Finite Group Databasebeta

← #15618900

Subgroups — #15618900

Order 2816.

1872 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#529C211yesmaximal, characteristic
2#13077784C212yesmaximal, complemented
3#13077781C212yesmaximal, complemented
4#13077778C211yesmaximal, characteristic, complemented
5#13077776C211yesmaximal, characteristic, complemented
6#13077772C211yesmaximal, characteristic, complemented
7#13077768C211yesmaximal, characteristic, complemented
8#13077766C211yesmaximal, characteristic, complemented
9#13077764C211yesmaximal, characteristic, complemented
10#13077760C211yesmaximal, characteristic, complemented
11#13077756C212yesmaximal, complemented
12#13077749C212yesmaximal, complemented
13#13077568C211yesmaximal, characteristic, complemented
14Q8×#4313C211yesmaximal, characteristic, complemented
15#13077352C211yesmaximal, characteristic, complemented
16#13077349C212yesmaximal, complemented
17D4×#4313C212yesmaximal, complemented
18D4×#4313C211yesmaximal, characteristic, complemented
19#13077250C212yesmaximal, complemented
20#13077244C211yesmaximal, characteristic, complemented
21#13077177C212yesmaximal, complemented
22C2×#10622450C211yesmaximal, characteristic, complemented
23C11×#2994C211yesmaximal, characteristic, complemented
24C11×#529C2211yescharacteristic
25C2×M16×D11C2212yes—
26C22×#4313C2212yes—
27C22×#4313C2212yes—
28#10623237C412yes—
29D11×#126C412yes—
30#10623222C411yescharacteristic
31D11×#125C411yescharacteristic
32#10623211C411yescharacteristic
33D11×#124C411yescharacteristic
34D11×#123C412yes—
35#10623180C412yes—
36D11×C22⋊Q8C411yescharacteristic
37#10623155C411yescharacteristic
38D11×#121C411yescharacteristic
39#10623131C411yescharacteristic
40#10623111C2211yescharacteristic
41C4×Q8×D11C2211yescharacteristic
42#10623088C2211yescharacteristic
43C4×D4×D11C2212yes—
44C4×D4×D11C2211yescharacteristic
45#10623069C2212yes—
46#10623059C2212yes—
47D11×#117C2212yes—
48#10623010C2211yescharacteristic
49C2×C42×D11C2211yescharacteristic
50C11×#446C2211yescharacteristic, complemented
51C8×Q8×C11C2211yescharacteristic, complemented
52C11×#436C2211yescharacteristic, complemented
53C11×#435C2212yescomplemented
54C8×D4×C11C2211yescharacteristic, complemented
55C8×D4×C11C2212yescomplemented
56C11×#433C2212yescomplemented
57C11×#431C2211yescharacteristic, complemented
58C11×#424C2212yescomplemented
59C2×C11×C4⋊C8C2211yescharacteristic, complemented
60#10622741C2212yescomplemented
61#10622740C2212yescomplemented
62#10622732C2212yescomplemented
63#10622724C2212yescomplemented
64#10622724C2212yescomplemented
65#10622724C2212yescomplemented
66C8×C22⋊D11C2212yescomplemented
67#10622715C2212yescomplemented
68C2×Dic11⋊C8C2212yescomplemented
69#10622637C2211yescharacteristic, complemented
70Q8×C11⋊C8C2211yescharacteristic, complemented
71#10622625C2211yescharacteristic, complemented
72#10622624C2212yescomplemented
73D4×C11⋊C8C2211yescharacteristic, complemented
74D4×C11⋊C8C2212yescomplemented
75#10622613C2212yescomplemented
76#10622612C2212yescomplemented
77#10622538C2211yescharacteristic, complemented
78C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
79#10622453C2212yescomplemented
80#10622453C2212yescomplemented
81#10622452C2212yescomplemented
82#10622452C2212yescomplemented
83#10622452C2212yescomplemented
84#10622452C2212yescomplemented
85#10622451C2211yescharacteristic, complemented
86#10622451C2212yescomplemented
87#10622450C2211yescharacteristic
88#10622450C2212yes—
89#10622450C2211yescharacteristic
90#10622450C2212yes—
91#10622450C2212yes—
92#10622450C2211yescharacteristic
93#10622450C2211yescharacteristic
94#10622450C2211yescharacteristic, complemented
95#10622450C2211yescharacteristic, complemented
96#10622450C2212yescomplemented
97#10622449C2212yescomplemented
98#10622448C2211yescharacteristic, complemented
