Finite Group Databasebeta

← #14914920

Subgroups — #14914920

Order 2816.

3586 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623205C211yesmaximal, characteristic
2C2×#10623105C211yesmaximal, characteristic, complemented
3C2×C4×D4×D11C211yesmaximal, characteristic, complemented
4#13071692C211yesmaximal, characteristic, complemented
5#13071691C211yesmaximal, characteristic, complemented
6#13071683C211yesmaximal, characteristic, complemented
7#13071680C211yesmaximal, characteristic, complemented
8#13071680C211yesmaximal, characteristic, complemented
9#13071678C211yesmaximal, characteristic, complemented
10#13071677C211yesmaximal, characteristic, complemented
11#13071655C212yesmaximal, complemented
12#13071649C212yesmaximal, complemented
13#13071635C212yesmaximal, complemented
14#13071629C212yesmaximal, complemented
15#13071278C212yesmaximal, complemented
16#13071269C212yesmaximal, complemented
17#13071195C211yesmaximal, characteristic, complemented
18C4×#66935C212yesmaximal, complemented
19#13071117C212yesmaximal, complemented
20#13071105C211yesmaximal, characteristic, complemented
21#13071096C211yesmaximal, characteristic, complemented
22#13070970C211yesmaximal, characteristic, complemented
23C11×#2367C211yesmaximal, characteristic, complemented
24C22×#4343C2211yescharacteristic
25C22×D4×D11C2211yescharacteristic
26C23×C4×D11C2212yes—
27C2×C11×#124C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic, complemented
29C2×C4×D4×C11C2211yescharacteristic
30C2×#67000C2211yescharacteristic
31C2×Q8×Dic11C2211yescharacteristic, complemented
32C2×#66993C2211yescharacteristic
33C2×D4×Dic11C2211yescharacteristic
34C2×C4×C22⋊D11C2212yes—
35C2×C4×C22⋊D11C2212yescomplemented
36#10623205C4116yescomplemented
37#10623105—28no—
38C4×D4×D11—28no—
39C2×#66946C2212yes—
40C2×#66946C2211yescharacteristic
41C2×#66946C2211yescharacteristic, complemented
42C2×#66946C2212yescomplemented
43C2×#66945C2211yescharacteristic
44C2×C4⋊C4×D11C2211yescharacteristic
45C2×C4⋊C4×D11C2212yescomplemented
46C2×#66937C2212yes—
47C2×#66937C2212yes—
48C2×#66935C2212yes—
49C2×#66935C2212yes—
50C2×(C22⋊D11)⋊C4C2212yes—
51C2×(C22⋊D11)⋊C4C2212yescomplemented
52C2×C22⋊C4×D11C2212yes—
53C2×#66927C2211yescharacteristic
54C2×C4×D44C2212yes—
55C2×C4×D44C2211yescharacteristic
56C2×C4×D44C2211yescharacteristic, complemented
57C2×C4×D44C2212yescomplemented
58C2×#66925C2211yescharacteristic
59C2×#66925C2211yescharacteristic
60C2×#66925C2212yescomplemented
61C2×C42×D11C2211yescharacteristic
62C11×#391C2211yescharacteristic, complemented
63C11×#390C2211yescharacteristic
64C11×#388C2212yescomplemented
65C11×#388C2212yescomplemented
66C11×#385C2212yescomplemented
67C4×C11×C4⋊C4C2211yescharacteristic, complemented
68C4×C11×C4⋊C4C2211yescharacteristic, complemented
69C4×C11×C22⋊C4C2212yescomplemented
70#10622843C2211yescharacteristic, complemented
71#10622834C2211yescharacteristic
72#10622826C2212yescomplemented
73#10622603C2212yescomplemented
74#10622602C2211yescharacteristic
75#10622602C2211yescharacteristic
76#10622602C2212yescomplemented
77#10622601C2211yescharacteristic
78#10622601C2211yescharacteristic, complemented
79#10622601C2212yescomplemented
80C4⋊C4×Dic11C2211yescharacteristic, complemented
81C4⋊C4×Dic11C2211yescharacteristic, complemented
82#10622585C2211yescharacteristic, complemented
83#10622585C2211yescharacteristic, complemented
84#10622571C2212yescomplemented
85#10622570C2212yes—
86#10622570C2212yes—
87#10622570C2212yescomplemented
88#10622570C2212yescomplemented
89#10622569C2212yescomplemented
90#10622569C2212yescomplemented
91#10622568C2212yes—
