Finite Group Databasebeta

← #14677147

Subgroups — #14677147

Order 2816.

2590 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2C2×#10622569C211yesmaximal, characteristic
3C2×#10622569C211yesmaximal, characteristic
4C2×#10622602C211yesmaximal, characteristic, complemented
5C2×D11×#95C211yesmaximal, characteristic, complemented
6#13066874C211yesmaximal, characteristic, complemented
7#13066871C211yesmaximal, characteristic, complemented
8#13066859C211yesmaximal, characteristic, complemented
9#13066851C211yesmaximal, characteristic, complemented
10#13066848C211yesmaximal, characteristic, complemented
11#13066838C211yesmaximal, characteristic, complemented
12#13066838C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C2×(C22⋊D11)⋊C4—24no—
34C2×(C22⋊D11)⋊C4—24no—
35C2×(C22⋊D11)⋊C4—24no—
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2211yescharacteristic
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#10622602—24no—
55#10622569—24no—
56#10622569C418yescomplemented
57D11×#95—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⋊D11C2×C414yes—
71C22×C22⋊D11D414yes—
72C22×C22⋊D11Q814yes—
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—22no—
92C22×C4×D11—22no—
93C22×C4×D11—22no—
94C22×C4×D11—22no—
95C22×C4×D11—22no—
96C22×C4×D11—22no—
97C22×C4×D11—22no—
98C22×C4×D11—41no—
99C22×C4×D11—41no—
100C22×C4×D11—41no—
101C22×C4×D11—41no—
102C22×C4×D11—41no—
103C22×C4×D11—41no—
104C22×C4×D11—41no—
105C22×C4×D11—41no—
106C22×C4×D11C2×C414yescomplemented
107C22×C4×D11D414yes—
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4—22no—
110C2×C11×C4⋊C4—41no—
111C2×C11×C22⋊C4—22no—
112C2×C11×C22⋊C4—22no—
113C2×C11×C22⋊C4—22no—
114C2×C11×C22⋊C4—22no—
115C2×C11×C22⋊C4—22no—
116C2×C11×C22⋊C4—41no—
117C2×C11×C22⋊C4—41no—
118C2×C11×C22⋊C4—41no—
119C2×C11×C22⋊C4C2×C414yescomplemented
120C2×C22⋊Dic11—22no—
121C2×C22⋊Dic11—22no—
122C2×C22⋊Dic11—41no—
123C2×C22⋊Dic11—41no—
124C2×C22⋊Dic11—41no—
125C2×C22⋊Dic11C2×C414yescomplemented
126C2×(C2×D11)⋊C4—22no—
127C2×(C2×D11)⋊C4—22no—
128C2×(C2×D11)⋊C4—22no—
129C2×(C2×D11)⋊C4—22no—
130C2×(C2×D11)⋊C4—22no—
131C2×(C2×D11)⋊C4—22no—
132C2×(C2×D11)⋊C4—22no—
133C2×(C2×D11)⋊C4C2×C414yescomplemented
134C2×(C2×D11)⋊C4D414yes—
135C2×Dic11⋊C4—22no—
136C2×Dic11⋊C4—22no—
137C2×Dic11⋊C4—22no—
138C2×Dic11⋊C4—22no—
139C2×Dic11⋊C4—22no—
140C2×Dic11⋊C4—41no—
141C2×C4×Dic11—22no—
142C2×C4×Dic11—22no—
143C2×C4×Dic11—22no—
144(C22⋊D11)⋊C4—232no—
145C11×#95—22no—
146C11×#95—41no—
147C11×#95—41no—
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—22no—
157C11⋊#95—41no—
158C11⋊#95—41no—
159C11⋊#95—41no—
160C11⋊#95—41no—
161C11⋊#95C2×C414yescomplemented
162C11⋊#95C2×C414yescomplemented
163#14016—111nomaximal, Sylow
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×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11C22×C412yes—
177C24×C11C2×D412yes—
178C24×C11C2×Q812yes—
179C24×C11C2411yescharacteristic
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×D11C2×D412yes—
191C23×D11C2×D412yes—
192C23×D11C2×Q812yes—
193C23×D11#4112yes—
194C23×D11#4112yes—
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×C11—21no—
229C22×C4×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11C22×C412yes—
233C22×C4×C11C22×C412yes—
