Finite Group Databasebeta

← #15619009

Subgroups — #15619009

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#13082170C211yesmaximal, characteristic
2#13077781C212yesmaximal, complemented
3#13077781C212yesmaximal, complemented
4#13077778C212yesmaximal, complemented
5#13077759C212yesmaximal, complemented
6#13077757C212yesmaximal, complemented
7#13077750C212yesmaximal, complemented
8#13077743C212yesmaximal, complemented
9#13077729C212yesmaximal, complemented
10#13077560C211yesmaximal, characteristic, complemented
11#13077554C211yesmaximal, characteristic, complemented
12#13077348C211yesmaximal, characteristic, complemented
13#13077344C211yesmaximal, characteristic, complemented
14#13077337C211yesmaximal, characteristic, complemented
15#13077321C211yesmaximal, characteristic, complemented
16#13077306C211yesmaximal, characteristic, complemented
17C2×#10622343C211yesmaximal, characteristic, complemented
18#13077273C211yesmaximal, characteristic, complemented
19#13077266C211yesmaximal, characteristic, complemented
20#13077183C211yesmaximal, characteristic, complemented
21#13077177C211yesmaximal, characteristic, complemented
22C2×#10622612C211yesmaximal, characteristic, complemented
23C11×#2924C211yesmaximal, characteristic, complemented
24C2×C11×#117C2211yescharacteristic
25#10623322C2211yescharacteristic
26C2×C4×C22⋊D11C2211yescharacteristic
27C22×#4318C2211yescharacteristic
28C23×C11⋊C8C2211yescharacteristic
29C2×#66960C2211yescharacteristic
30C2×M16×D11C2211yescharacteristic
31C2×#66954C2211yescharacteristic
32C22×#4313C2211yescharacteristic
33#10623064C411yescharacteristic
34#10623063C411yescharacteristic
35#10623062C412yes—
36#10623061C411yescharacteristic
37#10623060C411yescharacteristic
38#10623059C2212yes—
39#10623059C2212yes—
40#10623058C412yes—
41#10623055C2211yescharacteristic
42#10623053C2211yescharacteristic
43D11×#117C2211yescharacteristic
44#10623048C2211yescharacteristic
45#10623045C411yescharacteristic
46#10623044C411yescharacteristic
47#10623042C411yescharacteristic
48#10623038C411yescharacteristic
49#10623026C412yes—
50#10623021C412yes—
51#10623010C2212yes—
52C4×#4339C2212yes—
53C11×#433C2212yescomplemented
54C11×#433C2212yescomplemented
55C11×#432C2212yescomplemented
56C11×#431C2212yescomplemented
57C11×#424C2211yescharacteristic
58C11×#424C2211yescharacteristic
59C11×#407C2211yescharacteristic
60C2×C11×C22⋊C8C2211yescharacteristic
61C11×#405C2211yescharacteristic
62C11×#405C2211yescharacteristic
63#10622742C2211yescharacteristic
64#10622739C2211yescharacteristic
65#10622735C2211yescharacteristic
66#10622732C2211yescharacteristic
67#10622731C2211yescharacteristic
68M16×Dic11C2211yescharacteristic
69#10622723C2211yescharacteristic
70C2×(C2×D11)⋊C8C2211yescharacteristic
71#10622715C2211yescharacteristic
72#10622714C2211yescharacteristic
73C2×#66879C2211yescharacteristic
74C2×Dic11⋊C8C2211yescharacteristic
75#10622612C2211yescharacteristic
76#10622612C2211yescharacteristic
77#10622612C2211yescharacteristic
78#10622612C2211yescharacteristic
79#10622612C2212yescomplemented
80#10622612C2212yescomplemented
81C2×C4⋊(C11⋊C8)C2212yescomplemented
82C2×C4⋊(C11⋊C8)C2212yescomplemented
83#10622453C2212yescomplemented
84#10622453C2212yescomplemented
85#10622453C2212yescomplemented
86#10622453C2212yescomplemented
87#10622452C2212yescomplemented
88#10622452C2212yescomplemented
89#10622452C2212yescomplemented
