Finite Group Databasebeta

← #15618997

Subgroups — #15618997

Order 2816.

1882 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#13082176C211yesmaximal, characteristic
2#13077773C212yesmaximal, complemented
3#13077771C212yesmaximal, complemented
4#13077769C212yesmaximal, complemented
5#13077758C212yesmaximal, complemented
6#13077751C212yesmaximal, complemented
7#13077749C212yesmaximal, complemented
8#13077736C212yesmaximal, complemented
9#13077723C212yesmaximal, complemented
10#13077560C211yesmaximal, characteristic, complemented
11#13077549C211yesmaximal, characteristic, complemented
12#13077348C211yesmaximal, characteristic, complemented
13#13077343C211yesmaximal, characteristic, complemented
14#13077338C211yesmaximal, characteristic, complemented
15#13077313C211yesmaximal, characteristic, complemented
16C2×C8×C22⋊D11C211yesmaximal, characteristic, complemented
17#13077276C211yesmaximal, characteristic, complemented
18#13077271C211yesmaximal, characteristic, complemented
19#13077256C211yesmaximal, characteristic, complemented
20#13077182C211yesmaximal, characteristic, complemented
21C2×#10622715C211yesmaximal, characteristic, complemented
22D11×#424C211yesmaximal, characteristic, complemented
23C11×#2929C211yesmaximal, characteristic, complemented
24C2×C11×#131C2211yescharacteristic
25C23×C8×C11C2211yescharacteristic
26C11×#525C2211yescharacteristic
27#10623359C2211yescharacteristic
28#41×Dic11C2211yescharacteristic
29C2×#67001C2211yescharacteristic
30C2×C4×C22⋊D11C2211yescharacteristic
31C2×#66979C2211yescharacteristic
32C22×#4318C2211yescharacteristic
33C2×M16×D11C2211yescharacteristic
34C22×C8×D11C2211yescharacteristic
35#10623189C412yes—
36#10623181C412yes—
37#10623173C411yescharacteristic
38#10623172C411yescharacteristic
39#10623170C411yescharacteristic
40#10623166C411yescharacteristic
41#10623149C411yescharacteristic
42#10623147C411yescharacteristic
43#10623145C411yescharacteristic
44#10623142C411yescharacteristic
45#10623122C412yes—
46#10623118C412yes—
47#10623088C2212yes—
48#10623069C2212yes—
49#10623069C2212yes—
50C4×#4341C2212yes—
51D11×#117C2211yescharacteristic
52#10623048C2211yescharacteristic
53C11×#435C2212yescomplemented
54C11×#435C2212yescomplemented
55C8×D4×C11C2212yescomplemented
56C8×D4×C11C2212yescomplemented
57C11×#424C2211yescharacteristic
58C11×#408C2211yescharacteristic
59C11×#407C2211yescharacteristic
60C11×#405C2211yescharacteristic
61#10622847C2211yescharacteristic
62C2×C22⋊(C11⋊C8)C2211yescharacteristic
63#10622741C2212yescomplemented
64#10622740C2212yescomplemented
65#10622739C2211yescharacteristic
66#10622735C2211yescharacteristic
67#10622735C2211yescharacteristic
68#10622732C2211yescharacteristic
69#10622732C2211yescharacteristic
70#10622732C2212yescomplemented
71#10622731C2211yescharacteristic
72#10622731C2212yescomplemented
73M16×Dic11C2211yescharacteristic
74#10622724C2212yescomplemented
75C8×C22⋊D11C2211yescharacteristic
76C8×C22⋊D11C2211yescharacteristic
77C8×C22⋊D11C2211yescharacteristic
78C8×C22⋊D11C2211yescharacteristic
79C8×C22⋊D11C2211yescharacteristic
80C8×C22⋊D11C2211yescharacteristic
81C8×C22⋊D11C2211yescharacteristic
82C8×C22⋊D11C2211yescharacteristic
83C8×C22⋊D11C2212yescomplemented
84C2×(C2×D11)⋊C8C2211yescharacteristic
85#10622715C2211yescharacteristic
86#10622715C2211yescharacteristic
87#10622715C2211yescharacteristic
88#10622715C2211yescharacteristic
89#10622715C2212yescomplemented
90#10622715C2212yescomplemented
91#10622715C2212yescomplemented
92C2×Dic11⋊C8C2211yescharacteristic
93C2×Dic11⋊C8C2212yescomplemented
