Finite Group Databasebeta

← #15619015

Subgroups — #15619015

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#13082180C211yesmaximal, characteristic
2#13077784C212yesmaximal, complemented
3#13077783C212yesmaximal, complemented
4#13077774C212yesmaximal, complemented
5#13077763C212yesmaximal, complemented
6#13077753C212yesmaximal, complemented
7#13077752C212yesmaximal, complemented
8#13077738C212yesmaximal, complemented
9#13077730C212yesmaximal, complemented
10#13077559C211yesmaximal, characteristic, complemented
11#13077553C211yesmaximal, characteristic, complemented
12#13077351C211yesmaximal, characteristic, complemented
13#13077338C211yesmaximal, characteristic, complemented
14#13077338C211yesmaximal, characteristic, complemented
15#13077317C211yesmaximal, characteristic, complemented
16#13077308C211yesmaximal, characteristic, complemented
17C2×#10622449C211yesmaximal, characteristic, complemented
18#13077273C211yesmaximal, characteristic, complemented
19#13077273C211yesmaximal, characteristic, complemented
20#13077267C211yesmaximal, characteristic, complemented
21#13077177C211yesmaximal, characteristic, complemented
22D11×#424C211yesmaximal, characteristic, complemented
23C11×#2906C211yesmaximal, characteristic, complemented
24C2×C11×#131C2211yescharacteristic
25C2×C11×#131C2211yescharacteristic
26C4×C11×#41C2211yescharacteristic
27#10623359C2211yescharacteristic
28#10623359C2211yescharacteristic
29C2×M16×D11C2211yescharacteristic
30C2×M16×D11C2211yescharacteristic
31C22×#4313C2211yescharacteristic
32C22×C8×D11C2211yescharacteristic
33#10623115C411yescharacteristic
34#10623112C411yescharacteristic
35#10623112C411yescharacteristic
36#10623110C411yescharacteristic
37#10623094C411yescharacteristic
38#10623089C411yescharacteristic
39#10623089C411yescharacteristic
40#10623087C412yes—
41#10623087C412yes—
42#10623082C411yescharacteristic
43#10623081C412yes—
44#10623072C412yes—
45#10623059C2212yes—
46#10623059C2212yes—
47D11×#117C2211yescharacteristic
48D11×#117C2211yescharacteristic
49#10623010C2212yes—
50C4×#4339C2212yes—
51C2×C4×D44C2211yescharacteristic
52#10623001C2211yescharacteristic
53C11×#424C2211yescharacteristic
54C11×#424C2211yescharacteristic
55C11×#424C2212yescomplemented
56C11×#424C2212yescomplemented
57C11×#423C2211yescharacteristic
58C11×#423C2212yescomplemented
59C2×C11×C4⋊C8C2211yescharacteristic
60C2×C11×C4⋊C8C2212yescomplemented
61#10622847C2211yescharacteristic
62#10622847C2211yescharacteristic
63#10622741C2212yescomplemented
64#10622741C2212yescomplemented
65#10622741C2212yescomplemented
66#10622741C2212yescomplemented
67#10622740C2212yescomplemented
68#10622740C2212yescomplemented
69#10622740C2212yescomplemented
70#10622740C2212yescomplemented
71#10622739C2211yescharacteristic
72#10622739C2211yescharacteristic
73#10622735C2211yescharacteristic
74#10622735C2211yescharacteristic
75#10622732C2211yescharacteristic
76#10622732C2211yescharacteristic
77#10622724C2212yescomplemented
78#10622724C2212yescomplemented
79#10622724C2212yescomplemented
80#10622724C2212yescomplemented
81C8×C22⋊D11C2212yescomplemented
82C8×C22⋊D11C2212yescomplemented
83C8×C22⋊D11C2212yescomplemented
84C8×C22⋊D11C2212yescomplemented
85C2×(C2×D11)⋊C8C2211yescharacteristic
86C2×(C2×D11)⋊C8C2211yescharacteristic
87#10622715C2211yescharacteristic
88#10622715C2211yescharacteristic
89#10622714C2211yescharacteristic
