Finite Group Databasebeta

← #14915025

Subgroups — #14915025

Order 2816.

3578 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623136C211yesmaximal, characteristic
2C2×#10623076C212yesmaximal, complemented
3#13071613C212yesmaximal, complemented
4#13071609C212yesmaximal, complemented
5#13071607C212yesmaximal, complemented
6#13071603C212yesmaximal, complemented
7#13071598C212yesmaximal, complemented
8#13071597C212yesmaximal, complemented
9#13071594C212yesmaximal, complemented
10#13071593C212yesmaximal, complemented
11#13071321C211yesmaximal, characteristic, complemented
12#13071316C211yesmaximal, characteristic, complemented
13#13071314C212yesmaximal, complemented
14#13071229C211yesmaximal, characteristic, complemented
15C4×#66983C211yesmaximal, characteristic, complemented
16#13071126C212yesmaximal, complemented
17D11×#386C212yesmaximal, complemented
18C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
19C4×C11×#121C211yesmaximal, characteristic, complemented
20C22×D4×D11C2212yes—
21C23×C4×D11C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×C4×D4×C11C2212yescomplemented
24C2×C4×D4×C11C2211yescharacteristic, complemented
25C22×C42×C11C2211yescharacteristic, complemented
26C2×#66992C2212yes—
27C2×#66990C2212yes—
28C2×D4×Dic11C2212yescomplemented
29C2×#66983C2211yescharacteristic
30C2×C4×C22⋊D11C2212yes—
31C2×C4×C22⋊D11C2212yescomplemented
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2212yescomplemented
35C22×C4×Dic11C2211yescharacteristic, complemented
36#10623136C4116yescomplemented
37#10623076—216no—
38C2×#66947C2212yes—
39C2×#66946C2212yes—
40C2×#66945C2212yescomplemented
41C2×#66936C2212yes—
42C2×#66935C2212yes—
43C2×(C22⋊D11)⋊C4C2212yes—
44C2×(C22⋊D11)⋊C4C2212yescomplemented
45C2×(C22⋊D11)⋊C4C2212yescomplemented
46C2×C22⋊C4×D11C2212yes—
47C2×C22⋊C4×D11C2212yescomplemented
48C2×C22⋊C4×D11C2212yescomplemented
49C2×C22⋊C4×D11C2212yescomplemented
50C2×C4×D44C2212yes—
51C2×C4×D44C2211yescharacteristic, complemented
52C2×#66925C2212yescomplemented
53C11×#390C2211yescharacteristic, complemented
54C11×#389C2211yescharacteristic, complemented
55C11×#388C2212yescomplemented
56C11×#386C2212yescomplemented
57C11×#380C2211yescharacteristic, complemented
58C4×C11×C4⋊C4C2211yescharacteristic, complemented
59C4×C11×C22⋊C4C2212yescomplemented
60#10622833C2212yescomplemented
61#10622833C2212yescomplemented
62#10622826C2212yescomplemented
63#10622826C2212yescomplemented
64#10622825C2211yescharacteristic, complemented
65#10622823C2212yescomplemented
66C2×C11⋊#95C2211yescharacteristic, complemented
67C2×C11⋊#95C2211yescharacteristic, complemented
68#10622603C2212yescomplemented
69#10622602C2212yescomplemented
70#10622602C2212yescomplemented
71#10622602C2212yescomplemented
72#10622602C2212yescomplemented
73#10622594C2212yescomplemented
74#10622591C2212yescomplemented
75#10622571C2212yescomplemented
76#10622570C2212yescomplemented
77#10622569C2212yes—
78#10622569C2212yes—
79#10622569C2212yescomplemented
80#10622564C2212yescomplemented
81#10622563C2212yescomplemented
82#10622557C2212yescomplemented
83#10622557C2212yescomplemented
84#10622555C2212yescomplemented
85C22⋊C4×Dic11C2212yescomplemented
86#10622553C2212yescomplemented
87#10622553C2212yescomplemented
88#10622552C2211yescharacteristic, complemented
89C4×(C2×D11)⋊C4C2212yescomplemented
90C4×(C2×D11)⋊C4C2212yescomplemented
