Finite Group Databasebeta

← #14961137

Subgroups — #14961137

Order 2816.

2954 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623336C211yesmaximal, characteristic, complemented
2C2×#10623335C211yesmaximal, characteristic, complemented
3#13076898C212yesmaximal, complemented
4#13075454C211yesmaximal, characteristic, complemented
5#13075346C211yesmaximal, characteristic, complemented
6#13075332C212yesmaximal, complemented
7#13075050C212yesmaximal, complemented
8#13075020C212yesmaximal, complemented
9#13074995C211yesmaximal, characteristic, complemented
10#13074880C212yesmaximal, complemented
11#13074850C212yesmaximal, complemented
12#13074834C211yesmaximal, characteristic, complemented
13#13074822C212yesmaximal, complemented
14#13074350C212yesmaximal, complemented
15#13073060C212yesmaximal, complemented
16#13072226C212yesmaximal, complemented
17#13072006C212yesmaximal, complemented
18#13071984C212yesmaximal, complemented
19C2×C11×#386C211yesmaximal, characteristic, complemented
20C23×D4×C11C2211yescharacteristic
21C24×C4×C11C2211yescharacteristic, complemented
22C23×C22⋊D11C2211yescharacteristic
23C22×#4339C2211yescharacteristic, complemented
24C22×C11×C22⋊C4C2212yes—
25C22×C11×C22⋊C4C2211yescharacteristic, complemented
26C2×#67006C2212yes—
27C2×#67006C2212yes—
28C2×#67006C2212yescomplemented
29C22×C22⋊Dic11C2211yescharacteristic
30#10623336—28no—
31#10623335—28no—
32C2×#66993C2211yescharacteristic
33C2×#66993C2211yescharacteristic, complemented
34C2×#66992C2212yes—
35C2×#66992C2212yes—
36C2×#66991C2212yes—
37C2×#66991C2212yescomplemented
38C2×#66990C2211yescharacteristic
39C2×#66990C2211yescharacteristic
40C2×#66989C2211yescharacteristic
41C2×#66989C2211yescharacteristic, complemented
42C2×#66988C2211yescharacteristic
43C2×#66988C2211yescharacteristic
44C2×#66983C2212yes—
45C2×#66983C2212yes—
46C2×#66983C2212yescomplemented
47C2×#66983C2212yescomplemented
48C2×#66982C2212yes—
49C2×#66979C2211yescharacteristic, complemented
50C2×#66939C2212yescomplemented
51C2×#66935C2212yescomplemented
52C11×#386C2211yescharacteristic
53C11×#386C2212yes—
54C11×#386C2211yescharacteristic
55C11×#386C2212yescomplemented
56C11×#386C2211yescharacteristic, complemented
57C11×#386C2211yescharacteristic, complemented
58C2×C11×#95C2212yescomplemented
59#10622826C2212yes—
60#10622826C2212yes—
61#10622826C2212yescomplemented
62#10622826C2212yescomplemented
63#10622826C2212yescomplemented
64#10622826C2212yescomplemented
65#10622826C2212yescomplemented
66#10622826C2212yescomplemented
67#10622825C2212yescomplemented
68#10622825C2212yescomplemented
69#10622825C2212yescomplemented
70#10622825C2212yescomplemented
71#10622574C2212yescomplemented
72#10622574C2212yescomplemented
73#10622574C2212yescomplemented
74#10622574C2212yescomplemented
75#10622574C2212yescomplemented
76#10622574C2212yescomplemented
77#10622574C2212yescomplemented
78#10622574C2212yescomplemented
79#10622573C2212yescomplemented
80#10622573C2212yescomplemented
81#10622573C2212yescomplemented
82#10622573C2212yescomplemented
83#10622571C2212yescomplemented
84#10622571C2212yescomplemented
85#10622568C2212yescomplemented
86#10622566C2212yescomplemented
