Finite Group Databasebeta

← #14678219

Subgroups — #14678219

Order 2816.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C211yesmaximal, characteristic
2C2×#10622557C211yesmaximal, characteristic, complemented
3C2×#10622571C211yesmaximal, characteristic
4C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
5C2×#10622279C211yesmaximal, characteristic, complemented
6#13066882C211yesmaximal, characteristic, complemented
7#13066860C211yesmaximal, characteristic, complemented
8#13066855C211yesmaximal, characteristic
9#13066852C211yesmaximal, characteristic, complemented
10#13066850C211yesmaximal, characteristic, complemented
11#13066850C211yesmaximal, characteristic, complemented
12Dic11⋊#95C211yesmaximal, characteristic, complemented
13#13066838C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1440C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66936—24no—
36C2×#66936—24no—
37C2×#66936C418yescomplemented
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41C2×C11×#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49C2×C11⋊#95C2211yescharacteristic
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54#10622571—24no—
55#10622557—24no—
56C22⋊C4×Dic11—24no—
57#10622279—24no—
58C25×C11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—22no—
67C22×C22⋊D11—22no—
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11—41no—
71C22×C22⋊D11—41no—
72C22×C22⋊D11C2×C414yes—
73C23×Dic11—22no—
74C23×Dic11—22no—
75C23×Dic11—22no—
76C23×Dic11—22no—
77C23×Dic11—22no—
78C23×Dic11—41no—
79C23×Dic11—41no—
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C22×C4×D11—22no—
88C22×C4×D11—22no—
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—41no—
92C22×C4×D11—41no—
93C22×C4×D11C2×C414yescomplemented
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—41no—
102C2×C11×C22⋊C4C2×C414yes—
103C2×C22⋊Dic11—22no—
104C2×C22⋊Dic11—22no—
105C2×C22⋊Dic11—41no—
106C2×C22⋊Dic11C2×C414yes—
107C2×C22⋊Dic11D414yes—
108C2×C22⋊Dic11D414yes—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—22no—
117C2×(C2×D11)⋊C4—22no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—41no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4C2×C414yescomplemented
123C2×(C2×D11)⋊C4D414yes—
124C2×C4⋊Dic11—22no—
125C2×C4⋊Dic11—22no—
126C2×C4⋊Dic11C2×C414yescomplemented
127C2×Dic11⋊C4—22no—
128C2×Dic11⋊C4—22no—
129C2×Dic11⋊C4—22no—
130C2×Dic11⋊C4—22no—
131C2×Dic11⋊C4—41no—
132C2×Dic11⋊C4C2×C414yescomplemented
133C2×C4×Dic11—22no—
134C2×C4×Dic11—22no—
135C2×C4×Dic11—22no—
136C2×C4×Dic11—22no—
137C2×C4×Dic11—22no—
138C2×C4×Dic11—22no—
139C2×C4×Dic11—41no—
140C2×C4×Dic11—41no—
141C2×C4×Dic11—41no—
142#66936—232no—
143C11×#95—22no—
144C11×#95—22no—
145C11×#95—22no—
146C11×#95—41no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—22no—
156C11⋊#95—41no—
157C11⋊#95—41no—
158C11⋊#95—41no—
159#14096—111nomaximal, Sylow
160C24×C11—21no—
161C24×C11—21no—
162C24×C11—21no—
163C24×C11—21no—
164C24×C11—21no—
165C24×C11—21no—
166C24×C11—21no—
167C24×C11—21no—
168C24×C11—21no—
169C24×C11—21no—
170C24×C11—21no—
