Finite Group Databasebeta

← #14925901

Subgroups — #14925901

Order 2816.

3206 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623117C211yesmaximal, characteristic, complemented
2C22×D4×Dic11C211yesmaximal, characteristic, complemented
3#13074229C212yesmaximal, complemented
4#13074221C212yesmaximal, complemented
5#13074093C211yesmaximal, characteristic, complemented
6#13073993C211yesmaximal, characteristic, complemented
7#13073800C212yesmaximal, complemented
8#13073771C211yesmaximal, characteristic, complemented
9#13073574C212yesmaximal, complemented
10#13073544C211yesmaximal, characteristic, complemented
11#13072013C211yesmaximal, characteristic, complemented
12#13072006C211yesmaximal, characteristic, complemented
13#13071990C211yesmaximal, characteristic, complemented
14#13071872C212yesmaximal, complemented
15#13071828C212yesmaximal, complemented
16#13071141C211yesmaximal, characteristic, complemented
17#13071135C211yesmaximal, characteristic, complemented
18#121×Dic11C212yesmaximal, complemented
19#13071126C212yesmaximal, complemented
20#120×Dic11C211yesmaximal, characteristic, complemented
21#13071115C211yesmaximal, characteristic, complemented
22C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
23C11×#2410C211yesmaximal, characteristic, complemented
24C23×D4×C11C2211yescharacteristic
25C24×Dic11C2211yescharacteristic
26C24×Dic11C2211yescharacteristic
27C22×#4341C2211yescharacteristic, complemented
28C2×C11×#121C2212yes—
29C2×C11×#120C2211yescharacteristic
30C2×C11×#120C2211yescharacteristic
31C22×C11×C22⋊C4C2211yescharacteristic
32C2×#67006C2211yescharacteristic
33C2×#67006C2211yescharacteristic
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C2×#66992C2212yes—
38C2×#66992C2211yescharacteristic
39C2×#66992C2211yescharacteristic, complemented
40C2×#66988C2211yescharacteristic
41C2×#66988C2211yescharacteristic, complemented
42C2×D4×Dic11—28no—
43C2×D4×Dic11C2212yes—
44C2×D4×Dic11C2211yescharacteristic
45C2×D4×Dic11C2212yes—
46C2×D4×Dic11C2212yes—
47C2×D4×Dic11C2212yes—
48C2×D4×Dic11C2211yescharacteristic, complemented
49C2×D4×Dic11C2212yescomplemented
50C22×C4⋊Dic11C2211yescharacteristic
51C22×C4×Dic11C2211yescharacteristic
52C22×C4×Dic11C2212yescomplemented
53#10623117—28no—
54C2×#66939C2211yescharacteristic
55C2×#66939C2211yescharacteristic, complemented
56C2×(C22⋊D11)⋊C4C2211yescharacteristic
57C2×(C22⋊D11)⋊C4C2211yescharacteristic, complemented
58C2×(C22⋊D11)⋊C4C2212yescomplemented
59C2×#66931C2211yescharacteristic
60C2×#66931C2211yescharacteristic, complemented
61C2×#66930C2211yescharacteristic, complemented
62C11×#394C2212yes—
63C11×#392C2212yes—
64C11×#386C2212yes—
65C11×#386C2211yescharacteristic
66C11×#385C2211yescharacteristic
67C11×#379C2211yescharacteristic
68#10622860C2211yescharacteristic
69#10622836C2212yes—
70#10622836C2212yescomplemented
71#10622835C2212yes—
72#10622835C2212yescomplemented
73#10622834C2212yescomplemented
74#10622833C2211yescharacteristic
75#10622833C2212yes—
76#10622833C2212yescomplemented
77#10622833C2212yescomplemented
78#10622826C2211yescharacteristic
79#10622826C2212yescomplemented
80#10622825C2212yescomplemented
81#10622823C2211yescharacteristic
82C2×C11⋊#95C2212yescomplemented
83#10622603C2212yescomplemented
84#10622598C2212yescomplemented
85#10622597C2212yescomplemented
86C4⋊C4×Dic11C2212yescomplemented
87#10622574C2212yescomplemented
88#10622574C2212yescomplemented
89#10622571C2211yescharacteristic
90#10622571C2212yescomplemented
