Finite Group Databasebeta

← #15619020

Subgroups — #15619020

Order 2816.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082174C211yesmaximal, characteristic
2#13077782C212yesmaximal, complemented
3#13077780C212yesmaximal, complemented
4#13077773C212yesmaximal, complemented
5#13077762C212yesmaximal, complemented
6#13077751C212yesmaximal, complemented
7#13077749C212yesmaximal, complemented
8#13077736C212yesmaximal, complemented
9#13077728C212yesmaximal, complemented
10#13077563C211yesmaximal, characteristic, complemented
11#13077553C211yesmaximal, characteristic, complemented
12#13077341C211yesmaximal, characteristic, complemented
13#13077341C211yesmaximal, characteristic, complemented
14#13077315C211yesmaximal, characteristic, complemented
15#13077306C211yesmaximal, characteristic, complemented
16C2×#10622624C211yesmaximal, characteristic, complemented
17#13077276C211yesmaximal, characteristic, complemented
18#13077276C211yesmaximal, characteristic, complemented
19#13077268C211yesmaximal, characteristic, complemented
20#13077185C211yesmaximal, characteristic, complemented
21#13077179C211yesmaximal, characteristic, complemented
22C2×#10622732C211yesmaximal, characteristic, complemented
23D4×C11×M16C211yesmaximal, characteristic, complemented
24C22×C11×M16C2211yescharacteristic
25C22×C11×M16C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27#10623337C412yes—
28#10623322C2211yescharacteristic
29#10623322C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31C2×#66979C2211yescharacteristic
32C22×#4318C2211yescharacteristic
33C23×C11⋊C8C2211yescharacteristic
34C2×#66960C2211yescharacteristic
35C2×#66960C2211yescharacteristic
36#10623096C411yescharacteristic
37#10623096C411yescharacteristic
38#10623094C411yescharacteristic
39#10623088C2212yes—
40#10623086C411yescharacteristic
41#10623074C411yescharacteristic
42#10623073C411yescharacteristic
43#10623072C411yescharacteristic
44#10623072C411yescharacteristic
45#10623069C2212yes—
46#10623069C2212yes—
47C4×#4341C2212yes—
48#10623044C412yes—
49#10623026C412yes—
50#10623026C412yes—
51C4×#4339C2211yescharacteristic
52#10623001C2211yescharacteristic
53C11×#436C2212yes—
54C11×#435C2212yes—
55C11×#435C2212yes—
56C8×D4×C11C2212yes—
57C11×#423C2211yescharacteristic
58C11×#407C2211yescharacteristic
59C11×#407C2211yescharacteristic
60C4×C11×M16C2211yescharacteristic
61C2×C22⋊(C11⋊C8)C2211yescharacteristic
62C2×C22⋊(C11⋊C8)C2211yescharacteristic
63#10622742C2211yescharacteristic
64#10622742C2211yescharacteristic
65#10622741C2212yescomplemented
66#10622741C2212yescomplemented
67#10622740C2212yescomplemented
68#10622740C2212yescomplemented
69#10622735C2211yescharacteristic
70#10622735C2211yescharacteristic
71#10622735C2211yescharacteristic
72#10622735C2211yescharacteristic
73#10622732C2211yescharacteristic
74#10622732C2211yescharacteristic
75#10622732C2211yescharacteristic
76#10622732C2211yescharacteristic
77#10622732C2211yescharacteristic
78#10622732C2211yescharacteristic
79#10622732C2211yescharacteristic
80#10622732C2211yescharacteristic
81#10622732C2212yescomplemented
82#10622732C2212yescomplemented
83#10622731C2212yescomplemented
84#10622731C2212yescomplemented
85#10622724C2212yescomplemented
86#10622724C2212yescomplemented
87C8×C22⋊D11C2212yescomplemented
88C8×C22⋊D11C2212yescomplemented
89#10622715C2212yescomplemented
90#10622715C2212yescomplemented
91C2×Dic11⋊C8C2212yescomplemented
92C2×Dic11⋊C8C2212yescomplemented
93#10622624C2211yescharacteristic
94#10622624C2211yescharacteristic
95#10622624C2211yescharacteristic
96#10622624C2211yescharacteristic
97#10622624C2211yescharacteristic
98#10622624C2211yescharacteristic
99#10622624C2211yescharacteristic
100#10622624C2211yescharacteristic