171C24×C11—21no—
172C24×C11C22×C412yes—
173C24×C11C2×D412yes—
174C24×C11C2×D412yes—
175C24×C11C2411yescharacteristic
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11—21no—
182C23×D11—21no—
183C23×D11—21no—
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11—21no—
188C23×D11C22×C412yes—
189C23×D11C2×D412yes—
190C23×D11#4112yes—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—21no—
199C22×C4×C11—21no—
200C22×C4×C11—21no—
201C22×C4×C11—21no—
202C22×C4×C11—21no—
203C22×C4×C11—21no—
204C22×C4×C11—21no—
205C22×C4×C11—21no—
206C22×C4×C11—21no—
207C22×C4×C11—21no—
208C22×C4×C11—21no—
209C22×C4×C11—21no—
210C22×C4×C11—21no—
211C22×C4×C11—21no—
212C22×C4×C11—21no—
213C22×C4×C11—21no—
214C22×C4×C11—21no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11—21no—
221C22×C4×C11—21no—
222C22×C4×C11—21no—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11C22×C412yes—
229C22×C4×C11C22×C412yes—
230C22×C4×C11C2×D412yes—
231C22×C4×C11#4112yes—
232C22×C4×C11#4112yes—
233C2×C22⋊D11—28no—
234C2×C22⋊D11—28no—
235C2×C22⋊D11—44no—
236C2×C22⋊D11—44no—
237C2×C22⋊D11—44no—
238C2×C22⋊D11—44no—
239C2×C22⋊D11—44no—
240C22×Dic11—28no—
241C22×Dic11—21no—
242C22×Dic11—21no—
243C22×Dic11—21no—
244C22×Dic11—21no—
245C22×Dic11—21no—
246C22×Dic11—21no—
247C22×Dic11—21no—
248C22×Dic11—21no—
249C22×Dic11—21no—
250C22×Dic11—21no—
251C22×Dic11—21no—
252C22×Dic11—21no—
253C22×Dic11—21no—
254C22×Dic11—21no—
255C22×Dic11—21no—
256C22×Dic11—21no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—21no—
260C22×Dic11—21no—
261C22×Dic11—21no—
262C22×Dic11—21no—
263C22×Dic11—21no—
264C22×Dic11—21no—
265C22×Dic11—21no—
266C22×Dic11—21no—
267C22×Dic11—21no—
268C22×Dic11—21no—
269C22×Dic11—21no—
270C22×Dic11—21no—
271C22×Dic11—21no—
272C22×Dic11—21no—
273C22×Dic11—21no—
274C22×Dic11—21no—
275C22×Dic11—21no—
276C22×Dic11—21no—
277C22×Dic11—21no—
278C22×Dic11—44no—
279C22×Dic11—44no—
280C22×Dic11—44no—
281C22×Dic11—44no—
282C22×Dic11—44no—
283C22×Dic11—44no—
284C22×Dic11C22×C412yes—
285C22×Dic11C22×C412yes—
286C22×Dic11C22×C412yes—
287C22×Dic11C2×D412yes—
288C22×Dic11C2×D412yes—
289C22×Dic11C2×D412yes—
290C22×Dic11C2×D412yes—
291C22×Dic11C2×D412yes—
292C22×Dic11#4112yes—
293C22×Dic11#4112yes—
294C22×Dic11#4112yes—
295C22×Dic11#4112yes—
296C2×C4×D11—28no—
297C2×C4×D11—28no—
298C2×C4×D11—44no—
299C2×C4×D11—44no—
300C2×C4×D11—44no—
301C2×C4×D11—44no—
302C2×C4×D11—44no—
303C11×C22⋊C4—28no—
304C11×C22⋊C4—28no—
305C11×C22⋊C4—44no—
306C22⋊Dic11—44no—
307C22⋊Dic11C22⋊C4116yescomplemented
308(C2×D11)⋊C4—28no—
309(C2×D11)⋊C4—28no—
310(C2×D11)⋊C4—28no—
311(C2×D11)⋊C4—44no—
312(C2×D11)⋊C4—44no—
313C4⋊Dic11—28no—
314Dic11⋊C4—28no—
315Dic11⋊C4—44no—
316C4×Dic11—44no—
317C4×Dic11—44no—
318C4×Dic11—44no—
319C22×#123—111no—
320C2×#388—111no—
321C2×#386—111no—
322C2×C4×C22⋊C4—111no—
323C2×C4×C22⋊C4—111no—
324#1445—111no—
325#1440D1111yescharacteristic, complemented
326#1439—111no—
327#1438—111no—
328#1437—111no—
329#1436—111no—
330#1436—111no—
331C4⋊#95—111no—
332C22⋊#95—111no—