90#10622452C2212yescomplemented
91#10622450C2212yescomplemented
92#10622450C2212yescomplemented
93#10622450C2212yescomplemented
94#10622448C2212yescomplemented
95#10622448C2212yescomplemented
96#10622448C2212yescomplemented
97#10622446C2212yescomplemented
98D11×C4⋊C8C2212yescomplemented
99#10622343C2211yescharacteristic
100#10622343C2211yescharacteristic
101#10622343C2211yescharacteristic
102#10622343C2211yescharacteristic
103#10622343C2211yescharacteristic
104#10622343C2211yescharacteristic
105#10622343C2211yescharacteristic
106#10622343C2211yescharacteristic
107#10622343C2212yes—
108#10622343C2212yescomplemented
109#10622343C2212yescomplemented
110#10622343C2212yescomplemented
111#10622342C2212yes—
112#10622342C2212yescomplemented
113#10622341C2212yes—
114#10622341C2212yescomplemented
115(C22⋊D11)⋊C8C2212yes—
116(C22⋊D11)⋊C8C2212yescomplemented
117(C22⋊D11)⋊C8C2212yescomplemented
118(C22⋊D11)⋊C8C2212yescomplemented
119#10622319C2212yescomplemented
120#10622319C2212yescomplemented
121#10622319C2212yescomplemented
122#10622319C2212yescomplemented
123#10622314C2212yescomplemented
124#10622314C2212yescomplemented
125#10622314C2212yescomplemented
126#10622314C2212yescomplemented
127#10622301C2212yescomplemented
128#10622301C2212yescomplemented
129#10622301C2212yescomplemented
130C8×D44C2212yescomplemented
131#10622292C2212yescomplemented
132#10622292C2212yescomplemented
133#10622292C2212yescomplemented
134C8×Dic22C2212yescomplemented
135C23×C4×C11C2311yescharacteristic
136C22×C22⋊D11C2×C411yescharacteristic
137C2×#4339C2×C412yes—
138C2×#4339C2311yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C2×C11×M16C2311yescharacteristic
141C2×C11×M16C2311yescharacteristic
142C22×C8×C11C2311yescharacteristic
143C22×C8×C11C2311yescharacteristic
144C11×#117C2×C412yes—
145C11×#117C2×C411yescharacteristic
146C11×#117C2×C411yescharacteristic
147C11×#117C2311yescharacteristic
148C11×#117C2311yescharacteristic
149C11×#117C2312yes—
150C2×C11×C4⋊C4C2×C411yescharacteristic
151C2×C11×C4⋊C4C2×C411yescharacteristic
152C2×C11×C22⋊C4C2×C412yes—
153C2×C42×C11C2312yes—
154#67006C2×C412yes—
155C2×C22⋊Dic11C2×C411yescharacteristic
156#66983C2×C412yes—
157#66983C2×C411yescharacteristic
158#66983C2×C411yescharacteristic
159#66982C2×C412yes—
160#66982C2×C412yes—
161#66982C2×C412yes—
162C4×C22⋊D11C2×C412yes—
163C4×C22⋊D11C2×C412yes—
164C4×C22⋊D11C2×C411yescharacteristic
165C4×C22⋊D11C2×C411yescharacteristic
166C4×C22⋊D11C2×C411yescharacteristic
167C4×C22⋊D11C2×C411yescharacteristic
168C4×C22⋊D11C2311yescharacteristic
169C4×C22⋊D11C2312yes—
170C4×C22⋊D11C2311yescharacteristic
171C4×C22⋊D11C2311yescharacteristic
172C4×C22⋊D11C2311yescharacteristic
173C4×C22⋊D11C2312yes—
174C2×(C2×D11)⋊C4C2×C411yescharacteristic
175#66979C2×C412yes—
176#66979C2311yescharacteristic
177#66977C2×C412yes—
178#66977C2×C411yescharacteristic
179#66977C2×C411yescharacteristic
180C2×Dic11⋊C4C2×C411yescharacteristic
181C2×C4×Dic11C2311yescharacteristic
182C2×#4318—42no—
183C2×#4318C2311yescharacteristic
184C2×#4318C2311yescharacteristic
185C2×#4318C2312yes—
186C22×C11⋊C8—42no—
187C22×C11⋊C8C2311yescharacteristic
188C22×C11⋊C8C2311yescharacteristic
189C22×C11⋊C8C2311yescharacteristic
190C22×C11⋊C8C2311yescharacteristic
191C22×C11⋊C8C2312yes—
192C22×C11⋊C8C2311yescharacteristic
193C22×C11⋊C8C2311yescharacteristic
194#66960—42no—
195M16×D11—42no—
196#66954—42no—
197C2×#4313—42no—
