Finite Group Databasebeta

← #15619027

Subgroups — #15619027

Order 2816.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082180C211yesmaximal, characteristic
2#13077788C212yesmaximal, complemented
3#13077781C212yesmaximal, complemented
4#13077770C212yesmaximal, complemented
5#13077759C212yesmaximal, complemented
6#13077757C212yesmaximal, complemented
7#13077750C212yesmaximal, complemented
8#13077743C212yesmaximal, complemented
9#13077735C212yesmaximal, complemented
10#13077563C211yesmaximal, characteristic, complemented
11#13077556C211yesmaximal, characteristic, complemented
12M16×D44C211yesmaximal, characteristic, complemented
13#13077346C211yesmaximal, characteristic, complemented
14#13077346C211yesmaximal, characteristic, complemented
15#13077322C211yesmaximal, characteristic, complemented
16#13077313C211yesmaximal, characteristic, complemented
17C2×#10622319C211yesmaximal, characteristic, complemented
18#13077273C211yesmaximal, characteristic, complemented
19#13077273C211yesmaximal, characteristic, complemented
20#13077184C211yesmaximal, characteristic, complemented
21#13077177C211yesmaximal, characteristic, complemented
22D11×#424C211yesmaximal, characteristic, complemented
23C11×#2923C211yesmaximal, characteristic, complemented
24C4×C11×#41C2211yescharacteristic
25#10623359C2211yescharacteristic
26#10623359C2211yescharacteristic
27C2×#67001C2211yescharacteristic
28C2×#67001C2211yescharacteristic
29C2×M16×D11C2211yescharacteristic
30C2×M16×D11C2211yescharacteristic
31C22×#4313C2211yescharacteristic
32C22×C8×D11C2211yescharacteristic
33#10623115C411yescharacteristic
34#10623112C411yescharacteristic
35#10623112C411yescharacteristic
36#10623110C411yescharacteristic
37#10623094C411yescharacteristic
38#10623089C411yescharacteristic
39#10623089C411yescharacteristic
40#10623087C412yes—
41#10623087C412yes—
42#10623082C411yescharacteristic
43#10623081C412yes—
44#10623072C412yes—
45#10623059C2212yes—
46#10623059C2212yes—
47D11×#117C2211yescharacteristic
48D11×#117C2211yescharacteristic
49#10623010C2212yes—
50C4×#4339C2212yes—
51C2×C4×D44C2211yescharacteristic
52#10623001C2211yescharacteristic
53C11×#433C2212yescomplemented
54C11×#433C2212yescomplemented
55C11×#432C2212yescomplemented
56C11×#432C2212yescomplemented
57C11×#424C2211yescharacteristic
58C11×#424C2211yescharacteristic
59C11×#408C2211yescharacteristic
60C11×#408C2211yescharacteristic
61C4×C11×M16C2211yescharacteristic
62C2×C11×#97C2211yescharacteristic
63#10622739C2211yescharacteristic
64#10622739C2211yescharacteristic
65#10622735C2211yescharacteristic
66#10622735C2211yescharacteristic
67#10622732C2211yescharacteristic
68#10622732C2211yescharacteristic
69C2×(C2×D11)⋊C8C2211yescharacteristic
70C2×(C2×D11)⋊C8C2211yescharacteristic
71#10622715C2211yescharacteristic
72#10622715C2211yescharacteristic
73#10622714C2211yescharacteristic
74#10622714C2211yescharacteristic
75#10622612C2211yescharacteristic
76#10622612C2211yescharacteristic
77#10622612C2212yescomplemented
78#10622612C2212yescomplemented
79#10622537C2211yescharacteristic
80#10622537C2212yescomplemented
81C2×C4⋊(C11⋊C8)C2211yescharacteristic
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#10622448C2212yescomplemented
94#10622448C2212yescomplemented
95#10622446C2212yescomplemented
96#10622446C2212yescomplemented
97D11×C4⋊C8C2212yescomplemented