333C22⋊#95—111no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—41no—
353C23×C11—41no—
354C23×C11—41no—
355C23×C11—41no—
356C23×C11—41no—
357C23×C11—41no—
358C23×C11—41no—
359C23×C11—41no—
360C23×C11—41no—
361C23×C11—41no—
362C23×C11—41no—
363C23×C11—41no—
364C23×C11—41no—
365C23×C11—41no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11C2×C22⋊C414yes—
369C23×C11C23×C411yescharacteristic
370C23×C11C22×D411yescharacteristic
371C23×C11C22×D411yescharacteristic
372C23×C11C22×D411yescharacteristic
373C23×C11C2×#4111yescharacteristic
374C23×C11C2×#4111yescharacteristic
375C23×C11C2×#4111yescharacteristic
376C23×C11C2×#4111yescharacteristic
377C23×C11C2×#4111yescharacteristic
378C23×C11C2×#4111yescharacteristic
379C23×C11C2×#4111yescharacteristic
380C23×C11H(5,𝔽2)11yescharacteristic
381C23×C11H(5,𝔽2)11yescharacteristic
382C23×C11H(5,𝔽2)11yescharacteristic
383C23×C112−1+411yescharacteristic
384C22×D11—22no—
385C22×D11—22no—
386C22×D11—22no—
387C22×D11—22no—
388C22×D11—22no—
389C22×D11—22no—
390C22×D11—22no—
391C22×D11—22no—
392C22×D11—22no—
393C22×D11—22no—
394C22×D11—22no—
395C22×D11—22no—
396C22×D11—22no—
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—41no—
403C22×D11—41no—
404C22×D11—41no—
405C22×D11—41no—
406C22×D11—41no—
407C22×D11—41no—
408C22×D11—41no—
409C22×D11—41no—
410C22×D11—41no—
411C22×D11—41no—
412C22×D11—41no—
413C22×D11—41no—
414C22×D11—41no—
415C22×D11—41no—
416C22×D11—41no—
417C22×D11—41no—
418C22×D11C4×D414yes—
419C2×C4×C11—22no—
420C2×C4×C11—22no—
421C2×C4×C11—22no—
422C2×C4×C11—22no—
423C2×C4×C11—22no—
424C2×C4×C11—22no—
425C2×C4×C11—22no—
426C2×C4×C11—22no—
427C2×C4×C11—22no—
428C2×C4×C11—22no—
429C2×C4×C11—22no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
436C2×C4×C11—41no—
437C2×C4×C11—41no—
438C2×C4×C11—41no—
439C2×C4×C11—41no—
440C2×C4×C11—41no—
441C2×C4×C11—41no—
442C2×C4×C11—41no—
443C2×C4×C11—41no—
444C2×C4×C11—41no—
445C2×C4×C11—41no—
446C2×C4×C11—41no—
447C2×C4×C11—41no—
448C2×C4×C11—41no—
449C2×C4×C11—41no—
450C2×C4×C11—41no—
451C2×C4×C11—41no—
452C2×C4×C11—41no—
453C2×C4×C11—41no—
454C2×C4×C11—41no—
455C2×C4×C11—41no—
456C2×C4×C11—41no—
457C2×C4×C11—41no—
458C2×C4×C11—41no—
459C2×C4×C11—41no—
460C2×C4×C11—41no—
461C22⋊D11—416no—
462C2×Dic11—22no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—22no—
466C2×Dic11—22no—
467C2×Dic11—22no—
468C2×Dic11—22no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—416no—
490C2×Dic11—41no—
491C2×Dic11—41no—
492C2×Dic11—41no—
493C2×Dic11—41no—
494C2×Dic11—41no—
495C2×Dic11—41no—
496C2×Dic11—41no—
497C2×Dic11—41no—
498C2×Dic11—41no—
499C2×Dic11—41no—
500C2×Dic11—41no—
501C2×Dic11—41no—
502C2×Dic11—41no—
503C2×Dic11—41no—
504C2×Dic11—41no—
505C2×Dic11—41no—
506C2×Dic11—41no—
507C2×Dic11—41no—
508C2×Dic11—41no—
509C2×Dic11C2×C22⋊C414yes—
510C2×Dic11C2×C22⋊C414yes—
511C2×Dic11#12314yescomplemented
512C4×D11—416no—
513C23×D4—111no—
514C24×C4—111no—
515C24×C4—111no—
516C2×#123—118no—
517C2×#123—224no—
518C2×#123—224no—
519C22×C4⋊C4—111no—
520C22×C4⋊C4—111no—
521C22×C4⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4—111no—
