Finite Group Databasebeta

← #14675275

Subgroups — #14675275

Order 2816.

2882 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×#10622279C212yesmaximal, complemented
4C2×#10622279C211yesmaximal, characteristic, complemented
5C2×D11×#95C211yesmaximal, characteristic, complemented
6#13066852C212yesmaximal, complemented
7#13066850C212yesmaximal, complemented
8(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
9(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
10C4×C11⋊#95C211yesmaximal, characteristic, complemented
11C11×#1434C211yesmaximal, characteristic, complemented
12C23×D44C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C23×C4×D11C2212yes—
16C22×C42×C11C2211yescharacteristic
17C22×(C2×D11)⋊C4C2212yes—
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4×Dic11C2212yes—
24C22×C4×Dic11C2212yes—
25C2×C4×D44—28no—
26C2×C4×D44C418yescomplemented
27C2×C11×#95C2211yescharacteristic
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11×#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622279—28no—
38#10622279—24no—
39#10622278C4116yescomplemented
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×Dic11C2311yescharacteristic
51C23×Dic11C2312yes—
52C22×D44—24no—
53C22×D44—22no—
54C22×D44—22no—
55C22×D44C2×C414yes—
56C22×D44C2×C418yes—
57C22×C4×D11—24no—
58C22×C4×D11—24no—
59C22×C4×D11—24no—
60C22×C4×D11—22no—
61C22×C4×D11—22no—
62C22×C4×D11—22no—
63C22×C4×D11—22no—
64C22×C4×D11—24no—
65C22×C4×D11—24no—
66C22×C4×D11—24no—
67C22×C4×D11—42no—
68C22×C4×D11—42no—
69C22×C4×D11—42no—
70C22×C4×D11—42no—
71C22×C4×D11C2×C414yes—
72C22×C4×D11C2×C414yescomplemented
73C22×C4×D11C2×C418yescomplemented
74C2×C42×C11—24no—
75C2×C42×C11C2×C414yescomplemented
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—24no—
81C2×(C2×D11)⋊C4—42no—
82C2×(C2×D11)⋊C4—42no—
83C2×(C2×D11)⋊C4C2×C414yes—
84C2×(C2×D11)⋊C4C2×C414yescomplemented
85C2×(C2×D11)⋊C4C2×C418yescomplemented
86C2×(C2×D11)⋊C4C2×C418yescomplemented
87C2×(C2×D11)⋊C4C2×C418yescomplemented
88C2×(C2×D11)⋊C4D418yes—
89C2×C4⋊Dic11—24no—
90C2×C4⋊Dic11C2×C414yescomplemented
91C2×C4×Dic11—24no—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—24no—
94C2×C4×Dic11—24no—
95C2×C4×Dic11—42no—
96C2×C4×Dic11—42no—
97C4×D44—232no—
98C11×#95—22no—
99C11×#95—24no—
100C11×#95—22no—
101C11×#95C2×C418yescomplemented
102C11⋊#95—22no—
103C11⋊#95—24no—
104C11⋊#95—24no—
105C11⋊#95—42no—
106C11⋊#95C2×C418yescomplemented
107C11⋊#95D414yescomplemented
108#13813—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—21no—
121C23×D11—21no—
122C23×D11—21no—
123C23×D11—22no—
124C23×D11—21no—
125C23×D11C22×C414yes—
126C23×D11C22×C412yes—
127C23×D11C22×C412yes—
128C23×D11C22×C414yes—
129C23×D11C2×D414yes—
130C23×D11#4112yes—
131C23×D11#4112yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
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×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11C22×C414yes—
153C22×C4×C11C22×C414yes—
154C22×C4×C11C22×C414yes—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C22×C412yes—
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11#4112yes—
161C22×Dic11—22no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—21no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—21no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11C22×C414yes—
