Finite Group Databasebeta

← #14960556

Subgroups — #14960556

Order 2816.

3038 conjugacy classes of subgroups.

The subgroup lattice has 1272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623124C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic, complemented
3#13076901C211yesmaximal, characteristic, complemented
4#13076896C211yesmaximal, characteristic, complemented
5#13075094C212yesmaximal, complemented
6#13075090C212yesmaximal, complemented
7#13074918C212yesmaximal, complemented
8#13074910C212yesmaximal, complemented
9#13074906C212yesmaximal, complemented
10#13074905C212yesmaximal, complemented
11#13074846C212yesmaximal, complemented
12#13074845C212yesmaximal, complemented
13#13074427C211yesmaximal, characteristic, complemented
14#13074356C211yesmaximal, characteristic, complemented
15#13073968C211yesmaximal, characteristic, complemented
16#13073962C211yesmaximal, characteristic, complemented
17#13071991C211yesmaximal, characteristic, complemented
18#13071990C211yesmaximal, characteristic, complemented
19#13071984C211yesmaximal, characteristic, complemented
20#13071971C211yesmaximal, characteristic, complemented
21#13071969C211yesmaximal, characteristic, complemented
22#13071228C211yesmaximal, characteristic, complemented
23C11×#2410C211yesmaximal, characteristic, complemented
24C23×D4×C11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic
26C23×C22⋊D11C2211yescharacteristic
27C24×Dic11C2211yescharacteristic
28C2×C11×#121C2212yescomplemented
29C2×C11×#120C2211yescharacteristic
30C2×C11×#120C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C2×#67006C2211yescharacteristic
33C2×#67006C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C2×#66992—28no—
37C2×#66992C2211yescharacteristic
38C2×#66992C2212yes—
39C2×#66992C2212yes—
40C2×#66992C2212yes—
41C2×#66992C2212yes—
42C2×#66992C2211yescharacteristic, complemented
43C2×#66992C2212yescomplemented
44C2×#66992C2212yescomplemented
45C2×#66992C2212yescomplemented
46C2×#66992C2212yescomplemented
47C2×#66991C2211yescharacteristic, complemented
48C2×#66990C2211yescharacteristic
49C2×#66989C2211yescharacteristic, complemented
50C2×#66988C2211yescharacteristic, complemented
51C2×D4×Dic11C2211yescharacteristic
52C2×#66983C2212yescomplemented
53C22×(C2×D11)⋊C4C2211yescharacteristic
54C22×Dic11⋊C4C2211yescharacteristic
55#10623124—28no—
56C2×#66938C2211yescharacteristic, complemented
57C2×#66937C2212yescomplemented
58C2×#66936C2211yescharacteristic, complemented
59C2×#66935C2211yescharacteristic
60C2×(C22⋊D11)⋊C4C2211yescharacteristic
61C2×#66932C2211yescharacteristic, complemented
62C2×#66932C2211yescharacteristic, complemented
63C2×#66931C2211yescharacteristic
64C2×#66931C2212yescomplemented
65C11×#394C2212yescomplemented
66C11×#392C2212yescomplemented
67C11×#386C2211yescharacteristic
68C11×#386C2212yescomplemented
69C11×#385C2211yescharacteristic
70C11×#379C2211yescharacteristic
71#10622860C2211yescharacteristic
72#10622836C2212yescomplemented
73#10622836C2212yescomplemented
74#10622836C2212yescomplemented
75#10622835C2212yescomplemented
76#10622833C2211yescharacteristic
77#10622833C2212yescomplemented
78#10622833C2212yescomplemented
79#10622826C2211yescharacteristic
80#10622826C2212yescomplemented
81#10622823C2211yescharacteristic
82#10622823C2212yescomplemented
83#10622823C2212yescomplemented
84#10622607C2212yescomplemented
85#10622605C2212yescomplemented
86#10622602C2212yescomplemented
87#10622593C2212yescomplemented
88#10622574C2212yescomplemented
89#10622574C2212yescomplemented
90#10622573C2212yescomplemented
91#10622573C2212yescomplemented
92#10622573C2212yescomplemented
93#10622572C2212yescomplemented
94#10622572C2212yescomplemented
