Finite Group Databasebeta

← #14926310

Subgroups — #14926310

Order 2816.

7786 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D4×D11C211yesmaximal, characteristic, complemented
2C2×#10623184C212yesmaximal, complemented
3C22×#66935C211yesmaximal, characteristic, complemented
4#13076911C212yesmaximal, complemented
5#13076894C212yesmaximal, complemented
6#13074329C214yesmaximal, complemented
7#13071992C212yesmaximal, complemented
8#13071988C212yesmaximal, complemented
9#13071985C214yesmaximal, complemented
10#13071943C211yesmaximal, characteristic, complemented
11#13071940C212yesmaximal, complemented
12#13071929C211yesmaximal, characteristic, complemented
13#13071928C212yesmaximal, complemented
14#13071926C211yesmaximal, characteristic, complemented
15#13071190C212yesmaximal, complemented
16D11×#379C211yesmaximal, characteristic, complemented
17C11×#2405C211yesmaximal, characteristic, complemented
18C25×D11C2211yescharacteristic
19C25×D11C2211yescharacteristic, complemented
20C23×D4×C11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic, complemented
23C23×C22⋊D11C2211yescharacteristic, complemented
24C22×D4×D11—28no—
25C22×D4×D11—216no—
26C22×D4×D11C2212yes—
27C22×D4×D11C2212yes—
28C22×D4×D11C2212yescomplemented
29C22×D4×D11C2212yescomplemented
30C23×D44C2211yescharacteristic, complemented
31C23×D44C2211yescharacteristic, complemented
32C23×D44C2211yescharacteristic, complemented
33C23×C4×D11C2211yescharacteristic, complemented
34C2×C11×#123C2212yescomplemented
35C22×C11×C22⋊C4C2211yescharacteristic, complemented
36C2×#67006C2212yescomplemented
37C2×#66990C2212yescomplemented
38C2×#66982C2212yescomplemented
39C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
40C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
41#10623184—216no—
42C2×#66948C2214yescomplemented
43C2×#66947C2214yescomplemented
44C2×#66937C2214yescomplemented
45C2×#66935—28no—
46C2×#66935C2212yes—
47C2×#66935C2214yescomplemented
48C2×#66935C2212yescomplemented
49C2×#66935C2212yescomplemented
50C2×#66935C2212yescomplemented
51C2×#66935C2212yescomplemented
52C2×#66935C2214yescomplemented
53C2×#66935C2212yescomplemented
54C2×C22⋊C4×D11C2212yescomplemented
55C2×C22⋊C4×D11C2212yescomplemented
56C2×C22⋊C4×D11C2212yescomplemented
57C11×#394C2214yescomplemented
58C11×#386C2212yescomplemented
59C11×#385C2212yescomplemented
60C11×#379C2211yescharacteristic, complemented
61C11×#379C2212yescomplemented
62#10622860C2211yescharacteristic, complemented
63#10622836C2214yescomplemented
64#10622833C2212yescomplemented
65#10622826C2212yescomplemented
66#10622826C2212yescomplemented
67#10622604C2214yescomplemented
68#10622602C2214yescomplemented
69#10622573C2214yescomplemented
70#10622573C2214yescomplemented
71#10622572C2214yescomplemented
72#10622572C2214yescomplemented
73#10622571C2212yescomplemented
74#10622571C2212yescomplemented
75#10622569C2214yescomplemented
76#10622568C2212yescomplemented
77#10622568C2212yescomplemented
78#10622568C2214yescomplemented
79#10622568C2214yescomplemented
80#10622568C2212yescomplemented
81#10622568C2212yescomplemented
82#10622559C2212yescomplemented
83#10622284C2214yescomplemented
84#10622278C2214yescomplemented
85#10622278C2214yescomplemented
86#10622277C2214yescomplemented
87C25×C11C2311yescharacteristic
88C25×C11C2311yescharacteristic
89C24×D11—28no—
90C24×D11—24no—
91C24×D11—28no—
92C24×D11—44no—
93C24×D11—44no—
94C24×D11—44no—
95C24×D11—44no—
96C24×D11D418yescomplemented
97C24×D11C2311yescharacteristic
98C24×D11C2311yescharacteristic
99C24×D11C2312yes—
