Finite Group Databasebeta

← C4×#10623136 #14912782

Subgroups — C4×#10623136 #14912782

Order 2816.

3770 conjugacy classes of subgroups.

The subgroup lattice has 1108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623136C211yesmaximal, characteristic
2C2×C4×D4×D11C212yesmaximal, complemented
3#13071321C211yesmaximal, characteristic, complemented
4#13071317C212yesmaximal, complemented
5#13071316C211yesmaximal, characteristic, complemented
6#13071286C212yesmaximal, complemented
7#13071280C212yesmaximal, complemented
8#13071275C212yesmaximal, complemented
9#13071269C212yesmaximal, complemented
10#13071229C211yesmaximal, characteristic, complemented
11#13071190C212yesmaximal, complemented
12C4×#66947C212yesmaximal, complemented
13C4×#66936C212yesmaximal, complemented
14C4×#66983C211yesmaximal, characteristic, complemented
15C4×#66992C212yesmaximal, complemented
16C4×#66935C212yesmaximal, complemented
17C4×#66990C212yesmaximal, complemented
18C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
19C4×C11×#121C211yesmaximal, characteristic, complemented
20C22×D4×D11C2212yes—
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2212yescomplemented
23C2×C11×#121C2211yescharacteristic
24C2×C4×D4×C11C2212yescomplemented
25C2×C4×D4×C11C2211yescharacteristic, complemented
26C22×C42×C11C2211yescharacteristic, complemented
27C2×#66992C2212yes—
28C2×#66990C2212yes—
29C2×D4×Dic11C2212yescomplemented
30C2×#66983C2211yescharacteristic
31C2×C4×C22⋊D11C2212yes—
32C2×C4×C22⋊D11C2212yescomplemented
33C2×C4×C22⋊D11C2212yescomplemented
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic, complemented
37#10623136C4116yesdirect product factor
38C4×D4×D11—216no—
39C2×#66947C2212yes—
40C2×#66946C2212yes—
41C2×C4⋊C4×D11C2212yescomplemented
42C2×#66936C2212yes—
43C2×#66935C2212yes—
44C2×(C22⋊D11)⋊C4C2212yes—
45C2×(C22⋊D11)⋊C4C2212yescomplemented
46C2×C22⋊C4×D11C2212yes—
47C2×C22⋊C4×D11C2212yescomplemented
48C2×C4×D44C2212yes—
49C2×C4×D44C2211yescharacteristic, complemented
50C2×C42×D11C2212yescomplemented
51C11×#390C2211yescharacteristic, complemented
52C11×#389C2211yescharacteristic, complemented
53C11×#388C2212yescomplemented
54C11×#386C2212yescomplemented
55C11×#380C2211yescharacteristic, complemented
56C4×C11×C4⋊C4C2211yescharacteristic, complemented
57C4×C11×C22⋊C4C2212yescomplemented
58#10622833C2212yescomplemented
59#10622833C2212yescomplemented
60#10622826C2212yescomplemented
61#10622825C2211yescharacteristic, complemented
62C4×C22⋊Dic11C2212yescomplemented
63C2×C11⋊#95C2211yescharacteristic, complemented
64C2×C11⋊#95C2211yescharacteristic, complemented
65#10622603C2212yescomplemented
66#10622603C2212yescomplemented
67#10622602C2212yescomplemented
68#10622602C2212yescomplemented
69#10622602C2212yescomplemented
70#10622594C2212yescomplemented
71#10622585C2212yescomplemented
72#10622571C2212yescomplemented
73#10622571C2212yescomplemented
74#10622570C2212yescomplemented
75#10622569C2212yes—
76#10622569C2212yes—
77#10622569C2212yescomplemented
78#10622568C2212yescomplemented
79#10622568C2212yescomplemented
80#10622564C2212yescomplemented
81#10622563C2212yescomplemented
