Finite Group Databasebeta

← #15617563

Subgroups — #15617563

Order 2816.

2042 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13081815C211yesmaximal, characteristic
2#13077284C211yesmaximal, characteristic, complemented
3#13077282C211yesmaximal, characteristic, complemented
4#13077281C211yesmaximal, characteristic, complemented
5#13077280C211yesmaximal, characteristic, complemented
6#13077280C211yesmaximal, characteristic, complemented
7#13077278C211yesmaximal, characteristic, complemented
8#13077278C211yesmaximal, characteristic, complemented
9#13077275C212yesmaximal, complemented
10#13077272C212yesmaximal, complemented
11#13077272C212yesmaximal, complemented
12#13077269C212yesmaximal, complemented
13#13077264C212yesmaximal, complemented
14#13077262C212yesmaximal, complemented
15#13077257C212yesmaximal, complemented
16#13077255C212yesmaximal, complemented
17#13077178C211yesmaximal, characteristic, complemented
18C2×#10622452C211yesmaximal, characteristic, complemented
19#13077058C211yesmaximal, characteristic
20D11×#408C211yesmaximal, characteristic
21#13077032C211yesmaximal, characteristic, complemented
22D11×#405C211yesmaximal, characteristic, complemented
23C11×#2925C211yesmaximal, characteristic, complemented
24C2×#41×D11C2211yescharacteristic
25C4×C11×#41C2211yescharacteristic
26#41×Dic11C2211yescharacteristic
27C2×M16×D11C2211yescharacteristic
28C2×M16×D11C2211yescharacteristic
29C22×#4313C2211yescharacteristic
30C22×C8×D11C2211yescharacteristic
31#10623105C411yescharacteristic
32#10623105C411yescharacteristic
33#10623103C411yescharacteristic
34#10623103C411yescharacteristic
35#10623077C412yes—
36#10623077C412yes—
37#10623077C411yescharacteristic
38#10623077C411yescharacteristic
39#10623076C412yes—
40#10623076C412yes—
41#10623076C411yescharacteristic
42#10623076C411yescharacteristic
43#10623053C2212yes—
44#10623053C2211yescharacteristic
45D11×#117C2212yes—
46D11×#117C2211yescharacteristic
47C4×#4339C2212yes—
48C4×#4339C2211yescharacteristic
49C2×#66925C2212yes—
50C2×#66925C2211yescharacteristic
51C11×#433C2212yescomplemented
52C11×#433C2212yescomplemented
53C11×#432C2212yescomplemented
54C11×#431C2212yescomplemented
55C11×#423C2211yescharacteristic, complemented
56C2×C11×C4⋊C8C2211yescharacteristic, complemented
57C11×#408C2211yescharacteristic
58C11×#408C2211yescharacteristic
59C11×#405C2211yescharacteristic, complemented
60C11×#405C2211yescharacteristic, complemented
61#10622847C2211yescharacteristic
62#10622847C2211yescharacteristic
63#10622742C2211yescharacteristic
64#10622742C2211yescharacteristic
65#10622735C2211yescharacteristic, complemented
66#10622735C2211yescharacteristic, complemented
67#10622731C2211yescharacteristic, complemented
68#10622731C2211yescharacteristic, complemented
69#10622723C2211yescharacteristic
70#10622723C2211yescharacteristic
71#10622714C2211yescharacteristic, complemented
72#10622714C2211yescharacteristic, complemented
73C2×Dic11⋊C8C2211yescharacteristic, complemented
74C2×Dic11⋊C8C2211yescharacteristic, complemented
75#10622613C2212yescomplemented
76#10622613C2212yescomplemented
77#10622610C2211yescharacteristic, complemented
78#10622610C2211yescharacteristic, complemented
79#10622539C2212yescomplemented
80#10622538C2212yescomplemented
81#10622537C2211yescharacteristic, complemented
82C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
83#10622453C2212yescomplemented
84#10622453C2212yescomplemented
85#10622453C2212yescomplemented
86#10622453C2212yescomplemented
87#10622452C2211yescharacteristic
88#10622452C2212yes—
89#10622452C2211yescharacteristic
90#10622452C2211yescharacteristic
91#10622452C2212yes—
92#10622452C2211yescharacteristic
93#10622452C2211yescharacteristic, complemented
94#10622452C2212yescomplemented
95#10622452C2211yescharacteristic, complemented
