Finite Group Databasebeta

← #14676857

Subgroups — #14676857

Order 2816.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622586C211yesmaximal, characteristic, complemented
2C2×#10622600C211yesmaximal, characteristic
3C2×#10622600C211yesmaximal, characteristic
4C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
5#13066876C212yesmaximal, complemented
6#13066860C212yesmaximal
7#13066854C212yesmaximal
8#13066849C212yesmaximal, complemented
9#13066846C211yesmaximal, characteristic, complemented
10#13066845C211yesmaximal, characteristic, complemented
11C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C42×C11C2212yes—
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C4×C11×C4⋊C4—24no—
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36#10622600—24no—
37#10622600C418yescomplemented
38#10622586—24no—
39C4×(C2×D11)⋊C4—24no—
40C24×D11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×Dic11C2312yes—
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C22×C4×D11—22no—
52C22×C4×D11—22no—
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11—22no—
57C22×C4×D11C2×C414yes—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4C2×C414yes—
63C2×C11×C4⋊C4D414yes—
64C2×C42×C11—22no—
65C2×C42×C11—22no—
66C2×C42×C11—24no—
67C2×C42×C11—42no—
68C2×C42×C11—42no—
69C2×C42×C11D414yes—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—22no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—42no—
78C2×(C2×D11)⋊C4—42no—
79C2×(C2×D11)⋊C4—42no—
80C2×(C2×D11)⋊C4C2×C418yes—
81C2×(C2×D11)⋊C4Q814yes—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11C2×C414yes—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—42no—
91C2×C4×Dic11—22no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11—22no—
94C11×#95—24no—
95C11⋊#95—22no—
96C11⋊#95—22no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—42no—
101C11⋊#95—42no—
102C11⋊#95—42no—
103C11⋊#95C2×C418yes—
104#13993—111nomaximal, Sylow
105C24×C11C2411yescharacteristic
106C23×D11—21no—
107C23×D11—21no—
108C23×D11—21no—
109C23×D11—21no—
110C23×D11—21no—
111C23×D11—21no—
112C23×D11—21no—
113C23×D11—21no—
114C23×D11—21no—
115C23×D11—21no—
116C23×D11—21no—
117C23×D11—21no—
118C23×D11C22×C412yes—
119C23×D11C2×Q812yes—
120C23×D11#4112yes—
121C22×C4×C11—21no—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—22no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11C22×C414yes—
144C22×C4×C11C22×C412yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2×D412yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×Q812yes—
151C22×C4×C11#4112yes—
152C22×C4×C11#4112yes—
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11#4112yes—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—22no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—22no—
182C22×Dic11—21no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—21no—
187C22×Dic11C22×C412yes—
188C22×Dic11C22×C414yes—
189C22×Dic11C2×Q812yes—
190C22×Dic11#4112yes—
191C2×C4×D11—28no—
192C2×C4×D11—28no—
193C2×C4×D11—28no—
194C2×C4×D11—44no—
195C2×C4×D11—44no—
196C2×C4×D11—44no—
197C2×C4×D11—44no—
198C11×C4⋊C4—28no—
199C11×C4⋊C4—28no—
200C42×C11—28no—
201C42×C11—48no—
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—48no—
205(C2×D11)⋊C4—48no—
206C4⋊Dic11—28no—
207C4⋊Dic11—44no—
208Dic11⋊C4—48no—
209C4×Dic11—44no—
210C2×#389—111no—
211C2×#380—111no—
212C2×#380—111no—
213C2×C4×C4⋊C4D1111yescharacteristic, complemented
214C2×C4×C22⋊C4—111no—
215#1443—112no—
216#1439—112no—
217#1437—112no—
218#1436—112no—
219C4⋊#95—111no—
220C4⋊#95—111no—
221C23×C11C23×C411yescharacteristic
222C23×C11C22×D411yescharacteristic
223C23×C11C22×D411yescharacteristic
224C23×C11C22×Q811yescharacteristic
225C23×C11C2×#4111yescharacteristic
226C23×C11C2×#4111yescharacteristic
