Finite Group Databasebeta

← #14677260

Subgroups — #14677260

Order 2816.

2574 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66938C211yesmaximal, characteristic
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
3C2×#10622259C211yesmaximal, characteristic, complemented
4C2×#10622259C211yesmaximal, characteristic, complemented
5C2×#10622570C211yesmaximal, characteristic
6#13066864C211yesmaximal, characteristic, complemented
7#13066864C211yesmaximal, characteristic, complemented
8#13066863C211yesmaximal, characteristic, complemented
9Dic11⋊#95C211yesmaximal, characteristic, complemented
10#13066838C211yesmaximal, characteristic, complemented
11#13066838C211yesmaximal, characteristic, complemented
12(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1440C211yesmaximal, characteristic, complemented
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C22×C4×Dic11C2211yescharacteristic
35C2×#66938—24no—
36C2×#66938—24no—
37C2×#66938C418yescomplemented
38C2×(C22⋊D11)⋊C4—24no—
39C2×(C22⋊D11)⋊C4—24no—
40C2×(C22⋊D11)⋊C4—24no—
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
54C2×C11⋊#95C2211yescharacteristic
55C2×C11⋊#95C2211yescharacteristic
56C2×C11⋊#95C2211yescharacteristic
57#10622570—24no—
58#10622259—24no—
59#10622259—24no—
60C25×C11C2311yescharacteristic
61C24×D11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—22no—
69C22×C22⋊D11—22no—
70C22×C22⋊D11—22no—
71C22×C22⋊D11—22no—
72C22×C22⋊D11C2×C414yes—
73C22×C22⋊D11D414yes—
74C22×C22⋊D11D414yes—
75C23×Dic11—22no—
76C23×Dic11—22no—
77C23×Dic11—22no—
78C23×Dic11—22no—
79C23×Dic11—22no—
80C23×Dic11—41no—
81C23×Dic11—41no—
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C23×Dic11C2311yescharacteristic
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C22×C4×D11—22no—
90C22×C4×D11—22no—
91C22×C4×D11—22no—
92C22×C4×D11—22no—
93C22×C4×D11—22no—
94C22×C4×D11—41no—
95C22×C4×D11—41no—
96C22×Dic22—22no—
97C22×Dic22—22no—
98C22×Dic22—22no—
99C22×Dic22—22no—
100C22×Dic22—22no—
101C22×Dic22—22no—
102C22×Dic22C2×C414yescomplemented
103C2×C11×C22⋊C4—22no—
104C2×C11×C22⋊C4—22no—
105C2×C11×C22⋊C4—22no—
106C2×C11×C22⋊C4—22no—
107C2×C11×C22⋊C4—22no—
108C2×C11×C22⋊C4—22no—
109C2×C11×C22⋊C4—22no—
110C2×C11×C22⋊C4—41no—
111C2×C11×C22⋊C4C2×C414yescomplemented
112C2×C22⋊Dic11—22no—
113C2×C22⋊Dic11—22no—
114C2×C22⋊Dic11—22no—
115C2×C22⋊Dic11—22no—
116C2×C22⋊Dic11—41no—
117C2×C22⋊Dic11C2×C414yescomplemented
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—22no—
128C2×(C2×D11)⋊C4—22no—
129C2×(C2×D11)⋊C4—41no—
130C2×(C2×D11)⋊C4—41no—
131C2×(C2×D11)⋊C4C2×C414yescomplemented
132C2×(C2×D11)⋊C4C2×C414yescomplemented
133C2×Dic11⋊C4—22no—
134C2×Dic11⋊C4—22no—
135C2×Dic11⋊C4—22no—
136C2×Dic11⋊C4—22no—
137C2×Dic11⋊C4—22no—
138C2×Dic11⋊C4D414yes—
139C2×C4×Dic11—22no—
140C2×C4×Dic11—22no—
141C2×C4×Dic11—22no—
142C2×C4×Dic11—22no—
143C2×C4×Dic11—22no—
144C2×C4×Dic11—22no—
145C2×C4×Dic11—22no—
146C2×C4×Dic11C2×C414yescomplemented
147C2×C4×Dic11D414yes—
148#66938—232no—