82#10622559C2212yescomplemented
83#10622558C2212yescomplemented
84#10622558C2212yescomplemented
85#10622555C2212yescomplemented
86#10622553C2212yescomplemented
87#10622552C2211yescharacteristic, complemented
88C4×(C2×D11)⋊C4C2212yescomplemented
89C4×(C2×D11)⋊C4C2212yescomplemented
90C4×(C2×D11)⋊C4C2212yescomplemented
91C4×(C2×D11)⋊C4C2212yescomplemented
92C4×(C2×D11)⋊C4C2212yescomplemented
93C4×(C2×D11)⋊C4C2212yescomplemented
94C4×C4⋊Dic11C2211yescharacteristic, complemented
95C4×Dic11⋊C4C2212yescomplemented
96#10622541C2211yescharacteristic, complemented
97#10622282C2212yescomplemented
98#10622281C2212yescomplemented
99#10622281C2212yescomplemented
100#10622281C2212yescomplemented
101#10622278C2212yes—
102#10622278C2212yes—
103#10622278C2212yescomplemented
104#10622277C2212yescomplemented
105#10622277C2212yescomplemented
106#10622268C2212yescomplemented
107#10622267C2212yescomplemented
108#10622265C2212yescomplemented
109C24×D11C2312yes—
110C24×D11C2311yescharacteristic
111C22×D4×C11C2312yes—
112C22×D4×C11C2311yescharacteristic
113C23×C4×C11C2312yes—
114C23×C4×C11C2311yescharacteristic
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—28no—
130C22×C4×D11—42no—
131C22×C4×D11—42no—
132C22×C4×D11—44no—
133C22×C4×D11—44no—
134C22×C4×D11D418yescomplemented
135C22×C4×D11C2312yes—
136C22×C4×D11C2312yes—
137C22×C4×D11C2312yes—
138C22×C4×D11C2312yes—
139C22×C4×D11C2312yes—
140C22×C4×D11C2312yes—
141C22×C4×D11C2312yes—
142C11×#121C2×C418yescomplemented
143C4×D4×C11—28no—
144C4×D4×C11—42no—
145C2×C11×C4⋊C4C2312yes—
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C4⋊C4C2311yescharacteristic
148C2×C11×C4⋊C4C2311yescharacteristic
149C2×C11×C22⋊C4C2312yes—
150C2×C11×C22⋊C4C2312yes—
151C2×C11×C22⋊C4C2312yes—
152C2×C11×C22⋊C4C2312yes—
153C2×C11×C22⋊C4C2312yes—
154C2×C42×C11—42no—
155C2×C42×C11C2312yes—
156C2×C42×C11C2311yescharacteristic
157C2×C42×C11C2311yescharacteristic
158C2×C42×C11C2311yescharacteristic
159C2×C42×C11C2311yescharacteristic
160C2×C22⋊Dic11C2312yes—
161C2×C22⋊Dic11C2312yes—
162C2×C22⋊Dic11C2312yes—
163C2×C22⋊Dic11C2312yes—
164C2×C22⋊Dic11C2312yes—
165#66992C2×C4116yescomplemented
166#66990C2×C4116yescomplemented
167D4×Dic11—28no—
168#66983C2×C418yescomplemented
169C4×C22⋊D11—28no—
170C4×C22⋊D11—28no—
171C4×C22⋊D11—44no—
172C2×(C2×D11)⋊C4—24no—
173C2×(C2×D11)⋊C4C2×C418yescomplemented
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×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×C4⋊Dic11C2312yes—
189C2×C4⋊Dic11C2311yescharacteristic
190C2×C4⋊Dic11C2311yescharacteristic
191C2×C4⋊Dic11C2311yescharacteristic
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2312yes—
195C2×Dic11⋊C4C2312yes—
196C2×Dic11⋊C4C2312yes—
197C2×C4×Dic11—42no—
198C2×C4×Dic11C2312yes—
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2312yes—
201C2×C4×Dic11C2312yes—
202C2×C4×Dic11C2312yes—
203#66947C2×C4116yescomplemented
204#66946—28no—
205C4⋊C4×D11—28no—
206#66936C2×C4116yescomplemented
207#66935C2×C4116yescomplemented
208(C22⋊D11)⋊C4—28no—
209(C22⋊D11)⋊C4—28no—
210C22⋊C4×D11—28no—
211C22⋊C4×D11—28no—
212C4×D44—28no—
213C4×D44—42no—
