Finite Group Databasebeta

← #14680520

Subgroups — #14680520

Order 2816.

2566 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
2C2×#10622573C211yesmaximal, characteristic
3C2×#10622603C211yesmaximal, characteristic, complemented
4C2×#10622278C211yesmaximal, characteristic, complemented
5C2×#10622571C211yesmaximal, characteristic, complemented
6#13066874C211yesmaximal, characteristic, complemented
7#13066860C211yesmaximal, characteristic, complemented
8#13066858C211yesmaximal, characteristic, complemented
9#13066856C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic, complemented
11#13066855C211yesmaximal, characteristic, complemented
12#13066842C211yesmaximal, characteristic, complemented
13#13066838C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×(C22⋊D11)⋊C4—24no—
38C2×(C22⋊D11)⋊C4—24no—
39C2×(C22⋊D11)⋊C4—24no—
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#10622603—24no—
55#10622573C418yescomplemented
56#10622571—24no—
57#10622278—24no—
58C25×C11C2311yescharacteristic
59C24×D11C2311yescharacteristic
60C24×D11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—22no—
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—22no—
74C22×C22⋊D11—22no—
75C22×C22⋊D11—41no—
76C22×C22⋊D11—41no—
77C22×C22⋊D11—41no—
78C22×C22⋊D11—41no—
79C22×C22⋊D11C2×C414yes—
80C22×C22⋊D11C2×C414yescomplemented
81C23×Dic11—22no—
82C23×Dic11—22no—
83C23×Dic11—41no—
84C23×Dic11—41no—
85C23×Dic11—41no—
86C23×Dic11—41no—
87C23×Dic11D414yescomplemented
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2311yescharacteristic
92C23×Dic11C2311yescharacteristic
93C23×Dic11C2311yescharacteristic
94C22×D44—22no—
95C22×D44—22no—
96C22×D44—41no—
97C22×D44—41no—
98C22×D44—41no—
99C22×D44—41no—
100C22×D44C2×C414yescomplemented
101C22×C4×D11—22no—
102C22×C4×D11—22no—
103C22×C4×D11—41no—
104C22×C4×D11—41no—
105C22×C4×D11—41no—
106C22×C4×D11—41no—
107C22×C4×D11D414yescomplemented
108C2×C11×C4⋊C4—22no—
109C2×C11×C4⋊C4—41no—
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—41no—
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—41no—
122C2×C22⋊Dic11—41no—
123C2×(C2×D11)⋊C4—22no—
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—22no—
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)⋊C4—22no—
134C2×(C2×D11)⋊C4—22no—
135C2×(C2×D11)⋊C4—22no—
136C2×(C2×D11)⋊C4—41no—
137C2×(C2×D11)⋊C4—41no—
138C2×(C2×D11)⋊C4—41no—
139C2×(C2×D11)⋊C4—41no—
140C2×(C2×D11)⋊C4—41no—
141C2×(C2×D11)⋊C4—41no—
142C2×(C2×D11)⋊C4—41no—
143C2×(C2×D11)⋊C4—41no—
144C2×(C2×D11)⋊C4—41no—
145C2×(C2×D11)⋊C4—41no—
146C2×(C2×D11)⋊C4—41no—
147C2×(C2×D11)⋊C4—41no—
148C2×(C2×D11)⋊C4C2×C414yescomplemented
149C2×(C2×D11)⋊C4C2×C414yescomplemented
150C2×Dic11⋊C4—22no—
151C2×Dic11⋊C4—22no—
152C2×Dic11⋊C4—22no—
153C2×C4×Dic11—22no—
154C2×C4×Dic11—22no—
155C2×C4×Dic11D414yescomplemented
156(C22⋊D11)⋊C4—232no—
157C11×#95—22no—
158C11×#95—41no—
159C11×#95—41no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—22no—
164C11⋊#95—22no—
165C11⋊#95—22no—
166C11⋊#95—41no—
167C11⋊#95—41no—
168C11⋊#95—41no—
169C11⋊#95—41no—
