Finite Group Databasebeta

← #14926729

Subgroups — #14926729

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#13076983C211yesmaximal, characteristic, complemented
3#13076960C211yesmaximal, characteristic, complemented
4#13076946C211yesmaximal, characteristic, complemented
5#13074755C212yesmaximal, complemented
6#13074746C212yesmaximal, complemented
7#13073687C212yesmaximal, complemented
8#13073673C212yesmaximal, complemented
9#13073200C211yesmaximal, characteristic, complemented
10#13072982C211yesmaximal, characteristic, complemented
11#13072738C212yesmaximal, complemented
12#13072379C211yesmaximal, characteristic, complemented
13#13072314C211yesmaximal, characteristic, complemented
14#13072250C211yesmaximal, characteristic, complemented
15#13072207C211yesmaximal, characteristic, complemented
16#13072159C212yesmaximal, complemented
17#13072059C211yesmaximal, characteristic, complemented
18#13071970C211yesmaximal, characteristic, complemented
19#13071275C212yesmaximal, complemented
20#13071132C211yesmaximal, characteristic, complemented
21D11×#390C211yesmaximal, characteristic, complemented
22C42×D44C211yesmaximal, characteristic, complemented
23C11×#2858C211yesmaximal, characteristic, complemented
24C22×D4×D11C2211yescharacteristic
25C2×C11×C4⋊Q8C2211yescharacteristic, complemented
26C2×C11×#127C2211yescharacteristic
27C2×C11×#124C2212yescomplemented
28C2×C11×#124C2212yescomplemented
29C2×#67000C2212yescomplemented
30C2×#66999C2212yes—
31C2×#66993C2211yescharacteristic
32C2×#66992C2212yescomplemented
33C2×#66991C2211yescharacteristic
34C2×#66991C2211yescharacteristic
35C2×#66991C2211yescharacteristic, complemented
36C2×#66990C2212yes—
37C2×#66990C2212yes—
38C2×D4×Dic11C2211yescharacteristic, complemented
39#10623209—216no—
40C2×#66948C2211yescharacteristic
41C2×C4⋊C4×D11C2211yescharacteristic
42C2×#66939C2212yescomplemented
43C2×#66937C2212yes—
44C2×#66937C2212yescomplemented
45C2×#66937C2212yescomplemented
46C2×#66936C2212yescomplemented
47C2×#66935C2212yes—
48C2×(C22⋊D11)⋊C4C2212yes—
49C2×C22⋊C4×D11C2212yes—
50C2×C22⋊C4×D11C2212yes—
51C2×#66932C2212yescomplemented
52C2×#66929C2212yescomplemented
53C2×C4×D44C2211yescharacteristic
54C2×C4×D44C2211yescharacteristic
55C2×C4×D44C2211yescharacteristic
56C2×C42×D11C2211yescharacteristic
57C2×C42×D11C2211yescharacteristic, complemented
58C11×#390C2211yescharacteristic
59C11×#390C2211yescharacteristic
60C11×#390C2212yescomplemented
61C11×#390C2211yescharacteristic, complemented
62C11×#390C2212yescomplemented
63C11×#390C2211yescharacteristic, complemented
64C43×C11C2211yescharacteristic, complemented
65#10622844C2212yescomplemented
66#10622842C2212yescomplemented
67#10622836C2212yes—
68#10622836C2212yes—
69#10622836C2212yescomplemented
70#10622835C2212yescomplemented
71#10622834C2211yescharacteristic
72#10622834C2211yescharacteristic
73#10622833C2212yescomplemented
74#10622604C2212yescomplemented
75#10622603C2212yescomplemented
76#10622602C2212yes—
77#10622601C2211yescharacteristic
78#10622600C2211yescharacteristic
