Finite Group Databasebeta

← #15619029

Subgroups — #15619029

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#13082183C211yesmaximal, characteristic
2#13077785C212yesmaximal, complemented
3#13077785C212yesmaximal, complemented
4#13077779C212yesmaximal, complemented
5#13077768C212yesmaximal, complemented
6#13077754C212yesmaximal, complemented
7#13077754C212yesmaximal, complemented
8#13077740C212yesmaximal, complemented
9#13077732C212yesmaximal, complemented
10#13077565C211yesmaximal, characteristic, complemented
11#13077351C211yesmaximal, characteristic, complemented
12#13077344C211yesmaximal, characteristic, complemented
13#13077344C211yesmaximal, characteristic, complemented
14#13077318C211yesmaximal, characteristic, complemented
15#13077309C211yesmaximal, characteristic, complemented
16C2×#10622319C211yesmaximal, characteristic, complemented
17#13077271C211yesmaximal, characteristic, complemented
18#13077271C211yesmaximal, characteristic, complemented
19#13077265C211yesmaximal, characteristic, complemented
20#13077185C211yesmaximal, characteristic, complemented
21#13077177C211yesmaximal, characteristic, complemented
22D11×#424C211yesmaximal, characteristic, complemented
23C11×#2961C211yesmaximal, characteristic, complemented
24C11×#533C2211yescharacteristic
25C2×#66960C2211yescharacteristic
26C2×#66960C2211yescharacteristic
27C2×M16×D11C2211yescharacteristic
28C2×M16×D11C2211yescharacteristic
29C22×#4313C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
31#10623265C411yescharacteristic
32#10623263C411yescharacteristic
33#10623261C411yescharacteristic
34#10623257C411yescharacteristic
35#10623226C411yescharacteristic
36#10623226C411yescharacteristic
37#10623225C411yescharacteristic
38#10623225C411yescharacteristic
39#10623173C412yes—
40#10623168C412yes—
41#10623168C412yes—
42#10623161C412yes—
43#10623111C2212yes—
44#10623111C2212yes—
45#10623111C2212yes—
46C4×#4343C2212yes—
47#10623055C2211yescharacteristic
48#10623055C2211yescharacteristic
49D11×#117C2211yescharacteristic
50D11×#117C2211yescharacteristic
51C4×#4339C2211yescharacteristic
52C2×C4×D44C2211yescharacteristic
53C11×#446C2212yescomplemented
54C11×#446C2212yescomplemented
55C11×#446C2212yescomplemented
56C11×#446C2212yescomplemented
57C11×#424C2211yescharacteristic
58C11×#424C2211yescharacteristic
59C11×#423C2211yescharacteristic
60C11×#405C2211yescharacteristic
61C11×#405C2211yescharacteristic
62C2×C11×#97C2211yescharacteristic
63#10622739C2211yescharacteristic
64#10622739C2211yescharacteristic
65#10622732C2211yescharacteristic
66#10622732C2211yescharacteristic
67#10622723C2211yescharacteristic
68#10622723C2211yescharacteristic
69C2×(C2×D11)⋊C8C2211yescharacteristic
70C2×(C2×D11)⋊C8C2211yescharacteristic
71#10622715C2211yescharacteristic
72#10622715C2211yescharacteristic
73#10622637C2212yescomplemented
74#10622637C2212yescomplemented
75#10622637C2212yescomplemented
76Q8×C11⋊C8C2212yescomplemented
77#10622612C2211yescharacteristic
78#10622612C2211yescharacteristic
79#10622610C2211yescharacteristic
80#10622610C2211yescharacteristic
81C2×C4⋊(C11⋊C8)C2211yescharacteristic
82C4×#4318C2211yescharacteristic
83#10622452C2212yescomplemented
84#10622452C2212yescomplemented
85#10622452C2212yescomplemented
86#10622452C2212yescomplemented
