Finite Group Databasebeta

← #14926734

Subgroups — #14926734

Order 2816.

2756 conjugacy classes of subgroups.

The subgroup lattice has 1222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623209C212yesmaximal, complemented
2#13076980C211yesmaximal, characteristic, complemented
3#13076974C211yesmaximal, characteristic, complemented
4#13076959C211yesmaximal, characteristic, complemented
5#13076948C211yesmaximal, characteristic, complemented
6#13074762C212yesmaximal, complemented
7#13074743C212yesmaximal, complemented
8#13073687C212yesmaximal, complemented
9#13073682C212yesmaximal, complemented
10#13073196C211yesmaximal, characteristic, complemented
11#13072745C212yesmaximal, complemented
12#13072382C211yesmaximal, characteristic, complemented
13#13072314C211yesmaximal, characteristic, complemented
14#13072252C211yesmaximal, characteristic, complemented
15#13072204C211yesmaximal, characteristic, complemented
16#13072153C212yesmaximal, complemented
17#13072058C211yesmaximal, characteristic, complemented
18#13071968C211yesmaximal, characteristic, complemented
19#13071278C212yesmaximal, complemented
20C4×#66948C211yesmaximal, characteristic, complemented
21D11×#390C211yesmaximal, characteristic, complemented
22C4×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
23C11×#2491C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C2×C11×C4⋊Q8C2211yescharacteristic, complemented
26C2×C11×#124C2212yescomplemented
27C2×C11×#121C2211yescharacteristic
28C2×#67000C2212yescomplemented
29C2×#67000C2212yescomplemented
30C2×#66999C2212yes—
31C2×#66993C2211yescharacteristic
32C2×#66992C2212yescomplemented
33C2×#66992C2212yescomplemented
34C2×#66990C2212yes—
35C2×#66983C2211yescharacteristic
36C2×#66983C2211yescharacteristic, complemented
37C2×C4×C22⋊D11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic, complemented
39#10623209—216no—
40C2×#66948C2211yescharacteristic
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×#66939C2212yescomplemented
43C2×#66937C2212yes—
44C2×#66937C2212yescomplemented
45C2×#66936C2212yescomplemented
46C2×#66935C2212yes—
47C2×#66935C2212yes—
48C2×(C22⋊D11)⋊C4C2211yescharacteristic
49C2×(C22⋊D11)⋊C4C2211yescharacteristic
50C2×C22⋊C4×D11C2212yes—
51C2×C22⋊C4×D11C2212yes—
52C2×#66932C2212yescomplemented
53C2×#66929C2212yescomplemented
54C2×#66927C2211yescharacteristic
55C2×C4×D44C2212yes—
56C2×C4×D44C2211yescharacteristic, complemented
57C2×C42×D11C2211yescharacteristic
58C11×#394C2212yescomplemented
59C11×#393C2212yescomplemented
60C11×#390C2211yescharacteristic
61C11×#390C2211yescharacteristic
62C11×#388C2212yescomplemented
63C11×#380C2211yescharacteristic, complemented
64C4×C11×C4⋊C4C2211yescharacteristic, complemented
65C4×C11×C22⋊C4C2211yescharacteristic, complemented
66#10622842C2212yescomplemented
67#10622836C2212yes—
68#10622834C2211yescharacteristic
69#10622834C2211yescharacteristic
70#10622602C2212yes—
71#10622601C2211yescharacteristic
72#10622601C2211yescharacteristic
73#10622601C2211yescharacteristic
74#10622601C2212yescomplemented
75#10622601C2211yescharacteristic, complemented
76#10622601C2212yescomplemented
77#10622601C2211yescharacteristic, complemented
78#10622600C2211yescharacteristic
79#10622598C2211yescharacteristic, complemented
80#10622598C2211yescharacteristic, complemented
81#10622597C2212yescomplemented
82#10622589C2211yescharacteristic, complemented
83#10622586C2211yescharacteristic, complemented
