Finite Group Databasebeta

← #14680688

Subgroups — #14680688

Order 2816.

1614 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622288C211yesmaximal, characteristic
2C2×#10622585C211yesmaximal, characteristic, complemented
3C2×#10622281C211yesmaximal, characteristic
4C2×#10622602C211yesmaximal, characteristic
5C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
6#13066882C211yesmaximal, characteristic, complemented
7#13066880C211yesmaximal, characteristic, complemented
8#13066874C211yesmaximal, characteristic, complemented
9#13066873C211yesmaximal, characteristic, complemented
10#13066864C211yesmaximal, characteristic
11#13066864C211yesmaximal, characteristic
12#13066860C211yesmaximal, characteristic
13#13066849C211yesmaximal, characteristic, complemented
14#13066842C211yesmaximal, characteristic, complemented
15C11×#1436C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
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×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
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
51#10622602—24no—
52#10622585—24no—
53C4×(C2×D11)⋊C4—24no—
54#10622288C418yescomplemented
55#10622281—24no—
56C24×D11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C22×C4×D11—22no—
72C22×C4×D11—22no—
73C22×C4×D11—41no—
74C22×C4×D11—41no—
75C22×C4×D11—41no—
76C22×C4×D11—41no—
77C22×C4×D11D414yes—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—22no—
81C2×C42×C11—22no—
82C2×C42×C11—41no—
83C2×C42×C11—41no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—41no—
96C2×(C2×D11)⋊C4—41no—
97C2×(C2×D11)⋊C4—41no—
98C2×(C2×D11)⋊C4—41no—
99C2×(C2×D11)⋊C4C2×C414yes—
100C2×(C2×D11)⋊C4C2×C414yes—
101C2×(C2×D11)⋊C4C2×C414yes—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—41no—
104C2×C4⋊Dic11—41no—
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—22no—
109C2×Dic11⋊C4—22no—
110C2×Dic11⋊C4—22no—
111C2×Dic11⋊C4—22no—
112C2×Dic11⋊C4—41no—
113C2×Dic11⋊C4—41no—
114C2×Dic11⋊C4—41no—
115C2×Dic11⋊C4—41no—
116C2×Dic11⋊C4C2×C414yescomplemented
117C2×C4×Dic11—41no—
118C2×C4×Dic11—41no—
119C2×C4×Dic11D414yes—
120C11×#95—22no—
121C11×#95—22no—
122C11×#95—41no—
123C11×#95—41no—
124C11×#95C2×C414yescomplemented
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—22no—
129C11⋊#95—22no—
130C11⋊#95—22no—
131C11⋊#95—22no—
132C11⋊#95—22no—
133C11⋊#95—22no—
134C11⋊#95—41no—
135C11⋊#95—41no—
136C11⋊#95—41no—
137C11⋊#95—41no—
138C11⋊#95C2×C414yescomplemented
139C11⋊#95C2×C414yescomplemented
140#14313—111nomaximal, Sylow
141C24×C11C2411yescharacteristic
142C23×D11—21no—
143C23×D11—21no—
144C23×D11—21no—
145C23×D11—21no—
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11C22×C412yes—
155C23×D11C2×D412yes—
156C23×D11#4112yes—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
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×C11C22×C412yes—
200C22×C4×C11C22×C412yes—
201C22×C4×C11C22×C412yes—
202C22×C4×C11C2×D412yes—
203C22×C4×C11C2×D412yes—
204C22×C4×C11#4112yes—
205C22×C4×C11#4112yes—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
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×Dic11C22×C412yes—
249C22×Dic11C22×C412yes—
250C22×Dic11C22×C412yes—
251C22×Dic11C2×D412yes—