227C23×C11C2×#4111yescharacteristic
228C23×C11C2×#4111yescharacteristic
229C23×C11C2×#4111yescharacteristic
230C23×C11C2×#4111yescharacteristic
231C23×C11C2×#4111yescharacteristic
232C23×C11H(5,𝔽2)11yescharacteristic
233C23×C11H(5,𝔽2)11yescharacteristic
234C23×C11H(5,𝔽2)11yescharacteristic
235C23×C112−1+411yescharacteristic
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—22no—
251C22×D11—22no—
252C22×D11—22no—
253C22×D11—22no—
254C22×D11—41no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—41no—
260C22×D11—41no—
261C22×D11—41no—
262C22×D11—41no—
263C22×D11—41no—
264C22×D11—41no—
265C22×D11—41no—
266C22×D11—41no—
267C22×D11—41no—
268C22×D11—41no—
269C22×D11—41no—
270C22×D11C4×Q814yes—
271C2×C4×C11—22no—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—24no—
281C2×C4×C11—22no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—24no—
285C2×C4×C11—24no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11#11714yes—
299C2×C4×C11C4×D414yes—
300C2×C4×C11C4×D414yes—
301C2×C4×C11#12114yes—
302C2×C4×C11C22⋊Q814yes—
303C2×C4×C11#12314yes—
304C2×C4×C11#12414yes—
305C2×C4×C11#12614yes—
306C2×Dic11—22no—
307C2×Dic11—24no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—42no—
327C2×Dic11—41no—
328C2×Dic11—42no—
329C2×Dic11—41no—
330C2×Dic11—42no—
331C2×Dic11—41no—
332C2×Dic11—42no—
333C2×Dic11—41no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C4×D11—416no—
342C24×C4—111no—
343C22×C4⋊C4—111no—
344C22×C4⋊C4—111no—
345C22×C4⋊C4—112no—
346C22×C4⋊C4C2×D1111yescharacteristic
347C22×C4⋊C4C2×D1111yescharacteristic
348C22×C22⋊C4—111no—
349C22×C22⋊C4—112no—
350C22×C22⋊C4—111no—
351C22×C22⋊C4—112no—
352C22×C42—111no—
353C22×C42C2×D1111yescharacteristic
354C22×C42C2×D1112yes—
355#389—224no—
356#380—118no—
357#380—224no—
358C4×C4⋊C4—24no—
359C4×C22⋊C4—224no—
360C2×#95—112no—
361C2×#95—112no—
362C2×#95—111no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95—111no—
366C2×#95—112no—
367C2×#95—112no—
368C2×#95—112no—
369C2×#95C2×D1112yes—
370C22×C11C2×#11711yescharacteristic
371C22×C11C2×C4×D411yescharacteristic
372C22×C11C2×C4×D411yescharacteristic
373C22×C11C2×C4×Q811yescharacteristic
374C22×C11C4×#4111yescharacteristic
375C22×C11#51811yescharacteristic
376C22×C11#52011yescharacteristic
377C22×C11C2×#12111yescharacteristic
378C22×C11C2×C22⋊Q811yescharacteristic
379C22×C11C2×#12311yescharacteristic
380C22×C11#52511yescharacteristic
381C22×C11C2×#12411yescharacteristic
382C22×C11C2×#12611yescharacteristic
383C22×C11#52911yescharacteristic
384C22×C11#53311yescharacteristic
385C22×C11#53511yescharacteristic
386C22×C11#53711yescharacteristic
387C22×C11#54011yescharacteristic
388C22×C11#54211yescharacteristic
389C22×C11#54611yescharacteristic
390C22×C11#54611yescharacteristic
391C22×C11D4×Q811yescharacteristic
392C22×C11#55011yescharacteristic
393C22×C11#55211yescharacteristic
394C22×C11#55311yescharacteristic
395C22×C11#55311yescharacteristic
396C22×C11#55311yescharacteristic
397C22×C11#55311yescharacteristic
398C22×C11#55311yescharacteristic
399C22×C11#55411yescharacteristic
400C22×C11#55411yescharacteristic
401C22×C11#55411yescharacteristic
402C22×C11#55511yescharacteristic
403C22×C11#55611yescharacteristic
404C22×C11#55611yescharacteristic
405C2×D11—24no—
406C2×D11—24no—
407C2×D11—24no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—42no—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—42no—
417C2×D11—42no—
418C2×D11—42no—
419C2×D11—42no—
420C4×C11—24no—
421C4×C11—44no—
422C4×C11—42no—
423C4×C11—44no—
424C4×C11#38818yes—
425Dic11—44no—
426Dic11—42no—
427Dic11—42no—
428Dic11—42no—
429Dic11—82no—
430C25—111no—
431C23×C4—112no—
432C23×C4—111no—
433C23×C4—111no—
434C23×C4—111no—
435C23×C4—114no—
436C23×C4—112no—
437C23×C4—222no—
438C23×C4—222no—