214C42×D11—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—
231C4×#534—111nomaximal, Sylow
232C24×C11C2412yes—
233C24×C11C2411yescharacteristic
234C23×D11—24no—
235C23×D11—24no—
236C23×D11—41no—
237C23×D11—41no—
238C23×D11—42no—
239C23×D11—42no—
240C23×D11—41no—
241C23×D11—41no—
242C23×D11—42no—
243C23×D11—42no—
244C23×D11C22×C414yes—
245C23×D11C22×C418yescomplemented
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×C418yescomplemented
255C2×D4×C11C22×C414yescomplemented
256C22×C4×C11—22no—
257C22×C4×C11—22no—
258C22×C4×C11—22no—
259C22×C4×C11—24no—
260C22×C4×C11—24no—
261C22×C4×C11—24no—
262C22×C4×C11—41no—
263C22×C4×C11—41no—
264C22×C4×C11—41no—
265C22×C4×C11—41no—
266C22×C4×C11C22×C414yescomplemented
267C22×C4×C11C2×D414yes—
268C22×C4×C11C2411yescharacteristic
269C22×C4×C11C2411yescharacteristic
270C22×C4×C11C2412yes—
271C22×C4×C11C2412yes—
272C22×C4×C11C2411yescharacteristic
273C22×C4×C11C2412yes—
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×C418yescomplemented
285C2×C22⋊D11C22×C418yescomplemented
286C22×Dic11—24no—
287C22×Dic11—22no—
288C22×Dic11—41no—
289C22×Dic11—41no—
290C22×Dic11—41no—
291C22×Dic11—41no—
292C22×Dic11—42no—
293C22×Dic11—42no—
294C22×Dic11—41no—
295C22×Dic11—41no—
296C22×Dic11C22×C414yescomplemented
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—416no—
330C2×C4×D11—432no—
331C2×C4×D11C22×C418yescomplemented
332C2×C4×D11C2×D418yes—
333C2×C4×D11C2×D418yes—
334C11×C4⋊C4—24no—
335C11×C4⋊C4—41no—
336C11×C4⋊C4—41no—
337C11×C4⋊C4C22×C414yescomplemented
338C11×C22⋊C4—24no—
339C11×C22⋊C4—24no—
340C11×C22⋊C4—42no—
341C11×C22⋊C4—42no—
342C11×C22⋊C4C22×C418yescomplemented
343C42×C11—24no—
344C42×C11—22no—
345C42×C11—22no—
346C42×C11—41no—
347C42×C11—41no—
348C22⋊Dic11—24no—
349C22⋊Dic11—24no—
350C22⋊Dic11—42no—
351C22⋊Dic11—42no—
352C22⋊Dic11C22×C418yescomplemented
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—24no—
359(C2×D11)⋊C4—42no—
360(C2×D11)⋊C4—42no—
361(C2×D11)⋊C4—42no—
362(C2×D11)⋊C4—42no—
363(C2×D11)⋊C4C22×C418yescomplemented
364(C2×D11)⋊C4C22×C418yescomplemented
365(C2×D11)⋊C4C22×C418yescomplemented
366(C2×D11)⋊C4C22×C418yescomplemented
367C4⋊Dic11—24no—
368C4⋊Dic11—41no—
369C4⋊Dic11—41no—
370C4⋊Dic11C22×C414yescomplemented
371Dic11⋊C4—24no—
372Dic11⋊C4—24no—
373Dic11⋊C4—42no—
374Dic11⋊C4—42no—
375Dic11⋊C4C22×C418yescomplemented
376C4×Dic11—24no—
377C4×Dic11—24no—
378C4×Dic11—24no—
379C4×Dic11—24no—
380C4×Dic11—42no—
381C2×#534—111no—
382C22×C4×D4—112no—
383#2325—112no—
384#2325—111no—
385#2325—111no—
386#2322—112no—
387#2322—112no—
388#2321—112no—
389#2321—112no—
390#2315—111no—
391#2308—112no—
392C4×#123—112no—
393C4×#123—112no—
394C4×#121—111no—
395C4×#121—112no—
396C4×#121D1111yescharacteristic, complemented
397C4×#120—112no—
398C4×#120—112no—
399C2×C4×C22⋊C4—111no—
400C23×C11—21no—
401C23×C11—21no—
402C23×C11—21no—
403C23×C11—21no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—22no—
408C23×C11—22no—
409C23×C11—22no—
410C23×C11C23×C414yes—
411C23×C11C23×C412yes—
412C23×C11C22×D412yes—
413C23×C11C2×#4112yes—
414C23×C11C2511yescharacteristic
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—22no—