92#10622568C2212yes—
93#10622564C2212yescomplemented
94#10622564C2212yescomplemented
95#10622563C2212yescomplemented
96C22⋊C4×Dic11C2212yescomplemented
97#10622553C2212yescomplemented
98#10622552C2211yescharacteristic
99#10622552C2211yescharacteristic, complemented
100#10622552C2212yescomplemented
101C4×(C2×D11)⋊C4C2212yes—
102C4×(C2×D11)⋊C4C2212yescomplemented
103C4×C4⋊Dic11C2211yescharacteristic, complemented
104C4×C4⋊Dic11C2211yescharacteristic, complemented
105C4×Dic11⋊C4C2212yescomplemented
106C4×Dic11⋊C4C2211yescharacteristic, complemented
107C4×Dic11⋊C4C2211yescharacteristic, complemented
108#10622283C2212yescomplemented
109#10622282C2212yescomplemented
110#10622281C2211yescharacteristic
111#10622281C2211yescharacteristic
112#10622281C2212yescomplemented
113#10622279C2212yes—
114#10622279C2212yescomplemented
115#10622279C2212yescomplemented
116#10622279C2212yescomplemented
117#10622278C2212yes—
118#10622278C2212yes—
119#10622278C2212yescomplemented
120#10622278C2212yescomplemented
121#10622278C2212yescomplemented
122#10622278C2212yescomplemented
123#10622262C2212yescomplemented
124#10622260C2211yescharacteristic, complemented
125#10622260C2211yescharacteristic, complemented
126C24×D11C2312yes—
127C22×Q8×C11C2311yescharacteristic
128C22×D4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C23×Dic11C2312yes—
134C2×#4343—24no—
135C2×#4343—24no—
136C2×#4343C2×C418yescomplemented
137C2×D4×D11—24no—
138C2×D4×D11—24no—
139C2×D4×D11C2×C418yescomplemented
140C22×D44C2311yescharacteristic
141C22×D44C2312yes—
142C22×D44C2311yescharacteristic
143C22×D44C2312yes—
144C22×D44C2312yes—
145C22×C4×D11—28no—
146C22×C4×D11—44no—
147C22×C4×D11—44no—
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2312yes—
150C22×C4×D11C2312yes—
151C22×C4×D11C2312yes—
152C22×C4×D11C2311yescharacteristic
153C22×C4×D11C2312yes—
154C22×C4×D11C2312yes—
155C22×C4×D11C2312yes—
156C22×C4×D11C2311yescharacteristic
157C11×#124C2×C418yescomplemented
158C4×Q8×C11—24no—
159C4×D4×C11—24no—
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C4⋊C4C2311yescharacteristic
162C2×C11×C4⋊C4C2311yescharacteristic
163C2×C11×C4⋊C4C2311yescharacteristic
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C11×C22⋊C4C2312yes—
169C2×C11×C22⋊C4C2312yes—
170C2×C42×C11C2311yescharacteristic
171C2×C42×C11C2311yescharacteristic
172C2×C42×C11C2312yes—
173C2×C42×C11C2312yes—
174C2×C42×C11C2311yescharacteristic
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178#67000C2×C418yescomplemented
179Q8×Dic11—24no—
180#66993C2×C418yescomplemented
181D4×Dic11—24no—
182C4×C22⋊D11—28no—
183C4×C22⋊D11—44no—
184C2×(C2×D11)⋊C4C2311yescharacteristic
185C2×(C2×D11)⋊C4C2311yescharacteristic
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2311yescharacteristic
200C2×(C2×D11)⋊C4C2311yescharacteristic
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×C4⋊Dic11C2312yes—
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2311yescharacteristic
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2311yescharacteristic
208C2×Dic11⋊C4C2311yescharacteristic
209C2×Dic11⋊C4C2311yescharacteristic
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2311yescharacteristic
213C2×Dic11⋊C4C2311yescharacteristic
214C2×Dic11⋊C4C2311yescharacteristic
215C2×Dic11⋊C4C2311yescharacteristic
216C2×Dic11⋊C4C2312yes—
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2312yes—
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2312yes—
225C2×C4×Dic11C2312yes—
226C2×C4×Dic11C2311yescharacteristic
227#66946—28no—
228#66946—24no—
229#66946—24no—
230#66946—44no—
231#66945—24no—
232C4⋊C4×D11—28no—
233C4⋊C4×D11D418yescomplemented