96#10622452C2212yescomplemented
97#10622452C2211yescharacteristic, complemented
98#10622452C2211yescharacteristic, complemented
99#10622448C2212yescomplemented
100#10622448C2212yescomplemented
101#10622446C2212yescomplemented
102#10622446C2212yescomplemented
103#10622340C2212yes—
104#10622340C2212yes—
105#10622340C2212yes—
106#10622340C2212yes—
107#10622339C2212yes—
108#10622339C2212yes—
109D11×C22⋊C8C2212yes—
110D11×C22⋊C8C2212yes—
111#10622333C2212yescomplemented
112#10622333C2212yescomplemented
113#10622333C2212yescomplemented
114#10622333C2212yescomplemented
115#10622332C2212yescomplemented
116#10622332C2212yescomplemented
117#10622331C2212yescomplemented
118#10622331C2212yescomplemented
119#10622322C2212yescomplemented
120#10622322C2212yescomplemented
121#10622321C2212yes—
122#10622321C2212yes—
123#10622320C2212yescomplemented
124#10622318C2212yescomplemented
125#10622318C2212yescomplemented
126D11×#97C2212yescomplemented
127#10622303C2212yescomplemented
128#10622303C2212yescomplemented
129#10622302C2212yes—
130#10622302C2212yes—
131C4×#4313C2212yescomplemented
132#10622298C2212yescomplemented
133#10622298C2212yescomplemented
134C4×C8×D11C2212yescomplemented
135C2×C11×#41C2311yescharacteristic
136#41×D11—24no—
137#41×D11—24no—
138C2×#4343C2×C411yescharacteristic
139C2×Q8×D11C2×C411yescharacteristic
140C2×#4341C2×C412yes—
141C2×#4341C2×C411yescharacteristic
142C2×D4×D11C2×C412yes—
143C2×D4×D11C2×C411yescharacteristic
144C2×#4339C2311yescharacteristic
145C2×#4339C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2311yescharacteristic
148C2×C11×M16C2311yescharacteristic
149C2×C11×M16C2311yescharacteristic
150C22×C8×C11C2311yescharacteristic
151C22×C8×C11C2311yescharacteristic
152C4×Q8×C11C2×C411yescharacteristic
153C4×Q8×C11C2×C411yescharacteristic
154C4×D4×C11C2×C412yes—
155C4×D4×C11C2×C412yes—
156C4×D4×C11C2×C411yescharacteristic
157C4×D4×C11C2×C411yescharacteristic
158C11×#117C2311yescharacteristic
159C11×#117C2312yes—
160C2×C42×C11C2311yescharacteristic
161C2×C42×C11C2312yes—
162Q8×Dic11C2×C411yescharacteristic
163Q8×Dic11C2×C411yescharacteristic
164D4×Dic11C2×C412yes—
165D4×Dic11C2×C412yes—
166D4×Dic11C2×C411yescharacteristic
167D4×Dic11C2×C411yescharacteristic
168C4×C22⋊D11C2×C412yes—
169C4×C22⋊D11C2×C412yes—
170C4×C22⋊D11C2×C412yes—
171C4×C22⋊D11C2×C412yes—
172C4×C22⋊D11C2×C412yes—
173C4×C22⋊D11C2×C412yes—
174C2×(C2×D11)⋊C4C2×C412yes—
175C2×(C2×D11)⋊C4C2×C412yes—
176C2×(C2×D11)⋊C4C2×C411yescharacteristic
177C2×(C2×D11)⋊C4C2×C411yescharacteristic
178#66979C2311yescharacteristic
179#66979C2312yes—
180C2×Dic11⋊C4C2×C412yes—
181C2×Dic11⋊C4C2×C412yes—
182C2×Dic11⋊C4C2×C411yescharacteristic
183C2×Dic11⋊C4C2×C411yescharacteristic
184C2×C4×Dic11C2311yescharacteristic
185C2×C4×Dic11C2312yes—
186C2×#4318C2311yescharacteristic
187C2×#4318C2311yescharacteristic
188C22×C11⋊C8C2311yescharacteristic
189C22×C11⋊C8C2311yescharacteristic
190M16×D11—24no—
191M16×D11—24no—
192C2×#4313—24no—
193C2×#4313C2311yescharacteristic
194C2×#4313C2311yescharacteristic
195C2×#4313C2311yescharacteristic
196C2×#4313C2311yescharacteristic
197C2×#4313C2312yes—
198C2×#4313C2312yes—
199C2×C8×D11—24no—
200C2×C8×D11C2311yescharacteristic
201C2×C8×D11C2311yescharacteristic
202C2×C8×D11C2311yescharacteristic
203C2×C8×D11C2311yescharacteristic
204C2×C8×D11C2312yes—
205C2×C8×D11C2312yes—
206#66946C2×C412yes—
207#66946C2×C412yes—
208#66946C2×C411yescharacteristic
209#66946C2×C411yescharacteristic
210#66945C2×C412yes—
211#66945C2×C412yes—
212#66945C2×C411yescharacteristic
213#66945C2×C411yescharacteristic
214C4⋊C4×D11C2×C412yes—
215C4⋊C4×D11C2×C412yes—
216C4⋊C4×D11C2×C411yescharacteristic
217C4⋊C4×D11C2×C411yescharacteristic
218#66940C2×C412yes—
219#66940C2×C412yes—
220#66940C2×C411yescharacteristic
221#66940C2×C411yescharacteristic
222(C22⋊D11)⋊C4C2×C412yes—
