Finite Group Databasebeta

← #14926735

Subgroups — #14926735

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×#10623091C212yesmaximal, complemented
2#13076984C211yesmaximal, characteristic, complemented
3#13076970C211yesmaximal, characteristic, complemented
4#13076960C211yesmaximal, characteristic, complemented
5#13076949C211yesmaximal, characteristic, complemented
6#13074759C212yesmaximal, complemented
7#13074748C212yesmaximal, complemented
8#13073685C212yesmaximal, complemented
9#13073676C212yesmaximal, complemented
10#13073196C211yesmaximal, characteristic, complemented
11#13072973C211yesmaximal, characteristic, complemented
12#13072744C212yesmaximal, complemented
13#13072375C211yesmaximal, characteristic, complemented
14#13072319C211yesmaximal, characteristic, complemented
15#13072254C211yesmaximal, characteristic, complemented
16#13072198C211yesmaximal, characteristic, complemented
17#13072154C212yesmaximal, complemented
18#13072057C211yesmaximal, characteristic, complemented
19#13071973C211yesmaximal, characteristic, complemented
20#13071270C212yesmaximal, complemented
21C2×#10622552C211yesmaximal, characteristic, complemented
22C42×C22⋊D11C211yesmaximal, characteristic, complemented
23C4×C11×#121C211yesmaximal, characteristic, complemented
24C23×D44C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C4×D4×C11C2212yes—
27C2×C4×D4×C11C2211yescharacteristic, complemented
28C22×C42×C11C2211yescharacteristic
29C2×#66993C2211yescharacteristic
30C2×#66993C2211yescharacteristic
31C2×#66992C2212yes—
32C2×#66991C2211yescharacteristic, complemented
33C2×#66990C2212yes—
34C2×#66990C2212yes—
35C2×#66983C2212yescomplemented
36C2×#66982C2212yescomplemented
37C2×C4×C22⋊D11C2211yescharacteristic
38C2×C4×C22⋊D11C2211yescharacteristic
39C2×C4×C22⋊D11C2211yescharacteristic
40C22×(C2×D11)⋊C4C2212yes—
41C22×(C2×D11)⋊C4C2212yes—
42C22×C4⋊Dic11C2211yescharacteristic
43#10623091—216no—
44C2×#66951C2212yescomplemented
45C2×#66948C2211yescharacteristic
46C2×#66948C2211yescharacteristic
47C2×#66947C2212yescomplemented
48C2×#66941C2211yescharacteristic, complemented
49C2×#66938C2212yescomplemented
50C2×#66938C2212yescomplemented
51C2×#66937C2212yescomplemented
52C2×#66937C2212yescomplemented
53C2×#66935C2212yes—
54C2×#66931C2212yes—
55C2×#66929C2212yescomplemented
56C2×#66928C2212yescomplemented
57C2×C42×D11C2211yescharacteristic, complemented
58C11×#390C2211yescharacteristic, complemented
59C11×#389C2211yescharacteristic, complemented
60C11×#388C2212yescomplemented
61C11×#386C2212yes—
62C11×#380C2211yescharacteristic
63C4×C11×C4⋊C4C2211yescharacteristic, complemented
64C4×C11×C22⋊C4C2212yescomplemented
65#10622834C2211yescharacteristic, complemented
66#10622833C2212yes—
67#10622826C2212yescomplemented
68#10622826C2212yescomplemented
69C4×C22⋊Dic11C2211yescharacteristic
70C4×C22⋊Dic11C2211yescharacteristic
71C4×C22⋊Dic11C2211yescharacteristic
72#10622603C2212yescomplemented
73#10622603C2212yescomplemented
74#10622601C2211yescharacteristic
75#10622601C2211yescharacteristic
76#10622601C2211yescharacteristic
77#10622601C2211yescharacteristic
78#10622600C2211yescharacteristic, complemented
79#10622598C2211yescharacteristic, complemented
80#10622589C2211yescharacteristic, complemented
81#10622586C2211yescharacteristic, complemented
82#10622586C2211yescharacteristic, complemented
83#10622574C2212yescomplemented
84#10622574C2212yescomplemented
