Finite Group Databasebeta

← #14683123

Subgroups — #14683123

Order 2816.

2182 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622573C211yesmaximal, characteristic
2C2×#10622552C211yesmaximal, characteristic, complemented
3C2×#10622564C211yesmaximal, characteristic, complemented
4C2×#10622278C211yesmaximal, characteristic, complemented
5C2×#10622569C211yesmaximal, characteristic, complemented
6#13066872C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066855C211yesmaximal, characteristic, complemented
9#13066855C211yesmaximal, characteristic, complemented
10#13066855C211yesmaximal, characteristic, complemented
11#13066852C211yesmaximal, characteristic, complemented
12#13066852C211yesmaximal, characteristic, complemented
13#13066843C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1437C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
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×C4⋊Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
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#10622573C418yescomplemented
52#10622569—24no—
53#10622564—24no—
54#10622552—24no—
55#10622278—24no—
56C25×C11C2311yescharacteristic
57C24×D11C2311yescharacteristic
58C24×D11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11—22no—
66C22×C22⋊D11—22no—
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⋊D11C2×C414yes—
78C22×C22⋊D11C2×C414yescomplemented
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C22×D44—22no—
86C22×D44—22no—
87C22×D44—22no—
88C22×D44—22no—
89C22×D44—41no—
90C22×D44—41no—
91C22×D44C2×C414yes—
92C22×C4×D11—22no—
93C22×C4×D11—22no—
94C22×C4×D11—22no—
95C22×C4×D11—41no—
96C22×C4×D11—41no—
97C22×C4×D11—41no—
98C22×C4×D11—41no—
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⋊C4—41no—
106C2×C11×C22⋊C4—41no—
107C2×C11×C22⋊C4C2×C414yescomplemented
108C2×C42×C11—22no—
109C2×C42×C11—22no—
110C2×C42×C11—41no—
111C2×C22⋊Dic11—22no—
112C2×C22⋊Dic11—22no—
113C2×C22⋊Dic11—22no—
114C2×C22⋊Dic11—41no—
115C2×C22⋊Dic11—41no—
116C2×C22⋊Dic11—41no—
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—22no—
124C2×(C2×D11)⋊C4—22no—
125C2×(C2×D11)⋊C4—22no—
126C2×(C2×D11)⋊C4—22no—
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)⋊C4—41no—
133C2×(C2×D11)⋊C4—41no—
134C2×(C2×D11)⋊C4—41no—
135C2×(C2×D11)⋊C4—41no—
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)⋊C4C2×C414yes—
142C2×(C2×D11)⋊C4C2×C414yescomplemented
143C2×(C2×D11)⋊C4D414yescomplemented
144C2×C4⋊Dic11—22no—
145C2×C4⋊Dic11—22no—
146C2×C4⋊Dic11—41no—
147C2×C4×Dic11—22no—
148C2×C4×Dic11—41no—
149C2×C4×Dic11—41no—
150C11×#95—22no—
151C11×#95—41no—
152C11×#95—41no—
153C11⋊#95—22no—
154C11⋊#95—22no—
155C11⋊#95—22no—
156C11⋊#95—41no—
157C11⋊#95—41no—
158C11⋊#95—41no—
159C11⋊#95—41no—
160C11⋊#95—41no—
161C11⋊#95—41no—
162C11⋊#95C2×C414yescomplemented
163C11⋊#95D414yescomplemented
164#14520—111nomaximal, Sylow
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×C11C22×C412yes—
180C24×C11C2411yescharacteristic
181C23×D11—21no—
182C23×D11—21no—
183C23×D11—21no—
