Finite Group Databasebeta

← #14681908

Subgroups — #14681908

Order 2816.

2602 conjugacy classes of subgroups.

The subgroup lattice has 1354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66991C211yesmaximal, characteristic
2C2×#10622833C211yesmaximal, characteristic, complemented
3C2×#10622826C211yesmaximal, characteristic, complemented
4C2×#10622571C211yesmaximal, characteristic, complemented
5#13066885C211yesmaximal, characteristic, complemented
6#13066883C211yesmaximal, characteristic, complemented
7#13066863C211yesmaximal, characteristic, complemented
8#13066863C211yesmaximal, characteristic, complemented
9#13066855C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic, complemented
11#13066839C211yesmaximal, characteristic, complemented
12#13066838C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#386C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C22⋊D11C2211yescharacteristic
20C24×Dic11C2211yescharacteristic
21C23×C4×D11C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×C22⋊Dic11C2211yescharacteristic
30C2×#66991—24no—
31C2×#66991—24no—
32C2×#66991C418yescomplemented
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×(C2×D11)⋊C4C2211yescharacteristic
36C22×(C2×D11)⋊C4C2211yescharacteristic
37C22×C4⋊Dic11C2211yescharacteristic
38C11×#386—24no—
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41#10622833—24no—
42#10622826—24no—
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
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622571—24no—
58C25×C11C2311yescharacteristic
59C25×C11C2311yescharacteristic
60C24×D11C2311yescharacteristic
61C22×D4×C11—41no—
62C22×D4×C11—41no—
63C22×D4×C11—41no—
64C22×D4×C11—41no—
65C22×D4×C11C2×C414yes—
66C22×D4×C11D414yes—
67C22×D4×C11D414yes—
68C23×C4×C11—22no—
69C23×C4×C11—22no—
70C23×C4×C11—22no—
71C23×C4×C11—41no—
72C23×C4×C11—41no—
73C23×C4×C11—41no—
74C23×C4×C11—41no—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2311yescharacteristic
77C23×C4×C11C2311yescharacteristic
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2311yescharacteristic
80C22×C22⋊D11—22no—
81C22×C22⋊D11—22no—
82C22×C22⋊D11—22no—
83C22×C22⋊D11—22no—
84C22×C22⋊D11—22no—
85C22×C22⋊D11—22no—
86C22×C22⋊D11—22no—
87C22×C22⋊D11—22no—
88C22×C22⋊D11—41no—
89C22×C22⋊D11—41no—
90C22×C22⋊D11—41no—
91C22×C22⋊D11—41no—
92C22×C22⋊D11C2×C414yescomplemented
93C22×C22⋊D11C2×C414yescomplemented
94C23×Dic11—22no—
95C23×Dic11—22no—
96C23×Dic11—22no—
97C23×Dic11—41no—
98C23×Dic11—41no—
99C23×Dic11—41no—
100C23×Dic11—41no—
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2311yescharacteristic
107C23×Dic11C2311yescharacteristic
108C22×C4×D11—22no—
109C22×C4×D11—22no—
110C22×C4×D11—41no—
111C22×C4×D11—41no—
112C22×C4×D11—41no—
