Finite Group Databasebeta

← #14926302

Subgroups — #14926302

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×#10623120C212yesmaximal, complemented
3C22×#66990C211yesmaximal, characteristic, complemented
4#13076907C212yesmaximal, complemented
5#13076892C212yesmaximal, complemented
6#13074327C214yesmaximal, complemented
7#13071993C212yesmaximal, complemented
8#13071986C212yesmaximal, complemented
9#13071983C214yesmaximal, complemented
10#13071944C211yesmaximal, characteristic, complemented
11#13071942C212yesmaximal, complemented
12#13071939C211yesmaximal, characteristic, complemented
13#13071927C212yesmaximal, complemented
14#13071926C211yesmaximal, characteristic, complemented
15#13071190C212yesmaximal, complemented
16D11×#379C211yesmaximal, characteristic, complemented
17C11×#2403C211yesmaximal, characteristic, complemented
18C25×D11C2211yescharacteristic
19C25×D11C2211yescharacteristic, complemented
20C23×D4×C11C2211yescharacteristic
21C23×D4×C11C2211yescharacteristic, complemented
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic, complemented
24C23×C22⋊D11C2211yescharacteristic, complemented
25C23×C22⋊D11C2211yescharacteristic, complemented
26C22×D4×D11—28no—
27C22×D4×D11—216no—
28C22×D4×D11C2212yes—
29C22×D4×D11C2212yes—
30C22×D4×D11C2212yescomplemented
31C22×D4×D11C2212yescomplemented
32C23×D44C2211yescharacteristic, complemented
33C23×C4×D11C2211yescharacteristic, complemented
34C2×C11×#120C2212yescomplemented
35C2×C11×#120C2212yescomplemented
36C2×#67006C2212yescomplemented
37C22×C22⋊Dic11C2211yescharacteristic, complemented
38C2×#66991C2214yescomplemented
39C2×#66990—28no—
40C2×#66990C2212yes—
41C2×#66990C2214yescomplemented
42C2×#66990C2212yescomplemented
43C2×#66990C2212yescomplemented
44C2×#66990C2214yescomplemented
45C2×#66990C2212yescomplemented
46C2×#66990C2212yescomplemented
47C2×#66988C2212yescomplemented
48C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
49C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
50#10623120—216no—
51C2×#66939C2212yescomplemented
52C2×#66937C2214yescomplemented
53C2×#66936C2214yescomplemented
54C2×C22⋊C4×D11C2212yescomplemented
55C2×C22⋊C4×D11C2212yescomplemented
56C2×C22⋊C4×D11C2212yescomplemented
57C11×#392C2214yescomplemented
58C11×#386C2212yescomplemented
59C11×#386C2212yescomplemented
60C11×#379C2211yescharacteristic, complemented
61#10622860C2211yescharacteristic, complemented
62#10622860C2212yescomplemented
63#10622836C2214yescomplemented
64#10622836C2214yescomplemented
65#10622835C2214yescomplemented
66#10622833C2212yescomplemented
67#10622833C2212yescomplemented
68#10622826C2212yescomplemented
69#10622823C2212yescomplemented
70#10622574C2214yescomplemented
71#10622574C2214yescomplemented
72#10622573C2214yescomplemented
73#10622571C2212yescomplemented
74#10622569C2214yescomplemented
75#10622569C2214yescomplemented
76#10622568C2212yescomplemented
77#10622568C2212yescomplemented
78#10622568C2214yescomplemented
79#10622568C2214yescomplemented
80#10622568C2212yescomplemented
81#10622568C2212yescomplemented
82#10622563C2212yescomplemented
83#10622285C2214yescomplemented
84#10622281C2214yescomplemented
85#10622278C2214yescomplemented
86#10622277C2214yescomplemented