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×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×D11C22×C412yes—
208C23×D11C22×C412yes—
209C23×D11C2×D412yes—
210C23×D11#4112yes—
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×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×C11C22×C412yes—
247C22×C4×C11C22×C412yes—
248C22×C4×C11C2×D412yes—
249C22×C4×C11C2×D412yes—
250C22×C4×C11#4112yes—
251C22×C4×C11#4112yes—
252C22×C4×C11#4112yes—
253C2×C22⋊D11—28no—
254C2×C22⋊D11—44no—
255C2×C22⋊D11—44no—
256C2×C22⋊D11—44no—
257C2×C22⋊D11—44no—
258C2×C22⋊D11—44no—
259C2×C22⋊D11—44no—
260C2×C22⋊D11—44no—
261C2×C22⋊D11—44no—
262C2×C22⋊D11—44no—
263C2×C22⋊D11—44no—
264C2×C22⋊D11—44no—
265C2×C22⋊D11—44no—
266C2×C22⋊D11—44no—
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×Dic11—21no—
301C22×Dic11—21no—
302C22×Dic11—21no—
303C22×Dic11—21no—
304C22×Dic11C22×C412yes—
305C22×Dic11C22×C412yes—
306C22×Dic11C2×D412yes—
307C22×Dic11C2×D412yes—
308C22×Dic11C2×D412yes—
309C2×D44—28no—
310C2×D44—28no—
311C2×D44—44no—
312C2×D44—44no—
313C2×D44—44no—
314C2×D44—44no—
315C2×D44—44no—
316C2×C4×D11—44no—
317C2×C4×D11—44no—
318C2×C4×D11—44no—
319C2×C4×D11—44no—
320C2×C4×D11—44no—
321C2×C4×D11—44no—
322C2×C4×D11—44no—
323C11×C22⋊C4—28no—
324C11×C22⋊C4—44no—
325C11×C22⋊C4—44no—
326C42×C11—44no—
327C22⋊Dic11—44no—
328C22⋊Dic11—44no—
329(C2×D11)⋊C4—44no—
330(C2×D11)⋊C4—44no—
331(C2×D11)⋊C4—44no—
332(C2×D11)⋊C4—44no—
333(C2×D11)⋊C4—44no—
334(C2×D11)⋊C4—44no—
335(C2×D11)⋊C4—44no—
336(C2×D11)⋊C4—44no—
337(C2×D11)⋊C4—44no—
338C4⋊Dic11—44no—
339C4×Dic11—44no—
340C2×#392—111no—
341C2×#390—111no—
342C2×#388—111no—
343C2×#386—111no—
344C2×#386—111no—
345#1442—111no—
346#1440—111no—
347#1438—111no—
348#1438—111no—
349#1438—111no—
350#1437—111no—
351#1437—111no—
352#1437D1111yescharacteristic, complemented
353#1434—111no—
354C22⋊#95—111no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
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×C11C23×C411yescharacteristic
391C23×C11C22×D411yescharacteristic
392C23×C11C22×D411yescharacteristic
393C23×C11C2×#4111yescharacteristic
394C23×C11C2×#4111yescharacteristic
395C23×C11C2×#4111yescharacteristic
396C23×C11C2×#4111yescharacteristic
397C23×C11H(5,𝔽2)11yescharacteristic
398C23×C11H(5,𝔽2)11yescharacteristic
399C23×C11H(5,𝔽2)11yescharacteristic
400C23×C11H(5,𝔽2)11yescharacteristic
401C23×C11H(5,𝔽2)11yescharacteristic
402C23×C11H(5,𝔽2)11yescharacteristic
403C23×C11H(5,𝔽2)11yescharacteristic
404C23×C11H(5,𝔽2)11yescharacteristic
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—22no—
408C22×D11—22no—
409C22×D11—22no—
410C22×D11—22no—
411C22×D11—22no—
412C22×D11—22no—
413C22×D11—22no—
414C22×D11—22no—
415C22×D11—22no—
416C22×D11—22no—
417C22×D11—22no—
418C22×D11—22no—
419C22×D11—22no—
420C22×D11—22no—
421C22×D11—22no—
422C22×D11—22no—
423C22×D11—22no—
424C22×D11—22no—
425C22×D11—22no—
426C22×D11—22no—
427C22×D11—22no—
428C22×D11—22no—
429C22×D11—22no—
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—
