Finite Group Databasebeta

← #14926738

Subgroups — #14926738

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×#10623188C212yesmaximal, complemented
2#13076980C211yesmaximal, characteristic, complemented
3#13076970C211yesmaximal, characteristic, complemented
4#13076958C211yesmaximal, characteristic, complemented
5#13076949C211yesmaximal, characteristic, complemented
6#13074752C212yesmaximal, complemented
7#13074751C212yesmaximal, complemented
8#13073688C212yesmaximal, complemented
9#13073672C212yesmaximal, complemented
10#13073202C211yesmaximal, characteristic, complemented
11#13072980C211yesmaximal, characteristic, complemented
12#13072743C212yesmaximal, complemented
13#13072316C211yesmaximal, characteristic, complemented
14#13072250C211yesmaximal, characteristic, complemented
15#13072198C211yesmaximal, characteristic, complemented
16#13072145C212yesmaximal, complemented
17#13072059C211yesmaximal, characteristic, complemented
18#13071970C211yesmaximal, characteristic, complemented
19#13071272C212yesmaximal, complemented
20C4×#66991C211yesmaximal, characteristic, complemented
21D11×#390C211yesmaximal, characteristic, complemented
22C4×#66946C211yesmaximal, characteristic, complemented
23C11×#2445C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C2×C11×#127C2211yescharacteristic
26C2×C11×#123C2212yescomplemented
27C2×C4×D4×C11C2211yescharacteristic, complemented
28C2×#66993C2211yescharacteristic
29C2×#66991C2211yescharacteristic
30C2×#66991C2211yescharacteristic
31C2×#66991C2212yescomplemented
32C2×#66991C2212yescomplemented
33C2×#66991C2211yescharacteristic, complemented
34C2×#66990C2212yes—
35C2×#66990C2212yes—
36C2×#66983C2212yescomplemented
37C2×C4×C22⋊D11C2212yes—
38#10623188—216no—
39C2×#66951C2212yescomplemented
40C2×#66950C2212yes—
41C2×#66948C2211yescharacteristic
42C2×#66947C2212yescomplemented
43C2×#66946C2211yescharacteristic
44C2×#66946C2211yescharacteristic
45C2×C4⋊C4×D11C2211yescharacteristic
46C2×#66941C2211yescharacteristic, complemented
47C2×#66938C2212yescomplemented
48C2×#66938C2212yescomplemented
49C2×#66938C2212yescomplemented
50C2×#66937C2212yes—
51C2×#66935C2212yes—
52C2×C22⋊C4×D11C2212yes—
53C2×C22⋊C4×D11C2212yes—
54C2×#66932C2212yescomplemented
55C2×C4×D44C2211yescharacteristic
56C2×C42×D11C2211yescharacteristic
57C2×C42×D11C2211yescharacteristic, complemented
58C11×#394C2212yescomplemented
59C11×#394C2212yescomplemented
60C11×#390C2211yescharacteristic
61C11×#390C2211yescharacteristic
62C11×#390C2211yescharacteristic, complemented
63C11×#389C2211yescharacteristic, complemented
64C11×#386C2212yescomplemented
65C4×C11×C4⋊C4C2211yescharacteristic, complemented
66#10622836C2212yes—
67#10622836C2212yes—
68#10622834C2211yescharacteristic
69#10622834C2211yescharacteristic
70#10622834C2212yescomplemented
71#10622834C2211yescharacteristic, complemented
72#10622834C2212yescomplemented
73#10622826C2212yescomplemented
74C4×C22⋊Dic11C2212yescomplemented
75#10622607C2212yescomplemented
76#10622603C2212yescomplemented
77#10622601C2211yescharacteristic
78#10622600C2211yescharacteristic
79#10622600C2211yescharacteristic, complemented
80#10622598C2211yescharacteristic, complemented
81#10622596C2212yescomplemented
82C4⋊C4×Dic11C2211yescharacteristic, complemented
83C4⋊C4×Dic11C2211yescharacteristic, complemented
84#10622586C2211yescharacteristic, complemented
85#10622574C2212yes—
86#10622574C2212yescomplemented
