescharacteristic
209C42×C11C22×C411yescharacteristic
210C42×C11C22×C411yescharacteristic
211C42×C11C22×C411yescharacteristic
212C42×C11C22×C411yescharacteristic
213C42×C11C22×C411yescharacteristic
214C42×C11C22×C411yescharacteristic
215C42×C11C22×C411yescharacteristic
216C42×C11C22×C411yescharacteristic
217C42×C11C22×C411yescharacteristic
218C42×C11C22×C411yescharacteristic
219C42×C11C22×C411yescharacteristic
220C42×C11C2411yescharacteristic
221C42×C11C2411yescharacteristic
222C42×C11C2411yescharacteristic
223C42×C11C2411yescharacteristic
224C22⋊Dic11C22×C414yes—
225C22⋊Dic11C22×C414yes—
226(C2×D11)⋊C4C22×C414yes—
227(C2×D11)⋊C4C22×C414yes—
228(C2×D11)⋊C4C22×C414yes—
229(C2×D11)⋊C4C22×C414yes—
230(C2×D11)⋊C4C22×C414yes—
231(C2×D11)⋊C4C22×C414yes—
232(C2×D11)⋊C4C22×C414yes—
233(C2×D11)⋊C4C22×C414yes—
234C4⋊Dic11C22×C412yes—
235C4⋊Dic11C22×C412yes—
236C4⋊Dic11C22×C412yes—
237C4⋊Dic11C22×C412yes—
238Dic11⋊C4C22×C414yes—
239Dic11⋊C4C22×C414yes—
240Dic11⋊C4C22×C414yes—
241Dic11⋊C4C22×C414yes—
242Dic11⋊C4C22×C414yes—
243Dic11⋊C4C22×C414yes—
244Dic11⋊C4C22×C414yes—
245Dic11⋊C4C22×C414yes—
246C4×Dic11C22×C414yes—
247C4×Dic11C2414yes—
248#4318—28no—
249C2×C11⋊C8C2418yes—
250#4313—216no—
251C8×D11—216no—
252C2×#529—111no—
253#2969—114no—
254#2968—114no—
255#2967—114no—
256#2966—114no—
257Q8×M16—112no—
258D4×M16—112no—
259D4×M16—114no—
260#2921—112no—
261#2920—111no—
262#2873—112no—
263C2×C4×M16D1111yescharacteristic, complemented
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—41no—
267C23×C11C23×C411yescharacteristic
268C23×C11C23×C411yescharacteristic
269C23×C11C23×C411yescharacteristic
270C22×D11—24no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11C23×C414yes—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—41no—
285C2×C4×C11—41no—
286C2×C4×C11—41no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11C23×C411yescharacteristic
292C2×C4×C11C23×C411yescharacteristic
293C2×C4×C11C23×C411yescharacteristic
294C2×C4×C11C23×C411yescharacteristic
295C2×C4×C11C23×C411yescharacteristic
296C2×C4×C11C23×C411yescharacteristic
297C2×C4×C11C23×C411yescharacteristic
298C2×C4×C11C23×C411yescharacteristic
299C2×C4×C11C23×C411yescharacteristic
300C2×C4×C11C23×C411yescharacteristic
301C2×C4×C11C23×C411yescharacteristic
302C2×C4×C11C2×#4114yes—
303C2×C4×C11C2511yescharacteristic
304C22⋊D11—28no—
305C22⋊D11—44no—
306C2×Dic11—24no—
307C2×Dic11—42no—
308C2×Dic11—42no—
309C2×Dic11C23×C414yes—
310C2×Dic11C23×C414yes—
311C2×Dic11C23×C414yes—
312D44—24no—
313D44—42no—
314C4×D11—28no—
315C4×D11—24no—
316C4×D11—24no—
317Dic22—24no—
318Dic22—42no—
319C8×C11—24no—
320C8×C11C2×#4118yes—
321C11⋊C8—28no—
322C22×M16—114no—
323C22×M16C2×D1112yes—
324#529—112no—
325#529—112no—
326#529—112no—
327#529—112no—
328#529—112no—
329#529—112no—
330#529—112no—
331#529—112no—
332C2×#126—112no—
333C2×#125—111no—
334C2×#124—111no—
335C2×#123—112no—
336C2×C22⋊Q8—111no—
