Finite Group Databasebeta

← #14677136

Subgroups — #14677136

Order 2816.

2950 conjugacy classes of subgroups.

The subgroup lattice has 1252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
3C2×#10622569C211yesmaximal, characteristic
4C2×#10622569C211yesmaximal, characteristic
5C2×#10622563C211yesmaximal, characteristic, complemented
6C2×#10622281C211yesmaximal, characteristic, complemented
7C2×#10622559C211yesmaximal, characteristic, complemented
8#13066880C211yesmaximal, characteristic, complemented
9#13066879C211yesmaximal, characteristic, complemented
10#13066859C211yesmaximal, characteristic, complemented
11#13066850C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
15C11×#1439C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C23×C4×D11C2211yescharacteristic
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×C4⋊C4×D11—24no—
38C2×C4⋊C4×D11—24no—
39C2×C4⋊C4×D11—24no—
40C2×(C22⋊D11)⋊C4—24no—
41C2×(C22⋊D11)⋊C4—24no—
42C2×(C22⋊D11)⋊C4—24no—
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
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622569—24no—
58#10622569C418yescomplemented
59#10622563—24no—
60#10622559—24no—
61#10622281—24no—
62C25×C11C2311yescharacteristic
63C24×D11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11—22no—
73C22×C22⋊D11—22no—
74C22×C22⋊D11C2×C414yes—
75C22×C22⋊D11D414yes—
76C22×C22⋊D11Q814yes—
77C23×Dic11—22no—
78C23×Dic11—22no—
79C23×Dic11—22no—
80C23×Dic11—22no—
81C23×Dic11—22no—
82C23×Dic11—41no—
83C23×Dic11—41no—
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2311yescharacteristic
91C22×C4×D11—22no—
92C22×C4×D11—22no—
93C22×C4×D11—22no—
94C22×C4×D11—22no—
95C22×C4×D11—22no—
96C22×C4×D11—22no—
97C22×C4×D11—22no—
98C22×C4×D11—22no—
99C22×C4×D11—22no—
100C22×C4×D11—22no—
101C22×C4×D11—22no—
102C22×C4×D11—22no—
103C22×C4×D11—22no—
104C22×C4×D11—22no—
105C22×C4×D11—22no—
106C22×C4×D11—41no—
107C22×C4×D11—41no—
108C22×C4×D11—41no—
109C22×C4×D11—41no—
110C22×C4×D11C2×C414yescomplemented
111C22×C4×D11D414yes—
112C2×C11×C4⋊C4—22no—
113C2×C11×C4⋊C4—22no—
114C2×C11×C4⋊C4—22no—
115C2×C11×C22⋊C4—22no—
116C2×C11×C22⋊C4—22no—
117C2×C11×C22⋊C4—22no—
118C2×C11×C22⋊C4—22no—
119C2×C11×C22⋊C4—22no—
120C2×C11×C22⋊C4—22no—
121C2×C11×C22⋊C4—22no—
122C2×C11×C22⋊C4—41no—
123C2×C11×C22⋊C4C2×C414yescomplemented
124C2×C22⋊Dic11—22no—
125C2×C22⋊Dic11—22no—
126C2×C22⋊Dic11—22no—
127C2×C22⋊Dic11—22no—
128C2×C22⋊Dic11—41no—
129C2×C22⋊Dic11C2×C414yescomplemented
130C2×(C2×D11)⋊C4—22no—
131C2×(C2×D11)⋊C4—22no—
132C2×(C2×D11)⋊C4—22no—
133C2×(C2×D11)⋊C4—22no—
134C2×(C2×D11)⋊C4—22no—
135C2×(C2×D11)⋊C4—22no—
136C2×(C2×D11)⋊C4—22no—
137C2×(C2×D11)⋊C4C2×C414yescomplemented
138C2×(C2×D11)⋊C4D414yes—
139C2×C4⋊Dic11—22no—
140C2×C4⋊Dic11—22no—
141C2×C4⋊Dic11—22no—
142C2×C4⋊Dic11—22no—
143C2×C4⋊Dic11—41no—
144C2×C4⋊Dic11D414yescomplemented
145C2×Dic11⋊C4—22no—
146C2×Dic11⋊C4—22no—
147C2×Dic11⋊C4—22no—
148C2×Dic11⋊C4—22no—
149C2×Dic11⋊C4—22no—
150C2×Dic11⋊C4—22no—
151C2×Dic11⋊C4—22no—
