Finite Group Databasebeta

← #14926730

Subgroups — #14926730

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×#10623235C212yesmaximal, complemented
2#13076984C211yesmaximal, characteristic, complemented
3#13076970C211yesmaximal, characteristic, complemented
4#13076962C211yesmaximal, characteristic, complemented
5#13076946C211yesmaximal, characteristic, complemented
6#13074754C212yesmaximal, complemented
7#13074750C212yesmaximal, complemented
8#13073692C212yesmaximal, complemented
9#13073674C212yesmaximal, complemented
10#13072973C211yesmaximal, characteristic, complemented
11#13072735C212yesmaximal, complemented
12#13072381C211yesmaximal, characteristic, complemented
13#13072321C211yesmaximal, characteristic, complemented
14#13072252C211yesmaximal, characteristic, complemented
15#13072205C211yesmaximal, characteristic, complemented
16#13072147C212yesmaximal, complemented
17#13072054C211yesmaximal, characteristic, complemented
18#13071970C211yesmaximal, characteristic, complemented
19#13071278C212yesmaximal, complemented
20C4×#66948C211yesmaximal, characteristic, complemented
21D11×#390C211yesmaximal, characteristic, complemented
22C4×#66946C211yesmaximal, characteristic, complemented
23C11×#2512C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C2×C11×#126C2212yescomplemented
26C2×#66993C2211yescharacteristic
27C2×#66991C2211yescharacteristic
28#10623235—216no—
29C2×#66951C2212yescomplemented
30C2×#66949C2212yes—
31C2×#66948C2212yes—
32C2×#66948C2211yescharacteristic
33C2×#66948C2211yescharacteristic
34C2×#66948C2212yescomplemented
35C2×#66948C2212yescomplemented
36C2×#66948C2211yescharacteristic, complemented
37C2×#66947C2212yescomplemented
38C2×#66946C2211yescharacteristic
39C2×#66946C2211yescharacteristic
40C2×C4⋊C4×D11C2211yescharacteristic
41C2×#66941C2211yescharacteristic, complemented
42C2×#66938C2212yescomplemented
43C2×#66938C2212yescomplemented
44C2×#66937C2212yescomplemented
45C2×#66936C2212yescomplemented
46C2×#66935C2212yes—
47C2×#66935C2212yes—
48C2×#66935C2212yes—
49C2×C22⋊C4×D11C2212yes—
50C2×C22⋊C4×D11C2212yes—
51C2×#66928C2212yescomplemented
52C2×#66927C2211yescharacteristic
53C2×C4×D44C2212yes—
54C2×C4×D44C2211yescharacteristic
55C2×C4×D44C2211yescharacteristic, complemented
56C2×C42×D11C2211yescharacteristic
57C2×C42×D11C2211yescharacteristic, complemented
58C11×#397C2212yescomplemented
59C11×#396C2212yescomplemented
60C11×#390C2211yescharacteristic
61C11×#390C2211yescharacteristic
62C11×#390C2211yescharacteristic
63C11×#389C2211yescharacteristic, complemented
64C11×#388C2212yescomplemented
65C11×#384C2211yescharacteristic, complemented
66C4×C11×C4⋊C4C2211yescharacteristic, complemented
67C4×C11×C4⋊C4C2211yescharacteristic, complemented
68#10622834C2211yescharacteristic
69#10622607C2212yescomplemented
70#10622604C2212yescomplemented
71#10622603C2212yescomplemented
72#10622602C2212yes—
73#10622601C2211yescharacteristic
74#10622601C2211yescharacteristic
75#10622601C2212yescomplemented
76#10622601C2211yescharacteristic, complemented
77#10622601C2212yescomplemented
78#10622600C2211yescharacteristic