91C4×(C2×D11)⋊C4C2212yescomplemented
92C4×(C2×D11)⋊C4C2212yescomplemented
93C4×(C2×D11)⋊C4C2212yescomplemented
94C4×C4⋊Dic11C2211yescharacteristic, complemented
95#10622546C2212yescomplemented
96#10622541C2211yescharacteristic, complemented
97#10622283C2212yescomplemented
98#10622281C2212yescomplemented
99#10622281C2212yescomplemented
100#10622279C2212yescomplemented
101#10622278C2212yes—
102#10622278C2212yes—
103#10622278C2212yescomplemented
104D11×#95C2212yescomplemented
105D11×#95C2212yescomplemented
106#10622267C2212yescomplemented
107#10622262C2212yescomplemented
108#10622260C2212yescomplemented
109C24×D11C2312yes—
110C24×D11C2311yescharacteristic
111C22×D4×C11C2312yes—
112C22×D4×C11C2311yescharacteristic
113C23×C4×C11C2311yescharacteristic
114C23×C4×C11C2312yes—
115C23×C4×C11C2311yescharacteristic
116C23×C4×C11C2311yescharacteristic
117C22×C22⋊D11C2312yes—
118C22×C22⋊D11C2312yes—
119C22×C22⋊D11C2312yes—
120C23×Dic11C2312yes—
121C23×Dic11C2311yescharacteristic
122C23×Dic11C2311yescharacteristic
123C23×Dic11C2311yescharacteristic
124C2×D4×D11—28no—
125C2×D4×D11—28no—
126C2×D4×D11C2×C4116yescomplemented
127C22×D44C2312yes—
128C22×D44C2311yescharacteristic
129C22×C4×D11—24no—
130C22×C4×D11—42no—
131C22×C4×D11—42no—
132C22×C4×D11C2312yes—
133C22×C4×D11C2312yes—
134C22×C4×D11C2312yes—
135C22×C4×D11C2312yes—
136C22×C4×D11C2312yes—
137C22×C4×D11C2312yes—
138C22×C4×D11C2312yes—
139C11×#121C2×C418yescomplemented
140C4×D4×C11—28no—
141C4×D4×C11—42no—
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C4⋊C4C2311yescharacteristic
144C2×C11×C4⋊C4C2311yescharacteristic
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C11×C22⋊C4C2312yes—
147C2×C11×C22⋊C4C2312yes—
148C2×C11×C22⋊C4C2312yes—
149C2×C11×C22⋊C4C2312yes—
150C2×C11×C22⋊C4C2312yes—
151C2×C42×C11—42no—
152C2×C42×C11C2312yes—
153C2×C42×C11C2311yescharacteristic
154C2×C42×C11C2311yescharacteristic
155C2×C42×C11C2311yescharacteristic
156C2×C42×C11C2311yescharacteristic
157C2×C22⋊Dic11C2312yes—
158C2×C22⋊Dic11C2312yes—
159C2×C22⋊Dic11C2312yes—
160C2×C22⋊Dic11C2312yes—
161C2×C22⋊Dic11C2312yes—
162#66992C2×C4116yescomplemented
163#66990C2×C4116yescomplemented
164D4×Dic11—28no—
165#66983C2×C418yescomplemented
166C4×C22⋊D11—28no—
167C4×C22⋊D11—28no—
168C2×(C2×D11)⋊C4—28no—
169C2×(C2×D11)⋊C4C2×C418yescomplemented
170C2×(C2×D11)⋊C4D418yescomplemented
171C2×(C2×D11)⋊C4C2312yes—
172C2×(C2×D11)⋊C4C2312yes—
173C2×(C2×D11)⋊C4C2312yes—
174C2×(C2×D11)⋊C4C2312yes—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2312yes—
177C2×(C2×D11)⋊C4C2312yes—
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×C4⋊Dic11C2312yes—
186C2×C4⋊Dic11C2311yescharacteristic
187C2×C4⋊Dic11C2311yescharacteristic
188C2×C4⋊Dic11C2311yescharacteristic
189C2×Dic11⋊C4C2312yes—
190C2×Dic11⋊C4C2312yes—
191C2×Dic11⋊C4C2312yes—
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×C4×Dic11—42no—
195C2×C4×Dic11C2312yes—
196C2×C4×Dic11C2312yes—
197C2×C4×Dic11C2312yes—
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2312yes—
200#66947C2×C4116yescomplemented
201#66946—28no—
202#66945—28no—
203#66936C2×C4116yescomplemented
204#66935C2×C4116yescomplemented
205(C22⋊D11)⋊C4—28no—
206(C22⋊D11)⋊C4—28no—
207(C22⋊D11)⋊C4—44no—
208C22⋊C4×D11—28no—
209C22⋊C4×D11—28no—
210C22⋊C4×D11—44no—
211C22⋊C4×D11—44no—
212C4×D44—28no—
213C4×D44—42no—
214#66925—28no—
215C11×#95C2312yes—
216C11×#95C2312yes—
