Finite Group Databasebeta

← #14676625

Subgroups — #14676625

Order 2816.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622586C211yesmaximal, characteristic, complemented
2C2×#10622282C212yesmaximal
3C2×#10622600C211yesmaximal, characteristic
4C2×#10622600C211yesmaximal, characteristic
5C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
7#13066877C212yesmaximal, complemented
8#13066864C212yesmaximal
9#13066847C212yesmaximal, complemented
10#13066846C211yesmaximal, characteristic, complemented
11C11×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×(C2×D11)⋊C4C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4C2212yes—
23C22×C4×Dic11C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C2×C11×#95C2212yes—
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35#10622600—24no—
36#10622600C418yescomplemented
37C4⋊C4×Dic11—24no—
38#10622586—24no—
39C4×(C2×D11)⋊C4—24no—
40#10622282—28no—
41C24×D11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2312yes—
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2311yescharacteristic
52C22×C4×D11—22no—
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11—22no—
57C22×C4×D11—22no—
58C22×C4×D11C2×C414yes—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4C2×C414yes—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11—22no—
68C2×(C2×D11)⋊C4—24no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—24no—
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)⋊C4C2×C418yes—
79C2×(C2×D11)⋊C4D414yes—
80C2×C4⋊Dic11—22no—
81C2×C4⋊Dic11—22no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11C2×C414yes—
85C2×C4⋊Dic11D414yes—
86C2×Dic11⋊C4—24no—
87C2×Dic11⋊C4—24no—
88C2×Dic11⋊C4—24no—
89C2×C4×Dic11—22no—
90C2×C4×Dic11—22no—
91C2×C4×Dic11—24no—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—42no—
94C2×C4×Dic11D414yes—
95C11×#95—24no—
96C11×#95—42no—
97C11⋊#95—24no—
98C11⋊#95—24no—
99C11⋊#95—22no—
100C11⋊#95—22no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95—24no—
104C11⋊#95C2×C418yes—
105#13974—111nomaximal, Sylow
106C24×C11C2411yescharacteristic
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×D11—21no—
119C23×D11C22×C412yes—
120C23×D11C2×D412yes—
121C23×D11#4112yes—
122C22×C4×C11—22no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—21no—
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—21no—
131C22×C4×C11—21no—
132C22×C4×C11—21no—
133C22×C4×C11—22no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—22no—
147C22×C4×C11C22×C414yes—
148C22×C4×C11C22×C412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11#4112yes—
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11#4112yes—
156C22×C4×C11#4112yes—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—21no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—21no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—21no—
173C22×Dic11—22no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—22no—
184C22×Dic11—21no—
185C22×Dic11C22×C412yes—
186C22×Dic11C22×C414yes—
187C22×Dic11C2×D412yes—
188C22×Dic11C2×D414yes—
189C22×Dic11C2×D412yes—
190C22×Dic11C2×D412yes—
191C22×Dic11#4112yes—
192C2×C4×D11—28no—
193C2×C4×D11—28no—
194C2×C4×D11—28no—
195C2×C4×D11—44no—
196C2×C4×D11—44no—
197C2×C4×D11—44no—
198C2×C4×D11—44no—
199C11×C4⋊C4—28no—
200C11×C4⋊C4—44no—
201C42×C11—44no—
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—216no—
205(C2×D11)⋊C4—48no—
206C4⋊Dic11—28no—
207C4⋊Dic11—28no—
208Dic11⋊C4—48no—
209C4×Dic11—28no—
210C4×Dic11—48no—
211C2×#389—111no—
212C2×#388—112no—
213C2×#380—111no—
214C2×#380—111no—
215C2×C4×C4⋊C4—111no—
216C2×C4×C22⋊C4—111no—
217#1443—112no—
218#1440—112no—
219#1436—112no—
220C4⋊#95—111no—
221C4⋊#95D1111yescharacteristic, complemented
