Finite Group Databasebeta

← C2×#13082473 #15661847

Subgroups — C2×#13082473 #15661847

Order 2816.

7130 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082473C2132yesmaximal, direct product factor
2C2×#10623244C211yesmaximal, characteristic, complemented
3C2×#10623101C211yesmaximal, characteristic, complemented
4C2×#10623098C211yesmaximal, characteristic, complemented
5C2×#10623073C212yesmaximal, complemented
6C2×#10623202C212yesmaximal, complemented
7C2×#10623202C212yesmaximal, complemented
8C2×#10623070C212yesmaximal, complemented
9C2×#10623181C214yesmaximal, complemented
10C2×#10623191C214yesmaximal, complemented
11C2×#10623206C212yesmaximal, complemented
12C2×#10623109C211yesmaximal, characteristic, complemented
13C2×#10623247C211yesmaximal, characteristic
14C2×#10623088C212yesmaximal, complemented
15C2×#10623211C212yesmaximal, complemented
16C2×#10623077C212yesmaximal, complemented
17C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
18C2×C11×#559C211yesmaximal, characteristic, complemented
19C22×Q8×D11C2211yescharacteristic
20C22×#4341C2212yes—
21C11×#559C22116yescomplemented
22C2×C11×#127C2211yescharacteristic
23C2×C11×#124C2212yes—
24C2×C11×#124C2212yes—
25C2×C11×#123C2214yes—
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11C2212yes—
29C2×C4×D4×C11C2212yes—
30C2×#66999C2211yescharacteristic
31C2×Q8×Dic11C2212yes—
32C2×Q8×Dic11C2211yescharacteristic
33C2×#66997C2211yescharacteristic
34C2×#66997C2212yes—
35C2×#66991C2212yes—
36C2×#66991C2212yes—
37C2×#66989C2212yes—
38C2×#66989C2212yes—
39C2×#66989C2212yes—
40C2×#66988C2214yes—
41C2×D4×Dic11C2212yes—
42C2×D4×Dic11C2212yes—
43C2×D4×Dic11C2212yes—
44C2×D4×Dic11C2212yes—
45C2×C4×C22⋊D11C2214yes—
46C2×#66979C2214yes—
47C2×#66977C2214yes—
48C22×Dic11⋊C4C2214yes—
49#10623247C22116yes—
50#10623244C22116yescomplemented
51#10623211C22132yescomplemented
52#10623206C22132yescomplemented
53#10623202C22132yescomplemented
54#10623202C22132yescomplemented
55#10623191C22164yescomplemented
56#10623181C22164yescomplemented
57#10623109C22116yescomplemented
58C4×Q8×D11C22116yescomplemented
59#10623101C22116yescomplemented
60#10623098C22116yescomplemented
61#10623088C22132yescomplemented
62#10623077C22132yescomplemented
63#10623073C22132yescomplemented
64#10623070C22132yescomplemented
65C2×#66950C2211yescharacteristic
66C2×#66949C2212yes—
67C2×C4⋊C4×D11C2212yes—
68C2×C4⋊C4×D11C2211yescharacteristic
69C2×#66943C2214yes—
70C2×#66943C2212yes—
71C2×#66942C2212yes—
72C2×#66942C2214yes—