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—
231#34273—111nomaximal, Sylow
232C24×C11C2412yes—
233C24×C11C2411yescharacteristic
234C23×D11—24no—
235C23×D11—24no—
236C23×D11—41no—
237C23×D11—41no—
238C23×D11—41no—
239C23×D11—41no—
240C23×D11—42no—
241C23×D11—42no—
242C23×D11—42no—
243C23×D11—42no—
244C23×D11C22×C418yes—
245C23×D11C22×C414yes—
246C23×D11C2×D414yes—
247C23×D11#4114yes—
248C23×D11C2412yes—
249C23×D11C2412yes—
250C2×D4×C11—24no—
251C2×D4×C11—24no—
252C2×D4×C11—41no—
253C2×D4×C11—41no—
254C2×D4×C11C22×C418yes—
255C2×D4×C11C22×C414yescomplemented
256C22×C4×C11—22no—
257C22×C4×C11—22no—
258C22×C4×C11—22no—
259C22×C4×C11—24no—
260C22×C4×C11—41no—
261C22×C4×C11—41no—
262C22×C4×C11—41no—
263C22×C4×C11—41no—
264C22×C4×C11—42no—
265C22×C4×C11—42no—
266C22×C4×C11C22×C414yes—
267C22×C4×C11C2×D414yes—
268C22×C4×C11C2412yes—
269C22×C4×C11C2412yes—
270C22×C4×C11C2411yescharacteristic
271C22×C4×C11C2412yes—
272C22×C4×C11C2411yescharacteristic
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2411yescharacteristic
275C22×C4×C11C2411yescharacteristic
276C22×C4×C11C2411yescharacteristic
277C2×C22⋊D11—24no—
278C2×C22⋊D11—24no—
279C2×C22⋊D11—24no—
280C2×C22⋊D11—24no—
281C2×C22⋊D11—42no—
282C2×C22⋊D11—42no—
283C2×C22⋊D11C22×C418yes—
284C2×C22⋊D11C22×C418yes—
285C2×C22⋊D11C22×C418yescomplemented
286C22×Dic11—24no—
287C22×Dic11—22no—
288C22×Dic11—41no—
289C22×Dic11—41no—
290C22×Dic11—41no—
291C22×Dic11—41no—
292C22×Dic11—41no—
293C22×Dic11—41no—
294C22×Dic11—42no—
295C22×Dic11—42no—
296C22×Dic11C22×C414yes—
297C22×Dic11C2×D414yes—
298C22×Dic11C2412yes—
299C22×Dic11C2412yes—
300C22×Dic11C2412yes—
301C22×Dic11C2412yes—
302C22×Dic11C2412yes—
303C22×Dic11C2412yes—
304D4×D11—264no—
305C2×D44—24no—
306C2×D44—24no—
307C2×D44—41no—
308C2×D44—41no—
309C2×D44C22×C418yes—
310C2×D44C22×C414yescomplemented
311C2×C4×D11—24no—
312C2×C4×D11—24no—
313C2×C4×D11—24no—
314C2×C4×D11—24no—
315C2×C4×D11—24no—
316C2×C4×D11—24no—
317C2×C4×D11—24no—
318C2×C4×D11—24no—
319C2×C4×D11—24no—
320C2×C4×D11—24no—
321C2×C4×D11—42no—
322C2×C4×D11—42no—
323C2×C4×D11—42no—
324C2×C4×D11—42no—
325C2×C4×D11—42no—
326C2×C4×D11—42no—
327C2×C4×D11—42no—
328C2×C4×D11—42no—
329C2×C4×D11—42no—
330C2×C4×D11—42no—
331C2×C4×D11—416no—
332C2×C4×D11C22×C418yes—
333C11×C4⋊C4—24no—
334C11×C4⋊C4—41no—
335C11×C4⋊C4—41no—
336C11×C4⋊C4C22×C414yescomplemented
337C11×C22⋊C4—24no—
338C11×C22⋊C4—24no—
339C11×C22⋊C4—24no—
340C11×C22⋊C4—24no—
341C11×C22⋊C4C22×C418yescomplemented
342C42×C11—24no—
343C42×C11—22no—
344C42×C11—22no—
345C42×C11—41no—
346C42×C11—41no—
347C22⋊Dic11—24no—
348C22⋊Dic11—24no—
349C22⋊Dic11—42no—
350C22⋊Dic11—42no—
351C22⋊Dic11C22×C418yescomplemented
352(C2×D11)⋊C4—24no—
353(C2×D11)⋊C4—24no—
354(C2×D11)⋊C4—24no—
355(C2×D11)⋊C4—24no—
356(C2×D11)⋊C4—24no—
357(C2×D11)⋊C4—24no—
358(C2×D11)⋊C4—42no—
359(C2×D11)⋊C4—42no—
360(C2×D11)⋊C4C22×C418yes—
361(C2×D11)⋊C4C22×C418yes—
362(C2×D11)⋊C4C22×C418yescomplemented
363(C2×D11)⋊C4C22×C418yescomplemented
364(C2×D11)⋊C4C2×D418yes—
365(C2×D11)⋊C4C2×D418yes—
366C4⋊Dic11—24no—
367C4⋊Dic11—41no—
368C4⋊Dic11—41no—
369C4⋊Dic11C22×C414yescomplemented
370Dic11⋊C4—24no—
371Dic11⋊C4—24no—
372Dic11⋊C4—42no—
373Dic11⋊C4—42no—
374Dic11⋊C4C22×C418yescomplemented
375C4×Dic11—24no—
376C4×Dic11—24no—
377C4×Dic11—24no—
378C4×Dic11—24no—
379C4×Dic11—42no—
380C2×#534—111no—
381C2×#518—112no—
382#2359—112no—
383#2359—112no—