170C11⋊#95C2×C414yescomplemented
171#14299—111nomaximal, Sylow
172C24×C11—21no—
173C24×C11—21no—
174C24×C11—21no—
175C24×C11—21no—
176C24×C11—21no—
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11C22×C412yes—
185C24×C11C2×D412yes—
186C24×C11#4112yes—
187C24×C11C2411yescharacteristic
188C23×D11—21no—
189C23×D11—21no—
190C23×D11—21no—
191C23×D11—21no—
192C23×D11—21no—
193C23×D11—21no—
194C23×D11—21no—
195C23×D11—21no—
196C23×D11—21no—
197C23×D11—21no—
198C23×D11—21no—
199C23×D11—21no—
200C23×D11—21no—
201C23×D11—21no—
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—21no—
205C23×D11—21no—
206C23×D11—21no—
207C23×D11—21no—
208C23×D11—21no—
209C23×D11—21no—
210C23×D11—21no—
211C23×D11—21no—
212C23×D11—21no—
213C23×D11—21no—
214C23×D11C22×C412yes—
215C23×D11C22×C412yes—
216C23×D11C2×D412yes—
217C23×D11#4112yes—
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×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11—21no—
236C22×C4×C11—21no—
237C22×C4×C11—21no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11—21no—
249C22×C4×C11—21no—
250C22×C4×C11—21no—
251C22×C4×C11—21no—
252C22×C4×C11—21no—
253C22×C4×C11—21no—
254C22×C4×C11—21no—
255C22×C4×C11—21no—
256C22×C4×C11C22×C412yes—
257C22×C4×C11C22×C412yes—
258C22×C4×C11C2×D412yes—
259C22×C4×C11C2×D412yes—
260C2×C22⋊D11—28no—
261C2×C22⋊D11—28no—
262C2×C22⋊D11—28no—
263C2×C22⋊D11—28no—
264C2×C22⋊D11—28no—
265C2×C22⋊D11—28no—
266C2×C22⋊D11—28no—
267C2×C22⋊D11—28no—
268C2×C22⋊D11—44no—
269C2×C22⋊D11—44no—
270C2×C22⋊D11—44no—
271C2×C22⋊D11—44no—
272C2×C22⋊D11—44no—
273C2×C22⋊D11—44no—
274C22×Dic11—28no—
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—21no—
285C22×Dic11—21no—
286C22×Dic11—21no—
287C22×Dic11—21no—
288C22×Dic11—21no—
289C22×Dic11—21no—
290C22×Dic11—21no—
291C22×Dic11—21no—
292C22×Dic11—21no—
293C22×Dic11—21no—
294C22×Dic11—21no—
295C22×Dic11—21no—
296C22×Dic11—21no—
297C22×Dic11—21no—
298C22×Dic11—21no—
299C22×Dic11—21no—
300C22×Dic11—21no—
301C22×Dic11—21no—
302C22×Dic11—21no—
303C22×Dic11—21no—
304C22×Dic11—21no—
305C22×Dic11—21no—
306C22×Dic11—21no—
307C22×Dic11—21no—
308C22×Dic11—21no—
309C22×Dic11—44no—
310C22×Dic11—44no—
311C22×Dic11—44no—
312C22×Dic11—44no—
313C22×Dic11—44no—
314C22×Dic11—44no—
315C22×Dic11C22×C412yes—
316C22×Dic11C22×C412yes—
317C22×Dic11C2×D412yes—
318C22×Dic11C2×D412yes—
319C22×Dic11C2×D412yes—
320C22×Dic11C2×D412yes—
321C22×Dic11C2×D412yes—
322C22×Dic11#4112yes—
323C2×D44—28no—
324C2×D44—44no—
325C2×D44—44no—
326C2×D44—44no—
327C2×D44—44no—
328C2×D44—44no—
329C2×D44—44no—
330C2×C4×D11—28no—
331C2×C4×D11—44no—
332C2×C4×D11—44no—
333C2×C4×D11—44no—
334C2×C4×D11—44no—
335C2×C4×D11—44no—
336C2×C4×D11—44no—
337C11×C4⋊C4—44no—
338C11×C22⋊C4—28no—
339C11×C22⋊C4—44no—
340C11×C22⋊C4—44no—
341C22⋊Dic11—44no—
342(C2×D11)⋊C4—28no—
343(C2×D11)⋊C4—28no—
344(C2×D11)⋊C4—44no—
345(C2×D11)⋊C4—44no—
346(C2×D11)⋊C4—44no—
347(C2×D11)⋊C4—44no—
348(C2×D11)⋊C4—44no—
349(C2×D11)⋊C4—44no—
350(C2×D11)⋊C4—44no—
351Dic11⋊C4—28no—
352C4×Dic11—28no—
353C22×C4×D4—111no—
354C2×#392—111no—
355C2×#388—111no—