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×D11C4×D414yes—
475C2×C4×C11—22no—
476C2×C4×C11—22no—
477C2×C4×C11—22no—
478C2×C4×C11—22no—
479C2×C4×C11—22no—
480C2×C4×C11—22no—
481C2×C4×C11—22no—
482C2×C4×C11—22no—
483C2×C4×C11—22no—
484C2×C4×C11—22no—
485C2×C4×C11—22no—
486C2×C4×C11—22no—
487C2×C4×C11—22no—
488C2×C4×C11—22no—
489C2×C4×C11—22no—
490C2×C4×C11—22no—
491C2×C4×C11—22no—
492C2×C4×C11—22no—
493C2×C4×C11—41no—
494C2×C4×C11—41no—
495C2×C4×C11—41no—
496C2×C4×C11—41no—
497C2×C4×C11—41no—
498C2×C4×C11—41no—
499C2×C4×C11—41no—
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×C11C4×D414yes—
517C22⋊D11—416no—
518C22⋊D11—416no—
519C2×Dic11—22no—
520C2×Dic11—22no—
521C2×Dic11—22no—
522C2×Dic11—22no—
523C2×Dic11—22no—
524C2×Dic11—22no—
525C2×Dic11—22no—
526C2×Dic11—22no—
527C2×Dic11—22no—
528C2×Dic11—22no—
529C2×Dic11—22no—
530C2×Dic11—22no—
531C2×Dic11—22no—
532C2×Dic11—22no—
533C2×Dic11—22no—
534C2×Dic11—41no—
535C2×Dic11—41no—
536C2×Dic11—41no—
537C2×Dic11—41no—
538C2×Dic11—41no—
539C2×Dic11—41no—
540C2×Dic11—41no—
541C2×Dic11—41no—
542C2×Dic11—41no—
543C2×Dic11—41no—
544C2×Dic11—41no—
545C2×Dic11—41no—
546C2×Dic11—41no—
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—
561D44—416no—
562C4×D11—416no—
563C23×D4—111no—
564C23×D4—111no—
565C23×D4—111no—
566C24×C4—111no—
567C22×C4⋊C4—111no—
568C22×C22⋊C4—111no—
569C22×C22⋊C4—111no—
570C22×C22⋊C4—111no—
571C22×C22⋊C4—111no—
572C22×C22⋊C4—111no—
573C22×C22⋊C4—111no—
574C22×C22⋊C4—111no—
575C22×C22⋊C4—111no—
576C22×C22⋊C4—111no—
577C22×C22⋊C4—111no—
578C22×C22⋊C4—111no—
579C22×C22⋊C4C2×D1111yescharacteristic
580C22×C22⋊C4C2×D1111yescharacteristic
581C22×C22⋊C4C2×D1111yescharacteristic
582C22×C42—111no—
583C22×C42C2×D1111yescharacteristic
584#392—118no—
585#390—224no—
586#388—224no—
587#386—224no—
588#386—224no—
589C2×#95—111no—
590C2×#95—111no—
591C2×#95—111no—
592C2×#95—111no—
593C2×#95—111no—
594C2×#95—111no—
595C2×#95—111no—
596C2×#95—111no—
597C2×#95—111no—
598C2×#95—111no—
599C2×#95—111no—
600C2×#95C2×D1111yescharacteristic
601C2×#95C2×D1111yescharacteristic
602C2×#95C2×D1111yescharacteristic
603C22×C11—42no—
604C22×C11—42no—
605C22×C11—42no—
606C22×C11—42no—
607C22×C11—42no—
608C22×C11—42no—
609C22×C11—42no—
610C22×C11—81no—
611C22×C11—81no—
612C22×C11—81no—
613C22×C11—81no—
614C22×C11—81no—
615C22×C11—81no—
616C22×C11—81no—
617C22×C11—81no—
618C22×C11C2×C4×D411yescharacteristic
619C22×C11C2×C4×D411yescharacteristic
620C22×C11C4×#4111yescharacteristic
621C22×C11#51811yescharacteristic
622C22×C11#51811yescharacteristic
623C22×C11#51811yescharacteristic
624C22×C11#51811yescharacteristic
625C22×C11#53411yescharacteristic
626C22×C11#53511yescharacteristic
627C22×C11#53511yescharacteristic
628C22×C11#53511yescharacteristic
629C22×C11#53811yescharacteristic
630C22×C11#53811yescharacteristic
631C22×C11#53811yescharacteristic
632C22×C11#53811yescharacteristic
633C22×C11#54011yescharacteristic
634C22×C11#54011yescharacteristic
635C22×C11#54011yescharacteristic
636C22×C11#54011yescharacteristic
637C22×C11D4211yescharacteristic