73C2×#66941C2211yescharacteristic
74C2×#66940C2212yes—
75C2×#66940C2211yescharacteristic
76C2×#66940C2212yes—
77C2×#66936C2214yes—
78C2×#66936C2214yes—
79C2×(C22⋊D11)⋊C4C2214yes—
80C2×#66932C2214yes—
81C2×#66932C2214yes—
82C2×#66932C2214yes—
83C2×#66932C2214yes—
84C2×#66931C2214yes—
85C2×#66931C2214yes—
86C2×#66931C2214yes—
87C2×#66930C2214yes—
88C2×#66930C2214yes—
89C2×#66925C2212yes—
90C2×C42×D11C2212yes—
91C2×C42×D11C2211yescharacteristic
92C2×#66923C2212yes—
93C2×#66922C2211yescharacteristic
94C2×#66922C2212yes—
95C2×C4×Dic22C2212yes—
96C2×C4×Dic22C2212yes—
97C2×C4×Dic22C2212yes—
98C2×C4×Dic22C2211yescharacteristic
99C2×C4×Dic22C2212yes—
100C2×C4×Dic22C2211yescharacteristic
101C22×Q8×C11C2311yescharacteristic
102C22×Q8×C11C2311yescharacteristic
103C22×D4×C11C2312yes—
104C22×D4×C11C2312yes—
105C22×D4×C11C2312yes—
106C23×C4×C11C2314yes—
107C22×C22⋊D11C2314yes—
108C23×Dic11C2314yes—
109C23×Dic11C2314yes—
110C2×Q8×D11—28no—
111C2×Q8×D11C2318yes—
112C2×#4341—216no—
113C2×#4341C23116yes—
114C22×C4×D11C2311yescharacteristic
115C22×C4×D11C2312yes—
116C22×C4×D11C2312yes—
117C22×C4×D11C2311yescharacteristic
118C22×C4×D11C2311yescharacteristic
119C22×Dic22C2311yescharacteristic
120C22×Dic22C2311yescharacteristic
121C22×Dic22C2312yes—
122C22×Dic22C2312yes—
123C22×Dic22C2312yes—
124C11×#127C2318yes—
125C11×#124C23116yes—
126C11×#124C23116yes—
127C11×#123C23132yes—
128C4×Q8×C11C2318yes—
129C4×Q8×C11C2318yes—
130C4×D4×C11C23116yes—
131C4×D4×C11C23116yes—
132C2×C11×C4⋊C4C2311yescharacteristic
133C2×C11×C4⋊C4C2312yes—
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C4⋊C4C2312yes—
136C2×C11×C22⋊C4C2314yes—
137C2×C11×C22⋊C4C2314yes—
138C2×C11×C22⋊C4C2314yes—
139C2×C42×C11C2311yescharacteristic
140C2×C42×C11C2312yes—
141C2×C42×C11C2312yes—
142C2×C22⋊Dic11C2314yes—
143C2×C22⋊Dic11C2314yes—
144C2×C22⋊Dic11C2314yes—
145C2×C22⋊Dic11C2314yes—
146C2×C22⋊Dic11C2314yes—
147#66999C2318yes—
148Q8×Dic11C23116yes—
149Q8×Dic11C2318yes—
150#66997C23116yes—
151#66997C2318yes—
152#66991C23116yes—
153#66991C23116yes—
154#66989C23116yes—
155#66989C23116yes—
156#66989C23116yes—
157#66988C23132yes—
158D4×Dic11C23116yes—
159D4×Dic11C23116yes—
160D4×Dic11C23116yes—
161D4×Dic11C23116yes—
162C4×C22⋊D11C23132yes—
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2312yes—
165#66979C23132yes—
166C2×C4⋊Dic11C2311yescharacteristic
167C2×C4⋊Dic11C2312yes—
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2312yes—
170C2×C4⋊Dic11C2312yes—
171C2×C4⋊Dic11C2314yes—
172C2×C4⋊Dic11C2314yes—