90#10622714C2211yescharacteristic
91#10622613C2212yescomplemented
92#10622613C2212yescomplemented
93#10622612C2211yescharacteristic
94#10622612C2211yescharacteristic
95#10622539C2212yescomplemented
96#10622539C2212yescomplemented
97C4×#4318C2211yescharacteristic
98C2×#66867C2211yescharacteristic
99#10622453C2212yescomplemented
100#10622453C2212yescomplemented
101#10622453C2212yescomplemented
102#10622453C2212yescomplemented
103#10622452C2212yescomplemented
104#10622452C2212yescomplemented
105#10622452C2212yescomplemented
106#10622452C2212yescomplemented
107#10622451C2212yes—
108#10622450C2212yescomplemented
109#10622450C2212yescomplemented
110#10622449C2211yescharacteristic
111#10622449C2211yescharacteristic
112#10622449C2211yescharacteristic
113#10622449C2212yes—
114#10622449C2211yescharacteristic
115#10622449C2211yescharacteristic
116#10622449C2211yescharacteristic
117#10622449C2211yescharacteristic
118#10622449C2211yescharacteristic
119#10622449C2212yes—
120#10622448C2212yescomplemented
121#10622448C2212yescomplemented
122#10622447C2212yes—
123#10622446C2212yescomplemented
124#10622446C2212yescomplemented
125D11×C4⋊C8C2212yescomplemented
126D11×C4⋊C8C2212yescomplemented
127#10622444C2212yescomplemented
128#10622443C2212yescomplemented
129#10622441C2212yescomplemented
130#10622441C2212yescomplemented
131#10622441C2212yescomplemented
132#10622441C2212yescomplemented
133#10622441C2212yescomplemented
134#10622441C2212yescomplemented
135C2×C11×#41C2311yescharacteristic
136C2×#4339C2×C412yes—
137C22×D44C2×C411yescharacteristic
138C22×C4×D11C2311yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C11×#131—42no—
141C11×#131—42no—
142C2×C11×M16C2311yescharacteristic
143C2×C11×M16C2311yescharacteristic
144C2×C11×M16C2312yes—
145C2×C11×M16C2312yes—
146C22×C8×C11C2311yescharacteristic
147C22×C8×C11C2311yescharacteristic
148C22×C8×C11C2312yes—
149C22×C8×C11C2312yes—
150C4×Q8×C11C2×C411yescharacteristic
151C4×Q8×C11C2×C411yescharacteristic
152C4×D4×C11C2×C412yes—
153C4×D4×C11C2×C411yescharacteristic
154C4×D4×C11C2×C412yes—
155C4×D4×C11C2×C411yescharacteristic
156C11×#117C2311yescharacteristic
157C11×#117C2312yes—
158C2×C42×C11C2311yescharacteristic
159C2×C42×C11C2312yes—
160#66999C2×C411yescharacteristic
161#66999C2×C411yescharacteristic
162#66999C2×C411yescharacteristic
163#66999C2×C411yescharacteristic
164#66991C2×C411yescharacteristic
165#66991C2×C411yescharacteristic
166#66991C2×C411yescharacteristic
167#66991C2×C411yescharacteristic
168#66990C2×C412yes—
169#66990C2×C412yes—
170#66988C2×C412yes—
171#66988C2×C412yes—
172#66983C2×C412yes—
173#66982C2×C412yes—
174#66982C2×C412yes—
175C4×C22⋊D11C2×C412yes—
176C4×C22⋊D11C2×C412yes—
177C4×C22⋊D11C2312yes—
178C4×C22⋊D11C2312yes—
179C4×C22⋊D11C2312yes—
180C4×C22⋊D11C2312yes—
181C2×(C2×D11)⋊C4C2×C411yescharacteristic
182C2×(C2×D11)⋊C4C2×C411yescharacteristic
183#66979C2×C412yes—
184#66979C2311yescharacteristic
185#66979C2311yescharacteristic
186C2×C4⋊Dic11C2×C411yescharacteristic
187#66977C2×C412yes—
188#66977C2×C412yes—
189#66977C2×C412yes—
190C2×#4318C2311yescharacteristic
191C2×#4318C2311yescharacteristic
192C22×C11⋊C8C2311yescharacteristic
193C22×C11⋊C8C2311yescharacteristic
194M16×D11—42no—
195M16×D11—42no—
196C2×#4313—42no—
197C2×#4313C2311yescharacteristic
198C2×#4313C2311yescharacteristic
199C2×#4313C2312yes—
200C2×#4313C2312yes—
201C2×#4313C2311yescharacteristic