84#10622574C2212yescomplemented
85#10622573C2212yes—
86#10622573C2212yes—
87#10622573C2212yescomplemented
88#10622572C2212yes—
89#10622572C2212yescomplemented
90#10622572C2212yescomplemented
91#10622571C2212yescomplemented
92#10622570C2212yes—
93#10622570C2212yes—
94#10622570C2212yescomplemented
95#10622570C2212yescomplemented
96#10622569C2212yescomplemented
97#10622568C2212yes—
98#10622564C2212yescomplemented
99#10622558C2212yescomplemented
100#10622557C2212yescomplemented
101C22⋊C4×Dic11C2211yescharacteristic, complemented
102C22⋊C4×Dic11C2211yescharacteristic, complemented
103#10622553C2212yescomplemented
104#10622552C2211yescharacteristic
105C4×(C2×D11)⋊C4C2211yescharacteristic
106C4×(C2×D11)⋊C4C2212yescomplemented
107C4×Dic11⋊C4C2211yescharacteristic, complemented
108C42×Dic11C2211yescharacteristic, complemented
109#10622541C2211yescharacteristic, complemented
110#10622289C2212yescomplemented
111#10622289C2212yescomplemented
112#10622288C2212yescomplemented
113#10622285C2212yescomplemented
114#10622283C2212yescomplemented
115#10622283C2212yescomplemented
116#10622283C2212yescomplemented
117#10622279C2211yescharacteristic
118#10622279C2211yescharacteristic
119#10622278C2212yes—
120#10622278C2212yes—
121#10622278C2212yescomplemented
122#10622262C2211yescharacteristic, complemented
123#10622262C2211yescharacteristic, complemented
124C24×D11C2312yes—
125C22×Q8×C11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2312yes—
128C23×C4×C11C2311yescharacteristic
129C22×C22⋊D11C2311yescharacteristic
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C23×Dic11C2311yescharacteristic
136C23×Dic11C2311yescharacteristic
137C2×D4×D11—24no—
138C2×D4×D11—42no—
139C2×D4×D11—42no—
140C22×D44C2312yes—
141C22×D44C2311yescharacteristic
142C22×D44C2311yescharacteristic
143C22×D44C2312yes—
144C22×D44C2312yes—
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2312yes—
148C22×C4×D11C2312yes—
149C22×C4×D11C2311yescharacteristic
150C11×C4⋊Q8—42no—
151C11×#124—28no—
152C11×#121—42no—
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2311yescharacteristic
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2311yescharacteristic
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2312yes—
167C2×C42×C11C2311yescharacteristic
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2311yescharacteristic
172C2×C22⋊Dic11C2312yes—
173#67000—28no—
174#67000—44no—
175#66999—28no—
176#66993—42no—
177#66992—28no—
178#66992—44no—
179#66990—28no—
180#66983—42no—
181#66983—42no—
182C4×C22⋊D11—24no—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2312yes—
188C2×(C2×D11)⋊C4C2312yes—
189C2×(C2×D11)⋊C4C2312yes—
190C2×(C2×D11)⋊C4C2312yes—
191C2×(C2×D11)⋊C4C2312yes—
192C2×(C2×D11)⋊C4C2312yes—
193C2×(C2×D11)⋊C4C2311yescharacteristic
194C2×(C2×D11)⋊C4C2312yes—
195C2×(C2×D11)⋊C4C2312yes—
196C2×(C2×D11)⋊C4C2312yes—
197C2×(C2×D11)⋊C4C2312yes—
198C2×(C2×D11)⋊C4C2312yes—
199C2×(C2×D11)⋊C4C2312yes—
200C2×(C2×D11)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2311yescharacteristic
203C2×C4⋊Dic11C2312yes—
204C2×C4⋊Dic11C2311yescharacteristic
205C2×C4⋊Dic11C2312yes—
206C2×C4⋊Dic11C2311yescharacteristic
207C2×Dic11⋊C4C2312yes—
208C2×Dic11⋊C4C2312yes—
209C2×Dic11⋊C4C2312yes—
210C2×Dic11⋊C4C2311yescharacteristic
211C2×Dic11⋊C4C2311yescharacteristic
212C2×Dic11⋊C4C2312yes—
213C2×Dic11⋊C4C2312yes—
214C2×Dic11⋊C4C2311yescharacteristic
215C2×C4×Dic11—42no—