79#10622600C2211yescharacteristic, complemented
80#10622598C2211yescharacteristic, complemented
81#10622597C2212yescomplemented
82#10622589C2211yescharacteristic, complemented
83C4⋊C4×Dic11C2211yescharacteristic, complemented
84#10622574C2212yes—
85#10622574C2212yescomplemented
86#10622574C2212yescomplemented
87#10622573C2212yes—
88#10622572C2212yescomplemented
89#10622571C2212yescomplemented
90#10622570C2212yes—
91#10622570C2212yes—
92#10622570C2212yescomplemented
93#10622570C2212yescomplemented
94#10622569C2212yes—
95#10622569C2212yes—
96#10622569C2212yescomplemented
97#10622568C2212yes—
98#10622565C2212yescomplemented
99#10622564C2212yescomplemented
100#10622561C2212yescomplemented
101#10622561C2212yescomplemented
102#10622558C2212yescomplemented
103#10622558C2212yescomplemented
104#10622558C2212yescomplemented
105C22⋊C4×Dic11C2212yescomplemented
106#10622553C2212yescomplemented
107#10622553C2212yescomplemented
108#10622553C2212yescomplemented
109#10622552C2211yescharacteristic
110#10622552C2211yescharacteristic
111#10622552C2211yescharacteristic
112C4×(C2×D11)⋊C4C2211yescharacteristic
113C4×(C2×D11)⋊C4C2211yescharacteristic
114C4×(C2×D11)⋊C4C2211yescharacteristic
115C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
116C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
117C4×(C2×D11)⋊C4C2211yescharacteristic, complemented
118C4×C4⋊Dic11C2211yescharacteristic, complemented
119C4×C4⋊Dic11C2211yescharacteristic, complemented
120C4×C4⋊Dic11C2211yescharacteristic, complemented
121#10622541C2211yescharacteristic, complemented
122#10622541C2211yescharacteristic, complemented
123#10622541C2211yescharacteristic, complemented
124C24×D11C2312yes—
125C22×Q8×C11C2312yes—
126C22×D4×C11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C22×D4×C11C2312yes—
130C22×C22⋊D11C2312yes—
131C22×C22⋊D11C2312yes—
132C22×C22⋊D11C2312yes—
133C22×C22⋊D11C2312yes—
134C22×C22⋊D11C2312yes—
135C22×C22⋊D11C2312yes—
136C23×Dic11C2312yes—
137C2×D4×D11—24no—
138C2×D4×D11—42no—
139C2×D4×D11—42no—
140C22×D44C2311yescharacteristic
141C22×D44C2311yescharacteristic
142C22×D44C2312yes—
143C22×C4×D11C2311yescharacteristic
144C22×C4×D11C2311yescharacteristic
145C22×C4×D11C2311yescharacteristic
146C22×C4×D11C2311yescharacteristic
147C22×C4×D11C2312yes—
148C22×C4×D11C2311yescharacteristic
149C22×C4×D11C2311yescharacteristic
150C11×C4⋊Q8—42no—
151C11×#127—42no—
152C11×#124—28no—
153C11×#124—44no—
154C2×C11×C4⋊C4C2311yescharacteristic
155C2×C11×C4⋊C4C2311yescharacteristic
156C2×C11×C4⋊C4C2312yes—
157C2×C11×C22⋊C4C2312yes—
158C2×C11×C22⋊C4C2312yes—
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×C11C2311yescharacteristic
168C2×C42×C11C2311yescharacteristic
169C2×C42×C11C2311yescharacteristic
170C2×C42×C11C2311yescharacteristic
171C2×C42×C11C2311yescharacteristic
172C2×C22⋊Dic11C2312yes—
173C2×C22⋊Dic11C2312yes—
174C2×C22⋊Dic11C2312yes—
175C2×C22⋊Dic11C2312yes—
176C2×C22⋊Dic11C2312yes—
177C2×C22⋊Dic11C2312yes—
178C2×C22⋊Dic11C2312yes—
179C2×C22⋊Dic11C2312yes—
180#67000—28no—
181#66999—28no—
182#66993—42no—
183#66992—28no—
184#66991—24no—