152C2×Dic11⋊C4—22no—
153C2×Dic11⋊C4—22no—
154C2×Dic11⋊C4—22no—
155C2×Dic11⋊C4—41no—
156C2×Dic11⋊C4D414yescomplemented
157C2×C4×Dic11—22no—
158C2×C4×Dic11—22no—
159C2×C4×Dic11—22no—
160C4⋊C4×D11—232no—
161(C22⋊D11)⋊C4—232no—
162C11×#95—22no—
163C11×#95—22no—
164C11×#95—41no—
165C11⋊#95—22no—
166C11⋊#95—22no—
167C11⋊#95—22no—
168C11⋊#95—22no—
169C11⋊#95—22no—
170C11⋊#95—22no—
171C11⋊#95—22no—
172C11⋊#95—22no—
173C11⋊#95—41no—
174C11⋊#95C2×C414yescomplemented
175C11⋊#95C2×C414yescomplemented
176#14015—111nomaximal, Sylow
177C24×C11—21no—
178C24×C11—21no—
179C24×C11—21no—
180C24×C11—21no—
181C24×C11—21no—
182C24×C11—21no—
183C24×C11—21no—
184C24×C11—21no—
185C24×C11—21no—
186C24×C11—21no—
187C24×C11—21no—
188C24×C11—21no—
189C24×C11C22×C412yes—
190C24×C11C2×D412yes—
191C24×C11C2×Q812yes—
192C24×C11C2411yescharacteristic
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×D11C22×C412yes—
202C23×D11C2×D412yes—
203C23×D11C2×D412yes—
204C23×D11C2×D412yes—
205C23×D11C2×Q812yes—
206C23×D11#4112yes—
207C23×D11#4112yes—
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×C11—21no—
240C22×C4×C11—21no—
241C22×C4×C11—21no—
242C22×C4×C11—21no—
243C22×C4×C11C22×C412yes—
244C22×C4×C11C22×C412yes—
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2×D412yes—
247C22×C4×C11C2×D412yes—
248C22×C4×C11C2×D412yes—
249C22×C4×C11#4112yes—
250C2×C22⋊D11—28no—
251C2×C22⋊D11—28no—
252C2×C22⋊D11—28no—
253C2×C22⋊D11—28no—
254C2×C22⋊D11—28no—
255C2×C22⋊D11—28no—
256C2×C22⋊D11C4⋊C4116yescomplemented
257C22×Dic11—28no—
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—44no—
296C22×Dic11—44no—
297C22×Dic11—44no—
298C22×Dic11—44no—
299C22×Dic11—44no—
300C22×Dic11—44no—
301C22×Dic11C22×C412yes—
302C22×Dic11C22×C412yes—
303C22×Dic11C22×C412yes—
304C22×Dic11C2×D412yes—
305C22×Dic11C2×D412yes—
306C22×Dic11C2×D412yes—
307C22×Dic11C2×D412yes—
308C22×Dic11C2×D412yes—
309C22×Dic11C2×D412yes—
310C22×Dic11C2×D412yes—
311C22×Dic11C2×Q812yes—
312C22×Dic11#4112yes—
313C2×C4×D11—28no—
314C2×C4×D11—28no—
315C2×C4×D11—28no—
316C2×C4×D11—28no—
317C2×C4×D11—28no—
318C2×C4×D11—28no—
319C2×C4×D11—28no—
320C2×C4×D11—28no—
321C2×C4×D11—28no—
322C2×C4×D11—28no—
323C2×C4×D11—44no—
324C2×C4×D11—44no—
325C2×C4×D11—44no—
326C2×C4×D11—44no—
327C2×C4×D11—44no—
328C2×C4×D11—44no—
329C2×C4×D11—44no—
330C2×C4×D11—44no—
331C2×C4×D11—44no—
332C2×C4×D11—44no—
333C2×C4×D11—44no—
334C11×C4⋊C4—28no—
335C11×C22⋊C4—28no—
336C11×C22⋊C4—28no—
337C11×C22⋊C4—44no—
338C22⋊Dic11—28no—
339C22⋊Dic11—44no—
340(C2×D11)⋊C4—28no—
341(C2×D11)⋊C4—28no—
342(C2×D11)⋊C4—44no—
343C4⋊Dic11—28no—
344C4⋊Dic11—44no—
345Dic11⋊C4—28no—
346Dic11⋊C4—28no—
347Dic11⋊C4—28no—
348Dic11⋊C4—44no—
349C4×Dic11—28no—
350C22×C4×D4—111no—
351C23×C4⋊C4—111no—
352C2×#386—111no—
353C2×#386—111no—
354C2×#385—111no—
355C2×#385—111no—
356C2×#385—111no—
357#1444—111no—
358#1444—111no—
359#1439—111no—
360#1439D1111yescharacteristic, complemented
361#1436—111no—
362#1436—111no—
363C22⋊#95—111no—
364C22⋊#95—111no—
365C23×C11—22no—