198C2×#4313C2311yescharacteristic
199C2×#4313C2311yescharacteristic
200C2×#4313C2311yescharacteristic
201C2×#4313C2311yescharacteristic
202C2×#4313C2312yes—
203C2×#4313C2312yes—
204C2×#4313C2312yes—
205C2×C8×D11C2312yes—
206C2×C8×D11C2312yes—
207C2×C8×D11C2312yes—
208#66951C2×C412yes—
209#66951C2×C412yes—
210#66950C2×C411yescharacteristic
211#66950C2×C411yescharacteristic
212#66949C2×C412yes—
213#66949C2×C412yes—
214#66948C2×C411yescharacteristic
215#66948C2×C411yescharacteristic
216#66947C2×C412yes—
217#66947C2×C412yes—
218#66946C2×C411yescharacteristic
219#66946C2×C411yescharacteristic
220#66945C2×C411yescharacteristic
221#66945C2×C411yescharacteristic
222C4⋊C4×D11C2×C411yescharacteristic
223C4⋊C4×D11C2×C411yescharacteristic
224#66943C2×C411yescharacteristic
225#66943C2×C411yescharacteristic
226#66942C2×C412yes—
227#66942C2×C412yes—
228#66941C2×C411yescharacteristic
229#66941C2×C411yescharacteristic
230#66940C2×C411yescharacteristic
231#66940C2×C411yescharacteristic
232#66939C2×C412yes—
233#66938C2×C412yes—
234#66938C2×C412yes—
235#66937C2×C412yes—
236#66937C2×C412yes—
237#66936C2×C412yes—
238#66936C2×C412yes—
239#66935C2×C412yes—
240(C22⋊D11)⋊C4C2×C412yes—
241(C22⋊D11)⋊C4C2×C412yes—
242C22⋊C4×D11C2×C412yes—
243#66932C2×C412yes—
244#66932C2×C412yes—
245#66931C2×C412yes—
246#66931C2×C412yes—
247#66930C2×C412yes—
248#66929C2×C412yes—
249#66929C2×C412yes—
250#66928C2×C412yes—
251C4×D44C2×C412yes—
252C4×D44C2312yes—
253C4×D44C2312yes—
254#66925C2×C412yes—
255#66925C2×C412yes—
256#66925C2312yes—
257#66925C2312yes—
258C42×D11C2312yes—
259C42×D11C2312yes—
260#66923C2×C412yes—
261C4×Dic22C2×C412yes—
262C4×Dic22C2312yes—
263C4×Dic22C2312yes—
264C11×C4⋊C8C2312yes—
265C11×C4⋊C8C2312yes—
266C11×C4⋊C8C2312yes—
267C11×C4⋊C8C2312yes—
268C11×C22⋊C8C2312yes—
269C11×C22⋊C8C2311yescharacteristic
270C11×C22⋊C8C2312yes—
271C11×C22⋊C8C2311yescharacteristic
272C11×C22⋊C8C2311yescharacteristic
273C11×C22⋊C8C2311yescharacteristic
274C11×#97C2312yes—
275C11×#97C2312yes—
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)⋊C8C2312yes—
283(C2×D11)⋊C8C2312yes—
284(C2×D11)⋊C8C2312yes—
285(C2×D11)⋊C8C2312yes—
286(C2×D11)⋊C8C2312yes—
287(C2×D11)⋊C8C2312yes—
288#66879C2312yes—
289#66879C2312yes—
290#66879C2312yes—
291#66879C2311yescharacteristic
292#66879C2311yescharacteristic
293#66879C2311yescharacteristic
294#66879C2311yescharacteristic
295Dic11⋊C8C2312yes—
296Dic11⋊C8C2312yes—
297Dic11⋊C8C2312yes—
298Dic11⋊C8C2312yes—
299Dic11⋊C8C2311yescharacteristic
300Dic11⋊C8C2312yes—
301Dic11⋊C8C2311yescharacteristic
302Dic11⋊C8C2312yes—
303Dic11⋊C8C2311yescharacteristic
304Dic11⋊C8C2311yescharacteristic
305C8×Dic11C2312yes—
306C8×Dic11C2312yes—
307C8×Dic11C2312yes—
308C4⋊(C11⋊C8)C2312yes—
309C4⋊(C11⋊C8)C2312yes—
310C4⋊(C11⋊C8)C2312yes—
311C4⋊(C11⋊C8)C2312yes—
312C4⋊(C11⋊C8)C2312yes—
313C4⋊(C11⋊C8)C2312yes—
314C4⋊(C11⋊C8)C2312yes—
315C4⋊(C11⋊C8)C2312yes—
316#60272—111nomaximal, Sylow
317C24×C11C22×C411yescharacteristic
318C23×D11C22×C411yescharacteristic
319C22×C4×C11—22no—
320C22×C4×C11—22no—
321C22×C4×C11C22×C411yescharacteristic
322C22×C4×C11C22×C411yescharacteristic
323C22×C4×C11C22×C411yescharacteristic
324C22×C4×C11C22×C412yes—
325C22×C4×C11C22×C412yes—
326C22×C4×C11C2411yescharacteristic
327C22×C4×C11C2411yescharacteristic
328C22×C4×C11C2411yescharacteristic
329C2×C22⋊D11—42no—
330C2×C22⋊D11C22×C412yes—
331C2×C22⋊D11C22×C411yescharacteristic