223(C22⋊D11)⋊C4C2×C412yes—
224(C22⋊D11)⋊C4C2×C412yes—
225(C22⋊D11)⋊C4C2×C412yes—
226(C22⋊D11)⋊C4C2×C412yes—
227(C22⋊D11)⋊C4C2×C412yes—
228C22⋊C4×D11C2×C412yes—
229C22⋊C4×D11C2×C412yes—
230C22⋊C4×D11C2×C412yes—
231#66930C2×C412yes—
232#66930C2×C412yes—
233#66930C2×C412yes—
234C4×D44C2×C412yes—
235C4×D44C2×C412yes—
236C4×D44C2×C411yescharacteristic
237C4×D44C2×C411yescharacteristic
238#66925C2×C412yes—
239#66925C2×C412yes—
240#66925C2×C411yescharacteristic
241#66925C2×C411yescharacteristic
242#66925C2×C412yes—
243#66925C2×C412yes—
244#66925C2×C411yescharacteristic
245#66925C2×C411yescharacteristic
246#66925C2311yescharacteristic
247#66925C2311yescharacteristic
248#66925C2312yes—
249#66925C2312yes—
250#66925C2311yescharacteristic
251#66925C2312yes—
252#66925C2311yescharacteristic
253C42×D11C2312yes—
254C42×D11C2312yes—
255C42×D11C2312yes—
256C4×Dic22C2×C412yes—
257C4×Dic22C2×C412yes—
258C4×Dic22C2×C411yescharacteristic
259C4×Dic22C2×C411yescharacteristic
260C11×C4⋊C8C2311yescharacteristic
261C11×C4⋊C8C2311yescharacteristic
262C11×C4⋊C8C2311yescharacteristic
263C11×C4⋊C8C2311yescharacteristic
264C11×C4⋊C8C2312yes—
265C11×C4⋊C8C2312yes—
266C11×C22⋊C8C2312yes—
267C11×C22⋊C8C2312yes—
268C11×C22⋊C8C2312yes—
269C11×C22⋊C8C2312yes—
270C11×#97C2312yes—
271C11×#97C2312yes—
272C4×C8×C11C2312yes—
273C4×C8×C11C2312yes—
274C22⋊(C11⋊C8)C2312yes—
275C22⋊(C11⋊C8)C2312yes—
276C22⋊(C11⋊C8)C2312yes—
277C22⋊(C11⋊C8)C2312yes—
278(C2×D11)⋊C8C2312yes—
279(C2×D11)⋊C8C2312yes—
280(C2×D11)⋊C8C2312yes—
281(C2×D11)⋊C8C2312yes—
282(C2×D11)⋊C8C2312yes—
283(C2×D11)⋊C8C2312yes—
284(C2×D11)⋊C8C2312yes—
285(C2×D11)⋊C8C2312yes—
286#66879C2312yes—
287#66879C2312yes—
288#66879C2312yes—
289#66879C2312yes—
290Dic11⋊C8C2312yes—
291Dic11⋊C8C2312yes—
292Dic11⋊C8C2312yes—
293Dic11⋊C8C2312yes—
294Dic11⋊C8C2311yescharacteristic
295Dic11⋊C8C2311yescharacteristic
296Dic11⋊C8C2311yescharacteristic
297Dic11⋊C8C2311yescharacteristic
298Dic11⋊C8C2311yescharacteristic
299Dic11⋊C8C2311yescharacteristic
300Dic11⋊C8C2311yescharacteristic
301Dic11⋊C8C2311yescharacteristic
302C8×Dic11C2312yes—
303C8×Dic11C2312yes—
304C8×Dic11C2312yes—
305C8×Dic11C2312yes—
306C4⋊(C11⋊C8)C2311yescharacteristic
307C4⋊(C11⋊C8)C2311yescharacteristic
308C4⋊(C11⋊C8)C2311yescharacteristic
309C4⋊(C11⋊C8)C2311yescharacteristic
310C4⋊(C11⋊C8)C2312yes—
311C4⋊(C11⋊C8)C2312yes—
312#66867C2312yes—
313#66867C2312yes—
314C4×C11⋊C8C2312yes—
315C4×C11⋊C8C2312yes—
316#60126—111nomaximal, Sylow
317C23×D11C22×C412yes—
318C23×D11C22×C411yescharacteristic
319C11×#41—22no—
320C11×#41—22no—
321C2×Q8×C11C22×C411yescharacteristic
322C2×D4×C11C22×C412yes—
323C2×D4×C11C22×C411yescharacteristic
324C22×C4×C11C22×C412yes—
325C22×C4×C11C22×C412yes—
326C22×C4×C11C22×C411yescharacteristic
327C22×C4×C11C22×C411yescharacteristic
328C22×C4×C11C2412yes—
329C22×C4×C11C2411yescharacteristic
330C2×C22⋊D11C22×C412yes—
331C2×C22⋊D11C22×C412yes—
332C2×C22⋊D11C22×C412yes—
333C22×Dic11C22×C412yes—
334C22×Dic11C22×C412yes—
335C22×Dic11C22×C412yes—
336C22×Dic11C22×C411yescharacteristic
337C22×Dic11C22×C411yescharacteristic
338C22×Dic11C22×C411yescharacteristic
339#4343—24no—
340Q8×D11—24no—
341#4341—28no—
342#4341—24no—
343D4×D11—24no—
344D4×D11—28no—
345#4339—24no—
346#4339—24no—
347#4339—22no—
348#4339—22no—
349C2×D44C22×C412yes—
350C2×D44C22×C411yescharacteristic
351C2×C4×D11—24no—
352C2×C4×D11—24no—
353C2×C4×D11C22×C412yes—
354C2×C4×D11C22×C412yes—
355C2×C4×D11C22×C412yes—
356C2×C4×D11C22×C412yes—
357C2×C4×D11C22×C412yes—
358C2×C4×D11C22×C412yes—
359C2×C4×D11C22×C412yes—
360C2×C4×D11C22×C412yes—
361C2×C4×D11C22×C411yescharacteristic
362C2×C4×D11C22×C411yescharacteristic
363C2×C4×D11#4114yes—
364C2×C4×D11#4114yes—
365C2×C4×D11C2412yes—
366C2×C4×D11C2411yescharacteristic
367C2×C4×D11C2411yescharacteristic
368C2×Dic22C22×C412yes—
369C2×Dic22C22×C411yescharacteristic