425C22×D11—216no—
426C22×D11—44no—
427C22×D11—44no—
428C22×D11—44no—
429C22×D11—48no—
430C22×D11—48no—
431C22×D11—44no—
432C22×D11—44no—
433C22×D11—44no—
434C22×D11—48no—
435C22×D11—48no—
436C22×D11—48no—
437C22×D11—48no—
438C22×D11C4×D4116yescomplemented
439C22×D11C23×C414yes—
440C22×D11C23×C414yes—
441C22×D11C22×D414yes—
442C22×D11C2×#4114yes—
443D4×C11—216no—
444D4×C11—44no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—21no—
448C2×C4×C11—21no—
449C2×C4×C11—21no—
450C2×C4×C11—21no—
451C2×C4×C11—21no—
452C2×C4×C11—21no—
453C2×C4×C11—28no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—22no—
459C2×C4×C11—21no—
460C2×C4×C11—21no—
461C2×C4×C11—22no—
462C2×C4×C11—22no—
463C2×C4×C11—21no—
464C2×C4×C11—22no—
465C2×C4×C11—21no—
466C2×C4×C11—44no—
467C2×C4×C11—44no—
468C2×C4×C11—48no—
469C2×C4×C11C23×C414yes—
470C2×C4×C11C23×C412yes—
471C2×C4×C11C23×C412yes—
472C2×C4×C11C22×D412yes—
473C2×C4×C11C22×D412yes—
474C2×C4×C11H(5,𝔽2)12yes—
475C2×C4×C11H(5,𝔽2)12yes—
476C22⋊D11—216no—
477C22⋊D11—216no—
478C22⋊D11—48no—
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—22no—
494C2×Dic11—44no—
495C2×Dic11—44no—
496C2×Dic11—48no—
497C2×Dic11—44no—
498C2×Dic11C23×C414yes—
499C2×Dic11C23×C414yes—
500C2×Dic11C22×D414yes—
501D44—216no—
502D44—44no—
503C4×D11—216no—
504C4×D11—216no—
505C4×D11—48no—
506C4×D11—48no—
507C4×D11—48no—
508C4×D11—48no—
509C4×D11—48no—
510C23×D4—112no—
511C24×C4—111no—
512C24×C4—112no—
513#534—1116no—
514C2×#123—112no—
515C2×#123—112no—
516C2×#121—112no—
517C2×#121—111no—
518C2×#121C2×D1111yescharacteristic
519C2×#120—112no—
520C2×#120—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—112no—
529C2×C4×D4—111no—
530C2×C4×D4—2216no—
531C2×C4×D4C2×D1112yescomplemented
532C2×C4×D4C2×D1111yescharacteristic, complemented
533C22×C4⋊C4—112no—
534C22×C22⋊C4—111no—
535C22×C22⋊C4—111no—
536C22×C22⋊C4—112no—
537C22×C22⋊C4—112no—
538C22×C42—111no—
539C22×C42—112no—
540C22×C42C2×D1111yescharacteristic, complemented
541#390—112no—
542#390—111no—
543#390C2×D1111yescharacteristic, complemented
544#389—112no—
545#389—111no—
546#389C2×D1111yescharacteristic, complemented
547#388—112no—
548#388—112no—
549#388—112no—
550#388—112no—
551#388—112no—
552#388—112no—
553#388—112no—
554#388C2×D1112yescomplemented
555#387—112no—
556#387—112no—
557#387—112no—
558#387—112no—
559#386—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#386C2×D1112yescomplemented
571#385—112no—
572#385—112no—
573#385—112no—
574#385—112no—
575#385—112no—
576#385—112no—
577#385—112no—
578#385—112no—
579#381—112no—
580#381—112no—
581#380—111no—
582#380—112no—
583#380C2×D1111yescharacteristic, complemented
584#379—112no—
585#379—112no—
586C4×C4⋊C4—112no—
587C4×C4⋊C4—111no—
588C4×C4⋊C4C2×D1111yescharacteristic, complemented
589C4×C22⋊C4—112no—
590C4×C22⋊C4—112no—
591C4×C22⋊C4—112no—
592C4×C22⋊C4—112no—
593C4×C22⋊C4—112no—
594C4×C22⋊C4—112no—
595C4×C22⋊C4—112no—
596C4×C22⋊C4C2×D1112yescomplemented
597C2×#95—111no—
598C2×#95—111no—
599C22×C11—22no—
600C22×C11—22no—
601C22×C11—22no—
602C22×C11—22no—
603C22×C11—22no—
604C22×C11—22no—
605C22×C11—24no—
606C22×C11—24no—
607C22×C11—24no—