85#10622573C2212yes—
86#10622573C2212yes—
87#10622573C2212yescomplemented
88#10622572C2212yescomplemented
89#10622572C2212yescomplemented
90#10622570C2212yescomplemented
91#10622570C2212yescomplemented
92#10622570C2212yescomplemented
93#10622570C2212yescomplemented
94#10622568C2212yes—
95#10622561C2212yescomplemented
96#10622559C2212yes—
97#10622553C2212yescomplemented
98#10622553C2212yescomplemented
99#10622552C2212yes—
100#10622552C2211yescharacteristic
101#10622552C2212yes—
102#10622552C2211yescharacteristic
103#10622552C2211yescharacteristic
104#10622552C2211yescharacteristic
105C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
106C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
107C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
108C4×Dic11⋊C4C2211yescharacteristic, complemented
109C4×Dic11⋊C4C2211yescharacteristic, complemented
110C4×Dic11⋊C4C2211yescharacteristic, complemented
111C42×Dic11C2211yescharacteristic, complemented
112#10622289C2212yescomplemented
113#10622288C2212yescomplemented
114#10622286C2212yescomplemented
115#10622285C2212yes—
116#10622285C2212yescomplemented
117#10622284C2212yes—
118#10622283C2212yescomplemented
119#10622282C2212yescomplemented
120#10622282C2212yescomplemented
121#10622278C2212yescomplemented
122#10622270C2212yescomplemented
123#10622269C2212yescomplemented
124C24×D11C2312yes—
125C22×D4×C11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2312yes—
130C23×C4×C11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2312yes—
136C22×C22⋊D11C2312yes—
137C23×Dic11C2312yes—
138C22×D44—24no—
139C22×D44—42no—
140C22×D44—42no—
141C22×D44C2311yescharacteristic
142C22×D44C2311yescharacteristic
143C22×D44C2312yes—
144C22×D44C2312yes—
145C22×D44C2312yes—
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×Dic22C2312yes—
150C11×#121—24no—
151C4×D4×C11—28no—
152C4×D4×C11—42no—
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2311yescharacteristic
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C42×C11—42no—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2312yes—
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2311yescharacteristic
168C2×C22⋊Dic11C2312yes—
169C2×C22⋊Dic11C2311yescharacteristic
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172C2×C22⋊Dic11C2311yescharacteristic
173C2×C22⋊Dic11C2311yescharacteristic
174#66993—42no—
175#66993—42no—
176#66992—28no—
177#66991—42no—
178#66990—28no—
179#66990—28no—
180#66983—28no—
181#66982—28no—
182C4×C22⋊D11—24no—
183C4×C22⋊D11—24no—
184C4×C22⋊D11D418yescomplemented
185C2×(C2×D11)⋊C4—28no—
186C2×(C2×D11)⋊C4—44no—
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)⋊C4C2312yes—
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)⋊C4C2311yescharacteristic
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2312yes—
205C2×(C2×D11)⋊C4C2312yes—
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2311yescharacteristic
209C2×C4⋊Dic11—42no—
210C2×C4⋊Dic11C2312yes—
211C2×C4⋊Dic11C2311yescharacteristic
212C2×C4⋊Dic11C2311yescharacteristic
213C2×C4⋊Dic11C2312yes—
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2311yescharacteristic
218C2×Dic11⋊C4C2311yescharacteristic
219C2×Dic11⋊C4C2312yes—
220C2×Dic11⋊C4C2312yes—
221C2×Dic11⋊C4C2311yescharacteristic
222C2×C4×Dic11C2311yescharacteristic
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227C2×C4×Dic11C2311yescharacteristic
228C2×C4×Dic11C2311yescharacteristic