91#10622570C2212yescomplemented
92#10622566C2212yescomplemented
93#10622565C2212yescomplemented
94#10622565C2212yescomplemented
95#10622564C2212yescomplemented
96#10622564C2212yescomplemented
97#10622563C2211yescharacteristic
98#10622563C2212yescomplemented
99#10622562C2212yescomplemented
100#10622560C2212yescomplemented
101#10622559C2211yescharacteristic
102#10622559C2212yescomplemented
103#10622558C2212yescomplemented
104#10622557C2212yescomplemented
105#10622556C2211yescharacteristic
106#10622556C2211yescharacteristic
107#10622555C2212yescomplemented
108C22⋊C4×Dic11C2211yescharacteristic
109C22⋊C4×Dic11C2211yescharacteristic
110C22⋊C4×Dic11C2211yescharacteristic
111C22⋊C4×Dic11C2211yescharacteristic
112C22⋊C4×Dic11C2212yescomplemented
113C22⋊C4×Dic11C2212yescomplemented
114C22⋊C4×Dic11C2212yescomplemented
115C22⋊C4×Dic11C2212yescomplemented
116C22⋊C4×Dic11C2212yescomplemented
117#10622283C2212yescomplemented
118#10622279C2212yescomplemented
119#10622273C2212yescomplemented
120#10622269C2212yescomplemented
121#10622268C2212yescomplemented
122#10622267C2212yescomplemented
123#10622262C2212yescomplemented
124#10622260C2212yescomplemented
125C25×C11C2311yescharacteristic
126C25×C11C2311yescharacteristic
127C22×D4×C11—24no—
128C22×D4×C11—28no—
129C22×D4×C11C2312yes—
130C22×D4×C11C2311yescharacteristic
131C22×D4×C11C2311yescharacteristic
132C22×D4×C11C2312yes—
133C22×D4×C11C2312yes—
134C22×D4×C11C2311yescharacteristic
135C23×C4×C11C2311yescharacteristic
136C23×C4×C11C2312yes—
137C22×C22⋊D11C2311yescharacteristic
138C22×C22⋊D11C2311yescharacteristic
139C22×C22⋊D11C2312yes—
140C22×C22⋊D11C2311yescharacteristic
141C22×C22⋊D11C2311yescharacteristic
142C23×Dic11—24no—
143C23×Dic11—44no—
144C23×Dic11—44no—
145C23×Dic11D418yescomplemented
146C23×Dic11C2312yes—
147C23×Dic11C2311yescharacteristic
148C23×Dic11C2311yescharacteristic
149C23×Dic11C2312yes—
150C23×Dic11C2311yescharacteristic
151C23×Dic11C2311yescharacteristic
152C23×Dic11C2311yescharacteristic
153C23×Dic11C2311yescharacteristic
154C23×Dic11C2312yes—
155C23×Dic11C2311yescharacteristic
156C23×Dic11C2311yescharacteristic
157C23×Dic11C2311yescharacteristic
158C2×#4341—24no—
159C2×#4341—44no—
160C22×C4×D11C2311yescharacteristic
161C22×Dic22C2311yescharacteristic
162C11×#121—28no—
163C11×#120—24no—
164C11×#120—24no—
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C22⋊C4—24no—
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2311yescharacteristic
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C11×C22⋊C4C2312yes—
175C2×C11×C22⋊C4C2312yes—
176C2×C11×C22⋊C4C2311yescharacteristic
177#67006—24no—
178#67006—24no—
179C2×C22⋊Dic11—24no—
180C2×C22⋊Dic11—24no—
181C2×C22⋊Dic11—24no—
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2311yescharacteristic
184C2×C22⋊Dic11C2311yescharacteristic
185C2×C22⋊Dic11C2311yescharacteristic
186C2×C22⋊Dic11C2312yes—
187C2×C22⋊Dic11C2312yes—
188C2×C22⋊Dic11C2312yes—
189C2×C22⋊Dic11C2312yes—
190C2×C22⋊Dic11C2312yes—
191C2×C22⋊Dic11C2312yes—
192C2×C22⋊Dic11C2311yescharacteristic
193C2×C22⋊Dic11C2312yes—
194C2×C22⋊Dic11C2312yes—
195C2×C22⋊Dic11C2311yescharacteristic
196C2×C22⋊Dic11C2312yes—
197C2×C22⋊Dic11C2312yes—
198C2×C22⋊Dic11C2311yescharacteristic
199#66992—28no—
200#66992—24no—
201#66992—24no—
202#66988—24no—
203#66988—24no—
204D4×Dic11—28no—
205D4×Dic11—28no—
206D4×Dic11—28no—
207D4×Dic11—28no—
208D4×Dic11—24no—
209D4×Dic11—24no—
210D4×Dic11—44no—
211C2×(C2×D11)⋊C4C2311yescharacteristic