234#66937C2×C4116yescomplemented
235#66937C2×C4116yescomplemented
236#66935C2×C4116yescomplemented
237#66935C2×C4116yescomplemented
238(C22⋊D11)⋊C4—28no—
239(C22⋊D11)⋊C4—44no—
240C22⋊C4×D11—28no—
241#66927C2×C418yescomplemented
242C4×D44—28no—
243C4×D44—24no—
244C4×D44—24no—
245C4×D44—44no—
246#66925—24no—
247#66925—28no—
248#66925C2×C418yescomplemented
249C42×D11—24no—
250C11×#95C2311yescharacteristic
251C11×#95C2311yescharacteristic
252C11×#95C2312yes—
253C11×#95C2312yes—
254C11×#95C2312yes—
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2311yescharacteristic
262C11⋊#95C2311yescharacteristic
263C11⋊#95C2312yes—
264C11⋊#95C2311yescharacteristic
265C11⋊#95C2311yescharacteristic
266#34265—111nomaximal, Sylow
267C24×C11C2412yes—
268C23×D11—24no—
269C23×D11—24no—
270C23×D11—42no—
271C23×D11—42no—
272C23×D11—42no—
273C23×D11—42no—
274C23×D11C22×C418yes—
275C23×D11C2412yes—
276C23×D11C2412yes—
277C23×D11C2411yescharacteristic
278C2×Q8×C11—22no—
279C2×Q8×C11—22no—
280C2×Q8×C11C22×C414yescomplemented
281C2×D4×C11—22no—
282C2×D4×C11—22no—
283C2×D4×C11C22×C414yes—
284C22×C4×C11—24no—
285C22×C4×C11—24no—
286C22×C4×C11—42no—
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2412yes—
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C2×C22⋊D11—24no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11—42no—
300C2×C22⋊D11—42no—
301C2×C22⋊D11—42no—
302C2×C22⋊D11—42no—
303C2×C22⋊D11C22×C418yes—
304C2×C22⋊D11C22×C418yescomplemented
305C2×C22⋊D11C22×C418yescomplemented
306C22×Dic11—24no—
307C22×Dic11—24no—
308C22×Dic11—42no—
309C22×Dic11C2412yes—
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2411yescharacteristic
315C22×Dic11C2412yes—
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318#4343—232no—
319D4×D11—232no—
320C2×D44—24no—
321C2×D44—24no—
322C2×D44—22no—
323C2×D44—22no—
324C2×D44—22no—
325C2×D44—22no—
326C2×D44—42no—
327C2×D44—42no—
328C2×D44—42no—
329C2×D44—42no—
330C2×D44C22×C414yes—
331C2×D44C22×C418yes—
332C2×D44C22×C414yescomplemented
333C2×D44C22×C418yescomplemented
334C2×D44C22×C418yescomplemented
335C2×C4×D11—24no—
336C2×C4×D11—24no—
337C2×C4×D11—22no—
338C2×C4×D11—24no—
339C2×C4×D11—24no—
340C2×C4×D11—24no—
341C2×C4×D11—22no—
342C2×C4×D11—22no—
343C2×C4×D11—24no—
344C2×C4×D11—24no—
345C2×C4×D11—22no—
346C2×C4×D11—24no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11—41no—
352C2×C4×D11—41no—
353C2×C4×D11—42no—
354C2×C4×D11—42no—
355C2×C4×D11—42no—
356C2×C4×D11—42no—
357C2×C4×D11—432no—
358C2×C4×D11C22×C414yes—
359C2×C4×D11C22×C418yescomplemented
360C2×C4×D11C2×D418yes—
361C2×C4×D11C2×D414yes—
362C2×C4×D11#4114yes—
363C11×C4⋊C4—24no—
364C11×C4⋊C4—22no—
365C11×C4⋊C4—22no—
366C11×C4⋊C4—41no—
367C11×C4⋊C4C2×D414yes—
368C11×C22⋊C4—24no—
369C11×C22⋊C4—42no—
370C11×C22⋊C4—42no—
371C11×C22⋊C4C22×C418yescomplemented
372C11×C22⋊C4C22×C418yescomplemented
373C42×C11—22no—
374C42×C11—24no—
375C42×C11—22no—
376C42×C11—42no—
377C42×C11C22×C414yescomplemented
378C22⋊Dic11—24no—
379C22⋊Dic11—42no—
380C22⋊Dic11—42no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—22no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—24no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4—42no—
395(C2×D11)⋊C4—42no—
396(C2×D11)⋊C4C22×C414yes—
397(C2×D11)⋊C4C22×C414yes—
398(C2×D11)⋊C4C22×C418yescomplemented
399(C2×D11)⋊C4C22×C418yescomplemented
400C4⋊Dic11—24no—
401C4⋊Dic11—22no—
402C4⋊Dic11—22no—
403C4⋊Dic11—41no—
404C4⋊Dic11C2×D414yes—
405Dic11⋊C4—22no—
406Dic11⋊C4—22no—
407Dic11⋊C4—22no—
408Dic11⋊C4—22no—
409Dic11⋊C4—41no—
410Dic11⋊C4—41no—
411Dic11⋊C4C22×C414yescomplemented
412Dic11⋊C4C22×C414yescomplemented