229C2×C4×Dic11C2311yescharacteristic
230C2×C4×Dic11C2311yescharacteristic
231#66951—28no—
232#66948—42no—
233#66948—42no—
234#66947—28no—
235#66941—42no—
236#66938—28no—
237#66938—44no—
238#66937—28no—
239#66937—44no—
240#66935—28no—
241#66931—28no—
242#66929—28no—
243#66928—28no—
244C42×D11—42no—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2312yes—
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2312yes—
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2311yescharacteristic
257C11⋊#95C2311yescharacteristic
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×D4×C11—24no—
272C2×D4×C11—24no—
273C2×D4×C11—24no—
274C2×D4×C11—22no—
275C2×D4×C11—22no—
276C2×D4×C11—22no—
277C22×C4×C11—22no—
278C22×C4×C11—22no—
279C22×C4×C11—22no—
280C22×C4×C11—22no—
281C22×C4×C11—24no—
282C22×C4×C11—41no—
283C22×C4×C11—41no—
284C22×C4×C11—41no—
285C22×C4×C11—42no—
286C22×C4×C11—42no—
287C22×C4×C11C2×D414yes—
288C22×C4×C11#4114yes—
289C22×C4×C11C2412yes—
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2412yes—
292C22×C4×C11C2412yes—
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C22×C4×C11C2411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C2×C22⋊D11—24no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—22no—
303C2×C22⋊D11—22no—
304C2×C22⋊D11—24no—
305C2×C22⋊D11—42no—
306C2×C22⋊D11—42no—
307C2×C22⋊D11—42no—
308C2×C22⋊D11—42no—
309C2×C22⋊D11—42no—
310C2×C22⋊D11—42no—
311C2×C22⋊D11—42no—
312C2×C22⋊D11—42no—
313C2×C22⋊D11—42no—
314C2×C22⋊D11—42no—
315C2×C22⋊D11C2×D414yes—
316C22×Dic11—24no—
317C22×Dic11—42no—
318C22×Dic11—42no—
319C22×Dic11C2411yescharacteristic
320C22×Dic11C2411yescharacteristic
321C22×Dic11C2412yes—
322C22×Dic11C2412yes—
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2411yescharacteristic
325C22×Dic11C2411yescharacteristic
326C22×Dic11C2411yescharacteristic
327C22×Dic11C2411yescharacteristic
328C2×D44—24no—
329C2×D44—24no—
330C2×D44—24no—
331C2×D44—22no—
332C2×D44—22no—
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×D44—42no—
342C2×D44—42no—
343C2×D44—416no—
344C2×C4×D11—22no—
345C2×C4×D11—22no—
346C2×C4×D11—22no—
347C2×C4×D11—22no—
348C2×C4×D11—22no—
349C2×C4×D11—41no—
350C2×C4×D11—41no—
351C2×C4×D11—41no—
352C2×C4×D11C2×D414yescomplemented
353C2×Dic22—24no—
354C2×Dic22—42no—
355C2×Dic22—42no—
356C11×C4⋊C4—24no—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—22no—
360C11×C22⋊C4—24no—
361C11×C22⋊C4—24no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—42no—
365C42×C11—24no—
366C42×C11—22no—
367C42×C11—22no—
368C42×C11—41no—
369C42×C11—41no—
370C22⋊Dic11—24no—
371C22⋊Dic11—22no—
372C22⋊Dic11—42no—
373C22⋊Dic11—42no—
374C22⋊Dic11C2×D414yes—
375C22⋊Dic11#4114yes—
376(C2×D11)⋊C4—24no—
377(C2×D11)⋊C4—24no—
378(C2×D11)⋊C4—24no—
379(C2×D11)⋊C4—24no—
380(C2×D11)⋊C4—22no—
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—24no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—22no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—24no—
391(C2×D11)⋊C4—42no—
392(C2×D11)⋊C4—42no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4—42no—
395(C2×D11)⋊C4—42no—
396(C2×D11)⋊C4—42no—
397(C2×D11)⋊C4C2×D414yescomplemented
398C4⋊Dic11—24no—
399C4⋊Dic11—22no—
400C4⋊Dic11—22no—
401C4⋊Dic11—42no—
402Dic11⋊C4—24no—
403Dic11⋊C4—24no—
404Dic11⋊C4—24no—
405Dic11⋊C4—22no—
406Dic11⋊C4—22no—
407Dic11⋊C4—42no—
408Dic11⋊C4—42no—
409Dic11⋊C4C2×D414yescomplemented
410C4×Dic11—22no—