87#10622566C2212yescomplemented
88#10622566C2212yescomplemented
89#10622566C2212yescomplemented
90#10622563C2212yescomplemented
91#10622563C2212yescomplemented
92#10622556C2212yescomplemented
93#10622290C2212yescomplemented
94#10622287C2212yescomplemented
95#10622286C2212yescomplemented
96#10622285C2212yescomplemented
97#10622284C2212yescomplemented
98#10622283C2212yescomplemented
99#10622283C2212yescomplemented
100#10622281C2212yescomplemented
101#10622281C2212yescomplemented
102#10622278C2212yescomplemented
103#10622278C2212yescomplemented
104#10622274C2212yescomplemented
105#10622272C2212yescomplemented
106#10622269C2212yescomplemented
107#10622266C2212yescomplemented
108#10622266C2212yescomplemented
109C25×C11C2311yescharacteristic
110C25×C11C2311yescharacteristic
111C24×D11C2311yescharacteristic
112C22×D4×C11—42no—
113C22×D4×C11—42no—
114C22×D4×C11D418yescomplemented
115C22×D4×C11C2311yescharacteristic
116C22×D4×C11C2311yescharacteristic
117C22×D4×C11C2311yescharacteristic
118C22×D4×C11C2311yescharacteristic
119C23×C4×C11—44no—
120C23×C4×C11—42no—
121C23×C4×C11C2312yes—
122C23×C4×C11C2311yescharacteristic
123C23×C4×C11C2311yescharacteristic
124C23×C4×C11C2312yes—
125C23×C4×C11C2312yes—
126C23×C4×C11C2311yescharacteristic
127C22×C22⋊D11—24no—
128C22×C22⋊D11—42no—
129C22×C22⋊D11—42no—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2312yes—
137C22×C22⋊D11C2312yes—
138C22×C22⋊D11C2312yes—
139C23×Dic11C2312yes—
140C23×Dic11C2311yescharacteristic
141C2×#4339—24no—
142C2×#4339—42no—
143C2×#4339—42no—
144C22×D44C2312yes—
145C22×D44C2311yescharacteristic
146C22×D44C2312yes—
147C22×C4×D11C2312yes—
148C22×Dic22C2311yescharacteristic
149C2×C11×C22⋊C4—44no—
150C2×C11×C22⋊C4—42no—
151C2×C11×C22⋊C4C2312yes—
152C2×C11×C22⋊C4C2312yes—
153C2×C11×C22⋊C4C2312yes—
154C2×C11×C22⋊C4C2311yescharacteristic
155C2×C11×C22⋊C4C2312yes—
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2311yescharacteristic
158#67006—28no—
159#67006—28no—
160#67006—28no—
161C2×C22⋊Dic11—24no—
162C2×C22⋊Dic11C2312yes—
163C2×C22⋊Dic11C2312yes—
164C2×C22⋊Dic11C2312yes—
165C2×C22⋊Dic11C2311yescharacteristic
166C2×C22⋊Dic11C2311yescharacteristic
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172#66993—24no—
173#66993—24no—
174#66992—28no—
175#66992—28no—
176#66991—28no—
177#66991—28no—
178#66990—24no—
179#66990—24no—
180#66989—24no—
181#66989—24no—
182#66988—24no—
183#66988—24no—
184#66983—44no—
185#66983—44no—
186#66983—44no—
187#66983—44no—
188#66982—28no—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203#66979—24no—
204C2×C4⋊Dic11C2312yes—
205C2×C4⋊Dic11C2312yes—
206C2×C4⋊Dic11C2312yes—
207C2×C4⋊Dic11C2312yes—
208C2×C4⋊Dic11C2312yes—
209C2×C4⋊Dic11C2312yes—
210C2×C4⋊Dic11C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215#66939—44no—
216#66935—44no—
217C11×#95C2312yes—
218C11×#95C2312yes—
219C11×#95C2312yes—
220C11×#95C2312yes—
221C11⋊#95C2312yes—
222C11⋊#95C2312yes—
223C11⋊#95C2312yes—
224C11⋊#95C2312yes—
225C11⋊#95C2312yes—
226C11⋊#95C2312yes—
227C11⋊#95C2312yes—
228C11⋊#95C2312yes—
229C11⋊#95C2312yes—
230C11⋊#95C2312yes—
231C11⋊#95C2312yes—
232C11⋊#95C2312yes—
233#36737—111nomaximal, Sylow