370C11×M16—22no—
371C11×M16—22no—
372C2×C8×C11—22no—
373C2×C8×C11—22no—
374C2×C8×C11C2411yescharacteristic
375C2×C8×C11C2411yescharacteristic
376C2×C8×C11C2412yes—
377C2×C8×C11C2412yes—
378C2×C8×C11C2411yescharacteristic
379C2×C8×C11C2411yescharacteristic
380C11×C4⋊C4C22×C412yes—
381C11×C4⋊C4C22×C412yes—
382C11×C4⋊C4C22×C411yescharacteristic
383C11×C4⋊C4C22×C411yescharacteristic
384C11×C22⋊C4C22×C412yes—
385C11×C22⋊C4C22×C412yes—
386C11×C22⋊C4C22×C412yes—
387C42×C11C22×C412yes—
388C42×C11C22×C412yes—
389C42×C11C22×C411yescharacteristic
390C42×C11C22×C411yescharacteristic
391C42×C11C2412yes—
392C42×C11C2411yescharacteristic
393C42×C11C2411yescharacteristic
394C22⋊Dic11C22×C412yes—
395C22⋊Dic11C22×C412yes—
396C22⋊Dic11C22×C412yes—
397(C2×D11)⋊C4C22×C411yescharacteristic
398(C2×D11)⋊C4C22×C411yescharacteristic
399(C2×D11)⋊C4C22×C412yes—
400(C2×D11)⋊C4C22×C412yes—
401(C2×D11)⋊C4C22×C411yescharacteristic
402(C2×D11)⋊C4C22×C411yescharacteristic
403(C2×D11)⋊C4C22×C412yes—
404(C2×D11)⋊C4C22×C412yes—
405(C2×D11)⋊C4C22×C411yescharacteristic
406(C2×D11)⋊C4C22×C411yescharacteristic
407(C2×D11)⋊C4C22×C412yes—
408(C2×D11)⋊C4C22×C412yes—
409(C2×D11)⋊C4C22×C411yescharacteristic
410(C2×D11)⋊C4C22×C411yescharacteristic
411C4⋊Dic11C22×C412yes—
412C4⋊Dic11C22×C412yes—
413C4⋊Dic11C22×C411yescharacteristic
414C4⋊Dic11C22×C411yescharacteristic
415Dic11⋊C4C22×C412yes—
416Dic11⋊C4C22×C412yes—
417Dic11⋊C4C22×C411yescharacteristic
418Dic11⋊C4C22×C411yescharacteristic
419Dic11⋊C4C22×C411yescharacteristic
420Dic11⋊C4C22×C411yescharacteristic
421Dic11⋊C4C22×C412yes—
422Dic11⋊C4C22×C412yes—
423Dic11⋊C4C22×C411yescharacteristic
424Dic11⋊C4C22×C411yescharacteristic
425Dic11⋊C4C22×C412yes—
426Dic11⋊C4C22×C412yes—
427Dic11⋊C4C22×C411yescharacteristic
428Dic11⋊C4C22×C411yescharacteristic
429C4×Dic11C22×C412yes—
430C4×Dic11C22×C412yes—
431C4×Dic11C22×C412yes—
432C4×Dic11C22×C412yes—
433C4×Dic11C22×C412yes—
434C4×Dic11C22×C412yes—
435C4×Dic11C22×C412yes—
436C4×Dic11C22×C412yes—
437C4×Dic11C22×C411yescharacteristic
438C4×Dic11C22×C411yescharacteristic
439C4×Dic11C2412yes—
440C4×Dic11C2411yescharacteristic
441C4×Dic11C2411yescharacteristic
442#4318—22no—
443#4318—22no—
444C2×C11⋊C8—22no—
445C2×C11⋊C8—22no—
446C2×C11⋊C8C2411yescharacteristic
447C2×C11⋊C8C2411yescharacteristic
448C2×C11⋊C8C2412yes—
449C2×C11⋊C8C2412yes—
450C2×C11⋊C8C2411yescharacteristic
451C2×C11⋊C8C2411yescharacteristic
452#4313—22no—
453#4313—22no—
454#4313—22no—
455#4313—22no—
456#4313—24no—
457#4313—24no—
458C8×D11—22no—
459C8×D11—22no—
460C8×D11—22no—
461C8×D11—22no—
462C8×D11—24no—
463C8×D11—24no—
464#3428—111no—
465#2925—111no—
466#2925—111no—
467#2925—111no—
468#2925—111no—
469#2925—111no—
470#2925—111no—
471#2925—111no—
472#2925D1111yescharacteristic, complemented
473#2924—112no—
474#2924—112no—
475#2924—112no—
476#2924—112no—
477#2923—112no—
478#2923—112no—
479#2922—112no—
480#2922—112no—
481#2905—111no—
482C2×#424—111no—
483#2879—111no—
484C2×#408—111no—
485#2873—111no—
486C2×#405—111no—
487C23×C11C23×C412yes—
488C23×C11C23×C411yescharacteristic
489C22×D11—24no—
490C22×D11—41no—
491C22×D11—41no—
492C22×D11—42no—
493C22×D11—42no—
494C22×D11#11714yes—
495C22×D11C23×C412yes—
496C22×D11C23×C411yescharacteristic
497C22×D11C23×C411yescharacteristic
498Q8×C11—22no—
499D4×C11—24no—
500D4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—41no—
504C2×C4×C11—41no—
505C2×C4×C11—42no—
506C2×C4×C11—42no—
507C2×C4×C11C23×C412yes—
508C2×C4×C11C23×C412yes—
509C2×C4×C11C23×C411yescharacteristic
510C2×C4×C11C23×C411yescharacteristic
511C2×C4×C11C23×C412yes—
512C2×C4×C11C23×C411yescharacteristic
513C2×C4×C11C23×C411yescharacteristic
514C2×C4×C11C23×C411yescharacteristic
515C2×C4×C11C2×#4112yes—
516C2×C4×C11C2×#4112yes—
517C2×C4×C11C2511yescharacteristic
518C22⋊D11—24no—
519C22⋊D11—24no—
520C22⋊D11—24no—
