Finite Group Databasebeta

← #15624546

Subgroups — #15624546

Order 2816.

2362 conjugacy classes of subgroups.

The subgroup lattice has 1182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic, complemented
2#13079453C214yesmaximal, complemented
3#13079442C212yesmaximal, complemented
4#13079426C212yesmaximal, complemented
5#13079404C214yesmaximal, complemented
6#13079393C212yesmaximal, complemented
7#13079377C212yesmaximal, complemented
8#13078560C211yesmaximal, characteristic, complemented
9#13078552C211yesmaximal, characteristic, complemented
10#13078547C212yesmaximal, complemented
11#13078242C212yesmaximal, complemented
12#13078231C212yesmaximal, complemented
13#13077874C211yesmaximal, characteristic, complemented
14#13077866C211yesmaximal, characteristic, complemented
15#13077858C212yesmaximal, complemented
16C2×#10622820C211yesmaximal, characteristic, complemented
17C2×C11×#525C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic, complemented
19C24×C4×C11C2211yescharacteristic
20C22×#4339C2211yescharacteristic
21C11×#525—21no—
22C11×#525—21no—
23C11×#525—21no—
24C11×#525—21no—
25C11×#525C2212yes—
26C11×#525C2212yes—
27C11×#525C2212yescomplemented
28C11×#525C2212yescomplemented
29C2×C11×#123—21no—
30C2×C11×C22⋊Q8C2211yescharacteristic
31C2×C11×C22⋊Q8C2211yescharacteristic, complemented
32C2×C11×#121C2211yescharacteristic
33C2×C11×#121C2211yescharacteristic, complemented
34C2×C11×#120—21no—
35C2×C4×D4×C11—21no—
36C2×C4×D4×C11—21no—
37C2×C11×#117C2211yescharacteristic, complemented
38C2×#67006—21no—
39C2×#66995C2212yescomplemented
40C2×#66985C2212yescomplemented
41#10623322—21no—
42#10623322—21no—
43#10623322—21no—
44#10623322—21no—
45#10623322C2212yes—
46#10623322C2212yes—
47#10623322C2212yescomplemented
48#10623322C2212yescomplemented
49C2×#66983C2211yescharacteristic, complemented
50C2×#66983C2211yescharacteristic, complemented
51C2×#66982—21no—
52C2×C4×C22⋊D11—21no—
53C2×C4×C22⋊D11—21no—
54C2×#66979C2211yescharacteristic
55C2×#66977C2211yescharacteristic, complemented
56C2×#66977C2211yescharacteristic, complemented
57C22×#4318C2212yescomplemented
58#10622852C2214yescomplemented
59#10622852C2214yescomplemented
60#10622851C2214yescomplemented
61#10622851C2214yescomplemented
62#10622838C2212yescomplemented
63#10622828C2212yescomplemented
64#10622820C2211yescharacteristic
65#10622820C2211yescharacteristic
66#10622820C2212yescomplemented
67#10622820C2212yescomplemented
68#10622820C2212yescomplemented
69C2×C22⋊(C11⋊C8)C2212yescomplemented
70C2×C22⋊(C11⋊C8)C2212yescomplemented
71#10622665C2214yescomplemented
72#10622664C2214yescomplemented
73#10622663C2212yescomplemented
74#10622662C2214yescomplemented
75#10622661C2214yescomplemented
76#10622660C2214yescomplemented
77#10622659C2212yescomplemented
78#10622658C2214yescomplemented
79#10622657C2212yescomplemented
80#10622656C2212yescomplemented
81#10622655C2214yescomplemented
82#10622654C2214yescomplemented
83#10622653C2212yescomplemented
84#10622652C2214yescomplemented
85#10622651C2214yescomplemented
86#10622650C2214yescomplemented
87#10622649C2212yescomplemented
88#10622648C2214yescomplemented
89#10622647C2212yescomplemented
90#10622646C2212yescomplemented
91#10622616C2214yescomplemented
92#10622616C2214yescomplemented
93#10622609C2214yescomplemented
94#10622609C2214yescomplemented
95#10622579C2212yescomplemented
96#10622579C2212yescomplemented