212C2×(C2×D11)⋊C4C2311yescharacteristic
213C2×(C2×D11)⋊C4C2312yes—
214C2×(C2×D11)⋊C4C2312yes—
215C2×(C2×D11)⋊C4C2312yes—
216C2×C4⋊Dic11—24no—
217C2×C4⋊Dic11C2311yescharacteristic
218C2×C4⋊Dic11C2311yescharacteristic
219C2×C4⋊Dic11C2312yes—
220C2×C4⋊Dic11C2312yes—
221C2×C4⋊Dic11C2312yes—
222C2×C4⋊Dic11C2312yes—
223C2×Dic11⋊C4C2311yescharacteristic
224C2×Dic11⋊C4C2311yescharacteristic
225C2×Dic11⋊C4C2311yescharacteristic
226C2×Dic11⋊C4C2311yescharacteristic
227C2×Dic11⋊C4C2312yes—
228C2×Dic11⋊C4C2312yes—
229C2×Dic11⋊C4C2312yes—
230C2×C4×Dic11—24no—
231C2×C4×Dic11—44no—
232C2×C4×Dic11C2311yescharacteristic
233C2×C4×Dic11C2311yescharacteristic
234C2×C4×Dic11C2312yes—
235C2×C4×Dic11C2312yes—
236C2×C4×Dic11C2312yes—
237C2×C4×Dic11C2312yes—
238C2×C4×Dic11C2312yes—
239C2×C4×Dic11C2312yes—
240#66939—24no—
241#66939—24no—
242(C22⋊D11)⋊C4—24no—
243(C22⋊D11)⋊C4—24no—
244(C22⋊D11)⋊C4—44no—
245#66931—24no—
246#66931—24no—
247#66930—24no—
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—
261C11⋊#95C2312yes—
262C11⋊#95C2312yes—
263C11⋊#95C2312yes—
264#34957—111nomaximal, Sylow
265C24×C11—22no—
266C24×C11—22no—
267C24×C11—22no—
268C24×C11—24no—
269C24×C11—24no—
270C24×C11—22no—
271C24×C11—22no—
272C24×C11—42no—
273C24×C11—42no—
274C24×C11C2×D414yes—
275C24×C11C2411yescharacteristic
276C24×C11C2411yescharacteristic
277C24×C11C2412yes—
278C24×C11C2411yescharacteristic
279C24×C11C2411yescharacteristic
280C23×D11C2411yescharacteristic
281C2×D4×C11—232no—
282C2×D4×C11—24no—
283C2×D4×C11—24no—
284C2×D4×C11—24no—
285C2×D4×C11—24no—
286C2×D4×C11—22no—
287C2×D4×C11—22no—
288C2×D4×C11—22no—
289C2×D4×C11—22no—
290C2×D4×C11—22no—
291C2×D4×C11—24no—
292C2×D4×C11—24no—
293C2×D4×C11—24no—
294C2×D4×C11—24no—
295C2×D4×C11—42no—
296C2×D4×C11—42no—
297C2×D4×C11#4118yescomplemented
298C22×C4×C11—22no—
299C22×C4×C11—24no—
300C22×C4×C11—24no—
301C22×C4×C11—24no—
302C22×C4×C11—42no—
303C22×C4×C11C2412yes—
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C22×C4×C11C2412yes—
308C22×C4×C11C2412yes—
309C2×C22⋊D11—22no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—22no—
313C2×C22⋊D11—22no—
314C2×C22⋊D11—22no—
315C2×C22⋊D11—24no—
316C2×C22⋊D11—24no—
317C2×C22⋊D11—22no—
318C2×C22⋊D11—42no—
319C2×C22⋊D11—42no—
320C2×C22⋊D11—42no—
321C22×Dic11—24no—
322C22×Dic11—24no—
323C22×Dic11—24no—
324C22×Dic11—22no—
325C22×Dic11—24no—
326C22×Dic11—24no—
327C22×Dic11—24no—
328C22×Dic11—24no—
329C22×Dic11—24no—
330C22×Dic11—24no—
331C22×Dic11—22no—
332C22×Dic11—22no—
333C22×Dic11—22no—
334C22×Dic11—22no—
335C22×Dic11—24no—
336C22×Dic11—42no—
337C22×Dic11—42no—
338C22×Dic11—42no—
339C22×Dic11—42no—
340C22×Dic11—42no—
341C22×Dic11—42no—
342C22×Dic11—42no—
343C22×Dic11—416no—
344C22×Dic11—416no—
345C22×Dic11C2×D414yes—
346C22×Dic11C2×D414yes—
347C22×Dic11C2×D414yes—
348C22×Dic11C2×D414yes—
349C22×Dic11C2×D414yes—
350C22×Dic11C2×D414yes—
351C22×Dic11C2412yes—
352C22×Dic11C2412yes—
353C22×Dic11C2411yescharacteristic
354C22×Dic11C2411yescharacteristic
355C22×Dic11C2412yes—
356C22×Dic11C2411yescharacteristic
357C22×Dic11C2411yescharacteristic
358C22×Dic11C2411yescharacteristic
359C22×Dic11C2411yescharacteristic
360C22×Dic11C2412yes—
361C22×Dic11C2411yescharacteristic
362#4341—416no—
363C2×C4×D11—22no—
364C2×C4×D11—24no—
365C2×Dic22—22no—
366C2×Dic22—42no—
367C11×C4⋊C4—24no—
368C11×C22⋊C4—22no—
369C11×C22⋊C4—22no—
370C11×C22⋊C4—22no—
371C11×C22⋊C4—22no—
372C11×C22⋊C4—24no—
373C11×C22⋊C4—24no—
374C11×C22⋊C4—24no—
375C11×C22⋊C4—24no—