87#10622452C2212yescomplemented
88#10622452C2212yescomplemented
89#10622451C2212yes—
90#10622451C2212yescomplemented
91#10622451C2212yescomplemented
92#10622450C2212yescomplemented
93#10622450C2212yescomplemented
94#10622450C2212yescomplemented
95#10622449C2212yes—
96#10622449C2212yes—
97#10622449C2212yescomplemented
98#10622449C2212yescomplemented
99#10622449C2212yescomplemented
100#10622449C2212yescomplemented
101#10622447C2212yes—
102#10622447C2212yescomplemented
103#10622447C2212yescomplemented
104D11×C4⋊C8C2212yescomplemented
105D11×C4⋊C8C2212yescomplemented
106D11×C4⋊C8C2212yescomplemented
107#10622322C2212yescomplemented
108#10622322C2212yescomplemented
109#10622322C2212yescomplemented
110#10622322C2212yescomplemented
111#10622319C2211yescharacteristic
112#10622319C2211yescharacteristic
113#10622319C2211yescharacteristic
114#10622319C2211yescharacteristic
115#10622319C2211yescharacteristic
116#10622319C2211yescharacteristic
117#10622319C2211yescharacteristic
118#10622319C2211yescharacteristic
119#10622319C2212yescomplemented
120#10622319C2212yescomplemented
121#10622319C2212yescomplemented
122#10622319C2212yescomplemented
123#10622318C2212yescomplemented
124#10622318C2212yescomplemented
125#10622318C2212yescomplemented
126#10622318C2212yescomplemented
127#10622303C2212yescomplemented
128#10622303C2212yescomplemented
129#10622301C2212yescomplemented
130#10622301C2212yescomplemented
131C8×D44C2212yescomplemented
132C8×D44C2212yescomplemented
133#10622298C2212yescomplemented
134#10622298C2212yescomplemented
135C2×#4343C2×C412yes—
136C2×#4339C2311yescharacteristic
137C22×D44C2×C411yescharacteristic
138C22×C4×D11C2311yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C2×C11×M16C2311yescharacteristic
141C2×C11×M16C2311yescharacteristic
142C22×C8×C11C2311yescharacteristic
143C22×C8×C11C2311yescharacteristic
144C11×C4⋊Q8C2×C411yescharacteristic
145C11×C4⋊Q8C2×C411yescharacteristic
146C11×#125C2×C411yescharacteristic
147C11×#125C2×C411yescharacteristic
148C11×C22⋊Q8C2×C412yes—
149C11×C22⋊Q8C2×C412yes—
150C4×Q8×C11C2312yes—
151C4×Q8×C11C2312yes—
152C11×#117C2311yescharacteristic
153C11×#117C2311yescharacteristic
154C2×C42×C11C2311yescharacteristic
155#67000C2×C412yes—
156#67000C2×C412yes—
157#67000C2×C412yes—
158#66999C2×C412yes—
159#66999C2×C412yes—
160#66999C2×C412yes—
161Q8×Dic11C2×C412yes—
162C4×C22⋊D11C2×C412yes—
163C4×C22⋊D11C2×C412yes—
164C2×(C2×D11)⋊C4C2×C411yescharacteristic
165C2×(C2×D11)⋊C4C2×C411yescharacteristic
166#66979C2311yescharacteristic
167C2×C4⋊Dic11C2×C411yescharacteristic
168C2×#4318C2311yescharacteristic
169C2×#4318C2311yescharacteristic
170C22×C11⋊C8C2311yescharacteristic
171C22×C11⋊C8C2311yescharacteristic
172#66960—42no—
173#66960—42no—
174M16×D11—42no—
175M16×D11—42no—
176C2×#4313—42no—
177C2×#4313C2311yescharacteristic
178C2×#4313C2311yescharacteristic
179C2×#4313C2311yescharacteristic
180C2×#4313C2311yescharacteristic
181C2×#4313C2312yes—
182C2×#4313C2312yes—
183C2×#4313C2312yes—
184C2×#4313C2312yes—
185C2×C8×D11—42no—
186C2×C8×D11C2311yescharacteristic
187C2×C8×D11C2311yescharacteristic
188C2×C8×D11C2311yescharacteristic
189C2×C8×D11C2311yescharacteristic
190C2×C8×D11C2312yes—
191C2×C8×D11C2312yes—
192C2×C8×D11C2312yes—
193C2×C8×D11C2312yes—
194#66951C2×C412yes—
195#66951C2×C412yes—