411C4×Dic11—22no—
412C4×Dic11—22no—
413C4×Dic11—22no—
414C4×Dic11—22no—
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#2491—111no—
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×#121D1111yescharacteristic, complemented
440C2×#390—111no—
441C42×D4—111no—
442C23×C11—21no—
443C23×C11—21no—
444C23×C11—21no—
445C23×C11—21no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11C22×D412yes—
454C23×C11C2×#4112yes—
455C23×C11C2×#4112yes—
456C23×C11C2511yescharacteristic
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—21no—
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—22no—
476C22×D11—22no—
477C22×D11—48no—
478C22×D11—48no—
479C22×D11—48no—
480C22×D11—84no—
481C22×D11—84no—
482C22×D11—84no—
483C22×D11—84no—
484C22×D11C22×D412yes—
485D4×C11—48no—
486D4×C11—44no—
487C2×C4×C11—21no—
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—21no—
495C2×C4×C11—28no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—21no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—21no—
505C2×C4×C11—22no—
506C2×C4×C11—21no—
507C2×C4×C11—22no—
508C2×C4×C11—44no—
509C2×C4×C11—44no—
510C2×C4×C11—84no—
511C2×C4×C11C22×D412yes—
512C2×C4×C11C22×D412yes—
513C2×C4×C11C2×#4112yes—
514C2×C4×C11C2×#4112yes—
515C2×C4×C11H(5,𝔽2)12yes—
516C2×C4×C11H(5,𝔽2)12yes—
517C2×C4×C11H(5,𝔽2)12yes—
518C22⋊D11—28no—
519C22⋊D11—84no—
520C22⋊D11—84no—
521C22⋊D11—84no—
522C22⋊D11—84no—
523C22⋊D11—84no—
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—21no—
539C2×Dic11—21no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—21no—
545C2×Dic11—21no—
546C2×Dic11—84no—
547C2×Dic11C22×D412yes—
548C2×Dic11C22×D412yes—
549C2×Dic11C22×D412yes—
550C2×Dic11C2×#4112yes—
551C2×Dic11C2×#4112yes—
552D44—48no—
553D44—44no—
554D44—44no—
555D44—84no—
556D44—84no—
557C4×D11—44no—
558C4×D11—44no—
559C4×D11—44no—
560Dic22—84no—
561C23×D4—111no—
562#538—2216no—
563C2×C4⋊Q8—111no—
564C2×#127—111no—
565C2×#127—111no—
566C2×#126—112no—
567C2×#126—112no—
568C2×#124—112no—
569C2×#124—112no—
570C2×#124—112no—
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×D4C2×D1112yes—
589C2×C4×D4C2×D1111yescharacteristic, complemented
590C22×C4⋊C4—111no—
591C22×C22⋊C4—112no—
592C22×C22⋊C4—112no—
593C22×C42—111no—
594C22×C42C2×D1111yescharacteristic
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#394—112no—
606#393—112no—
607#392—112no—
608#392—112no—
609#392—112no—
610#392—112no—
611#390—111no—
612#390—111no—
613#390—111no—
614#390—111no—
615#390—111no—
616#390—112no—
617#390—112no—
618#390—112no—
619#390—112no—
620#390—111no—
621#390—111no—
622#390—112no—
623#390—111no—
624#390—111no—
625#390—112no—
626#390C2×D1111yescharacteristic, complemented
627#389—111no—
628#389—111no—
629#389—111no—
630#389C2×D1111yescharacteristic, complemented
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#386C2×D1112yes—
644#385—112no—
645#384—111no—
646#380—111no—
647#380C2×D1111yescharacteristic
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—111no—
657C4×C22⋊C4—111no—
658C4×C22⋊C4—111no—
659C4×C22⋊C4C2×D1112yescomplemented
660C43—111no—
661C22×C11—22no—
662C22×C11—22no—
663C22×C11—22no—
664C22×C11—22no—
665C22×C11—22no—
666C22×C11—22no—
667C22×C11—42no—
668C22×C11—42no—
669C22×C11—42no—
670C22×C11—42no—
671C22×C11—42no—
672C22×C11—42no—
673C22×C11—42no—
674C22×C11#53214yes—
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—41no—
686C2×D11—41no—
687C2×D11—41no—
688C2×D11—41no—
