Finite Group Databasebeta

← C2×#13082371 #15662206

Subgroups — C2×#13082371 #15662206

Order 2816.

7206 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082371C2132yesmaximal, direct product factor
2C2×#10623263C212yesmaximal, complemented
3C2×#10623261C212yesmaximal, complemented
4C2×#10623173C214yesmaximal, complemented
5C2×#10623225C212yesmaximal, complemented
6C2×#10623225C212yesmaximal, complemented
7C2×#10623168C214yesmaximal, complemented
8C2×#10623264C212yesmaximal, complemented
9C2×#10623228C212yesmaximal, complemented
10C2×#10623057C211yesmaximal, characteristic, complemented
11C2×#10623259C212yesmaximal, complemented
12C2×#10623222C212yesmaximal, complemented
13C2×#10623055C211yesmaximal, characteristic
14C22×#66950C211yesmaximal, characteristic, complemented
15C2×#10623035C211yesmaximal, characteristic, complemented
16C2×#10623047C211yesmaximal, characteristic, complemented
17C2×D11×#117C211yesmaximal, characteristic, complemented
18C2×C11×#544C211yesmaximal, characteristic, complemented
19C22×#4339C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C23×Dic22C2211yescharacteristic
22C11×#544C22116yescomplemented
23C2×C11×C4⋊Q8C2212yescomplemented
24C2×C11×C4⋊Q8C2212yescomplemented
25C2×C11×#125C2212yescomplemented
26C2×C11×#125C2212yescomplemented
27C2×C11×C22⋊Q8C2214yes—
28C2×C11×#117C2211yescharacteristic
29C2×C11×#117C2211yescharacteristic
30C22×C11×C4⋊C4C2211yescharacteristic
31C2×#67000C2214yes—
32C2×#66999C2214yes—
33C2×#66999C2214yescomplemented
34C2×Q8×Dic11C2214yescomplemented
35C2×C4×C22⋊D11C2214yes—
36C22×(C2×D11)⋊C4C2212yes—
37C2×#66979C2211yescharacteristic
38C22×C4⋊Dic11C2212yes—
39#10623264C22132yescomplemented
40#10623263C22132yescomplemented
41#10623261C22132yescomplemented
42#10623259C22132yescomplemented
43#10623228C22132yescomplemented
44#10623225C22132yescomplemented
45#10623225C22132yescomplemented
46#10623222C22132yescomplemented
47#10623173C22164yescomplemented
48#10623168C22164yescomplemented
49#10623057C22116yescomplemented
50#10623055C22116yes—
51D11×#117C22116yescomplemented
52#10623047C22116yescomplemented
53C2×#66951C2214yes—
54C2×#66951C2214yes—
55C2×#66951C2214yescomplemented
56C2×#66951C2214yescomplemented
57C2×#66950C2211yescharacteristic
58C2×#66950C2211yescharacteristic
59C2×#66950C2212yes—
60C2×#66950C2212yes—
61C2×#66950C2212yes—
62C2×#66950C2212yes—
63C2×#66950C22116yescomplemented
64C2×#66950C2212yescomplemented
65C2×#66950C2212yescomplemented
66C2×#66948C2211yescharacteristic
67C2×#66948C2211yescharacteristic
68C2×#66947C2214yes—
69C2×#66947C2214yes—
70#10623035C22116yescomplemented
71C2×#66946C2214yes—
72C2×#66946C2212yescomplemented
73C2×#66945C2214yes—
74C2×#66945C2211yescharacteristic
75C2×#66945C2211yescharacteristic
76C2×#66945C2214yescomplemented
77C2×#66945C2212yescomplemented
78C2×C4⋊C4×D11C2211yescharacteristic
79C2×C4⋊C4×D11C2211yescharacteristic