100C24×D11C2311yescharacteristic
101C24×D11C2311yescharacteristic
102C24×D11C2311yescharacteristic
103C24×D11C2311yescharacteristic
104C24×D11C2312yes—
105C24×D11C2311yescharacteristic
106C24×D11C2311yescharacteristic, complemented
107C22×D4×C11—24no—
108C22×D4×C11—28no—
109C22×D4×C11C2312yes—
110C22×D4×C11C2312yes—
111C23×C4×C11C2311yescharacteristic
112C23×C4×C11C2311yescharacteristic, complemented
113C23×C4×C11C2311yescharacteristic, complemented
114C22×C22⋊D11—24no—
115C22×C22⋊D11—24no—
116C22×C22⋊D11—28no—
117C22×C22⋊D11—28no—
118C22×C22⋊D11—24no—
119C22×C22⋊D11—44no—
120C22×C22⋊D11C2312yes—
121C22×C22⋊D11C2312yes—
122C22×C22⋊D11C2312yes—
123C22×C22⋊D11C2312yes—
124C22×C22⋊D11C2312yes—
125C22×C22⋊D11C2314yescomplemented
126C22×C22⋊D11C2312yescomplemented
127C23×Dic11C2311yescharacteristic
128C23×Dic11C2311yescharacteristic, complemented
129C2×D4×D11—2128no—
130C2×D4×D11—28no—
131C2×D4×D11—28no—
132C2×D4×D11—28no—
133C2×D4×D11—28no—
134C2×D4×D11—28no—
135C2×D4×D11—28no—
136C2×D4×D11—28no—
137C2×D4×D11—28no—
138C2×D4×D11—28no—
139C2×D4×D11—28no—
140C2×D4×D11—28no—
141C2×D4×D11D4116yescomplemented
142C22×D44—24no—
143C22×D44—28no—
144C22×D44—24no—
145C22×D44—24no—
146C22×D44—28no—
147C22×D44—44no—
148C22×D44C2312yes—
149C22×D44C2312yes—
150C22×D44C2312yes—
151C22×D44C2312yes—
152C22×D44C2312yescomplemented
153C22×D44C2314yescomplemented
154C22×D44C2312yescomplemented
155C22×C4×D11—24no—
156C22×C4×D11—28no—
157C22×C4×D11C2312yes—
158C22×C4×D11C2312yes—
159C22×C4×D11C2314yescomplemented
160C11×#123—28no—
161C2×C11×C4⋊C4C2314yescomplemented
162C2×C11×C22⋊C4—24no—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yescomplemented
166C2×C11×C22⋊C4C2312yescomplemented
167C2×C11×C22⋊C4C2314yescomplemented
168C2×C11×C22⋊C4C2312yescomplemented
169C2×C11×C22⋊C4C2314yescomplemented
170#67006—44no—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yescomplemented
173C2×C22⋊Dic11C2312yescomplemented
174C2×C22⋊Dic11C2314yescomplemented
175#66990—28no—
176#66982—28no—
177C2×(C2×D11)⋊C4—24no—
178C2×(C2×D11)⋊C4—24no—
179C2×(C2×D11)⋊C4C2314yes—
180C2×(C2×D11)⋊C4C2314yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yescomplemented
184C2×(C2×D11)⋊C4C2312yescomplemented
185C2×(C2×D11)⋊C4C2314yescomplemented
186C2×(C2×D11)⋊C4C2314yescomplemented
187C2×(C2×D11)⋊C4C2314yescomplemented
188C2×(C2×D11)⋊C4C2314yescomplemented
189C2×(C2×D11)⋊C4C2314yescomplemented
190C2×(C2×D11)⋊C4C2314yescomplemented
191C2×Dic11⋊C4C2314yescomplemented
192#66948—216no—
193#66947—216no—
194#66937—216no—
195#66935—28no—
196#66935—28no—
197#66935—28no—
198#66935—28no—
199#66935—216no—
200#66935—28no—
201#66935—48no—
202#66935—44no—
203C22⋊C4×D11—28no—
204C22⋊C4×D11—44no—
205C22⋊C4×D11—44no—
206C11×#95C2314yescomplemented
207C11⋊#95C2314yescomplemented
208C11⋊#95C2314yescomplemented
209C11⋊#95C2314yescomplemented
210#34980—111nomaximal, Sylow
211C24×C11—24no—
212C24×C11—24no—
213C24×C11—22no—
214C24×C11—24no—
215C24×C11—24no—
216C24×C11—42no—
217C24×C11—42no—
218C24×C11C2×D414yes—
219C24×C11C2411yescharacteristic
220C24×C11C2412yes—
221C24×C11C2411yescharacteristic
222C24×C11C2411yescharacteristic
223C23×D11—24no—
224C23×D11—24no—
225C23×D11—24no—
226C23×D11—232no—
227C23×D11—22no—
228C23×D11—24no—
229C23×D11—24no—
230C23×D11—24no—
231C23×D11—232no—
232C23×D11—24no—
233C23×D11—24no—
234C23×D11—24no—
235C23×D11—24no—
236C23×D11—24no—
237C23×D11—24no—
238C23×D11—24no—
239C23×D11—24no—
240C23×D11—24no—
241C23×D11—24no—
242C23×D11—22no—
243C23×D11—24no—
244C23×D11—24no—
245C23×D11—28no—
246C23×D11—416no—
