Finite Group Databasebeta

← #14680529

Subgroups — #14680529

Order 2816.

2242 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2C2×#10622572C211yesmaximal, characteristic
3C2×#10622268C211yesmaximal, characteristic, complemented
4C2×#10622563C211yesmaximal, characteristic, complemented
5C2×#10622281C211yesmaximal, characteristic, complemented
6#13066880C211yesmaximal, characteristic, complemented
7#13066867C211yesmaximal, characteristic, complemented
8#13066864C211yesmaximal, characteristic, complemented
9#13066862C211yesmaximal, characteristic, complemented
10#13066859C211yesmaximal, characteristic, complemented
11#13066855C211yesmaximal, characteristic
12#13066842C211yesmaximal, characteristic, complemented
13#13066838C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1440C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×(C22⋊D11)⋊C4—24no—
36C2×(C22⋊D11)⋊C4—24no—
37C2×(C22⋊D11)⋊C4—24no—
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
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54#10622572C418yescomplemented
55#10622563—24no—
56#10622281—24no—
57#10622268—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—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11C2×C414yes—
73C23×Dic11—22no—
74C23×Dic11—22no—
75C23×Dic11—41no—
76C23×Dic11—41no—
77C23×Dic11—41no—
78C23×Dic11—41no—
79C23×Dic11D414yes—
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—41no—
90C22×C4×D11—41no—
91C22×C4×D11—41no—
92C22×C4×D11—41no—
93C22×C4×D11D414yes—
94C2×C11×C22⋊C4—22no—
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4—41no—
101C2×C11×C22⋊C4—41no—
102C2×C11×C22⋊C4C2×C414yescomplemented
103C2×C22⋊Dic11—22no—
104C2×C22⋊Dic11—41no—
105C2×C22⋊Dic11—41no—
106C2×C22⋊Dic11—41no—
107C2×C22⋊Dic11—41no—
108C2×C22⋊Dic11C2×C414yescomplemented
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4—22no—
111C2×(C2×D11)⋊C4—22no—
112C2×(C2×D11)⋊C4—22no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—41no—
117C2×(C2×D11)⋊C4—41no—
118C2×(C2×D11)⋊C4—41no—
119C2×(C2×D11)⋊C4—41no—
120C2×(C2×D11)⋊C4—41no—
121C2×(C2×D11)⋊C4—41no—
122C2×(C2×D11)⋊C4C2×C414yescomplemented
123C2×(C2×D11)⋊C4C2×C414yescomplemented
124C2×C4⋊Dic11—22no—
125C2×C4⋊Dic11—22no—
126C2×C4⋊Dic11—22no—
127C2×C4⋊Dic11—22no—
128C2×C4⋊Dic11—41no—
129C2×C4⋊Dic11—41no—
130C2×Dic11⋊C4—22no—
131C2×Dic11⋊C4—22no—
132C2×Dic11⋊C4—22no—
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4—22no—
135C2×Dic11⋊C4—22no—
136C2×Dic11⋊C4—41no—
137C2×Dic11⋊C4—41no—
138C2×Dic11⋊C4C2×C414yescomplemented
139C2×C4×Dic11—22no—
140C2×C4×Dic11—22no—
141C2×C4×Dic11D414yes—
142(C22⋊D11)⋊C4—232no—
143C11×#95—22no—
144C11×#95—22no—
145C11×#95—41no—
146C11×#95—41no—
147C11⋊#95—22no—
148C11⋊#95—22no—
149C11⋊#95—22no—
150C11⋊#95—22no—
151C11⋊#95—22no—
152C11⋊#95—22no—
153C11⋊#95—22no—
154C11⋊#95—41no—
155C11⋊#95—41no—
156C11⋊#95—41no—
157C11⋊#95—41no—
158C11⋊#95C2×C414yescomplemented
159#14300—111nomaximal, Sylow
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×C11C22×C412yes—
173C24×C11C2×D412yes—
174C24×C11#4112yes—
175C24×C11C2411yescharacteristic
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×D11—21no—
188C23×D11C22×C412yes—
189C23×D11C2×D412yes—
190C23×D11#4112yes—
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×C11—21no—
226C22×C4×C11—21no—
227C22×C4×C11—21no—
228C22×C4×C11—21no—
229C22×C4×C11C22×C412yes—
230C22×C4×C11C22×C412yes—
