Finite Group Databasebeta

← #14960762

Subgroups — #14960762

Order 2816.

2490 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623196C211yesmaximal, characteristic, complemented
2C22×#66931C211yesmaximal, characteristic, complemented
3#13076901C211yesmaximal, characteristic, complemented
4#13076896C211yesmaximal, characteristic
5#13075271C212yesmaximal, complemented
6#13075267C212yesmaximal, complemented
7#13075241C212yesmaximal, complemented
8#13075237C212yesmaximal, complemented
9#13074988C212yesmaximal, complemented
10#13074985C212yesmaximal, complemented
11#13074974C212yesmaximal, complemented
12#13074965C212yesmaximal, complemented
13#13074435C211yesmaximal, characteristic, complemented
14#13074364C211yesmaximal, characteristic, complemented
15#13073509C211yesmaximal, characteristic, complemented
16#13073503C211yesmaximal, characteristic, complemented
17#13072024C211yesmaximal, characteristic, complemented
18#13072017C211yesmaximal, characteristic, complemented
19#13072001C211yesmaximal, characteristic, complemented
20#13071980C211yesmaximal, characteristic, complemented
21#13071978C211yesmaximal, characteristic, complemented
22#13071232C211yesmaximal, characteristic, complemented
23C11×#2411C211yesmaximal, characteristic, complemented
24C24×Dic11C2211yescharacteristic
25C23×Dic22C2211yescharacteristic
26C2×C11×#123C2211yescharacteristic
27C2×C11×#120C2211yescharacteristic
28C2×C11×#117C2211yescharacteristic
29C22×C11×C22⋊C4C2211yescharacteristic
30C2×#67006C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C2×#66992C2211yescharacteristic
33C2×#66992C2212yes—
34C2×#66988C2211yescharacteristic
35C2×D4×Dic11C2211yescharacteristic
36C2×#66982C2211yescharacteristic
37C2×#66979C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41#10623196—28no—
42C2×#66951C2211yescharacteristic, complemented
43C2×#66950C2211yescharacteristic, complemented
44C2×#66949C2212yescomplemented
45C2×#66943C2211yescharacteristic, complemented
46C2×#66942C2211yescharacteristic, complemented
47C2×#66939C2211yescharacteristic
48C2×#66939C2211yescharacteristic, complemented
49C2×#66936C2211yescharacteristic, complemented
50C2×(C22⋊D11)⋊C4C2211yescharacteristic
51C2×#66932C2211yescharacteristic, complemented
52C2×#66931—28no—
53C2×#66931C2211yescharacteristic
54C2×#66931C2212yes—
55C2×#66931C2212yes—
56C2×#66931C2212yes—
57C2×#66931C2212yes—
58C2×#66931C2212yes—
59C2×#66931C2211yescharacteristic, complemented
60C2×#66931C2212yescomplemented
61C11×#396C2212yes—
62C11×#394C2212yes—
63C11×#390C2212yes—
64C11×#388C2212yes—
65C11×#386C2211yescharacteristic
66C11×#385C2211yescharacteristic
67C11×#379C2211yescharacteristic
68#10622860C2211yescharacteristic
69#10622835C2212yes—
70#10622833C2212yes—
71#10622833C2212yes—
72#10622833C2211yescharacteristic
73#10622826C2211yescharacteristic
74#10622823C2211yescharacteristic
75#10622607C2212yescomplemented
76#10622597C2212yescomplemented
77#10622596C2212yescomplemented
78#10622593C2212yescomplemented
79#10622592C2212yescomplemented
80#10622592C2212yescomplemented
81#10622586C2212yescomplemented