149(C22⋊D11)⋊C4—232no—
150C11×#95—22no—
151C11×#95—22no—
152C11×#95—22no—
153C11×#95—41no—
154C11⋊#95—22no—
155C11⋊#95—22no—
156C11⋊#95—22no—
157C11⋊#95—22no—
158C11⋊#95—22no—
159C11⋊#95—22no—
160C11⋊#95—22no—
161C11⋊#95—22no—
162C11⋊#95—22no—
163C11⋊#95—41no—
164C11⋊#95—41no—
165C11⋊#95—41no—
166#14027—111nomaximal, Sylow
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×C11C2×D412yes—
181C24×C11C2×D412yes—
182C24×C11C2411yescharacteristic
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×D11C22×C412yes—
196C23×D11C2×D412yes—
197C23×D11C2×D412yes—
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×C11—21no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11—21no—
233C22×C4×C11—21no—
234C22×C4×C11—21no—
235C22×C4×C11C22×C412yes—
236C22×C4×C11C22×C412yes—
237C22×C4×C11C2×D412yes—
238C22×C4×C11C2×D412yes—
239C22×C4×C11#4112yes—
240C2×C22⋊D11—28no—
241C2×C22⋊D11—28no—
242C2×C22⋊D11—28no—
243C2×C22⋊D11—28no—
244C2×C22⋊D11—28no—
245C2×C22⋊D11—28no—
246C2×C22⋊D11C22⋊C4116yes—
247C22×Dic11—28no—
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—21no—
282C22×Dic11—21no—
283C22×Dic11—44no—
284C22×Dic11—44no—
285C22×Dic11—44no—
286C22×Dic11—44no—
287C22×Dic11—44no—
288C22×Dic11—44no—
289C22×Dic11C22×C412yes—
290C22×Dic11C22×C412yes—
291C22×Dic11C22×C412yes—
292C22×Dic11C2×D412yes—
293C22×Dic11C2×D412yes—
294C22×Dic11C2×D412yes—
295C22×Dic11C2×D412yes—
296C22×Dic11C2×D412yes—
297C22×Dic11C2×D412yes—
298C22×Dic11#4112yes—
299C22×Dic11#4112yes—
300C22×Dic11#4112yes—
301C22×Dic11#4112yes—
302C22×Dic11#4112yes—
303C2×C4×D11—28no—
304C2×C4×D11—44no—
305C2×C4×D11—44no—
306C2×C4×D11—44no—
307C2×C4×D11—44no—
308C2×C4×D11—44no—
309C2×C4×D11—44no—
310C2×Dic22—28no—
311C2×Dic22—28no—
312C2×Dic22—28no—
313C2×Dic22—44no—
314C2×Dic22—44no—
315C2×Dic22—44no—
316C2×Dic22—44no—
317C11×C22⋊C4—28no—
318C11×C22⋊C4—28no—
319C11×C22⋊C4—44no—
320C22⋊Dic11—28no—
321C22⋊Dic11—44no—
322(C2×D11)⋊C4—28no—
323(C2×D11)⋊C4—28no—
324(C2×D11)⋊C4—28no—
325(C2×D11)⋊C4—44no—
326(C2×D11)⋊C4—44no—
327Dic11⋊C4—28no—
328Dic11⋊C4—44no—
329C4×Dic11—28no—
330C4×Dic11—28no—
331C4×Dic11—44no—
332C22×#124—111no—
333C22×C4×D4—111no—
334C2×#391—111no—
335C2×#391—111no—
336C2×#390—111no—
337#1440—111no—
338#1440—111no—
339#1440—111no—
340#1440D1111yescharacteristic, complemented
341C4⋊#95—111no—
342C22⋊#95—111no—
343C22⋊#95—111no—
344C22⋊#95—111no—
345C22⋊#95—111no—
346C4×#95—111no—
347C23×C11—22no—
348C23×C11—22no—
349C23×C11—22no—
350C23×C11—22no—
351C23×C11—22no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—22no—
358C23×C11—22no—
359C23×C11—22no—
360C23×C11—22no—
361C23×C11—22no—
362C23×C11—22no—
363C23×C11—22no—
364C23×C11—22no—
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×C11C2×C22⋊C414yes—
382C23×C11C23×C411yescharacteristic
383C23×C11C22×D411yescharacteristic
384C23×C11C22×D411yescharacteristic
385C23×C11C22×D411yescharacteristic
386C23×C11C22×D411yescharacteristic
387C23×C11C2×#4111yescharacteristic
