Finite Group Databasebeta

← #14926716

Subgroups — #14926716

Order 2816.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623124C212yesmaximal, complemented
2#13076980C211yesmaximal, characteristic, complemented
3#13076970C211yesmaximal, characteristic, complemented
4#13076959C211yesmaximal, characteristic, complemented
5#13076942C211yesmaximal, characteristic, complemented
6#13074752C212yesmaximal, complemented
7#13074741C212yesmaximal, complemented
8#13073686C212yesmaximal, complemented
9#13073671C212yesmaximal, complemented
10#13073200C211yesmaximal, characteristic, complemented
11#13072981C211yesmaximal, characteristic, complemented
12#13072739C212yesmaximal, complemented
13#13072384C211yesmaximal, characteristic, complemented
14#13072319C211yesmaximal, characteristic, complemented
15#13072249C211yesmaximal, characteristic, complemented
16#13072200C211yesmaximal, characteristic, complemented
17#13072156C212yesmaximal, complemented
18#13072056C211yesmaximal, characteristic, complemented
19#13071271C212yesmaximal, complemented
20#13071122C211yesmaximal, characteristic, complemented
21C2×#10622834C211yesmaximal, characteristic, complemented
22C4×D4×Dic11C211yesmaximal, characteristic, complemented
23C11×#2408C211yesmaximal, characteristic, complemented
24C23×D4×C11C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C11×#120C2212yes—
28C2×C4×D4×C11C2211yescharacteristic
29C2×#67006C2212yes—
30C2×#67006C2212yes—
31C22×C22⋊Dic11C2212yes—
32C22×C22⋊Dic11C2212yes—
33C2×#66993C2211yescharacteristic
34C2×#66993C2211yescharacteristic
35C2×#66992C2212yes—
36C2×#66992C2212yescomplemented
37C2×#66992C2212yescomplemented
38C2×#66991C2212yescomplemented
39C2×#66989C2212yescomplemented
40C2×#66988C2212yescomplemented
41C2×D4×Dic11C2211yescharacteristic
42C2×D4×Dic11C2211yescharacteristic
43C2×#66983C2211yescharacteristic
44C2×#66983C2211yescharacteristic, complemented
45C22×C4⋊Dic11C2211yescharacteristic
46C22×C4×Dic11C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic, complemented
48#10623124—216no—
49C2×#66946C2211yescharacteristic, complemented
50C2×#66941C2211yescharacteristic, complemented
51C2×#66938C2212yescomplemented
52C2×#66938C2212yescomplemented
53C2×#66936C2212yescomplemented
54C2×(C22⋊D11)⋊C4C2212yes—
55C2×#66932C2212yescomplemented
56C2×#66932C2212yescomplemented
57C2×#66931C2212yes—
58C11×#394C2212yes—
59C11×#392C2212yes—
60C11×#390C2211yescharacteristic
61C11×#390C2211yescharacteristic
62C11×#380C2211yescharacteristic
63C11×#379C2212yes—
64#10622836C2212yes—
65#10622836C2212yes—
66#10622836C2212yescomplemented
67#10622835C2212yescomplemented
68#10622834C2211yescharacteristic
69#10622834C2212yes—
70#10622834C2211yescharacteristic
71#10622834C2211yescharacteristic
72#10622834C2212yes—
73#10622834C2211yescharacteristic
74#10622834C2211yescharacteristic
75#10622834C2211yescharacteristic
76#10622833C2212yescomplemented
77#10622825C2211yescharacteristic, complemented
78C4×C22⋊Dic11C2211yescharacteristic
79C4×C22⋊Dic11C2211yescharacteristic, complemented
80#10622607C2212yescomplemented
81#10622601C2211yescharacteristic, complemented
82#10622598C2211yescharacteristic, complemented
83#10622589C2211yescharacteristic, complemented
84C4⋊C4×Dic11C2211yescharacteristic, complemented
85C4⋊C4×Dic11C2211yescharacteristic, complemented