202C2×#4313C2311yescharacteristic
203C2×C8×D11—42no—
204C2×C8×D11C2311yescharacteristic
205C2×C8×D11C2311yescharacteristic
206C2×C8×D11C2312yes—
207C2×C8×D11C2312yes—
208C2×C8×D11C2311yescharacteristic
209C2×C8×D11C2311yescharacteristic
210#66951C2×C412yes—
211#66951C2×C412yes—
212#66949C2×C412yes—
213#66949C2×C412yes—
214#66947C2×C412yes—
215#66947C2×C412yes—
216#66945C2×C411yescharacteristic
217#66945C2×C411yescharacteristic
218#66945C2×C411yescharacteristic
219#66945C2×C411yescharacteristic
220C4⋊C4×D11C2×C411yescharacteristic
221C4⋊C4×D11C2×C411yescharacteristic
222C4⋊C4×D11C2×C411yescharacteristic
223C4⋊C4×D11C2×C411yescharacteristic
224#66942C2×C412yes—
225#66942C2×C412yes—
226#66938C2×C412yes—
227#66938C2×C412yes—
228#66937C2×C412yes—
229#66937C2×C412yes—
230#66936C2×C412yes—
231#66936C2×C412yes—
232C22⋊C4×D11C2×C412yes—
233C22⋊C4×D11C2×C412yes—
234#66932C2×C412yes—
235#66932C2×C412yes—
236#66930C2×C412yes—
237#66930C2×C412yes—
238#66929C2×C412yes—
239#66929C2×C412yes—
240#66928C2×C412yes—
241C4×D44C2×C411yescharacteristic
242C4×D44C2×C411yescharacteristic
243C4×D44C2×C411yescharacteristic
244C4×D44C2×C411yescharacteristic
245C4×D44C2×C412yes—
246C4×D44C2311yescharacteristic
247C4×D44C2311yescharacteristic
248C4×D44C2311yescharacteristic
249C4×D44C2311yescharacteristic
250#66925C2×C412yes—
251#66925C2×C412yes—
252#66925C2312yes—
253#66925C2312yes—
254C42×D11C2312yes—
255C42×D11C2312yes—
256#66923C2×C411yescharacteristic
257#66923C2×C411yescharacteristic
258#66923C2×C412yes—
259#66922C2×C411yescharacteristic
260#66922C2×C411yescharacteristic
261C4×Dic22C2×C412yes—
262C4×Dic22C2312yes—
263C4×Dic22C2312yes—
264C11×C4⋊C8C2311yescharacteristic
265C11×C4⋊C8C2311yescharacteristic
266C11×C4⋊C8C2311yescharacteristic
267C11×C4⋊C8C2311yescharacteristic
268C11×C4⋊C8C2312yes—
269C11×C4⋊C8C2312yes—
270C11×C4⋊C8C2312yes—
271C11×C4⋊C8C2312yes—
272C11×C4⋊C8C2312yes—
273C11×C4⋊C8C2312yes—
274C22⋊(C11⋊C8)C2312yes—
275C22⋊(C11⋊C8)C2312yes—
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)⋊C8C2311yescharacteristic
283(C2×D11)⋊C8C2311yescharacteristic
284(C2×D11)⋊C8C2311yescharacteristic
285(C2×D11)⋊C8C2311yescharacteristic
286(C2×D11)⋊C8C2312yes—
287(C2×D11)⋊C8C2312yes—
288(C2×D11)⋊C8C2312yes—
289(C2×D11)⋊C8C2312yes—
290#66879C2312yes—
291#66879C2312yes—
292#66879C2312yes—
293#66879C2312yes—
294Dic11⋊C8C2312yes—
295Dic11⋊C8C2312yes—
296Dic11⋊C8C2312yes—
297Dic11⋊C8C2312yes—
298Dic11⋊C8C2312yes—
299Dic11⋊C8C2312yes—
300Dic11⋊C8C2312yes—
301Dic11⋊C8C2312yes—
302C8×Dic11C2312yes—
303C8×Dic11C2312yes—
304C8×Dic11C2312yes—
305C8×Dic11C2312yes—
306C4⋊(C11⋊C8)C2312yes—
307C4⋊(C11⋊C8)C2312yes—
308C4⋊(C11⋊C8)C2312yes—
309C4⋊(C11⋊C8)C2312yes—
310#66867C2311yescharacteristic
311#66867C2311yescharacteristic
312#66867C2311yescharacteristic
313#66867C2311yescharacteristic
314#66867C2312yes—
315C4×C11⋊C8C2312yes—
316#60272—111nomaximal, Sylow
317C23×D11C22×C411yescharacteristic
318C23×D11C22×C411yescharacteristic
319C11×#41—22no—
320C11×#41—22no—
321C2×Q8×C11C22×C411yescharacteristic
322C2×D4×C11C22×C412yes—
323C2×D4×C11C22×C411yescharacteristic
324C22×C4×C11C22×C411yescharacteristic
325C22×C4×C11C22×C411yescharacteristic
326C22×C4×C11C22×C412yes—
327C22×C4×C11C22×C412yes—
328C22×C4×C11C2412yes—
329C22×C4×C11C2411yescharacteristic
330C2×C22⋊D11C22×C412yes—
331C2×C22⋊D11C22×C412yes—
332C2×C22⋊D11C22×C412yes—
333C2×C22⋊D11C22×C412yes—