185#66991—42no—
186#66991—42no—
187#66990—28no—
188#66990—28no—
189D4×Dic11—42no—
190C2×(C2×D11)⋊C4C2311yescharacteristic
191C2×(C2×D11)⋊C4C2311yescharacteristic
192C2×(C2×D11)⋊C4C2311yescharacteristic
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)⋊C4C2312yes—
201C2×(C2×D11)⋊C4C2312yes—
202C2×(C2×D11)⋊C4C2312yes—
203C2×(C2×D11)⋊C4C2312yes—
204C2×(C2×D11)⋊C4C2311yescharacteristic
205C2×(C2×D11)⋊C4C2311yescharacteristic
206C2×(C2×D11)⋊C4C2311yescharacteristic
207C2×C4⋊Dic11C2311yescharacteristic
208C2×C4⋊Dic11C2311yescharacteristic
209C2×C4⋊Dic11C2312yes—
210C2×C4⋊Dic11C2311yescharacteristic
211C2×C4⋊Dic11C2311yescharacteristic
212C2×C4⋊Dic11C2311yescharacteristic
213C2×C4⋊Dic11C2311yescharacteristic
214C2×Dic11⋊C4C2312yes—
215C2×Dic11⋊C4C2312yes—
216C2×Dic11⋊C4C2312yes—
217C2×Dic11⋊C4C2312yes—
218C2×Dic11⋊C4C2312yes—
219C2×Dic11⋊C4C2312yes—
220C2×C4×Dic11C2311yescharacteristic
221C2×C4×Dic11C2311yescharacteristic
222C2×C4×Dic11C2312yes—
223C2×C4×Dic11C2311yescharacteristic
224C2×C4×Dic11C2311yescharacteristic
225C2×C4×Dic11C2311yescharacteristic
226C2×C4×Dic11C2311yescharacteristic
227#66948—42no—
228C4⋊C4×D11—42no—
229#66939—28no—
230#66937—28no—
231#66937—28no—
232#66937—44no—
233#66936—28no—
234#66935—28no—
235(C22⋊D11)⋊C4—28no—
236C22⋊C4×D11—28no—
237C22⋊C4×D11—44no—
238#66932—28no—
239#66929—28no—
240C4×D44—24no—
241C4×D44—24no—
242C4×D44D418yescomplemented
243C42×D11—42no—
244C42×D11—42no—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2311yescharacteristic
249C11⋊#95C2311yescharacteristic
250C11⋊#95C2311yescharacteristic
251C11⋊#95C2311yescharacteristic
252C11⋊#95C2311yescharacteristic
253C11⋊#95C2311yescharacteristic
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258#35007—111nomaximal, Sylow
259C24×C11C2412yes—
260C24×C11C2412yes—
261C23×D11—24no—
262C23×D11—24no—
263C23×D11—24no—
264C23×D11—42no—
265C23×D11—42no—
266C23×D11—42no—
267C23×D11—42no—
268C23×D11C2412yes—
269C23×D11C2411yescharacteristic
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—24no—
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C2×D4×C11—42no—
283C2×D4×C11—42no—
284C2×D4×C11—42no—
285C2×D4×C11—42no—
286C22×C4×C11C2411yescharacteristic
287C22×C4×C11C2412yes—
288C22×C4×C11C2412yes—
289C22×C4×C11C2411yescharacteristic
290C22×C4×C11C2411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C22×C4×C11C2411yescharacteristic
295C2×C22⋊D11—24no—
296C2×C22⋊D11—24no—
297C2×C22⋊D11—24no—
298C2×C22⋊D11—24no—
299C2×C22⋊D11—24no—
300C2×C22⋊D11—24no—
301C2×C22⋊D11—24no—
302C2×C22⋊D11—24no—
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⋊D11—42no—
310C2×C22⋊D11—42no—
311C2×C22⋊D11—42no—
312C2×C22⋊D11—42no—
313C22×Dic11—24no—
314C22×Dic11—42no—
315C22×Dic11—42no—
316C22×Dic11C2411yescharacteristic
317C22×Dic11C2411yescharacteristic
318C22×Dic11C2412yes—
319C22×Dic11C2412yes—
320C22×Dic11C2412yes—
321C22×Dic11C2411yescharacteristic
322C22×Dic11C2411yescharacteristic
323C22×Dic11C2411yescharacteristic
324C22×Dic11C2411yescharacteristic
325D4×D11—416no—
326C2×D44—24no—
327C2×D44—22no—