231C22×C4×C11C2×D412yes—
232C22×C4×C11C2×D412yes—
233C2×C22⋊D11—28no—
234C2×C22⋊D11—28no—
235C2×C22⋊D11—28no—
236C2×C22⋊D11—28no—
237C2×C22⋊D11—28no—
238C2×C22⋊D11—28no—
239C2×C22⋊D11—28no—
240C22×Dic11—28no—
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—21no—
280C22×Dic11—21no—
281C22×Dic11—44no—
282C22×Dic11—44no—
283C22×Dic11—44no—
284C22×Dic11—44no—
285C22×Dic11—44no—
286C22×Dic11—44no—
287C22×Dic11C22×C412yes—
288C22×Dic11C22×C412yes—
289C22×Dic11C22×C412yes—
290C22×Dic11C2×D412yes—
291C22×Dic11C2×D412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11C2×D412yes—
294C22×Dic11C2×D412yes—
295C22×Dic11#4112yes—
296C2×C4×D11—28no—
297C2×C4×D11—44no—
298C2×C4×D11—44no—
299C2×C4×D11—44no—
300C2×C4×D11—44no—
301C2×C4×D11—44no—
302C2×C4×D11—44no—
303C11×C22⋊C4—28no—
304C11×C22⋊C4—28no—
305C11×C22⋊C4—44no—
306C22⋊Dic11—44no—
307C22⋊Dic11—44no—
308(C2×D11)⋊C4—28no—
309(C2×D11)⋊C4—28no—
310(C2×D11)⋊C4—44no—
311(C2×D11)⋊C4—44no—
312(C2×D11)⋊C4—44no—
313C4⋊Dic11—44no—
314C4⋊Dic11—44no—
315Dic11⋊C4—28no—
316Dic11⋊C4—28no—
317Dic11⋊C4—44no—
318C4×Dic11—28no—
319C22×C4×D4—111no—
320C2×#394—111no—
321C2×#387—111no—
322C2×#385—111no—
323C2×#385—111no—
324#1444—111no—
325#1441—111no—
326#1440—111no—
327#1440D1111yescharacteristic, complemented
328#1439—111no—
329#1439—111no—
330#1438—111no—
331#1434—111no—
332C22⋊#95—111no—
333C22⋊#95—111no—
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—22no—
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×C11C4×D414yes—
369C23×C11C23×C411yescharacteristic
370C23×C11C22×D411yescharacteristic
371C23×C11C22×D411yescharacteristic
372C23×C11C22×D411yescharacteristic
373C23×C11C2×#4111yescharacteristic
374C23×C11C2×#4111yescharacteristic
375C23×C11C2×#4111yescharacteristic
376C23×C11H(5,𝔽2)11yescharacteristic
377C23×C11H(5,𝔽2)11yescharacteristic
378C23×C11H(5,𝔽2)11yescharacteristic
379C23×C11H(5,𝔽2)11yescharacteristic
380C23×C11H(5,𝔽2)11yescharacteristic
381C23×C112−1+411yescharacteristic
382C23×C112−1+411yescharacteristic
383C23×C112−1+411yescharacteristic
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—22no—
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×D11—41no—
418C22×D11C4×D414yes—
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—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—
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×C11—41no—
460C2×C4×C11—41no—
461C22⋊D11—232no—
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—416no—
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—
503C2×Dic11—41no—
504C2×Dic11—41no—
505C2×Dic11—41no—
506C2×Dic11—41no—
507C2×Dic11—41no—
508C2×Dic11—41no—
509C2×Dic11—41no—
510C2×Dic11C4×D414yes—
511C2×Dic11#12014yes—
512C4×D11—416no—
513C23×D4—111no—
514C24×C4—111no—
515C24×C4—111no—
516C2×C4×D4—224no—
517C2×C4×D4—224no—
518C2×C4×D4—224no—
519C22×C4⋊C4—111no—
520C22×C4⋊C4—111no—
521C22×C4⋊C4—111no—
522C22×C4⋊C4—111no—
523C22×C4⋊C4—111no—
524C22×C22⋊C4—111no—
525C22×C22⋊C4—111no—
526C22×C22⋊C4—111no—
527C22×C22⋊C4—111no—
528C22×C22⋊C4—111no—
529C22×C22⋊C4—111no—
530C22×C22⋊C4—111no—
531C22×C22⋊C4C2×D1111yescharacteristic
532C22×C22⋊C4C2×D1111yescharacteristic
533C22×C22⋊C4C2×D1111yescharacteristic
534C22×C42—111no—
535#394—118no—
536#387—224no—
537#385—224no—
538#385—224no—
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
554C2×#95C2×D1111yescharacteristic
555C22×C11—24no—
556C22×C11—24no—
