Finite Group Databasebeta

← #14684736

Subgroups — #14684736

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622836C211yesmaximal, characteristic
2#13066877C211yesmaximal, characteristic, complemented
3#13066876C211yesmaximal, characteristic, complemented
4#13066864C211yesmaximal, characteristic, complemented
5#13066863C211yesmaximal, characteristic, complemented
6#13066863C211yesmaximal, characteristic, complemented
7#13066857C211yesmaximal, characteristic, complemented
8#13066855C211yesmaximal, characteristic, complemented
9#13066855C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic, complemented
11#13066855C211yesmaximal, characteristic, complemented
12#13066853C211yesmaximal, characteristic, complemented
13#13066853C211yesmaximal, characteristic, complemented
14#13066852C211yesmaximal, characteristic, complemented
15C11×#1438C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic
28C22×C22⋊Dic11C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2211yescharacteristic
37#10622836C418yescomplemented
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
52C25×C11C2311yescharacteristic
53C25×C11C2311yescharacteristic
54C24×D11C2311yescharacteristic
55C22×D4×C11—41no—
56C22×D4×C11—41no—
57C22×D4×C11—41no—
58C22×D4×C11—41no—
59C22×D4×C11—41no—
60C22×D4×C11—41no—
61C22×D4×C11C2×C414yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—41no—
68C22×C22⋊D11—41no—
69C22×C22⋊D11—41no—
70C22×C22⋊D11—41no—
71C22×C22⋊D11—41no—
72C22×C22⋊D11—41no—
73C22×C22⋊D11—41no—
74C22×C22⋊D11—41no—
75C22×C22⋊D11—41no—
76C22×C22⋊D11—41no—
77C22×C22⋊D11—41no—
78C22×C22⋊D11—41no—
79C22×C22⋊D11C2×C414yes—
80C22×C22⋊D11C2×C414yes—
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—41no—
91C2×C11×C22⋊C4—41no—
92C2×C11×C22⋊C4—41no—
93C2×C11×C22⋊C4—41no—
94C2×C11×C22⋊C4—41no—
95C2×C11×C22⋊C4—41no—
96C2×C11×C22⋊C4—41no—
97C2×C11×C22⋊C4—41no—
98C2×C11×C22⋊C4—41no—
99C2×C11×C22⋊C4—41no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—41no—
103C2×C22⋊Dic11—41no—
104C2×C22⋊Dic11—41no—
105C2×C22⋊Dic11—41no—
106C2×C22⋊Dic11—41no—
107C2×C22⋊Dic11—41no—
108C2×C22⋊Dic11—41no—
109C2×C22⋊Dic11—41no—
110C2×C22⋊Dic11—41no—
111C2×C22⋊Dic11—41no—
112C2×C22⋊Dic11—41no—
113C2×C22⋊Dic11—41no—
114C2×C22⋊Dic11—41no—
115C2×C22⋊Dic11—41no—
116C2×C22⋊Dic11C2×C414yes—
117C2×C22⋊Dic11C2×C414yes—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×(C2×D11)⋊C4—41no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4—41no—
123C2×(C2×D11)⋊C4—41no—
124C2×(C2×D11)⋊C4—41no—
125C2×(C2×D11)⋊C4—41no—
126C2×(C2×D11)⋊C4—41no—
127C2×(C2×D11)⋊C4—41no—
128C2×(C2×D11)⋊C4—41no—
129C2×(C2×D11)⋊C4—41no—
130C2×(C2×D11)⋊C4—41no—
131C2×(C2×D11)⋊C4—41no—
132C2×(C2×D11)⋊C4C2×C414yes—
133C2×C4×Dic11—41no—
134C2×C4×Dic11—41no—
135C2×C4×Dic11—41no—
136C11×#95—41no—
137C11×#95—41no—
138C11⋊#95—41no—