87#10622573C2212yes—
88#10622573C2212yescomplemented
89#10622572C2212yescomplemented
90#10622572C2212yescomplemented
91#10622570C2212yes—
92#10622570C2212yes—
93#10622570C2212yescomplemented
94#10622570C2212yescomplemented
95#10622569C2212yes—
96#10622569C2212yes—
97#10622568C2212yes—
98#10622564C2212yescomplemented
99#10622561C2212yescomplemented
100#10622560C2212yescomplemented
101#10622558C2212yescomplemented
102#10622557C2212yescomplemented
103#10622557C2212yescomplemented
104#10622557C2212yescomplemented
105#10622552C2211yescharacteristic
106#10622552C2211yescharacteristic
107#10622552C2211yescharacteristic
108C4×(C2×D11)⋊C4C2211yescharacteristic
109C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
110#10622548C2211yescharacteristic, complemented
111C4×C4⋊Dic11C2211yescharacteristic, complemented
112C42×Dic11C2211yescharacteristic, complemented
113#10622541C2211yescharacteristic, complemented
114#10622287C2212yescomplemented
115#10622283C2212yescomplemented
116#10622282C2212yescomplemented
117#10622281C2212yes—
118#10622279C2211yescharacteristic
119#10622279C2211yescharacteristic
120#10622279C2211yescharacteristic, complemented
121#10622279C2211yescharacteristic, complemented
122#10622278C2212yescomplemented
123#10622269C2212yescomplemented
124C24×D11C2312yes—
125C22×D4×C11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C22×D4×C11C2312yes—
129C23×C4×C11C2312yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2312yes—
136C2×D4×D11—24no—
137C2×D4×D11—42no—
138C2×D4×D11—42no—
139C22×D44C2311yescharacteristic
140C22×D44C2311yescharacteristic
141C22×D44C2312yes—
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2312yes—
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×Dic22C2312yes—
150C11×#127—42no—
151C11×#123—28no—
152C4×D4×C11—42no—
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2312yes—
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177#66993—42no—
178#66991—28no—
179#66991—24no—
180#66991—42no—
181#66991—42no—
182#66991—44no—
183#66990—28no—
184#66990—28no—
185#66983—28no—
186C4×C22⋊D11—28no—
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
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)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2311yescharacteristic
203C2×(C2×D11)⋊C4C2311yescharacteristic
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2312yes—
206C2×C4⋊Dic11C2311yescharacteristic
207C2×C4⋊Dic11C2311yescharacteristic
208C2×C4⋊Dic11C2312yes—
209C2×C4⋊Dic11C2311yescharacteristic
210C2×C4⋊Dic11C2312yes—
211C2×Dic11⋊C4C2312yes—
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2312yes—
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226#66951—28no—
227#66950—28no—
228#66948—42no—
229#66947—28no—
230#66946—24no—
231#66946D418yescomplemented
232C4⋊C4×D11—42no—
233#66941—42no—
234#66938—28no—
235#66938—28no—
236#66938—44no—
237#66937—28no—
238#66935—28no—
239C22⋊C4×D11—28no—
240C22⋊C4×D11—44no—
241#66932—28no—
242C4×D44—24no—
243C42×D11—42no—
244C42×D11—42no—
245C11×#95C2312yes—
246C11×#95C2311yescharacteristic
247C11×#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258#35007—111nomaximal, Sylow
259C24×C11C2412yes—
260C24×C11C2412yes—
261C23×D11—24no—
262C23×D11—24no—
263C23×D11—24no—
264C23×D11—42no—
265C23×D11—42no—
266C23×D11—42no—
267C23×D11—42no—
268C23×D11C2412yes—
269C23×D11C2411yescharacteristic
270C23×D11C2411yescharacteristic
271C2×D4×C11—24no—
272C2×D4×C11—22no—