94C2×Dic11⋊C8C2212yescomplemented
95C2×Dic11⋊C8C2212yescomplemented
96C2×C8×Dic11C2211yescharacteristic
97#10622625C2212yescomplemented
98#10622624C2212yescomplemented
99#10622624C2212yescomplemented
100D4×C11⋊C8C2212yescomplemented
101#10622612C2211yescharacteristic
102#10622610C2211yescharacteristic
103#10622452C2212yescomplemented
104#10622452C2212yescomplemented
105D11×C4⋊C8C2212yescomplemented
106D11×C4⋊C8C2212yescomplemented
107#10622443C2212yescomplemented
108#10622443C2212yescomplemented
109#10622441C2212yescomplemented
110#10622441C2212yescomplemented
111#10622343C2212yes—
112#10622342C2212yes—
113#10622341C2212yes—
114#10622341C2212yescomplemented
115#10622341C2212yescomplemented
116(C22⋊D11)⋊C8C2212yes—
117(C22⋊D11)⋊C8C2212yescomplemented
118(C22⋊D11)⋊C8C2212yescomplemented
119#10622333C2212yescomplemented
120#10622333C2212yescomplemented
121#10622333C2212yescomplemented
122#10622333C2212yescomplemented
123#10622332C2212yescomplemented
124#10622331C2212yescomplemented
125#10622331C2212yescomplemented
126#10622331C2212yescomplemented
127#10622322C2212yescomplemented
128#10622318C2212yescomplemented
129#10622314C2212yescomplemented
130#10622314C2212yescomplemented
131#10622303C2212yescomplemented
132#10622298C2212yescomplemented
133#10622292C2212yescomplemented
134C8×Dic22C2212yescomplemented
135C2×C11×#41C2311yescharacteristic
136C23×C4×C11C2311yescharacteristic
137C22×C22⋊D11C2×C411yescharacteristic
138C2×#4341C2×C412yes—
139C22×C4×D11C2311yescharacteristic
140C11×#131—42no—
141C2×C11×M16C2311yescharacteristic
142C2×C11×M16C2311yescharacteristic
143C2×C11×M16C2312yes—
144C22×C8×C11—42no—
145C22×C8×C11C2311yescharacteristic
146C22×C8×C11C2311yescharacteristic
147C22×C8×C11C2311yescharacteristic
148C22×C8×C11C2311yescharacteristic
149C22×C8×C11C2311yescharacteristic
150C22×C8×C11C2311yescharacteristic
151C22×C8×C11C2312yes—
152C11×#123C2×C412yes—
153C11×C22⋊Q8C2×C411yescharacteristic
154C11×C22⋊Q8C2×C411yescharacteristic
155C11×#121C2×C411yescharacteristic
156C11×#121C2×C411yescharacteristic
157C11×#120C2×C412yes—
158C4×D4×C11C2312yes—
159C4×D4×C11C2312yes—
160C11×#117C2311yescharacteristic
161C2×C22⋊Dic11C2×C412yes—
162C2×C22⋊Dic11C2×C411yescharacteristic
163#67001—42no—
164#66999C2×C411yescharacteristic
165#66999C2×C411yescharacteristic
166Q8×Dic11C2×C411yescharacteristic
167Q8×Dic11C2×C411yescharacteristic
168#66992C2×C412yes—
169#66992C2×C412yes—
170#66991C2×C412yes—
171#66991C2×C411yescharacteristic
172#66991C2×C411yescharacteristic
173#66990C2×C412yes—
174#66989C2×C412yes—
175#66988C2×C412yes—
176#66988C2×C412yes—
177#66988C2×C412yes—
178D4×Dic11C2×C412yes—
179D4×Dic11C2×C412yes—
180D4×Dic11C2×C412yes—
181D4×Dic11C2×C411yescharacteristic
182D4×Dic11C2×C411yescharacteristic
183C4×C22⋊D11C2×C411yescharacteristic
184C4×C22⋊D11C2×C411yescharacteristic
185C4×C22⋊D11C2×C411yescharacteristic
186C4×C22⋊D11C2×C411yescharacteristic
187C4×C22⋊D11C2311yescharacteristic
188C4×C22⋊D11C2311yescharacteristic
189C4×C22⋊D11C2311yescharacteristic
190C4×C22⋊D11C2311yescharacteristic
191C4×C22⋊D11C2312yes—
192C4×C22⋊D11C2312yes—
193C2×(C2×D11)⋊C4C2×C411yescharacteristic
194#66979C2×C411yescharacteristic
195#66979C2×C411yescharacteristic
196#66979C2×C412yes—
197#66979C2311yescharacteristic
198#66979C2312yes—
199#66979C2311yescharacteristic
200#66979C2312yes—
201C2×C4⋊Dic11C2×C411yescharacteristic
202C2×C4⋊Dic11C2×C411yescharacteristic
203C2×Dic11⋊C4C2×C411yescharacteristic
204C2×C4×Dic11C2311yescharacteristic
205C2×C4×Dic11C2312yes—
206C2×C4×Dic11C2312yes—
207C2×#4318—42no—