113C22×C4×D11—41no—
114C22×C4×D11C2×C414yescomplemented
115C2×C11×C22⋊C4—22no—
116C2×C11×C22⋊C4—22no—
117C2×C11×C22⋊C4—22no—
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—22no—
120C2×C11×C22⋊C4—41no—
121C2×C11×C22⋊C4—41no—
122C2×C11×C22⋊C4—41no—
123C2×C11×C22⋊C4—41no—
124C2×C22⋊Dic11—22no—
125C2×C22⋊Dic11—22no—
126C2×C22⋊Dic11—22no—
127C2×C22⋊Dic11—22no—
128C2×C22⋊Dic11—22no—
129C2×C22⋊Dic11—22no—
130C2×C22⋊Dic11—22no—
131C2×C22⋊Dic11—22no—
132C2×C22⋊Dic11—22no—
133C2×C22⋊Dic11—41no—
134C2×C22⋊Dic11—41no—
135C2×C22⋊Dic11—41no—
136C2×C22⋊Dic11—41no—
137C2×C22⋊Dic11C2×C414yescomplemented
138C2×C22⋊Dic11C2×C414yescomplemented
139#66991—232no—
140C2×(C2×D11)⋊C4—22no—
141C2×(C2×D11)⋊C4—22no—
142C2×(C2×D11)⋊C4—22no—
143C2×(C2×D11)⋊C4—22no—
144C2×(C2×D11)⋊C4—22no—
145C2×(C2×D11)⋊C4—41no—
146C2×(C2×D11)⋊C4—41no—
147C2×(C2×D11)⋊C4—41no—
148C2×(C2×D11)⋊C4—41no—
149C2×(C2×D11)⋊C4—41no—
150C2×(C2×D11)⋊C4—41no—
151C2×(C2×D11)⋊C4D414yescomplemented
152C2×C4⋊Dic11—22no—
153C2×C4⋊Dic11—22no—
154C2×C4⋊Dic11C2×C414yescomplemented
155C11×#95—22no—
156C11×#95—22no—
157C11⋊#95—22no—
158C11⋊#95—22no—
159C11⋊#95—22no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—41no—
164C11⋊#95—41no—
165C11⋊#95—41no—
166C11⋊#95—41no—
167C11⋊#95—41no—
168C11⋊#95—41no—
169C11⋊#95—41no—
170C11⋊#95—41no—
171#14417—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×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11—21no—
190C24×C11—21no—
191C24×C11—21no—
192C24×C11—21no—
193C24×C11—21no—
194C24×C11—21no—
195C24×C11—21no—
196C24×C11C22×C412yes—
197C24×C11C22×C412yes—
198C24×C11C2×D412yes—
199C24×C11C2×D412yes—
200C24×C11C2×D412yes—
201C24×C11C2×D412yes—
202C24×C11C2411yescharacteristic
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×D11—21no—
215C23×D11C22×C412yes—
216C23×D11C2×D412yes—
217C23×D11#4112yes—
218C2×D4×C11—44no—
219C2×D4×C11—44no—
220C2×D4×C11—44no—
221C2×D4×C11—44no—
222C2×D4×C11—44no—
223C2×D4×C11—44no—
224C2×D4×C11C22⋊C4116yescomplemented
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—44no—
256C22×C4×C11—44no—
257C22×C4×C11—44no—
258C22×C4×C11—44no—
259C22×C4×C11—44no—
260C22×C4×C11—44no—
261C22×C4×C11—44no—
262C22×C4×C11C22×C412yes—
263C22×C4×C11C2×D412yes—
264C22×C4×C11C2×D412yes—
265C22×C4×C11C2×D412yes—
266C22×C4×C11#4112yes—
267C2×C22⋊D11—28no—
268C2×C22⋊D11—28no—
269C2×C22⋊D11—28no—
270C2×C22⋊D11—28no—
271C2×C22⋊D11—44no—
272C2×C22⋊D11—44no—
273C2×C22⋊D11—44no—
274C2×C22⋊D11—44no—
275C2×C22⋊D11—44no—
276C2×C22⋊D11—44no—
277C2×C22⋊D11—44no—
278C2×C22⋊D11—44no—
279C2×C22⋊D11—44no—
280C2×C22⋊D11—44no—
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—21no—
310C22×Dic11—21no—
311C22×Dic11—21no—
312C22×Dic11—21no—
313C22×Dic11—21no—
314C22×Dic11—21no—
315C22×Dic11—21no—