139C11⋊#95—41no—
140C11⋊#95—41no—
141C11⋊#95—41no—
142C11⋊#95—41no—
143C11⋊#95—41no—
144C11⋊#95—41no—
145C11⋊#95—41no—
146C11⋊#95—41no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151C11⋊#95C2×C414yes—
152#14651—111nomaximal, Sylow
153C24×C11—21no—
154C24×C11—21no—
155C24×C11—21no—
156C24×C11—21no—
157C24×C11—21no—
158C24×C11—21no—
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×C11—21no—
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×C11C22×C412yes—
182C24×C11C22×C412yes—
183C24×C11C2411yescharacteristic
184C23×D11—21no—
185C23×D11—21no—
186C23×D11—21no—
187C23×D11—21no—
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×D11C22×C412yes—
199C2×D4×C11—44no—
200C2×D4×C11—44no—
201C2×D4×C11—44no—
202C2×D4×C11—44no—
203C2×D4×C11—44no—
204C2×D4×C11—44no—
205C2×D4×C11—44no—
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×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×C11C22×C412yes—
240C22×C4×C11#4112yes—
241C2×C22⋊D11—44no—
242C2×C22⋊D11—44no—
243C2×C22⋊D11—44no—
244C2×C22⋊D11—44no—
245C2×C22⋊D11—44no—
246C2×C22⋊D11—44no—
247C2×C22⋊D11—44no—
248C2×C22⋊D11—44no—
249C2×C22⋊D11—44no—
250C2×C22⋊D11—44no—
251C2×C22⋊D11—44no—
252C2×C22⋊D11—44no—
253C2×C22⋊D11—44no—
254C2×C22⋊D11—44no—
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—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×Dic11C22×C412yes—
301C22×Dic11C22×C412yes—
302C22×Dic11C22×C412yes—
303C22×Dic11#4112yes—
304C11×C22⋊C4—44no—
305C11×C22⋊C4—44no—
306C11×C22⋊C4—44no—
307C11×C22⋊C4—44no—
308C22⋊Dic11—44no—
309C22⋊Dic11—44no—
310C22⋊Dic11—44no—
311C22⋊Dic11—44no—
312C22⋊Dic11—44no—
313C22⋊Dic11—44no—
314(C2×D11)⋊C4—44no—
315(C2×D11)⋊C4—44no—
316(C2×D11)⋊C4—44no—
317(C2×D11)⋊C4—44no—
318(C2×D11)⋊C4—44no—
319C4×Dic11—44no—
320C2×#392—111no—
321#1443—111no—
322#1443—111no—
323#1440—111no—
324#1440—111no—
325#1440—111no—
326#1438—111no—
327#1438—111no—
328#1438—111no—
329#1438—111no—
330#1438—111no—
331#1438D1111yescharacteristic, complemented
332#1437—111no—
333#1437—111no—
334#1437—111no—
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—41no—
350C23×C11—41no—
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—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×C11—41no—
383C23×C11—41no—
384C23×C11—41no—
385C23×C11—41no—
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×C11—41no—
403C23×C11—41no—
404C23×C11—41no—
405C23×C11C23×C411yescharacteristic
406C23×C11C2×#4111yescharacteristic
407C23×C11C2×#4111yescharacteristic
408C23×C11H(5,𝔽2)11yescharacteristic
409C23×C11H(5,𝔽2)11yescharacteristic
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×C11H(5,𝔽2)11yescharacteristic
418C23×C11H(5,𝔽2)11yescharacteristic
419C23×C11H(5,𝔽2)11yescharacteristic
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—22no—
423C22×D11—22no—