82#10622586C2212yescomplemented
83#10622585C2212yescomplemented
84#10622574C2212yes—
85#10622572C2212yes—
86#10622572C2212yescomplemented
87#10622571C2212yes—
88#10622571C2211yescharacteristic
89#10622570C2212yes—
90#10622569C2212yes—
91#10622564C2212yes—
92#10622563C2212yes—
93#10622563C2211yescharacteristic
94#10622561C2212yes—
95#10622561C2212yes—
96#10622561C2212yes—
97#10622561C2212yescomplemented
98#10622561C2212yescomplemented
99#10622560C2212yescomplemented
100#10622559C2212yes—
101#10622559C2211yescharacteristic
102#10622558C2212yes—
103#10622558C2212yes—
104#10622558C2212yescomplemented
105#10622556C2211yescharacteristic
106#10622556C2211yescharacteristic
107#10622555C2211yescharacteristic
108#10622555C2212yes—
109#10622555C2212yes—
110#10622555C2211yescharacteristic
111#10622555C2211yescharacteristic
112#10622555C2211yescharacteristic
113#10622553C2212yescomplemented
114#10622541C2212yescomplemented
115#10622541C2212yescomplemented
116#10622541C2212yescomplemented
117#10622289C2212yescomplemented
118#10622286C2212yescomplemented
119#10622271C2212yescomplemented
120#10622270C2212yescomplemented
121#10622270C2212yescomplemented
122#10622269C2212yescomplemented
123#10622259C2212yescomplemented
124#10622259C2212yescomplemented
125C25×C11C2311yescharacteristic
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2312yes—
133C23×Dic11—24no—
134C23×Dic11—44no—
135C23×Dic11C2311yescharacteristic
136C23×Dic11C2311yescharacteristic
137C23×Dic11C2312yes—
138C23×Dic11C2312yes—
139C23×Dic11C2311yescharacteristic
140C23×Dic11C2311yescharacteristic
141C23×Dic11C2311yescharacteristic
142C22×C4×D11C2311yescharacteristic
143C22×Dic22—24no—
144C22×Dic22—44no—
145C22×Dic22C2312yes—
146C22×Dic22C2312yes—
147C22×Dic22C2311yescharacteristic
148C11×#123—24no—
149C11×#120—42no—
150C11×#117—42no—
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C22⋊C4—24no—
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2311yescharacteristic
161C2×C11×C22⋊C4C2311yescharacteristic
162C2×C11×C22⋊C4C2311yescharacteristic
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C11×C22⋊C4C2312yes—
166C2×C11×C22⋊C4C2312yes—
167C2×C42×C11C2312yes—
168#67006—42no—
169C2×C22⋊Dic11—24no—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2311yescharacteristic
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2311yescharacteristic
176C2×C22⋊Dic11C2311yescharacteristic
177C2×C22⋊Dic11C2311yescharacteristic
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182#66992—24no—
183#66992—44no—
184#66988—42no—
185D4×Dic11—24no—
186#66982—24no—
187C2×(C2×D11)⋊C4C2311yescharacteristic
188C2×(C2×D11)⋊C4C2311yescharacteristic
189C2×(C2×D11)⋊C4C2311yescharacteristic
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2312yes—
194#66979—42no—
195C2×C4⋊Dic11D418yescomplemented
196C2×C4⋊Dic11C2312yes—
197C2×C4⋊Dic11C2311yescharacteristic
198C2×C4⋊Dic11C2311yescharacteristic
199C2×C4⋊Dic11C2312yes—
200C2×C4⋊Dic11C2312yes—
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4⋊Dic11C2311yescharacteristic
203C2×C4⋊Dic11C2311yescharacteristic