557C22×C11—24no—
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×C11—42no—
570C22×C11C2×C4×D411yescharacteristic
571C22×C11C2×C4×D411yescharacteristic
572C22×C11C2×C4×D411yescharacteristic
573C22×C11#51811yescharacteristic
574C22×C11#52011yescharacteristic
575C22×C11#52011yescharacteristic
576C22×C11#52011yescharacteristic
577C22×C11C2×#12011yescharacteristic
578C22×C11#52511yescharacteristic
579C22×C11#52511yescharacteristic
580C22×C11#52511yescharacteristic
581C22×C11#53411yescharacteristic
582C22×C11#53411yescharacteristic
583C22×C11#53411yescharacteristic
584C22×C11#53411yescharacteristic
585C22×C11#53511yescharacteristic
586C22×C11#53511yescharacteristic
587C22×C11#53611yescharacteristic
588C22×C11#53611yescharacteristic
589C22×C11#53611yescharacteristic
590C22×C11#53711yescharacteristic
591C22×C11#53711yescharacteristic
592C22×C11#53711yescharacteristic
593C22×C11#53811yescharacteristic
594C22×C11#53811yescharacteristic
595C22×C11#53911yescharacteristic
596C22×C11#53911yescharacteristic
597C22×C11#53911yescharacteristic
598C22×C11#53911yescharacteristic
599C22×C11#53911yescharacteristic
600C22×C11#53911yescharacteristic
601C22×C11#54011yescharacteristic
602C22×C11#54211yescharacteristic
603C22×C11#54211yescharacteristic
604C22×C11#54211yescharacteristic
605C2×D11—24no—
606C2×D11—24no—
607C2×D11—24no—
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—
619C2×D11—42no—
620C4×C11—42no—
621C4×C11—42no—
622C4×C11—42no—
623C4×C11—42no—
624C4×C11—81no—
625C4×C11—81no—
626Dic11—24no—
627Dic11—24no—
628Dic11—42no—
629Dic11—42no—
630Dic11—42no—
631Dic11—81no—
632Dic11—81no—
633C25—111no—
634C25C22×D1111yescharacteristic
635C22×D4—114no—
636C22×D4—222no—
637C22×D4—222no—
638C22×D4—222no—
639C22×D4—222no—
640C22×D4—222no—
641C22×D4—222no—
642C23×C4—111no—
643C23×C4—111no—
644C23×C4—111no—
645C23×C4—111no—
646C23×C4—111no—
647C23×C4—114no—
648C23×C4—114no—
649C23×C4—111no—
650C23×C4—111no—
651C23×C4—222no—
652C23×C4—222no—
653C23×C4—222no—
654C23×C4—222no—
655C23×C4—441no—
656C23×C4—441no—
657C23×C4—441no—
658C23×C4—441no—
659C23×C4—441no—
660C23×C4—441no—
661C23×C4—441no—
662C23×C4—441no—
663C23×C4C22×D1111yescharacteristic
664C23×C4C22×D1111yescharacteristic
665C23×C4C22×D1111yescharacteristic
666C23×C4C22×D1111yescharacteristic
667C23×C4C22×D1111yescharacteristic
668C23×C4C22×D1111yescharacteristic
669C4×D4—2232no—
670C2×C4⋊C4—114no—
671C2×C4⋊C4—222no—
672C2×C4⋊C4—222no—
673C2×C4⋊C4—222no—
674C2×C4⋊C4—222no—
675C2×C4⋊C4—222no—
676C2×C4⋊C4—222no—
677C2×C4⋊C4—222no—
678C2×C4⋊C4—222no—
679C2×C4⋊C4—222no—
680C2×C4⋊C4—222no—
681C2×C4⋊C4—441no—
682C2×C4⋊C4—441no—
683C2×C4⋊C4—441no—
684C2×C4⋊C4—441no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—41no—
692C2×C22⋊C4—41no—
693C2×C22⋊C4—114no—
694C2×C22⋊C4—114no—
695C2×C22⋊C4—114no—
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—222no—
704C2×C22⋊C4—441no—
705C2×C22⋊C4—441no—
706C2×C22⋊C4—441no—
707C2×C22⋊C4—441no—
708C2×C22⋊C4—441no—
709C2×C22⋊C4—441no—
710C2×C22⋊C4—441no—
711C2×C22⋊C4—441no—
712C2×C22⋊C4—441no—
713C2×C22⋊C4—441no—
714C2×C22⋊C4C4×D1114yescomplemented
715C2×C42—114no—
716C2×C42—222no—
717C2×C42—222no—
718#95—22no—
719#95—22no—
720#95—41no—
721#95—41no—
722#95—114no—
723#95—222no—
724#95—222no—
725#95—222no—
726#95—222no—
727#95—222no—
728#95—222no—
729#95—222no—
730#95—441no—
731#95—441no—
732#95—441no—
733#95—441no—
734C2×C11—44no—