80C2×C4⋊C4×D11C2212yescomplemented
81C2×#66943C2214yescomplemented
82C2×#66943C2214yescomplemented
83C2×#66943C2214yescomplemented
84C2×#66940C2212yescomplemented
85C2×#66940C2212yescomplemented
86C2×#66940C2212yescomplemented
87C2×#66939C2214yes—
88C2×#66939C2212yes—
89C2×#66935C2212yes—
90C2×C22⋊C4×D11C2212yes—
91C2×#66930C2214yes—
92C2×#66930C2212yes—
93C2×#66928C2212yescomplemented
94C2×C4×D44C2212yes—
95C2×C4×D44C2212yes—
96C2×#66925C2212yes—
97C2×C42×D11C2212yes—
98C2×#66922C2212yescomplemented
99C2×C4×Dic22C2212yescomplemented
100C2×C4×Dic22C2212yescomplemented
101C24×D11C2311yescharacteristic
102C22×Q8×C11C2314yes—
103C23×C4×C11C2312yes—
104C23×C4×C11C2311yescharacteristic
105C22×C22⋊D11C2312yes—
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2312yes—
108C2×#4339—28no—
109C2×#4339C2318yes—
110C22×D44C2312yes—
111C22×D44C2311yescharacteristic
112C22×D44C2312yes—
113C22×C4×D11—28no—
114C22×C4×D11C2311yescharacteristic
115C22×C4×D11C2312yes—
116C22×C4×D11C2311yescharacteristic
117C22×C4×D11C2311yescharacteristic
118C22×C4×D11C2312yes—
119C22×C4×D11C2311yescharacteristic
120C22×C4×D11C2318yes—
121C22×C4×D11C2312yes—
122C22×C4×D11C2314yes—
123C22×Dic22—28no—
124C22×Dic22C2312yes—
125C22×Dic22C2311yescharacteristic
126C22×Dic22C2312yes—
127C22×Dic22C2318yes—
128C11×C4⋊Q8C23116yescomplemented
129C11×C4⋊Q8C23116yescomplemented
130C11×#125C23116yescomplemented
131C11×#125C23116yescomplemented
132C11×C22⋊Q8C23132yes—
133C11×#117C2318yes—
134C11×#117C2318yes—
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C4⋊C4C2311yescharacteristic
137C2×C11×C4⋊C4C2312yes—
138C2×C11×C4⋊C4C2314yes—
139C2×C11×C4⋊C4C2314yes—
140C2×C11×C4⋊C4C2314yes—
141C2×C11×C4⋊C4C2311yescharacteristic
142C2×C11×C4⋊C4C2311yescharacteristic
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C4⋊C4C2318yes—
145C2×C11×C22⋊C4C2312yes—
146C2×C11×C22⋊C4C2312yes—
147C2×C42×C11C2312yes—
148C2×C42×C11C2312yes—
149C2×C22⋊Dic11C2312yes—
150#67000C23132yes—
151#66999C23132yes—
152#66999C23132yescomplemented
153Q8×Dic11C23132yescomplemented
154C4×C22⋊D11C23132yes—
155C2×(C2×D11)⋊C4C2312yes—
156C2×(C2×D11)⋊C4C2312yes—
157C2×(C2×D11)⋊C4C2312yes—
158C2×(C2×D11)⋊C4C2312yes—
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161C2×(C2×D11)⋊C4C2314yes—
162C2×(C2×D11)⋊C4C2314yes—
163C2×(C2×D11)⋊C4C2314yes—
164C2×(C2×D11)⋊C4C2314yes—
165C2×(C2×D11)⋊C4C2314yes—
166C2×(C2×D11)⋊C4C23116yes—
167#66979C2318yes—
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2311yescharacteristic
170C2×C4⋊Dic11C2314yes—
171C2×C4⋊Dic11C2314yes—
172C2×C4⋊Dic11C2312yes—
173C2×C4⋊Dic11C2312yes—
174C2×C4⋊Dic11C2314yes—
175C2×C4⋊Dic11C2314yes—
176C2×C4⋊Dic11C23116yes—
177C2×Dic11⋊C4C2314yes—
178C2×Dic11⋊C4C2314yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2314yes—
182C2×C4×Dic11C2314yes—
183C2×C4×Dic11C2314yes—
184C2×C4×Dic11C2312yes—
