Finite Group Databasebeta

← #14676791

Subgroups — #14676791

Order 2816.

2170 conjugacy classes of subgroups.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622283C211yesmaximal, characteristic, complemented
2C2×#10622571C211yesmaximal, characteristic
3C2×#10622569C211yesmaximal, characteristic
4C2×#10622563C211yesmaximal, characteristic, complemented
5C2×#10622600C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
7C2×#10622279C211yesmaximal, characteristic, complemented
8#13066872C211yesmaximal, characteristic, complemented
9#13066864C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic
11#13066853C211yesmaximal, characteristic, complemented
12#13066850C211yesmaximal, characteristic, complemented
13#13066848C211yesmaximal, characteristic, complemented
14#13066842C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
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
51#10622600—24no—
52#10622571—24no—
53#10622569C418yescomplemented
54#10622563—24no—
55C22⋊C4×Dic11—24no—
56#10622283—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×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—41no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—22no—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—41no—
105C2×C11×C22⋊C4C2×C414yes—
106C2×C22⋊Dic11—22no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—22no—
110C2×C22⋊Dic11—41no—
111C2×C22⋊Dic11C2×C414yes—
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—22no—
121C2×(C2×D11)⋊C4—22no—
122C2×(C2×D11)⋊C4—22no—
123C2×(C2×D11)⋊C4—41no—
124C2×(C2×D11)⋊C4—41no—
125C2×(C2×D11)⋊C4C2×C414yescomplemented
126C2×(C2×D11)⋊C4D414yes—
127C2×C4⋊Dic11—22no—
128C2×C4⋊Dic11—22no—
129C2×C4⋊Dic11—22no—
130C2×C4⋊Dic11—22no—
131C2×C4⋊Dic11—22no—
132C2×C4⋊Dic11—41no—
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—
142C11×#95—22no—
143C11×#95—22no—
144C11×#95—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—41no—
152C11⋊#95—41no—
153C11⋊#95—41no—
154C11⋊#95C2×C414yescomplemented
155C11⋊#95C2×C414yescomplemented
156C11⋊#95D414yescomplemented
157C11⋊#95D414yescomplemented
158#13988—111nomaximal, Sylow
159C24×C11—21no—
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×C11C22×C412yes—
172C24×C11#4112yes—
173C24×C11#4112yes—
174C24×C11C2411yescharacteristic
175C23×D11—21no—
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×D11C22×C412yes—
188C23×D11C2×D412yes—
189C23×D11#4112yes—
190C22×C4×C11—21no—
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×C11C22×C412yes—
226C22×C4×C11C22×C412yes—
227C22×C4×C11C2×D412yes—
228C22×C4×C11C2×D412yes—
229C22×C4×C11C2×D412yes—
230C22×C4×C11#4112yes—
231C22×C4×C11#4112yes—
232C2×C22⋊D11—28no—
233C2×C22⋊D11—28no—
234C2×C22⋊D11—44no—
235C2×C22⋊D11—44no—
236C2×C22⋊D11—44no—
237C2×C22⋊D11—44no—
238C2×C22⋊D11—44no—
239C22×Dic11—28no—
240C22×Dic11—21no—
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—21no—
279C22×Dic11—44no—
280C22×Dic11—44no—
281C22×Dic11—44no—
282C22×Dic11—44no—
283C22×Dic11—44no—
284C22×Dic11—44no—
285C22×Dic11C22×C412yes—
286C22×Dic11C22×C412yes—
287C22×Dic11C22×C412yes—
288C22×Dic11C2×D412yes—
289C22×Dic11C2×D412yes—
290C22×Dic11C2×D412yes—
291C22×Dic11C2×D412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11#4112yes—
