Finite Group Databasebeta

← #15619008

Subgroups — #15619008

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#13082174C211yesmaximal, characteristic
2#13077787C212yesmaximal, complemented
3#13077782C212yesmaximal, complemented
4#13077769C212yesmaximal, complemented
5#13077758C212yesmaximal, complemented
6#13077756C212yesmaximal, complemented
7#13077751C212yesmaximal, complemented
8#13077736C212yesmaximal, complemented
9#13077728C212yesmaximal, complemented
10#13077559C211yesmaximal, characteristic, complemented
11#13077556C211yesmaximal, characteristic, complemented
12D4×#4318C211yesmaximal, characteristic, complemented
13#13077337C211yesmaximal, characteristic, complemented
14#13077337C211yesmaximal, characteristic, complemented
15#13077319C211yesmaximal, characteristic, complemented
16#13077310C211yesmaximal, characteristic, complemented
17#13077270C211yesmaximal, characteristic, complemented
18#13077270C211yesmaximal, characteristic, complemented
19#13077265C211yesmaximal, characteristic, complemented
20#13077181C211yesmaximal, characteristic, complemented
21#13077179C211yesmaximal, characteristic, complemented
22C2×#10622715C211yesmaximal, characteristic, complemented
23C2×C11×#435C211yesmaximal, characteristic, complemented
24C22×C11×M16C2211yescharacteristic
25C23×C8×C11C2211yescharacteristic
26C2×C4×D4×C11C2211yescharacteristic
27#10623337C412yes—
28#10623322C2211yescharacteristic
29#10623322C2211yescharacteristic
30C2×#66979C2211yescharacteristic
31C2×#66979C2211yescharacteristic
32C22×#4318C2211yescharacteristic
33C22×#4318C2211yescharacteristic
34C2×#66954C2211yescharacteristic
35C2×#66954C2211yescharacteristic
36#10623096C411yescharacteristic
37#10623096C411yescharacteristic
38#10623094C411yescharacteristic
39#10623088C2212yes—
40#10623086C411yescharacteristic
41#10623074C411yescharacteristic
42#10623073C411yescharacteristic
43#10623072C411yescharacteristic
44#10623072C411yescharacteristic
45#10623069C2212yes—
46#10623069C2212yes—
47C4×#4341C2212yes—
48#10623044C412yes—
49#10623026C412yes—
50#10623026C412yes—
51C4×#4339C2211yescharacteristic
52#10623001C2211yescharacteristic
53C11×#435C2211yescharacteristic
54C11×#435C2211yescharacteristic
55C11×#435C2211yescharacteristic
56C11×#435C2211yescharacteristic
57C11×#435C2211yescharacteristic
58C11×#435C2211yescharacteristic
59C11×#435C2211yescharacteristic
60C11×#435C2211yescharacteristic
61C2×C11×C4⋊C8C2211yescharacteristic
62C2×C11×C22⋊C8C2211yescharacteristic
63C2×C11×C22⋊C8C2211yescharacteristic
64C2×C11×#97C2211yescharacteristic
65#10622820C2211yescharacteristic
66#10622820C2211yescharacteristic
67#10622741C2212yescomplemented
68#10622741C2212yescomplemented
69#10622740C2212yescomplemented
70#10622740C2212yescomplemented
71#10622732C2212yescomplemented
72#10622732C2212yescomplemented
73#10622731C2212yescomplemented
74#10622731C2212yescomplemented
75#10622724C2212yescomplemented
76#10622724C2212yescomplemented
77#10622723C2211yescharacteristic
78#10622723C2211yescharacteristic
79C8×C22⋊D11C2212yescomplemented
80C8×C22⋊D11C2212yescomplemented
81#10622715C2211yescharacteristic
82#10622715C2211yescharacteristic
83#10622715C2211yescharacteristic
84#10622715C2211yescharacteristic
85#10622715C2211yescharacteristic
86#10622715C2211yescharacteristic
87#10622715C2211yescharacteristic
88#10622715C2211yescharacteristic
89#10622715C2212yescomplemented
90#10622715C2212yescomplemented
91#10622714C2211yescharacteristic
92#10622714C2211yescharacteristic
93#10622714C2211yescharacteristic