608C22×C11—42no—
609C22×C11—42no—
610C22×C11—42no—
611C22×C11—42no—
612C22×C11C2×C4×D414yes—
613C22×C11C24×C411yescharacteristic
614C22×C11C23×D411yescharacteristic
615C22×C11C22×#4111yescharacteristic
616C22×C11C2×H(5,𝔽2)11yescharacteristic
617C22×C11C2×H(5,𝔽2)11yescharacteristic
618C22×C11#58511yescharacteristic
619C22×C11#58511yescharacteristic
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—24no—
629C2×D11—416no—
630C2×D11—432no—
631C2×D11—42no—
632C2×D11—42no—
633C2×D11—42no—
634C2×D11—42no—
635C2×D11C2×C4×D418yes—
636C4×C11—24no—
637C4×C11—22no—
638C4×C11—22no—
639C4×C11—22no—
640C4×C11—42no—
641C4×C11—42no—
642C4×C11—41no—
643C4×C11—41no—
644C4×C11#53414yescomplemented
645Dic11—24no—
646Dic11—24no—
647Dic11—24no—
648Dic11—42no—
649Dic11—42no—
650Dic11—42no—
651C25—111no—
652C25—112no—
653C22×D4—112no—
654C22×D4—112no—
655C22×D4—112no—
656C22×D4—1116no—
657C22×D4—112no—
658C22×D4—111no—
659C22×D4—228no—
660C22×D4—228no—
661C22×D4C22×D1112yes—
662C22×D4C22×D1111yescharacteristic
663C23×C4—111no—
664C23×C4—111no—
665C23×C4—112no—
666C23×C4—112no—
667C23×C4—118no—
668C23×C4—112no—
669C23×C4—111no—
670C23×C4—112no—
671C23×C4—112no—
672C23×C4—112no—
673C23×C4—112no—
674C23×C4—112no—
675C23×C4—228no—
676C23×C4—442no—
677C23×C4—442no—
678C23×C4—444no—
679C23×C4—444no—
680C23×C4C22×D1112yes—
681C23×C4C22×D1111yescharacteristic
682C23×C4C22×D1111yescharacteristic
683C23×C4C22×D1111yescharacteristic
684#123—1116no—
685#123—1116no—
686#121—1116no—
687#121—118no—
688#121C4×D1118yescomplemented
689#120—1116no—
690#120—1116no—
691C4×D4—28no—
692C4×D4—42no—
693C4×D4—228no—
694C4×D4—228no—
695C4×D4—228no—
696C4×D4—228no—
697C4×D4—228no—
698C4×D4—228no—
699C4×D4—228no—
700C4×D4—442no—
701C4×D4—444no—
702C2×C4⋊C4—112no—
703C2×C4⋊C4—111no—
704C2×C4⋊C4—112no—
705C2×C4⋊C4—112no—
706C2×C4⋊C4—112no—
707C2×C4⋊C4—112no—
708C2×C4⋊C4—111no—
709C2×C4⋊C4—112no—
710C2×C4⋊C4—111no—
711C2×C4⋊C4—228no—
712C2×C4⋊C4C22×D1112yes—
713C2×C4⋊C4C22×D1111yescharacteristic
714C2×C4⋊C4C22×D1111yescharacteristic
715C2×C4⋊C4C22×D1111yescharacteristic
716C2×C22⋊C4—112no—
717C2×C22⋊C4—118no—
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—112no—
735C2×C22⋊C4—112no—
736C2×C22⋊C4—228no—
737C2×C22⋊C4—228no—
738C2×C22⋊C4—224no—
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—228no—
751C2×C42—442no—
752C2×C42C22×D1112yes—
753C2×C42C22×D1111yescharacteristic
754C2×C42C22×D1111yescharacteristic
755C2×C42C22×D1111yescharacteristic
756C2×C42C22×D1111yescharacteristic
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#95—112no—
770#95C22×D1112yes—
771#95C22×D1112yes—
772#95C22×D1112yes—
773C2×C11—24no—
774C2×C11—44no—
775C2×C11C22×C4×D411yescharacteristic
776C2×C11C4×H(5,𝔽2)11yescharacteristic
777C2×C11C4×H(5,𝔽2)11yescharacteristic
778C2×C11C2×#53411yescharacteristic
779C2×C11#344911yescharacteristic
780C2×C11#345911yescharacteristic
781C2×C11#345911yescharacteristic
782D11—28no—
783D11—44no—
784C24—112no—
785C24—114no—
786C24—114no—
787C24—114no—
788C24—112no—
789C24—118no—
790C24—224no—
791C24—224no—
792C24—441no—
793C24—441no—
794C24—442no—
795C24—442no—
796C24—441no—