366C23×C11—22no—
367C23×C11—22no—
368C23×C11—22no—
369C23×C11—22no—
370C23×C11—22no—
371C23×C11—22no—
372C23×C11—22no—
373C23×C11—22no—
374C23×C11—22no—
375C23×C11—22no—
376C23×C11—22no—
377C23×C11—22no—
378C23×C11—22no—
379C23×C11—22no—
380C23×C11—22no—
381C23×C11—22no—
382C23×C11—22no—
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×C11C2×C4⋊C414yescomplemented
400C23×C11C23×C411yescharacteristic
401C23×C11C22×D411yescharacteristic
402C23×C11C22×D411yescharacteristic
403C23×C11C22×D411yescharacteristic
404C23×C11C22×D411yescharacteristic
405C23×C11C22×D411yescharacteristic
406C23×C11C22×Q811yescharacteristic
407C23×C11C2×#4111yescharacteristic
408C23×C11C2×#4111yescharacteristic
409C23×C11C2×#4111yescharacteristic
410C23×C11C2×#4111yescharacteristic
411C23×C11H(5,𝔽2)11yescharacteristic
412C23×C11H(5,𝔽2)11yescharacteristic
413C23×C112−1+411yescharacteristic
414C23×C112−1+411yescharacteristic
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—22no—
431C22×D11—22no—
432C22×D11—22no—
433C22×D11—22no—
434C22×D11—22no—
435C22×D11—22no—
436C22×D11—22no—
437C22×D11—22no—
438C22×D11—22no—
439C22×D11—22no—
440C22×D11—22no—
441C22×D11—22no—
442C22×D11—22no—
443C22×D11C2×C4⋊C414yes—
444C22×D11C4×D414yes—
445C22×D11C4×D414yes—
446C22×D11#12014yes—
447C22×D11C22⋊Q814yes—
448C22×D11C22⋊Q814yes—
449C22×D11#12314yes—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—22no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
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—22no—
463C2×C4×C11—22no—
464C2×C4×C11—22no—
465C2×C4×C11—22no—
466C2×C4×C11—22no—
467C2×C4×C11—22no—
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—
491C2×C4×C11C4×D414yescomplemented
492C22⋊D11—232no—
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—22no—
506C2×Dic11—22no—
507C2×Dic11—22no—
508C2×Dic11—22no—
509C2×Dic11—22no—
510C2×Dic11—22no—
511C2×Dic11—22no—
512C2×Dic11—22no—
513C2×Dic11—22no—
514C2×Dic11—22no—
515C2×Dic11—22no—
516C2×Dic11—22no—
517C2×Dic11—22no—
518C2×Dic11—22no—
519C2×Dic11—22no—
520C2×Dic11—416no—
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×Dic11C2×C4⋊C414yescomplemented
541C2×Dic11C4×D414yescomplemented
542C2×Dic11#12014yes—
543C4×D11—232no—
544C4×D11—416no—
545C4×D11—416no—
546C23×D4—111no—
547C24×C4—111no—
548C24×C4—111no—
549C24×C4—111no—
550C24×C4—111no—
551C2×C4×D4—224no—
552C2×C4×D4—224no—
553C2×C4×D4—224no—
554C22×C4⋊C4—111no—
555C22×C4⋊C4—111no—
556C22×C4⋊C4—111no—
557C22×C4⋊C4—111no—
558C22×C4⋊C4—111no—
559C22×C4⋊C4—111no—
560C22×C4⋊C4—224no—
561C22×C4⋊C4—224no—
562C22×C4⋊C4—224no—
563C22×C4⋊C4C2×D1111yescharacteristic
564C22×C22⋊C4—111no—
565C22×C22⋊C4—111no—
566C22×C22⋊C4—111no—
567C22×C22⋊C4—111no—
568C22×C22⋊C4—111no—
569C22×C22⋊C4C2×D1111yescharacteristic
570C22×C22⋊C4C2×D1111yescharacteristic
571C22×C22⋊C4C2×D1111yescharacteristic
572C22×C42—111no—
573#386—118no—
574#386—224no—
575#385—224no—
576#385—224no—
577#385—224no—
578C2×#95—111no—
579C2×#95—111no—
580C2×#95—111no—
581C2×#95—111no—