439C23×C4—222no—
440C23×C4—222no—
441C23×C4—222no—
442C23×C4—222no—
443C23×C4C22×D1112yes—
444C23×C4C22×D1112yes—
445C23×C4C22×D1111yescharacteristic
446C23×C4C22×D1111yescharacteristic
447C23×C4C22×D1111yescharacteristic
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—114no—
453C2×C4⋊C4—222no—
454C2×C4⋊C4—222no—
455C2×C4⋊C4—224no—
456C2×C4⋊C4—222no—
457C2×C4⋊C4—224no—
458C2×C4⋊C4—222no—
459C2×C4⋊C4—222no—
460C2×C4⋊C4—442no—
461C2×C4⋊C4C4×D1114yes—
462C2×C4⋊C4D4414yes—
463C2×C22⋊C4—114no—
464C2×C22⋊C4—118no—
465C2×C22⋊C4—222no—
466C2×C22⋊C4—222no—
467C2×C22⋊C4—222no—
468C2×C22⋊C4—222no—
469C2×C22⋊C4—222no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—442no—
473C2×C22⋊C4—442no—
474C2×C22⋊C4—442no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—24no—
478C2×C42—42no—
479C2×C42—42no—
480C2×C42—222no—
481C2×C42—222no—
482C2×C42—222no—
483C2×C42C22⋊D1114yes—
484#95—24no—
485#95—118no—
486#95—224no—
487#95—224no—
488#95—224no—
489#95—222no—
490#95—222no—
491#95—442no—
492#95—442no—
493#95—442no—
494C2×C11C2×#38811yescharacteristic
495C2×C11C4×C22⋊Q811yescharacteristic
496C2×C11#232411yescharacteristic
497C2×C11#234511yescharacteristic
498C2×C11#234711yescharacteristic
499C2×C11#236011yescharacteristic
500C2×C11#236311yescharacteristic
501C2×C11#248511yescharacteristic
502C2×C11#248711yescharacteristic
503C2×C11#249011yescharacteristic
504C2×C11#249211yescharacteristic
505C2×C11#249411yescharacteristic
506C2×C11#249711yescharacteristic
507C2×C11#253511yescharacteristic
508C2×C11#253811yescharacteristic
509D11—44no—
510C24—112no—
511C24—112no—
512C24—112no—
513C24—221no—
514C24—221no—
515C24—221no—
516C24—221no—
517C24—221no—
518C24—221no—
519C24—221no—
520C24—221no—
521C24—221no—
522C24—221no—
523C24—221no—
524C24—221no—
525C24C23×D1111yescharacteristic
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—112no—
549C22×C4—114no—
550C22×C4—112no—
551C22×C4—112no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—222no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—222no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—222no—
565C22×C4—221no—
566C22×C4—222no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—222no—
570C22×C4—221no—
571C22×C4—222no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—228no—
577C22×C4—228no—
578C22×C4—228no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—444no—
587C22×C4—444no—
588C22×C4—444no—
589C22×C4—444no—
590C22×C4C2×C4×D1114yes—
591C22×C4C2×C4×D1112yes—
592C22×C4C2×D4414yes—
593C22×C4C2×D4412yes—
594C22×C4#433912yes—
595C22×C4#433912yes—
596C22×C4#433912yes—
597C22×C4#433912yes—
598C22×C4Q8×D1112yes—
599C22×C4#434312yes—
600C22×C4C2×C22⋊D1112yes—
601C22×C4C2×C22⋊D1112yes—
602C22×C4C2×C22⋊D1112yes—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—228no—
606C4⋊C4—448no—
607C4⋊C4—444no—
608C22⋊C4—228no—
609C22⋊C4—228no—
610C22⋊C4—448no—
611C22⋊C4—448no—
612C42—28no—
613C42—48no—
614C42—444no—
615C11#1399311yescharacteristic, complemented, Sylow
616C23—114no—
617C23—222no—
618C23—222no—
619C23—222no—
620C23—222no—
621C23—222no—
622C23—222no—
623C23—222no—
624C23—222no—
625C23—222no—
626C23—222no—
627C23—222no—
628C23—222no—
629C23—222no—
630C23—222no—
631C23—222no—
632C23—222no—
633C23—222no—
634C23—222no—
635C23—441no—
636C23—441no—
637C23—441no—
638C23—441no—
639C23—441no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23—441no—
644C23—441no—
645C23—441no—
646C23—441no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23—441no—
651C23C22×C4×D1111yescharacteristic
652C23C22×D4411yescharacteristic
653C23C2×#433911yescharacteristic
654C23C2×#433911yescharacteristic
655C23C2×#433911yescharacteristic
656C23C2×#433911yescharacteristic
657C23#6703711yescharacteristic