94#10622714C2211yescharacteristic
95C2×Dic11⋊C8C2212yescomplemented
96C2×Dic11⋊C8C2212yescomplemented
97#10622625C2212yes—
98#10622624C2212yes—
99#10622624C2212yes—
100D4×C11⋊C8C2212yes—
101#10622537C2211yescharacteristic
102C4×#4318C2211yescharacteristic
103#10622452C2212yescomplemented
104#10622452C2212yescomplemented
105#10622450C2212yescomplemented
106D11×C4⋊C8C2212yescomplemented
107#10622444C2212yescomplemented
108#10622443C2212yescomplemented
109#10622441C2212yescomplemented
110#10622441C2212yescomplemented
111#10622343C2212yescomplemented
112#10622343C2212yescomplemented
113#10622342C2212yescomplemented
114#10622342C2212yescomplemented
115#10622341C2212yescomplemented
116#10622341C2212yescomplemented
117(C22⋊D11)⋊C8C2212yescomplemented
118(C22⋊D11)⋊C8C2212yescomplemented
119#10622333C2212yescomplemented
120#10622333C2212yescomplemented
121#10622333C2212yescomplemented
122#10622333C2212yescomplemented
123#10622332C2212yescomplemented
124#10622332C2212yescomplemented
125#10622331C2212yescomplemented
126#10622331C2212yescomplemented
127#10622322C2212yescomplemented
128#10622322C2212yescomplemented
129#10622318C2212yescomplemented
130#10622318C2212yescomplemented
131#10622314C2212yescomplemented
132#10622314C2212yescomplemented
133#10622314C2212yescomplemented
134#10622314C2212yescomplemented
135C22×D4×C11C2×C411yescharacteristic
136C23×C4×C11C2311yescharacteristic
137C23×C4×C11C2311yescharacteristic
138C2×#4341C2×C412yes—
139C2×#4339C2311yescharacteristic
140C2×C11×M16—42no—
141C2×C11×M16C2311yescharacteristic
142C2×C11×M16C2311yescharacteristic
143C2×C11×M16C2311yescharacteristic
144C2×C11×M16C2311yescharacteristic
145C22×C8×C11—42no—
146C22×C8×C11C2311yescharacteristic
147C22×C8×C11C2311yescharacteristic
148C22×C8×C11C2311yescharacteristic
149C22×C8×C11C2311yescharacteristic
150C22×C8×C11C2311yescharacteristic
151C22×C8×C11C2311yescharacteristic
152C22×C8×C11C2311yescharacteristic
153C22×C8×C11C2311yescharacteristic
154C4×D4×C11C2×C411yescharacteristic
155C4×D4×C11C2×C411yescharacteristic
156C4×D4×C11C2×C411yescharacteristic
157C4×D4×C11C2×C411yescharacteristic
158C4×D4×C11C2311yescharacteristic
159C4×D4×C11C2311yescharacteristic
160C4×D4×C11C2311yescharacteristic
161C4×D4×C11C2311yescharacteristic
162C2×C11×C4⋊C4C2×C411yescharacteristic
163C2×C11×C22⋊C4C2×C411yescharacteristic
164C2×C11×C22⋊C4C2×C411yescharacteristic
165C2×C42×C11C2311yescharacteristic
166#67006C2×C412yes—
167#67006C2×C412yes—
168C2×C22⋊Dic11C2×C412yes—
169C2×C22⋊Dic11C2×C412yes—
170#66992C2×C412yes—
171#66992C2×C412yes—
172#66991C2×C412yes—
173#66989C2×C412yes—
174#66988C2×C412yes—
175#66988C2×C412yes—
176D4×Dic11C2×C412yes—
177#66983C2×C411yescharacteristic
178#66983C2×C411yescharacteristic
179#66983C2×C411yescharacteristic
180#66983C2×C411yescharacteristic
181#66982C2×C412yes—
182#66982C2×C412yes—
183C4×C22⋊D11C2×C412yes—
184C4×C22⋊D11C2×C412yes—
185C4×C22⋊D11C2312yes—
186C4×C22⋊D11C2312yes—
187C4×C22⋊D11C2312yes—
188C4×C22⋊D11C2312yes—
189#66979C2×C412yes—
190#66979C2×C412yes—
191#66979C2×C411yescharacteristic
192#66979C2×C411yescharacteristic
193#66979C2×C411yescharacteristic
194#66979C2×C411yescharacteristic
195#66979C2312yes—
196#66979C2311yescharacteristic
197#66979C2311yescharacteristic
198#66979C2311yescharacteristic
199#66979C2312yes—
200C2×C4⋊Dic11C2×C411yescharacteristic
201C2×C4⋊Dic11C2×C411yescharacteristic
202C2×C4⋊Dic11C2×C411yescharacteristic
203C2×C4⋊Dic11C2×C411yescharacteristic
204#66977C2×C412yes—
205#66977C2×C412yes—
206#66977C2×C411yescharacteristic