337C2×#121—111no—
338C2×C4×Q8—111no—
339C2×C4×D4—112no—
340C2×C4×D4—111no—
341C2×#117—112no—
342C22×C42C2×D1111yescharacteristic
343#446—118no—
344#446—114no—
345C8×Q8—114no—
346#436—118no—
347#436—114no—
348#435—118no—
349#435—118no—
350#435—118no—
351C8×D4—118no—
352C8×D4—114no—
353#433—118no—
354#433—118no—
355#432—112no—
356#432—112no—
357#431—112no—
358#431—112no—
359#423—114no—
360#423—112no—
361#407—112no—
362#407—114no—
363#405—118no—
364#405—118no—
365C4×M16—114no—
366C4×M16—112no—
367C4×M16C2×D1111yescharacteristic
368C4×M16C2×D1111yescharacteristic
369C4×M16C2×D1112yes—
370C4×M16C2×D1112yescomplemented
371C4×M16C2×D1112yescomplemented
372C2×#97C2×D1112yescomplemented
373C2×C4×C8C2×D1112yescomplemented
374C22×C11—21no—
375C22×C11—21no—
376C22×C11—21no—
377C22×C11—21no—
378C22×C11—21no—
379C22×C11—21no—
380C22×C11—21no—
381C22×C11—44no—
382C22×C11C4×#4112yes—
383C22×C11#56812yes—
384C22×C11C24×C411yescharacteristic
385C2×D11—24no—
386C2×D11—24no—
387C2×D11—24no—
388C2×D11—84no—
389C4×C11—21no—
390C4×C11—21no—
391C4×C11—21no—
392C4×C11—21no—
393C4×C11—21no—
394C4×C11—21no—
395C4×C11—21no—
396C4×C11—21no—
397C4×C11—21no—
398C4×C11C4×#4112yes—
399C4×C11#56812yes—
400C4×C11C22×#4112yes—
401Dic11—24no—
402Dic11—24no—
403Dic11—24no—
404C22×Q8—111no—
405C22×D4—112no—
406C22×D4—111no—
407C23×C4—112no—
408C23×C4C4×D1111yescharacteristic
409C23×C4C4×D1111yescharacteristic
410C23×C4C22×D1111yescharacteristic
411C2×M16—28no—
412C2×M16—114no—
413C2×M16—118no—
414C2×M16—2216no—
415C2×M16C22×D1112yes—
416C2×M16C22×D1114yes—
417C2×M16C22×D1112yes—
418C22×C8—118no—
419C22×C8C22×D1114yes—
420#126—114no—
421#126—114no—
422#126—114no—
423#126—114no—
424#125—112no—
425#125—112no—
426#125—112no—
427#125—112no—
428#124—112no—
429#124—112no—
430#124—112no—
431#124—112no—
432#123—114no—
433#123—114no—
434#123—114no—
435#123—114no—
436C22⋊Q8—112no—
437C22⋊Q8—112no—
438C22⋊Q8—112no—
439C22⋊Q8—112no—
440#121—112no—
441#121—112no—
442#121—112no—
443#121—112no—
444C4×Q8—112no—
445C4×Q8—112no—
446C4×Q8—112no—
447C4×Q8—112no—
448C4×D4—114no—
449C4×D4—114no—
450C4×D4—114no—
451C4×D4—114no—
452C4×D4—112no—
453C4×D4—112no—
454C4×D4—112no—
455C4×D4—112no—
456#117—114no—
457#117—114no—
458#117—114no—
459#117—114no—
460C2×C4⋊C4—112no—
461C2×C4⋊C4—112no—
462C2×C4⋊C4—111no—
463C2×C4⋊C4—112no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—112no—
466C2×C22⋊C4—112no—
467C2×C22⋊C4—112no—
468C2×C22⋊C4—112no—
469C2×C22⋊C4—112no—
470C2×C22⋊C4—112no—
471C2×C42—112no—
472C2×C42C4×D1111yescharacteristic
473C2×C42C4×D1111yescharacteristic
474C2×C42C4×D1111yescharacteristic
475C2×C42C4×D1111yescharacteristic
476C2×C42C4×D1111yescharacteristic
477C2×C42C4×D1111yescharacteristic
478C2×C42C22×D1111yescharacteristic
479C2×C42C22×D1111yescharacteristic
480C2×C42C22×D1111yescharacteristic
481C2×C42C22×D1111yescharacteristic
482C2×C42C22×D1111yescharacteristic
483C2×C42C22×D1111yescharacteristic