735C2×C11C4×#12011yescharacteristic
736C2×C11#232211yescharacteristic
737C2×C11#232211yescharacteristic
738C2×C11#232411yescharacteristic
739C2×C11#232511yescharacteristic
740C2×C11#232511yescharacteristic
741C2×C11#232611yescharacteristic
742C2×C11#261311yescharacteristic
743C2×C11#261611yescharacteristic
744C2×C11#263011yescharacteristic
745C2×C11#263011yescharacteristic
746C2×C11#263311yescharacteristic
747C2×C11#263611yescharacteristic
748C2×C11#263811yescharacteristic
749C2×C11#263811yescharacteristic
750D11—44no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—112no—
764C24—112no—
765C24—112no—
766C24—221no—
767C24—221no—
768C24—221no—
769C24—221no—
770C24—221no—
771C24—221no—
772C24—221no—
773C24—221no—
774C24—221no—
775C24—221no—
776C24—221no—
777C24—221no—
778C24C2×C4×D1112yes—
779C24D4×D1112yes—
780C24#434112yes—
781C24C23×D1111yescharacteristic
782C2×D4—228no—
783C2×D4—228no—
784C2×D4—228no—
785C2×D4—228no—
786C2×D4—228no—
787C2×D4—228no—
788C2×D4—228no—
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—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—112no—
828C22×C4—112no—
829C22×C4—112no—
830C22×C4—112no—
831C22×C4—112no—
832C22×C4—112no—
833C22×C4—112no—
834C22×C4—112no—
835C22×C4—112no—
836C22×C4—228no—
837C22×C4—228no—
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—221no—
860C22×C4—221no—
861C22×C4—221no—
862C22×C4—221no—
863C22×C4—221no—
864C22×C4—221no—
865C22×C4—221no—
866C22×C4—221no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—221no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—221no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—444no—
879C22×C4—444no—
880C22×C4—444no—
881C22×C4—444no—
882C22×C4—444no—
883C22×C4—444no—
884C22×C4—444no—
885C22×C4—444no—
886C22×C4—444no—
887C22×C4—444no—
888C22×C4—444no—
889C22×C4—444no—
890C22×C4C2×C4×D1112yes—
891C22×C4C2×C4×D1112yes—
892C22×C4D4×D1112yes—
893C22×C4D4×D1112yes—
894C4⋊C4—228no—
895C4⋊C4—228no—
896C4⋊C4—444no—
897C4⋊C4—444no—
898C4⋊C4—444no—
899C22⋊C4—28no—
900C22⋊C4—28no—
901C22⋊C4—44no—
902C22⋊C4—228no—
903C22⋊C4—228no—
904C22⋊C4—444no—
905C22⋊C4—444no—
906C22⋊C4—444no—
907C22⋊C4—444no—
908C22⋊C4—444no—
909C42—228no—
910C11#1430011yescharacteristic, complemented, Sylow
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—22no—
928C23—22no—
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—41no—
944C23—41no—
945C23—114no—
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—222no—
963C23—222no—
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—441no—
979C23—441no—
980C23(C22⋊D11)⋊C414yes—
981C23C22×C4×D1111yescharacteristic
982C23C2×D4×D1111yescharacteristic
983C23C2×D4×D1111yescharacteristic
984C23C2×D4×D1111yescharacteristic
985C23C2×#434111yescharacteristic
986C23#6703711yescharacteristic
987C23#6703711yescharacteristic
988C23#41×D1111yescharacteristic
989C23#41×D1111yescharacteristic
990C23#6704211yescharacteristic
991C23#6704211yescharacteristic
992C23#6704211yescharacteristic
993C23#6704311yescharacteristic
994C23#6704311yescharacteristic
995C23#6704311yescharacteristic
996D4—2232no—
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—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—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—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—114no—
1040C2×C4—114no—
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—441no—