207#66977C2×C411yescharacteristic
208#66977C2×C411yescharacteristic
209#66977C2×C411yescharacteristic
210C2×C4×Dic11C2312yes—
211C2×C4×Dic11C2312yes—
212C2×#4318—42no—
213C2×#4318—42no—
214C2×#4318C2311yescharacteristic
215C2×#4318C2311yescharacteristic
216C2×#4318C2311yescharacteristic
217C2×#4318C2311yescharacteristic
218C2×#4318C2312yes—
219C2×#4318C2312yes—
220C22×C11⋊C8C2312yes—
221C22×C11⋊C8C2312yes—
222#66954—42no—
223#66954—42no—
224C2×#4313C2312yes—
225C2×#4313C2312yes—
226C2×C8×D11C2312yes—
227C2×C8×D11C2312yes—
228#66951C2×C412yes—
229#66951C2×C412yes—
230#66950C2×C412yes—
231#66945C2×C412yes—
232#66943C2×C412yes—
233#66942C2×C412yes—
234#66942C2×C412yes—
235#66940C2×C412yes—
236#66939C2×C412yes—
237#66939C2×C412yes—
238#66938C2×C412yes—
239#66938C2×C412yes—
240#66936C2×C412yes—
241#66936C2×C412yes—
242(C22⋊D11)⋊C4C2×C412yes—
243(C22⋊D11)⋊C4C2×C412yes—
244#66932C2×C412yes—
245#66932C2×C412yes—
246#66932C2×C412yes—
247#66932C2×C412yes—
248#66931C2×C412yes—
249#66931C2×C412yes—
250#66930C2×C412yes—
251#66930C2×C412yes—
252C4×D44C2×C411yescharacteristic
253C4×D44C2×C411yescharacteristic
254#66925C2312yes—
255C42×D11C2312yes—
256#66923C2×C411yescharacteristic
257#66923C2×C411yescharacteristic
258#66922C2×C411yescharacteristic
259#66922C2×C411yescharacteristic
260C4×Dic22C2×C411yescharacteristic
261C4×Dic22C2×C411yescharacteristic
262C4×Dic22C2312yes—
263C4×Dic22C2312yes—
264C11×C4⋊C8C2311yescharacteristic
265C11×C4⋊C8C2311yescharacteristic
266C11×C4⋊C8C2311yescharacteristic
267C11×C4⋊C8C2311yescharacteristic
268C11×C22⋊C8C2311yescharacteristic
269C11×C22⋊C8C2311yescharacteristic
270C11×C22⋊C8C2311yescharacteristic
271C11×C22⋊C8C2311yescharacteristic
272C11×C22⋊C8C2311yescharacteristic
273C11×C22⋊C8C2311yescharacteristic
274C11×C22⋊C8C2311yescharacteristic
275C11×C22⋊C8C2311yescharacteristic
276C11×#97C2311yescharacteristic
277C11×#97C2311yescharacteristic
278C11×#97C2311yescharacteristic
279C11×#97C2311yescharacteristic
280C22⋊(C11⋊C8)C2312yes—
281C22⋊(C11⋊C8)C2312yes—
282C22⋊(C11⋊C8)C2312yes—
283C22⋊(C11⋊C8)C2312yes—
284(C2×D11)⋊C8C2312yes—
285(C2×D11)⋊C8C2312yes—
286(C2×D11)⋊C8C2312yes—
287(C2×D11)⋊C8C2312yes—
288#66879C2312yes—
289#66879C2312yes—
290#66879C2312yes—
291#66879C2312yes—
292Dic11⋊C8C2312yes—
293Dic11⋊C8C2312yes—
294Dic11⋊C8C2312yes—
295Dic11⋊C8C2312yes—
296Dic11⋊C8C2312yes—
297Dic11⋊C8C2312yes—
298Dic11⋊C8C2312yes—
299Dic11⋊C8C2312yes—
300Dic11⋊C8C2312yes—
301Dic11⋊C8C2312yes—
302Dic11⋊C8C2312yes—
303Dic11⋊C8C2312yes—
304Dic11⋊C8C2312yes—
305Dic11⋊C8C2312yes—
306Dic11⋊C8C2312yes—
307Dic11⋊C8C2312yes—
308C8×Dic11C2312yes—
309C8×Dic11C2312yes—
310C8×Dic11C2312yes—
311C8×Dic11C2312yes—
312C4⋊(C11⋊C8)C2312yes—
313C4⋊(C11⋊C8)C2312yes—
314#66867C2312yes—
315C4×C11⋊C8C2312yes—
316#60272—111nomaximal, Sylow
317C24×C11C22×C411yescharacteristic
318C24×C11C22×C411yescharacteristic
319C2×D4×C11—42no—
320C2×D4×C11C22×C411yescharacteristic
321C2×D4×C11C22×C411yescharacteristic
322C2×D4×C11C22×C411yescharacteristic
323C2×D4×C11C22×C411yescharacteristic
324C22×C4×C11—22no—
325C22×C4×C11—22no—
326C22×C4×C11—22no—
327C22×C4×C11—22no—
328C22×C4×C11C22×C411yescharacteristic
329C22×C4×C11C22×C411yescharacteristic
330C22×C4×C11C22×C411yescharacteristic
331C22×C4×C11C22×C411yescharacteristic
332C22×C4×C11C22×C411yescharacteristic
333C22×C4×C11C22×C411yescharacteristic
334C22×C4×C11C22×C411yescharacteristic
335C22×C4×C11C22×C411yescharacteristic
336C22×C4×C11C2411yescharacteristic
337C22×C4×C11C2411yescharacteristic
338C22×C4×C11C2411yescharacteristic
