Finite Group Databasebeta

← #14676384

Subgroups — #14676384

Order 2816.

1486 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622279C211yesmaximal, characteristic
2#13066877C211yesmaximal, characteristic, complemented
3#13066876C211yesmaximal, characteristic, complemented
4#13066864C211yesmaximal, characteristic
5#13066864C211yesmaximal, characteristic
6#13066854C211yesmaximal, characteristic
7#13066852C211yesmaximal, characteristic
8#13066842C211yesmaximal, characteristic, complemented
9#13066841C211yesmaximal, characteristic, complemented
10#13066841C211yesmaximal, characteristic, complemented
11#13066840C211yesmaximal, characteristic, complemented
12(C2×D11)⋊#95C211yesmaximal, characteristic
13(C2×D11)⋊#95C211yesmaximal, characteristic
14C4×C11⋊#95C211yesmaximal, characteristic, complemented
15C11×#1434C211yesmaximal, characteristic, complemented
16C23×C4×D11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×C4×Dic11C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11×#95C2211yescharacteristic
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#10622279C418yescomplemented
52C24×D11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2311yescharacteristic
67C22×C4×D11—22no—
68C22×C4×D11—22no—
69C22×C4×D11—41no—
70C22×C4×D11—41no—
71C22×C4×D11—41no—
72C22×C4×D11—41no—
73C22×C4×D11C2×C414yes—
74C2×C42×C11—22no—
75C2×C42×C11—22no—
76C2×C42×C11—41no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—22no—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—22no—
83C2×(C2×D11)⋊C4—22no—
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—41no—
90C2×(C2×D11)⋊C4—41no—
91C2×(C2×D11)⋊C4—41no—
92C2×(C2×D11)⋊C4—41no—
93C2×(C2×D11)⋊C4C2×C414yes—
94C2×(C2×D11)⋊C4C2×C414yes—
95C2×C4×Dic11—22no—
96C2×C4×Dic11—22no—
97C2×C4×Dic11—41no—
98C2×C4×Dic11—41no—
99C2×C4×Dic11—41no—
100C2×C4×Dic11—41no—
101C2×C4×Dic11—41no—
102C2×C4×Dic11C2×C414yes—
103C2×C4×Dic11C2×C414yes—
104C11×#95—22no—
105C11×#95—22no—
106C11×#95—41no—
107C11×#95—41no—
108C11×#95—41no—
109C11×#95C2×C414yes—
110C11⋊#95—22no—
111C11⋊#95—22no—
112C11⋊#95—22no—
113C11⋊#95—22no—
114C11⋊#95—22no—
115C11⋊#95—22no—
116C11⋊#95—22no—
117C11⋊#95—22no—
118C11⋊#95—22no—
119C11⋊#95—22no—
120C11⋊#95—41no—
121C11⋊#95—41no—
122C11⋊#95—41no—
123C11⋊#95—41no—
124C11⋊#95—41no—
125C11⋊#95—41no—
126C11⋊#95—41no—
127C11⋊#95C2×C414yes—
128#13947—111nomaximal, Sylow
129C24×C11C2411yescharacteristic
130C23×D11—21no—
131C23×D11—21no—
132C23×D11—21no—
133C23×D11—21no—
134C23×D11—21no—
135C23×D11—21no—
136C23×D11—21no—
137C23×D11—21no—
138C23×D11—21no—
139C23×D11—21no—
140C23×D11—21no—
141C23×D11—21no—
142C23×D11C22×C412yes—
143C23×D11#4112yes—
144C23×D11#4112yes—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—21no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
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×C11C22×C412yes—
188C22×C4×C11C22×C412yes—
189C22×C4×C11C22×C412yes—
190C22×C4×C11#4112yes—
191C22×C4×C11#4112yes—
192C22×C4×C11#4112yes—
193C22×C4×C11#4112yes—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
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×Dic11C22×C412yes—
