Finite Group Databasebeta

← #14926724

Subgroups — #14926724

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#13076972C211yesmaximal, characteristic, complemented
4#13076958C211yesmaximal, characteristic, complemented
5#13076946C211yesmaximal, characteristic, complemented
6#13074758C212yesmaximal, complemented
7#13074747C212yesmaximal, complemented
8#13073686C212yesmaximal, complemented
9#13073677C212yesmaximal, complemented
10#13073204C211yesmaximal, characteristic, complemented
11#13072977C211yesmaximal, characteristic, complemented
12#13072741C212yesmaximal, complemented
13#13072377C211yesmaximal, characteristic, complemented
14#13072318C211yesmaximal, characteristic, complemented
15#13072207C211yesmaximal, characteristic, complemented
16#13072148C212yesmaximal, complemented
17#13072057C211yesmaximal, characteristic, complemented
18#13071966C211yesmaximal, characteristic, complemented
19#13071277C212yesmaximal, complemented
20#121×Dic11C211yesmaximal, characteristic, complemented
21C2×#10622834C211yesmaximal, characteristic, complemented
22C4×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
23C11×#2433C211yesmaximal, characteristic, complemented
24C23×D4×C11C2211yescharacteristic
25C2×C11×#127C2211yescharacteristic
26C2×C11×#127C2211yescharacteristic
27C2×C11×#121C2211yescharacteristic
28C2×C11×#120C2212yes—
29C2×C11×#120C2212yes—
30C2×#67006C2212yes—
31C22×C22⋊Dic11C2212yes—
32C22×C22⋊Dic11C2212yes—
33C2×#66992C2212yes—
34C2×#66992C2212yescomplemented
35C2×#66991C2211yescharacteristic
36C2×#66991C2211yescharacteristic
37C2×#66991C2212yescomplemented
38C2×#66991C2212yescomplemented
39C2×#66991C2211yescharacteristic, complemented
40C2×#66989C2212yescomplemented
41C2×#66989C2212yescomplemented
42C2×#66988C2212yescomplemented
43C2×D4×Dic11C2212yes—
44C2×D4×Dic11C2211yescharacteristic, complemented
45C2×C4×C22⋊D11C2211yescharacteristic
46C22×C4⋊Dic11C2211yescharacteristic
47C22×C4×Dic11C2211yescharacteristic
48#10623124—216no—
49C2×#66938C2212yescomplemented
50C2×#66936C2212yescomplemented
51C2×(C22⋊D11)⋊C4C2211yescharacteristic
52C2×(C22⋊D11)⋊C4C2211yescharacteristic
53C2×#66932C2212yescomplemented
54C2×#66932C2212yescomplemented
55C2×#66931C2212yes—
56C2×C42×D11C2211yescharacteristic, complemented
57C2×#66922C2211yescharacteristic, complemented
58C11×#392C2212yes—
59C11×#392C2212yes—
60C11×#390C2211yescharacteristic
61C11×#390C2211yescharacteristic
62C4×C11×C22⋊C4C2211yescharacteristic
63#10622860C2212yes—
64#10622836C2212yes—
65#10622836C2212yescomplemented
66#10622835C2212yes—
67#10622835C2212yescomplemented
68#10622835C2212yescomplemented
69#10622835C2212yescomplemented
70#10622834C2212yes—
71#10622834C2211yescharacteristic
72#10622834C2211yescharacteristic
73#10622834C2212yes—
74#10622834C2211yescharacteristic
75#10622834C2211yescharacteristic
76#10622834C2211yescharacteristic
77#10622834C2211yescharacteristic
78#10622834C2212yescomplemented
79#10622834C2212yescomplemented
80#10622834C2211yescharacteristic, complemented
81#10622834C2212yescomplemented
82#10622834C2212yescomplemented
83#10622834C2211yescharacteristic, complemented
84#10622833C2212yes—
85#10622833C2212yes—
86#10622833C2212yescomplemented
87#10622833C2212yescomplemented
88#10622825C2211yescharacteristic
89#10622600C2211yescharacteristic, complemented
90#10622598C2211yescharacteristic, complemented