234C22×C4×C11C2×D412yes—
235C22×C4×C11C2×D412yes—
236C22×C4×C11#4112yes—
237C2×C22⋊D11—28no—
238C2×C22⋊D11—28no—
239C2×C22⋊D11—28no—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—28no—
242C2×C22⋊D11—28no—
243C2×C22⋊D11C4⋊C4116yescomplemented
244C22×Dic11—28no—
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—21no—
279C22×Dic11—21no—
280C22×Dic11—21no—
281C22×Dic11—21no—
282C22×Dic11—21no—
283C22×Dic11—21no—
284C22×Dic11—44no—
285C22×Dic11—44no—
286C22×Dic11—44no—
287C22×Dic11—44no—
288C22×Dic11—44no—
289C22×Dic11—44no—
290C22×Dic11C22×C412yes—
291C22×Dic11C22×C412yes—
292C22×Dic11C22×C412yes—
293C22×Dic11C2×D412yes—
294C22×Dic11C2×D412yes—
295C22×Dic11C2×D412yes—
296C22×Dic11C2×Q812yes—
297C22×Dic11#4112yes—
298C22×Dic11#4112yes—
299C22×Dic11#4112yes—
300C2×C4×D11—28no—
301C2×C4×D11—28no—
302C2×C4×D11—28no—
303C2×C4×D11—28no—
304C2×C4×D11—44no—
305C2×C4×D11—44no—
306C2×C4×D11—44no—
307C2×C4×D11—44no—
308C2×C4×D11—44no—
309C2×C4×D11—44no—
310C2×C4×D11—44no—
311C2×C4×D11—44no—
312C2×C4×D11—44no—
313C2×C4×D11—44no—
314C2×C4×D11—44no—
315C2×C4×D11—44no—
316C2×C4×D11—44no—
317C2×C4×D11—44no—
318C2×C4×D11—44no—
319C2×C4×D11—44no—
320C2×C4×D11—44no—
321C11×C4⋊C4—44no—
322C11×C22⋊C4—28no—
323C11×C22⋊C4—44no—
324C11×C22⋊C4—44no—
325C22⋊Dic11—44no—
326C22⋊Dic11—44no—
327(C2×D11)⋊C4—28no—
328(C2×D11)⋊C4—28no—
329(C2×D11)⋊C4—44no—
330Dic11⋊C4—28no—
331Dic11⋊C4—44no—
332C4×Dic11—28no—
333C22×C4×D4—111no—
334C2×#386—111no—
335C2×#386—111no—
336C2×#385—111no—
337C22×#95—111no—
338#1442—111no—
339#1442—111no—
340#1439—111no—
341#1439D1111yescharacteristic, complemented
342#1436—111no—
343#1436—111no—
344C22⋊#95—111no—
345C22⋊#95—111no—
346C22⋊#95—111no—
347C22⋊#95—111no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
365C23×C11—22no—
366C23×C11—41no—
367C23×C11—41no—
368C23×C11—41no—
369C23×C11—41no—
370C23×C11—41no—
371C23×C11—41no—
372C23×C11—41no—
373C23×C11—41no—
374C23×C11—41no—
375C23×C11—41no—
376C23×C11—41no—
377C23×C11—41no—
378C23×C11—41no—
379C23×C11—41no—
380C23×C11—41no—
381C23×C11—41no—
382C23×C11C2×C4⋊C414yes—
383C23×C11C23×C411yescharacteristic
384C23×C11C22×D411yescharacteristic
385C23×C11C22×D411yescharacteristic
386C23×C11C22×D411yescharacteristic
387C23×C11C22×Q811yescharacteristic
388C23×C11C2×#4111yescharacteristic
389C23×C11C2×#4111yescharacteristic
390C23×C11C2×#4111yescharacteristic
391C23×C11C2×#4111yescharacteristic
392C23×C11C2×#4111yescharacteristic
393C23×C11C2×#4111yescharacteristic
394C23×C11H(5,𝔽2)11yescharacteristic
395C23×C11H(5,𝔽2)11yescharacteristic
396C23×C11H(5,𝔽2)11yescharacteristic
397C23×C11H(5,𝔽2)11yescharacteristic
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—22no—
423C22×D11—22no—
424C22×D11—22no—
425C22×D11—22no—
426C22×D11C2×C4⋊C414yes—
427C22×D11C4×D414yes—
428C22×D11C4×D414yes—
429C22×D11#12014yes—
430C22×D11C22⋊Q814yes—
431C22×D11C22⋊Q814yes—
432C22×D11#12314yes—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
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—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C2×C4×C11—41no—
475C22⋊D11—232no—
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—22no—
490C2×Dic11—22no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—22no—