234C24×C11—22no—
235C24×C11—22no—
236C24×C11—22no—
237C24×C11—22no—
238C24×C11—42no—
239C24×C11—42no—
240C24×C11—42no—
241C24×C11—42no—
242C24×C11C2×D414yes—
243C24×C11C2×D414yes—
244C24×C11C2411yescharacteristic
245C24×C11C2411yescharacteristic
246C24×C11C2411yescharacteristic
247C24×C11C2411yescharacteristic
248C24×C11C2411yescharacteristic
249C23×D11—22no—
250C23×D11—41no—
251C23×D11—41no—
252C23×D11—42no—
253C23×D11—42no—
254C23×D11C2412yes—
255C23×D11C2412yes—
256C2×D4×C11—416no—
257C2×D4×C11—41no—
258C2×D4×C11—41no—
259C2×D4×C11—41no—
260C2×D4×C11—41no—
261C2×D4×C11—41no—
262C2×D4×C11—41no—
263C2×D4×C11—41no—
264C2×D4×C11—41no—
265C2×D4×C11C2×D414yes—
266C2×D4×C11C2×D414yes—
267C2×D4×C11C2×D414yes—
268C2×D4×C11C2×D414yes—
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—24no—
272C22×C4×C11—24no—
273C22×C4×C11—24no—
274C22×C4×C11—24no—
275C22×C4×C11—24no—
276C22×C4×C11—41no—
277C22×C4×C11—42no—
278C22×C4×C11—42no—
279C22×C4×C11—42no—
280C22×C4×C11—41no—
281C22×C4×C11—42no—
282C22×C4×C11—42no—
283C22×C4×C11—42no—
284C22×C4×C11—416no—
285C22×C4×C11C2×D414yes—
286C22×C4×C11C2412yes—
287C22×C4×C11C2412yes—
288C22×C4×C11C2412yes—
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2412yes—
292C2×C22⋊D11—24no—
293C2×C22⋊D11—24no—
294C2×C22⋊D11—24no—
295C2×C22⋊D11—24no—
296C2×C22⋊D11—24no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—24no—
303C2×C22⋊D11—24no—
304C2×C22⋊D11—24no—
305C2×C22⋊D11—42no—
306C2×C22⋊D11—42no—
307C2×C22⋊D11—42no—
308C2×C22⋊D11—42no—
309C2×C22⋊D11—42no—
310C2×C22⋊D11—42no—
311C2×C22⋊D11—42no—
312C2×C22⋊D11—42no—
313C2×C22⋊D11—42no—
314C2×C22⋊D11—42no—
315C2×C22⋊D11—42no—
316C2×C22⋊D11—42no—
317C2×C22⋊D11—42no—
318C2×C22⋊D11—42no—
319C2×C22⋊D11—416no—
320C22×Dic11—22no—
321C22×Dic11—24no—
322C22×Dic11—41no—
323C22×Dic11—41no—
324C22×Dic11—42no—
325C22×Dic11—42no—
326C22×Dic11C2412yes—
327C22×Dic11C2412yes—
328C22×Dic11C2412yes—
329C22×Dic11C2412yes—
330C22×Dic11C2412yes—
331C22×Dic11C2412yes—
332#4339—416no—
333C2×D44—22no—
334C2×D44—24no—
335C2×D44—41no—
336C2×D44—41no—
337C2×D44—42no—
338C2×D44—42no—
339C2×D44—42no—
340C2×D44—42no—
341C2×D44—42no—
342C2×C4×D11—24no—
343C2×C4×D11—42no—
344C2×C4×D11—42no—
345C2×Dic22—22no—
346C2×Dic22—41no—
347C2×Dic22—41no—
348C11×C22⋊C4—24no—
349C11×C22⋊C4—24no—
350C11×C22⋊C4—42no—
351C11×C22⋊C4—41no—
352C11×C22⋊C4—42no—
353C11×C22⋊C4—41no—
354C11×C22⋊C4—42no—
355C22⋊Dic11—24no—
356C22⋊Dic11—24no—
357C22⋊Dic11—22no—
358C22⋊Dic11—22no—
359C22⋊Dic11—24no—
360C22⋊Dic11—24no—
361C22⋊Dic11—24no—
362C22⋊Dic11—24no—
363C22⋊Dic11—24no—
364C22⋊Dic11—24no—
365(C2×D11)⋊C4—24no—
366(C2×D11)⋊C4—24no—
367(C2×D11)⋊C4—24no—
368(C2×D11)⋊C4—24no—
369(C2×D11)⋊C4—42no—
370(C2×D11)⋊C4—42no—
371(C2×D11)⋊C4—42no—
372(C2×D11)⋊C4—42no—
373(C2×D11)⋊C4—42no—
374(C2×D11)⋊C4—42no—
375(C2×D11)⋊C4—42no—
376(C2×D11)⋊C4—42no—
377(C2×D11)⋊C4—42no—
378(C2×D11)⋊C4—42no—
379C4⋊Dic11—24no—
380C4⋊Dic11—24no—
381C4⋊Dic11—42no—
382C4⋊Dic11—42no—
383C4⋊Dic11—42no—
384C4⋊Dic11—42no—
385C4⋊Dic11—42no—
386Dic11⋊C4—24no—
387Dic11⋊C4—24no—
388C4×Dic11—22no—
389C4×Dic11—22no—
390C2×#535—111no—
391C2×#534—111no—
392#2847—112no—
393#2717—111no—
394#2709—111no—