339C22×C4×C11C2411yescharacteristic
340C22×C4×C11C2411yescharacteristic
341C2×C22⋊D11C22×C412yes—
342C2×C22⋊D11C22×C412yes—
343C2×C22⋊D11C22×C412yes—
344C2×C22⋊D11C22×C412yes—
345C2×C22⋊D11C22×C412yes—
346C22×Dic11C22×C412yes—
347C22×Dic11C22×C412yes—
348C22×Dic11C22×C412yes—
349C22×Dic11C22×C412yes—
350#4341—44no—
351#4339—22no—
352#4339—22no—
353C2×D44C22×C411yescharacteristic
354C2×C4×D11C22×C412yes—
355C2×C4×D11C22×C412yes—
356C2×C4×D11C2412yes—
357C2×Dic22C22×C411yescharacteristic
358C2×Dic22C22×C412yes—
359C2×Dic22C22×C412yes—
360C11×M16—41no—
361C11×M16—41no—
362C11×M16—41no—
363C11×M16—41no—
364C2×C8×C11—22no—
365C2×C8×C11—22no—
366C2×C8×C11—22no—
367C2×C8×C11—22no—
368C2×C8×C11—41no—
369C2×C8×C11—41no—
370C2×C8×C11—41no—
371C2×C8×C11—41no—
372C2×C8×C11C2411yescharacteristic
373C2×C8×C11C2411yescharacteristic
374C2×C8×C11C2411yescharacteristic
375C2×C8×C11C2411yescharacteristic
376C2×C8×C11C2411yescharacteristic
377C2×C8×C11C2411yescharacteristic
378C2×C8×C11C2411yescharacteristic
379C2×C8×C11C2411yescharacteristic
380C11×C4⋊C4C22×C411yescharacteristic
381C11×C4⋊C4C22×C411yescharacteristic
382C11×C4⋊C4C22×C411yescharacteristic
383C11×C4⋊C4C22×C411yescharacteristic
384C11×C22⋊C4C22×C411yescharacteristic
385C11×C22⋊C4C22×C411yescharacteristic
386C11×C22⋊C4C22×C411yescharacteristic
387C11×C22⋊C4C22×C411yescharacteristic
388C11×C22⋊C4C22×C411yescharacteristic
389C11×C22⋊C4C22×C411yescharacteristic
390C11×C22⋊C4C22×C411yescharacteristic
391C11×C22⋊C4C22×C411yescharacteristic
392C42×C11C22×C411yescharacteristic
393C42×C11C22×C411yescharacteristic
394C42×C11C2411yescharacteristic
395C42×C11C2411yescharacteristic
396C22⋊Dic11C22×C412yes—
397C22⋊Dic11C22×C412yes—
398C22⋊Dic11C22×C412yes—
399C22⋊Dic11C22×C412yes—
400C22⋊Dic11C22×C412yes—
401C22⋊Dic11C22×C412yes—
402C22⋊Dic11C22×C412yes—
403C22⋊Dic11C22×C412yes—
404C22⋊Dic11C22×C412yes—
405C22⋊Dic11C22×C412yes—
406C22⋊Dic11C22×C412yes—
407(C2×D11)⋊C4C22×C412yes—
408(C2×D11)⋊C4C22×C412yes—
409(C2×D11)⋊C4C22×C412yes—
410(C2×D11)⋊C4C22×C412yes—
411(C2×D11)⋊C4C22×C412yes—
412(C2×D11)⋊C4C22×C412yes—
413C4⋊Dic11C22×C411yescharacteristic
414C4⋊Dic11C22×C411yescharacteristic
415C4⋊Dic11C22×C412yes—
416C4⋊Dic11C22×C412yes—
417C4⋊Dic11C22×C411yescharacteristic
418C4⋊Dic11C22×C411yescharacteristic
419C4⋊Dic11C22×C411yescharacteristic
420C4⋊Dic11C22×C411yescharacteristic
421C4⋊Dic11C22×C412yes—
422C4⋊Dic11C22×C412yes—
423C4⋊Dic11C22×C412yes—
424C4⋊Dic11C22×C412yes—
425Dic11⋊C4C22×C412yes—
426Dic11⋊C4C22×C412yes—
427Dic11⋊C4C22×C412yes—
428Dic11⋊C4C22×C412yes—
429Dic11⋊C4C22×C412yes—
430Dic11⋊C4C22×C412yes—
431Dic11⋊C4C22×C412yes—
432Dic11⋊C4C22×C412yes—
433Dic11⋊C4C22×C412yes—
434Dic11⋊C4C22×C412yes—
435C4×Dic11C22×C412yes—
436C4×Dic11C22×C412yes—
437C4×Dic11C22×C412yes—
438C4×Dic11C22×C412yes—
439C4×Dic11C22×C412yes—
440C4×Dic11C22×C412yes—
441C4×Dic11C2412yes—
442C4×Dic11C2412yes—
443C4×Dic11C2412yes—
444#4318—22no—
445#4318—22no—
446#4318—22no—
447#4318—22no—
448#4318—42no—
449#4318—42no—
450C2×C11⋊C8—42no—
451C2×C11⋊C8—42no—
452C2×C11⋊C8C2412yes—
453C2×C11⋊C8C2412yes—
454C2×C11⋊C8C2412yes—
455C2×C11⋊C8C2412yes—
456#4313—42no—
457#4313—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×#435D1111yescharacteristic, complemented
477#2924—111no—
478#2924—111no—
479#2923—111no—
480#2906—111no—
481#2905—111no—
482C2×#424—111no—
483C23×C11—22no—
484C23×C11—22no—
485C23×C11—22no—
486C23×C11—41no—
487C23×C11—41no—
488C23×C11—41no—
489C23×C11C23×C411yescharacteristic
490C23×C11C23×C411yescharacteristic
491C23×C11C23×C411yescharacteristic