413Dic11⋊C4C2×D418yes—
414C4×Dic11—22no—
415C4×Dic11—22no—
416C4×Dic11—24no—
417C4×Dic11—24no—
418C4×Dic11—22no—
419C4×Dic11—22no—
420C4×Dic11—42no—
421C4×Dic11—42no—
422C4×Dic11—42no—
423C4×Dic11C22×C414yescomplemented
424C2×#535—111no—
425C2×#520—111no—
426C22×C4×D4—111no—
427#2367—111no—
428#2367—111no—
429#2367—111no—
430#2367D1111yescharacteristic, complemented
431#2366—111no—
432#2366—111no—
433#2366—111no—
434#2366—111no—
435#2363—112no—
436#2363—112no—
437#2361—112no—
438#2361—112no—
439#2321—112no—
440#2321—112no—
441#2309—111no—
442C4×#120—112no—
443C4×#120—112no—
444#2297—111no—
445#2296—111no—
446#2274—111no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11C23×C414yes—
454C23×C11C2511yescharacteristic
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—216no—
472C22×D11—48no—
473C22×D11—48no—
474C22×D11—48no—
475C22×D11—48no—
476C22×D11—48no—
477C22×D11—48no—
478C22×D11C23×C414yes—
479C22×D11C23×C414yes—
480C22×D11C23×C412yes—
481C22×D11C22×D412yes—
482C22×D11C2×#4112yes—
483Q8×C11—28no—
484D4×C11—28no—
485C2×C4×C11—22no—
486C2×C4×C11—21no—
487C2×C4×C11—22no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
491C2×C4×C11—22no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—21no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—21no—
501C2×C4×C11—21no—
502C2×C4×C11—21no—
503C2×C4×C11—21no—
504C2×C4×C11—22no—
505C2×C4×C11—21no—
506C2×C4×C11—21no—
507C2×C4×C11—48no—
508C2×C4×C11C23×C412yes—
509C2×C4×C11C23×C412yes—
510C2×C4×C11C23×C414yes—
511C2×C4×C11C23×C412yes—
512C2×C4×C11C22×D414yes—
513C2×C4×C11C22×D412yes—
514C2×C4×C11C2×#4112yes—
515C2×C4×C11H(5,𝔽2)12yes—
516C22⋊D11—216no—
517C22⋊D11—48no—
518C22⋊D11—48no—
519C2×Dic11—21no—
520C2×Dic11—21no—
521C2×Dic11—21no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—21no—
535C2×Dic11—21no—
536C2×Dic11—21no—
537C2×Dic11—22no—
538C2×Dic11—21no—
539C2×Dic11—48no—
540C2×Dic11C23×C412yes—
541C2×Dic11C23×C412yes—
542C2×Dic11C23×C412yes—
543C2×Dic11C22×D414yes—
544C2×Dic11C22×D412yes—
545C2×Dic11C2×#4112yes—
546C2×Dic11H(5,𝔽2)12yes—
547D44—216no—
548D44—28no—
549D44—28no—
550D44—48no—
551D44—48no—
552C4×D11—28no—
553C4×D11—216no—
554C4×D11—48no—
555C4×D11—48no—
556C4×D11—48no—
557C4×D11—44no—
558C4×D11—84no—
559C4×D11—84no—
560C4×D11C4×D4116yescomplemented
561C22×#41—111no—
562C23×D4—111no—
563C24×C4—112no—
564#535—1116no—
565C2×#127—111no—
566C2×#127—111no—
567C2×#124—111no—
568C2×#124C2×D1111yescharacteristic
569C2×#121—112no—
570C2×#121—112no—
571C2×#120—112no—
572C2×#120—112no—
573#520—228no—
574C2×C4×Q8—111no—
575C2×C4×Q8C2×D1111yescharacteristic, complemented
576C2×C4×D4—111no—
577C2×C4×D4—112no—
578C2×C4×D4—112no—
579C2×C4×D4—112no—
580C2×C4×D4—111no—
581C2×C4×D4—111no—
582C2×C4×D4—112no—
583C2×C4×D4—112no—
584C2×C4×D4—112no—
585C2×C4×D4—112no—
586C2×C4×D4—111no—
587C2×C4×D4—111no—
588C2×C4×D4—112no—
589C2×C4×D4—228no—
590C2×C4×D4C2×D1111yescharacteristic
591C2×#117—111no—
592C2×#117—111no—
593C2×#117—111no—
594C2×#117—112no—
595C22×C4⋊C4—111no—
596C22×C4⋊C4—112no—
597C22×C22⋊C4—112no—
598C22×C42—111no—
599#391—111no—
600#391C2×D1111yescharacteristic, complemented
601#390—111no—
602#390—111no—
603#390—112no—
604#390—111no—
605#390—112no—
606#390—112no—
607#390—112no—
608#390—112no—
609#390—111no—
610#390—112no—
611#390—111no—
612#390C2×D1111yescharacteristic
613#389—111no—
614#389—111no—
615#389—111no—
616#389—111no—
617#388—112no—
618#388—112no—
619#388—112no—
620#388—112no—
621#388—112no—
622#388—112no—
623#388C2×D1112yescomplemented
624#388C2×D1112yescomplemented
625#386—112no—
626#386—112no—
627#386—112no—
628#386—112no—