395#2708—112no—
396#2688—112no—
397#2686—112no—
398#2684—111no—
399#2673—112no—
400#2671—112no—
401#2669—111no—
402#2668—112no—
403#2617—112no—
404#2498—112no—
405#2430—112no—
406#2412—112no—
407#2410—112no—
408C2×#386D1111yescharacteristic, complemented
409C23×C11—22no—
410C23×C11—22no—
411C23×C11—28no—
412C23×C11—22no—
413C23×C11—22no—
414C23×C11—21no—
415C23×C11—21no—
416C23×C11—21no—
417C23×C11—21no—
418C23×C11—22no—
419C23×C11—22no—
420C23×C11—21no—
421C23×C11—21no—
422C23×C11—21no—
423C23×C11—21no—
424C23×C11—22no—
425C23×C11—22no—
426C23×C11—22no—
427C23×C11—22no—
428C23×C11—28no—
429C23×C11—48no—
430C23×C11—48no—
431C23×C11—44no—
432C23×C11—44no—
433C23×C11—48no—
434C23×C11—82no—
435C23×C11—82no—
436C23×C11—84no—
437C23×C11C22×D412yes—
438C23×C11C22×D412yes—
439C23×C11C22×D412yes—
440C23×C11C22×D412yes—
441C23×C11C22×D412yes—
442C23×C11H(5,𝔽2)12yes—
443C23×C11H(5,𝔽2)12yes—
444C23×C11C2511yescharacteristic
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—22no—
448C22×D11—22no—
449C22×D11—22no—
450C22×D11—22no—
451C22×D11—22no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—22no—
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—44no—
460C22×D11—84no—
461C22×D11—82no—
462C22×D11—82no—
463C22×D11—84no—
464D4×C11—44no—
465D4×C11—44no—
466D4×C11—44no—
467D4×C11—44no—
468C2×C4×C11—28no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—21no—
472C2×C4×C11—21no—
473C2×C4×C11—21no—
474C2×C4×C11—21no—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—44no—
485C2×C4×C11—48no—
486C2×C4×C11—48no—
487C2×C4×C11—44no—
488C2×C4×C11—84no—
489C2×C4×C11C22×D412yes—
490C2×C4×C11C22×D412yes—
491C2×C4×C11H(5,𝔽2)14yes—
492C22⋊D11—48no—
493C22⋊D11—48no—
494C22⋊D11—48no—
495C22⋊D11—84no—
496C22⋊D11—84no—
497C22⋊D11—84no—
498C22⋊D11—84no—
499C22⋊D11—84no—
500C22⋊D11—84no—
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—22no—
504C2×Dic11—22no—
505C2×Dic11—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—44no—
520C2×Dic11—84no—
521D44—44no—
522D44—84no—
523D44—84no—
524C4×D11—48no—
525Dic22—44no—
526C22×#41—111no—
527C23×D4—111no—
528C23×D4C2×D1111yescharacteristic
529C24×C4C2×D1111yescharacteristic, complemented
530#535—228no—
531#534—228no—
532C2×#127—111no—
533C2×#127—111no—
534C2×#124—111no—
535C2×#124—111no—
536C2×#123—111no—
537C2×#123—111no—
538C2×#123—112no—
539C2×#123—112no—
540C2×#121—112no—
541C2×#121—112no—
542C2×#121—112no—
543C2×#121—112no—
544C2×#121—112no—
545C2×#121—112no—
546C2×#121—112no—
547C2×#121—112no—
548C2×#120—112no—
549C2×#120—112no—
550C2×#120—112no—
551C2×#120—111no—
552C2×#120—111no—
553C2×#120—112no—
554C2×#117—111no—
555C22×C22⋊C4—111no—
556C22×C22⋊C4C2×D1112yes—
557C22×C22⋊C4C2×D1111yescharacteristic, complemented
558#400—112no—
559#399—112no—
560#398—112no—
561#397—112no—
562#397—112no—
563#397—112no—
564#397—112no—
565#397—112no—
566#395—112no—
567#394—112no—
568#394—112no—
569#394—112no—
570#394—112no—
571#394—112no—
572#394—112no—
573#394—112no—
574#394—112no—
575#394—112no—
576#393—112no—
577#392—112no—
578#392—112no—
579#392—112no—
580#392—112no—
581#392—112no—
582#388—112no—
583#388—112no—
584#387—112no—
585#387—112no—
586#386—112no—