797C24—441no—
798C24—442no—
799C24—442no—
800C24C23×D1112yes—
801C24C23×D1111yescharacteristic
802C2×D4—24no—
803C2×D4—24no—
804C2×D4—41no—
805C2×D4—41no—
806C2×D4—118no—
807C2×D4—118no—
808C2×D4—118no—
809C2×D4—118no—
810C2×D4—114no—
811C2×D4—224no—
812C2×D4—224no—
813C2×D4—2264no—
814C2×D4—224no—
815C2×D4—224no—
816C2×D4—224no—
817C2×D4—224no—
818C2×D4—441no—
819C2×D4—441no—
820C2×D4—442no—
821C2×D4—442no—
822C2×D4C2×C4×D1118yescomplemented
823C2×D4C2×C4×D1114yescomplemented
824C22×C4—22no—
825C22×C4—22no—
826C22×C4—22no—
827C22×C4—24no—
828C22×C4—24no—
829C22×C4—24no—
830C22×C4—41no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—112no—
835C22×C4—112no—
836C22×C4—112no—
837C22×C4—114no—
838C22×C4—114no—
839C22×C4—118no—
840C22×C4—118no—
841C22×C4—118no—
842C22×C4—112no—
843C22×C4—112no—
844C22×C4—112no—
845C22×C4—224no—
846C22×C4—224no—
847C22×C4—224no—
848C22×C4—224no—
849C22×C4—224no—
850C22×C4—224no—
851C22×C4—224no—
852C22×C4—224no—
853C22×C4—222no—
854C22×C4—224no—
855C22×C4—224no—
856C22×C4—224no—
857C22×C4—4416no—
858C22×C4—442no—
859C22×C4—442no—
860C22×C4—442no—
861C22×C4—442no—
862C22×C4—442no—
863C22×C4—442no—
864C22×C4—442no—
865C22×C4—442no—
866C22×C4—4432no—
867C22×C4—441no—
868C22×C4—441no—
869C22×C4—441no—
870C22×C4—442no—
871C22×C4—441no—
872C22×C4—442no—
873C22×C4—441no—
874C22×C4—441no—
875C22×C4C2×C4×D1114yescomplemented
876C22×C4D4×D1114yes—
877C22×C4C23×D1111yescharacteristic
878C22×C4C23×D1111yescharacteristic
879C22×C4C23×D1112yes—
880C22×C4C23×D1112yes—
881C22×C4C23×D1111yescharacteristic
882C22×C4C23×D1112yes—
883C22×C4C23×D1111yescharacteristic
884C22×C4C23×D1111yescharacteristic
885C22×C4C23×D1111yescharacteristic
886C4⋊C4—24no—
887C4⋊C4—41no—
888C4⋊C4—41no—
889C4⋊C4—118no—
890C4⋊C4—114no—
891C4⋊C4—224no—
892C4⋊C4—224no—
893C4⋊C4—224no—
894C4⋊C4—442no—
895C4⋊C4—441no—
896C4⋊C4—442no—
897C4⋊C4—441no—
898C4⋊C4C2×C4×D1114yescomplemented
899C22⋊C4—24no—
900C22⋊C4—24no—
901C22⋊C4—42no—
902C22⋊C4—42no—
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⋊C4—442no—
921C22⋊C4—442no—
922C22⋊C4C2×C4×D1118yescomplemented
923C42—24no—
924C42—22no—
925C42—22no—
926C42—41no—
927C42—41no—
928C42—224no—
929C42—224no—
930C42—224no—
931C42—224no—
932C42—442no—
933C11C4×#53411yescharacteristic, complemented, Sylow
934C23—21no—
935C23—21no—
936C23—21no—
937C23—21no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—114no—
945C23—114no—
946C23—114no—
947C23—1116no—
948C23—114no—
949C23—2216no—
950C23—222no—
951C23—222no—
952C23—222no—
953C23—222no—
954C23—222no—
955C23—222no—
956C23—222no—
957C23—222no—
958C23—222no—
959C23—222no—
960C23—444no—
961C23—444no—
962C23—444no—
963C23—444no—
964C23—444no—
965C23—444no—
966C23—448no—
967C23—448no—
968C23—448no—
969C23—448no—
970C23—448no—
971C23—448no—
972C23C22×C4×D1114yes—
973C23C22×C4×D1112yes—
974C23C2×D4×D1112yes—
975C23#41×D1112yes—
976C23C24×D1111yescharacteristic
977D4—216no—
978D4—44no—
979D4—2216no—
980D4—2216no—
981D4—2216no—
982D4—444no—
983D4—448no—
984C2×C4—22no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—28no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—22no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—22no—