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×C4×Dic11C2311yescharacteristic
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227#66948—24no—
228C4⋊C4×D11—42no—
229#66939—28no—
230#66937—28no—
231#66937—28no—
232#66936—28no—
233#66935—28no—
234#66935—28no—
235(C22⋊D11)⋊C4—24no—
236(C22⋊D11)⋊C4D418yescomplemented
237C22⋊C4×D11—28no—
238C22⋊C4×D11—44no—
239#66932—28no—
240#66929—28no—
241#66927—42no—
242C4×D44—28no—
243C4×D44—42no—
244C42×D11—42no—
245C11×#95C2311yescharacteristic
246C11×#95C2311yescharacteristic
247C11×#95C2312yes—
248C11×#95C2312yes—
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258#35007—111nomaximal, Sylow
259C24×C11C2412yes—
260C24×C11C2411yescharacteristic
261C23×D11—24no—
262C23×D11—24no—
263C23×D11—24no—
264C23×D11—42no—
265C23×D11—42no—
266C23×D11—42no—
267C23×D11—42no—
268C23×D11C2412yes—
269C23×D11C2412yes—
270C23×D11C2411yescharacteristic
271C2×Q8×C11—24no—
272C2×Q8×C11—42no—
273C2×Q8×C11—42no—
274C2×D4×C11—24no—
275C2×D4×C11—22no—
276C2×D4×C11—22no—
277C2×D4×C11—22no—
278C2×D4×C11—42no—
279C2×D4×C11—42no—
280C22×C4×C11—22no—
281C22×C4×C11—22no—
282C22×C4×C11—22no—
283C22×C4×C11C2412yes—
284C22×C4×C11C2411yescharacteristic
285C22×C4×C11C2412yes—
286C22×C4×C11C2412yes—
287C22×C4×C11C2411yescharacteristic
288C22×C4×C11C2411yescharacteristic
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C2×C22⋊D11—24no—
293C2×C22⋊D11—24no—
294C2×C22⋊D11—24no—
295C2×C22⋊D11—24no—
296C2×C22⋊D11—24no—
297C2×C22⋊D11—22no—
298C2×C22⋊D11—22no—
299C2×C22⋊D11—42no—
300C2×C22⋊D11—42no—
301C2×C22⋊D11—42no—
302C2×C22⋊D11—42no—
303C2×C22⋊D11—42no—
304C2×C22⋊D11—42no—
305C2×C22⋊D11—42no—
306C2×C22⋊D11—42no—
307C2×C22⋊D11—42no—
308C2×C22⋊D11—42no—
309C2×C22⋊D11C2×D414yes—
310C22×Dic11—22no—
311C22×Dic11—22no—
312C22×Dic11—41no—
313C22×Dic11—41no—
314C22×Dic11—41no—
315C22×Dic11C2×D414yescomplemented
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2412yes—
318C22×Dic11C2412yes—
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2411yescharacteristic
322C22×Dic11C2411yescharacteristic
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2411yescharacteristic
325D4×D11—416no—
326C2×D44—24no—
327C2×D44—24no—
328C2×D44—24no—
329C2×D44—24no—
330C2×D44—22no—
331C2×D44—22no—
332C2×D44—24no—
333C2×D44—22no—
334C2×D44—22no—
335C2×D44—22no—
336C2×D44—22no—
337C2×D44—42no—
338C2×D44—42no—
339C2×D44—42no—
340C2×D44—42no—
341C2×C4×D11—22no—
342C2×C4×D11—24no—
343C2×C4×D11—22no—
344C2×C4×D11—24no—
345C2×C4×D11—22no—
346C2×C4×D11—22no—
347C2×C4×D11—41no—
348C2×C4×D11—41no—
349C2×C4×D11—41no—
350C2×C4×D11—42no—
351C2×C4×D11—42no—
352C2×C4×D11—42no—
353C2×C4×D11—42no—
354C2×C4×D11C2×D414yes—
355C2×C4×D11#4114yes—
356C11×C4⋊C4—22no—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—42no—
360C11×C22⋊C4—24no—
361C11×C22⋊C4—24no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4—42no—
367C11×C22⋊C4C2×D414yescomplemented
368C42×C11—24no—
369C42×C11—22no—
370C42×C11—22no—
371C22⋊Dic11—24no—
372C22⋊Dic11—24no—
373C22⋊Dic11—22no—
374C22⋊Dic11—24no—
375C22⋊Dic11—42no—
376(C2×D11)⋊C4—24no—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—24no—
380(C2×D11)⋊C4—24no—
381(C2×D11)⋊C4—24no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—24no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—22no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—42no—
389(C2×D11)⋊C4—42no—
390(C2×D11)⋊C4—42no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4C2×D414yes—
395(C2×D11)⋊C4#4114yes—
