Finite Group Databasebeta

← #14675964

Subgroups — #14675964

Order 2816.

2690 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D44C211yesmaximal, characteristic
2C2×#10622278C212yesmaximal
3C2×#10622602C212yesmaximal, complemented
4C2×#10622280C211yesmaximal, characteristic, complemented
5C2×D11×#95C211yesmaximal, characteristic, complemented
6#13066868C212yesmaximal, complemented
7#13066858C212yesmaximal, complemented
8#13066843C211yesmaximal, characteristic, complemented
9(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
11C11×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C4×D11C2212yes—
14C23×C4×D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C42×C11C2211yescharacteristic
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C22×Dic11⋊C4C2212yes—
25C2×C4×D44—28no—
26C2×C4×D44C418yescomplemented
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622602—28no—
38#10622280—24no—
39#10622278—28no—
40D11×#95—24no—
41C24×D11C2311yescharacteristic
42C24×D11C2311yescharacteristic
43C23×C4×C11C2312yes—
44C23×C4×C11C2312yes—
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×C4×C11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2312yes—
51C23×Dic11C2311yescharacteristic
52C22×D44—24no—
53C22×D44—24no—
54C22×D44C2×C414yes—
55C22×D44D414yes—
56C22×D44Q814yes—
57C22×C4×D11—24no—
58C22×C4×D11—24no—
59C22×C4×D11—22no—
60C22×C4×D11—22no—
61C22×C4×D11—24no—
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11—24no—
65C22×C4×D11—24no—
66C22×C4×D11—24no—
67C22×C4×D11—24no—
68C22×C4×D11—42no—
69C22×C4×D11—42no—
70C22×C4×D11—42no—
71C22×C4×D11—42no—
72C22×C4×D11C2×C414yes—
73C22×C4×D11C2×C414yescomplemented
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4—42no—
77C2×C42×C11—24no—
78C2×C42×C11C2×C414yescomplemented
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—24no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—24no—
85C2×(C2×D11)⋊C4—24no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—42no—
88C2×(C2×D11)⋊C4—42no—
89C2×(C2×D11)⋊C4C2×C414yes—
90C2×(C2×D11)⋊C4C2×C414yescomplemented
91C2×(C2×D11)⋊C4D418yes—
92C2×C4⋊Dic11—24no—
93C2×C4⋊Dic11C2×C414yescomplemented
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4—24no—
96C2×Dic11⋊C4—42no—
97C4×D44—232no—
98C11×#95—22no—
99C11×#95—24no—
100C11×#95—22no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95—22no—
104C11⋊#95—24no—
105C11⋊#95—24no—
106C11⋊#95—42no—
107C11⋊#95D414yescomplemented
108#13899—111nomaximal, Sylow
109C24×C11C2411yescharacteristic
110C23×D11—21no—
111C23×D11—21no—
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—21no—
115C23×D11—21no—
116C23×D11—21no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—21no—
120C23×D11—22no—
121C23×D11—21no—
122C23×D11—22no—
123C23×D11—21no—
124C23×D11C22×C412yes—
125C23×D11C22×C412yes—
126C23×D11C2×D412yes—
127C23×D11C2×D414yes—
128C23×D11C2×D412yes—
129C23×D11C2×Q812yes—
130C23×D11C2×Q812yes—
131C23×D11#4114yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
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×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11C22×C412yes—
153C22×C4×C11C22×C412yes—
154C22×C4×C11C22×C412yes—
155C22×C4×C11C2×D414yes—
156C22×C4×C11C2×D412yes—
157C22×C4×C11C2×D412yes—
158C22×C4×C11C2×Q812yes—
159C22×C4×C11#4114yes—
160C22×C4×C11#4112yes—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—21no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11C22×C412yes—
182C22×Dic11C22×C412yes—
183C22×Dic11C2×D414yes—
184C22×Dic11C2×D414yes—
185C2×D44—28no—
186C2×D44—28no—
187C2×D44—216no—
188C2×D44—216no—
189C2×D44C4⋊C4116yescomplemented
190C2×C4×D11—216no—
191C2×C4×D11—28no—
192C2×C4×D11—28no—
193C2×C4×D11—28no—
194C2×C4×D11—28no—
195C2×C4×D11—44no—