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—42no—
703C2×D11—816no—
704C4×C11—22no—
705C4×C11—22no—
706C4×C11—22no—
707C4×C11—22no—
708C4×C11—42no—
709C4×C11—42no—
710C4×C11—42no—
711C4×C11—41no—
712C4×C11#53814yescomplemented
713Dic11—22no—
714Dic11—22no—
715Dic11—22no—
716Dic11—22no—
717Dic11—22no—
718Dic11—41no—
719Dic11—41no—
720Dic11—42no—
721Dic11—42no—
722C25—112no—
723C22×Q8—112no—
724C22×D4—111no—
725C22×D4—112no—
726C22×D4—112no—
727C22×D4—112no—
728C22×D4—112no—
729C22×D4—112no—
730C22×D4—111no—
731C22×D4—111no—
732C22×D4—112no—
733C22×D4—112no—
734C22×D4—112no—
735C22×D4—224no—
736C22×D4—442no—
737C22×D4—442no—
738C22×D4C22×D1112yes—
739C22×D4C22×D1111yescharacteristic
740C23×C4—111no—
741C23×C4—112no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4C22×D1111yescharacteristic
745C23×C4C22×D1111yescharacteristic
746C23×C4C22×D1112yes—
747C23×C4C22×D1111yescharacteristic
748C4⋊Q8—442no—
749#127—442no—
750#127—442no—
751#126—228no—
752#126—228no—
753#124—228no—
754#124—228no—
755#124—444no—
756#123—228no—
757#123—228no—
758C22⋊Q8—228no—
759#121—24no—
760#121—228no—
761#121—228no—
762#121—228no—
763#121—444no—
764#121—442no—
765#121—442no—
766#121—442no—
767#120—228no—
768#120—228no—
769#120—228no—
770C4×D4—28no—
771C4×D4—42no—
772C4×D4—118no—
773C4×D4—224no—
774C4×D4—224no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—111no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—111no—
780C2×C4⋊C4—112no—
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×D1112yes—
789C2×C4⋊C4C22×D1111yescharacteristic
790C2×C4⋊C4C22×D1111yescharacteristic
791C2×C4⋊C4C22×D1111yescharacteristic
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—111no—
796C2×C22⋊C4—112no—
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—111no—
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—112no—
818C2×C22⋊C4—112no—
819C2×C22⋊C4—112no—
820C2×C22⋊C4—228no—
821C2×C22⋊C4—444no—
822C2×C22⋊C4C22×D1112yes—
823C2×C22⋊C4C22×D1112yes—
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1112yes—
826C2×C22⋊C4C22×D1112yes—
827C2×C42—42no—
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—442no—
838C2×C42C22×D1112yes—
839C2×C42C22×D1111yescharacteristic
840C2×C42C22×D1111yescharacteristic
841C2×C42C22×D1111yescharacteristic
842C2×C42C22×D1111yescharacteristic
843#95—111no—
844#95—111no—
845#95—111no—
846#95—111no—
847#95—111no—
848#95—111no—
849#95—112no—
850#95—112no—
851#95—112no—
852#95—112no—
853#95C22×D1112yes—
854#95C22×D1112yes—
855#95C22×D1112yes—
856C2×C11—24no—
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—42no—
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—224no—
881C2×Q8—442no—
882C2×Q8—442no—
883C2×D4—24no—
884C2×D4—24no—
885C2×D4—24no—
886C2×D4—22no—
887C2×D4—22no—
888C2×D4—22no—
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—222no—
901C2×D4—222no—
902C2×D4—222no—
903C2×D4—222no—
904C2×D4—222no—
905C2×D4—222no—
906C2×D4—442no—
907C2×D4—442no—
908C2×D4—4416no—
909C2×D4—442no—
910C2×D4—442no—
911C2×D4—442no—
912C2×D4—442no—
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—22no—
927C22×C4—24no—
928C22×C4—41no—
929C22×C4—41no—
930C22×C4—41no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—111no—
934C22×C4—111no—
935C22×C4—111no—
936C22×C4—111no—
937C22×C4—111no—
938C22×C4—114no—
939C22×C4—111no—
940C22×C4—111no—
941C22×C4—112no—
942C22×C4—112no—
943C22×C4—222no—
944C22×C4—224no—