273C2×D4×C11—22no—
274C2×D4×C11—24no—
275C2×D4×C11—22no—
276C2×D4×C11—22no—
277C2×D4×C11—22no—
278C2×D4×C11—22no—
279C2×D4×C11—42no—
280C2×D4×C11—42no—
281C2×D4×C11—42no—
282C2×D4×C11—42no—
283C22×C4×C11—24no—
284C22×C4×C11—42no—
285C22×C4×C11—42no—
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2412yes—
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2412yes—
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C2×C22⋊D11—24no—
296C2×C22⋊D11—24no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—24no—
303C2×C22⋊D11—42no—
304C2×C22⋊D11—42no—
305C2×C22⋊D11—42no—
306C2×C22⋊D11—42no—
307C2×C22⋊D11—42no—
308C2×C22⋊D11—42no—
309C2×C22⋊D11—42no—
310C2×C22⋊D11—42no—
311C2×C22⋊D11—42no—
312C2×C22⋊D11—42no—
313C22×Dic11C2411yescharacteristic
314C22×Dic11C2412yes—
315C22×Dic11C2412yes—
316C22×Dic11C2412yes—
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2411yescharacteristic
322D4×D11—416no—
323C2×D44—24no—
324C2×D44—22no—
325C2×D44—22no—
326C2×D44—22no—
327C2×D44—22no—
328C2×D44—22no—
329C2×D44—42no—
330C2×D44—42no—
331C2×D44C2×D414yes—
332C2×C4×D11—22no—
333C2×C4×D11—22no—
334C2×C4×D11—24no—
335C2×C4×D11—22no—
336C2×C4×D11—22no—
337C2×C4×D11—22no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—22no—
342C2×C4×D11—41no—
343C2×C4×D11—41no—
344C2×C4×D11—41no—
345C2×C4×D11—41no—
346C2×C4×D11—41no—
347C2×C4×D11—41no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11C2×D414yes—
351C2×C4×D11C2×D414yescomplemented
352C2×C4×D11#4114yes—
353C2×Dic22—24no—
354C2×Dic22—42no—
355C2×Dic22—42no—
356C11×C4⋊C4—24no—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—22no—
360C11×C4⋊C4C2×D414yescomplemented
361C11×C22⋊C4—24no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—42no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4—42no—
367C11×C22⋊C4—42no—
368C42×C11—22no—
369C42×C11—22no—
370C42×C11—22no—
371C22⋊Dic11—24no—
372C22⋊Dic11—24no—
373C22⋊Dic11—24no—
374C22⋊Dic11—24no—
375C22⋊Dic11—24no—
376C22⋊Dic11—24no—
377C22⋊Dic11—24no—
378C22⋊Dic11—42no—
379C22⋊Dic11—42no—
380(C2×D11)⋊C4—24no—
381(C2×D11)⋊C4—22no—
382(C2×D11)⋊C4—22no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—22no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4C2×D414yes—
395(C2×D11)⋊C4C2×D414yescomplemented
396(C2×D11)⋊C4#4114yes—
397C4⋊Dic11—24no—
398C4⋊Dic11—22no—
399C4⋊Dic11—24no—
400C4⋊Dic11—22no—
401C4⋊Dic11—22no—
402C4⋊Dic11—22no—
403C4⋊Dic11—42no—
404Dic11⋊C4—24no—
405Dic11⋊C4—24no—
406Dic11⋊C4—42no—
407Dic11⋊C4—42no—
408C4×Dic11—22no—
409C4×Dic11—22no—
410C4×Dic11—24no—
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#2445D1111yescharacteristic, complemented
432#2440—111no—
433#2433—111no—
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—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
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×C11C2511yescharacteristic
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—21no—
464C22×D11—21no—
465C22×D11—21no—
466C22×D11—21no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—48no—
475C22×D11—48no—
476C22×D11—48no—
477C22×D11—84no—
478C22×D11—84no—
479C22×D11—84no—
480C22×D11—84no—
481C22×D11C22×D412yes—
482C22×D11C22×D412yes—
483C22×D11C2×#4112yes—
484C22×D11C2×#4112yes—
485D4×C11—44no—
486D4×C11—44no—
487D4×C11—84no—
488D4×C11—84no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—21no—
500C2×C4×C11—21no—
501C2×C4×C11—21no—