196#66951C2×C412yes—
197#66951C2×C412yes—
198#66951C2×C412yes—
199#66951C2×C412yes—
200#66950C2×C411yescharacteristic
201#66950C2×C411yescharacteristic
202#66950C2×C411yescharacteristic
203#66950C2×C411yescharacteristic
204#66948C2×C411yescharacteristic
205#66948C2×C411yescharacteristic
206#66948C2×C411yescharacteristic
207#66948C2×C411yescharacteristic
208#66948C2×C412yes—
209#66948C2×C412yes—
210#66948C2×C412yes—
211#66947C2×C412yes—
212#66947C2×C412yes—
213#66947C2×C412yes—
214#66947C2×C412yes—
215#66947C2×C412yes—
216#66947C2×C412yes—
217#66946C2×C412yes—
218#66946C2×C412yes—
219#66946C2×C412yes—
220#66945C2×C411yescharacteristic
221#66945C2×C411yescharacteristic
222#66945C2×C411yescharacteristic
223#66945C2×C411yescharacteristic
224#66945C2×C412yes—
225#66945C2×C412yes—
226#66945C2×C412yes—
227C4⋊C4×D11C2×C411yescharacteristic
228C4⋊C4×D11C2×C411yescharacteristic
229C4⋊C4×D11C2×C411yescharacteristic
230C4⋊C4×D11C2×C411yescharacteristic
231#66943C2×C412yes—
232#66943C2×C412yes—
233#66943C2×C412yes—
234#66939C2×C412yes—
235#66939C2×C412yes—
236#66935C2×C412yes—
237#66935C2×C412yes—
238C22⋊C4×D11C2×C412yes—
239C22⋊C4×D11C2×C412yes—
240#66930C2×C412yes—
241#66930C2×C412yes—
242C4×D44C2×C411yescharacteristic
243C4×D44C2×C411yescharacteristic
244C4×D44C2×C411yescharacteristic
245C4×D44C2×C411yescharacteristic
246C4×D44C2×C411yescharacteristic
247C4×D44C2×C411yescharacteristic
248C4×D44C2311yescharacteristic
249C4×D44C2311yescharacteristic
250C4×D44C2311yescharacteristic
251C4×D44C2311yescharacteristic
252C4×D44C2312yes—
253C4×D44C2312yes—
254C4×D44C2312yes—
255C4×D44C2312yes—
256#66925C2312yes—
257#66925C2312yes—
258#66925C2312yes—
259C42×D11C2312yes—
260C42×D11C2312yes—
261C42×D11C2312yes—
262C4×Dic22C2×C411yescharacteristic
263C4×Dic22C2×C411yescharacteristic
264C11×C4⋊C8C2312yes—
265C11×C4⋊C8C2312yes—
266C11×C4⋊C8C2312yes—
267C11×C4⋊C8C2312yes—
268C11×C4⋊C8C2312yes—
269C11×C4⋊C8C2312yes—
270C11×#97C2311yescharacteristic
271C11×#97C2311yescharacteristic
272C11×#97C2312yes—
273C11×#97C2312yes—
274C11×#97C2311yescharacteristic
275C11×#97C2311yescharacteristic
276C4×C8×C11C2312yes—
277C4×C8×C11C2312yes—
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(C2×D11)⋊C8C2312yes—
291(C2×D11)⋊C8C2312yes—
292(C2×D11)⋊C8C2312yes—
293(C2×D11)⋊C8C2312yes—
294Dic11⋊C8C2312yes—
295Dic11⋊C8C2312yes—
296Dic11⋊C8C2312yes—
297Dic11⋊C8C2312yes—
298Dic11⋊C8C2312yes—
299Dic11⋊C8C2312yes—
300Dic11⋊C8C2312yes—
301Dic11⋊C8C2312yes—
302C4⋊(C11⋊C8)C2311yescharacteristic
303C4⋊(C11⋊C8)C2311yescharacteristic
304C4⋊(C11⋊C8)C2311yescharacteristic
305C4⋊(C11⋊C8)C2311yescharacteristic
306C4⋊(C11⋊C8)C2312yes—
307C4⋊(C11⋊C8)C2312yes—
308C4⋊(C11⋊C8)C2312yes—
309C4⋊(C11⋊C8)C2312yes—
310#66867C2312yes—
311#66867C2312yes—
312#66867C2312yes—
313C4×C11⋊C8C2312yes—
314C4×C11⋊C8C2312yes—
315C4×C11⋊C8C2312yes—
316#60272—111nomaximal, Sylow
317C23×D11C22×C411yescharacteristic
318C23×D11C22×C411yescharacteristic
319C2×Q8×C11C22×C412yes—
320C2×Q8×C11C22×C412yes—
321C22×C4×C11C22×C411yescharacteristic
322C22×C4×C11C22×C411yescharacteristic
323C22×C4×C11C2411yescharacteristic
324C2×C22⋊D11C22×C412yes—
325C22×Dic11C22×C411yescharacteristic
326C22×Dic11C22×C411yescharacteristic
327#4343—44no—
328#4339—22no—
329#4339—22no—
330C2×D44—42no—
331C2×D44C22×C411yescharacteristic