99#10622448C2211yescharacteristic, complemented
100#10622447C2211yescharacteristic, complemented
101#10622444C2211yescharacteristic, complemented
102#10622444C2212yescomplemented
103#10622443C2211yescharacteristic, complemented
104#10622441C2212yescomplemented
105#10622343C2212yescomplemented
106#10622343C2212yescomplemented
107#10622343C2212yescomplemented
108#10622342C2212yescomplemented
109#10622341C2212yescomplemented
110#10622339C2212yes—
111#10622339C2212yes—
112#10622339C2211yescharacteristic
113#10622339C2211yescharacteristic
114(C22⋊D11)⋊C8C2212yescomplemented
115#10622333C2212yescomplemented
116#10622333C2212yescomplemented
117#10622332C2211yescharacteristic, complemented
118#10622332C2211yescharacteristic, complemented
119#10622322C2212yescomplemented
120#10622320C2212yes—
121#10622319C2212yescomplemented
122#10622314C2212yescomplemented
123#10622303C2212yescomplemented
124#10622301C2212yescomplemented
125#10622301C2211yescharacteristic, complemented
126C4×#4313C2212yes—
127C4×#4313C2211yescharacteristic
128C4×#4313C2211yescharacteristic
129C8×D44C2211yescharacteristic, complemented
130#10622298C2211yescharacteristic, complemented
131#10622298C2211yescharacteristic, complemented
132#10622292C2211yescharacteristic, complemented
133#10622292C2212yescomplemented
134C8×Dic22C2211yescharacteristic, complemented
135C2×Q8×D11C2×C411yescharacteristic
136C2×D4×D11C2×C412yes—
137C2×D4×D11C2×C411yescharacteristic
138C22×C4×D11C2×C411yescharacteristic
139C22×C4×D11C2×C411yescharacteristic
140C22×C4×D11C2311yescharacteristic
141C22×C4×D11C2312yes—
142C2×C11×M16C2312yes—
143C22×C8×C11C2312yes—
144C22×C8×C11C2312yes—
145C11×#126C2×C412yes—
146C11×#125C2×C411yescharacteristic
147C11×#124C2×C411yescharacteristic
148C11×#123C2×C412yes—
149C11×C22⋊Q8C2×C411yescharacteristic
150C11×#121C2×C411yescharacteristic
151C4×Q8×C11C2311yescharacteristic
152C4×D4×C11C2312yes—
153C4×D4×C11C2311yescharacteristic
154C11×#117C2312yes—
155C2×C42×C11C2311yescharacteristic
156#67000C2×C411yescharacteristic
157#66999C2×C411yescharacteristic
158Q8×Dic11C2×C411yescharacteristic
159#66992C2×C412yes—
160#66991C2×C411yescharacteristic
161#66989C2×C411yescharacteristic
162#66988C2×C412yes—
163D4×Dic11C2×C412yes—
164D4×Dic11C2×C411yescharacteristic
165#66983C2×C411yescharacteristic
166#66982C2×C412yes—
167C4×C22⋊D11C2312yes—
168C4×C22⋊D11C2312yes—
169C4×C22⋊D11C2312yes—
170#66979C2312yes—
171#66977C2×C411yescharacteristic
172C2×C4×Dic11C2×C411yescharacteristic
173C2×C4×Dic11C2×C411yescharacteristic
174C2×C4×Dic11C2311yescharacteristic
175C2×#4318C2312yes—
176C22×C11⋊C8C2312yes—
177C22×C11⋊C8C2312yes—
178M16×D11—44no—
179C2×#4313—44no—
180C2×#4313—44no—
181C2×#4313C2311yescharacteristic
182C2×#4313C2312yes—
183C2×#4313C2312yes—
184C2×#4313C2311yescharacteristic
185C2×#4313C2311yescharacteristic
186C2×#4313C2311yescharacteristic
187C2×#4313C2312yes—
188C2×#4313C2312yes—
189C2×#4313C2312yes—
190C2×#4313C2312yes—
191C2×C8×D11C2312yes—
192C2×C8×D11C2312yes—
193#66951C2×C412yes—
194#66951C2×C412yes—
195#66951C2×C412yes—
196#66950C2×C411yescharacteristic
197#66949C2×C412yes—
198#66948C2×C411yescharacteristic
199#66947C2×C412yes—
200#66947C2×C412yes—
201#66946C2×C412yes—
202#66946C2×C411yescharacteristic
203#66945C2×C412yes—
204#66945C2×C412yes—
205C4⋊C4×D11C2×C412yes—
206C4⋊C4×D11C2×C412yes—
207C4⋊C4×D11C2×C412yes—
208C4⋊C4×D11C2×C412yes—
209C4⋊C4×D11C2×C411yescharacteristic
210C4⋊C4×D11C2×C411yescharacteristic
211#66943C2×C411yescharacteristic
212#66943C2×C411yescharacteristic
213#66942C2×C412yes—
214#66942C2×C412yes—
215#66940C2×C412yes—
216#66940C2×C411yescharacteristic
217#66939C2×C412yes—
218#66938C2×C412yes—
219#66938C2×C412yes—
220#66937C2×C412yes—
221#66936C2×C412yes—
222#66936C2×C412yes—
223(C22⋊D11)⋊C4C2×C412yes—
224(C22⋊D11)⋊C4C2×C412yes—