521C2×Dic11—24no—
522C2×Dic11—41no—
523C2×Dic11—41no—
524C2×Dic11—42no—
525C2×Dic11—42no—
526C2×Dic11#11714yes—
527C2×Dic11C23×C412yes—
528C2×Dic11C23×C411yescharacteristic
529C2×Dic11C23×C411yescharacteristic
530C2×Dic11C23×C412yes—
531C2×Dic11C23×C412yes—
532C2×Dic11C23×C411yescharacteristic
533C2×Dic11C23×C411yescharacteristic
534C2×Dic11C23×C411yescharacteristic
535C2×Dic11C23×C411yescharacteristic
536D44—24no—
537D44—22no—
538C4×D11—24no—
539C4×D11—22no—
540C4×D11—22no—
541C4×D11—24no—
542C4×D11—42no—
543C4×D11—42no—
544C4×D11—42no—
545C4×D11—42no—
546C4×D11—42no—
547C4×D11—42no—
548C4×D11#11714yes—
549C4×D11#11714yes—
550C4×D11C2×#4112yes—
551C4×D11C2×#4112yes—
552C4×D11C2×#4112yes—
553C4×D11C2×#4112yes—
554Dic22—22no—
555Dic22—24no—
556C8×C11—21no—
557C8×C11—21no—
558C8×C11—22no—
559C8×C11—22no—
560C8×C11—21no—
561C8×C11—21no—
562C11⋊C8—21no—
563C11⋊C8—21no—
564C11⋊C8—22no—
565C11⋊C8—22no—
566C11⋊C8—21no—
567C11⋊C8—21no—
568C22×#41—111no—
569C22×M16—111no—
570C22×M16—111no—
571C22×M16—111no—
572C23×C8—111no—
573#520—111no—
574#520—111no—
575#520—112no—
576#520—112no—
577#520—111no—
578#520—111no—
579#519—111no—
580#519—111no—
581#518—112no—
582#518—112no—
583#518—111no—
584#518—111no—
585C4×#41—111no—
586C4×#41—112no—
587C4×#41—111no—
588C4×#41—112no—
589C4×#41—111no—
590C4×#41C2×D1111yescharacteristic
591C2×#117—111no—
592C2×#117—112no—
593C2×#117—111no—
594C2×#117—112no—
595#433—112no—
596#433—112no—
597#433—112no—
598#433—112no—
599#433—112no—
600#433—112no—
601#433—112no—
602#433—112no—
603#433—112no—
604#433—112no—
605#433—112no—
606#433—112no—
607#433—112no—
608#433—112no—
609#433C2×D1112yescomplemented
610#433C2×D1112yescomplemented
611#432—112no—
612#432—112no—
613#432—112no—
614#432—112no—
615#432—112no—
616#432—112no—
617#432—112no—
618#432C2×D1112yescomplemented
619#431—112no—
620#431—112no—
621#431—112no—
622#431—112no—
623#431—112no—
624#431—112no—
625#431—112no—
626#431C2×D1112yescomplemented
627#424—111no—
628#424—111no—
629#424—111no—
630#424—111no—
631#424—111no—
632#424—111no—
633#424—111no—
634#424—111no—
635#424—112no—
636#424—112no—
637#424—112no—
638#424—112no—
639#423—111no—
640#423—111no—
641#423—111no—
642#423C2×D1111yescharacteristic, complemented
643C2×C4⋊C8—111no—
644C2×C4⋊C8—111no—
645C2×C4⋊C8—111no—
646C2×C4⋊C8C2×D1111yescharacteristic, complemented
647#408—111no—
648#408—111no—
649#408—111no—
650#408—111no—
651#408—111no—
652#408—111no—
653#408—112no—
654#408—112no—
655#408—112no—
656#408—112no—
657#408C2×D1111yescharacteristic
658#408C2×D1111yescharacteristic
659#407—112no—
660#407—112no—
661C2×C22⋊C8—112no—
662C2×C22⋊C8—112no—
663#405—111no—
664#405—111no—
665#405—111no—
666#405—111no—
667#405—111no—
668#405—111no—
669#405—112no—
670#405—112no—
671#405—112no—
672#405—112no—
673#405C2×D1111yescharacteristic, complemented
674#405C2×D1111yescharacteristic, complemented
675C4×M16—112no—
676C4×M16—112no—
677C2×#97—112no—
678C2×C4×C8—112no—
679C22×C11—21no—
680C22×C11—21no—
681C22×C11—22no—
682C22×C11—22no—
683C22×C11—22no—
684C22×C11C2×#11712yes—
685C22×C11C24×C411yescharacteristic
686C2×D11—21no—
687C2×D11—21no—
688C2×D11—21no—
689C2×D11—21no—
690C2×D11—22no—
691C2×D11—22no—
692C2×D11—22no—
693C2×D11—44no—
694C2×D11—84no—
695C2×D11C2×#11712yes—
696C2×D11C2×#11712yes—
697C4×C11—22no—
698C4×C11—21no—
699C4×C11—21no—
700C4×C11—21no—
701C4×C11—22no—
702C4×C11—21no—
703C4×C11—22no—
704C4×C11C2×#11712yes—
705C4×C11C22×#4111yescharacteristic
706C4×C11C22×#4111yescharacteristic
707Dic11—22no—
708Dic11—22no—
709Dic11—21no—
710Dic11—22no—
711Dic11—21no—
712Dic11—21no—
713Dic11—21no—
714Dic11C2×#11712yes—
715Dic11C2×#11712yes—
716C2×#41—111no—
717C2×#41—112no—
718C2×#41—111no—
719C2×#41—112no—
720C2×#41—111no—
721C2×#41—224no—
722C2×#41—224no—
723C2×#41C22×D1111yescharacteristic
724C22×Q8—111no—