79#10622600C2211yescharacteristic, complemented
80#10622598C2211yescharacteristic, complemented
81#10622593C2212yescomplemented
82#10622592C2212yescomplemented
83C4⋊C4×Dic11C2211yescharacteristic, complemented
84C4⋊C4×Dic11C2211yescharacteristic, complemented
85#10622586C2211yescharacteristic, complemented
86#10622574C2212yes—
87#10622573C2212yes—
88#10622573C2212yes—
89#10622573C2212yes—
90#10622573C2212yescomplemented
91#10622572C2212yescomplemented
92#10622570C2212yes—
93#10622570C2212yes—
94#10622570C2212yescomplemented
95#10622570C2212yescomplemented
96#10622569C2212yescomplemented
97#10622569C2212yescomplemented
98#10622568C2212yes—
99#10622564C2212yescomplemented
100#10622558C2212yescomplemented
101#10622553C2212yescomplemented
102#10622552C2211yescharacteristic
103#10622552C2211yescharacteristic
104#10622552C2211yescharacteristic, complemented
105C4×(C2×D11)⋊C4C2211yescharacteristic
106C4×(C2×D11)⋊C4C2212yescomplemented
107C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
108C42×Dic11C2211yescharacteristic, complemented
109#10622541C2211yescharacteristic, complemented
110#10622286C2212yescomplemented
111#10622285C2212yescomplemented
112#10622285C2212yescomplemented
113#10622285C2212yescomplemented
114#10622283C2212yescomplemented
115#10622283C2212yescomplemented
116#10622282C2212yescomplemented
117#10622279C2211yescharacteristic
118#10622279C2211yescharacteristic
119#10622279C2211yescharacteristic, complemented
120#10622279C2211yescharacteristic, complemented
121#10622278C2212yes—
122#10622278C2212yes—
123#10622278C2212yescomplemented
124C24×D11C2312yes—
125C22×D4×C11C2311yescharacteristic
126C22×C22⋊D11C2312yes—
127C22×C22⋊D11C2312yes—
128C22×C22⋊D11C2312yes—
129C22×C22⋊D11C2312yes—
130C2×D4×D11—24no—
131C2×D4×D11—42no—
132C2×D4×D11—42no—
133C22×D44C2312yes—
134C22×D44C2311yescharacteristic
135C22×D44C2311yescharacteristic
136C22×D44C2311yescharacteristic
137C22×D44C2312yes—
138C22×D44C2312yes—
139C22×D44C2312yes—
140C22×D44C2312yes—
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2312yes—
146C22×C4×D11C2312yes—
147C22×C4×D11C2311yescharacteristic
148C22×C4×D11C2311yescharacteristic
149C22×Dic22C2312yes—
150C11×#126—28no—
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2311yescharacteristic
153C2×C11×C4⋊C4C2311yescharacteristic
154C2×C11×C4⋊C4C2312yes—
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C4⋊C4C2312yes—
158C2×C11×C4⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2312yes—
160C2×C11×C22⋊C4C2312yes—
161C2×C11×C22⋊C4C2312yes—
162C2×C11×C22⋊C4C2312yes—
163C2×C11×C22⋊C4C2312yes—
164C2×C11×C22⋊C4C2312yes—
165C2×C42×C11C2311yescharacteristic
166C2×C42×C11C2311yescharacteristic
167C2×C42×C11C2312yes—
168C2×C42×C11C2311yescharacteristic
169C2×C22⋊Dic11C2312yes—
170C2×C22⋊Dic11C2312yes—
171C2×C22⋊Dic11C2312yes—
172#66993—42no—
173#66991—42no—
174C2×(C2×D11)⋊C4C2312yes—
175C2×(C2×D11)⋊C4C2312yes—
176C2×(C2×D11)⋊C4C2311yescharacteristic
177C2×(C2×D11)⋊C4C2311yescharacteristic
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×(C2×D11)⋊C4C2312yes—
183C2×(C2×D11)⋊C4C2312yes—
184C2×(C2×D11)⋊C4C2312yes—
185C2×(C2×D11)⋊C4C2312yes—