502C2×C4×C11—21no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—21no—
506C2×C4×C11—22no—
507C2×C4×C11—21no—
508C2×C4×C11—22no—
509C2×C4×C11—84no—
510C2×C4×C11C22×D412yes—
511C2×C4×C11C22×D412yes—
512C2×C4×C11C22×D412yes—
513C2×C4×C11C2×#4112yes—
514C2×C4×C11C2×#4112yes—
515C2×C4×C11H(5,𝔽2)12yes—
516C2×C4×C11H(5,𝔽2)12yes—
517C22⋊D11—48no—
518C22⋊D11—48no—
519C22⋊D11—84no—
520C22⋊D11—84no—
521C22⋊D11—84no—
522C22⋊D11—84no—
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—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—21no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—21no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—21no—
545C2×Dic11C22×D412yes—
546C2×Dic11C22×D412yes—
547C2×Dic11C2×#4112yes—
548C2×Dic11C2×#4112yes—
549C2×Dic11H(5,𝔽2)12yes—
550D44—28no—
551D44—44no—
552D44—84no—
553C4×D11—28no—
554C4×D11—44no—
555C4×D11—44no—
556C4×D11—44no—
557C4×D11—44no—
558C4×D11—44no—
559C4×D11—84no—
560Dic22—84no—
561C23×D4—111no—
562#538—2216no—
563C2×C4⋊Q8—111no—
564C2×#127—111no—
565C2×#127C2×D1111yescharacteristic
566C2×#126—112no—
567C2×#126—112no—
568C2×#124—112no—
569C2×#124—112no—
570C2×#124—112no—
571C2×#123—112no—
572C2×#123C2×D1112yescomplemented
573C2×C22⋊Q8—112no—
574C2×#121—112no—
575C2×#121—111no—
576C2×#121—112no—
577C2×#121—111no—
578C2×#121—111no—
579C2×#121—112no—
580C2×#121—111no—
581C2×#121—112no—
582C2×#120—112no—
583C2×#120—112no—
584C2×#120—112no—
585C2×C4×D4—112no—
586C2×C4×D4—111no—
587C2×C4×D4—111no—
588C2×C4×D4—111no—
589C2×C4×D4C2×D1111yescharacteristic, complemented
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#394C2×D1112yescomplemented
605#394C2×D1112yescomplemented
606#393—112no—
607#392—112no—
608#392—112no—
609#392—112no—
610#392—112no—
611#390—112no—
612#390—111no—
613#390—111no—
614#390—112no—
615#390—111no—
616#390—111no—
617#390—112no—
618#390—112no—
619#390—112no—
620#390—112no—
621#390—111no—
622#390—111no—
623#390—111no—
624#390C2×D1111yescharacteristic
625#390C2×D1111yescharacteristic
626#390C2×D1111yescharacteristic, complemented
627#389—111no—
628#389—111no—
629#389—111no—
630#389C2×D1111yescharacteristic, complemented
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#386C2×D1112yescomplemented
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⋊C4C2×D1111yescharacteristic, complemented
653C4×C22⋊C4—112no—
654C4×C22⋊C4—111no—
655C4×C22⋊C4—111no—
656C4×C22⋊C4—111no—
657C4×C22⋊C4—111no—
658C4×C22⋊C4—111no—
659C4×C22⋊C4—111no—
660C43—111no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11—42no—
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×C11C23×D411yescharacteristic
676C22×C11C22×#4111yescharacteristic
677C22×C11C22×#4111yescharacteristic
678C22×C11C2×H(5,𝔽2)11yescharacteristic
679C22×C11C2×H(5,𝔽2)11yescharacteristic
680C22×C11C2×H(5,𝔽2)11yescharacteristic
681C22×C11#58511yescharacteristic
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—22no—
685C2×D11—22no—
686C2×D11—22no—
687C2×D11—22no—
688C2×D11—22no—
689C2×D11—22no—
690C2×D11—22no—
691C2×D11—41no—
692C2×D11—41no—
693C2×D11—41no—
694C2×D11—41no—
695C2×D11—42no—
696C2×D11—42no—
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—816no—
703C2×D11#53214yes—
704C4×C11—22no—
705C4×C11—22no—
706C4×C11—22no—
707C4×C11—22no—
708C4×C11—41no—
709C4×C11—42no—
710C4×C11—42no—
711C4×C11—41no—
712C4×C11#53814yescomplemented
713Dic11—22no—
714Dic11—22no—
715Dic11—22no—
716Dic11—22no—
717Dic11—22no—
718Dic11—42no—
719Dic11—41no—
