Finite Group Databasebeta

← #14920193

Subgroups — #14920193

Order 2816.

2982 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623078C211yesmaximal, characteristic, complemented
2C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
3#13074537C212yesmaximal, complemented
4#13074504C212yesmaximal, complemented
5#13074461C212yesmaximal, complemented
6#13074459C212yesmaximal, complemented
7#13074435C211yesmaximal, characteristic, complemented
8#13074425C211yesmaximal, characteristic, complemented
9#13074394C211yesmaximal, characteristic, complemented
10#13074393C211yesmaximal, characteristic, complemented
11#13074364C211yesmaximal, characteristic, complemented
12#13074354C211yesmaximal, characteristic, complemented
13#13074331C211yesmaximal, characteristic, complemented
14#13074330C211yesmaximal, characteristic, complemented
15#13071877C212yesmaximal, complemented
16#13071860C212yesmaximal, complemented
17#13071854C212yesmaximal, complemented
18#13071831C212yesmaximal, complemented
19C4×#66939C211yesmaximal, characteristic, complemented
20C4×#66988C211yesmaximal, characteristic, complemented
21C4×#67006C211yesmaximal, characteristic, complemented
22#13070997C211yesmaximal, characteristic, complemented
23C4×C11×#120C211yesmaximal, characteristic, complemented
24C24×C4×C11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic
26C22×#4339C2211yescharacteristic, complemented
27C23×C4×D11C2211yescharacteristic
28C2×C11×#120C2211yescharacteristic
29C2×C4×D4×C11C2211yescharacteristic
30C2×C4×D4×C11C2212yescomplemented
31C2×#67006C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C2×#66992C2211yescharacteristic
34C2×#66990C2211yescharacteristic
35C2×#66988C2211yescharacteristic
36C2×C4×C22⋊D11—28no—
37C2×C4×C22⋊D11C2211yescharacteristic
38C2×C4×C22⋊D11C2212yes—
39C2×C4×C22⋊D11C2212yes—
40C2×C4×C22⋊D11C2212yes—
41C2×C4×C22⋊D11C2212yes—
42C2×C4×C22⋊D11C2211yescharacteristic, complemented
43C2×C4×C22⋊D11C2212yescomplemented
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×Dic11⋊C4C2211yescharacteristic
46C22×C4×Dic11C2211yescharacteristic
47#10623078—28no—
48C2×#66949C2211yescharacteristic, complemented
49C2×#66947C2211yescharacteristic, complemented
50C2×#66939C2211yescharacteristic
51C2×#66937C2211yescharacteristic, complemented
52C2×#66936C2211yescharacteristic, complemented
53C2×#66935C2211yescharacteristic
54C2×#66931C2211yescharacteristic
55C2×C4×D44C2211yescharacteristic, complemented
56C2×#66925C2211yescharacteristic, complemented
57C2×#66925C2212yescomplemented
58C11×#386C2211yescharacteristic
59C11×#386C2212yescomplemented
60C11×#385C2211yescharacteristic
61C11×#385C2212yescomplemented
62C11×#379C2211yescharacteristic
63C4×C11×C22⋊C4C2211yescharacteristic
64C4×C11×C22⋊C4C2212yescomplemented
65#10622860C2211yescharacteristic
66#10622836C2212yes—
67#10622836C2212yes—
68#10622836C2212yescomplemented
69#10622835C2212yescomplemented
70#10622833C2211yescharacteristic
71#10622826C2211yescharacteristic
72#10622826C2212yescomplemented
73#10622823C2211yescharacteristic
74#10622823C2212yescomplemented
75C4×C22⋊Dic11C2211yescharacteristic
76C4×C22⋊Dic11C2212yescomplemented
77C4×C22⋊Dic11C2212yescomplemented
78#10622606C2212yescomplemented
79#10622604C2212yescomplemented
80#10622593C2212yescomplemented
81#10622592C2212yescomplemented
82#10622591C2212yescomplemented
83#10622574C2212yes—
84#10622574C2212yes—
85#10622574C2212yescomplemented
86#10622573C2212yes—
87#10622573C2212yes—