204C2×C4⋊Dic11C2311yescharacteristic
205C2×Dic11⋊C4—24no—
206C2×Dic11⋊C4—24no—
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2312yes—
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2311yescharacteristic
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2311yescharacteristic
215C2×Dic11⋊C4C2311yescharacteristic
216C2×Dic11⋊C4C2311yescharacteristic
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2312yes—
222C2×Dic11⋊C4C2312yes—
223C2×Dic11⋊C4C2312yes—
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2312yes—
227#66951—24no—
228#66950—24no—
229#66949—44no—
230#66943—24no—
231#66942—24no—
232#66939—24no—
233#66939—42no—
234#66936—24no—
235(C22⋊D11)⋊C4—24no—
236#66932—24no—
237#66931—24no—
238#66931—28no—
239#66931—28no—
240#66931—28no—
241#66931—28no—
242#66931—24no—
243#66931—44no—
244#66931—44no—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261#36719—111nomaximal, Sylow
262C24×C11—22no—
263C24×C11—24no—
264C24×C11—22no—
265C24×C11—22no—
266C24×C11—42no—
267C24×C11C2411yescharacteristic
268C24×C11C2412yes—
269C24×C11C2411yescharacteristic
270C23×D11C2411yescharacteristic
271C2×D4×C11—22no—
272C2×D4×C11—22no—
273C2×D4×C11—22no—
274C2×D4×C11—24no—
275C2×D4×C11—42no—
276C2×D4×C11—42no—
277C22×C4×C11—22no—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11—42no—
281C22×C4×C11C2×D414yes—
282C22×C4×C11C2412yes—
283C22×C4×C11C2411yescharacteristic
284C22×C4×C11C2412yes—
285C22×C4×C11C2411yescharacteristic
286C22×C4×C11C2412yes—
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C2×C22⋊D11—22no—
291C2×C22⋊D11—22no—
292C2×C22⋊D11—22no—
293C2×C22⋊D11—22no—
294C2×C22⋊D11—24no—
295C2×C22⋊D11—42no—
296C2×C22⋊D11—42no—
297C2×C22⋊D11—42no—
298C22×Dic11—24no—
299C22×Dic11—24no—
300C22×Dic11—24no—
301C22×Dic11—24no—
302C22×Dic11—24no—
303C22×Dic11—22no—
304C22×Dic11—22no—
305C22×Dic11—22no—
306C22×Dic11—22no—
307C22×Dic11—22no—
308C22×Dic11—42no—
309C22×Dic11—42no—
310C22×Dic11—42no—
311C22×Dic11—42no—
312C22×Dic11—42no—
313C22×Dic11—416no—
314C22×Dic11C2×D414yes—
315C22×Dic11C2×D414yes—
316C22×Dic11C2412yes—
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2411yescharacteristic
319C22×Dic11C2412yes—
320C22×Dic11C2412yes—
321C22×Dic11C2411yescharacteristic
322C22×Dic11C2411yescharacteristic
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2411yescharacteristic
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2412yes—
327C2×C4×D11—22no—
328C2×C4×D11—42no—
329C2×Dic22—24no—
330C2×Dic22—24no—
331C2×Dic22—24no—
332C2×Dic22—24no—
333C2×Dic22—22no—
334C2×Dic22—42no—
335C2×Dic22—42no—
336C2×Dic22—42no—
337C2×Dic22—416no—
338C11×C4⋊C4—22no—
339C11×C4⋊C4—22no—
340C11×C4⋊C4—42no—
341C11×C4⋊C4—42no—
342C11×C22⋊C4—22no—
343C11×C22⋊C4—22no—
344C11×C22⋊C4—22no—
345C11×C22⋊C4—24no—
346C11×C22⋊C4—24no—
347C11×C22⋊C4—24no—
348C11×C22⋊C4—22no—
349C11×C22⋊C4—22no—
350C11×C22⋊C4—42no—
351C11×C22⋊C4—42no—
352C11×C22⋊C4—42no—
353C42×C11—42no—
354C22⋊Dic11—24no—
355C22⋊Dic11—24no—
356C22⋊Dic11—22no—
357C22⋊Dic11—22no—
358C22⋊Dic11—24no—
359C22⋊Dic11—22no—
360C22⋊Dic11—22no—
361C22⋊Dic11—22no—