720Dic11—42no—
721Dic11—42no—
722C25—112no—
723C22×Q8—112no—
724C22×D4—112no—
725C22×D4—112no—
726C22×D4—112no—
727C22×D4—112no—
728C22×D4—112no—
729C22×D4—112no—
730C22×D4—111no—
731C22×D4—111no—
732C22×D4—112no—
733C22×D4—224no—
734C22×D4—442no—
735C22×D4—442no—
736C22×D4C22×D1111yescharacteristic
737C22×D4C22×D1111yescharacteristic
738C22×D4C22×D1112yes—
739C22×D4C22×D1112yes—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—111no—
745C23×C4—111no—
746C23×C4—112no—
747C23×C4C22×D1112yes—
748C4⋊Q8—442no—
749#127—42no—
750#127—442no—
751#126—228no—
752#126—228no—
753#124—228no—
754#124—228no—
755#124—444no—
756#123—28no—
757#123—228no—
758C22⋊Q8—228no—
759#121—228no—
760#121—228no—
761#121—228no—
762#121—224no—
763#121—444no—
764#121—442no—
765#121—442no—
766#121—442no—
767#120—228no—
768#120—228no—
769#120—228no—
770C4×D4—42no—
771C4×D4—118no—
772C4×D4—224no—
773C4×D4—224no—
774C4×D4—228no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—111no—
782C2×C4⋊C4—111no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—442no—
787C2×C4⋊C4C22×D1111yescharacteristic
788C2×C4⋊C4C22×D1111yescharacteristic
789C2×C4⋊C4C22×D1111yescharacteristic
790C2×C4⋊C4C22×D1112yes—
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—112no—
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—111no—
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×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—442no—
839C2×C42—442no—
840C2×C42C22×D1111yescharacteristic
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#95C22×D1111yescharacteristic
854#95C22×D1111yescharacteristic
855#95C22×D1112yes—
856C2×C11—82no—
857C2×C11—82no—
858C2×C11C2×#53211yescharacteristic
859C2×C11C2×#53811yescharacteristic
860C2×C11#346011yescharacteristic
861C2×C11#349611yescharacteristic
862C2×C11#349811yescharacteristic
863C2×C11#351411yescharacteristic
864C2×C11#351911yescharacteristic
865D11—24no—
866D11—42no—
867D11—82no—
868C24—111no—
869C24—111no—
870C24—112no—
871C24—224no—
872C24—224no—
873C24—224no—
874C24—442no—
875C24—442no—
876C24—442no—
877C24—442no—
878C24C23×D1112yes—
879C24C23×D1112yes—
880C2×Q8—224no—
881C2×Q8—442no—
882C2×Q8—442no—
883C2×D4—24no—
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—22no—
887C2×D4—22no—
888C2×D4—24no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—114no—
896C2×D4—222no—
897C2×D4—222no—
898C2×D4—224no—
899C2×D4—224no—
900C2×D4—224no—
901C2×D4—224no—
902C2×D4—224no—
903C2×D4—224no—
904C2×D4—224no—
905C2×D4—224no—
906C2×D4—224no—
907C2×D4—222no—
908C2×D4—222no—
909C2×D4—222no—
910C2×D4—442no—
911C2×D4—442no—
912C2×D4—4416no—
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×D4—442no—
923C22×C4—24no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—111no—
927C22×C4—111no—
928C22×C4—111no—
929C22×C4—111no—
930C22×C4—111no—
931C22×C4—114no—
932C22×C4—114no—
933C22×C4—114no—
934C22×C4—111no—
935C22×C4—112no—
936C22×C4—112no—
937C22×C4—112no—
938C22×C4—222no—
939C22×C4—222no—
940C22×C4—222no—
941C22×C4—224no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—222no—
946C22×C4—222no—
947C22×C4—222no—
948C22×C4—441no—
949C22×C4—441no—
950C22×C4—441no—
951C22×C4—441no—
952C22×C4—441no—
953C22×C4—441no—
954C22×C4—442no—
955C22×C4—442no—
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1112yes—
958C22×C4C23×D1111yescharacteristic
959C22×C4C23×D1112yes—
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C4⋊C4—24no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—224no—