396C4⋊Dic11—24no—
397C4⋊Dic11—24no—
398C4⋊Dic11—22no—
399C4⋊Dic11—22no—
400Dic11⋊C4—24no—
401Dic11⋊C4—24no—
402Dic11⋊C4—22no—
403Dic11⋊C4—22no—
404Dic11⋊C4—24no—
405Dic11⋊C4—42no—
406Dic11⋊C4—42no—
407Dic11⋊C4C2×D414yescomplemented
408C4×Dic11—22no—
409C4×Dic11—22no—
410C4×Dic11—22no—
411C4×Dic11—22no—
412C4×Dic11—22no—
413C4×Dic11—41no—
414C4×Dic11—41no—
415C4×Dic11—41no—
416C4×Dic11—41no—
417C4×Dic11—41no—
418C4×Dic11C2×D414yescomplemented
419C2×#538—112no—
420#2860—111no—
421#2858—111no—
422#2856—111no—
423#2854—111no—
424#2662—112no—
425#2661—112no—
426#2555—112no—
427#2554—112no—
428#2512—111no—
429#2491D1111yescharacteristic, complemented
430#2472—112no—
431#2445—111no—
432#2440—111no—
433#2433—111no—
434#2428—111no—
435#2424—112no—
436#2416—111no—
437#2408—111no—
438#2321—112no—
439C4×#121—111no—
440C2×#390—111no—
441C42×D4—111no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11—21no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11C22×D412yes—
456C23×C11C2511yescharacteristic
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
475C22×D11—48no—
476C22×D11—48no—
477C22×D11—48no—
478C22×D11—84no—
479C22×D11—84no—
480C22×D11—84no—
481C22×D11—84no—
482C22×D11C22×D412yes—
483C22×D11C2×#4112yes—
484C22×D11C2×#4112yes—
485Q8×C11—84no—
486D4×C11—44no—
487D4×C11—84no—
488C2×C4×C11—21no—
489C2×C4×C11—21no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—21no—
498C2×C4×C11—21no—
499C2×C4×C11—22no—
500C2×C4×C11—22no—
501C2×C4×C11—21no—
502C2×C4×C11—21no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—21no—
507C2×C4×C11—21no—
508C2×C4×C11—22no—
509C2×C4×C11—44no—
510C2×C4×C11C22×D412yes—
511C2×C4×C11C22×D412yes—
512C2×C4×C11C2×#4112yes—
513C2×C4×C11C2×#4112yes—
514C2×C4×C11H(5,𝔽2)12yes—
515C2×C4×C11H(5,𝔽2)12yes—
516C22⋊D11—28no—
517C22⋊D11—48no—
518C22⋊D11—84no—
519C22⋊D11—84no—
520C22⋊D11—84no—
521C22⋊D11—84no—
522C2×Dic11—21no—
523C2×Dic11—21no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—21no—
527C2×Dic11—21no—
528C2×Dic11—21no—
529C2×Dic11—21no—
530C2×Dic11—21no—
531C2×Dic11—21no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—21no—
537C2×Dic11—21no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—21no—
542C2×Dic11—22no—
543C2×Dic11—44no—
544C2×Dic11—44no—
545C2×Dic11C22×D412yes—
546C2×Dic11C22×D412yes—
547C2×Dic11C22×D412yes—
548C2×Dic11C2×#4112yes—
549C2×Dic11C2×#4112yes—
550C2×Dic11H(5,𝔽2)12yes—
551D44—48no—
552D44—44no—
553D44—44no—
554D44—84no—
555D44—84no—
556C4×D11—28no—
557C4×D11—44no—
558C4×D11—44no—
559C4×D11—84no—
560C4×D11—84no—
561C23×D4—111no—
562#538—2216no—
563C2×C4⋊Q8C2×D1111yescharacteristic, complemented
564C2×#127—111no—
565C2×#127—111no—
566C2×#126—112no—
567C2×#126—112no—
568C2×#124—112no—
569C2×#124—112no—
570C2×#124C2×D1112yescomplemented
571C2×#123—112no—
572C2×#123—112no—
573C2×C22⋊Q8—112no—
574C2×#121—112no—
575C2×#121—112no—
576C2×#121—111no—
577C2×#121—111no—
578C2×#121—111no—
579C2×#121—112no—
580C2×#121—112no—
581C2×#121C2×D1111yescharacteristic
582C2×#120—112no—
583C2×#120—112no—
584C2×#120—112no—
585C2×C4×D4—111no—
586C2×C4×D4—111no—
587C2×C4×D4—111no—
588C2×C4×D4—112no—
589C2×C4×D4—111no—
590C22×C4⋊C4—111no—
591C22×C22⋊C4—112no—
592C22×C22⋊C4—112no—
593C22×C42—111no—
594C22×C42—111no—
595#398—112no—
596#397—112no—
597#396—112no—
598#396—112no—
599#395—112no—
600#394—112no—
601#394—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394C2×D1112yescomplemented