356C2×#386—111no—
357C2×#386—111no—
358#1442—111no—
359#1439—111no—
360#1439—111no—
361#1439D1111yescharacteristic, complemented
362#1438—111no—
363#1438—111no—
364#1438—111no—
365#1434—111no—
366C22⋊#95—111no—
367C22⋊#95—111no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
383C23×C11—22no—
384C23×C11—22no—
385C23×C11—22no—
386C23×C11—41no—
387C23×C11—41no—
388C23×C11—41no—
389C23×C11—41no—
390C23×C11—41no—
391C23×C11—41no—
392C23×C11—41no—
393C23×C11—41no—
394C23×C11—41no—
395C23×C11—41no—
396C23×C11—41no—
397C23×C11—41no—
398C23×C11—41no—
399C23×C11—41no—
400C23×C11—41no—
401C23×C11—41no—
402C23×C11C4×D414yes—
403C23×C11C23×C411yescharacteristic
404C23×C11C22×D411yescharacteristic
405C23×C11C22×D411yescharacteristic
406C23×C11C22×D411yescharacteristic
407C23×C11C2×#4111yescharacteristic
408C23×C11C2×#4111yescharacteristic
409C23×C11C2×#4111yescharacteristic
410C23×C11H(5,𝔽2)11yescharacteristic
411C23×C11H(5,𝔽2)11yescharacteristic
412C23×C11H(5,𝔽2)11yescharacteristic
413C23×C11H(5,𝔽2)11yescharacteristic
414C23×C11H(5,𝔽2)11yescharacteristic
415C23×C11H(5,𝔽2)11yescharacteristic
416C23×C11H(5,𝔽2)11yescharacteristic
417C23×C112−1+411yescharacteristic
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×D11—22no—
427C22×D11—22no—
428C22×D11—22no—
429C22×D11—22no—
430C22×D11—22no—
431C22×D11—22no—
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—22no—
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11—41no—
444C22×D11—41no—
445C22×D11—41no—
446C22×D11—41no—
447C22×D11—41no—
448C22×D11—41no—
449C22×D11—41no—
450C22×D11—41no—
451C22×D11—41no—
452C22×D11—41no—
453C22×D11—41no—
454C22×D11—41no—
455C22×D11—41no—
456C22×D11—41no—
457C22×D11—41no—
458C22×D11—41no—
459C22×D11—41no—
460C22×D11—41no—
461C22×D11—41no—
462C22×D11—41no—
463C22×D11—41no—
464C22×D11—41no—
465C22×D11—41no—
466C22×D11—41no—
467C22×D11—41no—
468C22×D11—41no—
469C22×D11—41no—
470C22×D11—41no—
471C22×D11—41no—
472C22×D11—41no—
473C22×D11—41no—
474C22×D11—41no—
475C22×D11—41no—
476C22×D11—41no—
477C22×D11—41no—
478C22×D11—41no—
479C22×D11—41no—
480C22×D11—41no—
481C22×D11—41no—
482C22×D11—41no—
483C22×D11—41no—
484C22×D11—41no—
485C22×D11—41no—
486C22×D11—41no—
487C22×D11C4×D414yes—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
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—41no—
501C2×C4×C11—41no—
502C2×C4×C11—41no—
503C2×C4×C11—41no—
504C2×C4×C11—41no—
505C2×C4×C11—41no—
506C2×C4×C11—41no—
507C2×C4×C11—41no—
508C2×C4×C11—41no—
509C2×C4×C11—41no—
510C2×C4×C11—41no—
511C2×C4×C11—41no—
512C2×C4×C11—41no—
513C2×C4×C11—41no—
514C2×C4×C11—41no—
515C2×C4×C11—41no—
516C2×C4×C11—41no—
517C2×C4×C11—41no—
518C2×C4×C11—41no—
519C2×C4×C11—41no—
520C2×C4×C11—41no—
521C2×C4×C11—41no—
522C2×C4×C11—41no—
523C2×C4×C11—41no—
524C2×C4×C11—41no—
525C2×C4×C11—41no—
526C2×C4×C11—41no—
527C2×C4×C11—41no—
528C2×C4×C11—41no—
529C2×C4×C11—41no—
530C22⋊D11—232no—
531C22⋊D11—416no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—22no—
535C2×Dic11—22no—
536C2×Dic11—22no—
537C2×Dic11—22no—
538C2×Dic11—22no—