225(C22⋊D11)⋊C4C2×C412yes—
226C22⋊C4×D11C2×C412yes—
227C22⋊C4×D11C2×C412yes—
228C22⋊C4×D11C2×C412yes—
229C22⋊C4×D11C2×C412yes—
230C22⋊C4×D11C2×C412yes—
231#66932C2×C412yes—
232#66932C2×C412yes—
233#66932C2×C412yes—
234#66931C2×C412yes—
235#66930C2×C412yes—
236#66930C2×C412yes—
237#66929C2×C412yes—
238#66928C2×C411yescharacteristic
239C4×D44C2311yescharacteristic
240C4×D44C2312yes—
241#66925C2312yes—
242#66925C2312yes—
243C42×D11C2×C411yescharacteristic
244C42×D11C2×C411yescharacteristic
245C42×D11C2×C411yescharacteristic
246C42×D11C2×C411yescharacteristic
247C42×D11C2311yescharacteristic
248C42×D11C2311yescharacteristic
249C42×D11C2311yescharacteristic
250C42×D11C2311yescharacteristic
251C42×D11C2312yes—
252#66923C2×C411yescharacteristic
253C4×Dic22C2311yescharacteristic
254C4×Dic22C2312yes—
255C11×C4⋊C8C2312yes—
256C11×C4⋊C8C2311yescharacteristic
257C11×C4⋊C8C2311yescharacteristic
258C11×C4⋊C8C2311yescharacteristic
259C11×C4⋊C8C2312yes—
260C11×C4⋊C8C2312yes—
261C11×C4⋊C8C2311yescharacteristic
262C11×C22⋊C8C2311yescharacteristic
263C11×C22⋊C8C2311yescharacteristic
264C11×C22⋊C8C2312yes—
265C11×C22⋊C8C2312yes—
266C11×#97C2312yes—
267C4×C8×C11C2311yescharacteristic
268C4×C8×C11C2311yescharacteristic
269C4×C8×C11C2312yes—
270C22⋊(C11⋊C8)C2311yescharacteristic
271C22⋊(C11⋊C8)C2311yescharacteristic
272C22⋊(C11⋊C8)C2312yes—
273C22⋊(C11⋊C8)C2312yes—
274(C2×D11)⋊C8C2312yes—
275(C2×D11)⋊C8C2311yescharacteristic
276(C2×D11)⋊C8C2312yes—
277(C2×D11)⋊C8C2311yescharacteristic
278(C2×D11)⋊C8C2311yescharacteristic
279(C2×D11)⋊C8C2311yescharacteristic
280(C2×D11)⋊C8C2312yes—
281(C2×D11)⋊C8C2312yes—
282#66879C2311yescharacteristic
283#66879C2312yes—
284#66879C2311yescharacteristic
285#66879C2311yescharacteristic
286#66879C2312yes—
287#66879C2311yescharacteristic
288Dic11⋊C8C2312yes—
289Dic11⋊C8C2312yes—
290Dic11⋊C8C2312yes—
291Dic11⋊C8C2312yes—
292Dic11⋊C8C2311yescharacteristic
293Dic11⋊C8C2312yes—
294Dic11⋊C8C2312yes—
295Dic11⋊C8C2312yes—
296Dic11⋊C8C2311yescharacteristic
297Dic11⋊C8C2311yescharacteristic
298Dic11⋊C8C2311yescharacteristic
299Dic11⋊C8C2312yes—
300C8×Dic11C2312yes—
301C8×Dic11C2312yes—
302C4⋊(C11⋊C8)C2311yescharacteristic
303C4⋊(C11⋊C8)C2311yescharacteristic
304C4⋊(C11⋊C8)C2312yes—
305C4⋊(C11⋊C8)C2311yescharacteristic
306C4⋊(C11⋊C8)C2311yescharacteristic
307C4⋊(C11⋊C8)C2312yes—
308C4⋊(C11⋊C8)C2312yes—
309#66867C2312yes—
310C4×C11⋊C8C2311yescharacteristic
311C4×C11⋊C8C2311yescharacteristic
312C4×C11⋊C8C2312yes—
313#60264—111nomaximal, Sylow
314C23×D11C22×C411yescharacteristic
315C23×D11C22×C412yes—
316C2×Q8×C11C22×C411yescharacteristic
317C2×D4×C11C22×C412yes—
318C2×D4×C11C22×C411yescharacteristic
319C22×C4×C11C22×C411yescharacteristic
320C22×C4×C11C22×C411yescharacteristic
321C22×C4×C11C2411yescharacteristic
322C22×C4×C11C2412yes—
323C2×C22⋊D11C22×C412yes—
324C2×C22⋊D11C22×C412yes—
325C2×C22⋊D11C22×C412yes—
326C22×Dic11C22×C412yes—
327C22×Dic11C22×C411yescharacteristic
328C22×Dic11C22×C411yescharacteristic
329C22×Dic11C22×C411yescharacteristic
330Q8×D11—42no—
331D4×D11—44no—
332D4×D11—42no—
333C2×D44C22×C411yescharacteristic
334C2×D44C22×C412yes—
335C2×C4×D11—22no—
336C2×C4×D11—24no—
337C2×C4×D11—22no—
338C2×C4×D11—24no—
339C2×C4×D11—42no—
340C2×C4×D11—42no—
341C2×C4×D11C22×C411yescharacteristic
342C2×C4×D11C22×C411yescharacteristic
343C2×C4×D11C22×C411yescharacteristic
344C2×C4×D11C22×C411yescharacteristic
345C2×C4×D11C22×C412yes—
346C2×C4×D11C22×C412yes—
347C2×C4×D11C22×C411yescharacteristic
348C2×C4×D11C22×C411yescharacteristic
349C2×C4×D11C22×C411yescharacteristic
350C2×C4×D11C22×C411yescharacteristic
351C2×C4×D11C22×C411yescharacteristic
352C2×C4×D11C22×C411yescharacteristic
353C2×C4×D11C22×C412yes—
354C2×C4×D11C22×C412yes—
355C2×C4×D11C2411yescharacteristic
356C2×C4×D11C2412yes—
357C2×C4×D11C2411yescharacteristic