98D11×C4⋊C8C2212yescomplemented
99#10622343C2212yescomplemented
100#10622343C2212yescomplemented
101#10622343C2212yescomplemented
102#10622343C2212yescomplemented
103#10622342C2212yescomplemented
104#10622342C2212yescomplemented
105#10622342C2212yescomplemented
106#10622342C2212yescomplemented
107#10622341C2212yescomplemented
108#10622341C2212yescomplemented
109#10622341C2212yescomplemented
110#10622341C2212yescomplemented
111(C22⋊D11)⋊C8C2212yescomplemented
112(C22⋊D11)⋊C8C2212yescomplemented
113(C22⋊D11)⋊C8C2212yescomplemented
114(C22⋊D11)⋊C8C2212yescomplemented
115#10622319C2211yescharacteristic
116#10622319C2211yescharacteristic
117#10622319C2211yescharacteristic
118#10622319C2212yes—
119#10622319C2211yescharacteristic
120#10622319C2211yescharacteristic
121#10622319C2211yescharacteristic
122#10622319C2211yescharacteristic
123#10622319C2211yescharacteristic
124#10622319C2212yes—
125#10622314C2212yescomplemented
126#10622314C2212yescomplemented
127#10622314C2212yescomplemented
128#10622314C2212yescomplemented
129#10622314C2212yescomplemented
130#10622314C2212yescomplemented
131#10622301C2212yes—
132C8×D44C2212yes—
133#10622292C2212yescomplemented
134C8×Dic22C2212yescomplemented
135C2×C11×#41C2311yescharacteristic
136C2×#4339C2×C412yes—
137C22×D44C2×C411yescharacteristic
138C22×C4×D11C2311yescharacteristic
139C22×C4×D11C2311yescharacteristic
140C2×C11×M16C2311yescharacteristic
141C2×C11×M16C2311yescharacteristic
142C22×C8×C11C2311yescharacteristic
143C22×C8×C11C2311yescharacteristic
144C4×Q8×C11C2×C411yescharacteristic
145C4×Q8×C11C2×C411yescharacteristic
146C4×D4×C11C2×C412yes—
147C4×D4×C11C2×C411yescharacteristic
148C4×D4×C11C2×C412yes—
149C4×D4×C11C2×C411yescharacteristic
150C11×#117C2311yescharacteristic
151C11×#117C2312yes—
152C2×C42×C11C2311yescharacteristic
153C2×C42×C11C2312yes—
154#67001—42no—
155#67001—42no—
156#66999C2×C411yescharacteristic
157#66999C2×C411yescharacteristic
158#66999C2×C411yescharacteristic
159#66999C2×C411yescharacteristic
160#66991C2×C411yescharacteristic
161#66991C2×C411yescharacteristic
162#66991C2×C411yescharacteristic
163#66991C2×C411yescharacteristic
164#66990C2×C412yes—
165#66990C2×C412yes—
166#66988C2×C412yes—
167#66988C2×C412yes—
168#66983C2×C412yes—
169#66982C2×C412yes—
170#66982C2×C412yes—
171C4×C22⋊D11C2×C412yes—
172C4×C22⋊D11C2×C412yes—
173C4×C22⋊D11C2312yes—
174C4×C22⋊D11C2312yes—
175C4×C22⋊D11C2312yes—
176C4×C22⋊D11C2312yes—
177C2×(C2×D11)⋊C4C2×C411yescharacteristic
178C2×(C2×D11)⋊C4C2×C411yescharacteristic
179#66979C2×C412yes—
180#66979C2311yescharacteristic
181#66979C2311yescharacteristic
182C2×C4⋊Dic11C2×C411yescharacteristic
183#66977C2×C412yes—
184#66977C2×C412yes—
185#66977C2×C412yes—
186C2×#4318C2311yescharacteristic
187C2×#4318C2311yescharacteristic
188C2×#4318C2312yes—
189C2×#4318C2312yes—
190C22×C11⋊C8C2311yescharacteristic
191C22×C11⋊C8C2311yescharacteristic
192C22×C11⋊C8C2312yes—
193C22×C11⋊C8C2312yes—
194M16×D11—42no—
195M16×D11—42no—
196C2×#4313—42no—
197C2×#4313C2311yescharacteristic
198C2×#4313C2311yescharacteristic
199C2×#4313C2311yescharacteristic
200C2×#4313C2311yescharacteristic
201C2×#4313C2312yes—
202C2×#4313C2312yes—
203C2×C8×D11—42no—
204C2×C8×D11C2311yescharacteristic
205C2×C8×D11C2311yescharacteristic
206C2×C8×D11C2311yescharacteristic
207C2×C8×D11C2311yescharacteristic