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2312yes—
187C2×C4×Dic11C2314yes—
188#66951C23132yes—
189#66951C23132yes—
190#66951C23132yescomplemented
191#66951C23132yescomplemented
192#66950C2318yes—
193#66950C23116yes—
194#66950C23116yes—
195#66950C23116yes—
196#66950C23116yes—
197#66950C2318yes—
198#66950C23116yescomplemented
199#66950C23116yescomplemented
200#66948C2318yes—
201#66948C2318yes—
202#66947C23132yes—
203#66947C23132yes—
204#66946C23132yes—
205#66946C23116yescomplemented
206#66945C23132yes—
207#66945C2318yes—
208#66945C2318yes—
209#66945C23116yescomplemented
210#66945C23132yescomplemented
211C4⋊C4×D11C2318yes—
212C4⋊C4×D11C2318yes—
213C4⋊C4×D11C23116yescomplemented
214#66943C23132yescomplemented
215#66943C23132yescomplemented
216#66943C23132yescomplemented
217#66940C23116yescomplemented
218#66940C23116yescomplemented
219#66940C23116yescomplemented
220#66939C23116yes—
221#66939C23132yes—
222#66935C23116yes—
223C22⋊C4×D11C23116yes—
224#66930C23132yes—
225#66930C23116yes—
226#66928C23116yescomplemented
227C4×D44C23116yes—
228C4×D44C23116yes—
229#66925C23116yes—
230C42×D11C23116yes—
231#66922C23116yescomplemented
232C4×Dic22C23116yescomplemented
233C4×Dic22C23116yescomplemented
234C2×#3495—111nomaximal, Sylow
235C24×C11C2411yescharacteristic
236C23×D11—24no—
237C23×D11—24no—
238C23×D11—42no—
239C23×D11C2411yescharacteristic
240C23×D11C2412yes—
241C23×D11C2414yes—
242C23×D11C2411yescharacteristic
243C2×Q8×C11—48no—
244C2×Q8×C11C24116yes—
245C22×C4×C11—44no—
246C22×C4×C11#4118yes—
247C22×C4×C11C2412yes—
248C22×C4×C11C2412yes—
249C22×C4×C11C2412yes—
250C22×C4×C11C2412yes—
251C22×C4×C11C2414yes—
252C22×C4×C11C2418yes—
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C22×C4×C11C2414yes—
256C2×C22⋊D11—28no—
257C2×C22⋊D11C2418yes—
258C22×Dic11—28no—
259C22×Dic11—24no—
260C22×Dic11C2414yes—
261C22×Dic11C2418yes—
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2411yescharacteristic
265C22×Dic11C2412yes—
266C22×Dic11C2414yes—
267C22×Dic11C2411yescharacteristic
268#4339—232no—
269C2×D44—28no—
270C2×D44—24no—
271C2×D44—44no—
272C2×D44C2418yes—
273C2×D44C2414yes—
274C2×D44C2418yes—
275C2×C4×D11—28no—
276C2×C4×D11—24no—
277C2×C4×D11—24no—
278C2×C4×D11—24no—
279C2×C4×D11—24no—
280C2×C4×D11—232no—
281C2×C4×D11—28no—
282C2×C4×D11—48no—
283C2×C4×D11—44no—
284C2×C4×D11C2414yes—
285C2×C4×D11C2418yes—
286C2×C4×D11C2414yes—
287C2×C4×D11C2414yes—
288C2×C4×D11C2418yes—
289C2×C4×D11C2414yes—
290C2×C4×D11C2418yes—
291C2×C4×D11C24116yes—
292C2×Dic22—28no—
293C2×Dic22—28no—
294C2×Dic22—232no—
295C2×Dic22—24no—
296C2×Dic22C2418yes—
297C2×Dic22C2414yes—
298C2×Dic22C2418yes—
299C11×C4⋊C4C2414yes—
300C11×C4⋊C4C2414yes—
301C11×C4⋊C4C2418yes—
302C11×C4⋊C4C24116yes—
303C11×C4⋊C4C24116yes—
304C11×C4⋊C4C24116yes—
305C11×C4⋊C4C2414yes—
306C11×C4⋊C4C2414yes—
307C11×C4⋊C4C2418yes—
308C11×C22⋊C4C2418yes—
309C11×C22⋊C4C2418yes—
310C42×C11C2418yes—