95#10622572C2212yescomplemented
96#10622571C2211yescharacteristic
97#10622571C2212yescomplemented
98#10622571C2212yescomplemented
99#10622570C2212yescomplemented
100#10622570C2212yescomplemented
101#10622568C2211yescharacteristic
102#10622568C2211yescharacteristic
103#10622563C2211yescharacteristic
104#10622563C2212yescomplemented
105#10622561C2212yescomplemented
106#10622559C2211yescharacteristic
107#10622559C2212yescomplemented
108#10622559C2212yescomplemented
109#10622559C2212yescomplemented
110#10622559C2212yescomplemented
111#10622555C2211yescharacteristic
112#10622555C2211yescharacteristic
113#10622555C2211yescharacteristic
114#10622555C2211yescharacteristic
115#10622555C2212yescomplemented
116#10622555C2212yescomplemented
117#10622289C2212yescomplemented
118#10622289C2212yescomplemented
119#10622288C2212yescomplemented
120#10622286C2212yescomplemented
121#10622285C2212yescomplemented
122#10622270C2212yescomplemented
123#10622267C2212yescomplemented
124#10622265C2212yescomplemented
125C25×C11C2311yescharacteristic
126C25×C11C2311yescharacteristic
127C24×D11C2311yescharacteristic
128C22×D4×C11—24no—
129C22×D4×C11—44no—
130C22×D4×C11C2311yescharacteristic
131C22×D4×C11C2312yes—
132C22×D4×C11C2312yes—
133C22×D4×C11C2311yescharacteristic
134C22×D4×C11C2311yescharacteristic
135C22×D4×C11C2312yes—
136C23×C4×C11C2311yescharacteristic
137C23×C4×C11C2312yes—
138C22×C22⋊D11—24no—
139C22×C22⋊D11—24no—
140C22×C22⋊D11—44no—
141C22×C22⋊D11—44no—
142C22×C22⋊D11C2311yescharacteristic
143C22×C22⋊D11C2312yes—
144C22×C22⋊D11C2312yes—
145C22×C22⋊D11C2312yes—
146C22×C22⋊D11C2312yes—
147C22×C22⋊D11C2311yescharacteristic
148C22×C22⋊D11C2312yes—
149C22×C22⋊D11C2311yescharacteristic
150C22×C22⋊D11C2311yescharacteristic
151C22×C22⋊D11C2312yes—
152C23×Dic11—24no—
153C23×Dic11—44no—
154C23×Dic11C2311yescharacteristic
155C23×Dic11C2312yes—
156C23×Dic11C2312yes—
157C23×Dic11C2311yescharacteristic
158C23×Dic11C2312yes—
159C23×Dic11C2311yescharacteristic
160C23×Dic11C2311yescharacteristic
161C22×D44C2312yes—
162C22×C4×D11C2311yescharacteristic
163C22×Dic22C2311yescharacteristic
164C11×#121—44no—
165C11×#120—24no—
166C11×#120—42no—
167C2×C11×C4⋊C4C2312yes—
168C2×C11×C22⋊C4—42no—
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2311yescharacteristic
172C2×C11×C22⋊C4C2311yescharacteristic
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2311yescharacteristic
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2312yes—
177C2×C11×C22⋊C4C2312yes—
178C2×C11×C22⋊C4C2312yes—
179#67006—24no—
180#67006—42no—
181C2×C22⋊Dic11—42no—
182C2×C22⋊Dic11D418yescomplemented
183C2×C22⋊Dic11C2311yescharacteristic
184C2×C22⋊Dic11C2311yescharacteristic
185C2×C22⋊Dic11C2311yescharacteristic
186C2×C22⋊Dic11C2311yescharacteristic
187C2×C22⋊Dic11C2311yescharacteristic
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2311yescharacteristic
190C2×C22⋊Dic11C2312yes—
191C2×C22⋊Dic11C2311yescharacteristic
192C2×C22⋊Dic11C2312yes—
193C2×C22⋊Dic11C2312yes—
194C2×C22⋊Dic11C2312yes—
195C2×C22⋊Dic11C2311yescharacteristic
196C2×C22⋊Dic11C2311yescharacteristic
197C2×C22⋊Dic11C2311yescharacteristic
198C2×C22⋊Dic11C2311yescharacteristic
199#66992—24no—
200#66992—28no—
201#66992—28no—
202#66992—28no—
203#66992—28no—
204#66992—24no—
205#66992—44no—
206#66992—44no—
207#66992—44no—
208#66992—44no—
209#66991—24no—
210#66990—42no—
211#66989—24no—
212#66988—24no—
213D4×Dic11—24no—
214#66983—44no—
215C2×(C2×D11)⋊C4—24no—
216C2×(C2×D11)⋊C4C2311yescharacteristic
217C2×(C2×D11)⋊C4C2311yescharacteristic
218C2×(C2×D11)⋊C4C2312yes—
219C2×(C2×D11)⋊C4C2312yes—
220C2×(C2×D11)⋊C4C2312yes—
221C2×(C2×D11)⋊C4C2312yes—
222C2×(C2×D11)⋊C4C2312yes—
223C2×(C2×D11)⋊C4C2312yes—