101C2×C4⋊(C11⋊C8)C2211yescharacteristic
102C2×#66867C2211yescharacteristic
103#10622452C2212yescomplemented
104#10622452C2212yescomplemented
105#10622450C2212yescomplemented
106D11×C4⋊C8C2212yescomplemented
107#10622441C2212yescomplemented
108#10622441C2212yescomplemented
109#10622441C2212yescomplemented
110#10622441C2212yescomplemented
111#10622343C2212yescomplemented
112#10622343C2212yescomplemented
113#10622342C2212yescomplemented
114#10622342C2212yescomplemented
115#10622341C2212yescomplemented
116#10622341C2212yescomplemented
117(C22⋊D11)⋊C8C2212yescomplemented
118(C22⋊D11)⋊C8C2212yescomplemented
119#10622333C2212yescomplemented
120#10622333C2212yescomplemented
121#10622333C2212yescomplemented
122#10622333C2212yescomplemented
123#10622332C2212yescomplemented
124#10622332C2212yescomplemented
125#10622331C2212yescomplemented
126#10622331C2212yescomplemented
127#10622318C2212yescomplemented
128#10622318C2212yescomplemented
129#10622314C2212yescomplemented
130#10622314C2212yescomplemented
131#10622303C2212yescomplemented
132#10622303C2212yescomplemented
133#10622292C2212yescomplemented
134C8×Dic22C2212yescomplemented
135C22×D4×C11C2×C411yescharacteristic
136C23×C4×C11C2311yescharacteristic
137C23×C4×C11C2311yescharacteristic
138C2×#4341C2×C412yes—
139C2×#4339C2311yescharacteristic
140C2×C11×M16—42no—
141C2×C11×M16—42no—
142C2×C11×M16C2311yescharacteristic
143C2×C11×M16C2311yescharacteristic
144C2×C11×M16C2311yescharacteristic
145C2×C11×M16C2311yescharacteristic
146C2×C11×M16C2312yes—
147C2×C11×M16C2312yes—
148C22×C8×C11C2312yes—
149C22×C8×C11C2312yes—
150C4×D4×C11C2×C411yescharacteristic
151C4×D4×C11C2×C411yescharacteristic
152C4×D4×C11C2×C411yescharacteristic
153C4×D4×C11C2×C411yescharacteristic
154C4×D4×C11C2311yescharacteristic
155C4×D4×C11C2311yescharacteristic
156C4×D4×C11C2311yescharacteristic
157C4×D4×C11C2311yescharacteristic
158C2×C11×C4⋊C4C2×C411yescharacteristic
159C2×C11×C22⋊C4C2×C411yescharacteristic
160C2×C11×C22⋊C4C2×C411yescharacteristic
161C2×C42×C11C2311yescharacteristic
162#67006C2×C412yes—
163#67006C2×C412yes—
164C2×C22⋊Dic11C2×C412yes—
165C2×C22⋊Dic11C2×C412yes—
166#66992C2×C412yes—
167#66992C2×C412yes—
168#66991C2×C412yes—
169#66989C2×C412yes—
170#66988C2×C412yes—
171#66988C2×C412yes—
172D4×Dic11C2×C412yes—
173#66983C2×C411yescharacteristic
174#66983C2×C411yescharacteristic
175#66983C2×C411yescharacteristic
176#66983C2×C411yescharacteristic
177#66982C2×C412yes—
178#66982C2×C412yes—
179C4×C22⋊D11C2×C412yes—
180C4×C22⋊D11C2×C412yes—
181C4×C22⋊D11C2312yes—
182C4×C22⋊D11C2312yes—
183C4×C22⋊D11C2312yes—
184C4×C22⋊D11C2312yes—
185#66979C2×C412yes—
186#66979C2×C412yes—
187#66979C2×C411yescharacteristic
188#66979C2×C411yescharacteristic
189#66979C2×C411yescharacteristic
190#66979C2×C411yescharacteristic
191#66979C2311yescharacteristic
192#66979C2311yescharacteristic
193#66979C2311yescharacteristic
194#66979C2312yes—
195#66979C2312yes—
196C2×C4⋊Dic11C2×C411yescharacteristic
197C2×C4⋊Dic11C2×C411yescharacteristic
198C2×C4⋊Dic11C2×C411yescharacteristic
199C2×C4⋊Dic11C2×C411yescharacteristic
200#66977C2×C412yes—
201#66977C2×C412yes—
202#66977C2×C411yescharacteristic
203#66977C2×C411yescharacteristic
204#66977C2×C411yescharacteristic
205#66977C2×C411yescharacteristic
206C2×C4×Dic11C2312yes—
207C2×C4×Dic11C2312yes—
208C2×#4318—42no—
209C2×#4318C2311yescharacteristic
210C2×#4318C2311yescharacteristic
211C2×#4318C2311yescharacteristic
212C2×#4318C2311yescharacteristic
213C22×C11⋊C8—42no—
214C22×C11⋊C8C2311yescharacteristic
215C22×C11⋊C8C2311yescharacteristic
216C22×C11⋊C8C2311yescharacteristic
217C22×C11⋊C8C2311yescharacteristic
218C22×C11⋊C8C2311yescharacteristic
219C22×C11⋊C8C2311yescharacteristic
220C22×C11⋊C8C2311yescharacteristic