388C23×C11C2×#4111yescharacteristic
389C23×C11C2×#4111yescharacteristic
390C23×C11C2×#4111yescharacteristic
391C23×C11C2×#4111yescharacteristic
392C23×C11C2×#4111yescharacteristic
393C23×C11H(5,𝔽2)11yescharacteristic
394C23×C11H(5,𝔽2)11yescharacteristic
395C23×C112−1+411yescharacteristic
396C23×C112−1+411yescharacteristic
397C22×D11—22no—
398C22×D11—22no—
399C22×D11—22no—
400C22×D11—22no—
401C22×D11—22no—
402C22×D11—22no—
403C22×D11—22no—
404C22×D11—22no—
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—41no—
416C22×D11—41no—
417C22×D11—41no—
418C22×D11—41no—
419C22×D11—41no—
420C22×D11—41no—
421C22×D11—41no—
422C22×D11—41no—
423C22×D11—41no—
424C22×D11—41no—
425C22×D11—41no—
426C22×D11—41no—
427C22×D11—41no—
428C22×D11—41no—
429C22×D11—41no—
430C22×D11—41no—
431C22×D11C2×C22⋊C414yes—
432C2×C4×C11—22no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—22no—
436C2×C4×C11—22no—
437C2×C4×C11—22no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
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—
461C2×C4×C11—41no—
462C2×C4×C11—41no—
463C2×C4×C11—41no—
464C2×C4×C11—41no—
465C2×C4×C11—41no—
466C2×C4×C11—41no—
467C2×C4×C11—41no—
468C2×C4×C11—41no—
469C2×C4×C11—41no—
470C2×C4×C11—41no—
471C2×C4×C11—41no—
472C2×C4×C11—41no—
473C2×C4×C11—41no—
474C22⋊D11—232no—
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—22no—
484C2×Dic11—22no—
485C2×Dic11—22no—
486C2×Dic11—22no—
487C2×Dic11—22no—
488C2×Dic11—22no—
489C2×Dic11—22no—
490C2×Dic11—22no—
491C2×Dic11—22no—
492C2×Dic11—22no—
493C2×Dic11—416no—
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×Dic11—41no—
511C2×Dic11—41no—
512C2×Dic11—41no—
513C2×Dic11—41no—
514C2×Dic11—41no—
515C2×Dic11—41no—
516C2×Dic11—41no—
517C2×Dic11C2×C22⋊C414yes—
518C2×Dic11C4×D414yes—
519C2×Dic11C4×D414yes—
520C2×Dic11#12014yes—
521C2×Dic11#12114yes—
522C2×Dic11#12114yes—
523C2×Dic11#12314yes—
524C2×Dic11#12414yescomplemented
525C4×D11—416no—
526Dic22—416no—
527C23×Q8—111no—
528C23×D4—111no—
529C24×C4—111no—
530C24×C4—111no—
531C2×#124—118no—
532C2×#124—224no—
533C2×#124—224no—
534C2×C4×D4—224no—
535C2×C4×D4—224no—
536C2×C4×D4—224no—
537C22×C4⋊C4—111no—
538C22×C4⋊C4—111no—
539C22×C22⋊C4—111no—
540C22×C22⋊C4—111no—
541C22×C22⋊C4—111no—
542C22×C22⋊C4—111no—
543C22×C22⋊C4—111no—
544C22×C22⋊C4—111no—
545C22×C22⋊C4—111no—
546C22×C22⋊C4C2×D1111yescharacteristic
547C22×C22⋊C4C2×D1111yescharacteristic
548C22×C22⋊C4C2×D1111yescharacteristic
549C22×C42—111no—
550C22×C42—111no—
551C22×C42—111no—
552#391—224no—
553#391—224no—
554#390—224no—
555C2×#95—111no—
556C2×#95—111no—
557C2×#95—111no—
558C2×#95—111no—
559C2×#95—111no—
560C2×#95—111no—
561C2×#95—111no—
562C2×#95—111no—
563C2×#95—111no—
564C2×#95—111no—
565C2×#95—111no—
566C2×#95—111no—
567C2×#95C2×D1111yescharacteristic
568C2×#95C2×D1111yescharacteristic
569C2×#95C2×D1111yescharacteristic
570C2×#95C2×D1111yescharacteristic
571C22×C11—24no—
572C22×C11—24no—
573C22×C11—24no—
574C22×C11—42no—
575C22×C11—42no—
576C22×C11—42no—
577C22×C11—42no—