334C22×Dic11C22×C411yescharacteristic
335C22×Dic11C22×C411yescharacteristic
336#4339—44no—
337C2×D44—42no—
338C2×D44C22×C411yescharacteristic
339C2×D44C22×C411yescharacteristic
340C2×D44C22×C411yescharacteristic
341C2×D44C22×C411yescharacteristic
342C2×C4×D11—22no—
343C2×C4×D11—22no—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11C22×C412yes—
347C2×C4×D11C22×C411yescharacteristic
348C2×C4×D11C22×C411yescharacteristic
349C2×C4×D11C22×C411yescharacteristic
350C2×C4×D11C22×C411yescharacteristic
351C2×C4×D11C22×C412yes—
352C2×C4×D11C22×C412yes—
353C2×C4×D11C22×C412yes—
354C2×C4×D11C2411yescharacteristic
355C2×C4×D11C2411yescharacteristic
356C2×C4×D11C2411yescharacteristic
357C2×C4×D11C2411yescharacteristic
358C2×Dic22C22×C412yes—
359C2×Dic22C22×C412yes—
360C11×M16—22no—
361C11×M16—22no—
362C11×M16—42no—
363C11×M16—42no—
364C2×C8×C11—22no—
365C2×C8×C11—22no—
366C2×C8×C11—42no—
367C2×C8×C11—42no—
368C2×C8×C11C2411yescharacteristic
369C2×C8×C11C2411yescharacteristic
370C2×C8×C11C2412yes—
371C2×C8×C11C2412yes—
372C2×C8×C11C2411yescharacteristic
373C2×C8×C11C2411yescharacteristic
374C11×C4⋊C4C22×C412yes—
375C11×C4⋊C4C22×C411yescharacteristic
376C11×C4⋊C4C22×C411yescharacteristic
377C11×C4⋊C4C22×C412yes—
378C11×C22⋊C4C22×C412yes—
379C11×C22⋊C4C22×C412yes—
380C11×C22⋊C4C22×C412yes—
381C42×C11C22×C412yes—
382C42×C11C22×C411yescharacteristic
383C42×C11C22×C411yescharacteristic
384C42×C11C22×C412yes—
385C42×C11C2411yescharacteristic
386C42×C11C2411yescharacteristic
387C42×C11C2412yes—
388C22⋊Dic11C22×C412yes—
389C22⋊Dic11C22×C412yes—
390C22⋊Dic11C22×C412yes—
391C22⋊Dic11C22×C412yes—
392C22⋊Dic11C22×C412yes—
393C22⋊Dic11C22×C412yes—
394(C2×D11)⋊C4C22×C411yescharacteristic
395(C2×D11)⋊C4C22×C411yescharacteristic
396(C2×D11)⋊C4C22×C412yes—
397(C2×D11)⋊C4C22×C412yes—
398(C2×D11)⋊C4C22×C412yes—
399(C2×D11)⋊C4C22×C412yes—
400(C2×D11)⋊C4C22×C412yes—
401(C2×D11)⋊C4C22×C412yes—
402(C2×D11)⋊C4C22×C411yescharacteristic
403(C2×D11)⋊C4C22×C411yescharacteristic
404(C2×D11)⋊C4C22×C411yescharacteristic
405(C2×D11)⋊C4C22×C411yescharacteristic
406(C2×D11)⋊C4C22×C411yescharacteristic
407(C2×D11)⋊C4C22×C411yescharacteristic
408(C2×D11)⋊C4C22×C412yes—
409(C2×D11)⋊C4C22×C412yes—
410C4⋊Dic11C22×C411yescharacteristic
411C4⋊Dic11C22×C412yes—
412C4⋊Dic11C22×C412yes—
413C4⋊Dic11C22×C411yescharacteristic
414C4⋊Dic11C22×C411yescharacteristic
415C4⋊Dic11C22×C411yescharacteristic
416C4⋊Dic11C22×C411yescharacteristic
417C4⋊Dic11C22×C411yescharacteristic
418C4⋊Dic11C22×C411yescharacteristic
419C4⋊Dic11C22×C411yescharacteristic
420Dic11⋊C4C22×C412yes—
421Dic11⋊C4C22×C412yes—
422Dic11⋊C4C22×C412yes—
423Dic11⋊C4C22×C412yes—
424Dic11⋊C4C22×C412yes—
425Dic11⋊C4C22×C412yes—
426Dic11⋊C4C22×C412yes—
427Dic11⋊C4C22×C412yes—
428Dic11⋊C4C22×C412yes—
429Dic11⋊C4C22×C412yes—
430Dic11⋊C4C22×C412yes—
431Dic11⋊C4C22×C412yes—
432C4×Dic11C22×C412yes—
433C4×Dic11C22×C412yes—
434C4×Dic11C22×C412yes—
435C4×Dic11C22×C412yes—
436C4×Dic11C2412yes—
437C4×Dic11C2412yes—
438#4318—22no—
439#4318—22no—
440C2×C11⋊C8—22no—
441C2×C11⋊C8—22no—
442C2×C11⋊C8C2412yes—
443C2×C11⋊C8C2412yes—
444C2×C11⋊C8C2411yescharacteristic
445C2×C11⋊C8C2411yescharacteristic
446C2×C11⋊C8C2411yescharacteristic
447C2×C11⋊C8C2411yescharacteristic
448#4313—41no—
449#4313—41no—
450#4313—41no—
451#4313—41no—
452#4313—42no—
453#4313—42no—
454C8×D11—41no—
455C8×D11—41no—
456C8×D11—41no—
457C8×D11—41no—