492C23×C11C23×C411yescharacteristic
493C23×C11C23×C411yescharacteristic
494C22×D11C23×C412yes—
495D4×C11—22no—
496D4×C11—22no—
497D4×C11—41no—
498D4×C11—41no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—21no—
506C2×C4×C11—21no—
507C2×C4×C11—21no—
508C2×C4×C11—21no—
509C2×C4×C11—21no—
510C2×C4×C11—21no—
511C2×C4×C11—21no—
512C2×C4×C11—21no—
513C2×C4×C11—41no—
514C2×C4×C11—41no—
515C2×C4×C11C23×C411yescharacteristic
516C2×C4×C11C23×C411yescharacteristic
517C2×C4×C11C23×C411yescharacteristic
518C2×C4×C11C23×C411yescharacteristic
519C2×C4×C11C23×C411yescharacteristic
520C2×C4×C11C23×C411yescharacteristic
521C2×C4×C11C23×C411yescharacteristic
522C2×C4×C11C23×C411yescharacteristic
523C2×C4×C11C23×C411yescharacteristic
524C2×C4×C11H(5,𝔽2)12yes—
525C2×C4×C112−1+412yes—
526C2×C4×C11C2511yescharacteristic
527C22⋊D11—24no—
528C22⋊D11—24no—
529C22⋊D11—42no—
530C22⋊D11—42no—
531C22⋊D11—42no—
532C2×Dic11—24no—
533C2×Dic11—42no—
534C2×Dic11—42no—
535C2×Dic11—42no—
536C2×Dic11C23×C412yes—
537C2×Dic11C23×C412yes—
538C2×Dic11C23×C412yes—
539C2×Dic11C23×C412yes—
540C2×Dic11C23×C412yes—
541C2×Dic11C23×C412yes—
542C2×Dic11C23×C412yes—
543D44—22no—
544C4×D11—22no—
545C4×D11—22no—
546C4×D11—42no—
547C4×D11—42no—
548Dic22—22no—
549Dic22—42no—
550Dic22—42no—
551C8×C11—21no—
552C8×C11—21no—
553C8×C11—21no—
554C8×C11—21no—
555C8×C11—21no—
556C8×C11—21no—
557C8×C11—21no—
558C8×C11—21no—
559C11⋊C8—22no—
560C11⋊C8—22no—
561C11⋊C8—22no—
562C11⋊C8—22no—
563C2×#131—111no—
564C2×#131—111no—
565C22×M16—111no—
566C22×M16—111no—
567C22×M16C2×D1111yescharacteristic
568C23×C8C2×D1111yescharacteristic
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×#41—111no—
589C2×C4×D4C2×D1111yescharacteristic
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—112no—
614#435—112no—
615#435C2×D1111yescharacteristic
616#435C2×D1111yescharacteristic
617#435C2×D1111yescharacteristic
618#435C2×D1111yescharacteristic
619#435C2×D1111yescharacteristic
620#435C2×D1111yescharacteristic
621#435C2×D1111yescharacteristic
622#435C2×D1111yescharacteristic
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—112no—
641#424—112no—
642#424—111no—
643#424—111no—
644#424—111no—
645#424—111no—
646#424—112no—
647#424—112no—
648#424—111no—
649#424—111no—
650#424—111no—
651#424—111no—
652#424—112no—
653#424—112no—
654#423—112no—
655#423—112no—
656#423—111no—
657#423—112no—
658C2×C4⋊C8—112no—
659C2×C4⋊C8—112no—
660C2×C4⋊C8—112no—
661C2×C4⋊C8C2×D1111yescharacteristic
662#408—111no—
663#408—111no—
664#407—111no—
665#407—111no—
666C2×C22⋊C8C2×D1111yescharacteristic
667C2×C22⋊C8C2×D1111yescharacteristic
668#405—111no—
669#405—111no—
670#405—111no—
671#405—111no—
672C4×M16—111no—
673C2×#97C2×D1111yescharacteristic
674C22×C11—21no—
675C22×C11—21no—
676C22×C11—21no—
677C22×C11—21no—
678C22×C11—21no—
679C22×C11—21no—
680C22×C11—21no—
681C22×C11—21no—
682C22×C11—21no—
683C22×C11—21no—
684C22×C11—21no—
685C22×C11—21no—
686C22×C11—21no—
687C22×C11—44no—
688C22×C11—82no—
689C22×C11#52012yes—
690C22×C11#56812yes—
691C22×C11C24×C411yescharacteristic
692C2×D11—22no—
693C2×D11—22no—
694C2×D11—22no—
695C4×C11—21no—
696C4×C11—21no—
697C4×C11—21no—
698C4×C11—21no—
699C4×C11—21no—
700C4×C11—21no—
701C4×C11—21no—
702C4×C11—21no—
703C4×C11#52012yes—
704C4×C11C2×H(5,𝔽2)11yescharacteristic
705C4×C11C2×2−1+411yescharacteristic
706Dic11—22no—
707Dic11—22no—
708Dic11—22no—
709Dic11—22no—
710Dic11—22no—
711Dic11—22no—
712Dic11—22no—
713C2×#41—112no—
714C2×#41—111no—
715C22×D4C4×D1111yescharacteristic
716C23×C4C22×D1111yescharacteristic