582C2×#95—111no—
583C2×#95—111no—
584C2×#95—111no—
585C2×#95—111no—
586C2×#95—111no—
587C2×#95—111no—
588C2×#95—111no—
589C2×#95C2×D1111yescharacteristic
590C2×#95C2×D1111yescharacteristic
591C2×#95C2×D1111yescharacteristic
592C22×C11—24no—
593C22×C11—24no—
594C22×C11—24no—
595C22×C11—42no—
596C22×C11—42no—
597C22×C11—42no—
598C22×C11—42no—
599C22×C11—42no—
600C22×C11—42no—
601C22×C11—42no—
602C22×C11—42no—
603C22×C11—42no—
604C22×C11—42no—
605C22×C11—42no—
606C22×C11—42no—
607C22×C11C22×C4⋊C411yescharacteristic
608C22×C11C2×C4×D411yescharacteristic
609C22×C11C2×C4×D411yescharacteristic
610C22×C11C2×C4×D411yescharacteristic
611C22×C11C2×C4×D411yescharacteristic
612C22×C11#52011yescharacteristic
613C22×C11#52011yescharacteristic
614C22×C11C2×#12011yescharacteristic
615C22×C11C2×#12011yescharacteristic
616C22×C11C2×C22⋊Q811yescharacteristic
617C22×C11C2×C22⋊Q811yescharacteristic
618C22×C11C2×#12311yescharacteristic
619C22×C11#52511yescharacteristic
620C22×C11#52511yescharacteristic
621C22×C11#52511yescharacteristic
622C22×C11#53411yescharacteristic
623C22×C11#53611yescharacteristic
624C22×C11#53911yescharacteristic
625C22×C11#53911yescharacteristic
626C22×C11D4211yescharacteristic
627C22×C11D4211yescharacteristic
628C22×C11D4211yescharacteristic
629C22×C11D4211yescharacteristic
630C22×C11#54711yescharacteristic
631C22×C11#54711yescharacteristic
632C22×C11#54711yescharacteristic
633C22×C11#54711yescharacteristic
634C22×C11#54811yescharacteristic
635C22×C11#54811yescharacteristic
636C22×C11D4×Q811yescharacteristic
637C22×C11D4×Q811yescharacteristic
638C22×C11#55311yescharacteristic
639C22×C11#55311yescharacteristic
640C22×C11#55411yescharacteristic
641C22×C11#55411yescharacteristic
642C2×D11—24no—
643C2×D11—24no—
644C2×D11—24no—
645C2×D11—24no—
646C2×D11—24no—
647C2×D11—24no—
648C2×D11—24no—
649C2×D11—24no—
650C2×D11—24no—
651C2×D11—24no—
652C2×D11—24no—
653C2×D11—24no—
654C2×D11—24no—
655C2×D11—24no—
656C2×D11#38518yescomplemented
657C4×C11—24no—
658C4×C11—42no—
659C4×C11—42no—
660C4×C11—42no—
661C4×C11—42no—
662C4×C11—81no—
663Dic11—24no—
664Dic11—24no—
665Dic11—24no—
666Dic11—42no—
667Dic11—42no—
668Dic11—42no—
669Dic11—81no—
670C25—111no—
671C25C22×D1111yescharacteristic
672C22×D4—114no—
673C22×D4—114no—
674C22×D4—114no—
675C22×D4—222no—
676C22×D4—222no—
677C22×D4—222no—
678C22×D4—222no—
679C23×C4—111no—
680C23×C4—111no—
681C23×C4—111no—
682C23×C4—111no—
683C23×C4—111no—
684C23×C4—111no—
685C23×C4—114no—
686C23×C4—114no—
687C23×C4—111no—
688C23×C4—222no—
689C23×C4—222no—
690C23×C4—222no—
691C23×C4—222no—
692C23×C4—222no—
693C23×C4—222no—
694C23×C4—222no—
695C23×C4—222no—
696C23×C4—222no—
697C23×C4—222no—
698C23×C4—222no—
699C23×C4—222no—
700C23×C4—222no—
701C23×C4—222no—
702C23×C4—222no—
703C23×C4—222no—
704C23×C4—222no—
705C23×C4—222no—
706C23×C4—222no—
707C23×C4—222no—
708C23×C4—441no—
709C23×C4—441no—
710C23×C4—441no—
711C23×C4—441no—
712C23×C4—441no—
713C23×C4—441no—
714C23×C4C22×D1111yescharacteristic