384#2359—112no—
385#2359—112no—
386#2358—112no—
387#2358—112no—
388#2358—112no—
389#2358—112no—
390#2325—111no—
391#2325—111no—
392#2325—112no—
393#2315—111no—
394C4×#121—111no—
395C4×#121—112no—
396C4×#121D1111yescharacteristic, complemented
397C2×#386—112no—
398C2×C4×C22⋊C4—111no—
399C23×C11—21no—
400C23×C11—21no—
401C23×C11—21no—
402C23×C11—21no—
403C23×C11—22no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—22no—
408C23×C11—22no—
409C23×C11C23×C414yes—
410C23×C11C23×C412yes—
411C23×C11C22×D412yes—
412C23×C11C2×#4112yes—
413C23×C11C2511yescharacteristic
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—22no—
423C22×D11—22no—
424C22×D11—216no—
425C22×D11—44no—
426C22×D11—44no—
427C22×D11—44no—
428C22×D11—44no—
429C22×D11—44no—
430C22×D11—44no—
431C22×D11—48no—
432C22×D11—48no—
433C22×D11—84no—
434C22×D11—84no—
435C22×D11—84no—
436C22×D11—84no—
437C22×D11C4×D4116yescomplemented
438C22×D11C23×C414yes—
439C22×D11C23×C414yes—
440C22×D11C22×D414yes—
441C22×D11C2×#4114yes—
442D4×C11—216no—
443D4×C11—44no—
444C2×C4×C11—28no—
445C2×C4×C11—22no—
446C2×C4×C11—21no—
447C2×C4×C11—21no—
448C2×C4×C11—22no—
449C2×C4×C11—21no—
450C2×C4×C11—21no—
451C2×C4×C11—21no—
452C2×C4×C11—21no—
453C2×C4×C11—21no—
454C2×C4×C11—21no—
455C2×C4×C11—21no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—21no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—44no—
466C2×C4×C11—44no—
467C2×C4×C11—84no—
468C2×C4×C11C23×C414yes—
469C2×C4×C11C23×C412yes—
470C2×C4×C11C23×C412yes—
471C2×C4×C11C22×D412yes—
472C2×C4×C11C22×D412yes—
473C2×C4×C11H(5,𝔽2)12yes—
474C2×C4×C11H(5,𝔽2)12yes—
475C22⋊D11—216no—
476C22⋊D11—216no—
477C22⋊D11—48no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—44no—
494C2×Dic11—44no—
495C2×Dic11—44no—
496C2×Dic11—84no—
497C2×Dic11C23×C414yes—
498C2×Dic11C23×C414yes—
499C2×Dic11C22×D414yes—
500D44—216no—
501D44—44no—
502C4×D11—216no—
503C4×D11—48no—
504C4×D11—48no—
505C4×D11—84no—
506C4×D11—84no—
507C4×D11—84no—
508C4×D11—84no—
509C23×D4—112no—
510C24×C4—111no—
511#534—1116no—
512C2×#123—112no—
513C2×#123—112no—
514C2×#121—112no—
515C2×#121—111no—
516C2×#121C2×D1111yescharacteristic
517C2×#120—112no—
518C2×#120—112no—
519#518—2216no—
520C2×C4×D4—112no—
521C2×C4×D4—112no—
522C2×C4×D4—112no—
523C2×C4×D4—112no—
524C2×C4×D4—112no—
525C2×C4×D4—112no—
526C2×C4×D4—112no—
527C2×C4×D4—112no—
528C2×C4×D4—111no—
529C2×C4×D4C2×D1112yescomplemented
530C2×C4×D4C2×D1111yescharacteristic, complemented
531C2×#117—112no—
532C2×#117—112no—
533C22×C22⋊C4—111no—
534C22×C22⋊C4—111no—
535C22×C22⋊C4—112no—
536C22×C22⋊C4—112no—
537C22×C22⋊C4—112no—
538C22×C22⋊C4—112no—
539C22×C22⋊C4—112no—
540C22×C42—111no—
541C22×C42C2×D1111yescharacteristic, complemented
542#390—112no—
543#390—111no—
544#390C2×D1111yescharacteristic, complemented
545#389—111no—
546#389—112no—
547#389C2×D1111yescharacteristic, complemented
548#388—112no—
549#388—112no—
550#388—112no—
551#388—112no—
552#388—112no—
553#388—112no—
554#388—112no—
555#388C2×D1112yescomplemented
556#387—112no—
557#387—112no—
558#387—112no—
559#387—112no—
560#386—112no—
561#386—112no—
562#386—112no—
563#386—112no—
564#386—112no—
565#386—112no—
566#386—112no—
567#386—112no—
568#386—112no—
569#386—112no—
570#386—112no—
571#386C2×D1112yescomplemented
572#385—112no—
573#385—112no—
574#385—112no—
575#385—112no—
576#385—112no—
577#385—112no—
578#385—112no—
579#385—112no—