208C2×#4318C2311yescharacteristic
209C2×#4318C2311yescharacteristic
210C2×#4318C2312yes—
211C2×#4318C2312yes—
212C22×C11⋊C8C2311yescharacteristic
213C22×C11⋊C8C2311yescharacteristic
214C22×C11⋊C8C2312yes—
215C22×C11⋊C8C2312yes—
216M16×D11—42no—
217C2×#4313C2312yes—
218C2×C8×D11—42no—
219C2×C8×D11C2311yescharacteristic
220C2×C8×D11C2311yescharacteristic
221C2×C8×D11C2311yescharacteristic
222C2×C8×D11C2311yescharacteristic
223C2×C8×D11C2312yes—
224#66951C2×C412yes—
225#66951C2×C412yes—
226#66950C2×C412yes—
227#66945C2×C411yescharacteristic
228#66945C2×C411yescharacteristic
229#66945C2×C412yes—
230C4⋊C4×D11C2×C411yescharacteristic
231C4⋊C4×D11C2×C411yescharacteristic
232#66943C2×C411yescharacteristic
233#66943C2×C411yescharacteristic
234#66943C2×C412yes—
235#66942C2×C412yes—
236#66942C2×C412yes—
237#66941C2×C411yescharacteristic
238#66941C2×C411yescharacteristic
239#66940C2×C412yes—
240#66939C2×C412yes—
241#66939C2×C412yes—
242#66938C2×C412yes—
243#66938C2×C412yes—
244#66936C2×C412yes—
245#66936C2×C412yes—
246(C22⋊D11)⋊C4C2×C412yes—
247(C22⋊D11)⋊C4C2×C412yes—
248C22⋊C4×D11C2×C412yes—
249#66932C2×C412yes—
250#66932C2×C412yes—
251#66932C2×C412yes—
252#66932C2×C412yes—
253#66931C2×C412yes—
254#66931C2×C412yes—
255#66931C2×C412yes—
256#66931C2×C412yes—
257#66930C2×C412yes—
258#66930C2×C412yes—
259#66930C2×C412yes—
260#66925C2312yes—
261C42×D11C2312yes—
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)C2312yes—
277C22⋊(C11⋊C8)C2312yes—
278(C2×D11)⋊C8C2311yescharacteristic
279(C2×D11)⋊C8C2311yescharacteristic
280(C2×D11)⋊C8C2311yescharacteristic
281(C2×D11)⋊C8C2311yescharacteristic
282(C2×D11)⋊C8C2312yes—
283(C2×D11)⋊C8C2312yes—
284#66879C2312yes—
285#66879C2312yes—
286#66879C2312yes—
287Dic11⋊C8C2311yescharacteristic
288Dic11⋊C8C2311yescharacteristic
289Dic11⋊C8C2311yescharacteristic
290Dic11⋊C8C2311yescharacteristic
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—
304Dic11⋊C8C2312yes—
305C8×Dic11C2311yescharacteristic
306C8×Dic11C2311yescharacteristic
307C8×Dic11C2311yescharacteristic
308C8×Dic11C2311yescharacteristic
309C8×Dic11C2312yes—
310C8×Dic11C2312yes—
311C8×Dic11C2312yes—
312C4⋊(C11⋊C8)C2312yes—
313C4⋊(C11⋊C8)C2312yes—
314#66867C2312yes—
315C4×C11⋊C8C2312yes—
316#60271—111nomaximal, Sylow
317C24×C11C22×C411yescharacteristic
318C23×D11C22×C411yescharacteristic
319C11×#41—22no—
320C11×#41—22no—
321C2×Q8×C11C22×C411yescharacteristic
322C2×D4×C11C22×C412yes—
323C2×D4×C11C22×C411yescharacteristic
324C2×D4×C11C22×C412yes—
325C2×D4×C11C22×C412yes—
326C22×C4×C11—22no—
327C22×C4×C11—22no—
328C22×C4×C11C22×C411yescharacteristic
329C22×C4×C11C22×C411yescharacteristic
330C22×C4×C11C22×C411yescharacteristic
331C22×C4×C11C2411yescharacteristic
332C22×C4×C11C2412yes—
333C22×C4×C11C2411yescharacteristic
334C22×C4×C11C2411yescharacteristic
335C2×C22⋊D11—24no—
336C2×C22⋊D11C22×C412yes—
337C2×C22⋊D11C22×C411yescharacteristic
338C2×C22⋊D11C22×C411yescharacteristic
339C2×C22⋊D11C22×C411yescharacteristic
340C2×C22⋊D11C22×C412yes—
341C2×C22⋊D11C22×C411yescharacteristic
342C22×Dic11C22×C411yescharacteristic
343C22×Dic11C22×C412yes—
344C22×Dic11C22×C412yes—
345C22×Dic11C22×C411yescharacteristic
346C22×Dic11C22×C411yescharacteristic
347C22×Dic11C22×C412yes—
348C22×Dic11C22×C412yes—
349#4341—28no—
350C2×C4×D11—22no—
351C2×C4×D11—22no—
352C2×C4×D11C22×C412yes—
353C2×C4×D11C22×C411yescharacteristic
354C2×C4×D11C22×C411yescharacteristic
355C2×C4×D11C22×C412yes—
356C2×C4×D11C2411yescharacteristic
357C2×C4×D11C2411yescharacteristic
358C2×Dic22C22×C412yes—
359C2×Dic22C22×C412yes—
360C11×M16—22no—