717C23×C4C22×D1111yescharacteristic
718#131—442no—
719#131—442no—
720C2×M16—42no—
721C2×M16—111no—
722C2×M16—111no—
723C2×M16—111no—
724C2×M16—111no—
725C2×M16—112no—
726C2×M16—112no—
727C2×M16—112no—
728C2×M16—112no—
729C2×M16—442no—
730C2×M16—442no—
731C2×M16C22×D1111yescharacteristic
732C2×M16C22×D1111yescharacteristic
733C2×M16C22×D1111yescharacteristic
734C2×M16C22×D1111yescharacteristic
735C22×C8—42no—
736C22×C8—112no—
737C22×C8—112no—
738C22×C8—112no—
739C22×C8—112no—
740C22×C8C22×D1111yescharacteristic
741C22×C8C22×D1111yescharacteristic
742C22×C8C22×D1111yescharacteristic
743C22×C8C22×D1111yescharacteristic
744C22×C8C22×D1111yescharacteristic
745C22×C8C22×D1111yescharacteristic
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—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—112no—
782#121—112no—
783#121—112no—
784#121—111no—
785#121—111no—
786#121—111no—
787#121—111no—
788#120—112no—
789#120—112no—
790C4×Q8—112no—
791C4×Q8—111no—
792C4×Q8—111no—
793C4×Q8—112no—
794C4×Q8—112no—
795C4×D4—112no—
796C4×D4—112no—
797C4×D4—112no—
798C4×D4—112no—
799C4×D4—112no—
800C4×D4—112no—
801C4×D4—112no—
802C4×D4—112no—
803C4×D4—112no—
804C4×D4—111no—
805C4×D4—111no—
806C4×D4C4×D1111yescharacteristic
807C4×D4C4×D1111yescharacteristic
808C4×D4C4×D1111yescharacteristic
809C4×D4C4×D1111yescharacteristic
810C4×D4C22×D1111yescharacteristic
811C4×D4C22×D1111yescharacteristic
812C4×D4C22×D1111yescharacteristic
813C4×D4C22×D1111yescharacteristic
814#117—112no—
815#117—112no—
816#117—111no—
817#117—111no—
818#117—111no—
819#117—111no—
820#117—111no—
821#117—111no—
822#117—111no—
823#117—112no—
824#117—112no—
825#117—112no—
826#117—112no—
827#117—112no—
828#117—112no—
829C2×C4⋊C4—111no—
830C2×C4⋊C4—111no—
831C2×C4⋊C4—111no—
832C2×C4⋊C4—111no—
833C2×C4⋊C4C4×D1111yescharacteristic
834C2×C22⋊C4—112no—
835C2×C22⋊C4—112no—
836C2×C22⋊C4C4×D1111yescharacteristic
837C2×C22⋊C4C4×D1111yescharacteristic
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—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×D1111yescharacteristic
861C4⋊C8C22×D1111yescharacteristic
862C4⋊C8C22×D1111yescharacteristic
863C4⋊C8C22×D1111yescharacteristic
864C22⋊C8—112no—
865C22⋊C8—112no—
866C22⋊C8—112no—
867C22⋊C8—112no—
868C22⋊C8—112no—
869C22⋊C8—112no—
870C22⋊C8—112no—
871C22⋊C8—112no—
872C22⋊C8C22×D1111yescharacteristic
873C22⋊C8C22×D1111yescharacteristic
874C22⋊C8C22×D1111yescharacteristic
875C22⋊C8C22×D1111yescharacteristic
876C22⋊C8C22×D1111yescharacteristic
877C22⋊C8C22×D1111yescharacteristic
878C22⋊C8C22×D1111yescharacteristic
879C22⋊C8C22×D1111yescharacteristic
880#97—112no—
881#97—112no—
882#97—112no—
883#97—112no—
884#97—112no—
885#97C22×D1111yescharacteristic
886#97C22×D1111yescharacteristic
887#97C22×D1111yescharacteristic
888#97C22×D1111yescharacteristic
889C4×C8—112no—
890C4×C8—112no—
891C4×C8—112no—
892C4×C8—112no—
893C4×C8—112no—
894C2×C11—22no—
895C2×C11—22no—
896C2×C11—41no—
897C2×C11—41no—
898C2×C11—41no—
899C2×C11C2×#52011yescharacteristic
900C2×C11C2×#56811yescharacteristic
901C2×C11#357311yescharacteristic
902D11—42no—
903C24C2×C4×D1111yescharacteristic
904C24C2×C4×D1111yescharacteristic
905#41—222no—
906#41—222no—
907#41—444no—
908C2×Q8—111no—
909C2×Q8—112no—
910C2×Q8—112no—
911C2×D4—42no—
912C2×D4—112no—
913C2×D4—112no—
914C2×D4—112no—
915C2×D4—112no—
916C2×D4—112no—
917C2×D4—111no—
918C2×D4C2×C4×D1111yescharacteristic
919C2×D4C2×C4×D1111yescharacteristic
920C2×D4C2×C4×D1111yescharacteristic
921C2×D4C2×C4×D1111yescharacteristic