362C22⋊Dic11—24no—
363C22⋊Dic11—42no—
364C22⋊Dic11—42no—
365C22⋊Dic11—42no—
366(C2×D11)⋊C4—22no—
367(C2×D11)⋊C4—22no—
368(C2×D11)⋊C4—24no—
369(C2×D11)⋊C4—22no—
370(C2×D11)⋊C4—22no—
371(C2×D11)⋊C4—42no—
372(C2×D11)⋊C4—42no—
373C4⋊Dic11—22no—
374C4⋊Dic11—22no—
375C4⋊Dic11—24no—
376C4⋊Dic11—42no—
377C4⋊Dic11—42no—
378C4⋊Dic11C2×D414yes—
379C4⋊Dic11C2×D414yes—
380C4⋊Dic11C2×D414yes—
381C4⋊Dic11C2×D414yes—
382Dic11⋊C4—24no—
383Dic11⋊C4—24no—
384Dic11⋊C4—22no—
385Dic11⋊C4—22no—
386Dic11⋊C4—22no—
387Dic11⋊C4—22no—
388Dic11⋊C4—24no—
389Dic11⋊C4—24no—
390Dic11⋊C4—24no—
391Dic11⋊C4—22no—
392Dic11⋊C4—22no—
393Dic11⋊C4—42no—
394Dic11⋊C4—42no—
395Dic11⋊C4—42no—
396Dic11⋊C4—42no—
397Dic11⋊C4—42no—
398Dic11⋊C4—42no—
399C4×Dic11—22no—
400C4×Dic11—22no—
401C4×Dic11—42no—
402C2×#539—111no—
403C22×C22⋊Q8—111no—
404#2848—111no—
405#2847—111no—
406#2704—112no—
407#2704—112no—
408#2702—112no—
409#2702—112no—
410#2683—112no—
411#2683—112no—
412#2681—112no—
413#2681—112no—
414#2627—111no—
415#2618—111no—
416#2534—111no—
417#2534—111no—
418#2413—111no—
419#2413—111no—
420#2411—111no—
421#2411D1111yescharacteristic, complemented
422#2409—111no—
423#2409—111no—
424#2316—111no—
425C23×C11—22no—
426C23×C11—22no—
427C23×C11—28no—
428C23×C11—22no—
429C23×C11—22no—
430C23×C11—22no—
431C23×C11—22no—
432C23×C11—22no—
433C23×C11—22no—
434C23×C11—21no—
435C23×C11—22no—
436C23×C11—21no—
437C23×C11—21no—
438C23×C11—22no—
439C23×C11—48no—
440C23×C11—48no—
441C23×C11—44no—
442C23×C11—44no—
443C23×C11C22×D412yes—
444C23×C11H(5,𝔽2)12yes—
445C23×C112−1+414yes—
446C23×C112−1+412yes—
447C23×C11C2511yescharacteristic
448C22×D11—21no—
449C22×D11—22no—
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—22no—
453D4×C11—44no—
454D4×C11—84no—
455C2×C4×C11—28no—
456C2×C4×C11—21no—
457C2×C4×C11—21no—
458C2×C4×C11—21no—
459C2×C4×C11—21no—
460C2×C4×C11—21no—
461C2×C4×C11—21no—
462C2×C4×C11—21no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—21no—
468C2×C4×C11—22no—
469C2×C4×C11—22no—
470C2×C4×C11—22no—
471C2×C4×C11—22no—
472C2×C4×C11—22no—
473C2×C4×C11—22no—
474C2×C4×C11—21no—
475C2×C4×C11—22no—
476C2×C4×C11—44no—
477C2×C4×C11C22×D412yes—
478C2×C4×C11C22×D412yes—
479C22⋊D11—44no—
480C22⋊D11—82no—
481C22⋊D11—84no—
482C2×Dic11—28no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—21no—
490C2×Dic11—21no—
491C2×Dic11—22no—
492C2×Dic11—21no—
493C2×Dic11—22no—
494C2×Dic11—22no—
495C2×Dic11—22no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—21no—
500C2×Dic11—22no—
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—21no—
504C2×Dic11—22no—
505C2×Dic11—44no—
506C2×Dic11—44no—
507C2×Dic11—48no—
508C2×Dic11—48no—
509C2×Dic11—44no—
510C2×Dic11—82no—
511C2×Dic11C22×D412yes—
512C2×Dic11C22×D412yes—
513C2×Dic11C22×D412yes—
514C2×Dic11C22×D412yes—
515C2×Dic11H(5,𝔽2)14yes—
516C4×D11—82no—
517Dic22—48no—
518Dic22—48no—
519Dic22—82no—
520C23×Q8—111no—
521C24×C4—111no—
522#539—228no—
523C2×#126—111no—
524C2×#126—111no—
525C2×#125—111no—
526C2×#125—111no—
527C2×#123—111no—
528C2×#123—111no—
529C2×#123—111no—
530C2×#123—111no—
531C2×#123—111no—
532C2×#123C2×D1111yescharacteristic