186C2×(C2×D11)⋊C4C2312yes—
187C2×(C2×D11)⋊C4C2311yescharacteristic
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)⋊C4C2311yescharacteristic
196C2×(C2×D11)⋊C4C2311yescharacteristic
197C2×(C2×D11)⋊C4C2311yescharacteristic
198C2×C4⋊Dic11C2312yes—
199C2×C4⋊Dic11C2311yescharacteristic
200C2×C4⋊Dic11C2311yescharacteristic
201C2×C4⋊Dic11C2311yescharacteristic
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×Dic11⋊C4C2312yes—
205C2×Dic11⋊C4C2312yes—
206C2×C4×Dic11C2311yescharacteristic
207C2×C4×Dic11C2311yescharacteristic
208C2×C4×Dic11C2311yescharacteristic
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216#66951—28no—
217#66949—28no—
218#66948—28no—
219#66948—28no—
220#66948—24no—
221#66948—44no—
222#66948—42no—
223#66948—42no—
224#66947—28no—
225#66946—24no—
226#66946D418yescomplemented
227C4⋊C4×D11—42no—
228#66941—42no—
229#66938—28no—
230#66938—44no—
231#66937—28no—
232#66936—28no—
233#66935—28no—
234#66935—28no—
235#66935—28no—
236C22⋊C4×D11—28no—
237C22⋊C4×D11—44no—
238#66928—28no—
239#66927—42no—
240C4×D44—28no—
241C4×D44—24no—
242C4×D44—42no—
243C42×D11—42no—
244C42×D11—42no—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2311yescharacteristic
248C11×#95C2311yescharacteristic
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2311yescharacteristic
255C11⋊#95C2311yescharacteristic
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258#35007—111nomaximal, Sylow
259C24×C11C2412yes—
260C23×D11—24no—
261C23×D11—24no—
262C23×D11—24no—
263C23×D11—42no—
264C23×D11—42no—
265C23×D11—42no—
266C23×D11—42no—
267C23×D11C2412yes—
268C23×D11C2412yes—
269C23×D11C2411yescharacteristic
270C23×D11C2411yescharacteristic
271C2×D4×C11—22no—
272C2×D4×C11—22no—
273C2×D4×C11—22no—
274C22×C4×C11C2412yes—
275C22×C4×C11C2411yescharacteristic
276C22×C4×C11C2412yes—
277C22×C4×C11C2412yes—
278C22×C4×C11C2411yescharacteristic
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2411yescharacteristic
282C22×C4×C11C2411yescharacteristic
283C22×C4×C11C2411yescharacteristic
284C2×C22⋊D11—24no—
285C2×C22⋊D11—24no—
286C2×C22⋊D11—24no—
287C2×C22⋊D11—24no—
288C2×C22⋊D11—42no—
289C2×C22⋊D11—42no—
290C2×C22⋊D11—42no—
291C2×C22⋊D11—42no—
292C2×C22⋊D11—42no—
293C2×C22⋊D11—42no—
294C2×C22⋊D11—42no—
295C2×C22⋊D11—42no—
296C22×Dic11C2411yescharacteristic
297C22×Dic11C2412yes—
298C22×Dic11C2412yes—
299C22×Dic11C2411yescharacteristic
300C22×Dic11C2411yescharacteristic
301C22×Dic11C2411yescharacteristic
302C22×Dic11C2411yescharacteristic
303C22×Dic11C2411yescharacteristic
304D4×D11—416no—
305C2×D44—24no—
306C2×D44—24no—
307C2×D44—24no—
308C2×D44—22no—
309C2×D44—22no—
310C2×D44—24no—
311C2×D44—24no—
312C2×D44—24no—
313C2×D44—22no—
314C2×D44—22no—
315C2×D44—24no—
316C2×D44—22no—
317C2×D44—22no—
318C2×D44—22no—
319C2×D44—22no—
320C2×D44—42no—
321C2×D44—42no—
322C2×D44—42no—
323C2×D44—42no—
324C2×D44—42no—
325C2×D44—42no—
326C2×D44—42no—
327C2×D44—42no—
328C2×D44C2×D414yes—
329C2×C4×D11—22no—
330C2×C4×D11—22no—
331C2×C4×D11—24no—
332C2×C4×D11—22no—
333C2×C4×D11—24no—
334C2×C4×D11—22no—
335C2×C4×D11—22no—
336C2×C4×D11—22no—
337C2×C4×D11—22no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—41no—