725C22×D4—111no—
726C22×D4—112no—
727C23×C4—111no—
728C23×C4—112no—
729C2×M16—111no—
730C2×M16—111no—
731C2×M16—111no—
732C2×M16—112no—
733C2×M16—111no—
734C2×M16—111no—
735C2×M16—112no—
736C2×M16—111no—
737C2×M16—224no—
738C2×M16—224no—
739C2×M16—224no—
740C2×M16C22×D1111yescharacteristic
741C2×M16C22×D1111yescharacteristic
742C22×C8—111no—
743C22×C8—111no—
744C22×C8—111no—
745C22×C8—111no—
746C22×C8—111no—
747C22×C8—111no—
748C22×C8—112no—
749C22×C8—112no—
750C22×C8—224no—
751C22×C8C22×D1111yescharacteristic
752C22×C8C22×D1111yescharacteristic
753C4×Q8—111no—
754C4×Q8—111no—
755C4×Q8—112no—
756C4×Q8—112no—
757C4×Q8—111no—
758C4×Q8—111no—
759C4×Q8—112no—
760C4×Q8—112no—
761C4×Q8—111no—
762C4×Q8—111no—
763C4×Q8C4×D1111yescharacteristic
764C4×Q8C4×D1111yescharacteristic
765C4×D4—112no—
766C4×D4—112no—
767C4×D4—111no—
768C4×D4—111no—
769C4×D4—112no—
770C4×D4—112no—
771C4×D4—112no—
772C4×D4—112no—
773C4×D4—112no—
774C4×D4—112no—
775C4×D4—112no—
776C4×D4—112no—
777C4×D4—111no—
778C4×D4—111no—
779C4×D4—112no—
780C4×D4—112no—
781C4×D4—112no—
782C4×D4—112no—
783C4×D4—112no—
784C4×D4—112no—
785C4×D4—112no—
786C4×D4—112no—
787C4×D4—111no—
788C4×D4—111no—
789C4×D4C4×D1112yes—
790C4×D4C4×D1112yes—
791C4×D4C4×D1111yescharacteristic
792C4×D4C4×D1111yescharacteristic
793#117—111no—
794#117—112no—
795#117—111no—
796#117—111no—
797#117—112no—
798#117—112no—
799#117—112no—
800#117—112no—
801#117—112no—
802#117—111no—
803#117—111no—
804#117—112no—
805#117—112no—
806#117—111no—
807#117—111no—
808#117—112no—
809#117—112no—
810#117—112no—
811#117—111no—
812#117—111no—
813#117—111no—
814#117—111no—
815#117—112no—
816#117—112no—
817#117C22×D1111yescharacteristic
818#117C22×D1112yes—
819C2×C4⋊C4—111no—
820C2×C4⋊C4—111no—
821C2×C4⋊C4—112no—
822C2×C4⋊C4—112no—
823C2×C4⋊C4—111no—
824C2×C4⋊C4—111no—
825C2×C4⋊C4—112no—
826C2×C4⋊C4—112no—
827C2×C22⋊C4—111no—
828C2×C22⋊C4—111no—
829C2×C22⋊C4—112no—
830C2×C22⋊C4—112no—
831C2×C22⋊C4—112no—
832C2×C22⋊C4—112no—
833C2×C22⋊C4—112no—
834C2×C42—111no—
835C2×C42—112no—
836C2×C42—112no—
837C2×C42—112no—
838C2×C42—112no—
839C2×C42C22×D1111yescharacteristic
840C2×C42C22×D1112yes—
841C4⋊C8—111no—
842C4⋊C8—111no—
843C4⋊C8—111no—
844C4⋊C8—111no—
845C4⋊C8—111no—
846C4⋊C8—111no—
847C4⋊C8—111no—
848C4⋊C8—111no—
849C4⋊C8—112no—
850C4⋊C8—112no—
851C4⋊C8—112no—
852C4⋊C8—112no—
853C4⋊C8—111no—
854C4⋊C8—111no—
855C4⋊C8—111no—
856C4⋊C8—111no—
857C4⋊C8—112no—
858C4⋊C8—112no—
859C4⋊C8C22×D1111yescharacteristic
860C4⋊C8C22×D1111yescharacteristic
861C4⋊C8C22×D1111yescharacteristic
862C4⋊C8C22×D1111yescharacteristic
863C4⋊C8C22×D1112yes—
864C4⋊C8C22×D1112yes—
865C22⋊C8—112no—
866C22⋊C8—112no—
867C22⋊C8—112no—
868C22⋊C8—112no—
869C22⋊C8—112no—
870C22⋊C8—112no—
871C22⋊C8—112no—
872C22⋊C8—112no—
873C22⋊C8—112no—
874C22⋊C8—112no—
875C22⋊C8—112no—
876C22⋊C8—112no—
877C22⋊C8C22×D1112yes—
878C22⋊C8C22×D1112yes—
879C22⋊C8C22×D1112yes—
880C22⋊C8C22×D1112yes—
881#97—112no—
882#97—112no—
883#97—112no—
884#97—112no—
885#97—112no—
886#97—112no—
887#97C22×D1112yes—
888#97C22×D1112yes—
889C4×C8—112no—
890C4×C8—112no—
891C4×C8—112no—
892C4×C8—112no—
893C4×C8—112no—
894C4×C8—112no—
895C4×C8C22×D1112yes—
896C4×C8C22×D1112yes—
897C2×C11—22no—
898C2×C11—42no—
899C2×C11C22×#11711yescharacteristic
900C2×C11#357311yescharacteristic
901C2×C11#357311yescharacteristic
902D11—22no—
903D11—22no—
904D11—42no—
905C24—111no—
906C24—112no—
907#41—22no—
908#41—22no—
909#41—224no—
910#41—224no—
911#41—228no—
912#41—224no—
913#41—224no—
914#41—222no—
915#41—222no—
916C2×Q8—112no—
917C2×Q8—111no—
918C2×Q8—224no—
919C2×Q8C2×C4×D1111yescharacteristic
920C2×D4—112no—
921C2×D4—112no—
922C2×D4—112no—
923C2×D4—112no—
924C2×D4—111no—
925C2×D4—224no—
926C2×D4—228no—
927C2×D4C2×C4×D1112yes—
928C2×D4C2×C4×D1111yescharacteristic
929C22×C4—111no—
930C22×C4—111no—
931C22×C4—111no—