970C4⋊C4—222no—
971C4⋊C4—224no—
972C4⋊C4—224no—
973C4⋊C4—224no—
974C4⋊C4—222no—
975C4⋊C4—222no—
976C4⋊C4—222no—
977C4⋊C4—442no—
978C4⋊C4—442no—
979C4⋊C4—442no—
980C4⋊C4D4×D1114yescomplemented
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—114no—
989C22⋊C4—114no—
990C22⋊C4—114no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—222no—
994C22⋊C4—222no—
995C22⋊C4—224no—
996C22⋊C4—222no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—224no—
1001C22⋊C4—224no—
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—22no—
1016C42—22no—
1017C42—114no—
1018C42—222no—
1019C42—222no—
1020C42—224no—
1021C42—222no—
1022C42—222no—
1023C42—441no—
1024C42—441no—
1025C42—441no—
1026C42—441no—
1027C42—441no—
1028C11#3500711yescharacteristic, complemented, Sylow
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—112no—
1044C23—112no—
1045C23—112no—
1046C23—112no—
1047C23—221no—
1048C23—221no—
1049C23—221no—
1050C23—221no—
1051C23—221no—
1052C23—221no—
1053C23—221no—
1054C23—221no—
1055C23—221no—
1056C23—221no—
1057C23—222no—
1058C23—222no—
1059C23—222no—
1060C23—222no—
1061C23—222no—
1062C23—222no—
1063C23—222no—
1064C23—448no—
1065C23—448no—
1066C23—448no—
1067C23—884no—
1068C23—884no—
1069C23—884no—
1070C23—884no—
1071C23C24×D1111yescharacteristic
1072Q8—884no—
1073D4—44no—
1074D4—44no—
1075D4—84no—
1076D4—84no—
1077D4—228no—
1078D4—448no—
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—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—22no—
1095C2×C4—22no—
1096C2×C4—21no—
1097C2×C4—22no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—22no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—22no—
1106C2×C4—84no—
1107C2×C4—112no—
1108C2×C4—112no—
1109C2×C4—112no—
1110C2×C4—112no—
1111C2×C4—112no—
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—228no—
1123C2×C4—222no—
1124C2×C4—222no—
1125C2×C4—222no—
1126C2×C4—221no—
1127C2×C4—222no—
1128C2×C4—221no—
1129C2×C4—222no—
1130C2×C4—221no—
1131C2×C4—222no—
1132C2×C4—222no—
1133C2×C4—222no—
1134C2×C4—222no—
1135C2×C4—444no—
1136C2×C4—444no—
1137C2×C4—444no—
1138C2×C4—444no—
1139C2×C4—444no—
1140C2×C4—884no—
1141C2×C4C2×D4×D1112yes—
1142C2×C4C2×D4×D1112yes—
1143C2×C4C2×D4×D1112yes—
1144C2×C4#6703712yes—
1145C2×C4#41×D1112yes—
1146C2×C4#41×D1112yes—
1147C2×C4#6704212yes—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—114no—
1163C22—222no—
1164C22—222no—
1165C22—222no—
1166C22—222no—
1167C22—222no—
1168C22—222no—
1169C22—222no—
1170C22—222no—
1171C22—222no—
1172C22—441no—
1173C22—441no—
1174C22—441no—
1175C22—441no—
1176C22—442no—
1177C22—442no—
1178C22—442no—
1179C22—442no—
1180C22—442no—
1181C22—442no—
1182C22—442no—
1183C22—8816no—
1184C22C22×D4×D1111yescharacteristic
1185C22C2×#6703711yescharacteristic
1186C22C2×#41×D1111yescharacteristic
1187C22C2×#41×D1111yescharacteristic
1188C22C2×#6704211yescharacteristic
1189C22D11×H(5,𝔽2)11yescharacteristic
1190C22#1062345511yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—42no—
1196C4—41no—
1197C4—42no—
1198C4—41no—
1199C4—222no—
1200C4—222no—
1201C4—222no—
1202C4—222no—
1203C4—222no—
1204C4—442no—
1205C4—442no—
1206C4—442no—
1207C4—441no—
1208C4#1062318814yescomplemented
1209C2—82no—
1210C2—82no—
1211C2—224no—
1212C2—442no—
1213C2—882no—
1214C2D11×#53211yescharacteristic
1215C2C2×#1062318811yescharacteristic
1216C2#1308203111yescharacteristic