328C2×D44—22no—
329C2×D44—22no—
330C2×D44—22no—
331C2×D44—22no—
332C2×D44—42no—
333C2×D44—42no—
334C2×D44C2×D414yes—
335C2×C4×D11—22no—
336C2×C4×D11—24no—
337C2×C4×D11—22no—
338C2×C4×D11—22no—
339C2×C4×D11—22no—
340C2×C4×D11—22no—
341C2×C4×D11—22no—
342C2×C4×D11—22no—
343C2×C4×D11—22no—
344C2×C4×D11—22no—
345C2×C4×D11—41no—
346C2×C4×D11—41no—
347C2×C4×D11—41no—
348C2×C4×D11—41no—
349C2×C4×D11—41no—
350C2×C4×D11—41no—
351C2×C4×D11—42no—
352C2×C4×D11—42no—
353C2×C4×D11C2×D414yes—
354C2×C4×D11C2×D414yescomplemented
355C2×C4×D11#4114yes—
356C11×C4⋊C4—22no—
357C11×C4⋊C4—22no—
358C11×C4⋊C4—42no—
359C11×C22⋊C4—24no—
360C11×C22⋊C4—24no—
361C11×C22⋊C4—24no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—24no—
364C11×C22⋊C4—24no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4—42no—
367C42×C11—22no—
368C42×C11—22no—
369C42×C11—22no—
370C42×C11—22no—
371C42×C11—22no—
372C42×C11—41no—
373C42×C11C2×D414yescomplemented
374C22⋊Dic11—24no—
375C22⋊Dic11—24no—
376C22⋊Dic11—24no—
377C22⋊Dic11—24no—
378C22⋊Dic11—42no—
379C22⋊Dic11—42no—
380C22⋊Dic11—42no—
381C22⋊Dic11—42no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—22no—
384(C2×D11)⋊C4—24no—
385(C2×D11)⋊C4—24no—
386(C2×D11)⋊C4—22no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—24no—
390(C2×D11)⋊C4—22no—
391(C2×D11)⋊C4—24no—
392(C2×D11)⋊C4—24no—
393(C2×D11)⋊C4—42no—
394(C2×D11)⋊C4—42no—
395(C2×D11)⋊C4—42no—
396(C2×D11)⋊C4C2×D414yes—
397(C2×D11)⋊C4C2×D414yescomplemented
398(C2×D11)⋊C4#4114yes—
399C4⋊Dic11—24no—
400C4⋊Dic11—22no—
401C4⋊Dic11—22no—
402C4⋊Dic11—22no—
403C4⋊Dic11—22no—
404C4⋊Dic11—22no—
405C4⋊Dic11C2×D414yescomplemented
406Dic11⋊C4—24no—
407Dic11⋊C4—24no—
408Dic11⋊C4—24no—
409Dic11⋊C4—24no—
410Dic11⋊C4—42no—
411Dic11⋊C4—42no—
412C4×Dic11—24no—
413C4×Dic11—22no—
414C4×Dic11—22no—
415C4×Dic11—41no—
416C4×Dic11—41no—
417C4×Dic11—41no—
418C4×Dic11—41no—
419C2×#538—112no—
420#2860—111no—
421#2858D1111yescharacteristic, complemented
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×#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×C11—22no—
450C23×C11—22no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—22no—
455C23×C11—22no—
456C23×C11C2511yescharacteristic
457C22×D11—21no—
458C22×D11—21no—
459C22×D11—21no—
460C22×D11—21no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—21no—
464C22×D11—21no—
465C22×D11—21no—
466C22×D11—21no—
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—
485Q8×C11—84no—
486D4×C11—44no—
487D4×C11—44no—
488D4×C11—84no—
489D4×C11—84no—
490C2×C4×C11—21no—
491C2×C4×C11—21no—
492C2×C4×C11—21no—
493C2×C4×C11—21no—
494C2×C4×C11—21no—
495C2×C4×C11—21no—
496C2×C4×C11—21no—
497C2×C4×C11—21no—
498C2×C4×C11—21no—
499C2×C4×C11—21no—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
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—
516C2×C4×C11H(5,𝔽2)12yes—
517C22⋊D11—48no—
518C22⋊D11—48no—
519C22⋊D11—84no—
520C22⋊D11—84no—
521C22⋊D11—84no—
522C22⋊D11—84no—
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—22no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—21no—