341C2×C4×D11—41no—
342C2×C4×D11—41no—
343C2×C4×D11—41no—
344C2×C4×D11—41no—
345C2×C4×D11—41no—
346C2×C4×D11—42no—
347C2×C4×D11—42no—
348C2×C4×D11—42no—
349C2×C4×D11—42no—
350C2×C4×D11C2×D414yes—
351C2×C4×D11C2×D414yescomplemented
352C2×C4×D11#4114yes—
353C2×Dic22—24no—
354C2×Dic22—42no—
355C2×Dic22—42no—
356C11×C4⋊C4—24no—
357C11×C4⋊C4—24no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—22no—
360C11×C4⋊C4—22no—
361C11×C4⋊C4—22no—
362C11×C4⋊C4—42no—
363C11×C4⋊C4C2×D414yescomplemented
364C11×C22⋊C4—24no—
365C11×C22⋊C4—24no—
366C11×C22⋊C4—24no—
367C11×C22⋊C4—24no—
368C11×C22⋊C4—42no—
369C11×C22⋊C4—42no—
370C42×C11—24no—
371C42×C11—22no—
372C42×C11—22no—
373C42×C11—22no—
374C22⋊Dic11—24no—
375C22⋊Dic11—24no—
376C22⋊Dic11—42no—
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—22no—
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—24no—
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)⋊C4—42no—
398(C2×D11)⋊C4C2×D414yes—
399(C2×D11)⋊C4C2×D414yescomplemented
400(C2×D11)⋊C4#4114yes—
401C4⋊Dic11—24no—
402C4⋊Dic11—22no—
403C4⋊Dic11—22no—
404C4⋊Dic11—22no—
405Dic11⋊C4—24no—
406Dic11⋊C4—24no—
407Dic11⋊C4—42no—
408Dic11⋊C4—42no—
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#2512D1111yescharacteristic, complemented
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×#121—111no—
440C2×#390—111no—
441C42×D4—111no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—22no—
447C23×C11—22no—
448C23×C11—22no—
449C23×C11C2511yescharacteristic
450C22×D11—21no—
451C22×D11—21no—
452C22×D11—21no—
453C22×D11—21no—
454C22×D11—21no—
455C22×D11—21no—
456C22×D11—21no—
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—22no—
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—48no—
475C22×D11—48no—
476C22×D11—48no—
477C22×D11—84no—
478C22×D11—84no—
479C22×D11—84no—
480C22×D11—84no—
481C22×D11C22×D412yes—
482C22×D11C22×D412yes—
483C22×D11C2×#4112yes—
484C22×D11C2×#4112yes—
485D4×C11—44no—
486C2×C4×C11—21no—
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—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—21no—
498C2×C4×C11—22no—
499C2×C4×C11—21no—
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—22no—
507C2×C4×C11—21no—
508C2×C4×C11—21no—
509C2×C4×C11C22×D412yes—
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—48no—
517C22⋊D11—84no—
518C22⋊D11—84no—
519C22⋊D11—84no—
520C2×Dic11—21no—
521C2×Dic11—21no—
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—22no—
531C2×Dic11—22no—
532C2×Dic11—21no—
533C2×Dic11—21no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—21no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11C22×D412yes—
540C2×Dic11C22×D412yes—
541C2×Dic11C2×#4112yes—
542C2×Dic11C2×#4112yes—
543C2×Dic11H(5,𝔽2)12yes—
544D44—28no—
545D44—48no—
546D44—44no—
547D44—44no—
548D44—84no—
549D44—84no—
550D44—84no—
551D44—84no—
552C4×D11—28no—
553C4×D11—44no—
554C4×D11—44no—
555C4×D11—44no—
556C4×D11—44no—
557C4×D11—44no—
558C4×D11—84no—
559C4×D11—84no—
560Dic22—84no—
561C23×D4—111no—
562#538—2216no—
563C2×C4⋊Q8—111no—
564C2×#127—111no—
565C2×#127—111no—
566C2×#126—112no—