332C2×C22⋊D11C22×C411yescharacteristic
333C2×C22⋊D11C22×C412yes—
334C2×C22⋊D11C22×C411yescharacteristic
335C2×C22⋊D11C22×C412yes—
336C2×C22⋊D11C22×C411yescharacteristic
337C22×Dic11C22×C411yescharacteristic
338C22×Dic11C22×C411yescharacteristic
339C22×Dic11C22×C411yescharacteristic
340#4339—22no—
341#4339—22no—
342#4339—44no—
343C2×D44C22×C411yescharacteristic
344C2×D44C22×C412yes—
345C2×D44C22×C412yes—
346C2×C4×D11—22no—
347C2×C4×D11—22no—
348C2×C4×D11C22×C411yescharacteristic
349C2×C4×D11C22×C411yescharacteristic
350C2×C4×D11C22×C412yes—
351C2×C4×D11C22×C412yes—
352C2×C4×D11C22×C412yes—
353C2×C4×D11C22×C412yes—
354C2×C4×D11C2411yescharacteristic
355C2×C4×D11C2412yes—
356C2×C4×D11C2411yescharacteristic
357C2×Dic22C22×C411yescharacteristic
358C2×Dic22C22×C412yes—
359C2×Dic22C22×C412yes—
360C11×M16—22no—
361C11×M16—22no—
362C2×C8×C11—22no—
363C2×C8×C11—22no—
364C2×C8×C11C2412yes—
365C2×C8×C11C2411yescharacteristic
366C2×C8×C11C2411yescharacteristic
367C2×C8×C11C2412yes—
368C2×C8×C11C2411yescharacteristic
369C2×C8×C11C2411yescharacteristic
370C11×C4⋊C4C22×C411yescharacteristic
371C11×C4⋊C4C22×C411yescharacteristic
372C11×C4⋊C4C22×C411yescharacteristic
373C11×C4⋊C4C22×C411yescharacteristic
374C11×C4⋊C4C22×C412yes—
375C11×C4⋊C4C22×C412yes—
376C11×C22⋊C4C22×C412yes—
377C11×C22⋊C4C22×C412yes—
378C11×C22⋊C4C22×C412yes—
379C11×C22⋊C4C22×C412yes—
380C42×C11C22×C412yes—
381C42×C11C22×C412yes—
382C42×C11C2412yes—
383C42×C11C2412yes—
384C22⋊Dic11C22×C412yes—
385C22⋊Dic11C22×C411yescharacteristic
386C22⋊Dic11C22×C412yes—
387C22⋊Dic11C22×C411yescharacteristic
388C22⋊Dic11C22×C412yes—
389C22⋊Dic11C22×C411yescharacteristic
390C22⋊Dic11C22×C411yescharacteristic
391(C2×D11)⋊C4C22×C411yescharacteristic
392(C2×D11)⋊C4C22×C412yes—
393(C2×D11)⋊C4C22×C412yes—
394(C2×D11)⋊C4C22×C412yes—
395(C2×D11)⋊C4C22×C412yes—
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×C411yescharacteristic
402(C2×D11)⋊C4C22×C411yescharacteristic
403(C2×D11)⋊C4C22×C412yes—
404(C2×D11)⋊C4C22×C411yescharacteristic
405C4⋊Dic11C22×C412yes—
406C4⋊Dic11C22×C412yes—
407C4⋊Dic11C22×C412yes—
408C4⋊Dic11C22×C412yes—
409C4⋊Dic11C22×C411yescharacteristic
410C4⋊Dic11C22×C411yescharacteristic
411Dic11⋊C4C22×C411yescharacteristic
412Dic11⋊C4C22×C412yes—
413Dic11⋊C4C22×C412yes—
414Dic11⋊C4C22×C412yes—
415Dic11⋊C4C22×C412yes—
416Dic11⋊C4C22×C412yes—
417Dic11⋊C4C22×C411yescharacteristic
418Dic11⋊C4C22×C412yes—
419Dic11⋊C4C22×C412yes—
420Dic11⋊C4C22×C412yes—
421Dic11⋊C4C22×C412yes—
422Dic11⋊C4C22×C411yescharacteristic
423Dic11⋊C4C22×C412yes—
424Dic11⋊C4C22×C411yescharacteristic
425C4×Dic11C22×C412yes—
426C4×Dic11C22×C412yes—
427C4×Dic11C22×C412yes—
428C4×Dic11C22×C412yes—
429C4×Dic11C22×C411yescharacteristic
430C4×Dic11C22×C411yescharacteristic
431C4×Dic11C2412yes—
432C4×Dic11C2411yescharacteristic
433C4×Dic11C2411yescharacteristic
434#4318—22no—
435#4318—22no—
436#4318—42no—
437C2×C11⋊C8—22no—
438C2×C11⋊C8—22no—
439C2×C11⋊C8—41no—
440C2×C11⋊C8—41no—
441C2×C11⋊C8—41no—
442C2×C11⋊C8—41no—
443C2×C11⋊C8—42no—
444C2×C11⋊C8C2411yescharacteristic
445C2×C11⋊C8C2412yes—
446C2×C11⋊C8C2412yes—
447C2×C11⋊C8C2411yescharacteristic
448C2×C11⋊C8C2411yescharacteristic
449C2×C11⋊C8C2411yescharacteristic
450#4313—41no—
451#4313—41no—
452#4313—41no—
453#4313—41no—
454#4313—42no—
455#4313—42no—
456#4313—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#2961—111no—
471D4×M16—111no—