221C22×C11⋊C8C2311yescharacteristic
222#66960—42no—
223#66960—42no—
224C2×#4313C2312yes—
225C2×#4313C2312yes—
226C2×C8×D11C2312yes—
227C2×C8×D11C2312yes—
228#66951C2×C412yes—
229#66951C2×C412yes—
230#66950C2×C412yes—
231#66945C2×C412yes—
232#66943C2×C412yes—
233#66942C2×C412yes—
234#66942C2×C412yes—
235#66940C2×C412yes—
236#66939C2×C412yes—
237#66939C2×C412yes—
238#66938C2×C412yes—
239#66938C2×C412yes—
240#66936C2×C412yes—
241#66936C2×C412yes—
242(C22⋊D11)⋊C4C2×C412yes—
243(C22⋊D11)⋊C4C2×C412yes—
244#66932C2×C412yes—
245#66932C2×C412yes—
246#66932C2×C412yes—
247#66932C2×C412yes—
248#66931C2×C412yes—
249#66931C2×C412yes—
250#66930C2×C412yes—
251#66930C2×C412yes—
252C4×D44C2×C411yescharacteristic
253C4×D44C2×C411yescharacteristic
254#66925C2312yes—
255C42×D11C2312yes—
256#66923C2×C411yescharacteristic
257#66923C2×C411yescharacteristic
258#66922C2×C411yescharacteristic
259#66922C2×C411yescharacteristic
260C4×Dic22C2×C411yescharacteristic
261C4×Dic22C2×C411yescharacteristic
262C4×Dic22C2312yes—
263C4×Dic22C2312yes—
264C11×C4⋊C8C2312yes—
265C11×C4⋊C8C2312yes—
266C11×C22⋊C8C2312yes—
267C11×C22⋊C8C2312yes—
268C11×C22⋊C8C2312yes—
269C11×C22⋊C8C2312yes—
270C11×#97C2312yes—
271C4×C8×C11C2312yes—
272C22⋊(C11⋊C8)C2311yescharacteristic
273C22⋊(C11⋊C8)C2311yescharacteristic
274C22⋊(C11⋊C8)C2311yescharacteristic
275C22⋊(C11⋊C8)C2311yescharacteristic
276C22⋊(C11⋊C8)C2311yescharacteristic
277C22⋊(C11⋊C8)C2311yescharacteristic
278C22⋊(C11⋊C8)C2311yescharacteristic
279C22⋊(C11⋊C8)C2311yescharacteristic
280(C2×D11)⋊C8C2312yes—
281(C2×D11)⋊C8C2312yes—
282(C2×D11)⋊C8C2312yes—
283(C2×D11)⋊C8C2312yes—
284#66879C2312yes—
285#66879C2312yes—
286#66879C2312yes—
287#66879C2312yes—
288Dic11⋊C8C2312yes—
289Dic11⋊C8C2312yes—
290Dic11⋊C8C2312yes—
291Dic11⋊C8C2312yes—
292Dic11⋊C8C2312yes—
293Dic11⋊C8C2312yes—
294Dic11⋊C8C2312yes—
295Dic11⋊C8C2312yes—
296Dic11⋊C8C2312yes—
297Dic11⋊C8C2312yes—
298Dic11⋊C8C2312yes—
299Dic11⋊C8C2312yes—
300Dic11⋊C8C2312yes—
301Dic11⋊C8C2312yes—
302Dic11⋊C8C2312yes—
303Dic11⋊C8C2312yes—
304C8×Dic11C2312yes—
305C8×Dic11C2312yes—
306C8×Dic11C2312yes—
307C8×Dic11C2312yes—
308C4⋊(C11⋊C8)C2311yescharacteristic
309C4⋊(C11⋊C8)C2311yescharacteristic
310C4⋊(C11⋊C8)C2311yescharacteristic
311C4⋊(C11⋊C8)C2311yescharacteristic
312#66867C2311yescharacteristic
313#66867C2311yescharacteristic
314#66867C2311yescharacteristic
315#66867C2311yescharacteristic
316#60272—111nomaximal, Sylow
317C24×C11C22×C411yescharacteristic
318C24×C11C22×C411yescharacteristic
319C2×D4×C11—42no—
320C2×D4×C11C22×C411yescharacteristic
321C2×D4×C11C22×C411yescharacteristic
322C2×D4×C11C22×C411yescharacteristic
323C2×D4×C11C22×C411yescharacteristic
324C22×C4×C11—22no—
325C22×C4×C11—22no—
326C22×C4×C11—22no—
327C22×C4×C11—22no—
328C22×C4×C11C22×C411yescharacteristic
329C22×C4×C11C22×C411yescharacteristic
330C22×C4×C11C22×C411yescharacteristic
331C22×C4×C11C22×C411yescharacteristic
332C22×C4×C11C22×C411yescharacteristic
333C22×C4×C11C22×C411yescharacteristic
334C22×C4×C11C22×C411yescharacteristic
335C22×C4×C11C22×C411yescharacteristic
336C22×C4×C11C2411yescharacteristic
337C22×C4×C11C2411yescharacteristic
338C22×C4×C11C2411yescharacteristic
339C22×C4×C11C2411yescharacteristic
340C22×C4×C11C2411yescharacteristic
341C2×C22⋊D11C22×C412yes—
342C2×C22⋊D11C22×C412yes—
343C2×C22⋊D11C22×C412yes—
344C2×C22⋊D11C22×C412yes—
345C2×C22⋊D11C22×C412yes—
346C22×Dic11C22×C412yes—
347C22×Dic11C22×C412yes—
348C22×Dic11C22×C412yes—
349C22×Dic11C22×C412yes—
350#4341—44no—
351#4339—22no—
352#4339—22no—
353C2×D44C22×C411yescharacteristic
354C2×C4×D11C22×C412yes—
355C2×C4×D11C22×C412yes—
356C2×C4×D11C2412yes—
357C2×Dic22C22×C411yescharacteristic
358C2×Dic22C22×C412yes—
359C2×Dic22C22×C412yes—
360C11×M16—22no—
