Finite Group Databasebeta

← #14685094

Subgroups — #14685094

Order 2816.

2430 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D11C211yesmaximal, characteristic
2C2×#10622281C211yesmaximal, characteristic
3C2×#10622602C211yesmaximal, characteristic
4C2×#10622277C211yesmaximal, characteristic
5C2×#10622277C211yesmaximal, characteristic
6#13066851C211yesmaximal, characteristic, complemented
7#13066850C211yesmaximal, characteristic, complemented
8#13066850C211yesmaximal, characteristic, complemented
9#13066849C211yesmaximal, characteristic, complemented
10#13066848C211yesmaximal, characteristic, complemented
11#13066847C211yesmaximal, characteristic, complemented
12#13066847C211yesmaximal, characteristic, complemented
13(C2×D11)⋊#95C211yesmaximal, characteristic
14(C2×D11)⋊#95C211yesmaximal, characteristic
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×C42×D11—24no—
32C2×C42×D11—24no—
33C2×C42×D11—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
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54#10622602—24no—
55#10622281—24no—
56#10622277—24no—
57#10622277C418yescomplemented
58C24×D11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—22no—
83C22×C4×D11—22no—
84C22×C4×D11—22no—
85C22×C4×D11—22no—
86C22×C4×D11—22no—
87C22×C4×D11—22no—
88C22×C4×D11—22no—
89C22×C4×D11C2×C414yes—
90C22×C4×D11D414yes—
91C22×C4×D11D414yes—
92C22×C4×D11D414yes—
93C22×C4×D11Q814yes—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—22no—
97C2×C42×C11—22no—
98C2×C42×C11—22no—
99C2×C42×C11—22no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
103C2×(C2×D11)⋊C4—22no—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—22no—
110C2×(C2×D11)⋊C4C2×C414yes—
111C2×(C2×D11)⋊C4C2×C414yes—
112C2×C4⋊Dic11—22no—
113C2×C4⋊Dic11—22no—
114C2×C4⋊Dic11—22no—
115C2×Dic11⋊C4—22no—
116C2×Dic11⋊C4—22no—
117C2×Dic11⋊C4—22no—
118C2×Dic11⋊C4—22no—
119C2×Dic11⋊C4—22no—
120C2×Dic11⋊C4—22no—
121C2×C4×Dic11—22no—
122C2×C4×Dic11—22no—
123C2×C4×Dic11—22no—
124C2×C4×Dic11—22no—
125C2×C4×Dic11—22no—
126C2×C4×Dic11—22no—
127C2×C4×Dic11—22no—
128C2×C4×Dic11—22no—
129C2×C4×Dic11—22no—
130C42×D11—232no—
131C11×#95—22no—
132C11×#95—22no—
133C11×#95—22no—
134C11×#95—22no—
135C11×#95C2×C414yescomplemented
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—22no—
145C11⋊#95—22no—
146C11⋊#95—22no—
147C11⋊#95—22no—
148C11⋊#95C2×C414yescomplemented
149C11⋊#95C2×C414yescomplemented
150C11⋊#95C2×C414yescomplemented
151#14705—111nomaximal, Sylow
152C24×C11C2411yescharacteristic
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11—21no—
159C23×D11—21no—
160C23×D11—21no—
161C23×D11C22×C412yes—
162C23×D11C2×D412yes—
163C23×D11C2×D412yes—
164C23×D11C2×D412yes—
165C23×D11C2×Q812yes—
166C23×D11#4112yes—
167C23×D11#4112yes—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
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×C11C22×C412yes—
207C22×C4×C11C22×C412yes—
208C22×C4×C11C22×C412yes—
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2×Q812yes—
213C22×C4×C11#4112yes—
214C22×C4×C11#4112yes—
215C22×C4×C11#4112yes—