311C42×C11C2418yes—
312C22⋊Dic11C2418yes—
313(C2×D11)⋊C4C2418yes—
314(C2×D11)⋊C4C2418yes—
315(C2×D11)⋊C4C2418yes—
316(C2×D11)⋊C4C2418yes—
317(C2×D11)⋊C4C2418yes—
318(C2×D11)⋊C4C2418yes—
319(C2×D11)⋊C4C24116yes—
320(C2×D11)⋊C4C24116yes—
321(C2×D11)⋊C4C24116yes—
322(C2×D11)⋊C4C24116yes—
323(C2×D11)⋊C4C24116yes—
324C4⋊Dic11C2414yes—
325C4⋊Dic11C2414yes—
326C4⋊Dic11C24116yes—
327C4⋊Dic11C24116yes—
328C4⋊Dic11C2418yes—
329C4⋊Dic11C2418yes—
330C4⋊Dic11C24116yes—
331C4⋊Dic11C24116yes—
332Dic11⋊C4C24116yes—
333Dic11⋊C4C24116yes—
334Dic11⋊C4C2418yes—
335Dic11⋊C4C2418yes—
336Dic11⋊C4C24116yes—
337C4×Dic11C24116yes—
338C4×Dic11C24116yes—
339C4×Dic11C2418yes—
340C4×Dic11C2418yes—
341C4×Dic11C2418yes—
342C4×Dic11C24116yes—
343#3495—1132no—
344C2×#556—112no—
345C2×#554—112no—
346C2×#552—112no—
347C2×#552—112no—
348C2×#552—114no—
349C2×#551—114no—
350C2×#544D1111yescharacteristic, complemented
351C2×#542—112no—
352C2×#541—112no—
353C2×#536—111no—
354C2×#533—112no—
355C2×#529—112no—
356C2×#525—111no—
357C22×C22⋊Q8—111no—
358C2×#520—111no—
359C2×#519—111no—
360C22×#117—111no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11C2×#4114yes—
364C23×C11C2512yes—
365C23×C11C2511yescharacteristic
366C22×D11—22no—
367C22×D11—22no—
368C22×D11—28no—
369C22×D11—22no—
370C22×D11—24no—
371C22×D11—24no—
372C22×D11—22no—
373C22×D11—24no—
374C22×D11—22no—
375C22×D11—28no—
376C22×D11—44no—
377C22×D11—416no—
378C22×D112−1+414yes—
379C22×D11C2512yes—
380C22×D11C2514yes—
381C22×D11C2512yes—
382Q8×C11—416no—
383C2×C4×C11—24no—
384C2×C4×C11—24no—
385C2×C4×C11—28no—
386C2×C4×C11—24no—
387C2×C4×C11—24no—
388C2×C4×C11—48no—
389C2×C4×C11C2×#4114yes—
390C2×C4×C11C2×#4114yes—
391C2×C4×C11C2×#41116yes—
392C2×C4×C11C2514yes—
393C2×C4×C11C2514yes—
394C2×C4×C11C2514yes—
395C2×C4×C11C2514yes—
396C2×C4×C11C2518yes—
397C2×C4×C11C2512yes—
398C2×C4×C11C2512yes—
399C22⋊D11—216no—
400C2×Dic11—216no—
401C2×Dic11—28no—
402C2×Dic11—24no—
403C2×Dic11—28no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—24no—
407C2×Dic11—24no—
408C2×Dic11C2514yes—
409C2×Dic11C2514yes—
410C2×Dic11C2512yes—
411C2×Dic11C2514yes—
412C2×Dic11C2518yes—
413C2×Dic11C2512yes—
414D44—216no—
415D44—28no—
416D44—48no—
417C4×D11—216no—
418C4×D11—28no—
419C4×D11—28no—
420C4×D11—28no—
421C4×D11—28no—
422C4×D11—216no—
423C4×D11—416no—
424C4×D11—48no—
425Dic22—216no—
426Dic22—216no—
427Dic22—28no—
428C22×#41—111no—
429C23×Q8—111no—
430C24×C4—111no—
431#556—1132no—
432#554—1132no—
433#552—1132no—
434#552—1132no—
435#552—1164no—
436#551—1164no—
437#544C2×D11116yescomplemented
438#542—1132no—
439#541—1132no—
440#536—1116no—
441#533—1132no—
442C2×C4⋊Q8—112no—
443C2×C4⋊Q8C2×D1112yescomplemented
444C2×C4⋊Q8C2×D1112yescomplemented
445#529—1132no—
446C2×#126—114no—
447C2×#126—114no—
448C2×#126—114no—
449C2×#126—114no—
450C2×#125—114no—
451C2×#125—114no—
452C2×#125—114no—
453C2×#125C2×D1112yescomplemented