539C2×Dic11—22no—
540C2×Dic11—22no—
541C2×Dic11—22no—
542C2×Dic11—22no—
543C2×Dic11—22no—
544C2×Dic11—22no—
545C2×Dic11—22no—
546C2×Dic11—22no—
547C2×Dic11—22no—
548C2×Dic11—22no—
549C2×Dic11—22no—
550C2×Dic11—416no—
551C2×Dic11—41no—
552C2×Dic11—41no—
553C2×Dic11—41no—
554C2×Dic11—41no—
555C2×Dic11—41no—
556C2×Dic11—41no—
557C2×Dic11—41no—
558C2×Dic11—41no—
559C2×Dic11—41no—
560C2×Dic11—41no—
561C2×Dic11—41no—
562C2×Dic11—41no—
563C2×Dic11—41no—
564C2×Dic11—41no—
565C2×Dic11—41no—
566C2×Dic11—41no—
567C2×Dic11—41no—
568C2×Dic11—41no—
569C2×Dic11—41no—
570C2×Dic11—41no—
571C2×Dic11—41no—
572C2×Dic11—41no—
573C2×Dic11C4×D414yes—
574C2×Dic11#12014yes—
575D44—416no—
576C4×D11—416no—
577C23×D4—111no—
578C23×D4—111no—
579C23×D4—111no—
580C24×C4—111no—
581C24×C4—111no—
582C2×C4×D4—224no—
583C2×C4×D4—224no—
584C2×C4×D4—224no—
585C22×C4⋊C4—111no—
586C22×C4⋊C4C2×D1111yescharacteristic
587C22×C22⋊C4—111no—
588C22×C22⋊C4—111no—
589C22×C22⋊C4—111no—
590C22×C22⋊C4—111no—
591C22×C22⋊C4—111no—
592C22×C22⋊C4—111no—
593C22×C22⋊C4—111no—
594C22×C22⋊C4—111no—
595C22×C22⋊C4—111no—
596C22×C22⋊C4—111no—
597C22×C22⋊C4C2×D1111yescharacteristic
598C22×C22⋊C4C2×D1111yescharacteristic
599C22×C22⋊C4C2×D1111yescharacteristic
600C22×C42—111no—
601#392—118no—
602#388—224no—
603#386—224no—
604#386—224no—
605C2×#95—111no—
606C2×#95—111no—
607C2×#95—111no—
608C2×#95—111no—
609C2×#95—111no—
610C2×#95—111no—
611C2×#95—111no—
612C2×#95—111no—
613C2×#95—111no—
614C2×#95—111no—
615C2×#95—111no—
616C2×#95C2×D1111yescharacteristic
617C2×#95C2×D1111yescharacteristic
618C2×#95C2×D1111yescharacteristic
619C22×C11—24no—
620C22×C11—24no—
621C22×C11—24no—
622C22×C11—42no—
623C22×C11—42no—
624C22×C11—42no—
625C22×C11—42no—
626C22×C11—42no—
627C22×C11—42no—
628C22×C11—42no—
629C22×C11—42no—
630C22×C11—42no—
631C22×C11—42no—
632C22×C11—42no—
633C22×C11—42no—
634C22×C11C2×C4×D411yescharacteristic
635C22×C11C2×C4×D411yescharacteristic
636C22×C11C2×C4×D411yescharacteristic
637C22×C11#51811yescharacteristic
638C22×C11#51811yescharacteristic
639C22×C11#51811yescharacteristic
640C22×C11#52011yescharacteristic
641C22×C11C2×#12011yescharacteristic
642C22×C11#52511yescharacteristic
643C22×C11#52511yescharacteristic
644C22×C11#52511yescharacteristic
645C22×C11#53411yescharacteristic
646C22×C11#53411yescharacteristic
647C22×C11#53411yescharacteristic
648C22×C11#53411yescharacteristic
649C22×C11#53511yescharacteristic
650C22×C11#53511yescharacteristic
651C22×C11#53511yescharacteristic
652C22×C11#53511yescharacteristic
653C22×C11#53511yescharacteristic
654C22×C11#53711yescharacteristic
655C22×C11#53711yescharacteristic
656C22×C11#53711yescharacteristic
657C22×C11#53811yescharacteristic
658C22×C11#53811yescharacteristic
659C22×C11#53811yescharacteristic
660C22×C11#53811yescharacteristic
661C22×C11#53811yescharacteristic
662C22×C11#53811yescharacteristic
663C22×C11#53911yescharacteristic
664C22×C11#53911yescharacteristic
665C22×C11#54011yescharacteristic
666C22×C11#54011yescharacteristic
667C22×C11#54011yescharacteristic