196C2×C4×D11—44no—
197C2×C4×D11—48no—
198C2×C4×D11—48no—
199C2×C4×D11—48no—
200C2×C4×D11—48no—
201C2×C4×D11—48no—
202C2×C4×D11—48no—
203C2×C4×D11—48no—
204C2×C4×D11—48no—
205C2×C4×D11—48no—
206C2×C4×D11—48no—
207C11×C4⋊C4—48no—
208C42×C11—28no—
209(C2×D11)⋊C4—28no—
210(C2×D11)⋊C4—48no—
211(C2×D11)⋊C4—48no—
212(C2×D11)⋊C4—48no—
213(C2×D11)⋊C4C22⋊C4116yescomplemented
214C4⋊Dic11—28no—
215Dic11⋊C4—48no—
216C22×C4×D4—111no—
217C2×#386—112no—
218C2×#385—112no—
219C2×#380—111no—
220C22×#95—111no—
221#1441—112no—
222#1439—112no—
223C4⋊#95D1111yescharacteristic, complemented
224#1434—111no—
225C22⋊#95—111no—
226C22⋊#95—111no—
227C23×C11C23×C411yescharacteristic
228C23×C11C22×D412yes—
229C23×C11C22×D411yescharacteristic
230C23×C11C22×D411yescharacteristic
231C23×C11C22×Q811yescharacteristic
232C23×C11C2×#4112yes—
233C23×C11C2×#4111yescharacteristic
234C23×C11C2×#4112yes—
235C23×C11H(5,𝔽2)11yescharacteristic
236C23×C11H(5,𝔽2)12yes—
237C23×C112−1+411yescharacteristic
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—24no—
243C22×D11—24no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—22no—
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—24no—
251C22×D11—22no—
252C22×D11—24no—
253C22×D11—22no—
254C22×D11—22no—
255C22×D11—24no—
256C22×D11—22no—
257C22×D11—22no—
258C22×D11—22no—
259C22×D11—22no—
260C22×D11—22no—
261C22×D11—22no—
262C22×D11—24no—
263C22×D11—24no—
264C22×D11—22no—
265C22×D11—24no—
266C22×D11—22no—
267C22×D11—22no—
268C22×D11—22no—
269C22×D11—24no—
270C22×D11—42no—
271C22×D11—42no—
272C22×D11—42no—
273C22×D11—42no—
274C22×D11—42no—
275C22×D11—42no—
276C22×D11—42no—
277C22×D11—42no—
278C22×D11C2×C22⋊C414yes—
279C22×D11C2×C4⋊C414yes—
280C22×D11C2×C4⋊C414yes—
281C22×D11#11714yes—
282C22×D11#12118yes—
283C22×D11C22⋊Q818yes—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—24no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—24no—
296C2×C4×C11—24no—
297C2×C4×C11—24no—
298C2×C4×C11—24no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11—42no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—42no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11C2×C22⋊C414yes—
311C2×C4×C11C2×C4⋊C414yes—
312C2×C4×C11C4×D414yes—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—42no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11—42no—
336C2×Dic11C2×C22⋊C414yes—
337D44—232no—
338C4×D11—416no—
339C4×D11—416no—
340C4×D11—432no—
341C23×D4—111no—
342C24×C4—111no—
343C24×C4—111no—
344C24×C4—112no—
345C2×C4×D4—118no—
346C2×C4×D4—228no—
347C22×C4⋊C4—111no—
348C22×C4⋊C4—112no—
349C22×C4⋊C4C2×D1112yes—
350C22×C22⋊C4—111no—
351C22×C22⋊C4—111no—
352C22×C22⋊C4—112no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4—112no—
355C22×C42C2×D1111yescharacteristic
356#386—228no—
357#385—228no—
358#380—224no—
359C2×#95—111no—
360C2×#95—111no—
361C2×#95—112no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95—112no—
366C2×#95—224no—
367C2×#95C2×D1111yescharacteristic
368C2×#95C2×D1111yescharacteristic
369C2×#95C2×D1112yes—
370C22×C11C22×C22⋊C411yescharacteristic
371C22×C11C22×C4⋊C411yescharacteristic
372C22×C11C2×#11711yescharacteristic
373C22×C11C2×C4×D411yescharacteristic
374C22×C11C4×#4111yescharacteristic
375C22×C11#51811yescharacteristic
376C22×C11#52011yescharacteristic
377C22×C11C2×#12112yes—
378C22×C11C2×C22⋊Q812yes—
379C22×C11#52512yes—
380C22×C11#52912yes—
381C22×C11#53812yes—
382C22×C11#53912yes—
383C22×C11D4211yescharacteristic
384C22×C11D4212yes—
385C22×C11#54612yes—
386C22×C11#54612yes—
387C22×C11#54612yes—
388C22×C11#54711yescharacteristic
389C22×C11#54712yes—
390C22×C11D4×Q811yescharacteristic
391C22×C11#55411yescharacteristic
392C22×C11#55412yes—
393C2×D11—24no—
394C2×D11—24no—
395C2×D11—24no—
396C2×D11—24no—
397C2×D11—24no—