294C22×Dic11#4112yes—
295C2×C4×D11—28no—
296C2×C4×D11—28no—
297C2×C4×D11—44no—
298C2×C4×D11—44no—
299C2×C4×D11—44no—
300C2×C4×D11—44no—
301C2×C4×D11—44no—
302C11×C4⋊C4—44no—
303C11×C22⋊C4—28no—
304C11×C22⋊C4—28no—
305C11×C22⋊C4—44no—
306C22⋊Dic11—28no—
307C22⋊Dic11—44no—
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—44no—
314C4⋊Dic11—44no—
315C4×Dic11—44no—
316C4×Dic11—44no—
317C4×Dic11—44no—
318C2×#388—111no—
319C2×#386—111no—
320C2×#386—111no—
321C2×#385—111no—
322C2×#380—111no—
323C2×C4×C22⋊C4—111no—
324C2×C4×C22⋊C4—111no—
325#1442—111no—
326#1440—111no—
327#1439D1111yescharacteristic, complemented
328#1438—111no—
329#1437—111no—
330#1436—111no—
331#1436—111no—
332#1434—111no—
333C23×C11—22no—
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—41no—
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#11714yes—
368C23×C11C23×C411yescharacteristic
369C23×C11C22×D411yescharacteristic
370C23×C11C22×D411yescharacteristic
371C23×C11C22×D411yescharacteristic
372C23×C11C2×#4111yescharacteristic
373C23×C11C2×#4111yescharacteristic
374C23×C11C2×#4111yescharacteristic
375C23×C11C2×#4111yescharacteristic
376C23×C11C2×#4111yescharacteristic
377C23×C11C2×#4111yescharacteristic
378C23×C11C2×#4111yescharacteristic
379C23×C11H(5,𝔽2)11yescharacteristic
380C23×C11H(5,𝔽2)11yescharacteristic
381C23×C11H(5,𝔽2)11yescharacteristic
382C23×C112−1+411yescharacteristic
383C22×D11—22no—
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—41no—
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×D11C4×D414yes—
418C2×C4×C11—22no—
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—22no—
435C2×C4×C11—22no—
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×C11C4×D414yes—
460C22⋊D11—416no—
461C2×Dic11—22no—
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—416no—
486C2×Dic11—41no—
487C2×Dic11—41no—
488C2×Dic11—41no—
489C2×Dic11—41no—
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×Dic11C4×D414yes—
510C2×Dic11#12114yes—
511C4×D11—416no—
512C23×D4—111no—
513C24×C4—111no—
514C24×C4—111no—
515C22×C4⋊C4—111no—
516C22×C4⋊C4—111no—
517C22×C4⋊C4C2×D1111yescharacteristic
518C22×C22⋊C4—111no—
519C22×C22⋊C4—111no—
520C22×C22⋊C4—111no—
521C22×C22⋊C4—111no—
522C22×C22⋊C4—111no—
523C22×C22⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4C2×D1111yescharacteristic
526C22×C22⋊C4C2×D1111yescharacteristic
527C22×C22⋊C4C2×D1111yescharacteristic
528C22×C42—111no—
529C22×C42—111no—
530C22×C42—111no—
531#388—224no—
532#386—118no—
533#386—224no—
534#385—224no—
535#380—224no—
536C4×C22⋊C4—224no—
537C4×C22⋊C4—224no—
538C2×#95—111no—
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
554C22×C11—24no—
555C22×C11—24no—
556C22×C11—24no—
557C22×C11—42no—
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×C11C2×#11711yescharacteristic
570C22×C11C2×C4×D411yescharacteristic
571C22×C11C2×C4×D411yescharacteristic
572C22×C11C2×C4×D411yescharacteristic
573C22×C11C4×#4111yescharacteristic
574C22×C11#51811yescharacteristic
575C22×C11#52011yescharacteristic
576C22×C11C2×#12111yescharacteristic
577C22×C11#52511yescharacteristic
578C22×C11#52511yescharacteristic
579C22×C11#52511yescharacteristic
580C22×C11#52911yescharacteristic