533C2×C22⋊Q8—111no—
534C2×C22⋊Q8—112no—
535C2×C22⋊Q8—111no—
536C2×C22⋊Q8—112no—
537C2×C22⋊Q8—112no—
538C2×C22⋊Q8—112no—
539C2×C22⋊Q8—112no—
540C2×C22⋊Q8—111no—
541C2×C22⋊Q8—112no—
542C2×C22⋊Q8—112no—
543C2×C22⋊Q8—228no—
544C2×#121—111no—
545C2×#121—112no—
546C2×#120—111no—
547C2×#120C2×D1111yescharacteristic
548C2×C4×D4—111no—
549C2×C4×D4—111no—
550C2×#117—111no—
551C2×#117C2×D1111yescharacteristic
552C22×C4⋊C4—111no—
553C22×C4⋊C4—111no—
554C22×C4⋊C4—111no—
555C22×C22⋊C4—111no—
556C22×C22⋊C4C2×D1111yescharacteristic
557#400—112no—
558#398—112no—
559#398—112no—
560#398—112no—
561#398—112no—
562#398—112no—
563#396—112no—
564#396—112no—
565#396—112no—
566#396—112no—
567#396—112no—
568#396—112no—
569#396—112no—
570#396C2×D1112yes—
571#395—112no—
572#395—112no—
573#395—112no—
574#394—112no—
575#394—112no—
576#394—112no—
577#394—112no—
578#394C2×D1112yes—
579#393—112no—
580#393—112no—
581#391—112no—
582#391—112no—
583#390—112no—
584#390C2×D1112yes—
585#389—112no—
586#389—112no—
587#389—112no—
588#389—112no—
589#389—112no—
590#389—112no—
591#388—112no—
592#388—112no—
593#388—112no—
594#388—112no—
595#388—112no—
596#388C2×D1112yes—
597#386—111no—
598#386—112no—
599#386—112no—
600#386—111no—
601#386—111no—
602#386—112no—
603#386—112no—
604#386C2×D1111yescharacteristic
605#385—111no—
606#385—111no—
607#385—112no—
608#385—111no—
609#385—112no—
610#385C2×D1111yescharacteristic
611#381—111no—
612#381—111no—
613#380—111no—
614#380—111no—
615#380—111no—
616#380—111no—
617#380—112no—
618#380—112no—
619#379—111no—
620#379C2×D1111yescharacteristic
621C22×C11—22no—
622C22×C11—22no—
623C22×C11—24no—
624C22×C11—24no—
625C22×C11—24no—
626C22×C11—24no—
627C22×C11—24no—
628C22×C11—416no—
629C22×C11—42no—
630C22×C11—42no—
631C22×C11—42no—
632C22×C11—42no—
633C22×C11—41no—
634C22×C11—41no—
635C22×C11—41no—
636C22×C11—42no—
637C22×C11—42no—
638C22×C11#53714yes—
639C22×C11C23×D411yescharacteristic
640C22×C11C2×H(5,𝔽2)11yescharacteristic
641C22×C11C2×H(5,𝔽2)12yes—
642C22×C11C2×2−1+411yescharacteristic
643C22×C11C2×2−1+412yes—
644C2×D11—41no—
645C2×D11—41no—
646C2×D11—41no—
647C2×D11—42no—
648C2×D11—42no—
649C4×C11—22no—
650C4×C11—22no—
651C4×C11—41no—
652C4×C11—42no—
653C4×C11—41no—
654C4×C11—41no—
655C4×C11—42no—
656C4×C11—42no—
657Dic11—22no—
658Dic11—24no—
659Dic11—22no—
660Dic11—22no—
661Dic11—22no—
662Dic11—42no—
663Dic11—41no—
664Dic11—41no—
665Dic11—41no—
666Dic11—42no—
667Dic11—42no—
668C25C22×D1111yescharacteristic
669C22×Q8—112no—
670C22×Q8—112no—
671C22×Q8—111no—
672C22×Q8—224no—
673C22×Q8—444no—
674C22×D4—111no—
675C22×D4—112no—
676C22×D4—111no—
677C22×D4C22×D1111yescharacteristic
678C22×D4C22×D1112yes—
679C23×C4—111no—
680C23×C4—111no—
681C23×C4—111no—
682C23×C4—111no—
683C23×C4—112no—
684C23×C4—112no—
685C23×C4—111no—
686C23×C4—111no—
687C23×C4—224no—
688C23×C4—444no—
689C23×C4C22×D1111yescharacteristic
690C23×C4C22×D1111yescharacteristic
691#126—224no—
692#126—224no—
693#125—224no—
694#125—224no—
695#123—24no—
696#123—224no—
697#123—224no—
698#123—224no—
699#123—442no—
700#123—442no—
701C22⋊Q8—228no—