629#386—112no—
630#386—112no—
631#386—112no—
632#386—112no—
633#386—112no—
634#386—112no—
635#385—111no—
636#385—112no—
637#385—111no—
638#385—112no—
639#385—111no—
640#385—112no—
641#385—111no—
642#385C2×D1112yescomplemented
643#379—112no—
644#379—112no—
645C4×C4⋊C4—111no—
646C4×C4⋊C4—111no—
647C4×C4⋊C4—112no—
648C4×C4⋊C4—111no—
649C4×C4⋊C4—111no—
650C4×C4⋊C4—111no—
651C4×C4⋊C4—111no—
652C4×C4⋊C4—112no—
653C4×C4⋊C4C2×D1111yescharacteristic, complemented
654C4×C4⋊C4C2×D1111yescharacteristic, complemented
655C4×C22⋊C4—112no—
656C4×C22⋊C4—112no—
657C4×C22⋊C4—112no—
658C4×C22⋊C4—112no—
659C4×C22⋊C4—112no—
660C4×C22⋊C4—112no—
661C4×C22⋊C4—112no—
662C4×C22⋊C4C2×D1112yescomplemented
663C22×C11—24no—
664C22×C11—24no—
665C22×C11—24no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11C24×C411yescharacteristic
671C22×C11C23×D411yescharacteristic
672C22×C11C22×#4111yescharacteristic
673C22×C11C2×H(5,𝔽2)11yescharacteristic
674C22×C11C2×H(5,𝔽2)11yescharacteristic
675C22×C11#58511yescharacteristic
676C22×C11#58511yescharacteristic
677C2×D11—22no—
678C2×D11—22no—
679C2×D11—22no—
680C2×D11—22no—
681C2×D11—22no—
682C2×D11—22no—
683C2×D11—24no—
684C2×D11—24no—
685C2×D11—24no—
686C2×D11—24no—
687C2×D11—24no—
688C2×D11—24no—
689C2×D11—432no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—42no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11—42no—
697C2×D11—42no—
698C2×D11C2×C4×D414yes—
699C4×C11—24no—
700C4×C11—22no—
701C4×C11—22no—
702C4×C11—22no—
703C4×C11—24no—
704C4×C11—41no—
705C4×C11—41no—
706C4×C11—41no—
707C4×C11—42no—
708C4×C11C2×C4×D414yes—
709Dic11—22no—
710Dic11—22no—
711Dic11—22no—
712Dic11—24no—
713Dic11—41no—
714Dic11—41no—
715Dic11—41no—
716Dic11—42no—
717Dic11C2×C4×D414yes—
718C25—112no—
719C2×#41—118no—
720C2×#41—224no—
721C2×#41—224no—
722C22×Q8C22×D1111yescharacteristic
723C22×D4—112no—
724C22×D4—112no—
725C22×D4—112no—
726C22×D4—118no—
727C22×D4—112no—
728C22×D4—111no—
729C22×D4—111no—
730C22×D4—112no—
731C22×D4—112no—
732C22×D4—224no—
733C22×D4—224no—
734C22×D4C22×D1111yescharacteristic
735C23×C4—111no—
736C23×C4—112no—
737C23×C4—112no—
738C23×C4—112no—
739C23×C4—111no—
740C23×C4—112no—
741C23×C4—112no—
742C23×C4—111no—
743C23×C4—112no—
744C23×C4—112no—
745C23×C4—228no—
746C23×C4—444no—
747C23×C4—444no—
748C23×C4C22×D1112yes—
749#127—118no—
750#127—118no—
751#124—118no—
752#124C4×D1118yescomplemented
753#121—1116no—
754#121—1116no—
755#120—1116no—
756#120—1116no—
757C4×Q8—24no—
758C4×Q8—224no—
759C4×D4—24no—
760C4×D4—224no—
761C4×D4—224no—
762C4×D4—228no—
763C4×D4—228no—
764C4×D4—228no—
765C4×D4—228no—
766C4×D4—224no—
767C4×D4—224no—
768C4×D4—224no—
769C4×D4—444no—
770C4×D4—444no—
771C4×D4—444no—
772C4×D4—444no—
773#117—118no—
774#117—228no—
775#117—224no—
776#117—224no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—118no—
782C2×C4⋊C4—111no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—111no—
785C2×C4⋊C4—111no—
786C2×C4⋊C4—111no—
787C2×C4⋊C4—111no—
788C2×C4⋊C4—111no—
789C2×C4⋊C4—111no—
790C2×C4⋊C4—111no—
791C2×C4⋊C4—111no—
792C2×C4⋊C4—228no—
793C2×C4⋊C4C22×D1112yes—
794C2×C4⋊C4C22×D1111yescharacteristic
795C2×C4⋊C4C22×D1111yescharacteristic
796C2×C4⋊C4C22×D1111yescharacteristic
797C2×C4⋊C4C22×D1111yescharacteristic
798C2×C22⋊C4—111no—
799C2×C22⋊C4—111no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—111no—
806C2×C22⋊C4—111no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—112no—
818C2×C22⋊C4—112no—
819C2×C22⋊C4—112no—
820C2×C22⋊C4—228no—
821C2×C22⋊C4C22×D1112yes—
822C2×C22⋊C4C22×D1112yes—
823C2×C22⋊C4C22×D1112yes—
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1112yes—
826C2×C42—111no—