237C22×Dic11C22×C412yes—
238C22×Dic11C22×C412yes—
239C22×Dic11#4112yes—
240C22×Dic11#4112yes—
241C22×Dic11#4112yes—
242C22×Dic11#4112yes—
243C2×C4×D11—28no—
244C2×C4×D11—44no—
245C2×C4×D11—44no—
246C2×C4×D11—44no—
247C2×C4×D11—44no—
248C2×C4×D11—44no—
249C2×C4×D11—44no—
250C42×C11—44no—
251(C2×D11)⋊C4—28no—
252(C2×D11)⋊C4—28no—
253(C2×D11)⋊C4—44no—
254(C2×D11)⋊C4—44no—
255(C2×D11)⋊C4—44no—
256(C2×D11)⋊C4—44no—
257C4×Dic11—44no—
258C4×Dic11—44no—
259C4×Dic11—44no—
260C2×C4×C22⋊C4—111no—
261#1443—111no—
262#1443—111no—
263#1440—111no—
264#1440—111no—
265#1437—111no—
266#1437—111no—
267#1434—111no—
268#1434—111no—
269#1434—111no—
270#1434—111no—
271#1434D1111yescharacteristic, complemented
272C22⋊#95—111no—
273C22⋊#95—111no—
274C4×#95—111no—
275C23×C11C23×C411yescharacteristic
276C23×C11C2×#4111yescharacteristic
277C23×C11C2×#4111yescharacteristic
278C23×C11C2×#4111yescharacteristic
279C23×C11C2×#4111yescharacteristic
280C23×C11C2×#4111yescharacteristic
281C23×C11C2×#4111yescharacteristic
282C23×C11C2×#4111yescharacteristic
283C23×C11C2×#4111yescharacteristic
284C23×C11C2×#4111yescharacteristic
285C23×C11C2×#4111yescharacteristic
286C23×C11H(5,𝔽2)11yescharacteristic
287C23×C11H(5,𝔽2)11yescharacteristic
288C23×C11H(5,𝔽2)11yescharacteristic
289C23×C11H(5,𝔽2)11yescharacteristic
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—22no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—22no—
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—41no—
309C22×D11—41no—
310C22×D11—41no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11#11714yes—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11—41no—
350C2×C4×C11—41no—
351C2×C4×C11—41no—
352C2×C4×C11—41no—
353C2×C4×C11—41no—
354C2×C4×C11—41no—
355C2×C4×C11—41no—
356C2×C4×C11—41no—
357C2×C4×C11—41no—
358C2×C4×C11—41no—
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#11714yes—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
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—41no—
393C2×Dic11—41no—
394C2×Dic11—41no—
395C2×Dic11—41no—
396C2×Dic11—41no—
397C2×Dic11—41no—
398C2×Dic11—41no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—41no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
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#11714yes—
423C4×D11—416no—
424C24×C4—111no—
425C22×C22⋊C4—111no—
426C22×C22⋊C4—111no—
427C22×C22⋊C4—111no—
428C22×C22⋊C4—111no—
429C22×C22⋊C4—111no—
430C22×C22⋊C4—111no—
431C22×C42—111no—
432C22×C42—111no—
433C22×C42—111no—
434C22×C42C2×D1111yescharacteristic
435C4×C22⋊C4—118no—
436C2×#95—111no—
437C2×#95—111no—
438C2×#95—111no—
439C2×#95—111no—
440C2×#95—111no—
441C2×#95—111no—
442C2×#95—111no—
443C2×#95—111no—
444C2×#95—111no—
445C2×#95—111no—
446C2×#95—111no—
447C2×#95—111no—
448C2×#95—111no—
449C2×#95—111no—
450C2×#95—111no—
451C2×#95—111no—
452C2×#95—111no—
453C2×#95—111no—
454C2×#95C2×D1111yescharacteristic
455C2×#95C2×D1111yescharacteristic
456C2×#95C2×D1111yescharacteristic
457C2×#95C2×D1111yescharacteristic
458C2×#95C2×D1111yescharacteristic
459C2×#95C2×D1111yescharacteristic
460C22×C11C2×#11711yescharacteristic