580#380—111no—
581#380—112no—
582#380C2×D1111yescharacteristic, complemented
583C4×C4⋊C4—111no—
584C4×C4⋊C4—112no—
585C4×C4⋊C4C2×D1111yescharacteristic, complemented
586C4×C22⋊C4—112no—
587C4×C22⋊C4—112no—
588C4×C22⋊C4—112no—
589C4×C22⋊C4—112no—
590C4×C22⋊C4—112no—
591C4×C22⋊C4—112no—
592C4×C22⋊C4—112no—
593C4×C22⋊C4C2×D1112yescomplemented
594C2×#95—111no—
595C2×#95—111no—
596C2×#95—112no—
597C2×#95—112no—
598C22×C11—22no—
599C22×C11—22no—
600C22×C11—22no—
601C22×C11—22no—
602C22×C11—22no—
603C22×C11—22no—
604C22×C11—24no—
605C22×C11—24no—
606C22×C11—24no—
607C22×C11—42no—
608C22×C11—42no—
609C22×C11—42no—
610C22×C11—42no—
611C22×C11C2×C4×D414yes—
612C22×C11C24×C411yescharacteristic
613C22×C11C23×D411yescharacteristic
614C22×C11C22×#4111yescharacteristic
615C22×C11C2×H(5,𝔽2)11yescharacteristic
616C22×C11C2×H(5,𝔽2)11yescharacteristic
617C22×C11#58511yescharacteristic
618C22×C11#58511yescharacteristic
619C2×D11—24no—
620C2×D11—24no—
621C2×D11—24no—
622C2×D11—24no—
623C2×D11—24no—
624C2×D11—24no—
625C2×D11—24no—
626C2×D11—24no—
627C2×D11—24no—
628C2×D11—416no—
629C2×D11—42no—
630C2×D11—42no—
631C2×D11—42no—
632C2×D11—42no—
633C2×D11—816no—
634C2×D11C2×C4×D418yes—
635C4×C11—24no—
636C4×C11—22no—
637C4×C11—22no—
638C4×C11—22no—
639C4×C11—22no—
640C4×C11—22no—
641C4×C11—22no—
642C4×C11—42no—
643C4×C11—42no—
644Dic11—24no—
645Dic11—24no—
646Dic11—24no—
647Dic11—42no—
648Dic11—42no—
649Dic11—42no—
650C25—111no—
651C25—112no—
652C22×D4—112no—
653C22×D4—112no—
654C22×D4—112no—
655C22×D4—1116no—
656C22×D4—112no—
657C22×D4—111no—
658C22×D4—228no—
659C22×D4—228no—
660C22×D4C22×D1112yes—
661C22×D4C22×D1111yescharacteristic
662C23×C4—111no—
663C23×C4—111no—
664C23×C4—112no—
665C23×C4—112no—
666C23×C4—111no—
667C23×C4—112no—
668C23×C4—112no—
669C23×C4—112no—
670C23×C4—112no—
671C23×C4—112no—
672C23×C4—112no—
673C23×C4—224no—
674C23×C4—442no—
675C23×C4—442no—
676C23×C4C22×D1111yescharacteristic
677C23×C4C22×D1112yes—
678C23×C4C22×D1111yescharacteristic
679C23×C4C22×D1111yescharacteristic
680#123—1116no—
681#123—1116no—
682#121—1116no—
683#121—118no—
684#121C4×D1118yescomplemented
685#120—1116no—
686#120—1116no—
687C4×D4—28no—
688C4×D4—42no—
689C4×D4—228no—
690C4×D4—228no—
691C4×D4—228no—
692C4×D4—228no—
693C4×D4—228no—
694C4×D4—228no—
695C4×D4—228no—
696C4×D4—442no—
697C4×D4—444no—
698#117—228no—
699#117—228no—
700C2×C4⋊C4—112no—
701C2×C4⋊C4—111no—
702C2×C4⋊C4—112no—
703C2×C4⋊C4—112no—
704C2×C4⋊C4—112no—
705C2×C4⋊C4—112no—
706C2×C4⋊C4—111no—
707C2×C4⋊C4—112no—
708C2×C4⋊C4—111no—
709C2×C4⋊C4C22×D1112yes—
710C2×C4⋊C4C22×D1111yescharacteristic
711C2×C4⋊C4C22×D1111yescharacteristic
712C2×C4⋊C4C22×D1111yescharacteristic
713C2×C22⋊C4—112no—
714C2×C22⋊C4—118no—
715C2×C22⋊C4—118no—
716C2×C22⋊C4—112no—
717C2×C22⋊C4—112no—
718C2×C22⋊C4—112no—
719C2×C22⋊C4—112no—
720C2×C22⋊C4—112no—
721C2×C22⋊C4—112no—
722C2×C22⋊C4—112no—
723C2×C22⋊C4—112no—
724C2×C22⋊C4—112no—
725C2×C22⋊C4—112no—
726C2×C22⋊C4—112no—
727C2×C22⋊C4—112no—
728C2×C22⋊C4—112no—
729C2×C22⋊C4—112no—
730C2×C22⋊C4—112no—
731C2×C22⋊C4—112no—
732C2×C22⋊C4—112no—
733C2×C22⋊C4—112no—
734C2×C22⋊C4—228no—
735C2×C22⋊C4—228no—
736C2×C22⋊C4—228no—
737C2×C22⋊C4—444no—
738C2×C22⋊C4—444no—
739C2×C22⋊C4C22×D1112yes—
740C2×C22⋊C4C22×D1112yes—
741C2×C22⋊C4C22×D1112yes—
742C2×C22⋊C4C22×D1112yes—
743C2×C22⋊C4C22×D1112yes—
744C2×C42—42no—
745C2×C42—112no—
746C2×C42—112no—