535C2×Dic11—21no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—21no—
539C2×Dic11—21no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—21no—
544C2×Dic11—21no—
545C2×Dic11—22no—
546C2×Dic11—84no—
547C2×Dic11C22×D412yes—
548C2×Dic11C22×D412yes—
549C2×Dic11C2×#4112yes—
550C2×Dic11C2×#4112yes—
551D44—28no—
552D44—44no—
553D44—84no—
554C4×D11—28no—
555C4×D11—44no—
556C4×D11—44no—
557C4×D11—44no—
558C4×D11—44no—
559C4×D11—44no—
560C4×D11—84no—
561C23×D4—111no—
562#538—2216no—
563C2×C4⋊Q8C2×D1111yescharacteristic, complemented
564C2×#127—111no—
565C2×#127C2×D1111yescharacteristic
566C2×#126—112no—
567C2×#126—112no—
568C2×#124—112no—
569C2×#124C2×D1112yescomplemented
570C2×#124C2×D1112yescomplemented
571C2×#123—112no—
572C2×#123—112no—
573C2×C22⋊Q8—112no—
574C2×#121—111no—
575C2×#121—112no—
576C2×#121—111no—
577C2×#121—111no—
578C2×#121—111no—
579C2×#121—112no—
580C2×#121—112no—
581C2×#121—112no—
582C2×#120—112no—
583C2×#120—112no—
584C2×#120—112no—
585C2×C4×D4—111no—
586C2×C4×D4—112no—
587C2×C4×D4—111no—
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#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—112no—
615#390—112no—
616#390—112no—
617#390—112no—
618#390—111no—
619#390—111no—
620#390—111no—
621#390C2×D1111yescharacteristic
622#390C2×D1111yescharacteristic
623#390C2×D1112yescomplemented
624#390C2×D1111yescharacteristic, complemented
625#390C2×D1111yescharacteristic, complemented
626#390C2×D1112yescomplemented
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#388—112no—
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#380—111no—
648#379—112no—
649C4×C4⋊C4—111no—
650C4×C4⋊C4—111no—
651C4×C4⋊C4—111no—
652C4×C4⋊C4—111no—
653C4×C22⋊C4—112no—
654C4×C22⋊C4—111no—
655C4×C22⋊C4—111no—
656C4×C22⋊C4—111no—
657C4×C22⋊C4—111no—
658C4×C22⋊C4—111no—
659C4×C22⋊C4—111no—
660C43C2×D1111yescharacteristic, complemented
661C22×C11—42no—
662C22×C11—42no—
663C22×C11—42no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11—42no—
667C22×C11—42no—
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—22no—
689C2×D11—22no—
690C2×D11—22no—
691C2×D11—41no—
692C2×D11—41no—
693C2×D11—41no—
694C2×D11—41no—
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—22no—
709C4×C11—41no—
710C4×C11—42no—
711C4×C11—42no—
712C4×C11#53814yescomplemented
713Dic11—22no—
714Dic11—22no—
715Dic11—22no—
716Dic11—22no—
717Dic11—42no—
718Dic11—41no—
719Dic11—42no—
720Dic11—42no—
721Dic11—41no—
722C25—112no—
723C22×Q8C22×D1112yes—
724C22×D4—112no—
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—224no—
734C22×D4—442no—
735C22×D4—442no—
736C22×D4C22×D1111yescharacteristic
737C22×D4C22×D1111yescharacteristic
738C22×D4C22×D1112yes—
739C22×D4C22×D1112yes—
740C23×C4—111no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—112no—
744C23×C4—111no—
745C23×C4—111no—
746C23×C4—111no—
747C23×C4—112no—
748C4⋊Q8—42no—
749#127—42no—
750#127—442no—
751#126—228no—
752#126—228no—
753#124—28no—
754#124—44no—
755#124—228no—
756#123—228no—
757#123—228no—
758C22⋊Q8—228no—
759#121—228no—
760#121—228no—
761#121—228no—