332C2×D44C22×C411yescharacteristic
333C2×D44C22×C411yescharacteristic
334C2×D44C22×C412yes—
335C2×D44C22×C411yescharacteristic
336C2×D44C22×C411yescharacteristic
337C2×D44C22×C412yes—
338C2×D44C22×C412yes—
339C2×D44C22×C412yes—
340C2×C4×D11—22no—
341C2×C4×D11—22no—
342C2×C4×D11—22no—
343C2×C4×D11—22no—
344C2×C4×D11C22×C412yes—
345C2×C4×D11C22×C411yescharacteristic
346C2×C4×D11C22×C411yescharacteristic
347C2×C4×D11C22×C411yescharacteristic
348C2×C4×D11C22×C411yescharacteristic
349C2×C4×D11C22×C412yes—
350C2×C4×D11C22×C412yes—
351C2×C4×D11C22×C412yes—
352C2×C4×D11C22×C412yes—
353C2×C4×D11C22×C412yes—
354C2×C4×D11C2411yescharacteristic
355C2×C4×D11C2411yescharacteristic
356C2×C4×D11C2412yes—
357C2×C4×D11C2411yescharacteristic
358C2×C4×D11C2411yescharacteristic
359C2×Dic22C22×C411yescharacteristic
360C11×M16—22no—
361C11×M16—22no—
362C2×C8×C11—22no—
363C2×C8×C11—22no—
364C2×C8×C11C2411yescharacteristic
365C2×C8×C11C2411yescharacteristic
366C2×C8×C11C2412yes—
367C2×C8×C11C2412yes—
368C2×C8×C11C2411yescharacteristic
369C2×C8×C11C2411yescharacteristic
370C11×C4⋊C4C22×C412yes—
371C11×C4⋊C4C22×C412yes—
372C11×C4⋊C4C22×C412yes—
373C11×C4⋊C4C22×C411yescharacteristic
374C11×C4⋊C4C22×C411yescharacteristic
375C11×C4⋊C4C22×C411yescharacteristic
376C11×C4⋊C4C22×C411yescharacteristic
377C11×C4⋊C4C22×C412yes—
378C11×C4⋊C4C22×C412yes—
379C11×C4⋊C4C22×C412yes—
380C11×C22⋊C4C22×C412yes—
381C11×C22⋊C4C22×C412yes—
382C42×C11C22×C411yescharacteristic
383C42×C11C22×C411yescharacteristic
384C42×C11C2411yescharacteristic
385C42×C11C2412yes—
386C42×C11C2412yes—
387C42×C11C2411yescharacteristic
388C22⋊Dic11C22×C412yes—
389(C2×D11)⋊C4C22×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×C411yescharacteristic
396(C2×D11)⋊C4C22×C411yescharacteristic
397(C2×D11)⋊C4C22×C411yescharacteristic
398(C2×D11)⋊C4C22×C411yescharacteristic
399(C2×D11)⋊C4C22×C411yescharacteristic
400(C2×D11)⋊C4C22×C411yescharacteristic
401(C2×D11)⋊C4C22×C411yescharacteristic
402(C2×D11)⋊C4C22×C411yescharacteristic
403(C2×D11)⋊C4C22×C412yes—
404(C2×D11)⋊C4C22×C412yes—
405(C2×D11)⋊C4C22×C412yes—
406(C2×D11)⋊C4C22×C412yes—
407(C2×D11)⋊C4C22×C412yes—
408(C2×D11)⋊C4C22×C412yes—
409(C2×D11)⋊C4C22×C412yes—
410(C2×D11)⋊C4C22×C412yes—
411C4⋊Dic11C22×C411yescharacteristic
412C4⋊Dic11C22×C411yescharacteristic
413C4⋊Dic11C22×C411yescharacteristic
414C4⋊Dic11C22×C411yescharacteristic
415C4⋊Dic11C22×C411yescharacteristic
416C4⋊Dic11C22×C411yescharacteristic
417C4⋊Dic11C22×C412yes—
418C4⋊Dic11C22×C412yes—
419C4⋊Dic11C22×C412yes—
420C4⋊Dic11C22×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—
434#4318—22no—
435#4318—22no—
436C2×C11⋊C8—22no—
437C2×C11⋊C8—22no—
438C2×C11⋊C8C2412yes—
439C2×C11⋊C8C2411yescharacteristic
440C2×C11⋊C8C2411yescharacteristic
441C2×C11⋊C8C2412yes—
442C2×C11⋊C8C2411yescharacteristic
443C2×C11⋊C8C2411yescharacteristic
444#4313—41no—
445#4313—41no—
446#4313—41no—
447#4313—41no—
448#4313—42no—
449#4313—42no—
450#4313—42no—
451#4313—42no—
452C8×D11—41no—
453C8×D11—41no—
454C8×D11—41no—
455C8×D11—41no—
456C8×D11—42no—
457C8×D11—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#2961D1111yescharacteristic, complemented
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#2906—111no—
481#2905—111no—
482C2×#424—111no—
483C23×C11C23×C411yescharacteristic