252C22×Dic11C2×D412yes—
253C22×Dic11C2×D412yes—
254C22×Dic11#4112yes—
255C2×C4×D11—28no—
256C2×C4×D11—44no—
257C2×C4×D11—44no—
258C2×C4×D11—44no—
259C2×C4×D11—44no—
260C2×C4×D11—44no—
261C2×C4×D11—44no—
262C11×C4⋊C4—44no—
263C42×C11—44no—
264(C2×D11)⋊C4—28no—
265(C2×D11)⋊C4—28no—
266(C2×D11)⋊C4—28no—
267(C2×D11)⋊C4—28no—
268(C2×D11)⋊C4—44no—
269(C2×D11)⋊C4—44no—
270C4⋊Dic11—44no—
271Dic11⋊C4—28no—
272Dic11⋊C4—44no—
273Dic11⋊C4—44no—
274Dic11⋊C4—44no—
275C4×Dic11—44no—
276C2×#397—111no—
277C2×#389—111no—
278C2×#385—111no—
279C2×#385—111no—
280C2×C4×C22⋊C4—111no—
281#1445—111no—
282#1444—111no—
283#1442—111no—
284#1442—111no—
285#1440—111no—
286#1440—111no—
287#1439—111no—
288#1436—111no—
289#1436D1111yescharacteristic, complemented
290#1434—111no—
291C23×C11C23×C411yescharacteristic
292C23×C11C22×D411yescharacteristic
293C23×C11C22×D411yescharacteristic
294C23×C11C2×#4111yescharacteristic
295C23×C11C2×#4111yescharacteristic
296C23×C11C2×#4111yescharacteristic
297C23×C11C2×#4111yescharacteristic
298C23×C11H(5,𝔽2)11yescharacteristic
299C23×C11H(5,𝔽2)11yescharacteristic
300C23×C11H(5,𝔽2)11yescharacteristic
301C23×C11H(5,𝔽2)11yescharacteristic
302C23×C112−1+411yescharacteristic
303C23×C112−1+411yescharacteristic
304C23×C112−1+411yescharacteristic
305C23×C112−1+411yescharacteristic
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—22no—
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—22no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—41no—
330C22×D11—41no—
331C22×D11—41no—
332C22×D11—41no—
333C22×D11—41no—
334C22×D11—41no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—41no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11C4×D414yes—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—41no—
360C2×C4×C11—41no—
361C2×C4×C11—41no—
362C2×C4×C11—41no—
363C2×C4×C11—41no—
364C2×C4×C11—41no—
365C2×C4×C11—41no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11—41no—
383C2×C4×C11—41no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11—41no—
389C2×C4×C11#12114yes—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11—41no—
426C2×Dic11—41no—
427C2×Dic11—41no—
428C2×Dic11—41no—
429C2×Dic11—41no—
430C2×Dic11—41no—
431C2×Dic11—41no—
432C2×Dic11—41no—
433C2×Dic11—41no—
434C2×Dic11—41no—
435C2×Dic11—41no—
436C2×Dic11—41no—
437C2×Dic11—41no—
438C2×Dic11C4×D414yes—
439C4×D11—416no—
440C24×C4—111no—
441C22×C4⋊C4—111no—
442C22×C4⋊C4—111no—
443C22×C4⋊C4—111no—
444C22×C4⋊C4—111no—
445C22×C4⋊C4—111no—
446C22×C4⋊C4C2×D1111yescharacteristic
447C22×C22⋊C4—111no—
448C22×C22⋊C4—111no—
449C22×C22⋊C4—111no—
450C22×C22⋊C4—111no—
451C22×C22⋊C4—111no—
452C22×C22⋊C4—111no—
453C22×C42—111no—
454C22×C42C2×D1111yescharacteristic
455#397—118no—
456#389—224no—
457#385—224no—
458#385—224no—
459C4×C22⋊C4—224no—
460C2×#95—111no—
461C2×#95—111no—
462C2×#95—111no—
463C2×#95—111no—
464C2×#95—111no—
465C2×#95—111no—
466C2×#95—111no—
467C2×#95—111no—
468C2×#95—111no—
469C2×#95—111no—
470C2×#95—111no—
471C2×#95—111no—
472C2×#95—111no—
473C2×#95—111no—
474C2×#95—111no—
475C2×#95C2×D1111yescharacteristic
476C2×#95C2×D1111yescharacteristic
477C2×#95C2×D1111yescharacteristic
478C2×#95C2×D1111yescharacteristic