88#10622572C2212yes—
89#10622572C2212yes—
90#10622572C2212yescomplemented
91#10622572C2212yescomplemented
92#10622572C2212yescomplemented
93#10622571C2211yescharacteristic
94#10622568C2211yescharacteristic
95#10622568C2211yescharacteristic
96#10622565C2212yescomplemented
97#10622563C2211yescharacteristic
98#10622562C2212yescomplemented
99#10622561C2212yescomplemented
100#10622561C2212yescomplemented
101#10622561C2212yescomplemented
102#10622560C2212yescomplemented
103#10622559C2211yescharacteristic
104#10622557C2212yescomplemented
105#10622556C2211yescharacteristic
106#10622556C2211yescharacteristic
107#10622555C2211yescharacteristic
108#10622555C2211yescharacteristic
109C4×(C2×D11)⋊C4C2212yescomplemented
110C4×(C2×D11)⋊C4C2212yescomplemented
111C4×C4⋊Dic11C2212yescomplemented
112C4×Dic11⋊C4C2212yescomplemented
113#10622289C2212yescomplemented
114#10622288C2212yescomplemented
115#10622288C2212yescomplemented
116#10622287C2212yescomplemented
117#10622285C2212yescomplemented
118#10622283C2212yescomplemented
119#10622280C2212yescomplemented
120#10622277C2212yescomplemented
121#10622271C2212yescomplemented
122#10622270C2212yescomplemented
123#10622270C2212yescomplemented
124#10622266C2212yescomplemented
125C25×C11C2311yescharacteristic
126C24×D11C2311yescharacteristic
127C22×D4×C11C2311yescharacteristic
128C22×D4×C11C2312yes—
129C23×C4×C11—24no—
130C23×C4×C11—44no—
131C23×C4×C11C2312yes—
132C23×C4×C11C2311yescharacteristic
133C23×C4×C11C2311yescharacteristic
134C23×C4×C11C2311yescharacteristic
135C23×C4×C11C2312yes—
136C22×C22⋊D11—24no—
137C22×C22⋊D11—24no—
138C22×C22⋊D11—24no—
139C22×C22⋊D11C2311yescharacteristic
140C22×C22⋊D11C2312yes—
141C22×C22⋊D11C2312yes—
142C22×C22⋊D11C2311yescharacteristic
143C22×C22⋊D11C2311yescharacteristic
144C22×C22⋊D11C2311yescharacteristic
145C22×C22⋊D11C2312yes—
146C23×Dic11C2311yescharacteristic
147C23×Dic11C2311yescharacteristic
148C23×Dic11C2311yescharacteristic
149C2×#4339—24no—
150C2×#4339—44no—
151C22×D44C2311yescharacteristic
152C22×D44C2311yescharacteristic
153C22×C4×D11—44no—
154C22×C4×D11D418yescomplemented
155C22×C4×D11C2311yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C22×C4×D11C2311yescharacteristic
158C22×C4×D11C2311yescharacteristic
159C22×C4×D11C2311yescharacteristic
160C22×Dic22C2311yescharacteristic
161C11×#120—24no—
162C4×D4×C11—24no—
163C4×D4×C11—44no—
164C2×C11×C4⋊C4C2311yescharacteristic
165C2×C11×C4⋊C4C2312yes—
166C2×C11×C22⋊C4C2311yescharacteristic
167C2×C11×C22⋊C4C2311yescharacteristic
168C2×C11×C22⋊C4C2311yescharacteristic
169C2×C11×C22⋊C4C2311yescharacteristic
170C2×C11×C22⋊C4C2312yes—
171C2×C11×C22⋊C4C2312yes—
172C2×C11×C22⋊C4C2312yes—
173C2×C11×C22⋊C4C2312yes—
174C2×C42×C11C2311yescharacteristic
175C2×C42×C11C2312yes—
176#67006—24no—
177C2×C22⋊Dic11—24no—
178C2×C22⋊Dic11C2311yescharacteristic
179C2×C22⋊Dic11C2311yescharacteristic
180C2×C22⋊Dic11C2312yes—
181C2×C22⋊Dic11C2312yes—
182C2×C22⋊Dic11C2311yescharacteristic
183C2×C22⋊Dic11C2311yescharacteristic
184C2×C22⋊Dic11C2312yes—
185C2×C22⋊Dic11C2312yes—
186C2×C22⋊Dic11C2312yes—
187C2×C22⋊Dic11C2312yes—
188C2×C22⋊Dic11C2312yes—
189#66992—24no—
190#66990—24no—
191#66988—24no—
192C4×C22⋊D11—24no—
193C4×C22⋊D11—28no—
194C4×C22⋊D11—28no—
195C4×C22⋊D11—28no—
196C4×C22⋊D11—28no—
197C4×C22⋊D11—24no—
198C4×C22⋊D11—44no—
199C2×(C2×D11)⋊C4—24no—
200C2×(C2×D11)⋊C4C2311yescharacteristic
201C2×(C2×D11)⋊C4C2311yescharacteristic
202C2×(C2×D11)⋊C4C2311yescharacteristic
203C2×(C2×D11)⋊C4C2311yescharacteristic
