Finite Group Databasebeta

← #14912783

Subgroups — #14912783

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#13071319C211yesmaximal, characteristic, complemented
4#13071314C212yesmaximal, complemented
5#13071289C212yesmaximal, complemented
6#13071283C212yesmaximal, complemented
7#13071278C212yesmaximal, complemented
8#13071272C212yesmaximal, complemented
9#13071229C211yesmaximal, characteristic, complemented
10#13071190C212yesmaximal, complemented
11#13071143C212yesmaximal, complemented
12#13071137C212yesmaximal, complemented
13#121×Dic11C211yesmaximal, characteristic, complemented
14#13071126C212yesmaximal, complemented
15#13071122C211yesmaximal, characteristic, complemented
16#13071121C212yesmaximal, complemented
17#13071117C212yesmaximal, complemented
18C2×#10622279C211yesmaximal, characteristic, complemented
19C11×#2325C211yesmaximal, characteristic, complemented
20C22×D4×D11C2212yes—
21C23×C4×D11C2211yescharacteristic
22C23×C4×D11C2212yescomplemented
23C2×C11×#121C2211yescharacteristic
24C2×C4×D4×C11C2212yescomplemented
25C2×#66992C2212yes—
26C2×#66990C2212yes—
27C2×D4×Dic11C2212yescomplemented
28C2×D4×Dic11C2211yescharacteristic, complemented
29C2×#66983C2211yescharacteristic
30C2×C4×C22⋊D11C2212yes—
31C2×C4×C22⋊D11C2212yescomplemented
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic, complemented
35C22×C4×Dic11C2211yescharacteristic, complemented
36#10623136C4116yescomplemented
37C4×D4×D11—216no—
38C2×#66947C2212yes—
39C2×#66946C2212yes—
40C2×#66946C2211yescharacteristic, complemented
41C2×C4⋊C4×D11C2212yescomplemented
42C2×#66936C2212yes—
43C2×#66935C2212yes—
44C2×(C22⋊D11)⋊C4C2212yes—
45C2×(C22⋊D11)⋊C4C2212yescomplemented
46C2×(C22⋊D11)⋊C4C2212yescomplemented
47C2×C22⋊C4×D11C2212yes—
48C2×C22⋊C4×D11C2212yescomplemented
49C2×C4×D44C2212yes—
50C2×C42×D11C2212yescomplemented
51C11×#388C2212yescomplemented
52C11×#387C2212yescomplemented
53C11×#386C2212yescomplemented
54C11×#386C2212yescomplemented
55C11×#385C2212yescomplemented
56C11×#380C2211yescharacteristic, complemented
57C2×C11×#95C2211yescharacteristic, complemented
58#10622834C2211yescharacteristic, complemented
59#10622833C2212yescomplemented
60#10622826C2212yescomplemented
61#10622826C2212yescomplemented
62#10622825C2211yescharacteristic, complemented
63#10622823C2212yescomplemented
64C2×C11⋊#95C2211yescharacteristic, complemented
65#10622602C2212yescomplemented
66#10622602C2212yescomplemented
67#10622602C2212yescomplemented
68#10622601C2211yescharacteristic, complemented
69#10622598C2211yescharacteristic, complemented
70#10622591C2212yescomplemented
71C4⋊C4×Dic11C2211yescharacteristic, complemented
72C4⋊C4×Dic11C2211yescharacteristic, complemented
73#10622586C2211yescharacteristic, complemented
74#10622571C2212yescomplemented
75#10622570C2212yescomplemented
76#10622569C2212yes—
77#10622569C2212yes—
78#10622569C2212yescomplemented
79#10622568C2212yescomplemented
80#10622568C2212yescomplemented