97#10622577C2212yescomplemented
98#10622577C2212yescomplemented
99C25×C11D411yescharacteristic
100C2×C11×#41—21no—
101C2×C11×#41—21no—
102C2×C11×#41—44no—
103C2×C11×#41C2312yes—
104C2×C11×#41C2312yes—
105C22×Q8×C11C2311yescharacteristic
106C22×D4×C11—21no—
107C22×D4×C11—21no—
108C22×D4×C11—21no—
109C22×D4×C11C2311yescharacteristic
110C23×C4×C11—21no—
111C23×C4×C11—44no—
112C23×C4×C11D411yescharacteristic
113C23×C4×C11D411yescharacteristic
114C23×C4×C11D411yescharacteristic
115C23×C4×C11D411yescharacteristic
116C23×C4×C11D411yescharacteristic
117C23×C4×C11D411yescharacteristic
118C23×C4×C11D411yescharacteristic
119C23×C4×C11C2311yescharacteristic
120C23×C4×C11C2311yescharacteristic
121C23×C4×C11C2311yescharacteristic
122C23×C4×C11C2311yescharacteristic
123C23×C4×C11C2311yescharacteristic
124C23×C4×C11C2311yescharacteristic
125C23×C4×C11C2311yescharacteristic
126C22×C22⋊D11—21no—
127C22×C22⋊D11—21no—
128C22×C22⋊D11—21no—
129C2×#4339—21no—
130C2×#4339—21no—
131C2×#4339—44no—
132C2×#4339C2312yes—
133C2×#4339C2312yes—
134C22×D44C2311yescharacteristic
135C22×C4×D11—21no—
136C22×Dic22C2311yescharacteristic
137C11×#123—22no—
138C11×#123—22no—
139C11×#123—22no—
140C11×#123—22no—
141C11×C22⋊Q8—21no—
142C11×C22⋊Q8—21no—
143C11×C22⋊Q8—21no—
144C11×C22⋊Q8—21no—
145C11×C22⋊Q8C2312yes—
146C11×C22⋊Q8C2312yes—
147C11×C22⋊Q8C2312yes—
148C11×C22⋊Q8C2312yes—
149C11×#121—21no—
150C11×#121—21no—
151C11×#121—21no—
152C11×#121—21no—
153C11×#121C2312yes—
154C11×#121C2312yes—
155C11×#121C2312yes—
156C11×#121C2312yes—
157C11×#120—22no—
158C11×#120—22no—
159C11×#120—22no—
160C11×#120—22no—
161C4×D4×C11—22no—
162C4×D4×C11—22no—
163C4×D4×C11—22no—
164C4×D4×C11—22no—
165C4×D4×C11—22no—
166C4×D4×C11—22no—
167C4×D4×C11—22no—
168C4×D4×C11—22no—
169C11×#117—21no—
170C11×#117—21no—
171C11×#117C2312yes—
172C11×#117C2312yes—
173C2×C11×C4⋊C4—21no—
174C2×C11×C4⋊C4—21no—
175C2×C11×C4⋊C4C2311yescharacteristic
176C2×C11×C4⋊C4C2311yescharacteristic
177C2×C11×C22⋊C4—21no—
178C2×C11×C22⋊C4—21no—
179C2×C11×C22⋊C4—21no—
180C2×C11×C22⋊C4—21no—
181C2×C11×C22⋊C4—21no—
182C2×C42×C11—21no—
183#67006—22no—
184#67006—22no—
185#67006—22no—
186#67006—22no—
187C2×C22⋊Dic11—21no—
188C2×C22⋊Dic11—21no—
189C2×C22⋊Dic11—21no—
190C2×#4326C2314yescomplemented
191#66995—44no—
192C2×#4325C2314yescomplemented
193C2×#4324C2314yescomplemented
194#66985—44no—
195C2×#4323C2314yescomplemented
196#66983—21no—
197#66983—21no—
198#66983—21no—
199#66983—21no—
200#66983C2312yes—
201#66983C2312yes—
202#66983C2312yes—
203#66983C2312yes—
204#66982—22no—
205#66982—22no—
206#66982—22no—
207#66982—22no—
208C4×C22⋊D11—22no—
209C4×C22⋊D11—22no—
210C4×C22⋊D11—22no—
211C4×C22⋊D11—22no—
212C4×C22⋊D11—22no—
213C4×C22⋊D11—22no—
214C4×C22⋊D11—22no—
215C4×C22⋊D11—22no—
216C2×(C2×D11)⋊C4—21no—
217C2×(C2×D11)⋊C4—21no—
218#66979—21no—
219#66979—21no—
220#66979C2312yes—
221#66979C2312yes—
222C2×C4⋊Dic11C2311yescharacteristic
223C2×C4⋊Dic11C2311yescharacteristic
224#66977—21no—
225#66977—21no—
226#66977—21no—
227#66977—21no—
228#66977C2312yes—
229#66977C2312yes—
230#66977C2312yes—
231#66977C2312yes—
232C2×Dic11⋊C4—21no—
233C2×Dic11⋊C4—21no—
234C2×C4×Dic11—21no—
235C2×#4318—44no—
236C2×#4318C2312yes—
237C2×#4318C2312yes—
238C2×#4318C2314yes—
239C22×C11⋊C8C2314yes—
240#66899C2314yescomplemented
241#66899C2314yescomplemented
242#66896C2314yescomplemented
243#66896C2314yescomplemented
244C22⋊(C11⋊C8)C2312yes—