208C2×C8×D11C2312yes—
209C2×C8×D11C2312yes—
210#66951C2×C412yes—
211#66951C2×C412yes—
212#66949C2×C412yes—
213#66949C2×C412yes—
214#66947C2×C412yes—
215#66947C2×C412yes—
216#66945C2×C411yescharacteristic
217#66945C2×C411yescharacteristic
218#66945C2×C411yescharacteristic
219#66945C2×C411yescharacteristic
220C4⋊C4×D11C2×C411yescharacteristic
221C4⋊C4×D11C2×C411yescharacteristic
222C4⋊C4×D11C2×C411yescharacteristic
223C4⋊C4×D11C2×C411yescharacteristic
224#66942C2×C412yes—
225#66942C2×C412yes—
226#66938C2×C412yes—
227#66938C2×C412yes—
228#66937C2×C412yes—
229#66937C2×C412yes—
230#66936C2×C412yes—
231#66936C2×C412yes—
232C22⋊C4×D11C2×C412yes—
233C22⋊C4×D11C2×C412yes—
234#66932C2×C412yes—
235#66932C2×C412yes—
236#66930C2×C412yes—
237#66930C2×C412yes—
238#66929C2×C412yes—
239#66929C2×C412yes—
240#66928C2×C412yes—
241C4×D44C2×C411yescharacteristic
242C4×D44C2×C411yescharacteristic
243C4×D44C2×C411yescharacteristic
244C4×D44C2×C411yescharacteristic
245C4×D44C2×C412yes—
246C4×D44C2311yescharacteristic
247C4×D44C2311yescharacteristic
248C4×D44C2311yescharacteristic
249C4×D44C2311yescharacteristic
250#66925C2×C412yes—
251#66925C2×C412yes—
252#66925C2312yes—
253#66925C2312yes—
254C42×D11C2312yes—
255C42×D11C2312yes—
256#66923C2×C411yescharacteristic
257#66923C2×C411yescharacteristic
258#66923C2×C412yes—
259#66922C2×C411yescharacteristic
260#66922C2×C411yescharacteristic
261C4×Dic22C2×C412yes—
262C4×Dic22C2312yes—
263C4×Dic22C2312yes—
264C11×C4⋊C8C2312yes—
265C11×C4⋊C8C2312yes—
266C11×C4⋊C8C2312yes—
267C11×C4⋊C8C2312yes—
268C11×C22⋊C8C2312yes—
269C11×C22⋊C8C2312yes—
270C11×C22⋊C8C2312yes—
271C11×C22⋊C8C2312yes—
272C11×#97C2311yescharacteristic
273C11×#97C2311yescharacteristic
274C11×#97C2311yescharacteristic
275C11×#97C2311yescharacteristic
276C11×#97C2312yes—
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#66879C2312yes—
291#66879C2312yes—
292#66879C2312yes—
293#66879C2312yes—
294Dic11⋊C8C2312yes—
295Dic11⋊C8C2312yes—
296Dic11⋊C8C2312yes—
297Dic11⋊C8C2312yes—
298Dic11⋊C8C2312yes—
299Dic11⋊C8C2312yes—
300Dic11⋊C8C2312yes—
301Dic11⋊C8C2312yes—
302C8×Dic11C2312yes—
303C8×Dic11C2312yes—
304C8×Dic11C2312yes—
305C8×Dic11C2312yes—
306C4⋊(C11⋊C8)C2311yescharacteristic
307C4⋊(C11⋊C8)C2311yescharacteristic
308C4⋊(C11⋊C8)C2311yescharacteristic
309C4⋊(C11⋊C8)C2311yescharacteristic
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
317C23×D11C22×C411yescharacteristic
318C23×D11C22×C411yescharacteristic
319C11×#41—22no—
320C11×#41—22no—
321C2×Q8×C11C22×C411yescharacteristic
322C2×D4×C11C22×C412yes—
323C2×D4×C11C22×C411yescharacteristic
324C22×C4×C11C22×C411yescharacteristic
325C22×C4×C11C22×C411yescharacteristic
326C22×C4×C11C22×C412yes—
327C22×C4×C11C22×C412yes—
328C22×C4×C11C2412yes—
329C22×C4×C11C2411yescharacteristic
330C2×C22⋊D11C22×C412yes—
331C2×C22⋊D11C22×C412yes—
332C2×C22⋊D11C22×C412yes—
333C2×C22⋊D11C22×C412yes—
334C22×Dic11C22×C411yescharacteristic
335C22×Dic11C22×C411yescharacteristic
336#4339—44no—
337C2×D44—42no—
338C2×D44C22×C411yescharacteristic
339C2×D44C22×C411yescharacteristic
340C2×D44C22×C411yescharacteristic
341C2×D44C22×C411yescharacteristic
342C2×C4×D11—22no—
343C2×C4×D11—22no—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11C22×C412yes—
347C2×C4×D11C22×C411yescharacteristic
348C2×C4×D11C22×C411yescharacteristic
349C2×C4×D11C22×C411yescharacteristic