358C2×Dic22C22×C411yescharacteristic
359C2×Dic22C22×C412yes—
360C11×M16—42no—
361C2×C8×C11—42no—
362C2×C8×C11—42no—
363C2×C8×C11C2411yescharacteristic
364C2×C8×C11C2412yes—
365C2×C8×C11C2411yescharacteristic
366C2×C8×C11C2412yes—
367C2×C8×C11C2411yescharacteristic
368C2×C8×C11C2411yescharacteristic
369C11×C4⋊C4C22×C411yescharacteristic
370C11×C4⋊C4C22×C412yes—
371C11×C4⋊C4C22×C412yes—
372C11×C4⋊C4C22×C412yes—
373C11×C4⋊C4C22×C411yescharacteristic
374C11×C4⋊C4C22×C412yes—
375C11×C22⋊C4C22×C412yes—
376C11×C22⋊C4C22×C412yes—
377C11×C22⋊C4C22×C412yes—
378C11×C22⋊C4C22×C412yes—
379C11×C22⋊C4C22×C412yes—
380C42×C11C22×C411yescharacteristic
381C42×C11C22×C411yescharacteristic
382C42×C11C2411yescharacteristic
383C42×C11C2412yes—
384C42×C11C2411yescharacteristic
385C22⋊Dic11C22×C412yes—
386C22⋊Dic11C22×C412yes—
387C22⋊Dic11C22×C412yes—
388C22⋊Dic11C22×C412yes—
389C22⋊Dic11C22×C412yes—
390(C2×D11)⋊C4C22×C412yes—
391(C2×D11)⋊C4C22×C412yes—
392(C2×D11)⋊C4C22×C412yes—
393(C2×D11)⋊C4C22×C412yes—
394(C2×D11)⋊C4C22×C412yes—
395(C2×D11)⋊C4C22×C412yes—
396(C2×D11)⋊C4C22×C412yes—
397(C2×D11)⋊C4C22×C412yes—
398(C2×D11)⋊C4C22×C412yes—
399(C2×D11)⋊C4C22×C412yes—
400C4⋊Dic11C22×C411yescharacteristic
401C4⋊Dic11C22×C412yes—
402C4⋊Dic11C22×C411yescharacteristic
403C4⋊Dic11C22×C412yes—
404C4⋊Dic11C22×C412yes—
405C4⋊Dic11C22×C412yes—
406Dic11⋊C4C22×C412yes—
407Dic11⋊C4C22×C412yes—
408Dic11⋊C4C22×C412yes—
409Dic11⋊C4C22×C412yes—
410Dic11⋊C4C22×C412yes—
411Dic11⋊C4C22×C412yes—
412Dic11⋊C4C22×C412yes—
413Dic11⋊C4C22×C412yes—
414Dic11⋊C4C22×C412yes—
415Dic11⋊C4C22×C412yes—
416C4×Dic11C22×C411yescharacteristic
417C4×Dic11C22×C411yescharacteristic
418C4×Dic11C22×C411yescharacteristic
419C4×Dic11C22×C411yescharacteristic
420C4×Dic11C22×C411yescharacteristic
421C4×Dic11C22×C411yescharacteristic
422C4×Dic11C22×C411yescharacteristic
423C4×Dic11C22×C411yescharacteristic
424C4×Dic11C22×C411yescharacteristic
425C4×Dic11C22×C411yescharacteristic
426C4×Dic11C22×C412yes—
427C4×Dic11C22×C412yes—
428C4×Dic11C2412yes—
429C4×Dic11C2411yescharacteristic
430C4×Dic11C2411yescharacteristic
431#4318—42no—
432C2×C11⋊C8—42no—
433C2×C11⋊C8—42no—
434C2×C11⋊C8C2411yescharacteristic
435C2×C11⋊C8C2411yescharacteristic
436C2×C11⋊C8C2411yescharacteristic
437C2×C11⋊C8C2411yescharacteristic
438C2×C11⋊C8C2412yes—
439C2×C11⋊C8C2412yes—
440#4313—22no—
441#4313—24no—
442#4313—24no—
443#4313—22no—
444#4313—22no—
445#4313—22no—
446#4313—42no—
447#4313—42no—
448#4313—42no—
449#4313—42no—
450C8×D11—42no—
451C8×D11—42no—
452C2×#529—111no—
453#2995—112no—
454#2995—112no—
455#2994—111no—
456#2994—111no—
457#2994—111no—
458#2994D1111yescharacteristic, complemented
459#2993—111no—
460#2993—111no—
461#2993—111no—
462#2993—111no—
463#2992—112no—
464#2992—112no—
465Q8×M16—111no—
466Q8×M16—111no—
467D4×M16—111no—
468D4×M16—112no—
469D4×M16—112no—
470D4×M16—111no—
471#2921—112no—
472#2920—111no—
473#2905—112no—
474C2×#423—111no—
475C23×C11C23×C412yes—
476C23×C11C23×C411yescharacteristic
477C22×D11—22no—
478C22×D11—22no—
479C22×D11—24no—
480C22×D11—41no—
481C22×D11—42no—
482C22×D11—42no—
483C22×D11C23×C412yes—
484C22×D11C23×C411yescharacteristic
485C22×D11C23×C411yescharacteristic
486Q8×C11—22no—
487D4×C11—24no—
488D4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—21no—
492C2×C4×C11—22no—
493C2×C4×C11—21no—
494C2×C4×C11—22no—
495C2×C4×C11C23×C411yescharacteristic
496C2×C4×C11C23×C411yescharacteristic
497C2×C4×C11C23×C411yescharacteristic
498C2×C4×C11C23×C411yescharacteristic
499C2×C4×C11C23×C412yes—
500C2×C4×C11C23×C412yes—
501C2×C4×C11C23×C412yes—
502C2×C4×C11C23×C411yescharacteristic
503C2×C4×C11C2511yescharacteristic
504C22⋊D11—24no—
505C22⋊D11—42no—
506C22⋊D11—42no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—24no—
510C2×Dic11—41no—
511C2×Dic11C23×C411yescharacteristic