216C22×C4×C11#4112yes—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—21no—
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×Dic11C22×C412yes—
256C22×Dic11C22×C412yes—
257C22×Dic11C22×C412yes—
258C22×Dic11C2×D412yes—
259C22×Dic11C2×D412yes—
260C22×Dic11C2×D412yes—
261C22×Dic11C2×Q812yes—
262C22×Dic11#4112yes—
263C22×Dic11#4112yes—
264C22×Dic11#4112yes—
265C22×Dic11#4112yes—
266C2×C4×D11—28no—
267C2×C4×D11—28no—
268C2×C4×D11—28no—
269C2×C4×D11—28no—
270C2×C4×D11—28no—
271C2×C4×D11—28no—
272C2×C4×D11—28no—
273C2×C4×D11—28no—
274C2×C4×D11—28no—
275C2×C4×D11—28no—
276C2×C4×D11—28no—
277C2×C4×D11—28no—
278C2×C4×D11—28no—
279C2×C4×D11—28no—
280C2×C4×D11—28no—
281C2×C4×D11—28no—
282C2×C4×D11—28no—
283C2×C4×D11—28no—
284C2×C4×D11—28no—
285C2×C4×D11—28no—
286C2×C4×D11C4⋊C4116yescomplemented
287C11×C4⋊C4—44no—
288C42×C11—28no—
289(C2×D11)⋊C4—28no—
290(C2×D11)⋊C4—28no—
291(C2×D11)⋊C4—44no—
292(C2×D11)⋊C4—44no—
293C4⋊Dic11—44no—
294Dic11⋊C4—44no—
295Dic11⋊C4—44no—
296C4×Dic11—28no—
297C4×Dic11—28no—
298C4×Dic11—28no—
299C23×C42—111no—
300C2×#385—111no—
301C2×#385—111no—
302C2×#381—111no—
303C2×#381—111no—
304#1436—111no—
305#1436—111no—
306#1436—111no—
307#1436—111no—
308#1436—111no—
309#1436—111no—
310#1436—111no—
311#1436D1111yescharacteristic, complemented
312C22⋊#95—111no—
313C22⋊#95—111no—
314C23×C11C23×C411yescharacteristic
315C23×C11C22×D411yescharacteristic
316C23×C11C22×D411yescharacteristic
317C23×C11C22×D411yescharacteristic
318C23×C11C22×Q811yescharacteristic
319C23×C11C2×#4111yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11C2×#4111yescharacteristic
322C23×C11C2×#4111yescharacteristic
323C23×C11C2×#4111yescharacteristic
324C23×C11C2×#4111yescharacteristic
325C23×C11C2×#4111yescharacteristic
326C23×C11C2×#4111yescharacteristic
327C23×C11C2×#4111yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—22no—
344C22×D11—22no—
345C22×D11—22no—
346C22×D11—22no—
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11—22no—
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11C2×C4⋊C414yes—
358C22×D11C4×D414yes—
359C22×D11C4×D414yes—
360C22×D11#12014yes—
361C22×D11C22⋊Q814yes—
362C22×D11C22⋊Q814yes—
363C22×D11#12314yes—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—22no—
380C2×C4×C11—22no—
381C2×C4×C11—22no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—41no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—41no—
394C2×C4×C11—41no—
395C2×C4×C11—41no—
396C2×C4×C11—41no—
397C2×C4×C11—41no—
398C2×C4×C11—41no—
399C2×C4×C11—41no—
400C2×C4×C11—41no—
401C2×C4×C11—41no—
402C2×C4×C11—41no—
403C2×C4×C11—41no—
404C2×C4×C11—41no—
405C2×C4×C11—41no—
406C2×C4×C11—41no—
407C2×C4×C11—41no—
408C2×C4×C11—41no—
409C2×C4×C11—41no—
410C2×C4×C11C2×C4⋊C414yes—
411C2×C4×C11#12314yes—
412C2×C4×C11#12314yes—
413C2×Dic11—22no—
414C2×Dic11—22no—
415C2×Dic11—22no—
416C2×Dic11—22no—
417C2×Dic11—22no—
418C2×Dic11—22no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—22no—
423C2×Dic11—22no—
424C2×Dic11—22no—
425C2×Dic11—22no—
426C2×Dic11—22no—
427C2×Dic11—22no—
428C2×Dic11—22no—
429C2×Dic11—22no—
430C2×Dic11—22no—
431C2×Dic11—22no—