461C22×C11C2×#11711yescharacteristic
462C22×C11C2×#11711yescharacteristic
463C22×C11C4×#4111yescharacteristic
464C22×C11C4×#4111yescharacteristic
465C22×C11#51811yescharacteristic
466C22×C11#51811yescharacteristic
467C22×C11#52911yescharacteristic
468C22×C11#52911yescharacteristic
469C22×C11#52911yescharacteristic
470C22×C11#52911yescharacteristic
471C22×C11#52911yescharacteristic
472C22×C11#52911yescharacteristic
473C22×C11#52911yescharacteristic
474C22×C11#52911yescharacteristic
475C22×C11#53811yescharacteristic
476C22×C11#53811yescharacteristic
477C22×C11#53811yescharacteristic
478C22×C11#53811yescharacteristic
479C22×C11#55111yescharacteristic
480C22×C11#55111yescharacteristic
481C22×C11#55111yescharacteristic
482C22×C11#55111yescharacteristic
483C22×C11#55111yescharacteristic
484C22×C11#55111yescharacteristic
485C22×C11#55311yescharacteristic
486C22×C11#55311yescharacteristic
487C22×C11#55311yescharacteristic
488C22×C11#55311yescharacteristic
489C22×C11#55311yescharacteristic
490C22×C11#55311yescharacteristic
491C22×C11#55311yescharacteristic
492C22×C11#55311yescharacteristic
493C22×C11#55911yescharacteristic
494C22×C11#55911yescharacteristic
495C2×D11—24no—
496C2×D11—24no—
497C2×D11—24no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—42no—
506C2×D11—42no—
507C2×D11—42no—
508C2×D11—42no—
509C2×D11—42no—
510C4×C11—24no—
511C4×C11—42no—
512C4×C11—42no—
513C4×C11—42no—
514C4×C11—42no—
515C4×C11—81no—
516C4×C11—81no—
517Dic11—24no—
518Dic11—42no—
519Dic11—42no—
520Dic11—42no—
521Dic11—42no—
522Dic11—81no—
523Dic11—81no—
524C25—111no—
525C23×C4—111no—
526C23×C4—111no—
527C23×C4—111no—
528C23×C4—111no—
529C23×C4—111no—
530C23×C4—114no—
531C23×C4—111no—
532C23×C4—111no—
533C23×C4—222no—
534C23×C4—222no—
535C23×C4—441no—
536C23×C4—441no—
537C23×C4—441no—
538C23×C4—441no—
539C23×C4C22×D1111yescharacteristic
540C23×C4C22×D1111yescharacteristic
541C23×C4C22×D1111yescharacteristic
542C23×C4C22×D1111yescharacteristic
543C23×C4C22×D1111yescharacteristic
544C23×C4C22×D1111yescharacteristic
545C23×C4C22×D1111yescharacteristic
546C2×C22⋊C4—114no—
547C2×C22⋊C4—114no—
548C2×C22⋊C4—222no—
549C2×C22⋊C4—222no—
550C2×C22⋊C4—222no—
551C2×C22⋊C4—222no—
552C2×C22⋊C4—222no—
553C2×C22⋊C4—222no—
554C2×C22⋊C4—222no—
555C2×C22⋊C4—222no—
556C2×C22⋊C4—222no—
557C2×C22⋊C4—222no—
558C2×C22⋊C4—222no—
559C2×C22⋊C4—222no—
560C2×C22⋊C4—441no—
561C2×C22⋊C4—441no—
562C2×C22⋊C4—441no—
563C2×C22⋊C4—441no—
564C2×C42—22no—
565C2×C42—22no—
566C2×C42—41no—
567C2×C42—114no—
568C2×C42—114no—
569C2×C42—222no—
570C2×C42—222no—
571C2×C42—441no—
572C2×C42—441no—
573C2×C42—441no—
574C2×C42—441no—
575C2×C42—441no—
576#95—22no—
577#95—22no—
578#95—41no—
579#95—41no—
580#95—41no—
581#95—114no—
582#95—222no—
583#95—222no—
584#95—222no—
585#95—222no—
586#95—222no—
587#95—222no—
588#95—222no—
589#95—222no—
590#95—222no—
591#95—222no—
592#95—441no—
593#95—441no—
594#95—441no—
595#95—441no—
596#95—441no—
597#95—441no—
598#95—441no—
599#95C4×D1114yes—
600C2×C11#228311yescharacteristic
601C2×C11#229811yescharacteristic
602C2×C11#231211yescharacteristic
603C2×C11#235311yescharacteristic
