Finite Group Databasebeta

← #14683826

Subgroups — #14683826

Order 2816.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622572C211yesmaximal, characteristic
2C2×#10622553C211yesmaximal, characteristic, complemented
3C2×#10622571C211yesmaximal, characteristic
4C2×#10622569C211yesmaximal, characteristic
5#13066882C211yesmaximal, characteristic, complemented
6#13066875C211yesmaximal, characteristic, complemented
7#13066871C211yesmaximal, characteristic, complemented
8#13066859C211yesmaximal, characteristic, complemented
9#13066858C211yesmaximal, characteristic, complemented
10#13066849C211yesmaximal, characteristic, complemented
11#13066838C211yesmaximal, characteristic, complemented
12#13066838C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#388C211yesmaximal, 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×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×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C11×#388—24no—
34C2×C11×#95C2211yescharacteristic
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
51C2×C11⋊#95C2211yescharacteristic
52#10622572C418yescomplemented
53#10622571—24no—
54#10622569—24no—
55#10622553—24no—
56C25×C11C2311yescharacteristic
57C24×D11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—22no—
65C22×C22⋊D11—22no—
66C22×C22⋊D11—22no—
67C22×C22⋊D11—22no—
68C22×C22⋊D11—41no—
69C22×C22⋊D11—41no—
70C22×C22⋊D11C2×C414yes—
71C23×Dic11—22no—
72C23×Dic11—22no—
73C23×Dic11—22no—
74C23×Dic11—41no—
75C23×Dic11—41no—
76C23×Dic11—41no—
77C23×Dic11—41no—
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2311yescharacteristic
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C22×C4×D11—22no—
86C22×C4×D11—22no—
87C22×C4×D11—22no—
88C22×C4×D11—41no—
89C22×C4×D11—41no—
90C22×C4×D11—41no—
91C22×C4×D11—41no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—41no—
94C2×C11×C4⋊C4—41no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—41no—
100C2×C11×C22⋊C4—41no—
101C2×C11×C22⋊C4—41no—
102C2×C11×C22⋊C4C2×C414yescomplemented
103C2×C11×C22⋊C4D414yes—
104C2×C42×C11—22no—
105C2×C42×C11—22no—
106C2×C42×C11—41no—
107C2×C22⋊Dic11—22no—
108C2×C22⋊Dic11—22no—
109C2×C22⋊Dic11—41no—
110C2×C22⋊Dic11—41no—
111C2×C22⋊Dic11—41no—
112C2×C22⋊Dic11C2×C414yescomplemented
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—41no—
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)⋊C4C2×C414yescomplemented
126C2×(C2×D11)⋊C4C2×C414yescomplemented
127C2×(C2×D11)⋊C4D414yes—
128C2×Dic11⋊C4—22no—
129C2×Dic11⋊C4—41no—
130C2×Dic11⋊C4—41no—
131C2×Dic11⋊C4—41no—
132C2×Dic11⋊C4—41no—
133C2×Dic11⋊C4C2×C414yescomplemented
134C11×#95—22no—
135C11×#95—22no—
136C11⋊#95—22no—
137C11⋊#95—22no—
138C11⋊#95—22no—
139C11⋊#95—22no—
140C11⋊#95—22no—
141C11⋊#95—22no—
142C11⋊#95—22no—
143C11⋊#95—22no—
144C11⋊#95—41no—
145C11⋊#95—41no—
146C11⋊#95—41no—
147C11⋊#95—41no—
148C11⋊#95—41no—
149C11⋊#95—41no—
150C11⋊#95—41no—
151C11⋊#95C2×C414yescomplemented
152#14571—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×C11C22×C412yes—
166C24×C11C2×D412yes—
167C24×C11#4112yes—
168C24×C11C2411yescharacteristic
169C23×D11—21no—
170C23×D11—21no—
171C23×D11—21no—
172C23×D11—21no—
173C23×D11—21no—
174C23×D11—21no—
175C23×D11—21no—
176C23×D11—21no—
177C23×D11—21no—
178C23×D11—21no—