87C25×C11C2311yescharacteristic
88C25×C11C2311yescharacteristic
89C25×C11C2311yescharacteristic, complemented
90C24×D11—28no—
91C24×D11—24no—
92C24×D11—28no—
93C24×D11—44no—
94C24×D11—44no—
95C24×D11—44no—
96C24×D11—44no—
97C24×D11D418yescomplemented
98C24×D11C2311yescharacteristic
99C24×D11C2311yescharacteristic
100C24×D11C2312yes—
101C24×D11C2311yescharacteristic
102C24×D11C2311yescharacteristic
103C24×D11C2311yescharacteristic
104C24×D11C2311yescharacteristic
105C24×D11C2312yes—
106C24×D11C2311yescharacteristic
107C22×D4×C11—24no—
108C22×D4×C11—28no—
109C22×D4×C11—24no—
110C22×D4×C11—44no—
111C22×D4×C11C2312yes—
112C22×D4×C11C2312yes—
113C22×D4×C11C2312yes—
114C22×D4×C11C2314yescomplemented
115C22×D4×C11C2312yescomplemented
116C23×C4×C11C2311yescharacteristic
117C23×C4×C11C2311yescharacteristic, complemented
118C22×C22⋊D11—24no—
119C22×C22⋊D11—24no—
120C22×C22⋊D11—28no—
121C22×C22⋊D11—28no—
122C22×C22⋊D11—24no—
123C22×C22⋊D11—24no—
124C22×C22⋊D11—28no—
125C22×C22⋊D11—44no—
126C22×C22⋊D11C2312yes—
127C22×C22⋊D11C2312yes—
128C22×C22⋊D11C2312yes—
129C22×C22⋊D11C2312yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yescomplemented
133C22×C22⋊D11C2314yescomplemented
134C22×C22⋊D11C2312yescomplemented
135C23×Dic11C2311yescharacteristic
136C23×Dic11C2311yescharacteristic, complemented
137C23×Dic11C2311yescharacteristic, complemented
138C2×D4×D11—2128no—
139C2×D4×D11—28no—
140C2×D4×D11—28no—
141C2×D4×D11—28no—
142C2×D4×D11—28no—
143C2×D4×D11—28no—
144C2×D4×D11—28no—
145C2×D4×D11—28no—
146C2×D4×D11—28no—
147C2×D4×D11—28no—
148C2×D4×D11—28no—
149C2×D4×D11—28no—
150C2×D4×D11D4116yescomplemented
151C22×D44—24no—
152C22×D44—28no—
153C22×D44C2312yes—
154C22×D44C2312yes—
155C22×C4×D11—24no—
156C22×C4×D11—28no—
157C22×C4×D11C2312yes—
158C22×C4×D11C2312yes—
159C22×C4×D11C2314yescomplemented
160C11×#120—28no—
161C11×#120—44no—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yescomplemented
164C2×C11×C22⋊C4C2314yescomplemented
165C2×C11×C22⋊C4C2312yescomplemented
166C2×C11×C22⋊C4C2314yescomplemented
167#67006—28no—
168C2×C22⋊Dic11—24no—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yescomplemented
172C2×C22⋊Dic11C2314yescomplemented
173C2×C22⋊Dic11C2314yescomplemented
174C2×C22⋊Dic11C2312yescomplemented
175C2×C22⋊Dic11C2312yescomplemented
176C2×C22⋊Dic11C2314yescomplemented
177#66991—216no—
178#66990—28no—
179#66990—28no—
180#66990—28no—
181#66990—28no—
182#66990—216no—
183#66990—48no—
184#66990—44no—
185#66988—28no—
186C2×(C2×D11)⋊C4—24no—
187C2×(C2×D11)⋊C4—24no—
188C2×(C2×D11)⋊C4C2314yes—
189C2×(C2×D11)⋊C4C2314yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2314yescomplemented
193C2×(C2×D11)⋊C4C2312yescomplemented
194C2×(C2×D11)⋊C4C2312yescomplemented
195C2×(C2×D11)⋊C4C2314yescomplemented
196C2×(C2×D11)⋊C4C2314yescomplemented
197C2×(C2×D11)⋊C4C2314yescomplemented
198C2×C4⋊Dic11C2314yescomplemented
199C2×Dic11⋊C4C2314yescomplemented
200#66939—28no—
201#66937—216no—
202#66936—216no—
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—22no—
216C24×C11—24no—
217C24×C11—24no—
218C24×C11—42no—
219C24×C11—42no—
220C24×C11—42no—
221C24×C11—42no—
222C24×C11C2×D414yes—
223C24×C11C2412yes—
224C24×C11C2411yescharacteristic
225C24×C11C2412yes—