668C22×C11#54211yescharacteristic
669C2×D11—24no—
670C2×D11—24no—
671C2×D11—24no—
672C2×D11—42no—
673C2×D11—42no—
674C2×D11—42no—
675C2×D11—42no—
676C2×D11—42no—
677C2×D11—42no—
678C2×D11—42no—
679C2×D11—42no—
680C2×D11—42no—
681C2×D11—42no—
682C2×D11—42no—
683C2×D11—42no—
684C2×D11—42no—
685C2×D11—42no—
686C2×D11—42no—
687C2×D11—42no—
688C2×D11—42no—
689C2×D11—42no—
690C2×D11—42no—
691C2×D11—81no—
692C2×D11—81no—
693C2×D11—81no—
694C2×D11—81no—
695C2×D11—81no—
696C2×D11—81no—
697C2×D11—81no—
698C2×D11—81no—
699C4×C11—42no—
700C4×C11—42no—
701C4×C11—42no—
702C4×C11—42no—
703C4×C11—81no—
704C4×C11—81no—
705Dic11—24no—
706Dic11—24no—
707Dic11—42no—
708Dic11—42no—
709Dic11—81no—
710Dic11—81no—
711C25—111no—
712C25—111no—
713C25C22×D1111yescharacteristic
714C22×D4—114no—
715C22×D4—114no—
716C22×D4—114no—
717C22×D4—222no—
718C22×D4—222no—
719C22×D4—222no—
720C22×D4—222no—
721C22×D4—222no—
722C22×D4—222no—
723C22×D4—222no—
724C22×D4—222no—
725C22×D4—222no—
726C22×D4—222no—
727C22×D4—441no—
728C22×D4—441no—
729C22×D4—441no—
730C22×D4—441no—
731C22×D4—441no—
732C22×D4—441no—
733C22×D4—441no—
734C22×D4—441no—
735C23×C4—111no—
736C23×C4—111no—
737C23×C4—111no—
738C23×C4—111no—
739C23×C4—114no—
740C23×C4—114no—
741C23×C4—111no—
742C23×C4—111no—
743C23×C4—222no—
744C23×C4—222no—
745C23×C4—222no—
746C23×C4—222no—
747C23×C4—441no—
748C23×C4—441no—
749C23×C4—441no—
750C23×C4—441no—
751C23×C4—441no—
752C23×C4—441no—
753C23×C4—441no—
754C23×C4—441no—
755C23×C4C22×D1111yescharacteristic
756C23×C4C22×D1111yescharacteristic
757C23×C4C22×D1111yescharacteristic
758C23×C4C22×D1111yescharacteristic
759C23×C4C22×D1111yescharacteristic
760C23×C4C22×D1111yescharacteristic
761C4×D4—2232no—
762C2×C4⋊C4—22no—
763C2×C4⋊C4—41no—
764C2×C4⋊C4—41no—
765C2×C4⋊C4—222no—
766C2×C4⋊C4—222no—
767C2×C4⋊C4—222no—
768C2×C22⋊C4—22no—
769C2×C22⋊C4—22no—
770C2×C22⋊C4—22no—
771C2×C22⋊C4—22no—
772C2×C22⋊C4—41no—
773C2×C22⋊C4—41no—
774C2×C22⋊C4—41no—
775C2×C22⋊C4—41no—
776C2×C22⋊C4—114no—
777C2×C22⋊C4—114no—
778C2×C22⋊C4—222no—
779C2×C22⋊C4—222no—
780C2×C22⋊C4—222no—
781C2×C22⋊C4—222no—
782C2×C22⋊C4—222no—
783C2×C22⋊C4—222no—
784C2×C22⋊C4—222no—
785C2×C22⋊C4—222no—
786C2×C22⋊C4—222no—
787C2×C22⋊C4—222no—
788C2×C22⋊C4—222no—
789C2×C22⋊C4—222no—
790C2×C22⋊C4—222no—
791C2×C22⋊C4—222no—
792C2×C22⋊C4—441no—
793C2×C22⋊C4—441no—
794C2×C22⋊C4—441no—
795C2×C22⋊C4—441no—
796C2×C22⋊C4—441no—
797C2×C22⋊C4—441no—
798C2×C22⋊C4—441no—
799C2×C22⋊C4—441no—
800C2×C22⋊C4—441no—
801C2×C22⋊C4—441no—
802C2×C22⋊C4—441no—
803C2×C22⋊C4—441no—
804C2×C22⋊C4—441no—
805C2×C22⋊C4—441no—
806C2×C22⋊C4C4×D1114yescomplemented
807C2×C42—114no—
808C2×C42—222no—
809C2×C42—222no—
810#95—22no—
811#95—41no—
812#95—41no—
813#95—114no—
814#95—222no—
815#95—222no—
816#95—222no—
817#95—222no—
818#95—222no—
819#95—222no—
820#95—441no—
821#95—441no—
822#95—441no—
823#95—441no—
824C2×C11—44no—
825C2×C11C4×#12011yescharacteristic
826C2×C11#232111yescharacteristic
827C2×C11#232111yescharacteristic
828C2×C11#232411yescharacteristic
829C2×C11#232511yescharacteristic