361C11×M16—22no—
362C11×M16—42no—
363C2×C8×C11—22no—
364C2×C8×C11—22no—
365C2×C8×C11—41no—
366C2×C8×C11—41no—
367C2×C8×C11—41no—
368C2×C8×C11—41no—
369C2×C8×C11—42no—
370C2×C8×C11C2411yescharacteristic
371C2×C8×C11C2411yescharacteristic
372C2×C8×C11C2412yes—
373C2×C8×C11C2412yes—
374C2×C8×C11C2411yescharacteristic
375C2×C8×C11C2411yescharacteristic
376C11×C4⋊C4C22×C412yes—
377C11×C4⋊C4C22×C411yescharacteristic
378C11×C4⋊C4C22×C411yescharacteristic
379C11×C4⋊C4C22×C412yes—
380C11×C22⋊C4C22×C412yes—
381C11×C22⋊C4C22×C412yes—
382C11×C22⋊C4C22×C412yes—
383C11×C22⋊C4C22×C412yes—
384C11×C22⋊C4C22×C412yes—
385C42×C11C2412yes—
386C22⋊Dic11C22×C411yescharacteristic
387C22⋊Dic11C22×C412yes—
388C22⋊Dic11C22×C412yes—
389C22⋊Dic11C22×C412yes—
390C22⋊Dic11C22×C411yescharacteristic
391C22⋊Dic11C22×C412yes—
392C22⋊Dic11C22×C412yes—
393C22⋊Dic11C22×C411yescharacteristic
394C22⋊Dic11C22×C411yescharacteristic
395C22⋊Dic11C22×C412yes—
396C22⋊Dic11C22×C412yes—
397C22⋊Dic11C22×C412yes—
398(C2×D11)⋊C4C22×C412yes—
399(C2×D11)⋊C4C22×C412yes—
400(C2×D11)⋊C4C22×C411yescharacteristic
401(C2×D11)⋊C4C22×C412yes—
402(C2×D11)⋊C4C22×C411yescharacteristic
403(C2×D11)⋊C4C22×C411yescharacteristic
404(C2×D11)⋊C4C22×C412yes—
405(C2×D11)⋊C4C22×C411yescharacteristic
406C4⋊Dic11C22×C412yes—
407C4⋊Dic11C22×C412yes—
408C4⋊Dic11C22×C412yes—
409C4⋊Dic11C22×C412yes—
410C4⋊Dic11C22×C412yes—
411C4⋊Dic11C22×C412yes—
412C4⋊Dic11C22×C411yescharacteristic
413C4⋊Dic11C22×C411yescharacteristic
414C4⋊Dic11C22×C411yescharacteristic
415C4⋊Dic11C22×C411yescharacteristic
416Dic11⋊C4C22×C412yes—
417Dic11⋊C4C22×C412yes—
418Dic11⋊C4C22×C412yes—
419Dic11⋊C4C22×C412yes—
420Dic11⋊C4C22×C412yes—
421Dic11⋊C4C22×C412yes—
422Dic11⋊C4C22×C411yescharacteristic
423Dic11⋊C4C22×C412yes—
424Dic11⋊C4C22×C411yescharacteristic
425Dic11⋊C4C22×C412yes—
426Dic11⋊C4C22×C411yescharacteristic
427Dic11⋊C4C22×C411yescharacteristic
428C4×Dic11C22×C412yes—
429C4×Dic11C22×C412yes—
430C4×Dic11C22×C412yes—
431C4×Dic11C22×C412yes—
432C4×Dic11C22×C412yes—
433C4×Dic11C22×C412yes—
434C4×Dic11C22×C411yescharacteristic
435C4×Dic11C22×C411yescharacteristic
436C4×Dic11C2411yescharacteristic
437C4×Dic11C2411yescharacteristic
438C4×Dic11C2412yes—
439C4×Dic11C2412yes—
440#4318—22no—
441#4318—22no—
442#4318—42no—
443#4318—42no—
444C2×C11⋊C8—22no—
445C2×C11⋊C8—22no—
446C2×C11⋊C8—42no—
447C2×C11⋊C8—42no—
448C2×C11⋊C8C2411yescharacteristic
449C2×C11⋊C8C2412yes—
450C2×C11⋊C8C2411yescharacteristic
451C2×C11⋊C8C2411yescharacteristic
452C2×C11⋊C8C2412yes—
453C2×C11⋊C8C2411yescharacteristic
454#4313—42no—
455C8×D11—41no—
456C8×D11—41no—
457C8×D11—41no—
458C8×D11—41no—
459C8×D11—42no—
460#3475—111no—
461#2994—112no—
462#2994—112no—
463#2994—112no—
464#2993—112no—
465#2992—112no—
466#2992—112no—
467#2990—112no—
468#2988—112no—
469#2962—111no—
470#2960—111no—
471D4×M16—111no—
472#2933—111no—
473#2933—111no—
474#2929—111no—
475#2929D1111yescharacteristic, complemented
476C2×C8×D4—111no—
477#2924—111no—
478#2924—111no—
479#2922—111no—
480#2906—111no—
481C2×#424—111no—
482C2×#424—111no—
483C23×C11—22no—
484C23×C11—22no—
485C23×C11—41no—
486C23×C11C23×C411yescharacteristic
487C23×C11C23×C412yes—
488C23×C11C23×C411yescharacteristic
489C23×C11C23×C411yescharacteristic
490C22×D11—22no—
491C22×D11—22no—
492C22×D11—41no—
493C22×D11C23×C411yescharacteristic
494C22×D11C23×C411yescharacteristic
495Q8×C11—22no—
496D4×C11—24no—
497D4×C11—24no—
498D4×C11—22no—
499D4×C11—42no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—21no—
504C2×C4×C11—22no—
505C2×C4×C11—21no—
506C2×C4×C11—21no—
507C2×C4×C11—21no—
