Finite Group Databasebeta

← #14926732

Subgroups — #14926732

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×#10623148C212yesmaximal, complemented
2#13076984C211yesmaximal, characteristic, complemented
3#13076970C211yesmaximal, characteristic, complemented
4#13076959C211yesmaximal, characteristic, complemented
5#13076948C211yesmaximal, characteristic, complemented
6#13074754C212yesmaximal, complemented
7#13074743C212yesmaximal, complemented
8#13073684C212yesmaximal, complemented
9#13073669C212yesmaximal, complemented
10#13073205C211yesmaximal, characteristic, complemented
11#13072975C211yesmaximal, characteristic, complemented
12#13072747C212yesmaximal, complemented
13#13072379C211yesmaximal, characteristic, complemented
14#13072312C211yesmaximal, characteristic, complemented
15#13072254C211yesmaximal, characteristic, complemented
16#13072206C211yesmaximal, characteristic, complemented
17#13072158C212yesmaximal, complemented
18#13071972C211yesmaximal, characteristic, complemented
19#13071279C212yesmaximal, complemented
20#121×Dic11C211yesmaximal, characteristic, complemented
21C2×#10622601C211yesmaximal, characteristic, complemented
22C4×D4×Dic11C211yesmaximal, characteristic, complemented
23C11×#2416C211yesmaximal, characteristic, complemented
24C23×D44C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C11×#121C2212yes—
27C2×C11×#121C2211yescharacteristic, complemented
28C2×C4×D4×C11C2211yescharacteristic
29C22×C11×C4⋊C4C2211yescharacteristic
30C2×#66993C2211yescharacteristic
31C2×#66993C2211yescharacteristic
32C2×#66992C2212yescomplemented
33C2×#66992C2212yescomplemented
34C2×#66992C2212yescomplemented
35C2×#66990C2212yes—
36C2×#66990C2212yes—
37C2×#66990C2212yes—
38C2×D4×Dic11C2212yes—
39C2×D4×Dic11C2211yescharacteristic
40C2×D4×Dic11C2211yescharacteristic
41C2×D4×Dic11C2211yescharacteristic, complemented
42C2×#66983C2211yescharacteristic
43C2×#66983C2211yescharacteristic
44C22×(C2×D11)⋊C4C2212yes—
45C22×(C2×D11)⋊C4C2212yes—
46C2×#66977C2212yes—
47C22×C4×Dic11C2211yescharacteristic
48C22×C4×Dic11C2211yescharacteristic, complemented
49#10623148—216no—
50C2×#66951C2212yescomplemented
51C2×#66951C2212yescomplemented
52C2×#66941C2211yescharacteristic, complemented
53C2×#66939C2212yescomplemented
54C2×#66939C2212yescomplemented
55C2×#66938C2212yescomplemented
56C2×#66938C2212yescomplemented
57C2×#66938C2212yescomplemented
58C11×#396C2212yescomplemented
59C11×#394C2212yescomplemented
60C11×#390C2211yescharacteristic, complemented
61C11×#389C2211yescharacteristic, complemented
62C11×#386C2212yes—
63C11×#380C2211yescharacteristic, complemented
64#10622836C2212yescomplemented
65#10622834C2211yescharacteristic, complemented
66#10622833C2212yes—
67#10622825C2211yescharacteristic
68#10622823C2212yes—
69C4×C22⋊Dic11C2211yescharacteristic
70C4×C22⋊Dic11C2211yescharacteristic, complemented
71#10622607C2212yescomplemented
72#10622604C2212yes—
73#10622603C2212yescomplemented
74#10622601C2212yes—
75#10622601C2211yescharacteristic
76#10622601C2211yescharacteristic
77#10622601C2212yes—
78#10622601C2211yescharacteristic
79#10622601C2211yescharacteristic
80#10622601C2211yescharacteristic
81#10622601C2211yescharacteristic
82#10622598C2211yescharacteristic, complemented