604C2×C11#235311yescharacteristic
605C2×C11#235311yescharacteristic
606C2×C11#235711yescharacteristic
607C2×C11#257611yescharacteristic
608C2×C11#257611yescharacteristic
609C2×C11#257811yescharacteristic
610C2×C11#257811yescharacteristic
611C2×C11#259511yescharacteristic
612C2×C11#259511yescharacteristic
613C2×C11#259711yescharacteristic
614C2×C11#259711yescharacteristic
615D11—44no—
616C24—112no—
617C24—112no—
618C24—112no—
619C24—221no—
620C24—221no—
621C24—221no—
622C24—221no—
623C24—221no—
624C24—221no—
625C24—221no—
626C24—221no—
627C24—221no—
628C24—221no—
629C24—221no—
630C24—221no—
631C24C23×D1111yescharacteristic
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
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—112no—
675C22×C4—112no—
676C22×C4—112no—
677C22×C4—112no—
678C22×C4—112no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—228no—
682C22×C4—221no—
683C22×C4—221no—
684C22×C4—221no—
685C22×C4—221no—
686C22×C4—221no—
687C22×C4—221no—
688C22×C4—221no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—221no—
692C22×C4—221no—
693C22×C4—221no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—221no—
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—444no—
725C22×C4—444no—
726C22×C4—444no—
727C22×C4—444no—
728C22×C4—444no—
729C22×C4—444no—
730C22×C4C2×C4×D1112yes—
731C22×C4C2×C4×D1112yes—
732C22×C4C2×C4×D1112yes—
733C22×C4#433912yes—
734C22×C4#433912yes—
735C22×C4#434112yes—
736C22×C4#434312yes—
737C22⋊C4—228no—
738C22⋊C4—228no—
739C22⋊C4—444no—
740C22⋊C4—444no—
741C22⋊C4—444no—
742C22⋊C4—444no—
743C42—44no—
744C42—444no—
745C42—444no—
746C42—444no—
747C11#1394711yescharacteristic, complemented, Sylow
748C23—114no—
749C23—222no—
750C23—222no—
751C23—222no—
752C23—222no—
753C23—222no—
754C23—222no—
755C23—222no—
756C23—222no—
757C23—222no—
758C23—222no—
759C23—222no—
760C23—222no—
761C23—222no—
762C23—222no—
763C23—222no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23—441no—
768C23—441no—
769C23—441no—
770C23—441no—
771C23—441no—
772C23—441no—
773C23—441no—
774C23—441no—
775C23—441no—
776C23—441no—
777C23—441no—
778C23—441no—
779C23—441no—
780C23—441no—
781C23—441no—
782C23—441no—
783C23C22×C4×D1111yescharacteristic
784C23C2×#433911yescharacteristic
785C23C2×#433911yescharacteristic
786C23C2×#434111yescharacteristic
787C23#6703711yescharacteristic
788C23#6703711yescharacteristic
789C23C2×#434311yescharacteristic
790C23#41×D1111yescharacteristic
791C23#41×D1111yescharacteristic
792C23#41×D1111yescharacteristic
793C23#41×D1111yescharacteristic
794C23#41×D1111yescharacteristic
795C23#41×D1111yescharacteristic
796C23#6704211yescharacteristic
797C23#6704211yescharacteristic
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—114no—
847C2×C4—222no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—222no—
852C2×C4—222no—
853C2×C4—222no—
854C2×C4—222no—
855C2×C4—222no—
856C2×C4—222no—
857C2×C4—222no—
858C2×C4—222no—
859C2×C4—222no—
860C2×C4—222no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—4416no—
866C2×C4—441no—
867C2×C4—441no—
868C2×C4—441no—
869C2×C4—441no—
870C2×C4—441no—
871C2×C4—441no—