715C23×C4C22×D1111yescharacteristic
716C23×C4C22×D1111yescharacteristic
717C23×C4C22×D1111yescharacteristic
718C23×C4C22×D1111yescharacteristic
719C23×C4C22×D1111yescharacteristic
720C4×D4—2232no—
721C2×C4⋊C4—22no—
722C2×C4⋊C4—22no—
723C2×C4⋊C4—22no—
724C2×C4⋊C4—114no—
725C2×C4⋊C4—114no—
726C2×C4⋊C4—2232no—
727C2×C4⋊C4—222no—
728C2×C4⋊C4—222no—
729C2×C4⋊C4—222no—
730C2×C4⋊C4—222no—
731C2×C4⋊C4—222no—
732C2×C4⋊C4—222no—
733C2×C4⋊C4—222no—
734C2×C4⋊C4—222no—
735C2×C4⋊C4—222no—
736C2×C4⋊C4—222no—
737C2×C4⋊C4—222no—
738C2×C4⋊C4—222no—
739C2×C4⋊C4—222no—
740C2×C4⋊C4—222no—
741C2×C4⋊C4—441no—
742C2×C4⋊C4—441no—
743C2×C22⋊C4—22no—
744C2×C22⋊C4—22no—
745C2×C22⋊C4—22no—
746C2×C22⋊C4—22no—
747C2×C22⋊C4—22no—
748C2×C22⋊C4—22no—
749C2×C22⋊C4—22no—
750C2×C22⋊C4—41no—
751C2×C22⋊C4—114no—
752C2×C22⋊C4—114no—
753C2×C22⋊C4—114no—
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⋊C4C4×D1114yescomplemented
767C2×C42—222no—
768C2×C42—222no—
769C2×C42—222no—
770#95—22no—
771#95—22no—
772#95—41no—
773#95—114no—
774#95—114no—
775#95—222no—
776#95—222no—
777#95—222no—
778#95—222no—
779#95—222no—
780#95—222no—
781#95—222no—
782#95—222no—
783#95—441no—
784C2×C11—44no—
785C2×C11C2×#38511yescharacteristic
786C2×C11C4×#12011yescharacteristic
787C2×C11#232211yescharacteristic
788C2×C11D4×C4⋊C411yescharacteristic
789C2×C11D4×C4⋊C411yescharacteristic
790C2×C11#236111yescharacteristic
791C2×C11#236111yescharacteristic
792C2×C11#240311yescharacteristic
793C2×C11#240611yescharacteristic
794C2×C11#240911yescharacteristic
795C2×C11#244311yescharacteristic
796C2×C11#244311yescharacteristic
797C2×C11#244911yescharacteristic
798C2×C11#244911yescharacteristic
799C2×C11#257911yescharacteristic
800D11—28no—
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—112no—
814C24—112no—
815C24—112no—
816C24—112no—
817C24—112no—
818C24—112no—
819C24—112no—
820C24—221no—
821C24—221no—
822C24—221no—
823C24—221no—
824C24—221no—
825C24—221no—
826C24—221no—
827C24—221no—
828C24C2×C4×D1112yes—
829C24D4×D1112yes—
830C24Q8×D1112yes—
831C24C23×D1111yescharacteristic
832C2×D4—1116no—
833C2×D4—228no—
834C2×D4—228no—
835C2×D4—228no—
836C2×D4—228no—
837C2×D4—228no—
838C2×D4—228no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
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—112no—
875C22×C4—112no—
876C22×C4—112no—
877C22×C4—112no—
878C22×C4—112no—
879C22×C4—112no—
880C22×C4—112no—
881C22×C4—112no—
882C22×C4—112no—
883C22×C4—112no—
884C22×C4—112no—
885C22×C4—112no—
886C22×C4—228no—
887C22×C4—228no—
888C22×C4—228no—
889C22×C4—228no—
890C22×C4—228no—
891C22×C4—228no—
892C22×C4—228no—
893C22×C4—228no—
894C22×C4—228no—
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—228no—
908C22×C4—228no—
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—444no—
935C22×C4—444no—
936C22×C4—444no—
937C22×C4—444no—
938C22×C4—444no—
939C22×C4—444no—
940C22×C4—444no—
941C22×C4—444no—
942C22×C4—444no—
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×C4C2×C4×D1112yes—