179C22×Dic11C22×C412yes—
180C22×Dic11C22×C412yes—
181C22×Dic11C22×C414yes—
182C22×Dic11C2×D414yes—
183C22×Dic11C2×D414yes—
184C22×Dic11#4114yes—
185C2×D44—28no—
186C2×D44—28no—
187C2×D44—216no—
188C2×D44—216no—
189C2×D44C42116yescomplemented
190C2×C4×D11—28no—
191C2×C4×D11—216no—
192C2×C4×D11—28no—
193C2×C4×D11—216no—
194C2×C4×D11—28no—
195C2×C4×D11—28no—
196C2×C4×D11—44no—
197C2×C4×D11—44no—
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—
207C42×C11—28no—
208(C2×D11)⋊C4—216no—
209(C2×D11)⋊C4—216no—
210(C2×D11)⋊C4—28no—
211(C2×D11)⋊C4—48no—
212(C2×D11)⋊C4C22⋊C4116yescomplemented
213C4⋊Dic11—28no—
214C4×Dic11—48no—
215C4×Dic11—48no—
216C22×C4×D4—111no—
217C2×#386—112no—
218C2×C4×C22⋊C4—112no—
219C2×C4×C22⋊C4—111no—
220C22×#95—111no—
221#1437—112no—
222#1436—112no—
223#1434D1111yescharacteristic, complemented
224C22⋊#95—111no—
225C22⋊#95—111no—
226C4×#95—111no—
227C23×C11C23×C411yescharacteristic
228C23×C11C23×C412yes—
229C23×C11C22×D412yes—
230C23×C11C22×D411yescharacteristic
231C23×C11C2×#4111yescharacteristic
232C23×C11C2×#4111yescharacteristic
233C23×C11C2×#4111yescharacteristic
234C23×C11C2×#4112yes—
235C23×C11H(5,𝔽2)12yes—
236C23×C11H(5,𝔽2)11yescharacteristic
237C23×C112−1+411yescharacteristic
238C22×D11—22no—
239C22×D11—24no—
240C22×D11—22no—
241C22×D11—24no—
242C22×D11—22no—
243C22×D11—24no—
244C22×D11—22no—
245C22×D11—24no—
246C22×D11—24no—
247C22×D11—22no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—24no—
251C22×D11—22no—
252C22×D11—24no—
253C22×D11—22no—
254C22×D11—24no—
255C22×D11—22no—
256C22×D11—22no—
257C22×D11—22no—
258C22×D11—24no—
259C22×D11—22no—
260C22×D11—24no—
261C22×D11—24no—
262C22×D11—22no—
263C22×D11—24no—
264C22×D11—24no—
265C22×D11—22no—
266C22×D11—22no—
267C22×D11—24no—
268C22×D11—42no—
269C22×D11—42no—
270C22×D11—42no—
271C22×D11—41no—
272C22×D11—42no—
273C22×D11—41no—
274C22×D11—42no—
275C22×D11—41no—
276C22×D11—42no—
277C22×D11—41no—
278C22×D11C2×C4214yes—
279C22×D11C2×C4214yes—
280C22×D11C2×C22⋊C414yes—
281C22×D11#11714yes—
282C22×D11C4×D418yes—
283C22×D11C4×D418yes—
284C2×C4×C11—22no—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—24no—
288C2×C4×C11—24no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
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—24no—
300C2×C4×C11—24no—
301C2×C4×C11—24no—
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×C4214yes—
311C2×C4×C11C2×C22⋊C414yes—
312C2×C4×C11C4×D414yes—
313C2×Dic11—22no—
314C2×Dic11—24no—
315C2×Dic11—22no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—24no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—22no—
324C2×Dic11—24no—
325C2×Dic11—22no—
326C2×Dic11—24no—
327C2×Dic11—24no—
328C2×Dic11—22no—
329C2×Dic11—42no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11—42no—
333C2×Dic11—42no—
334C2×Dic11—42no—
335C2×Dic11C2×C22⋊C414yes—
336C2×Dic11C4×D418yescomplemented
337D44—232no—
338C4×D11—416no—
339C4×D11—432no—
340C4×D11—416no—
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×C22⋊C4—111no—
349C22×C22⋊C4—111no—
350C22×C22⋊C4—112no—
351C22×C22⋊C4—112no—
352C22×C22⋊C4—112no—
353C22×C42—112no—
354C22×C42—112no—
355C22×C42C2×D1111yescharacteristic
356#386—1116no—
357C4×C22⋊C4—224no—