932C22×C4—114no—
933C22×C4—114no—
934C22×C4—111no—
935C22×C4—111no—
936C22×C4—112no—
937C22×C4—112no—
938C22×C4—112no—
939C22×C4—111no—
940C22×C4—111no—
941C22×C4—112no—
942C22×C4—112no—
943C22×C4—112no—
944C22×C4—112no—
945C22×C4—112no—
946C22×C4—112no—
947C22×C4—112no—
948C22×C4—112no—
949C22×C4—112no—
950C22×C4—224no—
951C22×C4—224no—
952C22×C4C2×C4×D1112yes—
953C22×C4C2×C4×D1112yes—
954C22×C4C2×C4×D1111yescharacteristic
955C22×C4C2×C4×D1111yescharacteristic
956C22×C4C23×D1112yes—
957C22×C4C23×D1111yescharacteristic
958M16—22no—
959M16—22no—
960M16—222no—
961M16—222no—
962M16—222no—
963M16—222no—
964M16—224no—
965M16—224no—
966M16—222no—
967M16—222no—
968C2×C8—22no—
969C2×C8—22no—
970C2×C8—111no—
971C2×C8—112no—
972C2×C8—111no—
973C2×C8—112no—
974C2×C8—111no—
975C2×C8—111no—
976C2×C8—222no—
977C2×C8—222no—
978C2×C8—222no—
979C2×C8—222no—
980C2×C8—224no—
981C2×C8—224no—
982C2×C8—222no—
983C2×C8—222no—
984C2×C8C23×D1111yescharacteristic
985C2×C8C23×D1111yescharacteristic
986C2×C8C23×D1112yes—
987C2×C8C23×D1112yes—
988C2×C8C23×D1111yescharacteristic
989C2×C8C23×D1111yescharacteristic
990C4⋊C4—112no—
991C4⋊C4—112no—
992C4⋊C4—111no—
993C4⋊C4—111no—
994C4⋊C4—111no—
995C4⋊C4—111no—
996C4⋊C4—111no—
997C4⋊C4—111no—
998C4⋊C4—111no—
999C4⋊C4—111no—
1000C4⋊C4—112no—
1001C4⋊C4—112no—
1002C4⋊C4—112no—
1003C4⋊C4—112no—
1004C4⋊C4—112no—
1005C4⋊C4—112no—
1006C4⋊C4—111no—
1007C4⋊C4—111no—
1008C4⋊C4C2×C4×D1112yes—
1009C4⋊C4C2×C4×D1112yes—
1010C4⋊C4C2×C4×D1111yescharacteristic
1011C4⋊C4C2×C4×D1111yescharacteristic
1012C22⋊C4—112no—
1013C22⋊C4—112no—
1014C22⋊C4—112no—
1015C22⋊C4—112no—
1016C22⋊C4—112no—
1017C22⋊C4—111no—
1018C22⋊C4—111no—
1019C22⋊C4—111no—
1020C22⋊C4—111no—
1021C22⋊C4—111no—
1022C22⋊C4—111no—
1023C22⋊C4—112no—
1024C22⋊C4—112no—
1025C22⋊C4—111no—
1026C22⋊C4—111no—
1027C22⋊C4—112no—
1028C22⋊C4—112no—
1029C22⋊C4C2×C4×D1112yes—
1030C22⋊C4C2×C4×D1112yes—
1031C22⋊C4C2×C4×D1112yes—
1032C42—112no—
1033C42—112no—
1034C42—112no—
1035C42—112no—
1036C42—111no—
1037C42—111no—
1038C42—112no—
1039C42—112no—
1040C42—112no—
1041C42—112no—
1042C42—112no—
1043C42—111no—
1044C42—111no—
1045C42C2×C4×D1112yes—
1046C42C2×C4×D1112yes—
1047C42C2×C4×D1111yescharacteristic
1048C42C2×C4×D1111yescharacteristic
1049C42C23×D1112yes—
1050C42C23×D1111yescharacteristic
1051C42C23×D1111yescharacteristic
1052C11#6012611yescharacteristic, complemented, Sylow
1053C23—111no—
1054C23—111no—
1055C23—114no—
1056C23—112no—
1057C23—224no—
1058C23—441no—
1059C23—441no—
1060C23—442no—
1061C23—442no—
1062C23C22×C4×D1112yes—
1063C23C22×C4×D1111yescharacteristic
1064Q8—22no—
1065Q8—224no—
1066Q8—222no—
1067D4—24no—
1068D4—22no—
1069D4—224no—
1070D4—224no—
1071D4—224no—
1072D4—224no—
1073D4—222no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—41no—
1077C2×C4—42no—
1078C2×C4—41no—
1079C2×C4—42no—
1080C2×C4—114no—
1081C2×C4—111no—
1082C2×C4—111no—
1083C2×C4—114no—
1084C2×C4—114no—
1085C2×C4—112no—
1086C2×C4—112no—
1087C2×C4—112no—
1088C2×C4—112no—
1089C2×C4—112no—
1090C2×C4—111no—
1091C2×C4—111no—
1092C2×C4—112no—
1093C2×C4—111no—
1094C2×C4—111no—
1095C2×C4—112no—
1096C2×C4—224no—
1097C2×C4—224no—
1098C2×C4—224no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—442no—
1102C2×C4—442no—
1103C2×C4—442no—
1104C2×C4—442no—
1105C2×C4—442no—
1106C2×C4—442no—
1107C2×C4—441no—
1108C2×C4—442no—
1109C2×C4—441no—
1110C2×C4—442no—
1111C2×C4C22×C4×D1112yes—
1112C2×C4C22×C4×D1112yes—
1113C2×C4C22×C4×D1111yescharacteristic
1114C2×C4C22×C4×D1112yes—
1115C2×C4C22×C4×D1111yescharacteristic
1116C2×C4C22×C4×D1111yescharacteristic
1117C2×C4C22×C4×D1111yescharacteristic
1118C2×C4C22×C4×D1111yescharacteristic
1119C2×C4#41×D1112yes—
1120C2×C4#41×D1112yes—
1121C2×C4C24×D1111yescharacteristic
1122C8—21no—
1123C8—21no—
1124C8—21no—
1125C8—21no—
1126C8—22no—
1127C8—22no—
1128C8—221no—
1129C8—221no—