376C11×C22⋊C4—42no—
377C11×C22⋊C4#4114yescomplemented
378C22⋊Dic11—24no—
379C22⋊Dic11—24no—
380C22⋊Dic11—22no—
381C22⋊Dic11—22no—
382C22⋊Dic11—24no—
383C22⋊Dic11—24no—
384C22⋊Dic11—24no—
385C22⋊Dic11—22no—
386C22⋊Dic11—22no—
387C22⋊Dic11—22no—
388C22⋊Dic11—24no—
389C22⋊Dic11—24no—
390C22⋊Dic11—24no—
391C22⋊Dic11—22no—
392C22⋊Dic11—42no—
393C22⋊Dic11—42no—
394C22⋊Dic11#4114yescomplemented
395(C2×D11)⋊C4—22no—
396(C2×D11)⋊C4—22no—
397(C2×D11)⋊C4—24no—
398(C2×D11)⋊C4—24no—
399(C2×D11)⋊C4—42no—
400C4⋊Dic11—22no—
401C4⋊Dic11—22no—
402C4⋊Dic11—24no—
403C4⋊Dic11—24no—
404C4⋊Dic11—24no—
405C4⋊Dic11—42no—
406Dic11⋊C4—22no—
407Dic11⋊C4—22no—
408Dic11⋊C4—22no—
409Dic11⋊C4—22no—
410Dic11⋊C4—24no—
411Dic11⋊C4—24no—
412Dic11⋊C4—42no—
413C4×Dic11—22no—
414C4×Dic11—22no—
415C4×Dic11—24no—
416C4×Dic11—24no—
417C4×Dic11—24no—
418C4×Dic11—24no—
419C4×Dic11—42no—
420C4×Dic11—42no—
421C2×#525—111no—
422C22×C4×D4—111no—
423#2602—112no—
424#2602—112no—
425#2591—111no—
426#2583—111no—
427#2564—112no—
428#2561—111no—
429#2543—112no—
430#2539—111no—
431#2412—111no—
432#2412—111no—
433#2410—111no—
434#2410D1111yescharacteristic, complemented
435#2395—112no—
436#2388—112no—
437C4×#123—111no—
438C4×#123—111no—
439C4×#121—112no—
440C4×#121—112no—
441C4×#120—111no—
442C4×#120—111no—
443C2×C4×C22⋊C4—111no—
444C23×C11—21no—
445C23×C11—21no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—28no—
450C23×C11—28no—
451C23×C11—28no—
452C23×C11—22no—
453C23×C11—21no—
454C23×C11—22no—
455C23×C11—21no—
456C23×C11—22no—
457C23×C11—22no—
458C23×C11—22no—
459C23×C11—22no—
460C23×C11—22no—
461C23×C11—22no—
462C23×C11—21no—
463C23×C11—21no—
464C23×C11—22no—
465C23×C11—21no—
466C23×C11—22no—
467C23×C11—44no—
468C23×C11—48no—
469C23×C11—48no—
470C23×C11—48no—
471C23×C11—48no—
472C23×C11—44no—
473C23×C11—44no—
474C23×C11C22×D412yes—
475C23×C11C22×D412yes—
476C23×C11C22×D412yes—
477C23×C11C2×#4114yes—
478C23×C11C2×#4114yes—
479C23×C11C2×#4112yes—
480C23×C11C2×#4112yes—
481C23×C11C2511yescharacteristic
482C22×D11—21no—
483C22×D11—21no—
484C22×D11—22no—
485C22×D11—21no—
486C22×D11—22no—
487D4×C11—216no—
488D4×C11—216no—
489D4×C11—48no—
490D4×C11—44no—
491D4×C11—44no—
492D4×C11—44no—
493C2×C4×C11—28no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—21no—
499C2×C4×C11—21no—
500C2×C4×C11—21no—
501C2×C4×C11—21no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—21no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—48no—
509C2×C4×C11C2×#4114yes—
510C2×C4×C11C2×#4114yes—
511C22⋊D11—48no—
512C22⋊D11—44no—
513C22⋊D11—44no—
514C22⋊D11—44no—
515C22⋊D11—44no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—28no—
522C2×Dic11—28no—
523C2×Dic11—28no—
524C2×Dic11—22no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—21no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—21no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—44no—
541C2×Dic11—44no—
542C2×Dic11—44no—
543C2×Dic11—48no—
544C2×Dic11—48no—
545C2×Dic11—44no—
546C2×Dic11—44no—
547C2×Dic11—44no—
548C2×Dic11—48no—
549C2×Dic11C22×D412yes—
550C2×Dic11C22×D412yes—
551C2×Dic11C22×D412yes—
552C2×Dic11C22×D412yes—
553C2×Dic11C2×#4114yes—
554C2×Dic11H(5,𝔽2)14yes—
555C4×D11—44no—
556Dic22—44no—
557C22×#41—111no—
558C23×D4C2×D1111yescharacteristic
559C24×C4—111no—
560C24×C4—111no—
561#525—228no—
562C2×#123—111no—
563C2×#123—111no—
564C2×#123—111no—
565C2×#123—111no—
566C2×C22⋊Q8—111no—
567C2×C22⋊Q8—111no—
568C2×#121—111no—
569C2×#121—112no—
570C2×#121—111no—
571C2×#121C2×D1112yes—