638C22×C11#54611yescharacteristic
639C22×C11#54611yescharacteristic
640C22×C11#54611yescharacteristic
641C22×C11#54611yescharacteristic
642C22×C11#54611yescharacteristic
643C22×C11#55011yescharacteristic
644C22×C11#55111yescharacteristic
645C22×C11#55311yescharacteristic
646C22×C11#55311yescharacteristic
647C22×C11#55311yescharacteristic
648C22×C11#55511yescharacteristic
649C22×C11#56011yescharacteristic
650C22×C11#56011yescharacteristic
651C22×C11#56011yescharacteristic
652C22×C11H(3,𝔽4)11yescharacteristic
653C2×D11—24no—
654C2×D11—24no—
655C2×D11—24no—
656C2×D11—42no—
657C2×D11—42no—
658C2×D11—42no—
659C2×D11—42no—
660C2×D11—42no—
661C2×D11—42no—
662C2×D11—42no—
663C2×D11—42no—
664C2×D11—42no—
665C2×D11—42no—
666C2×D11—42no—
667C2×D11—42no—
668C2×D11—42no—
669C2×D11—42no—
670C2×D11—42no—
671C2×D11—42no—
672C2×D11—42no—
673C2×D11—42no—
674C2×D11—42no—
675C2×D11—81no—
676C2×D11—81no—
677C2×D11—81no—
678C2×D11—81no—
679C2×D11—81no—
680C2×D11—81no—
681C2×D11—81no—
682C2×D11—81no—
683C4×C11—24no—
684C4×C11—42no—
685C4×C11—42no—
686C4×C11—42no—
687C4×C11—42no—
688C4×C11—81no—
689Dic11—42no—
690Dic11—42no—
691Dic11—42no—
692Dic11—42no—
693Dic11—42no—
694Dic11—81no—
695C25—111no—
696C25—111no—
697C25C22×D1111yescharacteristic
698C22×D4—114no—
699C22×D4—114no—
700C22×D4—114no—
701C22×D4—222no—
702C22×D4—222no—
703C22×D4—222no—
704C22×D4—222no—
705C22×D4—222no—
706C22×D4—222no—
707C22×D4—441no—
708C22×D4—441no—
709C22×D4—441no—
710C22×D4—441no—
711C22×D4—441no—
712C22×D4—441no—
713C22×D4—441no—
714C22×D4—441no—
715C22×D4—441no—
716C22×D4—441no—
717C22×D4—441no—
718C22×D4—441no—
719C23×C4—111no—
720C23×C4—111no—
721C23×C4—111no—
722C23×C4—111no—
723C23×C4—111no—
724C23×C4—111no—
725C23×C4—222no—
726C23×C4—222no—
727C23×C4—222no—
728C23×C4—441no—
729C23×C4—441no—
730C23×C4—441no—
731C23×C4—441no—
732C23×C4C22×D1111yescharacteristic
733C23×C4C22×D1111yescharacteristic
734C23×C4C22×D1111yescharacteristic
735C23×C4C22×D1111yescharacteristic
736C23×C4C22×D1111yescharacteristic
737C23×C4C22×D1111yescharacteristic
738C2×C4⋊C4—222no—
739C2×C4⋊C4—222no—
740C2×C4⋊C4—441no—
741C2×C22⋊C4—22no—
742C2×C22⋊C4—22no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—41no—
747C2×C22⋊C4—41no—
748C2×C22⋊C4—41no—
749C2×C22⋊C4—114no—
750C2×C22⋊C4—114no—
751C2×C22⋊C4—114no—
752C2×C22⋊C4—222no—
753C2×C22⋊C4—222no—
754C2×C22⋊C4—222no—
755C2×C22⋊C4—222no—
756C2×C22⋊C4—222no—
757C2×C22⋊C4—222no—
758C2×C22⋊C4—222no—
759C2×C22⋊C4—222no—
760C2×C22⋊C4—222no—
761C2×C22⋊C4—222no—
762C2×C22⋊C4—222no—
763C2×C22⋊C4—222no—
764C2×C22⋊C4—222no—
765C2×C22⋊C4—441no—
766C2×C22⋊C4—441no—
767C2×C22⋊C4—441no—
768C2×C22⋊C4—441no—
769C2×C22⋊C4—441no—
770C2×C22⋊C4—441no—
771C2×C22⋊C4—441no—
772C2×C22⋊C4—441no—
773C2×C22⋊C4—441no—
774C2×C22⋊C4—441no—
775C2×C22⋊C4—441no—
776C2×C22⋊C4—441no—
777C2×C22⋊C4—441no—
778C2×C22⋊C4—441no—
779C2×C22⋊C4—441no—
780C2×C22⋊C4—441no—
781C2×C22⋊C4—441no—
782C2×C22⋊C4C4×D1114yescomplemented
783C2×C42—22no—
784C2×C42—22no—
785C2×C42—41no—
786C2×C42—222no—
787C2×C42—441no—