827C2×C42—112no—
828C2×C42—111no—
829C2×C42—112no—
830C2×C42—111no—
831C2×C42—111no—
832C2×C42—111no—
833C2×C42—112no—
834C2×C42—112no—
835C2×C42—112no—
836C2×C42—224no—
837C2×C42C22×D1112yes—
838C2×C42C22×D1111yescharacteristic
839C2×C42C22×D1111yescharacteristic
840C2×C42C22×D1112yes—
841C2×C42C22×D1111yescharacteristic
842#95—112no—
843#95—111no—
844#95—111no—
845#95—111no—
846#95—112no—
847#95—112no—
848#95—112no—
849#95—112no—
850#95—111no—
851#95—111no—
852#95—111no—
853#95C22×D1112yes—
854#95C22×D1112yes—
855#95C22×D1112yes—
856#95C22×D1111yescharacteristic
857#95C22×D1111yescharacteristic
858C2×C11—44no—
859C2×C11C22×C4×D411yescharacteristic
860C2×C11C4×H(5,𝔽2)11yescharacteristic
861C2×C11C4×H(5,𝔽2)11yescharacteristic
862C2×C11#348411yescharacteristic
863C2×C11#348711yescharacteristic
864C2×C11#350611yescharacteristic
865C2×C11#350611yescharacteristic
866D11—24no—
867D11—44no—
868D11—44no—
869C24—111no—
870C24—112no—
871C24—112no—
872C24—118no—
873C24—224no—
874C24—224no—
875C24—442no—
876C24—442no—
877C24—442no—
878C24—442no—
879C24C23×D1112yes—
880#41—2232no—
881C2×Q8—22no—
882C2×Q8—22no—
883C2×Q8C2×C4×D1114yescomplemented
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—118no—
887C2×D4—118no—
888C2×D4—118no—
889C2×D4—118no—
890C2×D4—114no—
891C2×D4—114no—
892C2×D4—118no—
893C2×D4—118no—
894C2×D4—224no—
895C2×D4—224no—
896C2×D4—2232no—
897C2×D4—224no—
898C2×D4—224no—
899C2×D4—222no—
900C2×D4—222no—
901C2×D4—222no—
902C2×D4—222no—
903C2×D4—442no—
904C2×D4—442no—
905C2×D4—442no—
906C2×D4—442no—
907C2×D4—442no—
908C2×D4—442no—
909C2×D4—442no—
910C2×D4—442no—
911C2×D4C2×C4×D1114yes—
912C22×C4—24no—
913C22×C4—24no—
914C22×C4—42no—
915C22×C4—111no—
916C22×C4—114no—
917C22×C4—114no—
918C22×C4—114no—
919C22×C4—111no—
920C22×C4—111no—
921C22×C4—111no—
922C22×C4—112no—
923C22×C4—118no—
924C22×C4—118no—
925C22×C4—112no—
926C22×C4—111no—
927C22×C4—111no—
928C22×C4—111no—
929C22×C4—224no—
930C22×C4—222no—
931C22×C4—224no—
932C22×C4—224no—
933C22×C4—224no—
934C22×C4—224no—
935C22×C4—222no—
936C22×C4—222no—
937C22×C4—224no—
938C22×C4—224no—
939C22×C4—222no—
940C22×C4—224no—
941C22×C4—224no—
942C22×C4—224no—
943C22×C4—442no—
944C22×C4—442no—
945C22×C4—442no—
946C22×C4—442no—
947C22×C4—441no—
948C22×C4—441no—
949C22×C4—442no—
950C22×C4—442no—
951C22×C4—442no—
952C22×C4—442no—
953C22×C4—4432no—
954C22×C4—442no—
955C22×C4C23×D1112yes—
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1111yescharacteristic
959C22×C4C23×D1111yescharacteristic
960C22×C4C23×D1112yes—
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1112yes—
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C4⋊C4—24no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—41no—
969C4⋊C4—114no—
970C4⋊C4—114no—
971C4⋊C4—118no—
972C4⋊C4—114no—
973C4⋊C4—222no—
974C4⋊C4—224no—
975C4⋊C4—222no—
976C4⋊C4—222no—
977C4⋊C4—222no—
978C4⋊C4—222no—
979C4⋊C4—222no—
980C4⋊C4—441no—
981C4⋊C4—441no—
982C4⋊C4—441no—
983C4⋊C4D4×D1114yes—
984C22⋊C4—24no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—114no—
988C22⋊C4—114no—
989C22⋊C4—118no—
990C22⋊C4—118no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—224no—
994C22⋊C4—222no—
995C22⋊C4—222no—
996C22⋊C4—224no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—224no—
1001C22⋊C4—442no—
1002C22⋊C4—442no—
1003C22⋊C4—442no—
1004C22⋊C4—442no—
1005C22⋊C4—442no—
1006C22⋊C4—442no—
1007C22⋊C4—442no—
1008C22⋊C4—442no—
1009C22⋊C4C2×C4×D1118yescomplemented
1010C22⋊C4C2×C4×D1118yescomplemented
1011C42—22no—
1012C42—24no—
1013C42—22no—
1014C42—42no—
1015C42—114no—
1016C42—222no—
1017C42—222no—
1018C42—224no—
1019C42—224no—