572C2×#120—111no—
573C2×#120—111no—
574C2×#120C2×D1111yescharacteristic
575C2×#120C2×D1111yescharacteristic
576C2×C4×D4—112no—
577C2×C4×D4—112no—
578C2×C4×D4—112no—
579C2×C4×D4—112no—
580C2×C4×D4—111no—
581C2×C4×D4—111no—
582C2×C4×D4—112no—
583C2×C4×D4—111no—
584C2×C4×D4—111no—
585C2×C4×D4—112no—
586C2×C4×D4—228no—
587C2×#117—111no—
588C22×C4⋊C4—111no—
589C22×C22⋊C4—111no—
590C22×C22⋊C4—111no—
591C22×C22⋊C4—111no—
592C22×C22⋊C4C2×D1111yescharacteristic
593C22×C42—111no—
594C22×C42—112no—
595#400—112no—
596#399—112no—
597#398—112no—
598#397—112no—
599#397—112no—
600#397—112no—
601#395—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394—112no—
606#394C2×D1112yes—
607#393—112no—
608#392—112no—
609#392—112no—
610#392C2×D1112yes—
611#390—112no—
612#390—112no—
613#389—112no—
614#389—112no—
615#388—112no—
616#388—112no—
617#388—112no—
618#388—112no—
619#388—112no—
620#388—112no—
621#387—112no—
622#387—112no—
623#386—112no—
624#386—111no—
625#386—112no—
626#386—112no—
627#386—111no—
628#386—112no—
629#386—111no—
630#386—112no—
631#386C2×D1112yes—
632#386C2×D1111yescharacteristic
633#385—111no—
634#385—112no—
635#385—112no—
636#385—111no—
637#385—111no—
638#385C2×D1111yescharacteristic
639#381—111no—
640#381—111no—
641#380—112no—
642#380—112no—
643#379—111no—
644#379C2×D1111yescharacteristic
645C4×C4⋊C4—112no—
646C4×C4⋊C4—112no—
647C4×C22⋊C4—111no—
648C4×C22⋊C4—111no—
649C4×C22⋊C4—112no—
650C4×C22⋊C4—112no—
651C4×C22⋊C4—112no—
652C4×C22⋊C4—111no—
653C4×C22⋊C4—111no—
654C4×C22⋊C4—112no—
655C4×C22⋊C4—112no—
656C4×C22⋊C4—112no—
657C2×#95—112no—
658C22×C11—22no—
659C22×C11—22no—
660C22×C11—22no—
661C22×C11—22no—
662C22×C11—24no—
663C22×C11—24no—
664C22×C11—24no—
665C22×C11—24no—
666C22×C11—22no—
667C22×C11—24no—
668C22×C11—22no—
669C22×C11—22no—
670C22×C11—24no—
671C22×C11—24no—
672C22×C11—416no—
673C22×C11—416no—
674C22×C11—42no—
675C22×C11—42no—
676C22×C11—42no—
677C22×C11—42no—
678C22×C11—42no—
679C22×C11—42no—
680C22×C11—41no—
681C22×C11—41no—
682C22×C11—41no—
683C22×C11—42no—
684C22×C11—42no—
685C22×C11#52514yes—
686C22×C11#53214yes—
687C22×C11C23×D411yescharacteristic
688C22×C11C22×#4112yes—
689C22×C11C22×#4111yescharacteristic
690C22×C11C22×#4111yescharacteristic
691C22×C11C2×H(5,𝔽2)12yes—
692C2×D11—41no—
693C2×D11—41no—
694C2×D11—41no—
695C2×D11—42no—
696C2×D11—42no—
697C4×C11—24no—
698C4×C11—24no—
699C4×C11—41no—
700C4×C11—41no—
701C4×C11—41no—
702C4×C11—42no—
703Dic11—22no—
704Dic11—22no—
705Dic11—22no—
706Dic11—24no—
707Dic11—41no—
708Dic11—42no—
709Dic11—41no—
710Dic11—41no—
711Dic11—42no—
712Dic11—42no—
713Dic11#53414yes—
714C25C22×D1111yescharacteristic
715C25C22×D1111yescharacteristic
716C2×#41—224no—
717C2×#41—444no—
718C22×Q8—111no—
719C22×D4—24no—
720C22×D4—28no—
721C22×D4—111no—
722C22×D4—111no—
723C22×D4—112no—
724C22×D4—111no—
725C22×D4—111no—
726C22×D4C22×D1112yes—
727C22×D4C22×D1111yescharacteristic
728C22×D4C22×D1111yescharacteristic
729C22×D4C22×D1112yes—
730C22×D4C22×D1112yes—
731C22×D4C22×D1111yescharacteristic
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—118no—
736C23×C4—111no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—111no—
740C23×C4—112no—
741C23×C4—111no—
742C23×C4—112no—
743C23×C4—111no—
744C23×C4—112no—
745C23×C4—111no—
746C23×C4—224no—
747C23×C4—444no—
748C23×C4—444no—
749C23×C4C22×D1111yescharacteristic
750C23×C4C22×D1112yes—
751#123—224no—
752#123—224no—
753#123—224no—
754#123—224no—
755C22⋊Q8—224no—
756C22⋊Q8—224no—
757#121—28no—
758#121—224no—