222C23×C11C23×C411yescharacteristic
223C23×C11C22×D411yescharacteristic
224C23×C11C22×D411yescharacteristic
225C23×C11C22×D411yescharacteristic
226C23×C11C2×#4111yescharacteristic
227C23×C11C2×#4111yescharacteristic
228C23×C11C2×#4111yescharacteristic
229C23×C11C2×#4111yescharacteristic
230C23×C11C2×#4111yescharacteristic
231C23×C11C2×#4111yescharacteristic
232C23×C11C2×#4111yescharacteristic
233C23×C11H(5,𝔽2)11yescharacteristic
234C23×C112−1+411yescharacteristic
235C23×C112−1+411yescharacteristic
236C23×C112−1+411yescharacteristic
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—22no—
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×D11—41no—
271C22×D11C4×D414yes—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11—24no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—41no—
282C2×C4×C11—41no—
283C2×C4×C11—41no—
284C2×C4×C11—41no—
285C2×C4×C11—42no—
286C2×C4×C11—42no—
287C2×C4×C11—42no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—42no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—42no—
294C2×C4×C11—42no—
295C2×C4×C11—42no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
299C2×C4×C11—42no—
300C2×C4×C11#11714yes—
301C2×C4×C11C4×D414yes—
302C2×C4×C11C4×D414yes—
303C2×C4×C11#12114yes—
304C2×C4×C11#12314yes—
305C2×C4×C11#12414yes—
306C2×C4×C11#12614yes—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—22no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—24no—
319C2×Dic11—22no—
320C2×Dic11—24no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—42no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—42no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—41no—
336C2×Dic11—42no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—42no—
340C2×Dic11—41no—
341C2×Dic11#12114yes—
342C4×D11—416no—
343C24×C4—111no—
344C22×C4⋊C4—111no—
345C22×C4⋊C4—111no—
346C22×C4⋊C4—112no—
347C22×C4⋊C4C2×D1111yescharacteristic
348C22×C4⋊C4C2×D1111yescharacteristic
349C22×C22⋊C4—112no—
350C22×C22⋊C4—111no—
351C22×C22⋊C4—111no—
352C22×C22⋊C4—112no—
353C22×C42—111no—
354C22×C42—112no—
355C22×C42C2×D1111yescharacteristic
356#389—224no—
357#388—228no—
358#380—118no—
359#380—224no—
360C4×C4⋊C4—224no—
361C4×C22⋊C4—224no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95—111no—
366C2×#95—112no—
367C2×#95—112no—
368C2×#95—112no—
369C2×#95—111no—
370C2×#95C2×D1112yes—
371C2×#95C2×D1112yes—
372C22×C11C2×#11711yescharacteristic
373C22×C11C2×C4×D411yescharacteristic
374C22×C11C2×C4×D411yescharacteristic
375C22×C11C2×C4×D411yescharacteristic
376C22×C11C4×#4111yescharacteristic
377C22×C11#51911yescharacteristic
378C22×C11#52011yescharacteristic
379C22×C11C2×#12111yescharacteristic
380C22×C11C2×#12111yescharacteristic
381C22×C11C2×#12311yescharacteristic
382C22×C11#52511yescharacteristic
383C22×C11C2×#12411yescharacteristic
384C22×C11C2×#12611yescharacteristic
385C22×C11#52911yescharacteristic
386C22×C11#53211yescharacteristic
387C22×C11#53611yescharacteristic
388C22×C11#53711yescharacteristic
389C22×C11#54111yescharacteristic
390C22×C11#54211yescharacteristic
391C22×C11D4211yescharacteristic
392C22×C11#54711yescharacteristic
393C22×C11#54711yescharacteristic
394C22×C11#54711yescharacteristic
395C22×C11#54711yescharacteristic
396C22×C11#54811yescharacteristic
397C22×C11#54811yescharacteristic
398C22×C11#55211yescharacteristic
399C22×C11#55211yescharacteristic
400C22×C11#55211yescharacteristic
401C22×C11#55311yescharacteristic
402C22×C11#55311yescharacteristic
403C22×C11#55311yescharacteristic
404C22×C11#55611yescharacteristic
405C22×C11#55611yescharacteristic
406C22×C11#55611yescharacteristic
407C2×D11—24no—
408C2×D11—24no—
409C2×D11—24no—
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—