788C2×C42—441no—
789#95—22no—
790#95—41no—
791#95—41no—
792#95—114no—
793#95—114no—
794#95—222no—
795#95—222no—
796#95—222no—
797#95—441no—
798#95—441no—
799#95—441no—
800#95—441no—
801#95—441no—
802#95—441no—
803C2×C11—82no—
804C2×C11#232111yescharacteristic
805C2×C11#232811yescharacteristic
806C2×C11#233311yescharacteristic
807C2×C11#235811yescharacteristic
808C2×C11#236311yescharacteristic
809C2×C11#236411yescharacteristic
810C2×C11#237511yescharacteristic
811C2×C11#267011yescharacteristic
812C2×C11#267311yescharacteristic
813C2×C11#269911yescharacteristic
814C2×C11#270311yescharacteristic
815C2×C11#270311yescharacteristic
816C2×C11#271411yescharacteristic
817C2×C11#275311yescharacteristic
818C2×C11#275611yescharacteristic
819D11—44no—
820D11—82no—
821C24—21no—
822C24—21no—
823C24—21no—
824C24—21no—
825C24—21no—
826C24—21no—
827C24—21no—
828C24—21no—
829C24—21no—
830C24—21no—
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—112no—
836C24—112no—
837C24—112no—
838C24—112no—
839C24—221no—
840C24—221no—
841C24—221no—
842C24—221no—
843C24—221no—
844C24—221no—
845C24—221no—
846C24—221no—
847C24—221no—
848C24—221no—
849C24—221no—
850C24—221no—
851C24—221no—
852C24—221no—
853C24—221no—
854C24—221no—
855C24—221no—
856C24—221no—
857C24—221no—
858C24—221no—
859C24—221no—
860C24—221no—
861C24—221no—
862C24—221no—
863C24—221no—
864C24—221no—
865C24C2×C4×D1112yes—
866C24C23×D1111yescharacteristic
867C2×D4—228no—
868C2×D4—228no—
869C2×D4—228no—
870C2×D4—444no—
871C2×D4—444no—
872C2×D4—444no—
873C2×D4—444no—
874C2×D4—444no—
875C2×D4—444no—
876C2×D4—444no—
877C2×D4—444no—
878C2×D4—444no—
879C2×D4—444no—
880C2×D4—444no—
881C2×D4—444no—
882C2×D4—444no—
883C2×D4—444no—
884C2×D4—444no—
885C2×D4—444no—
886C2×D4—444no—
887C2×D4—444no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
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—112no—
924C22×C4—112no—
925C22×C4—112no—
926C22×C4—112no—
927C22×C4—112no—
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×C4—221no—
938C22×C4—221no—
939C22×C4—221no—
940C22×C4—221no—
941C22×C4—221no—
942C22×C4—221no—
943C22×C4—221no—
944C22×C4—221no—
945C22×C4—221no—
946C22×C4—221no—
947C22×C4—221no—
948C22×C4—221no—
949C22×C4—221no—
950C22×C4—221no—
951C22×C4—221no—
952C22×C4—221no—
953C22×C4—221no—
954C22×C4—221no—
955C22×C4—221no—
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—444no—
966C22×C4—444no—
967C22×C4—444no—
968C22×C4—444no—
969C22×C4—444no—
970C22×C4—444no—
971C22×C4—444no—
972C22×C4C2×C4×D1112yes—
973C22×C4C2×C4×D1112yes—
974C22×C4#433912yes—
975C22×C4#433912yes—
976C22×C4D4×D1112yes—
977C22×C4D4×D1112yes—
978C22×C4#434112yes—
979C4⋊C4—444no—
980C22⋊C4—28no—
981C22⋊C4—44no—
982C22⋊C4—44no—
983C22⋊C4—444no—
984C22⋊C4—444no—
985C22⋊C4—444no—
986C22⋊C4—444no—
987C22⋊C4—444no—
988C22⋊C4—444no—
989C22⋊C4—444no—
990C22⋊C4—444no—
991C22⋊C4—444no—
992C22⋊C4—444no—
993C22⋊C4—444no—
994C42—44no—
995C42—444no—
996C11#1452011yescharacteristic, complemented, Sylow
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—22no—