245C22⋊(C11⋊C8)C2312yes—
246C22⋊(C11⋊C8)C2312yes—
247C22⋊(C11⋊C8)C2312yes—
248C22⋊(C11⋊C8)C2314yes—
249C22⋊(C11⋊C8)C2314yes—
250#66874C2314yescomplemented
251#66874C2314yescomplemented
252#66873C2314yescomplemented
253#66873C2314yescomplemented
254#66872C2314yescomplemented
255#66872C2314yescomplemented
256#66871C2314yescomplemented
257#66871C2314yescomplemented
258#60752—111nomaximal, Sylow
259C24×C11—21no—
260C24×C11—42no—
261C24×C11—42no—
262C24×C11—42no—
263C24×C11C2×D411yescharacteristic
264C24×C11C2×D411yescharacteristic
265C24×C11C2×D411yescharacteristic
266C24×C11C2×D411yescharacteristic
267C24×C11C2×D411yescharacteristic
268C24×C11C2×D411yescharacteristic
269C24×C11C2×D411yescharacteristic
270C23×D11—21no—
271C11×#41—44no—
272C11×#41—44no—
273C11×#41—44no—
274C11×#41—44no—
275C2×Q8×C11—21no—
276C2×Q8×C11—24no—
277C2×Q8×C11C2412yes—
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C2×D4×C11—22no—
283C2×D4×C11—22no—
284C2×D4×C11—21no—
285C2×D4×C11—24no—
286C2×D4×C11—44no—
287C2×D4×C11—44no—
288C2×D4×C11—44no—
289C2×D4×C11C2412yes—
290C22×C4×C11—24no—
291C22×C4×C11—24no—
292C22×C4×C11—24no—
293C22×C4×C11—21no—
294C22×C4×C11—21no—
295C22×C4×C11—21no—
296C22×C4×C11—22no—
297C22×C4×C11—22no—
298C22×C4×C11—42no—
299C22×C4×C11—42no—
300C22×C4×C11—42no—
301C22×C4×C11—42no—
302C22×C4×C11—42no—
303C22×C4×C11—42no—
304C22×C4×C11—42no—
305C22×C4×C11—42no—
306C22×C4×C11—42no—
307C22×C4×C11—42no—
308C22×C4×C11—42no—
309C22×C4×C11—44no—
310C22×C4×C11C2×D411yescharacteristic
311C22×C4×C11C2×D411yescharacteristic
312C22×C4×C11C2×D411yescharacteristic
313C22×C4×C11C2×D411yescharacteristic
314C22×C4×C11C2×D411yescharacteristic
315C22×C4×C11C2×D411yescharacteristic
316C22×C4×C11C2×D411yescharacteristic
317C22×C4×C11C2×D411yescharacteristic
318C22×C4×C11C2×D411yescharacteristic
319C22×C4×C11C2×D411yescharacteristic
320C22×C4×C11C2×D411yescharacteristic
321C22×C4×C11C2×D411yescharacteristic
322C22×C4×C11C2×D411yescharacteristic
323C22×C4×C11C2×D411yescharacteristic
324C22×C4×C11C2×D411yescharacteristic
325C22×C4×C11C2×D411yescharacteristic
326C22×C4×C11C2×D411yescharacteristic
327C22×C4×C11C2×D411yescharacteristic
328C22×C4×C11C2×D411yescharacteristic
329C22×C4×C11C2×D411yescharacteristic
330C22×C4×C11C2×D411yescharacteristic
331C22×C4×C11C2411yescharacteristic
332C22×C4×C11C2411yescharacteristic
333C22×C4×C11C2411yescharacteristic
334C22×C4×C11C2411yescharacteristic
335C22×C4×C11C2411yescharacteristic
336C22×C4×C11C2411yescharacteristic
337C22×C4×C11C2411yescharacteristic
338C2×C22⋊D11—22no—
339C2×C22⋊D11—22no—
340C2×C22⋊D11—22no—
341C2×C22⋊D11—22no—
342C2×C22⋊D11—22no—
343C2×C22⋊D11—22no—
344C2×C22⋊D11—44no—
345C2×C22⋊D11—44no—
346C2×C22⋊D11—44no—
347C22×Dic11—21no—
348C22×Dic11—21no—
349C22×Dic11—21no—
350#4339—24no—
351#4339—24no—
352#4339—42no—
353#4339—42no—
354#4339—44no—
355#4339—44no—
356C2×D44—21no—
357C2×D44—42no—
358C2×D44C2412yes—
359C2×C4×D11—22no—
360C2×C4×D11—22no—
361C2×C4×D11—44no—
362C2×Dic22—21no—
363C2×Dic22—42no—
364C2×Dic22C2412yes—
365C11×C4⋊C4—22no—
366C11×C4⋊C4—22no—
367C11×C4⋊C4—22no—
368C11×C4⋊C4—22no—
369C11×C4⋊C4—21no—
370C11×C4⋊C4—21no—
371C11×C4⋊C4C2412yes—
372C11×C4⋊C4C2412yes—
373C11×C22⋊C4—22no—
374C11×C22⋊C4—22no—
375C11×C22⋊C4—22no—
376C11×C22⋊C4—22no—
377C11×C22⋊C4—22no—
378C11×C22⋊C4—22no—
379C11×C22⋊C4—22no—
380C11×C22⋊C4—22no—
381C11×C22⋊C4—22no—
382C11×C22⋊C4—22no—
383C42×C11—22no—