316C22×Dic11—21no—
317C22×Dic11—21no—
318C22×Dic11—21no—
319C22×Dic11—21no—
320C22×Dic11—21no—
321C22×Dic11—21no—
322C22×Dic11—21no—
323C22×Dic11—21no—
324C22×Dic11—21no—
325C22×Dic11—44no—
326C22×Dic11—44no—
327C22×Dic11—44no—
328C22×Dic11—44no—
329C22×Dic11—44no—
330C22×Dic11—44no—
331C22×Dic11—44no—
332C22×Dic11C22×C412yes—
333C22×Dic11C22×C412yes—
334C22×Dic11C22×C412yes—
335C22×Dic11C2×D412yes—
336C22×Dic11#4112yes—
337C2×C4×D11—28no—
338C2×C4×D11—44no—
339C2×C4×D11—44no—
340C2×C4×D11—44no—
341C2×C4×D11—44no—
342C2×C4×D11—44no—
343C2×C4×D11—44no—
344C11×C22⋊C4—44no—
345C11×C22⋊C4—44no—
346C11×C22⋊C4—44no—
347C22⋊Dic11—28no—
348C22⋊Dic11—28no—
349C22⋊Dic11—44no—
350C22⋊Dic11—44no—
351C22⋊Dic11—44no—
352(C2×D11)⋊C4—44no—
353(C2×D11)⋊C4—44no—
354(C2×D11)⋊C4—44no—
355(C2×D11)⋊C4—44no—
356C4⋊Dic11—28no—
357C22×#121—111no—
358C2×#386—111no—
359C2×#386—111no—
360C2×#386—111no—
361C2×#386D1111yescharacteristic, complemented
362#1445—111no—
363#1445—111no—
364#1440—111no—
365#1440—111no—
366#1438—111no—
367#1438—111no—
368C22⋊#95—111no—
369C22⋊#95—111no—
370C22⋊#95—111no—
371C22⋊#95—111no—
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—22no—
387C23×C11—22no—
388C23×C11—22no—
389C23×C11—22no—
390C23×C11—22no—
391C23×C11—22no—
392C23×C11—22no—
393C23×C11—22no—
394C23×C11—22no—
395C23×C11—22no—
396C23×C11—22no—
397C23×C11—22no—
398C23×C11—22no—
399C23×C11—22no—
400C23×C11—22no—
401C23×C11—22no—
402C23×C11—22no—
403C23×C11—22no—
404C23×C11—22no—
405C23×C11—22no—
406C23×C11—22no—
407C23×C11—22no—
408C23×C11—41no—
409C23×C11—41no—
410C23×C11—41no—
411C23×C11—41no—
412C23×C11—41no—
413C23×C11—41no—
414C23×C11—41no—
415C23×C11—41no—
416C23×C11—41no—
417C23×C11—41no—
418C23×C11—41no—
419C23×C11—41no—
420C23×C11—41no—
421C23×C11—41no—
422C23×C11—41no—
423C23×C11—41no—
424C23×C11—41no—
425C23×C11—41no—
426C23×C11—41no—
427C23×C11—41no—
428C23×C11—41no—
429C23×C11—41no—
430C23×C11—41no—
431C23×C11—41no—
432C23×C11—41no—
433C23×C11—41no—
434C23×C11—41no—
435C23×C11—41no—
436C23×C11—41no—
437C23×C11—41no—
438C23×C11—41no—
439C23×C11—41no—
440C23×C11C2×C22⋊C414yes—
441C23×C11C2×C22⋊C414yes—
442C23×C11C23×C411yescharacteristic
443C23×C11C22×D411yescharacteristic
444C23×C11C22×D411yescharacteristic
445C23×C11C22×D411yescharacteristic
446C23×C11C2×#4111yescharacteristic
447C23×C11C2×#4111yescharacteristic
448C23×C11C2×#4111yescharacteristic
449C23×C11H(5,𝔽2)11yescharacteristic
450C23×C11H(5,𝔽2)11yescharacteristic
451C23×C11H(5,𝔽2)11yescharacteristic
452C23×C11H(5,𝔽2)11yescharacteristic
453C23×C11H(5,𝔽2)11yescharacteristic
454C23×C11H(5,𝔽2)11yescharacteristic
455C23×C11H(5,𝔽2)11yescharacteristic
456C23×C112−1+411yescharacteristic
457C22×D11—22no—
458C22×D11—22no—
459C22×D11—22no—