83#10622598C2211yescharacteristic, complemented
84#10622597C2212yescomplemented
85#10622592C2212yescomplemented
86#10622589C2211yescharacteristic, complemented
87C4⋊C4×Dic11C2211yescharacteristic, complemented
88C4⋊C4×Dic11C2211yescharacteristic, complemented
89C4⋊C4×Dic11C2211yescharacteristic, complemented
90#10622586C2211yescharacteristic, complemented
91#10622574C2212yescomplemented
92#10622574C2212yescomplemented
93#10622573C2212yes—
94#10622573C2212yes—
95#10622573C2212yes—
96#10622572C2212yescomplemented
97#10622572C2212yescomplemented
98#10622571C2212yescomplemented
99#10622571C2212yescomplemented
100#10622571C2212yescomplemented
101#10622570C2212yescomplemented
102#10622570C2212yescomplemented
103#10622570C2212yescomplemented
104#10622570C2212yescomplemented
105#10622568C2212yes—
106#10622564C2212yescomplemented
107C22⋊C4×Dic11C2211yescharacteristic
108C22⋊C4×Dic11C2211yescharacteristic
109C22⋊C4×Dic11C2212yescomplemented
110C22⋊C4×Dic11C2211yescharacteristic, complemented
111C22⋊C4×Dic11C2211yescharacteristic, complemented
112#10622552C2211yescharacteristic
113#10622552C2211yescharacteristic
114C4×C4⋊Dic11C2211yescharacteristic, complemented
115C42×Dic11C2211yescharacteristic, complemented
116#10622288C2212yescomplemented
117#10622286C2212yescomplemented
118#10622283C2212yescomplemented
119#10622283C2212yescomplemented
120#10622283C2212yescomplemented
121#10622282C2212yescomplemented
122#10622282C2212yescomplemented
123#10622282C2212yescomplemented
124C24×D11C2312yes—
125C22×D4×C11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C23×C4×C11C2311yescharacteristic
130C23×C4×C11C2311yescharacteristic
131C23×C4×C11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2312yes—
137C22×C22⋊D11C2312yes—
138C23×Dic11C2311yescharacteristic
139C23×Dic11C2311yescharacteristic
140C23×Dic11C2312yes—
141C23×Dic11C2311yescharacteristic
142C23×Dic11C2311yescharacteristic
143C22×D44—24no—
144C22×D44—42no—
145C22×D44—42no—
146C22×D44C2311yescharacteristic
147C22×D44C2311yescharacteristic
148C22×D44C2312yes—
149C22×Dic22C2312yes—
150C11×#121—28no—
151C11×#121—24no—
152C11×#121—42no—
153C4×D4×C11—24no—
154C2×C11×C4⋊C4—42no—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2311yescharacteristic
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C4⋊C4C2311yescharacteristic
160C2×C11×C4⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2311yescharacteristic
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C11×C22⋊C4C2312yes—
168C2×C42×C11C2311yescharacteristic
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2311yescharacteristic
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2311yescharacteristic
177#66993—42no—
178#66993—42no—
179#66992—28no—
180#66992—28no—
181#66992—44no—
182#66990—28no—
183#66990—28no—
184#66990—28no—
185D4×Dic11—28no—
186D4×Dic11—24no—
187D4×Dic11—42no—
188D4×Dic11D418yescomplemented
189#66983—42no—
190#66983—42no—
191C2×(C2×D11)⋊C4—28no—
192C2×(C2×D11)⋊C4—44no—
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)⋊C4C2312yes—
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×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210C2×(C2×D11)⋊C4C2312yes—
211C2×C4⋊Dic11C2312yes—
212C2×C4⋊Dic11C2312yes—
213C2×C4⋊Dic11C2311yescharacteristic