484C22×D11—22no—
485C22×D11—22no—
486C22×D11—22no—
487C22×D11—41no—
488C22×D11—41no—
489C22×D11—41no—
490C22×D11C23×C411yescharacteristic
491C22×D11C23×C411yescharacteristic
492C22×D11C23×C412yes—
493C22×D11C23×C411yescharacteristic
494C22×D11C23×C411yescharacteristic
495Q8×C11—42no—
496Q8×C11—42no—
497C2×C4×C11—41no—
498C2×C4×C11—41no—
499C2×C4×C11C23×C411yescharacteristic
500C2×C4×C11C23×C411yescharacteristic
501C2×C4×C11C23×C412yes—
502C2×C4×C11C23×C412yes—
503C2×C4×C11C23×C412yes—
504C2×C4×C11C23×C412yes—
505C2×C4×C11C23×C411yescharacteristic
506C2×C4×C11C23×C411yescharacteristic
507C2×C4×C11C23×C411yescharacteristic
508C2×C4×C11H(5,𝔽2)12yes—
509C2×C4×C112−1+412yes—
510C2×C4×C11C2511yescharacteristic
511C22⋊D11—24no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11C23×C411yescharacteristic
515C2×Dic11C23×C411yescharacteristic
516C2×Dic11C23×C412yes—
517C2×Dic11C23×C412yes—
518C2×Dic11C23×C412yes—
519C2×Dic11C23×C411yescharacteristic
520C2×Dic11C23×C411yescharacteristic
521D44—22no—
522D44—22no—
523D44—24no—
524D44—22no—
525D44—41no—
526D44—41no—
527D44—42no—
528D44—42no—
529D44—42no—
530C4×D11—24no—
531C4×D11—22no—
532C4×D11—22no—
533C4×D11—22no—
534C4×D11—22no—
535C4×D11—21no—
536C4×D11—21no—
537C4×D11—21no—
538C4×D11—22no—
539C4×D11—21no—
540C4×D11—21no—
541C4×D11—21no—
542C4×D11—21no—
543C4×D11—21no—
544C4×D11—22no—
545C4×D11—42no—
546C4×D11—42no—
547C4×D11—42no—
548C4×D11—42no—
549C4×D11—42no—
550Dic22—22no—
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—21no—
560C11⋊C8—22no—
561C11⋊C8—21no—
562C11⋊C8—22no—
563C2×#131—111no—
564C2×#131—111no—
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#533C2×D1111yescharacteristic
582#529—112no—
583#529—112no—
584#529—112no—
585#525—111no—
586#525—111no—
587C4×#41—112no—
588C4×#41—111no—
589C2×C4×D4—111no—
590C2×#117—111no—
591C2×#117—111no—
592#446—112no—
593#446—112no—
594#446—112no—
595#446C2×D1112yescomplemented
596#446C2×D1112yescomplemented
597#446C2×D1112yescomplemented
598#446C2×D1112yescomplemented
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—111no—
612#435—111no—
613#435—111no—
614#435—111no—
615#435—111no—
616#435—111no—
617#435—111no—
618#435—111no—
619#435—112no—
620#435—112no—
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#424—112no—
651#424—112no—
652#424C2×D1111yescharacteristic
653#424C2×D1111yescharacteristic
654#423—112no—
655#423—112no—
656#423—112no—
657#423C2×D1111yescharacteristic
658C2×C4⋊C8—111no—
659C2×C4⋊C8—112no—
660C2×C4⋊C8—112no—
661C2×C4⋊C8—112no—
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#405C2×D1111yescharacteristic
671#405C2×D1111yescharacteristic
672C4×M16—111no—
673C2×#97C2×D1111yescharacteristic
674C22×C11—21no—
675C22×C11—21no—
676C22×C11#52012yes—
677C22×C11C24×C411yescharacteristic
678C2×D11—21no—
679C2×D11—21no—
680C2×D11—21no—
681C2×D11—21no—
682C2×D11—21no—
683C2×D11—22no—
684C2×D11—21no—
685C2×D11—21no—
686C2×D11—21no—
687C2×D11—22no—
688C2×D11—21no—
689C2×D11—21no—
690C2×D11—21no—
691C2×D11—22no—
692C2×D11—44no—
693C2×D11—82no—
694C2×D11#56812yes—
695C4×C11—21no—
696C4×C11—21no—
697C4×C11—22no—
698C4×C11—22no—
699C4×C11—21no—
700C4×C11—21no—
701C4×C11—22no—
702C4×C11—22no—
703C4×C11#52012yes—
704C4×C11C2×H(5,𝔽2)11yescharacteristic
705C4×C11C2×2−1+411yescharacteristic