747C2×C42—112no—
748C2×C42—112no—
749C2×C42—112no—
750C2×C42—442no—
751C2×C42C22×D1112yes—
752C2×C42C22×D1111yescharacteristic
753C2×C42C22×D1111yescharacteristic
754C2×C42C22×D1111yescharacteristic
755C2×C42C22×D1111yescharacteristic
756#95—112no—
757#95—112no—
758#95—112no—
759#95—112no—
760#95—112no—
761#95—112no—
762#95—112no—
763#95—112no—
764#95—112no—
765#95—112no—
766#95—112no—
767#95—112no—
768#95—112no—
769#95C22×D1112yes—
770#95C22×D1112yes—
771#95C22×D1112yes—
772C2×C11—24no—
773C2×C11—44no—
774C2×C11C22×C4×D411yescharacteristic
775C2×C11C4×H(5,𝔽2)11yescharacteristic
776C2×C11C4×H(5,𝔽2)11yescharacteristic
777C2×C11#349011yescharacteristic
778C2×C11#349111yescharacteristic
779C2×C11#349611yescharacteristic
780C2×C11#349611yescharacteristic
781D11—28no—
782D11—44no—
783C24—112no—
784C24—114no—
785C24—114no—
786C24—114no—
787C24—112no—
788C24—118no—
789C24—224no—
790C24—224no—
791C24—441no—
792C24—441no—
793C24—441no—
794C24—441no—
795C24—442no—
796C24—442no—
797C24—442no—
798C24—442no—
799C24C23×D1112yes—
800C24C23×D1111yescharacteristic
801C2×D4—24no—
802C2×D4—24no—
803C2×D4—41no—
804C2×D4—41no—
805C2×D4—118no—
806C2×D4—118no—
807C2×D4—118no—
808C2×D4—118no—
809C2×D4—114no—
810C2×D4—224no—
811C2×D4—224no—
812C2×D4—2264no—
813C2×D4—224no—
814C2×D4—224no—
815C2×D4—224no—
816C2×D4—224no—
817C2×D4—441no—
818C2×D4—441no—
819C2×D4—442no—
820C2×D4—442no—
821C2×D4C2×C4×D1118yes—
822C2×D4C2×C4×D1114yescomplemented
823C22×C4—22no—
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—24no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—41no—
831C22×C4—42no—
832C22×C4—42no—
833C22×C4—112no—
834C22×C4—112no—
835C22×C4—112no—
836C22×C4—114no—
837C22×C4—114no—
838C22×C4—118no—
839C22×C4—112no—
840C22×C4—112no—
841C22×C4—112no—
842C22×C4—224no—
843C22×C4—224no—
844C22×C4—224no—
845C22×C4—224no—
846C22×C4—224no—
847C22×C4—224no—
848C22×C4—224no—
849C22×C4—224no—
850C22×C4—222no—
851C22×C4—224no—
852C22×C4—224no—
853C22×C4—224no—
854C22×C4—442no—
855C22×C4—442no—
856C22×C4—442no—
857C22×C4—442no—
858C22×C4—442no—
859C22×C4—442no—
860C22×C4—442no—
861C22×C4—442no—
862C22×C4—442no—
863C22×C4—442no—
864C22×C4—4416no—
865C22×C4—441no—
866C22×C4—441no—
867C22×C4—441no—
868C22×C4—441no—
869C22×C4—441no—
870C22×C4—441no—
871C22×C4—442no—
872C22×C4—442no—
873C22×C4C2×C4×D1114yes—
874C22×C4D4×D1114yes—
875C22×C4C23×D1112yes—
876C22×C4C23×D1112yes—
877C22×C4C23×D1111yescharacteristic
878C22×C4C23×D1112yes—
879C22×C4C23×D1111yescharacteristic
880C22×C4C23×D1111yescharacteristic
881C22×C4C23×D1111yescharacteristic
882C22×C4C23×D1111yescharacteristic
883C22×C4C23×D1111yescharacteristic
884C4⋊C4—24no—
885C4⋊C4—41no—
886C4⋊C4—41no—
887C4⋊C4—118no—
888C4⋊C4—114no—
889C4⋊C4—224no—
890C4⋊C4—224no—
891C4⋊C4—224no—
892C4⋊C4—442no—
893C4⋊C4—441no—
894C4⋊C4—442no—
895C4⋊C4—441no—
896C4⋊C4C2×C4×D1114yescomplemented
897C22⋊C4—24no—
898C22⋊C4—24no—
899C22⋊C4—24no—
900C22⋊C4—24no—
901C22⋊C4—118no—
902C22⋊C4—118no—
903C22⋊C4—118no—
904C22⋊C4—118no—
905C22⋊C4—118no—
906C22⋊C4—118no—
907C22⋊C4—118no—
908C22⋊C4—224no—
909C22⋊C4—224no—
910C22⋊C4—224no—
911C22⋊C4—224no—
912C22⋊C4—224no—
913C22⋊C4—224no—
914C22⋊C4—224no—
915C22⋊C4—224no—
916C22⋊C4—442no—
917C22⋊C4—442no—
918C22⋊C4—442no—
919C22⋊C4—442no—
920C22⋊C4C2×C4×D1118yescomplemented
921C42—24no—
922C42—22no—
923C42—22no—
924C42—41no—
925C42—41no—
926C42—224no—
927C42—224no—