214C2×C4⋊Dic11C2311yescharacteristic
215C2×C4⋊Dic11C2311yescharacteristic
216C2×C4⋊Dic11C2311yescharacteristic
217#66977—28no—
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×C4×Dic11—42no—
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
236C2×C4×Dic11C2311yescharacteristic
237#66951—28no—
238#66951—28no—
239#66941—42no—
240#66939—28no—
241#66939—28no—
242#66938—28no—
243#66938—28no—
244#66938—44no—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11⋊#95C2311yescharacteristic
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2312yes—
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2312yes—
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2311yescharacteristic
258#35007—111nomaximal, Sylow
259C24×C11C2412yes—
260C24×C11C2411yescharacteristic
261C24×C11C2411yescharacteristic
262C23×D11—24no—
263C23×D11—24no—
264C23×D11—24no—
265C23×D11—42no—
266C23×D11—42no—
267C23×D11—42no—
268C23×D11—42no—
269C23×D11C2412yes—
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—24no—
277C2×D4×C11—22no—
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—42no—
281C2×D4×C11—42no—
282C2×D4×C11C2×D414yes—
283C22×C4×C11—22no—
284C22×C4×C11—22no—
285C22×C4×C11—24no—
286C22×C4×C11—22no—
287C22×C4×C11—22no—
288C22×C4×C11—22no—
289C22×C4×C11—42no—
290C22×C4×C11—42no—
291C22×C4×C11#4114yes—
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2412yes—
295C22×C4×C11C2412yes—
296C22×C4×C11C2412yes—
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—24no—
303C2×C22⋊D11—24no—
304C2×C22⋊D11—24no—
305C2×C22⋊D11—24no—
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—
313C2×C22⋊D11—42no—
314C2×C22⋊D11—42no—
315C2×C22⋊D11—42no—
316C2×C22⋊D11—42no—
317C2×C22⋊D11—42no—
318C22×Dic11—22no—
319C22×Dic11—22no—
320C22×Dic11—22no—
321C22×Dic11—24no—
322C22×Dic11—22no—
323C22×Dic11—41no—
324C22×Dic11—41no—
325C22×Dic11—41no—
326C22×Dic11—41no—
327C22×Dic11—41no—
328C22×Dic11—41no—
329C22×Dic11—42no—
330C22×Dic11—42no—
331C22×Dic11C2×D414yes—
332C22×Dic11C2×D414yescomplemented
333C22×Dic11C2411yescharacteristic
334C22×Dic11C2412yes—
335C22×Dic11C2412yes—
336C22×Dic11C2411yescharacteristic
337C22×Dic11C2411yescharacteristic
338C22×Dic11C2411yescharacteristic
339C22×Dic11C2411yescharacteristic
340C22×Dic11C2411yescharacteristic
341C22×Dic11C2411yescharacteristic
342C22×Dic11C2411yescharacteristic
343C2×D44—24no—
344C2×D44—22no—
345C2×D44—22no—
346C2×D44—22no—
347C2×D44—22no—
348C2×D44—22no—
349C2×D44—22no—
350C2×D44—42no—
351C2×D44—42no—
352C2×D44—416no—
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⋊C4—22no—
361C11×C4⋊C4—42no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—22no—
366C11×C22⋊C4—24no—
367C11×C22⋊C4—42no—
368C11×C22⋊C4—42no—
369C42×C11—22no—
370C22⋊Dic11—24no—
371C22⋊Dic11—22no—
372C22⋊Dic11—24no—
373C22⋊Dic11—24no—
374C22⋊Dic11—42no—
375C22⋊Dic11C2×D414yes—
376C22⋊Dic11C2×D414yescomplemented
377C22⋊Dic11#4114yes—
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—24no—
380(C2×D11)⋊C4—24no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—24no—
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—
396C4⋊Dic11—24no—
397C4⋊Dic11—24no—
398C4⋊Dic11—22no—
399C4⋊Dic11—22no—
400C4⋊Dic11—22no—
401C4⋊Dic11C2×D414yescomplemented
