Finite Group Databasebeta

← #14675596

Subgroups — #14675596

Order 2816.

1790 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×#10622565C211yesmaximal, characteristic
2C2×#10622262C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic11C211yesmaximal, characteristic
4C2×C22⋊C4×Dic11C211yesmaximal, characteristic
5C2×C22⋊C4×Dic11C211yesmaximal, characteristic
6#13066882C211yesmaximal, characteristic, complemented
7#13066877C211yesmaximal, characteristic, complemented
8#13066876C211yesmaximal, characteristic, complemented
9#13066874C211yesmaximal, characteristic, complemented
10#13066863C211yesmaximal, characteristic
11#13066859C211yesmaximal, characteristic
12#95×Dic11C211yesmaximal, characteristic, complemented
13#95×Dic11C211yesmaximal, characteristic, complemented
14#95×Dic11C211yesmaximal, characteristic, complemented
15C11×#1440C211yesmaximal, characteristic
16C24×Dic11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
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#10622565C418yescomplemented
52C22⋊C4×Dic11—24no—
53C22⋊C4×Dic11—24no—
54C22⋊C4×Dic11—24no—
55#10622262—24no—
56C25×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—22no—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11D414yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C2×C11×C22⋊C4—22no—
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4C2×C414yes—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11C2×C414yes—
95C2×C22⋊Dic11C2×C414yes—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—22no—
101C2×Dic11⋊C4C2×C414yescomplemented
102C2×C4×Dic11—22no—
103C2×C4×Dic11—22no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—22no—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—22no—
112C2×C4×Dic11—22no—
113C2×C4×Dic11—22no—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11D414yes—
120C11×#95—22no—
121C11×#95—22no—
122C11×#95—22no—
123C11×#95—22no—
124C11⋊#95—22no—
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—22no—
135C11⋊#95—22no—
136C11⋊#95—22no—
137C11⋊#95C2×C414yescomplemented
138C11⋊#95C2×C414yescomplemented
139C11⋊#95C2×C414yescomplemented
140C4×#397—111nomaximal, Sylow
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—21no—
144C24×C11—21no—
145C24×C11—21no—
146C24×C11—21no—
147C24×C11—21no—
148C24×C11—21no—
149C24×C11—21no—
150C24×C11—21no—
151C24×C11—21no—
152C24×C11—21no—
153C24×C11C22×C412yes—
154C24×C11C2×D412yes—
155C24×C11#4112yes—
156C24×C11C2411yescharacteristic
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×C11C22×C412yes—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C2×D412yes—
196C22×C4×C11#4112yes—
197C22×C4×C11#4112yes—
198C22×C4×C11#4112yes—
199C22×Dic11—28no—
200C22×Dic11—28no—
201C22×Dic11—28no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
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—44no—
243C22×Dic11—44no—
244C22×Dic11—44no—
245C22×Dic11—44no—
246C22×Dic11C22×C412yes—
247C22×Dic11C22×C412yes—
248C22×Dic11C22×C412yes—
249C22×Dic11C22×C412yes—
250C22×Dic11C2×D412yes—
251C22×Dic11C2×D412yes—
252C22×Dic11C2×D412yes—
253C22×Dic11C2×D412yes—
254C22×Dic11#4112yes—
255C22×Dic11#4112yes—
256C22×Dic11#4112yes—
257C22×Dic11#4112yes—
258C22×Dic11#4112yes—
259C22×Dic11#4112yes—
260C22×Dic11#4112yes—
261C22×Dic11#4112yes—
262C11×C22⋊C4—28no—
263C11×C22⋊C4—28no—
264C11×C22⋊C4—28no—
265C22⋊Dic11—28no—
266C22⋊Dic11—28no—
267C22⋊Dic11—28no—
268Dic11⋊C4—28no—
269Dic11⋊C4—28no—
270C4×Dic11—28no—
271C4×Dic11—44no—
272C4×Dic11—44no—
273C4×Dic11—44no—