706Dic11—22no—
707Dic11—21no—
708Dic11—21no—
709Dic11—21no—
710Dic11—21no—
711Dic11—22no—
712Dic11—22no—
713C2×#41—112no—
714C2×#41—111no—
715C22×D4—111no—
716C23×C4—111no—
717C23×C4—111no—
718#131—442no—
719#131—442no—
720C2×M16—111no—
721C2×M16—111no—
722C2×M16—111no—
723C2×M16—111no—
724C2×M16—112no—
725C2×M16—111no—
726C2×M16—111no—
727C2×M16—112no—
728C2×M16—112no—
729C2×M16—112no—
730C2×M16—442no—
731C2×M16—442no—
732C2×M16—442no—
733C2×M16C22×D1111yescharacteristic
734C2×M16C22×D1111yescharacteristic
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—112no—
744C22×C8—112no—
745C22×C8—442no—
746C22×C8C22×D1111yescharacteristic
747C22×C8C22×D1111yescharacteristic
748C4⋊Q8C4×D1111yescharacteristic
749C4⋊Q8C4×D1111yescharacteristic
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#125C4×D1111yescharacteristic
760#125C4×D1111yescharacteristic
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—112no—
773C22⋊Q8—112no—
774C22⋊Q8—112no—
775C22⋊Q8—111no—
776C22⋊Q8—111no—
777C22⋊Q8—111no—
778C22⋊Q8—111no—
779C22⋊Q8C4×D1112yes—
780C22⋊Q8C4×D1112yes—
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—111no—
792C4×Q8—111no—
793C4×Q8C22×D1112yes—
794C4×Q8C22×D1112yes—
795C4×D4—112no—
796C4×D4—112no—
797C4×D4—112no—
798C4×D4—112no—
799C4×D4—112no—
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—111no—
809C4×D4—111no—
810C4×D4—112no—
811C4×D4—112no—
812C4×D4—112no—
813C4×D4—112no—
814#117—111no—
815#117—111no—
816#117—111no—
817#117—111no—
818#117—111no—
819#117—112no—
820#117—112no—
821#117—112no—
822#117—112no—
823#117—112no—
824#117—112no—
825#117—112no—
826#117—112no—
827#117C22×D1111yescharacteristic
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—111no—
835C2×C22⋊C4—111no—
836C2×C22⋊C4—112no—
837C2×C22⋊C4—112no—
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—111no—
851C4⋊C8—111no—
852C4⋊C8—112no—
853C4⋊C8—111no—
854C4⋊C8—111no—
855C4⋊C8—112no—
856C4⋊C8—112no—
857C4⋊C8—112no—
858C4⋊C8C22×D1112yes—
859C4⋊C8C22×D1112yes—
860C4⋊C8C22×D1112yes—
861C4⋊C8C22×D1112yes—
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⋊C8—112no—
877C22⋊C8—112no—
878C22⋊C8—112no—
879C22⋊C8—112no—
880#97—112no—
881#97—112no—
882#97—112no—
883#97C22×D1111yescharacteristic
884#97C22×D1111yescharacteristic
885#97C22×D1111yescharacteristic
886#97C22×D1111yescharacteristic
887#97C22×D1112yes—
888#97C22×D1112yes—
889C4×C8—112no—
890C4×C8—112no—
891C4×C8—112no—
892C4×C8C22×D1112yes—
893C4×C8C22×D1112yes—
894C2×C11—22no—
895C2×C11C2×#52011yescharacteristic
896C2×C11C2×#56811yescharacteristic
897C2×C11#357311yescharacteristic
898D11—22no—
899D11—42no—
900D11—41no—
901D11—41no—
902D11—41no—
903C24—111no—
904C24—111no—
905#41—222no—
906#41—222no—
907#41—444no—
908C2×Q8—111no—
909C2×Q8C2×C4×D1112yes—
910C2×Q8C2×C4×D1112yes—
911C2×D4—112no—
912C2×D4—111no—
913C2×D4—112no—
914C2×D4—111no—
915C2×D4—111no—
916C2×D4—112no—
917C2×D4—111no—
918C2×D4—111no—
919C2×D4—112no—
920C2×D4—112no—
921C2×D4—442no—
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—112no—
932C22×C4—111no—
933C22×C4—111no—
934C22×C4—112no—
935C22×C4—112no—
936C22×C4—112no—
937C22×C4—112no—
938C22×C4—112no—
939C22×C4—222no—
940C22×C4—222no—
941C22×C4—222no—
942C22×C4—222no—
943C22×C4C2×C4×D1111yescharacteristic
944C22×C4C2×C4×D1111yescharacteristic