247C23×D11—416no—
248C23×D11—42no—
249C23×D11—42no—
250C23×D11—42no—
251C23×D11—42no—
252C23×D11—42no—
253C23×D11—42no—
254C23×D11—44no—
255C23×D11—44no—
256C23×D11—44no—
257C23×D11—42no—
258C23×D11—42no—
259C23×D11—42no—
260C23×D11—42no—
261C23×D11—464no—
262C23×D11—464no—
263C23×D11—416no—
264C23×D11—416no—
265C23×D11C2×D414yes—
266C23×D11C2×D414yes—
267C23×D11C2×D414yes—
268C23×D11C2×D414yes—
269C23×D11C2×D414yes—
270C23×D11C2×D418yes—
271C23×D11C2×D414yes—
272C23×D11C2×D418yescomplemented
273C23×D11C2412yes—
274C23×D11C2411yescharacteristic
275C23×D11C2412yes—
276C23×D11C2411yescharacteristic
277C23×D11C2411yescharacteristic
278C23×D11C2411yescharacteristic
279C2×D4×C11—232no—
280C2×D4×C11—24no—
281C2×D4×C11—24no—
282C2×D4×C11—24no—
283C2×D4×C11—24no—
284C2×D4×C11—24no—
285C2×D4×C11C2×D418yes—
286C22×C4×C11—22no—
287C22×C4×C11—24no—
288C22×C4×C11—22no—
289C22×C4×C11—22no—
290C22×C4×C11—24no—
291C22×C4×C11—42no—
292C22×C4×C11C2412yes—
293C22×C4×C11C2414yes—
294C22×C4×C11C2412yes—
295C22×C4×C11C2412yes—
296C2×C22⋊D11—232no—
297C2×C22⋊D11—232no—
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—24no—
306C2×C22⋊D11—28no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—24no—
312C2×C22⋊D11—24no—
313C2×C22⋊D11—42no—
314C2×C22⋊D11—42no—
315C2×C22⋊D11—44no—
316C2×C22⋊D11—44no—
317C2×C22⋊D11—416no—
318C2×C22⋊D11C2×D418yes—
319C2×C22⋊D11C2×D418yescomplemented
320C22×Dic11—24no—
321C22×Dic11—22no—
322C22×Dic11—22no—
323C22×Dic11—42no—
324C22×Dic11C2412yes—
325C22×Dic11C2414yes—
326C22×Dic11C2412yes—
327D4×D11—264no—
328D4×D11—264no—
329D4×D11—264no—
330D4×D11—264no—
331C2×D44—232no—
332C2×D44—24no—
333C2×D44—24no—
334C2×D44—24no—
335C2×D44—24no—
336C2×D44—24no—
337C2×D44—24no—
338C2×D44—24no—
339C2×D44—24no—
340C2×D44—28no—
341C2×D44—28no—
342C2×D44—28no—
343C2×D44—28no—
344C2×D44—24no—
345C2×D44—44no—
346C2×D44—44no—
347C2×D44—44no—
348C2×D44—416no—
349C2×D44—416no—
350C2×D44C2×D418yescomplemented
351C2×C4×D11—232no—
352C2×C4×D11—24no—
353C2×C4×D11—24no—
354C2×C4×D11—24no—
355C2×C4×D11—24no—
356C2×C4×D11—28no—
357C2×C4×D11—24no—
358C2×C4×D11—44no—
359C2×C4×D11—44no—
360C2×C4×D11C2×D418yescomplemented
361C11×C4⋊C4—28no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—28no—
366C11×C22⋊C4—24no—
367C11×C22⋊C4—42no—
368C11×C22⋊C4—44no—
369C22⋊Dic11—24no—
370C22⋊Dic11—24no—
371C22⋊Dic11—42no—
372C22⋊Dic11—44no—
373(C2×D11)⋊C4—28no—
374(C2×D11)⋊C4—28no—
375(C2×D11)⋊C4—24no—
376(C2×D11)⋊C4—24no—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—28no—
380(C2×D11)⋊C4—28no—
381(C2×D11)⋊C4—28no—
382(C2×D11)⋊C4—44no—
383(C2×D11)⋊C4—44no—
384(C2×D11)⋊C4—44no—
385Dic11⋊C4—28no—
386C24×D4—111no—
387C2×#534—112no—
388C22×#120—111no—
389#2849—112no—
390#2846—112no—
391#2613—114no—
392#2410—114no—
393#2410—112no—
394#2410—112no—
395#2405—112no—
396#2405—111no—
397#2405D1111yescharacteristic, complemented
398#2403—112no—
399#2403—111no—
400#2403—111no—
401#2308—112no—
402C2×#379—111no—
403C23×C11—22no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—28no—
408C23×C11—28no—
409C23×C11—28no—
410C23×C11—22no—
411C23×C11—22no—
412C23×C11—22no—
413C23×C11—22no—
414C23×C11—24no—
415C23×C11—24no—
416C23×C11—22no—
417C23×C11—44no—
418C23×C11—416no—
419C23×C11—416no—
420C23×C11—44no—
421C23×C11—44no—
422C23×C11C22×D412yes—
423C23×C11C22×D414yes—
424C23×C11C22×D414yes—
425C23×C11C22×D412yes—
426C23×C11C22×D412yes—
427C23×C11H(5,𝔽2)14yes—
428C23×C11C2511yescharacteristic
429C22×D11—232no—
430C22×D11—28no—
431C22×D11—22no—
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—28no—