484C4⋊C8—118no—
485C4⋊C8—118no—
486C4⋊C8—114no—
487C4⋊C8—114no—
488C22⋊C8—114no—
489C22⋊C8—114no—
490C22⋊C8—118no—
491C22⋊C8—118no—
492#97—118no—
493#97—114no—
494#97C22×D1112yes—
495#97C22×D1112yes—
496#97C22×D1114yes—
497C4×C8—118no—
498C4×C8—114no—
499C4×C8C22×D1112yes—
500C4×C8C22×D1112yes—
501C4×C8C22×D1114yes—
502C2×C11—22no—
503C2×C11—22no—
504C2×C11—41no—
505C2×C11C2×C4×#4111yescharacteristic
506C2×C11C2×#56811yescharacteristic
507C2×C11C2×#56811yescharacteristic
508D11—44no—
509C24—112no—
510C24C2×C4×D1111yescharacteristic
511C2×Q8—112no—
512C2×Q8—112no—
513C2×Q8—442no—
514C2×D4—114no—
515C2×D4—114no—
516C2×D4—112no—
517C2×D4—112no—
518C2×D4—442no—
519C2×D4—444no—
520C22×C4—24no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—112no—
524C22×C4—112no—
525C22×C4—112no—
526C22×C4—114no—
527C22×C4—114no—
528C22×C4—228no—
529C22×C4C2×C4×D1111yescharacteristic
530C22×C4C2×C4×D1111yescharacteristic
531C22×C4C2×C4×D1111yescharacteristic
532C22×C4C2×C4×D1111yescharacteristic
533C22×C4C2×C4×D1111yescharacteristic
534C22×C4C2×C4×D1111yescharacteristic
535C22×C4C2×C4×D1111yescharacteristic
536C22×C4C2×C4×D1111yescharacteristic
537C22×C4C2×C4×D1111yescharacteristic
538C22×C4C2×C4×D1111yescharacteristic
539C22×C4C2×C4×D1111yescharacteristic
540C22×C4C2×C4×D1111yescharacteristic
541C22×C4C2×C4×D1111yescharacteristic
542C22×C4C2×C4×D1111yescharacteristic
543C22×C4C2×C4×D1111yescharacteristic
544C22×C4C23×D1111yescharacteristic
545C22×C4C23×D1111yescharacteristic
546C22×C4C23×D1111yescharacteristic
547M16—24no—
548M16—28no—
549M16—228no—
550M16—2216no—
551M16#433918yes—
552C2×C8—28no—
553C2×C8—118no—
554C2×C8—2216no—
555C2×C8C23×D1114yes—
556C2×C8C23×D1114yes—
557C4⋊C4—114no—
558C4⋊C4—114no—
559C4⋊C4—114no—
560C4⋊C4—114no—
561C4⋊C4—112no—
562C4⋊C4—112no—
563C4⋊C4—114no—
564C4⋊C4—114no—
565C4⋊C4—112no—
566C4⋊C4—112no—
567C4⋊C4—114no—
568C4⋊C4—114no—
569C22⋊C4—114no—
570C22⋊C4—114no—
571C22⋊C4—114no—
572C22⋊C4—114no—
573C22⋊C4—114no—
574C22⋊C4—114no—
575C22⋊C4—114no—
576C22⋊C4—114no—
577C22⋊C4—114no—
578C22⋊C4—114no—
579C42—114no—
580C42—114no—
581C42C2×C4×D1111yescharacteristic
582C42C2×C4×D1111yescharacteristic
583C42C2×C4×D1111yescharacteristic
584C42C2×C4×D1111yescharacteristic
585C42C2×C4×D1111yescharacteristic
586C42C2×C4×D1111yescharacteristic
587C42C2×C4×D1111yescharacteristic
588C42C2×C4×D1111yescharacteristic
589C42C2×C4×D1111yescharacteristic
590C42C2×C4×D1111yescharacteristic
591C42C2×C4×D1111yescharacteristic
592C42C2×C4×D1111yescharacteristic
593C42C23×D1111yescharacteristic
594C42C23×D1111yescharacteristic
595C42C23×D1111yescharacteristic
596C42C23×D1111yescharacteristic
597C11#6021411yescharacteristic, complemented, Sylow
598C23—22no—
599C23—22no—
600C23—41no—
601C23—114no—
602C23—224no—
603C23—442no—
604C23—442no—
605C23C22×C4×D1111yescharacteristic
606C23C22×C4×D1111yescharacteristic
607C23C22×C4×D1111yescharacteristic