226C24×C11C2411yescharacteristic
227C24×C11C2411yescharacteristic
228C23×D11—24no—
229C23×D11—24no—
230C23×D11—24no—
231C23×D11—232no—
232C23×D11—22no—
233C23×D11—24no—
234C23×D11—24no—
235C23×D11—24no—
236C23×D11—232no—
237C23×D11—24no—
238C23×D11—24no—
239C23×D11—24no—
240C23×D11—24no—
241C23×D11—24no—
242C23×D11—24no—
243C23×D11—24no—
244C23×D11—24no—
245C23×D11—24no—
246C23×D11—24no—
247C23×D11—24no—
248C23×D11—28no—
249C23×D11—416no—
250C23×D11—416no—
251C23×D11—42no—
252C23×D11—42no—
253C23×D11—42no—
254C23×D11—42no—
255C23×D11—42no—
256C23×D11—42no—
257C23×D11—44no—
258C23×D11—44no—
259C23×D11—44no—
260C23×D11—42no—
261C23×D11—42no—
262C23×D11—464no—
263C23×D11—464no—
264C23×D11—416no—
265C23×D11—416no—
266C23×D11C2×D414yes—
267C23×D11C2×D414yes—
268C23×D11C2×D414yes—
269C23×D11C2×D414yes—
270C23×D11C2×D414yes—
271C23×D11C2×D418yes—
272C23×D11C2×D414yes—
273C23×D11C2×D418yescomplemented
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×C11—24no—
286C2×D4×C11—24no—
287C2×D4×C11—24no—
288C2×D4×C11—28no—
289C2×D4×C11—24no—
290C2×D4×C11—42no—
291C2×D4×C11—42no—
292C2×D4×C11—44no—
293C2×D4×C11—44no—
294C2×D4×C11—416no—
295C2×D4×C11C2×D418yes—
296C22×C4×C11—22no—
297C22×C4×C11—24no—
298C22×C4×C11—22no—
299C22×C4×C11—42no—
300C22×C4×C11C2412yes—
301C22×C4×C11C2414yes—
302C22×C4×C11C2412yes—
303C2×C22⋊D11—232no—
304C2×C22⋊D11—232no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—24no—
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—24no—
314C2×C22⋊D11—24no—
315C2×C22⋊D11—28no—
316C2×C22⋊D11—28no—
317C2×C22⋊D11—24no—
318C2×C22⋊D11—24no—
319C2×C22⋊D11—24no—
320C2×C22⋊D11—24no—
321C2×C22⋊D11—28no—
322C2×C22⋊D11—28no—
323C2×C22⋊D11—44no—
324C2×C22⋊D11—44no—
325C2×C22⋊D11—44no—
326C2×C22⋊D11—416no—
327C2×C22⋊D11—416no—
328C2×C22⋊D11C2×D418yes—
329C2×C22⋊D11C2×D418yescomplemented
330C22×Dic11—24no—
331C22×Dic11—22no—
332C22×Dic11—24no—
333C22×Dic11—22no—
334C22×Dic11—22no—
335C22×Dic11—42no—
336C22×Dic11C2412yes—
337C22×Dic11C2414yes—
338C22×Dic11C2412yes—
339C22×Dic11C2412yes—
340D4×D11—264no—
341D4×D11—264no—
342D4×D11—264no—
343D4×D11—264no—
344C2×D44—232no—
345C2×D44—24no—
346C2×D44—24no—
347C2×D44—24no—
348C2×D44—24no—
349C2×D44—24no—
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×C22⋊C4—24no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—28no—
364C11×C22⋊C4—42no—
365C11×C22⋊C4—44no—
366C22⋊Dic11—28no—
367C22⋊Dic11—24no—
368C22⋊Dic11—28no—
369C22⋊Dic11—24no—
370C22⋊Dic11—24no—
371C22⋊Dic11—24no—
372C22⋊Dic11—42no—
373C22⋊Dic11—44no—
374(C2×D11)⋊C4—28no—
375(C2×D11)⋊C4—28no—
376(C2×D11)⋊C4—24no—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—24no—
380(C2×D11)⋊C4—28no—
381(C2×D11)⋊C4—44no—
382(C2×D11)⋊C4—44no—
383(C2×D11)⋊C4—44no—
384C4⋊Dic11—28no—
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#2405—111no—
398#2403—111no—
399#2403—112no—
400#2403D1111yescharacteristic, complemented
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—24no—
418C23×C11—22no—
419C23×C11—24no—
420C23×C11—22no—
421C23×C11—22no—
422C23×C11—44no—
423C23×C11—416no—
424C23×C11—416no—
425C23×C11—44no—
426C23×C11—44no—
427C23×C11—44no—
428C23×C11—44no—
429C23×C11—44no—
430C23×C11—88no—
431C23×C11C22×D412yes—