578C22×C11—42no—
579C22×C11—42no—
580C22×C11—42no—
581C22×C11—42no—
582C22×C11—42no—
583C22×C11—42no—
584C22×C11—42no—
585C22×C11—42no—
586C22×C11C22×C22⋊C411yescharacteristic
587C22×C11C2×C4×D411yescharacteristic
588C22×C11C2×C4×D411yescharacteristic
589C22×C11C4×#4111yescharacteristic
590C22×C11C4×#4111yescharacteristic
591C22×C11#52011yescharacteristic
592C22×C11#52011yescharacteristic
593C22×C11C2×#12011yescharacteristic
594C22×C11C2×#12111yescharacteristic
595C22×C11C2×#12111yescharacteristic
596C22×C11C2×#12311yescharacteristic
597C22×C11C2×#12411yescharacteristic
598C22×C11#52911yescharacteristic
599C22×C11#52911yescharacteristic
600C22×C11#53211yescharacteristic
601C22×C11#53511yescharacteristic
602C22×C11#53611yescharacteristic
603C22×C11#54211yescharacteristic
604C22×C11#54211yescharacteristic
605C22×C11#54611yescharacteristic
606C22×C11#54611yescharacteristic
607C22×C11#54611yescharacteristic
608C22×C11#54611yescharacteristic
609C22×C11#54611yescharacteristic
610C22×C11#54611yescharacteristic
611C22×C11#54711yescharacteristic
612C22×C11#54711yescharacteristic
613C22×C11#54711yescharacteristic
614C22×C11#54711yescharacteristic
615C22×C11#54811yescharacteristic
616C22×C11#54811yescharacteristic
617C22×C11#55611yescharacteristic
618C22×C11#55611yescharacteristic
619C22×C11#55911yescharacteristic
620C22×C11#55911yescharacteristic
621C2×D11—24no—
622C2×D11—24no—
623C2×D11—24no—
624C2×D11—42no—
625C2×D11—42no—
626C2×D11—42no—
627C2×D11—42no—
628C2×D11—42no—
629C2×D11—42no—
630C2×D11—42no—
631C2×D11—42no—
632C2×D11—42no—
633C2×D11—42no—
634C2×D11—42no—
635C2×D11—42no—
636C4×C11—42no—
637C4×C11—42no—
638C4×C11—42no—
639C4×C11—42no—
640C4×C11—42no—
641C4×C11—81no—
642Dic11—24no—
643Dic11—42no—
644Dic11—42no—
645Dic11—42no—
646Dic11—42no—
647Dic11—81no—
648Dic11#38618yes—
649C25—111no—
650C25C22×D1111yescharacteristic
651C22×Q8—114no—
652C22×Q8—222no—
653C22×Q8—222no—
654C22×Q8—222no—
655C22×Q8—222no—
656C22×Q8—222no—
657C22×Q8—222no—
658C22×D4—114no—
659C22×D4—114no—
660C22×D4—114no—
661C22×D4—222no—
662C22×D4—222no—
663C22×D4—222no—
664C22×D4—222no—
665C23×C4—111no—
666C23×C4—111no—
667C23×C4—111no—
668C23×C4—111no—
669C23×C4—111no—
670C23×C4—111no—
671C23×C4—111no—
672C23×C4—222no—
673C23×C4—222no—
674C23×C4—222no—
675C23×C4—222no—
676C23×C4—222no—
677C23×C4—222no—
678C23×C4—222no—
679C23×C4—222no—
680C23×C4—222no—
681C23×C4—222no—
682C23×C4—441no—
683C23×C4—441no—
684C23×C4—441no—
685C23×C4—441no—
686C23×C4C22×D1111yescharacteristic
687C23×C4C22×D1111yescharacteristic
688C23×C4C22×D1111yescharacteristic
689C23×C4C22×D1111yescharacteristic
690C23×C4C22×D1111yescharacteristic
691C23×C4C22×D1111yescharacteristic
692#124—2232no—
693C4×D4—2232no—
694C2×C4⋊C4—114no—
695C2×C4⋊C4—222no—
696C2×C4⋊C4—222no—
697C2×C4⋊C4—222no—
698C2×C4⋊C4—222no—
699C2×C4⋊C4—222no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—41no—
708C2×C22⋊C4—114no—
709C2×C22⋊C4—114no—
710C2×C22⋊C4—114no—
711C2×C22⋊C4—222no—
712C2×C22⋊C4—222no—