91C4⋊C4×Dic11C2211yescharacteristic, complemented
92#10622586C2211yescharacteristic, complemented
93#10622574C2212yescomplemented
94#10622574C2212yescomplemented
95#10622569C2212yescomplemented
96#10622566C2212yescomplemented
97#10622564C2212yescomplemented
98#10622564C2212yescomplemented
99#10622564C2212yescomplemented
100#10622564C2212yescomplemented
101#10622564C2212yescomplemented
102#10622563C2212yes—
103#10622561C2212yescomplemented
104#10622561C2212yescomplemented
105#10622560C2212yescomplemented
106#10622558C2212yescomplemented
107#10622558C2212yescomplemented
108#10622557C2212yescomplemented
109C22⋊C4×Dic11C2211yescharacteristic
110C22⋊C4×Dic11C2211yescharacteristic
111C22⋊C4×Dic11C2212yescomplemented
112C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
113#10622548C2211yescharacteristic, complemented
114C4×Dic11⋊C4C2211yescharacteristic, complemented
115C42×Dic11C2211yescharacteristic, complemented
116#10622541C2211yescharacteristic, complemented
117#10622541C2211yescharacteristic, complemented
118#10622279C2211yescharacteristic, complemented
119#10622279C2211yescharacteristic, complemented
120#10622274C2212yescomplemented
121#10622269C2212yescomplemented
122#10622262C2211yescharacteristic, complemented
123#10622262C2211yescharacteristic, complemented
124C25×C11C2312yes—
125C22×D4×C11—24no—
126C22×D4×C11—42no—
127C22×D4×C11—42no—
128C22×D4×C11C2312yes—
129C22×D4×C11C2311yescharacteristic
130C22×D4×C11C2311yescharacteristic
131C22×D4×C11C2311yescharacteristic
132C22×D4×C11C2312yes—
133C22×D4×C11C2312yes—
134C22×D4×C11C2312yes—
135C22×D4×C11C2312yes—
136C22×D4×C11C2312yes—
137C23×C4×C11C2311yescharacteristic
138C22×C22⋊D11C2311yescharacteristic
139C22×C22⋊D11C2312yes—
140C22×C22⋊D11C2312yes—
141C22×C22⋊D11C2312yes—
142C23×Dic11C2311yescharacteristic
143C23×Dic11C2312yes—
144C23×Dic11C2312yes—
145C23×Dic11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×Dic22C2312yes—
150C11×#127—42no—
151C11×#127—42no—
152C11×#121—24no—
153C11×#120—28no—
154C11×#120—28no—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2311yescharacteristic
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2311yescharacteristic
165#67006—28no—
166C2×C22⋊Dic11—28no—
167C2×C22⋊Dic11—44no—
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2312yes—
183C2×C22⋊Dic11C2312yes—
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2312yes—
186C2×C22⋊Dic11C2312yes—
187C2×C22⋊Dic11C2312yes—
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2312yes—
190#66992—28no—
191#66992—28no—
192#66991—28no—
193#66991—42no—
194#66991—42no—
195#66991—42no—
196#66991—44no—
197#66989—28no—
198#66989—44no—
199#66988—28no—
200D4×Dic11—28no—
201D4×Dic11—42no—
202C4×C22⋊D11—24no—
203C2×(C2×D11)⋊C4C2311yescharacteristic
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2311yescharacteristic
206C2×(C2×D11)⋊C4C2311yescharacteristic
207C2×C4⋊Dic11—42no—
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2311yescharacteristic
210C2×C4⋊Dic11C2312yes—
211C2×C4⋊Dic11C2312yes—
212C2×C4⋊Dic11C2311yescharacteristic
213C2×C4⋊Dic11C2311yescharacteristic
214C2×C4⋊Dic11C2312yes—
215C2×C4⋊Dic11C2312yes—
216C2×C4⋊Dic11C2312yes—
217C2×Dic11⋊C4C2312yes—
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2311yescharacteristic
221C2×Dic11⋊C4C2311yescharacteristic
222C2×Dic11⋊C4C2311yescharacteristic
223C2×C4×Dic11—42no—