606#393C2×D1112yescomplemented
607#392—112no—
608#392—112no—
609#392—112no—
610#392—112no—
611#390—111no—
612#390—111no—
613#390—112no—
614#390—111no—
615#390—111no—
616#390—111no—
617#390—111no—
618#390—111no—
619#390—112no—
620#390—112no—
621#390—112no—
622#390—112no—
623#390—112no—
624#390—111no—
625#390C2×D1111yescharacteristic
626#390C2×D1111yescharacteristic
627#389—111no—
628#389—111no—
629#389—111no—
630#389—111no—
631#388—112no—
632#388—112no—
633#388—112no—
634#388—112no—
635#388—112no—
636#388—112no—
637#388—112no—
638#388C2×D1112yescomplemented
639#386—112no—
640#386—112no—
641#386—112no—
642#386—112no—
643#386—112no—
644#385—112no—
645#384—111no—
646#380—111no—
647#380C2×D1111yescharacteristic, complemented
648#379—112no—
649C4×C4⋊C4—111no—
650C4×C4⋊C4—111no—
651C4×C4⋊C4—111no—
652C4×C4⋊C4C2×D1111yescharacteristic, complemented
653C4×C22⋊C4—111no—
654C4×C22⋊C4—111no—
655C4×C22⋊C4—111no—
656C4×C22⋊C4—112no—
657C4×C22⋊C4—111no—
658C4×C22⋊C4—111no—
659C4×C22⋊C4C2×D1111yescharacteristic, complemented
660C43—111no—
661C22×C11—22no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—41no—
665C22×C11—41no—
666C22×C11—41no—
667C22×C11—41no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—42no—
673C22×C11—42no—
674C22×C11—42no—
675C22×C11C23×D411yescharacteristic
676C22×C11C22×#4111yescharacteristic
677C22×C11C22×#4111yescharacteristic
678C22×C11C2×H(5,𝔽2)11yescharacteristic
679C22×C11C2×H(5,𝔽2)11yescharacteristic
680C22×C11C2×H(5,𝔽2)11yescharacteristic
681C22×C11#58511yescharacteristic
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—22no—
685C2×D11—22no—
686C2×D11—22no—
687C2×D11—22no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—42no—
692C2×D11—42no—
693C2×D11—42no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11—42no—
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—816no—
703C2×D11#53214yes—
704C4×C11—22no—
705C4×C11—22no—
706C4×C11—22no—
707C4×C11—42no—
708C4×C11—41no—
709C4×C11—42no—
710C4×C11—42no—
711C4×C11—41no—
712C4×C11#53814yescomplemented
713Dic11—22no—
714Dic11—22no—
715Dic11—22no—
716Dic11—22no—
717Dic11—22no—
718Dic11—22no—
719Dic11—41no—
720Dic11—42no—
721Dic11—42no—
722C25—112no—
723C22×Q8C22×D1112yes—
724C22×D4—111no—
725C22×D4—112no—
726C22×D4—112no—
727C22×D4—112no—
728C22×D4—112no—
729C22×D4—112no—
730C22×D4—112no—
731C22×D4—111no—
732C22×D4—111no—
733C22×D4—112no—
734C22×D4—112no—
735C22×D4—224no—
736C22×D4—442no—
737C22×D4—442no—
738C22×D4C22×D1111yescharacteristic
739C22×D4C22×D1112yes—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—111no—
745C23×C4—112no—
746C23×C4—112no—
747C23×C4C22×D1111yescharacteristic
748C4⋊Q8—42no—
749#127—442no—
750#127—442no—
751#126—228no—
752#126—228no—
753#124—28no—
754#124—228no—
755#124—444no—
756#123—228no—
757#123—228no—
758C22⋊Q8—228no—
759#121—42no—
760#121—228no—
761#121—224no—
762#121—228no—
763#121—228no—
764#121—444no—
765#121—442no—
766#121—442no—
767#120—228no—
768#120—228no—
769#120—228no—
770C4×D4—118no—
771C4×D4—228no—
772C4×D4—224no—
773C4×D4—224no—
774C4×D4—442no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—111no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—112no—
784C2×C4⋊C4—112no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—442no—
788C2×C4⋊C4C22×D1111yescharacteristic
789C2×C4⋊C4C22×D1111yescharacteristic
790C2×C4⋊C4C22×D1111yescharacteristic
791C2×C4⋊C4C22×D1112yes—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—112no—