204C2×(C2×D11)⋊C4C2311yescharacteristic
205C2×(C2×D11)⋊C4C2311yescharacteristic
206C2×(C2×D11)⋊C4C2312yes—
207C2×(C2×D11)⋊C4C2312yes—
208C2×(C2×D11)⋊C4C2312yes—
209C2×(C2×D11)⋊C4C2312yes—
210C2×(C2×D11)⋊C4C2312yes—
211C2×(C2×D11)⋊C4C2312yes—
212C2×(C2×D11)⋊C4C2312yes—
213C2×(C2×D11)⋊C4C2312yes—
214C2×(C2×D11)⋊C4C2312yes—
215C2×C4⋊Dic11C2311yescharacteristic
216C2×C4⋊Dic11C2312yes—
217C2×C4⋊Dic11C2312yes—
218C2×Dic11⋊C4—24no—
219C2×Dic11⋊C4C2311yescharacteristic
220C2×Dic11⋊C4C2311yescharacteristic
221C2×Dic11⋊C4C2311yescharacteristic
222C2×Dic11⋊C4C2311yescharacteristic
223C2×Dic11⋊C4C2312yes—
224C2×Dic11⋊C4C2312yes—
225C2×Dic11⋊C4C2312yes—
226C2×Dic11⋊C4C2312yes—
227C2×Dic11⋊C4C2312yes—
228C2×Dic11⋊C4C2312yes—
229C2×Dic11⋊C4C2312yes—
230C2×C4×Dic11—24no—
231C2×C4×Dic11C2312yes—
232C2×C4×Dic11C2311yescharacteristic
233C2×C4×Dic11C2312yes—
234C2×C4×Dic11C2312yes—
235#66949—24no—
236#66947—24no—
237#66939—24no—
238#66937—24no—
239#66936—24no—
240#66935—24no—
241#66931—24no—
242C4×D44—24no—
243#66925—24no—
244#66925—44no—
245C11×#95C2312yes—
246C11×#95C2312yes—
247C11×#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258C11⋊#95C2312yes—
259C11⋊#95C2312yes—
260C11⋊#95C2312yes—
261#34562—111nomaximal, Sylow
262C24×C11—22no—
263C24×C11—22no—
264C24×C11—42no—
265C24×C11—42no—
266C24×C11#4114yescomplemented
267C24×C11C2411yescharacteristic
268C24×C11C2412yes—
269C24×C11C2411yescharacteristic
270C23×D11—22no—
271C23×D11—22no—
272C23×D11—42no—
273C23×D11—42no—
274C23×D11C2×D414yes—
275C23×D11C2411yescharacteristic
276C23×D11C2411yescharacteristic
277C23×D11C2411yescharacteristic
278C2×D4×C11—22no—
279C2×D4×C11—22no—
280C2×D4×C11—24no—
281C2×D4×C11—22no—
282C2×D4×C11—42no—
283C2×D4×C11—42no—
284C22×C4×C11—24no—
285C22×C4×C11—22no—
286C22×C4×C11—24no—
287C22×C4×C11—24no—
288C22×C4×C11—22no—
289C22×C4×C11—24no—
290C22×C4×C11—24no—
291C22×C4×C11—24no—
292C22×C4×C11—42no—
293C22×C4×C11—42no—
294C22×C4×C11—42no—
295C22×C4×C11—416no—
296C22×C4×C11C2×D414yes—
297C22×C4×C11C2412yes—
298C22×C4×C11C2411yescharacteristic
299C22×C4×C11C2411yescharacteristic
300C22×C4×C11C2411yescharacteristic
301C22×C4×C11C2412yes—
302C22×C4×C11C2412yes—
303C22×C4×C11C2411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C2×C22⋊D11—232no—
306C2×C22⋊D11—22no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—22no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—24no—
312C2×C22⋊D11—22no—
313C2×C22⋊D11—24no—
314C2×C22⋊D11—22no—
315C2×C22⋊D11—24no—
316C2×C22⋊D11—24no—
317C2×C22⋊D11—22no—
318C2×C22⋊D11—22no—
319C2×C22⋊D11—42no—
320C2×C22⋊D11—42no—
321C2×C22⋊D11—42no—
322C2×C22⋊D11—42no—
323C2×C22⋊D11—42no—
324C22×Dic11—22no—
325C22×Dic11—22no—
326C22×Dic11—22no—
327C22×Dic11—42no—
328C22×Dic11—42no—
329C22×Dic11C2×D414yes—
330C22×Dic11#4114yescomplemented
331C22×Dic11C2412yes—
332C22×Dic11C2412yes—
333C22×Dic11C2412yes—
334C22×Dic11C2411yescharacteristic
335C22×Dic11C2411yescharacteristic
336C22×Dic11C2411yescharacteristic
337C22×Dic11C2411yescharacteristic
338C22×Dic11C2411yescharacteristic
339C22×Dic11C2412yes—
340#4339—416no—
341C2×D44—22no—
342C2×D44—22no—
343C2×D44—42no—
344C2×D44—42no—
345C2×C4×D11—22no—
346C2×C4×D11—24no—
347C2×C4×D11—24no—
348C2×C4×D11—24no—
349C2×C4×D11—42no—
350C2×C4×D11—42no—
351C2×C4×D11—416no—
352C2×C4×D11C2×D414yes—
353C2×C4×D11C2×D414yes—
354C2×C4×D11C2×D414yes—
355C2×C4×D11C2×D414yes—
356C2×Dic22—22no—
357C2×Dic22—42no—
358C11×C4⋊C4—22no—
359C11×C4⋊C4—42no—
360C11×C22⋊C4—22no—