494C2×Dic11—22no—
495C2×Dic11—22no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—416no—
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×Dic11—41no—
510C2×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—41no—
513C2×Dic11—41no—
514C2×Dic11—41no—
515C2×Dic11—41no—
516C2×Dic11—41no—
517C2×Dic11—41no—
518C2×Dic11—41no—
519C2×Dic11—41no—
520C2×Dic11—41no—
521C2×Dic11—41no—
522C2×Dic11—41no—
523C2×Dic11—41no—
524C2×Dic11C2×C4⋊C414yes—
525C2×Dic11#12314yes—
526C4×D11—416no—
527C4×D11—416no—
528C4×D11—416no—
529C23×D4—111no—
530C24×C4—111no—
531C24×C4—111no—
532C24×C4—111no—
533C24×C4—111no—
534C2×C4×D4—224no—
535C2×C4×D4—224no—
536C2×C4×D4—224no—
537C22×C4⋊C4—111no—
538C22×C4⋊C4—111no—
539C22×C4⋊C4C2×D1111yescharacteristic
540C22×C22⋊C4—111no—
541C22×C22⋊C4—111no—
542C22×C22⋊C4—111no—
543C22×C22⋊C4—111no—
544C22×C22⋊C4—111no—
545C22×C22⋊C4C2×D1111yescharacteristic
546C22×C22⋊C4C2×D1111yescharacteristic
547C22×C22⋊C4C2×D1111yescharacteristic
548C22×C42—111no—
549#386—118no—
550#386—224no—
551#385—224no—
552C2×#95—111no—
553C2×#95—111no—
554C2×#95—111no—
555C2×#95—111no—
556C2×#95—111no—
557C2×#95—111no—
558C2×#95—111no—
559C2×#95—111no—
560C2×#95—111no—
561C2×#95—111no—
562C2×#95—111no—
563C2×#95—111no—
564C2×#95—111no—
565C2×#95—111no—
566C2×#95—111no—
567C2×#95—224no—
568C2×#95C2×D1111yescharacteristic
569C2×#95C2×D1111yescharacteristic
570C2×#95C2×D1111yescharacteristic
571C22×C11—24no—
572C22×C11—24no—
573C22×C11—24no—
574C22×C11—42no—
575C22×C11—42no—
576C22×C11—42no—
577C22×C11—42no—
578C22×C11—42no—
579C22×C11—42no—
580C22×C11—42no—
581C22×C11—42no—
582C22×C11—42no—
583C22×C11—42no—
584C22×C11—42no—
585C22×C11—42no—
586C22×C11C22×C4⋊C411yescharacteristic
587C22×C11C2×C4×D411yescharacteristic
588C22×C11C2×C4×D411yescharacteristic
589C22×C11C4×#4111yescharacteristic
590C22×C11C4×#4111yescharacteristic
591C22×C11#51811yescharacteristic
592C22×C11#51811yescharacteristic
593C22×C11C2×#12011yescharacteristic
594C22×C11C2×C22⋊Q811yescharacteristic
595C22×C11C2×C22⋊Q811yescharacteristic
596C22×C11C2×#12311yescharacteristic
597C22×C11C2×#12311yescharacteristic
598C22×C11#52511yescharacteristic
599C22×C11#52911yescharacteristic
600C22×C11#52911yescharacteristic
601C22×C11#53411yescharacteristic
602C22×C11#53511yescharacteristic
603C22×C11#53811yescharacteristic
604C22×C11#53811yescharacteristic
605C22×C11#54611yescharacteristic
606C22×C11#54611yescharacteristic
607C22×C11#54611yescharacteristic
608C22×C11#54611yescharacteristic
609C22×C11#54611yescharacteristic
610C22×C11#54611yescharacteristic
611C22×C11#54611yescharacteristic
612C22×C11#54611yescharacteristic
613C22×C11#55311yescharacteristic
614C22×C11#55311yescharacteristic
615C22×C11#55311yescharacteristic
616C22×C11#55311yescharacteristic
617C22×C11#55411yescharacteristic
618C22×C11#55411yescharacteristic
619C22×C11#55411yescharacteristic
620C22×C11#55411yescharacteristic
621C2×D11—24no—
622C2×D11—24no—
623C2×D11—24no—
624C2×D11—24no—
625C2×D11—24no—
626C2×D11—24no—
627C2×D11—24no—
628C2×D11—24no—
629C2×D11—24no—
630C2×D11—24no—
631C2×D11—24no—
632C2×D11—24no—
633C2×D11—24no—
634C2×D11—24no—
635C2×D11#38518yes—
636C4×C11—42no—
637C4×C11—42no—
638C4×C11—42no—
639C4×C11—42no—
640C4×C11—42no—