587#386—112no—
588#386—112no—
589#386—112no—
590#386—112no—
591#386—112no—
592#386—112no—
593#386—112no—
594#386—112no—
595#386—112no—
596#386—112no—
597#386—112no—
598#386C2×D1112yes—
599#386C2×D1111yescharacteristic
600#386C2×D1111yescharacteristic
601#386C2×D1111yescharacteristic, complemented
602#386C2×D1112yescomplemented
603#386C2×D1111yescharacteristic, complemented
604#385—112no—
605#385—112no—
606#385—112no—
607#385—112no—
608#381—112no—
609#380—112no—
610#380—112no—
611#380—112no—
612#380—112no—
613#379—112no—
614C2×#95C2×D1112yescomplemented
615C22×C11—24no—
616C22×C11—22no—
617C22×C11—22no—
618C22×C11—24no—
619C22×C11—22no—
620C22×C11—22no—
621C22×C11—22no—
622C22×C11—22no—
623C22×C11—24no—
624C22×C11—24no—
625C22×C11—24no—
626C22×C11—24no—
627C22×C11—416no—
628C22×C11—41no—
629C22×C11—41no—
630C22×C11—41no—
631C22×C11—41no—
632C22×C11—41no—
633C22×C11—41no—
634C22×C11—41no—
635C22×C11—41no—
636C22×C11—42no—
637C22×C11—42no—
638C22×C11—42no—
639C22×C11—42no—
640C22×C11—88no—
641C22×C11#53414yes—
642C22×C11C23×D411yescharacteristic
643C22×C11C2×H(5,𝔽2)11yescharacteristic
644C22×C11C2×H(5,𝔽2)11yescharacteristic
645C22×C11C2×H(5,𝔽2)12yes—
646C22×C11#58512yes—
647C2×D11—42no—
648C2×D11—42no—
649C2×D11—42no—
650C2×D11—42no—
651C2×D11—42no—
652C2×D11—42no—
653C2×D11—42no—
654C2×D11—42no—
655C2×D11—42no—
656C2×D11—42no—
657C2×D11—42no—
658C2×D11—42no—
659C2×D11—42no—
660C2×D11—42no—
661C2×D11—88no—
662C4×C11—22no—
663C4×C11—22no—
664C4×C11—24no—
665C4×C11—42no—
666C4×C11—42no—
667C4×C11—42no—
668Dic11—42no—
669Dic11—42no—
670Dic11—42no—
671Dic11—42no—
672Dic11—42no—
673Dic11—42no—
674C25—111no—
675C25C22×D1111yescharacteristic
676C25C22×D1111yescharacteristic
677C2×#41—224no—
678C2×#41—442no—
679C2×#41—442no—
680C22×Q8—111no—
681C22×D4—42no—
682C22×D4—42no—
683C22×D4—112no—
684C22×D4—112no—
685C22×D4—112no—
686C22×D4—112no—
687C22×D4—112no—
688C22×D4—112no—
689C22×D4—112no—
690C22×D4—112no—
691C22×D4—112no—
692C22×D4—112no—
693C22×D4—111no—
694C22×D4—112no—
695C22×D4—224no—
696C22×D4—442no—
697C22×D4—442no—
698C22×D4D4418yescomplemented
699C22×D4C22×D1111yescharacteristic
700C22×D4C22×D1111yescharacteristic
701C22×D4C22×D1111yescharacteristic
702C22×D4C22×D1111yescharacteristic
703C23×C4—44no—
704C23×C4—42no—
705C23×C4—112no—
706C23×C4—111no—
707C23×C4—112no—
708C23×C4C22×D1112yes—
709C23×C4C22×D1111yescharacteristic
710C23×C4C22×D1111yescharacteristic
711C23×C4C22×D1112yes—
712C23×C4C22×D1112yes—
713C23×C4C22×D1111yescharacteristic
714#127—224no—
715#127—224no—
716#124—224no—
717#124—224no—
718#123—224no—
719#123—224no—
720#123—228no—
721#123—444no—
722#121—228no—
723#121—228no—
724#121—228no—
725#121—228no—
726#121—444no—
727#121—444no—
728#121—444no—
729#121—444no—
730#120—228no—
731#120—228no—
732#120—228no—
733#120—224no—
734#120—224no—
735#120—444no—
736#117—224no—
737C2×C4⋊C4—112no—
738C2×C4⋊C4—112no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—112no—
741C2×C4⋊C4—112no—
742C2×C4⋊C4—112no—
743C2×C4⋊C4—112no—
744C2×C4⋊C4—112no—
745C2×C4⋊C4—112no—
746C2×C22⋊C4—44no—
747C2×C22⋊C4—42no—
748C2×C22⋊C4—112no—
749C2×C22⋊C4—111no—
750C2×C22⋊C4—111no—
751C2×C22⋊C4—112no—