432C2×Dic11—22no—
433C2×Dic11—22no—
434C2×Dic11—22no—
435C2×Dic11—22no—
436C2×Dic11—22no—
437C2×Dic11—41no—
438C2×Dic11—41no—
439C2×Dic11—41no—
440C2×Dic11—41no—
441C2×Dic11—41no—
442C2×Dic11—41no—
443C2×Dic11—41no—
444C2×Dic11—41no—
445C2×Dic11—41no—
446C2×Dic11—41no—
447C2×Dic11—41no—
448C2×Dic11—41no—
449C2×Dic11—41no—
450C2×Dic11—41no—
451C2×Dic11—41no—
452C2×Dic11—41no—
453C2×Dic11—41no—
454C2×Dic11—41no—
455C2×Dic11—41no—
456C2×Dic11—41no—
457C2×Dic11—41no—
458C2×Dic11—41no—
459C2×Dic11C2×C4⋊C414yes—
460C2×Dic11#12314yes—
461C2×Dic11#12314yes—
462C4×D11—232no—
463C4×D11—232no—
464C4×D11—232no—
465C24×C4—111no—
466C24×C4—111no—
467C24×C4—111no—
468C22×C4⋊C4—111no—
469C22×C4⋊C4—111no—
470C22×C4⋊C4—111no—
471C22×C4⋊C4C2×D1111yescharacteristic
472C22×C22⋊C4—111no—
473C22×C22⋊C4—111no—
474C22×C22⋊C4—111no—
475C22×C22⋊C4—111no—
476C22×C42—111no—
477C22×C42—111no—
478C22×C42—111no—
479C22×C42—224no—
480C22×C42—224no—
481C22×C42—224no—
482C22×C42C2×D1111yescharacteristic
483#385—224no—
484#385—224no—
485#381—118no—
486#381—224no—
487C2×#95—111no—
488C2×#95—111no—
489C2×#95—111no—
490C2×#95—111no—
491C2×#95—111no—
492C2×#95—111no—
493C2×#95—111no—
494C2×#95—111no—
495C2×#95—111no—
496C2×#95—111no—
497C2×#95—111no—
498C2×#95—111no—
499C2×#95—111no—
500C2×#95—111no—
501C2×#95—111no—
502C2×#95C2×D1111yescharacteristic
503C2×#95C2×D1111yescharacteristic
504C2×#95C2×D1111yescharacteristic
505C2×#95C2×D1111yescharacteristic
506C2×#95C2×D1111yescharacteristic
507C22×C11C22×C4⋊C411yescharacteristic
508C22×C11C2×C4×D411yescharacteristic
509C22×C11C2×C4×D411yescharacteristic
510C22×C11C4×#4111yescharacteristic
511C22×C11C4×#4111yescharacteristic
512C22×C11C4×#4111yescharacteristic
513C22×C11C4×#4111yescharacteristic
514C22×C11C2×#12011yescharacteristic
515C22×C11C2×C22⋊Q811yescharacteristic
516C22×C11C2×C22⋊Q811yescharacteristic
517C22×C11C2×#12311yescharacteristic
518C22×C11C2×#12311yescharacteristic
519C22×C11C2×#12311yescharacteristic
520C22×C11C2×#12311yescharacteristic
521C22×C11C2×#12311yescharacteristic
522C22×C11#52511yescharacteristic
523C22×C11#52511yescharacteristic
524C22×C11#52511yescharacteristic
525C22×C11#52511yescharacteristic
526C22×C11#52511yescharacteristic
527C22×C11#52511yescharacteristic
528C22×C11#52511yescharacteristic
529C22×C11#52511yescharacteristic
530C22×C11#52911yescharacteristic
531C22×C11#52911yescharacteristic
532C22×C11#52911yescharacteristic
533C22×C11#52911yescharacteristic
534C22×C11#52911yescharacteristic
535C22×C11#52911yescharacteristic
536C22×C11#52911yescharacteristic
537C22×C11#52911yescharacteristic
538C22×C11#53311yescharacteristic
539C22×C11#53311yescharacteristic
540C22×C11#53311yescharacteristic
541C22×C11#53311yescharacteristic
542C2×D11—24no—
543C2×D11—24no—
544C2×D11—24no—
545C2×D11—24no—
546C2×D11—24no—
547C2×D11—24no—
548C2×D11—24no—
549C2×D11—24no—
550C2×D11—24no—
551C2×D11—24no—
552C2×D11—24no—
553C2×D11—24no—
554C2×D11—24no—
555C2×D11—24no—
556C2×D11#38518yes—
557C4×C11—24no—
558C4×C11—24no—
559C4×C11—24no—
560C4×C11—42no—
561C4×C11—42no—
562C4×C11—81no—
563C4×C11—81no—