173C2×C4⋊Dic11C2312yes—
174#66977C23132yes—
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2314yes—
178C2×Dic11⋊C4C2314yes—
179C2×Dic11⋊C4C2312yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2312yes—
182C2×Dic11⋊C4C2312yes—
183C2×Dic11⋊C4C2314yes—
184C2×Dic11⋊C4C2314yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C23132yes—
188C2×C4×Dic11C2311yescharacteristic
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C2312yes—
192C2×C4×Dic11C2314yes—
193C2×C4×Dic11C2314yes—
194C2×C4×Dic11C2312yes—
195C2×C4×Dic11C2312yes—
196C2×C4×Dic11C2311yescharacteristic
197#66950C2318yes—
198#66949C23116yes—
199C4⋊C4×D11C2318yes—
200C4⋊C4×D11C23116yes—
201#66943C23116yes—
202#66943C23132yes—
203#66942C23132yes—
204#66942C23116yes—
205#66941C2318yes—
206#66940C2318yes—
207#66940C23116yes—
208#66940C23116yes—
209#66936C23132yes—
210#66936C23132yes—
211(C22⋊D11)⋊C4C23132yes—
212#66932C23132yes—
213#66932C23132yes—
214#66932C23132yes—
215#66932C23132yes—
216#66931C23132yes—
217#66931C23132yes—
218#66931C23132yes—
219#66930C23132yes—
220#66930C23132yes—
221#66925C23116yes—
222C42×D11C2318yes—
223C42×D11C23116yes—
224#66923C23116yes—
225#66922C2318yes—
226#66922C23116yes—
227C4×Dic22C2318yes—
228C4×Dic22C2318yes—
229C4×Dic22C23116yes—
230C4×Dic22C23116yes—
231C4×Dic22C23116yes—
232C4×Dic22C23116yes—
233C2×#3507—111nomaximal, Sylow
234C24×C11C2414yes—
235C23×D11C2411yescharacteristic
236C2×Q8×C11—24no—
237C2×Q8×C11—24no—
238C2×Q8×C11C2414yes—
239C2×Q8×C11C2414yes—
240C2×D4×C11—28no—
241C2×D4×C11—28no—
242C2×D4×C11—44no—
243C2×D4×C11C2418yes—
244C2×D4×C11C2418yes—
245C2×D4×C11C2418yes—
246C22×C4×C11—48no—
247C22×C4×C11C2412yes—
248C22×C4×C11C2412yes—
249C22×C4×C11C2411yescharacteristic
250C22×C4×C11C2412yes—
251C22×C4×C11C2412yes—
252C22×C4×C11C24116yes—
253C22×C4×C11C2411yescharacteristic
254C22×C4×C11C2411yescharacteristic
255C2×C22⋊D11—216no—
256C2×C22⋊D11C24116yes—
257C22×Dic11—216no—
258C22×Dic11—48no—
259C22×Dic11C24116yes—
260C22×Dic11C2411yescharacteristic
261C22×Dic11C2412yes—
262C22×Dic11C2412yes—
263C22×Dic11C2414yes—
264C22×Dic11C2411yescharacteristic
265C22×Dic11C2412yes—
266C22×Dic11C2412yes—
267C22×Dic11C24116yes—
268C22×Dic11C2411yescharacteristic
269Q8×D11—232no—
270#4341—264no—
271C2×C4×D11—28no—
272C2×C4×D11—24no—
273C2×C4×D11—44no—
274C2×C4×D11—42no—
275C2×C4×D11#4118yes—
276C2×C4×D11C2414yes—
277C2×C4×D11C2418yes—
278C2×C4×D11C2418yes—
279C2×C4×D11C2414yes—
280C2×C4×D11C2414yes—
281C2×Dic22—28no—
282C2×Dic22—28no—
283C2×Dic22—24no—