179C23×D11—21no—
180C23×D11—21no—
181C23×D11C22×C412yes—
182C23×D11C2×D412yes—
183C23×D11#4112yes—
184C22×C4×C11—21no—
185C22×C4×C11—21no—
186C22×C4×C11—21no—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
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×C11C22×C412yes—
222C22×C4×C11C22×C412yes—
223C22×C4×C11C2×D412yes—
224C22×C4×C11C2×D412yes—
225C22×C4×C11C2×D412yes—
226C2×C22⋊D11—28no—
227C2×C22⋊D11—28no—
228C2×C22⋊D11—44no—
229C2×C22⋊D11—44no—
230C2×C22⋊D11—44no—
231C2×C22⋊D11—44no—
232C2×C22⋊D11—44no—
233C22×Dic11—21no—
234C22×Dic11—21no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—21no—
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—44no—
277C22×Dic11—44no—
278C22×Dic11—44no—
279C22×Dic11—44no—
280C22×Dic11—44no—
281C22×Dic11—44no—
282C22×Dic11—44no—
283C22×Dic11C22×C412yes—
284C22×Dic11C22×C412yes—
285C22×Dic11C22×C412yes—
286C22×Dic11C2×D412yes—
287C22×Dic11#4112yes—
288C22×Dic11#4112yes—
289C2×C4×D11—44no—
290C2×C4×D11—44no—
291C2×C4×D11—44no—
292C2×C4×D11—44no—
293C2×C4×D11—44no—
294C2×C4×D11—44no—
295C2×C4×D11—44no—
296C11×C4⋊C4—44no—
297C11×C22⋊C4—28no—
298C11×C22⋊C4—44no—
299C11×C22⋊C4—44no—
300C42×C11—44no—
301C22⋊Dic11—44no—
302C22⋊Dic11—44no—
303(C2×D11)⋊C4—28no—
304(C2×D11)⋊C4—44no—
305(C2×D11)⋊C4—44no—
306(C2×D11)⋊C4—44no—
307(C2×D11)⋊C4—44no—
308Dic11⋊C4—44no—
309Dic11⋊C4—44no—
310C2×#394—111no—
311C2×#388—111no—
312C2×#388D1111yescharacteristic, complemented
313C2×#386—111no—
314C2×#386—111no—
315#1445—111no—
316#1442—111no—
317#1442—111no—
318#1439—111no—
319#1439—111no—
320#1436—111no—
321C22⋊#95—111no—
322C22⋊#95—111no—
323C22⋊#95—111no—
324C22⋊#95—111no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
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—41no—
344C23×C11—41no—
345C23×C11—41no—
346C23×C11—41no—
347C23×C11—41no—
348C23×C11—41no—
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×C11C4×D414yes—
360C23×C11C23×C411yescharacteristic
361C23×C11C22×D411yescharacteristic
362C23×C11C22×D411yescharacteristic
363C23×C11C2×#4111yescharacteristic
364C23×C11C2×#4111yescharacteristic
365C23×C11C2×#4111yescharacteristic
366C23×C11C2×#4111yescharacteristic
367C23×C11H(5,𝔽2)11yescharacteristic
368C23×C11H(5,𝔽2)11yescharacteristic
369C23×C11H(5,𝔽2)11yescharacteristic
370C23×C11H(5,𝔽2)11yescharacteristic
371C23×C11H(5,𝔽2)11yescharacteristic
372C23×C11H(5,𝔽2)11yescharacteristic
373C23×C112−1+411yescharacteristic
374C23×C112−1+411yescharacteristic
375C22×D11—22no—
376C22×D11—22no—
377C22×D11—22no—
378C22×D11—22no—
379C22×D11—22no—
380C22×D11—22no—
381C22×D11—22no—
382C22×D11—22no—
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—41no—
394C22×D11—41no—
395C22×D11—41no—
396C22×D11—41no—
397C22×D11—41no—
398C22×D11—41no—
399C22×D11—41no—
400C22×D11—41no—
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×D11C4×D414yes—
410C2×C4×C11—22no—
411C2×C4×C11—22no—
412C2×C4×C11—22no—
413C2×C4×C11—22no—
414C2×C4×C11—22no—
415C2×C4×C11—22no—
416C2×C4×C11—22no—
417C2×C4×C11—22no—
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—41no—
426C2×C4×C11—41no—
427C2×C4×C11—41no—
428C2×C4×C11—41no—
429C2×C4×C11—41no—
430C2×C4×C11—41no—
431C2×C4×C11—41no—
432C2×C4×C11—41no—
433C2×C4×C11—41no—
434C2×C4×C11—41no—