945C22×C4C23×D1111yescharacteristic
946M16—22no—
947M16—22no—
948M16—222no—
949M16—222no—
950M16—441no—
951M16—441no—
952M16—441no—
953M16—441no—
954M16—442no—
955M16—442no—
956M16—442no—
957M16—442no—
958C2×C8—22no—
959C2×C8—22no—
960C2×C8—112no—
961C2×C8—111no—
962C2×C8—111no—
963C2×C8—112no—
964C2×C8—111no—
965C2×C8—111no—
966C2×C8—222no—
967C2×C8—222no—
968C2×C8—441no—
969C2×C8—441no—
970C2×C8—441no—
971C2×C8—441no—
972C2×C8—442no—
973C2×C8—442no—
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—112no—
986C4⋊C4—112no—
987C4⋊C4—112no—
988C4⋊C4—112no—
989C4⋊C4—111no—
990C4⋊C4—111no—
991C4⋊C4—111no—
992C4⋊C4—112no—
993C4⋊C4—112no—
994C4⋊C4—112no—
995C4⋊C4—112no—
996C4⋊C4—112no—
997C4⋊C4—112no—
998C4⋊C4C2×C4×D1111yescharacteristic
999C4⋊C4C2×C4×D1111yescharacteristic
1000C4⋊C4C2×C4×D1111yescharacteristic
1001C4⋊C4C2×C4×D1111yescharacteristic
1002C4⋊C4C2×C4×D1112yes—
1003C4⋊C4C2×C4×D1112yes—
1004C4⋊C4C2×C4×D1112yes—
1005C4⋊C4C2×C4×D1112yes—
1006C4⋊C4C2×C4×D1112yes—
1007C4⋊C4C2×C4×D1112yes—
1008C22⋊C4—112no—
1009C22⋊C4—111no—
1010C22⋊C4—111no—
1011C22⋊C4—112no—
1012C22⋊C4—112no—
1013C22⋊C4—112no—
1014C22⋊C4—112no—
1015C22⋊C4—111no—
1016C22⋊C4—111no—
1017C22⋊C4—111no—
1018C22⋊C4—111no—
1019C22⋊C4—111no—
1020C22⋊C4—111no—
1021C22⋊C4—112no—
1022C22⋊C4—112no—
1023C22⋊C4—112no—
1024C22⋊C4—112no—
1025C22⋊C4—112no—
1026C22⋊C4—112no—
1027C22⋊C4—112no—
1028C22⋊C4—112no—
1029C22⋊C4—112no—
1030C22⋊C4—112no—
1031C22⋊C4C2×C4×D1112yes—
1032C22⋊C4C2×C4×D1112yes—
1033C42—112no—
1034C42—112no—
1035C42—112no—
1036C42—112no—
1037C42—112no—
1038C42—112no—
1039C42—112no—
1040C42C2×C4×D1111yescharacteristic
1041C42C2×C4×D1111yescharacteristic
1042C42C23×D1111yescharacteristic
1043C42C23×D1112yes—
1044C42C23×D1112yes—
1045C42C23×D1111yescharacteristic
1046C11#6027211yescharacteristic, complemented, Sylow
1047C23—111no—
1048C23—111no—
1049C23—111no—
1050C23—112no—
1051C23—111no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—441no—
1056C23—441no—
1057C23—441no—
1058C23C22×C4×D1111yescharacteristic
1059Q8—42no—
1060Q8—42no—
1061Q8—222no—
1062D4—222no—
1063D4—222no—
1064D4—224no—
1065D4—224no—
1066D4—222no—
1067D4—441no—
1068D4—441no—
1069D4—442no—
1070D4—442no—
1071D4—442no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—112no—
1075C2×C4—112no—
1076C2×C4—111no—
1077C2×C4—111no—
1078C2×C4—112no—
1079C2×C4—111no—
1080C2×C4—111no—
1081C2×C4—224no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—221no—
1089C2×C4—221no—
1090C2×C4—221no—
1091C2×C4—221no—
1092C2×C4—222no—
1093C2×C4—221no—
1094C2×C4—221no—
1095C2×C4—221no—
1096C2×C4—222no—
1097C2×C4—221no—
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×D1112yes—
1106C2×C4C22×C4×D1112yes—
1107C2×C4C22×C4×D1112yes—
1108C2×C4C22×C4×D1112yes—
1109C2×C4C22×C4×D1111yescharacteristic
1110C2×C4C22×C4×D1111yescharacteristic
1111C2×C4C22×C4×D1111yescharacteristic
1112C2×C4#6704012yes—
1113C2×C4#6704212yes—
1114C2×C4C24×D1111yescharacteristic
1115C8—21no—
1116C8—21no—
1117C8—21no—
1118C8—21no—
1119C8—22no—
1120C8—22no—
1121C8—222no—
1122C8—221no—
1123C8—221no—
1124C8—221no—
1125C8—221no—
1126C8—222no—
1127C22—21no—
1128C22—21no—
1129C22—112no—
1130C22—221no—
1131C22—221no—
1132C22—221no—
1133C22—222no—
1134C22—221no—
1135C22—221no—
1136C22—221no—
1137C22—222no—
1138C22—221no—