702C22⋊Q8—228no—
703C22⋊Q8—228no—
704C22⋊Q8—228no—
705C22⋊Q8—224no—
706C22⋊Q8—224no—
707C22⋊Q8—224no—
708C22⋊Q8—444no—
709C22⋊Q8—444no—
710C22⋊Q8—444no—
711#121—224no—
712#121—444no—
713#120—42no—
714#120—442no—
715C4×D4—224no—
716C4×D4—224no—
717#117—42no—
718#117—442no—
719C2×C4⋊C4—118no—
720C2×C4⋊C4—111no—
721C2×C4⋊C4—111no—
722C2×C4⋊C4—111no—
723C2×C4⋊C4—111no—
724C2×C4⋊C4—112no—
725C2×C4⋊C4—112no—
726C2×C4⋊C4—112no—
727C2×C4⋊C4—112no—
728C2×C4⋊C4—111no—
729C2×C4⋊C4—111no—
730C2×C4⋊C4—111no—
731C2×C4⋊C4—112no—
732C2×C4⋊C4—112no—
733C2×C4⋊C4—111no—
734C2×C4⋊C4—111no—
735C2×C4⋊C4—111no—
736C2×C4⋊C4—111no—
737C2×C4⋊C4—111no—
738C2×C4⋊C4—112no—
739C2×C4⋊C4—112no—
740C2×C4⋊C4—112no—
741C2×C4⋊C4—112no—
742C2×C4⋊C4—112no—
743C2×C4⋊C4—112no—
744C2×C4⋊C4—112no—
745C2×C4⋊C4—112no—
746C2×C4⋊C4—224no—
747C2×C4⋊C4—224no—
748C2×C4⋊C4C22×D1111yescharacteristic
749C2×C4⋊C4C22×D1111yescharacteristic
750C2×C4⋊C4C22×D1112yes—
751C2×C4⋊C4C22×D1112yes—
752C2×C22⋊C4—24no—
753C2×C22⋊C4—112no—
754C2×C22⋊C4—112no—
755C2×C22⋊C4—111no—
756C2×C22⋊C4—111no—
757C2×C22⋊C4—111no—
758C2×C22⋊C4—111no—
759C2×C22⋊C4—111no—
760C2×C22⋊C4—112no—
761C2×C22⋊C4—112no—
762C2×C22⋊C4—111no—
763C2×C22⋊C4—111no—
764C2×C22⋊C4—112no—
765C2×C22⋊C4—111no—
766C2×C22⋊C4—111no—
767C2×C22⋊C4—112no—
768C2×C22⋊C4—112no—
769C2×C22⋊C4—112no—
770C2×C22⋊C4—112no—
771C2×C22⋊C4—112no—
772C2×C22⋊C4—224no—
773C2×C22⋊C4C22×D1112yes—
774C2×C22⋊C4C22×D1112yes—
775C2×C22⋊C4C22×D1111yescharacteristic
776C2×C22⋊C4C22×D1111yescharacteristic
777C2×C22⋊C4C22×D1111yescharacteristic
778C2×C22⋊C4C22×D1111yescharacteristic
779C2×C22⋊C4C22×D1111yescharacteristic
780C2×C22⋊C4C22×D1112yes—
781C2×C22⋊C4C22×D1112yes—
782C2×C22⋊C4C22×D1112yes—
783C2×C22⋊C4C22×D1112yes—
784C2×C42—111no—
785C2×C42—111no—
786C2×C42—112no—
787C2×C42C22×D1112yes—
788#95—112no—
789#95—112no—
790#95—112no—
791#95—112no—
792#95—112no—
793#95—112no—
794#95—112no—
795#95—112no—
796#95—112no—
797#95—112no—
798#95—112no—
799#95—112no—
800#95—112no—
801#95—112no—
802#95C22×D1112yes—
803#95C22×D1112yes—
804C2×C11—24no—
805C2×C11—44no—
806C2×C11—81no—
807C2×C11C2×#53711yescharacteristic
808C2×C11#348411yescharacteristic
809C2×C11#348611yescharacteristic
810C2×C11#353612yes—
811C2×C11#353812yes—
812D11—81no—
813C24—22no—
814C24—24no—
815C24—22no—
816C24—22no—
817C24—42no—
818C24—111no—
819C24C23×D1111yescharacteristic
820C24C23×D1112yes—
821C24C23×D1111yescharacteristic
822C2×Q8—224no—
823C2×Q8—224no—
824C2×Q8—224no—
825C2×Q8—224no—
826C2×Q8—222no—
827C2×Q8—442no—
828C2×Q8—442no—
829C2×Q8—442no—
830C2×Q8—4416no—
831C2×D4—22no—
832C2×D4—22no—
833C2×D4—22no—
834C2×D4—24no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—222no—
838C2×D4—222no—
839C2×D4—222no—
840C2×D4—222no—
841C2×D4—224no—
842C2×D4—442no—
843C2×D4—442no—
844C2×D4—442no—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—42no—
849C22×C4—112no—
850C22×C4—111no—
851C22×C4—111no—
852C22×C4—111no—
853C22×C4—111no—
854C22×C4—114no—
855C22×C4—114no—
856C22×C4—111no—
857C22×C4—112no—
858C22×C4—112no—
859C22×C4—111no—
860C22×C4—112no—
861C22×C4—111no—
862C22×C4—222no—