361C11×C22⋊C4—22no—
362C11×C22⋊C4—24no—
363C11×C22⋊C4—22no—
364C11×C22⋊C4—22no—
365C11×C22⋊C4—42no—
366C11×C22⋊C4—42no—
367C11×C22⋊C4—42no—
368C42×C11—22no—
369C42×C11—24no—
370C22⋊Dic11—22no—
371C22⋊Dic11—24no—
372C22⋊Dic11—24no—
373C22⋊Dic11—24no—
374C22⋊Dic11—22no—
375C22⋊Dic11—22no—
376C22⋊Dic11—24no—
377C22⋊Dic11—22no—
378C22⋊Dic11—42no—
379C22⋊Dic11—42no—
380C22⋊Dic11—42no—
381(C2×D11)⋊C4—22no—
382(C2×D11)⋊C4—24no—
383(C2×D11)⋊C4—22no—
384(C2×D11)⋊C4—22no—
385(C2×D11)⋊C4—22no—
386(C2×D11)⋊C4—22no—
387(C2×D11)⋊C4—24no—
388(C2×D11)⋊C4—24no—
389(C2×D11)⋊C4—22no—
390(C2×D11)⋊C4—42no—
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—
396C4⋊Dic11—22no—
397C4⋊Dic11—24no—
398C4⋊Dic11—42no—
399Dic11⋊C4—22no—
400Dic11⋊C4—22no—
401Dic11⋊C4—22no—
402Dic11⋊C4—24no—
403Dic11⋊C4—24no—
404Dic11⋊C4—24no—
405Dic11⋊C4—22no—
406Dic11⋊C4—42no—
407Dic11⋊C4—42no—
408Dic11⋊C4—42no—
409Dic11⋊C4—42no—
410C4×Dic11—22no—
411C4×Dic11—24no—
412C4×Dic11—24no—
413C4×Dic11—24no—
414C2×#525—111no—
415C22×C4×D4—111no—
416#2638—112no—
417#2635—112no—
418#2630—112no—
419#2630—112no—
420#2627—111no—
421#2626—111no—
422#2622—111no—
423#2622—111no—
424#2618—111no—
425#2617—111no—
426#2613—111no—
427#2613—111no—
428#2395—112no—
429#2392—112no—
430#2392—112no—
431#2388—112no—
432C4×#123—111no—
433C4×#123—111no—
434C4×#120—111no—
435C4×#120D1111yescharacteristic, complemented
436#2280—111no—
437C23×C11—22no—
438C23×C11—22no—
439C23×C11—28no—
440C23×C11—22no—
441C23×C11—22no—
442C23×C11—22no—
443C23×C11—22no—
444C23×C11—22no—
445C23×C11—22no—
446C23×C11—21no—
447C23×C11—21no—
448C23×C11—21no—
449C23×C11—22no—
450C23×C11—22no—
451C23×C11—48no—
452C23×C11—44no—
453C23×C11—44no—
454C23×C11—48no—
455C23×C11C22×D412yes—
456C23×C11C2×#4114yes—
457C23×C11C2×#4112yes—
458C23×C11C2×#4112yes—
459C23×C11C2511yescharacteristic
460C22×D11—28no—
461C22×D11—21no—
462C22×D11—21no—
463C22×D11—21no—
464C22×D11—21no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—21no—
470C22×D11—21no—
471C22×D11—21no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—44no—
475C22×D11—44no—
476C22×D11—48no—
477C22×D11—48no—
478C22×D11C22×D412yes—
479C22×D11C22×D412yes—
480D4×C11—48no—
481D4×C11—44no—
482C2×C4×C11—22no—
483C2×C4×C11—28no—
484C2×C4×C11—22no—
485C2×C4×C11—21no—
486C2×C4×C11—21no—
487C2×C4×C11—21no—
488C2×C4×C11—21no—
489C2×C4×C11—22no—
490C2×C4×C11—21no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—22no—
494C2×C4×C11—22no—
495C2×C4×C11—22no—
496C2×C4×C11—22no—
497C2×C4×C11—22no—
498C2×C4×C11—22no—
499C2×C4×C11—22no—
500C2×C4×C11—48no—
501C2×C4×C11—44no—
502C2×C4×C11—44no—
503C2×C4×C11—48no—
504C2×C4×C11C22×D412yes—
505C2×C4×C11C22×D412yes—
506C2×C4×C11H(5,𝔽2)14yes—
507C22⋊D11—216no—
508C22⋊D11—216no—
509C22⋊D11—44no—
510C22⋊D11—44no—
511C22⋊D11—44no—
512C22⋊D11—48no—
513C22⋊D11—44no—
514C2×Dic11—28no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—21no—
521C2×Dic11—21no—
522C2×Dic11—21no—
523C2×Dic11—22no—
524C2×Dic11—21no—
525C2×Dic11—21no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—44no—
536C2×Dic11—44no—
537C2×Dic11C22×D412yes—
538C2×Dic11C22×D412yes—
539C2×Dic11C2×#4114yes—
540D44—44no—
541D44—44no—
542C4×D11—28no—
543C4×D11—28no—
544C4×D11—44no—
545C4×D11—44no—
546C4×D11—44no—
547Dic22—44no—
548C22×#41—111no—
549C23×D4—111no—
550C24×C4—111no—
551C24×C4C2×D1111yescharacteristic
552#525—228no—
553C2×#123—111no—
554C2×#123—111no—
555C2×#123—111no—
556C2×#123—111no—
557C2×C22⋊Q8—111no—
558C2×C22⋊Q8—111no—