1139C22—221no—
1140C22—221no—
1141C22—221no—
1142C22—221no—
1143C22—222no—
1144C22—444no—
1145C22—882no—
1146C22#1062310512yes—
1147C22C23×C4×D1111yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—22no—
1151C4—22no—
1152C4—21no—
1153C4—21no—
1154C4—22no—
1155C4—22no—
1156C4—222no—
1157C4—222no—
1158C4—221no—
1159C4—221no—
1160C4—221no—
1161C4—221no—
1162C4—222no—
1163C4#1062310512yes—
1164C4C2×#6704011yescharacteristic
1165C4C2×#6704211yescharacteristic
1166C2—22no—
1167C2—222no—
1168C2—441no—
1169C2—441no—
1170C2—441no—
1171C2—442no—
1172C2C2×#1062310511yescharacteristic
1173C2D11×#56811yescharacteristic
1174C2#1308332911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2961C2
prime radical#13082183C2
cosocleC2×C4×C11C25
hypercenter#2961D11
hypocenterC11#60272
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2961

Complements

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

NH ≅ G/Ntype
2. #13077785C2semidirect
3. #13077785C2semidirect
4. #13077779C2semidirect
5. #13077768C2semidirect
6. #13077754C2semidirect
7. #13077754C2semidirect
8. #13077740C2semidirect
9. #13077732C2semidirect
10. #13077565C2semidirect
11. #13077351C2semidirect
12. #13077344C2semidirect
13. #13077344C2semidirect
14. #13077318C2semidirect
15. #13077309C2semidirect
16. C2×#10622319C2semidirect
17. #13077271C2semidirect
18. #13077271C2semidirect
19. #13077265C2semidirect
20. #13077185C2semidirect
21. #13077177C2semidirect
22. D11×#424C2semidirect
23. C11×#2961C2semidirect
53. C11×#446C22semidirect
54. C11×#446C22semidirect
55. C11×#446C22semidirect
56. C11×#446C22semidirect
73. #10622637C22semidirect
74. #10622637C22semidirect
75. #10622637C22semidirect
76. Q8×C11⋊C8C22semidirect
83. #10622452C22semidirect
84. #10622452C22semidirect
85. #10622452C22semidirect
86. #10622452C22semidirect
87. #10622452C22semidirect
88. #10622452C22semidirect
90. #10622451C22semidirect
91. #10622451C22semidirect
92. #10622450C22semidirect
93. #10622450C22semidirect
94. #10622450C22semidirect
97. #10622449C22semidirect
98. #10622449C22semidirect
99. #10622449C22semidirect
100. #10622449C22semidirect
102. #10622447C22semidirect
103. #10622447C22semidirect
104. D11×C4⋊C8C22semidirect
105. D11×C4⋊C8C22semidirect
106. D11×C4⋊C8C22semidirect
107. #10622322C22semidirect
108. #10622322C22semidirect
109. #10622322C22semidirect
110. #10622322C22semidirect
119. #10622319C22semidirect
120. #10622319C22semidirect
121. #10622319C22semidirect
122. #10622319C22semidirect
123. #10622318C22semidirect
124. #10622318C22semidirect
125. #10622318C22semidirect
126. #10622318C22semidirect
127. #10622303C22semidirect
128. #10622303C22semidirect
129. #10622301C22semidirect
130. #10622301C22semidirect
131. C8×D44C22semidirect
132. C8×D44C22semidirect
133. #10622298C22semidirect
134. #10622298C22semidirect
470. #2961D11semidirect
595. #446C2×D11semidirect
596. #446C2×D11semidirect
597. #446C2×D11semidirect
598. #446C2×D11semidirect
1046. C11#60272semidirect

Maximal subgroups

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

subgroupindex
#130821832
#130777852
#130777792
#130777682
#130777542
#130777402
#130777322
#130775652
#130773512
#130773442
#130773182
#130773092
C2×#106223192
#130772712
#130772652
#130771852
#130771772
D11×#4242
C11×#29612
#6027211