435C2×C4×C11—41no—
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—
452C22⋊D11—416no—
453C2×Dic11—22no—
454C2×Dic11—22no—
455C2×Dic11—22no—
456C2×Dic11—22no—
457C2×Dic11—22no—
458C2×Dic11—22no—
459C2×Dic11—22no—
460C2×Dic11—22no—
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—416no—
472C2×Dic11—41no—
473C2×Dic11—41no—
474C2×Dic11—41no—
475C2×Dic11—41no—
476C2×Dic11—41no—
477C2×Dic11—41no—
478C2×Dic11—41no—
479C2×Dic11—41no—
480C2×Dic11—41no—
481C2×Dic11—41no—
482C2×Dic11—41no—
483C2×Dic11—41no—
484C2×Dic11—41no—
485C2×Dic11—41no—
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—
503C4×D11—416no—
504C23×D4—111no—
505C24×C4—111no—
506C24×C4—111no—
507C22×C4⋊C4—111no—
508C22×C4⋊C4—111no—
509C22×C4⋊C4C2×D1111yescharacteristic
510C22×C22⋊C4—111no—
511C22×C22⋊C4—111no—
512C22×C22⋊C4—111no—
513C22×C22⋊C4—111no—
514C22×C22⋊C4—111no—
515C22×C22⋊C4—111no—
516C22×C22⋊C4—111no—
517C22×C22⋊C4C2×D1111yescharacteristic
518C22×C22⋊C4C2×D1111yescharacteristic
519C22×C22⋊C4C2×D1111yescharacteristic
520C22×C42C2×D1111yescharacteristic
521#394—118no—
522#388—24no—
523#388—224no—
524#386—224no—
525#386—224no—
526C2×#95—111no—
527C2×#95—111no—
528C2×#95—111no—
529C2×#95—111no—
530C2×#95—111no—
531C2×#95—111no—
532C2×#95—111no—
533C2×#95—111no—
534C2×#95—111no—
535C2×#95—111no—
536C2×#95—111no—
537C2×#95—111no—
538C2×#95—111no—
539C2×#95—111no—
540C2×#95—111no—
541C2×#95—111no—
542C2×#95C2×D1111yescharacteristic
543C2×#95C2×D1111yescharacteristic
544C22×C11—24no—
545C22×C11—24no—
546C22×C11—24no—
547C22×C11—42no—
548C22×C11—42no—
549C22×C11—42no—
550C22×C11—42no—
551C22×C11—42no—
552C22×C11—42no—
553C22×C11—42no—
554C22×C11—42no—
555C22×C11—42no—
556C22×C11—42no—
557C22×C11—42no—
558C22×C11—42no—
559C22×C11C2×C4×D411yescharacteristic
560C22×C11C2×C4×D411yescharacteristic
561C22×C11C4×#4111yescharacteristic
562C22×C11#51811yescharacteristic
563C22×C11#51811yescharacteristic
564C22×C11#52011yescharacteristic
565C22×C11#52011yescharacteristic
566C22×C11#53411yescharacteristic
567C22×C11#53411yescharacteristic
568C22×C11#53711yescharacteristic
569C22×C11#53711yescharacteristic
570C22×C11#53811yescharacteristic
571C22×C11#53811yescharacteristic
572C22×C11#53811yescharacteristic
573C22×C11#53811yescharacteristic
574C22×C11#53911yescharacteristic
575C22×C11#53911yescharacteristic
576C22×C11#54011yescharacteristic
577C22×C11#54011yescharacteristic
578C22×C11D4211yescharacteristic
579C22×C11#54611yescharacteristic
580C22×C11#54611yescharacteristic
581C22×C11#54611yescharacteristic
582C22×C11#54611yescharacteristic
583C22×C11#54711yescharacteristic
584C22×C11#54711yescharacteristic
585C22×C11#55111yescharacteristic
586C22×C11#55111yescharacteristic
587C22×C11#55111yescharacteristic
588C22×C11#55211yescharacteristic
589C22×C11#55211yescharacteristic
590C22×C11H(3,𝔽4)11yescharacteristic
591C22×C11#56211yescharacteristic
592C22×C11#56211yescharacteristic
593C22×C11#56311yescharacteristic
594C2×D11—24no—
595C2×D11—24no—
596C2×D11—24no—
597C2×D11—42no—
598C2×D11—42no—
599C2×D11—42no—
600C2×D11—42no—
601C2×D11—42no—
602C2×D11—42no—
603C2×D11—42no—
604C2×D11—42no—
605C2×D11—42no—
606C2×D11—42no—
607C2×D11—42no—
608C2×D11—42no—
609C4×C11—42no—
610C4×C11—42no—
611C4×C11—42no—
612C4×C11—42no—