274C4×Dic11—44no—
275C4×Dic11—44no—
276C2×#397—111no—
277C2×C4×C4⋊C4—111no—
278C2×C4×C22⋊C4—111no—
279C2×C4×C22⋊C4—111no—
280C2×C4×C22⋊C4—111no—
281#1445—111no—
282#1443—111no—
283#1443—111no—
284#1442—111no—
285#1440—111no—
286#1440D1111yescharacteristic
287#1439—111no—
288C4×#95—111no—
289C4×#95—111no—
290C4×#95—111no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—22no—
305C23×C11—22no—
306C23×C11—22no—
307C23×C11—22no—
308C23×C11—22no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—41no—
312C23×C11—41no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—41no—
323C23×C11—41no—
324C23×C11—41no—
325C23×C11C4×D414yes—
326C23×C11C23×C411yescharacteristic
327C23×C11C22×D411yescharacteristic
328C23×C11C22×D411yescharacteristic
329C23×C11C2×#4111yescharacteristic
330C23×C11C2×#4111yescharacteristic
331C23×C11C2×#4111yescharacteristic
332C23×C11C2×#4111yescharacteristic
333C23×C11C2×#4111yescharacteristic
334C23×C11C2×#4111yescharacteristic
335C23×C11C2×#4111yescharacteristic
336C23×C11C2×#4111yescharacteristic
337C23×C11C2×#4111yescharacteristic
338C23×C11C2×#4111yescharacteristic
339C23×C11C2×#4111yescharacteristic
340C23×C11C2×#4111yescharacteristic
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×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
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—41no—
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—416no—
432C2×Dic11C4×D414yes—
433C2×Dic11#12114yes—
434C2×Dic11#12314yes—
435C2×Dic11#12314yes—
436C2×Dic11#12314yes—
437C2×Dic11#12414yes—
438C2×Dic11#12614yes—
439C2×Dic11#12614yes—
440C24×C4—111no—
441C22×C4⋊C4—111no—
442C22×C4⋊C4—111no—
443C22×C22⋊C4—111no—
444C22×C22⋊C4—111no—
445C22×C22⋊C4—111no—
446C22×C22⋊C4C2×D1111yescharacteristic
447C22×C22⋊C4C2×D1111yescharacteristic
448C22×C22⋊C4C2×D1111yescharacteristic
449C22×C42—111no—
450C22×C42—111no—
451C22×C42—111no—
452C22×C42—111no—
453C22×C42—111no—
454C22×C42—111no—
455#397—118no—
456C4×C4⋊C4—224no—
457C4×C22⋊C4—224no—
458C4×C22⋊C4—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×#95—111no—
476C2×#95C2×D1111yescharacteristic
477C2×#95C2×D1111yescharacteristic
478C2×#95C2×D1111yescharacteristic
479C2×#95C2×D1111yescharacteristic
480C22×C11—24no—
481C22×C11—24no—
482C22×C11—24no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11C2×C4×D411yescharacteristic
496C22×C11C2×C4×D411yescharacteristic
497C22×C11C4×#4111yescharacteristic
498C22×C11C4×#4111yescharacteristic
499C22×C11C4×#4111yescharacteristic
500C22×C11C4×#4111yescharacteristic
501C22×C11C4×#4111yescharacteristic
502C22×C11C2×#12111yescharacteristic
503C22×C11C2×#12311yescharacteristic
504C22×C11C2×#12311yescharacteristic
505C22×C11C2×#12311yescharacteristic
506C22×C11#52511yescharacteristic
507C22×C11#52511yescharacteristic
508C22×C11#52511yescharacteristic
509C22×C11#52511yescharacteristic
510C22×C11C2×#12411yescharacteristic
511C22×C11C2×#12611yescharacteristic
512C22×C11C2×#12611yescharacteristic
513C22×C11#52911yescharacteristic
514C22×C11#52911yescharacteristic
515C22×C11#52911yescharacteristic
516C22×C11#52911yescharacteristic
517C22×C11#52911yescharacteristic
518C22×C11#52911yescharacteristic
519C22×C11#52911yescharacteristic
520C22×C11#52911yescharacteristic
521C22×C11#52911yescharacteristic
522C22×C11#52911yescharacteristic
523C22×C11#52911yescharacteristic
524C22×C11#52911yescharacteristic
525C22×C11#52911yescharacteristic
526C22×C11#52911yescharacteristic
527C22×C11#52911yescharacteristic
528C22×C11#53211yescharacteristic