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×M16—111no—
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#2906D1111yescharacteristic, complemented
481#2905—111no—
482C2×#424—111no—
483C23×C11C23×C412yes—
484C23×C11C23×C411yescharacteristic
485C22×D11—22no—
486C22×D11—22no—
487C22×D11—22no—
488C22×D11—41no—
489C22×D11—41no—
490C22×D11—41no—
491C22×D11C23×C411yescharacteristic
492C22×D11C23×C411yescharacteristic
493C22×D11C23×C411yescharacteristic
494C22×D11C23×C411yescharacteristic
495Q8×C11—22no—
496D4×C11—24no—
497D4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—41no—
501C2×C4×C11—42no—
502C2×C4×C11—41no—
503C2×C4×C11—42no—
504C2×C4×C11C23×C412yes—
505C2×C4×C11C23×C412yes—
506C2×C4×C11C23×C411yescharacteristic
507C2×C4×C11C23×C411yescharacteristic
508C2×C4×C11C23×C412yes—
509C2×C4×C11C23×C411yescharacteristic
510C2×C4×C11C23×C411yescharacteristic
511C2×C4×C11C23×C411yescharacteristic
512C2×C4×C11H(5,𝔽2)12yes—
513C2×C4×C112−1+412yes—
514C2×C4×C11C2511yescharacteristic
515C22⋊D11—24no—
516C22⋊D11—42no—
517C22⋊D11—42no—
518C22⋊D11—42no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11C23×C411yescharacteristic
522C2×Dic11C23×C411yescharacteristic
523C2×Dic11C23×C412yes—
524C2×Dic11C23×C412yes—
525C2×Dic11C23×C412yes—
526C2×Dic11C23×C412yes—
527C2×Dic11C23×C411yescharacteristic
528C2×Dic11C23×C411yescharacteristic
529D44—22no—
530D44—22no—
531D44—41no—
532D44—41no—
533C4×D11—24no—
534C4×D11—22no—
535C4×D11—22no—
536C4×D11—22no—
537C4×D11—22no—
538C4×D11—21no—
539C4×D11—21no—
540C4×D11—21no—
541C4×D11—21no—
542C4×D11—21no—
543C4×D11—21no—
544C4×D11—21no—
545C4×D11—21no—
546C4×D11—42no—
547C4×D11—42no—
548C4×D11—42no—
549Dic22—42no—
550Dic22—42no—
551C8×C11—21no—
552C8×C11—21no—
553C8×C11—22no—
554C8×C11—22no—
555C8×C11—21no—
556C8×C11—21no—
557C11⋊C8—21no—
558C11⋊C8—21no—
559C11⋊C8—22no—
560C11⋊C8—21no—
561C11⋊C8—21no—
562C11⋊C8—22no—
563C2×#131C2×D1111yescharacteristic
564C2×#131C2×D1111yescharacteristic
565C22×M16—111no—
566C22×M16—111no—
567C22×M16—111no—
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×#41C2×D1111yescharacteristic
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—
597#446—112no—
598#446—112no—
599C8×Q8—112no—
600#436—112no—
601#436—112no—
602#436—112no—
603#436—112no—
604#436—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#435—111no—
614#435—111no—
615#435—111no—
616#435—111no—
617#435—111no—
618#435—111no—
619#435—111no—
620#435—111no—
621#435—112no—
622#435—112no—
623C8×D4—112no—
624C8×D4—112no—
625C8×D4—112no—
626C8×D4—112no—
627C8×D4—112no—
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—112no—
647#424—112no—
648#424—112no—
649#424—112no—
650#424C2×D1111yescharacteristic
651#424C2×D1111yescharacteristic
652#424C2×D1112yescomplemented
653#424C2×D1112yescomplemented
654#423—112no—
655#423—112no—
656#423C2×D1111yescharacteristic
657#423C2×D1112yescomplemented
658C2×C4⋊C8—112no—
659C2×C4⋊C8—112no—
660C2×C4⋊C8C2×D1111yescharacteristic
661C2×C4⋊C8C2×D1112yescomplemented
662#408—111no—
663#408—111no—
664#407—111no—
665#407—111no—
666C2×C22⋊C8—111no—
667C2×C22⋊C8—111no—
668#405—111no—
669#405—111no—
670#405—111no—
671#405—111no—
672C4×M16—111no—
673C2×#97—111no—
674C22×C11—21no—
675C22×C11—21no—
676C22×C11—22no—
677C22×C11—22no—
678C22×C11—22no—
679C22×C11#52012yes—
680C22×C11C24×C411yescharacteristic
681C2×D11—21no—
682C2×D11—21no—
683C2×D11—21no—