86C4⋊C4×Dic11C2211yescharacteristic, complemented
87#10622586C2211yescharacteristic, complemented
88#10622586C2211yescharacteristic, complemented
89#10622574C2212yescomplemented
90#10622574C2212yescomplemented
91#10622574C2212yescomplemented
92#10622572C2212yescomplemented
93#10622571C2212yes—
94#10622571C2212yes—
95#10622570C2212yescomplemented
96#10622570C2212yescomplemented
97#10622570C2212yescomplemented
98#10622570C2212yescomplemented
99#10622569C2212yescomplemented
100#10622569C2212yescomplemented
101#10622565C2212yescomplemented
102#10622564C2212yescomplemented
103#10622561C2212yescomplemented
104#10622560C2212yescomplemented
105#10622559C2212yes—
106#10622558C2212yescomplemented
107#10622558C2212yescomplemented
108#10622558C2212yescomplemented
109#10622557C2212yescomplemented
110#10622557C2212yescomplemented
111#10622557C2212yescomplemented
112C22⋊C4×Dic11C2211yescharacteristic
113C22⋊C4×Dic11C2211yescharacteristic
114C22⋊C4×Dic11C2211yescharacteristic, complemented
115C22⋊C4×Dic11C2211yescharacteristic, complemented
116#10622552C2211yescharacteristic, complemented
117C4×C4⋊Dic11C2211yescharacteristic, complemented
118C42×Dic11C2211yescharacteristic, complemented
119#10622541C2211yescharacteristic, complemented
120#10622282C2212yescomplemented
121#10622279C2212yescomplemented
122#10622270C2212yescomplemented
123#10622269C2212yescomplemented
124C25×C11C2312yes—
125C22×D4×C11—24no—
126C22×D4×C11—42no—
127C22×D4×C11—42no—
128C22×D4×C11C2311yescharacteristic
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2311yescharacteristic
131C22×D4×C11C2312yes—
132C22×D4×C11C2312yes—
133C22×D4×C11C2312yes—
134C23×C4×C11C2311yescharacteristic
135C23×C4×C11C2311yescharacteristic
136C22×C22⋊D11C2312yes—
137C22×C22⋊D11C2312yes—
138C22×C22⋊D11C2312yes—
139C22×C22⋊D11C2312yes—
140C22×C22⋊D11C2312yes—
141C22×C22⋊D11C2312yes—
142C23×Dic11C2311yescharacteristic
143C23×Dic11C2311yescharacteristic
144C23×Dic11C2312yes—
145C23×Dic11C2311yescharacteristic
146C23×Dic11C2311yescharacteristic
147C22×D44C2311yescharacteristic
148C22×C4×D11C2312yes—
149C22×Dic22C2312yes—
150C11×#121—42no—
151C11×#121—42no—
152C11×#120—28no—
153C4×D4×C11—24no—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C42×C11C2311yescharacteristic
167#67006—28no—
168#67006—28no—
169C2×C22⋊Dic11—28no—
170C2×C22⋊Dic11—44no—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2311yescharacteristic
186C2×C22⋊Dic11C2311yescharacteristic
187C2×C22⋊Dic11C2311yescharacteristic
188#66993—42no—
189#66993—42no—
190#66992—28no—
191#66992—28no—
192#66992—44no—
193#66991—28no—
194#66989—28no—
195#66988—28no—
196D4×Dic11—24no—
197D4×Dic11D418yescomplemented
198#66983—24no—
199#66983—42no—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×C4⋊Dic11—42no—
208C2×C4⋊Dic11C2312yes—
209C2×C4⋊Dic11C2311yescharacteristic
210C2×C4⋊Dic11C2311yescharacteristic
211C2×C4⋊Dic11C2311yescharacteristic
212C2×C4⋊Dic11C2311yescharacteristic
213C2×C4⋊Dic11C2312yes—
214C2×C4⋊Dic11C2311yescharacteristic
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2312yes—
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×C4×Dic11—42no—
222C2×C4×Dic11—42no—
223C2×C4×Dic11C2312yes—
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2311yescharacteristic
230C2×C4×Dic11C2311yescharacteristic
231C2×C4×Dic11C2311yescharacteristic
232C2×C4×Dic11C2311yescharacteristic