432C23×C11C22×D414yes—
433C23×C11C22×D414yes—
434C23×C11C22×D412yes—
435C23×C11C22×D412yes—
436C23×C11H(5,𝔽2)14yes—
437C23×C11C2511yescharacteristic
438C22×D11—232no—
439C22×D11—28no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—22no—
444C22×D11—22no—
445C22×D11—22no—
446C22×D11—28no—
447C22×D11—28no—
448C22×D11—28no—
449C22×D11—216no—
450C22×D11—28no—
451C22×D11—28no—
452C22×D11—22no—
453C22×D11—22no—
454C22×D11—22no—
455C22×D11—22no—
456C22×D11—24no—
457C22×D11—24no—
458C22×D11—22no—
459C22×D11—28no—
460C22×D11—28no—
461C22×D11—28no—
462C22×D11—216no—
463C22×D11—28no—
464C22×D11—28no—
465C22×D11—44no—
466C22×D11—44no—
467C22×D11—44no—
468C22×D11—44no—
469C22×D11—44no—
470C22×D11—44no—
471C22×D11—44no—
472C22×D11—416no—
473C22×D11—416no—
474C22×D11—416no—
475C22×D11—416no—
476C22×D11—416no—
477C22×D11—416no—
478C22×D11—416no—
479C22×D11—416no—
480C22×D11—4128no—
481C22×D11—4128no—
482C22×D11—48no—
483C22×D11—48no—
484C22×D11—48no—
485C22×D11—416no—
486C22×D11—416no—
487C22×D11—44no—
488C22×D11—44no—
489C22×D11—48no—
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—
501D4×C11—48no—
502D4×C11—48no—
503D4×C11—88no—
504C2×C4×C11—28no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—24no—
508C2×C4×C11—22no—
509C2×C4×C11—24no—
510C2×C4×C11—22no—
511C2×C4×C11—24no—
512C2×C4×C11—22no—
513C2×C4×C11—44no—
514C2×C4×C11C22×D414yes—
515C22⋊D11—216no—
516C22⋊D11—216no—
517C22⋊D11—216no—
518C22⋊D11—216no—
519C22⋊D11—48no—
520C22⋊D11—48no—
521C22⋊D11—48no—
522C22⋊D11—48no—
523C22⋊D11—88no—
524C2×Dic11—28no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—24no—
528C2×Dic11—24no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—24no—
532C2×Dic11—24no—
533C2×Dic11—24no—
534C2×Dic11—44no—
535C2×Dic11—44no—
536C2×Dic11C22×D414yes—
537D44—216no—
538D44—216no—
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—111no—
549C23×D4—112no—
550C23×D4—112no—
551C23×D4—112no—
552C23×D4—111no—
553C23×D4—2216no—
554C23×D4—228no—
555C23×D4C2×D1111yescharacteristic
556C23×D4C2×D1111yescharacteristic, complemented
557C24×C4—111no—
558#534—2216no—
559C2×#123—112no—
560C2×#123—114no—
561C2×#123—112no—
562C2×#121—114no—
563C2×#121—114no—
564C2×#120—112no—
565C2×#120—112no—
566C2×#120—112no—
567C2×#120—114no—
568C2×#120—112no—
569C2×#120—112no—
570C2×#120—112no—
571C2×#120—114no—
572C2×#120—228no—
573C2×#120C2×D1112yescomplemented
574C2×#120C2×D1112yescomplemented
575C22×C22⋊C4—111no—
576C22×C22⋊C4—111no—
577C22×C22⋊C4—111no—
578C22×C22⋊C4—112no—
579C22×C22⋊C4—112no—
580C22×C22⋊C4—112no—
581#394—114no—
582#394—114no—
583#394—114no—
584#394—114no—
585#392—114no—
586#392—114no—
587#392—114no—
588#392C2×D1114yescomplemented
589#386—112no—
590#386—112no—
591#386—112no—
592#386—112no—
593#386—114no—
594#386—114no—
595#386—114no—
596#386C2×D1112yescomplemented
597#386C2×D1112yescomplemented
598#385—112no—
599#385—112no—
600#385—114no—
601#381—114no—
602#379—112no—
603#379—111no—
604#379—112no—
605#379—112no—
606#379—114no—
607#379—114no—
608#379—112no—
609#379—112no—
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×C11—42no—
629C22×C11—42no—
630C22×C11—42no—
631C22×C11—44no—
632C22×C11—44no—
633C22×C11—88no—
634C22×C11C2×#12014yes—
635C22×C11#53414yescomplemented