762#121—224no—
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—224no—
772C4×D4—224no—
773C4×D4—228no—
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—111no—
785C2×C4⋊C4—112no—
786C2×C4⋊C4—112no—
787C2×C4⋊C4—112no—
788C2×C4⋊C4—442no—
789C2×C4⋊C4C22×D1111yescharacteristic
790C2×C4⋊C4C22×D1111yescharacteristic
791C2×C4⋊C4C22×D1112yes—
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—112no—
803C2×C22⋊C4—111no—
804C2×C22⋊C4—111no—
805C2×C22⋊C4—111no—
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×D1112yes—
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—112no—
828C2×C42—111no—
829C2×C42—111no—
830C2×C42—111no—
831C2×C42—111no—
832C2×C42—111no—
833C2×C42—111no—
834C2×C42—442no—
835C2×C42—442no—
836C2×C42C22×D1111yescharacteristic
837C2×C42C22×D1111yescharacteristic
838C2×C42C22×D1111yescharacteristic
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#95—112no—
854#95—112no—
855#95—112no—
856C2×C11—82no—
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—42no—
867D11—82no—
868C24—111no—
869C24—111no—
870C24—112no—
871C24—224no—
872C24—224no—
873C24—224no—
874C24—442no—
875C24—442no—
876C24—442no—
877C24—442no—
878C24C23×D1112yes—
879C24C23×D1112yes—
880C2×Q8—24no—
881C2×Q8—42no—
882C2×Q8—42no—
883C2×D4—24no—
884C2×D4—22no—
885C2×D4—22no—
886C2×D4—22no—
887C2×D4—22no—
888C2×D4—24no—
889C2×D4—22no—
890C2×D4—22no—
891C2×D4—42no—
892C2×D4—42no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—114no—
896C2×D4—222no—
897C2×D4—222no—
898C2×D4—224no—
899C2×D4—224no—
900C2×D4—224no—
901C2×D4—224no—
902C2×D4—224no—
903C2×D4—224no—
904C2×D4—224no—
905C2×D4—224no—
906C2×D4—224no—
907C2×D4—222no—
908C2×D4—222no—
909C2×D4—222no—
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—111no—
924C22×C4—111no—
925C22×C4—111no—
926C22×C4—111no—
927C22×C4—114no—
928C22×C4—114no—
929C22×C4—114no—
930C22×C4—111no—
931C22×C4—111no—
932C22×C4—112no—
933C22×C4—112no—
934C22×C4—112no—
935C22×C4—222no—
936C22×C4—222no—
937C22×C4—224no—
938C22×C4—224no—
939C22×C4—222no—
940C22×C4—222no—
941C22×C4—222no—
942C22×C4—222no—
943C22×C4—222no—
944C22×C4—222no—
945C22×C4—222no—
946C22×C4—441no—
947C22×C4—441no—
948C22×C4—441no—
949C22×C4—441no—
950C22×C4—441no—
951C22×C4—441no—
952C22×C4—442no—
953C22×C4—442no—
954C22×C4—442no—
955C22×C4—442no—
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—22no—
966C4⋊C4—22no—
967C4⋊C4—42no—
968C4⋊C4—114no—
969C4⋊C4—222no—
970C4⋊C4—222no—
971C4⋊C4—224no—
972C4⋊C4—224no—
973C4⋊C4—224no—
974C4⋊C4—224no—
975C4⋊C4—224no—
976C4⋊C4—222no—
977C4⋊C4—222no—
978C4⋊C4—222no—
979C4⋊C4—442no—
980C4⋊C4—442no—
981C22⋊C4—24no—
982C22⋊C4—24no—
983C22⋊C4—24no—
984C22⋊C4—24no—
985C22⋊C4—24no—
986C22⋊C4—24no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—114no—
990C22⋊C4—114no—
991C22⋊C4—114no—
992C22⋊C4—224no—
993C22⋊C4—222no—
994C22⋊C4—224no—
995C22⋊C4—222no—
996C22⋊C4—224no—
997C22⋊C4—224no—
998C22⋊C4—224no—
999C22⋊C4—224no—
1000C22⋊C4—224no—
1001C22⋊C4—224no—
1002C22⋊C4—224no—
1003C22⋊C4—224no—
1004C22⋊C4—224no—
1005C22⋊C4—222no—
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—22no—