479C2×#95C2×D1111yescharacteristic
480C22×C11C2×C4×D411yescharacteristic
481C22×C11C2×C4×D411yescharacteristic
482C22×C11C4×#4111yescharacteristic
483C22×C11#52011yescharacteristic
484C22×C11#52011yescharacteristic
485C22×C11#52011yescharacteristic
486C22×C11#52011yescharacteristic
487C22×C11C2×#12111yescharacteristic
488C22×C11#52511yescharacteristic
489C22×C11#52911yescharacteristic
490C22×C11#53211yescharacteristic
491C22×C11#53411yescharacteristic
492C22×C11#53411yescharacteristic
493C22×C11#53411yescharacteristic
494C22×C11#53511yescharacteristic
495C22×C11#53611yescharacteristic
496C22×C11#53611yescharacteristic
497C22×C11#53611yescharacteristic
498C22×C11#53611yescharacteristic
499C22×C11#53811yescharacteristic
500C22×C11#53811yescharacteristic
501C22×C11#53911yescharacteristic
502C22×C11#53911yescharacteristic
503C22×C11#53911yescharacteristic
504C22×C11#53911yescharacteristic
505C22×C11#53911yescharacteristic
506C22×C11#53911yescharacteristic
507C22×C11#53911yescharacteristic
508C22×C11#53911yescharacteristic
509C22×C11#54111yescharacteristic
510C22×C11#54111yescharacteristic
511C22×C11#54211yescharacteristic
512C22×C11#54211yescharacteristic
513C22×C11#54211yescharacteristic
514C22×C11#54211yescharacteristic
515C2×D11—24no—
516C2×D11—24no—
517C2×D11—24no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—42no—
524C2×D11—42no—
525C2×D11—42no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—42no—
530C4×C11—24no—
531C4×C11—42no—
532C4×C11—42no—
533C4×C11—42no—
534C4×C11—42no—
535C4×C11—81no—
536C4×C11—81no—
537Dic11—24no—
538Dic11—42no—
539Dic11—42no—
540Dic11—42no—
541Dic11—42no—
542Dic11—81no—
543Dic11—81no—
544C25—111no—
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—111no—
548C23×C4—111no—
549C23×C4—111no—
550C23×C4—114no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—222no—
554C23×C4—222no—
555C23×C4—441no—
556C23×C4—441no—
557C23×C4—441no—
558C23×C4—441no—
559C23×C4C22×D1111yescharacteristic
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562C23×C4C22×D1111yescharacteristic
563C23×C4C22×D1111yescharacteristic
564C23×C4C22×D1111yescharacteristic
565C23×C4C22×D1111yescharacteristic
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—114no—
570C2×C4⋊C4—222no—
571C2×C4⋊C4—222no—
572C2×C4⋊C4—222no—
573C2×C4⋊C4—222no—
574C2×C4⋊C4—222no—
575C2×C4⋊C4—222no—
576C2×C4⋊C4—222no—
577C2×C4⋊C4—222no—
578C2×C4⋊C4—441no—
579C2×C4⋊C4—441no—
580C2×C4⋊C4—441no—
581C2×C4⋊C4—441no—
582C2×C4⋊C4—441no—
583C2×C4⋊C4—441no—
584C2×C22⋊C4—114no—
585C2×C22⋊C4—114no—
586C2×C22⋊C4—114no—
587C2×C22⋊C4—222no—
588C2×C22⋊C4—222no—
589C2×C22⋊C4—222no—
590C2×C22⋊C4—222no—
591C2×C22⋊C4—222no—
592C2×C22⋊C4—222no—
593C2×C22⋊C4—222no—
594C2×C22⋊C4—222no—
595C2×C22⋊C4—222no—
596C2×C22⋊C4—222no—
597C2×C22⋊C4—222no—
598C2×C22⋊C4—441no—
599C2×C22⋊C4—441no—
600C2×C22⋊C4—441no—
601C2×C22⋊C4—441no—
602C2×C42—22no—
603C2×C42—41no—
604C2×C42—41no—
605C2×C42—114no—
606C2×C42—441no—
607C2×C42—441no—
608#95—22no—
609#95—22no—
610#95—41no—
611#95—41no—
612#95—114no—
613#95—114no—
614#95—222no—
615#95—222no—
616#95—222no—
617#95—222no—
618#95—222no—
619#95—222no—
620#95—222no—
621#95—222no—
622#95—222no—
623#95—441no—
624#95—441no—