1020C42—222no—
1021C42—222no—
1022C42—442no—
1023C42—442no—
1024C42—442no—
1025C42C2×C4×D1114yescomplemented
1026C11#3426511yescharacteristic, complemented, Sylow
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—112no—
1034C23—112no—
1035C23—112no—
1036C23—114no—
1037C23—114no—
1038C23—2216no—
1039C23—221no—
1040C23—221no—
1041C23—221no—
1042C23—221no—
1043C23—222no—
1044C23—222no—
1045C23—222no—
1046C23—222no—
1047C23—222no—
1048C23—222no—
1049C23—222no—
1050C23—222no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—448no—
1056C23—448no—
1057C23—448no—
1058C23—448no—
1059C23—448no—
1060C23—448no—
1061C23C22×C4×D1114yes—
1062C23C24×D1111yescharacteristic
1063Q8—28no—
1064D4—28no—
1065D4—2216no—
1066D4—2216no—
1067D4—228no—
1068D4—228no—
1069D4—448no—
1070D4—448no—
1071D4—448no—
1072D4—448no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—22no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—22no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—48no—
1096C2×C4—112no—
1097C2×C4—112no—
1098C2×C4—112no—
1099C2×C4—1116no—
1100C2×C4—112no—
1101C2×C4—112no—
1102C2×C4—114no—
1103C2×C4—112no—
1104C2×C4—2216no—
1105C2×C4—228no—
1106C2×C4—221no—
1107C2×C4—221no—
1108C2×C4—222no—
1109C2×C4—221no—
1110C2×C4—221no—
1111C2×C4—221no—
1112C2×C4—222no—
1113C2×C4—221no—
1114C2×C4—221no—
1115C2×C4—221no—
1116C2×C4—221no—
1117C2×C4—222no—
1118C2×C4—222no—
1119C2×C4—221no—
1120C2×C4—221no—
1121C2×C4—221no—
1122C2×C4—221no—
1123C2×C4—222no—
1124C2×C4—221no—
1125C2×C4—221no—
1126C2×C4—448no—
1127C2×C4—448no—
1128C2×C4—448no—
1129C2×C4—444no—
1130C2×C4—448no—
1131C2×C4—884no—
1132C2×C4—884no—
1133C2×C4C22×C4×D1112yes—
1134C2×C4C22×C4×D1112yes—
1135C2×C4C22×C4×D1114yes—
1136C2×C4C22×C4×D1112yes—
1137C2×C4C2×D4×D1114yes—
1138C2×C4C2×D4×D1112yes—
1139C2×C4#41×D1112yes—
1140C2×C4#6704212yes—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—42no—
1145C22—42no—
1146C22—42no—
1147C22—42no—
1148C22—114no—
1149C22—222no—
1150C22—222no—
1151C22—222no—
1152C22—222no—
1153C22—222no—
1154C22—222no—
1155C22—224no—
1156C22—224no—
1157C22—224no—
1158C22—224no—
1159C22—224no—
1160C22—224no—
1161C22—4432no—
1162C22—442no—
1163C22—442no—
1164C22—442no—
1165C22—442no—
1166C22—442no—
1167C22—442no—
1168C22—442no—
1169C22—442no—
1170C22C23×C4×D1111yescharacteristic
1171C22C22×D4×D1111yescharacteristic
1172C22C2×#41×D1111yescharacteristic
1173C22C2×#6704211yescharacteristic
1174C22#1062345311yescharacteristic
1175C22D11×H(5,𝔽2)11yescharacteristic
1176C22#1062345711yescharacteristic
1177C4—22no—
1178C4—24no—
1179C4—24no—
1180C4—22no—
1181C4—22no—
1182C4—42no—
1183C4—41no—
1184C4—41no—
1185C4—41no—
1186C4—114no—
1187C4—222no—
1188C4—224no—
1189C4—222no—
1190C4—222no—
1191C4—442no—
1192C4—441no—
1193C4—441no—
1194C4—441no—
1195C4C4×D4×D1114yes—
1196C2—44no—
1197C2—224no—
1198C2—444no—
1199C2—444no—
1200C2C2×C4×D4×D1111yescharacteristic
1201C2#1308182211yescharacteristic
1202C2C4×#6704211yescharacteristic
1203C2#1308224611yescharacteristic
1204C2#1308227311yescharacteristic
1205C2#1308246411yescharacteristic
1206C2#1308246911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2367C2
socle, cosocleC23×C11C25
prime radicalC2×#10623205C2
hypercenter#2367D11
hypocenterC11#34265
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2367

Complements

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

NH ≅ G/Ntype
2. C2×#10623105C2semidirect
3. C2×C4×D4×D11C2semidirect
4. #13071692C2semidirect
5. #13071691C2semidirect
6. #13071683C2semidirect
7. #13071680C2semidirect
8. #13071680C2semidirect
9. #13071678C2semidirect
10. #13071677C2semidirect