863C22×C4—224no—
864C22×C4—224no—
865C22×C4—224no—
866C22×C4—224no—
867C22×C4—224no—
868C22×C4—222no—
869C22×C4—222no—
870C22×C4—222no—
871C22×C4—222no—
872C22×C4—222no—
873C22×C4—442no—
874C22×C4—442no—
875C22×C4—442no—
876C22×C4—442no—
877C22×C4—442no—
878C22×C4—442no—
879C22×C4—4416no—
880C22×C4D4×D1114yes—
881C22×C4C23×D1112yes—
882C22×C4C23×D1111yescharacteristic
883C22×C4C23×D1112yes—
884C22×C4C23×D1111yescharacteristic
885C22×C4C23×D1112yes—
886C22×C4C23×D1111yescharacteristic
887C22×C4C23×D1111yescharacteristic
888C22×C4C23×D1111yescharacteristic
889C4⋊C4—22no—
890C4⋊C4—22no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—114no—
894C4⋊C4—114no—
895C4⋊C4—114no—
896C4⋊C4—114no—
897C4⋊C4—224no—
898C4⋊C4—224no—
899C4⋊C4—222no—
900C4⋊C4—222no—
901C4⋊C4—222no—
902C4⋊C4—222no—
903C4⋊C4—222no—
904C4⋊C4—222no—
905C4⋊C4—224no—
906C4⋊C4—224no—
907C4⋊C4—224no—
908C4⋊C4—224no—
909C4⋊C4—222no—
910C4⋊C4—222no—
911C4⋊C4—442no—
912C4⋊C4—442no—
913C4⋊C4—442no—
914C4⋊C4—442no—
915C4⋊C4—442no—
916C4⋊C4—442no—
917C4⋊C4—442no—
918C4⋊C4—442no—
919C22⋊C4—22no—
920C22⋊C4—22no—
921C22⋊C4—22no—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—24no—
925C22⋊C4—22no—
926C22⋊C4—22no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—222no—
931C22⋊C4—222no—
932C22⋊C4—224no—
933C22⋊C4—224no—
934C22⋊C4—224no—
935C22⋊C4—222no—
936C22⋊C4—222no—
937C22⋊C4—224no—
938C22⋊C4—222no—
939C22⋊C4—222no—
940C22⋊C4—222no—
941C22⋊C4—224no—
942C22⋊C4—222no—
943C22⋊C4—222no—
944C22⋊C4—442no—
945C22⋊C4—442no—
946C22⋊C4—442no—
947C22⋊C4—442no—
948C22⋊C4—442no—
949C42—42no—
950C42—222no—
951C42—222no—
952C42—442no—
953C11#3671911yescharacteristic, complemented, Sylow
954C23—22no—
955C23—22no—
956C23—28no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—21no—
964C23—21no—
965C23—21no—
966C23—22no—
967C23—22no—
968C23—48no—
969C23—48no—
970C23—44no—
971C23—44no—
972C23—221no—
973C23—221no—
974C23—221no—
975C23—222no—
976C23—222no—
977C23C2×D4×D1112yes—
978C23#6703712yes—
979C23#6704314yes—
980C23#6704312yes—
981C23C24×D1111yescharacteristic
982Q8—448no—
983Q8—448no—
984Q8—882no—
985D4—44no—
986D4—84no—
987D4—444no—
988D4—882no—
989D4—884no—
990C2×C4—28no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—21no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—44no—
1012C2×C4—112no—
1013C2×C4—112no—
1014C2×C4—112no—
1015C2×C4—112no—
1016C2×C4—114no—
1017C2×C4—228no—
1018C2×C4—222no—
1019C2×C4—222no—
1020C2×C4—222no—
1021C2×C4—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—221no—
1025C2×C4—221no—
1026C2×C4—222no—
1027C2×C4—221no—
1028C2×C4—222no—
1029C2×C4—222no—
1030C2×C4—222no—
1031C2×C4—221no—
1032C2×C4—222no—
1033C2×C4—222no—
1034C2×C4—222no—
1035C2×C4—221no—
1036C2×C4—222no—
1037C2×C4—222no—
1038C2×C4—222no—
1039C2×C4—222no—
1040C2×C4—444no—
1041C2×C4—444no—
1042C2×C4—448no—
1043C2×C4—448no—
1044C2×C4—444no—
1045C2×C4—882no—
1046C2×C4—882no—
1047C2×C4C2×D4×D1112yes—
1048C2×C4C2×D4×D1112yes—
1049C22—22no—
1050C22—22no—
1051C22—24no—
1052C22—24no—
1053C22—24no—
1054C22—24no—
1055C22—24no—