438C22×D11—28no—
439C22×D11—28no—
440C22×D11—216no—
441C22×D11—28no—
442C22×D11—28no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—22no—
447C22×D11—24no—
448C22×D11—24no—
449C22×D11—22no—
450C22×D11—28no—
451C22×D11—28no—
452C22×D11—28no—
453C22×D11—216no—
454C22×D11—28no—
455C22×D11—28no—
456C22×D11—24no—
457C22×D11—22no—
458C22×D11—24no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—44no—
462C22×D11—44no—
463C22×D11—44no—
464C22×D11—44no—
465C22×D11—44no—
466C22×D11—44no—
467C22×D11—44no—
468C22×D11—416no—
469C22×D11—416no—
470C22×D11—416no—
471C22×D11—416no—
472C22×D11—416no—
473C22×D11—416no—
474C22×D11—416no—
475C22×D11—416no—
476C22×D11—4128no—
477C22×D11—4128no—
478C22×D11—48no—
479C22×D11—48no—
480C22×D11—48no—
481C22×D11—416no—
482C22×D11—416no—
483C22×D11—44no—
484C22×D11—44no—
485C22×D11—48no—
486C22×D11—44no—
487C22×D11—44no—
488C22×D11—44no—
489C22×D11—88no—
490C22×D11#120116yescomplemented
491C22×D11C22×D412yes—
492C22×D11C22×D414yes—
493C22×D11C22×D412yes—
494C22×D11C22×D414yes—
495C22×D11C22×D412yes—
496C22×D11C22×D414yes—
497C22×D11C22×D412yes—
498C22×D11H(5,𝔽2)14yes—
499D4×C11—216no—
500D4×C11—216no—
501C2×C4×C11—28no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—24no—
505C2×C4×C11—24no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—24no—
509C2×C4×C11—24no—
510C2×C4×C11—24no—
511C2×C4×C11—44no—
512C2×C4×C11—44no—
513C2×C4×C11C22×D414yes—
514C22⋊D11—216no—
515C22⋊D11—216no—
516C22⋊D11—216no—
517C22⋊D11—216no—
518C22⋊D11—48no—
519C22⋊D11—48no—
520C22⋊D11—88no—
521C2×Dic11—28no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—24no—
525C2×Dic11—22no—
526C2×Dic11—24no—
527C2×Dic11—22no—
528C2×Dic11—24no—
529C2×Dic11—22no—
530C2×Dic11—44no—
531C2×Dic11C22×D414yes—
532D44—216no—
533D44—216no—
534D44—48no—
535D44—48no—
536D44—48no—
537D44—48no—
538D44—88no—
539C4×D11—216no—
540C4×D11—216no—
541C4×D11—88no—
542C26—111no—
543C26—111no—
544C23×D4—112no—
545C23×D4—111no—
546C23×D4—111no—
547C23×D4—111no—
548C23×D4—112no—
549C23×D4—112no—
550C23×D4—112no—
551C23×D4—111no—
552C23×D4—111no—
553C23×D4—111no—
554C23×D4—2216no—
555C23×D4—228no—
556C23×D4C2×D1111yescharacteristic
557C24×C4—111no—
558#534—2216no—
559C2×#123—112no—
560C2×#123—114no—
561C2×#123C2×D1112yescomplemented
562C2×#121—114no—
563C2×#121—114no—
564C2×#120—112no—
565C2×#120—112no—
566C2×#120—112no—
567C2×#120—112no—
568C2×#120—112no—
569C2×#120—114no—
570C2×#120—112no—
571C2×#120—112no—
572C2×#120—112no—
573C2×#120—114no—
574C2×#120—228no—
575C22×C22⋊C4—111no—
576C22×C22⋊C4—111no—
577C22×C22⋊C4—112no—
578C22×C22⋊C4—112no—
579C22×C22⋊C4—112no—
580C22×C22⋊C4C2×D1111yescharacteristic, complemented
581#394—114no—
582#394—114no—
583#394—114no—
584#394C2×D1114yescomplemented
585#392—114no—
586#392—114no—
587#392—114no—
588#392—114no—
589#386—112no—
590#386—112no—
591#386—112no—
592#386—112no—
593#386—112no—
594#386—114no—
595#386—114no—
596#386—114no—
597#386C2×D1112yescomplemented
598#385—114no—
599#385—112no—
600#385C2×D1112yescomplemented
601#381—114no—
602#379—111no—
603#379—112no—
604#379—112no—
605#379—114no—
606#379—114no—
607#379—112no—
608#379—112no—
609#379C2×D1112yescomplemented
610#379C2×D1111yescharacteristic, complemented
611C22×C11—22no—
612C22×C11—22no—
613C22×C11—22no—
614C22×C11—22no—
615C22×C11—28no—
616C22×C11—28no—
617C22×C11—22no—
618C22×C11—24no—
619C22×C11—22no—
620C22×C11—22no—
621C22×C11—28no—
622C22×C11—416no—
623C22×C11—416no—
624C22×C11—42no—
625C22×C11—42no—
626C22×C11—44no—
627C22×C11—44no—
628C22×C11C2×#12014yes—
629C22×C11#53414yescomplemented