613C4×C11—42no—
614C4×C11—81no—
615Dic11—42no—
616Dic11—42no—
617Dic11—42no—
618Dic11—42no—
619Dic11—42no—
620Dic11—42no—
621Dic11—81no—
622C25—111no—
623C25C22×D1111yescharacteristic
624C22×D4—114no—
625C22×D4—222no—
626C22×D4—222no—
627C22×D4—222no—
628C22×D4—222no—
629C22×D4—441no—
630C22×D4—441no—
631C23×C4—111no—
632C23×C4—111no—
633C23×C4—111no—
634C23×C4—111no—
635C23×C4—111no—
636C23×C4—111no—
637C23×C4—111no—
638C23×C4—222no—
639C23×C4—222no—
640C23×C4—222no—
641C23×C4—222no—
642C23×C4—222no—
643C23×C4—222no—
644C23×C4—441no—
645C23×C4—441no—
646C23×C4—441no—
647C23×C4—441no—
648C23×C4—441no—
649C23×C4—441no—
650C23×C4—441no—
651C23×C4—441no—
652C23×C4C22×D1111yescharacteristic
653C23×C4C22×D1111yescharacteristic
654C23×C4C22×D1111yescharacteristic
655C23×C4C22×D1111yescharacteristic
656C23×C4C22×D1111yescharacteristic
657C23×C4C22×D1111yescharacteristic
658C2×C4⋊C4—22no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—114no—
662C2×C4⋊C4—222no—
663C2×C4⋊C4—441no—
664C2×C4⋊C4—441no—
665C2×C4⋊C4—441no—
666C2×C4⋊C4—441no—
667C2×C22⋊C4—22no—
668C2×C22⋊C4—22no—
669C2×C22⋊C4—22no—
670C2×C22⋊C4—22no—
671C2×C22⋊C4—41no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—114no—
675C2×C22⋊C4—114no—
676C2×C22⋊C4—114no—
677C2×C22⋊C4—114no—
678C2×C22⋊C4—222no—
679C2×C22⋊C4—222no—
680C2×C22⋊C4—222no—
681C2×C22⋊C4—222no—
682C2×C22⋊C4—222no—
683C2×C22⋊C4—222no—
684C2×C22⋊C4—222no—
685C2×C22⋊C4—222no—
686C2×C22⋊C4—441no—
687C2×C22⋊C4—441no—
688C2×C22⋊C4—441no—
689C2×C22⋊C4—441no—
690C2×C22⋊C4—441no—
691C2×C22⋊C4—441no—
692C2×C22⋊C4—441no—
693C2×C22⋊C4—441no—
694C2×C22⋊C4—441no—
695C2×C22⋊C4C4×D1114yescomplemented
696C2×C22⋊C4C22⋊D1114yes—
697C2×C42—22no—
698C2×C42—22no—
699C2×C42—41no—
700#95—22no—
701#95—22no—
702#95—114no—
703#95—222no—
704#95—222no—
705#95—222no—
706#95—222no—
707#95—222no—
708#95—222no—
709#95—222no—
710#95—222no—
711#95—441no—
712#95—441no—
713#95—441no—
714#95—441no—
715#95—441no—
716#95—441no—
717#95—441no—
718C2×C11—44no—
719C2×C11#232511yescharacteristic
720C2×C11#232511yescharacteristic
721C2×C11#233311yescharacteristic
722C2×C11#235811yescharacteristic
723C2×C11#235911yescharacteristic
724C2×C11#235911yescharacteristic
725C2×C11#237911yescharacteristic
726C2×C11#267111yescharacteristic
727C2×C11#267111yescharacteristic
728C2×C11#268411yescharacteristic
729C2×C11#268411yescharacteristic
730C2×C11#269511yescharacteristic
731C2×C11#269511yescharacteristic
732C2×C11#274311yescharacteristic
733C2×C11#274311yescharacteristic
734D11—44no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—112no—
748C24—112no—
749C24—112no—
750C24—221no—
751C24—221no—
752C24—221no—
753C24—221no—
754C24—221no—
755C24—221no—
756C24—221no—
757C24—221no—
758C24—221no—
759C24—221no—
760C24—221no—
761C24—221no—
762C24C2×C4×D1112yes—
763C24#433912yes—
764C24C2×C22⋊D1112yes—
765C24C23×D1111yescharacteristic
766C2×D4—228no—
767C2×D4—228no—
768C2×D4—444no—
769C2×D4—444no—
770C2×D4—444no—
771C2×D4—444no—
772C2×D4—444no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
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—112no—
811C22×C4—112no—
812C22×C4—112no—
813C22×C4—112no—
814C22×C4—112no—
815C22×C4—112no—
816C22×C4—221no—
817C22×C4—221no—
818C22×C4—221no—