361C11×M16—22no—
362C11×M16—22no—
363C11×M16—22no—
364C11×M16—42no—
365C11×M16—42no—
366C2×C8×C11—42no—
367C2×C8×C11—42no—
368C2×C8×C11C2412yes—
369C2×C8×C11C2412yes—
370C2×C8×C11C2412yes—
371C2×C8×C11C2412yes—
372C11×C4⋊C4C22×C411yescharacteristic
373C11×C4⋊C4C22×C411yescharacteristic
374C11×C4⋊C4C22×C411yescharacteristic
375C11×C4⋊C4C22×C411yescharacteristic
376C11×C22⋊C4C22×C411yescharacteristic
377C11×C22⋊C4C22×C411yescharacteristic
378C11×C22⋊C4C22×C411yescharacteristic
379C11×C22⋊C4C22×C411yescharacteristic
380C11×C22⋊C4C22×C411yescharacteristic
381C11×C22⋊C4C22×C411yescharacteristic
382C11×C22⋊C4C22×C411yescharacteristic
383C11×C22⋊C4C22×C411yescharacteristic
384C42×C11C22×C411yescharacteristic
385C42×C11C22×C411yescharacteristic
386C42×C11C2411yescharacteristic
387C42×C11C2411yescharacteristic
388C22⋊Dic11C22×C412yes—
389C22⋊Dic11C22×C412yes—
390C22⋊Dic11C22×C412yes—
391C22⋊Dic11C22×C412yes—
392C22⋊Dic11C22×C412yes—
393C22⋊Dic11C22×C412yes—
394C22⋊Dic11C22×C412yes—
395C22⋊Dic11C22×C412yes—
396C22⋊Dic11C22×C412yes—
397C22⋊Dic11C22×C412yes—
398C22⋊Dic11C22×C412yes—
399(C2×D11)⋊C4C22×C412yes—
400(C2×D11)⋊C4C22×C412yes—
401(C2×D11)⋊C4C22×C412yes—
402(C2×D11)⋊C4C22×C412yes—
403(C2×D11)⋊C4C22×C412yes—
404(C2×D11)⋊C4C22×C412yes—
405C4⋊Dic11C22×C411yescharacteristic
406C4⋊Dic11C22×C411yescharacteristic
407C4⋊Dic11C22×C412yes—
408C4⋊Dic11C22×C412yes—
409C4⋊Dic11C22×C411yescharacteristic
410C4⋊Dic11C22×C411yescharacteristic
411C4⋊Dic11C22×C411yescharacteristic
412C4⋊Dic11C22×C411yescharacteristic
413C4⋊Dic11C22×C412yes—
414C4⋊Dic11C22×C412yes—
415C4⋊Dic11C22×C412yes—
416C4⋊Dic11C22×C412yes—
417Dic11⋊C4C22×C412yes—
418Dic11⋊C4C22×C412yes—
419Dic11⋊C4C22×C412yes—
420Dic11⋊C4C22×C412yes—
421Dic11⋊C4C22×C412yes—
422Dic11⋊C4C22×C412yes—
423Dic11⋊C4C22×C412yes—
424Dic11⋊C4C22×C412yes—
425Dic11⋊C4C22×C412yes—
426Dic11⋊C4C22×C412yes—
427C4×Dic11C22×C412yes—
428C4×Dic11C22×C412yes—
429C4×Dic11C22×C412yes—
430C4×Dic11C22×C412yes—
431C4×Dic11C22×C412yes—
432C4×Dic11C22×C412yes—
433C4×Dic11C2412yes—
434C4×Dic11C2412yes—
435C4×Dic11C2412yes—
436#4318—41no—
437#4318—41no—
438#4318—41no—
439#4318—41no—
440C2×C11⋊C8—22no—
441C2×C11⋊C8—22no—
442C2×C11⋊C8—22no—
443C2×C11⋊C8—22no—
444C2×C11⋊C8—41no—
445C2×C11⋊C8—41no—
446C2×C11⋊C8—41no—
447C2×C11⋊C8—41no—
448C2×C11⋊C8C2411yescharacteristic
449C2×C11⋊C8C2411yescharacteristic
450C2×C11⋊C8C2411yescharacteristic
451C2×C11⋊C8C2411yescharacteristic
452C2×C11⋊C8C2411yescharacteristic
453C2×C11⋊C8C2411yescharacteristic
454C2×C11⋊C8C2411yescharacteristic
455C2×C11⋊C8C2411yescharacteristic
456#4313—42no—
457#4313—42no—
458C8×D11—42no—
459C8×D11—42no—
460#3475—111no—
461#2995—112no—
462#2995—112no—
463#2994—112no—
464#2993—112no—
465#2992—112no—
466#2992—112no—
467#2990—112no—
468#2989—112no—
469#2962—111no—
470#2961—111no—
471D4×M16D1111yescharacteristic, complemented
472#2933—111no—
473#2933—111no—
474#2930—111no—
475#2929—111no—
476C2×#435—111no—
477#2924—111no—
478#2924—111no—
479#2923—111no—
480#2906—111no—
481#2905—111no—
482C2×#424—111no—
483C23×C11—22no—
484C23×C11—22no—
485C23×C11—22no—
486C23×C11—41no—
487C23×C11—41no—
488C23×C11—41no—
489C23×C11C23×C411yescharacteristic
490C23×C11C23×C411yescharacteristic
491C23×C11C23×C411yescharacteristic
492C23×C11C23×C411yescharacteristic
493C23×C11C23×C411yescharacteristic
494C22×D11C23×C412yes—
495D4×C11—22no—
496D4×C11—22no—
497D4×C11—41no—
498D4×C11—41no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—21no—
506C2×C4×C11—21no—
507C2×C4×C11—21no—
508C2×C4×C11—21no—
509C2×C4×C11—21no—
510C2×C4×C11—21no—
511C2×C4×C11—21no—
512C2×C4×C11—21no—
513C2×C4×C11—41no—
514C2×C4×C11—41no—
515C2×C4×C11C23×C411yescharacteristic
516C2×C4×C11C23×C411yescharacteristic