384C42×C11—22no—
385C22⋊Dic11—22no—
386C22⋊Dic11—22no—
387C22⋊Dic11—22no—
388C22⋊Dic11—22no—
389C22⋊Dic11—22no—
390C22⋊Dic11—22no—
391#4326—44no—
392#4325—44no—
393#4324—44no—
394#4323—44no—
395(C2×D11)⋊C4—22no—
396(C2×D11)⋊C4—22no—
397(C2×D11)⋊C4—22no—
398(C2×D11)⋊C4—22no—
399C4⋊Dic11—21no—
400C4⋊Dic11—21no—
401C4⋊Dic11C2412yes—
402C4⋊Dic11C2412yes—
403Dic11⋊C4—22no—
404Dic11⋊C4—22no—
405Dic11⋊C4—22no—
406Dic11⋊C4—22no—
407C4×Dic11—22no—
408C4×Dic11—22no—
409#4318—24no—
410#4318—24no—
411#4318—44no—
412C2×C11⋊C8—44no—
413C2×C11⋊C8C2414yes—
414C2×C11⋊C8C2414yes—
415C2×#525—111no—
416C2×#525D1111yescharacteristic, complemented
417#3197—114no—
418#3196—112no—
419#3194—112no—
420#3191—114no—
421#3190—112no—
422#3188—112no—
423#3095—111no—
424#3094—111no—
425#3093—112no—
426#3056—112no—
427#3055—112no—
428#3007—111no—
429#3006—111no—
430#3005—112no—
431C2×#407—111no—
432C23×C11—22no—
433C23×C11—22no—
434C23×C11—22no—
435C23×C11—22no—
436C23×C11—22no—
437C23×C11—22no—
438C23×C11—22no—
439C23×C11—22no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—41no—
443C23×C11—41no—
444C23×C11—41no—
445C23×C11—41no—
446C23×C11—41no—
447C23×C11—41no—
448C23×C11—41no—
449C23×C11—41no—
450C23×C11—41no—
451C23×C11—41no—
452C23×C11—41no—
453C23×C11—41no—
454C23×C11—42no—
455C23×C11—42no—
456C23×C11—416no—
457C23×C11—42no—
458C23×C11C22×D411yescharacteristic
459C23×C11C22×D411yescharacteristic
460C23×C11C22×D411yescharacteristic
461C23×C11C22×D411yescharacteristic
462C23×C11C22×D411yescharacteristic
463C23×C11C22×D411yescharacteristic
464C23×C11C22×D411yescharacteristic
465C22×D11—22no—
466C22×D11—42no—
467C22×D11—42no—
468C22×D11—42no—
469Q8×C11—24no—
470Q8×C11—42no—
471D4×C11—24no—
472D4×C11—44no—
473D4×C11—44no—
474D4×C11—44no—
475D4×C11—44no—
476D4×C11—44no—
477D4×C11—44no—
478D4×C11—42no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—41no—
498C2×C4×C11—41no—
499C2×C4×C11—41no—
500C2×C4×C11—41no—
501C2×C4×C11—41no—
502C2×C4×C11—41no—
503C2×C4×C11—41no—
504C2×C4×C11—41no—
505C2×C4×C11—41no—
506C2×C4×C11—41no—
507C2×C4×C11—41no—
508C2×C4×C11—41no—
509C2×C4×C11—44no—
510C2×C4×C11—44no—
511C2×C4×C11—42no—
512C2×C4×C11—42no—
513C2×C4×C11—42no—
514C2×C4×C11C22×D411yescharacteristic
515C2×C4×C11C22×D411yescharacteristic
516C2×C4×C11C22×D411yescharacteristic
517C2×C4×C11C22×D411yescharacteristic
518C2×C4×C11C22×D411yescharacteristic
519C2×C4×C11C22×D411yescharacteristic
520C2×C4×C11C22×D411yescharacteristic
521C2×C4×C11H(5,𝔽2)14yes—
522C2×C4×C11C2511yescharacteristic
523C22⋊D11—44no—
524C22⋊D11—44no—
525C22⋊D11—44no—
526C22⋊D11—44no—
527C22⋊D11—44no—
528C22⋊D11—44no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—42no—
533C2×Dic11—42no—
534C2×Dic11—42no—
535D44—22no—
536D44—22no—
537D44—42no—
538C4×D11—44no—
539C4×D11—44no—
540Dic22—22no—
541Dic22—22no—
542Dic22—42no—
543C11⋊C8—24no—
544C11⋊C8—24no—
545C22×#41—111no—
546C22×#41C2×D1111yescharacteristic, complemented
547C24×C4C2×D1111yescharacteristic
548C2×#137—112no—
549C2×AGL(1,ℤ/8)—112no—
550C22×M16—112no—
551#525—21no—
552#525—21no—
553#525—21no—
554#525—21no—
555#525—112no—
556#525—112no—
557#525—112no—
558#525—112no—
559#525—221no—
560#525—221no—
561#525—221no—
562#525—221no—
563#525C2×D1112yes—
564#525C2×D1112yes—
565#525C2×D1112yescomplemented
566#525C2×D1112yescomplemented
567C2×#123—21no—
568C2×#123—221no—
569C2×C22⋊Q8—111no—
570C2×C22⋊Q8—111no—