636C22×C11C23×D411yescharacteristic
637C22×C11C23×D412yes—
638C22×C11C2×H(5,𝔽2)12yes—
639C22×C11C2×H(5,𝔽2)12yes—
640C2×D11—232no—
641C2×D11—22no—
642C2×D11—22no—
643C2×D11—22no—
644C2×D11—22no—
645C2×D11—22no—
646C2×D11—22no—
647C2×D11—28no—
648C2×D11—28no—
649C2×D11—28no—
650C2×D11—24no—
651C2×D11—22no—
652C2×D11—22no—
653C2×D11—22no—
654C2×D11—28no—
655C2×D11—416no—
656C2×D11—416no—
657C2×D11—416no—
658C2×D11—416no—
659C2×D11—416no—
660C2×D11—432no—
661C2×D11—432no—
662C2×D11—416no—
663C2×D11—42no—
664C2×D11—42no—
665C2×D11—44no—
666C2×D11—44no—
667C2×D11C2×#12014yes—
668C2×D11C2×#12014yes—
669C2×D11#53414yescomplemented
670C4×C11—24no—
671C4×C11—42no—
672C4×C11—44no—
673Dic11—24no—
674Dic11—42no—
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—228no—
688C25—224no—
689C25—228no—
690C25—444no—
691C25—444no—
692C25—444no—
693C25—444no—
694C25C22×D1111yescharacteristic
695C25C22×D1111yescharacteristic
696C25C22×D1111yescharacteristic, complemented
697C22×D4—24no—
698C22×D4—28no—
699C22×D4—24no—
700C22×D4—44no—
701C22×D4—112no—
702C22×D4—112no—
703C22×D4—1116no—
704C22×D4—112no—
705C22×D4—112no—
706C22×D4—112no—
707C22×D4—112no—
708C22×D4—112no—
709C22×D4—114no—
710C22×D4—112no—
711C22×D4—112no—
712C22×D4—112no—
713C22×D4—228no—
714C22×D4—224no—
715C22×D4—228no—
716C22×D4—228no—
717C22×D4—228no—
718C22×D4—228no—
719C22×D4—228no—
720C22×D4—228no—
721C22×D4—228no—
722C22×D4—228no—
723C22×D4—228no—
724C22×D4—228no—
725C22×D4—22128no—
726C22×D4—228no—
727C22×D4—228no—
728C22×D4—224no—
729C22×D4—224no—
730C22×D4—228no—
731C22×D4—224no—
732C22×D4—224no—
733C22×D4—228no—
734C22×D4—444no—
735C22×D4C22×D1112yes—
736C22×D4C22×D1112yes—
737C22×D4C22×D1112yes—
738C22×D4C22×D1114yescomplemented
739C22×D4C22×D1112yescomplemented
740C23×C4—112no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—112no—
745C23×C4—114no—
746C23×C4—228no—
747C23×C4—224no—
748C23×C4C22×D1111yescharacteristic
749C23×C4C22×D1111yescharacteristic, complemented
750#123—2216no—
751#123—228no—
752#123—228no—
753#121—2216no—
754#121—2216no—
755#120—28no—
756#120—44no—
757#120—228no—
758#120—228no—
759#120—228no—
760#120—228no—
761#120—2216no—
762#120—228no—
763#120—444no—
764#120—448no—
765C2×C4⋊C4—114no—
766C2×C4⋊C4—114no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—114no—
772C2×C22⋊C4—114no—
773C2×C22⋊C4—112no—
774C2×C22⋊C4—112no—
775C2×C22⋊C4—112no—
776C2×C22⋊C4—112no—
777C2×C22⋊C4—114no—
778C2×C22⋊C4—114no—
779C2×C22⋊C4—114no—
780C2×C22⋊C4—112no—
781C2×C22⋊C4—114no—
782C2×C22⋊C4—114no—
783C2×C22⋊C4—114no—
784C2×C22⋊C4—114no—
785C2×C22⋊C4—228no—
786C2×C22⋊C4—224no—
787C2×C22⋊C4—224no—
788C2×C22⋊C4—224no—
789C2×C22⋊C4—444no—
790C2×C22⋊C4—444no—
791C2×C22⋊C4C22×D1112yes—
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×C11—82no—
805C2×C11C22×#12011yescharacteristic
806C2×C11C2×#53411yescharacteristic
807C2×C11C2×#53411yescharacteristic
808C2×C11#348414yes—
809D11—24no—
810D11—24no—
811D11—24no—
812D11—42no—
813D11—44no—
814C24—24no—
815C24—24no—
816C24—22no—
817C24—24no—
818C24—22no—
819C24—24no—
820C24—24no—
821C24—42no—
822C24—42no—
823C24—42no—
824C24—42no—
825C24—111no—
826C24—111no—
827C24—111no—
828C24—118no—
829C24—114no—
830C24—114no—