424C22×D11—22no—
425C22×D11—22no—
426C22×D11—22no—
427C22×D11—41no—
428C22×D11—41no—
429C22×D11—41no—
430C22×D11—41no—
431C22×D11—41no—
432C22×D11—41no—
433C22×D11—41no—
434C22×D11—41no—
435C22×D11—41no—
436C22×D11—41no—
437C22×D11—41no—
438C22×D11—41no—
439C22×D11—41no—
440C22×D11—41no—
441C22×D11—41no—
442C22×D11—41no—
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—
455D4×C11—416no—
456C2×C4×C11—22no—
457C2×C4×C11—22no—
458C2×C4×C11—22no—
459C2×C4×C11—22no—
460C2×C4×C11—22no—
461C2×C4×C11—22no—
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—
475C2×C4×C11—41no—
476C2×C4×C11—41no—
477C2×C4×C11—41no—
478C2×C4×C11—41no—
479C2×C4×C11—41no—
480C2×C4×C11—41no—
481C2×C4×C11—41no—
482C2×C4×C11—41no—
483C2×C4×C11—41no—
484C2×C4×C11—41no—
485C2×C4×C11—41no—
486C2×C4×C11—41no—
487C2×C4×C11—41no—
488C2×C4×C11—41no—
489C2×C4×C11—41no—
490C2×C4×C11—41no—
491C22⋊D11—416no—
492C22⋊D11—416no—
493C2×Dic11—22no—
494C2×Dic11—22no—
495C2×Dic11—22no—
496C2×Dic11—22no—
497C2×Dic11—22no—
498C2×Dic11—22no—
499C2×Dic11—22no—
500C2×Dic11—22no—
501C2×Dic11—22no—
502C2×Dic11—22no—
503C2×Dic11—22no—
504C2×Dic11—22no—
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×Dic11—41no—
525C2×Dic11—41no—
526C2×Dic11—41no—
527C2×Dic11—41no—
528C2×Dic11—41no—
529C2×Dic11—41no—
530C2×Dic11—41no—
531C2×Dic11—41no—
532C2×Dic11—41no—
533C2×Dic11—41no—
534C2×Dic11—41no—
535C2×Dic11—41no—
536C2×Dic11—41no—
537C2×Dic11—41no—
538C2×Dic11—41no—
539C2×Dic11—41no—
540C2×Dic11—41no—
541C2×Dic11—41no—
542C23×D4—111no—
543C23×D4—111no—
544C23×D4C2×D1111yescharacteristic
545C22×C22⋊C4—111no—
546C22×C22⋊C4—111no—
547C22×C22⋊C4—111no—
548C22×C22⋊C4—111no—
549C22×C22⋊C4—111no—
550C22×C22⋊C4—111no—
551C22×C22⋊C4—111no—
552C22×C22⋊C4—111no—
553C22×C22⋊C4—111no—
554C22×C22⋊C4—111no—
555C22×C22⋊C4—111no—
556C22×C22⋊C4C2×D1111yescharacteristic
557C22×C22⋊C4C2×D1111yescharacteristic
558C22×C22⋊C4C2×D1111yescharacteristic
559C22×C22⋊C4C2×D1111yescharacteristic
560C22×C42—111no—
561#392—118no—
562C2×#95—111no—
563C2×#95—111no—
564C2×#95—111no—
565C2×#95—111no—
566C2×#95—111no—
567C2×#95—111no—
568C2×#95—111no—
569C2×#95—111no—
570C2×#95—111no—
571C2×#95—111no—
572C2×#95—111no—
573C2×#95—111no—
574C2×#95—111no—
575C2×#95—111no—
576C2×#95C2×D1111yescharacteristic
577C2×#95C2×D1111yescharacteristic
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×C11—42no—
587C22×C11—42no—
588C22×C11—42no—
589C22×C11—42no—
590C22×C11—42no—
591C22×C11—42no—
592C22×C11—81no—
593C22×C11—81no—
594C22×C11—81no—
595C22×C11—81no—
596C22×C11—81no—
597C22×C11—81no—
598C22×C11—81no—
599C22×C11—81no—
600C22×C11—81no—
601C22×C11—81no—
602C22×C11—81no—
603C22×C11—81no—
604C22×C11—81no—
605C22×C11—81no—
606C22×C11—81no—
607C22×C11—81no—
608C22×C11C4×#4111yescharacteristic
609C22×C11#51811yescharacteristic