454C2×#125C2×D1112yescomplemented
455C2×#124—114no—
456C2×#124—112no—
457#525—1116no—
458C2×#123—114no—
459C2×#123—114no—
460C2×#123—112no—
461C2×#123—114no—
462C2×C22⋊Q8—114no—
463C2×C22⋊Q8—114no—
464C2×C22⋊Q8—112no—
465C2×C22⋊Q8—112no—
466C2×C22⋊Q8—112no—
467C2×C22⋊Q8—112no—
468C2×C22⋊Q8—111no—
469C2×C22⋊Q8—111no—
470C2×C22⋊Q8—1116no—
471C2×C22⋊Q8—112no—
472C2×C22⋊Q8—112no—
473C2×C22⋊Q8C2×D1114yes—
474C2×#121—111no—
475C2×#121—111no—
476C2×#120—112no—
477#520—1116no—
478#519—1116no—
479C2×C4×Q8—114no—
480C2×C4×Q8—112no—
481C2×C4×Q8—112no—
482C2×C4×Q8—112no—
483C2×C4×Q8—112no—
484C2×C4×Q8—112no—
485C2×C4×D4—114no—
486C2×C4×D4—114no—
487C2×C4×D4—112no—
488C2×C4×D4—112no—
489C2×C4×D4—112no—
490C2×#117—111no—
491C2×#117—1116no—
492C2×#117—111no—
493C2×#117—111no—
494C2×#117—114no—
495C2×#117—112no—
496C2×#117—114no—
497C2×#117—112no—
498C2×#117—114no—
499C2×#117—112no—
500C2×#117C2×D1111yescharacteristic
501C2×#117C2×D1111yescharacteristic
502C22×C4⋊C4—112no—
503C22×C4⋊C4—111no—
504C22×C4⋊C4—111no—
505C22×C4⋊C4—112no—
506C22×C4⋊C4C2×D1111yescharacteristic
507C22×C22⋊C4—112no—
508C22×C22⋊C4—112no—
509C22×C42—112no—
510C22×C11—22no—
511C22×C11—22no—
512C22×C11—28no—
513C22×C11C22×#4114yes—
514C22×C11C22×#4112yes—
515C22×C11C2×2−1+412yes—
516C22×C11#58512yes—
517C22×C11C2611yescharacteristic
518C2×D11—22no—
519C2×D11—22no—
520C2×D11—28no—
521C2×D11—22no—
522C2×D11—24no—
523C2×D11—22no—
524C2×D11—24no—
525C2×D11—22no—
526C2×D11—24no—
527C2×D11—416no—
528C2×D11—48no—
529C2×D11—44no—
530C2×D11C2×2−1+414yes—
531C4×C11—24no—
532C4×C11—24no—
533C4×C11—28no—
534C4×C11—24no—
535C4×C11—24no—
536C4×C11C22×#4114yes—
537C4×C11C22×#4114yes—
538Dic11—28no—
539Dic11—24no—
540Dic11—22no—
541Dic11—22no—
542Dic11—24no—
543Dic11—24no—
544C25—111no—
545C2×#41—118no—
546C2×#41—228no—
547C22×Q8—112no—
548C22×Q8—112no—
549C22×Q8—111no—
550C22×Q8—118no—
551C22×Q8—228no—
552C22×Q8C22×D1114yes—
553C22×D4—112no—
554C22×D4—112no—
555C22×D4—111no—
556C22×D4—112no—
557C23×C4—112no—
558C23×C4—111no—
559C23×C4—112no—
560C23×C4—111no—
561C23×C4—112no—
562C23×C4—111no—
563C23×C4—111no—
564C23×C4—118no—
565C23×C4—111no—
566C23×C4—112no—
567C23×C4—114no—
568C23×C4—228no—
569C23×C4C22×D1112yes—
570C23×C4C22×D1111yescharacteristic
571C4⋊Q8—1116no—
572C4⋊Q8C22×D11116yescomplemented
573C4⋊Q8C22×D11116yescomplemented
574#126—1132no—
575#126—1132no—
576#126—1132no—
577#126—1132no—
578#125—1132no—
579#125—1132no—
580#125—1132no—
581#125C22×D11116yescomplemented
582#125C22×D11116yescomplemented
583#124—1132no—
584#124—1116no—
585#123—1132no—
586#123—1132no—
587#123—1116no—
588#123—1132no—
589C22⋊Q8—1132no—
590C22⋊Q8—1132no—
591C22⋊Q8—1116no—
592C22⋊Q8—1116no—
593C22⋊Q8—1116no—
594C22⋊Q8—1116no—
595C22⋊Q8—118no—
596C22⋊Q8—118no—
597C22⋊Q8—1116no—
598C22⋊Q8—1116no—
599C22⋊Q8C22×D11132yes—
600#121—118no—
601#121—118no—
602#120—1116no—
603C4×Q8—1132no—