945C22×C4—222no—
946C22×C4—222no—
947C22×C4—222no—
948C22×C4—222no—
949C22×C4—441no—
950C22×C4—441no—
951C22×C4—441no—
952C22×C4—442no—
953C22×C4—442no—
954C22×C4#433914yes—
955C22×C4D4×D1114yes—
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1112yes—
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—24no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—114no—
970C4⋊C4—222no—
971C4⋊C4—224no—
972C4⋊C4—224no—
973C4⋊C4—224no—
974C4⋊C4—224no—
975C4⋊C4—222no—
976C4⋊C4—222no—
977C4⋊C4—222no—
978C4⋊C4—442no—
979C4⋊C4—442no—
980C4⋊C4—442no—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—42no—
986C22⋊C4—114no—
987C22⋊C4—114no—
988C22⋊C4—114no—
989C22⋊C4—222no—
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—222no—
999C22⋊C4—222no—
1000C22⋊C4—224no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—224no—
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⋊C4—442no—
1014C42—24no—
1015C42—22no—
1016C42—22no—
1017C42—41no—
1018C42—41no—
1019C42—114no—
1020C42—222no—
1021C42—222no—
1022C42—222no—
1023C42—222no—
1024C42—222no—
1025C42—441no—
1026C42—441no—
1027C42—441no—
1028C11#3500711yescharacteristic, complemented, Sylow
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—112no—
1041C23—221no—
1042C23—221no—
1043C23—221no—
1044C23—221no—
1045C23—221no—
1046C23—221no—
1047C23—222no—
1048C23—222no—
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—448no—
1062C23—448no—
1063C23—448no—
1064C23—884no—
1065C23—884no—
1066C23—884no—
1067C23—884no—
1068C23C2×#433912yes—
1069C23C2×D4×D1112yes—
1070C23#41×D1112yes—
1071C23C24×D1111yescharacteristic
1072Q8—884no—
1073D4—48no—
1074D4—44no—
1075D4—228no—
1076D4—448no—
1077D4—444no—
1078D4—444no—
1079D4—884no—
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—21no—
1093C2×C4—21no—
1094C2×C4—28no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—21no—
1103C2×C4—22no—
1104C2×C4—21no—
1105C2×C4—22no—
1106C2×C4—22no—
1107C2×C4—44no—
1108C2×C4—44no—
1109C2×C4—84no—
1110C2×C4—112no—
1111C2×C4—112no—
1112C2×C4—112no—
1113C2×C4—112no—
1114C2×C4—112no—
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—221no—
1127C2×C4—222no—
1128C2×C4—222no—
1129C2×C4—221no—
1130C2×C4—221no—
1131C2×C4—222no—
1132C2×C4—222no—
1133C2×C4—221no—
1134C2×C4—222no—
1135C2×C4—222no—
1136C2×C4—221no—
1137C2×C4—444no—
1138C2×C4—444no—
1139C2×C4—444no—
1140C2×C4—884no—
1141C2×C4C2×#433912yes—
1142C2×C4C2×#433912yes—
1143C2×C4C2×D4×D1112yes—
1144C2×C4C2×D4×D1112yes—
1145C2×C4#6703712yes—
1146C2×C4#6704212yes—
1147C2×C4#6704212yes—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—22no—
1154C22—42no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—222no—
1162C22—222no—
1163C22—222no—
1164C22—441no—
1165C22—441no—
1166C22—441no—
1167C22—441no—
1168C22—442no—
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—8816no—
1183C22#1062307914yes—
1184C22C22×#433911yescharacteristic
1185C22C22×D4×D1111yescharacteristic
1186C22C2×#6703711yescharacteristic
1187C22C2×#41×D1111yescharacteristic
1188C22C2×#6704211yescharacteristic
1189C22C2×#6704211yescharacteristic
1190C22#1062345311yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—42no—
1196C4—41no—
1197C4—42no—
1198C4—42no—
1199C4—222no—
1200C4—222no—
1201C4—222no—
1202C4—222no—
1203C4—222no—
1204C4—442no—
1205C4—442no—
1206C4—441no—
1207C4—441no—
1208C4#1062309114yescomplemented
1209C2—24no—
1210C2—82no—
1211C2—442no—
1212C2—882no—
1213C2—882no—