641C4×C11—81no—
642Dic11—24no—
643Dic11—24no—
644Dic11—42no—
645Dic11—42no—
646Dic11—42no—
647Dic11—42no—
648Dic11—81no—
649C25—111no—
650C25C22×D1111yescharacteristic
651C22×D4—114no—
652C22×D4—114no—
653C22×D4—114no—
654C22×D4—222no—
655C22×D4—222no—
656C22×D4—222no—
657C22×D4—222no—
658C23×C4—111no—
659C23×C4—111no—
660C23×C4—111no—
661C23×C4—111no—
662C23×C4—111no—
663C23×C4—111no—
664C23×C4—114no—
665C23×C4—114no—
666C23×C4—111no—
667C23×C4—222no—
668C23×C4—222no—
669C23×C4—222no—
670C23×C4—222no—
671C23×C4—222no—
672C23×C4—222no—
673C23×C4—222no—
674C23×C4—222no—
675C23×C4—222no—
676C23×C4—222no—
677C23×C4—222no—
678C23×C4—222no—
679C23×C4—222no—
680C23×C4—222no—
681C23×C4—222no—
682C23×C4—222no—
683C23×C4—441no—
684C23×C4—441no—
685C23×C4—441no—
686C23×C4—441no—
687C23×C4—441no—
688C23×C4—441no—
689C23×C4—441no—
690C23×C4—441no—
691C23×C4—441no—
692C23×C4—441no—
693C23×C4C22×D1111yescharacteristic
694C23×C4C22×D1111yescharacteristic
695C23×C4C22×D1111yescharacteristic
696C23×C4C22×D1111yescharacteristic
697C23×C4C22×D1111yescharacteristic
698C23×C4C22×D1111yescharacteristic
699C4×D4—2232no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—41no—
703C2×C4⋊C4—222no—
704C2×C4⋊C4—222no—
705C2×C4⋊C4—222no—
706C2×C4⋊C4—222no—
707C2×C4⋊C4—222no—
708C2×C4⋊C4—441no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4—114no—
718C2×C22⋊C4—114no—
719C2×C22⋊C4—114no—
720C2×C22⋊C4—222no—
721C2×C22⋊C4—222no—
722C2×C22⋊C4—222no—
723C2×C22⋊C4—222no—
724C2×C22⋊C4—222no—
725C2×C22⋊C4—222no—
726C2×C22⋊C4—222no—
727C2×C22⋊C4—222no—
728C2×C22⋊C4—222no—
729C2×C22⋊C4—441no—
730C2×C22⋊C4—441no—
731C2×C22⋊C4—441no—
732C2×C22⋊C4C4×D1114yescomplemented
733C2×C42—222no—
734C2×C42—222no—
735C2×C42—222no—
736#95—22no—
737#95—41no—
738#95—41no—
739#95—114no—
740#95—114no—
741#95—222no—
742#95—222no—
743#95—222no—
744#95—222no—
745#95—222no—
746#95—222no—
747#95—222no—
748#95—222no—
749#95—222no—
750#95—441no—
751#95—441no—
752#95—441no—
753#95—441no—
754C2×C11—44no—
755C2×C11C2×#38511yescharacteristic
756C2×C11C4×#12311yescharacteristic
757C2×C11#232111yescharacteristic
758C2×C11#234911yescharacteristic
759C2×C11#234911yescharacteristic
760C2×C11#236411yescharacteristic
761C2×C11#236411yescharacteristic
762C2×C11#240411yescharacteristic
763C2×C11#240511yescharacteristic
764C2×C11#244411yescharacteristic
765C2×C11#244411yescharacteristic
766C2×C11#245011yescharacteristic
767C2×C11#245011yescharacteristic
768C2×C11#248711yescharacteristic
769C2×C11#257911yescharacteristic
770D11—28no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—112no—
784C24—112no—
785C24—112no—
786C24—112no—
787C24—112no—
788C24—112no—
789C24—112no—
790C24—221no—
791C24—221no—
792C24—221no—
793C24—221no—
794C24—221no—
795C24—221no—
796C24—221no—
797C24—221no—
798C24C2×C4×D1112yes—
799C24D4×D1112yes—
800C24Q8×D1112yes—
801C24C23×D1111yescharacteristic
802C2×D4—1116no—
803C2×D4—228no—
804C2×D4—228no—
805C2×D4—228no—
806C2×D4—228no—
807C2×D4—228no—
808C2×D4—228no—
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—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—112no—
847C22×C4—112no—
848C22×C4—112no—
849C22×C4—112no—
850C22×C4—112no—
851C22×C4—112no—
852C22×C4—112no—
853C22×C4—112no—