529C22×C11#53211yescharacteristic
530C4×C11—42no—
531C4×C11—42no—
532C4×C11—42no—
533C4×C11—42no—
534C4×C11—42no—
535C4×C11—42no—
536Dic11—24no—
537Dic11—42no—
538Dic11—42no—
539Dic11—42no—
540Dic11—42no—
541Dic11—42no—
542Dic11—42no—
543Dic11#39718yescomplemented
544C25C22×D1111yescharacteristic
545C23×C4—111no—
546C23×C4—111no—
547C23×C4—114no—
548C23×C4—111no—
549C23×C4—111no—
550C23×C4—111no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—111no—
554C23×C4—222no—
555C23×C4—222no—
556C23×C4—222no—
557C23×C4—222no—
558C23×C4—222no—
559C23×C4—222no—
560C23×C4C22×D1111yescharacteristic
561C23×C4C22×D1111yescharacteristic
562C23×C4C22×D1111yescharacteristic
563C23×C4C22×D1111yescharacteristic
564C23×C4C22×D1111yescharacteristic
565C23×C4C22×D1111yescharacteristic
566C2×C4⋊C4—114no—
567C2×C4⋊C4—222no—
568C2×C4⋊C4—222no—
569C2×C4⋊C4—222no—
570C2×C4⋊C4—222no—
571C2×C4⋊C4—222no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—114no—
581C2×C22⋊C4—114no—
582C2×C22⋊C4—222no—
583C2×C22⋊C4—222no—
584C2×C22⋊C4—222no—
585C2×C22⋊C4—222no—
586C2×C22⋊C4—222no—
587C2×C22⋊C4—222no—
588C2×C22⋊C4—222no—
589C2×C22⋊C4C4×D1114yes—
590C2×C42—114no—
591C2×C42—222no—
592C2×C42—222no—
593C2×C42—222no—
594C2×C42—222no—
595C2×C42—222no—
596C2×C42—222no—
597C2×C42—222no—
598C2×C42—222no—
599C2×C42—222no—
600C2×C42—222no—
601C2×C42—222no—
602C2×C42—222no—
603C2×C42—222no—
604C2×C42—222no—
605C2×C42—222no—
606C2×C42—222no—
607C2×C42—222no—
608#95—22no—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—114no—
613#95—114no—
614#95—114no—
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—222no—
624#95—222no—
625#95—222no—
626#95—222no—
627#95—222no—
628C2×C11—44no—
629C2×C11C4×#12111yescharacteristic
630C2×C11C4×#12311yescharacteristic
631C2×C11C4×#12311yescharacteristic
632C2×C11C4×#12311yescharacteristic
633C2×C11C4×#12411yescharacteristic
634C2×C11C4×#12611yescharacteristic
635C2×C11C4×#12611yescharacteristic
636C2×C11C2×#39711yescharacteristic
637C2×C11#239211yescharacteristic
638C2×C11#239511yescharacteristic
639C2×C11#239511yescharacteristic
640C2×C11#239511yescharacteristic
641C2×C11#239811yescharacteristic
642C2×C11#240111yescharacteristic
643C2×C11#240111yescharacteristic
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24C2×C4×D1112yes—
657C24D4×D1112yes—
658C24#434112yes—
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—112no—
697C22×C4—112no—
698C22×C4—112no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—112no—
709C22×C4—112no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—228no—
713C22×C4—228no—
714C22×C4—228no—
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—221no—
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—221no—
753C22×C4—221no—
754C22×C4—221no—
755C22×C4—444no—
756C22×C4—444no—
757C22×C4—444no—
758C22×C4—444no—
759C22×C4C2×C4×D1112yes—
760C22×C4C2×C4×D1112yes—
761C22×C4D4×D1112yes—
762C22×C4#434112yes—
763C22×C4#434112yes—
764C22×C4#434112yes—
765C4⋊C4—228no—
766C4⋊C4—228no—
767C22⋊C4—28no—
768C22⋊C4—28no—
769C22⋊C4—28no—
770C22⋊C4—228no—
771C22⋊C4—228no—
772C22⋊C4—228no—
773C42—228no—
774C42—444no—
775C42—444no—
776C42—444no—
777C42—444no—
778C42—444no—
779C11C4×#39711yescharacteristic, complemented, Sylow
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23(C22⋊D11)⋊C414yes—
815C23C22×C4×D1111yescharacteristic
816C23C2×D4×D1111yescharacteristic
817C23C2×D4×D1111yescharacteristic
818C23C2×#434111yescharacteristic
819C23C2×#434111yescharacteristic
820C23C2×#434111yescharacteristic