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2312yes—
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#66938—28no—
237#66936—28no—
238(C22⋊D11)⋊C4—24no—
239(C22⋊D11)⋊C4D418yescomplemented
240#66932—28no—
241#66932—28no—
242#66931—28no—
243C42×D11—42no—
244#66922—42no—
245C11×#95C2311yescharacteristic
246C11×#95C2311yescharacteristic
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
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×C11C2412yes—
269C24×C11C2411yescharacteristic
270C23×D11C2411yescharacteristic
271C2×D4×C11—24no—
272C2×D4×C11—24no—
273C2×D4×C11—24no—
274C2×D4×C11—24no—
275C2×D4×C11—24no—
276C2×D4×C11—22no—
277C2×D4×C11—24no—
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—24no—
281C2×D4×C11—24no—
282C2×D4×C11—22no—
283C2×D4×C11—22no—
284C2×D4×C11—22no—
285C2×D4×C11—22no—
286C2×D4×C11—22no—
287C2×D4×C11—22no—
288C2×D4×C11—42no—
289C2×D4×C11—42no—
290C2×D4×C11—416no—
291C2×D4×C11—42no—
292C2×D4×C11—42no—
293C2×D4×C11—42no—
294C2×D4×C11—42no—
295C2×D4×C11—42no—
296C2×D4×C11—42no—
297C2×D4×C11—42no—
298C2×D4×C11—42no—
299C22×C4×C11—22no—
300C22×C4×C11—22no—
301C22×C4×C11#4114yes—
302C22×C4×C11C2412yes—
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2411yescharacteristic
308C22×C4×C11C2411yescharacteristic
309C2×C22⋊D11—22no—
310C2×C22⋊D11—22no—
311C2×C22⋊D11—24no—
312C2×C22⋊D11—24no—
313C2×C22⋊D11—24no—
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⋊D11C2×D414yes—
321C22×Dic11—22no—
322C22×Dic11—24no—
323C22×Dic11—24no—
324C22×Dic11—22no—
325C22×Dic11—41no—
326C22×Dic11—41no—
327C22×Dic11—41no—
328C22×Dic11—42no—
329C22×Dic11—42no—
330C22×Dic11—42no—
331C22×Dic11—42no—
332C22×Dic11C2×D414yes—
333C22×Dic11C2411yescharacteristic
334C22×Dic11C2411yescharacteristic
335C22×Dic11C2411yescharacteristic
336C22×Dic11C2412yes—
337C22×Dic11C2412yes—
338C22×Dic11C2412yes—
339C22×Dic11C2412yes—
340C22×Dic11C2411yescharacteristic
341C22×Dic11C2411yescharacteristic
342C22×Dic11C2411yescharacteristic
343C22×Dic11C2411yescharacteristic
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11—22no—
347C2×C4×D11—22no—
348C2×C4×D11—22no—
349C2×C4×D11—41no—
350C2×C4×D11—41no—
351C2×C4×D11—41no—
352C2×C4×D11C2×D414yescomplemented
353C2×Dic22—24no—
354C2×Dic22—42no—
355C2×Dic22—42no—
356C11×C4⋊C4—22no—
357C11×C22⋊C4—24no—
358C11×C22⋊C4—24no—
359C11×C22⋊C4—24no—
360C11×C22⋊C4—24no—
361C11×C22⋊C4—24no—
362C11×C22⋊C4C2×D414yes—
363C11×C22⋊C4#4114yes—
364C42×C11—22no—
365C42×C11—22no—
366C22⋊Dic11—24no—
367C22⋊Dic11—24no—
368C22⋊Dic11—24no—
369C22⋊Dic11—24no—
370C22⋊Dic11—24no—
371C22⋊Dic11—24no—
372C22⋊Dic11—24no—
373C22⋊Dic11—24no—
374C22⋊Dic11—24no—
375C22⋊Dic11—24no—
376C22⋊Dic11—24no—
377C22⋊Dic11—24no—
378C22⋊Dic11—22no—
379C22⋊Dic11—42no—
380C22⋊Dic11—42no—
381C22⋊Dic11—42no—
382C22⋊Dic11—42no—
383C22⋊Dic11—42no—
384C22⋊Dic11—42no—
385C22⋊Dic11—42no—
386C22⋊Dic11—42no—
387C22⋊Dic11—42no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—22no—
390(C2×D11)⋊C4—22no—
391(C2×D11)⋊C4C2×D414yescomplemented
392C4⋊Dic11—24no—
393C4⋊Dic11—24no—
394C4⋊Dic11—22no—
395C4⋊Dic11—22no—
396C4⋊Dic11—22no—
397C4⋊Dic11—22no—
398C4⋊Dic11—42no—
399C4⋊Dic11—42no—
400C4⋊Dic11—42no—
401Dic11⋊C4—24no—
402Dic11⋊C4—24no—
403Dic11⋊C4—24no—
404Dic11⋊C4—22no—
405Dic11⋊C4—22no—
406Dic11⋊C4C2×D414yescomplemented
407C4×Dic11—24no—
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#2433D1111yescharacteristic, complemented