508C2×C4×C11—22no—
509C2×C4×C11C23×C411yescharacteristic
510C2×C4×C11C23×C412yes—
511C2×C4×C11C23×C412yes—
512C2×C4×C11C23×C412yes—
513C2×C4×C11C23×C411yescharacteristic
514C2×C4×C11C23×C411yescharacteristic
515C2×C4×C11H(5,𝔽2)12yes—
516C2×C4×C112−1+412yes—
517C2×C4×C11C2511yescharacteristic
518C22⋊D11—22no—
519C22⋊D11—24no—
520C22⋊D11—22no—
521C22⋊D11—22no—
522C22⋊D11—42no—
523C22⋊D11#13114yescomplemented
524C2×Dic11—22no—
525C2×Dic11—24no—
526C2×Dic11—24no—
527C2×Dic11—22no—
528C2×Dic11—41no—
529C2×Dic11—42no—
530C2×Dic11—42no—
531C2×Dic11C23×C411yescharacteristic
532C2×Dic11C23×C411yescharacteristic
533C2×Dic11C23×C412yes—
534C2×Dic11C23×C412yes—
535C2×Dic11C23×C411yescharacteristic
536C2×Dic11C23×C412yes—
537C2×Dic11C23×C412yes—
538C2×Dic11C23×C411yescharacteristic
539C2×Dic11C23×C411yescharacteristic
540C2×Dic11C23×C411yescharacteristic
541C4×D11—24no—
542C4×D11—22no—
543C4×D11—22no—
544C4×D11—21no—
545C4×D11—21no—
546C4×D11—21no—
547C4×D11—21no—
548C4×D11—42no—
549Dic22—24no—
550Dic22—42no—
551C8×C11—21no—
552C8×C11—21no—
553C8×C11—22no—
554C8×C11—21no—
555C8×C11—21no—
556C8×C11—22no—
557C11⋊C8—21no—
558C11⋊C8—21no—
559C11⋊C8—22no—
560C11⋊C8—22no—
561C11⋊C8—21no—
562C11⋊C8—21no—
563C2×#131—111no—
564C2×#131C2×D1111yescharacteristic
565C22×M16—111no—
566C22×M16—111no—
567C23×C8—111no—
568C23×C8C2×D1111yescharacteristic
569#556—111no—
570#555—111no—
571#554—111no—
572#553—111no—
573#553—111no—
574#552—112no—
575#552—111no—
576#552—111no—
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#525C2×D1111yescharacteristic
587C4×#41—111no—
588C4×#41—112no—
589C2×C4×D4—111no—
590C2×#117—111no—
591C2×#117—111no—
592#446—112no—
593#446—112no—
594#446—112no—
595#446—112no—
596#446—112no—
597C8×Q8—112no—
598C8×Q8—112no—
599C8×Q8—112no—
600#436—112no—
601#436—112no—
602#436—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#435C2×D1112yescomplemented
612#435C2×D1112yescomplemented
613C8×D4—111no—
614C8×D4—111no—
615C8×D4—111no—
616C8×D4—111no—
617C8×D4—111no—
618C8×D4—111no—
619C8×D4—111no—
620C8×D4—111no—
621C8×D4—112no—
622C8×D4—112no—
623C8×D4—112no—
624C8×D4—112no—
625C8×D4—112no—
626C8×D4C2×D1112yescomplemented
627C8×D4C2×D1112yescomplemented
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#431—112no—
637#431—112no—
638#431—112no—
639#431—112no—
640#424—111no—
641#424—111no—
642#424—112no—
643#424—111no—
644#424—111no—
645#424—111no—
646#424—111no—
647#424—112no—
648#424—112no—
649#424—112no—
650#424—111no—
651#424—112no—
652#424—112no—
653#424C2×D1111yescharacteristic
654#423—111no—
655#423—112no—
656C2×C4⋊C8—112no—
657C2×C4⋊C8—112no—
658C2×C4⋊C8—111no—
659C2×C4⋊C8—112no—
660C2×C4⋊C8—112no—
661C2×C4⋊C8—112no—
662#408—111no—
663#408C2×D1111yescharacteristic
664#407—111no—
665#407C2×D1111yescharacteristic
666C2×C22⋊C8—111no—
667C2×C22⋊C8—111no—
668#405—111no—
669#405—111no—
670#405—111no—
671#405C2×D1111yescharacteristic
672C4×M16—111no—
673C2×C4×C8—111no—
674C22×C11—21no—
675C22×C11—21no—
676C22×C11—21no—
677C22×C11—21no—
678C22×C11—21no—
679C22×C11—22no—
680C22×C11—22no—
681C22×C11—21no—
682C22×C11—21no—
683C22×C11—22no—
684C22×C11—44no—
685C22×C11#52012yes—
686C22×C11C2×#13112yes—
687C22×C11C24×C411yescharacteristic
688C2×D11—21no—
689C2×D11—21no—
690C2×D11—21no—
691C2×D11—21no—
692C2×D11—21no—
693C2×D11—44no—
694C2×D11C2×#13112yes—
695C4×C11—21no—
696C4×C11—21no—
697C4×C11—22no—
698C4×C11—22no—
699C4×C11—22no—
700C4×C11#52012yes—
701C4×C11C2×H(5,𝔽2)11yescharacteristic
702C4×C11C2×2−1+411yescharacteristic
703Dic11—21no—
704Dic11—21no—
705Dic11—22no—