1056C22—416no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—41no—
1062C22—41no—
1063C22—41no—
1064C22—42no—
1065C22—42no—
1066C22—441no—
1067C22—441no—
1068C22—441no—
1069C22—442no—
1070C22—442no—
1071C22#1062312814yes—
1072C22C22×D4×D1111yescharacteristic
1073C22C2×#6703711yescharacteristic
1074C22C2×#6704311yescharacteristic
1075C22C2×#6704312yes—
1076C22D11×H(5,𝔽2)12yes—
1077C4—22no—
1078C4—22no—
1079C4—41no—
1080C4—42no—
1081C4—41no—
1082C4—41no—
1083C4—42no—
1084C4—42no—
1085C4—224no—
1086C4—222no—
1087C4—222no—
1088C4—222no—
1089C4—222no—
1090C4—442no—
1091C4—441no—
1092C4—441no—
1093C4—441no—
1094C4—442no—
1095C4—442no—
1096C2—24no—
1097C2—44no—
1098C2—81no—
1099C2—881no—
1100C2C2×#1062312811yescharacteristic
1101C2#1308225011yescharacteristic
1102C2#1308226311yescharacteristic
1103C2#1308283112yes—
1104C2#1308285612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2411C2
prime radical#13076896C2
hypercenter#2411D11
hypocenterC11#36719
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2411

Complements

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

NH ≅ G/Ntype
1. C2×#10623196C2semidirect
2. C22×#66931C2semidirect
3. #13076901C2semidirect
5. #13075271C2semidirect
6. #13075267C2semidirect
7. #13075241C2semidirect
8. #13075237C2semidirect
9. #13074988C2semidirect
10. #13074985C2semidirect
11. #13074974C2semidirect
12. #13074965C2semidirect
13. #13074435C2semidirect
14. #13074364C2semidirect
15. #13073509C2semidirect
16. #13073503C2semidirect
17. #13072024C2semidirect
18. #13072017C2semidirect
19. #13072001C2semidirect
20. #13071980C2semidirect
21. #13071978C2semidirect
22. #13071232C2semidirect
23. C11×#2411C2semidirect
42. C2×#66951C22semidirect
43. C2×#66950C22semidirect
44. C2×#66949C22semidirect
45. C2×#66943C22semidirect
46. C2×#66942C22semidirect
48. C2×#66939C22semidirect
49. C2×#66936C22semidirect
51. C2×#66932C22semidirect
59. C2×#66931C22semidirect
60. C2×#66931C22semidirect
75. #10622607C22semidirect
76. #10622597C22semidirect
77. #10622596C22semidirect
78. #10622593C22semidirect
79. #10622592C22semidirect
80. #10622592C22semidirect
81. #10622586C22semidirect
82. #10622586C22semidirect
83. #10622585C22semidirect
86. #10622572C22semidirect
97. #10622561C22semidirect
98. #10622561C22semidirect
99. #10622560C22semidirect
104. #10622558C22semidirect
113. #10622553C22semidirect
114. #10622541C22semidirect
115. #10622541C22semidirect
116. #10622541C22semidirect
117. #10622289C22semidirect
118. #10622286C22semidirect
119. #10622271C22semidirect
120. #10622270C22semidirect
121. #10622270C22semidirect
122. #10622269C22semidirect
123. #10622259C22semidirect
124. #10622259C22semidirect
195. C2×C4⋊Dic11D4semidirect
421. #2411D11semidirect
953. C11#36719semidirect

Maximal subgroups

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

subgroupindex
C2×#106231962
C22×#669312
#130769012
#130768962
#130752712
#130752672
#130752412
#130752372
#130749882
#130749852
#130749742
#130749652
#130744352
#130743642
#130735092
#130735032
#130720242
#130720172
#130720012
#130719802
#130719782
#130712322
C11×#24112
#3671911