795C2×C22⋊C4—112no—
796C2×C22⋊C4—111no—
797C2×C22⋊C4—112no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—111no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—112no—
809C2×C22⋊C4—112no—
810C2×C22⋊C4—112no—
811C2×C22⋊C4—112no—
812C2×C22⋊C4—112no—
813C2×C22⋊C4—112no—
814C2×C22⋊C4—112no—
815C2×C22⋊C4—112no—
816C2×C22⋊C4—112no—
817C2×C22⋊C4—228no—
818C2×C22⋊C4—444no—
819C2×C22⋊C4C22×D1112yes—
820C2×C22⋊C4C22×D1111yescharacteristic
821C2×C22⋊C4C22×D1112yes—
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—111no—
830C2×C42—111no—
831C2×C42—111no—
832C2×C42—111no—
833C2×C42—111no—
834C2×C42—111no—
835C2×C42—111no—
836C2×C42—111no—
837C2×C42—111no—
838C2×C42—442no—
839C2×C42—442no—
840C2×C42C22×D1112yes—
841C2×C42C22×D1111yescharacteristic
842C2×C42C22×D1111yescharacteristic
843#95—111no—
844#95—111no—
845#95—111no—
846#95—111no—
847#95—112no—
848#95—112no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95C22×D1111yescharacteristic
853#95C22×D1111yescharacteristic
854#95C22×D1112yes—
855#95C22×D1112yes—
856C2×C11—42no—
857C2×C11—82no—
858C2×C11C2×#53211yescharacteristic
859C2×C11C2×#53811yescharacteristic
860C2×C11#346011yescharacteristic
861C2×C11#349611yescharacteristic
862C2×C11#349811yescharacteristic
863C2×C11#351411yescharacteristic
864C2×C11#351911yescharacteristic
865D11—24no—
866D11—82no—
867D11—82no—
868C24—111no—
869C24—112no—
870C24—112no—
871C24—224no—
872C24—224no—
873C24—224no—
874C24—442no—
875C24—442no—
876C24—442no—
877C24—442no—
878C24C23×D1112yes—
879C24C23×D1111yescharacteristic
880C2×Q8—24no—
881C2×Q8—42no—
882C2×Q8—42no—
883C2×D4—24no—
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—22no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—114no—
890C2×D4—224no—
891C2×D4—224no—
892C2×D4—224no—
893C2×D4—224no—
894C2×D4—224no—
895C2×D4—224no—
896C2×D4—222no—
897C2×D4—222no—
898C2×D4—224no—
899C2×D4—224no—
900C2×D4—224no—
901C2×D4—222no—
902C2×D4—222no—
903C2×D4—222no—
904C2×D4—222no—
905C2×D4—224no—
906C2×D4—222no—
907C2×D4—222no—
908C2×D4—442no—
909C2×D4—442no—
910C2×D4—442no—
911C2×D4—442no—
912C2×D4—4416no—
913C2×D4—442no—
914C2×D4—442no—
915C2×D4—442no—
916C2×D4—442no—
917C2×D4—442no—
918C2×D4—442no—
919C2×D4—442no—
920C2×D4—442no—
921C2×D4—442no—
922C2×D4—442no—
923C22×C4—22no—
924C22×C4—22no—
925C22×C4—22no—
926C22×C4—111no—
927C22×C4—111no—
928C22×C4—111no—
929C22×C4—111no—
930C22×C4—111no—
931C22×C4—111no—
932C22×C4—114no—
933C22×C4—114no—
934C22×C4—114no—
935C22×C4—111no—
936C22×C4—112no—
937C22×C4—112no—
938C22×C4—222no—
939C22×C4—222no—
940C22×C4—224no—
941C22×C4—222no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—224no—
946C22×C4—441no—
947C22×C4—441no—
948C22×C4—441no—
949C22×C4—442no—
950C22×C4—442no—
951C22×C4—442no—
952C22×C4—442no—
953C22×C4—441no—
954C22×C4—441no—
955C22×C4—441no—
956C22×C4C23×D1112yes—
957C22×C4C23×D1111yescharacteristic
958C22×C4C23×D1112yes—
959C22×C4C23×D1112yes—
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—22no—
968C4⋊C4—42no—
969C4⋊C4—114no—
970C4⋊C4—224no—
971C4⋊C4—222no—
972C4⋊C4—222no—
973C4⋊C4—224no—
974C4⋊C4—224no—
975C4⋊C4—224no—
976C4⋊C4—224no—
977C4⋊C4—222no—
978C4⋊C4—222no—
979C4⋊C4—442no—
980C4⋊C4—442no—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—22no—
985C22⋊C4—24no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—114no—
989C22⋊C4—114no—
990C22⋊C4—224no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—224no—