1088C2×C4—441no—
1089C2×C4—441no—
1090C22—24no—
1091C22—24no—
1092C22—24no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—224no—
1106C22—224no—
1107C22—224no—
1108C22—442no—
1109C22—442no—
1110C22—442no—
1111C22—442no—
1112C22—442no—
1113C22—442no—
1114C22—442no—
1115C22—442no—
1116C22—442no—
1117C22—442no—
1118C22—442no—
1119C22—442no—
1120C22C2×(C22⋊D11)⋊C411yescharacteristic
1121C22#1062305411yescharacteristic
1122C22#1062305411yescharacteristic
1123C22C4×D4×D1111yescharacteristic
1124C22C4×D4×D1111yescharacteristic
1125C22#1062307611yescharacteristic
1126C22#1062307711yescharacteristic
1127C22D11×#12011yescharacteristic
1128C22#1062312411yescharacteristic
1129C22#1062312811yescharacteristic
1130C22#1062312811yescharacteristic
1131C22#1062313611yescharacteristic
1132C22#1062313611yescharacteristic
1133C22#1062313711yescharacteristic
1134C22#1062313711yescharacteristic
1135C22#1062313811yescharacteristic
1136C22#1062313911yescharacteristic
1137C22#1062317911yescharacteristic
1138C22#1062317911yescharacteristic
1139C22#1062318411yescharacteristic
1140C22#1062318411yescharacteristic
1141C22#1062318711yescharacteristic
1142C22#1062319111yescharacteristic
1143C22#1062319411yescharacteristic
1144C22#1062319611yescharacteristic
1145C22#1062319611yescharacteristic
1146C22#1062319611yescharacteristic
1147C22#1062320011yescharacteristic
1148C22#1062320511yescharacteristic
1149C22#1062320611yescharacteristic
1150C22#1062320911yescharacteristic
1151C22#1062323811yescharacteristic
1152C22#1062323811yescharacteristic
1153C22#1062324111yescharacteristic
1154C22#1062324111yescharacteristic
1155C4—42no—
1156C4—42no—
1157C4—42no—
1158C4—42no—
1159C4—81no—
1160C4—81no—
1161C4—224no—
1162C4—224no—
1163C4—442no—
1164C4—442no—
1165C4—442no—
1166C4—881no—
1167C4—881no—
1168C2—44no—
1169C2—444no—
1170C2#1307112111yescharacteristic
1171C2#1307128211yescharacteristic
1172C2#1307128611yescharacteristic
1173C2#1307130411yescharacteristic
1174C2#1307131711yescharacteristic
1175C2#1307132011yescharacteristic
1176C2#1307132511yescharacteristic
1177C2#1307432911yescharacteristic
1178C2#1307434411yescharacteristic
1179C2#1307445811yescharacteristic
1180C2#1307446011yescharacteristic
1181C2#1307448911yescharacteristic
1182C2#1307451811yescharacteristic
1183C2#1307453511yescharacteristic
1184C2#1307453811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1440C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1440D11
hypocenterC11#14300
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
3. C2×#10622268C2semidirect
4. C2×#10622563C2semidirect
5. C2×#10622281C2semidirect
6. #13066880C2semidirect
7. #13066867C2semidirect
8. #13066864C2semidirect
9. #13066862C2semidirect
10. #13066859C2semidirect
12. #13066842C2semidirect
13. #13066838C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1440C2semidirect
54. #10622572C4semidirect
102. C2×C11×C22⋊C4C2×C4semidirect
108. C2×C22⋊Dic11C2×C4semidirect
122. C2×(C2×D11)⋊C4C2×C4semidirect
123. C2×(C2×D11)⋊C4C2×C4semidirect
138. C2×Dic11⋊C4C2×C4semidirect
158. C11⋊#95C2×C4semidirect
327. #1440D11semidirect
714. C2×C22⋊C4C4×D11semidirect
910. C11#14300semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
C2×#106225722
C2×#106222682
C2×#106225632
C2×#106222812
#130668802
#130668672
#130668642
#130668622
#130668592
#130668552
#130668422
#130668382
(C2×D11)⋊#952
C11×#14402
#1430011