81#10622564C2212yescomplemented
82#10622557C2212yescomplemented
83#10622557C2212yescomplemented
84#10622555C2212yescomplemented
85C22⋊C4×Dic11C2212yescomplemented
86C22⋊C4×Dic11C2212yescomplemented
87#10622553C2212yescomplemented
88#10622546C2212yescomplemented
89#10622283C2212yescomplemented
90#10622283C2212yescomplemented
91#10622282C2212yescomplemented
92#10622281C2212yescomplemented
93#10622281C2212yescomplemented
94#10622281C2212yescomplemented
95#10622279C2212yescomplemented
96#10622279C2212yescomplemented
97#10622279C2212yescomplemented
98#10622279C2212yescomplemented
99#10622279C2212yescomplemented
100#10622279C2212yescomplemented
101#10622278C2212yes—
102#10622278C2212yes—
103#10622278C2212yescomplemented
104#10622277C2212yescomplemented
105#10622277C2212yescomplemented
106#10622266C2212yescomplemented
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—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—
144C2×C11×C4⋊C4C2312yes—
145C2×C11×C4⋊C4C2311yescharacteristic
146C2×C11×C4⋊C4C2311yescharacteristic
147C2×C11×C4⋊C4C2311yescharacteristic
148C2×C11×C22⋊C4C2312yes—
149C2×C11×C22⋊C4C2312yes—
150C2×C11×C22⋊C4C2312yes—
151C2×C11×C22⋊C4C2312yes—
152C2×C11×C22⋊C4C2312yes—
153C2×C42×C11C2312yes—
154C2×C22⋊Dic11C2312yes—
155C2×C22⋊Dic11C2312yes—
156C2×C22⋊Dic11C2312yes—
157C2×C22⋊Dic11C2312yes—
158C2×C22⋊Dic11C2312yes—
159#66992C2×C4116yescomplemented
160#66990C2×C4116yescomplemented
161D4×Dic11—28no—
162D4×Dic11—42no—
163#66983C2×C418yescomplemented
164C4×C22⋊D11—28no—
165C4×C22⋊D11—28no—
166C2×(C2×D11)⋊C4—24no—
167C2×(C2×D11)⋊C4C2×C418yescomplemented
168C2×(C2×D11)⋊C4C2312yes—
169C2×(C2×D11)⋊C4C2312yes—
170C2×(C2×D11)⋊C4C2312yes—
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×C4⋊Dic11C2312yes—
183C2×C4⋊Dic11C2311yescharacteristic
184C2×C4⋊Dic11C2311yescharacteristic
185C2×C4⋊Dic11C2311yescharacteristic
186C2×Dic11⋊C4C2312yes—
187C2×Dic11⋊C4C2312yes—
188C2×Dic11⋊C4C2312yes—
189C2×Dic11⋊C4C2312yes—
190C2×Dic11⋊C4C2312yes—
191C2×C4×Dic11—42no—
192C2×C4×Dic11—42no—
193C2×C4×Dic11C2312yes—
194C2×C4×Dic11C2312yes—
195C2×C4×Dic11C2312yes—
196C2×C4×Dic11C2312yes—
197C2×C4×Dic11C2311yescharacteristic
198C2×C4×Dic11C2311yescharacteristic
199C2×C4×Dic11C2312yes—
200C2×C4×Dic11C2311yescharacteristic
201C2×C4×Dic11C2311yescharacteristic
202#66947C2×C4116yescomplemented
203#66946—28no—
204#66946—42no—
205C4⋊C4×D11—28no—
206#66936C2×C4116yescomplemented
207#66935C2×C4116yescomplemented
208(C22⋊D11)⋊C4—28no—
209(C22⋊D11)⋊C4—28no—
210(C22⋊D11)⋊C4—44no—
211C22⋊C4×D11—28no—
212C22⋊C4×D11—28no—
213C4×D44—28no—
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—24no—
258C22×C4×C11—41no—
259C22×C4×C11—41no—
260C22×C4×C11—41no—
261C22×C4×C11—41no—
262C22×C4×C11—42no—
263C22×C4×C11—42no—
264C22×C4×C11—41no—
265C22×C4×C11—41no—
266C22×C4×C11C22×C414yescomplemented
267C22×C4×C11C2×D414yes—
268C22×C4×C11C2412yes—
269C22×C4×C11C2412yes—
270C22×C4×C11C2412yes—