559C2×#121—111no—
560C2×#121—111no—
561C2×#120—111no—
562C2×#120—111no—
563C2×#120—111no—
564C2×#120C2×D1111yescharacteristic
565C2×C4×D4—112no—
566C2×C4×D4—112no—
567C2×C4×D4—112no—
568C2×C4×D4—112no—
569C2×C4×D4—111no—
570C2×C4×D4—111no—
571C2×C4×D4—112no—
572C2×C4×D4—111no—
573C2×C4×D4—228no—
574C2×C4×D4C2×D1111yescharacteristic
575C2×C4×D4C2×D1112yescomplemented
576C2×#117—111no—
577C2×#117—112no—
578C22×C4⋊C4—111no—
579C22×C22⋊C4—111no—
580C22×C22⋊C4—111no—
581C22×C42—111no—
582#400—112no—
583#399—112no—
584#398—112no—
585#398—112no—
586#398—112no—
587#397—112no—
588#397—112no—
589#397—112no—
590#397—112no—
591#397—112no—
592#396—112no—
593#396—112no—
594#396—112no—
595#396—112no—
596#395—112no—
597#394—112no—
598#394—112no—
599#394—112no—
600#394—112no—
601#394—112no—
602#394—112no—
603#394—112no—
604#394—112no—
605#394—112no—
606#394—112no—
607#394—112no—
608#393—112no—
609#392—112no—
610#392—112no—
611#392—112no—
612#392—112no—
613#392—112no—
614#388—112no—
615#388—112no—
616#387—112no—
617#387—112no—
618#386—111no—
619#386—111no—
620#386—112no—
621#386—111no—
622#386C2×D1111yescharacteristic
623#386C2×D1112yescomplemented
624#385—111no—
625#385—112no—
626#385—111no—
627#385—111no—
628#385C2×D1111yescharacteristic
629#385C2×D1112yescomplemented
630#381—111no—
631#381—111no—
632#381—112no—
633#380—111no—
634#380—111no—
635#380—112no—
636#379—111no—
637#379—111no—
638#379—111no—
639#379C2×D1111yescharacteristic
640C4×C4⋊C4—112no—
641C4×C4⋊C4—112no—
642C4×C22⋊C4—112no—
643C4×C22⋊C4—112no—
644C4×C22⋊C4—111no—
645C4×C22⋊C4—112no—
646C4×C22⋊C4—112no—
647C4×C22⋊C4C2×D1111yescharacteristic
648C4×C22⋊C4C2×D1112yescomplemented
649C22×C11—22no—
650C22×C11—22no—
651C22×C11—24no—
652C22×C11—24no—
653C22×C11—24no—
654C22×C11—24no—
655C22×C11—24no—
656C22×C11—416no—
657C22×C11—42no—
658C22×C11—42no—
659C22×C11—42no—
660C22×C11—42no—
661C22×C11—41no—
662C22×C11—41no—
663C22×C11—41no—
664C22×C11—42no—
665C22×C11—42no—
666C22×C11#52514yes—
667C22×C11C23×D411yescharacteristic
668C22×C11C22×#4111yescharacteristic
669C22×C11C22×#4111yescharacteristic
670C22×C11C2×H(5,𝔽2)12yes—
671C22×C11#58512yes—
672C2×D11—22no—
673C2×D11—22no—
674C2×D11—22no—
675C2×D11—22no—
676C2×D11—22no—
677C2×D11—22no—
678C2×D11—416no—
679C2×D11—42no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—42no—
683C2×D11—41no—
684C2×D11—41no—
685C2×D11—41no—
686C2×D11—42no—
687C2×D11—42no—
688C4×C11—22no—
689C4×C11—41no—
690C4×C11—42no—
691C4×C11—41no—
692C4×C11—41no—
693C4×C11—42no—
694C4×C11—42no—
695C4×C11#53414yes—
696Dic11—24no—
697Dic11—22no—
698Dic11—22no—
699Dic11—41no—
700Dic11—41no—
701Dic11—42no—
702Dic11—41no—
703Dic11—42no—
704Dic11—42no—
705C25—111no—
706C25C22×D1111yescharacteristic
707C2×#41—224no—
708C2×#41—444no—
709C22×Q8—111no—
710C22×D4—112no—
711C22×D4—112no—
712C22×D4—111no—
713C22×D4—111no—
714C22×D4—112no—
715C22×D4—111no—
716C22×D4—111no—
717C22×D4—111no—
718C22×D4—111no—
719C22×D4—224no—
720C22×D4—224no—
721C22×D4—224no—
722C22×D4C22×D1111yescharacteristic
723C22×D4C22×D1112yes—
724C23×C4—24no—
725C23×C4—44no—
726C23×C4—111no—
727C23×C4—111no—
728C23×C4—111no—
729C23×C4—111no—
730C23×C4—118no—
731C23×C4—111no—
732C23×C4—111no—
733C23×C4—111no—
734C23×C4—111no—
735C23×C4—444no—
736C23×C4C22×D1112yes—
737C23×C4C22×D1111yescharacteristic
738C23×C4C22×D1111yescharacteristic
739C23×C4C22×D1111yescharacteristic
740C23×C4C22×D1112yes—
741#123—224no—
742#123—224no—
743#123—224no—
744#123—224no—
745C22⋊Q8—224no—