284C2×Dic22—24no—
285C2×Dic22—44no—
286C2×Dic22C2414yes—
287C2×Dic22C2414yes—
288C2×Dic22C2418yes—
289C2×Dic22C2418yes—
290C2×Dic22C2418yes—
291C11×C4⋊C4C2414yes—
292C11×C4⋊C4C2418yes—
293C11×C4⋊C4C2414yes—
294C11×C4⋊C4C2418yes—
295C11×C22⋊C4C24116yes—
296C11×C22⋊C4C24116yes—
297C11×C22⋊C4C24116yes—
298C42×C11C2414yes—
299C42×C11C2418yes—
300C42×C11C2418yes—
301C22⋊Dic11C24116yes—
302C22⋊Dic11C24116yes—
303C22⋊Dic11C24116yes—
304C22⋊Dic11C24116yes—
305C22⋊Dic11C24116yes—
306(C2×D11)⋊C4C2418yes—
307(C2×D11)⋊C4C2418yes—
308C4⋊Dic11C2414yes—
309C4⋊Dic11C2418yes—
310C4⋊Dic11C2414yes—
311C4⋊Dic11C2418yes—
312C4⋊Dic11C2418yes—
313C4⋊Dic11C24116yes—
314C4⋊Dic11C24116yes—
315C4⋊Dic11C2418yes—
316Dic11⋊C4C2418yes—
317Dic11⋊C4C2418yes—
318Dic11⋊C4C24116yes—
319Dic11⋊C4C24116yes—
320Dic11⋊C4C2418yes—
321Dic11⋊C4C2418yes—
322Dic11⋊C4C2418yes—
323Dic11⋊C4C2418yes—
324Dic11⋊C4C24116yes—
325Dic11⋊C4C24116yes—
326Dic11⋊C4C2418yes—
327Dic11⋊C4C2418yes—
328C4×Dic11C2414yes—
329C4×Dic11C2414yes—
330C4×Dic11C2418yes—
331C4×Dic11C2418yes—
332C4×Dic11C24116yes—
333C4×Dic11C24116yes—
334C4×Dic11C2418yes—
335C4×Dic11C2418yes—
336C4×Dic11C2414yes—
337#3507—1132no—
338C2×#559—111no—
339C2×#559D1111yescharacteristic, complemented
340C2×#557—111no—
341C2×#557—111no—
342C2×#556—112no—
343C2×#556—112no—
344C2×#556—112no—
345C2×#554—112no—
346C2×#552—114no—
347C2×#539—114no—
348C2×#536—112no—
349C2×#533—111no—
350C2×#532—111no—
351C2×#529—112no—
352C2×#529—112no—
353C2×#520—112no—
354C22×C4×Q8—111no—
355C23×C11—28no—
356C23×C11—28no—
357C23×C11—28no—
358C23×C11C2518yes—
359C23×C11C2511yescharacteristic
360C22×D11—22no—
361C22×D11—22no—
362C22×D11C2×#4114yes—
363C22×D11C2512yes—
364Q8×C11—28no—
365Q8×C11—28no—
366D4×C11—216no—
367D4×C11—216no—
368D4×C11—48no—
369C2×C4×C11—24no—
370C2×C4×C11—24no—
371C2×C4×C11—24no—
372C2×C4×C11—24no—
373C2×C4×C11—22no—
374C2×C4×C11—416no—
375C2×C4×C11C2×#4114yes—
376C2×C4×C112−1+414yes—
377C2×C4×C11C2514yes—
378C2×C4×C11C2514yes—
379C2×C4×C11C2512yes—
380C2×C4×C11C2514yes—
381C2×C4×C11C2514yes—
382C2×C4×C11C2512yes—
383C2×C4×C11C2512yes—
384C22⋊D11—232no—
385C2×Dic11—24no—
386C2×Dic11—28no—
387C2×Dic11—24no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—24no—
391C2×Dic11—24no—
392C2×Dic11—232no—
393C2×Dic11—416no—
394C2×Dic11C2×#4114yes—
395C2×Dic11C2512yes—
396C2×Dic11C2514yes—
397C2×Dic11C2514yes—
398C2×Dic11C2518yes—
399C2×Dic11C2512yes—
400C2×Dic11C2514yes—
401C2×Dic11C2514yes—
402C2×Dic11C2512yes—
403C4×D11—216no—
404C4×D11—28no—