350C2×C4×D11C22×C411yescharacteristic
351C2×C4×D11C22×C412yes—
352C2×C4×D11C22×C412yes—
353C2×C4×D11C22×C412yes—
354C2×C4×D11C2411yescharacteristic
355C2×C4×D11C2411yescharacteristic
356C2×C4×D11C2411yescharacteristic
357C2×C4×D11C2411yescharacteristic
358C2×Dic22C22×C412yes—
359C2×Dic22C22×C412yes—
360C11×M16—22no—
361C11×M16—22no—
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×C412yes—
371C11×C4⋊C4C22×C411yescharacteristic
372C11×C4⋊C4C22×C411yescharacteristic
373C11×C4⋊C4C22×C412yes—
374C11×C22⋊C4C22×C412yes—
375C11×C22⋊C4C22×C412yes—
376C11×C22⋊C4C22×C412yes—
377C42×C11C22×C412yes—
378C42×C11C22×C411yescharacteristic
379C42×C11C22×C411yescharacteristic
380C42×C11C22×C412yes—
381C42×C11C2411yescharacteristic
382C42×C11C2411yescharacteristic
383C42×C11C2412yes—
384C22⋊Dic11C22×C412yes—
385C22⋊Dic11C22×C412yes—
386C22⋊Dic11C22×C412yes—
387C22⋊Dic11C22×C412yes—
388C22⋊Dic11C22×C412yes—
389C22⋊Dic11C22×C412yes—
390(C2×D11)⋊C4C22×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×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×C411yescharacteristic
404(C2×D11)⋊C4C22×C412yes—
405(C2×D11)⋊C4C22×C412yes—
406C4⋊Dic11C22×C411yescharacteristic
407C4⋊Dic11C22×C412yes—
408C4⋊Dic11C22×C412yes—
409C4⋊Dic11C22×C411yescharacteristic
410C4⋊Dic11C22×C411yescharacteristic
411C4⋊Dic11C22×C411yescharacteristic
412C4⋊Dic11C22×C411yescharacteristic
413C4⋊Dic11C22×C411yescharacteristic
414C4⋊Dic11C22×C411yescharacteristic
415C4⋊Dic11C22×C411yescharacteristic
416Dic11⋊C4C22×C412yes—
417Dic11⋊C4C22×C412yes—
418Dic11⋊C4C22×C412yes—
419Dic11⋊C4C22×C412yes—
420Dic11⋊C4C22×C412yes—
421Dic11⋊C4C22×C412yes—
422Dic11⋊C4C22×C412yes—
423Dic11⋊C4C22×C412yes—
424Dic11⋊C4C22×C412yes—
425Dic11⋊C4C22×C412yes—
426Dic11⋊C4C22×C412yes—
427Dic11⋊C4C22×C412yes—
428C4×Dic11C22×C412yes—
429C4×Dic11C22×C412yes—
430C4×Dic11C22×C412yes—
431C4×Dic11C22×C412yes—
432C4×Dic11C2412yes—
433C4×Dic11C2412yes—
434#4318—22no—
435#4318—22no—
436#4318—42no—
437#4318—42no—
438C2×C11⋊C8—22no—
439C2×C11⋊C8—22no—
440C2×C11⋊C8—42no—
441C2×C11⋊C8—42no—
442C2×C11⋊C8C2411yescharacteristic
443C2×C11⋊C8C2411yescharacteristic
444C2×C11⋊C8C2412yes—
445C2×C11⋊C8C2412yes—
446C2×C11⋊C8C2411yescharacteristic
447C2×C11⋊C8C2411yescharacteristic
448#4313—41no—
449#4313—41no—
450#4313—41no—
451#4313—41no—
452#4313—42no—
453#4313—42no—
454C8×D11—41no—
455C8×D11—41no—
456C8×D11—41no—
457C8×D11—41no—
458C8×D11—42no—
459C8×D11—42no—
460#3475—111no—
461#2995—112no—
462#2995—112no—
463#2994—112no—
464#2993—112no—
465#2992—112no—
466#2992—112no—
467#2990—112no—
468#2989—112no—
469#2962—111no—
470#2961—111no—
471D4×M16—111no—
472#2933—111no—
473#2933—111no—
474#2930—111no—
475#2929—111no—
476C2×#435—111no—
477#2924—111no—
478#2924—111no—
479#2923D1111yescharacteristic, complemented
480#2906—111no—
481#2905—111no—
482C2×#424—111no—
483C23×C11C23×C412yes—
484C23×C11C23×C411yescharacteristic
485C22×D11—22no—
486C22×D11—22no—
487C22×D11—22no—
488C22×D11—41no—
489C22×D11—41no—
490C22×D11—41no—
491C22×D11C23×C411yescharacteristic
492C22×D11C23×C411yescharacteristic
493C22×D11C23×C411yescharacteristic
494C22×D11C23×C411yescharacteristic
495Q8×C11—22no—
496D4×C11—24no—
497D4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—41no—
501C2×C4×C11—42no—
502C2×C4×C11—41no—
503C2×C4×C11—42no—
504C2×C4×C11C23×C412yes—