512C2×Dic11C23×C411yescharacteristic
513C2×Dic11C23×C411yescharacteristic
514C2×Dic11C23×C411yescharacteristic
515C2×Dic11C23×C411yescharacteristic
516C2×Dic11C23×C412yes—
517C2×Dic11C23×C412yes—
518C2×Dic11C23×C412yes—
519C2×Dic11C23×C411yescharacteristic
520D44—22no—
521D44—42no—
522C4×D11—22no—
523C4×D11—24no—
524C4×D11—22no—
525C4×D11—22no—
526C4×D11—22no—
527C4×D11—21no—
528C4×D11—21no—
529C4×D11—22no—
530C4×D11—22no—
531C4×D11—24no—
532C4×D11—41no—
533C4×D11—41no—
534C4×D11—41no—
535C4×D11—41no—
536C4×D11—41no—
537C4×D11—41no—
538C4×D11—42no—
539C4×D11—42no—
540C4×D11H(5,𝔽2)12yes—
541C4×D112−1+412yes—
542Dic22—22no—
543Dic22—42no—
544C8×C11—21no—
545C8×C11—22no—
546C8×C11—22no—
547C8×C11—21no—
548C8×C11—21no—
549C8×C11—21no—
550C11⋊C8—21no—
551C11⋊C8—22no—
552C11⋊C8—22no—
553C11⋊C8—21no—
554C11⋊C8—21no—
555C11⋊C8—21no—
556C22×M16—112no—
557C22×M16—112no—
558C22×M16—112no—
559#529—112no—
560#529—111no—
561#529—111no—
562#529—112no—
563#529—111no—
564#529—111no—
565#529—111no—
566#529—112no—
567#529—111no—
568#529—112no—
569#529—111no—
570#529C2×D1111yescharacteristic
571C2×#126—112no—
572C2×#125—111no—
573C2×#124—111no—
574C2×#123—112no—
575C2×C22⋊Q8—111no—
576C2×#121—111no—
577C2×C4×Q8—111no—
578C2×C4×D4—112no—
579C2×C4×D4—111no—
580C2×#117—112no—
581C22×C42—111no—
582#446—111no—
583#446—112no—
584#446—112no—
585#446—111no—
586#446—112no—
587#446—112no—
588#446—111no—
589#446C2×D1111yescharacteristic, complemented
590C8×Q8—111no—
591C8×Q8—111no—
592C8×Q8—111no—
593C8×Q8C2×D1111yescharacteristic, complemented
594#436—112no—
595#436—111no—
596#436—111no—
597#436—112no—
598#436—112no—
599#436—111no—
600#436—112no—
601#436C2×D1111yescharacteristic, complemented
602#435—112no—
603#435—112no—
604#435—112no—
605#435—112no—
606#435—112no—
607#435—112no—
608#435—112no—
609#435—112no—
610#435—112no—
611#435—112no—
612#435—112no—
613#435C2×D1112yescomplemented
614C8×D4—112no—
615C8×D4—112no—
616C8×D4—111no—
617C8×D4—111no—
618C8×D4—112no—
619C8×D4—111no—
620C8×D4C2×D1112yescomplemented
621C8×D4C2×D1111yescharacteristic, complemented
622#433—112no—
623#433—112no—
624#433—112no—
625#433—112no—
626#433—112no—
627#433—112no—
628#433—112no—
629#433C2×D1112yescomplemented
630#432—111no—
631#432—111no—
632#432—111no—
633#432—111no—
634#431—111no—
635#431—111no—
636#431—111no—
637#431C2×D1111yescharacteristic, complemented
638#424—112no—
639#424—112no—
640#424—112no—
641#424—112no—
642#424—112no—
643#424—112no—
644#424—112no—
645#424C2×D1112yescomplemented
646#423—112no—
647#423—111no—
648#423—111no—
649#423—111no—
650#423—111no—
651#423—112no—
652#423—111no—
653#423—112no—
654#423—112no—
655#423—111no—
656C2×C4⋊C8—112no—
657C2×C4⋊C8—111no—
658C2×C4⋊C8C2×D1111yescharacteristic, complemented
659#407—111no—
660#407—111no—
661#407—112no—
662#407—112no—
663C4×M16—112no—
664C4×M16—111no—
665C4×M16—111no—
666C4×M16—112no—
667C22×C11—21no—
668C22×C11—21no—
669C22×C11—22no—
670C22×C11—22no—
671C22×C11—22no—
672C22×C11#56812yes—
673C22×C11C24×C411yescharacteristic
674C2×D11—21no—
675C2×D11—21no—
676C2×D11—21no—
677C2×D11—22no—
678C2×D11—21no—
679C2×D11—21no—
680C2×D11—22no—
681C2×D11—22no—
682C2×D11—44no—
683C2×D11—84no—
684C2×D11#52012yes—
685C4×C11—21no—
686C4×C11—22no—
687C4×C11—21no—
688C4×C11—21no—
689C4×C11—21no—
690C4×C11—22no—
691C4×C11—22no—
692C4×C11#56812yes—
693C4×C11C2×H(5,𝔽2)11yescharacteristic
694C4×C11C2×2−1+411yescharacteristic
695Dic11—22no—
696Dic11—21no—
697Dic11—22no—
698Dic11—21no—
699Dic11—21no—
700Dic11—21no—
701Dic11—21no—
702Dic11—22no—
703Dic11#52012yes—
704C22×Q8—111no—
705C22×D4—112no—
706C22×D4—111no—
707C23×C4—112no—
708C23×C4—111no—
709C23×C4—111no—
710C23×C4—111no—
711C2×M16—112no—
712C2×M16—112no—
713C2×M16—111no—
714C2×M16—112no—
715C2×M16—111no—
716C2×M16—111no—
717C2×M16—111no—
718C2×M16—112no—
719C2×M16—112no—
720C2×M16—112no—