526C22×C22⋊C4—111no—
527C22×C22⋊C4—111no—
528C22×C22⋊C4—111no—
529C22×C22⋊C4C2×D1111yescharacteristic
530C22×C22⋊C4C2×D1111yescharacteristic
531C22×C22⋊C4C2×D1111yescharacteristic
532C22×C42—111no—
533C22×C42—111no—
534C22×C42—111no—
535#388—224no—
536#386—224no—
537C4×C22⋊C4—224no—
538C4×C22⋊C4—224no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95—111no—
543C2×#95—111no—
544C2×#95—111no—
545C2×#95—111no—
546C2×#95—111no—
547C2×#95—111no—
548C2×#95—111no—
549C2×#95—111no—
550C2×#95—111no—
551C2×#95C2×D1111yescharacteristic
552C2×#95C2×D1111yescharacteristic
553C2×#95C2×D1111yescharacteristic
554C2×#95C2×D1111yescharacteristic
555C22×C11—24no—
556C22×C11—24no—
557C22×C11—24no—
558C22×C11—42no—
559C22×C11—42no—
560C22×C11—42no—
561C22×C11—42no—
562C22×C11—42no—
563C22×C11—42no—
564C22×C11—42no—
565C22×C11—42no—
566C22×C11—42no—
567C22×C11—42no—
568C22×C11—42no—
569C22×C11—42no—
570C22×C11C22×C22⋊C411yescharacteristic
571C22×C11C2×C4×D411yescharacteristic
572C22×C11C4×#4111yescharacteristic
573C22×C11C4×#4111yescharacteristic
574C22×C11C4×#4111yescharacteristic
575C22×C11#51811yescharacteristic
576C22×C11#52011yescharacteristic
577C22×C11C2×#12311yescharacteristic
578C22×C11#52511yescharacteristic
579C22×C11#52511yescharacteristic
580C22×C11#52511yescharacteristic
581C22×C11#52911yescharacteristic
582C22×C11#52911yescharacteristic
583C22×C11#53211yescharacteristic
584C22×C11#53211yescharacteristic
585C22×C11#53811yescharacteristic
586C22×C11#53911yescharacteristic
587C22×C11#54011yescharacteristic
588C22×C11#54211yescharacteristic
589C22×C11D4211yescharacteristic
590C22×C11D4211yescharacteristic
591C22×C11#54611yescharacteristic
592C22×C11#54611yescharacteristic
593C22×C11#54611yescharacteristic
594C22×C11#54611yescharacteristic
595C22×C11#54611yescharacteristic
596C22×C11#54711yescharacteristic
597C22×C11#54711yescharacteristic
598C22×C11#54711yescharacteristic
599C22×C11#55111yescharacteristic
600C22×C11#55111yescharacteristic
601C22×C11#55211yescharacteristic
602C22×C11#55311yescharacteristic
603C22×C11#55311yescharacteristic
604C22×C11#55911yescharacteristic
605C2×D11—24no—
606C2×D11—24no—
607C2×D11—24no—
608C2×D11—42no—
609C2×D11—42no—
610C2×D11—42no—
611C2×D11—42no—
612C2×D11—42no—
613C2×D11—42no—
614C2×D11—42no—
615C2×D11—42no—
616C2×D11—42no—
617C2×D11—42no—
618C2×D11—42no—
619C2×D11—42no—
620C4×C11—42no—
621C4×C11—42no—
622C4×C11—42no—
623C4×C11—42no—
624C4×C11—42no—
625C4×C11—81no—
626Dic11—24no—
627Dic11—24no—
628Dic11—24no—
629Dic11—42no—
630Dic11—42no—
631Dic11—42no—
632Dic11—81no—
633C25—111no—
634C25C22×D1111yescharacteristic
635C22×D4—114no—
636C22×D4—222no—
637C22×D4—222no—
638C22×D4—222no—
639C22×D4—222no—
640C22×D4—441no—
641C22×D4—441no—
642C23×C4—111no—
643C23×C4—111no—
644C23×C4—111no—
645C23×C4—111no—
646C23×C4—111no—
647C23×C4—111no—
648C23×C4—114no—
649C23×C4—111no—
650C23×C4—222no—
651C23×C4—222no—
652C23×C4—222no—
653C23×C4—222no—
654C23×C4—222no—
655C23×C4—222no—
656C23×C4—222no—
657C23×C4—222no—
658C23×C4—222no—