610C22×C11#51811yescharacteristic
611C22×C11#51811yescharacteristic
612C22×C11#51811yescharacteristic
613C22×C11#51811yescharacteristic
614C22×C11#51811yescharacteristic
615C22×C11#53811yescharacteristic
616C22×C11#53811yescharacteristic
617C22×C11#53811yescharacteristic
618C22×C11#53811yescharacteristic
619C22×C11#53811yescharacteristic
620C22×C11#53811yescharacteristic
621C22×C11#54011yescharacteristic
622C22×C11#54011yescharacteristic
623C22×C11#54011yescharacteristic
624C22×C11#54011yescharacteristic
625C22×C11#54011yescharacteristic
626C22×C11#54011yescharacteristic
627C22×C11#56011yescharacteristic
628C22×C11#56011yescharacteristic
629C22×C11#56011yescharacteristic
630C22×C11#56011yescharacteristic
631C22×C11#56011yescharacteristic
632C22×C11#56011yescharacteristic
633C22×C11#56011yescharacteristic
634C22×C11#56011yescharacteristic
635C22×C11#56011yescharacteristic
636C22×C11#56011yescharacteristic
637C22×C11#56011yescharacteristic
638C22×C11#56011yescharacteristic
639C22×C11#56011yescharacteristic
640C22×C11H(3,𝔽4)11yescharacteristic
641C22×C11H(3,𝔽4)11yescharacteristic
642C22×C11H(3,𝔽4)11yescharacteristic
643C2×D11—42no—
644C2×D11—42no—
645C2×D11—42no—
646C2×D11—42no—
647C2×D11—42no—
648C2×D11—42no—
649C2×D11—42no—
650C2×D11—81no—
651C2×D11—81no—
652C2×D11—81no—
653C2×D11—81no—
654C2×D11—81no—
655C2×D11—81no—
656C2×D11—81no—
657C2×D11—81no—
658C4×C11—42no—
659C4×C11—42no—
660C4×C11—81no—
661C4×C11—81no—
662C4×C11—81no—
663Dic11—42no—
664Dic11—42no—
665Dic11—42no—
666Dic11—42no—
667Dic11—81no—
668Dic11—81no—
669Dic11—81no—
670C25—111no—
671C25C22×D1111yescharacteristic
672C25C22×D1111yescharacteristic
673C22×D4—41no—
674C22×D4—41no—
675C22×D4—41no—
676C22×D4—41no—
677C22×D4—41no—
678C22×D4—41no—
679C22×D4—114no—
680C22×D4—114no—
681C22×D4—441no—
682C22×D4—441no—
683C22×D4—441no—
684C22×D4—441no—
685C22×D4—441no—
686C22×D4—441no—
687C22×D4—441no—
688C22×D4—441no—
689C22×D4—441no—
690C22×D4—441no—
691C22×D4—441no—
692C22×D4—441no—
693C22×D4C4×D1114yes—
694C23×C4—111no—
695C23×C4—111no—
696C23×C4—111no—
697C23×C4—111no—
698C23×C4—111no—
699C23×C4—111no—
700C23×C4—111no—
701C23×C4C22×D1111yescharacteristic
702C23×C4C22×D1111yescharacteristic
703C23×C4C22×D1111yescharacteristic
704C23×C4C22×D1111yescharacteristic
705C23×C4C22×D1111yescharacteristic
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—41no—
709C2×C22⋊C4—41no—
710C2×C22⋊C4—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4—41no—
718C2×C22⋊C4—114no—
719C2×C22⋊C4—114no—
720C2×C22⋊C4—114no—
721C2×C22⋊C4—222no—
722C2×C22⋊C4—222no—
723C2×C22⋊C4—222no—
724C2×C22⋊C4—222no—
725C2×C22⋊C4—441no—
726C2×C22⋊C4—441no—
727C2×C22⋊C4—441no—
728C2×C22⋊C4—441no—
729C2×C22⋊C4—441no—
730C2×C22⋊C4—441no—
731C2×C22⋊C4—441no—
732C2×C22⋊C4—441no—
733C2×C22⋊C4—441no—
734C2×C22⋊C4—441no—
735C2×C22⋊C4—441no—