819C22×C4—221no—
820C22×C4—221no—
821C22×C4—221no—
822C22×C4—221no—
823C22×C4—221no—
824C22×C4—221no—
825C22×C4—221no—
826C22×C4—221no—
827C22×C4—221no—
828C22×C4—221no—
829C22×C4—221no—
830C22×C4—221no—
831C22×C4—221no—
832C22×C4—221no—
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—221no—
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—444no—
860C22×C4—444no—
861C22×C4—444no—
862C22×C4—444no—
863C22×C4—444no—
864C22×C4—444no—
865C22×C4—444no—
866C22×C4—444no—
867C22×C4—444no—
868C22×C4—444no—
869C22×C4—444no—
870C22×C4—444no—
871C22×C4—444no—
872C22×C4—444no—
873C22×C4C2×C4×D1112yes—
874C22×C4C2×C4×D1112yes—
875C22×C4D4×D1112yes—
876C22×C4C2×C22⋊D1112yes—
877C22×C4C2×C22⋊D1112yes—
878C4⋊C4—44no—
879C4⋊C4—444no—
880C4⋊C4—444no—
881C22⋊C4—28no—
882C22⋊C4—44no—
883C22⋊C4—44no—
884C22⋊C4—228no—
885C22⋊C4—444no—
886C22⋊C4—444no—
887C22⋊C4—444no—
888C22⋊C4—444no—
889C22⋊C4—444no—
890C22⋊C4—444no—
891C42—44no—
892C11#1457111yescharacteristic, complemented, Sylow
893C23—22no—
894C23—22no—
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—114no—
928C23—222no—
929C23—222no—
930C23—222no—
931C23—222no—
932C23—222no—
933C23—222no—
934C23—222no—
935C23—222no—
936C23—222no—
937C23—222no—
938C23—222no—
939C23—222no—
940C23—222no—
941C23—222no—
942C23—222no—
943C23—222no—
944C23—222no—
945C23—222no—
946C23—441no—
947C23—441no—
948C23—441no—
949C23—441no—
950C23—441no—
951C23—441no—
952C23—441no—
953C23—441no—
954C23—441no—
955C23—441no—
956C23—441no—
957C23—441no—
958C23—441no—
959C23—441no—
960C23—441no—
961C23—441no—
962C23C4×C22⋊D1114yes—
963C23C22×C4×D1111yescharacteristic
964C23C2×#433911yescharacteristic
965C23C2×D4×D1111yescharacteristic
966C23#6703711yescharacteristic
967C23#6703711yescharacteristic
968C23#6703711yescharacteristic
969C23#41×D1111yescharacteristic
970C23#41×D1111yescharacteristic
971C23#41×D1111yescharacteristic
972C23#6704211yescharacteristic
973C23#6704211yescharacteristic
974C23#6704211yescharacteristic
975C23#6704311yescharacteristic
976C23#6704311yescharacteristic
977C23C22×C22⋊D1111yescharacteristic
978D4—4416no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
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—222no—
1022C2×C4—222no—
1023C2×C4—222no—
1024C2×C4—222no—
1025C2×C4—222no—
1026C2×C4—222no—
1027C2×C4—222no—
1028C2×C4—222no—
1029C2×C4—222no—
1030C2×C4—222no—
1031C2×C4—222no—
1032C2×C4—222no—
1033C2×C4—222no—
1034C2×C4—222no—
1035C2×C4—222no—
1036C2×C4—222no—
1037C2×C4—222no—
1038C2×C4—222no—
1039C2×C4—4416no—
1040C2×C4—4416no—
1041C2×C4—441no—
1042C2×C4—441no—
1043C2×C4—441no—
1044C2×C4—441no—
1045C2×C4—441no—
1046C2×C4—441no—
1047C2×C4—441no—
1048C2×C4—441no—
1049C2×C4—441no—
1050C2×C4—441no—
1051C2×C4—441no—
1052C2×C4—441no—
1053C2×C4—441no—
1054C2×C4—441no—
1055C2×C4—441no—
1056C2×C4—441no—
1057C2×C4—441no—
1058C2×C4—441no—
1059C2×C4—441no—
1060C2×C4—441no—
1061C2×C4—441no—
1062C2×C4—441no—
1063C2×C4—441no—
1064C2×C4—441no—
1065C2×C4—441no—
1066C2×C4—441no—
1067C2×C4—441no—
1068C2×C4—441no—
1069C2×C4—441no—
1070C2×C4—441no—
1071C2×C4—441no—
1072C22—24no—
1073C22—24no—
1074C22—24no—
1075C22—42no—
1076C22—42no—
1077C22—42no—
1078C22—42no—
1079C22—42no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—224no—
1088C22—224no—