571C2×C22⋊Q8C2×D1111yescharacteristic
572C2×C22⋊Q8C2×D1111yescharacteristic, complemented
573C2×#121—111no—
574C2×#121—111no—
575C2×#121C2×D1111yescharacteristic
576C2×#121C2×D1111yescharacteristic, complemented
577C2×#120—21no—
578C2×#120—221no—
579C2×C4×D4—21no—
580C2×C4×D4—21no—
581C2×C4×D4—221no—
582C2×C4×D4—221no—
583C2×#117—111no—
584C2×#117C2×D1111yescharacteristic, complemented
585#485—114no—
586#485—114no—
587#485—114no—
588#484—112no—
589#483—112no—
590#482—114no—
591#482—114no—
592#482—114no—
593#481—112no—
594#480—112no—
595#470—114no—
596#469—114no—
597#468—114no—
598#468—114no—
599#467—114no—
600#466—114no—
601#465—114no—
602#465—114no—
603#452—114no—
604#452—114no—
605#452—114no—
606#451—112no—
607#450—112no—
608#449—114no—
609#449—114no—
610#449—114no—
611#448—112no—
612#447—112no—
613#428—112no—
614#428—112no—
615#419—112no—
616#418—112no—
617#417—112no—
618#417—112no—
619#407—112no—
620#407—111no—
621#407—111no—
622#407—112no—
623#407—112no—
624C2×C22⋊C8—112no—
625C2×C22⋊C8—112no—
626C22×C11—21no—
627C22×C11—21no—
628C22×C11—21no—
629C22×C11—21no—
630C22×C11—21no—
631C22×C11—21no—
632C22×C11—21no—
633C22×C11—21no—
634C22×C11—21no—
635C22×C11—21no—
636C22×C11—21no—
637C22×C11—21no—
638C22×C11—21no—
639C22×C11—21no—
640C22×C11—21no—
641C22×C11—21no—
642C22×C11—21no—
643C22×C11—21no—
644C22×C11—44no—
645C22×C11—44no—
646C22×C11—44no—
647C22×C11—44no—
648C22×C11—44no—
649C22×C11—44no—
650C22×C11—44no—
651C22×C11—42no—
652C22×C11—42no—
653C22×C11—42no—
654C22×C11—84no—
655C22×C11#53412yes—
656C22×C11#57512yes—
657C22×C11#57512yes—
658C22×C11C23×D411yescharacteristic
659C2×D11—42no—
660C2×D11—42no—
661C2×D11—42no—
662C2×D11—84no—
663C4×C11—21no—
664C4×C11—21no—
665C4×C11—21no—
666C4×C11—21no—
667C4×C11—21no—
668C4×C11—21no—
669C4×C11—42no—
670C4×C11—42no—
671C4×C11—42no—
672C4×C11#53412yes—
673C4×C11C2×H(5,𝔽2)12yes—
674Dic11—42no—
675Dic11—42no—
676Dic11—42no—
677C25C22⋊D1111yescharacteristic
678C2×#41—21no—
679C2×#41—21no—
680C2×#41—44no—
681C2×#41—112no—
682C2×#41—112no—
683C2×#41—221no—
684C2×#41—221no—
685C2×#41—444no—
686C2×#41C22×D1112yes—
687C2×#41C22×D1112yes—
688C22×Q8—111no—
689C22×Q8C22×D1111yescharacteristic
690C22×D4—21no—
691C22×D4—21no—
692C22×D4—21no—
693C22×D4—111no—
694C22×D4—221no—
695C22×D4—221no—
696C22×D4—221no—
697C22×D4C22×D1111yescharacteristic
698C23×C4—21no—
699C23×C4—44no—
700C23×C4—221no—
701C23×C4C22⋊D1111yescharacteristic
702C23×C4C22⋊D1111yescharacteristic
703C23×C4C22⋊D1111yescharacteristic
704C23×C4C22⋊D1111yescharacteristic
705C23×C4C22⋊D1111yescharacteristic
706C23×C4C22⋊D1111yescharacteristic
707C23×C4C22⋊D1111yescharacteristic
708C23×C4C22×D1111yescharacteristic
709C23×C4C22×D1111yescharacteristic
710C23×C4C22×D1111yescharacteristic
711C23×C4C22×D1111yescharacteristic
712C23×C4C22×D1111yescharacteristic
713C23×C4C22×D1111yescharacteristic
714C23×C4C22×D1111yescharacteristic
715#137—444no—
716AGL(1,ℤ/8)—444no—
717C2×Q16—114no—
718C2×SD16—114no—
719C2×SD16—114no—
720C2×D8—114no—
721C2×M16—112no—
722C2×M16—112no—
723C2×M16—114no—
724C2×M16—444no—
725C22×C8—114no—
726#123—22no—
727#123—22no—
728#123—22no—
729#123—22no—
730#123—222no—
731#123—222no—
732#123—222no—
733#123—222no—
734C22⋊Q8—21no—
735C22⋊Q8—21no—
736C22⋊Q8—21no—
737C22⋊Q8—21no—
738C22⋊Q8—112no—
739C22⋊Q8—112no—
740C22⋊Q8—112no—
741C22⋊Q8—112no—
742C22⋊Q8—221no—
743C22⋊Q8—221no—
744C22⋊Q8—221no—
745C22⋊Q8—221no—