233C2×C4×Dic11C2311yescharacteristic
234C2×C4×Dic11C2311yescharacteristic
235C2×C4×Dic11C2311yescharacteristic
236#66946—42no—
237#66941—42no—
238#66938—28no—
239#66938—44no—
240#66936—28no—
241(C22⋊D11)⋊C4—28no—
242#66932—28no—
243#66932—28no—
244#66931—28no—
245C11×#95C2312yes—
246C11⋊#95C2311yescharacteristic
247C11⋊#95C2312yes—
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2312yes—
258#35007—111nomaximal, Sylow
259C24×C11—24no—
260C24×C11—24no—
261C24×C11—24no—
262C24×C11—42no—
263C24×C11—42no—
264C24×C11—42no—
265C24×C11—42no—
266C24×C11C2412yes—
267C24×C11C2412yes—
268C24×C11C2411yescharacteristic
269C24×C11C2411yescharacteristic
270C23×D11C2412yes—
271C2×D4×C11—22no—
272C2×D4×C11—22no—
273C2×D4×C11—24no—
274C2×D4×C11—24no—
275C2×D4×C11—24no—
276C2×D4×C11—22no—
277C2×D4×C11—22no—
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C2×D4×C11—42no—
283C2×D4×C11—42no—
284C2×D4×C11—416no—
285C2×D4×C11—42no—
286C2×D4×C11—42no—
287C2×D4×C11—42no—
288C2×D4×C11—42no—
289C2×D4×C11C2×D414yes—
290C22×C4×C11—22no—
291C22×C4×C11—22no—
292C22×C4×C11—22no—
293C22×C4×C11—22no—
294C22×C4×C11—22no—
295C22×C4×C11#4114yes—
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2412yes—
299C22×C4×C11C2412yes—
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2411yescharacteristic
302C22×C4×C11C2411yescharacteristic
303C2×C22⋊D11—24no—
304C2×C22⋊D11—24no—
305C2×C22⋊D11—24no—
306C2×C22⋊D11—24no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—42no—
312C2×C22⋊D11—42no—
313C2×C22⋊D11—42no—
314C2×C22⋊D11—42no—
315C2×C22⋊D11—42no—
316C2×C22⋊D11—42no—
317C2×C22⋊D11—42no—
318C2×C22⋊D11—42no—
319C2×C22⋊D11—42no—
320C2×C22⋊D11—42no—
321C22×Dic11—22no—
322C22×Dic11—22no—
323C22×Dic11—22no—
324C22×Dic11—24no—
325C22×Dic11—22no—
326C22×Dic11—41no—
327C22×Dic11—41no—
328C22×Dic11—41no—
329C22×Dic11—41no—
330C22×Dic11—41no—
331C22×Dic11—41no—
332C22×Dic11—42no—
333C22×Dic11—42no—
334C22×Dic11C2×D414yes—
335C22×Dic11C2×D414yescomplemented
336C22×Dic11C2411yescharacteristic
337C22×Dic11C2412yes—
338C22×Dic11C2412yes—
339C22×Dic11C2412yes—
340C22×Dic11C2411yescharacteristic
341C22×Dic11C2411yescharacteristic
342C22×Dic11C2411yescharacteristic
343C22×Dic11C2411yescharacteristic
344C22×Dic11C2411yescharacteristic
345C22×Dic11C2411yescharacteristic
346C22×Dic11C2411yescharacteristic
347C2×D44—22no—
348C2×D44—22no—
349C2×D44—22no—
350C2×C4×D11—24no—
351C2×C4×D11—42no—
352C2×C4×D11—42no—
353C2×Dic22—24no—
354C2×Dic22—42no—
355C2×Dic22—42no—
356C11×C4⋊C4—22no—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—22no—
359C11×C22⋊C4—24no—
360C11×C22⋊C4—22no—
361C11×C22⋊C4—24no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—42no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4—42no—
367C11×C22⋊C4—42no—
368C42×C11—22no—
369C22⋊Dic11—24no—
370C22⋊Dic11—24no—
371C22⋊Dic11—24no—
372C22⋊Dic11—24no—
373C22⋊Dic11—24no—
374C22⋊Dic11—24no—
375C22⋊Dic11—22no—
376C22⋊Dic11—24no—
377C22⋊Dic11—24no—
378C22⋊Dic11—24no—
379C22⋊Dic11—24no—
380C22⋊Dic11—24no—
381C22⋊Dic11—42no—
382C22⋊Dic11—42no—
383C22⋊Dic11C2×D414yes—
384C22⋊Dic11C2×D414yescomplemented
385C22⋊Dic11#4114yes—
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—
393C4⋊Dic11—24no—
394C4⋊Dic11—22no—
395C4⋊Dic11—22no—
396C4⋊Dic11—22no—
397C4⋊Dic11—22no—
398C4⋊Dic11—42no—
399C4⋊Dic11C2×D414yescomplemented