11. #13071655C2semidirect
12. #13071649C2semidirect
13. #13071635C2semidirect
14. #13071629C2semidirect
15. #13071278C2semidirect
16. #13071269C2semidirect
17. #13071195C2semidirect
18. C4×#66935C2semidirect
19. #13071117C2semidirect
20. #13071105C2semidirect
21. #13071096C2semidirect
22. #13070970C2semidirect
23. C11×#2367C2semidirect
28. C2×C4×Q8×C11C22semidirect
31. C2×Q8×Dic11C22semidirect
35. C2×C4×C22⋊D11C22semidirect
36. #10623205C4semidirect
41. C2×#66946C22semidirect
42. C2×#66946C22semidirect
45. C2×C4⋊C4×D11C22semidirect
51. C2×(C22⋊D11)⋊C4C22semidirect
56. C2×C4×D44C22semidirect
57. C2×C4×D44C22semidirect
60. C2×#66925C22semidirect
62. C11×#391C22semidirect
64. C11×#388C22semidirect
65. C11×#388C22semidirect
66. C11×#385C22semidirect
67. C4×C11×C4⋊C4C22semidirect
68. C4×C11×C4⋊C4C22semidirect
69. C4×C11×C22⋊C4C22semidirect
70. #10622843C22semidirect
72. #10622826C22semidirect
73. #10622603C22semidirect
76. #10622602C22semidirect
78. #10622601C22semidirect
79. #10622601C22semidirect
80. C4⋊C4×Dic11C22semidirect
81. C4⋊C4×Dic11C22semidirect
82. #10622585C22semidirect
83. #10622585C22semidirect
84. #10622571C22semidirect
87. #10622570C22semidirect
88. #10622570C22semidirect
89. #10622569C22semidirect
90. #10622569C22semidirect
93. #10622564C22semidirect
94. #10622564C22semidirect
95. #10622563C22semidirect
96. C22⋊C4×Dic11C22semidirect
97. #10622553C22semidirect
99. #10622552C22semidirect
100. #10622552C22semidirect
102. C4×(C2×D11)⋊C4C22semidirect
103. C4×C4⋊Dic11C22semidirect
104. C4×C4⋊Dic11C22semidirect
105. C4×Dic11⋊C4C22semidirect
106. C4×Dic11⋊C4C22semidirect
107. C4×Dic11⋊C4C22semidirect
108. #10622283C22semidirect
109. #10622282C22semidirect
112. #10622281C22semidirect
114. #10622279C22semidirect
115. #10622279C22semidirect
116. #10622279C22semidirect
119. #10622278C22semidirect
120. #10622278C22semidirect
121. #10622278C22semidirect
122. #10622278C22semidirect
123. #10622262C22semidirect
124. #10622260C22semidirect
125. #10622260C22semidirect
136. C2×#4343C2×C4semidirect
139. C2×D4×D11C2×C4semidirect
157. C11×#124C2×C4semidirect
178. #67000C2×C4semidirect
180. #66993C2×C4semidirect
233. C4⋊C4×D11D4semidirect
234. #66937C2×C4semidirect
235. #66937C2×C4semidirect
236. #66935C2×C4semidirect
237. #66935C2×C4semidirect
241. #66927C2×C4semidirect
248. #66925C2×C4semidirect
280. C2×Q8×C11C22×C4semidirect
304. C2×C22⋊D11C22×C4semidirect
305. C2×C22⋊D11C22×C4semidirect
332. C2×D44C22×C4semidirect
333. C2×D44C22×C4semidirect
334. C2×D44C22×C4semidirect
359. C2×C4×D11C22×C4semidirect
371. C11×C22⋊C4C22×C4semidirect
372. C11×C22⋊C4C22×C4semidirect
377. C42×C11C22×C4semidirect
398. (C2×D11)⋊C4C22×C4semidirect
399. (C2×D11)⋊C4C22×C4semidirect
411. Dic11⋊C4C22×C4semidirect
412. Dic11⋊C4C22×C4semidirect
423. C4×Dic11C22×C4semidirect
430. #2367D11semidirect
560. C4×D11C4×D4semidirect
575. C2×C4×Q8C2×D11semidirect
600. #391C2×D11semidirect
623. #388C2×D11semidirect
624. #388C2×D11semidirect
642. #385C2×D11semidirect
653. C4×C4⋊C4C2×D11semidirect
654. C4×C4⋊C4C2×D11semidirect
662. C4×C22⋊C4C2×D11semidirect
752. #124C4×D11semidirect
883. C2×Q8C2×C4×D11semidirect
1009. C22⋊C4C2×C4×D11semidirect
1010. C22⋊C4C2×C4×D11semidirect
1025. C42C2×C4×D11semidirect
1026. C11#34265semidirect

Maximal subgroups

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

subgroupindex
C2×#106232052
C2×#106231052
C2×C4×D4×D112
#130716922
#130716912
#130716832
#130716802
#130716782
#130716772
#130716552
#130716492
#130716352
#130716292
#130712782
#130712692
#130711952
C4×#669352
#130711172
#130711052
#130710962
#130709702
C11×#23672
#3426511