567C2×#126C2×D1112yescomplemented
568C2×#124—112no—
569C2×#124—112no—
570C2×#124—112no—
571C2×#123—112no—
572C2×#123—112no—
573C2×C22⋊Q8—112no—
574C2×#121—111no—
575C2×#121—112no—
576C2×#121—112no—
577C2×#121—111no—
578C2×#121—111no—
579C2×#121—111no—
580C2×#121—112no—
581C2×#121—112no—
582C2×#120—112no—
583C2×#120—112no—
584C2×#120—112no—
585C2×C4×D4—111no—
586C2×C4×D4—111no—
587C2×C4×D4—112no—
588C2×C4×D4—111no—
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#397C2×D1112yescomplemented
597#396—112no—
598#396C2×D1112yescomplemented
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—112no—
613#390—111no—
614#390—111no—
615#390—112no—
616#390—111no—
617#390—112no—
618#390—112no—
619#390—112no—
620#390—112no—
621#390—111no—
622#390—111no—
623#390—111no—
624#390C2×D1111yescharacteristic
625#390C2×D1111yescharacteristic
626#390C2×D1111yescharacteristic
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#386—112no—
644#385—112no—
645#384C2×D1111yescharacteristic, complemented
646#380—111no—
647#380—111no—
648#379—112no—
649C4×C4⋊C4—111no—
650C4×C4⋊C4—111no—
651C4×C4⋊C4C2×D1111yescharacteristic, complemented
652C4×C4⋊C4C2×D1111yescharacteristic, complemented
653C4×C22⋊C4—111no—
654C4×C22⋊C4—111no—
655C4×C22⋊C4—112no—
656C4×C22⋊C4—111no—
657C4×C22⋊C4—111no—
658C4×C22⋊C4—111no—
659C4×C22⋊C4—111no—
660C43—111no—
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11—42no—
668C22×C11C23×D411yescharacteristic
669C22×C11C22×#4111yescharacteristic
670C22×C11C22×#4111yescharacteristic
671C22×C11C2×H(5,𝔽2)11yescharacteristic
672C22×C11C2×H(5,𝔽2)11yescharacteristic
673C22×C11C2×H(5,𝔽2)11yescharacteristic
674C22×C11#58511yescharacteristic
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—22no—
679C2×D11—22no—
680C2×D11—22no—
681C2×D11—22no—
682C2×D11—22no—
683C2×D11—22no—
684C2×D11—41no—
685C2×D11—41no—
686C2×D11—41no—
687C2×D11—41no—
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—22no—
708C4×C11—42no—
709C4×C11—41no—
710C4×C11—42no—
711C4×C11—42no—
712C4×C11—41no—
713C4×C11#53814yescomplemented
714Dic11—22no—
715Dic11—22no—
716Dic11—22no—
717Dic11—22no—
718Dic11—22no—
719Dic11—41no—
720Dic11—42no—
721Dic11—42no—
722C25—112no—
723C22×Q8—112no—
724C22×D4—112no—
725C22×D4—112no—
726C22×D4—112no—
727C22×D4—112no—
728C22×D4—111no—
729C22×D4—112no—
730C22×D4—111no—
731C22×D4—111no—
732C22×D4—112no—
733C22×D4—112no—
734C22×D4—112no—
735C22×D4—112no—
736C22×D4—224no—
737C22×D4—442no—
738C22×D4—442no—
739C22×D4C22×D1111yescharacteristic
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—111no—
744C23×C4—111no—
745C23×C4—111no—
746C23×C4—112no—
747C23×C4—112no—
748C4⋊Q8—442no—
749#127—442no—
750#127—442no—
751#126—28no—
752#126—228no—
753#124—228no—
754#124—228no—
755#124—444no—
756#123—228no—
757#123—228no—
758C22⋊Q8—228no—
759#121—228no—
760#121—228no—
761#121—224no—
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—118no—
771C4×D4—228no—
772C4×D4—224no—
773C4×D4—224no—
774C4×D4—442no—
775C2×C4⋊C4—111no—
776C2×C4⋊C4—111no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—111no—
779C2×C4⋊C4—112no—
780C2×C4⋊C4—112no—
781C2×C4⋊C4—112no—
782C2×C4⋊C4—112no—