400Dic11⋊C4—24no—
401Dic11⋊C4—24no—
402Dic11⋊C4—24no—
403Dic11⋊C4—24no—
404Dic11⋊C4—42no—
405Dic11⋊C4—42no—
406C4×Dic11—24no—
407C4×Dic11—22no—
408C4×Dic11—22no—
409C4×Dic11—22no—
410C4×Dic11—22no—
411C4×Dic11—22no—
412C4×Dic11—22no—
413C4×Dic11—41no—
414C4×Dic11—41no—
415C4×Dic11—41no—
416C4×Dic11—41no—
417C4×Dic11—41no—
418C4×Dic11C2×D414yescomplemented
419C2×#538—112no—
420#2860—111no—
421#2858—111no—
422#2856—111no—
423#2854—111no—
424#2662—112no—
425#2661—112no—
426#2555—112no—
427#2554—112no—
428#2512—111no—
429#2491—111no—
430#2472—112no—
431#2445—111no—
432#2440—111no—
433#2433—111no—
434#2428—111no—
435#2424—112no—
436#2416—111no—
437#2408D1111yescharacteristic, complemented
438#2321—112no—
439C4×#121—111no—
440C2×#390—111no—
441C42×D4—111no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11—21no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—21no—
449C23×C11—21no—
450C23×C11—21no—
451C23×C11—21no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—22no—
456C23×C11—22no—
457C23×C11—22no—
458C23×C11—22no—
459C23×C11—22no—
460C23×C11—22no—
461C23×C11—22no—
462C23×C11—22no—
463C23×C11—22no—
464C23×C11—22no—
465C23×C11—22no—
466C23×C11—48no—
467C23×C11—48no—
468C23×C11—48no—
469C23×C11—84no—
470C23×C11—84no—
471C23×C11—84no—
472C23×C11—84no—
473C23×C11C22×D412yes—
474C23×C11C22×D412yes—
475C23×C11C2×#4112yes—
476C23×C11C2×#4112yes—
477C23×C11C2511yescharacteristic
478C22×D11—22no—
479C22×D11—22no—
480C22×D11—22no—
481C22×D11—22no—
482C22×D11—22no—
483C22×D11—22no—
484C22×D11—22no—
485D4×C11—28no—
486D4×C11—48no—
487D4×C11—44no—
488D4×C11—44no—
489D4×C11—84no—
490D4×C11—84no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—28no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—21no—
499C2×C4×C11—21no—
500C2×C4×C11—21no—
501C2×C4×C11—21no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—21no—
505C2×C4×C11—22no—
506C2×C4×C11—21no—
507C2×C4×C11—22no—
508C2×C4×C11—44no—
509C2×C4×C11C22×D412yes—
510C2×C4×C11C2×#4112yes—
511C2×C4×C11C2×#4112yes—
512C2×C4×C11H(5,𝔽2)12yes—
513C2×C4×C11H(5,𝔽2)12yes—
514C22⋊D11—48no—
515C22⋊D11—84no—
516C22⋊D11—84no—
517C22⋊D11—84no—
518C22⋊D11—84no—
519C22⋊D11—84no—
520C2×Dic11—21no—
521C2×Dic11—21no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—21no—
539C2×Dic11—22no—
540C2×Dic11—21no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—21no—
546C2×Dic11—44no—
547C2×Dic11—44no—
548C2×Dic11—44no—
549C2×Dic11—44no—
550C2×Dic11—84no—
551C2×Dic11C22×D412yes—
552C2×Dic11C22×D412yes—
553C2×Dic11C22×D412yes—
554C2×Dic11C22×D412yes—
555C2×Dic11C2×#4112yes—
556C2×Dic11C2×#4112yes—
557C2×Dic11H(5,𝔽2)12yes—
558D44—44no—
559C4×D11—84no—
560Dic22—84no—
561C23×D4C2×D1111yescharacteristic
562#538—2216no—
563C2×C4⋊Q8—111no—
564C2×#127—111no—
565C2×#127—111no—
566C2×#126—112no—
567C2×#126—112no—
568C2×#124—112no—
569C2×#124—112no—
570C2×#124—112no—
571C2×#123—112no—
572C2×#123—112no—
573C2×C22⋊Q8—112no—
574C2×#121—112no—
575C2×#121—112no—
576C2×#121—112no—
577C2×#121—111no—
578C2×#121—112no—
579C2×#121—111no—
580C2×#121C2×D1111yescharacteristic
581C2×#121C2×D1111yescharacteristic
582C2×#120—112no—
583C2×#120—112no—
584C2×#120C2×D1112yes—
585C2×C4×D4—111no—
586C2×C4×D4—111no—
587C2×C4×D4—111no—
588C2×C4×D4—112no—
589C2×C4×D4C2×D1111yescharacteristic
590C22×C4⋊C4—111no—
591C22×C22⋊C4—112no—
592C22×C22⋊C4—112no—