831C24—112no—
832C24—111no—
833C24—114no—
834C24—114no—
835C24—114no—
836C24—118no—
837C24—114no—
838C24—224no—
839C24—224no—
840C24—224no—
841C24—224no—
842C24—224no—
843C24—2232no—
844C24—224no—
845C24—224no—
846C24—224no—
847C24—224no—
848C24—224no—
849C24—224no—
850C24—224no—
851C24—228no—
852C24—2232no—
853C24—224no—
854C24—224no—
855C24—222no—
856C24—224no—
857C24—224no—
858C24—224no—
859C24—442no—
860C24—442no—
861C24—442no—
862C24—442no—
863C24—442no—
864C24—4416no—
865C24—444no—
866C24—444no—
867C24—442no—
868C24—442no—
869C24—442no—
870C24—444no—
871C24—4416no—
872C24—4464no—
873C24—4464no—
874C24—4416no—
875C24—4416no—
876C24D4×D1114yes—
877C24C23×D1112yes—
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—24no—
889C2×D4—24no—
890C2×D4—24no—
891C2×D4—28no—
892C2×D4—24no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—416no—
898C2×D4—118no—
899C2×D4—118no—
900C2×D4—118no—
901C2×D4—224no—
902C2×D4—224no—
903C2×D4—224no—
904C2×D4—224no—
905C2×D4—2232no—
906C2×D4—224no—
907C2×D4—224no—
908C2×D4—2264no—
909C2×D4—2264no—
910C2×D4—2264no—
911C2×D4—2264no—
912C2×D4—224no—
913C2×D4—224no—
914C2×D4—224no—
915C2×D4—224no—
916C2×D4—2232no—
917C2×D4—2232no—
918C2×D4—224no—
919C2×D4—224no—
920C2×D4—224no—
921C2×D4—224no—
922C2×D4—224no—
923C2×D4—224no—
924C2×D4—224no—
925C2×D4—224no—
926C2×D4—228no—
927C2×D4—228no—
928C2×D4—228no—
929C2×D4—228no—
930C2×D4—224no—
931C2×D4—444no—
932C2×D4—444no—
933C2×D4—444no—
934C2×D4—4416no—
935C2×D4—4416no—
936C2×D4D4×D1118yes—
937C22×C4—22no—
938C22×C4—24no—
939C22×C4—22no—
940C22×C4—42no—
941C22×C4—112no—
942C22×C4—118no—
943C22×C4—112no—
944C22×C4—114no—
945C22×C4—112no—
946C22×C4—224no—
947C22×C4—224no—
948C22×C4—224no—
949C22×C4—224no—
950C22×C4—2232no—
951C22×C4—228no—
952C22×C4—224no—
953C22×C4—222no—
954C22×C4—224no—
955C22×C4—222no—
956C22×C4—222no—
957C22×C4—224no—
958C22×C4—444no—
959C22×C4—444no—
960C22×C4—442no—
961C22×C4C23×D1112yes—
962C22×C4C23×D1114yes—
963C22×C4C23×D1112yes—
964C4⋊C4—228no—
965C4⋊C4—228no—
966C22⋊C4—24no—
967C22⋊C4—24no—
968C22⋊C4—28no—
969C22⋊C4—42no—
970C22⋊C4—44no—
971C22⋊C4—224no—
972C22⋊C4—224no—
973C22⋊C4—224no—
974C22⋊C4—224no—
975C22⋊C4—228no—
976C22⋊C4—228no—
977C22⋊C4—228no—
978C22⋊C4—228no—
979C22⋊C4—224no—
980C22⋊C4—224no—
981C22⋊C4—224no—
982C22⋊C4—228no—
983C22⋊C4—224no—
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—24no—
1005C23—22no—
1006C23—22no—
1007C23—22no—
1008C23—24no—
1009C23—44no—
1010C23—416no—
1011C23—416no—
1012C23—44no—
1013C23—44no—
1014C23—44no—
1015C23—44no—
1016C23—44no—
1017C23—88no—
1018C23—114no—
1019C23—112no—
1020C23—112no—
1021C23—112no—
1022C23—114no—
1023C23—114no—
1024C23—1116no—
1025C23—114no—
1026C23—112no—
1027C23—228no—
1028C23—228no—
1029C23—228no—
1030C23—228no—
1031C23—2216no—
1032C23—228no—
1033C23—228no—
1034C23—228no—
1035C23—2232no—
1036C23—228no—
1037C23—2216no—
1038C23—228no—
1039C23—222no—
1040C23—222no—
1041C23—222no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—228no—
1046C23—228no—
1047C23—222no—
1048C23—222no—
1049C23—222no—
1050C23—222no—
1051C23—224no—
1052C23—224no—
1053C23—222no—
1054C23—444no—
1055C23—444no—
1056C23—444no—
1057C23—444no—
1058C23—4416no—
1059C23—444no—
1060C23—444no—