659C23×C4—441no—
660C23×C4—441no—
661C23×C4—441no—
662C23×C4—441no—
663C23×C4C22×D1111yescharacteristic
664C23×C4C22×D1111yescharacteristic
665C23×C4C22×D1111yescharacteristic
666C23×C4C22×D1111yescharacteristic
667C23×C4C22×D1111yescharacteristic
668C23×C4C22×D1111yescharacteristic
669#123—2232no—
670C2×C4⋊C4—114no—
671C2×C4⋊C4—114no—
672C2×C4⋊C4—222no—
673C2×C4⋊C4—222no—
674C2×C4⋊C4—222no—
675C2×C4⋊C4—222no—
676C2×C4⋊C4—222no—
677C2×C4⋊C4—222no—
678C2×C4⋊C4—441no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—41no—
687C2×C22⋊C4—114no—
688C2×C22⋊C4—114no—
689C2×C22⋊C4—114no—
690C2×C22⋊C4—114no—
691C2×C22⋊C4—114no—
692C2×C22⋊C4—222no—
693C2×C22⋊C4—222no—
694C2×C22⋊C4—222no—
695C2×C22⋊C4—222no—
696C2×C22⋊C4—222no—
697C2×C22⋊C4—222no—
698C2×C22⋊C4—222no—
699C2×C22⋊C4—222no—
700C2×C22⋊C4—222no—
701C2×C22⋊C4—222no—
702C2×C22⋊C4—222no—
703C2×C22⋊C4—222no—
704C2×C22⋊C4—222no—
705C2×C22⋊C4—441no—
706C2×C22⋊C4—441no—
707C2×C22⋊C4—441no—
708C2×C22⋊C4C4×D1114yes—
709C2×C42—222no—
710C2×C42—222no—
711C2×C42—222no—
712C2×C42—222no—
713C2×C42—222no—
714C2×C42—222no—
715C2×C42—441no—
716C2×C42—441no—
717C2×C42—441no—
718#95—22no—
719#95—22no—
720#95—22no—
721#95—41no—
722#95—222no—
723#95—222no—
724#95—222no—
725#95—222no—
726#95—222no—
727#95—222no—
728#95—222no—
729#95—222no—
730#95—222no—
731#95—441no—
732#95—441no—
733#95—441no—
734C2×C11—44no—
735C2×C11#229711yescharacteristic
736C2×C11C4×#12311yescharacteristic
737C2×C11#233511yescharacteristic
738C2×C11D4×C22⋊C411yescharacteristic
739C2×C11#233911yescharacteristic
740C2×C11#235911yescharacteristic
741C2×C11#237411yescharacteristic
742C2×C11#241811yescharacteristic
743C2×C11#242211yescharacteristic
744C2×C11#245511yescharacteristic
745C2×C11#245711yescharacteristic
746C2×C11#246411yescharacteristic
747C2×C11#247011yescharacteristic
748C2×C11#255311yescharacteristic
749C2×C11#255711yescharacteristic
750D11—44no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—112no—
764C24—112no—
765C24—112no—
766C24—221no—
767C24—221no—
768C24—221no—
769C24—221no—
770C24—221no—
771C24—221no—
772C24—221no—
773C24—221no—
774C24—221no—
775C24—221no—
776C24—221no—
777C24—221no—
778C24C2×C4×D1112yes—
779C24D4×D1112yes—
780C24D4×D1112yes—
781C24C23×D1111yescharacteristic
782C2×D4—228no—
783C2×D4—228no—
784C2×D4—444no—
785C2×D4—444no—
786C2×D4—444no—
787C2×D4—444no—
788C2×D4—444no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—112no—
827C22×C4—112no—
828C22×C4—112no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—112no—
832C22×C4—112no—
833C22×C4—112no—
834C22×C4—112no—
835C22×C4—112no—
836C22×C4—112no—
837C22×C4—112no—
838C22×C4—228no—
839C22×C4—228no—
840C22×C4—221no—
841C22×C4—221no—
842C22×C4—221no—
843C22×C4—221no—
844C22×C4—221no—
845C22×C4—221no—
846C22×C4—221no—
847C22×C4—221no—
848C22×C4—221no—
849C22×C4—221no—
850C22×C4—221no—
851C22×C4—221no—
852C22×C4—228no—
853C22×C4—221no—
854C22×C4—221no—
855C22×C4—221no—
856C22×C4—221no—
857C22×C4—221no—
858C22×C4—221no—
859C22×C4—221no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—221no—