398C2×D11—28no—
399C2×D11—28no—
400C2×D11—28no—
401C2×D11—28no—
402C2×D11—24no—
403C2×D11—24no—
404C2×D11—24no—
405C2×D11—24no—
406C2×D11—42no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—44no—
410C2×D11—44no—
411C2×D11—44no—
412C2×D11—44no—
413C2×D11—42no—
414C2×D11#38018yescomplemented
415C4×C11—24no—
416C4×C11—24no—
417C4×C11—24no—
418C4×C11—44no—
419C4×C11—82no—
420Dic11—24no—
421Dic11—42no—
422Dic11—44no—
423Dic11—82no—
424C25—111no—
425C25—111no—
426C22×D4—114no—
427C22×D4—114no—
428C22×D4—114no—
429C22×D4—224no—
430C22×D4—224no—
431C23×C4—111no—
432C23×C4—111no—
433C23×C4—112no—
434C23×C4—114no—
435C23×C4—114no—
436C23×C4—112no—
437C23×C4—224no—
438C23×C4—224no—
439C23×C4—224no—
440C23×C4—224no—
441C23×C4—224no—
442C23×C4—224no—
443C23×C4—224no—
444C23×C4—222no—
445C23×C4—222no—
446C23×C4—222no—
447C23×C4—222no—
448C23×C4—442no—
449C23×C4—442no—
450C23×C4—442no—
451C23×C4—442no—
452C23×C4C22×D1112yes—
453C23×C4C22×D1112yes—
454C23×C4C22×D1111yescharacteristic
455C23×C4C22×D1111yescharacteristic
456C23×C4C22×D1111yescharacteristic
457C4×D4—2232no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—42no—
461C2×C4⋊C4—114no—
462C2×C4⋊C4—224no—
463C2×C4⋊C4—224no—
464C2×C4⋊C4—224no—
465C2×C4⋊C4—442no—
466C2×C22⋊C4—114no—
467C2×C22⋊C4—118no—
468C2×C22⋊C4—114no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—224no—
472C2×C22⋊C4—224no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—442no—
478C2×C22⋊C4—442no—
479C2×C42—24no—
480C2×C42C4×D1114yescomplemented
481#95—22no—
482#95—22no—
483#95—24no—
484#95—114no—
485#95—224no—
486#95—224no—
487#95—224no—
488#95—224no—
489#95—222no—
490#95—442no—
491C2×C11C2×#38011yescharacteristic
492C2×C11#229011yescharacteristic
493C2×C11#231811yescharacteristic
494C2×C11D4×C22⋊C411yescharacteristic
495C2×C11#233911yescharacteristic
496C2×C11D4×C4⋊C411yescharacteristic
497C2×C11#234911yescharacteristic
498C2×C11#242412yes—
499C2×C11#242512yes—
500C2×C11#244912yes—
501C2×C11#245012yes—
502D11—28no—
503D11—44no—
504C24—112no—
505C24—114no—
506C24—112no—
507C24—112no—
508C24—114no—
509C24—112no—
510C24—112no—
511C24—112no—
512C24—222no—
513C24—221no—
514C24—221no—
515C24—221no—
516C24—221no—
517C24—222no—
518C24—222no—
519C24—221no—
520C24—222no—
521C24—221no—
522C24—221no—
523C24—221no—
524C24—222no—
525C24—222no—
526C24C23×D1111yescharacteristic
527C2×D4—1116no—
528C2×D4—228no—
529C2×D4—228no—
530C2×D4—2216no—
531C2×D4—2216no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—112no—
553C22×C4—114no—
554C22×C4—112no—
555C22×C4—114no—
556C22×C4—228no—
557C22×C4—228no—
558C22×C4—2216no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—222no—
562C22×C4—222no—
563C22×C4—221no—
564C22×C4—222no—
565C22×C4—222no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—221no—
569C22×C4—222no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—228no—
573C22×C4—228no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—222no—
578C22×C4—222no—
579C22×C4—222no—
580C22×C4—222no—
581C22×C4—444no—
582C22×C4—444no—
583C22×C4—448no—
584C22×C4—448no—
585C22×C4—448no—
586C22×C4—448no—
587C22×C4—448no—
588C22×C4—448no—
589C22×C4—448no—
590C22×C4—448no—
591C22×C4—448no—
592C22×C4—448no—
593C22×C4C2×C4×D1112yes—
594C22×C4C2×C4×D1112yes—
595C22×C4C2×C4×D1112yes—
596C22×C4#433914yes—
597C22×C4D4×D1114yes—
598C22×C4D4×D1112yes—
599C22×C4D4×D1112yes—
600C22×C4Q8×D1112yes—
601C22×C4#434312yes—
602C4⋊C4—48no—
603C4⋊C4—228no—
604C4⋊C4—448no—
605C22⋊C4—1116no—
606C22⋊C4—228no—
607C22⋊C4—448no—
608C22⋊C4—448no—
609C22⋊C4—448no—
610C42—28no—
611C11#1389911yescharacteristic, complemented, Sylow
612C23—114no—
613C23—114no—
614C23—114no—
615C23—118no—
616C23—118no—
617C23—114no—
618C23—222no—
619C23—222no—
620C23—222no—