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—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—114no—
1033C23—222no—
1034C23—222no—
1035C23—222no—
1036C23—222no—
1037C23—222no—
1038C23—222no—
1039C23—222no—
1040C23—222no—
1041C23—222no—
1042C23—222no—
1043C23—222no—
1044C23—222no—
1045C23—222no—
1046C23—222no—
1047C23—222no—
1048C23—222no—
1049C23—222no—
1050C23—222no—
1051C23—222no—
1052C23—222no—
1053C23—222no—
1054C23—222no—
1055C23—222no—
1056C23—222no—
1057C23—222no—
1058C23—441no—
1059C23—441no—
1060C23—441no—
1061C23—441no—
1062C23—441no—
1063C23—441no—
1064C23—441no—
1065C23—441no—
1066C23—441no—
1067C23—441no—
1068C23—441no—
1069C23—441no—
1070C23—441no—
1071C23—441no—
1072C23—441no—
1073C23—441no—
1074C23—441no—
1075C23—441no—
1076C23—441no—
1077C23—441no—
1078C23—441no—
1079C23—441no—
1080C23—441no—
1081C23—441no—
1082C23—441no—
1083C23—441no—
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—
1102C23C22×C4×D1111yescharacteristic
1103C23C2×#433911yescharacteristic
1104C23C2×#433911yescharacteristic
1105C23C2×D4×D1111yescharacteristic
1106C23C2×D4×D1111yescharacteristic
1107C23C2×#434111yescharacteristic
1108C23#6703711yescharacteristic
1109C23#6703711yescharacteristic
1110C23#6703711yescharacteristic
1111C23#41×D1111yescharacteristic
1112C23#6704211yescharacteristic
1113C23#6704211yescharacteristic
1114C23#6704211yescharacteristic
1115C23#6704211yescharacteristic
1116C23#6704211yescharacteristic
1117D4—4416no—
1118D4—4416no—
1119D4—4416no—
1120C2×C4—22no—
1121C2×C4—22no—
1122C2×C4—22no—
1123C2×C4—22no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—222no—
1162C2×C4—222no—
1163C2×C4—222no—
1164C2×C4—222no—
1165C2×C4—222no—
1166C2×C4—222no—
1167C2×C4—222no—
1168C2×C4—222no—
1169C2×C4—222no—
1170C2×C4—222no—
1171C2×C4—222no—
1172C2×C4—222no—
1173C2×C4—222no—
1174C2×C4—222no—
1175C2×C4—222no—
1176C2×C4—4416no—
1177C2×C4—441no—
1178C2×C4—441no—
1179C2×C4—441no—
1180C2×C4—441no—
1181C2×C4—441no—
1182C2×C4—441no—
1183C2×C4—441no—
1184C2×C4—441no—
1185C2×C4—441no—
1186C2×C4—441no—
1187C2×C4—441no—
1188C2×C4—441no—
1189C2×C4—441no—
1190C2×C4—441no—
1191C2×C4—441no—
1192C2×C4—441no—
1193C2×C4—441no—
1194C2×C4—441no—
1195C2×C4—441no—
1196C2×C4—441no—
1197C2×C4—441no—
1198C2×C4—441no—
1199C2×C4—441no—
1200C2×C4—441no—
1201C2×C4—441no—
1202C2×C4—441no—
1203C2×C4—441no—
1204C2×C4(C22⋊D11)⋊C414yes—
1205C22—42no—
1206C22—42no—
1207C22—42no—
1208C22—42no—
1209C22—42no—
1210C22—42no—
1211C22—42no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—224no—
1221C22—224no—
1222C22—224no—
1223C22—442no—
1224C22—442no—
1225C22—442no—
1226C22—442no—
1227C22—442no—
1228C22—442no—
1229C22—442no—
1230C22—442no—
1231C22—442no—
1232C22—442no—
1233C22—442no—
1234C22—442no—
1235C22—442no—
1236C22—442no—
1237C22—442no—
1238C22—442no—
1239C22—442no—
1240C22—442no—
1241C22—442no—
1242C22—881no—
1243C22—881no—
1244C22—881no—
1245C22—881no—
1246C22—881no—
1247C22—881no—
1248C22—881no—
1249C22—881no—
1250C22C4×#433911yescharacteristic