746C22⋊Q8C22×D1112yes—
747C22⋊Q8C22×D1112yes—
748C22⋊Q8C22×D1112yes—
749C22⋊Q8C22×D1112yes—
750#121—21no—
751#121—21no—
752#121—21no—
753#121—21no—
754#121—112no—
755#121—112no—
756#121—112no—
757#121—112no—
758#121—221no—
759#121—221no—
760#121—221no—
761#121—221no—
762#121C22×D1112yes—
763#121C22×D1112yes—
764#121C22×D1112yes—
765#121C22×D1112yes—
766#120—22no—
767#120—22no—
768#120—22no—
769#120—22no—
770#120—222no—
771#120—222no—
772#120—222no—
773#120—222no—
774C4×D4—22no—
775C4×D4—22no—
776C4×D4—22no—
777C4×D4—22no—
778C4×D4—22no—
779C4×D4—22no—
780C4×D4—22no—
781C4×D4—22no—
782C4×D4—222no—
783C4×D4—222no—
784C4×D4—222no—
785C4×D4—222no—
786C4×D4—222no—
787C4×D4—222no—
788C4×D4—222no—
789C4×D4—222no—
790#117—21no—
791#117—21no—
792#117—112no—
793#117—112no—
794#117—221no—
795#117—221no—
796#117C22×D1112yes—
797#117C22×D1112yes—
798C2×C4⋊C4—21no—
799C2×C4⋊C4—21no—
800C2×C4⋊C4—111no—
801C2×C4⋊C4—111no—
802C2×C4⋊C4—221no—
803C2×C4⋊C4—221no—
804C2×C4⋊C4C22×D1111yescharacteristic
805C2×C4⋊C4C22×D1111yescharacteristic
806C2×C22⋊C4—21no—
807C2×C22⋊C4—21no—
808C2×C22⋊C4—21no—
809C2×C22⋊C4—21no—
810C2×C22⋊C4—21no—
811C2×C22⋊C4—221no—
812C2×C22⋊C4—221no—
813C2×C22⋊C4—221no—
814C2×C22⋊C4—221no—
815C2×C22⋊C4—221no—
816C2×C42—21no—
817C2×C42—221no—
818#107—114no—
819#107—114no—
820#106—114no—
821#106—114no—
822#103—114no—
823#103—114no—
824#103—114no—
825#103—114no—
826#102—114no—
827#102—114no—
828#102—114no—
829#102—114no—
830C22⋊C8—112no—
831C22⋊C8—112no—
832C22⋊C8—114no—
833C22⋊C8—114no—
834C22⋊C8—112no—
835C22⋊C8—112no—
836C2×C11—22no—
837C2×C11—22no—
838C2×C11—22no—
839C2×C11—41no—
840C2×C11—41no—
841C2×C11—41no—
842C2×C11—41no—
843C2×C11—82no—
844C2×C11C2×#53411yescharacteristic
845C2×C11C2×#57511yescharacteristic
846C2×C11C2×#57511yescharacteristic
847D11—82no—
848C24—21no—
849C24—42no—
850C24—42no—
851C24—42no—
852C24—221no—
853C24C2×C22⋊D1111yescharacteristic
854C24C2×C22⋊D1111yescharacteristic
855C24C2×C22⋊D1111yescharacteristic
856C24C2×C22⋊D1111yescharacteristic
857C24C2×C22⋊D1111yescharacteristic
858C24C2×C22⋊D1111yescharacteristic
859C24C2×C22⋊D1111yescharacteristic
860#41—44no—
861#41—44no—
862#41—44no—
863#41—44no—
864#41—224no—
865#41—224no—
866#41—442no—
867#41—442no—
868#41—444no—
869#41—444no—
870C2×Q8—21no—
871C2×Q8—24no—
872C2×Q8—112no—
873C2×Q8—221no—
874C2×Q8—442no—
875C2×Q8C23×D1112yes—
876C2×D4—22no—
877C2×D4—22no—
878C2×D4—22no—
879C2×D4—22no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—24no—
883C2×D4—21no—
884C2×D4—44no—
885C2×D4—44no—
886C2×D4—44no—
887C2×D4—112no—
888C2×D4—222no—
889C2×D4—222no—
890C2×D4—222no—
891C2×D4—222no—
892C2×D4—222no—
893C2×D4—222no—
894C2×D4—221no—
895C2×D4—442no—
896C2×D4—444no—
897C2×D4—444no—
898C2×D4—444no—
899C2×D4C23×D1112yes—
900C22×C4—24no—
901C22×C4—24no—
902C22×C4—24no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—22no—
907C22×C4—22no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—42no—
912C22×C4—42no—
913C22×C4—42no—
914C22×C4—42no—
915C22×C4—42no—
916C22×C4—42no—
917C22×C4—42no—
918C22×C4—42no—
919C22×C4—44no—
920C22×C4—221no—
921C22×C4—221no—
922C22×C4—221no—
923C22×C4—222no—
924C22×C4—222no—
925C22×C4—444no—
926C22×C4C2×C22⋊D1111yescharacteristic
927C22×C4C2×C22⋊D1111yescharacteristic
928C22×C4C2×C22⋊D1111yescharacteristic
929C22×C4C2×C22⋊D1111yescharacteristic
930C22×C4C2×C22⋊D1111yescharacteristic
931C22×C4C2×C22⋊D1111yescharacteristic