517C2×C4×C11C23×C411yescharacteristic
518C2×C4×C11C23×C411yescharacteristic
519C2×C4×C11C23×C411yescharacteristic
520C2×C4×C11C23×C411yescharacteristic
521C2×C4×C11C23×C411yescharacteristic
522C2×C4×C11C23×C411yescharacteristic
523C2×C4×C11C23×C411yescharacteristic
524C2×C4×C11H(5,𝔽2)12yes—
525C2×C4×C112−1+412yes—
526C2×C4×C11C2511yescharacteristic
527C22⋊D11—24no—
528C22⋊D11—24no—
529C22⋊D11—42no—
530C22⋊D11—42no—
531C22⋊D11—42no—
532C2×Dic11—24no—
533C2×Dic11—42no—
534C2×Dic11—42no—
535C2×Dic11—42no—
536C2×Dic11C23×C412yes—
537C2×Dic11C23×C412yes—
538C2×Dic11C23×C412yes—
539C2×Dic11C23×C412yes—
540C2×Dic11C23×C412yes—
541C2×Dic11C23×C412yes—
542C2×Dic11C23×C412yes—
543D44—22no—
544C4×D11—22no—
545C4×D11—22no—
546C4×D11—42no—
547C4×D11—42no—
548Dic22—22no—
549Dic22—42no—
550Dic22—42no—
551C8×C11—22no—
552C8×C11—22no—
553C8×C11—22no—
554C8×C11—22no—
555C11⋊C8—21no—
556C11⋊C8—21no—
557C11⋊C8—21no—
558C11⋊C8—21no—
559C11⋊C8—21no—
560C11⋊C8—21no—
561C11⋊C8—21no—
562C11⋊C8—21no—
563C2×#131—111no—
564C2×#131—111no—
565C22×M16—111no—
566C22×M16C2×D1111yescharacteristic
567C22×M16C2×D1111yescharacteristic
568C23×C8—111no—
569#556—111no—
570#555—111no—
571#554—111no—
572#553—111no—
573#553—111no—
574#552—111no—
575#552—111no—
576#552—112no—
577#551—112no—
578#551—112no—
579#547—111no—
580#546—112no—
581#533—111no—
582#529—112no—
583#529—112no—
584#529—112no—
585#525—111no—
586#525—111no—
587C4×#41—112no—
588C4×#41—111no—
589C2×C4×D4C2×D1111yescharacteristic
590C2×#117—111no—
591C2×#117—111no—
592#446—112no—
593#446—112no—
594#446—112no—
595#446—112no—
596#446—112no—
597#446—112no—
598#446—112no—
599C8×Q8—112no—
600#436—112no—
601#436—112no—
602#436—112no—
603#436—112no—
604#436C2×D1112yes—
605#435—112no—
606#435—112no—
607#435—112no—
608#435—112no—
609#435—111no—
610#435—111no—
611#435—111no—
612#435—111no—
613#435—111no—
614#435—111no—
615#435—111no—
616#435—111no—
617#435—112no—
618#435—112no—
619#435—112no—
620#435—112no—
621#435C2×D1112yes—
622#435C2×D1112yes—
623C8×D4—112no—
624C8×D4—112no—
625C8×D4—112no—
626C8×D4—112no—
627C8×D4C2×D1112yes—
628#433—112no—
629#433—112no—
630#433—112no—
631#433—112no—
632#433—112no—
633#433—112no—
634#432—112no—
635#432—112no—
636#432—112no—
637#432—112no—
638#431—112no—
639#431—112no—
640#424—111no—
641#424—111no—
642#424—111no—
643#424—111no—
644#424—111no—
645#424—111no—
646#424—111no—
647#424—111no—
648#424—112no—
649#424—112no—
650#424—112no—
651#424—112no—
652#424—112no—
653#424—112no—
654#423—112no—
655#423—112no—
656#423—112no—
657#423C2×D1111yescharacteristic
658C2×C4⋊C8—112no—
659C2×C4⋊C8—112no—
660C2×C4⋊C8—111no—
661C2×C4⋊C8—112no—
662#408—111no—
663#408—111no—
664#407C2×D1111yescharacteristic
665#407C2×D1111yescharacteristic
666C2×C22⋊C8—111no—
667C2×C22⋊C8—111no—
668#405—111no—
669#405—111no—
670#405—111no—
671#405—111no—
672C4×M16C2×D1111yescharacteristic
673C2×#97—111no—
674C22×C11—21no—
675C22×C11—21no—
676C22×C11—21no—
677C22×C11—21no—
678C22×C11—21no—
679C22×C11—21no—
680C22×C11—21no—
681C22×C11—21no—
682C22×C11—21no—
683C22×C11—21no—
684C22×C11—21no—
685C22×C11—21no—
686C22×C11—21no—
687C22×C11—44no—
688C22×C11—82no—
689C22×C11#52012yes—
690C22×C11#56812yes—
691C22×C11C24×C411yescharacteristic
692C2×D11—22no—
693C2×D11—22no—
694C2×D11—22no—
695C4×C11—21no—
696C4×C11—21no—
697C4×C11—21no—
698C4×C11—21no—
699C4×C11—21no—
700C4×C11—21no—
701C4×C11—21no—
702C4×C11—21no—
703C4×C11#52012yes—
704C4×C11C2×H(5,𝔽2)11yescharacteristic
705C4×C11C2×2−1+411yescharacteristic
706Dic11—22no—
707Dic11—22no—
708Dic11—22no—
709Dic11—22no—
710Dic11—22no—
711Dic11—22no—
712Dic11—22no—
713C2×#41—112no—
714C2×#41—111no—
715C22×D4C4×D1111yescharacteristic
716C23×C4C22×D1111yescharacteristic
717C23×C4C22×D1111yescharacteristic