630C22×C11C23×D411yescharacteristic
631C22×C11C23×D412yes—
632C22×C11C2×H(5,𝔽2)12yes—
633C22×C11C2×H(5,𝔽2)12yes—
634C2×D11—232no—
635C2×D11—22no—
636C2×D11—22no—
637C2×D11—22no—
638C2×D11—22no—
639C2×D11—22no—
640C2×D11—22no—
641C2×D11—28no—
642C2×D11—28no—
643C2×D11—28no—
644C2×D11—24no—
645C2×D11—22no—
646C2×D11—22no—
647C2×D11—22no—
648C2×D11—28no—
649C2×D11—416no—
650C2×D11—416no—
651C2×D11—416no—
652C2×D11—416no—
653C2×D11—416no—
654C2×D11—432no—
655C2×D11—432no—
656C2×D11—416no—
657C2×D11—42no—
658C2×D11—42no—
659C2×D11—44no—
660C2×D11—44no—
661C2×D11—42no—
662C2×D11—42no—
663C2×D11—42no—
664C2×D11—44no—
665C2×D11—44no—
666C2×D11—88no—
667C2×D11C2×#12014yes—
668C2×D11C2×#12014yes—
669C2×D11#53414yescomplemented
670C4×C11—24no—
671C4×C11—42no—
672C4×C11—42no—
673C4×C11—44no—
674Dic11—24no—
675Dic11—42no—
676Dic11—44no—
677C25—111no—
678C25—111no—
679C25—111no—
680C25—111no—
681C25—111no—
682C25—118no—
683C25—112no—
684C25—111no—
685C25—112no—
686C25—111no—
687C25—111no—
688C25—228no—
689C25—224no—
690C25—228no—
691C25—444no—
692C25—444no—
693C25—444no—
694C25—444no—
695C25C22×D1111yescharacteristic
696C25C22×D1111yescharacteristic
697C22×D4—24no—
698C22×D4—28no—
699C22×D4—112no—
700C22×D4—112no—
701C22×D4—1116no—
702C22×D4—112no—
703C22×D4—112no—
704C22×D4—112no—
705C22×D4—114no—
706C22×D4—112no—
707C22×D4—112no—
708C22×D4—112no—
709C22×D4—112no—
710C22×D4—112no—
711C22×D4—112no—
712C22×D4—114no—
713C22×D4—112no—
714C22×D4—228no—
715C22×D4—224no—
716C22×D4—224no—
717C22×D4—224no—
718C22×D4—228no—
719C22×D4—228no—
720C22×D4—228no—
721C22×D4—228no—
722C22×D4—228no—
723C22×D4—228no—
724C22×D4—228no—
725C22×D4—228no—
726C22×D4—228no—
727C22×D4—228no—
728C22×D4—228no—
729C22×D4—22128no—
730C22×D4—228no—
731C22×D4—228no—
732C22×D4—224no—
733C22×D4—224no—
734C22×D4—228no—
735C22×D4—224no—
736C22×D4—444no—
737C22×D4—444no—
738C22×D4C22×D1112yes—
739C22×D4C22×D1112yes—
740C23×C4—112no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—112no—
744C23×C4—114no—
745C23×C4—228no—
746C23×C4—224no—
747C23×C4C22×D1111yescharacteristic
748C23×C4C22×D1111yescharacteristic, complemented
749C23×C4C22×D1111yescharacteristic, complemented
750#123—28no—
751#123—2216no—
752#123—228no—
753#121—2216no—
754#121—2216no—
755#120—228no—
756#120—228no—
757#120—228no—
758#120—228no—
759#120—228no—
760#120—2216no—
761#120—228no—
762#120—444no—
763#120—448no—
764#120—444no—
765C2×C4⋊C4—114no—
766C2×C4⋊C4C22×D1114yescomplemented
767C2×C22⋊C4—24no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—112no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—114no—
775C2×C22⋊C4—114no—
776C2×C22⋊C4—114no—
777C2×C22⋊C4—114no—
778C2×C22⋊C4—114no—
779C2×C22⋊C4—112no—
780C2×C22⋊C4—114no—
781C2×C22⋊C4—114no—
782C2×C22⋊C4—114no—
783C2×C22⋊C4—114no—
784C2×C22⋊C4—228no—
785C2×C22⋊C4—224no—
786C2×C22⋊C4—224no—
787C2×C22⋊C4—444no—
788C2×C22⋊C4—444no—
789C2×C22⋊C4C22×D1112yes—
790C2×C22⋊C4C22×D1112yes—
791C2×C22⋊C4C22×D1112yescomplemented
792C2×C22⋊C4C22×D1112yescomplemented
793C2×C22⋊C4C22×D1114yescomplemented
794C2×C22⋊C4C22×D1112yescomplemented
795C2×C22⋊C4C22×D1114yescomplemented
796#95—114no—
797#95—114no—
798#95—114no—
799#95C22×D1114yescomplemented
800C2×C11—24no—
801C2×C11—24no—
802C2×C11—42no—
803C2×C11—44no—
804C2×C11C22×#12011yescharacteristic
805C2×C11C2×#53411yescharacteristic
806C2×C11C2×#53411yescharacteristic
807C2×C11#348414yes—
808D11—24no—
809D11—24no—
810D11—24no—
811D11—42no—
812D11—44no—
813D11—82no—
814C24—24no—
815C24—24no—
816C24—22no—
817C24—24no—
818C24—24no—
819C24—42no—