581C22×C11#52911yescharacteristic
582C22×C11#52911yescharacteristic
583C22×C11#53211yescharacteristic
584C22×C11#53811yescharacteristic
585C22×C11#53911yescharacteristic
586C22×C11#54011yescharacteristic
587C22×C11#54211yescharacteristic
588C22×C11D4211yescharacteristic
589C22×C11D4211yescharacteristic
590C22×C11#54611yescharacteristic
591C22×C11#54611yescharacteristic
592C22×C11#54611yescharacteristic
593C22×C11#54611yescharacteristic
594C22×C11#54611yescharacteristic
595C22×C11#54711yescharacteristic
596C22×C11#54811yescharacteristic
597C22×C11#54811yescharacteristic
598C22×C11#55111yescharacteristic
599C22×C11#55111yescharacteristic
600C22×C11#55111yescharacteristic
601C22×C11#55211yescharacteristic
602C22×C11#55311yescharacteristic
603C22×C11#55311yescharacteristic
604C2×D11—24no—
605C2×D11—24no—
606C2×D11—24no—
607C2×D11—42no—
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—
619C4×C11—24no—
620C4×C11—42no—
621C4×C11—42no—
622C4×C11—42no—
623C4×C11—42no—
624C4×C11—81no—
625Dic11—24no—
626Dic11—24no—
627Dic11—42no—
628Dic11—42no—
629Dic11—42no—
630Dic11—42no—
631Dic11—81no—
632C25—111no—
633C25C22×D1111yescharacteristic
634C22×D4—114no—
635C22×D4—222no—
636C22×D4—222no—
637C22×D4—222no—
638C22×D4—222no—
639C22×D4—441no—
640C22×D4—441no—
641C23×C4—111no—
642C23×C4—111no—
643C23×C4—111no—
644C23×C4—111no—
645C23×C4—111no—
646C23×C4—111no—
647C23×C4—114no—
648C23×C4—111no—
649C23×C4—222no—
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—441no—
659C23×C4—441no—
660C23×C4—441no—
661C23×C4—441no—
662C23×C4C22×D1111yescharacteristic
663C23×C4C22×D1111yescharacteristic
664C23×C4C22×D1111yescharacteristic
665C23×C4C22×D1111yescharacteristic
666C23×C4C22×D1111yescharacteristic
667C23×C4C22×D1111yescharacteristic
668C2×C4⋊C4—22no—
669C2×C4⋊C4—22no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—222no—
672C2×C4⋊C4—222no—
673C2×C4⋊C4—222no—
674C2×C4⋊C4—222no—
675C2×C4⋊C4—222no—
676C2×C4⋊C4—441no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—41no—
685C2×C22⋊C4—114no—
686C2×C22⋊C4—114no—
687C2×C22⋊C4—114no—
688C2×C22⋊C4—222no—
689C2×C22⋊C4—222no—
690C2×C22⋊C4—222no—
691C2×C22⋊C4—222no—
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—441no—
704C2×C22⋊C4—441no—
705C2×C22⋊C4—441no—
706C2×C22⋊C4C4×D1114yes—
707C2×C42—222no—
708C2×C42—222no—
709C2×C42—222no—
710C2×C42—222no—
711C2×C42—222no—
712C2×C42—222no—
713C2×C42—441no—
714C2×C42—441no—
715C2×C42—441no—
716#95—22no—
717#95—22no—
718#95—22no—
719#95—114no—
720#95—114no—
721#95—114no—
722#95—114no—
723#95—222no—
724#95—222no—
725#95—222no—
726#95—222no—
727#95—222no—
728#95—222no—
729#95—441no—
730#95—441no—
731#95—441no—
732C2×C11—44no—
733C2×C11#229011yescharacteristic
734C2×C11C4×#12111yescharacteristic
735C2×C11#233511yescharacteristic
736C2×C11#234211yescharacteristic
737C2×C11#235211yescharacteristic
738C2×C11#235811yescharacteristic
739C2×C11#236111yescharacteristic
740C2×C11#242411yescharacteristic
741C2×C11#242711yescharacteristic
742C2×C11#245711yescharacteristic
743C2×C11#246311yescharacteristic
744C2×C11#246411yescharacteristic
745C2×C11#247711yescharacteristic
746C2×C11#255311yescharacteristic
747C2×C11#257811yescharacteristic