718#131—442no—
719#131—442no—
720C2×M16—42no—
721C2×M16—42no—
722C2×M16—111no—
723C2×M16—111no—
724C2×M16—111no—
725C2×M16—111no—
726C2×M16—112no—
727C2×M16—112no—
728C2×M16—442no—
729C2×M16C22×D1111yescharacteristic
730C2×M16C22×D1111yescharacteristic
731C2×M16C22×D1111yescharacteristic
732C2×M16C22×D1111yescharacteristic
733C2×M16C22×D1112yes—
734C2×M16C22×D1112yes—
735C22×C8—111no—
736C22×C8—111no—
737C22×C8—111no—
738C22×C8—111no—
739C22×C8—111no—
740C22×C8—111no—
741C22×C8—111no—
742C22×C8—111no—
743C22×C8—112no—
744C22×C8—112no—
745C22×C8—442no—
746C22×C8C22×D1112yes—
747C22×C8C22×D1112yes—
748C4⋊Q8—111no—
749C4⋊Q8—111no—
750#126—112no—
751#126—112no—
752#126—112no—
753#126—112no—
754#126—112no—
755#126—112no—
756#125—112no—
757#125—112no—
758#125—112no—
759#125—111no—
760#125—111no—
761#124—112no—
762#124—112no—
763#124—112no—
764#123—112no—
765#123—112no—
766#123—112no—
767#123—112no—
768#123—112no—
769#123—112no—
770#123—112no—
771#123—112no—
772C22⋊Q8—111no—
773C22⋊Q8—111no—
774C22⋊Q8—111no—
775C22⋊Q8—111no—
776C22⋊Q8—112no—
777C22⋊Q8—112no—
778C22⋊Q8—112no—
779C22⋊Q8—112no—
780C22⋊Q8—112no—
781#121—112no—
782#121—112no—
783#121—112no—
784#121—111no—
785#121—111no—
786#121—111no—
787#121—111no—
788#120—112no—
789#120—112no—
790C4×Q8—112no—
791C4×Q8—111no—
792C4×Q8—111no—
793C4×Q8—112no—
794C4×Q8—112no—
795C4×D4—112no—
796C4×D4—112no—
797C4×D4—112no—
798C4×D4—112no—
799C4×D4—112no—
800C4×D4—112no—
801C4×D4—112no—
802C4×D4—112no—
803C4×D4—112no—
804C4×D4—111no—
805C4×D4—111no—
806C4×D4C4×D1111yescharacteristic
807C4×D4C4×D1111yescharacteristic
808C4×D4C4×D1111yescharacteristic
809C4×D4C4×D1111yescharacteristic
810C4×D4C22×D1111yescharacteristic
811C4×D4C22×D1111yescharacteristic
812C4×D4C22×D1111yescharacteristic
813C4×D4C22×D1111yescharacteristic
814#117—112no—
815#117—112no—
816#117—111no—
817#117—111no—
818#117—111no—
819#117—111no—
820#117—111no—
821#117—111no—
822#117—111no—
823#117—112no—
824#117—112no—
825#117—112no—
826#117—112no—
827#117—112no—
828#117—112no—
829C2×C4⋊C4—111no—
830C2×C4⋊C4—111no—
831C2×C4⋊C4—111no—
832C2×C4⋊C4—111no—
833C2×C4⋊C4C4×D1111yescharacteristic
834C2×C22⋊C4—112no—
835C2×C22⋊C4—112no—
836C2×C22⋊C4C4×D1111yescharacteristic
837C2×C22⋊C4C4×D1111yescharacteristic
838C2×C42—112no—
839C2×C42—112no—
840C2×C42—112no—
841C2×C42C22×D1111yescharacteristic
842C4⋊C8—112no—
843C4⋊C8—112no—
844C4⋊C8—112no—
845C4⋊C8—112no—
846C4⋊C8—112no—
847C4⋊C8—112no—
848C4⋊C8—112no—
849C4⋊C8—112no—
850C4⋊C8—112no—
851C4⋊C8—112no—
852C4⋊C8—112no—
853C4⋊C8—112no—
854C4⋊C8—112no—
855C4⋊C8—112no—
856C4⋊C8—112no—
857C4⋊C8—112no—
858C4⋊C8—111no—
859C4⋊C8—111no—
860C4⋊C8—111no—
861C4⋊C8—111no—
862C4⋊C8C22×D1112yes—
863C4⋊C8C22×D1112yes—
864C22⋊C8—111no—
865C22⋊C8—111no—
866C22⋊C8—111no—
867C22⋊C8—111no—
868C22⋊C8—111no—
869C22⋊C8—111no—
870C22⋊C8—111no—
871C22⋊C8—111no—
872C22⋊C8—112no—
873C22⋊C8—112no—
874C22⋊C8—112no—
875C22⋊C8—112no—
876C22⋊C8C22×D1112yes—
877C22⋊C8C22×D1112yes—
878C22⋊C8C22×D1112yes—
879C22⋊C8C22×D1112yes—
880#97—112no—
881#97—112no—
882#97—112no—
883#97—112no—
884#97—111no—
885#97—111no—
886#97—111no—
887#97—111no—
888#97C22×D1112yes—
889C4×C8—112no—
890C4×C8—112no—
891C4×C8—112no—
892C4×C8—112no—
893C4×C8C22×D1112yes—
894C2×C11—22no—
895C2×C11—22no—
896C2×C11—41no—
897C2×C11—41no—
898C2×C11—41no—
899C2×C11C2×#52011yescharacteristic
900C2×C11C2×#56811yescharacteristic
901C2×C11#357311yescharacteristic
902D11—42no—
903C24C2×C4×D1111yescharacteristic
904C24C2×C4×D1111yescharacteristic
905#41—222no—
906#41—222no—
907#41—444no—
908C2×Q8—111no—
909C2×Q8—112no—
910C2×Q8—112no—
911C2×D4—42no—
912C2×D4—112no—
913C2×D4—112no—
914C2×D4—112no—
915C2×D4—112no—
916C2×D4—112no—
917C2×D4—111no—
918C2×D4C2×C4×D1111yescharacteristic