405C4×D11—44no—
406C4×D11—48no—
407C4×D11C2×#41116yes—
408Dic22—216no—
409Dic22—28no—
410Dic22—28no—
411Dic22—216no—
412Dic22—48no—
413C22×#41—112no—
414C23×Q8—111no—
415#559—1116no—
416#559C2×D11116yescomplemented
417#557—1116no—
418#557—1116no—
419#556—1132no—
420#556—1132no—
421#556—1132no—
422#554—1132no—
423#552—1164no—
424#539—1164no—
425#536—1132no—
426#533—1116no—
427#532—1116no—
428C2×C4⋊Q8—111no—
429C2×C4⋊Q8—112no—
430C2×C4⋊Q8—111no—
431C2×C4⋊Q8—111no—
432C2×C4⋊Q8—112no—
433C2×#127C2×D1111yescharacteristic
434#529—1132no—
435#529—1132no—
436C2×#126—114no—
437C2×#126—114no—
438C2×#126—114no—
439C2×#126—114no—
440C2×#125—112no—
441C2×#125—114no—
442C2×#125—112no—
443C2×#125—114no—
444C2×#125—112no—
445C2×#124—112no—
446C2×#124—112no—
447C2×#124—112no—
448C2×#124C2×D1112yes—
449C2×#124C2×D1112yes—
450C2×#123—114no—
451C2×#123—114no—
452C2×#123—114no—
453C2×#123C2×D1114yes—
454C2×C22⋊Q8—111no—
455C2×C22⋊Q8—114no—
456C2×C22⋊Q8—112no—
457C2×C22⋊Q8—111no—
458C2×C22⋊Q8—114no—
459C2×C22⋊Q8—114no—
460C2×C22⋊Q8—114no—
461C2×#121—112no—
462C2×#121—112no—
463#520—1132no—
464C2×C4×Q8—111no—
465C2×C4×Q8—112no—
466C2×C4×Q8—1116no—
467C2×C4×Q8—112no—
468C2×C4×Q8—111no—
469C2×C4×Q8—112no—
470C2×C4×Q8—112no—
471C2×C4×Q8—111no—
472C2×C4×Q8—112no—
473C2×C4×Q8—112no—
474C2×C4×Q8—112no—
475C2×C4×Q8—111no—
476C2×C4×Q8C2×D1111yescharacteristic
477C2×C4×Q8C2×D1111yescharacteristic
478C2×C4×D4—112no—
479C2×C4×D4—112no—
480C2×C4×D4—112no—
481C2×C4×D4—112no—
482C2×C4×D4—114no—
483C2×C4×D4—114no—
484C2×C4×D4C2×D1112yes—
485C2×C4×D4C2×D1112yes—
486C2×#117—114no—
487C2×#117—114no—
488C2×#117—114no—
489C2×#117—112no—
490C22×C4⋊C4—114no—
491C22×C4⋊C4—111no—
492C22×C4⋊C4—112no—
493C22×C42—112no—
494C22×C42—111no—
495C22×C11—28no—
496C22×C11—28no—
497C22×C11—28no—
498C22×C11—416no—
499C22×C11C22×#4112yes—
500C22×C11C2×2−1+412yes—
501C22×C11#58512yes—
502C22×C11C2611yescharacteristic
503C2×D11—22no—
504C2×D11—22no—
505C2×D11—28no—
506C2×D11C22×#4114yes—
507C4×C11—24no—
508C4×C11—24no—
509C4×C11—24no—
510C4×C11—24no—
511C4×C11—22no—
512C4×C11C22×#4114yes—
513C4×C11C2×2−1+414yes—
514Dic11—24no—
515Dic11—28no—
516Dic11—24no—
517Dic11—22no—
518Dic11—22no—
519Dic11—24no—
520Dic11—24no—
521Dic11C22×#4114yes—
522C2×#41—1116no—
523C2×#41—2216no—
524C22×Q8—118no—
525C22×Q8—111no—
526C22×Q8—112no—
527C22×Q8—111no—
528C22×Q8—112no—
529C22×Q8—112no—
530C22×Q8—228no—
531C22×Q8C22×D1111yescharacteristic
532C22×Q8C22×D1111yescharacteristic
533C22×D4—114no—
534C22×D4C22×D1112yes—
535C22×D4C22×D1112yes—