748D11—44no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—112no—
762C24—112no—
763C24—112no—
764C24—221no—
765C24—221no—
766C24—221no—
767C24—221no—
768C24—221no—
769C24—221no—
770C24—221no—
771C24—221no—
772C24—221no—
773C24—221no—
774C24—221no—
775C24—221no—
776C24C2×C4×D1112yes—
777C24#434112yes—
778C24#434312yes—
779C24C23×D1111yescharacteristic
780C2×D4—228no—
781C2×D4—228no—
782C2×D4—444no—
783C2×D4—444no—
784C2×D4—444no—
785C2×D4—444no—
786C2×D4—444no—
787C22×C4—21no—
788C22×C4—21no—
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—112no—
823C22×C4—112no—
824C22×C4—112no—
825C22×C4—112no—
826C22×C4—112no—
827C22×C4—112no—
828C22×C4—112no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—112no—
832C22×C4—228no—
833C22×C4—221no—
834C22×C4—221no—
835C22×C4—221no—
836C22×C4—221no—
837C22×C4—221no—
838C22×C4—221no—
839C22×C4—221no—
840C22×C4—221no—
841C22×C4—228no—
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—221no—
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—228no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—221no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—444no—
875C22×C4—444no—
876C22×C4—444no—
877C22×C4—444no—
878C22×C4—444no—
879C22×C4—444no—
880C22×C4—444no—
881C22×C4—444no—
882C22×C4—444no—
883C22×C4—444no—
884C22×C4—444no—
885C22×C4C2×C4×D1112yes—
886C22×C4C2×C4×D1112yes—
887C22×C4D4×D1112yes—
888C22×C4D4×D1112yes—
889C22×C4D4×D1112yes—
890C22×C4#434112yes—
891C22×C4#434112yes—
892C4⋊C4—44no—
893C4⋊C4—444no—
894C4⋊C4—444no—
895C22⋊C4—28no—
896C22⋊C4—28no—
897C22⋊C4—44no—
898C22⋊C4—228no—
899C22⋊C4—228no—
900C22⋊C4—228no—
901C22⋊C4—228no—
902C22⋊C4—444no—
903C22⋊C4—444no—
904C22⋊C4—444no—
905C42—444no—
906C42—444no—
907C42—444no—
908C11#1398811yescharacteristic, complemented, Sylow
909C23—22no—
910C23—22no—
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—41no—
928C23—41no—
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—114no—
944C23—222no—
945C23—222no—
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—441no—
963C23—441no—
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#6694514yes—
979C23C22×C4×D1111yescharacteristic
980C23C2×D4×D1111yescharacteristic
981C23C2×D4×D1111yescharacteristic
982C23C2×D4×D1111yescharacteristic
983C23C2×#434111yescharacteristic
984C23C2×#434111yescharacteristic
985C23C2×#434111yescharacteristic
986C23#6703711yescharacteristic
987C23C2×#434311yescharacteristic
988C23#41×D1111yescharacteristic
989C23#41×D1111yescharacteristic
990C23#41×D1111yescharacteristic
991C23#6704211yescharacteristic
992C23#6704211yescharacteristic
993C23#6704311yescharacteristic
994D4—4416no—
995C2×C4—22no—
996C2×C4—22no—
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—22no—
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—114no—
1037C2×C4—114no—
1038C2×C4—222no—
1039C2×C4—222no—
1040C2×C4—222no—
1041C2×C4—222no—
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—4416no—
1063C2×C4—4416no—
1064C2×C4—441no—
1065C2×C4—441no—
1066C2×C4—441no—
1067C2×C4—441no—
1068C2×C4—441no—
1069C2×C4—441no—
1070C2×C4—441no—
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(C22⋊D11)⋊C414yes—
1088C22—24no—
1089C22—24no—
1090C22—24no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—224no—