922C22×C4—22no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—112no—
927C22×C4—112no—
928C22×C4—112no—
929C22×C4—112no—
930C22×C4—112no—
931C22×C4—112no—
932C22×C4—112no—
933C22×C4C2×C4×D1111yescharacteristic
934C22×C4C2×C4×D1111yescharacteristic
935C22×C4C2×C4×D1111yescharacteristic
936C22×C4C2×C4×D1111yescharacteristic
937C22×C4C2×C4×D1111yescharacteristic
938C22×C4C2×C4×D1111yescharacteristic
939C22×C4C2×C4×D1111yescharacteristic
940C22×C4C2×C4×D1111yescharacteristic
941C22×C4C23×D1111yescharacteristic
942C22×C4C23×D1111yescharacteristic
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1111yescharacteristic
946M16—41no—
947M16—41no—
948M16—41no—
949M16—41no—
950M16—222no—
951M16—222no—
952M16—222no—
953M16—222no—
954M16—442no—
955M16—442no—
956M16—442no—
957M16—442no—
958C2×C8—22no—
959C2×C8—22no—
960C2×C8—22no—
961C2×C8—22no—
962C2×C8—41no—
963C2×C8—41no—
964C2×C8—41no—
965C2×C8—41no—
966C2×C8—112no—
967C2×C8—112no—
968C2×C8—112no—
969C2×C8—112no—
970C2×C8—442no—
971C2×C8—442no—
972C2×C8—442no—
973C2×C8—442no—
974C2×C8C23×D1111yescharacteristic
975C2×C8C23×D1111yescharacteristic
976C2×C8C23×D1111yescharacteristic
977C2×C8C23×D1111yescharacteristic
978C2×C8C23×D1111yescharacteristic
979C2×C8C23×D1111yescharacteristic
980C2×C8C23×D1111yescharacteristic
981C2×C8C23×D1111yescharacteristic
982C4⋊C4—111no—
983C4⋊C4—111no—
984C4⋊C4—111no—
985C4⋊C4—111no—
986C4⋊C4—111no—
987C4⋊C4—111no—
988C4⋊C4—112no—
989C4⋊C4—112no—
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⋊C4—112no—
1003C4⋊C4—112no—
1004C4⋊C4C2×C4×D1111yescharacteristic
1005C4⋊C4C2×C4×D1111yescharacteristic
1006C4⋊C4C2×C4×D1111yescharacteristic
1007C4⋊C4C2×C4×D1111yescharacteristic
1008C22⋊C4—112no—
1009C22⋊C4—112no—
1010C22⋊C4—112no—
1011C22⋊C4—112no—
1012C22⋊C4—112no—
1013C22⋊C4—112no—
1014C22⋊C4—112no—
1015C22⋊C4—112no—
1016C22⋊C4—112no—
1017C22⋊C4—112no—
1018C22⋊C4—112no—
1019C22⋊C4—112no—
1020C22⋊C4—112no—
1021C22⋊C4—112no—
1022C22⋊C4—112no—
1023C22⋊C4—112no—
1024C22⋊C4—112no—
1025C22⋊C4C2×C4×D1111yescharacteristic
1026C22⋊C4C2×C4×D1111yescharacteristic
1027C22⋊C4C2×C4×D1111yescharacteristic
1028C22⋊C4C2×C4×D1111yescharacteristic
1029C22⋊C4C2×C4×D1111yescharacteristic
1030C22⋊C4C2×C4×D1111yescharacteristic
1031C22⋊C4C2×C4×D1111yescharacteristic
1032C22⋊C4C2×C4×D1111yescharacteristic
1033C42—112no—
1034C42—112no—
1035C42—112no—
1036C42—112no—
1037C42—112no—
1038C42—112no—
1039C42—112no—
1040C42—112no—
1041C42—112no—
1042C42C2×C4×D1111yescharacteristic
1043C42C2×C4×D1111yescharacteristic
1044C42C23×D1111yescharacteristic
1045C42C23×D1111yescharacteristic
1046C11#6027211yescharacteristic, complemented, Sylow
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—112no—
1054C23C22×C4×D1111yescharacteristic
1055C23C22×C4×D1111yescharacteristic
1056C23C22×C4×D1111yescharacteristic
1057C23C22×C4×D1111yescharacteristic
1058C23C22×C4×D1111yescharacteristic
1059Q8—222no—
1060Q8—442no—
1061Q8—442no—
1062D4—22no—
1063D4—22no—
1064D4—41no—
1065D4—41no—
1066D4—224no—
1067D4—224no—
1068D4—222no—
1069D4—442no—
1070D4—442no—
1071D4—442no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—112no—
1089C2×C4—112no—
1090C2×C4—112no—
1091C2×C4—112no—
1092C2×C4—112no—
1093C2×C4—112no—
1094C2×C4—112no—
1095C2×C4—224no—
1096C2×C4—222no—
1097C2×C4—222no—
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×D1111yescharacteristic
1106C2×C4C22×C4×D1111yescharacteristic
1107C2×C4C22×C4×D1111yescharacteristic
1108C2×C4C22×C4×D1111yescharacteristic
1109C2×C4C22×C4×D1111yescharacteristic
1110C2×C4C22×C4×D1111yescharacteristic