1089C22—224no—
1090C22—442no—
1091C22—442no—
1092C22—442no—
1093C22—442no—
1094C22—442no—
1095C22—442no—
1096C22—442no—
1097C22—442no—
1098C22—442no—
1099C22—442no—
1100C22—442no—
1101C22—442no—
1102C22#1062305311yescharacteristic
1103C22#1062305411yescharacteristic
1104C22#1062305811yescharacteristic
1105C22#1062306211yescharacteristic
1106C22C4×D4×D1111yescharacteristic
1107C22#1062307611yescharacteristic
1108C22#1062307611yescharacteristic
1109C22#1062307711yescharacteristic
1110C22#1062308111yescharacteristic
1111C22#1062308711yescharacteristic
1112C22#1062309111yescharacteristic
1113C22#1062309511yescharacteristic
1114C22#1062313911yescharacteristic
1115C22#1062314311yescharacteristic
1116C22#1062314611yescharacteristic
1117C22#1062315211yescharacteristic
1118C22#1062318411yescharacteristic
1119C22#1062318611yescharacteristic
1120C22#1062319411yescharacteristic
1121C22#1062319811yescharacteristic
1122C22#1062320911yescharacteristic
1123C22#1062320911yescharacteristic
1124C22#1062321011yescharacteristic
1125C22#1062321411yescharacteristic
1126C22#1062323511yescharacteristic
1127C22#1062323811yescharacteristic
1128C22#1062323911yescharacteristic
1129C22#1062324311yescharacteristic
1130C22C2×C4×C22⋊D1111yescharacteristic
1131C22D4×C22⋊D1111yescharacteristic
1132C22#1062333511yescharacteristic
1133C22#1062335511yescharacteristic
1134C22#1062336011yescharacteristic
1135C22#1062336011yescharacteristic
1136C22#1062336411yescharacteristic
1137C4—42no—
1138C4—42no—
1139C4—42no—
1140C4—42no—
1141C4—42no—
1142C4—81no—
1143C4—442no—
1144C4—442no—
1145C4—442no—
1146C4—442no—
1147C4—442no—
1148C4—442no—
1149C4—881no—
1150C2—44no—
1151C2—444no—
1152C2#1307131411yescharacteristic
1153C2#1307132011yescharacteristic
1154C2#1307137911yescharacteristic
1155C2#1307159311yescharacteristic
1156C2#1307160511yescharacteristic
1157C2#1307160811yescharacteristic
1158C2#1307178511yescharacteristic
1159C2#1307484811yescharacteristic
1160C2#1307485211yescharacteristic
1161C2#1307499211yescharacteristic
1162C2#1307499711yescharacteristic
1163C2#1307514511yescharacteristic
1164C2#1307515411yescharacteristic
1165C2#1307574911yescharacteristic
1166C2#1307575611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#388C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#388D11
hypocenterC11#14571
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C2×#10622553C2semidirect
5. #13066882C2semidirect
6. #13066875C2semidirect
7. #13066871C2semidirect
8. #13066859C2semidirect
9. #13066858C2semidirect
10. #13066849C2semidirect
11. #13066838C2semidirect
12. #13066838C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C2×C11×#388C2semidirect
52. #10622572C4semidirect
102. C2×C11×C22⋊C4C2×C4semidirect
112. C2×C22⋊Dic11C2×C4semidirect
125. C2×(C2×D11)⋊C4C2×C4semidirect
126. C2×(C2×D11)⋊C4C2×C4semidirect
133. C2×Dic11⋊C4C2×C4semidirect
151. C11⋊#95C2×C4semidirect
312. C2×#388D11semidirect
695. C2×C22⋊C4C4×D11semidirect
892. C11#14571semidirect

Maximal subgroups

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

subgroupindex
C2×#106225722
C2×#106225532
C2×#106225712
C2×#106225692
#130668822
#130668752
#130668712
#130668592
#130668582
#130668492
#130668382
(C2×D11)⋊#952
C2×C11×#3882
#1457111