1001C2×C4—21no—
1002C2×C4—22no—
1003C2×C4—21no—
1004C2×C4—22no—
1005C2×C4—44no—
1006C2×C4—44no—
1007C2×C4—48no—
1008C2×C4—114no—
1009C2×C4—114no—
1010C2×C4—114no—
1011C2×C4—2216no—
1012C2×C4—222no—
1013C2×C4—222no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—222no—
1018C2×C4—2216no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—222no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—448no—
1029C2×C4—448no—
1030C2×C4—448no—
1031C2×C4—448no—
1032C2×C4—444no—
1033C2×C4—444no—
1034C2×C4—448no—
1035C2×C4—444no—
1036C2×C4—448no—
1037C2×C4C22×C4×D1112yes—
1038C2×C4C22×C4×D1112yes—
1039C2×C4C22×C4×D1114yes—
1040C2×C4C2×D4×D1112yes—
1041C2×C4C2×D4×D1112yes—
1042C2×C4#6703712yes—
1043C2×C4#6704212yes—
1044C22—22no—
1045C22—22no—
1046C22—22no—
1047C22—22no—
1048C22—22no—
1049C22—22no—
1050C22—24no—
1051C22—24no—
1052C22—24no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—118no—
1058C22—224no—
1059C22—224no—
1060C22—224no—
1061C22—224no—
1062C22—224no—
1063C22—224no—
1064C22—224no—
1065C22—224no—
1066C22—224no—
1067C22—4416no—
1068C22—4432no—
1069C22—442no—
1070C22—442no—
1071C22—442no—
1072C22—442no—
1073C22C4×D4×D1114yes—
1074C22C23×C4×D1111yescharacteristic
1075C22C22×D4×D1111yescharacteristic
1076C22C2×#6703711yescharacteristic
1077C22C2×#41×D1111yescharacteristic
1078C22C2×#6704211yescharacteristic
1079C22#1062345311yescharacteristic
1080C22#1062345311yescharacteristic
1081C4—22no—
1082C4—24no—
1083C4—22no—
1084C4—22no—
1085C4—42no—
1086C4—42no—
1087C4—41no—
1088C4—41no—
1089C4—224no—
1090C4—224no—
1091C4—224no—
1092C4—442no—
1093C4—442no—
1094C4—442no—
1095C4#1062313614yesdirect product factor
1096C2—24no—
1097C2—44no—
1098C2—228no—
1099C2—444no—
1100C2C2×C4×D4×D1111yescharacteristic
1101C2C4×#6703711yescharacteristic
1102C2C4×#6704211yescharacteristic
1103C2C2×#1062313611yescharacteristic
1104C2#1308194311yescharacteristic
1105C2#1308202311yescharacteristic
1106C2#1308202611yescharacteristic
subgroupG/H
centerC22×C4C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC4×C11×#121C2
socle, cosocleC23×C11C25
prime radicalC2×#10623136C2
hypercenterC4×#121D11
hypocenterC11C4×#534
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
2. C2×C4×D4×D11C2semidirect
3. #13071321C2semidirect
4. #13071317C2semidirect
5. #13071316C2semidirect
6. #13071286C2semidirect
7. #13071280C2semidirect
8. #13071275C2semidirect
9. #13071269C2semidirect
10. #13071229C2semidirect
11. #13071190C2semidirect
12. C4×#66947C2semidirect
13. C4×#66936C2semidirect
14. C4×#66983C2semidirect
15. C4×#66992C2semidirect
16. C4×#66935C2semidirect
17. C4×#66990C2semidirect
18. C2×C4×(C2×D11)⋊C4C2semidirect
19. C4×C11×#121C2semidirect
22. C23×C4×D11C22semidirect
24. C2×C4×D4×C11C22semidirect
25. C2×C4×D4×C11C22semidirect
26. C22×C42×C11C22semidirect
29. C2×D4×Dic11C22semidirect
32. C2×C4×C22⋊D11C22semidirect
33. C2×C4×C22⋊D11C22semidirect
36. C22×C4×Dic11C22semidirect
37. #10623136C4direct (N × H)
41. C2×C4⋊C4×D11C22semidirect
45. C2×(C22⋊D11)⋊C4C22semidirect
47. C2×C22⋊C4×D11C22semidirect
49. C2×C4×D44C22semidirect