224C2×(C2×D11)⋊C4C2312yes—
225C2×(C2×D11)⋊C4C2312yes—
226C2×(C2×D11)⋊C4C2312yes—
227C2×(C2×D11)⋊C4C2312yes—
228C2×C4⋊Dic11C2311yescharacteristic
229C2×C4⋊Dic11C2312yes—
230C2×C4⋊Dic11C2311yescharacteristic
231C2×Dic11⋊C4—24no—
232C2×Dic11⋊C4C2311yescharacteristic
233C2×Dic11⋊C4C2311yescharacteristic
234C2×Dic11⋊C4C2312yes—
235C2×Dic11⋊C4C2311yescharacteristic
236C2×Dic11⋊C4C2311yescharacteristic
237C2×Dic11⋊C4C2312yes—
238C2×Dic11⋊C4C2312yes—
239C2×Dic11⋊C4C2312yes—
240C2×Dic11⋊C4C2312yes—
241C2×Dic11⋊C4C2312yes—
242C2×Dic11⋊C4C2312yes—
243C2×Dic11⋊C4C2312yes—
244C2×C4×Dic11C2311yescharacteristic
245C2×C4×Dic11C2311yescharacteristic
246#66938—24no—
247#66937—44no—
248#66936—24no—
249#66935—42no—
250(C22⋊D11)⋊C4—24no—
251#66932—24no—
252#66932—24no—
253#66931—24no—
254#66931—44no—
255C11×#95C2312yes—
256C11×#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264C11⋊#95C2312yes—
265C11⋊#95C2312yes—
266C11⋊#95C2312yes—
267#36706—111nomaximal, Sylow
268C24×C11—22no—
269C24×C11—24no—
270C24×C11—22no—
271C24×C11—22no—
272C24×C11—22no—
273C24×C11—22no—
274C24×C11—42no—
275C24×C11—42no—
276C24×C11—42no—
277C24×C11C2×D414yes—
278C24×C11C2411yescharacteristic
279C24×C11C2411yescharacteristic
280C24×C11C2411yescharacteristic
281C24×C11C2412yes—
282C24×C11C2411yescharacteristic
283C23×D11—22no—
284C23×D11—22no—
285C23×D11—22no—
286C23×D11—42no—
287C23×D11—42no—
288C23×D11C2412yes—
289C23×D11C2411yescharacteristic
290C2×D4×C11—22no—
291C2×D4×C11—24no—
292C2×D4×C11—24no—
293C2×D4×C11—22no—
294C2×D4×C11—24no—
295C2×D4×C11—24no—
296C2×D4×C11—22no—
297C2×D4×C11—22no—
298C2×D4×C11—22no—
299C2×D4×C11—24no—
300C2×D4×C11—42no—
301C2×D4×C11—42no—
302C2×D4×C11—42no—
303C2×D4×C11—42no—
304C2×D4×C11—42no—
305C2×D4×C11—42no—
306C2×D4×C11—416no—
307C22×C4×C11—22no—
308C22×C4×C11—42no—
309C22×C4×C11—42no—
310C22×C4×C11—42no—
311C22×C4×C11—42no—
312C22×C4×C11C2412yes—
313C22×C4×C11C2412yes—
314C22×C4×C11C2411yescharacteristic
315C22×C4×C11C2412yes—
316C22×C4×C11C2411yescharacteristic
317C22×C4×C11C2411yescharacteristic
318C2×C22⋊D11—24no—
319C2×C22⋊D11—24no—
320C2×C22⋊D11—22no—
321C2×C22⋊D11—24no—
322C2×C22⋊D11—24no—
323C2×C22⋊D11—22no—
324C2×C22⋊D11—24no—
325C2×C22⋊D11—24no—
326C2×C22⋊D11—22no—
327C2×C22⋊D11—22no—
328C2×C22⋊D11—22no—
329C2×C22⋊D11—24no—
330C2×C22⋊D11—24no—
331C2×C22⋊D11—24no—
332C2×C22⋊D11—22no—
333C2×C22⋊D11—42no—
334C2×C22⋊D11—42no—
335C2×C22⋊D11—42no—
336C2×C22⋊D11—42no—
337C2×C22⋊D11—42no—
338C2×C22⋊D11—42no—
339C2×C22⋊D11—42no—
340C2×C22⋊D11—42no—
341C2×C22⋊D11—42no—
342C2×C22⋊D11—42no—
343C2×C22⋊D11—42no—
344C2×C22⋊D11—42no—
345C2×C22⋊D11—416no—
346C2×C22⋊D11—416no—
347C22×Dic11—24no—
348C22×Dic11—24no—
349C22×Dic11—24no—
350C22×Dic11—24no—
351C22×Dic11—24no—
352C22×Dic11—22no—
353C22×Dic11—22no—
354C22×Dic11—42no—
355C22×Dic11—42no—
356C22×Dic11—42no—
357C22×Dic11—42no—
358C22×Dic11—42no—
359C22×Dic11—42no—
360C22×Dic11—42no—
361C22×Dic11—42no—
362C22×Dic11—416no—
363C22×Dic11C2×D414yes—
364C22×Dic11C2×D414yes—
365C22×Dic11C2411yescharacteristic
366C22×Dic11C2412yes—
367C22×Dic11C2412yes—
368C22×Dic11C2411yescharacteristic
369C22×Dic11C2411yescharacteristic
370C22×Dic11C2411yescharacteristic
371C22×Dic11C2411yescharacteristic
372C22×Dic11C2411yescharacteristic
373C22×Dic11C2411yescharacteristic
374C22×Dic11C2412yes—
375C2×D44—42no—
376C2×D44—42no—
377C2×D44—42no—
378C2×C4×D11—22no—
379C2×C4×D11—42no—
380C2×Dic22—22no—
381C2×Dic22—42no—
382C11×C4⋊C4—42no—
383C11×C22⋊C4—22no—
384C11×C22⋊C4—22no—
385C11×C22⋊C4—22no—
386C11×C22⋊C4—22no—
387C11×C22⋊C4—24no—
388C11×C22⋊C4—22no—
389C11×C22⋊C4—42no—
390C11×C22⋊C4—42no—
391C11×C22⋊C4—42no—
392C11×C22⋊C4—42no—
393C22⋊Dic11—22no—
394C22⋊Dic11—22no—
395C22⋊Dic11—24no—
396C22⋊Dic11—22no—