271C22×C4×C11C2411yescharacteristic
272C22×C4×C11C2412yes—
273C22×C4×C11C2411yescharacteristic
274C22×C4×C11C2412yes—
275C2×C22⋊D11—24no—
276C2×C22⋊D11—24no—
277C2×C22⋊D11—24no—
278C2×C22⋊D11—24no—
279C2×C22⋊D11—42no—
280C2×C22⋊D11—42no—
281C2×C22⋊D11C22×C418yes—
282C2×C22⋊D11C22×C418yescomplemented
283C2×C22⋊D11C22×C418yescomplemented
284C22×Dic11—22no—
285C22×Dic11—22no—
286C22×Dic11—24no—
287C22×Dic11—24no—
288C22×Dic11—24no—
289C22×Dic11—22no—
290C22×Dic11—41no—
291C22×Dic11—41no—
292C22×Dic11—41no—
293C22×Dic11—41no—
294C22×Dic11C22×C414yescomplemented
295C22×Dic11C2×D414yes—
296C22×Dic11C2411yescharacteristic
297C22×Dic11C2411yescharacteristic
298C22×Dic11C2412yes—
299C22×Dic11C2412yes—
300C22×Dic11C2412yes—
301C22×Dic11C2412yes—
302C22×Dic11C2411yescharacteristic
303C22×Dic11C2411yescharacteristic
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—
344C22⋊Dic11—24no—
345C22⋊Dic11—24no—
346C22⋊Dic11—42no—
347C22⋊Dic11—42no—
348C22⋊Dic11C22×C418yescomplemented
349(C2×D11)⋊C4—24no—
350(C2×D11)⋊C4—24no—
351(C2×D11)⋊C4—24no—
352(C2×D11)⋊C4—24no—
353(C2×D11)⋊C4—24no—
354(C2×D11)⋊C4—24no—
355(C2×D11)⋊C4—42no—
356(C2×D11)⋊C4—42no—
357(C2×D11)⋊C4—42no—
358(C2×D11)⋊C4—42no—
359(C2×D11)⋊C4C22×C418yescomplemented
360(C2×D11)⋊C4C22×C418yescomplemented
361(C2×D11)⋊C4C22×C418yescomplemented
362(C2×D11)⋊C4C22×C418yescomplemented
363C4⋊Dic11—24no—
364C4⋊Dic11—41no—
365C4⋊Dic11—41no—
366C4⋊Dic11C22×C414yescomplemented
367Dic11⋊C4—24no—
368Dic11⋊C4—24no—
369Dic11⋊C4—42no—
370Dic11⋊C4—42no—
371Dic11⋊C4C22×C418yescomplemented
372C4×Dic11—24no—
373C4×Dic11—24no—
374C4×Dic11—24no—
375C4×Dic11—22no—
376C4×Dic11—22no—
377C4×Dic11—24no—
378C4×Dic11—41no—
379C4×Dic11—41no—
380C4×Dic11—42no—
381C2×#534—111no—
382C22×C4×D4—112no—
383#2325—111no—
384#2325—112no—
385#2325D1111yescharacteristic, complemented
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—112no—
395C4×#121—111no—
396C4×#121—111no—
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—22no—
450C2×C4×C11—22no—
451C2×C4×C11—21no—
452C2×C4×C11—21no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
462C2×C4×C11—44no—
463C2×C4×C11—44no—
464C2×C4×C11—48no—
465C2×C4×C11—44no—
466C2×C4×C11C23×C414yes—
467C2×C4×C11C23×C412yes—
468C2×C4×C11C23×C412yes—
469C2×C4×C11C22×D414yes—
470C22⋊D11—216no—
471C22⋊D11—216no—
472C22⋊D11—48no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—21no—
477C2×Dic11—21no—
478C2×Dic11—22no—
479C2×Dic11—28no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—21no—
483C2×Dic11—21no—
484C2×Dic11—21no—
485C2×Dic11—21no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—21no—
491C2×Dic11—21no—
492C2×Dic11—44no—
493C2×Dic11—44no—
494C2×Dic11—48no—
495C2×Dic11C23×C414yes—
496C2×Dic11C23×C414yes—
497C2×Dic11C22×D412yes—
498C2×Dic11C22×D412yes—
499C2×Dic11H(5,𝔽2)12yes—
500C2×Dic11H(5,𝔽2)12yes—
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—111no—
525C2×C4×D4—112no—
526C2×C4×D4—111no—