928C42—224no—
929C42—224no—
930C42—442no—
931C11#3427311yescharacteristic, complemented, Sylow
932C23—21no—
933C23—21no—
934C23—21no—
935C23—21no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—114no—
943C23—114no—
944C23—114no—
945C23—1116no—
946C23—114no—
947C23—2216no—
948C23—222no—
949C23—222no—
950C23—222no—
951C23—222no—
952C23—222no—
953C23—222no—
954C23—222no—
955C23—222no—
956C23—222no—
957C23—222no—
958C23—444no—
959C23—444no—
960C23—444no—
961C23—444no—
962C23—444no—
963C23—444no—
964C23—448no—
965C23—448no—
966C23—884no—
967C23—884no—
968C23—884no—
969C23—884no—
970C23C22×C4×D1114yes—
971C23C22×C4×D1112yes—
972C23C2×D4×D1112yes—
973C23#41×D1112yes—
974C23C24×D1111yescharacteristic
975D4—216no—
976D4—44no—
977D4—2216no—
978D4—2216no—
979D4—2216no—
980D4—444no—
981D4—448no—
982C2×C4—28no—
983C2×C4—22no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—22no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—44no—
1004C2×C4—44no—
1005C2×C4—84no—
1006C2×C4—114no—
1007C2×C4—114no—
1008C2×C4—114no—
1009C2×C4—2216no—
1010C2×C4—222no—
1011C2×C4—222no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—222no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—448no—
1026C2×C4—448no—
1027C2×C4—444no—
1028C2×C4—444no—
1029C2×C4—444no—
1030C2×C4—884no—
1031C2×C4—884no—
1032C2×C4—884no—
1033C2×C4—884no—
1034C2×C4—884no—
1035C2×C4C22×C4×D1112yes—
1036C2×C4C22×C4×D1112yes—
1037C2×C4C22×C4×D1114yes—
1038C2×C4C2×D4×D1112yes—
1039C2×C4C2×D4×D1112yes—
1040C2×C4#6703712yes—
1041C2×C4#6704212yes—
1042C22—22no—
1043C22—22no—
1044C22—22no—
1045C22—22no—
1046C22—22no—
1047C22—22no—
1048C22—24no—
1049C22—24no—
1050C22—24no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—118no—
1056C22—224no—
1057C22—224no—
1058C22—224no—
1059C22—224no—
1060C22—224no—
1061C22—224no—
1062C22—224no—
1063C22—224no—
1064C22—224no—
1065C22—4416no—
1066C22—442no—
1067C22—442no—
1068C22—442no—
1069C22—442no—
1070C22—8816no—
1071C22C4×D4×D1114yes—
1072C22C23×C4×D1111yescharacteristic
1073C22C22×D4×D1111yescharacteristic
1074C22C2×#6703711yescharacteristic
1075C22C2×#41×D1111yescharacteristic
1076C22C2×#6704211yescharacteristic
1077C22#1062345311yescharacteristic
1078C22#1062345311yescharacteristic
1079C4—22no—
1080C4—22no—
1081C4—24no—
1082C4—22no—
1083C4—22no—
1084C4—22no—
1085C4—22no—
1086C4—42no—
1087C4—42no—
1088C4—224no—
1089C4—224no—
1090C4—224no—
1091C4—442no—
1092C4—442no—
1093C4—442no—
1094C2—24no—
1095C2—44no—
1096C2—228no—
1097C2—444no—
1098C2C2×C4×D4×D1111yescharacteristic
1099C2C4×#6703711yescharacteristic
1100C2C4×#6704211yescharacteristic
1101C2#1308229911yescharacteristic
1102C2#1308230811yescharacteristic
1103C2#1308237311yescharacteristic
1104C2#1308237811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC4×C11×#121C2
socle, cosocleC23×C11C25
prime radicalC2×#10623136C2
hypercenterC4×#121D11
hypocenterC11#34273
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. C2×#10623076C2semidirect
3. #13071613C2semidirect
4. #13071609C2semidirect
5. #13071607C2semidirect
6. #13071603C2semidirect
7. #13071598C2semidirect
8. #13071597C2semidirect
9. #13071594C2semidirect
10. #13071593C2semidirect
11. #13071321C2semidirect
12. #13071316C2semidirect
13. #13071314C2semidirect
14. #13071229C2semidirect
15. C4×#66983C2semidirect
16. #13071126C2semidirect
17. D11×#386C2semidirect
18. C2×C4×(C2×D11)⋊C4C2semidirect