684C2×D11—21no—
685C2×D11—21no—
686C2×D11—21no—
687C2×D11—21no—
688C2×D11—21no—
689C2×D11—21no—
690C2×D11—21no—
691C2×D11—21no—
692C2×D11—44no—
693C2×D11—82no—
694C2×D11#56812yes—
695C4×C11—22no—
696C4×C11—21no—
697C4×C11—22no—
698C4×C11—21no—
699C4×C11—21no—
700C4×C11—21no—
701C4×C11—22no—
702C4×C11#52012yes—
703C4×C11C2×H(5,𝔽2)11yescharacteristic
704C4×C11C2×2−1+411yescharacteristic
705Dic11—21no—
706Dic11—21no—
707Dic11—21no—
708Dic11—21no—
709Dic11—22no—
710Dic11—22no—
711Dic11—22no—
712Dic11—22no—
713C2×#41—112no—
714C2×#41C22×D1111yescharacteristic
715C22×D4—111no—
716C23×C4—111no—
717C23×C4—111no—
718#131—42no—
719#131—42no—
720C2×M16—111no—
721C2×M16—111no—
722C2×M16—111no—
723C2×M16—112no—
724C2×M16—111no—
725C2×M16—111no—
726C2×M16—112no—
727C2×M16—111no—
728C2×M16—442no—
729C2×M16—442no—
730C2×M16—442no—
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—112no—
742C22×C8—112no—
743C22×C8—442no—
744C22×C8C22×D1111yescharacteristic
745C22×C8C22×D1111yescharacteristic
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—111no—
782#121—111no—
783#121—111no—
784#121—111no—
785#121—112no—
786#121—112no—
787#121—112no—
788#120—112no—
789#120—112no—
790C4×Q8—112no—
791C4×Q8—112no—
792C4×Q8—112no—
793C4×Q8C4×D1111yescharacteristic
794C4×Q8C4×D1111yescharacteristic
795C4×D4—112no—
796C4×D4—112no—
797C4×D4—112no—
798C4×D4—112no—
799C4×D4—112no—
800C4×D4—112no—
801C4×D4—111no—
802C4×D4—111no—
803C4×D4—111no—
804C4×D4—111no—
805C4×D4—112no—
806C4×D4—111no—
807C4×D4—111no—
808C4×D4—111no—
809C4×D4—111no—
810C4×D4C4×D1112yes—
811C4×D4C4×D1111yescharacteristic
812C4×D4C4×D1112yes—
813C4×D4C4×D1111yescharacteristic
814#117—112no—
815#117—111no—
816#117—111no—
817#117—111no—
818#117—111no—
819#117—111no—
820#117—111no—
821#117—112no—
822#117—112no—
823#117—112no—
824#117—112no—
825#117—112no—
826#117—112no—
827#117C22×D1111yescharacteristic
828#117C22×D1112yes—
829C2×C4⋊C4—111no—
830C2×C4⋊C4—111no—
831C2×C4⋊C4—111no—
832C2×C4⋊C4—111no—
833C2×C4⋊C4—111no—
834C2×C22⋊C4—111no—
835C2×C22⋊C4—111no—
836C2×C22⋊C4—112no—
837C2×C22⋊C4—112no—
838C2×C42—112no—
839C2×C42—112no—
840C2×C42C22×D1111yescharacteristic
841C2×C42C22×D1112yes—
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⋊C8C22×D1112yes—
855C4⋊C8C22×D1112yes—
856C4⋊C8C22×D1111yescharacteristic
857C4⋊C8C22×D1111yescharacteristic
858C4⋊C8C22×D1111yescharacteristic
859C4⋊C8C22×D1111yescharacteristic
860C4⋊C8C22×D1112yes—
861C4⋊C8C22×D1112yes—
862C4⋊C8C22×D1112yes—
863C4⋊C8C22×D1112yes—
864C22⋊C8—112no—
865C22⋊C8—112no—
866C22⋊C8—112no—
867C22⋊C8—112no—
868C22⋊C8—111no—
869C22⋊C8—111no—
870C22⋊C8—111no—
871C22⋊C8—111no—
872C22⋊C8—111no—
873C22⋊C8—111no—
874C22⋊C8—111no—
875C22⋊C8—111no—
876C22⋊C8—112no—
877C22⋊C8—112no—
878C22⋊C8—112no—
879C22⋊C8—112no—
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#97—112no—
889C4×C8—112no—
890C4×C8—112no—
891C4×C8—112no—
892C4×C8—112no—
893C4×C8—112no—
894C2×C11—22no—
895C2×C11—42no—
896C2×C11C2×#52011yescharacteristic
897C2×C11C2×#56811yescharacteristic
898C2×C11#357311yescharacteristic
899D11—22no—
900D11—41no—
901D11—41no—
902D11—41no—
903C24—111no—
904C24—111no—
905#41—22no—
906#41—22no—
907#41—444no—
908C2×Q8—112no—
909C2×Q8—112no—
910C2×Q8C2×C4×D1111yescharacteristic
911C2×D4—112no—
912C2×D4—112no—
913C2×D4—112no—
914C2×D4—112no—
915C2×D4—111no—
916C2×D4—111no—
917C2×D4—111no—
918C2×D4—111no—