952C22×C4C2×C4×D1112yes—
953C22×C4D4×D1112yes—
954C22×C4D4×D1112yes—
955C22×C4D4×D1112yes—
956C22×C4D4×D1112yes—
957C22×C4#434112yes—
958C4⋊C4—28no—
959C4⋊C4—228no—
960C4⋊C4—228no—
961C4⋊C4—228no—
962C4⋊C4—228no—
963C4⋊C4—444no—
964C4⋊C4—444no—
965C22⋊C4—28no—
966C22⋊C4—28no—
967C22⋊C4—44no—
968C22⋊C4—228no—
969C22⋊C4—228no—
970C22⋊C4—228no—
971C22⋊C4—444no—
972C22⋊C4—444no—
973C42—228no—
974C11#1401511yescharacteristic, complemented, Sylow
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
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—114no—
1010C23—114no—
1011C23—114no—
1012C23—114no—
1013C23—114no—
1014C23—114no—
1015C23—114no—
1016C23—222no—
1017C23—222no—
1018C23—222no—
1019C23—222no—
1020C23—222no—
1021C23—222no—
1022C23—222no—
1023C23—222no—
1024C23—222no—
1025C23—222no—
1026C23—222no—
1027C23—222no—
1028C23—222no—
1029C23—222no—
1030C23—222no—
1031C23—222no—
1032C23—222no—
1033C23—222no—
1034C23—222no—
1035C23—222no—
1036C23—222no—
1037C23—222no—
1038C23—222no—
1039C23—222no—
1040C23—222no—
1041C23—222no—
1042C23—222no—
1043C23—222no—
1044C23C4⋊C4×D1114yescomplemented
1045C23C22×C4×D1111yescharacteristic
1046C23C2×D4×D1111yescharacteristic
1047C23C2×D4×D1111yescharacteristic
1048C23C2×D4×D1111yescharacteristic
1049C23C2×D4×D1111yescharacteristic
1050C23C2×D4×D1111yescharacteristic
1051C23C2×#434111yescharacteristic
1052C23#6703711yescharacteristic
1053C23C2×Q8×D1111yescharacteristic
1054C23#41×D1111yescharacteristic
1055C23#41×D1111yescharacteristic
1056C23#41×D1111yescharacteristic
1057C23#6704211yescharacteristic
1058C23#6704311yescharacteristic
1059C23#6704311yescharacteristic
1060D4—2232no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
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—114no—
1103C2×C4—114no—
1104C2×C4—114no—
1105C2×C4—2232no—
1106C2×C4—222no—
1107C2×C4—222no—
1108C2×C4—222no—
1109C2×C4—222no—
1110C2×C4—222no—
1111C2×C4—222no—
1112C2×C4—222no—
1113C2×C4—222no—
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—222no—
1127C2×C4—222no—
1128C2×C4—222no—
1129C2×C4—222no—
1130C2×C4—222no—
1131C2×C4—222no—
1132C2×C4—222no—
1133C2×C4—4416no—
1134C2×C4—4416no—
1135C2×C4—4416no—
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(C22⋊D11)⋊C414yescomplemented
1156C22—24no—
1157C22—24no—
1158C22—24no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—42no—
1169C22—42no—
1170C22—42no—
1171C22—118no—
1172C22—224no—
1173C22—224no—
1174C22—224no—
1175C22—224no—
1176C22—224no—
1177C22—224no—
1178C22—224no—
1179C22—224no—
1180C22—224no—
1181C22—224no—
1182C22—224no—
1183C22—224no—
1184C22—224no—
1185C22—224no—
1186C22C2×(C22⋊D11)⋊C411yescharacteristic
1187C22C2×C4⋊C4×D1111yescharacteristic
1188C22#1062305411yescharacteristic
1189C22C4×D4×D1111yescharacteristic
1190C22C4×D4×D1111yescharacteristic
1191C22C4×D4×D1111yescharacteristic
1192C22#1062307711yescharacteristic
1193C22D11×#12011yescharacteristic
1194C22D11×#12011yescharacteristic
1195C22#1062312111yescharacteristic