721C2×M16—112no—
722C2×M16—444no—
723C2×M16—444no—
724C2×M16—444no—
725C2×M16C22×D1112yes—
726C22×C8—112no—
727C22×C8—112no—
728C22×C8—112no—
729C22×C8—112no—
730C22×C8C22×D1112yes—
731C22×C8C22×D1112yes—
732#126—112no—
733#126—112no—
734#126—112no—
735#126—112no—
736#126—112no—
737#126—112no—
738#126—112no—
739#126C4×D1112yes—
740#125—112no—
741#125—112no—
742#125—111no—
743#125—111no—
744#125—111no—
745#125C4×D1111yescharacteristic
746#124—111no—
747#124—111no—
748#124—112no—
749#124—112no—
750#124—111no—
751#124C4×D1111yescharacteristic
752#123—112no—
753#123—112no—
754#123—112no—
755#123—112no—
756#123—112no—
757#123—112no—
758#123—112no—
759#123C4×D1112yes—
760C22⋊Q8—111no—
761C22⋊Q8—111no—
762C22⋊Q8—112no—
763C22⋊Q8—111no—
764C22⋊Q8—112no—
765C22⋊Q8C4×D1111yescharacteristic
766#121—111no—
767#121—112no—
768#121—111no—
769#121—111no—
770#121—112no—
771#121C4×D1111yescharacteristic
772C4×Q8—111no—
773C4×Q8—112no—
774C4×Q8—111no—
775C4×Q8—111no—
776C4×Q8—112no—
777C4×Q8C22×D1111yescharacteristic
778C4×D4—111no—
779C4×D4—112no—
780C4×D4—112no—
781C4×D4—112no—
782C4×D4—112no—
783C4×D4—111no—
784C4×D4—112no—
785C4×D4—112no—
786C4×D4—112no—
787C4×D4—112no—
788C4×D4—111no—
789C4×D4—112no—
790C4×D4C22×D1112yes—
791C4×D4C22×D1111yescharacteristic
792#117—112no—
793#117—112no—
794#117—112no—
795#117—112no—
796#117—112no—
797#117—112no—
798#117—112no—
799#117C22×D1112yes—
800C2×C4⋊C4—112no—
801C2×C4⋊C4—112no—
802C2×C4⋊C4—111no—
803C2×C4⋊C4—112no—
804C2×C4⋊C4—111no—
805C2×C4⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C42—111no—
812C2×C42—111no—
813C2×C42—111no—
814C2×C42—111no—
815C2×C42—111no—
816C2×C42—111no—
817C2×C42—111no—
818C2×C42—111no—
819C2×C42—112no—
820C2×C42—111no—
821C2×C42—111no—
822C2×C42—111no—
823C2×C42C22×D1111yescharacteristic
824C4⋊C8—112no—
825C4⋊C8—112no—
826C4⋊C8—112no—
827C4⋊C8—112no—
828C4⋊C8—111no—
829C4⋊C8—111no—
830C4⋊C8—112no—
831C4⋊C8—112no—
832C4⋊C8—112no—
833C4⋊C8—112no—
834C4⋊C8—111no—
835C4⋊C8—111no—
836C4⋊C8—112no—
837C4⋊C8—111no—
838C4⋊C8—111no—
839C4⋊C8—111no—
840C4⋊C8—112no—
841C4⋊C8—112no—
842C4⋊C8—111no—
843C4⋊C8C22×D1112yes—
844C4⋊C8C22×D1111yescharacteristic
845C4⋊C8C22×D1111yescharacteristic
846C4⋊C8C22×D1111yescharacteristic
847C4⋊C8C22×D1112yes—
848C4⋊C8C22×D1112yes—
849C4⋊C8C22×D1111yescharacteristic
850C22⋊C8—111no—
851C22⋊C8—111no—
852C22⋊C8—112no—
853C22⋊C8—112no—
854C22⋊C8—111no—
855C22⋊C8—111no—
856C22⋊C8—111no—
857C22⋊C8—111no—
858C22⋊C8—112no—
859C22⋊C8—112no—
860C22⋊C8—112no—
861C22⋊C8—112no—
862C22⋊C8C22×D1111yescharacteristic
863C22⋊C8C22×D1111yescharacteristic
864C22⋊C8C22×D1112yes—
865C22⋊C8C22×D1112yes—
866#97—111no—
867#97—111no—
868#97—111no—
869#97—111no—
870#97—112no—
871#97—112no—
872#97—112no—
873#97C22×D1112yes—
874C4×C8—112no—
875C4×C8—112no—
876C4×C8—111no—
877C4×C8—111no—
878C4×C8—112no—
879C4×C8C22×D1111yescharacteristic
880C4×C8C22×D1111yescharacteristic
881C4×C8C22×D1112yes—
882C2×C11—22no—
883C2×C11—42no—
884C2×C11C2×#52011yescharacteristic
885C2×C11C2×#56811yescharacteristic
886C2×C11C2×#56811yescharacteristic
887D11—22no—
888D11—41no—
889D11—42no—
890C24—111no—
891C24—112no—
892C2×Q8—111no—
893C2×Q8—112no—
894C2×Q8—442no—
895C2×Q8C2×C4×D1111yescharacteristic
896C2×D4—112no—
897C2×D4—112no—
898C2×D4—112no—
899C2×D4—111no—
900C2×D4—112no—
901C2×D4—442no—
902C2×D4—444no—
903C2×D4C2×C4×D1112yes—
904C2×D4C2×C4×D1111yescharacteristic
905C22×C4—111no—
906C22×C4—111no—
907C22×C4—111no—
908C22×C4—112no—
909C22×C4—111no—
910C22×C4—111no—
911C22×C4—111no—
912C22×C4—111no—
913C22×C4—111no—
914C22×C4—112no—
915C22×C4—112no—
916C22×C4—111no—
917C22×C4—112no—
918C22×C4—111no—
919C22×C4—111no—
920C22×C4—111no—
921C22×C4—111no—
922C22×C4—111no—
923C22×C4—111no—
924C22×C4—112no—
925C22×C4—112no—
926C22×C4—222no—
927C22×C4—224no—
928C22×C4—222no—