472#2933—111no—
473#2933—111no—
474#2930—111no—
475#2929—111no—
476C2×#435—111no—
477#2924—111no—
478#2924D1111yescharacteristic, complemented
479#2923—111no—
480#2906—111no—
481#2905—111no—
482C2×#424—111no—
483C23×C11—22no—
484C23×C11—22no—
485C23×C11—41no—
486C23×C11C23×C411yescharacteristic
487C23×C11C23×C411yescharacteristic
488C23×C11C23×C411yescharacteristic
489C22×D11—22no—
490C22×D11—41no—
491C22×D11—41no—
492C22×D11C23×C411yescharacteristic
493C22×D11C23×C412yes—
494C22×D11C23×C411yescharacteristic
495C2×C4×C11—22no—
496C2×C4×C11—24no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—21no—
500C2×C4×C11—21no—
501C2×C4×C11—21no—
502C2×C4×C11—21no—
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×C412yes—
510C2×C4×C11C23×C411yescharacteristic
511C2×C4×C11H(5,𝔽2)12yes—
512C2×C4×C112−1+412yes—
513C2×C4×C11C2511yescharacteristic
514C22⋊D11—24no—
515C22⋊D11—22no—
516C22⋊D11—24no—
517C22⋊D11—22no—
518C22⋊D11—41no—
519C22⋊D11—41no—
520C22⋊D11—42no—
521C2×Dic11—22no—
522C2×Dic11—41no—
523C2×Dic11—41no—
524C2×Dic11C23×C411yescharacteristic
525C2×Dic11C23×C411yescharacteristic
526C2×Dic11C23×C411yescharacteristic
527C2×Dic11C23×C412yes—
528C2×Dic11C23×C411yescharacteristic
529C2×Dic11C23×C412yes—
530C2×Dic11C23×C412yes—
531C2×Dic11C23×C411yescharacteristic
532C2×Dic11C23×C411yescharacteristic
533D44—22no—
534D44—42no—
535D44—42no—
536C4×D11—22no—
537C4×D11—22no—
538C4×D11—21no—
539C4×D11—22no—
540C4×D11—21no—
541C4×D11—21no—
542C4×D11—21no—
543C4×D11—22no—
544C4×D11—42no—
545C4×D11—42no—
546C4×D11—42no—
547C4×D11—42no—
548Dic22—22no—
549Dic22—42no—
550Dic22—42no—
551C8×C11—21no—
552C8×C11—22no—
553C8×C11—21no—
554C8×C11—21no—
555C8×C11—21no—
556C8×C11—22no—
557C11⋊C8—21no—
558C11⋊C8—22no—
559C11⋊C8—22no—
560C11⋊C8—21no—
561C11⋊C8—21no—
562C11⋊C8—21no—
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—112no—
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#525—111no—
587C4×#41—111no—
588C4×#41—112no—
589C2×C4×D4—111no—
590C2×#117—111no—
591C2×#117C2×D1111yescharacteristic
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—111no—
606#435—111no—
607#435—111no—
608#435—111no—
609#435—111no—
610#435—111no—
611#435—111no—
612#435—111no—
613#435—112no—
614#435—112no—
615#435—112no—
616#435—112no—
617#435—112no—
618#435—112no—
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#433C2×D1112yescomplemented
633#433C2×D1112yescomplemented
634#432—112no—
635#432—112no—
636#432—112no—
637#432C2×D1112yescomplemented
638#431—112no—
639#431C2×D1112yescomplemented
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—111no—
655#423—112no—
656#423—112no—
657#423—112no—
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#407C2×D1111yescharacteristic
666C2×C22⋊C8—111no—
667C2×C22⋊C8C2×D1111yescharacteristic
668#405—111no—
669#405—111no—
670#405C2×D1111yescharacteristic
671#405C2×D1111yescharacteristic
672C4×M16—111no—
673C2×#97—111no—
674C22×C11—21no—
675C22×C11—21no—
676C22×C11—21no—
677C22×C11—21no—
678C22×C11—21no—
679C22×C11—21no—
680C22×C11—21no—
681C22×C11—44no—
682C22×C11#52012yes—
683C22×C11#56812yes—
684C22×C11C24×C411yescharacteristic
685C2×D11—21no—
686C2×D11—21no—
687C2×D11—22no—
688C2×D11—21no—
689C2×D11—21no—
690C2×D11—22no—
691C2×D11—21no—
692C2×D11—21no—
693C2×D11—22no—
694C2×D11—82no—
695C4×C11—21no—
696C4×C11—21no—
697C4×C11—22no—
698C4×C11—22no—
699C4×C11—22no—
700C4×C11—22no—
701C4×C11#52012yes—