854C22×C4—112no—
855C22×C4—112no—
856C22×C4—228no—
857C22×C4—228no—
858C22×C4—228no—
859C22×C4—228no—
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—228no—
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—221no—
879C22×C4—221no—
880C22×C4—221no—
881C22×C4—221no—
882C22×C4—221no—
883C22×C4—221no—
884C22×C4—221no—
885C22×C4—221no—
886C22×C4—221no—
887C22×C4—221no—
888C22×C4—221no—
889C22×C4—221no—
890C22×C4—221no—
891C22×C4—221no—
892C22×C4—221no—
893C22×C4—221no—
894C22×C4—221no—
895C22×C4—221no—
896C22×C4—221no—
897C22×C4—221no—
898C22×C4—221no—
899C22×C4—221no—
900C22×C4—444no—
901C22×C4—444no—
902C22×C4—444no—
903C22×C4—444no—
904C22×C4—444no—
905C22×C4—444no—
906C22×C4—444no—
907C22×C4—444no—
908C22×C4—444no—
909C22×C4—444no—
910C22×C4—444no—
911C22×C4—444no—
912C22×C4—444no—
913C22×C4—444no—
914C22×C4—444no—
915C22×C4—444no—
916C22×C4—444no—
917C22×C4—444no—
918C22×C4—444no—
919C22×C4—444no—
920C22×C4—444no—
921C22×C4—444no—
922C22×C4—444no—
923C22×C4C2×C4×D1112yes—
924C22×C4C2×C4×D1112yes—
925C22×C4D4×D1112yes—
926C22×C4D4×D1112yes—
927C22×C4#434112yes—
928C4⋊C4—44no—
929C4⋊C4—228no—
930C4⋊C4—444no—
931C22⋊C4—28no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—228no—
935C22⋊C4—228no—
936C22⋊C4—444no—
937C22⋊C4—444no—
938C22⋊C4—444no—
939C42—228no—
940C11#1401611yescharacteristic, complemented, Sylow
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—114no—
976C23—114no—
977C23—114no—
978C23—114no—
979C23—114no—
980C23—114no—
981C23—114no—
982C23—222no—
983C23—222no—
984C23—222no—
985C23—222no—
986C23—222no—
987C23—222no—
988C23—222no—
989C23—222no—
990C23—222no—
991C23—222no—
992C23—222no—
993C23—222no—
994C23—222no—
995C23—222no—
996C23—222no—
997C23—222no—
998C23—222no—
999C23—222no—
1000C23—222no—
1001C23—222no—
1002C23—222no—
1003C23—222no—
1004C23—222no—
1005C23—222no—
1006C23—222no—
1007C23—222no—
1008C23—222no—
1009C23—222no—
1010C23C4⋊C4×D1114yes—
1011C23C22×C4×D1111yescharacteristic
1012C23C2×D4×D1111yescharacteristic
1013C23C2×D4×D1111yescharacteristic
1014C23C2×D4×D1111yescharacteristic
1015C23C2×#434111yescharacteristic
1016C23#6703711yescharacteristic
1017C23#6703711yescharacteristic
1018C23#6703711yescharacteristic
1019C23C2×Q8×D1111yescharacteristic
1020C23#41×D1111yescharacteristic
1021C23#41×D1111yescharacteristic
1022C23#41×D1111yescharacteristic
1023C23#41×D1111yescharacteristic
1024C23#41×D1111yescharacteristic
1025C23#6704211yescharacteristic
1026D4—2232no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—114no—
1070C2×C4—114no—
1071C2×C4—222no—
1072C2×C4—222no—
1073C2×C4—222no—
1074C2×C4—222no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—222no—
1081C2×C4—222no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—222no—
1094C2×C4—222no—
1095C2×C4—4416no—
1096C2×C4—4416no—
1097C2×C4—4416no—
1098C2×C4—4416no—
1099C2×C4—441no—
1100C2×C4—441no—
1101C2×C4—441no—
1102C2×C4—441no—
1103C2×C4—441no—
1104C2×C4—441no—
1105C2×C4—441no—
1106C2×C4—441no—
1107C2×C4—441no—
1108C2×C4—441no—
1109C2×C4—441no—
1110C2×C4—441no—
1111C2×C4—441no—
1112C2×C4—441no—
1113C2×C4—441no—
1114C2×C4—441no—
1115C2×C4—441no—
1116C2×C4—441no—
1117C2×C4—441no—
1118C2×C4—441no—
1119C2×C4—441no—
1120C2×C4—441no—
1121C2×C4—441no—