358C4×C22⋊C4—228no—
359C2×#95—112no—
360C2×#95—111no—
361C2×#95—111no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95—224no—
366C2×#95C2×D1111yescharacteristic
367C2×#95C2×D1111yescharacteristic
368C2×#95C2×D1112yes—
369C2×#95C2×D1112yes—
370C22×C11C22×C4211yescharacteristic
371C22×C11C22×C22⋊C411yescharacteristic
372C22×C11C2×#11711yescharacteristic
373C22×C11C2×C4×D411yescharacteristic
374C22×C11C2×C4×D412yes—
375C22×C11C2×C4×D412yes—
376C22×C11C2×C4×D412yes—
377C22×C11C4×#4111yescharacteristic
378C22×C11C4×#4112yes—
379C22×C11#51811yescharacteristic
380C22×C11#51812yes—
381C22×C11#52011yescharacteristic
382C22×C11#52012yes—
383C22×C11D4212yes—
384C22×C11#54612yes—
385C22×C11#54612yes—
386C22×C11#54611yescharacteristic
387C22×C11#54712yes—
388C22×C11#54811yescharacteristic
389C22×C11#55112yes—
390C22×C11#55211yescharacteristic
391C22×C11#55312yes—
392C22×C11#55311yescharacteristic
393C2×D11—24no—
394C2×D11—24no—
395C2×D11—24no—
396C2×D11—24no—
397C2×D11—28no—
398C2×D11—28no—
399C2×D11—28no—
400C2×D11—28no—
401C2×D11—24no—
402C2×D11—24no—
403C2×D11—24no—
404C2×D11—24no—
405C2×D11—24no—
406C2×D11—42no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—44no—
411C2×D11—44no—
412C2×D11—44no—
413C2×D11—44no—
414C2×D11C4×C22⋊C418yescomplemented
415C4×C11—24no—
416C4×C11—24no—
417C4×C11—24no—
418C4×C11—44no—
419C4×C11—44no—
420Dic11—24no—
421Dic11—28no—
422Dic11—42no—
423Dic11—44no—
424C25—111no—
425C25—111no—
426C22×D4—114no—
427C22×D4—118no—
428C22×D4—224no—
429C22×D4—222no—
430C22×D4—222no—
431C23×C4—111no—
432C23×C4—112no—
433C23×C4—112no—
434C23×C4—111no—
435C23×C4—114no—
436C23×C4—114no—
437C23×C4—118no—
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—114no—
459C2×C4⋊C4—224no—
460C2×C22⋊C4—114no—
461C2×C22⋊C4—118no—
462C2×C22⋊C4—114no—
463C2×C22⋊C4—118no—
464C2×C22⋊C4—118no—
465C2×C22⋊C4—118no—
466C2×C22⋊C4—224no—
467C2×C22⋊C4—224no—
468C2×C22⋊C4—224no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—224no—
471C2×C22⋊C4—442no—
472C2×C22⋊C4—442no—
473C2×C42—24no—
474C2×C42—224no—
475C2×C42—224no—
476C2×C42—224no—
477C2×C42—224no—
478C2×C42—442no—
479C2×C42—442no—
480C2×C42C4×D1114yescomplemented
481#95—22no—
482#95—24no—
483#95—22no—
484#95—118no—
485#95—114no—
486#95—224no—
487#95—224no—
488#95—222no—
489#95—442no—
490#95C4×D1118yescomplemented
491C2×C11C2×C4×C22⋊C411yescharacteristic
492C2×C11C42×D411yescharacteristic
493C2×C11#227511yescharacteristic
494C2×C11D4×C22⋊C411yescharacteristic
495C2×C11#233911yescharacteristic
496C2×C11#235211yescharacteristic
497C2×C11#235311yescharacteristic
498C2×C11#235812yes—
499C2×C11#235912yes—
500C2×C11#236112yes—
501C2×C11#236412yes—
502D11—28no—
503D11—44no—
504C24—112no—
505C24—114no—
506C24—114no—
507C24—112no—
508C24—112no—
509C24—114no—
510C24—112no—
511C24—221no—
512C24—221no—
513C24—222no—
514C24—222no—
515C24—221no—
516C24—221no—
517C24—221no—
518C24—222no—
519C24—221no—
520C24—222no—
521C24—221no—
522C24—221no—
523C24—221no—
524C24—222no—
525C24—221no—
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—21no—
538C22×C4—22no—
539C22×C4—21no—
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—114no—
553C22×C4—112no—
554C22×C4—114no—
555C22×C4—114no—
556C22×C4—114no—
557C22×C4—114no—
558C22×C4—112no—