929C22×C4—224no—
930C22×C4—442no—
931C22×C4—442no—
932C22×C4C2×C4×D1111yescharacteristic
933C22×C4C2×C4×D1111yescharacteristic
934C22×C4C23×D1111yescharacteristic
935C22×C4C23×D1112yes—
936M16—42no—
937M16—224no—
938M16—222no—
939M16—224no—
940M16—222no—
941M16—222no—
942M16—222no—
943M16—442no—
944M16—442no—
945M16—442no—
946M16—442no—
947M16—442no—
948C2×C8—42no—
949C2×C8—42no—
950C2×C8—111no—
951C2×C8—111no—
952C2×C8—112no—
953C2×C8—111no—
954C2×C8—111no—
955C2×C8—112no—
956C2×C8—442no—
957C2×C8—442no—
958C2×C8—442no—
959C2×C8—442no—
960C2×C8C23×D1111yescharacteristic
961C2×C8C23×D1112yes—
962C2×C8C23×D1111yescharacteristic
963C2×C8C23×D1111yescharacteristic
964C2×C8C23×D1111yescharacteristic
965C2×C8C23×D1112yes—
966C4⋊C4—112no—
967C4⋊C4—112no—
968C4⋊C4—112no—
969C4⋊C4—112no—
970C4⋊C4—112no—
971C4⋊C4—112no—
972C4⋊C4—112no—
973C4⋊C4—111no—
974C4⋊C4—112no—
975C4⋊C4—112no—
976C4⋊C4—112no—
977C4⋊C4—112no—
978C4⋊C4—111no—
979C4⋊C4—112no—
980C4⋊C4—112no—
981C4⋊C4—112no—
982C4⋊C4C2×C4×D1112yes—
983C4⋊C4C2×C4×D1112yes—
984C4⋊C4C2×C4×D1111yescharacteristic
985C4⋊C4C2×C4×D1112yes—
986C4⋊C4C2×C4×D1111yescharacteristic
987C4⋊C4C2×C4×D1112yes—
988C22⋊C4—112no—
989C22⋊C4—112no—
990C22⋊C4—112no—
991C22⋊C4—112no—
992C22⋊C4—112no—
993C22⋊C4—112no—
994C22⋊C4—112no—
995C22⋊C4—112no—
996C22⋊C4—112no—
997C22⋊C4—112no—
998C22⋊C4—112no—
999C22⋊C4—112no—
1000C22⋊C4—112no—
1001C22⋊C4—112no—
1002C22⋊C4—112no—
1003C22⋊C4C2×C4×D1112yes—
1004C22⋊C4C2×C4×D1112yes—
1005C22⋊C4C2×C4×D1112yes—
1006C22⋊C4C2×C4×D1112yes—
1007C22⋊C4C2×C4×D1112yes—
1008C42—111no—
1009C42—111no—
1010C42—111no—
1011C42—111no—
1012C42—111no—
1013C42—111no—
1014C42—111no—
1015C42—111no—
1016C42—111no—
1017C42—111no—
1018C42—112no—
1019C42—112no—
1020C42—112no—
1021C42—111no—
1022C42—111no—
1023C42C2×C4×D1111yescharacteristic
1024C42C2×C4×D1111yescharacteristic
1025C42C23×D1111yescharacteristic
1026C42C23×D1112yes—
1027C42C23×D1111yescharacteristic
1028C11#6026411yescharacteristic, complemented, Sylow
1029C23—111no—
1030C23—112no—
1031C23—111no—
1032C23—222no—
1033C23—224no—
1034C23—222no—
1035C23—441no—
1036C23—442no—
1037C23—442no—
1038C23C22×C4×D1112yes—
1039C23C22×C4×D1111yescharacteristic
1040Q8—22no—
1041Q8—222no—
1042Q8—442no—
1043D4—24no—
1044D4—22no—
1045D4—224no—
1046D4—222no—
1047D4—442no—
1048D4—442no—
1049D4—442no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—21no—
1055C2×C4—22no—
1056C2×C4—111no—
1057C2×C4—112no—
1058C2×C4—112no—
1059C2×C4—111no—
1060C2×C4—111no—
1061C2×C4—111no—
1062C2×C4—111no—
1063C2×C4—111no—
1064C2×C4—112no—
1065C2×C4—112no—
1066C2×C4—112no—
1067C2×C4—222no—
1068C2×C4—224no—
1069C2×C4—222no—
1070C2×C4—224no—
1071C2×C4—222no—
1072C2×C4—224no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—221no—
1078C2×C4—221no—
1079C2×C4—222no—
1080C2×C4—441no—
1081C2×C4—441no—
1082C2×C4—441no—
1083C2×C4—441no—
1084C2×C4—441no—
1085C2×C4—441no—
1086C2×C4—442no—
1087C2×C4—442no—
1088C2×C4—441no—
1089C2×C4C22×C4×D1111yescharacteristic
1090C2×C4C22×C4×D1111yescharacteristic
1091C2×C4C22×C4×D1111yescharacteristic
1092C2×C4C22×C4×D1111yescharacteristic
1093C2×C4C22×C4×D1112yes—
1094C2×C4C22×C4×D1112yes—
1095C2×C4C22×C4×D1112yes—
1096C2×C4C22×C4×D1111yescharacteristic
1097C2×C4C24×D1111yescharacteristic
1098C8—21no—
1099C8—22no—
1100C8—22no—
1101C8—21no—
1102C8—21no—
1103C8—21no—
1104C8—221no—
1105C8—222no—
1106C8—221no—
1107C8—222no—
1108C8—221no—
1109C8—221no—
1110C22—21no—
1111C22—21no—
1112C22—22no—
1113C22—22no—
1114C22—22no—
1115C22—112no—
1116C22—221no—
1117C22—221no—
1118C22—221no—
1119C22—221no—
1120C22—222no—
1121C22—222no—
1122C22—221no—
1123C22—222no—
1124C22—444no—
1125C22—884no—
1126C22#1062328112yes—
1127C22C23×C4×D1111yescharacteristic
1128C4—21no—
1129C4—21no—
1130C4—21no—
1131C4—22no—
1132C4—22no—
1133C4—21no—
1134C4—22no—
1135C4—112no—