434#2428—111no—
435#2424—112no—
436#2416—111no—
437#2408—111no—
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—22no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
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—22no—
467C23×C11—48no—
468C23×C11—48no—
469C23×C11—48no—
470C23×C11—84no—
471C23×C11—84no—
472C23×C11—84no—
473C23×C11—84no—
474C23×C11C22×D412yes—
475C23×C11C2×#4112yes—
476C23×C11C2×#4112yes—
477C23×C11C2511yescharacteristic
478C22×D11—21no—
479C22×D11—21no—
480C22×D11—21no—
481C22×D11—21no—
482C22×D11—21no—
483C22×D11—21no—
484C22×D11C22×D412yes—
485D4×C11—48no—
486D4×C11—48no—
487D4×C11—44no—
488D4×C11—44no—
489D4×C11—44no—
490D4×C11—84no—
491D4×C11—84no—
492D4×C11—84no—
493D4×C11—84no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—21no—
498C2×C4×C11—21no—
499C2×C4×C11—21no—
500C2×C4×C11—21no—
501C2×C4×C11—21no—
502C2×C4×C11—21no—
503C2×C4×C11—21no—
504C2×C4×C11—28no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11C22×D412yes—
509C2×C4×C11C22×D412yes—
510C2×C4×C11C2×#4112yes—
511C2×C4×C11C2×#4112yes—
512C2×C4×C11C2×#4112yes—
513C2×C4×C11C2×#4112yes—
514C2×C4×C11H(5,𝔽2)12yes—
515C2×C4×C11H(5,𝔽2)12yes—
516C22⋊D11—28no—
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—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—21no—
535C2×Dic11—21no—
536C2×Dic11—21no—
537C2×Dic11—21no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—21no—
546C2×Dic11—21no—
547C2×Dic11—21no—
548C2×Dic11—22no—
549C2×Dic11—44no—
550C2×Dic11—44no—
551C2×Dic11—84no—
552C2×Dic11—84no—
553C2×Dic11C22×D412yes—
554C2×Dic11C22×D412yes—
555C2×Dic11C22×D412yes—
556C2×Dic11H(5,𝔽2)12yes—
557C4×D11—44no—
558C4×D11—44no—
559C4×D11—44no—
560Dic22—84no—
561C23×D4C2×D1111yescharacteristic
562#538—2216no—
563C2×C4⋊Q8—111no—
564C2×#127C2×D1111yescharacteristic
565C2×#127C2×D1111yescharacteristic
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—111no—
579C2×#121—111no—
580C2×#121—112no—
581C2×#121C2×D1111yescharacteristic
582C2×#120—112no—
583C2×#120C2×D1112yes—
584C2×#120C2×D1112yes—
585C2×C4×D4—112no—
586C2×C4×D4—111no—
587C2×C4×D4—111no—
588C2×C4×D4—111no—
589C2×C4×D4—111no—
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#394—112no—
606#393—112no—
607#392—112no—
608#392—112no—
609#392C2×D1112yes—
610#392C2×D1112yes—
611#390—112no—
612#390—112no—
613#390—111no—
614#390—111no—
615#390—111no—
616#390—112no—
617#390—111no—
618#390—111no—
619#390—112no—
620#390—111no—
621#390—112no—
622#390—111no—
623#390—111no—
624#390—112no—
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#380—111no—
648#379—112no—
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—112no—
656C4×C22⋊C4—111no—
657C4×C22⋊C4—111no—
658C4×C22⋊C4—111no—
659C4×C22⋊C4C2×D1111yescharacteristic
660C43—111no—
661C22×C11—22no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—22no—
665C22×C11—22no—
666C22×C11—22no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—42no—
673C22×C11—42no—
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—22no—
698C2×D11—22no—
699C2×D11—22no—
700C2×D11—41no—
701C2×D11—41no—
702C2×D11—41no—
703C2×D11—41no—
704C4×C11—22no—
705C4×C11—22no—
706C4×C11—22no—
707C4×C11—22no—
708C4×C11—22no—
709C4×C11—42no—
710C4×C11#53814yescomplemented
711Dic11—22no—
712Dic11—22no—
713Dic11—22no—
714Dic11—22no—
715Dic11—41no—
716Dic11—41no—
717Dic11—42no—
718Dic11—42no—
719Dic11—42no—