752C2×C22⋊C4—112no—
753C2×C22⋊C4—112no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—112no—
756C2×C22⋊C4—112no—
757C2×C22⋊C4—112no—
758C2×C22⋊C4—112no—
759C2×C22⋊C4—112no—
760C2×C22⋊C4—112no—
761C2×C22⋊C4—112no—
762C2×C22⋊C4—112no—
763C2×C22⋊C4—112no—
764C2×C22⋊C4—112no—
765C2×C22⋊C4—112no—
766C2×C22⋊C4—112no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—224no—
773C2×C22⋊C4C22×D1112yes—
774C2×C22⋊C4C22×D1112yes—
775C2×C22⋊C4C22×D1112yes—
776C2×C22⋊C4C22×D1112yes—
777C2×C22⋊C4C22×D1111yescharacteristic
778C2×C22⋊C4C22×D1112yes—
779C2×C22⋊C4C22×D1111yescharacteristic
780C2×C42—111no—
781C2×C42—111no—
782#95—112no—
783#95—112no—
784#95—112no—
785#95—112no—
786#95—112no—
787#95—112no—
788#95—112no—
789#95—112no—
790#95—112no—
791#95—112no—
792#95—112no—
793#95—112no—
794#95C22×D1112yes—
795#95C22×D1112yes—
796#95C22×D1112yes—
797#95C22×D1112yes—
798C2×C11—24no—
799C2×C11—42no—
800C2×C11—42no—
801C2×C11—42no—
802C2×C11—42no—
803C2×C11C2×#53411yescharacteristic
804C2×C11#349612yes—
805C2×C11#353211yescharacteristic
806C2×C11#353311yescharacteristic
807C2×C11#354212yes—
808D11—82no—
809D11—82no—
810C24—22no—
811C24—22no—
812C24—22no—
813C24—22no—
814C24—42no—
815C24—42no—
816C24—42no—
817C24—42no—
818C24—112no—
819C24—112no—
820C24—222no—
821C24—441no—
822C24—441no—
823C24—442no—
824C24—442no—
825C24C2×D4414yes—
826C24C2×D4414yes—
827C24C23×D1111yescharacteristic
828C24C23×D1111yescharacteristic
829C24C23×D1111yescharacteristic
830C24C23×D1111yescharacteristic
831C24C23×D1111yescharacteristic
832#41—4416no—
833C2×Q8—222no—
834C2×Q8—441no—
835C2×Q8—441no—
836C2×D4—41no—
837C2×D4—41no—
838C2×D4—41no—
839C2×D4—41no—
840C2×D4—41no—
841C2×D4—41no—
842C2×D4—41no—
843C2×D4—41no—
844C2×D4—416no—
845C2×D4—224no—
846C2×D4—224no—
847C2×D4—224no—
848C2×D4—224no—
849C2×D4—224no—
850C2×D4—224no—
851C2×D4—224no—
852C2×D4—224no—
853C2×D4—224no—
854C2×D4—224no—
855C2×D4—224no—
856C2×D4—224no—
857C2×D4—224no—
858C2×D4—222no—
859C2×D4—224no—
860C2×D4—441no—
861C2×D4—441no—
862C2×D4—442no—
863C2×D4—442no—
864C2×D4—442no—
865C2×D4—442no—
866C2×D4—442no—
867C2×D4—442no—
868C2×D4—442no—
869C2×D4—442no—
870C2×D4—442no—
871C2×D4—442no—
872C2×D4—442no—
873C2×D4—442no—
874C2×D4—442no—
875C2×D4—442no—
876C2×D4—442no—
877C2×D4—442no—
878C2×D4—442no—
879C2×D4—442no—
880C2×D4—442no—
881C2×D4—4416no—
882C2×D4C2×D4414yes—
883C2×D4C2×D4414yes—
884C2×D4C2×D4414yes—
885C2×D4C2×D4414yes—
886C22×C4—22no—
887C22×C4—22no—
888C22×C4—24no—
889C22×C4—24no—
890C22×C4—24no—
891C22×C4—24no—
892C22×C4—24no—
893C22×C4—41no—
894C22×C4—42no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—41no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—416no—
902C22×C4—112no—
903C22×C4—112no—
904C22×C4—112no—
905C22×C4—112no—
906C22×C4—112no—
907C22×C4—112no—
908C22×C4—222no—
909C22×C4—224no—
910C22×C4—224no—
911C22×C4—442no—
912C22×C4—442no—
913C22×C4—441no—
914C22×C4—441no—
915C22×C4—442no—
916C22×C4—442no—
917C22×C4C2×D4414yes—
918C22×C4C23×D1112yes—
919C22×C4C23×D1112yes—
920C22×C4C23×D1112yes—
921C22×C4C23×D1111yescharacteristic
922C22×C4C23×D1111yescharacteristic
923C22×C4C23×D1112yes—
924C4⋊C4—224no—
925C4⋊C4—224no—