736C2×C22⋊C4—441no—
737C2×C22⋊C4—441no—
738C2×C22⋊C4—441no—
739C2×C22⋊C4—441no—
740C2×C22⋊C4—441no—
741C2×C22⋊C4—441no—
742C2×C22⋊C4—441no—
743C2×C22⋊C4—441no—
744C2×C22⋊C4—441no—
745C2×C22⋊C4—441no—
746C2×C22⋊C4—441no—
747C2×C22⋊C4—441no—
748C2×C22⋊C4—441no—
749C2×C22⋊C4—441no—
750C2×C22⋊C4—441no—
751C2×C42—441no—
752C2×C42—441no—
753C2×C42—441no—
754#95—41no—
755#95—41no—
756#95—114no—
757#95—441no—
758#95—441no—
759#95—441no—
760#95—441no—
761#95—441no—
762#95—441no—
763#95—441no—
764#95—441no—
765#95—441no—
766#95—441no—
767#95—441no—
768#95—441no—
769#95—441no—
770C2×C11—82no—
771C2×C11—82no—
772C2×C11#233311yescharacteristic
773C2×C11#233311yescharacteristic
774C2×C11#233311yescharacteristic
775C2×C11#237511yescharacteristic
776C2×C11#237511yescharacteristic
777C2×C11#237511yescharacteristic
778C2×C11#238011yescharacteristic
779C2×C11#282511yescharacteristic
780C2×C11#282511yescharacteristic
781C2×C11#282811yescharacteristic
782C2×C11#282811yescharacteristic
783C2×C11#282811yescharacteristic
784C2×C11#282811yescharacteristic
785C2×C11#282811yescharacteristic
786C2×C11#282811yescharacteristic
787D11—82no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—21no—
806C24—21no—
807C24—21no—
808C24—21no—
809C24—21no—
810C24—21no—
811C24—21no—
812C24—21no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—112no—
817C24—221no—
818C24—221no—
819C24—221no—
820C24—221no—
821C24—221no—
822C24—221no—
823C24—221no—
824C24—221no—
825C24—221no—
826C24—221no—
827C24—221no—
828C24—221no—
829C24—221no—
830C24—221no—
831C24C2×C4×D1112yes—
832C24C2×C4×D1112yes—
833C24C23×D1111yescharacteristic
834C2×D4—44no—
835C2×D4—44no—
836C2×D4—44no—
837C2×D4—44no—
838C2×D4—44no—
839C2×D4—44no—
840C2×D4—44no—
841C2×D4—444no—
842C2×D4—444no—
843C2×D4—444no—
844C2×D4—444no—
845C2×D4—444no—
846C2×D4—444no—
847C2×D4—444no—
848C2×D4—444no—
849C2×D4—444no—
850C2×D4—444no—
851C2×D4—444no—
852C2×D4—444no—
853C2×D4—444no—
854C2×D4—444no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—112no—
889C22×C4—112no—
890C22×C4—112no—
891C22×C4—112no—
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—221no—
901C22×C4—221no—
902C22×C4—221no—
903C22×C4—221no—
904C22×C4—221no—
905C22×C4—221no—
906C22×C4—221no—
907C22×C4—221no—
908C22×C4—221no—
909C22×C4—221no—
910C22×C4—221no—
911C22×C4—221no—
912C22×C4—221no—
913C22×C4—221no—
914C22×C4—221no—
915C22×C4—221no—
916C22×C4—221no—
917C22×C4—221no—
918C22×C4—221no—
919C22×C4—221no—
920C22×C4—221no—
921C22×C4—221no—
922C22×C4—221no—
923C22×C4—221no—
924C22×C4—221no—
925C22×C4—221no—
926C22×C4—221no—
927C22×C4—221no—
928C22×C4—221no—
929C22×C4—221no—
930C22×C4—221no—
931C22×C4—221no—
932C22×C4—221no—
933C22×C4—221no—
934C22×C4—221no—
935C22×C4—221no—
936C22×C4—221no—
937C22×C4C2×C4×D1112yes—
938C22×C4#434112yes—
939C22⋊C4—44no—