720Dic11—42no—
721Dic11—41no—
722C25C22×D1112yes—
723C22×Q8—112no—
724C22×D4—24no—
725C22×D4—42no—
726C22×D4—42no—
727C22×D4—111no—
728C22×D4—112no—
729C22×D4—112no—
730C22×D4—112no—
731C22×D4C22×D1112yes—
732C22×D4C22×D1111yescharacteristic
733C22×D4C22×D1111yescharacteristic
734C22×D4C22×D1111yescharacteristic
735C22×D4C22×D1112yes—
736C22×D4C22×D1112yes—
737C22×D4C22×D1112yes—
738C22×D4C22×D1112yes—
739C22×D4C22×D1112yes—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—112no—
744C23×C4—112no—
745C23×C4—111no—
746C23×C4—111no—
747C23×C4C22×D1111yescharacteristic
748C4⋊Q8—442no—
749#127—42no—
750#127—42no—
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—24no—
760#121—228no—
761#121—228no—
762#121—228no—
763#121—444no—
764#121—442no—
765#121—442no—
766#121—442no—
767#120—28no—
768#120—28no—
769#120—228no—
770C4×D4—118no—
771C4×D4—228no—
772C4×D4—224no—
773C4×D4—224no—
774C4×D4—442no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—111no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—111no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—112no—
788C2×C4⋊C4—112no—
789C2×C4⋊C4—112no—
790C2×C4⋊C4—442no—
791C2×C4⋊C4C22×D1111yescharacteristic
792C2×C22⋊C4—111no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
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—111no—
807C2×C22⋊C4—111no—
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—228no—
819C2×C22⋊C4—444no—
820C2×C22⋊C4C22×D1112yes—
821C2×C22⋊C4C22×D1112yes—
822C2×C22⋊C4C22×D1112yes—
823C2×C22⋊C4C22×D1112yes—
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1111yescharacteristic
826C2×C22⋊C4C22×D1111yescharacteristic
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—442no—
840C2×C42—442no—
841C2×C42C22×D1111yescharacteristic
842C2×C42C22×D1111yescharacteristic
843#95—111no—
844#95—111no—
845#95—111no—
846#95—111no—
847#95—112no—
848#95—112no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95—112no—
853#95—112no—
854#95C22×D1111yescharacteristic
855#95C22×D1111yescharacteristic
856C2×C11—24no—
857C2×C11—82no—
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—42no—
868C24—24no—
869C24—24no—
870C24—24no—
871C24—42no—
872C24—42no—
873C24—42no—
874C24—42no—
875C24—111no—
876C24C23×D1112yes—
877C24C23×D1112yes—
878C24C23×D1112yes—
879C24C23×D1111yescharacteristic
880C2×Q8—224no—
881C2×Q8—442no—
882C2×Q8—442no—
883C2×D4—24no—
884C2×D4—24no—
885C2×D4—24no—
886C2×D4—24no—
887C2×D4—24no—
888C2×D4—22no—
889C2×D4—24no—
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—24no—
893C2×D4—24no—
894C2×D4—22no—
895C2×D4—22no—
896C2×D4—22no—
897C2×D4—22no—
898C2×D4—22no—
899C2×D4—22no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—416no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—114no—
912C2×D4—222no—
913C2×D4—222no—
914C2×D4—224no—
915C2×D4—224no—
916C2×D4—224no—
917C2×D4—442no—
918C2×D4—442no—
919C2×D4—442no—
920C2×D4—442no—
921C2×D4—442no—
922C2×D4—442no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—111no—
926C22×C4—111no—
927C22×C4—111no—
928C22×C4—111no—
929C22×C4—114no—
930C22×C4—114no—
931C22×C4—111no—
932C22×C4—111no—
933C22×C4—111no—
934C22×C4—112no—
935C22×C4—112no—
936C22×C4—112no—
937C22×C4—112no—
938C22×C4—222no—
939C22×C4—222no—
940C22×C4—224no—
941C22×C4—222no—
942C22×C4—224no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—222no—
946C22×C4—222no—