759#121—224no—
760#121—228no—
761#120—24no—
762#120—24no—
763#120—224no—
764#120—224no—
765C4×D4—224no—
766C4×D4—224no—
767C4×D4—228no—
768C4×D4—228no—
769C4×D4—228no—
770C4×D4—228no—
771C4×D4—224no—
772C4×D4—224no—
773C4×D4—444no—
774C4×D4—444no—
775#117—224no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—111no—
782C2×C4⋊C4—111no—
783C2×C4⋊C4—111no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—112no—
788C2×C4⋊C4—112no—
789C2×C4⋊C4—224no—
790C2×C4⋊C4C22×D1112yes—
791C2×C22⋊C4—24no—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—112no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—112no—
797C2×C22⋊C4—111no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—111no—
800C2×C22⋊C4—111no—
801C2×C22⋊C4—111no—
802C2×C22⋊C4—111no—
803C2×C22⋊C4—111no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—111no—
808C2×C22⋊C4—111no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—224no—
815C2×C22⋊C4—224no—
816C2×C22⋊C4—224no—
817C2×C22⋊C4C22×D1111yescharacteristic
818C2×C22⋊C4C22×D1112yes—
819C2×C22⋊C4C22×D1111yescharacteristic
820C2×C22⋊C4C22×D1111yescharacteristic
821C2×C22⋊C4C22×D1111yescharacteristic
822C2×C22⋊C4C22×D1112yes—
823C2×C22⋊C4C22×D1112yes—
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1112yes—
826C2×C22⋊C4C22×D1111yescharacteristic
827C2×C42—111no—
828C2×C42—111no—
829C2×C42—112no—
830C2×C42—112no—
831C2×C42—112no—
832C2×C42—112no—
833C2×C42—112no—
834C2×C42—112no—
835C2×C42—224no—
836C2×C42—444no—
837#95—112no—
838#95—112no—
839#95—112no—
840#95—112no—
841#95—112no—
842#95—112no—
843#95—112no—
844#95—112no—
845#95—112no—
846#95—112no—
847#95—112no—
848#95—112no—
849#95—112no—
850#95—112no—
851#95C22×D1112yes—
852#95C22×D1112yes—
853C2×C11—24no—
854C2×C11—24no—
855C2×C11—42no—
856C2×C11—44no—
857C2×C11—81no—
858C2×C11C2×#52511yescharacteristic
859C2×C11C2×#53211yescharacteristic
860C2×C11C2×#53411yescharacteristic
861C2×C11#348112yes—
862C2×C11#348112yes—
863D11—81no—
864C24—22no—
865C24—22no—
866C24—24no—
867C24—24no—
868C24—22no—
869C24—22no—
870C24—22no—
871C24—42no—
872C24—42no—
873C24—111no—
874C24D4×D1114yes—
875C24C23×D1111yescharacteristic
876C24C23×D1111yescharacteristic
877C24C23×D1112yes—
878C24C23×D1111yescharacteristic
879C24C23×D1111yescharacteristic
880#41—4416no—
881C2×Q8—222no—
882C2×Q8—442no—
883C2×D4—232no—
884C2×D4—24no—
885C2×D4—24no—
886C2×D4—24no—
887C2×D4—24no—
888C2×D4—22no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—22no—
892C2×D4—24no—
893C2×D4—24no—
894C2×D4—22no—
895C2×D4—24no—
896C2×D4—24no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—224no—
900C2×D4—222no—
901C2×D4—222no—
902C2×D4—222no—
903C2×D4—222no—
904C2×D4—224no—
905C2×D4—224no—
906C2×D4—222no—
907C2×D4—222no—
908C2×D4—442no—
909C2×D4—442no—
910C2×D4—442no—
911C2×D4#434118yescomplemented
912C22×C4—22no—
913C22×C4—24no—
914C22×C4—24no—
915C22×C4—24no—
916C22×C4—42no—
917C22×C4—111no—
918C22×C4—114no—
919C22×C4—114no—
920C22×C4—114no—
921C22×C4—112no—
922C22×C4—111no—
923C22×C4—111no—
924C22×C4—111no—
925C22×C4—114no—
926C22×C4—114no—
927C22×C4—114no—
928C22×C4—112no—
929C22×C4—112no—
930C22×C4—111no—
931C22×C4—111no—
932C22×C4—112no—
933C22×C4—111no—
934C22×C4—222no—
935C22×C4—224no—
936C22×C4—224no—
937C22×C4—224no—
938C22×C4—224no—
939C22×C4—224no—
940C22×C4—224no—
941C22×C4—224no—
942C22×C4—222no—
943C22×C4—224no—
944C22×C4—224no—
945C22×C4—224no—
946C22×C4—222no—
947C22×C4—222no—
948C22×C4—224no—
949C22×C4—222no—
950C22×C4—222no—