604C4×Q8—1116no—
605C4×Q8—1116no—
606C4×Q8—1116no—
607C4×Q8—1116no—
608C4×Q8—1116no—
609C4×D4—1132no—
610C4×D4—1116no—
611C4×D4—1132no—
612C4×D4—1116no—
613C4×D4—1116no—
614#117—118no—
615#117—118no—
616#117—118no—
617#117—1116no—
618#117—1132no—
619#117—1132no—
620#117—1116no—
621#117—1132no—
622#117—1116no—
623#117C22×D1118yes—
624#117C22×D1118yes—
625C2×C4⋊C4—111no—
626C2×C4⋊C4—111no—
627C2×C4⋊C4—112no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4—114no—
630C2×C4⋊C4—114no—
631C2×C4⋊C4—114no—
632C2×C4⋊C4—1116no—
633C2×C4⋊C4—114no—
634C2×C4⋊C4—114no—
635C2×C4⋊C4—114no—
636C2×C4⋊C4—112no—
637C2×C4⋊C4—112no—
638C2×C4⋊C4—114no—
639C2×C4⋊C4—118no—
640C2×C4⋊C4—118no—
641C2×C4⋊C4—1116no—
642C2×C4⋊C4C22×D1112yes—
643C2×C4⋊C4C22×D1111yescharacteristic
644C2×C4⋊C4C22×D1111yescharacteristic
645C2×C4⋊C4C22×D1112yes—
646C2×C4⋊C4C22×D1118yes—
647C2×C4⋊C4C22×D1114yes—
648C2×C4⋊C4C22×D1114yes—
649C2×C4⋊C4C22×D1111yescharacteristic
650C2×C4⋊C4C22×D1111yescharacteristic
651C2×C4⋊C4C22×D1114yes—
652C2×C22⋊C4—112no—
653C2×C22⋊C4—112no—
654C2×C22⋊C4—112no—
655C2×C22⋊C4—114no—
656C2×C22⋊C4—114no—
657C2×C22⋊C4—1116no—
658C2×C22⋊C4—112no—
659C2×C22⋊C4—112no—
660C2×C22⋊C4—114no—
661C2×C22⋊C4—114no—
662C2×C22⋊C4—112no—
663C2×C22⋊C4—112no—
664C2×C22⋊C4—114no—
665C2×C22⋊C4—1116no—
666C2×C22⋊C4C22×D1112yes—
667C2×C22⋊C4C22×D1112yes—
668C2×C42—112no—
669C2×C42—112no—
670C2×C42—114no—
671C2×C42—114no—
672C2×C42—114no—
673C2×C42—112no—
674C2×C42—1116no—
675C2×C42C22×D1112yes—
676C2×C42C22×D1112yes—
677C2×C11—24no—
678C2×C11#349514yescomplemented
679C2×C11C23×#4111yescharacteristic
680C2×C11C22×2−1+411yescharacteristic
681C2×C11C2×#58511yescharacteristic
682D11—24no—
683D11—44no—
684D11—42no—
685C24—111no—
686C24—111no—
687C24—112no—
688C24—114no—
689C24—224no—
690C24—224no—
691C24—442no—
692C24C23×D1111yescharacteristic
693#41—2232no—
694C2×Q8—48no—
695C2×Q8—118no—
696C2×Q8—118no—
697C2×Q8—114no—
698C2×Q8—228no—
699C2×Q8—228no—
700C2×Q8—2232no—
701C2×Q8—224no—
702C2×Q8C23×D11116yes—
703C2×D4—118no—
704C2×D4—118no—
705C2×D4—114no—
706C2×D4—118no—
707C2×D4—228no—
708C2×D4—228no—
709C2×D4—224no—
710C2×D4—444no—
711C22×C4—44no—
712C22×C4—118no—
713C22×C4—114no—
714C22×C4—112no—
715C22×C4—111no—
716C22×C4—112no—
717C22×C4—114no—
718C22×C4—112no—
719C22×C4—111no—
720C22×C4—114no—
721C22×C4—118no—
722C22×C4—114no—
723C22×C4—118no—
724C22×C4—114no—
725C22×C4—114no—
726C22×C4—118no—
727C22×C4—1116no—
728C22×C4—228no—
729C22×C4—224no—
730C22×C4—228no—
731C22×C4—224no—
732C22×C4—224no—
733C22×C4—224no—
734C22×C4—224no—
735C22×C4—2232no—
736C22×C4—228no—
737C22×C4—448no—
738C22×C4—444no—
739C22×C4#434318yes—
740C22×C4C23×D1112yes—
741C22×C4C23×D1112yes—
742C22×C4C23×D1112yes—
743C22×C4C23×D1112yes—
744C22×C4C23×D1114yes—
745C22×C4C23×D1118yes—
746C22×C4C23×D1114yes—
747C22×C4C23×D1111yescharacteristic
748C22×C4C23×D1111yescharacteristic
749C4⋊C4—114no—