919C2×D4—442no—
920C2×D4C2×C4×D1112yes—
921C2×D4C2×C4×D1111yescharacteristic
922C22×C4—111no—
923C22×C4—111no—
924C22×C4—112no—
925C22×C4—111no—
926C22×C4—111no—
927C22×C4—111no—
928C22×C4—111no—
929C22×C4—111no—
930C22×C4—111no—
931C22×C4—111no—
932C22×C4—111no—
933C22×C4—112no—
934C22×C4—112no—
935C22×C4—112no—
936C22×C4—222no—
937C22×C4—222no—
938C22×C4—222no—
939C22×C4—222no—
940C22×C4C2×C4×D1111yescharacteristic
941C22×C4C2×C4×D1111yescharacteristic
942C22×C4C2×C4×D1112yes—
943C22×C4C2×C4×D1112yes—
944C22×C4C23×D1112yes—
945C22×C4C23×D1111yescharacteristic
946M16—22no—
947M16—22no—
948M16—42no—
949M16—42no—
950M16—222no—
951M16—222no—
952M16—441no—
953M16—441no—
954M16—441no—
955M16—441no—
956M16—442no—
957M16—442no—
958C2×C8—22no—
959C2×C8—22no—
960C2×C8—42no—
961C2×C8—42no—
962C2×C8—112no—
963C2×C8—111no—
964C2×C8—111no—
965C2×C8—112no—
966C2×C8—111no—
967C2×C8—111no—
968C2×C8—222no—
969C2×C8—222no—
970C2×C8—441no—
971C2×C8—441no—
972C2×C8—441no—
973C2×C8—441no—
974C2×C8—442no—
975C2×C8—442no—
976C2×C8C23×D1111yescharacteristic
977C2×C8C23×D1111yescharacteristic
978C2×C8C23×D1112yes—
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—112no—
1010C22⋊C4—112no—
1011C22⋊C4—112no—
1012C22⋊C4—112no—
1013C22⋊C4—112no—
1014C22⋊C4—111no—
1015C22⋊C4—111no—
1016C22⋊C4—112no—
1017C22⋊C4—112no—
1018C22⋊C4—112no—
1019C22⋊C4—112no—
1020C22⋊C4—111no—
1021C22⋊C4—111no—
1022C22⋊C4—111no—
1023C22⋊C4—111no—
1024C22⋊C4—111no—
1025C22⋊C4—111no—
1026C22⋊C4—112no—
1027C22⋊C4—112no—
1028C22⋊C4—112no—
1029C22⋊C4—112no—
1030C22⋊C4C2×C4×D1112yes—
1031C22⋊C4C2×C4×D1112yes—
1032C22⋊C4C2×C4×D1112yes—
1033C42—112no—
1034C42—112no—
1035C42—112no—
1036C42—112no—
1037C42—112no—
1038C42—112no—
1039C42C2×C4×D1112yes—
1040C42C2×C4×D1111yescharacteristic
1041C42C2×C4×D1111yescharacteristic
1042C42C2×C4×D1112yes—
1043C42C23×D1111yescharacteristic
1044C42C23×D1111yescharacteristic
1045C42C23×D1112yes—
1046C11#6027211yescharacteristic, complemented, Sylow
1047C23—111no—
1048C23—111no—
1049C23—111no—
1050C23—111no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—441no—
1055C23—441no—
1056C23—441no—
1057C23C22×C4×D1112yes—
1058C23C22×C4×D1111yescharacteristic
1059Q8—22no—
1060Q8—442no—
1061Q8—442no—
1062D4—24no—
1063D4—22no—
1064D4—222no—
1065D4—222no—
1066D4—224no—
1067D4—441no—
1068D4—441no—
1069D4—442no—
1070D4—442no—
1071D4—442no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—42no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—42no—
1078C2×C4—111no—
1079C2×C4—111no—
1080C2×C4—112no—
1081C2×C4—112no—
1082C2×C4—112no—
1083C2×C4—112no—
1084C2×C4—111no—
1085C2×C4—111no—
1086C2×C4—224no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—221no—
1094C2×C4—221no—
1095C2×C4—221no—
1096C2×C4—221no—
1097C2×C4—221no—
1098C2×C4—221no—
1099C2×C4—221no—
1100C2×C4—221no—
1101C2×C4—442no—
1102C2×C4—442no—
1103C2×C4—442no—
1104C2×C4C22×C4×D1112yes—
1105C2×C4C22×C4×D1112yes—
1106C2×C4C22×C4×D1111yescharacteristic
1107C2×C4C22×C4×D1111yescharacteristic
1108C2×C4C22×C4×D1112yes—
1109C2×C4C22×C4×D1111yescharacteristic
1110C2×C4C22×C4×D1111yescharacteristic
1111C2×C4C22×C4×D1111yescharacteristic
1112C2×C4#6703712yes—
1113C2×C4#6704012yes—
1114C2×C4C24×D1111yescharacteristic
1115C8—21no—
1116C8—21no—
1117C8—21no—
1118C8—21no—
1119C8—22no—
1120C8—22no—
1121C8—221no—
1122C8—221no—
1123C8—222no—
1124C8—221no—
1125C8—221no—
1126C8—222no—
1127C22—21no—