50. C2×C42×D11C22semidirect
51. C11×#390C22semidirect
52. C11×#389C22semidirect
53. C11×#388C22semidirect
54. C11×#386C22semidirect
55. C11×#380C22semidirect
56. C4×C11×C4⋊C4C22semidirect
57. C4×C11×C22⋊C4C22semidirect
58. #10622833C22semidirect
59. #10622833C22semidirect
60. #10622826C22semidirect
61. #10622825C22semidirect
62. C4×C22⋊Dic11C22semidirect
63. C2×C11⋊#95C22semidirect
64. C2×C11⋊#95C22semidirect
65. #10622603C22semidirect
66. #10622603C22semidirect
67. #10622602C22semidirect
68. #10622602C22semidirect
69. #10622602C22semidirect
70. #10622594C22semidirect
71. #10622585C22semidirect
72. #10622571C22semidirect
73. #10622571C22semidirect
74. #10622570C22semidirect
77. #10622569C22semidirect
78. #10622568C22semidirect
79. #10622568C22semidirect
80. #10622564C22semidirect
81. #10622563C22semidirect
82. #10622559C22semidirect
83. #10622558C22semidirect
84. #10622558C22semidirect
85. #10622555C22semidirect
86. #10622553C22semidirect
87. #10622552C22semidirect
88. C4×(C2×D11)⋊C4C22semidirect
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. C4×Dic11⋊C4C22semidirect
96. #10622541C22semidirect
97. #10622282C22semidirect
98. #10622281C22semidirect
99. #10622281C22semidirect
100. #10622281C22semidirect
103. #10622278C22semidirect
104. #10622277C22semidirect
105. #10622277C22semidirect
106. #10622268C22semidirect
107. #10622267C22semidirect
108. #10622265C22semidirect
126. C2×D4×D11C2×C4semidirect
134. C22×C4×D11D4semidirect
142. C11×#121C2×C4semidirect
165. #66992C2×C4semidirect
166. #66990C2×C4semidirect
168. #66983C2×C4semidirect
173. C2×(C2×D11)⋊C4C2×C4semidirect
203. #66947C2×C4semidirect
206. #66936C2×C4semidirect
207. #66935C2×C4semidirect
245. C23×D11C22×C4semidirect
254. C2×D4×C11C22×C4semidirect
255. C2×D4×C11C22×C4semidirect
266. C22×C4×C11C22×C4semidirect
284. C2×C22⋊D11C22×C4semidirect
285. C2×C22⋊D11C22×C4semidirect
296. C22×Dic11C22×C4semidirect
310. C2×D44C22×C4semidirect
331. C2×C4×D11C22×C4semidirect
337. C11×C4⋊C4C22×C4semidirect
342. C11×C22⋊C4C22×C4semidirect
352. C22⋊Dic11C22×C4semidirect
363. (C2×D11)⋊C4C22×C4semidirect
364. (C2×D11)⋊C4C22×C4semidirect
365. (C2×D11)⋊C4C22×C4semidirect
366. (C2×D11)⋊C4C22×C4semidirect
370. C4⋊Dic11C22×C4semidirect
375. Dic11⋊C4C22×C4semidirect
396. C4×#121D11semidirect
438. C22×D11C4×D4semidirect
531. C2×C4×D4C2×D11semidirect
532. C2×C4×D4C2×D11semidirect
540. C22×C42C2×D11semidirect
543. #390C2×D11semidirect
546. #389C2×D11semidirect
554. #388C2×D11semidirect
570. #386C2×D11semidirect
583. #380C2×D11semidirect
588. C4×C4⋊C4C2×D11semidirect
596. C4×C22⋊C4C2×D11semidirect
644. C4×C11#534semidirect
688. #121C4×D11semidirect
822. C2×D4C2×C4×D11semidirect
823. C2×D4C2×C4×D11semidirect
875. C22×C4C2×C4×D11semidirect
898. C4⋊C4C2×C4×D11semidirect
922. C22⋊C4C2×C4×D11semidirect
933. C11C4×#534semidirect
1095. C4#10623136direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231362
C2×C4×D4×D112
#130713212
#130713172
#130713162
#130712862
#130712802
#130712752
#130712692
#130712292
#130711902
C4×#669472
C4×#669362
C4×#669832
C4×#669922
C4×#669352
C4×#669902
C2×C4×(C2×D11)⋊C42
C4×C11×#1212
C4×#53411