397C22⋊Dic11—22no—
398C22⋊Dic11—22no—
399C22⋊Dic11—22no—
400C22⋊Dic11—24no—
401C22⋊Dic11—22no—
402C22⋊Dic11—42no—
403C22⋊Dic11—42no—
404C22⋊Dic11—42no—
405C22⋊Dic11C2×D414yes—
406C22⋊Dic11C2×D414yes—
407C22⋊Dic11C2×D414yes—
408C22⋊Dic11C2×D414yes—
409(C2×D11)⋊C4—22no—
410(C2×D11)⋊C4—22no—
411(C2×D11)⋊C4—24no—
412(C2×D11)⋊C4—24no—
413(C2×D11)⋊C4—24no—
414(C2×D11)⋊C4—42no—
415(C2×D11)⋊C4—42no—
416(C2×D11)⋊C4—42no—
417(C2×D11)⋊C4—42no—
418(C2×D11)⋊C4—42no—
419(C2×D11)⋊C4—42no—
420(C2×D11)⋊C4—42no—
421C4⋊Dic11—22no—
422C4⋊Dic11—22no—
423C4⋊Dic11—24no—
424Dic11⋊C4—22no—
425Dic11⋊C4—22no—
426Dic11⋊C4—22no—
427Dic11⋊C4—22no—
428Dic11⋊C4—24no—
429Dic11⋊C4—24no—
430Dic11⋊C4—24no—
431Dic11⋊C4—42no—
432Dic11⋊C4—42no—
433Dic11⋊C4—42no—
434Dic11⋊C4—42no—
435Dic11⋊C4—42no—
436C4×Dic11—22no—
437C4×Dic11—22no—
438C2×#538—111no—
439C22×#121—111no—
440#2848—111no—
441#2847—111no—
442#2691—112no—
443#2691—112no—
444#2676—112no—
445#2676—112no—
446#2675—112no—
447#2675—112no—
448#2671—112no—
449#2671—112no—
450#2626—111no—
451#2617—111no—
452#2579—111no—
453#2579—111no—
454#2410—111no—
455#2410—111no—
456#2410—111no—
457#2410D1111yescharacteristic, complemented
458#2408—111no—
459#2408—111no—
460#2315—111no—
461C23×C11—22no—
462C23×C11—22no—
463C23×C11—28no—
464C23×C11—22no—
465C23×C11—21no—
466C23×C11—22no—
467C23×C11—22no—
468C23×C11—21no—
469C23×C11—22no—
470C23×C11—22no—
471C23×C11—22no—
472C23×C11—22no—
473C23×C11—22no—
474C23×C11—22no—
475C23×C11—21no—
476C23×C11—21no—
477C23×C11—22no—
478C23×C11—28no—
479C23×C11—21no—
480C23×C11—22no—
481C23×C11—22no—
482C23×C11—21no—
483C23×C11—21no—
484C23×C11—44no—
485C23×C11—44no—
486C23×C11—48no—
487C23×C11—48no—
488C23×C11—44no—
489C23×C11—44no—
490C23×C11—84no—
491C23×C11—84no—
492C23×C11C22×D412yes—
493C23×C11C22×D412yes—
494C23×C11C22×D412yes—
495C23×C11H(5,𝔽2)14yes—
496C23×C11H(5,𝔽2)12yes—
497C23×C112−1+412yes—
498C23×C11C2511yescharacteristic
499C22×D11—21no—
500C22×D11—22no—
501C22×D11—22no—
502C22×D11—22no—
503C22×D11—22no—
504C22×D11—22no—
505C22×D11—22no—
506C22×D11—22no—
507C22×D11—22no—
508C22×D11—21no—
509C22×D11—21no—
510C22×D11—22no—
511C22×D11—44no—
512C22×D11—44no—
513C22×D11—44no—
514C22×D11—84no—
515C22×D11—84no—
516D4×C11—48no—
517D4×C11—48no—
518D4×C11—44no—
519D4×C11—82no—
520D4×C11—82no—
521D4×C11—84no—
522C2×C4×C11—21no—
523C2×C4×C11—21no—
524C2×C4×C11—21no—
525C2×C4×C11—22no—
526C2×C4×C11—22no—
527C2×C4×C11—22no—
528C2×C4×C11—22no—
529C2×C4×C11—22no—
530C2×C4×C11—22no—
531C2×C4×C11—22no—
532C2×C4×C11—21no—
533C2×C4×C11—22no—
534C2×C4×C11—22no—
535C2×C4×C11—22no—
536C2×C4×C11—22no—
537C2×C4×C11—21no—
538C2×C4×C11—44no—
539C2×C4×C11—84no—
540C22⋊D11—48no—
541C22⋊D11—48no—
542C22⋊D11—48no—
543C22⋊D11—48no—
544C22⋊D11—44no—
545C22⋊D11—82no—
546C22⋊D11—82no—
547C22⋊D11—82no—
548C22⋊D11—84no—
549C22⋊D11—84no—
550C2×Dic11—28no—
551C2×Dic11—22no—
552C2×Dic11—22no—
553C2×Dic11—22no—
554C2×Dic11—22no—
555C2×Dic11—22no—
556C2×Dic11—22no—
557C2×Dic11—21no—
558C2×Dic11—21no—
559C2×Dic11—21no—
560C2×Dic11—22no—
561C2×Dic11—22no—
562C2×Dic11—22no—
563C2×Dic11—22no—
564C2×Dic11—22no—
565C2×Dic11—22no—
566C2×Dic11—21no—
567C2×Dic11—22no—
568C2×Dic11—22no—
569C2×Dic11—21no—
570C2×Dic11—44no—
571C2×Dic11—44no—
572C2×Dic11—48no—
573C2×Dic11—48no—
574C2×Dic11—82no—
575C2×Dic11—84no—
576C2×Dic11C22×D412yes—
577C2×Dic11C22×D412yes—
578C2×Dic11C22×D412yes—
579C2×Dic11C22×D412yes—
580C2×Dic11H(5,𝔽2)14yes—
581D44—84no—
582C4×D11—82no—
583Dic22—82no—
584C23×D4—111no—
585C23×D4—111no—
586C23×D4C2×D1111yescharacteristic
587C24×C4—111no—
588#538—228no—
589C2×#126—111no—
590C2×#126—111no—
591C2×#124—111no—
592C2×#124—111no—
593C2×#123—111no—
594C2×#123—111no—
595C2×C22⋊Q8—111no—