505C2×C4×C11C23×C412yes—
506C2×C4×C11C23×C411yescharacteristic
507C2×C4×C11C23×C411yescharacteristic
508C2×C4×C11C23×C412yes—
509C2×C4×C11C23×C411yescharacteristic
510C2×C4×C11C23×C411yescharacteristic
511C2×C4×C11C23×C411yescharacteristic
512C2×C4×C11H(5,𝔽2)12yes—
513C2×C4×C112−1+412yes—
514C2×C4×C11C2511yescharacteristic
515C22⋊D11—24no—
516C22⋊D11—42no—
517C22⋊D11—42no—
518C22⋊D11—42no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11C23×C411yescharacteristic
522C2×Dic11C23×C411yescharacteristic
523C2×Dic11C23×C412yes—
524C2×Dic11C23×C412yes—
525C2×Dic11C23×C412yes—
526C2×Dic11C23×C412yes—
527C2×Dic11C23×C411yescharacteristic
528C2×Dic11C23×C411yescharacteristic
529D44—22no—
530D44—22no—
531D44—41no—
532D44—41no—
533C4×D11—24no—
534C4×D11—22no—
535C4×D11—22no—
536C4×D11—22no—
537C4×D11—22no—
538C4×D11—21no—
539C4×D11—21no—
540C4×D11—21no—
541C4×D11—21no—
542C4×D11—21no—
543C4×D11—21no—
544C4×D11—21no—
545C4×D11—21no—
546C4×D11—42no—
547C4×D11—42no—
548C4×D11—42no—
549Dic22—42no—
550Dic22—42no—
551C8×C11—21no—
552C8×C11—21no—
553C8×C11—22no—
554C8×C11—21no—
555C8×C11—21no—
556C8×C11—22no—
557C11⋊C8—21no—
558C11⋊C8—21no—
559C11⋊C8—22no—
560C11⋊C8—22no—
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—111no—
576#552—112no—
577#551—112no—
578#551—112no—
579#547—111no—
580#546—112no—
581#533—111no—
582#529—112no—
583#529—112no—
584#529—112no—
585#525—111no—
586#525—111no—
587C4×#41—112no—
588C4×#41C2×D1111yescharacteristic
589C2×C4×D4—111no—
590C2×#117—111no—
591C2×#117—111no—
592#446—112no—
593#446—112no—
594#446—112no—
595#446—112no—
596#446—112no—
597#446—112no—
598#446—112no—
599C8×Q8—112no—
600#436—112no—
601#436—112no—
602#436—112no—
603#436—112no—
604#436—112no—
605#435—112no—
606#435—112no—
607#435—112no—
608#435—112no—
609#435—112no—
610#435—112no—
611#435—112no—
612#435—112no—
613#435—111no—
614#435—111no—
615#435—111no—
616#435—111no—
617#435—111no—
618#435—111no—
619#435—111no—
620#435—111no—
621#435—112no—
622#435—112no—
623C8×D4—112no—
624C8×D4—112no—
625C8×D4—112no—
626C8×D4—112no—
627C8×D4—112no—
628#433—112no—
629#433—112no—
630#433—112no—
631#433—112no—
632#433C2×D1112yescomplemented
633#433C2×D1112yescomplemented
634#432—112no—
635#432—112no—
636#432C2×D1112yescomplemented
637#432C2×D1112yescomplemented
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—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#408C2×D1111yescharacteristic
663#408C2×D1111yescharacteristic
664#407—111no—
665#407—111no—
666C2×C22⋊C8—111no—
667C2×C22⋊C8—111no—
668#405—111no—
669#405—111no—
670#405—111no—
671#405—111no—
672C4×M16C2×D1111yescharacteristic
673C2×#97C2×D1111yescharacteristic
674C22×C11—21no—
675C22×C11—21no—
676C22×C11—22no—
677C22×C11—22no—
678C22×C11—22no—
679C22×C11#52012yes—
680C22×C11C24×C411yescharacteristic
681C2×D11—21no—
682C2×D11—21no—
683C2×D11—21no—
684C2×D11—21no—
685C2×D11—21no—
686C2×D11—21no—
687C2×D11—21no—
688C2×D11—21no—
689C2×D11—21no—
690C2×D11—21no—
691C2×D11—21no—
692C2×D11—44no—
693C2×D11—82no—
694C2×D11#56812yes—
695C4×C11—22no—
696C4×C11—21no—
697C4×C11—22no—
698C4×C11—21no—
699C4×C11—21no—
700C4×C11—21no—
701C4×C11—22no—
702C4×C11#52012yes—
703C4×C11C2×H(5,𝔽2)11yescharacteristic
704C4×C11C2×2−1+411yescharacteristic
705Dic11—21no—
706Dic11—21no—
707Dic11—21no—
708Dic11—21no—
709Dic11—22no—
710Dic11—22no—