1128C22—21no—
1129C22—22no—
1130C22—22no—
1131C22—22no—
1132C22—112no—
1133C22—221no—
1134C22—221no—
1135C22—221no—
1136C22—221no—
1137C22—221no—
1138C22—221no—
1139C22—221no—
1140C22—221no—
1141C22—221no—
1142C22—221no—
1143C22—221no—
1144C22—444no—
1145C22—882no—
1146C22#1062303512yes—
1147C22C23×C4×D1111yescharacteristic
1148C4—21no—
1149C4—22no—
1150C4—21no—
1151C4—21no—
1152C4—22no—
1153C4—21no—
1154C4—22no—
1155C4—222no—
1156C4—222no—
1157C4—222no—
1158C4—222no—
1159C4—221no—
1160C4—221no—
1161C4—221no—
1162C4—221no—
1163C4#1062303512yes—
1164C4C2×#6703711yescharacteristic
1165C4C2×#6704011yescharacteristic
1166C2—22no—
1167C2—42no—
1168C2—222no—
1169C2—441no—
1170C2—441no—
1171C2—441no—
1172C2C2×#1062303511yescharacteristic
1173C2D11×#56811yescharacteristic
1174C2#1308332711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2906C2
prime radical#13082180C2
cosocleC2×C4×C11C25
hypercenter#2906D11
hypocenterC11#60272
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #13077784C2semidirect
3. #13077783C2semidirect
4. #13077774C2semidirect
5. #13077763C2semidirect
6. #13077753C2semidirect
7. #13077752C2semidirect
8. #13077738C2semidirect
9. #13077730C2semidirect
10. #13077559C2semidirect
11. #13077553C2semidirect
12. #13077351C2semidirect
13. #13077338C2semidirect
14. #13077338C2semidirect
15. #13077317C2semidirect
16. #13077308C2semidirect
17. C2×#10622449C2semidirect
18. #13077273C2semidirect
19. #13077273C2semidirect
20. #13077267C2semidirect
21. #13077177C2semidirect
22. D11×#424C2semidirect
23. C11×#2906C2semidirect
55. C11×#424C22semidirect
56. C11×#424C22semidirect
58. C11×#423C22semidirect
60. C2×C11×C4⋊C8C22semidirect
63. #10622741C22semidirect
64. #10622741C22semidirect
65. #10622741C22semidirect
66. #10622741C22semidirect
67. #10622740C22semidirect
68. #10622740C22semidirect
69. #10622740C22semidirect
70. #10622740C22semidirect
77. #10622724C22semidirect
78. #10622724C22semidirect
79. #10622724C22semidirect
80. #10622724C22semidirect
81. C8×C22⋊D11C22semidirect
82. C8×C22⋊D11C22semidirect
83. C8×C22⋊D11C22semidirect
84. C8×C22⋊D11C22semidirect
91. #10622613C22semidirect
92. #10622613C22semidirect
95. #10622539C22semidirect
96. #10622539C22semidirect
99. #10622453C22semidirect
100. #10622453C22semidirect
101. #10622453C22semidirect
102. #10622453C22semidirect
103. #10622452C22semidirect
104. #10622452C22semidirect
105. #10622452C22semidirect
106. #10622452C22semidirect
108. #10622450C22semidirect
109. #10622450C22semidirect
120. #10622448C22semidirect
121. #10622448C22semidirect
123. #10622446C22semidirect
124. #10622446C22semidirect
125. D11×C4⋊C8C22semidirect
126. D11×C4⋊C8C22semidirect
127. #10622444C22semidirect
128. #10622443C22semidirect
129. #10622441C22semidirect
130. #10622441C22semidirect
131. #10622441C22semidirect
132. #10622441C22semidirect
133. #10622441C22semidirect
134. #10622441C22semidirect
480. #2906D11semidirect
652. #424C2×D11semidirect
653. #424C2×D11semidirect
657. #423C2×D11semidirect
661. C2×C4⋊C8C2×D11semidirect
1046. C11#60272semidirect

Maximal subgroups

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

subgroupindex
#130821802
#130777842
#130777832
#130777742
#130777632
#130777532
#130777522
#130777382
#130777302
#130775592
#130775532
#130773512
#130773382
#130773172
#130773082
C2×#106224492
#130772732
#130772672
#130771772
D11×#4242
C11×#29062
#6027211