608Q8—224no—
609Q8—442no—
610D4—228no—
611D4—224no—
612D4—442no—
613D4—444no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—114no—
632C2×C4—114no—
633C2×C4—114no—
634C2×C4—224no—
635C2×C4—228no—
636C2×C4—224no—
637C2×C4—224no—
638C2×C4—442no—
639C2×C4—442no—
640C2×C4C22×C4×D1111yescharacteristic
641C2×C4C22×C4×D1111yescharacteristic
642C2×C4C22×C4×D1111yescharacteristic
643C2×C4C22×C4×D1111yescharacteristic
644C2×C4C22×C4×D1111yescharacteristic
645C2×C4C22×C4×D1111yescharacteristic
646C2×C4C22×C4×D1111yescharacteristic
647C2×C4C22×C4×D1111yescharacteristic
648C2×C4C22×C4×D1111yescharacteristic
649C2×C4C22×C4×D1111yescharacteristic
650C2×C4C22×C4×D1111yescharacteristic
651C2×C4C2×#433914yes—
652C2×C4C24×D1111yescharacteristic
653C8—24no—
654C8—228no—
655C8C2×#433918yes—
656C22—21no—
657C22—21no—
658C22—21no—
659C22—21no—
660C22—21no—
661C22—21no—
662C22—21no—
663C22—44no—
664C22—224no—
665C22—224no—
666C22—224no—
667C22—884no—
668C22C4×#433912yes—
669C22#1062327612yes—
670C22C23×C4×D1111yescharacteristic
671C4—21no—
672C4—21no—
673C4—21no—
674C4—21no—
675C4—21no—
676C4—21no—
677C4—21no—
678C4—21no—
679C4—21no—
680C4—224no—
681C4—224no—
682C4—224no—
683C4C4×#433912yes—
684C4#1062327612yes—
685C4C22×#433912yes—
686C2—22no—
687C2—22no—
688C2—41no—
689C2—444no—
690C2C2×C4×#433911yescharacteristic
691C2C2×#1062327611yescharacteristic
692C2C2×#1062327611yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC2×C4×C11×M16C2
prime radicalC2×#66983C4
cosocleC2×C4×C11C25
hypercenterC2×C4×M16D11
hypocenterC11#60214
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
2. #13077620C2semidirect
3. #13077610C2semidirect
4. #13077601C2semidirect
5. #13077591C2semidirect
6. M16×Dic22C2semidirect
7. M16×D44C2semidirect
8. M16×C22⋊D11C2semidirect
9. #13077252C2semidirect
10. #13077249C2semidirect
11. #13077033C2semidirect
12. C2×C4×C11×M16C2semidirect
37. C4×C11×M16C22semidirect
38. C4×C11×M16C22semidirect
39. C2×C11×#97C22semidirect
40. C2×C4×C8×C11C22semidirect
42. #10622741C22semidirect
43. #10622740C22semidirect
47. #10622724C22semidirect
48. C8×C22⋊D11C22semidirect
49. #10622539C22semidirect
50. #10622539C22semidirect
51. #10622538C22semidirect
52. #10622538C22semidirect
55. #10622322C22semidirect
56. #10622321C22semidirect
57. #10622319C22semidirect
58. #10622314C22semidirect
59. #10622303C22semidirect
60. #10622302C22semidirect
61. #10622301C22semidirect
62. C8×D44C22semidirect
63. #10622292C22semidirect
64. C8×Dic22C22semidirect
263. C2×C4×M16D11semidirect
370. C4×M16C2×D11semidirect
371. C4×M16C2×D11semidirect
372. C2×#97C2×D11semidirect
373. C2×C4×C8C2×D11semidirect
597. C11#60214semidirect

Maximal subgroups

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

subgroupindex
C2×#106230102
#130776202
#130776102
#130776012
#130775912
M16×Dic222
M16×D442
M16×C22⋊D112
#130772522
#130772492
#130770332
C2×C4×C11×M162
#6021411