564Dic11—24no—
565Dic11—24no—
566Dic11—24no—
567Dic11—42no—
568Dic11—42no—
569Dic11—81no—
570Dic11—81no—
571C25—111no—
572C23×C4—111no—
573C23×C4—111no—
574C23×C4—111no—
575C23×C4—114no—
576C23×C4—114no—
577C23×C4—114no—
578C23×C4—111no—
579C23×C4—111no—
580C23×C4—114no—
581C23×C4—114no—
582C23×C4—111no—
583C23×C4—111no—
584C23×C4—222no—
585C23×C4—222no—
586C23×C4—222no—
587C23×C4—222no—
588C23×C4—222no—
589C23×C4—222no—
590C23×C4—222no—
591C23×C4—222no—
592C23×C4—222no—
593C23×C4—222no—
594C23×C4—222no—
595C23×C4—222no—
596C23×C4—222no—
597C23×C4—222no—
598C23×C4—222no—
599C23×C4—222no—
600C23×C4C22×D1111yescharacteristic
601C23×C4C22×D1111yescharacteristic
602C23×C4C22×D1111yescharacteristic
603C23×C4C22×D1111yescharacteristic
604C23×C4C22×D1111yescharacteristic
605C23×C4C22×D1111yescharacteristic
606C23×C4C22×D1111yescharacteristic
607C2×C4⋊C4—22no—
608C2×C4⋊C4—22no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—222no—
611C2×C4⋊C4—222no—
612C2×C4⋊C4—222no—
613C2×C4⋊C4—222no—
614C2×C4⋊C4—222no—
615C2×C4⋊C4—222no—
616C2×C4⋊C4—222no—
617C2×C4⋊C4—222no—
618C2×C4⋊C4—222no—
619C2×C22⋊C4—114no—
620C2×C22⋊C4—114no—
621C2×C22⋊C4—222no—
622C2×C22⋊C4—222no—
623C2×C22⋊C4—222no—
624C2×C22⋊C4—222no—
625C2×C22⋊C4—222no—
626C2×C22⋊C4—222no—
627C2×C22⋊C4—222no—
628C2×C22⋊C4—222no—
629C2×C22⋊C4—222no—
630C2×C22⋊C4—222no—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—2232no—
635C2×C42—222no—
636C2×C42—222no—
637C2×C42—222no—
638C2×C42—222no—
639C2×C42—222no—
640C2×C42—222no—
641C2×C42—222no—
642C2×C42—222no—
643C2×C42—222no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—114no—
649#95—114no—
650#95—114no—
651#95—222no—
652#95—222no—
653#95—222no—
654#95—222no—
655#95—222no—
656#95—222no—
657#95—222no—
658#95—222no—
659#95—222no—
660#95—222no—
661#95—222no—
662#95—222no—
663#95C4×D1114yescomplemented
664C2×C11C2×#38511yescharacteristic
665C2×C11#229611yescharacteristic
666C2×C11#229611yescharacteristic
667C2×C11C4×#12311yescharacteristic
668C2×C11C4×#12311yescharacteristic
669C2×C11C4×#12311yescharacteristic
670C2×C11C4×#12311yescharacteristic
671C2×C11#284911yescharacteristic
672C2×C11#284911yescharacteristic
673C2×C11#285311yescharacteristic
674C2×C11#285311yescharacteristic
675C2×C11#285511yescharacteristic
676C2×C11#285511yescharacteristic
677C2×C11#285511yescharacteristic
678C2×C11#285511yescharacteristic
679D11—28no—
680C24—112no—
681C24—112no—
682C24—112no—
683C24—112no—
684C24—112no—
685C24—112no—
686C24—112no—
687C24—221no—
688C24—221no—
689C24—221no—
690C24—221no—
691C24—221no—
692C24—221no—
693C24—221no—
694C24—221no—
695C24C23×D1111yescharacteristic
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—112no—
735C22×C4—112no—
736C22×C4—112no—
737C22×C4—112no—
738C22×C4—112no—
739C22×C4—112no—
740C22×C4—112no—
741C22×C4—112no—
742C22×C4—112no—
743C22×C4—1116no—
744C22×C4—112no—
745C22×C4—112no—
746C22×C4—228no—
747C22×C4—228no—
748C22×C4—228no—
749C22×C4—228no—
750C22×C4—228no—
751C22×C4—228no—
752C22×C4—228no—
753C22×C4—228no—
754C22×C4—228no—
755C22×C4—228no—
756C22×C4—228no—
757C22×C4—228no—