527C2×C4×D4—112no—
528C2×C4×D4—112no—
529C2×C4×D4—112no—
530C2×C4×D4—112no—
531C2×C4×D4—2216no—
532C2×C4×D4C2×D1112yescomplemented
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—111no—
540C22×C42—112no—
541#390—111no—
542#390—111no—
543#390—112no—
544#389—111no—
545#389—111no—
546#389—112no—
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#387C2×D1112yescomplemented
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#386C2×D1112yescomplemented
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#385C2×D1112yescomplemented
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—111no—
587C4×C4⋊C4—111no—
588C4×C4⋊C4—112no—
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⋊C4—112no—
597C2×#95—111no—
598C2×#95C2×D1111yescharacteristic, complemented
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—24no—
640C4×C11—42no—
641C4×C11—42no—
642C4×C11—42no—
643Dic11—24no—
644Dic11—24no—
645Dic11—22no—
646Dic11—42no—
647Dic11—42no—
648Dic11—41no—
649Dic11—41no—
650Dic11#53414yescomplemented
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—112no—
670C23×C4—111no—
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×D1111yescharacteristic
681C23×C4C22×D1112yes—
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—228no—
693C4×D4—228no—
694C4×D4—228no—
695C4×D4—228no—
696C4×D4—228no—
697C4×D4—228no—
698C4×D4—228no—
699C4×D4—444no—
700C4×D4—442no—
701C4×D4—442no—
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—112no—
745C2×C42—112no—
746C2×C42—112no—
747C2×C42—112no—
748C2×C42—111no—
749C2×C42—111no—
750C2×C42—112no—
751C2×C42—111no—
752C2×C42—111no—
753C2×C42—228no—
754C2×C42—442no—
755C2×C42—442no—
756C2×C42C22×D1112yes—
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#95C22×D1112yes—
769#95C22×D1112yes—
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—24no—
826C22×C4—41no—
827C22×C4—41no—
828C22×C4—41no—
829C22×C4—41no—
830C22×C4—42no—
831C22×C4—42no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—111no—
835C22×C4—114no—
836C22×C4—112no—
837C22×C4—112no—
838C22×C4—111no—
839C22×C4—114no—
840C22×C4—118no—
841C22×C4—118no—
842C22×C4—118no—
843C22×C4—111no—
844C22×C4—111no—
845C22×C4—112no—
846C22×C4—112no—
847C22×C4—224no—
848C22×C4—224no—
849C22×C4—224no—
850C22×C4—224no—
851C22×C4—224no—
852C22×C4—224no—
853C22×C4—224no—
854C22×C4—224no—
855C22×C4—224no—
856C22×C4—222no—
857C22×C4—222no—
858C22×C4—224no—
859C22×C4—224no—
860C22×C4—224no—
861C22×C4—222no—
862C22×C4—224no—
863C22×C4—442no—
864C22×C4—442no—
865C22×C4—442no—
866C22×C4—442no—
867C22×C4—442no—
868C22×C4—442no—
869C22×C4—442no—
870C22×C4—442no—
871C22×C4—4416no—
872C22×C4—4432no—
873C22×C4—441no—
874C22×C4—441no—
875C22×C4—441no—
876C22×C4—441no—
877C22×C4C2×C4×D1114yescomplemented
878C22×C4D4×D1114yes—
879C22×C4C23×D1112yes—
880C22×C4C23×D1112yes—
881C22×C4C23×D1112yes—
882C22×C4C23×D1111yescharacteristic
883C22×C4C23×D1112yes—
884C22×C4C23×D1111yescharacteristic
885C22×C4C23×D1112yes—