593C22×C42—111no—
594C22×C42—111no—
595#398—112no—
596#397—112no—
597#396—112no—
598#396—112no—
599#395—112no—
600#394—112no—
601#394—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394C2×D1112yes—
606#393—112no—
607#392—112no—
608#392—112no—
609#392—112no—
610#392C2×D1112yes—
611#390—111no—
612#390—111no—
613#390—111no—
614#390—111no—
615#390—112no—
616#390—111no—
617#390—111no—
618#390—112no—
619#390—111no—
620#390—112no—
621#390—112no—
622#390—112no—
623#390—112no—
624#390—111no—
625#390C2×D1111yescharacteristic
626#390C2×D1111yescharacteristic
627#389—111no—
628#389—111no—
629#389—111no—
630#389—111no—
631#388—112no—
632#388—112no—
633#388—112no—
634#388—112no—
635#388—112no—
636#388—112no—
637#388—112no—
638#388—112no—
639#386—112no—
640#386—112no—
641#386—112no—
642#386—112no—
643#386—112no—
644#385—112no—
645#384—111no—
646#380—111no—
647#380C2×D1111yescharacteristic
648#379C2×D1112yes—
649C4×C4⋊C4—111no—
650C4×C4⋊C4—111no—
651C4×C4⋊C4—111no—
652C4×C4⋊C4—111no—
653C4×C22⋊C4—111no—
654C4×C22⋊C4—111no—
655C4×C22⋊C4—111no—
656C4×C22⋊C4—111no—
657C4×C22⋊C4—111no—
658C4×C22⋊C4—111no—
659C4×C22⋊C4—112no—
660C43—111no—
661C22×C11—22no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—22no—
665C22×C11—22no—
666C22×C11—22no—
667C22×C11—22no—
668C22×C11—22no—
669C22×C11—22no—
670C22×C11—41no—
671C22×C11—41no—
672C22×C11—41no—
673C22×C11—41no—
674C22×C11—42no—
675C22×C11—42no—
676C22×C11—42no—
677C22×C11—42no—
678C22×C11—42no—
679C22×C11—42no—
680C22×C11—42no—
681C22×C11—42no—
682C22×C11—42no—
683C22×C11—42no—
684C22×C11—42no—
685C22×C11—42no—
686C22×C11—42no—
687C22×C11—42no—
688C22×C11—816no—
689C22×C11#53214yes—
690C22×C11C23×D411yescharacteristic
691C22×C11C22×#4111yescharacteristic
692C22×C11C22×#4111yescharacteristic
693C22×C11C2×H(5,𝔽2)11yescharacteristic
694C22×C11C2×H(5,𝔽2)11yescharacteristic
695C22×C11C2×H(5,𝔽2)11yescharacteristic
696C22×C11#58511yescharacteristic
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—42no—
703C2×D11—42no—
704C4×C11—22no—
705C4×C11—22no—
706C4×C11—41no—
707C4×C11—41no—
708C4×C11—42no—
709C4×C11—42no—
710C4×C11#53814yescomplemented
711Dic11—22no—
712Dic11—22no—
713Dic11—22no—
714Dic11—22no—
715Dic11—22no—
716Dic11—22no—
717Dic11—22no—
718Dic11—42no—
719Dic11—42no—
720Dic11—42no—
721Dic11—41no—
722C25C22×D1112yes—
723C22×Q8—112no—
724C22×D4—24no—
725C22×D4—42no—
726C22×D4—42no—
727C22×D4—112no—
728C22×D4—112no—
729C22×D4—112no—
730C22×D4—112no—
731C22×D4—112no—
732C22×D4—112no—
733C22×D4—111no—
734C22×D4C22×D1111yescharacteristic
735C22×D4C22×D1111yescharacteristic
736C22×D4C22×D1111yescharacteristic
737C22×D4C22×D1112yes—
738C22×D4C22×D1112yes—
739C22×D4C22×D1112yes—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—112no—
745C23×C4—112no—
746C23×C4C22×D1111yescharacteristic
747C23×C4C22×D1111yescharacteristic
748C4⋊Q8—442no—
749#127—442no—
750#127—442no—
751#126—228no—
752#126—228no—
753#124—228no—
754#124—228no—
755#124—444no—
756#123—228no—
757#123—228no—
758C22⋊Q8—228no—
759#121—42no—
760#121—42no—
761#121—228no—
762#121—228no—
763#121—228no—
764#121—224no—
765#121—444no—
766#121—442no—
767#120—28no—
768#120—228no—
769#120—228no—
770C4×D4—24no—
771C4×D4—118no—
772C4×D4—228no—
773C4×D4—224no—
774C4×D4—442no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—111no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—112no—