19. C4×C11×#121C2semidirect
23. C2×C4×D4×C11C22semidirect
24. C2×C4×D4×C11C22semidirect
25. C22×C42×C11C22semidirect
28. C2×D4×Dic11C22semidirect
31. C2×C4×C22⋊D11C22semidirect
34. C22×(C2×D11)⋊C4C22semidirect
35. C22×C4×Dic11C22semidirect
36. #10623136C4semidirect
40. C2×#66945C22semidirect
44. C2×(C22⋊D11)⋊C4C22semidirect
45. C2×(C22⋊D11)⋊C4C22semidirect
47. C2×C22⋊C4×D11C22semidirect
48. C2×C22⋊C4×D11C22semidirect
49. C2×C22⋊C4×D11C22semidirect
51. C2×C4×D44C22semidirect
52. C2×#66925C22semidirect
53. C11×#390C22semidirect
54. C11×#389C22semidirect
55. C11×#388C22semidirect
56. C11×#386C22semidirect
57. C11×#380C22semidirect
58. C4×C11×C4⋊C4C22semidirect
59. C4×C11×C22⋊C4C22semidirect
60. #10622833C22semidirect
61. #10622833C22semidirect
62. #10622826C22semidirect
63. #10622826C22semidirect
64. #10622825C22semidirect
65. #10622823C22semidirect
66. C2×C11⋊#95C22semidirect
67. C2×C11⋊#95C22semidirect
68. #10622603C22semidirect
69. #10622602C22semidirect
70. #10622602C22semidirect
71. #10622602C22semidirect
72. #10622602C22semidirect
73. #10622594C22semidirect
74. #10622591C22semidirect
75. #10622571C22semidirect
76. #10622570C22semidirect
79. #10622569C22semidirect
80. #10622564C22semidirect
81. #10622563C22semidirect
82. #10622557C22semidirect
83. #10622557C22semidirect
84. #10622555C22semidirect
85. C22⋊C4×Dic11C22semidirect
86. #10622553C22semidirect
87. #10622553C22semidirect
88. #10622552C22semidirect
89. C4×(C2×D11)⋊C4C22semidirect
90. C4×(C2×D11)⋊C4C22semidirect
91. C4×(C2×D11)⋊C4C22semidirect
92. C4×(C2×D11)⋊C4C22semidirect
93. C4×(C2×D11)⋊C4C22semidirect
94. C4×C4⋊Dic11C22semidirect
95. #10622546C22semidirect
96. #10622541C22semidirect
97. #10622283C22semidirect
98. #10622281C22semidirect
99. #10622281C22semidirect
100. #10622279C22semidirect
103. #10622278C22semidirect
104. D11×#95C22semidirect
105. D11×#95C22semidirect
106. #10622267C22semidirect
107. #10622262C22semidirect
108. #10622260C22semidirect
126. C2×D4×D11C2×C4semidirect
139. C11×#121C2×C4semidirect
162. #66992C2×C4semidirect
163. #66990C2×C4semidirect
165. #66983C2×C4semidirect
169. C2×(C2×D11)⋊C4C2×C4semidirect
170. C2×(C2×D11)⋊C4D4semidirect
200. #66947C2×C4semidirect
203. #66936C2×C4semidirect
204. #66935C2×C4semidirect
255. C2×D4×C11C22×C4semidirect
285. C2×C22⋊D11C22×C4semidirect
310. C2×D44C22×C4semidirect
336. C11×C4⋊C4C22×C4semidirect
341. C11×C22⋊C4C22×C4semidirect
351. C22⋊Dic11C22×C4semidirect
362. (C2×D11)⋊C4C22×C4semidirect
363. (C2×D11)⋊C4C22×C4semidirect
369. C4⋊Dic11C22×C4semidirect
374. Dic11⋊C4C22×C4semidirect
396. C4×#121D11semidirect
437. C22×D11C4×D4semidirect
529. C2×C4×D4C2×D11semidirect
530. C2×C4×D4C2×D11semidirect
541. C22×C42C2×D11semidirect
544. #390C2×D11semidirect
547. #389C2×D11semidirect
555. #388C2×D11semidirect
571. #386C2×D11semidirect
582. #380C2×D11semidirect
585. C4×C4⋊C4C2×D11semidirect
593. C4×C22⋊C4C2×D11semidirect
684. #121C4×D11semidirect
822. C2×D4C2×C4×D11semidirect
896. C4⋊C4C2×C4×D11semidirect
920. C22⋊C4C2×C4×D11semidirect
931. C11#34273semidirect

Maximal subgroups

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

subgroupindex
C2×#106231362
C2×#106230762
#130716132
#130716092
#130716072
#130716032
#130715982
#130715972
#130715942
#130715932
#130713212
#130713162
#130713142
#130712292
C4×#669832
#130711262
D11×#3862
C2×C4×(C2×D11)⋊C42
C4×C11×#1212
#3427311