947C22×C4—441no—
948C22×C4—441no—
949C22×C4—441no—
950C22×C4—441no—
951C22×C4—441no—
952C22×C4—441no—
953C22×C4—442no—
954C22×C4—442no—
955C22×C4—442no—
956C22×C4—442no—
957C22×C4#434114yes—
958C22×C4C23×D1112yes—
959C22×C4C23×D1111yescharacteristic
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C4⋊C4—22no—
966C4⋊C4—114no—
967C4⋊C4—224no—
968C4⋊C4—224no—
969C4⋊C4—224no—
970C4⋊C4—224no—
971C4⋊C4—224no—
972C4⋊C4—222no—
973C4⋊C4—222no—
974C4⋊C4—222no—
975C4⋊C4—222no—
976C4⋊C4—222no—
977C4⋊C4—222no—
978C4⋊C4—442no—
979C4⋊C4—442no—
980C4⋊C4—442no—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—114no—
987C22⋊C4—224no—
988C22⋊C4—224no—
989C22⋊C4—224no—
990C22⋊C4—224no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—224no—
994C22⋊C4—224no—
995C22⋊C4—224no—
996C22⋊C4—224no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—222no—
1001C22⋊C4—222no—
1002C22⋊C4—222no—
1003C22⋊C4—442no—
1004C22⋊C4—442no—
1005C22⋊C4—442no—
1006C22⋊C4—442no—
1007C22⋊C4—442no—
1008C22⋊C4—442no—
1009C22⋊C4—442no—
1010C22⋊C4—442no—
1011C22⋊C4—442no—
1012C22⋊C4D4×D1114yes—
1013C22⋊C4#434114yes—
1014C42—22no—
1015C42—22no—
1016C42—114no—
1017C42—224no—
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—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
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—22no—
1054C23—48no—
1055C23—48no—
1056C23—48no—
1057C23—84no—
1058C23—84no—
1059C23—84no—
1060C23—84no—
1061C23—112no—
1062C23—221no—
1063C23—221no—
1064C23—221no—
1065C23—221no—
1066C23—221no—
1067C23—221no—
1068C23C2×D4×D1112yes—
1069C23C2×#434112yes—
1070C23C2×#434112yes—
1071C23C24×D1111yescharacteristic
1072Q8—884no—
1073D4—48no—
1074D4—48no—
1075D4—44no—
1076D4—44no—
1077D4—44no—
1078D4—84no—
1079D4—84no—
1080D4—84no—
1081D4—84no—
1082D4—228no—
1083D4—884no—
1084D4—884no—
1085D4—884no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—28no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—112no—
1101C2×C4—112no—
1102C2×C4—112no—
1103C2×C4—112no—
1104C2×C4—221no—
1105C2×C4—221no—
1106C2×C4—221no—
1107C2×C4—221no—
1108C2×C4—221no—
1109C2×C4—221no—
1110C2×C4—221no—
1111C2×C4—221no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—222no—
1115C2×C4—222no—
1116C2×C4—221no—
1117C2×C4—221no—
1118C2×C4—221no—
1119C2×C4—221no—
1120C2×C4—221no—
1121C2×C4—221no—
1122C2×C4—222no—
1123C2×C4—222no—
1124C2×C4—222no—
1125C2×C4—222no—
1126C2×C4—221no—
1127C2×C4—222no—
1128C2×C4—222no—
1129C2×C4—222no—
1130C2×C4—221no—
1131C2×C4—221no—
1132C2×C4—222no—
1133C2×C4—444no—
1134C2×C4—444no—
1135C2×C4—444no—
1136C2×C4—444no—
1137C2×C4—444no—
1138C2×C4—884no—
1139C2×C4—884no—
1140C2×C4C2×D4×D1112yes—
1141C2×C4C2×D4×D1112yes—
1142C2×C4C2×#434112yes—
1143C2×C4C2×#434112yes—
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—42no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
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—222no—
1177C22—222no—
1178C22—222no—
1179C22—441no—
1180C22—441no—
1181C22—441no—
1182C22—441no—
1183C22#1062324714yes—
1184C22C22×D4×D1111yescharacteristic
1185C22C22×#434111yescharacteristic
1186C22C22×#434111yescharacteristic
1187C22C2×#6703711yescharacteristic
1188C22C2×#6703711yescharacteristic
1189C22D11×H(5,𝔽2)11yescharacteristic
1190C22#1062345511yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—22no—
1196C4—42no—
1197C4—222no—
1198C4—222no—
1199C4—222no—
1200C4—222no—