713C2×C22⋊C4—222no—
714C2×C22⋊C4—222no—
715C2×C22⋊C4—222no—
716C2×C22⋊C4—222no—
717C2×C22⋊C4—222no—
718C2×C22⋊C4—222no—
719C2×C22⋊C4—222no—
720C2×C22⋊C4—222no—
721C2×C22⋊C4—222no—
722C2×C22⋊C4—222no—
723C2×C22⋊C4—222no—
724C2×C22⋊C4—222no—
725C2×C22⋊C4—222no—
726C2×C22⋊C4—441no—
727C2×C22⋊C4—441no—
728C2×C22⋊C4—441no—
729C2×C22⋊C4C4×D1114yescomplemented
730C2×C42—114no—
731C2×C42—114no—
732C2×C42—222no—
733C2×C42—222no—
734C2×C42—222no—
735C2×C42—222no—
736C2×C42—222no—
737C2×C42—222no—
738C2×C42—222no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—41no—
743#95—222no—
744#95—222no—
745#95—222no—
746#95—222no—
747#95—222no—
748#95—222no—
749#95—222no—
750#95—222no—
751#95—222no—
752#95—441no—
753#95—441no—
754#95—441no—
755C2×C11—44no—
756C2×C11C2×#38611yescharacteristic
757C2×C11C4×#12411yescharacteristic
758C2×C11#232611yescharacteristic
759C2×C11#233911yescharacteristic
760C2×C11#233911yescharacteristic
761C2×C11#236711yescharacteristic
762C2×C11#236711yescharacteristic
763C2×C11#242711yescharacteristic
764C2×C11#242711yescharacteristic
765C2×C11#243211yescharacteristic
766C2×C11#243511yescharacteristic
767C2×C11#244711yescharacteristic
768C2×C11#244711yescharacteristic
769C2×C11#254411yescharacteristic
770C2×C11#254711yescharacteristic
771D11—44no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—112no—
785C24—112no—
786C24—112no—
787C24—221no—
788C24—221no—
789C24—221no—
790C24—221no—
791C24—221no—
792C24—221no—
793C24—221no—
794C24—221no—
795C24—221no—
796C24—221no—
797C24—221no—
798C24—221no—
799C24C2×C4×D1112yes—
800C24D4×D1112yes—
801C24D4×D1112yes—
802C24C23×D1111yescharacteristic
803C2×Q8—228no—
804C2×Q8—228no—
805C2×Q8—228no—
806C2×Q8—444no—
807C2×Q8—444no—
808C2×Q8—444no—
809C2×Q8—444no—
810C2×D4—1116no—
811C2×D4—228no—
812C2×D4—228no—
813C2×D4—228no—
814C2×D4—228no—
815C2×D4—228no—
816C2×D4—228no—
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—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
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—112no—
855C22×C4—112no—
856C22×C4—112no—
857C22×C4—112no—
858C22×C4—112no—
859C22×C4—112no—
860C22×C4—112no—
861C22×C4—112no—
862C22×C4—112no—
863C22×C4—112no—
864C22×C4—112no—
865C22×C4—112no—
866C22×C4—112no—
867C22×C4—112no—
868C22×C4—228no—
869C22×C4—221no—
870C22×C4—221no—
871C22×C4—221no—
872C22×C4—221no—
873C22×C4—228no—
874C22×C4—221no—
875C22×C4—221no—
876C22×C4—221no—
877C22×C4—221no—
878C22×C4—221no—
879C22×C4—221no—
880C22×C4—221no—
881C22×C4—221no—
882C22×C4—221no—
883C22×C4—221no—
884C22×C4—221no—
885C22×C4—221no—
886C22×C4—221no—
887C22×C4—221no—
888C22×C4—221no—
889C22×C4—221no—
890C22×C4—221no—
891C22×C4—221no—
892C22×C4—221no—
893C22×C4—221no—
894C22×C4—221no—
895C22×C4—221no—
896C22×C4—221no—
897C22×C4—221no—
898C22×C4—221no—
899C22×C4—221no—
900C22×C4—221no—
901C22×C4—221no—
902C22×C4—221no—
903C22×C4—221no—
904C22×C4—221no—
905C22×C4—444no—
906C22×C4—444no—
907C22×C4—444no—
908C22×C4—444no—
909C22×C4—444no—