821C23C2×#434111yescharacteristic
822C23#41×D1111yescharacteristic
823C23#41×D1111yescharacteristic
824C23#41×D1111yescharacteristic
825C23#41×D1111yescharacteristic
826C23#41×D1111yescharacteristic
827C23#41×D1111yescharacteristic
828C23#41×D1111yescharacteristic
829C23#41×D1111yescharacteristic
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—114no—
873C2×C4—114no—
874C2×C4—114no—
875C2×C4—114no—
876C2×C4—114no—
877C2×C4—114no—
878C2×C4—114no—
879C2×C4—114no—
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—222no—
898C2×C4—222no—
899C2×C4—222no—
900C2×C4—222no—
901C2×C4—222no—
902C2×C4—222no—
903C2×C4—222no—
904C2×C4—4416no—
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—441no—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22C2×(C22⋊D11)⋊C411yescharacteristic
945C22#1062305311yescharacteristic
946C22#1062305311yescharacteristic
947C22C4×#434111yescharacteristic
948C22C4×#434111yescharacteristic
949C22C4×#434111yescharacteristic
950C22C4×D4×D1111yescharacteristic
951C22#1062311711yescharacteristic
952C22#1062311711yescharacteristic
953C22#1062312711yescharacteristic
954C22#1062312711yescharacteristic
955C22#1062313111yescharacteristic
956C22#1062313111yescharacteristic
957C22#1062313111yescharacteristic
958C22#1062313111yescharacteristic
959C22D11×#12111yescharacteristic
960C22#1062313711yescharacteristic
961C22#1062318011yescharacteristic
962C22#1062318011yescharacteristic
963C22#1062318011yescharacteristic
964C22#1062318011yescharacteristic
965C22#1062318011yescharacteristic
966C22#1062318011yescharacteristic
967C22D11×#12311yescharacteristic
968C22D11×#12311yescharacteristic
969C22D11×#12311yescharacteristic
970C22#1062318711yescharacteristic
971C22D11×#12411yescharacteristic
972C22#1062321111yescharacteristic
973C22#1062321111yescharacteristic
974C22#1062321111yescharacteristic
975C22D11×#12611yescharacteristic
976C22D11×#12611yescharacteristic
977C22#1062323711yescharacteristic
978C22#1062323711yescharacteristic
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—118no—
986C4—224no—
987C4—442no—
988C4—442no—
989C4—442no—
990C4—442no—
991C4—442no—
992C4—442no—
993C2—44no—
994C2#1307112611yescharacteristic
995C2#1307113311yescharacteristic
996C2#1307114111yescharacteristic
997C2#1307114311yescharacteristic
998C2#1307115711yescharacteristic
999C2#1307117011yescharacteristic
1000C2#1307117011yescharacteristic
1001C2D11×#39711yescharacteristic
1002C2#1307185911yescharacteristic
1003C2#1307187211yescharacteristic
1004C2#1307187211yescharacteristic
1005C2#1307187411yescharacteristic
1006C2#1307190411yescharacteristic
1007C2#1307191311yescharacteristic
1008C2#1307191311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1440C2
socle, cosocleC24×C11C24
prime radicalC25×C11C23
hypercenter#1440D11
hypocenterC11C4×#397
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
2. C2×#10622262C2semidirect
6. #13066882C2semidirect
7. #13066877C2semidirect
8. #13066876C2semidirect
9. #13066874C2semidirect
12. #95×Dic11C2semidirect
13. #95×Dic11C2semidirect
14. #95×Dic11C2semidirect
51. #10622565C4semidirect
101. C2×Dic11⋊C4C2×C4semidirect
137. C11⋊#95C2×C4semidirect
138. C11⋊#95C2×C4semidirect
139. C11⋊#95C2×C4semidirect
543. Dic11#397semidirect
779. C11C4×#397semidirect

Maximal subgroups

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

subgroupindex
C2×#106225652
C2×#106222622
C2×C22⋊C4×Dic112
#130668822
#130668772
#130668762
#130668742
#130668632
#130668592
#95×Dic112
C11×#14402
C4×#39711