536C22×D4C22×D1112yes—
537C23×C4—111no—
538C23×C4—114no—
539C23×C4—114no—
540C23×C4—112no—
541C23×C4—111no—
542C23×C4—112no—
543C23×C4—111no—
544C23×C4C22×D1114yes—
545C4⋊Q8—118no—
546C4⋊Q8—1116no—
547C4⋊Q8—118no—
548C4⋊Q8—118no—
549C4⋊Q8—1116no—
550#127C22×D1118yes—
551#126—1132no—
552#126—1132no—
553#126—1132no—
554#126—1132no—
555#125—1116no—
556#125—1116no—
557#125—1132no—
558#125—1132no—
559#125—1116no—
560#124—1116no—
561#124—1116no—
562#124—1116no—
563#124C22×D11116yes—
564#124C22×D11116yes—
565#123—1132no—
566#123—1132no—
567#123—1132no—
568#123C22×D11132yes—
569C22⋊Q8—118no—
570C22⋊Q8—1132no—
571C22⋊Q8—118no—
572C22⋊Q8—1116no—
573C22⋊Q8—1132no—
574C22⋊Q8—1132no—
575C22⋊Q8—1132no—
576#121—1116no—
577#121—1116no—
578C4×Q8—118no—
579C4×Q8—1116no—
580C4×Q8—1116no—
581C4×Q8—118no—
582C4×Q8—1116no—
583C4×Q8—1116no—
584C4×Q8—118no—
585C4×Q8—1116no—
586C4×Q8—1116no—
587C4×Q8—1116no—
588C4×Q8—118no—
589C4×Q8C22×D1118yes—
590C4×Q8C22×D1118yes—
591C4×D4—1116no—
592C4×D4—1116no—
593C4×D4—1116no—
594C4×D4—1116no—
595C4×D4—1132no—
596C4×D4—1132no—
597C4×D4C22×D11116yes—
598C4×D4C22×D11116yes—
599#117—1132no—
600#117—1132no—
601#117—1132no—
602#117—1116no—
603C2×C4⋊C4—112no—
604C2×C4⋊C4—112no—
605C2×C4⋊C4—111no—
606C2×C4⋊C4—114no—
607C2×C4⋊C4—114no—
608C2×C4⋊C4—112no—
609C2×C4⋊C4—112no—
610C2×C4⋊C4—112no—
611C2×C4⋊C4—1132no—
612C2×C4⋊C4—112no—
613C2×C4⋊C4—112no—
614C2×C4⋊C4—112no—
615C2×C4⋊C4—114no—
616C2×C4⋊C4—114no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—112no—
619C2×C4⋊C4—112no—
620C2×C4⋊C4—112no—
621C2×C4⋊C4—114no—
622C2×C4⋊C4—114no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—118no—
625C2×C4⋊C4—1116no—
626C2×C4⋊C4C22×D1111yescharacteristic
627C2×C4⋊C4C22×D1112yes—
628C2×C4⋊C4C22×D1111yescharacteristic
629C2×C4⋊C4C22×D1112yes—
630C2×C22⋊C4—114no—
631C2×C22⋊C4—114no—
632C2×C22⋊C4—114no—
633C2×C22⋊C4—114no—
634C2×C22⋊C4—114no—
635C2×C22⋊C4—112no—
636C2×C22⋊C4—112no—
637C2×C22⋊C4C22×D1114yes—
638C2×C22⋊C4C22×D1114yes—
639C2×C22⋊C4C22×D1114yes—
640C2×C42—114no—
641C2×C42—114no—
642C2×C42—112no—
643C2×C42—112no—
644C2×C42—112no—
645C2×C42—111no—
646C2×C42—111no—
647C2×C42—112no—
648C2×C42—111no—
649C2×C42—1116no—
650C2×C42—118no—
651C2×C42C22×D1112yes—
652C2×C42C22×D1112yes—
653C2×C42C22×D1111yescharacteristic
654C2×C11—48no—
655C2×C11#350714yescomplemented
656C2×C11C23×#4111yescharacteristic
657C2×C11C22×2−1+411yescharacteristic
658C2×C11C2×#58511yescharacteristic
659D11—24no—
660C24—111no—
661C24C23×D1114yes—
662#41—2264no—