994C22⋊C4—224no—
995C22⋊C4—224no—
996C22⋊C4—224no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—222no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—222no—
1004C22⋊C4—224no—
1005C22⋊C4—224no—
1006C22⋊C4—442no—
1007C22⋊C4—442no—
1008C22⋊C4—442no—
1009C22⋊C4—442no—
1010C22⋊C4—442no—
1011C22⋊C4—442no—
1012C22⋊C4—442no—
1013C22⋊C4D4×D1114yescomplemented
1014C42—24no—
1015C42—22no—
1016C42—22no—
1017C42—114no—
1018C42—222no—
1019C42—222no—
1020C42—222no—
1021C42—222no—
1022C42—222no—
1023C42—441no—
1024C42—441no—
1025C42—441no—
1026C42—441no—
1027C42—441no—
1028C11#3500711yescharacteristic, complemented, Sylow
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—21no—
1034C23—21no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—112no—
1043C23—112no—
1044C23—112no—
1045C23—221no—
1046C23—221no—
1047C23—221no—
1048C23—221no—
1049C23—222no—
1050C23—222no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—222no—
1056C23—222no—
1057C23—222no—
1058C23—222no—
1059C23—222no—
1060C23—222no—
1061C23—222no—
1062C23—222no—
1063C23—448no—
1064C23—448no—
1065C23—448no—
1066C23—884no—
1067C23—884no—
1068C23—884no—
1069C23—884no—
1070C23C2×D4×D1112yes—
1071C23C24×D1111yescharacteristic
1072Q8—84no—
1073D4—44no—
1074D4—84no—
1075D4—228no—
1076D4—448no—
1077D4—448no—
1078D4—444no—
1079D4—444no—
1080D4—884no—
1081D4—884no—
1082D4—884no—
1083D4—884no—
1084D4—884no—
1085D4—884no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—21no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—44no—
1108C2×C4—112no—
1109C2×C4—112no—
1110C2×C4—112no—
1111C2×C4—112no—
1112C2×C4—112no—
1113C2×C4—112no—
1114C2×C4—221no—
1115C2×C4—221no—
1116C2×C4—221no—
1117C2×C4—221no—
1118C2×C4—221no—
1119C2×C4—221no—
1120C2×C4—221no—
1121C2×C4—221no—
1122C2×C4—221no—
1123C2×C4—221no—
1124C2×C4—221no—
1125C2×C4—221no—
1126C2×C4—228no—
1127C2×C4—222no—
1128C2×C4—222no—
1129C2×C4—222no—
1130C2×C4—221no—
1131C2×C4—222no—
1132C2×C4—221no—
1133C2×C4—222no—
1134C2×C4—221no—
1135C2×C4—222no—
1136C2×C4—444no—
1137C2×C4—444no—
1138C2×C4—444no—
1139C2×C4—444no—
1140C2×C4—884no—
1141C2×C4—884no—
1142C2×C4C2×D4×D1112yes—
1143C2×C4C2×D4×D1112yes—
1144C2×C4#6703712yes—
1145C2×C4#41×D1112yes—
1146C2×C4#41×D1112yes—
1147C2×C4#6704212yes—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—41no—
1152C22—41no—
1153C22—41no—
1154C22—41no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—114no—
1163C22—222no—
1164C22—222no—
1165C22—222no—
1166C22—222no—
1167C22—222no—
1168C22—222no—
1169C22—442no—
1170C22—442no—
1171C22—442no—
1172C22—442no—
1173C22—442no—
1174C22—442no—
1175C22—442no—
1176C22—442no—
1177C22—442no—
1178C22—442no—
1179C22—442no—
1180C22—442no—
1181C22—442no—
1182C22—442no—
1183C22—8816no—
1184C22C22×D4×D1111yescharacteristic
1185C22C2×#6703711yescharacteristic
1186C22C2×#41×D1111yescharacteristic
1187C22C2×#41×D1111yescharacteristic
1188C22C2×#6704211yescharacteristic
1189C22D11×H(5,𝔽2)11yescharacteristic
1190C22#1062345711yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—42no—
1195C4—42no—
1196C4—41no—
1197C4—42no—
1198C4—41no—
1199C4—222no—
1200C4—222no—
1201C4—222no—
1202C4—222no—
1203C4—222no—
1204C4—222no—
1205C4—442no—
1206C4—442no—
1207C4—441no—
1208C4#1062320914yescomplemented
1209C2—42no—
1210C2—82no—
1211C2—224no—
1212C2—882no—
1213C2—882no—
1214C2D11×#53211yescharacteristic
1215C2C2×#1062320911yescharacteristic
1216C2#1308203611yescharacteristic
1217C2#1308237411yescharacteristic