830C2×C11#232511yescharacteristic
831C2×C11#232811yescharacteristic
832C2×C11#261311yescharacteristic
833C2×C11#261511yescharacteristic
834C2×C11#263011yescharacteristic
835C2×C11#263011yescharacteristic
836C2×C11#263111yescharacteristic
837C2×C11#263511yescharacteristic
838C2×C11#263511yescharacteristic
839C2×C11#263611yescharacteristic
840D11—44no—
841D11—82no—
842C24—21no—
843C24—21no—
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—112no—
855C24—112no—
856C24—112no—
857C24—112no—
858C24—221no—
859C24—221no—
860C24—221no—
861C24—221no—
862C24—221no—
863C24—221no—
864C24—221no—
865C24—221no—
866C24—221no—
867C24—221no—
868C24—221no—
869C24—221no—
870C24—221no—
871C24—221no—
872C24—221no—
873C24—221no—
874C24—221no—
875C24—221no—
876C24—221no—
877C24—221no—
878C24—221no—
879C24—221no—
880C24—221no—
881C24—221no—
882C24—221no—
883C24—221no—
884C24C2×C4×D1112yes—
885C24D4×D1112yes—
886C24#434312yes—
887C24C23×D1111yescharacteristic
888C2×D4—228no—
889C2×D4—228no—
890C2×D4—228no—
891C2×D4—228no—
892C2×D4—228no—
893C2×D4—228no—
894C2×D4—228no—
895C2×D4—228no—
896C2×D4—228no—
897C2×D4—444no—
898C2×D4—444no—
899C2×D4—444no—
900C2×D4—444no—
901C2×D4—444no—
902C2×D4—444no—
903C2×D4—444no—
904C2×D4—444no—
905C2×D4—444no—
906C2×D4—444no—
907C2×D4—444no—
908C2×D4—444no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—112no—
948C22×C4—112no—
949C22×C4—112no—
950C22×C4—112no—
951C22×C4—112no—
952C22×C4—112no—
953C22×C4—112no—
954C22×C4—112no—
955C22×C4—228no—
956C22×C4—228no—
957C22×C4—221no—
958C22×C4—221no—
959C22×C4—221no—
960C22×C4—221no—
961C22×C4—221no—
962C22×C4—221no—
963C22×C4—221no—
964C22×C4—221no—
965C22×C4—221no—
966C22×C4—221no—
967C22×C4—221no—
968C22×C4—221no—
969C22×C4—221no—
970C22×C4—221no—
971C22×C4—221no—
972C22×C4—221no—
973C22×C4—221no—
974C22×C4—221no—
975C22×C4—221no—
976C22×C4—221no—
977C22×C4—221no—
978C22×C4—221no—
979C22×C4—221no—
980C22×C4—221no—
981C22×C4—221no—
982C22×C4—221no—
983C22×C4—221no—
984C22×C4—221no—
985C22×C4—221no—
986C22×C4—221no—
987C22×C4—221no—
988C22×C4—221no—
989C22×C4—221no—
990C22×C4—221no—
991C22×C4—444no—
992C22×C4—444no—
993C22×C4—444no—
994C22×C4—444no—
995C22×C4—444no—
996C22×C4—444no—
997C22×C4—444no—
998C22×C4—444no—
999C22×C4—444no—
1000C22×C4—444no—
1001C22×C4—444no—
1002C22×C4—444no—
1003C22×C4C2×C4×D1112yes—
1004C22×C4C2×C4×D1112yes—
1005C22×C4D4×D1112yes—
1006C22×C4D4×D1112yes—
1007C4⋊C4—44no—
1008C4⋊C4—228no—
1009C22⋊C4—28no—
1010C22⋊C4—44no—
1011C22⋊C4—44no—
1012C22⋊C4—228no—
1013C22⋊C4—228no—
1014C22⋊C4—444no—
1015C22⋊C4—444no—
1016C22⋊C4—444no—
1017C22⋊C4—444no—
1018C22⋊C4—444no—
1019C22⋊C4—444no—
1020C22⋊C4—444no—
1021C22⋊C4—444no—
1022C42—228no—
1023C11#1429911yescharacteristic, complemented, Sylow
1024C23—22no—
1025C23—22no—
1026C23—22no—
1027C23—22no—
1028C23—22no—
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—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—41no—
1048C23—41no—
1049C23—41no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—114no—
1059C23—222no—
1060C23—222no—
1061C23—222no—