940C22⋊C4—44no—
941C22⋊C4—44no—
942C22⋊C4—44no—
943C22⋊C4—444no—
944C22⋊C4—444no—
945C22⋊C4—444no—
946C22⋊C4—444no—
947C22⋊C4—444no—
948C22⋊C4—444no—
949C22⋊C4—444no—
950C22⋊C4—444no—
951C22⋊C4—444no—
952C22⋊C4—444no—
953C22⋊C4—444no—
954C42—444no—
955C11#1465111yescharacteristic, complemented, Sylow
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—222no—
1027C23—222no—
1028C23—222no—
1029C23—222no—
1030C23—222no—
1031C23—222no—
1032C23—222no—
1033C23—441no—
1034C23—441no—
1035C23—441no—
1036C23—441no—
1037C23—441no—
1038C23—441no—
1039C23—441no—
1040C23—441no—
1041C23—441no—
1042C23—441no—
1043C23—441no—
1044C23—441no—
1045C23—441no—
1046C23—441no—
1047C23—441no—
1048C23—441no—
1049C23—441no—
1050C23—441no—
1051C23—441no—
1052C23—441no—
1053C23—441no—
1054C23—441no—
1055C23—441no—
1056C23—441no—
1057C23—441no—
1058C23—441no—
1059C23—441no—
1060C23—441no—
1061C23C22×C4×D1111yescharacteristic
1062C23C2×#434111yescharacteristic
1063C23#6703711yescharacteristic
1064C23#6703711yescharacteristic
1065C23#6703711yescharacteristic
1066C23#6703711yescharacteristic
1067C23#6703711yescharacteristic
1068C23#6703711yescharacteristic
1069C23#6703711yescharacteristic
1070C23#6703711yescharacteristic
1071C23#6703711yescharacteristic
1072C23#41×D1111yescharacteristic
1073C23#6704211yescharacteristic
1074C23#6704211yescharacteristic
1075C23#6704211yescharacteristic
1076D4—416no—
1077D4—4416no—
1078D4—4416no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—222no—
1115C2×C4—222no—
1116C2×C4—222no—
1117C2×C4—222no—
1118C2×C4—222no—
1119C2×C4—222no—
1120C2×C4—222no—
1121C2×C4—222no—
1122C2×C4—222no—
1123C2×C4—222no—
1124C2×C4—222no—
1125C2×C4—222no—
1126C2×C4—441no—
1127C2×C4—441no—
1128C2×C4—441no—
1129C2×C4—441no—
1130C2×C4—441no—
1131C2×C4—441no—
1132C2×C4—441no—
1133C2×C4—441no—
1134C2×C4—441no—
1135C2×C4—441no—
1136C2×C4—441no—
1137C2×C4—441no—
1138C2×C4—441no—
1139C2×C4—441no—
1140C2×C4—441no—
1141C2×C4—441no—
1142C2×C4—441no—
1143C2×C4—441no—
1144C2×C4—441no—
1145C2×C4—441no—
1146C2×C4—441no—
1147C2×C4—441no—
1148C2×C4—441no—
1149C2×C4—441no—
1150C2×C4—441no—
1151C2×C4—441no—
1152C2×C4—441no—
1153C2×C4—441no—
1154C2×C4—441no—
1155C2×C4—441no—
1156C2×C4—441no—
1157C2×C4—441no—
1158C2×C4—441no—
1159C2×C4—441no—
1160C2×C4—441no—
1161C2×C4—441no—
1162C2×C4—441no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—42no—
1170C22—42no—
1171C22—42no—
1172C22—42no—
1173C22—42no—
1174C22—42no—
1175C22—42no—
1176C22—42no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22—81no—
1192C22—81no—
1193C22—442no—
1194C22—442no—
1195C22—442no—
1196C22—442no—
1197C22—442no—
1198C22—442no—
1199C22—442no—
1200C22—881no—
1201C22—881no—
1202C22—881no—
1203C22—881no—
1204C22—881no—
1205C22—881no—
1206C22—881no—
1207C22—881no—
1208C22#1062301711yescharacteristic