702C4×C11C2×H(5,𝔽2)11yescharacteristic
703C4×C11C2×2−1+411yescharacteristic
704Dic11—22no—
705Dic11—21no—
706Dic11—21no—
707Dic11—21no—
708Dic11—22no—
709Dic11—21no—
710Dic11—21no—
711Dic11—22no—
712Dic11—21no—
713C2×#41—112no—
714C2×#41—111no—
715C22×D4—111no—
716C23×C4—111no—
717C23×C4C22×D1111yescharacteristic
718#131—442no—
719#131—442no—
720C2×M16—111no—
721C2×M16—111no—
722C2×M16—112no—
723C2×M16—111no—
724C2×M16—112no—
725C2×M16—111no—
726C2×M16—111no—
727C2×M16—111no—
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⋊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—111no—
759#125—111no—
760#125—112no—
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—112no—
775C22⋊Q8—111no—
776C22⋊Q8—111no—
777C22⋊Q8—112no—
778C22⋊Q8—112no—
779C22⋊Q8—112no—
780C22⋊Q8—112no—
781#121—111no—
782#121—111no—
783#121—112no—
784#121—111no—
785#121—111no—
786#121—112no—
787#121—112no—
788#120—112no—
789#120—112no—
790C4×Q8—111no—
791C4×Q8—111no—
792C4×Q8—112no—
793C4×Q8—112no—
794C4×Q8—112no—
795C4×D4—111no—
796C4×D4—111no—
797C4×D4—111no—
798C4×D4—111no—
799C4×D4—112no—
800C4×D4—112no—
801C4×D4—111no—
802C4×D4—111no—
803C4×D4—111no—
804C4×D4—111no—
805C4×D4—112no—
806C4×D4—112no—
807C4×D4—111no—
808C4×D4—111no—
809C4×D4—112no—
810C4×D4—112no—
811C4×D4—112no—
812C4×D4—112no—
813C4×D4—112no—
814#117—112no—
815#117—111no—
816#117—111no—
817#117—111no—
818#117—112no—
819#117—112no—
820#117—112no—
821#117—112no—
822#117—112no—
823#117C4×D1112yes—
824#117C4×D1111yescharacteristic
825#117C4×D1111yescharacteristic
826#117C22×D1111yescharacteristic
827#117C22×D1111yescharacteristic
828#117C22×D1112yes—
829C2×C4⋊C4—111no—
830C2×C4⋊C4—111no—
831C2×C4⋊C4—111no—
832C2×C4⋊C4C4×D1111yescharacteristic
833C2×C4⋊C4C4×D1111yescharacteristic
834C2×C22⋊C4—111no—
835C2×C22⋊C4—111no—
836C2×C22⋊C4—112no—
837C2×C22⋊C4C4×D1112yes—
838C2×C42—111no—
839C2×C42—112no—
840C2×C42—112no—
841C2×C42C22×D1112yes—
842C4⋊C8—111no—
843C4⋊C8—112no—
844C4⋊C8—111no—
845C4⋊C8—111no—
846C4⋊C8—111no—
847C4⋊C8—112no—
848C4⋊C8—112no—
849C4⋊C8—112no—
850C4⋊C8—112no—
851C4⋊C8—112no—
852C4⋊C8—112no—
853C4⋊C8—112no—
854C4⋊C8—112no—
855C4⋊C8—112no—
856C4⋊C8—112no—
857C4⋊C8—112no—
858C4⋊C8—112no—
859C4⋊C8—112no—
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—112no—
869C22⋊C8—112no—
870C22⋊C8—112no—
871C22⋊C8—112no—
872C22⋊C8—112no—
873C22⋊C8—112no—
874C22⋊C8C22×D1111yescharacteristic
875C22⋊C8C22×D1111yescharacteristic
876C22⋊C8C22×D1111yescharacteristic
877C22⋊C8C22×D1111yescharacteristic
878C22⋊C8C22×D1112yes—
879C22⋊C8C22×D1112yes—
880#97—111no—
881#97—111no—
882#97—111no—
883#97—111no—
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×C8C22×D1112yes—
893C4×C8C22×D1112yes—
894C2×C11—22no—
895C2×C11—22no—
896C2×C11—41no—
897C2×C11C2×#52011yescharacteristic
898C2×C11C2×#56811yescharacteristic
899C2×C11#357311yescharacteristic
900D11—42no—
901D11—41no—
902D11—41no—
903C24—111no—
904C24C2×C4×D1111yescharacteristic
905#41—222no—
906#41—222no—
907#41—444no—
908C2×Q8—111no—
909C2×Q8—112no—
910C2×Q8—112no—
911C2×D4—111no—
912C2×D4—112no—
913C2×D4—112no—
914C2×D4—111no—
915C2×D4—111no—
916C2×D4—111no—
917C2×D4—112no—
918C2×D4—111no—
919C2×D4—112no—
920C2×D4—112no—
921C2×D4—442no—
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—111no—
925C22×C4—111no—
926C22×C4—111no—
927C22×C4—111no—
928C22×C4—111no—
929C22×C4—111no—
930C22×C4—112no—
931C22×C4—111no—