1104C22—224no—
1105C22—224no—
1106C22—442no—
1107C22—442no—
1108C22—442no—
1109C22—442no—
1110C22—442no—
1111C22—442no—
1112C22—442no—
1113C22—442no—
1114C22—442no—
1115C22—442no—
1116C22—442no—
1117C22—442no—
1118C22C2×(C22⋊D11)⋊C411yescharacteristic
1119C22C2×#6694511yescharacteristic
1120C22#1062305411yescharacteristic
1121C22C4×#434111yescharacteristic
1122C22C4×D4×D1111yescharacteristic
1123C22C4×D4×D1111yescharacteristic
1124C22#1062307611yescharacteristic
1125C22#1062311711yescharacteristic
1126C22#1062312211yescharacteristic
1127C22#1062312211yescharacteristic
1128C22#1062312911yescharacteristic
1129C22D11×#12111yescharacteristic
1130C22#1062313711yescharacteristic
1131C22#1062314011yescharacteristic
1132C22#1062314011yescharacteristic
1133C22#1062314111yescharacteristic
1134C22#1062314911yescharacteristic
1135C22#1062315011yescharacteristic
1136C22#1062315511yescharacteristic
1137C22#1062315811yescharacteristic
1138C22#1062316111yescharacteristic
1139C22#1062316111yescharacteristic
1140C22#1062316811yescharacteristic
1141C22#1062317311yescharacteristic
1142C22#1062318011yescharacteristic
1143C22#1062318611yescharacteristic
1144C22#1062318911yescharacteristic
1145C22#1062318911yescharacteristic
1146C22#1062319611yescharacteristic
1147C22#1062320011yescharacteristic
1148C22#1062320811yescharacteristic
1149C22#1062321111yescharacteristic
1150C22#1062323511yescharacteristic
1151C22#1062324011yescharacteristic
1152C22#1062324711yescharacteristic
1153C4—24no—
1154C4—42no—
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—81no—
1159C4—224no—
1160C4—224no—
1161C4—442no—
1162C4—442no—
1163C4—442no—
1164C4—442no—
1165C4—881no—
1166C2—44no—
1167C2—444no—
1168C2#1307105211yescharacteristic
1169C2#1307113211yescharacteristic
1170C2#1307141311yescharacteristic
1171C2#1307146311yescharacteristic
1172C2#1307154711yescharacteristic
1173C2#1307159611yescharacteristic
1174C2#1307162911yescharacteristic
1175C2#1307214711yescharacteristic
1176C2#1307218611yescharacteristic
1177C2#1307252411yescharacteristic
1178C2#1307260811yescharacteristic
1179C2#1307261711yescharacteristic
1180C2#1307282011yescharacteristic
1181C2#1307366211yescharacteristic
1182C2#1307395311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#13988
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
1. C2×#10622283C2semidirect
4. C2×#10622563C2semidirect
5. C2×#10622600C2semidirect
6. C2×C22⋊C4×Dic11C2semidirect
7. C2×#10622279C2semidirect
8. #13066872C2semidirect
9. #13066864C2semidirect
11. #13066853C2semidirect
12. #13066850C2semidirect
13. #13066848C2semidirect
14. #13066842C2semidirect
15. C11×#1439C2semidirect
53. #10622569C4semidirect
93. C22×C4×D11C2×C4semidirect
125. C2×(C2×D11)⋊C4C2×C4semidirect
154. C11⋊#95C2×C4semidirect
155. C11⋊#95C2×C4semidirect
156. C11⋊#95D4semidirect
157. C11⋊#95D4semidirect
327. #1439D11semidirect
908. C11#13988semidirect

Maximal subgroups

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

subgroupindex
C2×#106222832
C2×#106225712
C2×#106225692
C2×#106225632
C2×#106226002
C2×C22⋊C4×Dic112
C2×#106222792
#130668722
#130668642
#130668552
#130668532
#130668502
#130668482
#130668422
C11×#14392
#1398811