420C2×D11—42no—
421C2×D11—42no—
422C4×C11—42no—
423C4×C11—44no—
424C4×C11—42no—
425C4×C11—82no—
426C4×C11#38818yescomplemented
427Dic11—24no—
428Dic11—42no—
429Dic11—44no—
430Dic11—42no—
431Dic11—44no—
432C25—111no—
433C23×C4—111no—
434C23×C4—112no—
435C23×C4—112no—
436C23×C4—111no—
437C23×C4—111no—
438C23×C4—114no—
439C23×C4—222no—
440C23×C4—222no—
441C23×C4—222no—
442C23×C4—222no—
443C23×C4—222no—
444C23×C4—222no—
445C23×C4C22×D1112yes—
446C23×C4C22×D1112yes—
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—114no—
456C2×C4⋊C4—114no—
457C2×C4⋊C4—222no—
458C2×C4⋊C4—222no—
459C2×C4⋊C4—222no—
460C2×C4⋊C4—222no—
461C2×C4⋊C4—224no—
462C2×C4⋊C4—224no—
463C2×C4⋊C4—224no—
464C2×C4⋊C4C4×D1114yes—
465C2×C22⋊C4—118no—
466C2×C22⋊C4—114no—
467C2×C22⋊C4—222no—
468C2×C22⋊C4—222no—
469C2×C22⋊C4—222no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—222no—
473C2×C22⋊C4—222no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—442no—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—22no—
480C2×C42—114no—
481C2×C42—222no—
482C2×C42—222no—
483C2×C42—224no—
484C2×C42—224no—
485C2×C42—442no—
486#95—24no—
487#95—42no—
488#95—118no—
489#95—222no—
490#95—222no—
491#95—224no—
492#95—224no—
493#95—224no—
494#95—224no—
495#95—224no—
496C2×C11C2×#38811yescharacteristic
497C2×C11C4×#12111yescharacteristic
498C2×C11#232311yescharacteristic
499C2×C11#234411yescharacteristic
500C2×C11#234711yescharacteristic
501C2×C11#236111yescharacteristic
502C2×C11#236211yescharacteristic
503C2×C11#241511yescharacteristic
504C2×C11#241611yescharacteristic
505C2×C11#242111yescharacteristic
506C2×C11#242211yescharacteristic
507C2×C11#249411yescharacteristic
508C2×C11#249611yescharacteristic
509C2×C11#254711yescharacteristic
510C2×C11#256211yescharacteristic
511D11—44no—
512C24—112no—
513C24—112no—
514C24—112no—
515C24—221no—
516C24—221no—
517C24—221no—
518C24—221no—
519C24—221no—
520C24—221no—
521C24—221no—
522C24—221no—
523C24—221no—
524C24—221no—
525C24—221no—
526C24—221no—
527C24C23×D1111yescharacteristic
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—112no—
554C22×C4—112no—
555C22×C4—112no—
556C22×C4—112no—
557C22×C4—114no—
558C22×C4—112no—
559C22×C4—114no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—222no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—221no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—221no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—221no—
582C22×C4—222no—
583C22×C4—221no—
584C22×C4—222no—
585C22×C4—221no—
586C22×C4—222no—
587C22×C4—221no—
588C22×C4—228no—
589C22×C4—228no—
590C22×C4—228no—
591C22×C4—444no—
592C22×C4—444no—
593C22×C4—444no—
594C22×C4—444no—
595C22×C4C2×C4×D1114yes—
596C22×C4C2×C4×D1112yes—
597C22×C4#433912yes—
598C22×C4#433912yes—
599C22×C4D4×D1112yes—
600C22×C4D4×D1112yes—
601C22×C4D4×D1112yes—
602C22×C4#434112yes—
603C22×C4#434312yes—
604C22×C4#434312yes—
605C4⋊C4—28no—
606C4⋊C4—44no—
607C4⋊C4—228no—
608C4⋊C4—228no—
609C4⋊C4—448no—
610C22⋊C4—228no—
611C22⋊C4—2216no—
612C22⋊C4—228no—
613C22⋊C4—448no—
614C42—44no—
615C42—228no—
616C42—448no—
617C11#1397411yescharacteristic, complemented, Sylow
618C23—114no—
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—222no—
636C23—222no—
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—
651C23—441no—
652C23—441no—
653C23C22×C4×D1111yescharacteristic
654C23C2×#433911yescharacteristic
655C23C2×#433911yescharacteristic
656C23C2×D4×D1111yescharacteristic
657C23C2×D4×D1111yescharacteristic
658C23C2×D4×D1111yescharacteristic
659C23C2×#434111yescharacteristic
660C23#6703711yescharacteristic
661C23C2×#434311yescharacteristic
662C23C2×#434311yescharacteristic
663C23#6704011yescharacteristic