1061C23—444no—
1062C23—4416no—
1063C23—4416no—
1064C23—4416no—
1065C23—4416no—
1066C23—4416no—
1067C23—444no—
1068C23—448no—
1069C23—4416no—
1070C23—4416no—
1071C23—44128no—
1072C23—44128no—
1073C23—448no—
1074C23—448no—
1075C23—448no—
1076C23—4416no—
1077C23—4416no—
1078C23—444no—
1079C23C2×D4×D1112yes—
1080C23C2×D4×D1114yes—
1081C23C2×D4×D1114yes—
1082C23C2×D4×D1112yes—
1083C23C2×D4×D1112yes—
1084C23#6703714yes—
1085C23C24×D1111yescharacteristic
1086D4—216no—
1087D4—216no—
1088D4—48no—
1089D4—48no—
1090D4—88no—
1091D4—2216no—
1092D4—2216no—
1093D4—2216no—
1094D4—2216no—
1095D4—2216no—
1096D4—2216no—
1097D4—448no—
1098D4—448no—
1099D4—448no—
1100D4—448no—
1101D4—888no—
1102C2×C4—28no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—24no—
1106C2×C4—22no—
1107C2×C4—24no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—44no—
1112C2×C4—114no—
1113C2×C4—2216no—
1114C2×C4—2216no—
1115C2×C4—228no—
1116C2×C4—222no—
1117C2×C4—222no—
1118C2×C4—224no—
1119C2×C4—222no—
1120C2×C4—222no—
1121C2×C4—224no—
1122C2×C4—224no—
1123C2×C4—224no—
1124C2×C4—224no—
1125C2×C4—444no—
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—42no—
1147C22—42no—
1148C22—44no—
1149C22—44no—
1150C22—42no—
1151C22—88no—
1152C22—114no—
1153C22—114no—
1154C22—114no—
1155C22—2232no—
1156C22—222no—
1157C22—222no—
1158C22—222no—
1159C22—222no—
1160C22—222no—
1161C22—228no—
1162C22—228no—
1163C22—228no—
1164C22—222no—
1165C22—222no—
1166C22—222no—
1167C22—228no—
1168C22—224no—
1169C22—222no—
1170C22—4416no—
1171C22—4416no—
1172C22—4416no—
1173C22—4416no—
1174C22—4416no—
1175C22—4416no—
1176C22—4432no—
1177C22—4432no—
1178C22—442no—
1179C22—442no—
1180C22—444no—
1181C22—444no—
1182C22D11×#12014yes—
1183C22#1062312014yescomplemented
1184C22C22×D4×D1111yescharacteristic
1185C22C22×D4×D1112yes—
1186C22C2×#6703712yes—
1187C22D11×H(5,𝔽2)12yes—
1188C4—24no—
1189C4—42no—
1190C4—44no—
1191C4—224no—
1192C4—442no—
1193C4—444no—
1194C4—442no—
1195C2—24no—
1196C2—24no—
1197C2—42no—
1198C2—44no—
1199C2—82no—
1200C2—224no—
1201C2—224no—
1202C2—224no—
1203C2—442no—
1204C2—444no—
1205C2C2×D11×#12011yescharacteristic
1206C2D11×#53411yescharacteristic
1207C2C2×#1062312011yescharacteristic
1208C2#1308224414yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2403C2
hypercenter#2403D11
hypocenterC11#34980
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2403

Complements

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

NH ≅ G/Ntype
1. C23×D4×D11C2semidirect
2. C2×#10623120C2semidirect
3. C22×#66990C2semidirect
4. #13076907C2semidirect
5. #13076892C2semidirect
6. #13074327C2semidirect
7. #13071993C2semidirect
8. #13071986C2semidirect
9. #13071983C2semidirect
10. #13071944C2semidirect
11. #13071942C2semidirect
12. #13071939C2semidirect
13. #13071927C2semidirect
14. #13071926C2semidirect
15. #13071190C2semidirect
16. D11×#379C2semidirect
17. C11×#2403C2semidirect
19. C25×D11C22semidirect
21. C23×D4×C11C22semidirect
23. C23×C22⋊D11C22semidirect
24. C23×C22⋊D11C22semidirect
25. C23×C22⋊D11C22semidirect
30. C22×D4×D11C22semidirect
31. C22×D4×D11C22semidirect
32. C23×D44C22semidirect
33. C23×C4×D11C22semidirect
34. C2×C11×#120C22semidirect
35. C2×C11×#120C22semidirect