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—224no—
925C42—224no—
926C42—222no—
927C42—222no—
928C42—224no—
929C42—224no—
930C42—441no—
931C42—441no—
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—22no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—44no—
1002C2×C4—44no—
1003C2×C4—48no—
1004C2×C4—44no—
1005C2×C4—112no—
1006C2×C4—112no—
1007C2×C4—112no—
1008C2×C4—114no—
1009C2×C4—114no—
1010C2×C4—112no—
1011C2×C4—2216no—
1012C2×C4—2216no—
1013C2×C4—228no—
1014C2×C4—222no—
1015C2×C4—222no—
1016C2×C4—222no—
1017C2×C4—221no—
1018C2×C4—221no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—221no—
1023C2×C4—221no—
1024C2×C4—221no—
1025C2×C4—221no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—221no—
1030C2×C4—221no—
1031C2×C4—222no—
1032C2×C4—448no—
1033C2×C4—448no—
1034C2×C4—448no—
1035C2×C4—448no—
1036C2×C4—448no—
1037C2×C4—448no—
1038C2×C4—444no—
1039C2×C4—444no—
1040C2×C4C22×C4×D1112yes—
1041C2×C4C22×C4×D1112yes—
1042C2×C4C22×C4×D1114yes—
1043C2×C4C2×D4×D1114yes—
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×#41×D1111yescharacteristic
1077C22D11×H(5,𝔽2)11yescharacteristic
1078C22D11×H(5,𝔽2)11yescharacteristic
1079C22#1062345511yescharacteristic
1080C22#1062345711yescharacteristic
1081C4—24no—
1082C4—24no—
1083C4—22no—
1084C4—22no—
1085C4—42no—
1086C4—42no—
1087C4—42no—
1088C4—114no—
1089C4—222no—
1090C4—224no—
1091C4—224no—
1092C4—442no—
1093C4—442no—
1094C4—441no—
1095C4—441no—
1096C2—24no—
1097C2—44no—
1098C2—228no—
1099C2—444no—
1100C2C2×C4×D4×D1111yescharacteristic
1101C2#1308182011yescharacteristic
1102C2#1308182211yescharacteristic
1103C2D11×#53411yescharacteristic
1104C2#1308194411yescharacteristic
1105C2#1308202411yescharacteristic
1106C2#1308202711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2325C2
socle, cosocleC23×C11C25
prime radicalC2×#10623136C2
hypercenter#2325D11
hypocenterC11C4×#534
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2325

Complements

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

NH ≅ G/Ntype
2. C2×C4×D4×D11C2semidirect
3. #13071319C2semidirect
4. #13071314C2semidirect
5. #13071289C2semidirect
6. #13071283C2semidirect
7. #13071278C2semidirect
8. #13071272C2semidirect
9. #13071229C2semidirect
10. #13071190C2semidirect
11. #13071143C2semidirect
12. #13071137C2semidirect
13. #121×Dic11C2semidirect
14. #13071126C2semidirect
15. #13071122C2semidirect
16. #13071121C2semidirect
17. #13071117C2semidirect
18. C2×#10622279C2semidirect
19. C11×#2325C2semidirect
22. C23×C4×D11C22semidirect
24. C2×C4×D4×C11C22semidirect
27. C2×D4×Dic11C22semidirect
28. C2×D4×Dic11C22semidirect
31. C2×C4×C22⋊D11C22semidirect
34. C22×C4×Dic11C22semidirect
35. C22×C4×Dic11C22semidirect
36. #10623136C4semidirect
40. C2×#66946C22semidirect
41. C2×C4⋊C4×D11C22semidirect
45. C2×(C22⋊D11)⋊C4C22semidirect
46. C2×(C22⋊D11)⋊C4C22semidirect
48. C2×C22⋊C4×D11C22semidirect
50. C2×C42×D11C22semidirect