1201C4—442no—
1202C4—441no—
1203C4—442no—
1204C4—442no—
1205C4—442no—
1206C4—441no—
1207C4—441no—
1208C4#1062312414yescomplemented
1209C2—24no—
1210C2—82no—
1211C2—82no—
1212C2—82no—
1213C2—442no—
1214C2C2×#1062324711yescharacteristic
1215C2C2×#1062312411yescharacteristic
1216C2#1308202911yescharacteristic
1217C2#1308237211yescharacteristic
1218C2#1308238811yescharacteristic
1219C2#1308256811yescharacteristic
1220C2#1308263911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2433C2
hypercenter#2433D11
hypocenterC11#35007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2433

Complements

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

NH ≅ G/Ntype
1. C2×#10623124C2semidirect
2. #13076980C2semidirect
3. #13076972C2semidirect
4. #13076958C2semidirect
5. #13076946C2semidirect
6. #13074758C2semidirect
7. #13074747C2semidirect
8. #13073686C2semidirect
9. #13073677C2semidirect
10. #13073204C2semidirect
11. #13072977C2semidirect
12. #13072741C2semidirect
13. #13072377C2semidirect
14. #13072318C2semidirect
15. #13072207C2semidirect
16. #13072148C2semidirect
17. #13072057C2semidirect
18. #13071966C2semidirect
19. #13071277C2semidirect
20. #121×Dic11C2semidirect
21. C2×#10622834C2semidirect
22. C4×(C22⋊D11)⋊C4C2semidirect
23. C11×#2433C2semidirect
34. C2×#66992C22semidirect
37. C2×#66991C22semidirect
38. C2×#66991C22semidirect
39. C2×#66991C22semidirect
40. C2×#66989C22semidirect
41. C2×#66989C22semidirect
42. C2×#66988C22semidirect
44. C2×D4×Dic11C22semidirect
49. C2×#66938C22semidirect
50. C2×#66936C22semidirect
53. C2×#66932C22semidirect
54. C2×#66932C22semidirect
56. C2×C42×D11C22semidirect
57. C2×#66922C22semidirect
65. #10622836C22semidirect
67. #10622835C22semidirect
68. #10622835C22semidirect
69. #10622835C22semidirect
78. #10622834C22semidirect
79. #10622834C22semidirect
80. #10622834C22semidirect
81. #10622834C22semidirect
82. #10622834C22semidirect
83. #10622834C22semidirect
86. #10622833C22semidirect
87. #10622833C22semidirect
89. #10622600C22semidirect
90. #10622598C22semidirect
91. C4⋊C4×Dic11C22semidirect
92. #10622586C22semidirect
93. #10622574C22semidirect
94. #10622574C22semidirect
95. #10622569C22semidirect
96. #10622566C22semidirect
97. #10622564C22semidirect
98. #10622564C22semidirect
99. #10622564C22semidirect
100. #10622564C22semidirect
101. #10622564C22semidirect
103. #10622561C22semidirect
104. #10622561C22semidirect
105. #10622560C22semidirect
106. #10622558C22semidirect
107. #10622558C22semidirect
108. #10622557C22semidirect
111. C22⋊C4×Dic11C22semidirect
112. C4×(C2×D11)⋊C4C22semidirect
113. #10622548C22semidirect
114. C4×Dic11⋊C4C22semidirect
115. C42×Dic11C22semidirect
116. #10622541C22semidirect
117. #10622541C22semidirect
118. #10622279C22semidirect
119. #10622279C22semidirect
120. #10622274C22semidirect
121. #10622269C22semidirect
122. #10622262C22semidirect
123. #10622262C22semidirect
239. (C22⋊D11)⋊C4D4semidirect
352. C2×C4×D11C2×D4semidirect
391. (C2×D11)⋊C4C2×D4semidirect
406. Dic11⋊C4C2×D4semidirect
418. C4×Dic11C2×D4semidirect
433. #2433D11semidirect
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
#130769722
#130769582
#130769462
#130747582
#130747472
#130736862
#130736772
#130732042
#130729772
#130727412
#130723772
#130723182
#130722072
#130721482
#130720572
#130719662
#130712772
#121×Dic112
C2×#106228342
C4×(C22⋊D11)⋊C42
C11×#24332
#3500711