926C4⋊C4—224no—
927C4⋊C4—224no—
928C4⋊C4—442no—
929C4⋊C4—442no—
930C4⋊C4—442no—
931C4⋊C4—442no—
932C4⋊C4—442no—
933C22⋊C4—24no—
934C22⋊C4—24no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C22⋊C4—41no—
938C22⋊C4—42no—
939C22⋊C4—41no—
940C22⋊C4—222no—
941C22⋊C4—222no—
942C22⋊C4—224no—
943C22⋊C4—224no—
944C22⋊C4—224no—
945C22⋊C4—224no—
946C22⋊C4—224no—
947C22⋊C4—224no—
948C22⋊C4—224no—
949C22⋊C4—224no—
950C22⋊C4—224no—
951C22⋊C4—224no—
952C22⋊C4—224no—
953C22⋊C4—224no—
954C22⋊C4—442no—
955C22⋊C4—442no—
956C22⋊C4—442no—
957C22⋊C4—442no—
958C22⋊C4—442no—
959C22⋊C4—442no—
960C22⋊C4—442no—
961C22⋊C4—442no—
962C22⋊C4—442no—
963C22⋊C4—442no—
964C42—222no—
965C42—222no—
966C11#3673711yescharacteristic, complemented, Sylow
967C23—22no—
968C23—22no—
969C23—28no—
970C23—22no—
971C23—22no—
972C23—21no—
973C23—21no—
974C23—22no—
975C23—22no—
976C23—21no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—28no—
987C23—48no—
988C23—48no—
989C23—44no—
990C23—48no—
991C23—44no—
992C23—84no—
993C23—82no—
994C23—82no—
995C23—222no—
996C23—222no—
997C23—222no—
998C23—222no—
999C23—222no—
1000C23—222no—
1001C23—222no—
1002C23—222no—
1003C23—222no—
1004C23—222no—
1005C23—222no—
1006C23—222no—
1007C23—222no—
1008C23—222no—
1009C23—444no—
1010C23—884no—
1011C23—884no—
1012C23—882no—
1013C23—882no—
1014C23C22×D4412yes—
1015C23C22×D4412yes—
1016C23C22×D4412yes—
1017C23C22×D4412yes—
1018C23C22×D4412yes—
1019C23#6703712yes—
1020C23#6703712yes—
1021C23C24×D1111yescharacteristic
1022Q8—444no—
1023D4—44no—
1024D4—44no—
1025D4—44no—
1026D4—44no—
1027D4—444no—
1028D4—448no—
1029D4—448no—
1030D4—448no—
1031D4—884no—
1032D4—884no—
1033D4—884no—
1034D4—884no—
1035D4—884no—
1036D4—884no—
1037D4—884no—
1038D4—884no—
1039C2×C4—28no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—44no—
1056C2×C4—48no—
1057C2×C4—48no—
1058C2×C4—44no—
1059C2×C4—84no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—222no—
1070C2×C4—222no—
1071C2×C4—222no—
1072C2×C4—222no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—222no—
1078C2×C4—448no—
1079C2×C4—444no—
1080C2×C4—884no—
1081C2×C4C22×D4412yes—
1082C2×C4C22×D4412yes—
1083C2×C4#6703714yes—
1084C22—24no—
1085C22—24no—
1086C22—22no—
1087C22—22no—
1088C22—24no—
1089C22—24no—
1090C22—24no—
1091C22—24no—
1092C22—22no—
1093C22—22no—
1094C22—22no—
1095C22—22no—
1096C22—416no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—41no—
1102C22—41no—
1103C22—41no—
1104C22—41no—
1105C22—41no—
1106C22—41no—
1107C22—41no—
1108C22—41no—
1109C22—88no—
1110C22—442no—
1111C22—442no—
1112C22—442no—
1113C22—442no—
1114C22—442no—
1115C22—442no—
1116C22—442no—
1117C22—442no—
1118C22—442no—
1119C22—442no—
1120C22—442no—
1121C22—442no—
1122C22—442no—
1123C22—442no—
1124C22—888no—
1125C22#1062302414yes—
1126C22C23×D4411yescharacteristic
1127C22C2×#6703712yes—
1128C22C2×#6703711yescharacteristic
1129C22C2×#6703711yescharacteristic
1130C22#1062345312yes—
1131C4—22no—
1132C4—22no—
1133C4—24no—
1134C4—42no—
1135C4—42no—
1136C4—42no—
1137C4—442no—
1138C4—442no—
1139C4—442no—
1140C4—442no—
1141C4—442no—
1142C4—442no—
1143C2—24no—
1144C2—42no—
1145C2—42no—
1146C2—42no—
1147C2—42no—
1148C2—882no—