706Dic11—22no—
707Dic11—21no—
708Dic11—21no—
709Dic11—22no—
710Dic11—22no—
711Dic11—21no—
712Dic11C2×#13112yes—
713C2×#41—112no—
714C2×#41C22×D1111yescharacteristic
715C22×D4—111no—
716C23×C4—111no—
717C23×C4C22×D1111yescharacteristic
718#131—42no—
719#131—442no—
720C2×M16—111no—
721C2×M16—111no—
722C2×M16—112no—
723C2×M16—112no—
724C2×M16—112no—
725C2×M16—442no—
726C2×M16—442no—
727C2×M16C22×D1111yescharacteristic
728C2×M16C22×D1111yescharacteristic
729C2×M16C22×D1112yes—
730C22×C8—42no—
731C22×C8—111no—
732C22×C8—111no—
733C22×C8—112no—
734C22×C8—112no—
735C22×C8—111no—
736C22×C8—111no—
737C22×C8—111no—
738C22×C8—111no—
739C22×C8—112no—
740C22×C8—442no—
741C22×C8C22×D1111yescharacteristic
742C22×C8C22×D1111yescharacteristic
743C22×C8C22×D1111yescharacteristic
744C22×C8C22×D1111yescharacteristic
745C22×C8C22×D1111yescharacteristic
746C22×C8C22×D1111yescharacteristic
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#123C4×D1112yes—
772C22⋊Q8—111no—
773C22⋊Q8—111no—
774C22⋊Q8—112no—
775C22⋊Q8—112no—
776C22⋊Q8—112no—
777C22⋊Q8—112no—
778C22⋊Q8—112no—
779C22⋊Q8C4×D1111yescharacteristic
780C22⋊Q8C4×D1111yescharacteristic
781#121—111no—
782#121—111no—
783#121—112no—
784#121—112no—
785#121—112no—
786#121C4×D1111yescharacteristic
787#121C4×D1111yescharacteristic
788#120—112no—
789#120C4×D1112yes—
790C4×Q8—111no—
791C4×Q8—111no—
792C4×Q8—112no—
793C4×Q8—112no—
794C4×Q8—112no—
795C4×D4—112no—
796C4×D4—111no—
797C4×D4—112no—
798C4×D4—112no—
799C4×D4—111no—
800C4×D4—111no—
801C4×D4—111no—
802C4×D4—111no—
803C4×D4—111no—
804C4×D4—111no—
805C4×D4—111no—
806C4×D4—111no—
807C4×D4—111no—
808C4×D4—112no—
809C4×D4—112no—
810C4×D4—112no—
811C4×D4—112no—
812C4×D4C22×D1112yes—
813C4×D4C22×D1112yes—
814#117—112no—
815#117—111no—
816#117—111no—
817#117—111no—
818#117—111no—
819#117—112no—
820#117—112no—
821#117—111no—
822#117—111no—
823#117—112no—
824#117—112no—
825#117—112no—
826#117—112no—
827#117—112no—
828#117C22×D1111yescharacteristic
829C2×C4⋊C4—111no—
830C2×C4⋊C4—111no—
831C2×C4⋊C4—111no—
832C2×C4⋊C4—111no—
833C2×C4⋊C4—111no—
834C2×C22⋊C4—112no—
835C2×C22⋊C4—111no—
836C2×C22⋊C4—111no—
837C2×C22⋊C4—112no—
838C2×C42—112no—
839C2×C42—111no—
840C2×C42—112no—
841C2×C42—112no—
842C4⋊C8—111no—
843C4⋊C8—112no—
844C4⋊C8—112no—
845C4⋊C8—112no—
846C4⋊C8—112no—
847C4⋊C8—111no—
848C4⋊C8—112no—
849C4⋊C8—112no—
850C4⋊C8—112no—
851C4⋊C8—111no—
852C4⋊C8—111no—
853C4⋊C8—112no—
854C4⋊C8—112no—
855C4⋊C8—112no—
856C4⋊C8—112no—
857C4⋊C8—112no—
858C4⋊C8—112no—
859C4⋊C8—112no—
860C4⋊C8—112no—
861C4⋊C8—112no—
862C4⋊C8C22×D1112yes—
863C4⋊C8C22×D1112yes—
864C22⋊C8—111no—
865C22⋊C8—111no—
866C22⋊C8—111no—
867C22⋊C8—111no—
868C22⋊C8—112no—
869C22⋊C8—112no—
870C22⋊C8—111no—
871C22⋊C8—111no—
872C22⋊C8—111no—
873C22⋊C8—111no—
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#97C22×D1112yes—
885C4×C8—111no—
886C4×C8—111no—
887C4×C8—111no—
888C4×C8—111no—
889C4×C8—112no—
890C4×C8—112no—
891C4×C8—112no—
892C4×C8—112no—
893C4×C8C22×D1112yes—
894C2×C11—22no—
895C2×C11—22no—
896C2×C11—42no—
897C2×C11—41no—
898C2×C11C2×#52011yescharacteristic
899C2×C11C22×#13111yescharacteristic
900C2×C11#357311yescharacteristic
901D11—22no—
902D11—41no—
903C24—111no—
904C24C2×C4×D1111yescharacteristic
905#41—22no—
906#41—22no—
907#41—228no—
908C2×Q8—112no—
909C2×Q8—112no—
910C2×Q8C2×C4×D1111yescharacteristic
911C2×D4—111no—
912C2×D4—112no—
913C2×D4—111no—
914C2×D4—111no—
915C2×D4—111no—
916C2×D4—112no—
917C2×D4—224no—
918C2×D4C2×C4×D1112yes—
919C2×D4C2×C4×D1111yescharacteristic
920C2×D4C2×C4×D1112yes—