783C2×C4⋊C4—442no—
784C2×C4⋊C4C22×D1111yescharacteristic
785C2×C4⋊C4C22×D1111yescharacteristic
786C2×C4⋊C4C22×D1112yes—
787C2×C4⋊C4C22×D1112yes—
788C2×C4⋊C4C22×D1111yescharacteristic
789C2×C4⋊C4C22×D1111yescharacteristic
790C2×C4⋊C4C22×D1112yes—
791C2×C4⋊C4C22×D1111yescharacteristic
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—112no—
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—111no—
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—228no—
820C2×C22⋊C4—444no—
821C2×C22⋊C4C22×D1112yes—
822C2×C22⋊C4C22×D1112yes—
823C2×C22⋊C4C22×D1112yes—
824C2×C22⋊C4C22×D1112yes—
825C2×C22⋊C4C22×D1112yes—
826C2×C22⋊C4C22×D1112yes—
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—442no—
838C2×C42—442no—
839C2×C42C22×D1112yes—
840C2×C42C22×D1111yescharacteristic
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—82no—
857C2×C11C2×#53211yescharacteristic
858C2×C11C2×#53811yescharacteristic
859C2×C11#346011yescharacteristic
860C2×C11#349611yescharacteristic
861C2×C11#349811yescharacteristic
862C2×C11#351411yescharacteristic
863C2×C11#351911yescharacteristic
864D11—24no—
865D11—42no—
866D11—82no—
867D11—82no—
868C24—111no—
869C24—111no—
870C24—112no—
871C24—112no—
872C24—224no—
873C24—224no—
874C24—224no—
875C24—442no—
876C24—442no—
877C24—442no—
878C24—442no—
879C24C23×D1112yes—
880C2×Q8—224no—
881C2×Q8—442no—
882C2×Q8—442no—
883C2×D4—22no—
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—114no—
887C2×D4—222no—
888C2×D4—222no—
889C2×D4—224no—
890C2×D4—224no—
891C2×D4—224no—
892C2×D4—224no—
893C2×D4—224no—
894C2×D4—224no—
895C2×D4—224no—
896C2×D4—224no—
897C2×D4—224no—
898C2×D4—224no—
899C2×D4—222no—
900C2×D4—222no—
901C2×D4—224no—
902C2×D4—222no—
903C2×D4—222no—
904C2×D4—222no—
905C2×D4—222no—
906C2×D4—442no—
907C2×D4—442no—
908C2×D4—442no—
909C2×D4—442no—
910C2×D4—442no—
911C2×D4—442no—
912C2×D4—442no—
913C2×D4—442no—
914C2×D4—4416no—
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—111no—
924C22×C4—111no—
925C22×C4—111no—
926C22×C4—111no—
927C22×C4—111no—
928C22×C4—114no—
929C22×C4—114no—
930C22×C4—114no—
931C22×C4—111no—
932C22×C4—112no—
933C22×C4—112no—
934C22×C4—222no—
935C22×C4—222no—
936C22×C4—222no—
937C22×C4—224no—
938C22×C4—222no—
939C22×C4—222no—
940C22×C4—222no—
941C22×C4—222no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—224no—
945C22×C4—441no—
946C22×C4—441no—
947C22×C4—441no—
948C22×C4—441no—
949C22×C4—441no—
950C22×C4—441no—
951C22×C4—442no—
952C22×C4—442no—
953C22×C4—442no—
954C22×C4—442no—
955C22×C4C23×D1112yes—
956C22×C4C23×D1111yescharacteristic
957C22×C4C23×D1112yes—
958C22×C4C23×D1112yes—
959C22×C4C23×D1111yescharacteristic
960C22×C4C23×D1111yescharacteristic
961C22×C4C23×D1111yescharacteristic
962C22×C4C23×D1111yescharacteristic
963C22×C4C23×D1111yescharacteristic
964C22×C4C23×D1111yescharacteristic
965C4⋊C4—24no—
966C4⋊C4—24no—
967C4⋊C4—22no—
968C4⋊C4—22no—
969C4⋊C4—22no—
970C4⋊C4—22no—
971C4⋊C4—42no—
972C4⋊C4—224no—
973C4⋊C4—222no—
974C4⋊C4—224no—
975C4⋊C4—224no—
976C4⋊C4—222no—
977C4⋊C4—222no—
978C4⋊C4—442no—
979C4⋊C4—442no—
980C4⋊C4D4×D1114yescomplemented