460C22×D11—22no—
461C22×D11—22no—
462C22×D11—22no—
463C22×D11—22no—
464C22×D11—22no—
465C22×D11—22no—
466C22×D11—22no—
467C22×D11—22no—
468C22×D11—22no—
469C22×D11—22no—
470C22×D11—22no—
471C22×D11—22no—
472C22×D11—22no—
473C22×D11—22no—
474C22×D11—22no—
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×D11—41no—
488C22×D11—41no—
489C22×D11—41no—
490C22×D11—41no—
491C22×D11C4×D414yes—
492D4×C11—416no—
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—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—416no—
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×C11C2×C22⋊C414yes—
529C22⋊D11—416no—
530C22⋊D11—416no—
531C2×Dic11—22no—
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—416no—
547C2×Dic11—41no—
548C2×Dic11—41no—
549C2×Dic11—41no—
550C2×Dic11—41no—
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×Dic11—41no—
574C2×Dic11—41no—
575C2×Dic11—41no—
576C2×Dic11—41no—
577C2×Dic11—41no—
578C2×Dic11—41no—
579C2×Dic11—41no—
580C2×Dic11—41no—
581C4×D11—416no—
582C23×D4—111no—
583C23×D4—111no—
584C23×D4C2×D1111yescharacteristic
585C24×C4—111no—
586C24×C4—111no—
587C24×C4C2×D1111yescharacteristic
588C2×#121—118no—
589C2×#121—224no—
590C2×#121—224no—
591C22×C4⋊C4—111no—
592C22×C22⋊C4—111no—
593C22×C22⋊C4—111no—
594C22×C22⋊C4—111no—
595C22×C22⋊C4—111no—
596C22×C22⋊C4—111no—
597C22×C22⋊C4—111no—
598C22×C22⋊C4—111no—
599C22×C22⋊C4—111no—
600C22×C22⋊C4—111no—
601C22×C22⋊C4C2×D1111yescharacteristic
602C22×C22⋊C4C2×D1111yescharacteristic
603C22×C22⋊C4C2×D1111yescharacteristic
604#386—24no—
605#386—224no—
606#386—224no—
607#386—224no—
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×#95—111no—
617C2×#95—111no—
618C2×#95—111no—
619C2×#95—111no—
620C2×#95—111no—
621C2×#95—111no—
622C2×#95C2×D1111yescharacteristic
623C2×#95C2×D1111yescharacteristic
624C22×C11—24no—
625C22×C11—24no—
626C22×C11—24no—
627C22×C11—24no—
628C22×C11—24no—
629C22×C11—24no—
630C22×C11—42no—
631C22×C11—42no—
632C22×C11—42no—
633C22×C11—42no—
634C22×C11—42no—
635C22×C11—42no—
636C22×C11—42no—
637C22×C11—42no—
638C22×C11—42no—
639C22×C11—42no—
640C22×C11—42no—
641C22×C11—42no—
642C22×C11—42no—
643C22×C11—42no—
644C22×C11—42no—
645C22×C11—42no—
646C22×C11—42no—
647C22×C11—42no—
648C22×C11—42no—
649C22×C11—42no—
650C22×C11—42no—
651C22×C11—42no—
652C22×C11—42no—
653C22×C11—42no—
654C22×C11C22×C22⋊C411yescharacteristic
655C22×C11C2×C4×D411yescharacteristic
656C22×C11C4×#4111yescharacteristic
657C22×C11#51811yescharacteristic
658C22×C11#51811yescharacteristic
659C22×C11#51811yescharacteristic
660C22×C11#52011yescharacteristic
661C22×C11#53411yescharacteristic
662C22×C11#53411yescharacteristic
663C22×C11#53411yescharacteristic
664C22×C11#53411yescharacteristic
665C22×C11#53411yescharacteristic