788C2×C4⋊C4—442no—
789C2×C4⋊C4C22×D1111yescharacteristic
790C2×C4⋊C4C22×D1111yescharacteristic
791C2×C4⋊C4C22×D1111yescharacteristic
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—111no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
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—228no—
817C2×C22⋊C4—444no—
818C2×C22⋊C4C22×D1112yes—
819C2×C22⋊C4C22×D1111yescharacteristic
820C2×C22⋊C4C22×D1111yescharacteristic
821C2×C22⋊C4C22×D1112yes—
822C2×C22⋊C4C22×D1112yes—
823C2×C22⋊C4C22×D1112yes—
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1112yes—
826C2×C22⋊C4C22×D1112yes—
827C2×C42—111no—
828C2×C42—112no—
829C2×C42—111no—
830C2×C42—111no—
831C2×C42—111no—
832C2×C42—111no—
833C2×C42—111no—
834C2×C42—111no—
835C2×C42—111no—
836C2×C42—111no—
837C2×C42—111no—
838C2×C42—111no—
839C2×C42—111no—
840C2×C42—442no—
841C2×C42—442no—
842C2×C42C22×D1111yescharacteristic
843#95—111no—
844#95—111no—
845#95—111no—
846#95—111no—
847#95—111no—
848#95—111no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95—112no—
853#95—112no—
854#95—112no—
855#95C22×D1112yes—
856C2×C11—24no—
857C2×C11—42no—
858C2×C11—82no—
859C2×C11—82no—
860C2×C11C2×#53211yescharacteristic
861C2×C11C2×#53811yescharacteristic
862C2×C11#346011yescharacteristic
863C2×C11#349611yescharacteristic
864C2×C11#349811yescharacteristic
865C2×C11#351411yescharacteristic
866C2×C11#351911yescharacteristic
867D11—82no—
868C24—24no—
869C24—24no—
870C24—24no—
871C24—42no—
872C24—42no—
873C24—42no—
874C24—42no—
875C24—112no—
876C24C23×D1112yes—
877C24C23×D1112yes—
878C24C23×D1111yescharacteristic
879C24C23×D1111yescharacteristic
880C2×Q8—224no—
881C2×Q8—442no—
882C2×Q8—442no—
883C2×D4—22no—
884C2×D4—22no—
885C2×D4—24no—
886C2×D4—24no—
887C2×D4—24no—
888C2×D4—22no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—22no—
893C2×D4—22no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—416no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—224no—
902C2×D4—224no—
903C2×D4—224no—
904C2×D4—224no—
905C2×D4—224no—
906C2×D4—224no—
907C2×D4—224no—
908C2×D4—224no—
909C2×D4—222no—
910C2×D4—222no—
911C2×D4—222no—
912C2×D4—442no—
913C2×D4—442no—
914C2×D4—442no—
915C2×D4—442no—
916C2×D4—442no—
917C2×D4—442no—
918C2×D4—442no—
919C2×D4—442no—
920C2×D4—442no—
921C2×D4—442no—
922C2×D4D4×D1114yes—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—111no—
929C22×C4—111no—
930C22×C4—111no—
931C22×C4—111no—
932C22×C4—111no—
933C22×C4—111no—
934C22×C4—111no—
935C22×C4—114no—
936C22×C4—114no—
937C22×C4—111no—
938C22×C4—112no—
939C22×C4—112no—
940C22×C4—112no—
941C22×C4—224no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—222no—
946C22×C4—224no—
947C22×C4—442no—
948C22×C4—442no—
949C22×C4—441no—
950C22×C4—441no—
951C22×C4—441no—
952C22×C4—441no—
953C22×C4—441no—
954C22×C4—441no—
955C22×C4—442no—
956C22×C4—442no—
957C22×C4#434114yes—
958C22×C4C23×D1111yescharacteristic
959C22×C4C23×D1111yescharacteristic
960C22×C4C23×D1112yes—
961C22×C4C23×D1112yes—
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—114no—
969C4⋊C4—224no—
970C4⋊C4—222no—
971C4⋊C4—224no—
972C4⋊C4—224no—
973C4⋊C4—224no—
974C4⋊C4—224no—
975C4⋊C4—222no—
976C4⋊C4—222no—
977C4⋊C4—222no—
978C4⋊C4—442no—
979C4⋊C4—442no—
980C4⋊C4—442no—
981C22⋊C4—24no—
982C22⋊C4—22no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—22no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—114no—