596C2×C22⋊Q8—112no—
597C2×#121—111no—
598C2×#121—111no—
599C2×#121—112no—
600C2×#121—112no—
601C2×#121—112no—
602C2×#121—112no—
603C2×#121—111no—
604C2×#121—112no—
605C2×#121—112no—
606C2×#121—112no—
607C2×#121—112no—
608C2×#121—112no—
609C2×#121—112no—
610C2×#121—228no—
611C2×#121C2×D1112yescomplemented
612C2×#120—111no—
613C2×#120—111no—
614C2×#120—111no—
615C2×#120—111no—
616C2×#120C2×D1111yescharacteristic
617C2×#120C2×D1111yescharacteristic
618C2×C4×D4—111no—
619C2×C4×D4—111no—
620C22×C4⋊C4—111no—
621C22×C22⋊C4—111no—
622C22×C22⋊C4—111no—
623C22×C22⋊C4—111no—
624C22×C22⋊C4C2×D1111yescharacteristic
625#399—112no—
626#398—112no—
627#398—112no—
628#397—112no—
629#396—112no—
630#396—112no—
631#396—112no—
632#396—112no—
633#394—112no—
634#394—112no—
635#394—112no—
636#394—112no—
637#394—112no—
638#394—112no—
639#394—112no—
640#394C2×D1112yescomplemented
641#393—112no—
642#392—112no—
643#392—112no—
644#392—112no—
645#392—112no—
646#392—112no—
647#392—112no—
648#392C2×D1112yescomplemented
649#390—112no—
650#390—112no—
651#387—112no—
652#387—112no—
653#386—111no—
654#386—112no—
655#386—112no—
656#386—111no—
657#386—112no—
658#386—111no—
659#386—112no—
660#386—112no—
661#386C2×D1111yescharacteristic
662#386C2×D1112yescomplemented
663#385—112no—
664#385—112no—
665#385—111no—
666#385—112no—
667#385—112no—
668#385—112no—
669#385—111no—
670#385—111no—
671#385—112no—
672#385—112no—
673#385—112no—
674#385C2×D1111yescharacteristic
675#380—111no—
676#380—111no—
677#380—111no—
678#380—111no—
679#380—112no—
680#380—112no—
681#379—111no—
682#379—111no—
683#379—111no—
684#379C2×D1111yescharacteristic
685C22×C11—22no—
686C22×C11—22no—
687C22×C11—24no—
688C22×C11—24no—
689C22×C11—22no—
690C22×C11—22no—
691C22×C11—22no—
692C22×C11—24no—
693C22×C11—22no—
694C22×C11—22no—
695C22×C11—22no—
696C22×C11—24no—
697C22×C11—24no—
698C22×C11—416no—
699C22×C11—42no—
700C22×C11—42no—
701C22×C11—42no—
702C22×C11—42no—
703C22×C11—42no—
704C22×C11—42no—
705C22×C11—42no—
706C22×C11—42no—
707C22×C11—41no—
708C22×C11—41no—
709C22×C11—41no—
710C22×C11—42no—
711C22×C11—42no—
712C22×C11—88no—
713C22×C11#53714yes—
714C22×C11C23×D411yescharacteristic
715C22×C11C2×H(5,𝔽2)11yescharacteristic
716C22×C11C2×H(5,𝔽2)12yes—
717C22×C11C2×H(5,𝔽2)12yes—
718C22×C11C2×2−1+411yescharacteristic
719C2×D11—42no—
720C2×D11—41no—
721C2×D11—42no—
722C2×D11—42no—
723C2×D11—41no—
724C2×D11—41no—
725C2×D11—42no—
726C2×D11—42no—
727C2×D11—42no—
728C2×D11—42no—
729C2×D11—42no—
730C2×D11—42no—
731C2×D11—88no—
732C4×C11—41no—
733C4×C11—42no—
734C4×C11—41no—
735C4×C11—41no—
736C4×C11—42no—
737C4×C11—42no—
738Dic11—22no—
739Dic11—22no—
740Dic11—24no—
741Dic11—22no—
742Dic11—22no—
743Dic11—41no—
744Dic11—41no—
745Dic11—41no—
746Dic11—42no—
747Dic11—42no—
748C25—111no—
749C25C22×D1111yescharacteristic
750C25C22×D1111yescharacteristic
751C22×Q8—111no—
752C22×D4—24no—
753C22×D4—44no—
754C22×D4—111no—
755C22×D4—112no—
756C22×D4—112no—
757C22×D4—112no—
758C22×D4—112no—
759C22×D4—111no—
760C22×D4—111no—
761C22×D4—112no—
762C22×D4—111no—
763C22×D4—112no—
764C22×D4—112no—
765C22×D4—224no—
766C22×D4—224no—
767C22×D4—444no—
768C22×D4—444no—
769C22×D4C22×D1111yescharacteristic
770C22×D4C22×D1112yes—
771C22×D4C22×D1112yes—
772C22×D4C22×D1111yescharacteristic
773C22×D4C22×D1112yes—
774C22×D4C22×D1111yescharacteristic
775C23×C4—111no—
776C23×C4—111no—
777C23×C4—111no—
778C23×C4—112no—
779C23×C4—112no—
780C23×C4—111no—
781C23×C4—112no—
782C23×C4—111no—
783C23×C4—224no—
784C23×C4—444no—
785C23×C4C22×D1111yescharacteristic
786C23×C4C22×D1112yes—
787#126—224no—
788#126—224no—
789#124—224no—
790#124—224no—
791#123—224no—
792#123—224no—
793C22⋊Q8—224no—
794C22⋊Q8—444no—
795#121—44no—
796#121—228no—