921C2×D4C2×C4×D1112yes—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—112no—
925C22×C4—111no—
926C22×C4—112no—
927C22×C4—111no—
928C22×C4—111no—
929C22×C4—112no—
930C22×C4—112no—
931C22×C4—112no—
932C22×C4—111no—
933C22×C4—111no—
934C22×C4—111no—
935C22×C4—111no—
936C22×C4—112no—
937C22×C4—222no—
938C22×C4—222no—
939C22×C4C2×C4×D1111yescharacteristic
940C22×C4C2×C4×D1111yescharacteristic
941C22×C4C2×C4×D1111yescharacteristic
942C22×C4C23×D1111yescharacteristic
943C22×C4C23×D1112yes—
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1111yescharacteristic
946M16—22no—
947M16—22no—
948M16—42no—
949M16—222no—
950M16—222no—
951M16—442no—
952M16—442no—
953M16—442no—
954C2×C8—22no—
955C2×C8—22no—
956C2×C8—41no—
957C2×C8—41no—
958C2×C8—41no—
959C2×C8—41no—
960C2×C8—42no—
961C2×C8—111no—
962C2×C8—111no—
963C2×C8—111no—
964C2×C8—112no—
965C2×C8—112no—
966C2×C8—111no—
967C2×C8—222no—
968C2×C8—222no—
969C2×C8—441no—
970C2×C8—441no—
971C2×C8—441no—
972C2×C8—441no—
973C2×C8—442no—
974C2×C8—442no—
975C2×C8—442no—
976C2×C8C23×D1112yes—
977C2×C8C23×D1111yescharacteristic
978C2×C8C23×D1111yescharacteristic
979C2×C8C23×D1112yes—
980C2×C8C23×D1111yescharacteristic
981C2×C8C23×D1111yescharacteristic
982C4⋊C4—111no—
983C4⋊C4—111no—
984C4⋊C4—111no—
985C4⋊C4—111no—
986C4⋊C4—111no—
987C4⋊C4—112no—
988C4⋊C4—112no—
989C4⋊C4—112no—
990C4⋊C4—112no—
991C4⋊C4—111no—
992C4⋊C4—111no—
993C4⋊C4—111no—
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×D1112yes—
1007C4⋊C4C2×C4×D1112yes—
1008C22⋊C4—112no—
1009C22⋊C4—111no—
1010C22⋊C4—112no—
1011C22⋊C4—112no—
1012C22⋊C4—112no—
1013C22⋊C4—111no—
1014C22⋊C4—111no—
1015C22⋊C4—111no—
1016C22⋊C4—112no—
1017C22⋊C4—112no—
1018C22⋊C4—112no—
1019C22⋊C4—112no—
1020C22⋊C4—111no—
1021C22⋊C4—112no—
1022C22⋊C4—112no—
1023C22⋊C4—111no—
1024C22⋊C4—111no—
1025C22⋊C4—111no—
1026C22⋊C4—112no—
1027C22⋊C4—112no—
1028C22⋊C4C2×C4×D1112yes—
1029C22⋊C4C2×C4×D1112yes—
1030C22⋊C4C2×C4×D1112yes—
1031C22⋊C4C2×C4×D1112yes—
1032C22⋊C4C2×C4×D1112yes—
1033C42—112no—
1034C42—112no—
1035C42—112no—
1036C42—112no—
1037C42—112no—
1038C42—111no—
1039C42—111no—
1040C42—112no—
1041C42—111no—
1042C42—111no—
1043C42—112no—
1044C42—112no—
1045C42C23×D1112yes—
1046C11#6027111yescharacteristic, complemented, Sylow
1047C23—22no—
1048C23—22no—
1049C23—41no—
1050C23—111no—
1051C23—111no—
1052C23—222no—
1053C23—222no—
1054C23—441no—
1055C23C22×C4×D1111yescharacteristic
1056C23C22×C4×D1112yes—
1057C23C22×C4×D1111yescharacteristic
1058C23C22×C4×D1111yescharacteristic
1059Q8—22no—
1060Q8—224no—
1061Q8—442no—
1062D4—24no—
1063D4—24no—
1064D4—22no—
1065D4—42no—
1066D4—114no—
1067D4—222no—
1068D4—222no—
1069D4—224no—
1070D4—222no—
1071D4—442no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—22no—
1081C2×C4—111no—
1082C2×C4—112no—
1083C2×C4—111no—
1084C2×C4—112no—
1085C2×C4—111no—
1086C2×C4—111no—
1087C2×C4—112no—
1088C2×C4—112no—
1089C2×C4—111no—
1090C2×C4—111no—
1091C2×C4—224no—
1092C2×C4—222no—
1093C2×C4—224no—
1094C2×C4—224no—
1095C2×C4—222no—
1096C2×C4—222no—
1097C2×C4—222no—
1098C2×C4—221no—
1099C2×C4—221no—
1100C2×C4—221no—
1101C2×C4—221no—
1102C2×C4—442no—
1103C2×C4—442no—
1104C2×C4—442no—
1105C2×C4—441no—
1106C2×C4C22×C4×D1111yescharacteristic
1107C2×C4C22×C4×D1112yes—
1108C2×C4C22×C4×D1112yes—
1109C2×C4C22×C4×D1112yes—
1110C2×C4C22×C4×D1111yescharacteristic
1111C2×C4C22×C4×D1111yescharacteristic
1112C2×C4#6703712yes—
1113C2×C4#6704312yes—
1114C2×C4C24×D1111yescharacteristic
1115C8—21no—
1116C8—21no—
1117C8—21no—
1118C8—21no—
1119C8—22no—
1120C8—22no—
1121C8—221no—
1122C8—221no—
1123C8—222no—
1124C8—222no—
1125C8—221no—