919C2×D4C2×C4×D1111yescharacteristic
920C2×D4C2×C4×D1111yescharacteristic
921C2×D4C2×C4×D1111yescharacteristic
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—112no—
927C22×C4—112no—
928C22×C4—112no—
929C22×C4—112no—
930C22×C4—112no—
931C22×C4—112no—
932C22×C4—112no—
933C22×C4C2×C4×D1111yescharacteristic
934C22×C4C2×C4×D1111yescharacteristic
935C22×C4C2×C4×D1111yescharacteristic
936C22×C4C2×C4×D1111yescharacteristic
937C22×C4C2×C4×D1111yescharacteristic
938C22×C4C2×C4×D1111yescharacteristic
939C22×C4C2×C4×D1111yescharacteristic
940C22×C4C2×C4×D1111yescharacteristic
941C22×C4C23×D1111yescharacteristic
942C22×C4C23×D1111yescharacteristic
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1111yescharacteristic
946M16—22no—
947M16—22no—
948M16—22no—
949M16—22no—
950M16—42no—
951M16—42no—
952M16—442no—
953M16—442no—
954M16—441no—
955M16—441no—
956M16—441no—
957M16—441no—
958C2×C8—42no—
959C2×C8—42no—
960C2×C8—111no—
961C2×C8—111no—
962C2×C8—111no—
963C2×C8—111no—
964C2×C8—111no—
965C2×C8—111no—
966C2×C8—111no—
967C2×C8—111no—
968C2×C8—222no—
969C2×C8—222no—
970C2×C8—222no—
971C2×C8—222no—
972C2×C8—442no—
973C2×C8—442no—
974C2×C8—441no—
975C2×C8—441no—
976C2×C8—441no—
977C2×C8—441no—
978C2×C8C23×D1112yes—
979C2×C8C23×D1112yes—
980C2×C8C23×D1112yes—
981C2×C8C23×D1112yes—
982C4⋊C4—111no—
983C4⋊C4—111no—
984C4⋊C4—111no—
985C4⋊C4—111no—
986C4⋊C4—111no—
987C4⋊C4—111no—
988C4⋊C4—112no—
989C4⋊C4—112no—
990C4⋊C4—112no—
991C4⋊C4—112no—
992C4⋊C4—112no—
993C4⋊C4—112no—
994C4⋊C4—112no—
995C4⋊C4—112no—
996C4⋊C4—112no—
997C4⋊C4—112no—
998C4⋊C4—112no—
999C4⋊C4—112no—
1000C4⋊C4—112no—
1001C4⋊C4—112no—
1002C4⋊C4—112no—
1003C4⋊C4—112no—
1004C4⋊C4C2×C4×D1111yescharacteristic
1005C4⋊C4C2×C4×D1111yescharacteristic
1006C4⋊C4C2×C4×D1111yescharacteristic
1007C4⋊C4C2×C4×D1111yescharacteristic
1008C22⋊C4—112no—
1009C22⋊C4—112no—
1010C22⋊C4—112no—
1011C22⋊C4—112no—
1012C22⋊C4—112no—
1013C22⋊C4—112no—
1014C22⋊C4—112no—
1015C22⋊C4—112no—
1016C22⋊C4—112no—
1017C22⋊C4—112no—
1018C22⋊C4—112no—
1019C22⋊C4—112no—
1020C22⋊C4—112no—
1021C22⋊C4—112no—
1022C22⋊C4—112no—
1023C22⋊C4—112no—
1024C22⋊C4—112no—
1025C22⋊C4C2×C4×D1111yescharacteristic
1026C22⋊C4C2×C4×D1111yescharacteristic
1027C22⋊C4C2×C4×D1111yescharacteristic
1028C22⋊C4C2×C4×D1111yescharacteristic
1029C22⋊C4C2×C4×D1111yescharacteristic
1030C22⋊C4C2×C4×D1111yescharacteristic
1031C22⋊C4C2×C4×D1111yescharacteristic
1032C22⋊C4C2×C4×D1111yescharacteristic
1033C42—112no—
1034C42—112no—
1035C42—112no—
1036C42—112no—
1037C42—112no—
1038C42—112no—
1039C42—112no—
1040C42—112no—
1041C42—112no—
1042C42C2×C4×D1111yescharacteristic
1043C42C2×C4×D1111yescharacteristic
1044C42C23×D1111yescharacteristic
1045C42C23×D1111yescharacteristic
1046C11#6027211yescharacteristic, complemented, Sylow
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—112no—
1054C23C22×C4×D1111yescharacteristic
1055C23C22×C4×D1111yescharacteristic
1056C23C22×C4×D1111yescharacteristic
1057C23C22×C4×D1111yescharacteristic
1058C23C22×C4×D1111yescharacteristic
1059Q8—222no—
1060Q8—442no—
1061Q8—442no—
1062D4—22no—
1063D4—22no—
1064D4—41no—
1065D4—41no—
1066D4—224no—
1067D4—224no—
1068D4—222no—
1069D4—442no—
1070D4—442no—
1071D4—442no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—112no—
1089C2×C4—112no—
1090C2×C4—112no—
1091C2×C4—112no—
1092C2×C4—112no—
1093C2×C4—112no—
1094C2×C4—112no—
1095C2×C4—224no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—442no—
1099C2×C4—442no—
1100C2×C4—442no—
1101C2×C4—442no—
1102C2×C4—442no—
1103C2×C4C22×C4×D1111yescharacteristic
1104C2×C4C22×C4×D1111yescharacteristic
1105C2×C4C22×C4×D1111yescharacteristic
1106C2×C4C22×C4×D1111yescharacteristic
1107C2×C4C22×C4×D1111yescharacteristic