797#121—228no—
798#121—228no—
799#121—228no—
800#121—224no—
801#121—224no—
802#121—224no—
803#121—444no—
804#121—444no—
805#121—444no—
806#121—444no—
807#121—444no—
808#121—444no—
809#120—24no—
810#120—42no—
811#120—224no—
812#120—442no—
813#120—442no—
814#120—442no—
815C4×D4—224no—
816C4×D4—224no—
817C2×C4⋊C4—112no—
818C2×C4⋊C4—112no—
819C2×C4⋊C4—111no—
820C2×C4⋊C4—111no—
821C2×C4⋊C4—111no—
822C2×C4⋊C4—111no—
823C2×C4⋊C4—112no—
824C2×C4⋊C4—112no—
825C2×C4⋊C4—111no—
826C2×C4⋊C4—111no—
827C2×C4⋊C4—112no—
828C2×C4⋊C4—112no—
829C2×C4⋊C4—112no—
830C2×C4⋊C4—112no—
831C2×C4⋊C4—112no—
832C2×C4⋊C4—224no—
833C2×C4⋊C4C22×D1112yes—
834C2×C22⋊C4—42no—
835C2×C22⋊C4—118no—
836C2×C22⋊C4—111no—
837C2×C22⋊C4—111no—
838C2×C22⋊C4—111no—
839C2×C22⋊C4—111no—
840C2×C22⋊C4—111no—
841C2×C22⋊C4—111no—
842C2×C22⋊C4—111no—
843C2×C22⋊C4—111no—
844C2×C22⋊C4—111no—
845C2×C22⋊C4—111no—
846C2×C22⋊C4—112no—
847C2×C22⋊C4—112no—
848C2×C22⋊C4—111no—
849C2×C22⋊C4—112no—
850C2×C22⋊C4—112no—
851C2×C22⋊C4—111no—
852C2×C22⋊C4—112no—
853C2×C22⋊C4—111no—
854C2×C22⋊C4—112no—
855C2×C22⋊C4—112no—
856C2×C22⋊C4—112no—
857C2×C22⋊C4—112no—
858C2×C22⋊C4—112no—
859C2×C22⋊C4—112no—
860C2×C22⋊C4—112no—
861C2×C22⋊C4—112no—
862C2×C22⋊C4—112no—
863C2×C22⋊C4—112no—
864C2×C22⋊C4—224no—
865C2×C22⋊C4—442no—
866C2×C22⋊C4C22×D1111yescharacteristic
867C2×C22⋊C4C22×D1111yescharacteristic
868C2×C22⋊C4C22×D1111yescharacteristic
869C2×C22⋊C4C22×D1111yescharacteristic
870C2×C22⋊C4C22×D1111yescharacteristic
871C2×C22⋊C4C22×D1112yes—
872C2×C22⋊C4C22×D1112yes—
873C2×C22⋊C4C22×D1112yes—
874C2×C22⋊C4C22×D1112yes—
875C2×C22⋊C4C22×D1112yes—
876C2×C42—111no—
877C2×C42—111no—
878#95—112no—
879#95—112no—
880#95—112no—
881#95—112no—
882#95—112no—
883#95—112no—
884#95—112no—
885#95—112no—
886#95—112no—
887#95—112no—
888#95C22×D1112yes—
889#95C22×D1112yes—
890C2×C11—24no—
891C2×C11—44no—
892C2×C11—42no—
893C2×C11—42no—
894C2×C11—81no—
895C2×C11C2×#53711yescharacteristic
896C2×C11#348411yescharacteristic
897C2×C11#348411yescharacteristic
898C2×C11#353612yes—
899C2×C11#353712yes—
900D11—81no—
901D11—82no—
902C24—22no—
903C24—24no—
904C24—22no—
905C24—22no—
906C24—22no—
907C24—22no—
908C24—42no—
909C24—42no—
910C24—42no—
911C24—112no—
912C24—111no—
913C24—222no—
914C24—222no—
915C24—222no—
916C24—442no—
917C24—442no—
918C24D4×D1114yes—
919C24C23×D1111yescharacteristic
920C24C23×D1111yescharacteristic
921C24C23×D1111yescharacteristic
922C24C23×D1112yes—
923C24C23×D1111yescharacteristic
924C2×Q8—222no—
925C2×Q8—442no—
926C2×D4—22no—
927C2×D4—24no—
928C2×D4—24no—
929C2×D4—22no—
930C2×D4—24no—
931C2×D4—24no—
932C2×D4—22no—
933C2×D4—22no—
934C2×D4—22no—
935C2×D4—24no—
936C2×D4—42no—
937C2×D4—42no—
938C2×D4—42no—
939C2×D4—42no—
940C2×D4—42no—
941C2×D4—42no—
942C2×D4—416no—
943C2×D4—224no—
944C2×D4—224no—
945C2×D4—224no—
946C2×D4—224no—
947C2×D4—222no—
948C2×D4—222no—
949C2×D4—224no—
950C2×D4—224no—
951C2×D4—222no—
952C2×D4—224no—
953C2×D4—224no—
954C2×D4—222no—
955C2×D4—222no—
956C2×D4—222no—
957C2×D4—224no—
958C2×D4—442no—
959C2×D4—442no—
960C2×D4—442no—
961C2×D4—442no—
962C2×D4—442no—
963C2×D4—442no—
964C2×D4—442no—
965C2×D4—4416no—
966C2×D4—442no—
967C2×D4—442no—
968C2×D4—442no—
969C2×D4—442no—
970C2×D4—442no—
971C2×D4—442no—
972C2×D4—442no—
973C2×D4—442no—
974C2×D4—4416no—
975C22×C4—22no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—112no—
981C22×C4—111no—
982C22×C4—111no—
983C22×C4—111no—
984C22×C4—111no—
985C22×C4—114no—
986C22×C4—114no—
987C22×C4—111no—
988C22×C4—112no—
989C22×C4—112no—
990C22×C4—111no—
991C22×C4—111no—
992C22×C4—222no—
993C22×C4—224no—
994C22×C4—224no—
995C22×C4—224no—
996C22×C4—224no—
997C22×C4—224no—
998C22×C4—222no—
999C22×C4—222no—
1000C22×C4—442no—