1136C4—221no—
1137C4—221no—
1138C4—221no—
1139C4—221no—
1140C4—222no—
1141C4—222no—
1142C4—221no—
1143C4—222no—
1144C4#1062328112yes—
1145C4D11×H(5,𝔽2)11yescharacteristic
1146C4D11×2−1+411yescharacteristic
1147C2—22no—
1148C2—42no—
1149C2—222no—
1150C2—441no—
1151C2—442no—
1152C2D11×#52011yescharacteristic
1153C2C2×#1062328111yescharacteristic
1154C2C2×#1062328111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2994C2
prime radicalD11×#121C4
cosocleC2×C4×C11C25
hypercenter#2994D11
hypocenterC11#60264
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2994

Complements

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

NH ≅ G/Ntype
2. #13077784C2semidirect
3. #13077781C2semidirect
4. #13077778C2semidirect
5. #13077776C2semidirect
6. #13077772C2semidirect
7. #13077768C2semidirect
8. #13077766C2semidirect
9. #13077764C2semidirect
10. #13077760C2semidirect
11. #13077756C2semidirect
12. #13077749C2semidirect
13. #13077568C2semidirect
14. Q8×#4313C2semidirect
15. #13077352C2semidirect
16. #13077349C2semidirect
17. D4×#4313C2semidirect
18. D4×#4313C2semidirect
19. #13077250C2semidirect
20. #13077244C2semidirect
21. #13077177C2semidirect
22. C2×#10622450C2semidirect
23. C11×#2994C2semidirect
50. C11×#446C22semidirect
51. C8×Q8×C11C22semidirect
52. C11×#436C22semidirect
53. C11×#435C22semidirect
54. C8×D4×C11C22semidirect
55. C8×D4×C11C22semidirect
56. C11×#433C22semidirect
57. C11×#431C22semidirect
58. C11×#424C22semidirect
59. C2×C11×C4⋊C8C22semidirect
60. #10622741C22semidirect
61. #10622740C22semidirect
62. #10622732C22semidirect
63. #10622724C22semidirect
64. #10622724C22semidirect
65. #10622724C22semidirect
66. C8×C22⋊D11C22semidirect
67. #10622715C22semidirect
68. C2×Dic11⋊C8C22semidirect
69. #10622637C22semidirect
70. Q8×C11⋊C8C22semidirect
71. #10622625C22semidirect
72. #10622624C22semidirect
73. D4×C11⋊C8C22semidirect
74. D4×C11⋊C8C22semidirect
75. #10622613C22semidirect
76. #10622612C22semidirect
77. #10622538C22semidirect
78. C2×C4⋊(C11⋊C8)C22semidirect
79. #10622453C22semidirect
80. #10622453C22semidirect
81. #10622452C22semidirect
82. #10622452C22semidirect
83. #10622452C22semidirect
84. #10622452C22semidirect
85. #10622451C22semidirect
86. #10622451C22semidirect
94. #10622450C22semidirect
95. #10622450C22semidirect
96. #10622450C22semidirect
97. #10622449C22semidirect
98. #10622448C22semidirect
99. #10622448C22semidirect
100. #10622447C22semidirect
101. #10622444C22semidirect
102. #10622444C22semidirect
103. #10622443C22semidirect
104. #10622441C22semidirect
105. #10622343C22semidirect
106. #10622343C22semidirect
107. #10622343C22semidirect
108. #10622342C22semidirect
109. #10622341C22semidirect
114. (C22⋊D11)⋊C8C22semidirect
115. #10622333C22semidirect
116. #10622333C22semidirect
117. #10622332C22semidirect
118. #10622332C22semidirect
119. #10622322C22semidirect
121. #10622319C22semidirect
122. #10622314C22semidirect
123. #10622303C22semidirect
124. #10622301C22semidirect
125. #10622301C22semidirect
129. C8×D44C22semidirect
130. #10622298C22semidirect
131. #10622298C22semidirect
132. #10622292C22semidirect
133. #10622292C22semidirect
134. C8×Dic22C22semidirect
458. #2994D11semidirect
589. #446C2×D11semidirect
593. C8×Q8C2×D11semidirect
601. #436C2×D11semidirect
613. #435C2×D11semidirect
620. C8×D4C2×D11semidirect
621. C8×D4C2×D11semidirect
629. #433C2×D11semidirect
637. #431C2×D11semidirect
645. #424C2×D11semidirect
658. C2×C4⋊C8C2×D11semidirect
1028. C11#60264semidirect

Maximal subgroups

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

subgroupindex
D11×#5292
#130777842
#130777812
#130777782
#130777762
#130777722
#130777682
#130777662
#130777642
#130777602
#130777562
#130777492
#130775682
Q8×#43132
#130773522
#130773492
D4×#43132
#130772502
#130772442
#130771772
C2×#106224502
C11×#29942
#6026411