51. C11×#388C22semidirect
52. C11×#387C22semidirect
53. C11×#386C22semidirect
54. C11×#386C22semidirect
55. C11×#385C22semidirect
56. C11×#380C22semidirect
57. C2×C11×#95C22semidirect
58. #10622834C22semidirect
59. #10622833C22semidirect
60. #10622826C22semidirect
61. #10622826C22semidirect
62. #10622825C22semidirect
63. #10622823C22semidirect
64. C2×C11⋊#95C22semidirect
65. #10622602C22semidirect
66. #10622602C22semidirect
67. #10622602C22semidirect
68. #10622601C22semidirect
69. #10622598C22semidirect
70. #10622591C22semidirect
71. C4⋊C4×Dic11C22semidirect
72. C4⋊C4×Dic11C22semidirect
73. #10622586C22semidirect
74. #10622571C22semidirect
75. #10622570C22semidirect
78. #10622569C22semidirect
79. #10622568C22semidirect
80. #10622568C22semidirect
81. #10622564C22semidirect
82. #10622557C22semidirect
83. #10622557C22semidirect
84. #10622555C22semidirect
85. C22⋊C4×Dic11C22semidirect
86. C22⋊C4×Dic11C22semidirect
87. #10622553C22semidirect
88. #10622546C22semidirect
89. #10622283C22semidirect
90. #10622283C22semidirect
91. #10622282C22semidirect
92. #10622281C22semidirect
93. #10622281C22semidirect
94. #10622281C22semidirect
95. #10622279C22semidirect
96. #10622279C22semidirect
97. #10622279C22semidirect
98. #10622279C22semidirect
99. #10622279C22semidirect
100. #10622279C22semidirect
103. #10622278C22semidirect
104. #10622277C22semidirect
105. #10622277C22semidirect
106. #10622266C22semidirect
107. #10622262C22semidirect
108. #10622260C22semidirect
126. C2×D4×D11C2×C4semidirect
134. C22×C4×D11D4semidirect
142. C11×#121C2×C4semidirect
159. #66992C2×C4semidirect
160. #66990C2×C4semidirect
163. #66983C2×C4semidirect
167. C2×(C2×D11)⋊C4C2×C4semidirect
202. #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
282. C2×C22⋊D11C22×C4semidirect
283. C2×C22⋊D11C22×C4semidirect
294. C22×Dic11C22×C4semidirect
310. C2×D44C22×C4semidirect
331. C2×C4×D11C22×C4semidirect
337. C11×C4⋊C4C22×C4semidirect
342. C11×C22⋊C4C22×C4semidirect
348. C22⋊Dic11C22×C4semidirect
359. (C2×D11)⋊C4C22×C4semidirect
360. (C2×D11)⋊C4C22×C4semidirect
361. (C2×D11)⋊C4C22×C4semidirect
362. (C2×D11)⋊C4C22×C4semidirect
366. C4⋊Dic11C22×C4semidirect
371. Dic11⋊C4C22×C4semidirect
385. #2325D11semidirect
438. C22×D11C4×D4semidirect
532. C2×C4×D4C2×D11semidirect
554. #388C2×D11semidirect
558. #387C2×D11semidirect
569. #386C2×D11semidirect
570. #386C2×D11semidirect
578. #385C2×D11semidirect
583. #380C2×D11semidirect
598. C2×#95C2×D11semidirect
650. Dic11#534semidirect
688. #121C4×D11semidirect
822. C2×D4C2×C4×D11semidirect
823. C2×D4C2×C4×D11semidirect
877. C22×C4C2×C4×D11semidirect
898. C4⋊C4C2×C4×D11semidirect
922. C22⋊C4C2×C4×D11semidirect
933. C11C4×#534semidirect

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
#130713192
#130713142
#130712892
#130712832
#130712782
#130712722
#130712292
#130711902
#130711432
#130711372
#121×Dic112
#130711262
#130711222
#130711212
#130711172
C2×#106222792
C11×#23252
C4×#53411