1001C22×C4—442no—
1002C22×C4—442no—
1003C22×C4—442no—
1004C22×C4—442no—
1005C22×C4—442no—
1006C22×C4—442no—
1007C22×C4—442no—
1008C22×C4—442no—
1009C22×C4—4416no—
1010C22×C4C23×D1112yes—
1011C22×C4C23×D1112yes—
1012C22×C4C23×D1111yescharacteristic
1013C22×C4C23×D1112yes—
1014C22×C4C23×D1111yescharacteristic
1015C22×C4C23×D1111yescharacteristic
1016C4⋊C4—42no—
1017C4⋊C4—224no—
1018C4⋊C4—224no—
1019C4⋊C4—222no—
1020C4⋊C4—222no—
1021C4⋊C4—222no—
1022C4⋊C4—222no—
1023C4⋊C4—222no—
1024C4⋊C4—224no—
1025C4⋊C4—224no—
1026C4⋊C4—222no—
1027C4⋊C4—442no—
1028C4⋊C4—442no—
1029C4⋊C4—442no—
1030C4⋊C4—442no—
1031C4⋊C4—442no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—24no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—114no—
1043C22⋊C4—114no—
1044C22⋊C4—114no—
1045C22⋊C4—114no—
1046C22⋊C4—224no—
1047C22⋊C4—224no—
1048C22⋊C4—222no—
1049C22⋊C4—222no—
1050C22⋊C4—224no—
1051C22⋊C4—222no—
1052C22⋊C4—222no—
1053C22⋊C4—224no—
1054C22⋊C4—222no—
1055C22⋊C4—222no—
1056C22⋊C4—222no—
1057C22⋊C4—222no—
1058C22⋊C4—222no—
1059C22⋊C4—224no—
1060C22⋊C4—442no—
1061C22⋊C4—442no—
1062C22⋊C4—442no—
1063C22⋊C4—442no—
1064C22⋊C4—442no—
1065C22⋊C4—442no—
1066C22⋊C4—442no—
1067C22⋊C4—442no—
1068C22⋊C4—442no—
1069C22⋊C4—442no—
1070C42—222no—
1071C42—222no—
1072C11#3670611yescharacteristic, complemented, Sylow
1073C23—22no—
1074C23—22no—
1075C23—28no—
1076C23—22no—
1077C23—21no—
1078C23—22no—
1079C23—21no—
1080C23—22no—
1081C23—22no—
1082C23—22no—
1083C23—21no—
1084C23—21no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—28no—
1091C23—21no—
1092C23—22no—
1093C23—21no—
1094C23—21no—
1095C23—22no—
1096C23—44no—
1097C23—44no—
1098C23—48no—
1099C23—48no—
1100C23—44no—
1101C23—44no—
1102C23—84no—
1103C23—84no—
1104C23—221no—
1105C23—222no—
1106C23—222no—
1107C23—222no—
1108C23—222no—
1109C23—222no—
1110C23—221no—
1111C23—221no—
1112C23—222no—
1113C23—222no—
1114C23—222no—
1115C23—222no—
1116C23—444no—
1117C23—444no—
1118C23—444no—
1119C23—884no—
1120C23—884no—
1121C23C2×D4×D1112yes—
1122C23C2×D4×D1112yes—
1123C23C2×D4×D1112yes—
1124C23#6703714yes—
1125C23#6703712yes—
1126C23#6704312yes—
1127C23C24×D1111yescharacteristic
1128Q8—882no—
1129D4—48no—
1130D4—48no—
1131D4—44no—
1132D4—82no—
1133D4—82no—
1134D4—84no—
1135D4—448no—
1136D4—448no—
1137D4—448no—
1138D4—448no—
1139D4—444no—
1140D4—884no—
1141D4—882no—
1142D4—882no—
1143D4—882no—
1144D4—884no—
1145D4—884no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—21no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—21no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—44no—
1163C2×C4—84no—
1164C2×C4—112no—
1165C2×C4—112no—
1166C2×C4—112no—
1167C2×C4—112no—
1168C2×C4—114no—
1169C2×C4—228no—
1170C2×C4—222no—
1171C2×C4—222no—
1172C2×C4—222no—
1173C2×C4—222no—
1174C2×C4—222no—
1175C2×C4—222no—
1176C2×C4—221no—
1177C2×C4—221no—
1178C2×C4—221no—
1179C2×C4—222no—
1180C2×C4—222no—
1181C2×C4—222no—
1182C2×C4—222no—
1183C2×C4—221no—
1184C2×C4—222no—
1185C2×C4—221no—
1186C2×C4—222no—
1187C2×C4—222no—
1188C2×C4—222no—
1189C2×C4—444no—
1190C2×C4—444no—
1191C2×C4—448no—
1192C2×C4—448no—
1193C2×C4—882no—
1194C2×C4—882no—
1195C2×C4—884no—
1196C22—22no—
1197C22—22no—
1198C22—24no—
1199C22—24no—
1200C22—22no—
1201C22—22no—
1202C22—22no—
1203C22—24no—
1204C22—22no—
1205C22—22no—
1206C22—22no—
1207C22—24no—
1208C22—24no—
1209C22—416no—
1210C22—42no—
1211C22—42no—
1212C22—42no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—42no—
1217C22—42no—
1218C22—41no—
1219C22—41no—
1220C22—41no—
1221C22—42no—
1222C22—42no—
1223C22—88no—
1224C22—441no—
1225C22—442no—
1226C22—441no—
1227C22—442no—
1228C22—442no—
1229C22—441no—
1230C22—442no—
1231C22—442no—
1232C22—442no—
1233C22—442no—
1234C22—442no—