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—114no—
988C22⋊C4—114no—
989C22⋊C4—114no—
990C22⋊C4—224no—
991C22⋊C4—224no—
992C22⋊C4—224no—
993C22⋊C4—222no—
994C22⋊C4—222no—
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—224no—
1004C22⋊C4—224no—
1005C22⋊C4—224no—
1006C22⋊C4—224no—
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—22no—
1018C42—114no—
1019C42—222no—
1020C42—222no—
1021C42—222no—
1022C42—222no—
1023C42—441no—
1024C42—441no—
1025C42—441no—
1026C42—441no—
1027C42—441no—
1028C11#3500711yescharacteristic, complemented, Sylow
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—112no—
1037C23—112no—
1038C23—112no—
1039C23—112no—
1040C23—221no—
1041C23—221no—
1042C23—221no—
1043C23—221no—
1044C23—221no—
1045C23—221no—
1046C23—221no—
1047C23—221no—
1048C23—221no—
1049C23—221no—
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—222no—
1064C23—448no—
1065C23—448no—
1066C23—448no—
1067C23—884no—
1068C23—884no—
1069C23—884no—
1070C23—884no—
1071C23C24×D1111yescharacteristic
1072Q8—884no—
1073D4—44no—
1074D4—228no—
1075D4—448no—
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—22no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—21no—
1098C2×C4—22no—
1099C2×C4—21no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—22no—
1103C2×C4—22no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—22no—
1107C2×C4—22no—
1108C2×C4—21no—
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—228no—
1125C2×C4—222no—
1126C2×C4—222no—
1127C2×C4—221no—
1128C2×C4—221no—
1129C2×C4—221no—
1130C2×C4—222no—
1131C2×C4—222no—
1132C2×C4—222no—
1133C2×C4—222no—
1134C2×C4—444no—
1135C2×C4—444no—
1136C2×C4—444no—
1137C2×C4—444no—
1138C2×C4—444no—
1139C2×C4—884no—
1140C2×C4—884no—
1141C2×C4C2×D4×D1112yes—
1142C2×C4C2×D4×D1112yes—
1143C2×C4C2×D4×D1112yes—
1144C2×C4#41×D1112yes—
1145C2×C4#41×D1112yes—
1146C2×C4#6704212yes—
1147C2×C4#6704212yes—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
1155C22—114no—
1156C22—222no—
1157C22—222no—
1158C22—222no—
1159C22—222no—
1160C22—222no—
1161C22—222no—
1162C22—222no—
1163C22—222no—
1164C22—222no—
1165C22—441no—
1166C22—441no—
1167C22—441no—
1168C22—441no—
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×#41×D1111yescharacteristic
1186C22C2×#41×D1111yescharacteristic
1187C22C2×#6704211yescharacteristic
1188C22C2×#6704211yescharacteristic
1189C22D11×H(5,𝔽2)11yescharacteristic
1190C22#1062345711yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—41no—
1196C4—42no—
1197C4—42no—
1198C4—42no—
1199C4—41no—
1200C4—222no—
1201C4—222no—
1202C4—222no—
1203C4—222no—
1204C4—222no—
1205C4—442no—
1206C4—442no—
1207C4—441no—
1208C4#1062323514yescomplemented
1209C2—82no—
1210C2—224no—
1211C2—442no—
1212C2—882no—
1213C2—882no—
1214C2D11×#53211yescharacteristic
1215C2C2×#1062323511yescharacteristic
1216C2#1308203611yescharacteristic
1217C2#1308237411yescharacteristic
1218C2#1308239311yescharacteristic
1219C2#1308258011yescharacteristic
1220C2#1308264111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2512C2
hypercenter#2512D11
hypocenterC11#35007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2512

Complements