951C22×C4—4416no—
952C22×C4—442no—
953C22×C4—442no—
954C22×C4—442no—
955C22×C4—442no—
956C22×C4—442no—
957C22×C4—442no—
958C22×C4—442no—
959C22×C4—4416no—
960C22×C4C23×D1112yes—
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1112yes—
965C22×C4C23×D1112yes—
966C4⋊C4—24no—
967C4⋊C4—224no—
968C4⋊C4—224no—
969C4⋊C4—222no—
970C4⋊C4—222no—
971C4⋊C4—222no—
972C4⋊C4—222no—
973C4⋊C4—222no—
974C4⋊C4—222no—
975C4⋊C4—224no—
976C4⋊C4—224no—
977C4⋊C4—224no—
978C4⋊C4—442no—
979C4⋊C4—442no—
980C22⋊C4—22no—
981C22⋊C4—22no—
982C22⋊C4—22no—
983C22⋊C4—22no—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—24no—
987C22⋊C4—24no—
988C22⋊C4—42no—
989C22⋊C4—114no—
990C22⋊C4—222no—
991C22⋊C4—222no—
992C22⋊C4—224no—
993C22⋊C4—224no—
994C22⋊C4—224no—
995C22⋊C4—222no—
996C22⋊C4—222no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—224no—
1001C22⋊C4—222no—
1002C22⋊C4—222no—
1003C22⋊C4—222no—
1004C22⋊C4—224no—
1005C22⋊C4—222no—
1006C22⋊C4—224no—
1007C22⋊C4—224no—
1008C22⋊C4—442no—
1009C22⋊C4—442no—
1010C22⋊C4—442no—
1011C22⋊C4#434114yescomplemented
1012C42—224no—
1013C42—224no—
1014C42—224no—
1015C42—224no—
1016C42—222no—
1017C42—222no—
1018C42—442no—
1019C42—442no—
1020C11#3495711yescharacteristic, complemented, Sylow
1021C23—21no—
1022C23—22no—
1023C23—21no—
1024C23—22no—
1025C23—22no—
1026C23—28no—
1027C23—28no—
1028C23—28no—
1029C23—22no—
1030C23—21no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—21no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—21no—
1040C23—22no—
1041C23—21no—
1042C23—21no—
1043C23—22no—
1044C23—44no—
1045C23—48no—
1046C23—48no—
1047C23—48no—
1048C23—48no—
1049C23—44no—
1050C23—44no—
1051C23—221no—
1052C23—221no—
1053C23—222no—
1054C23—221no—
1055C23—222no—
1056C23C2×D4×D1112yes—
1057C23C2×D4×D1112yes—
1058C23C2×D4×D1112yes—
1059C23C2×#434114yes—
1060C23C2×#434114yes—
1061C23C2×#434112yes—
1062C23#41×D1112yes—
1063C23C24×D1111yescharacteristic
1064Q8—444no—
1065D4—216no—
1066D4—216no—
1067D4—48no—
1068D4—44no—
1069D4—44no—
1070D4—44no—
1071D4—448no—
1072D4—444no—
1073D4—444no—
1074D4—444no—
1075D4—444no—
1076C2×C4—28no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—21no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—48no—
1092C2×C4—112no—
1093C2×C4—114no—
1094C2×C4—112no—
1095C2×C4—112no—
1096C2×C4—112no—
1097C2×C4—114no—
1098C2×C4—228no—
1099C2×C4—228no—
1100C2×C4—228no—
1101C2×C4—222no—
1102C2×C4—222no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—222no—
1107C2×C4—221no—
1108C2×C4—221no—
1109C2×C4—222no—
1110C2×C4—221no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—222no—
1114C2×C4—221no—
1115C2×C4—222no—
1116C2×C4—221no—
1117C2×C4—222no—
1118C2×C4—222no—
1119C2×C4—222no—
1120C2×C4—222no—
1121C2×C4—222no—
1122C2×C4—444no—
1123C2×C4—448no—
1124C2×C4—444no—
1125C2×C4—444no—
1126C2×C4—444no—
1127C2×C4—444no—
1128C2×C4—448no—
1129C2×C4—448no—
1130C2×C4—444no—
1131C2×C4—444no—
1132C2×C4C2×#434114yes—
1133C2×C4C2×#434114yes—
1134C22—22no—
1135C22—22no—
1136C22—22no—
1137C22—24no—
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—22no—
1142C22—22no—
1143C22—22no—
1144C22—24no—
1145C22—24no—
1146C22—22no—
1147C22—24no—
1148C22—416no—
1149C22—416no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—42no—
1156C22—41no—
1157C22—41no—
1158C22—42no—
1159C22—42no—
1160C22—41no—
1161C22—441no—
1162C22—441no—
1163C22—442no—
1164C22—442no—
1165C22—441no—
1166C22#1062311714yes—
1167C22#1062312714yes—
1168C22C22×D4×D1111yescharacteristic