991C22⋊C4—114no—
992C22⋊C4—114no—
993C22⋊C4—224no—
994C22⋊C4—224no—
995C22⋊C4—224no—
996C22⋊C4—224no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—224no—
1001C22⋊C4—222no—
1002C22⋊C4—224no—
1003C22⋊C4—224no—
1004C22⋊C4—224no—
1005C22⋊C4—224no—
1006C22⋊C4—224no—
1007C22⋊C4—224no—
1008C22⋊C4—224no—
1009C22⋊C4—442no—
1010C22⋊C4—442no—
1011C22⋊C4—442no—
1012C22⋊C4—442no—
1013C22⋊C4—442no—
1014C42—22no—
1015C42—114no—
1016C42—224no—
1017C42—222no—
1018C42—222no—
1019C42—222no—
1020C42—222no—
1021C42—222no—
1022C42—222no—
1023C42—441no—
1024C42—441no—
1025C42—441no—
1026C42—441no—
1027C42—441no—
1028C11#3500711yescharacteristic, complemented, Sylow
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—21no—
1036C23—21no—
1037C23—21no—
1038C23—21no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—48no—
1054C23—48no—
1055C23—48no—
1056C23—84no—
1057C23—84no—
1058C23—84no—
1059C23—84no—
1060C23—222no—
1061C23—222no—
1062C23—222no—
1063C23—222no—
1064C23—222no—
1065C23—222no—
1066C23—222no—
1067C23C2×D4×D1112yes—
1068C23C2×D4×D1112yes—
1069C23C2×#434112yes—
1070C23#41×D1112yes—
1071C23C24×D1111yescharacteristic
1072Q8—884no—
1073D4—28no—
1074D4—48no—
1075D4—44no—
1076D4—44no—
1077D4—84no—
1078D4—84no—
1079D4—448no—
1080D4—444no—
1081D4—884no—
1082D4—884no—
1083D4—884no—
1084D4—884no—
1085D4—884no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—28no—
1091C2×C4—22no—
1092C2×C4—22no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—22no—
1103C2×C4—44no—
1104C2×C4—112no—
1105C2×C4—112no—
1106C2×C4—112no—
1107C2×C4—112no—
1108C2×C4—112no—
1109C2×C4—112no—
1110C2×C4—112no—
1111C2×C4—221no—
1112C2×C4—221no—
1113C2×C4—221no—
1114C2×C4—221no—
1115C2×C4—221no—
1116C2×C4—221no—
1117C2×C4—221no—
1118C2×C4—221no—
1119C2×C4—221no—
1120C2×C4—221no—
1121C2×C4—221no—
1122C2×C4—221no—
1123C2×C4—221no—
1124C2×C4—221no—
1125C2×C4—222no—
1126C2×C4—222no—
1127C2×C4—222no—
1128C2×C4—222no—
1129C2×C4—221no—
1130C2×C4—222no—
1131C2×C4—222no—
1132C2×C4—222no—
1133C2×C4—221no—
1134C2×C4—222no—
1135C2×C4—222no—
1136C2×C4—221no—
1137C2×C4—444no—
1138C2×C4—444no—
1139C2×C4—444no—
1140C2×C4—444no—
1141C2×C4—884no—
1142C2×C4—884no—
1143C2×C4C2×D4×D1112yes—
1144C2×C4C2×#434112yes—
1145C2×C4C2×#434112yes—
1146C2×C4#6703712yes—
1147C2×C4#6703712yes—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—22no—
1154C22—22no—
1155C22—22no—
1156C22—22no—
1157C22—41no—
1158C22—41no—
1159C22—41no—
1160C22—41no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—42no—
1170C22—42no—
1171C22—42no—
1172C22—42no—
1173C22—42no—
1174C22—42no—
1175C22—816no—
1176C22—442no—
1177C22—442no—
1178C22—442no—
1179C22—442no—
1180C22—442no—
1181C22—442no—
1182C22—442no—
1183C22#1062312714yes—
1184C22C22×D4×D1111yescharacteristic
1185C22C22×#434111yescharacteristic
1186C22C2×#6703711yescharacteristic
1187C22C2×#6703711yescharacteristic
1188C22C2×#41×D1111yescharacteristic
1189C22D11×H(5,𝔽2)11yescharacteristic
1190C22#1062345511yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—42no—
1194C4—42no—
1195C4—41no—
1196C4—41no—
1197C4—222no—
1198C4—222no—
1199C4—222no—
1200C4—222no—
1201C4—222no—
1202C4—222no—
1203C4—222no—
1204C4—442no—
1205C4—442no—
1206C4—441no—
1207C4—442no—
1208C4#1062312414yescomplemented
1209C2—24no—
1210C2—42no—
1211C2—82no—