711Dic11—22no—
712Dic11—22no—
713C2×#41—112no—
714C2×#41C22×D1111yescharacteristic
715C22×D4—111no—
716C23×C4—111no—
717C23×C4—111no—
718#131—442no—
719#131—442no—
720C2×M16—111no—
721C2×M16—111no—
722C2×M16—112no—
723C2×M16—112no—
724C2×M16—111no—
725C2×M16—111no—
726C2×M16—112no—
727C2×M16—111no—
728C2×M16—111no—
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—112no—
738C22×C8—112no—
739C22×C8—111no—
740C22×C8—111no—
741C22×C8—111no—
742C22×C8—111no—
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—112no—
759#125—111no—
760#125—111no—
761#124—112no—
762#124—112no—
763#124—112no—
764#123—112no—
765#123—112no—
766#123—112no—
767#123—112no—
768#123—112no—
769#123—112no—
770#123—112no—
771#123—112no—
772C22⋊Q8—111no—
773C22⋊Q8—111no—
774C22⋊Q8—111no—
775C22⋊Q8—111no—
776C22⋊Q8—112no—
777C22⋊Q8—112no—
778C22⋊Q8—112no—
779C22⋊Q8—112no—
780C22⋊Q8—112no—
781#121—111no—
782#121—111no—
783#121—111no—
784#121—111no—
785#121—112no—
786#121—112no—
787#121—112no—
788#120—112no—
789#120—112no—
790C4×Q8—112no—
791C4×Q8—112no—
792C4×Q8—112no—
793C4×Q8C4×D1111yescharacteristic
794C4×Q8C4×D1111yescharacteristic
795C4×D4—112no—
796C4×D4—112no—
797C4×D4—112no—
798C4×D4—112no—
799C4×D4—112no—
800C4×D4—112no—
801C4×D4—111no—
802C4×D4—111no—
803C4×D4—111no—
804C4×D4—111no—
805C4×D4—112no—
806C4×D4—111no—
807C4×D4—111no—
808C4×D4—111no—
809C4×D4—111no—
810C4×D4C4×D1112yes—
811C4×D4C4×D1111yescharacteristic
812C4×D4C4×D1112yes—
813C4×D4C4×D1111yescharacteristic
814#117—112no—
815#117—111no—
816#117—111no—
817#117—111no—
818#117—111no—
819#117—111no—
820#117—111no—
821#117—112no—
822#117—112no—
823#117—112no—
824#117—112no—
825#117—112no—
826#117—112no—
827#117C22×D1111yescharacteristic
828#117C22×D1112yes—
829C2×C4⋊C4—111no—
830C2×C4⋊C4—111no—
831C2×C4⋊C4—111no—
832C2×C4⋊C4—111no—
833C2×C4⋊C4—111no—
834C2×C22⋊C4—111no—
835C2×C22⋊C4—111no—
836C2×C22⋊C4—112no—
837C2×C22⋊C4—112no—
838C2×C42—112no—
839C2×C42—112no—
840C2×C42C22×D1111yescharacteristic
841C2×C42C22×D1112yes—
842C4⋊C8—112no—
843C4⋊C8—112no—
844C4⋊C8—112no—
845C4⋊C8—112no—
846C4⋊C8—112no—
847C4⋊C8—112no—
848C4⋊C8—112no—
849C4⋊C8—112no—
850C4⋊C8—111no—
851C4⋊C8—112no—
852C4⋊C8—111no—
853C4⋊C8—112no—
854C4⋊C8—112no—
855C4⋊C8—112no—
856C4⋊C8—111no—
857C4⋊C8—111no—
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—111no—
869C22⋊C8—111no—
870C22⋊C8—111no—
871C22⋊C8—111no—
872C22⋊C8—112no—
873C22⋊C8—112no—
874C22⋊C8—112no—
875C22⋊C8—112no—
876C22⋊C8C22×D1112yes—
877C22⋊C8C22×D1112yes—
878C22⋊C8C22×D1112yes—
879C22⋊C8C22×D1112yes—
880#97—112no—
881#97—112no—
882#97—112no—
883#97—112no—
884#97C22×D1111yescharacteristic
885#97C22×D1111yescharacteristic
886#97C22×D1111yescharacteristic
887#97C22×D1111yescharacteristic
888#97C22×D1112yes—
889C4×C8—112no—
890C4×C8—112no—
891C4×C8—112no—
892C4×C8—112no—
893C4×C8C22×D1112yes—
894C2×C11—22no—
895C2×C11—42no—
896C2×C11C2×#52011yescharacteristic
897C2×C11C2×#56811yescharacteristic
898C2×C11#357311yescharacteristic
899D11—22no—
900D11—41no—
901D11—41no—
902D11—41no—
903C24—111no—
904C24—111no—
905#41—22no—
906#41—22no—
907#41—444no—
908C2×Q8—112no—
909C2×Q8—112no—
910C2×Q8C2×C4×D1111yescharacteristic
911C2×D4—112no—
912C2×D4—112no—
913C2×D4—112no—
914C2×D4—112no—
915C2×D4—111no—
916C2×D4—111no—
917C2×D4—111no—
918C2×D4—111no—
919C2×D4—442no—
920C2×D4C2×C4×D1112yes—