1218C2#1308238811yescharacteristic
1219C2#1308257011yescharacteristic
1220C2#1308265111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2491C2
hypercenter#2491D11
hypocenterC11#35007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2491

Complements

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

NH ≅ G/Ntype
1. C2×#10623209C2semidirect
2. #13076980C2semidirect
3. #13076974C2semidirect
4. #13076959C2semidirect
5. #13076948C2semidirect
6. #13074762C2semidirect
7. #13074743C2semidirect
8. #13073687C2semidirect
9. #13073682C2semidirect
10. #13073196C2semidirect
11. #13072745C2semidirect
12. #13072382C2semidirect
13. #13072314C2semidirect
14. #13072252C2semidirect
15. #13072204C2semidirect
16. #13072153C2semidirect
17. #13072058C2semidirect
18. #13071968C2semidirect
19. #13071278C2semidirect
20. C4×#66948C2semidirect
21. D11×#390C2semidirect
22. C4×(C22⋊D11)⋊C4C2semidirect
23. C11×#2491C2semidirect
25. C2×C11×C4⋊Q8C22semidirect
26. C2×C11×#124C22semidirect
28. C2×#67000C22semidirect
29. C2×#67000C22semidirect
32. C2×#66992C22semidirect
33. C2×#66992C22semidirect
36. C2×#66983C22semidirect
38. C22×C4×Dic11C22semidirect
42. C2×#66939C22semidirect
44. C2×#66937C22semidirect
45. C2×#66936C22semidirect
52. C2×#66932C22semidirect
53. C2×#66929C22semidirect
56. C2×C4×D44C22semidirect
58. C11×#394C22semidirect
59. C11×#393C22semidirect
62. C11×#388C22semidirect
63. C11×#380C22semidirect
64. C4×C11×C4⋊C4C22semidirect
65. C4×C11×C22⋊C4C22semidirect
66. #10622842C22semidirect
74. #10622601C22semidirect
75. #10622601C22semidirect
76. #10622601C22semidirect
77. #10622601C22semidirect
79. #10622598C22semidirect
80. #10622598C22semidirect
81. #10622597C22semidirect
82. #10622589C22semidirect
83. #10622586C22semidirect
84. #10622574C22semidirect
87. #10622573C22semidirect
89. #10622572C22semidirect
90. #10622572C22semidirect
91. #10622571C22semidirect
94. #10622570C22semidirect
95. #10622570C22semidirect
96. #10622569C22semidirect
98. #10622564C22semidirect
99. #10622558C22semidirect
100. #10622557C22semidirect
101. C22⋊C4×Dic11C22semidirect
102. C22⋊C4×Dic11C22semidirect
103. #10622553C22semidirect
106. C4×(C2×D11)⋊C4C22semidirect
107. C4×Dic11⋊C4C22semidirect
108. C42×Dic11C22semidirect
109. #10622541C22semidirect
110. #10622289C22semidirect
111. #10622289C22semidirect
112. #10622288C22semidirect
113. #10622285C22semidirect
114. #10622283C22semidirect
115. #10622283C22semidirect
116. #10622283C22semidirect
121. #10622278C22semidirect
122. #10622262C22semidirect
123. #10622262C22semidirect
236. (C22⋊D11)⋊C4D4semidirect
315. C22×Dic11C2×D4semidirect
367. C11×C22⋊C4C2×D4semidirect
407. Dic11⋊C4C2×D4semidirect
418. C4×Dic11C2×D4semidirect
429. #2491D11semidirect
563. C2×C4⋊Q8C2×D11semidirect
570. C2×#124C2×D11semidirect
605. #394C2×D11semidirect
606. #393C2×D11semidirect
638. #388C2×D11semidirect
647. #380C2×D11semidirect
652. C4×C4⋊C4C2×D11semidirect
659. C4×C22⋊C4C2×D11semidirect
712. C4×C11#538semidirect
1013. C22⋊C4D4×D11semidirect
1028. C11#35007semidirect
1208. C4#10623209semidirect

Maximal subgroups

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

subgroupindex
C2×#106232092
#130769802
#130769742
#130769592
#130769482
#130747622
#130747432
#130736872
#130736822
#130731962
#130727452
#130723822
#130723142
#130722522
#130722042
#130721532
#130720582
#130719682
#130712782
C4×#669482
D11×#3902
C4×(C22⋊D11)⋊C42
C11×#24912
#3500711