932C22×C4—112no—
933C22×C4—112no—
934C22×C4—112no—
935C22×C4—112no—
936C22×C4—222no—
937C22×C4—222no—
938C22×C4C2×C4×D1112yes—
939C22×C4C2×C4×D1111yescharacteristic
940C22×C4C2×C4×D1111yescharacteristic
941C22×C4C2×C4×D1111yescharacteristic
942C22×C4C2×C4×D1112yes—
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×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—111no—
961C2×C8—112no—
962C2×C8—112no—
963C2×C8—111no—
964C2×C8—111no—
965C2×C8—111no—
966C2×C8—222no—
967C2×C8—222no—
968C2×C8—442no—
969C2×C8—442no—
970C2×C8—442no—
971C2×C8—441no—
972C2×C8—441no—
973C2×C8—441no—
974C2×C8—441no—
975C2×C8—442no—
976C2×C8C23×D1112yes—
977C2×C8C23×D1111yescharacteristic
978C2×C8C23×D1111yescharacteristic
979C2×C8C23×D1111yescharacteristic
980C2×C8C23×D1112yes—
981C2×C8C23×D1111yescharacteristic
982C4⋊C4—111no—
983C4⋊C4—111no—
984C4⋊C4—111no—
985C4⋊C4—112no—
986C4⋊C4—112no—
987C4⋊C4—111no—
988C4⋊C4—111no—
989C4⋊C4—111no—
990C4⋊C4—112no—
991C4⋊C4—112no—
992C4⋊C4—112no—
993C4⋊C4—112no—
994C4⋊C4—112no—
995C4⋊C4—112no—
996C4⋊C4—112no—
997C4⋊C4—112no—
998C4⋊C4—112no—
999C4⋊C4—112no—
1000C4⋊C4—112no—
1001C4⋊C4—112no—
1002C4⋊C4C2×C4×D1111yescharacteristic
1003C4⋊C4C2×C4×D1111yescharacteristic
1004C4⋊C4C2×C4×D1111yescharacteristic
1005C4⋊C4C2×C4×D1111yescharacteristic
1006C4⋊C4C2×C4×D1112yes—
1007C4⋊C4C2×C4×D1112yes—
1008C22⋊C4—111no—
1009C22⋊C4—112no—
1010C22⋊C4—111no—
1011C22⋊C4—111no—
1012C22⋊C4—111no—
1013C22⋊C4—112no—
1014C22⋊C4—112no—
1015C22⋊C4—111no—
1016C22⋊C4—112no—
1017C22⋊C4—112no—
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⋊C4C2×C4×D1112yes—
1030C22⋊C4C2×C4×D1112yes—
1031C22⋊C4C2×C4×D1112yes—
1032C22⋊C4C2×C4×D1112yes—
1033C42—112no—
1034C42—112no—
1035C42—112no—
1036C42—111no—
1037C42—111no—
1038C42—112no—
1039C42—111no—
1040C42—112no—
1041C42—111no—
1042C42C2×C4×D1112yes—
1043C42C2×C4×D1112yes—
1044C42C23×D1112yes—
1045C42C23×D1112yes—
1046C11#6027211yescharacteristic, complemented, Sylow
1047C23—22no—
1048C23—22no—
1049C23—41no—
1050C23—111no—
1051C23—112no—
1052C23—111no—
1053C23—222no—
1054C23—441no—
1055C23—441no—
1056C23C22×C4×D1111yescharacteristic
1057C23C22×C4×D1111yescharacteristic
1058C23C22×C4×D1111yescharacteristic
1059Q8—222no—
1060Q8—442no—
1061Q8—442no—
1062D4—222no—
1063D4—222no—
1064D4—224no—
1065D4—224no—
1066D4—222no—
1067D4—442no—
1068D4—442no—
1069D4—441no—
1070D4—441no—
1071D4—442no—
1072C2×C4—24no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—42no—
1081C2×C4—111no—
1082C2×C4—111no—
1083C2×C4—111no—
1084C2×C4—111no—
1085C2×C4—112no—
1086C2×C4—112no—
1087C2×C4—112no—
1088C2×C4—111no—
1089C2×C4—111no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—221no—
1094C2×C4—222no—
1095C2×C4—221no—
1096C2×C4—221no—
1097C2×C4—221no—
1098C2×C4—222no—
1099C2×C4—442no—
1100C2×C4—442no—
1101C2×C4—442no—
1102C2×C4—442no—
1103C2×C4—441no—
1104C2×C4—441no—
1105C2×C4C22×C4×D1112yes—
1106C2×C4C22×C4×D1112yes—
1107C2×C4C22×C4×D1111yescharacteristic
1108C2×C4C22×C4×D1112yes—
1109C2×C4C22×C4×D1112yes—
1110C2×C4C22×C4×D1111yescharacteristic
1111C2×C4C22×C4×D1111yescharacteristic
1112C2×C4#6704212yes—
1113C2×C4#6704312yes—
1114C2×C4C24×D1111yescharacteristic
1115C8—21no—
1116C8—21no—
1117C8—22no—
1118C8—21no—
1119C8—21no—
1120C8—22no—
1121C8—221no—
1122C8—221no—
1123C8—221no—
1124C8—221no—
1125C8—222no—
1126C8—222no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—44no—
1135C22—221no—