820C24—42no—
821C24—111no—
822C24—111no—
823C24—111no—
824C24—118no—
825C24—114no—
826C24—114no—
827C24—112no—
828C24—111no—
829C24—114no—
830C24—114no—
831C24—114no—
832C24—118no—
833C24—114no—
834C24—112no—
835C24—224no—
836C24—224no—
837C24—224no—
838C24—224no—
839C24—224no—
840C24—2232no—
841C24—224no—
842C24—224no—
843C24—224no—
844C24—224no—
845C24—224no—
846C24—224no—
847C24—224no—
848C24—228no—
849C24—2232no—
850C24—224no—
851C24—224no—
852C24—222no—
853C24—224no—
854C24—224no—
855C24—222no—
856C24—224no—
857C24—224no—
858C24—442no—
859C24—442no—
860C24—442no—
861C24—442no—
862C24—442no—
863C24—4416no—
864C24—444no—
865C24—444no—
866C24—442no—
867C24—442no—
868C24—442no—
869C24—444no—
870C24—442no—
871C24—442no—
872C24—4416no—
873C24—4464no—
874C24—4464no—
875C24—4416no—
876C24—4416no—
877C24D4×D1114yes—
878C24C23×D1112yes—
879C24C23×D1111yescharacteristic
880C24C23×D1111yescharacteristic
881C24C23×D1111yescharacteristic
882C2×D4—232no—
883C2×D4—24no—
884C2×D4—24no—
885C2×D4—24no—
886C2×D4—24no—
887C2×D4—24no—
888C2×D4—118no—
889C2×D4—118no—
890C2×D4—118no—
891C2×D4—224no—
892C2×D4—224no—
893C2×D4—224no—
894C2×D4—224no—
895C2×D4—2232no—
896C2×D4—224no—
897C2×D4—224no—
898C2×D4—224no—
899C2×D4—224no—
900C2×D4—228no—
901C2×D4—228no—
902C2×D4—228no—
903C2×D4—228no—
904C2×D4—224no—
905C2×D4—224no—
906C2×D4—2264no—
907C2×D4—2264no—
908C2×D4—2264no—
909C2×D4—2264no—
910C2×D4—224no—
911C2×D4—224no—
912C2×D4—224no—
913C2×D4—224no—
914C2×D4—2232no—
915C2×D4—2232no—
916C2×D4—224no—
917C2×D4—224no—
918C2×D4—224no—
919C2×D4—224no—
920C2×D4—224no—
921C2×D4—224no—
922C2×D4—224no—
923C2×D4—224no—
924C2×D4—228no—
925C2×D4—224no—
926C2×D4—444no—
927C2×D4—444no—
928C2×D4—444no—
929C2×D4—4416no—
930C2×D4—4416no—
931C2×D4—442no—
932C2×D4—442no—
933C2×D4—444no—
934C2×D4—444no—
935C2×D4—4416no—
936C2×D4D4×D1118yes—
937C22×C4—22no—
938C22×C4—24no—
939C22×C4—22no—
940C22×C4—22no—
941C22×C4—24no—
942C22×C4—42no—
943C22×C4—112no—
944C22×C4—118no—
945C22×C4—112no—
946C22×C4—114no—
947C22×C4—224no—
948C22×C4—224no—
949C22×C4—224no—
950C22×C4—224no—
951C22×C4—2232no—
952C22×C4—228no—
953C22×C4—224no—
954C22×C4—222no—
955C22×C4—224no—
956C22×C4—222no—
957C22×C4—444no—
958C22×C4—444no—
959C22×C4—442no—
960C22×C4C23×D1112yes—
961C22×C4C23×D1114yes—
962C22×C4C23×D1112yes—
963C22×C4C23×D1112yes—
964C4⋊C4—28no—
965C4⋊C4—228no—
966C22⋊C4—24no—
967C22⋊C4—24no—
968C22⋊C4—24no—
969C22⋊C4—28no—
970C22⋊C4—24no—
971C22⋊C4—42no—
972C22⋊C4—44no—
973C22⋊C4—228no—
974C22⋊C4—224no—
975C22⋊C4—224no—
976C22⋊C4—224no—
977C22⋊C4—224no—
978C22⋊C4—228no—
979C22⋊C4—228no—
980C22⋊C4—228no—
981C22⋊C4—224no—
982C22⋊C4—224no—
983C22⋊C4—228no—
984C22⋊C4—444no—
985C22⋊C4—444no—
986C22⋊C4—444no—
987C22⋊C4—442no—
988C22⋊C4—444no—
989C11#3498011yescharacteristic, complemented, Sylow
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—28no—
995C23—28no—
996C23—28no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—24no—
1001C23—22no—
1002C23—22no—
1003C23—24no—
1004C23—44no—
1005C23—416no—
1006C23—416no—
1007C23—44no—
1008C23—44no—
1009C23—114no—
1010C23—112no—
1011C23—112no—
1012C23—112no—
1013C23—114no—
1014C23—114no—
1015C23—1116no—
1016C23—114no—
1017C23—112no—
1018C23—228no—
1019C23—228no—
1020C23—228no—
1021C23—228no—
1022C23—2216no—
1023C23—228no—
1024C23—228no—
1025C23—228no—
1026C23—2232no—
1027C23—228no—
1028C23—2216no—
1029C23—228no—
1030C23—222no—
1031C23—222no—
1032C23—222no—
1033C23—222no—
1034C23—222no—
1035C23—222no—
1036C23—228no—
1037C23—228no—
1038C23—222no—
1039C23—222no—
1040C23—222no—
1041C23—222no—