666C22×C11#53711yescharacteristic
667C22×C11#53811yescharacteristic
668C22×C11#53811yescharacteristic
669C22×C11#53811yescharacteristic
670C22×C11#53911yescharacteristic
671C22×C11#54011yescharacteristic
672C22×C11#54011yescharacteristic
673C22×C11D4211yescharacteristic
674C22×C11D4211yescharacteristic
675C22×C11#54611yescharacteristic
676C22×C11#54611yescharacteristic
677C22×C11#54611yescharacteristic
678C22×C11#54611yescharacteristic
679C22×C11#54611yescharacteristic
680C22×C11#54611yescharacteristic
681C22×C11#54711yescharacteristic
682C22×C11#54711yescharacteristic
683C22×C11#55311yescharacteristic
684C22×C11#55311yescharacteristic
685C22×C11#56011yescharacteristic
686C22×C11#56011yescharacteristic
687C22×C11#56211yescharacteristic
688C22×C11#56211yescharacteristic
689C2×D11—24no—
690C2×D11—24no—
691C2×D11—24no—
692C2×D11—42no—
693C2×D11—42no—
694C2×D11—42no—
695C2×D11—42no—
696C2×D11—42no—
697C2×D11—42no—
698C2×D11—42no—
699C2×D11—42no—
700C2×D11—42no—
701C2×D11—42no—
702C2×D11—42no—
703C2×D11—42no—
704C4×C11—24no—
705C4×C11—42no—
706C4×C11—42no—
707C4×C11—81no—
708C4×C11—81no—
709Dic11—42no—
710Dic11—42no—
711Dic11—42no—
712Dic11—42no—
713Dic11—42no—
714Dic11—81no—
715Dic11—81no—
716C25—111no—
717C25C22×D1111yescharacteristic
718C25C22×D1111yescharacteristic
719C22×D4—41no—
720C22×D4—41no—
721C22×D4—41no—
722C22×D4—41no—
723C22×D4—114no—
724C22×D4—114no—
725C22×D4—222no—
726C22×D4—222no—
727C22×D4—222no—
728C22×D4—222no—
729C22×D4—222no—
730C22×D4—222no—
731C22×D4—222no—
732C22×D4—222no—
733C22×D4—441no—
734C22×D4—441no—
735C22×D4—441no—
736C22×D4—441no—
737C22×D4C4×D1114yes—
738C22×D4D4414yes—
739C22×D4C22⋊D1114yes—
740C23×C4—22no—
741C23×C4—22no—
742C23×C4—22no—
743C23×C4—41no—
744C23×C4—41no—
745C23×C4—41no—
746C23×C4—41no—
747C23×C4—111no—
748C23×C4—111no—
749C23×C4—111no—
750C23×C4—111no—
751C23×C4—111no—
752C23×C4—114no—
753C23×C4—111no—
754C23×C4—111no—
755C23×C4—222no—
756C23×C4—222no—
757C23×C4—222no—
758C23×C4—222no—
759C23×C4—222no—
760C23×C4—441no—
761C23×C4—441no—
762C23×C4—441no—
763C23×C4—441no—
764C23×C4—441no—
765C23×C4—441no—
766C23×C4—441no—
767C23×C4—441no—
768C23×C4C22×D1111yescharacteristic
769C23×C4C22×D1111yescharacteristic
770C23×C4C22×D1111yescharacteristic
771C23×C4C22×D1111yescharacteristic
772C23×C4C22×D1111yescharacteristic
773#121—2232no—
774C2×C4⋊C4—114no—
775C2×C4⋊C4—222no—
776C2×C4⋊C4—222no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—41no—
783C2×C22⋊C4—41no—
784C2×C22⋊C4—41no—
785C2×C22⋊C4—41no—
786C2×C22⋊C4—114no—
787C2×C22⋊C4—114no—
788C2×C22⋊C4—114no—
789C2×C22⋊C4—222no—
790C2×C22⋊C4—222no—
791C2×C22⋊C4—222no—
792C2×C22⋊C4—222no—
793C2×C22⋊C4—222no—
794C2×C22⋊C4—222no—
795C2×C22⋊C4—222no—
796C2×C22⋊C4—222no—
797C2×C22⋊C4—222no—