750C4⋊C4—114no—
751C4⋊C4—118no—
752C4⋊C4—118no—
753C4⋊C4—1116no—
754C4⋊C4—1116no—
755C4⋊C4—1116no—
756C4⋊C4—1116no—
757C4⋊C4—1116no—
758C4⋊C4—1116no—
759C4⋊C4—118no—
760C4⋊C4—118no—
761C4⋊C4—1116no—
762C4⋊C4C23×D1118yes—
763C4⋊C4C23×D1114yes—
764C4⋊C4C23×D1114yes—
765C4⋊C4C23×D1118yes—
766C4⋊C4C23×D11116yes—
767C4⋊C4C23×D11116yes—
768C4⋊C4C23×D1114yes—
769C4⋊C4C23×D1114yes—
770C4⋊C4C23×D11116yes—
771C22⋊C4—118no—
772C22⋊C4—118no—
773C22⋊C4—118no—
774C22⋊C4—1116no—
775C22⋊C4—1116no—
776C22⋊C4—118no—
777C22⋊C4—118no—
778C22⋊C4—1116no—
779C22⋊C4—1116no—
780C22⋊C4—118no—
781C22⋊C4—118no—
782C22⋊C4—1116no—
783C22⋊C4C23×D1118yes—
784C22⋊C4C23×D1118yes—
785C42—118no—
786C42—118no—
787C42—118no—
788C42—1116no—
789C42—1116no—
790C42—1116no—
791C42C23×D1118yes—
792C42C23×D1118yes—
793C11C2×#349511yescharacteristic, complemented, Sylow
794C23—22no—
795C23—22no—
796C23—114no—
797C23—112no—
798C23—112no—
799C23—114no—
800C23—228no—
801C23—222no—
802C23—222no—
803C23—228no—
804C23—222no—
805C23—224no—
806C23—224no—
807C23—222no—
808C23—224no—
809C23—222no—
810C23—444no—
811C23—4416no—
812C23C2×#434314yes—
813C23C24×D1112yes—
814C23C24×D1111yescharacteristic
815Q8—416no—
816Q8—2216no—
817Q8—2216no—
818Q8—228no—
819D4—2216no—
820D4—2216no—
821D4—228no—
822D4—448no—
823C2×C4—28no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—48no—
829C2×C4—114no—
830C2×C4—112no—
831C2×C4—114no—
832C2×C4—118no—
833C2×C4—114no—
834C2×C4—112no—
835C2×C4—2216no—
836C2×C4—228no—
837C2×C4—222no—
838C2×C4—222no—
839C2×C4—224no—
840C2×C4—2216no—
841C2×C4—228no—
842C2×C4—224no—
843C2×C4—224no—
844C2×C4—228no—
845C2×C4—228no—
846C2×C4—228no—
847C2×C4—228no—
848C2×C4—2216no—
849C2×C4—4416no—
850C2×C4—448no—
851C2×C4C2×#434314yes—
852C2×C4C2×#434314yes—
853C2×C4C2×#4343116yes—
854C2×C4C24×D1114yes—
855C2×C4C24×D1114yes—
856C2×C4C24×D1114yes—
857C2×C4C24×D1114yes—
858C2×C4C24×D1118yes—
859C2×C4C24×D1112yes—
860C2×C4C24×D1112yes—
861C22—28no—
862C22—22no—
863C22—22no—
864C22—114no—
865C22—228no—
866C22—222no—
867C22—222no—
868C22—222no—
869C22—224no—
870C22—224no—
871C22—222no—
872C22—224no—
873C22—222no—
874C22—4416no—
875C22—444no—
876C22—448no—
877C22C22×#434314yes—
878C22C22×#434312yes—
879C22#1062345512yes—
880C22D11×2−1+412yes—
881C22C25×D1111yescharacteristic
882C4—24no—
883C4—24no—
884C4—28no—
885C4—24no—
886C4—24no—
887C4—222no—
888C4—222no—
889C4—224no—
890C4—228no—
891C4—224no—
892C4—224no—
893C4C22×#434314yes—
894C4C22×#434314yes—
895C2—24no—
896C2—224no—
897C2—442no—
898C2—444no—
899C2#1308237114yesdirect product factor
900C2C23×#434311yescharacteristic
901C2C2×D11×2−1+411yescharacteristic
902C2C2×#1062345511yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#544C2
socleC23×C11C25
prime radicalC2×#10623055C2
hypercenterC2×#544D11
hypocenterC11C2×#3495
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #13082371C2direct (N × H)