872C2×C4—441no—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—441no—
878C2×C4—441no—
879C2×C4—441no—
880C2×C4—441no—
881C2×C4—441no—
882C2×C4—441no—
883C2×C4—441no—
884C2×C4—441no—
885C2×C4—441no—
886C2×C4—441no—
887C2×C4—441no—
888C2×C4—441no—
889C2×C4—441no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—441no—
896C2×C4#6692514yes—
897C22—224no—
898C22—224no—
899C22—224no—
900C22—442no—
901C22—442no—
902C22—442no—
903C22—442no—
904C22—442no—
905C22—442no—
906C22—442no—
907C22—442no—
908C22—442no—
909C22—442no—
910C22—442no—
911C22—442no—
912C22C2×#6692511yescharacteristic
913C22#1062302611yescharacteristic
914C22#1062304511yescharacteristic
915C22D11×#11711yescharacteristic
916C22D11×#11711yescharacteristic
917C22#1062305811yescharacteristic
918C22#1062305911yescharacteristic
919C22#1062305911yescharacteristic
920C22#1062305911yescharacteristic
921C22#1062305911yescharacteristic
922C22#1062306111yescharacteristic
923C22C4×#434111yescharacteristic
924C22#1062307111yescharacteristic
925C22#1062307611yescharacteristic
926C22#1062307611yescharacteristic
927C22#1062309011yescharacteristic
928C22#1062309611yescharacteristic
929C22C4×#434311yescharacteristic
930C22#1062311611yescharacteristic
931C22#1062314411yescharacteristic
932C22#1062314511yescharacteristic
933C22#1062315511yescharacteristic
934C22#1062316811yescharacteristic
935C22#1062318011yescharacteristic
936C22#1062318811yescharacteristic
937C22#1062318911yescharacteristic
938C22#1062319211yescharacteristic
939C22#1062320911yescharacteristic
940C22#1062321011yescharacteristic
941C22#1062322211yescharacteristic
942C22#1062322611yescharacteristic
943C22#1062323511yescharacteristic
944C22#1062323611yescharacteristic
945C22#1062323711yescharacteristic
946C22#1062324011yescharacteristic
947C4—24no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—81no—
953C4—81no—
954C4—224no—
955C4—442no—
956C4—442no—
957C4—442no—
958C4—442no—
959C4—881no—
960C4—881no—
961C2—444no—
962C2#1307100811yescharacteristic
963C2#1307110811yescharacteristic
964C2#1307121011yescharacteristic
965C2#1307155011yescharacteristic
966C2#1307155111yescharacteristic
967C2#1307155511yescharacteristic
968C2#1307158511yescharacteristic
969C2#1307391611yescharacteristic
970C2#1307391811yescharacteristic
971C2#1307394611yescharacteristic
972C2#1307394811yescharacteristic
973C2#1307413311yescharacteristic
974C2#1307413511yescharacteristic
975C2#1307416311yescharacteristic
976C2#1307416511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenter#1434D11
hypocenterC11#13947
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. #13066877C2semidirect
3. #13066876C2semidirect
8. #13066842C2semidirect
9. #13066841C2semidirect
10. #13066841C2semidirect
11. #13066840C2semidirect
14. C4×C11⋊#95C2semidirect
15. C11×#1434C2semidirect
51. #10622279C4semidirect
271. #1434D11semidirect
747. C11#13947semidirect

Maximal subgroups

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

subgroupindex
C2×#106222792
#130668772
#130668762
#130668642
#130668542
#130668522
#130668422
#130668412
#130668402
(C2×D11)⋊#952
C4×C11⋊#952
C11×#14342
#1394711