1149C2—882no—
1150C2C2×#1062302411yescharacteristic
1151C2#1308238012yes—
1152C2#1308277111yescharacteristic
1153C2#1308278711yescharacteristic
1154C2#1308293612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#386C2
hypercenterC2×#386D11
hypocenterC11#36737
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
1. C2×#10623336C2semidirect
2. C2×#10623335C2semidirect
3. #13076898C2semidirect
4. #13075454C2semidirect
5. #13075346C2semidirect
6. #13075332C2semidirect
7. #13075050C2semidirect
8. #13075020C2semidirect
9. #13074995C2semidirect
10. #13074880C2semidirect
11. #13074850C2semidirect
12. #13074834C2semidirect
13. #13074822C2semidirect
14. #13074350C2semidirect
15. #13073060C2semidirect
16. #13072226C2semidirect
17. #13072006C2semidirect
18. #13071984C2semidirect
19. C2×C11×#386C2semidirect
21. C24×C4×C11C22semidirect
23. C22×#4339C22semidirect
25. C22×C11×C22⋊C4C22semidirect
28. C2×#67006C22semidirect
33. C2×#66993C22semidirect
37. C2×#66991C22semidirect
41. C2×#66989C22semidirect
46. C2×#66983C22semidirect
47. C2×#66983C22semidirect
49. C2×#66979C22semidirect
50. C2×#66939C22semidirect
51. C2×#66935C22semidirect
55. C11×#386C22semidirect
56. C11×#386C22semidirect
57. C11×#386C22semidirect
58. C2×C11×#95C22semidirect
61. #10622826C22semidirect
62. #10622826C22semidirect
63. #10622826C22semidirect
64. #10622826C22semidirect
65. #10622826C22semidirect
66. #10622826C22semidirect
67. #10622825C22semidirect
68. #10622825C22semidirect
69. #10622825C22semidirect
70. #10622825C22semidirect
71. #10622574C22semidirect
72. #10622574C22semidirect
73. #10622574C22semidirect
74. #10622574C22semidirect
75. #10622574C22semidirect
76. #10622574C22semidirect
77. #10622574C22semidirect
78. #10622574C22semidirect
79. #10622573C22semidirect
80. #10622573C22semidirect
81. #10622573C22semidirect
82. #10622573C22semidirect
83. #10622571C22semidirect
84. #10622571C22semidirect
85. #10622568C22semidirect
86. #10622566C22semidirect
87. #10622566C22semidirect
88. #10622566C22semidirect
89. #10622566C22semidirect
90. #10622563C22semidirect
91. #10622563C22semidirect
92. #10622556C22semidirect
93. #10622290C22semidirect
94. #10622287C22semidirect
95. #10622286C22semidirect
96. #10622285C22semidirect
97. #10622284C22semidirect
98. #10622283C22semidirect
99. #10622283C22semidirect
100. #10622281C22semidirect
101. #10622281C22semidirect
102. #10622278C22semidirect
103. #10622278C22semidirect
104. #10622274C22semidirect
105. #10622272C22semidirect
106. #10622269C22semidirect
107. #10622266C22semidirect
108. #10622266C22semidirect
114. C22×D4×C11D4semidirect
408. C2×#386D11semidirect
529. C24×C4C2×D11semidirect
557. C22×C22⋊C4C2×D11semidirect
601. #386C2×D11semidirect
602. #386C2×D11semidirect
603. #386C2×D11semidirect
614. C2×#95C2×D11semidirect
698. C22×D4D44semidirect
966. C11#36737semidirect

Maximal subgroups

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

subgroupindex
C2×#106233362
C2×#106233352
#130768982
#130754542
#130753462
#130753322
#130750502
#130750202
#130749952
#130748802
#130748502
#130748342
#130748222
#130743502
#130730602
#130722262
#130720062
#130719842
C2×C11×#3862
#3673711