1042C23—224no—
1043C23—224no—
1044C23—222no—
1045C23—224no—
1046C23—222no—
1047C23—222no—
1048C23—222no—
1049C23—224no—
1050C23—444no—
1051C23—444no—
1052C23—444no—
1053C23—444no—
1054C23—4416no—
1055C23—444no—
1056C23—444no—
1057C23—444no—
1058C23—4416no—
1059C23—4416no—
1060C23—4416no—
1061C23—4416no—
1062C23—4416no—
1063C23—444no—
1064C23—444no—
1065C23—444no—
1066C23—448no—
1067C23—4416no—
1068C23—4416no—
1069C23—44128no—
1070C23—44128no—
1071C23—448no—
1072C23—448no—
1073C23—448no—
1074C23—4416no—
1075C23—4416no—
1076C23—444no—
1077C23—444no—
1078C23—888no—
1079C23C2×D4×D1112yes—
1080C23C2×D4×D1114yes—
1081C23C2×D4×D1114yes—
1082C23C2×D4×D1112yes—
1083C23C2×D4×D1112yes—
1084C23#6704214yes—
1085C23C24×D1111yescharacteristic
1086D4—216no—
1087D4—216no—
1088D4—2216no—
1089D4—2216no—
1090D4—2216no—
1091D4—2216no—
1092D4—2216no—
1093D4—2216no—
1094D4—448no—
1095D4—448no—
1096D4—448no—
1097D4—448no—
1098D4—448no—
1099D4—448no—
1100D4—888no—
1101D4—888no—
1102C2×C4—28no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—24no—
1109C2×C4—24no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—44no—
1113C2×C4—44no—
1114C2×C4—114no—
1115C2×C4—2216no—
1116C2×C4—2216no—
1117C2×C4—228no—
1118C2×C4—222no—
1119C2×C4—222no—
1120C2×C4—224no—
1121C2×C4—222no—
1122C2×C4—224no—
1123C2×C4—222no—
1124C2×C4—222no—
1125C2×C4—224no—
1126C2×C4—444no—
1127C2×C4—888no—
1128C2×C4C2×D4×D1114yes—
1129C22—22no—
1130C22—22no—
1131C22—22no—
1132C22—28no—
1133C22—28no—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—28no—
1138C22—22no—
1139C22—24no—
1140C22—416no—
1141C22—416no—
1142C22—42no—
1143C22—42no—
1144C22—44no—
1145C22—44no—
1146C22—114no—
1147C22—114no—
1148C22—114no—
1149C22—2232no—
1150C22—222no—
1151C22—222no—
1152C22—222no—
1153C22—222no—
1154C22—222no—
1155C22—228no—
1156C22—228no—
1157C22—228no—
1158C22—222no—
1159C22—222no—
1160C22—222no—
1161C22—228no—
1162C22—224no—
1163C22—222no—
1164C22—4416no—
1165C22—4416no—
1166C22—4416no—
1167C22—4416no—
1168C22—4416no—
1169C22—4416no—
1170C22—4432no—
1171C22—4432no—
1172C22—442no—
1173C22—442no—
1174C22—444no—
1175C22—444no—
1176C22—442no—
1177C22—442no—
1178C22—444no—
1179C22—444no—
1180C22—442no—
1181C22—888no—
1182C22D11×#12014yes—
1183C22#1062318414yescomplemented
1184C22C22×D4×D1111yescharacteristic
1185C22C22×D4×D1112yes—
1186C22C2×#6704212yes—
1187C22D11×H(5,𝔽2)12yes—
1188C4—24no—
1189C4—42no—
1190C4—44no—
1191C4—42no—
1192C4—224no—
1193C4—442no—
1194C4—444no—
1195C2—24no—
1196C2—24no—
1197C2—42no—
1198C2—44no—
1199C2—224no—
1200C2—224no—
1201C2—224no—
1202C2—442no—
1203C2—444no—
1204C2—882no—
1205C2C2×D11×#12011yescharacteristic
1206C2D11×#53411yescharacteristic
1207C2C2×#1062318411yescharacteristic
1208C2#1308224614yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2405C2
hypercenter#2405D11
hypocenterC11#34980
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2405

Complements

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

NH ≅ G/Ntype
1. C23×D4×D11C2semidirect
2. C2×#10623184C2semidirect
3. C22×#66935C2semidirect
4. #13076911C2semidirect
5. #13076894C2semidirect
6. #13074329C2semidirect
7. #13071992C2semidirect
8. #13071988C2semidirect
9. #13071985C2semidirect
10. #13071943C2semidirect
11. #13071940C2semidirect
12. #13071929C2semidirect
13. #13071928C2semidirect
14. #13071926C2semidirect
15. #13071190C2semidirect
16. D11×#379C2semidirect
17. C11×#2405C2semidirect
19. C25×D11C22semidirect
22. C23×C22⋊D11C22semidirect
23. C23×C22⋊D11C22semidirect
28. C22×D4×D11C22semidirect
29. C22×D4×D11C22semidirect