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#2416D1111yescharacteristic, complemented
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—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×C11C22×D412yes—
460C23×C11C22×D412yes—
461C23×C11C2×#4112yes—
462C23×C11C2×#4112yes—
463C23×C11C2511yescharacteristic
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—22no—
476C22×D11—22no—
477C22×D11—22no—
478C22×D11—48no—
479C22×D11—48no—
480C22×D11—48no—
481C22×D11—84no—
482C22×D11—84no—
483C22×D11—84no—
484C22×D11—84no—
485D4×C11—28no—
486D4×C11—48no—
487D4×C11—44no—
488D4×C11—84no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—28no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—21no—
499C2×C4×C11—21no—
500C2×C4×C11—22no—
501C2×C4×C11—21no—
502C2×C4×C11—21no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—21no—
507C2×C4×C11—22no—
508C2×C4×C11—21no—
509C2×C4×C11—44no—
510C2×C4×C11—84no—
511C2×C4×C11C22×D412yes—
512C2×C4×C11C2×#4112yes—
513C2×C4×C11C2×#4112yes—
514C2×C4×C11H(5,𝔽2)12yes—
515C2×C4×C11H(5,𝔽2)12yes—
516C22⋊D11—84no—
517C22⋊D11—84no—
518C22⋊D11—84no—
519C22⋊D11—84no—
520C22⋊D11—84no—
521C22⋊D11—84no—
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—21no—
535C2×Dic11—21no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—21no—
539C2×Dic11—21no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—21no—
544C2×Dic11—22no—
545C2×Dic11—44no—
546C2×Dic11—44no—
547C2×Dic11—44no—
548C2×Dic11—44no—
549C2×Dic11—84no—
550C2×Dic11C22×D412yes—
551C2×Dic11C22×D412yes—
552C2×Dic11C22×D412yes—
553C2×Dic11C22×D412yes—
554C2×Dic11C2×#4112yes—
555C2×Dic11C2×#4112yes—
556C2×Dic11H(5,𝔽2)12yes—
557D44—48no—
558D44—44no—
559D44—44no—
560Dic22—84no—
561C23×D4—111no—
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—111no—
579C2×#121C2×D1112yes—
580C2×#121C2×D1111yescharacteristic
581C2×#121C2×D1111yescharacteristic, complemented
582C2×#120—112no—
583C2×#120—112no—
584C2×#120—112no—
585C2×C4×D4—111no—
586C2×C4×D4—112no—
587C2×C4×D4—111no—
588C2×C4×D4—111no—
589C2×C4×D4C2×D1111yescharacteristic
590C22×C4⋊C4C2×D1111yescharacteristic
591C22×C22⋊C4—112no—
592C22×C22⋊C4—112no—
593C22×C42—111no—
594C22×C42—111no—
595#398—112no—
596#397—112no—
597#396—112no—
598#396C2×D1112yescomplemented
599#395—112no—
600#394—112no—
601#394—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394C2×D1112yescomplemented
606#393—112no—
607#392—112no—
608#392—112no—
609#392—112no—
610#392—112no—
611#390—111no—
612#390—111no—
613#390—111no—
614#390—111no—
615#390—111no—
616#390—112no—
617#390—111no—
618#390—111no—
619#390—112no—
620#390—112no—
621#390—112no—
622#390—112no—
623#390—112no—
624#390—111no—
625#390—111no—
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×D1112yes—
644#385—112no—
645#384—111no—
646#380—111no—
647#380C2×D1111yescharacteristic, complemented
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—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#53214yes—
682C22×C11C23×D411yescharacteristic
683C22×C11C22×#4111yescharacteristic
684C22×C11C22×#4111yescharacteristic
685C22×C11C2×H(5,𝔽2)11yescharacteristic
686C22×C11C2×H(5,𝔽2)11yescharacteristic
687C22×C11C2×H(5,𝔽2)11yescharacteristic
688C22×C11#58511yescharacteristic
689C2×D11—42no—