1209C22#1062301711yescharacteristic
1210C22#1062301711yescharacteristic
1211C22C4×#434111yescharacteristic
1212C22#1062307611yescharacteristic
1213C22#1062307611yescharacteristic
1214C22#1062307611yescharacteristic
1215C22#1062312411yescharacteristic
1216C22#1062312411yescharacteristic
1217C22#1062312511yescharacteristic
1218C22#1062312511yescharacteristic
1219C22#1062312611yescharacteristic
1220C22#1062312611yescharacteristic
1221C22#1062312611yescharacteristic
1222C22#1062312611yescharacteristic
1223C22#1062314411yescharacteristic
1224C22#1062314611yescharacteristic
1225C22#1062314611yescharacteristic
1226C22#1062314811yescharacteristic
1227C22#1062315011yescharacteristic
1228C22#1062315011yescharacteristic
1229C22#1062315111yescharacteristic
1230C22#1062315111yescharacteristic
1231C22#1062315111yescharacteristic
1232C22#1062315111yescharacteristic
1233C22#1062315111yescharacteristic
1234C22#1062315111yescharacteristic
1235C22#1062318811yescharacteristic
1236C22#1062319411yescharacteristic
1237C22#1062319711yescharacteristic
1238C22#1062319711yescharacteristic
1239C22#1062320911yescharacteristic
1240C22#1062321411yescharacteristic
1241C22#1062325011yescharacteristic
1242C22#1062325111yescharacteristic
1243C4—42no—
1244C4—42no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—442no—
1249C4—442no—
1250C4—442no—
1251C4—442no—
1252C4—881no—
1253C4—881no—
1254C4—881no—
1255C2—82no—
1256C2—82no—
1257C2—882no—
1258C2#1307137511yescharacteristic
1259C2#1307137711yescharacteristic
1260C2#1307138211yescharacteristic
1261C2#1307175311yescharacteristic
1262C2#1307175411yescharacteristic
1263C2#1307175511yescharacteristic
1264C2#1307179111yescharacteristic
1265C2#1307670111yescharacteristic
1266C2#1307670411yescharacteristic
1267C2#1307673211yescharacteristic
1268C2#1307673411yescharacteristic
1269C2#1307673611yescharacteristic
1270C2#1307673811yescharacteristic
1271C2#1307673811yescharacteristic
1272C2#1307673911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1438C2
socle, cosocleC24×C11C24
prime radicalC2×#10622836C2
hypercenter#1438D11
hypocenterC11#14651
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
2. #13066877C2semidirect
3. #13066876C2semidirect
4. #13066864C2semidirect
5. #13066863C2semidirect
6. #13066863C2semidirect
7. #13066857C2semidirect
8. #13066855C2semidirect
9. #13066855C2semidirect
10. #13066855C2semidirect
11. #13066855C2semidirect
12. #13066853C2semidirect
13. #13066853C2semidirect
14. #13066852C2semidirect
15. C11×#1438C2semidirect
37. #10622836C4semidirect
331. #1438D11semidirect
955. C11#14651semidirect

Maximal subgroups

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

subgroupindex
C2×#106228362
#130668772
#130668762
#130668642
#130668632
#130668572
#130668552
#130668532
#130668522
C11×#14382
#1465111