663C2×Q8—24no—
664C2×Q8—24no—
665C2×Q8—114no—
666C2×Q8—118no—
667C2×Q8—114no—
668C2×Q8—118no—
669C2×Q8—118no—
670C2×Q8—228no—
671C2×Q8—2232no—
672C2×Q8—224no—
673C2×Q8—228no—
674C2×Q8—224no—
675C2×Q8—444no—
676C2×Q8C23×D1114yes—
677C2×Q8C23×D1114yes—
678C2×D4—28no—
679C2×D4—28no—
680C2×D4—44no—
681C2×D4—1116no—
682C2×D4—2216no—
683C2×D4C23×D1118yes—
684C2×D4C23×D1118yes—
685C2×D4C23×D1118yes—
686C22×C4—48no—
687C22×C4—111no—
688C22×C4—118no—
689C22×C4—114no—
690C22×C4—1116no—
691C22×C4—111no—
692C22×C4—112no—
693C22×C4—112no—
694C22×C4—112no—
695C22×C4—111no—
696C22×C4—114no—
697C22×C4—112no—
698C22×C4—1116no—
699C22×C4—114no—
700C22×C4—118no—
701C22×C4—118no—
702C22×C4—114no—
703C22×C4—228no—
704C22×C4—2216no—
705C22×C4—224no—
706C22×C4—444no—
707C22×C4—442no—
708C22×C4—448no—
709C22×C4C23×D1112yes—
710C22×C4C23×D1112yes—
711C22×C4C23×D1112yes—
712C22×C4C23×D1111yescharacteristic
713C22×C4C23×D1112yes—
714C22×C4C23×D11116yes—
715C22×C4C23×D1111yescharacteristic
716C22×C4C23×D1111yescharacteristic
717C4⋊C4—118no—
718C4⋊C4—118no—
719C4⋊C4—114no—
720C4⋊C4—1116no—
721C4⋊C4—1116no—
722C4⋊C4—118no—
723C4⋊C4—118no—
724C4⋊C4—118no—
725C4⋊C4—118no—
726C4⋊C4—118no—
727C4⋊C4—118no—
728C4⋊C4—1116no—
729C4⋊C4—1116no—
730C4⋊C4—114no—
731C4⋊C4—118no—
732C4⋊C4—118no—
733C4⋊C4—118no—
734C4⋊C4—1116no—
735C4⋊C4—1116no—
736C4⋊C4—118no—
737C4⋊C4C23×D1114yes—
738C4⋊C4C23×D1118yes—
739C4⋊C4C23×D1114yes—
740C4⋊C4C23×D1118yes—
741C22⋊C4—1116no—
742C22⋊C4—1116no—
743C22⋊C4—1116no—
744C22⋊C4—1116no—
745C22⋊C4—1116no—
746C22⋊C4—118no—
747C22⋊C4—118no—
748C22⋊C4C23×D11116yes—
749C22⋊C4C23×D11116yes—
750C22⋊C4C23×D11116yes—
751C42—118no—
752C42—118no—
753C42—114no—
754C42—114no—
755C42—118no—
756C42—114no—
757C42—1116no—
758C42—1116no—
759C42—118no—
760C42C23×D1118yes—
761C42C23×D1114yes—
762C42C23×D1118yes—
763C11C2×#350711yescharacteristic, complemented, Sylow
764C23—28no—
765C23—28no—
766C23—28no—
767C23—114no—
768C23—112no—
769C23—222no—
770C23—222no—
771C23C24×D1118yes—
772C23C24×D1111yescharacteristic
773Q8—28no—
774Q8—28no—
775Q8—2216no—
776Q8—228no—
777Q8—2216no—
778Q8—228no—
779Q8—448no—
780D4—216no—
781D4—216no—
782D4—48no—
783D4—2232no—
784C2×C4—24no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—22no—
789C2×C4—416no—
790C2×C4—114no—
791C2×C4—112no—
792C2×C4—1116no—
793C2×C4—112no—
794C2×C4—114no—
795C2×C4—114no—
796C2×C4—114no—
797C2×C4—112no—
798C2×C4—118no—
799C2×C4—114no—
800C2×C4—2216no—
801C2×C4—2232no—
802C2×C4—228no—
803C2×C4—224no—
804C2×C4—222no—