1212C2—82no—
1213C2—882no—
1214C2C2×#1062312711yescharacteristic
1215C2C2×#1062312411yescharacteristic
1216C2#1308202911yescharacteristic
1217C2#1308237211yescharacteristic
1218C2#1308238811yescharacteristic
1219C2#1308257411yescharacteristic
1220C2#1308264511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2408C2
hypercenter#2408D11
hypocenterC11#35007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2408

Complements

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

NH ≅ G/Ntype
1. C2×#10623124C2semidirect
2. #13076980C2semidirect
3. #13076970C2semidirect
4. #13076959C2semidirect
5. #13076942C2semidirect
6. #13074752C2semidirect
7. #13074741C2semidirect
8. #13073686C2semidirect
9. #13073671C2semidirect
10. #13073200C2semidirect
11. #13072981C2semidirect
12. #13072739C2semidirect
13. #13072384C2semidirect
14. #13072319C2semidirect
15. #13072249C2semidirect
16. #13072200C2semidirect
17. #13072156C2semidirect
18. #13072056C2semidirect
19. #13071271C2semidirect
20. #13071122C2semidirect
21. C2×#10622834C2semidirect
22. C4×D4×Dic11C2semidirect
23. C11×#2408C2semidirect
36. C2×#66992C22semidirect
37. C2×#66992C22semidirect
38. C2×#66991C22semidirect
39. C2×#66989C22semidirect
40. C2×#66988C22semidirect
44. C2×#66983C22semidirect
47. C22×C4×Dic11C22semidirect
49. C2×#66946C22semidirect
50. C2×#66941C22semidirect
51. C2×#66938C22semidirect
52. C2×#66938C22semidirect
53. C2×#66936C22semidirect
55. C2×#66932C22semidirect
56. C2×#66932C22semidirect
66. #10622836C22semidirect
67. #10622835C22semidirect
76. #10622833C22semidirect
77. #10622825C22semidirect
79. C4×C22⋊Dic11C22semidirect
80. #10622607C22semidirect
81. #10622601C22semidirect
82. #10622598C22semidirect
83. #10622589C22semidirect
84. C4⋊C4×Dic11C22semidirect
85. C4⋊C4×Dic11C22semidirect
86. C4⋊C4×Dic11C22semidirect
87. #10622586C22semidirect
88. #10622586C22semidirect
89. #10622574C22semidirect
90. #10622574C22semidirect
91. #10622574C22semidirect
92. #10622572C22semidirect
95. #10622570C22semidirect
96. #10622570C22semidirect
97. #10622570C22semidirect
98. #10622570C22semidirect
99. #10622569C22semidirect
100. #10622569C22semidirect
101. #10622565C22semidirect
102. #10622564C22semidirect
103. #10622561C22semidirect
104. #10622560C22semidirect
106. #10622558C22semidirect
107. #10622558C22semidirect
108. #10622558C22semidirect
109. #10622557C22semidirect
110. #10622557C22semidirect
111. #10622557C22semidirect
114. C22⋊C4×Dic11C22semidirect
115. C22⋊C4×Dic11C22semidirect
116. #10622552C22semidirect
117. C4×C4⋊Dic11C22semidirect
118. C42×Dic11C22semidirect
119. #10622541C22semidirect
120. #10622282C22semidirect
121. #10622279C22semidirect
122. #10622270C22semidirect
123. #10622269C22semidirect
197. D4×Dic11D4semidirect
335. C22×Dic11C2×D4semidirect
384. C22⋊Dic11C2×D4semidirect
399. C4⋊Dic11C2×D4semidirect
418. C4×Dic11C2×D4semidirect
437. #2408D11semidirect
710. C4×C11#538semidirect
1028. C11#35007semidirect
1208. C4#10623124semidirect

Maximal subgroups

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

subgroupindex
C2×#106231242
#130769802
#130769702
#130769592
#130769422
#130747522
#130747412
#130736862
#130736712
#130732002
#130729812
#130727392
#130723842
#130723192
#130722492
#130722002
#130721562
#130720562
#130712712
#130711222
C2×#106228342
C4×D4×Dic112
C11×#24082
#3500711