1130C8—222no—
1131C8—222no—
1132C8—221no—
1133C8—221no—
1134C22—21no—
1135C22—21no—
1136C22—22no—
1137C22—22no—
1138C22—22no—
1139C22—112no—
1140C22—112no—
1141C22—221no—
1142C22—221no—
1143C22—221no—
1144C22—221no—
1145C22—222no—
1146C22—222no—
1147C22—222no—
1148C22—444no—
1149C22—884no—
1150C22D11×#11712yes—
1151C22C23×C4×D1111yescharacteristic
1152C4—22no—
1153C4—21no—
1154C4—21no—
1155C4—22no—
1156C4—21no—
1157C4—21no—
1158C4—22no—
1159C4—112no—
1160C4—112no—
1161C4—222no—
1162C4—222no—
1163C4—221no—
1164C4—221no—
1165C4—222no—
1166C4—221no—
1167C4—221no—
1168C4D11×#11712yes—
1169C4C2×#41×D1111yescharacteristic
1170C4C2×#41×D1111yescharacteristic
1171C2—22no—
1172C2—42no—
1173C2—222no—
1174C2—222no—
1175C2—442no—
1176C2C2×D11×#11711yescharacteristic
1177C2#1308332711yescharacteristic
1178C2#1308332911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2925C2
prime radicalC2×#41×D11C22
cosocleC2×C4×C11C25
hypercenter#2925D11
hypocenterC11#60126
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2925

Complements

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

NH ≅ G/Ntype
2. #13077284C2semidirect
3. #13077282C2semidirect
4. #13077281C2semidirect
5. #13077280C2semidirect
6. #13077280C2semidirect
7. #13077278C2semidirect
8. #13077278C2semidirect
9. #13077275C2semidirect
10. #13077272C2semidirect
11. #13077272C2semidirect
12. #13077269C2semidirect
13. #13077264C2semidirect
14. #13077262C2semidirect
15. #13077257C2semidirect
16. #13077255C2semidirect
17. #13077178C2semidirect
18. C2×#10622452C2semidirect
21. #13077032C2semidirect
22. D11×#405C2semidirect
23. C11×#2925C2semidirect
51. C11×#433C22semidirect
52. C11×#433C22semidirect
53. C11×#432C22semidirect
54. C11×#431C22semidirect
55. C11×#423C22semidirect
56. C2×C11×C4⋊C8C22semidirect
59. C11×#405C22semidirect
60. C11×#405C22semidirect
65. #10622735C22semidirect
66. #10622735C22semidirect
67. #10622731C22semidirect
68. #10622731C22semidirect
71. #10622714C22semidirect
72. #10622714C22semidirect
73. C2×Dic11⋊C8C22semidirect
74. C2×Dic11⋊C8C22semidirect
75. #10622613C22semidirect
76. #10622613C22semidirect
77. #10622610C22semidirect
78. #10622610C22semidirect
79. #10622539C22semidirect
80. #10622538C22semidirect
81. #10622537C22semidirect
82. C2×C4⋊(C11⋊C8)C22semidirect
83. #10622453C22semidirect
84. #10622453C22semidirect
85. #10622453C22semidirect
86. #10622453C22semidirect
93. #10622452C22semidirect
94. #10622452C22semidirect
95. #10622452C22semidirect
96. #10622452C22semidirect
97. #10622452C22semidirect
98. #10622452C22semidirect
99. #10622448C22semidirect
100. #10622448C22semidirect
101. #10622446C22semidirect
102. #10622446C22semidirect
111. #10622333C22semidirect
112. #10622333C22semidirect
113. #10622333C22semidirect
114. #10622333C22semidirect
115. #10622332C22semidirect
116. #10622332C22semidirect
117. #10622331C22semidirect
118. #10622331C22semidirect
119. #10622322C22semidirect
120. #10622322C22semidirect
123. #10622320C22semidirect
124. #10622318C22semidirect
125. #10622318C22semidirect
126. D11×#97C22semidirect
127. #10622303C22semidirect
128. #10622303C22semidirect
131. C4×#4313C22semidirect
132. #10622298C22semidirect
133. #10622298C22semidirect
134. C4×C8×D11C22semidirect
472. #2925D11semidirect
609. #433C2×D11semidirect
610. #433C2×D11semidirect
618. #432C2×D11semidirect
626. #431C2×D11semidirect
642. #423C2×D11semidirect
646. C2×C4⋊C8C2×D11semidirect
673. #405C2×D11semidirect
674. #405C2×D11semidirect
1052. C11#60126semidirect

Maximal subgroups

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

subgroupindex
#130818152
#130772842
#130772822
#130772812
#130772802
#130772782
#130772752
#130772722
#130772692
#130772642
#130772622
#130772572
#130772552
#130771782
C2×#106224522
#130770582
D11×#4082
#130770322
D11×#4052
C11×#29252
#6012611