758C22×C4—228no—
759C22×C4—228no—
760C22×C4—228no—
761C22×C4—228no—
762C22×C4—228no—
763C22×C4—228no—
764C22×C4—221no—
765C22×C4—221no—
766C22×C4—221no—
767C22×C4—221no—
768C22×C4—221no—
769C22×C4—221no—
770C22×C4—221no—
771C22×C4—221no—
772C22×C4—221no—
773C22×C4—221no—
774C22×C4—221no—
775C22×C4—221no—
776C22×C4—228no—
777C22×C4—228no—
778C22×C4—221no—
779C22×C4—221no—
780C22×C4—221no—
781C22×C4—221no—
782C22×C4—221no—
783C22×C4—221no—
784C22×C4—221no—
785C22×C4—221no—
786C22×C4—221no—
787C22×C4—221no—
788C22×C4—221no—
789C22×C4—221no—
790C22×C4—221no—
791C22×C4—221no—
792C22×C4—221no—
793C22×C4—221no—
794C22×C4—221no—
795C22×C4—221no—
796C22×C4—221no—
797C22×C4—221no—
798C22×C4—221no—
799C22×C4—221no—
800C22×C4—221no—
801C22×C4—221no—
802C22×C4—221no—
803C22×C4—221no—
804C22×C4C2×C4×D1112yes—
805C22×C4C2×C4×D1112yes—
806C22×C4C2×C4×D1112yes—
807C22×C4#433912yes—
808C22×C4#433912yes—
809C22×C4D4×D1112yes—
810C22×C4D4×D1112yes—
811C22×C4D4×D1112yes—
812C22×C4#434112yes—
813C22×C4Q8×D1112yes—
814C22×C4#434312yes—
815C4⋊C4—44no—
816C4⋊C4—444no—
817C4⋊C4—444no—
818C4⋊C4—444no—
819C22⋊C4—228no—
820C22⋊C4—228no—
821C22⋊C4—444no—
822C22⋊C4—444no—
823C42—28no—
824C42—228no—
825C42—228no—
826C42—228no—
827C11#1470511yescharacteristic, complemented, Sylow
828C23—114no—
829C23—114no—
830C23—114no—
831C23—114no—
832C23—114no—
833C23—114no—
834C23—114no—
835C23—222no—
836C23—222no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—222no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—222no—
845C23—222no—
846C23—222no—
847C23—222no—
848C23—222no—
849C23—222no—
850C23—222no—
851C23—222no—
852C23—222no—
853C23—222no—
854C23—222no—
855C23—222no—
856C23—222no—
857C23—222no—
858C23—222no—
859C23—222no—
860C23—222no—
861C23—222no—
862C23—222no—
863C23C22×C4×D1111yescharacteristic
864C23C2×#433911yescharacteristic
865C23C2×#433911yescharacteristic
866C23C2×D4×D1111yescharacteristic
867C23C2×D4×D1111yescharacteristic
868C23C2×D4×D1111yescharacteristic
869C23C2×#434111yescharacteristic
870C23C2×Q8×D1111yescharacteristic
871C23C2×#434311yescharacteristic
872C23#41×D1111yescharacteristic
873C23#41×D1111yescharacteristic
874C23#41×D1111yescharacteristic
875C23#41×D1111yescharacteristic
876C23#41×D1111yescharacteristic
877C23#41×D1111yescharacteristic
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—114no—
925C2×C4—114no—
926C2×C4—114no—
927C2×C4—2232no—
928C2×C4—2232no—
929C2×C4—2232no—
930C2×C4—222no—
931C2×C4—222no—
932C2×C4—222no—
933C2×C4—222no—
934C2×C4—222no—
935C2×C4—222no—
936C2×C4—222no—
937C2×C4—222no—
938C2×C4—222no—
939C2×C4—222no—
940C2×C4—222no—
941C2×C4—222no—
942C2×C4—222no—
943C2×C4—222no—
944C2×C4—222no—
945C2×C4—222no—
946C2×C4—222no—
947C2×C4—222no—
948C2×C4—222no—
949C2×C4—222no—
950C2×C4—222no—
951C2×C4—222no—
952C2×C4—222no—
953C2×C4—222no—
954C2×C4—441no—
955C2×C4—441no—
956C2×C4—441no—
957C2×C4—441no—
958C2×C4—441no—
959C2×C4—441no—
960C2×C4—441no—
961C2×C4—441no—
962C2×C4—441no—
963C2×C4—441no—
964C2×C4—441no—
965C2×C4—441no—
966C2×C4—441no—
967C2×C4—441no—
968C2×C4—441no—
969C2×C4—441no—
970C2×C4—441no—