1108C2×C4C22×C4×D1111yescharacteristic
1109C2×C4C22×C4×D1111yescharacteristic
1110C2×C4C22×C4×D1111yescharacteristic
1111C2×C4C22×C4×D1111yescharacteristic
1112C2×C4#6703712yes—
1113C2×C4#6704312yes—
1114C2×C4C24×D1111yescharacteristic
1115C8—22no—
1116C8—22no—
1117C8—22no—
1118C8—22no—
1119C8—221no—
1120C8—221no—
1121C8—221no—
1122C8—221no—
1123C8—221no—
1124C8—221no—
1125C8—221no—
1126C8—221no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—21no—
1137C22—21no—
1138C22—21no—
1139C22—21no—
1140C22—44no—
1141C22—82no—
1142C22—222no—
1143C22—222no—
1144C22—222no—
1145C22#1062307712yes—
1146C22#1062327612yes—
1147C22C23×C4×D1111yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—21no—
1151C4—21no—
1152C4—21no—
1153C4—21no—
1154C4—21no—
1155C4—21no—
1156C4—222no—
1157C4—222no—
1158C4—222no—
1159C4—222no—
1160C4—222no—
1161C4—222no—
1162C4—222no—
1163C4#1062307712yes—
1164C4C2×#6703711yescharacteristic
1165C4C2×#6704311yescharacteristic
1166C2—22no—
1167C2—22no—
1168C2—41no—
1169C2—41no—
1170C2—41no—
1171C2—442no—
1172C2C2×#1062307711yescharacteristic
1173C2C2×#1062327611yescharacteristic
1174C2#1308332911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingD4×C11×M16C2
prime radical#13082174C2
cosocleC2×C4×C11C25
hypercenterD4×M16D11
hypocenterC11#60272
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ D4×M16

Complements

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

NH ≅ G/Ntype
2. #13077782C2semidirect
3. #13077780C2semidirect
4. #13077773C2semidirect
5. #13077762C2semidirect
6. #13077751C2semidirect
7. #13077749C2semidirect
8. #13077736C2semidirect
9. #13077728C2semidirect
10. #13077563C2semidirect
11. #13077553C2semidirect
12. #13077341C2semidirect
13. #13077341C2semidirect
14. #13077315C2semidirect
15. #13077306C2semidirect
16. C2×#10622624C2semidirect
17. #13077276C2semidirect
18. #13077276C2semidirect
19. #13077268C2semidirect
20. #13077185C2semidirect
21. #13077179C2semidirect
22. C2×#10622732C2semidirect
23. D4×C11×M16C2semidirect
65. #10622741C22semidirect
66. #10622741C22semidirect
67. #10622740C22semidirect
68. #10622740C22semidirect
81. #10622732C22semidirect
82. #10622732C22semidirect
83. #10622731C22semidirect
84. #10622731C22semidirect
85. #10622724C22semidirect
86. #10622724C22semidirect
87. C8×C22⋊D11C22semidirect
88. C8×C22⋊D11C22semidirect
89. #10622715C22semidirect
90. #10622715C22semidirect
91. C2×Dic11⋊C8C22semidirect
92. C2×Dic11⋊C8C22semidirect
103. #10622452C22semidirect
104. #10622452C22semidirect
105. #10622450C22semidirect
106. D11×C4⋊C8C22semidirect
107. #10622441C22semidirect
108. #10622441C22semidirect
109. #10622441C22semidirect
110. #10622441C22semidirect
111. #10622343C22semidirect
112. #10622343C22semidirect
113. #10622342C22semidirect
114. #10622342C22semidirect
115. #10622341C22semidirect
116. #10622341C22semidirect
117. (C22⋊D11)⋊C8C22semidirect
118. (C22⋊D11)⋊C8C22semidirect
119. #10622333C22semidirect
120. #10622333C22semidirect
121. #10622333C22semidirect
122. #10622333C22semidirect
123. #10622332C22semidirect
124. #10622332C22semidirect
125. #10622331C22semidirect
126. #10622331C22semidirect
127. #10622318C22semidirect
128. #10622318C22semidirect
129. #10622314C22semidirect
130. #10622314C22semidirect
131. #10622303C22semidirect
132. #10622303C22semidirect
133. #10622292C22semidirect
134. C8×Dic22C22semidirect
471. D4×M16D11semidirect
1046. C11#60272semidirect

Maximal subgroups

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

subgroupindex
#130821742
#130777822
#130777802
#130777732
#130777622
#130777512
#130777492
#130777362
#130777282
#130775632
#130775532
#130773412
#130773152
#130773062
C2×#106226242
#130772762
#130772682
#130771852
#130771792
C2×#106227322
D4×C11×M162
#6027211