746C22⋊Q8—224no—
747#121—224no—
748#121—224no—
749#120—24no—
750#120—224no—
751#120—224no—
752#120—224no—
753C4×D4—24no—
754C4×D4—44no—
755C4×D4—224no—
756C4×D4—228no—
757C4×D4—228no—
758C4×D4—228no—
759C4×D4—228no—
760C4×D4—224no—
761C4×D4—224no—
762C4×D4—444no—
763#117—224no—
764#117—444no—
765C2×C4⋊C4—112no—
766C2×C4⋊C4—112no—
767C2×C4⋊C4—111no—
768C2×C4⋊C4—111no—
769C2×C4⋊C4—111no—
770C2×C4⋊C4—111no—
771C2×C4⋊C4—111no—
772C2×C4⋊C4—112no—
773C2×C4⋊C4—112no—
774C2×C4⋊C4—112no—
775C2×C4⋊C4—112no—
776C2×C4⋊C4—112no—
777C2×C4⋊C4—112no—
778C2×C4⋊C4—112no—
779C2×C4⋊C4—224no—
780C2×C4⋊C4C22×D1111yescharacteristic
781C2×C4⋊C4C22×D1112yes—
782C2×C22⋊C4—112no—
783C2×C22⋊C4—112no—
784C2×C22⋊C4—111no—
785C2×C22⋊C4—111no—
786C2×C22⋊C4—111no—
787C2×C22⋊C4—112no—
788C2×C22⋊C4—111no—
789C2×C22⋊C4—112no—
790C2×C22⋊C4—112no—
791C2×C22⋊C4—112no—
792C2×C22⋊C4—111no—
793C2×C22⋊C4—111no—
794C2×C22⋊C4—111no—
795C2×C22⋊C4—111no—
796C2×C22⋊C4—111no—
797C2×C22⋊C4—111no—
798C2×C22⋊C4—112no—
799C2×C22⋊C4—112no—
800C2×C22⋊C4—112no—
801C2×C22⋊C4—112no—
802C2×C22⋊C4—112no—
803C2×C22⋊C4—112no—
804C2×C22⋊C4—112no—
805C2×C22⋊C4—112no—
806C2×C22⋊C4—112no—
807C2×C22⋊C4—112no—
808C2×C22⋊C4—224no—
809C2×C22⋊C4—224no—
810C2×C22⋊C4C22×D1111yescharacteristic
811C2×C22⋊C4C22×D1111yescharacteristic
812C2×C22⋊C4C22×D1111yescharacteristic
813C2×C22⋊C4C22×D1112yes—
814C2×C22⋊C4C22×D1111yescharacteristic
815C2×C22⋊C4C22×D1112yes—
816C2×C22⋊C4C22×D1112yes—
817C2×C22⋊C4C22×D1112yes—
818C2×C42—112no—
819C2×C42—111no—
820C2×C42—112no—
821C2×C42—112no—
822C2×C42—224no—
823C2×C42C22×D1111yescharacteristic
824C2×C42C22×D1112yes—
825#95—112no—
826#95—112no—
827#95—112no—
828#95—112no—
829#95—112no—
830#95—112no—
831#95—112no—
832#95—112no—
833#95—112no—
834#95—112no—
835#95—112no—
836#95—112no—
837#95—112no—
838#95C22×D1112yes—
839#95C22×D1112yes—
840#95C22×D1112yes—
841C2×C11—24no—
842C2×C11—44no—
843C2×C11—81no—
844C2×C11C2×#52511yescharacteristic
845C2×C11C2×#53411yescharacteristic
846C2×C11#344911yescharacteristic
847C2×C11#345912yes—
848C2×C11#346012yes—
849D11—42no—
850D11—42no—
851D11—81no—
852C24—22no—
853C24—22no—
854C24—42no—
855C24—42no—
856C24—111no—
857C24—111no—
858C24—114no—
859C24—111no—
860C24—222no—
861C24—222no—
862C24—442no—
863C24—442no—
864C24#433914yescomplemented
865C24C23×D1111yescharacteristic
866C24C23×D1112yes—
867C24C23×D1111yescharacteristic
868#41—4416no—
869C2×Q8—222no—
870C2×Q8—442no—
871C2×D4—24no—
872C2×D4—22no—
873C2×D4—22no—
874C2×D4—22no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—222no—
878C2×D4—222no—
879C2×D4—224no—
880C2×D4—224no—
881C2×D4—222no—
882C2×D4—224no—
883C2×D4—224no—
884C2×D4—2232no—
885C2×D4—224no—
886C2×D4—224no—
887C2×D4—222no—
888C2×D4—222no—
889C2×D4—224no—
890C2×D4—222no—
891C2×D4—222no—
892C2×D4—222no—
893C2×D4—442no—
894C2×D4—442no—
895C2×D4—442no—
896C2×D4—442no—
897C2×D4—442no—
898C2×D4—442no—
899C2×D4—442no—
900C22×C4—24no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—24no—
904C22×C4—24no—
905C22×C4—24no—
906C22×C4—24no—
907C22×C4—24no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—416no—
912C22×C4—114no—
913C22×C4—112no—
914C22×C4—111no—
915C22×C4—111no—
916C22×C4—114no—
917C22×C4—114no—
918C22×C4—114no—
919C22×C4—114no—
920C22×C4—114no—
921C22×C4—112no—
922C22×C4—112no—
923C22×C4—112no—
924C22×C4—111no—
925C22×C4—111no—
926C22×C4—111no—
927C22×C4—222no—
928C22×C4—222no—
929C22×C4—224no—
930C22×C4—224no—
931C22×C4—222no—
932C22×C4—222no—
933C22×C4—224no—