798C2×C22⋊C4—222no—
799C2×C22⋊C4—222no—
800C2×C22⋊C4—222no—
801C2×C22⋊C4—222no—
802C2×C22⋊C4—222no—
803C2×C22⋊C4—441no—
804C2×C22⋊C4—441no—
805C2×C22⋊C4—441no—
806C2×C22⋊C4—441no—
807C2×C22⋊C4—441no—
808C2×C22⋊C4—441no—
809C2×C22⋊C4—441no—
810C2×C22⋊C4—441no—
811C2×C22⋊C4—441no—
812C2×C22⋊C4—441no—
813#95—22no—
814#95—22no—
815#95—222no—
816#95—222no—
817#95—222no—
818#95—222no—
819#95—222no—
820#95—222no—
821#95—441no—
822#95—441no—
823#95—441no—
824#95—441no—
825#95—441no—
826#95—441no—
827#95—441no—
828#95—441no—
829C2×C11—44no—
830C2×C11—44no—
831C2×C11#230811yescharacteristic
832C2×C11#232511yescharacteristic
833C2×C11#233311yescharacteristic
834C2×C11D4×C22⋊C411yescharacteristic
835C2×C11#233911yescharacteristic
836C2×C11#236411yescharacteristic
837C2×C11#237711yescharacteristic
838C2×C11#266811yescharacteristic
839C2×C11#266811yescharacteristic
840C2×C11#267111yescharacteristic
841C2×C11#267111yescharacteristic
842C2×C11#268811yescharacteristic
843C2×C11#268811yescharacteristic
844C2×C11#270811yescharacteristic
845C2×C11#270811yescharacteristic
846D11—44no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—112no—
872C24—112no—
873C24—112no—
874C24—221no—
875C24—221no—
876C24—221no—
877C24—221no—
878C24—221no—
879C24—221no—
880C24—221no—
881C24—221no—
882C24—221no—
883C24—221no—
884C24—221no—
885C24—221no—
886C24C2×C4×D1112yes—
887C24C2×C4×D1112yes—
888C24C2×D4412yes—
889C24C2×D4412yes—
890C24C2×C22⋊D1112yes—
891C24C2×C22⋊D1112yes—
892C24C23×D1111yescharacteristic
893C2×D4—44no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—228no—
900C2×D4—228no—
901C2×D4—228no—
902C2×D4—228no—
903C2×D4—444no—
904C2×D4—444no—
905C2×D4—444no—
906C2×D4—444no—
907C2×D4—444no—
908C2×D4—444no—
909C2×D4—444no—
910C2×D4—444no—
911C2×D4—444no—
912C2×D4—444no—
913C2×D4(C2×D11)⋊C4116yescomplemented
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—44no—
945C22×C4—44no—
946C22×C4—44no—
947C22×C4—44no—
948C22×C4—44no—
949C22×C4—44no—
950C22×C4—44no—
951C22×C4—112no—
952C22×C4—112no—
953C22×C4—112no—
954C22×C4—112no—
955C22×C4—112no—
956C22×C4—221no—
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—228no—
987C22×C4—221no—
988C22×C4—221no—
989C22×C4—221no—
990C22×C4—221no—
991C22×C4—221no—
992C22×C4—221no—
993C22×C4—221no—
994C22×C4—221no—
995C22×C4—221no—
996C22×C4—221no—
997C22×C4—221no—
998C22×C4—221no—
999C22×C4—221no—
1000C22×C4—221no—
1001C22×C4—444no—
1002C22×C4—444no—
1003C22×C4—444no—
1004C22×C4—444no—
1005C22×C4—444no—
1006C22×C4—444no—
1007C22×C4—444no—
1008C22×C4—444no—
1009C22×C4—444no—
1010C22×C4—444no—
1011C22×C4—444no—
1012C22×C4—444no—
1013C22×C4—444no—
1014C22×C4C2×C4×D1112yes—
1015C22×C4C2×D4412yes—
1016C22×C4D4×D1112yes—
1017C22×C4#434112yes—