1235C22—442no—
1236C22—888no—
1237C22#1062312814yes—
1238C22C22×D4×D1111yescharacteristic
1239C22C2×#6703711yescharacteristic
1240C22C2×#6703712yes—
1241C22C2×#6704311yescharacteristic
1242C22D11×H(5,𝔽2)12yes—
1243C4—41no—
1244C4—42no—
1245C4—41no—
1246C4—41no—
1247C4—42no—
1248C4—42no—
1249C4—222no—
1250C4—222no—
1251C4—224no—
1252C4—222no—
1253C4—222no—
1254C4—441no—
1255C4—441no—
1256C4—441no—
1257C4—442no—
1258C4—442no—
1259C2—24no—
1260C2—44no—
1261C2—42no—
1262C2—42no—
1263C2—81no—
1264C2—882no—
1265C2—881no—
1266C2C2×#1062312811yescharacteristic
1267C2#1308224511yescharacteristic
1268C2#1308224811yescharacteristic
1269C2#1308283112yes—
1270C2#1308284612yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2410C2
hypercenter#2410D11
hypocenterC11#36706
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2410

Complements

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

NH ≅ G/Ntype
1. C2×#10623124C2semidirect
2. C22×#66992C2semidirect
3. #13076901C2semidirect
4. #13076896C2semidirect
5. #13075094C2semidirect
6. #13075090C2semidirect
7. #13074918C2semidirect
8. #13074910C2semidirect
9. #13074906C2semidirect
10. #13074905C2semidirect
11. #13074846C2semidirect
12. #13074845C2semidirect
13. #13074427C2semidirect
14. #13074356C2semidirect
15. #13073968C2semidirect
16. #13073962C2semidirect
17. #13071991C2semidirect
18. #13071990C2semidirect
19. #13071984C2semidirect
20. #13071971C2semidirect
21. #13071969C2semidirect
22. #13071228C2semidirect
23. C11×#2410C2semidirect
28. C2×C11×#121C22semidirect
42. C2×#66992C22semidirect
43. C2×#66992C22semidirect
44. C2×#66992C22semidirect
45. C2×#66992C22semidirect
46. C2×#66992C22semidirect
47. C2×#66991C22semidirect
49. C2×#66989C22semidirect
50. C2×#66988C22semidirect
52. C2×#66983C22semidirect
56. C2×#66938C22semidirect
57. C2×#66937C22semidirect
58. C2×#66936C22semidirect
61. C2×#66932C22semidirect
62. C2×#66932C22semidirect
64. C2×#66931C22semidirect
65. C11×#394C22semidirect
66. C11×#392C22semidirect
68. C11×#386C22semidirect
72. #10622836C22semidirect
73. #10622836C22semidirect
74. #10622836C22semidirect
75. #10622835C22semidirect
77. #10622833C22semidirect
78. #10622833C22semidirect
80. #10622826C22semidirect
82. #10622823C22semidirect
83. #10622823C22semidirect
84. #10622607C22semidirect
85. #10622605C22semidirect
86. #10622602C22semidirect
87. #10622593C22semidirect
88. #10622574C22semidirect
89. #10622574C22semidirect
90. #10622573C22semidirect
91. #10622573C22semidirect
92. #10622573C22semidirect
93. #10622572C22semidirect
94. #10622572C22semidirect
95. #10622572C22semidirect
97. #10622571C22semidirect
98. #10622571C22semidirect
99. #10622570C22semidirect
100. #10622570C22semidirect
104. #10622563C22semidirect
105. #10622561C22semidirect
107. #10622559C22semidirect
108. #10622559C22semidirect
109. #10622559C22semidirect
110. #10622559C22semidirect
115. #10622555C22semidirect
116. #10622555C22semidirect
117. #10622289C22semidirect
118. #10622289C22semidirect
119. #10622288C22semidirect
120. #10622286C22semidirect
121. #10622285C22semidirect
122. #10622270C22semidirect
123. #10622267C22semidirect
124. #10622265C22semidirect
182. C2×C22⋊Dic11D4semidirect
457. #2410D11semidirect
611. C2×#121C2×D11semidirect
640. #394C2×D11semidirect
648. #392C2×D11semidirect
662. #386C2×D11semidirect
1072. C11#36706semidirect

Maximal subgroups

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

subgroupindex
C2×#106231242
C22×#669922
#130769012
#130768962
#130750942
#130750902
#130749182
#130749102
#130749062
#130749052
#130748462
#130748452
#130744272
#130743562
#130739682
#130739622
#130719912
#130719902
#130719842
#130719712
#130719692
#130712282
C11×#24102
#3670611