658C23#6703711yescharacteristic
659C23C2×Q8×D1111yescharacteristic
660C23C2×#434311yescharacteristic
661C23#41×D1111yescharacteristic
662C23#41×D1111yescharacteristic
663C23#6704211yescharacteristic
664C23#6704311yescharacteristic
665C23C22×C22⋊D1111yescharacteristic
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—222no—
694C2×C4—224no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—224no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—224no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—441no—
706C2×C4—441no—
707C2×C4—442no—
708C2×C4—442no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—441no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—442no—
715C2×C4—441no—
716C2×C4—441no—
717C2×C4—442no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—4416no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4#6692514yes—
730C2×C4C4×D4414yes—
731C2×C4#6692814yes—
732C2×C4#6692914yes—
733C2×C4C4×C22⋊D1114yes—
734C2×C4#6698214yes—
735C2×C4#6698314yes—
736C2×C4#6699914yes—
737C22—224no—
738C22—224no—
739C22—224no—
740C22—442no—
741C22—442no—
742C22—442no—
743C22—442no—
744C22—442no—
745C22—442no—
746C22—442no—
747C22—442no—
748C22—442no—
749C22—442no—
750C22—442no—
751C22—442no—
752C22C2×#6692511yescharacteristic
753C22C2×C4×D4411yescharacteristic
754C22C2×#6692811yescharacteristic
755C22C2×#6692911yescharacteristic
756C22#1062304211yescharacteristic
757C22#1062304211yescharacteristic
758C22#1062304511yescharacteristic
759C22#1062304511yescharacteristic
760C22#1062306011yescharacteristic
761C22#1062306111yescharacteristic
762C22#1062306311yescharacteristic
763C22#1062306411yescharacteristic
764C22#1062307611yescharacteristic
765C22#1062307711yescharacteristic
766C22#1062308511yescharacteristic
767C22#1062308511yescharacteristic
768C22#1062308911yescharacteristic
769C22#1062308911yescharacteristic
770C22#1062309211yescharacteristic
771C22#1062309311yescharacteristic
772C22C4×Q8×D1111yescharacteristic
773C22C4×#434311yescharacteristic
774C22Q8×D4411yescharacteristic
775C22#1062310811yescharacteristic
776C22#1062310911yescharacteristic
777C22#1062311011yescharacteristic
778C22#1062311111yescharacteristic
779C22#1062311511yescharacteristic
780C22C2×C4×C22⋊D1111yescharacteristic
781C22C2×#6698211yescharacteristic
782C22C2×#6698311yescharacteristic
783C22#1062333611yescharacteristic
784C22C2×#6699911yescharacteristic
785C22#1062335911yescharacteristic
786C22#1062336411yescharacteristic
787C4—24no—
788C4—42no—
789C4—44no—
790C4—44no—
791C4—444no—
792C4—442no—
793C4—442no—
794C4—442no—
795C4—882no—
796C4#1062255318yes—
797C2—444no—
798C2C2×#1062255311yescharacteristic
799C2C4×#6699911yescharacteristic
800C2#1307130311yescharacteristic
801C2#1307148911yescharacteristic
802C2#1307150511yescharacteristic
803C2#1307162311yescharacteristic
804C2#1307165611yescharacteristic
805C2#1307290711yescharacteristic
806C2#1307292711yescharacteristic
807C2#1307296211yescharacteristic
808C2#1307298411yescharacteristic
809C2#1307301011yescharacteristic
810C2#1307304311yescharacteristic
811C2#1307351311yescharacteristic
812C2#1307353411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C4⋊C4C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#13993
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622586C2semidirect
5. #13066876C2semidirect
8. #13066849C2semidirect
9. #13066846C2semidirect
10. #13066845C2semidirect
11. C2×C4×C11×C4⋊C4C2semidirect
37. #10622600C4semidirect
213. C2×C4×C4⋊C4D11semidirect
615. C11#13993semidirect

Maximal subgroups

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

subgroupindex
C2×#106225862
C2×#106226002
C2×C4×(C2×D11)⋊C42
#130668762
#130668602
#130668542
#130668492
#130668462
#130668452
C2×C4×C11×C4⋊C42
#1399311