1018C22×C4C2×C22⋊D1112yes—
1019C4⋊C4—228no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—228no—
1024C22⋊C4—228no—
1025C22⋊C4—444no—
1026C22⋊C4—444no—
1027C22⋊C4—444no—
1028C22⋊C4—444no—
1029C22⋊C4—444no—
1030C22⋊C4—444no—
1031C22⋊C4—444no—
1032C11#1441711yescharacteristic, complemented, Sylow
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—114no—
1102C23—222no—
1103C23—222no—
1104C23—222no—
1105C23—222no—
1106C23—222no—
1107C23—222no—
1108C23—222no—
1109C23—222no—
1110C23—222no—
1111C23—222no—
1112C23—222no—
1113C23—222no—
1114C23—222no—
1115C23—222no—
1116C23—222no—
1117C23—222no—
1118C23—222no—
1119C23—222no—
1120C23—441no—
1121C23—441no—
1122C23—441no—
1123C23—441no—
1124C23—441no—
1125C23—441no—
1126C23—441no—
1127C23—441no—
1128C23—441no—
1129C23—441no—
1130C23—441no—
1131C23—441no—
1132C23—441no—
1133C23—441no—
1134C23—441no—
1135C23—441no—
1136C23C2×(C2×D11)⋊C414yes—
1137C23C2×(C2×D11)⋊C414yes—
1138C23C22×C4×D1111yescharacteristic
1139C23C22×D4411yescharacteristic
1140C23C2×D4×D1111yescharacteristic
1141C23C2×#434111yescharacteristic
1142C23#6703711yescharacteristic
1143C23#6703711yescharacteristic
1144C23#6703711yescharacteristic
1145C23#6703711yescharacteristic
1146C23#6703711yescharacteristic
1147C23#6703711yescharacteristic
1148C23#41×D1111yescharacteristic
1149C23#41×D1111yescharacteristic
1150C23#6704211yescharacteristic
1151C23#6704311yescharacteristic
1152C23C22×C22⋊D1111yescharacteristic
1153D4—416no—
1154D4—4416no—
1155D4—4416no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—416no—
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—41no—
1190C2×C4—41no—
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—4416no—
1207C2×C4—4416no—
1208C2×C4—441no—
1209C2×C4—441no—
1210C2×C4—441no—
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—
1233C2×C4—441no—
1234C2×C4—441no—
1235C2×C4—441no—
1236C2×C4—441no—
1237C2×C4—441no—
1238C2×C4—441no—
1239C2×C4—441no—
1240C2×C4—441no—
1241C2×C4—441no—
1242C2×C4C2×(C2×D11)⋊C414yes—
1243C22—24no—
1244C22—24no—
1245C22—24no—
1246C22—24no—
1247C22—24no—
1248C22—24no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—42no—
1273C22—224no—
1274C22—224no—
1275C22—224no—
1276C22—442no—
1277C22—442no—
1278C22—442no—
1279C22—442no—
1280C22—442no—
1281C22—442no—
1282C22—442no—
1283C22—442no—
1284C22—442no—
1285C22—442no—
1286C22—442no—
1287C22—442no—
1288C22#1062301711yescharacteristic
1289C22#1062301711yescharacteristic
1290C22#1062302411yescharacteristic
1291C22#1062302411yescharacteristic
1292C22C4×#434111yescharacteristic
1293C22C4×D4×D1111yescharacteristic
1294C22#1062307611yescharacteristic
1295C22#1062307711yescharacteristic
1296C22D4×D4411yescharacteristic
1297C22#1062308511yescharacteristic
1298C22#1062308511yescharacteristic