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×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—42no—
703C2×D11—816no—
704C4×C11—22no—
705C4×C11—22no—
706C4×C11—42no—
707C4×C11—41no—
708C4×C11—41no—
709C4×C11—42no—
710C4×C11—42no—
711C4×C11#53814yescomplemented
712Dic11—22no—
713Dic11—22no—
714Dic11—22no—
715Dic11—22no—
716Dic11—22no—
717Dic11—22no—
718Dic11—22no—
719Dic11—42no—
720Dic11—42no—
721Dic11—41no—
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×D1112yes—
737C22×D4C22×D1111yescharacteristic
738C22×D4C22×D1111yescharacteristic
739C22×D4C22×D1112yes—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—112no—
745C23×C4C22×D1111yescharacteristic
746C23×C4C22×D1111yescharacteristic
747C23×C4C22×D1112yes—
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—28no—
760#121—24no—
761#121—42no—
762#121—228no—
763#121—228no—
764#121—444no—
765#121—442no—
766#121—442no—
767#120—228no—
768#120—228no—
769#120—228no—
770C4×D4—24no—
771C4×D4—118no—
772C4×D4—224no—
773C4×D4—228no—
774C4×D4—442no—
775C2×C4⋊C4—42no—
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—111no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4C22×D1111yescharacteristic
787C2×C4⋊C4C22×D1111yescharacteristic
788C2×C4⋊C4C22×D1111yescharacteristic
789C2×C4⋊C4C22×D1112yes—
790C2×C4⋊C4C22×D1111yescharacteristic
791C2×C4⋊C4C22×D1112yes—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—111no—
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—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—112no—
817C2×C22⋊C4—112no—
818C2×C22⋊C4—228no—
819C2×C22⋊C4—444no—
820C2×C22⋊C4C22×D1111yescharacteristic
821C2×C22⋊C4C22×D1111yescharacteristic
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#95C22×D1112yes—
855#95C22×D1112yes—
856C2×C11—24no—
857C2×C11—42no—
858C2×C11—82no—
859C2×C11C2×#53211yescharacteristic
860C2×C11C2×#53811yescharacteristic
861C2×C11#346011yescharacteristic
862C2×C11#349611yescharacteristic
863C2×C11#349811yescharacteristic
864C2×C11#351411yescharacteristic
865C2×C11#351911yescharacteristic
866D11—82no—
867D11—82no—
868C24—112no—
869C24—112no—
870C24—224no—
871C24—224no—
872C24—224no—
873C24—442no—
874C24—442no—
875C24—442no—
876C24—442no—
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—24no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—224no—
895C2×D4—224no—
896C2×D4—224no—
897C2×D4—224no—
898C2×D4—224no—
899C2×D4—224no—
900C2×D4—224no—
901C2×D4—222no—
902C2×D4—222no—
903C2×D4—222no—
904C2×D4—222no—
905C2×D4—222no—
906C2×D4—222no—
907C2×D4—442no—
908C2×D4—442no—
909C2×D4—4416no—
910C2×D4—442no—
911C2×D4—442no—
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—24no—
926C22×C4—22no—
927C22×C4—22no—
928C22×C4—22no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—111no—
932C22×C4—111no—
933C22×C4—111no—
934C22×C4—111no—
935C22×C4—111no—
936C22×C4—111no—
937C22×C4—111no—
938C22×C4—114no—
939C22×C4—114no—
940C22×C4—111no—
941C22×C4—112no—
942C22×C4—112no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—222no—
946C22×C4—224no—
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×C4#434114yes—
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1111yescharacteristic
959C22×C4C23×D1112yes—
960C22×C4C23×D1112yes—
961C22×C4C23×D1112yes—