1015C42—22no—
1016C42—22no—
1017C42—22no—
1018C42—22no—
1019C42—41no—
1020C42—224no—
1021C42—222no—
1022C42—222no—
1023C42—441no—
1024C42—441no—
1025C42—441no—
1026C42—441no—
1027C42D4×D1114yescomplemented
1028C11#3500711yescharacteristic, complemented, Sylow
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—112no—
1044C23—112no—
1045C23—112no—
1046C23—112no—
1047C23—221no—
1048C23—221no—
1049C23—221no—
1050C23—221no—
1051C23—221no—
1052C23—221no—
1053C23—221no—
1054C23—221no—
1055C23—221no—
1056C23—221no—
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—84no—
1073D4—44no—
1074D4—44no—
1075D4—84no—
1076D4—84no—
1077D4—228no—
1078D4—448no—
1079D4—448no—
1080D4—444no—
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—21no—
1095C2×C4—21no—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—21no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—22no—
1102C2×C4—22no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—112no—
1106C2×C4—112no—
1107C2×C4—112no—
1108C2×C4—112no—
1109C2×C4—221no—
1110C2×C4—221no—
1111C2×C4—221no—
1112C2×C4—221no—
1113C2×C4—221no—
1114C2×C4—221no—
1115C2×C4—221no—
1116C2×C4—221no—
1117C2×C4—228no—
1118C2×C4—222no—
1119C2×C4—222no—
1120C2×C4—222no—
1121C2×C4—222no—
1122C2×C4—221no—
1123C2×C4—221no—
1124C2×C4—222no—
1125C2×C4—222no—
1126C2×C4—221no—
1127C2×C4—221no—
1128C2×C4—222no—
1129C2×C4—221no—
1130C2×C4—221no—
1131C2×C4—222no—
1132C2×C4—222no—
1133C2×C4—444no—
1134C2×C4—444no—
1135C2×C4—444no—
1136C2×C4—444no—
1137C2×C4—444no—
1138C2×C4—884no—
1139C2×C4—884no—
1140C2×C4C2×D4×D1112yes—
1141C2×C4C2×D4×D1112yes—
1142C2×C4C2×D4×D1112yes—
1143C2×C4#6703712yes—
1144C2×C4#6703712yes—
1145C2×C4#41×D1112yes—
1146C2×C4#41×D1112yes—
1147C2×C4#6704212yes—
1148C22—42no—
1149C22—42no—
1150C22—42no—
1151C22—42no—
1152C22—42no—
1153C22—42no—
1154C22—42no—
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—222no—
1170C22—222no—
1171C22—222no—
1172C22—441no—
1173C22—441no—
1174C22—441no—
1175C22—441no—
1176C22—442no—
1177C22—442no—
1178C22—442no—
1179C22—442no—
1180C22—442no—
1181C22—442no—
1182C22—442no—
1183C22—8816no—
1184C22C22×D4×D1111yescharacteristic
1185C22C2×#6703711yescharacteristic
1186C22C2×#6703711yescharacteristic
1187C22C2×#41×D1111yescharacteristic
1188C22C2×#41×D1111yescharacteristic
1189C22C2×#6704211yescharacteristic
1190C22#1062345311yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—22no—
1196C4—42no—
1197C4—42no—
1198C4—41no—
1199C4—222no—
1200C4—222no—
1201C4—222no—
1202C4—222no—
1203C4—442no—
1204C4—441no—
1205C4—442no—
1206C4—442no—
1207C4—441no—
1208C4#1062320914yescomplemented
1209C2—82no—
1210C2—82no—
1211C2—224no—
1212C2—442no—
1213C2—882no—
1214C2D11×#53211yescharacteristic
1215C2C2×#1062320911yescharacteristic
1216C2#1308203011yescharacteristic
1217C2#1308237811yescharacteristic
1218C2#1308239211yescharacteristic
1219C2#1308257111yescharacteristic
1220C2#1308264311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2858C2
hypercenter#2858D11
hypocenterC11#35007