910C22×C4—444no—
911C22×C4—444no—
912C22×C4—444no—
913C22×C4—444no—
914C22×C4—444no—
915C22×C4—444no—
916C22×C4—444no—
917C22×C4C2×C4×D1112yes—
918C22×C4C2×C4×D1112yes—
919C22×C4D4×D1112yes—
920C22×C4D4×D1112yes—
921C22×C4#434112yes—
922C4⋊C4—228no—
923C4⋊C4—444no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—44no—
927C22⋊C4—228no—
928C22⋊C4—228no—
929C22⋊C4—228no—
930C22⋊C4—228no—
931C22⋊C4—444no—
932C22⋊C4—444no—
933C22⋊C4—444no—
934C42—228no—
935C42—228no—
936C42—444no—
937C11#1402711yescharacteristic, complemented, Sylow
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—114no—
973C23—222no—
974C23—222no—
975C23—222no—
976C23—222no—
977C23—222no—
978C23—222no—
979C23—222no—
980C23—222no—
981C23—222no—
982C23—222no—
983C23—222no—
984C23—222no—
985C23—222no—
986C23—222no—
987C23—222no—
988C23—222no—
989C23—222no—
990C23—222no—
991C23—441no—
992C23—441no—
993C23—441no—
994C23—441no—
995C23—441no—
996C23—441no—
997C23—441no—
998C23—441no—
999C23—441no—
1000C23—441no—
1001C23—441no—
1002C23—441no—
1003C23—441no—
1004C23—441no—
1005C23—441no—
1006C23—441no—
1007C23C22⋊C4×D1114yes—
1008C23C22×C4×D1111yescharacteristic
1009C23C2×D4×D1111yescharacteristic
1010C23C2×D4×D1111yescharacteristic
1011C23C2×D4×D1111yescharacteristic
1012C23C2×D4×D1111yescharacteristic
1013C23C2×#434111yescharacteristic
1014C23#6703711yescharacteristic
1015C23#41×D1111yescharacteristic
1016C23#41×D1111yescharacteristic
1017C23#41×D1111yescharacteristic
1018C23#41×D1111yescharacteristic
1019C23#41×D1111yescharacteristic
1020C23#6704211yescharacteristic
1021C23#6704311yescharacteristic
1022C23#6704311yescharacteristic
1023Q8—4416no—
1024D4—2232no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—114no—
1068C2×C4—114no—
1069C2×C4—114no—
1070C2×C4—114no—
1071C2×C4—114no—
1072C2×C4—114no—
1073C2×C4—114no—
1074C2×C4—114no—
1075C2×C4—222no—
1076C2×C4—222no—
1077C2×C4—222no—
1078C2×C4—222no—
1079C2×C4—222no—
1080C2×C4—222no—
1081C2×C4—222no—
1082C2×C4—222no—
1083C2×C4—222no—
1084C2×C4—222no—
1085C2×C4—222no—
1086C2×C4—222no—
1087C2×C4—222no—
1088C2×C4—222no—
1089C2×C4—222no—
1090C2×C4—222no—
1091C2×C4—222no—
1092C2×C4—222no—
1093C2×C4—4416no—
1094C2×C4—4416no—
1095C2×C4—441no—
1096C2×C4—441no—
1097C2×C4—441no—
1098C2×C4—441no—
1099C2×C4—441no—
1100C2×C4—441no—
1101C2×C4—441no—
1102C2×C4—441no—
1103C2×C4—441no—
1104C2×C4—441no—
1105C2×C4—441no—
1106C2×C4—441no—
1107C2×C4—441no—
1108C2×C4—441no—
1109C2×C4—441no—
1110C2×C4—441no—
1111C2×C4—441no—
1112C2×C4—441no—
1113C2×C4—441no—
1114C2×C4—441no—
1115C2×C4—441no—
1116C2×C4—441no—
1117C2×C4—441no—
1118C22—24no—
1119C22—24no—
1120C22—24no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—224no—
1134C22—224no—
1135C22—224no—
1136C22—442no—
1137C22—442no—
1138C22—442no—
1139C22—442no—
1140C22—442no—
1141C22—442no—
1142C22—442no—
1143C22—442no—
1144C22—442no—
1145C22—442no—
1146C22—442no—
1147C22—442no—
1148C22C2×C22⋊C4×D1111yescharacteristic
1149C22#1062305311yescharacteristic