921C2×D4C2×C4×D1111yescharacteristic
922C22×C4—111no—
923C22×C4—111no—
924C22×C4—112no—
925C22×C4—111no—
926C22×C4—111no—
927C22×C4—111no—
928C22×C4—111no—
929C22×C4—111no—
930C22×C4—111no—
931C22×C4—111no—
932C22×C4—111no—
933C22×C4—112no—
934C22×C4—112no—
935C22×C4—112no—
936C22×C4—222no—
937C22×C4—222no—
938C22×C4—222no—
939C22×C4—222no—
940C22×C4C2×C4×D1111yescharacteristic
941C22×C4C2×C4×D1111yescharacteristic
942C22×C4C2×C4×D1112yes—
943C22×C4C2×C4×D1112yes—
944C22×C4C23×D1112yes—
945C22×C4C23×D1111yescharacteristic
946M16—22no—
947M16—22no—
948M16—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—111no—
962C2×C8—112no—
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×D1112yes—
977C2×C8C23×D1111yescharacteristic
978C2×C8C23×D1111yescharacteristic
979C2×C8C23×D1112yes—
980C2×C8C23×D1111yescharacteristic
981C2×C8C23×D1111yescharacteristic
982C4⋊C4—111no—
983C4⋊C4—111no—
984C4⋊C4—111no—
985C4⋊C4—111no—
986C4⋊C4—111no—
987C4⋊C4—112no—
988C4⋊C4—112no—
989C4⋊C4—112no—
990C4⋊C4—112no—
991C4⋊C4—111no—
992C4⋊C4—111no—
993C4⋊C4—111no—
994C4⋊C4—112no—
995C4⋊C4—112no—
996C4⋊C4—112no—
997C4⋊C4—112no—
998C4⋊C4—112no—
999C4⋊C4—112no—
1000C4⋊C4—112no—
1001C4⋊C4—112no—
1002C4⋊C4—112no—
1003C4⋊C4—112no—
1004C4⋊C4C2×C4×D1111yescharacteristic
1005C4⋊C4C2×C4×D1111yescharacteristic
1006C4⋊C4C2×C4×D1112yes—
1007C4⋊C4C2×C4×D1112yes—
1008C22⋊C4—112no—
1009C22⋊C4—112no—
1010C22⋊C4—112no—
1011C22⋊C4—112no—
1012C22⋊C4—112no—
1013C22⋊C4—112no—
1014C22⋊C4—111no—
1015C22⋊C4—111no—
1016C22⋊C4—112no—
1017C22⋊C4—112no—
1018C22⋊C4—112no—
1019C22⋊C4—112no—
1020C22⋊C4—111no—
1021C22⋊C4—111no—
1022C22⋊C4—111no—
1023C22⋊C4—111no—
1024C22⋊C4—111no—
1025C22⋊C4—111no—
1026C22⋊C4—112no—
1027C22⋊C4—112no—
1028C22⋊C4—112no—
1029C22⋊C4—112no—
1030C22⋊C4C2×C4×D1112yes—
1031C22⋊C4C2×C4×D1112yes—
1032C22⋊C4C2×C4×D1112yes—
1033C42—112no—
1034C42—112no—
1035C42—112no—
1036C42—112no—
1037C42—112no—
1038C42—112no—
1039C42C2×C4×D1112yes—
1040C42C2×C4×D1111yescharacteristic
1041C42C2×C4×D1111yescharacteristic
1042C42C2×C4×D1112yes—
1043C42C23×D1111yescharacteristic
1044C42C23×D1111yescharacteristic
1045C42C23×D1112yes—
1046C11#6027211yescharacteristic, complemented, Sylow
1047C23—111no—
1048C23—111no—
1049C23—111no—
1050C23—111no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—441no—
1055C23—441no—
1056C23—441no—
1057C23C22×C4×D1112yes—
1058C23C22×C4×D1111yescharacteristic
1059Q8—22no—
1060Q8—442no—
1061Q8—442no—
1062D4—24no—
1063D4—22no—
1064D4—222no—
1065D4—222no—
1066D4—224no—
1067D4—441no—
1068D4—441no—
1069D4—442no—
1070D4—442no—
1071D4—442no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—42no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—42no—
1078C2×C4—111no—
1079C2×C4—111no—
1080C2×C4—112no—
1081C2×C4—112no—
1082C2×C4—112no—
1083C2×C4—112no—
1084C2×C4—111no—
1085C2×C4—111no—
1086C2×C4—224no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—221no—
1094C2×C4—221no—
1095C2×C4—221no—
1096C2×C4—221no—
1097C2×C4—221no—
1098C2×C4—221no—
1099C2×C4—221no—
1100C2×C4—221no—
1101C2×C4—442no—
1102C2×C4—442no—
1103C2×C4—442no—
1104C2×C4C22×C4×D1112yes—
1105C2×C4C22×C4×D1112yes—
1106C2×C4C22×C4×D1111yescharacteristic
1107C2×C4C22×C4×D1111yescharacteristic
1108C2×C4C22×C4×D1112yes—
1109C2×C4C22×C4×D1111yescharacteristic
1110C2×C4C22×C4×D1111yescharacteristic
1111C2×C4C22×C4×D1111yescharacteristic