1251C22C2×(C22⋊D11)⋊C411yescharacteristic
1252C22#1062302111yescharacteristic
1253C22#1062302511yescharacteristic
1254C22#1062305211yescharacteristic
1255C22#1062306111yescharacteristic
1256C22#1062306611yescharacteristic
1257C22C4×D4×D1111yescharacteristic
1258C22#1062307611yescharacteristic
1259C22#1062307611yescharacteristic
1260C22#1062307611yescharacteristic
1261C22#1062308111yescharacteristic
1262C22#1062308111yescharacteristic
1263C22#1062308411yescharacteristic
1264C22#1062308911yescharacteristic
1265C22#1062309111yescharacteristic
1266C22#1062309311yescharacteristic
1267C22#1062309411yescharacteristic
1268C22#1062309611yescharacteristic
1269C22#1062312211yescharacteristic
1270C22#1062313811yescharacteristic
1271C22#1062314011yescharacteristic
1272C22#1062314111yescharacteristic
1273C22#1062315011yescharacteristic
1274C22#1062315011yescharacteristic
1275C22#1062315111yescharacteristic
1276C22#1062318411yescharacteristic
1277C22#1062318911yescharacteristic
1278C22#1062319711yescharacteristic
1279C22#1062320511yescharacteristic
1280C22#1062320911yescharacteristic
1281C22#1062321411yescharacteristic
1282C22#1062323511yescharacteristic
1283C22#1062324211yescharacteristic
1284C22#1062324611yescharacteristic
1285C4—24no—
1286C4—42no—
1287C4—42no—
1288C4—42no—
1289C4—42no—
1290C4—81no—
1291C4—442no—
1292C4—442no—
1293C4—442no—
1294C4—442no—
1295C4—442no—
1296C4—881no—
1297C2—82no—
1298C2—444no—
1299C2—882no—
1300C2#1307127811yescharacteristic
1301C2#1307134011yescharacteristic
1302C2#1307137611yescharacteristic
1303C2#1307159611yescharacteristic
1304C2#1307165211yescharacteristic
1305C2#1307166711yescharacteristic
1306C2#1307175611yescharacteristic
1307C2#1307483911yescharacteristic
1308C2#1307488311yescharacteristic
1309C2#1307520511yescharacteristic
1310C2#1307525411yescharacteristic
1311C2#1307526311yescharacteristic
1312C2#1307540911yescharacteristic
1313C2#1307589711yescharacteristic
1314C2#1307594211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC2×#10622573C2
hypercenter#1437D11
hypocenterC11#14520
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C2×#10622552C2semidirect
3. C2×#10622564C2semidirect
4. C2×#10622278C2semidirect
5. C2×#10622569C2semidirect
6. #13066872C2semidirect
7. #13066864C2semidirect
8. #13066855C2semidirect
9. #13066855C2semidirect
10. #13066855C2semidirect
11. #13066852C2semidirect
12. #13066852C2semidirect
13. #13066843C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1437C2semidirect
51. #10622573C4semidirect
78. C22×C22⋊D11C2×C4semidirect
107. C2×C11×C22⋊C4C2×C4semidirect
142. C2×(C2×D11)⋊C4C2×C4semidirect
143. C2×(C2×D11)⋊C4D4semidirect
162. C11⋊#95C2×C4semidirect
163. C11⋊#95D4semidirect
352. #1437D11semidirect
782. C2×C22⋊C4C4×D11semidirect
996. C11#14520semidirect

Maximal subgroups

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

subgroupindex
C2×#106225732
C2×#106225522
C2×#106225642
C2×#106222782
C2×#106225692
#130668722
#130668642
#130668552
#130668522
#130668432
(C2×D11)⋊#952
C11×#14372
#1452011