1150C22#1062305411yescharacteristic
1151C22C4×#434111yescharacteristic
1152C22C4×D4×D1111yescharacteristic
1153C22C4×D4×D1111yescharacteristic
1154C22#1062307711yescharacteristic
1155C22D11×#12011yescharacteristic
1156C22#1062312211yescharacteristic
1157C22#1062312711yescharacteristic
1158C22#1062312911yescharacteristic
1159C22D11×#12111yescharacteristic
1160C22D11×#12111yescharacteristic
1161C22#1062313811yescharacteristic
1162C22#1062314111yescharacteristic
1163C22#1062314111yescharacteristic
1164C22#1062314211yescharacteristic
1165C22#1062317911yescharacteristic
1166C22#1062318011yescharacteristic
1167C22D11×#12311yescharacteristic
1168C22#1062318511yescharacteristic
1169C22#1062318511yescharacteristic
1170C22#1062318511yescharacteristic
1171C22#1062318611yescharacteristic
1172C22#1062318611yescharacteristic
1173C22#1062318611yescharacteristic
1174C22#1062319511yescharacteristic
1175C22#1062320011yescharacteristic
1176C22D11×#12411yescharacteristic
1177C22#1062320811yescharacteristic
1178C22#1062321211yescharacteristic
1179C22#1062323311yescharacteristic
1180C22#1062323311yescharacteristic
1181C22#1062323711yescharacteristic
1182C22#1062324111yescharacteristic
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—81no—
1189C4—118no—
1190C4—224no—
1191C4—442no—
1192C4—442no—
1193C4—442no—
1194C4—442no—
1195C4—881no—
1196C2—44no—
1197C2—444no—
1198C2D11×#38611yescharacteristic
1199C2#1307115711yescharacteristic
1200C2#1307132511yescharacteristic
1201C2#1307144011yescharacteristic
1202C2#1307144211yescharacteristic
1203C2#1307168211yescharacteristic
1204C2#1307169011yescharacteristic
1205C2#1307218611yescharacteristic
1206C2#1307218811yescharacteristic
1207C2#1307223911yescharacteristic
1208C2#1307226211yescharacteristic
1209C2#1307239611yescharacteristic
1210C2#1307239811yescharacteristic
1211C2#1307358211yescharacteristic
1212C2#1307360711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1440C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenter#1440D11
hypocenterC11#14027
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
3. C2×#10622259C2semidirect
4. C2×#10622259C2semidirect
6. #13066864C2semidirect
7. #13066864C2semidirect
8. #13066863C2semidirect
9. Dic11⋊#95C2semidirect
10. #13066838C2semidirect
11. #13066838C2semidirect
12. (C2×D11)⋊#95C2semidirect
13. (C2×D11)⋊#95C2semidirect
14. #95×Dic11C2semidirect
15. C11×#1440C2semidirect
37. C2×#66938C4semidirect
102. C22×Dic22C2×C4semidirect
111. C2×C11×C22⋊C4C2×C4semidirect
117. C2×C22⋊Dic11C2×C4semidirect
131. C2×(C2×D11)⋊C4C2×C4semidirect
132. C2×(C2×D11)⋊C4C2×C4semidirect
146. C2×C4×Dic11C2×C4semidirect
340. #1440D11semidirect
524. C2×Dic11#124semidirect
729. C2×C22⋊C4C4×D11semidirect
937. C11#14027semidirect

Maximal subgroups

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

subgroupindex
C22×#669382
C22×(C22⋊D11)⋊C42
C2×#106222592
C2×#106225702
#130668642
#130668632
Dic11⋊#952
#130668382
(C2×D11)⋊#952
#95×Dic112
C11×#14402
#1402711