2. C2×#10623263C2semidirect
3. C2×#10623261C2semidirect
4. C2×#10623173C2semidirect
5. C2×#10623225C2semidirect
6. C2×#10623225C2semidirect
7. C2×#10623168C2semidirect
8. C2×#10623264C2semidirect
9. C2×#10623228C2semidirect
10. C2×#10623057C2semidirect
11. C2×#10623259C2semidirect
12. C2×#10623222C2semidirect
14. C22×#66950C2semidirect
15. C2×#10623035C2semidirect
16. C2×#10623047C2semidirect
17. C2×D11×#117C2semidirect
18. C2×C11×#544C2semidirect
22. C11×#544C22semidirect
23. C2×C11×C4⋊Q8C22semidirect
24. C2×C11×C4⋊Q8C22semidirect
25. C2×C11×#125C22semidirect
26. C2×C11×#125C22semidirect
33. C2×#66999C22semidirect
34. C2×Q8×Dic11C22semidirect
39. #10623264C22semidirect
40. #10623263C22semidirect
41. #10623261C22semidirect
42. #10623259C22semidirect
43. #10623228C22semidirect
44. #10623225C22semidirect
45. #10623225C22semidirect
46. #10623222C22semidirect
47. #10623173C22semidirect
48. #10623168C22semidirect
49. #10623057C22semidirect
51. D11×#117C22semidirect
52. #10623047C22semidirect
55. C2×#66951C22semidirect
56. C2×#66951C22semidirect
63. C2×#66950C22semidirect
64. C2×#66950C22semidirect
65. C2×#66950C22semidirect
70. #10623035C22semidirect
72. C2×#66946C22semidirect
76. C2×#66945C22semidirect
77. C2×#66945C22semidirect
80. C2×C4⋊C4×D11C22semidirect
81. C2×#66943C22semidirect
82. C2×#66943C22semidirect
83. C2×#66943C22semidirect
84. C2×#66940C22semidirect
85. C2×#66940C22semidirect
86. C2×#66940C22semidirect
93. C2×#66928C22semidirect
98. C2×#66922C22semidirect
99. C2×C4×Dic22C22semidirect
100. C2×C4×Dic22C22semidirect
128. C11×C4⋊Q8C23semidirect
129. C11×C4⋊Q8C23semidirect
130. C11×#125C23semidirect
131. C11×#125C23semidirect
152. #66999C23semidirect
153. Q8×Dic11C23semidirect
190. #66951C23semidirect
191. #66951C23semidirect
198. #66950C23semidirect
199. #66950C23semidirect
205. #66946C23semidirect
209. #66945C23semidirect
210. #66945C23semidirect
213. C4⋊C4×D11C23semidirect
214. #66943C23semidirect
215. #66943C23semidirect
216. #66943C23semidirect
217. #66940C23semidirect
218. #66940C23semidirect
219. #66940C23semidirect
226. #66928C23semidirect
231. #66922C23semidirect
232. C4×Dic22C23semidirect
233. C4×Dic22C23semidirect
350. C2×#544D11semidirect
437. #544C2×D11semidirect
443. C2×C4⋊Q8C2×D11semidirect
444. C2×C4⋊Q8C2×D11semidirect
453. C2×#125C2×D11semidirect
454. C2×#125C2×D11semidirect
572. C4⋊Q8C22×D11semidirect
573. C4⋊Q8C22×D11semidirect
581. #125C22×D11semidirect
582. #125C22×D11semidirect
678. C2×C11#3495semidirect
793. C11C2×#3495semidirect
899. C2#13082371direct (N × H)

Maximal subgroups

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

subgroupindex
#130823712
C2×#106232632
C2×#106232612
C2×#106231732
C2×#106232252
C2×#106231682
C2×#106232642
C2×#106232282
C2×#106230572
C2×#106232592
C2×#106232222
C2×#106230552
C22×#669502
C2×#106230352
C2×#106230472
C2×D11×#1172
C2×C11×#5442
C2×#349511