865C22×C4—221no—
866C22×C4—221no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—221no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—444no—
879C22×C4—444no—
880C22×C4—444no—
881C22×C4—444no—
882C22×C4—444no—
883C22×C4—444no—
884C22×C4—444no—
885C22×C4—444no—
886C22×C4—444no—
887C22×C4—444no—
888C22×C4—444no—
889C22×C4C2×C4×D1112yes—
890C22×C4C2×C4×D1112yes—
891C22×C4D4×D1112yes—
892C22×C4#434112yes—
893C22×C4#434112yes—
894C4⋊C4—228no—
895C4⋊C4—228no—
896C4⋊C4—444no—
897C22⋊C4—28no—
898C22⋊C4—28no—
899C22⋊C4—44no—
900C22⋊C4—1116no—
901C22⋊C4—228no—
902C22⋊C4—228no—
903C22⋊C4—228no—
904C22⋊C4—444no—
905C22⋊C4—444no—
906C22⋊C4—444no—
907C42—444no—
908C42—444no—
909C42—444no—
910C11#1409611yescharacteristic, complemented, Sylow
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—114no—
946C23—222no—
947C23—222no—
948C23—222no—
949C23—222no—
950C23—222no—
951C23—222no—
952C23—222no—
953C23—222no—
954C23—222no—
955C23—222no—
956C23—222no—
957C23—222no—
958C23—222no—
959C23—222no—
960C23—222no—
961C23—222no—
962C23—222no—
963C23—222no—
964C23—441no—
965C23—441no—
966C23—441no—
967C23—441no—
968C23—441no—
969C23—441no—
970C23—441no—
971C23—441no—
972C23—441no—
973C23—441no—
974C23—441no—
975C23—441no—
976C23—441no—
977C23—441no—
978C23—441no—
979C23—441no—
980C23C22⋊C4×D1114yes—
981C23C22×C4×D1111yescharacteristic
982C23C2×D4×D1111yescharacteristic
983C23C2×D4×D1111yescharacteristic
984C23C2×D4×D1111yescharacteristic
985C23C2×#434111yescharacteristic
986C23C2×#434111yescharacteristic
987C23#6703711yescharacteristic
988C23#41×D1111yescharacteristic
989C23#41×D1111yescharacteristic
990C23#41×D1111yescharacteristic
991C23#41×D1111yescharacteristic
992C23#41×D1111yescharacteristic
993C23#6704211yescharacteristic
994C23#6704211yescharacteristic
995C23#6704311yescharacteristic
996D4—4416no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—114no—
1040C2×C4—114no—
1041C2×C4—114no—
1042C2×C4—222no—
1043C2×C4—222no—
1044C2×C4—222no—
1045C2×C4—222no—
1046C2×C4—222no—
1047C2×C4—222no—
1048C2×C4—222no—
1049C2×C4—222no—
1050C2×C4—222no—
1051C2×C4—222no—
1052C2×C4—222no—
1053C2×C4—222no—
1054C2×C4—222no—
1055C2×C4—222no—
1056C2×C4—222no—
1057C2×C4—222no—
1058C2×C4—222no—
1059C2×C4—222no—
1060C2×C4—222no—
1061C2×C4—222no—
1062C2×C4—222no—
1063C2×C4—222no—
1064C2×C4—222no—
1065C2×C4—222no—
1066C2×C4—222no—
1067C2×C4—222no—
1068C2×C4—222no—
1069C2×C4—4416no—
1070C2×C4—4416no—
1071C2×C4—441no—
1072C2×C4—441no—
1073C2×C4—441no—
1074C2×C4—441no—
1075C2×C4—441no—
1076C2×C4—441no—
1077C2×C4—441no—
1078C2×C4—441no—
1079C2×C4—441no—
1080C2×C4—441no—
1081C2×C4—441no—
1082C2×C4—441no—
1083C2×C4—441no—
1084C2×C4—441no—
1085C2×C4—441no—
1086C2×C4—441no—
1087C2×C4—441no—
1088C2×C4—441no—
1089C2×C4—441no—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—224no—
1106C22—224no—
1107C22—224no—
1108C22—442no—
1109C22—442no—
1110C22—442no—
1111C22—442no—
1112C22—442no—
1113C22—442no—
1114C22—442no—
1115C22—442no—
1116C22—442no—
1117C22—442no—
1118C22—442no—
1119C22—442no—