1111C2×C4C22×C4×D1111yescharacteristic
1112C2×C4#6703712yes—
1113C2×C4#6704312yes—
1114C2×C4C24×D1111yescharacteristic
1115C8—21no—
1116C8—21no—
1117C8—21no—
1118C8—21no—
1119C8—21no—
1120C8—21no—
1121C8—21no—
1122C8—21no—
1123C8—222no—
1124C8—222no—
1125C8—222no—
1126C8—222no—
1127C22—21no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—21no—
1137C22—21no—
1138C22—21no—
1139C22—21no—
1140C22—44no—
1141C22—82no—
1142C22—222no—
1143C22—222no—
1144C22—222no—
1145C22#1062307712yes—
1146C22#1062327612yes—
1147C22C23×C4×D1111yescharacteristic
1148C4—21no—
1149C4—21no—
1150C4—21no—
1151C4—21no—
1152C4—21no—
1153C4—21no—
1154C4—21no—
1155C4—21no—
1156C4—222no—
1157C4—222no—
1158C4—222no—
1159C4—222no—
1160C4—222no—
1161C4—222no—
1162C4—222no—
1163C4#1062307712yes—
1164C4C2×#6703711yescharacteristic
1165C4C2×#6704311yescharacteristic
1166C2—22no—
1167C2—22no—
1168C2—41no—
1169C2—41no—
1170C2—41no—
1171C2—442no—
1172C2C2×#1062307711yescharacteristic
1173C2C2×#1062327611yescharacteristic
1174C2#1308332711yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC2×C11×#435C2
prime radical#13082174C2
cosocleC2×C4×C11C25
hypercenterC2×#435D11
hypocenterC11#60272
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #13077787C2semidirect
3. #13077782C2semidirect
4. #13077769C2semidirect
5. #13077758C2semidirect
6. #13077756C2semidirect
7. #13077751C2semidirect
8. #13077736C2semidirect
9. #13077728C2semidirect
10. #13077559C2semidirect
11. #13077556C2semidirect
12. D4×#4318C2semidirect
13. #13077337C2semidirect
14. #13077337C2semidirect
15. #13077319C2semidirect
16. #13077310C2semidirect
17. #13077270C2semidirect
18. #13077270C2semidirect
19. #13077265C2semidirect
20. #13077181C2semidirect
21. #13077179C2semidirect
22. C2×#10622715C2semidirect
23. C2×C11×#435C2semidirect
67. #10622741C22semidirect
68. #10622741C22semidirect
69. #10622740C22semidirect
70. #10622740C22semidirect
71. #10622732C22semidirect
72. #10622732C22semidirect
73. #10622731C22semidirect
74. #10622731C22semidirect
75. #10622724C22semidirect
76. #10622724C22semidirect
79. C8×C22⋊D11C22semidirect
80. C8×C22⋊D11C22semidirect
89. #10622715C22semidirect
90. #10622715C22semidirect
95. C2×Dic11⋊C8C22semidirect
96. C2×Dic11⋊C8C22semidirect
103. #10622452C22semidirect
104. #10622452C22semidirect
105. #10622450C22semidirect
106. D11×C4⋊C8C22semidirect
107. #10622444C22semidirect
108. #10622443C22semidirect
109. #10622441C22semidirect
110. #10622441C22semidirect
111. #10622343C22semidirect
112. #10622343C22semidirect
113. #10622342C22semidirect
114. #10622342C22semidirect
115. #10622341C22semidirect
116. #10622341C22semidirect
117. (C22⋊D11)⋊C8C22semidirect
118. (C22⋊D11)⋊C8C22semidirect
119. #10622333C22semidirect
120. #10622333C22semidirect
121. #10622333C22semidirect
122. #10622333C22semidirect
123. #10622332C22semidirect
124. #10622332C22semidirect
125. #10622331C22semidirect
126. #10622331C22semidirect
127. #10622322C22semidirect
128. #10622322C22semidirect
129. #10622318C22semidirect
130. #10622318C22semidirect
131. #10622314C22semidirect
132. #10622314C22semidirect
133. #10622314C22semidirect
134. #10622314C22semidirect
476. C2×#435D11semidirect
1046. C11#60272semidirect

Maximal subgroups

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

subgroupindex
#130821742
#130777872
#130777822
#130777692
#130777582
#130777562
#130777512
#130777362
#130777282
#130775592
#130775562
D4×#43182
#130773372
#130773192
#130773102
#130772702
#130772652
#130771812
#130771792
C2×#106227152
C2×C11×#4352
#6027211