30. C23×D44C22semidirect
31. C23×D44C22semidirect
32. C23×D44C22semidirect
33. C23×C4×D11C22semidirect
34. C2×C11×#123C22semidirect
35. C22×C11×C22⋊C4C22semidirect
36. C2×#67006C22semidirect
37. C2×#66990C22semidirect
38. C2×#66982C22semidirect
39. C22×(C2×D11)⋊C4C22semidirect
40. C22×(C2×D11)⋊C4C22semidirect
42. C2×#66948C22semidirect
43. C2×#66947C22semidirect
44. C2×#66937C22semidirect
47. C2×#66935C22semidirect
48. C2×#66935C22semidirect
49. C2×#66935C22semidirect
50. C2×#66935C22semidirect
51. C2×#66935C22semidirect
52. C2×#66935C22semidirect
53. C2×#66935C22semidirect
54. C2×C22⋊C4×D11C22semidirect
55. C2×C22⋊C4×D11C22semidirect
56. C2×C22⋊C4×D11C22semidirect
57. C11×#394C22semidirect
58. C11×#386C22semidirect
59. C11×#385C22semidirect
60. C11×#379C22semidirect
61. C11×#379C22semidirect
62. #10622860C22semidirect
63. #10622836C22semidirect
64. #10622833C22semidirect
65. #10622826C22semidirect
66. #10622826C22semidirect
67. #10622604C22semidirect
68. #10622602C22semidirect
69. #10622573C22semidirect
70. #10622573C22semidirect
71. #10622572C22semidirect
72. #10622572C22semidirect
73. #10622571C22semidirect
74. #10622571C22semidirect
75. #10622569C22semidirect
76. #10622568C22semidirect
77. #10622568C22semidirect
78. #10622568C22semidirect
79. #10622568C22semidirect
80. #10622568C22semidirect
81. #10622568C22semidirect
82. #10622559C22semidirect
83. #10622284C22semidirect
84. #10622278C22semidirect
85. #10622278C22semidirect
86. #10622277C22semidirect
96. C24×D11D4semidirect
106. C24×D11C23semidirect
112. C23×C4×C11C23semidirect
113. C23×C4×C11C23semidirect
125. C22×C22⋊D11C23semidirect
126. C22×C22⋊D11C23semidirect
128. C23×Dic11C23semidirect
141. C2×D4×D11D4semidirect
152. C22×D44C23semidirect
153. C22×D44C23semidirect
154. C22×D44C23semidirect
159. C22×C4×D11C23semidirect
161. C2×C11×C4⋊C4C23semidirect
165. C2×C11×C22⋊C4C23semidirect
166. C2×C11×C22⋊C4C23semidirect
167. C2×C11×C22⋊C4C23semidirect
168. C2×C11×C22⋊C4C23semidirect
169. C2×C11×C22⋊C4C23semidirect
172. C2×C22⋊Dic11C23semidirect
173. C2×C22⋊Dic11C23semidirect
174. C2×C22⋊Dic11C23semidirect
183. C2×(C2×D11)⋊C4C23semidirect
184. C2×(C2×D11)⋊C4C23semidirect
185. C2×(C2×D11)⋊C4C23semidirect
186. C2×(C2×D11)⋊C4C23semidirect
187. C2×(C2×D11)⋊C4C23semidirect
188. C2×(C2×D11)⋊C4C23semidirect
189. C2×(C2×D11)⋊C4C23semidirect
190. C2×(C2×D11)⋊C4C23semidirect
191. C2×Dic11⋊C4C23semidirect
206. C11×#95C23semidirect
207. C11⋊#95C23semidirect
208. C11⋊#95C23semidirect
209. C11⋊#95C23semidirect
272. C23×D11C2×D4semidirect
319. C2×C22⋊D11C2×D4semidirect
350. C2×D44C2×D4semidirect
360. C2×C4×D11C2×D4semidirect
397. #2405D11semidirect
490. C22×D11#120semidirect
561. C2×#123C2×D11semidirect
580. C22×C22⋊C4C2×D11semidirect
584. #394C2×D11semidirect
597. #386C2×D11semidirect
600. #385C2×D11semidirect
609. #379C2×D11semidirect
610. #379C2×D11semidirect
629. C22×C11#534semidirect
669. C2×D11#534semidirect
748. C23×C4C22×D11semidirect
749. C23×C4C22×D11semidirect
766. C2×C4⋊C4C22×D11semidirect
791. C2×C22⋊C4C22×D11semidirect
792. C2×C22⋊C4C22×D11semidirect
793. C2×C22⋊C4C22×D11semidirect
794. C2×C22⋊C4C22×D11semidirect
795. C2×C22⋊C4C22×D11semidirect
799. #95C22×D11semidirect
989. C11#34980semidirect
1183. C22#10623184semidirect

Maximal subgroups

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

subgroupindex
C23×D4×D112
C2×#106231842
C22×#669352
#130769112
#130768942
#130743292
#130719922
#130719882
#130719852
#130719432
#130719402
#130719292
#130719282
#130719262
#130711902
D11×#3792
C11×#24052
#3498011