1120C22C2×C22⋊C4×D1111yescharacteristic
1121C22#1062305311yescharacteristic
1122C22#1062305411yescharacteristic
1123C22C4×#434111yescharacteristic
1124C22C4×#434111yescharacteristic
1125C22C4×D4×D1111yescharacteristic
1126C22#1062307611yescharacteristic
1127C22#1062311711yescharacteristic
1128C22#1062312111yescharacteristic
1129C22#1062312711yescharacteristic
1130C22#1062312711yescharacteristic
1131C22#1062313211yescharacteristic
1132C22#1062313711yescharacteristic
1133C22#1062314011yescharacteristic
1134C22#1062314111yescharacteristic
1135C22#1062314211yescharacteristic
1136C22#1062315011yescharacteristic
1137C22D11×#12311yescharacteristic
1138C22#1062318511yescharacteristic
1139C22#1062318511yescharacteristic
1140C22#1062318511yescharacteristic
1141C22#1062318611yescharacteristic
1142C22#1062318611yescharacteristic
1143C22#1062318711yescharacteristic
1144C22#1062318911yescharacteristic
1145C22#1062319211yescharacteristic
1146C22#1062319611yescharacteristic
1147C22#1062320011yescharacteristic
1148C22#1062320711yescharacteristic
1149C22#1062321111yescharacteristic
1150C22#1062321211yescharacteristic
1151C22#1062323511yescharacteristic
1152C22#1062323611yescharacteristic
1153C22#1062323711yescharacteristic
1154C22#1062323911yescharacteristic
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—42no—
1160C4—81no—
1161C4—224no—
1162C4—224no—
1163C4—224no—
1164C4—442no—
1165C4—442no—
1166C4—442no—
1167C4—881no—
1168C2—44no—
1169C2—444no—
1170C2#1307110111yescharacteristic
1171C2#1307114311yescharacteristic
1172C2#1307141311yescharacteristic
1173C2#1307143411yescharacteristic
1174C2#1307144011yescharacteristic
1175C2#1307160711yescharacteristic
1176C2#1307174411yescharacteristic
1177C2#1307207911yescharacteristic
1178C2#1307212311yescharacteristic
1179C2#1307249411yescharacteristic
1180C2#1307251811yescharacteristic
1181C2#1307262311yescharacteristic
1182C2#1307270711yescharacteristic
1183C2#1307365611yescharacteristic
1184C2#1307371011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1440C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1440D11
hypocenterC11#14096
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. C2×#10622557C2semidirect
4. C2×C22⋊C4×Dic11C2semidirect
5. C2×#10622279C2semidirect
6. #13066882C2semidirect
7. #13066860C2semidirect
9. #13066852C2semidirect
10. #13066850C2semidirect
11. #13066850C2semidirect
12. Dic11⋊#95C2semidirect
13. #13066838C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1440C2semidirect
37. C2×#66936C4semidirect
93. C22×C4×D11C2×C4semidirect
122. C2×(C2×D11)⋊C4C2×C4semidirect
126. C2×C4⋊Dic11C2×C4semidirect
132. C2×Dic11⋊C4C2×C4semidirect
307. C22⋊Dic11C22⋊C4semidirect
325. #1440D11semidirect
511. C2×Dic11#123semidirect
910. C11#14096semidirect

Maximal subgroups

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

subgroupindex
C22×#669362
C2×#106225572
C2×#106225712
C2×C22⋊C4×Dic112
C2×#106222792
#130668822
#130668602
#130668552
#130668522
#130668502
Dic11⋊#952
#130668382
(C2×D11)⋊#952
C11×#14402
#1409611