932C22×C4C2×C22⋊D1111yescharacteristic
933C22×C4C2×C22⋊D1111yescharacteristic
934C22×C4C2×C22⋊D1111yescharacteristic
935C22×C4C2×C22⋊D1111yescharacteristic
936C22×C4C2×C22⋊D1111yescharacteristic
937C22×C4C2×C22⋊D1111yescharacteristic
938C22×C4C2×C22⋊D1111yescharacteristic
939C22×C4C2×C22⋊D1111yescharacteristic
940C22×C4C2×C22⋊D1111yescharacteristic
941C22×C4C2×C22⋊D1111yescharacteristic
942C22×C4C2×C22⋊D1111yescharacteristic
943C22×C4C2×C22⋊D1111yescharacteristic
944C22×C4C2×C22⋊D1111yescharacteristic
945C22×C4C2×C22⋊D1111yescharacteristic
946C22×C4C2×C22⋊D1111yescharacteristic
947C22×C4C23×D1111yescharacteristic
948C22×C4C23×D1111yescharacteristic
949C22×C4C23×D1111yescharacteristic
950C22×C4C23×D1111yescharacteristic
951C22×C4C23×D1111yescharacteristic
952C22×C4C23×D1111yescharacteristic
953C22×C4C23×D1111yescharacteristic
954Q16—444no—
955SD16—444no—
956SD16—444no—
957D8—444no—
958M16—224no—
959M16—224no—
960M16—444no—
961C2×C8—114no—
962C2×C8—114no—
963C2×C8—444no—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—112no—
971C4⋊C4—112no—
972C4⋊C4—221no—
973C4⋊C4—221no—
974C4⋊C4—222no—
975C4⋊C4—222no—
976C4⋊C4—222no—
977C4⋊C4—222no—
978C4⋊C4C23×D1112yes—
979C4⋊C4C23×D1112yes—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—222no—
991C22⋊C4—222no—
992C22⋊C4—222no—
993C22⋊C4—222no—
994C22⋊C4—222no—
995C22⋊C4—222no—
996C22⋊C4—222no—
997C22⋊C4—222no—
998C22⋊C4—222no—
999C22⋊C4—222no—
1000C42—22no—
1001C42—22no—
1002C42—222no—
1003C42—222no—
1004C11#6075211yescharacteristic, complemented, Sylow
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—22no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—42no—
1028C23—42no—
1029C23—416no—
1030C23—42no—
1031C23—222no—
1032C23—442no—
1033C23—442no—
1034C23—442no—
1035C23C22×C22⋊D1111yescharacteristic
1036C23C22×C22⋊D1111yescharacteristic
1037C23C22×C22⋊D1111yescharacteristic
1038C23C22×C22⋊D1111yescharacteristic
1039C23C22×C22⋊D1111yescharacteristic
1040C23C22×C22⋊D1111yescharacteristic
1041C23C22×C22⋊D1111yescharacteristic
1042Q8—24no—
1043Q8—42no—
1044Q8—222no—
1045Q8—222no—
1046Q8—442no—
1047D4—24no—
1048D4—44no—
1049D4—44no—
1050D4—44no—
1051D4—44no—
1052D4—44no—
1053D4—44no—
1054D4—42no—
1055D4—222no—
1056D4—222no—
1057D4—442no—
1058D4—444no—
1059D4—444no—
1060D4—444no—
1061D4—444no—
1062D4—444no—
1063D4—444no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—44no—
1095C2×C4—44no—
1096C2×C4—42no—
1097C2×C4—42no—
1098C2×C4—42no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—444no—
1103C2×C4—442no—
1104C2×C4—442no—
1105C2×C4—442no—
1106C2×C4—444no—
1107C2×C4#6703714yes—
1108C2×C4C22×C22⋊D1111yescharacteristic
1109C2×C4C22×C22⋊D1111yescharacteristic
1110C2×C4C22×C22⋊D1111yescharacteristic
1111C2×C4C22×C22⋊D1111yescharacteristic
1112C2×C4C22×C22⋊D1111yescharacteristic
1113C2×C4C22×C22⋊D1111yescharacteristic
1114C2×C4C22×C22⋊D1111yescharacteristic
1115C2×C4C24×D1111yescharacteristic
1116C8—224no—
1117C8—224no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—21no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—44no—
1137C22—44no—
1138C22—44no—
1139C22—44no—
1140C22—44no—
1141C22—44no—
1142C22—44no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—84no—
1147C22—442no—
1148C22—442no—
1149C22—442no—
1150C22—884no—
1151C22#1062333512yes—
1152C22#1062335312yes—
1153C22#1062335312yes—
1154C22C23×C22⋊D1111yescharacteristic
1155C4—21no—