1112C2×C4#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—22no—
1130C22—22no—
1131C22—22no—
1132C22—112no—
1133C22—221no—
1134C22—221no—
1135C22—221no—
1136C22—221no—
1137C22—221no—
1138C22—221no—
1139C22—221no—
1140C22—221no—
1141C22—221no—
1142C22—221no—
1143C22—221no—
1144C22—444no—
1145C22—882no—
1146C22#1062305412yes—
1147C22C23×C4×D1111yescharacteristic
1148C4—21no—
1149C4—22no—
1150C4—21no—
1151C4—21no—
1152C4—22no—
1153C4—21no—
1154C4—22no—
1155C4—222no—
1156C4—222no—
1157C4—222no—
1158C4—222no—
1159C4—221no—
1160C4—221no—
1161C4—221no—
1162C4—221no—
1163C4#1062305412yes—
1164C4C2×#6704211yescharacteristic
1165C4C2×#6704311yescharacteristic
1166C2—22no—
1167C2—42no—
1168C2—222no—
1169C2—441no—
1170C2—441no—
1171C2—441no—
1172C2C2×#1062305411yescharacteristic
1173C2D11×#56811yescharacteristic
1174C2#1308332911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D11
commutator, socleC22×C11C24×C4
FittingC11×#2923C2
prime radical#13082180C2
cosocleC2×C4×C11C25
hypercenter#2923D11
hypocenterC11#60272
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ #2923

Complements

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

NH ≅ G/Ntype
2. #13077788C2semidirect
3. #13077781C2semidirect
4. #13077770C2semidirect
5. #13077759C2semidirect
6. #13077757C2semidirect
7. #13077750C2semidirect
8. #13077743C2semidirect
9. #13077735C2semidirect
10. #13077563C2semidirect
11. #13077556C2semidirect
12. M16×D44C2semidirect
13. #13077346C2semidirect
14. #13077346C2semidirect
15. #13077322C2semidirect
16. #13077313C2semidirect
17. C2×#10622319C2semidirect
18. #13077273C2semidirect
19. #13077273C2semidirect
20. #13077184C2semidirect
21. #13077177C2semidirect
22. D11×#424C2semidirect
23. C11×#2923C2semidirect
53. C11×#433C22semidirect
54. C11×#433C22semidirect
55. C11×#432C22semidirect
56. C11×#432C22semidirect
77. #10622612C22semidirect
78. #10622612C22semidirect
80. #10622537C22semidirect
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. #10622448C22semidirect
94. #10622448C22semidirect
95. #10622446C22semidirect
96. #10622446C22semidirect
97. D11×C4⋊C8C22semidirect
98. D11×C4⋊C8C22semidirect
99. #10622343C22semidirect
100. #10622343C22semidirect
101. #10622343C22semidirect
102. #10622343C22semidirect
103. #10622342C22semidirect
104. #10622342C22semidirect
105. #10622342C22semidirect
106. #10622342C22semidirect
107. #10622341C22semidirect
108. #10622341C22semidirect
109. #10622341C22semidirect
110. #10622341C22semidirect
111. (C22⋊D11)⋊C8C22semidirect
112. (C22⋊D11)⋊C8C22semidirect
113. (C22⋊D11)⋊C8C22semidirect
114. (C22⋊D11)⋊C8C22semidirect
125. #10622314C22semidirect
126. #10622314C22semidirect
127. #10622314C22semidirect
128. #10622314C22semidirect
129. #10622314C22semidirect
130. #10622314C22semidirect
133. #10622292C22semidirect
134. C8×Dic22C22semidirect
479. #2923D11semidirect
632. #433C2×D11semidirect
633. #433C2×D11semidirect
636. #432C2×D11semidirect
637. #432C2×D11semidirect
1046. C11#60272semidirect

Maximal subgroups

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

subgroupindex
#130821802
#130777882
#130777812
#130777702
#130777592
#130777572
#130777502
#130777432
#130777352
#130775632
#130775562
M16×D442
#130773462
#130773222
#130773132
C2×#106223192
#130772732
#130771842
#130771772
D11×#4242
C11×#29232
#6027211