934C22×C4—4416no—
935C22×C4—442no—
936C22×C4—442no—
937C22×C4—442no—
938C22×C4—442no—
939C22×C4D4×D1114yes—
940C22×C4C23×D1112yes—
941C22×C4C23×D1111yescharacteristic
942C22×C4C23×D1112yes—
943C22×C4C23×D1111yescharacteristic
944C22×C4C23×D1111yescharacteristic
945C22×C4C23×D1112yes—
946C22×C4C23×D1111yescharacteristic
947C22×C4C23×D1111yescharacteristic
948C4⋊C4—22no—
949C4⋊C4—42no—
950C4⋊C4—224no—
951C4⋊C4—224no—
952C4⋊C4—222no—
953C4⋊C4—222no—
954C4⋊C4—222no—
955C4⋊C4—222no—
956C4⋊C4—224no—
957C4⋊C4—224no—
958C4⋊C4—222no—
959C4⋊C4—442no—
960C4⋊C4—442no—
961C4⋊C4—442no—
962C4⋊C4—442no—
963C4⋊C4—442no—
964C22⋊C4—24no—
965C22⋊C4—22no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—222no—
973C22⋊C4—224no—
974C22⋊C4—224no—
975C22⋊C4—224no—
976C22⋊C4—222no—
977C22⋊C4—222no—
978C22⋊C4—222no—
979C22⋊C4—222no—
980C22⋊C4—224no—
981C22⋊C4—224no—
982C22⋊C4—222no—
983C22⋊C4—224no—
984C22⋊C4—224no—
985C22⋊C4—222no—
986C22⋊C4—222no—
987C22⋊C4—222no—
988C22⋊C4—222no—
989C22⋊C4—442no—
990C22⋊C4—442no—
991C22⋊C4—442no—
992C22⋊C4—442no—
993C22⋊C4—442no—
994C22⋊C4—442no—
995C22⋊C4—442no—
996C22⋊C4—442no—
997C22⋊C4—442no—
998C42—22no—
999C42—24no—
1000C42—224no—
1001C42—224no—
1002C42—222no—
1003C42—224no—
1004C11#3456211yescharacteristic, complemented, Sylow
1005C23—22no—
1006C23—22no—
1007C23—28no—
1008C23—22no—
1009C23—22no—
1010C23—22no—
1011C23—22no—
1012C23—22no—
1013C23—22no—
1014C23—21no—
1015C23—21no—
1016C23—22no—
1017C23—21no—
1018C23—22no—
1019C23—48no—
1020C23—44no—
1021C23—44no—
1022C23—48no—
1023C23—112no—
1024C23—112no—
1025C23—228no—
1026C23—221no—
1027C23—221no—
1028C23—222no—
1029C23—222no—
1030C23—221no—
1031C23—221no—
1032C23—222no—
1033C23—222no—
1034C23—221no—
1035C23—221no—
1036C23—222no—
1037C23—221no—
1038C23—222no—
1039C23—444no—
1040C23—444no—
1041C23—448no—
1042C23—448no—
1043C23C2×#433914yes—
1044C23C2×#433912yes—
1045C23C2×D4×D1112yes—
1046C23#41×D1112yes—
1047C23C24×D1111yescharacteristic
1048Q8—444no—
1049D4—48no—
1050D4—44no—
1051D4—2216no—
1052D4—2216no—
1053D4—444no—
1054D4—444no—
1055D4—444no—
1056D4—448no—
1057D4—444no—
1058D4—444no—
1059D4—444no—
1060C2×C4—22no—
1061C2×C4—28no—
1062C2×C4—21no—
1063C2×C4—22no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—48no—
1079C2×C4—44no—
1080C2×C4—48no—
1081C2×C4—44no—
1082C2×C4—112no—
1083C2×C4—112no—
1084C2×C4—114no—
1085C2×C4—228no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—228no—
1091C2×C4—228no—
1092C2×C4—221no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—221no—
1096C2×C4—221no—
1097C2×C4—221no—
1098C2×C4—222no—
1099C2×C4—222no—
1100C2×C4—222no—
1101C2×C4—222no—
1102C2×C4—221no—
1103C2×C4—222no—
1104C2×C4—222no—
1105C2×C4—222no—
1106C2×C4—222no—
1107C2×C4—222no—
1108C2×C4—444no—
1109C2×C4—444no—
1110C2×C4—444no—
1111C2×C4—444no—
1112C2×C4—444no—
1113C2×C4C2×D4×D1112yes—
1114C2×C4C2×D4×D1112yes—
1115C2×C4#6703714yes—
1116C22—22no—
1117C22—22no—
1118C22—24no—
1119C22—24no—
1120C22—24no—
1121C22—24no—
1122C22—24no—
1123C22—416no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—41no—
1129C22—41no—
1130C22—41no—
1131C22—42no—
1132C22—42no—
1133C22—222no—
1134C22—222no—
1135C22—222no—
1136C22—222no—
1137C22—222no—
1138C22—222no—
1139C22—4416no—
1140C22—442no—
1141C22—442no—
1142C22—442no—
1143C22—442no—
1144C22—441no—
1145C22—441no—
1146C22—441no—
1147C22—442no—
1148C22—442no—
1149C22#1062307814yes—
1150C22C22×#433911yescharacteristic
1151C22C22×D4×D1111yescharacteristic
1152C22C2×#6703712yes—