971C2×C4—441no—
972C2×C4—441no—
973C2×C4—441no—
974C2×C4—441no—
975C2×C4—441no—
976C2×C4#6693614yes—
977C2×C4C4⋊C4×D1114yes—
978C2×C4#6694714yes—
979C22—118no—
980C22—224no—
981C22—224no—
982C22—224no—
983C22—224no—
984C22—224no—
985C22—224no—
986C22—224no—
987C22—224no—
988C22—224no—
989C22—224no—
990C22—224no—
991C22—224no—
992C22—224no—
993C22—224no—
994C22C4×#433911yescharacteristic
995C22C2×#6693611yescharacteristic
996C22C2×C4⋊C4×D1111yescharacteristic
997C22C2×#6694711yescharacteristic
998C22#1062305311yescharacteristic
999C22#1062305911yescharacteristic
1000C22#1062305911yescharacteristic
1001C22C4×#434111yescharacteristic
1002C22C4×D4×D1111yescharacteristic
1003C22C4×D4×D1111yescharacteristic
1004C22#1062307811yescharacteristic
1005C22#1062307811yescharacteristic
1006C22#1062307811yescharacteristic
1007C22#1062307811yescharacteristic
1008C22#1062308811yescharacteristic
1009C22C4×#434311yescharacteristic
1010C22#1062310911yescharacteristic
1011C22#1062310911yescharacteristic
1012C22#1062311111yescharacteristic
1013C22D11×#12011yescharacteristic
1014C22#1062313711yescharacteristic
1015C22#1062313711yescharacteristic
1016C22D11×C22⋊Q811yescharacteristic
1017C22D11×C22⋊Q811yescharacteristic
1018C22#1062315811yescharacteristic
1019C22#1062315811yescharacteristic
1020C22D11×#12311yescharacteristic
1021C22D11×#12311yescharacteristic
1022C22D11×#12311yescharacteristic
1023C22#1062321111yescharacteristic
1024C22#1062321911yescharacteristic
1025C22#1062322211yescharacteristic
1026C22#1062323711yescharacteristic
1027C22#1062323711yescharacteristic
1028C22#1062325911yescharacteristic
1029C4—24no—
1030C4—24no—
1031C4—24no—
1032C4—42no—
1033C4—42no—
1034C4—81no—
1035C4—81no—
1036C4—224no—
1037C4—224no—
1038C4—224no—
1039C4—442no—
1040C4—442no—
1041C4—881no—
1042C4—881no—
1043C2—228no—
1044C2D11×#38511yescharacteristic
1045C2#1307109611yescharacteristic
1046C2#1307109711yescharacteristic
1047C2C4×#6693611yescharacteristic
1048C2#1307113711yescharacteristic
1049C2C4×#6694711yescharacteristic
1050C2#1307114311yescharacteristic
1051C2#1307690711yescharacteristic
1052C2#1307691111yescharacteristic
1053C2#1307693611yescharacteristic
1054C2#1307694011yescharacteristic
1055C2#1307695111yescharacteristic
1056C2#1307695111yescharacteristic
1057C2#1307695411yescharacteristic
1058C2#1307695711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#14705
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
6. #13066851C2semidirect
7. #13066850C2semidirect
8. #13066850C2semidirect
9. #13066849C2semidirect
10. #13066848C2semidirect
11. #13066847C2semidirect
12. #13066847C2semidirect
15. C11×#1436C2semidirect
57. #10622277C4semidirect
135. C11×#95C2×C4semidirect
148. C11⋊#95C2×C4semidirect
149. C11⋊#95C2×C4semidirect
150. C11⋊#95C2×C4semidirect
286. C2×C4×D11C4⋊C4semidirect
311. #1436D11semidirect
663. #95C4×D11semidirect
827. C11#14705semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D112
C2×#106222812
C2×#106226022
C2×#106222772
#130668512
#130668502
#130668492
#130668482
#130668472
(C2×D11)⋊#952
C11×#14362
#1470511