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

NH ≅ G/Ntype
1. C2×#10623235C2semidirect
2. #13076984C2semidirect
3. #13076970C2semidirect
4. #13076962C2semidirect
5. #13076946C2semidirect
6. #13074754C2semidirect
7. #13074750C2semidirect
8. #13073692C2semidirect
9. #13073674C2semidirect
10. #13072973C2semidirect
11. #13072735C2semidirect
12. #13072381C2semidirect
13. #13072321C2semidirect
14. #13072252C2semidirect
15. #13072205C2semidirect
16. #13072147C2semidirect
17. #13072054C2semidirect
18. #13071970C2semidirect
19. #13071278C2semidirect
20. C4×#66948C2semidirect
21. D11×#390C2semidirect
22. C4×#66946C2semidirect
23. C11×#2512C2semidirect
25. C2×C11×#126C22semidirect
29. C2×#66951C22semidirect
34. C2×#66948C22semidirect
35. C2×#66948C22semidirect
36. C2×#66948C22semidirect
37. C2×#66947C22semidirect
41. C2×#66941C22semidirect
42. C2×#66938C22semidirect
43. C2×#66938C22semidirect
44. C2×#66937C22semidirect
45. C2×#66936C22semidirect
51. C2×#66928C22semidirect
55. C2×C4×D44C22semidirect
57. C2×C42×D11C22semidirect
58. C11×#397C22semidirect
59. C11×#396C22semidirect
63. C11×#389C22semidirect
64. C11×#388C22semidirect
65. C11×#384C22semidirect
66. C4×C11×C4⋊C4C22semidirect
67. C4×C11×C4⋊C4C22semidirect
69. #10622607C22semidirect
70. #10622604C22semidirect
71. #10622603C22semidirect
75. #10622601C22semidirect
76. #10622601C22semidirect
77. #10622601C22semidirect
79. #10622600C22semidirect
80. #10622598C22semidirect
81. #10622593C22semidirect
82. #10622592C22semidirect
83. C4⋊C4×Dic11C22semidirect
84. C4⋊C4×Dic11C22semidirect
85. #10622586C22semidirect
90. #10622573C22semidirect
91. #10622572C22semidirect
94. #10622570C22semidirect
95. #10622570C22semidirect
96. #10622569C22semidirect
97. #10622569C22semidirect
99. #10622564C22semidirect
100. #10622558C22semidirect
101. #10622553C22semidirect
104. #10622552C22semidirect
106. C4×(C2×D11)⋊C4C22semidirect
107. C4×(C2×D11)⋊C4C22semidirect
108. C42×Dic11C22semidirect
109. #10622541C22semidirect
110. #10622286C22semidirect
111. #10622285C22semidirect
112. #10622285C22semidirect
113. #10622285C22semidirect
114. #10622283C22semidirect
115. #10622283C22semidirect
116. #10622282C22semidirect
119. #10622279C22semidirect
120. #10622279C22semidirect
123. #10622278C22semidirect
226. #66946D4semidirect
351. C2×C4×D11C2×D4semidirect
363. C11×C4⋊C4C2×D4semidirect
399. (C2×D11)⋊C4C2×D4semidirect
418. C4×Dic11C2×D4semidirect
428. #2512D11semidirect
567. C2×#126C2×D11semidirect
596. #397C2×D11semidirect
598. #396C2×D11semidirect
630. #389C2×D11semidirect
638. #388C2×D11semidirect
645. #384C2×D11semidirect
651. C4×C4⋊C4C2×D11semidirect
652. C4×C4⋊C4C2×D11semidirect
713. C4×C11#538semidirect
980. C4⋊C4D4×D11semidirect
1028. C11#35007semidirect
1208. C4#10623235semidirect

Maximal subgroups

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

subgroupindex
C2×#106232352
#130769842
#130769702
#130769622
#130769462
#130747542
#130747502
#130736922
#130736742
#130729732
#130727352
#130723812
#130723212
#130722522
#130722052
#130721472
#130720542
#130719702
#130712782
C4×#669482
D11×#3902
C4×#669462
C11×#25122
#3500711