1299C22#1062308611yescharacteristic
1300C22#1062312011yescharacteristic
1301C22#1062312211yescharacteristic
1302C22#1062312411yescharacteristic
1303C22#1062312611yescharacteristic
1304C22#1062313911yescharacteristic
1305C22#1062314311yescharacteristic
1306C22#1062314411yescharacteristic
1307C22#1062314511yescharacteristic
1308C22#1062314611yescharacteristic
1309C22#1062315011yescharacteristic
1310C22#1062315111yescharacteristic
1311C22#1062315211yescharacteristic
1312C22#1062318811yescharacteristic
1313C22#1062319111yescharacteristic
1314C22#1062319211yescharacteristic
1315C22#1062319811yescharacteristic
1316C22C22×(C2×D11)⋊C411yescharacteristic
1317C22D4×C22⋊D1111yescharacteristic
1318C22#1062333511yescharacteristic
1319C22#1062333511yescharacteristic
1320C22#1062333711yescharacteristic
1321C22#1062335511yescharacteristic
1322C22#1062336011yescharacteristic
1323C4—24no—
1324C4—42no—
1325C4—42no—
1326C4—81no—
1327C4—81no—
1328C4—442no—
1329C4—442no—
1330C4—442no—
1331C4—442no—
1332C4—442no—
1333C4—881no—
1334C4—881no—
1335C2—44no—
1336C2—44no—
1337C2—444no—
1338C2#1307119111yescharacteristic
1339C2#1307131811yescharacteristic
1340C2#1307137711yescharacteristic
1341C2D4×(C2×D11)⋊C411yescharacteristic
1342C2#1307144111yescharacteristic
1343C2#1307166511yescharacteristic
1344C2#1307176811yescharacteristic
1345C2#1307482011yescharacteristic
1346C2#1307482211yescharacteristic
1347C2#1307484811yescharacteristic
1348C2#1307485011yescharacteristic
1349C2#1307504811yescharacteristic
1350C2#1307505011yescharacteristic
1351C2#1307533011yescharacteristic
1352C2#1307533211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC22×#66991C2
hypercenterC2×#386D11
hypocenterC11#14417
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C2×#10622833C2semidirect
3. C2×#10622826C2semidirect
4. C2×#10622571C2semidirect
5. #13066885C2semidirect
6. #13066883C2semidirect
7. #13066863C2semidirect
8. #13066863C2semidirect
9. #13066855C2semidirect
10. #13066855C2semidirect
11. #13066839C2semidirect
12. #13066838C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C2×C11×#386C2semidirect
32. C2×#66991C4semidirect
92. C22×C22⋊D11C2×C4semidirect
93. C22×C22⋊D11C2×C4semidirect
114. C22×C4×D11C2×C4semidirect
137. C2×C22⋊Dic11C2×C4semidirect
138. C2×C22⋊Dic11C2×C4semidirect
151. C2×(C2×D11)⋊C4D4semidirect
154. C2×C4⋊Dic11C2×C4semidirect
224. C2×D4×C11C22⋊C4semidirect
361. C2×#386D11semidirect
913. C2×D4(C2×D11)⋊C4semidirect
1032. C11#14417semidirect

Maximal subgroups

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

subgroupindex
C22×#669912
C2×#106228332
C2×#106228262
C2×#106225712
#130668852
#130668832
#130668632
#130668552
#130668392
#130668382
(C2×D11)⋊#952
C2×C11×#3862
#1441711