1126C8—221no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—22no—
1132C22—21no—
1133C22—22no—
1134C22—21no—
1135C22—21no—
1136C22—22no—
1137C22—44no—
1138C22—112no—
1139C22—221no—
1140C22—221no—
1141C22—221no—
1142C22—221no—
1143C22—221no—
1144C22—444no—
1145C22#1062307712yes—
1146C22D11×#13112yes—
1147C22C23×C4×D1111yescharacteristic
1148C4—22no—
1149C4—22no—
1150C4—21no—
1151C4—21no—
1152C4—22no—
1153C4—112no—
1154C4—222no—
1155C4—221no—
1156C4—222no—
1157C4—222no—
1158C4—221no—
1159C4—222no—
1160C4—221no—
1161C4—221no—
1162C4—221no—
1163C4#1062307712yes—
1164C4C2×#6703711yescharacteristic
1165C4C2×#6704311yescharacteristic
1166C2—22no—
1167C2—22no—
1168C2—41no—
1169C2—42no—
1170C2—222no—
1171C2—441no—
1172C2C2×#1062307711yescharacteristic
1173C2C2×D11×#13111yescharacteristic
1174C2#1308332711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2929C2
prime radical#13082176C2
cosocleC2×C4×C11C25
hypercenter#2929D11
hypocenterC11#60271
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2929

Complements

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

NH ≅ G/Ntype
2. #13077773C2semidirect
3. #13077771C2semidirect
4. #13077769C2semidirect
5. #13077758C2semidirect
6. #13077751C2semidirect
7. #13077749C2semidirect
8. #13077736C2semidirect
9. #13077723C2semidirect
10. #13077560C2semidirect
11. #13077549C2semidirect
12. #13077348C2semidirect
13. #13077343C2semidirect
14. #13077338C2semidirect
15. #13077313C2semidirect
16. C2×C8×C22⋊D11C2semidirect
17. #13077276C2semidirect
18. #13077271C2semidirect
19. #13077256C2semidirect
20. #13077182C2semidirect
21. C2×#10622715C2semidirect
22. D11×#424C2semidirect
23. C11×#2929C2semidirect
53. C11×#435C22semidirect
54. C11×#435C22semidirect
55. C8×D4×C11C22semidirect
56. C8×D4×C11C22semidirect
63. #10622741C22semidirect
64. #10622740C22semidirect
70. #10622732C22semidirect
72. #10622731C22semidirect
74. #10622724C22semidirect
83. C8×C22⋊D11C22semidirect
89. #10622715C22semidirect
90. #10622715C22semidirect
91. #10622715C22semidirect
93. C2×Dic11⋊C8C22semidirect
94. C2×Dic11⋊C8C22semidirect
95. C2×Dic11⋊C8C22semidirect
97. #10622625C22semidirect
98. #10622624C22semidirect
99. #10622624C22semidirect
100. D4×C11⋊C8C22semidirect
103. #10622452C22semidirect
104. #10622452C22semidirect
105. D11×C4⋊C8C22semidirect
106. D11×C4⋊C8C22semidirect
107. #10622443C22semidirect
108. #10622443C22semidirect
109. #10622441C22semidirect
110. #10622441C22semidirect
114. #10622341C22semidirect
115. #10622341C22semidirect
117. (C22⋊D11)⋊C8C22semidirect
118. (C22⋊D11)⋊C8C22semidirect
119. #10622333C22semidirect
120. #10622333C22semidirect
121. #10622333C22semidirect
122. #10622333C22semidirect
123. #10622332C22semidirect
124. #10622331C22semidirect
125. #10622331C22semidirect
126. #10622331C22semidirect
127. #10622322C22semidirect
128. #10622318C22semidirect
129. #10622314C22semidirect
130. #10622314C22semidirect
131. #10622303C22semidirect
132. #10622298C22semidirect
133. #10622292C22semidirect
134. C8×Dic22C22semidirect
475. #2929D11semidirect
523. C22⋊D11#131semidirect
611. #435C2×D11semidirect
612. #435C2×D11semidirect
626. C8×D4C2×D11semidirect
627. C8×D4C2×D11semidirect
1046. C11#60271semidirect

Maximal subgroups

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

subgroupindex
#130821762
#130777732
#130777712
#130777692
#130777582
#130777512
#130777492
#130777362
#130777232
#130775602
#130775492
#130773482
#130773432
#130773382
#130773132
C2×C8×C22⋊D112
#130772762
#130772712
#130772562
#130771822
C2×#106227152
D11×#4242
C11×#29292
#6027111