664C23#41×D1111yescharacteristic
665C23#41×D1111yescharacteristic
666C23#6704311yescharacteristic
667C23#6704311yescharacteristic
668C2×C4—24no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—42no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—114no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—224no—
704C2×C4—224no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—222no—
708C2×C4—224no—
709C2×C4—222no—
710C2×C4—224no—
711C2×C4—224no—
712C2×C4—224no—
713C2×C4—222no—
714C2×C4—222no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—441no—
718C2×C4—442no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—442no—
723C2×C4—441no—
724C2×C4—442no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—441no—
730C2×C4—442no—
731C2×C4—4416no—
732C2×C4#6692514yes—
733C2×C4(C22⋊D11)⋊C414yes—
734C2×C4#6693714yes—
735C2×C4#6693814yes—
736C2×C4#6694614yes—
737C2×C4#6694714yes—
738C2×C4#6695114yes—
739C22—224no—
740C22—224no—
741C22—224no—
742C22—442no—
743C22—442no—
744C22—442no—
745C22—442no—
746C22—442no—
747C22—442no—
748C22—442no—
749C22—442no—
750C22—442no—
751C22—442no—
752C22—442no—
753C22—442no—
754C22C2×#6692511yescharacteristic
755C22C2×(C22⋊D11)⋊C411yescharacteristic
756C22C2×#6693711yescharacteristic
757C22C2×#6693811yescharacteristic
758C22C2×#6694611yescharacteristic
759C22C2×#6694711yescharacteristic
760C22#1062303811yescharacteristic
761C22C2×#6695111yescharacteristic
762C22#1062304511yescharacteristic
763C22#1062306011yescharacteristic
764C22#1062306411yescharacteristic
765C22C4×D4×D1111yescharacteristic
766C22#1062307711yescharacteristic
767C22#1062308211yescharacteristic
768C22#1062308911yescharacteristic
769C22#1062310311yescharacteristic
770C22C4×#434311yescharacteristic
771C22#1062311211yescharacteristic
772C22#1062311511yescharacteristic
773C22D11×#12111yescharacteristic
774C22#1062313911yescharacteristic
775C22#1062314211yescharacteristic
776C22#1062314511yescharacteristic
777C22#1062315811yescharacteristic
778C22#1062315911yescharacteristic
779C22#1062317211yescharacteristic
780C22#1062317311yescharacteristic
781C22#1062320811yescharacteristic
782C22#1062320811yescharacteristic
783C22#1062322211yescharacteristic
784C22#1062322811yescharacteristic
785C22#1062324811yescharacteristic
786C22#1062325611yescharacteristic
787C22#1062325711yescharacteristic
788C22#1062326411yescharacteristic
789C4—44no—
790C4—42no—
791C4—42no—
792C4—82no—
793C4—224no—
794C4—444no—
795C4—444no—
796C4—442no—
797C4—442no—
798C4#1062228218yescomplemented
799C2—444no—
800C2C2×#1062228211yescharacteristic
801C2#1307112411yescharacteristic
802C2#1307129611yescharacteristic
803C2#1307148111yescharacteristic
804C2#1307150511yescharacteristic
805C2#1307163711yescharacteristic
806C2#1307164811yescharacteristic
807C2#1307204811yescharacteristic
808C2#1307205911yescharacteristic
809C2#1307212211yescharacteristic
810C2#1307213311yescharacteristic
811C2#1307301411yescharacteristic
812C2#1307303611yescharacteristic
813C2#1307361011yescharacteristic
814C2#1307378111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC4⋊#95D11
hypocenterC11#13974
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
1. C2×#10622586C2semidirect
5. C2×C4⋊C4×Dic11C2semidirect
7. #13066877C2semidirect
9. #13066847C2semidirect
10. #13066846C2semidirect
11. C11×C4⋊#95C2semidirect
36. #10622600C4semidirect
221. C4⋊#95D11semidirect
426. C4×C11#388semidirect
617. C11#13974semidirect
798. C4#10622282semidirect

Maximal subgroups

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

subgroupindex
C2×#106225862
C2×#106222822
C2×#106226002
C2×C4⋊C4×Dic112
C2×C4×(C2×D11)⋊C42
#130668772
#130668642
#130668472
#130668462
C11×C4⋊#952
#1397411