1062C23—222no—
1063C23—222no—
1064C23—222no—
1065C23—222no—
1066C23—222no—
1067C23—222no—
1068C23—222no—
1069C23—222no—
1070C23—222no—
1071C23—222no—
1072C23—222no—
1073C23—222no—
1074C23—222no—
1075C23—222no—
1076C23—222no—
1077C23—222no—
1078C23—222no—
1079C23—222no—
1080C23—222no—
1081C23—222no—
1082C23—222no—
1083C23—222no—
1084C23—441no—
1085C23—441no—
1086C23—441no—
1087C23—441no—
1088C23—441no—
1089C23—441no—
1090C23—441no—
1091C23—441no—
1092C23—441no—
1093C23—441no—
1094C23—441no—
1095C23—441no—
1096C23—441no—
1097C23—441no—
1098C23—441no—
1099C23—441no—
1100C23—441no—
1101C23—441no—
1102C23—441no—
1103C23—441no—
1104C23—441no—
1105C23—441no—
1106C23—441no—
1107C23—441no—
1108C23—441no—
1109C23—441no—
1110C23—441no—
1111C23—441no—
1112C23—441no—
1113C23—441no—
1114C23—441no—
1115C23—441no—
1116C23—441no—
1117C23—441no—
1118C23—441no—
1119C23—441no—
1120C23—441no—
1121C23—441no—
1122C23—441no—
1123C23—441no—
1124C23—441no—
1125C23—441no—
1126C23—441no—
1127C23—441no—
1128C23#6694614yes—
1129C23C22×C4×D1111yescharacteristic
1130C23C2×D4×D1111yescharacteristic
1131C23C2×D4×D1111yescharacteristic
1132C23C2×D4×D1111yescharacteristic
1133C23#6703711yescharacteristic
1134C23#6703711yescharacteristic
1135C23#6703711yescharacteristic
1136C23#6703711yescharacteristic
1137C23C2×#434311yescharacteristic
1138C23#41×D1111yescharacteristic
1139C23#41×D1111yescharacteristic
1140C23#6704211yescharacteristic
1141C23#6704211yescharacteristic
1142C23#6704211yescharacteristic
1143C23#6704311yescharacteristic
1144D4—2232no—
1145D4—4416no—
1146D4—4416no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—114no—
1190C2×C4—114no—
1191C2×C4—222no—
1192C2×C4—222no—
1193C2×C4—222no—
1194C2×C4—222no—
1195C2×C4—222no—
1196C2×C4—222no—
1197C2×C4—222no—
1198C2×C4—222no—
1199C2×C4—222no—
1200C2×C4—222no—
1201C2×C4—222no—
1202C2×C4—222no—
1203C2×C4—222no—
1204C2×C4—222no—
1205C2×C4—222no—
1206C2×C4—222no—
1207C2×C4—222no—
1208C2×C4—222no—
1209C2×C4—4416no—
1210C2×C4—4416no—
1211C2×C4—441no—
1212C2×C4—441no—
1213C2×C4—441no—
1214C2×C4—441no—
1215C2×C4—441no—
1216C2×C4—441no—
1217C2×C4—441no—
1218C2×C4—441no—
1219C2×C4—441no—
1220C2×C4—441no—
1221C2×C4—441no—
1222C2×C4—441no—
1223C2×C4—441no—
1224C2×C4—441no—
1225C2×C4—441no—
1226C2×C4—441no—
1227C2×C4—441no—
1228C2×C4—441no—
1229C2×C4—441no—
1230C2×C4—441no—
1231C2×C4—441no—
1232C2×C4—441no—
1233C22—24no—
1234C22—24no—
1235C22—24no—
1236C22—42no—
1237C22—42no—
1238C22—42no—
1239C22—42no—
1240C22—42no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—224no—
1249C22—224no—
1250C22—224no—
1251C22—442no—
1252C22—442no—
1253C22—442no—
1254C22—442no—
1255C22—442no—
1256C22—442no—
1257C22—442no—
1258C22—442no—
1259C22—442no—
1260C22—442no—
1261C22—442no—
1262C22—442no—
1263C22—442no—
1264C22—442no—
1265C22—442no—
1266C22—442no—
1267C22—442no—
1268C22—442no—
1269C22—442no—
1270C22—881no—
1271C22—881no—
1272C22—881no—
1273C22—881no—
1274C22—881no—
1275C22—881no—
1276C22—881no—
1277C22—881no—
1278C22#1062301711yescharacteristic
1279C22C2×#6694611yescharacteristic