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2858

Complements

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

NH ≅ G/Ntype
1. C2×#10623209C2semidirect
2. #13076983C2semidirect
3. #13076960C2semidirect
4. #13076946C2semidirect
5. #13074755C2semidirect
6. #13074746C2semidirect
7. #13073687C2semidirect
8. #13073673C2semidirect
9. #13073200C2semidirect
10. #13072982C2semidirect
11. #13072738C2semidirect
12. #13072379C2semidirect
13. #13072314C2semidirect
14. #13072250C2semidirect
15. #13072207C2semidirect
16. #13072159C2semidirect
17. #13072059C2semidirect
18. #13071970C2semidirect
19. #13071275C2semidirect
20. #13071132C2semidirect
21. D11×#390C2semidirect
22. C42×D44C2semidirect
23. C11×#2858C2semidirect
25. C2×C11×C4⋊Q8C22semidirect
27. C2×C11×#124C22semidirect
28. C2×C11×#124C22semidirect
29. C2×#67000C22semidirect
32. C2×#66992C22semidirect
35. C2×#66991C22semidirect
38. C2×D4×Dic11C22semidirect
42. C2×#66939C22semidirect
44. C2×#66937C22semidirect
45. C2×#66937C22semidirect
46. C2×#66936C22semidirect
51. C2×#66932C22semidirect
52. C2×#66929C22semidirect
57. C2×C42×D11C22semidirect
60. C11×#390C22semidirect
61. C11×#390C22semidirect
62. C11×#390C22semidirect
63. C11×#390C22semidirect
64. C43×C11C22semidirect
65. #10622844C22semidirect
66. #10622842C22semidirect
69. #10622836C22semidirect
70. #10622835C22semidirect
73. #10622833C22semidirect
74. #10622604C22semidirect
75. #10622603C22semidirect
79. #10622600C22semidirect
80. #10622598C22semidirect
81. #10622597C22semidirect
82. #10622589C22semidirect
83. C4⋊C4×Dic11C22semidirect
85. #10622574C22semidirect
86. #10622574C22semidirect
88. #10622572C22semidirect
89. #10622571C22semidirect
92. #10622570C22semidirect
93. #10622570C22semidirect
96. #10622569C22semidirect
98. #10622565C22semidirect
99. #10622564C22semidirect
100. #10622561C22semidirect
101. #10622561C22semidirect
102. #10622558C22semidirect
103. #10622558C22semidirect
104. #10622558C22semidirect
105. C22⋊C4×Dic11C22semidirect
106. #10622553C22semidirect
107. #10622553C22semidirect
108. #10622553C22semidirect
115. C4×(C2×D11)⋊C4C22semidirect
116. C4×(C2×D11)⋊C4C22semidirect
117. C4×(C2×D11)⋊C4C22semidirect
118. C4×C4⋊Dic11C22semidirect
119. C4×C4⋊Dic11C22semidirect
120. C4×C4⋊Dic11C22semidirect
121. #10622541C22semidirect
122. #10622541C22semidirect
123. #10622541C22semidirect
242. C4×D44D4semidirect
354. C2×C4×D11C2×D4semidirect
373. C42×C11C2×D4semidirect
397. (C2×D11)⋊C4C2×D4semidirect
405. C4⋊Dic11C2×D4semidirect
421. #2858D11semidirect
563. C2×C4⋊Q8C2×D11semidirect
569. C2×#124C2×D11semidirect
570. C2×#124C2×D11semidirect
623. #390C2×D11semidirect
624. #390C2×D11semidirect
625. #390C2×D11semidirect
626. #390C2×D11semidirect
660. C43C2×D11semidirect
712. C4×C11#538semidirect
1027. C42D4×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
#130769832
#130769602
#130769462
#130747552
#130747462
#130736872
#130736732
#130732002
#130729822
#130727382
#130723792
#130723142
#130722502
#130722072
#130721592
#130720592
#130719702
#130712752
#130711322
D11×#3902
C42×D442
C11×#28582
#3500711