1156C4—21no—
1157C4—21no—
1158C4—21no—
1159C4—21no—
1160C4—21no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—442no—
1165C4—442no—
1166C4—442no—
1167C4#1062333512yes—
1168C4C2×#6703712yes—
1169C2—22no—
1170C2—22no—
1171C2—22no—
1172C2—41no—
1173C2—41no—
1174C2—41no—
1175C2—41no—
1176C2—82no—
1177C2—882no—
1178C2C2×#1062333511yescharacteristic
1179C2C2×#1062335311yescharacteristic
1180C2C2×#1062335311yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#525C2
socleC22×C11C23×D4
hypercenterC2×#525D11
hypocenterC11#60752
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#10623322C2semidirect
2. #13079453C2semidirect
3. #13079442C2semidirect
4. #13079426C2semidirect
5. #13079404C2semidirect
6. #13079393C2semidirect
7. #13079377C2semidirect
8. #13078560C2semidirect
9. #13078552C2semidirect
10. #13078547C2semidirect
11. #13078242C2semidirect
12. #13078231C2semidirect
13. #13077874C2semidirect
14. #13077866C2semidirect
15. #13077858C2semidirect
16. C2×#10622820C2semidirect
17. C2×C11×#525C2semidirect
18. C22×C11×#41C22semidirect
27. C11×#525C22semidirect
28. C11×#525C22semidirect
31. C2×C11×C22⋊Q8C22semidirect
33. C2×C11×#121C22semidirect
37. C2×C11×#117C22semidirect
39. C2×#66995C22semidirect
40. C2×#66985C22semidirect
47. #10623322C22semidirect
48. #10623322C22semidirect
49. C2×#66983C22semidirect
50. C2×#66983C22semidirect
55. C2×#66977C22semidirect
56. C2×#66977C22semidirect
57. C22×#4318C22semidirect
58. #10622852C22semidirect
59. #10622852C22semidirect
60. #10622851C22semidirect
61. #10622851C22semidirect
62. #10622838C22semidirect
63. #10622828C22semidirect
66. #10622820C22semidirect
67. #10622820C22semidirect
68. #10622820C22semidirect
69. C2×C22⋊(C11⋊C8)C22semidirect
70. C2×C22⋊(C11⋊C8)C22semidirect
71. #10622665C22semidirect
72. #10622664C22semidirect
73. #10622663C22semidirect
74. #10622662C22semidirect
75. #10622661C22semidirect
76. #10622660C22semidirect
77. #10622659C22semidirect
78. #10622658C22semidirect
79. #10622657C22semidirect
80. #10622656C22semidirect
81. #10622655C22semidirect
82. #10622654C22semidirect
83. #10622653C22semidirect
84. #10622652C22semidirect
85. #10622651C22semidirect
86. #10622650C22semidirect
87. #10622649C22semidirect
88. #10622648C22semidirect
89. #10622647C22semidirect
90. #10622646C22semidirect
91. #10622616C22semidirect
92. #10622616C22semidirect
93. #10622609C22semidirect
94. #10622609C22semidirect
95. #10622579C22semidirect
96. #10622579C22semidirect
97. #10622577C22semidirect
98. #10622577C22semidirect
190. C2×#4326C23semidirect
192. C2×#4325C23semidirect
193. C2×#4324C23semidirect
195. C2×#4323C23semidirect
240. #66899C23semidirect
241. #66899C23semidirect
242. #66896C23semidirect
243. #66896C23semidirect
250. #66874C23semidirect
251. #66874C23semidirect
252. #66873C23semidirect
253. #66873C23semidirect
254. #66872C23semidirect
255. #66872C23semidirect
256. #66871C23semidirect
257. #66871C23semidirect
416. C2×#525D11semidirect
546. C22×#41C2×D11semidirect
565. #525C2×D11semidirect
566. #525C2×D11semidirect
572. C2×C22⋊Q8C2×D11semidirect
576. C2×#121C2×D11semidirect
584. C2×#117C2×D11semidirect
1004. C11#60752semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
#130794532
#130794422
#130794262
#130794042
#130793932
#130793772
#130785602
#130785522
#130785472
#130782422
#130782312
#130778742
#130778662
#130778582
C2×#106228202
C2×C11×#5252
#6075211