805C2×C4—224no—
806C2×C4—224no—
807C2×C4—224no—
808C2×C4—222no—
809C2×C4—228no—
810C2×C4—448no—
811C2×C4—444no—
812C2×C4—4416no—
813C2×C4#41×D1114yes—
814C2×C4#6704314yes—
815C2×C4C24×D1114yes—
816C2×C4C24×D1114yes—
817C2×C4C24×D1114yes—
818C2×C4C24×D1112yes—
819C2×C4C24×D1114yes—
820C2×C4C24×D1112yes—
821C2×C4C24×D1112yes—
822C22—28no—
823C22—28no—
824C22—28no—
825C22—416no—
826C22—114no—
827C22—222no—
828C22—222no—
829C22—228no—
830C22C2×#41×D1112yes—
831C22C2×#6704312yes—
832C22#1062345512yes—
833C22C25×D1111yescharacteristic
834C4—24no—
835C4—24no—
836C4—24no—
837C4—24no—
838C4—22no—
839C4—114no—
840C4—228no—
841C4—224no—
842C4—222no—
843C4—224no—
844C4—224no—
845C4—224no—
846C4—222no—
847C4C2×#41×D1114yes—
848C4C2×#6704314yes—
849C2—48no—
850C2—224no—
851C2#1308247314yesdirect product factor
852C2C22×#41×D1111yescharacteristic
853C2C22×#6704311yescharacteristic
854C2C2×#1062345511yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#559C2
socleC23×C11C25
prime radicalC2×#10623247C2
hypercenterC2×#559D11
hypocenterC11C2×#3507
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. #13082473C2direct (N × H)
2. C2×#10623244C2semidirect
3. C2×#10623101C2semidirect
4. C2×#10623098C2semidirect
5. C2×#10623073C2semidirect
6. C2×#10623202C2semidirect
7. C2×#10623202C2semidirect
8. C2×#10623070C2semidirect
9. C2×#10623181C2semidirect
10. C2×#10623191C2semidirect
11. C2×#10623206C2semidirect
12. C2×#10623109C2semidirect
14. C2×#10623088C2semidirect
15. C2×#10623211C2semidirect
16. C2×#10623077C2semidirect
17. C2×C4×Q8×D11C2semidirect
18. C2×C11×#559C2semidirect
21. C11×#559C22semidirect
50. #10623244C22semidirect
51. #10623211C22semidirect
52. #10623206C22semidirect
53. #10623202C22semidirect
54. #10623202C22semidirect
55. #10623191C22semidirect
56. #10623181C22semidirect
57. #10623109C22semidirect
58. C4×Q8×D11C22semidirect
59. #10623101C22semidirect
60. #10623098C22semidirect
61. #10623088C22semidirect
62. #10623077C22semidirect
63. #10623073C22semidirect
64. #10623070C22semidirect
339. C2×#559D11semidirect
416. #559C2×D11semidirect
655. C2×C11#3507semidirect
763. C11C2×#3507semidirect
851. C2#13082473direct (N × H)

Maximal subgroups

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

subgroupindex
#130824732
C2×#106232442
C2×#106231012
C2×#106230982
C2×#106230732
C2×#106232022
C2×#106230702
C2×#106231812
C2×#106231912
C2×#106232062
C2×#106231092
C2×#106232472
C2×#106230882
C2×#106232112
C2×#106230772
C2×C4×Q8×D112
C2×C11×#5592
C2×#350711