1122C22—24no—
1123C22—24no—
1124C22—24no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—118no—
1138C22—224no—
1139C22—224no—
1140C22—224no—
1141C22—224no—
1142C22—224no—
1143C22—224no—
1144C22—224no—
1145C22—224no—
1146C22—224no—
1147C22—224no—
1148C22—224no—
1149C22—224no—
1150C22—224no—
1151C22—224no—
1152C22#1062301711yescharacteristic
1153C22C2×C4⋊C4×D1111yescharacteristic
1154C22#1062305311yescharacteristic
1155C22C4×#434111yescharacteristic
1156C22C4×D4×D1111yescharacteristic
1157C22C4×D4×D1111yescharacteristic
1158C22#1062307611yescharacteristic
1159C22D11×#12011yescharacteristic
1160C22#1062312211yescharacteristic
1161C22#1062312211yescharacteristic
1162C22#1062313611yescharacteristic
1163C22#1062313711yescharacteristic
1164C22#1062314111yescharacteristic
1165C22#1062314111yescharacteristic
1166C22#1062314111yescharacteristic
1167C22#1062314311yescharacteristic
1168C22#1062314411yescharacteristic
1169C22#1062314511yescharacteristic
1170C22D11×C22⋊Q811yescharacteristic
1171C22D11×C22⋊Q811yescharacteristic
1172C22#1062316611yescharacteristic
1173C22#1062316711yescharacteristic
1174C22#1062316711yescharacteristic
1175C22#1062316711yescharacteristic
1176C22D11×#12311yescharacteristic
1177C22D11×#12311yescharacteristic
1178C22#1062318511yescharacteristic
1179C22#1062319211yescharacteristic
1180C22#1062319211yescharacteristic
1181C22#1062320711yescharacteristic
1182C22#1062320911yescharacteristic
1183C22#1062321111yescharacteristic
1184C22#1062323711yescharacteristic
1185C22#1062324011yescharacteristic
1186C22#1062324611yescharacteristic
1187C4—42no—
1188C4—42no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—81no—
1193C4—224no—
1194C4—224no—
1195C4—442no—
1196C4—442no—
1197C4—442no—
1198C4—442no—
1199C4—881no—
1200C2—44no—
1201C2—228no—
1202C2D11×#38511yescharacteristic
1203C2#1307114311yescharacteristic
1204C2#1307127511yescharacteristic
1205C2#1307152011yescharacteristic
1206C2#1307152211yescharacteristic
1207C2#1307166011yescharacteristic
1208C2#1307166511yescharacteristic
1209C2#1307193011yescharacteristic
1210C2#1307193811yescharacteristic
1211C2#1307235911yescharacteristic
1212C2#1307236111yescharacteristic
1213C2#1307243311yescharacteristic
1214C2#1307243511yescharacteristic
1215C2#1307292611yescharacteristic
1216C2#1307395811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#14016
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
4. C2×#10622602C2semidirect
5. C2×D11×#95C2semidirect
6. #13066874C2semidirect
7. #13066871C2semidirect
8. #13066859C2semidirect
9. #13066851C2semidirect
10. #13066848C2semidirect
11. #13066838C2semidirect
12. #13066838C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1439C2semidirect
56. #10622569C4semidirect
106. C22×C4×D11C2×C4semidirect
119. C2×C11×C22⋊C4C2×C4semidirect
125. C2×C22⋊Dic11C2×C4semidirect
133. C2×(C2×D11)⋊C4C2×C4semidirect
161. C11⋊#95C2×C4semidirect
162. C11⋊#95C2×C4semidirect
243. C2×C22⋊D11C4⋊C4semidirect
341. #1439D11semidirect
732. C2×C22⋊C4C4×D11semidirect
940. C11#14016semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
C2×#106225692
C2×#106226022
C2×D11×#952
#130668742
#130668712
#130668592
#130668512
#130668482
#130668382
(C2×D11)⋊#952
C11×#14392
#1401611