1280C22#1062305411yescharacteristic
1281C22C4×D4×D1111yescharacteristic
1282C22C4×D4×D1111yescharacteristic
1283C22#1062307611yescharacteristic
1284C22#1062307611yescharacteristic
1285C22D11×#12011yescharacteristic
1286C22#1062312311yescharacteristic
1287C22#1062312311yescharacteristic
1288C22#1062312811yescharacteristic
1289C22#1062312811yescharacteristic
1290C22#1062313611yescharacteristic
1291C22#1062313611yescharacteristic
1292C22#1062313811yescharacteristic
1293C22#1062313911yescharacteristic
1294C22#1062314411yescharacteristic
1295C22#1062314611yescharacteristic
1296C22#1062315811yescharacteristic
1297C22#1062315811yescharacteristic
1298C22#1062317511yescharacteristic
1299C22#1062317511yescharacteristic
1300C22#1062317511yescharacteristic
1301C22#1062317611yescharacteristic
1302C22#1062318411yescharacteristic
1303C22#1062318411yescharacteristic
1304C22#1062318711yescharacteristic
1305C22#1062319411yescharacteristic
1306C22#1062319411yescharacteristic
1307C22#1062320511yescharacteristic
1308C22#1062320911yescharacteristic
1309C22#1062320911yescharacteristic
1310C22#1062323811yescharacteristic
1311C22#1062324111yescharacteristic
1312C22#1062324611yescharacteristic
1313C4—42no—
1314C4—42no—
1315C4—42no—
1316C4—42no—
1317C4—81no—
1318C4—81no—
1319C4—224no—
1320C4—224no—
1321C4—442no—
1322C4—442no—
1323C4—881no—
1324C4—881no—
1325C2—44no—
1326C2—444no—
1327C2—882no—
1328C2#1307111711yescharacteristic
1329C2#1307127311yescharacteristic
1330C2#1307127511yescharacteristic
1331C2#1307130411yescharacteristic
1332C2#1307131611yescharacteristic
1333C2#1307132011yescharacteristic
1334C2#1307133711yescharacteristic
1335C2#1307432911yescharacteristic
1336C2#1307433911yescharacteristic
1337C2#1307445811yescharacteristic
1338C2#1307446211yescharacteristic
1339C2#1307447411yescharacteristic
1340C2#1307450211yescharacteristic
1341C2#1307450611yescharacteristic
1342C2#1307452011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenter#1439D11
hypocenterC11#14299
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C22×(C22⋊D11)⋊C4C2semidirect
3. C2×#10622603C2semidirect
4. C2×#10622278C2semidirect
5. C2×#10622571C2semidirect
6. #13066874C2semidirect
7. #13066860C2semidirect
8. #13066858C2semidirect
9. #13066856C2semidirect
10. #13066855C2semidirect
11. #13066855C2semidirect
12. #13066842C2semidirect
13. #13066838C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1439C2semidirect
55. #10622573C4semidirect
80. C22×C22⋊D11C2×C4semidirect
87. C23×Dic11D4semidirect
100. C22×D44C2×C4semidirect
107. C22×C4×D11D4semidirect
119. C2×C11×C22⋊C4C2×C4semidirect
148. C2×(C2×D11)⋊C4C2×C4semidirect
149. C2×(C2×D11)⋊C4C2×C4semidirect
155. C2×C4×Dic11D4semidirect
170. C11⋊#95C2×C4semidirect
361. #1439D11semidirect
806. C2×C22⋊C4C4×D11semidirect
1023. C11#14299semidirect

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×#106225732
C2×#106226032
C2×#106222782
C2×#106225712
#130668742
#130668602
#130668582
#130668562
#130668552
#130668422
#130668382
(C2×D11)⋊#952
C11×#14392
#1429911