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C4⋊C4—24no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—22no—
970C4⋊C4—42no—
971C4⋊C4—114no—
972C4⋊C4—224no—
973C4⋊C4—222no—
974C4⋊C4—224no—
975C4⋊C4—224no—
976C4⋊C4—224no—
977C4⋊C4—222no—
978C4⋊C4—222no—
979C4⋊C4—442no—
980C4⋊C4—442no—
981C22⋊C4—24no—
982C22⋊C4—22no—
983C22⋊C4—24no—
984C22⋊C4—22no—
985C22⋊C4—24no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—114no—
989C22⋊C4—114no—
990C22⋊C4—114no—
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—224no—
1001C22⋊C4—224no—
1002C22⋊C4—222no—
1003C22⋊C4—224no—
1004C22⋊C4—224no—
1005C22⋊C4—224no—
1006C22⋊C4—224no—
1007C22⋊C4—442no—
1008C22⋊C4—442no—
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—222no—
1047C23—222no—
1048C23—222no—
1049C23—222no—
1050C23—222no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—222no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—222no—
1060C23—448no—
1061C23—448no—
1062C23—448no—
1063C23—884no—
1064C23—884no—
1065C23—884no—
1066C23—884no—
1067C23C2×D4×D1112yes—
1068C23C2×D4×D1112yes—
1069C23C2×#434112yes—
1070C23#41×D1112yes—
1071C23C24×D1111yescharacteristic
1072Q8—884no—
1073D4—28no—
1074D4—48no—
1075D4—44no—
1076D4—84no—
1077D4—448no—
1078D4—444no—
1079D4—444no—
1080D4—884no—
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—22no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—22no—
1097C2×C4—21no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—22no—
1104C2×C4—22no—
1105C2×C4—21no—
1106C2×C4—44no—
1107C2×C4—84no—
1108C2×C4—112no—
1109C2×C4—112no—
1110C2×C4—112no—
1111C2×C4—112no—
1112C2×C4—112no—
1113C2×C4—112no—
1114C2×C4—112no—
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—221no—
1126C2×C4—221no—
1127C2×C4—221no—
1128C2×C4—221no—
1129C2×C4—222no—
1130C2×C4—222no—
1131C2×C4—222no—
1132C2×C4—221no—
1133C2×C4—221no—
1134C2×C4—222no—
1135C2×C4—222no—
1136C2×C4—221no—
1137C2×C4—222no—
1138C2×C4—444no—
1139C2×C4—444no—
1140C2×C4—444no—
1141C2×C4—444no—
1142C2×C4—884no—
1143C2×C4C2×D4×D1112yes—
1144C2×C4C2×#434112yes—
1145C2×C4C2×#434112yes—
1146C2×C4#6703712yes—
1147C2×C4#6704212yes—
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—442no—
1169C22—442no—
1170C22—442no—
1171C22—442no—
1172C22—442no—
1173C22—442no—
1174C22—442no—
1175C22—442no—
1176C22—442no—
1177C22—442no—
1178C22—442no—
1179C22—442no—
1180C22—442no—
1181C22—442no—
1182C22—8816no—
1183C22#1062312714yes—
1184C22C22×D4×D1111yescharacteristic
1185C22C22×#434111yescharacteristic
1186C22C2×#6703711yescharacteristic
1187C22C2×#41×D1111yescharacteristic
1188C22C2×#6704211yescharacteristic
1189C22D11×H(5,𝔽2)11yescharacteristic
1190C22#1062345711yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—42no—
1194C4—42no—
1195C4—42no—
1196C4—41no—
1197C4—41no—
1198C4—222no—
1199C4—222no—
1200C4—222no—
1201C4—222no—
1202C4—222no—
1203C4—222no—
1204C4—222no—
1205C4—442no—
1206C4—441no—
1207C4—442no—
1208C4#1062314814yescomplemented
1209C2—24no—
1210C2—42no—
1211C2—82no—
1212C2—882no—
1213C2—882no—
1214C2C2×#1062312711yescharacteristic
1215C2C2×#1062314811yescharacteristic
1216C2#1308203311yescharacteristic
1217C2#1308237411yescharacteristic
1218C2#1308238811yescharacteristic
1219C2#1308257011yescharacteristic