1196C22#1062313611yescharacteristic
1197C22#1062313711yescharacteristic
1198C22#1062313711yescharacteristic
1199C22#1062314011yescharacteristic
1200C22#1062314011yescharacteristic
1201C22#1062314211yescharacteristic
1202C22#1062314211yescharacteristic
1203C22#1062314511yescharacteristic
1204C22D11×C22⋊Q811yescharacteristic
1205C22D11×C22⋊Q811yescharacteristic
1206C22#1062316311yescharacteristic
1207C22#1062316311yescharacteristic
1208C22#1062316611yescharacteristic
1209C22#1062316711yescharacteristic
1210C22D11×#12311yescharacteristic
1211C22#1062318611yescharacteristic
1212C22#1062318611yescharacteristic
1213C22#1062318711yescharacteristic
1214C22#1062319111yescharacteristic
1215C22#1062320611yescharacteristic
1216C22#1062320811yescharacteristic
1217C22#1062320811yescharacteristic
1218C22#1062323811yescharacteristic
1219C22#1062324011yescharacteristic
1220C22#1062324811yescharacteristic
1221C4—24no—
1222C4—42no—
1223C4—42no—
1224C4—42no—
1225C4—42no—
1226C4—81no—
1227C4—224no—
1228C4—224no—
1229C4—224no—
1230C4—442no—
1231C4—442no—
1232C4—442no—
1233C4—881no—
1234C2—44no—
1235C2—228no—
1236C2D11×#38511yescharacteristic
1237C2#1307112111yescharacteristic
1238C2#1307128611yescharacteristic
1239C2#1307151211yescharacteristic
1240C2#1307151411yescharacteristic
1241C2#1307162911yescharacteristic
1242C2#1307163711yescharacteristic
1243C2#1307192511yescharacteristic
1244C2#1307194611yescharacteristic
1245C2#1307197411yescharacteristic
1246C2#1307234411yescharacteristic
1247C2#1307234611yescharacteristic
1248C2#1307242611yescharacteristic
1249C2#1307242811yescharacteristic
1250C2#1307395811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1439C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1439D11
hypocenterC11#14015
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1439

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D11C2semidirect
5. C2×#10622563C2semidirect
6. C2×#10622281C2semidirect
7. C2×#10622559C2semidirect
8. #13066880C2semidirect
9. #13066879C2semidirect
10. #13066859C2semidirect
11. #13066850C2semidirect
12. #13066847C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. (C2×D11)⋊#95C2semidirect
15. C11×#1439C2semidirect
58. #10622569C4semidirect
110. C22×C4×D11C2×C4semidirect
123. C2×C11×C22⋊C4C2×C4semidirect
129. C2×C22⋊Dic11C2×C4semidirect
137. C2×(C2×D11)⋊C4C2×C4semidirect
144. C2×C4⋊Dic11D4semidirect
156. C2×Dic11⋊C4D4semidirect
174. C11⋊#95C2×C4semidirect
175. C11⋊#95C2×C4semidirect
256. C2×C22⋊D11C4⋊C4semidirect
360. #1439D11semidirect
399. C23×C11C2×C4⋊C4semidirect
491. C2×C4×C11C4×D4semidirect
540. C2×Dic11C2×C4⋊C4semidirect
541. C2×Dic11C4×D4semidirect
656. C2×D11#385semidirect
766. C2×C22⋊C4C4×D11semidirect
974. C11#14015semidirect
1044. C23C4⋊C4×D11semidirect
1155. C2×C4(C22⋊D11)⋊C4semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
C22×C4⋊C4×D112
C2×#106225692
C2×#106225632
C2×#106222812
C2×#106225592
#130668802
#130668792
#130668592
#130668502
#130668472
(C2×D11)⋊#952
C11×#14392
#1401511