1217C2#1308237211yescharacteristic
1218C2#1308239311yescharacteristic
1219C2#1308257611yescharacteristic
1220C2#1308264511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2445C2
hypercenter#2445D11
hypocenterC11#35007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2445

Complements

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

NH ≅ G/Ntype
1. C2×#10623188C2semidirect
2. #13076980C2semidirect
3. #13076970C2semidirect
4. #13076958C2semidirect
5. #13076949C2semidirect
6. #13074752C2semidirect
7. #13074751C2semidirect
8. #13073688C2semidirect
9. #13073672C2semidirect
10. #13073202C2semidirect
11. #13072980C2semidirect
12. #13072743C2semidirect
13. #13072316C2semidirect
14. #13072250C2semidirect
15. #13072198C2semidirect
16. #13072145C2semidirect
17. #13072059C2semidirect
18. #13071970C2semidirect
19. #13071272C2semidirect
20. C4×#66991C2semidirect
21. D11×#390C2semidirect
22. C4×#66946C2semidirect
23. C11×#2445C2semidirect
26. C2×C11×#123C22semidirect
27. C2×C4×D4×C11C22semidirect
31. C2×#66991C22semidirect
32. C2×#66991C22semidirect
33. C2×#66991C22semidirect
36. C2×#66983C22semidirect
39. C2×#66951C22semidirect
42. C2×#66947C22semidirect
46. C2×#66941C22semidirect
47. C2×#66938C22semidirect
48. C2×#66938C22semidirect
49. C2×#66938C22semidirect
54. C2×#66932C22semidirect
57. C2×C42×D11C22semidirect
58. C11×#394C22semidirect
59. C11×#394C22semidirect
62. C11×#390C22semidirect
63. C11×#389C22semidirect
64. C11×#386C22semidirect
65. C4×C11×C4⋊C4C22semidirect
70. #10622834C22semidirect
71. #10622834C22semidirect
72. #10622834C22semidirect
73. #10622826C22semidirect
74. C4×C22⋊Dic11C22semidirect
75. #10622607C22semidirect
76. #10622603C22semidirect
79. #10622600C22semidirect
80. #10622598C22semidirect
81. #10622596C22semidirect
82. C4⋊C4×Dic11C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. #10622586C22semidirect
86. #10622574C22semidirect
88. #10622573C22semidirect
89. #10622572C22semidirect
90. #10622572C22semidirect
93. #10622570C22semidirect
94. #10622570C22semidirect
98. #10622564C22semidirect
99. #10622561C22semidirect
100. #10622560C22semidirect
101. #10622558C22semidirect
102. #10622557C22semidirect
103. #10622557C22semidirect
104. #10622557C22semidirect
109. C4×(C2×D11)⋊C4C22semidirect
110. #10622548C22semidirect
111. C4×C4⋊Dic11C22semidirect
112. C42×Dic11C22semidirect
113. #10622541C22semidirect
114. #10622287C22semidirect
115. #10622283C22semidirect
116. #10622282C22semidirect
120. #10622279C22semidirect
121. #10622279C22semidirect
122. #10622278C22semidirect
123. #10622269C22semidirect
231. #66946D4semidirect
351. C2×C4×D11C2×D4semidirect
360. C11×C4⋊C4C2×D4semidirect
395. (C2×D11)⋊C4C2×D4semidirect
418. C4×Dic11C2×D4semidirect
431. #2445D11semidirect
572. C2×#123C2×D11semidirect
589. C2×C4×D4C2×D11semidirect
604. #394C2×D11semidirect
605. #394C2×D11semidirect
626. #390C2×D11semidirect
630. #389C2×D11semidirect
643. #386C2×D11semidirect
652. C4×C4⋊C4C2×D11semidirect
712. C4×C11#538semidirect
980. C4⋊C4D4×D11semidirect
1028. C11#35007semidirect
1208. C4#10623188semidirect

Maximal subgroups

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

subgroupindex
C2×#106231882
#130769802
#130769702
#130769582
#130769492
#130747522
#130747512
#130736882
#130736722
#130732022
#130729802
#130727432
#130723162
#130722502
#130721982
#130721452
#130720592
#130719702
#130712722
C4×#669912
D11×#3902
C4×#669462
C11×#24452
#3500711