1153C22C2×#41×D1111yescharacteristic
1154C22#1062345312yes—
1155C4—22no—
1156C4—41no—
1157C4—42no—
1158C4—41no—
1159C4—41no—
1160C4—42no—
1161C4—42no—
1162C4—224no—
1163C4—222no—
1164C4—222no—
1165C4—441no—
1166C4—441no—
1167C4—442no—
1168C4—441no—
1169C4—442no—
1170C4—442no—
1171C4#1062312014yes—
1172C2—24no—
1173C2—44no—
1174C2—81no—
1175C2—442no—
1176C2—442no—
1177C2—881no—
1178C2C2×#1062307811yescharacteristic
1179C2C2×#1062312011yescharacteristic
1180C2#1308194611yescharacteristic
1181C2#1308202512yes—
1182C2#1308203412yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#120C2
hypercenterC4×#120D11
hypocenterC11#34562
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#120

Complements

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

NH ≅ G/Ntype
1. C2×#10623078C2semidirect
2. C22×C4×C22⋊D11C2semidirect
3. #13074537C2semidirect
4. #13074504C2semidirect
5. #13074461C2semidirect
6. #13074459C2semidirect
7. #13074435C2semidirect
8. #13074425C2semidirect
9. #13074394C2semidirect
10. #13074393C2semidirect
11. #13074364C2semidirect
12. #13074354C2semidirect
13. #13074331C2semidirect
14. #13074330C2semidirect
15. #13071877C2semidirect
16. #13071860C2semidirect
17. #13071854C2semidirect
18. #13071831C2semidirect
19. C4×#66939C2semidirect
20. C4×#66988C2semidirect
21. C4×#67006C2semidirect
22. #13070997C2semidirect
23. C4×C11×#120C2semidirect
26. C22×#4339C22semidirect
30. C2×C4×D4×C11C22semidirect
42. C2×C4×C22⋊D11C22semidirect
43. C2×C4×C22⋊D11C22semidirect
48. C2×#66949C22semidirect
49. C2×#66947C22semidirect
51. C2×#66937C22semidirect
52. C2×#66936C22semidirect
55. C2×C4×D44C22semidirect
56. C2×#66925C22semidirect
57. C2×#66925C22semidirect
59. C11×#386C22semidirect
61. C11×#385C22semidirect
64. C4×C11×C22⋊C4C22semidirect
68. #10622836C22semidirect
69. #10622835C22semidirect
72. #10622826C22semidirect
74. #10622823C22semidirect
76. C4×C22⋊Dic11C22semidirect
77. C4×C22⋊Dic11C22semidirect
78. #10622606C22semidirect
79. #10622604C22semidirect
80. #10622593C22semidirect
81. #10622592C22semidirect
82. #10622591C22semidirect
85. #10622574C22semidirect
90. #10622572C22semidirect
91. #10622572C22semidirect
92. #10622572C22semidirect
96. #10622565C22semidirect
98. #10622562C22semidirect
99. #10622561C22semidirect
100. #10622561C22semidirect
101. #10622561C22semidirect
102. #10622560C22semidirect
104. #10622557C22semidirect
109. C4×(C2×D11)⋊C4C22semidirect
110. C4×(C2×D11)⋊C4C22semidirect
111. C4×C4⋊Dic11C22semidirect
112. C4×Dic11⋊C4C22semidirect
113. #10622289C22semidirect
114. #10622288C22semidirect
115. #10622288C22semidirect
116. #10622287C22semidirect
117. #10622285C22semidirect
118. #10622283C22semidirect
119. #10622280C22semidirect
120. #10622277C22semidirect
121. #10622271C22semidirect
122. #10622270C22semidirect
123. #10622270C22semidirect
124. #10622266C22semidirect
154. C22×C4×D11D4semidirect
266. C24×C11#41semidirect
330. C22×Dic11#41semidirect
435. C4×#120D11semidirect
575. C2×C4×D4C2×D11semidirect
623. #386C2×D11semidirect
629. #385C2×D11semidirect
648. C4×C22⋊C4C2×D11semidirect
864. C24#4339semidirect
1004. C11#34562semidirect

Maximal subgroups

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

subgroupindex
C2×#106230782
C22×C4×C22⋊D112
#130745372
#130745042
#130744612
#130744592
#130744352
#130744252
#130743942
#130743932
#130743642
#130743542
#130743312
#130743302
#130718772
#130718602
#130718542
#130718312
C4×#669392
C4×#669882
C4×#670062
#130709972
C4×C11×#1202
#3456211