1169C22C22×#434111yescharacteristic
1170C22C22×#434112yes—
1171C22C2×#41×D1111yescharacteristic
1172C22D11×H(5,𝔽2)12yes—
1173C4—24no—
1174C4—24no—
1175C4—41no—
1176C4—41no—
1177C4—42no—
1178C4—41no—
1179C4—114no—
1180C4—222no—
1181C4—222no—
1182C4—222no—
1183C4—224no—
1184C4—442no—
1185C4—441no—
1186C4—442no—
1187C4—441no—
1188C4—442no—
1189C4—441no—
1190C2—24no—
1191C2—24no—
1192C2—42no—
1193C2—44no—
1194C2—81no—
1195C2—881no—
1196C2C2×#1062311711yescharacteristic
1197C2C2×#1062312711yescharacteristic
1198C2D11×#53411yescharacteristic
1199C2#1308221712yes—
1200C2#1308222112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2410C2
hypercenter#2410D11
hypocenterC11#34957
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2410

Complements

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

NH ≅ G/Ntype
1. C2×#10623117C2semidirect
2. C22×D4×Dic11C2semidirect
3. #13074229C2semidirect
4. #13074221C2semidirect
5. #13074093C2semidirect
6. #13073993C2semidirect
7. #13073800C2semidirect
8. #13073771C2semidirect
9. #13073574C2semidirect
10. #13073544C2semidirect
11. #13072013C2semidirect
12. #13072006C2semidirect
13. #13071990C2semidirect
14. #13071872C2semidirect
15. #13071828C2semidirect
16. #13071141C2semidirect
17. #13071135C2semidirect
18. #121×Dic11C2semidirect
19. #13071126C2semidirect
20. #120×Dic11C2semidirect
21. #13071115C2semidirect
22. C2×C22⋊C4×Dic11C2semidirect
23. C11×#2410C2semidirect
27. C22×#4341C22semidirect
39. C2×#66992C22semidirect
41. C2×#66988C22semidirect
48. C2×D4×Dic11C22semidirect
49. C2×D4×Dic11C22semidirect
52. C22×C4×Dic11C22semidirect
55. C2×#66939C22semidirect
57. C2×(C22⋊D11)⋊C4C22semidirect
58. C2×(C22⋊D11)⋊C4C22semidirect
60. C2×#66931C22semidirect
61. C2×#66930C22semidirect
70. #10622836C22semidirect
72. #10622835C22semidirect
73. #10622834C22semidirect
76. #10622833C22semidirect
77. #10622833C22semidirect
79. #10622826C22semidirect
80. #10622825C22semidirect
82. C2×C11⋊#95C22semidirect
83. #10622603C22semidirect
84. #10622598C22semidirect
85. #10622597C22semidirect
86. C4⋊C4×Dic11C22semidirect
87. #10622574C22semidirect
88. #10622574C22semidirect
90. #10622571C22semidirect
91. #10622570C22semidirect
92. #10622566C22semidirect
93. #10622565C22semidirect
94. #10622565C22semidirect
95. #10622564C22semidirect
96. #10622564C22semidirect
98. #10622563C22semidirect
99. #10622562C22semidirect
100. #10622560C22semidirect
102. #10622559C22semidirect
103. #10622558C22semidirect
104. #10622557C22semidirect
107. #10622555C22semidirect
112. C22⋊C4×Dic11C22semidirect
113. C22⋊C4×Dic11C22semidirect
114. C22⋊C4×Dic11C22semidirect
115. C22⋊C4×Dic11C22semidirect
116. C22⋊C4×Dic11C22semidirect
117. #10622283C22semidirect
118. #10622279C22semidirect
119. #10622273C22semidirect
120. #10622269C22semidirect
121. #10622268C22semidirect
122. #10622267C22semidirect
123. #10622262C22semidirect
124. #10622260C22semidirect
145. C23×Dic11D4semidirect
297. C2×D4×C11#41semidirect
377. C11×C22⋊C4#41semidirect
394. C22⋊Dic11#41semidirect
434. #2410D11semidirect
911. C2×D4#4341semidirect
1011. C22⋊C4#4341semidirect
1020. C11#34957semidirect

Maximal subgroups

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

subgroupindex
C2×#106231172
C22×D4×Dic112
#130742292
#130742212
#130740932
#130739932
#130738002
#130737712
#130735742
#130735442
#130720132
#130720062
#130719902
#130718722
#130718282
#130711412
#130711352
#121×Dic112
#130711262
#120×Dic112
#130711152
C2×C22⋊C4×Dic112
C11×#24102
#3495711