625#95—441no—
626#95—441no—
627#95C4×D1114yescomplemented
628C2×C11C4×#12111yescharacteristic
629C2×C11#232211yescharacteristic
630C2×C11#232211yescharacteristic
631C2×C11#232211yescharacteristic
632C2×C11#232611yescharacteristic
633C2×C11#233411yescharacteristic
634C2×C11#233411yescharacteristic
635C2×C11#261711yescharacteristic
636C2×C11#262111yescharacteristic
637C2×C11#263311yescharacteristic
638C2×C11#263811yescharacteristic
639C2×C11#265211yescharacteristic
640C2×C11#265211yescharacteristic
641C2×C11#266311yescharacteristic
642C2×C11#266311yescharacteristic
643D11—44no—
644C24—112no—
645C24—112no—
646C24—112no—
647C24—221no—
648C24—221no—
649C24—221no—
650C24—221no—
651C24—221no—
652C24—221no—
653C24—221no—
654C24—221no—
655C24—221no—
656C24—221no—
657C24—221no—
658C24—221no—
659C24C23×D1111yescharacteristic
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—112no—
709C22×C4—221no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—228no—
738C22×C4—221no—
739C22×C4—221no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—221no—
743C22×C4—221no—
744C22×C4—221no—
745C22×C4—221no—
746C22×C4—221no—
747C22×C4—221no—
748C22×C4—221no—
749C22×C4—221no—
750C22×C4—221no—
751C22×C4—221no—
752C22×C4—444no—
753C22×C4—444no—
754C22×C4—444no—
755C22×C4—444no—
756C22×C4—444no—
757C22×C4—444no—
758C22×C4C2×C4×D1112yes—
759C22×C4C2×C4×D1112yes—
760C22×C4C2×C4×D1112yes—
761C22×C4#433912yes—
762C22×C4#433912yes—
763C22×C4D4×D1112yes—
764C22×C4D4×D1112yes—
765C4⋊C4—44no—
766C4⋊C4—228no—
767C4⋊C4—444no—
768C4⋊C4—444no—
769C4⋊C4—444no—
770C4⋊C4—444no—
771C22⋊C4—228no—
772C22⋊C4—228no—
773C22⋊C4—228no—
774C22⋊C4—228no—
775C22⋊C4—444no—
776C22⋊C4—444no—
777C42—44no—
778C42—444no—
779C11#1431311yescharacteristic, complemented, Sylow
780C23—114no—
781C23—222no—
782C23—222no—
783C23—222no—
784C23—222no—
785C23—222no—
786C23—222no—
787C23—222no—
788C23—222no—
789C23—222no—
790C23—222no—
791C23—222no—
792C23—222no—
793C23—222no—
794C23—222no—
795C23—222no—
796C23—222no—
797C23—222no—
798C23—222no—
799C23—441no—
800C23—441no—
801C23—441no—
802C23—441no—
803C23—441no—
804C23—441no—
805C23—441no—
806C23—441no—
807C23—441no—
808C23—441no—
809C23—441no—
810C23—441no—
811C23—441no—
812C23—441no—
813C23—441no—
814C23—441no—
815C23C22×C4×D1111yescharacteristic
816C23C2×#433911yescharacteristic
817C23C2×#433911yescharacteristic
818C23C2×D4×D1111yescharacteristic
819C23C2×D4×D1111yescharacteristic
820C23#6703711yescharacteristic
821C23#6703711yescharacteristic
822C23#6704011yescharacteristic
823C23#6704011yescharacteristic
824C23#41×D1111yescharacteristic
825C23#41×D1111yescharacteristic
826C23#6704211yescharacteristic
827C23#6704211yescharacteristic
828C23#6704311yescharacteristic
829C23#6704311yescharacteristic
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—114no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—4416no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4—441no—
904C2×C4—441no—
905C2×C4—441no—
906C2×C4—441no—
907C2×C4—441no—
908C2×C4—441no—
909C2×C4—441no—
910C2×C4—441no—
911C2×C4—441no—
912C2×C4—441no—
913C2×C4—441no—
914C2×C4—441no—
915C2×C4—441no—
916C2×C4—441no—
917C2×C4—441no—
918C2×C4—441no—
919C2×C4—441no—