36. C2×#67006C22semidirect
37. C22×C22⋊Dic11C22semidirect
38. C2×#66991C22semidirect
41. C2×#66990C22semidirect
42. C2×#66990C22semidirect
43. C2×#66990C22semidirect
44. C2×#66990C22semidirect
45. C2×#66990C22semidirect
46. C2×#66990C22semidirect
47. C2×#66988C22semidirect
48. C22×(C2×D11)⋊C4C22semidirect
49. C22×(C2×D11)⋊C4C22semidirect
51. C2×#66939C22semidirect
52. C2×#66937C22semidirect
53. C2×#66936C22semidirect
54. C2×C22⋊C4×D11C22semidirect
55. C2×C22⋊C4×D11C22semidirect
56. C2×C22⋊C4×D11C22semidirect
57. C11×#392C22semidirect
58. C11×#386C22semidirect
59. C11×#386C22semidirect
60. C11×#379C22semidirect
61. #10622860C22semidirect
62. #10622860C22semidirect
63. #10622836C22semidirect
64. #10622836C22semidirect
65. #10622835C22semidirect
66. #10622833C22semidirect
67. #10622833C22semidirect
68. #10622826C22semidirect
69. #10622823C22semidirect
70. #10622574C22semidirect
71. #10622574C22semidirect
72. #10622573C22semidirect
73. #10622571C22semidirect
74. #10622569C22semidirect
75. #10622569C22semidirect
76. #10622568C22semidirect
77. #10622568C22semidirect
78. #10622568C22semidirect
79. #10622568C22semidirect
80. #10622568C22semidirect
81. #10622568C22semidirect
82. #10622563C22semidirect
83. #10622285C22semidirect
84. #10622281C22semidirect
85. #10622278C22semidirect
86. #10622277C22semidirect
89. C25×C11C23semidirect
97. C24×D11D4semidirect
114. C22×D4×C11C23semidirect
115. C22×D4×C11C23semidirect
117. C23×C4×C11C23semidirect
132. C22×C22⋊D11C23semidirect
133. C22×C22⋊D11C23semidirect
134. C22×C22⋊D11C23semidirect
136. C23×Dic11C23semidirect
137. C23×Dic11C23semidirect
150. C2×D4×D11D4semidirect
159. C22×C4×D11C23semidirect
163. C2×C11×C22⋊C4C23semidirect
164. C2×C11×C22⋊C4C23semidirect
165. C2×C11×C22⋊C4C23semidirect
166. C2×C11×C22⋊C4C23semidirect
171. C2×C22⋊Dic11C23semidirect
172. C2×C22⋊Dic11C23semidirect
173. C2×C22⋊Dic11C23semidirect
174. C2×C22⋊Dic11C23semidirect
175. C2×C22⋊Dic11C23semidirect
176. C2×C22⋊Dic11C23semidirect
192. C2×(C2×D11)⋊C4C23semidirect
193. C2×(C2×D11)⋊C4C23semidirect
194. C2×(C2×D11)⋊C4C23semidirect
195. C2×(C2×D11)⋊C4C23semidirect
196. C2×(C2×D11)⋊C4C23semidirect
197. C2×(C2×D11)⋊C4C23semidirect
198. C2×C4⋊Dic11C23semidirect
199. C2×Dic11⋊C4C23semidirect
206. C11×#95C23semidirect
207. C11⋊#95C23semidirect
208. C11⋊#95C23semidirect
209. C11⋊#95C23semidirect
273. C23×D11C2×D4semidirect
329. C2×C22⋊D11C2×D4semidirect
350. C2×D44C2×D4semidirect
360. C2×C4×D11C2×D4semidirect
400. #2403D11semidirect
490. C22×D11#120semidirect
556. C23×D4C2×D11semidirect
573. C2×#120C2×D11semidirect
574. C2×#120C2×D11semidirect
588. #392C2×D11semidirect
596. #386C2×D11semidirect
597. #386C2×D11semidirect
610. #379C2×D11semidirect
635. C22×C11#534semidirect
669. C2×D11#534semidirect
696. C25C22×D11semidirect
738. C22×D4C22×D11semidirect
739. C22×D4C22×D11semidirect
749. C23×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#10623120semidirect

Maximal subgroups

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

subgroupindex
C23×D4×D112
C2×#106231202
C22×#669902
#130769072
#130768922
#130743272
#130719932
#130719862
#130719832
#130719442
#130719422
#130719392
#130719272
#130719262
#130711902
D11×#3792
C11×#24032
#3498011