1136C22—222no—
1137C22—221no—
1138C22—221no—
1139C22—222no—
1140C22—221no—
1141C22—221no—
1142C22—221no—
1143C22—222no—
1144C22—882no—
1145C22#1062305412yes—
1146C22#1062328112yes—
1147C22C23×C4×D1111yescharacteristic
1148C4—22no—
1149C4—22no—
1150C4—22no—
1151C4—22no—
1152C4—21no—
1153C4—21no—
1154C4—221no—
1155C4—221no—
1156C4—222no—
1157C4—221no—
1158C4—222no—
1159C4—221no—
1160C4—221no—
1161C4—221no—
1162C4—222no—
1163C4#1062305412yes—
1164C4C2×#6704211yescharacteristic
1165C4C2×#6704311yescharacteristic
1166C2—22no—
1167C2—22no—
1168C2—41no—
1169C2—441no—
1170C2—441no—
1171C2—442no—
1172C2C2×#1062305411yescharacteristic
1173C2C2×#1062328111yescharacteristic
1174C2#1308332911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2924C2
prime radical#13082170C2
cosocleC2×C4×C11C25
hypercenter#2924D11
hypocenterC11#60272
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2924

Complements

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

NH ≅ G/Ntype
2. #13077781C2semidirect
3. #13077781C2semidirect
4. #13077778C2semidirect
5. #13077759C2semidirect
6. #13077757C2semidirect
7. #13077750C2semidirect
8. #13077743C2semidirect
9. #13077729C2semidirect
10. #13077560C2semidirect
11. #13077554C2semidirect
12. #13077348C2semidirect
13. #13077344C2semidirect
14. #13077337C2semidirect
15. #13077321C2semidirect
16. #13077306C2semidirect
17. C2×#10622343C2semidirect
18. #13077273C2semidirect
19. #13077266C2semidirect
20. #13077183C2semidirect
21. #13077177C2semidirect
22. C2×#10622612C2semidirect
23. C11×#2924C2semidirect
53. C11×#433C22semidirect
54. C11×#433C22semidirect
55. C11×#432C22semidirect
56. C11×#431C22semidirect
79. #10622612C22semidirect
80. #10622612C22semidirect
81. C2×C4⋊(C11⋊C8)C22semidirect
82. C2×C4⋊(C11⋊C8)C22semidirect
83. #10622453C22semidirect
84. #10622453C22semidirect
85. #10622453C22semidirect
86. #10622453C22semidirect
87. #10622452C22semidirect
88. #10622452C22semidirect
89. #10622452C22semidirect
90. #10622452C22semidirect
91. #10622450C22semidirect
92. #10622450C22semidirect
93. #10622450C22semidirect
94. #10622448C22semidirect
95. #10622448C22semidirect
96. #10622448C22semidirect
97. #10622446C22semidirect
98. D11×C4⋊C8C22semidirect
108. #10622343C22semidirect
109. #10622343C22semidirect
110. #10622343C22semidirect
112. #10622342C22semidirect
114. #10622341C22semidirect
116. (C22⋊D11)⋊C8C22semidirect
117. (C22⋊D11)⋊C8C22semidirect
118. (C22⋊D11)⋊C8C22semidirect
119. #10622319C22semidirect
120. #10622319C22semidirect
121. #10622319C22semidirect
122. #10622319C22semidirect
123. #10622314C22semidirect
124. #10622314C22semidirect
125. #10622314C22semidirect
126. #10622314C22semidirect
127. #10622301C22semidirect
128. #10622301C22semidirect
129. #10622301C22semidirect
130. C8×D44C22semidirect
131. #10622292C22semidirect
132. #10622292C22semidirect
133. #10622292C22semidirect
134. C8×Dic22C22semidirect
478. #2924D11semidirect
632. #433C2×D11semidirect
633. #433C2×D11semidirect
637. #432C2×D11semidirect
639. #431C2×D11semidirect
1046. C11#60272semidirect

Maximal subgroups

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

subgroupindex
#130821702
#130777812
#130777782
#130777592
#130777572
#130777502
#130777432
#130777292
#130775602
#130775542
#130773482
#130773442
#130773372
#130773212
#130773062
C2×#106223432
#130772732
#130772662
#130771832
#130771772
C2×#106226122
C11×#29242
#6027211