621C23—222no—
622C23—222no—
623C23—224no—
624C23—222no—
625C23—222no—
626C23—224no—
627C23—222no—
628C23—224no—
629C23—224no—
630C23—224no—
631C23—224no—
632C23—224no—
633C23—224no—
634C23—224no—
635C23—224no—
636C23—222no—
637C23—222no—
638C23—222no—
639C23—222no—
640C23—222no—
641C23—222no—
642C23—222no—
643C23—222no—
644C23—222no—
645C23—222no—
646C23—224no—
647C23—224no—
648C23—224no—
649C23—224no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23—442no—
657C23—442no—
658C23C22×C4×D1111yescharacteristic
659C23C2×#433912yes—
660C23C2×D4×D1111yescharacteristic
661C23C2×D4×D1111yescharacteristic
662C23C2×D4×D1112yes—
663C23#6703711yescharacteristic
664C23C2×Q8×D1111yescharacteristic
665C23C2×#434311yescharacteristic
666C23#6704011yescharacteristic
667C23#41×D1112yes—
668C23#6704212yes—
669D4—2232no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
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—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—114no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—224no—
700C2×C4—224no—
701C2×C4—224no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—4416no—
708C2×C4—4416no—
709C2×C4—4432no—
710C2×C4—442no—
711C2×C4—442no—
712C2×C4—442no—
713C2×C4—442no—
714C2×C4—442no—
715C2×C4—442no—
716C2×C4—442no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4C22⋊C4×D1114yes—
724C2×C4C4⋊C4×D1114yes—
725C2×C4#6694614yes—
726C22—118no—
727C22—228no—
728C22—228no—
729C22—228no—
730C22—228no—
731C22—224no—
732C22—224no—
733C22—224no—
734C22—224no—
735C22—224no—
736C22—224no—
737C22—224no—
738C22—224no—
739C22—224no—
740C22—444no—
741C22—444no—
742C22—444no—
743C22—444no—
744C22—442no—
745C22—442no—
746C22—442no—
747C22—442no—
748C22C4×#433911yescharacteristic
749C22C2×C22⋊C4×D1111yescharacteristic
750C22#1062302112yes—
751C22C2×C4⋊C4×D1111yescharacteristic
752C22C2×#6694611yescharacteristic
753C22#1062303511yescharacteristic
754C22#1062303812yes—
755C22D11×#11711yescharacteristic
756C22#1062305211yescharacteristic
757C22#1062307812yes—
758C22#1062308112yes—
759C22#1062311012yes—
760C22#1062311112yes—
761C22D11×#12112yes—
762C22#1062314012yes—
763C22D11×C22⋊Q812yes—
764C22#1062316112yes—
765C22#1062320912yes—
766C22#1062322312yes—
767C22#1062324811yescharacteristic
768C22#1062325711yescharacteristic
769C22#1062325811yescharacteristic
770C22#1062326111yescharacteristic
771C4—24no—
772C4—24no—
773C4—24no—
774C4—44no—
775C4—82no—
776C4—224no—
777C4—444no—
778C4—442no—
779C4—882no—
780C2—228no—
781C2—444no—
782C2D11×#38011yescharacteristic
783C2#1307105711yescharacteristic
784C2#1307125211yescharacteristic
785C2#1307143611yescharacteristic
786C2#1307144311yescharacteristic
787C2#1307151611yescharacteristic
788C2#1307152711yescharacteristic
789C2#1307215912yes—
790C2#1307217412yes—
791C2#1307243212yes—
792C2#1307243712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenterC4⋊#95D11
hypocenterC11#13899
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#10622602C2semidirect
4. C2×#10622280C2semidirect
5. C2×D11×#95C2semidirect
6. #13066868C2semidirect
7. #13066858C2semidirect
8. #13066843C2semidirect
9. (C2×D11)⋊#95C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C11×C4⋊#95C2semidirect
26. C2×C4×D44C4semidirect
73. C22×C4×D11C2×C4semidirect
78. C2×C42×C11C2×C4semidirect
90. C2×(C2×D11)⋊C4C2×C4semidirect
93. C2×C4⋊Dic11C2×C4semidirect
107. C11⋊#95D4semidirect
189. C2×D44C4⋊C4semidirect
213. (C2×D11)⋊C4C22⋊C4semidirect
223. C4⋊#95D11semidirect
414. C2×D11#380semidirect
480. C2×C42C4×D11semidirect
611. C11#13899semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D442
C2×#106222782
C2×#106226022
C2×#106222802
C2×D11×#952
#130668682
#130668582
#130668432
(C2×D11)⋊#952
C11×C4⋊#952
#1389911