920C2×C4—441no—
921C2×C4—441no—
922C2×C4—441no—
923C2×C4—441no—
924C2×C4—441no—
925C2×C4—441no—
926C2×C4—441no—
927C2×C4—441no—
928C2×C4#6693714yes—
929C22—224no—
930C22—224no—
931C22—224no—
932C22—442no—
933C22—442no—
934C22—442no—
935C22—442no—
936C22—442no—
937C22—442no—
938C22—442no—
939C22—442no—
940C22—442no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22C4×#433911yescharacteristic
945C22C2×#6693711yescharacteristic
946C22#1062303511yescharacteristic
947C22#1062304611yescharacteristic
948C22#1062305411yescharacteristic
949C22#1062305911yescharacteristic
950C22#1062306511yescharacteristic
951C22C4×D4×D1111yescharacteristic
952C22C4×D4×D1111yescharacteristic
953C22#1062307711yescharacteristic
954C22#1062307811yescharacteristic
955C22#1062307911yescharacteristic
956C22#1062309111yescharacteristic
957C22#1062309111yescharacteristic
958C22#1062309511yescharacteristic
959C22#1062310511yescharacteristic
960C22#1062311311yescharacteristic
961C22#1062311411yescharacteristic
962C22#1062311411yescharacteristic
963C22#1062312311yescharacteristic
964C22#1062313611yescharacteristic
965C22#1062313611yescharacteristic
966C22#1062315911yescharacteristic
967C22#1062315911yescharacteristic
968C22#1062316911yescharacteristic
969C22#1062317111yescharacteristic
970C22#1062318411yescharacteristic
971C22#1062319111yescharacteristic
972C22#1062319311yescharacteristic
973C22#1062320611yescharacteristic
974C22#1062322311yescharacteristic
975C22#1062322311yescharacteristic
976C22#1062323811yescharacteristic
977C22#1062323811yescharacteristic
978C22#1062325511yescharacteristic
979C4—24no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—81no—
985C4—81no—
986C4—224no—
987C4—442no—
988C4—442no—
989C4—442no—
990C4—442no—
991C4—881no—
992C4—881no—
993C2—444no—
994C2C4×#6693711yescharacteristic
995C2#1307128011yescharacteristic
996C2#1307128611yescharacteristic
997C2#1307128911yescharacteristic
998C2#1307132211yescharacteristic
999C2#1307138511yescharacteristic
1000C2#1307139111yescharacteristic
1001C2#1307435611yescharacteristic
1002C2#1307438711yescharacteristic
1003C2#1307448811yescharacteristic
1004C2#1307454011yescharacteristic
1005C2#1307466011yescharacteristic
1006C2#1307466211yescharacteristic
1007C2#1307476811yescharacteristic
1008C2#1307477011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1436C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1436D11
hypocenterC11#14313
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
2. C2×#10622585C2semidirect
6. #13066882C2semidirect
7. #13066880C2semidirect
8. #13066874C2semidirect
9. #13066873C2semidirect
13. #13066849C2semidirect
14. #13066842C2semidirect
15. C11×#1436C2semidirect
54. #10622288C4semidirect
116. C2×Dic11⋊C4C2×C4semidirect
124. C11×#95C2×C4semidirect
138. C11⋊#95C2×C4semidirect
139. C11⋊#95C2×C4semidirect
289. #1436D11semidirect
627. #95C4×D11semidirect
779. C11#14313semidirect

Maximal subgroups

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

subgroupindex
C2×#106222882
C2×#106225852
C2×#106222812
C2×#106226022
C2×C4×(C2×D11)⋊C42
#130668822
#130668802
#130668742
#130668732
#130668642
#130668602
#130668492
#130668422
C11×#14362
#1431311