1220C2#1308264111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2416C2
hypercenter#2416D11
hypocenterC11#35007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2416

Complements

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

NH ≅ G/Ntype
1. C2×#10623148C2semidirect
2. #13076984C2semidirect
3. #13076970C2semidirect
4. #13076959C2semidirect
5. #13076948C2semidirect
6. #13074754C2semidirect
7. #13074743C2semidirect
8. #13073684C2semidirect
9. #13073669C2semidirect
10. #13073205C2semidirect
11. #13072975C2semidirect
12. #13072747C2semidirect
13. #13072379C2semidirect
14. #13072312C2semidirect
15. #13072254C2semidirect
16. #13072206C2semidirect
17. #13072158C2semidirect
18. #13071972C2semidirect
19. #13071279C2semidirect
20. #121×Dic11C2semidirect
21. C2×#10622601C2semidirect
22. C4×D4×Dic11C2semidirect
23. C11×#2416C2semidirect
27. C2×C11×#121C22semidirect
32. C2×#66992C22semidirect
33. C2×#66992C22semidirect
34. C2×#66992C22semidirect
41. C2×D4×Dic11C22semidirect
48. C22×C4×Dic11C22semidirect
50. C2×#66951C22semidirect
51. C2×#66951C22semidirect
52. C2×#66941C22semidirect
53. C2×#66939C22semidirect
54. C2×#66939C22semidirect
55. C2×#66938C22semidirect
56. C2×#66938C22semidirect
57. C2×#66938C22semidirect
58. C11×#396C22semidirect
59. C11×#394C22semidirect
60. C11×#390C22semidirect
61. C11×#389C22semidirect
63. C11×#380C22semidirect
64. #10622836C22semidirect
65. #10622834C22semidirect
70. C4×C22⋊Dic11C22semidirect
71. #10622607C22semidirect
73. #10622603C22semidirect
82. #10622598C22semidirect
83. #10622598C22semidirect
84. #10622597C22semidirect
85. #10622592C22semidirect
86. #10622589C22semidirect
87. C4⋊C4×Dic11C22semidirect
88. C4⋊C4×Dic11C22semidirect
89. C4⋊C4×Dic11C22semidirect
90. #10622586C22semidirect
91. #10622574C22semidirect
92. #10622574C22semidirect
96. #10622572C22semidirect
97. #10622572C22semidirect
98. #10622571C22semidirect
99. #10622571C22semidirect
100. #10622571C22semidirect
101. #10622570C22semidirect
102. #10622570C22semidirect
103. #10622570C22semidirect
104. #10622570C22semidirect
106. #10622564C22semidirect
109. C22⋊C4×Dic11C22semidirect
110. C22⋊C4×Dic11C22semidirect
111. C22⋊C4×Dic11C22semidirect
114. C4×C4⋊Dic11C22semidirect
115. C42×Dic11C22semidirect
116. #10622288C22semidirect
117. #10622286C22semidirect
118. #10622283C22semidirect
119. #10622283C22semidirect
120. #10622283C22semidirect
121. #10622282C22semidirect
122. #10622282C22semidirect
123. #10622282C22semidirect
188. D4×Dic11D4semidirect
332. C22×Dic11C2×D4semidirect
376. C22⋊Dic11C2×D4semidirect
401. C4⋊Dic11C2×D4semidirect
418. C4×Dic11C2×D4semidirect
436. #2416D11semidirect
581. C2×#121C2×D11semidirect
598. #396C2×D11semidirect
605. #394C2×D11semidirect
626. #390C2×D11semidirect
630. #389C2×D11semidirect
647. #380C2×D11semidirect
711. C4×C11#538semidirect
1028. C11#35007semidirect
1208. C4#10623148semidirect

Maximal subgroups

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

subgroupindex
C2×#106231482
#130769842
#130769702
#130769592
#130769482
#130747542
#130747432
#130736842
#130736692
#130732052
#130729752
#130727472
#130723792
#130723122
#130722542
#130722062
#130721582
#130719722
#130712792
#121×Dic112
C2×#106226012
C4×D4×Dic112
C11×#24162
#3500711