1214C2C2×#1062307911yescharacteristic
1215C2C2×#1062309111yescharacteristic
1216C2#1308203211yescharacteristic
1217C2#1308237311yescharacteristic
1218C2#1308238911yescharacteristic
1219C2#1308256511yescharacteristic
1220C2#1308263611yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC4×C11×#121C2
hypercenterC4×#121D11
hypocenterC11#35007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10623091C2semidirect
2. #13076984C2semidirect
3. #13076970C2semidirect
4. #13076960C2semidirect
5. #13076949C2semidirect
6. #13074759C2semidirect
7. #13074748C2semidirect
8. #13073685C2semidirect
9. #13073676C2semidirect
10. #13073196C2semidirect
11. #13072973C2semidirect
12. #13072744C2semidirect
13. #13072375C2semidirect
14. #13072319C2semidirect
15. #13072254C2semidirect
16. #13072198C2semidirect
17. #13072154C2semidirect
18. #13072057C2semidirect
19. #13071973C2semidirect
20. #13071270C2semidirect
21. C2×#10622552C2semidirect
22. C42×C22⋊D11C2semidirect
23. C4×C11×#121C2semidirect
27. C2×C4×D4×C11C22semidirect
32. C2×#66991C22semidirect
35. C2×#66983C22semidirect
36. C2×#66982C22semidirect
44. C2×#66951C22semidirect
47. C2×#66947C22semidirect
48. C2×#66941C22semidirect
49. C2×#66938C22semidirect
50. C2×#66938C22semidirect
51. C2×#66937C22semidirect
52. C2×#66937C22semidirect
55. C2×#66929C22semidirect
56. C2×#66928C22semidirect
57. C2×C42×D11C22semidirect
58. C11×#390C22semidirect
59. C11×#389C22semidirect
60. C11×#388C22semidirect
63. C4×C11×C4⋊C4C22semidirect
64. C4×C11×C22⋊C4C22semidirect
65. #10622834C22semidirect
67. #10622826C22semidirect
68. #10622826C22semidirect
72. #10622603C22semidirect
73. #10622603C22semidirect
78. #10622600C22semidirect
79. #10622598C22semidirect
80. #10622589C22semidirect
81. #10622586C22semidirect
82. #10622586C22semidirect
83. #10622574C22semidirect
84. #10622574C22semidirect
87. #10622573C22semidirect
88. #10622572C22semidirect
89. #10622572C22semidirect
90. #10622570C22semidirect
91. #10622570C22semidirect
92. #10622570C22semidirect
93. #10622570C22semidirect
95. #10622561C22semidirect
97. #10622553C22semidirect
98. #10622553C22semidirect
105. C4×(C2×D11)⋊C4C22semidirect
106. C4×(C2×D11)⋊C4C22semidirect
107. C4×(C2×D11)⋊C4C22semidirect
108. C4×Dic11⋊C4C22semidirect
109. C4×Dic11⋊C4C22semidirect
110. C4×Dic11⋊C4C22semidirect
111. C42×Dic11C22semidirect
112. #10622289C22semidirect
113. #10622288C22semidirect
114. #10622286C22semidirect
116. #10622285C22semidirect
118. #10622283C22semidirect
119. #10622282C22semidirect
120. #10622282C22semidirect
121. #10622278C22semidirect
122. #10622270C22semidirect
123. #10622269C22semidirect
184. C4×C22⋊D11D4semidirect
352. C2×C4×D11C2×D4semidirect
397. (C2×D11)⋊C4C2×D4semidirect
409. Dic11⋊C4C2×D4semidirect
418. C4×Dic11C2×D4semidirect
439. C4×#121D11semidirect
589. C2×C4×D4C2×D11semidirect
626. #390C2×D11semidirect
630. #389C2×D11semidirect
638. #388C2×D11semidirect
652. C4×C4⋊C4C2×D11semidirect
659. C4×C22⋊C4C2×D11semidirect
712. C4×C11#538semidirect
1028. C11#35007semidirect
1208. C4#10623091semidirect

Maximal subgroups

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

subgroupindex
C2×#106230912
#130769842
#130769702
#130769602
#130769492
#130747592
#130747482
#130736852
#130736762
#130731962
#130729732
#130727442
#130723752
#130723192
#130722542
#130721982
#130721542
#130720572
#130719732
#130712702
C2×#106225522
C42×C22⋊D112
C4×C11×#1212
#3500711