559C22×C4—228no—
560C22×C4—2216no—
561C22×C4—228no—
562C22×C4—2216no—
563C22×C4—221no—
564C22×C4—222no—
565C22×C4—221no—
566C22×C4—222no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—222no—
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—222no—
579C22×C4—222no—
580C22×C4—228no—
581C22×C4—228no—
582C22×C4—444no—
583C22×C4—444no—
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×D1114yes—
594C22×C4C2×C4×D1114yes—
595C22×C4C2×C4×D1114yes—
596C22×C4C2×C4×D1112yes—
597C22×C4C2×C4×D1112yes—
598C22×C4C2×C4×D1112yes—
599C22×C4D4×D1114yes—
600C22×C4D4×D1112yes—
601C22×C4#434312yes—
602C4⋊C4—228no—
603C22⋊C4—1116no—
604C22⋊C4—2216no—
605C22⋊C4—2216no—
606C22⋊C4—228no—
607C22⋊C4—448no—
608C42—28no—
609C42—448no—
610C42—448no—
611C11#1381311yescharacteristic, complemented, Sylow
612C23—114no—
613C23—114no—
614C23—114no—
615C23—118no—
616C23—118no—
617C23—114no—
618C23—224no—
619C23—224no—
620C23—222no—
621C23—224no—
622C23—222no—
623C23—222no—
624C23—224no—
625C23—222no—
626C23—224no—
627C23—224no—
628C23—224no—
629C23—224no—
630C23—224no—
631C23—224no—
632C23—222no—
633C23—222no—
634C23—222no—
635C23—222no—
636C23—222no—
637C23—222no—
638C23—222no—
639C23—224no—
640C23—222no—
641C23—222no—
642C23—224no—
643C23—222no—
644C23—224no—
645C23—224no—
646C23—224no—
647C23—224no—
648C23—442no—
649C23—442no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23—442no—
654C23—441no—
655C23—441no—
656C23—441no—
657C23—441no—
658C23C22×C4×D1111yescharacteristic
659C23C22×C4×D1112yes—
660C23C2×D4×D1112yes—
661C23C2×D4×D1111yescharacteristic
662C23C2×#434311yescharacteristic
663C23#41×D1111yescharacteristic
664C23#41×D1112yes—
665C23#41×D1111yescharacteristic
666C23#6704212yes—
667C23#6704211yescharacteristic
668C23#6704311yescharacteristic
669D4—2232no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
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—118no—
698C2×C4—224no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—224no—
702C2×C4—224no—
703C2×C4—224no—
704C2×C4—224no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—222no—
709C2×C4—222no—
710C2×C4—224no—
711C2×C4—222no—
712C2×C4—224no—
713C2×C4—224no—
714C2×C4—4416no—
715C2×C4—4416no—
716C2×C4—4432no—
717C2×C4—442no—
718C2×C4—442no—
719C2×C4—442no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4C42×D1114yes—
724C2×C4C22⋊C4×D1114yes—
725C2×C4#6694614yes—
726C22—118no—
727C22—228no—
728C22—228no—
729C22—224no—
730C22—224no—
731C22—224no—
732C22—224no—
733C22—224no—
734C22—224no—
735C22—228no—
736C22—228no—
737C22—224no—
738C22—224no—
739C22—224no—
740C22—444no—
741C22—444no—
742C22—442no—
743C22—442no—
744C22—442no—
745C22—442no—
746C22—444no—
747C22—444no—
748C22C2×C42×D1111yescharacteristic
749C22C2×C22⋊C4×D1111yescharacteristic
750C22C2×#6694611yescharacteristic
751C22D11×#11711yescharacteristic
752C22#1062305212yes—
753C22#1062305211yescharacteristic
754C22#1062305311yescharacteristic
755C22#1062305412yes—
756C22#1062305411yescharacteristic
757C22C4×D4×D1112yes—
758C22C4×D4×D1112yes—
759C22C4×D4×D1112yes—
760C22C4×#434312yes—
761C22#1062314012yes—
762C22#1062316112yes—
763C22#1062318512yes—
764C22#1062318612yes—
765C22#1062320711yescharacteristic
766C22#1062320811yescharacteristic
767C22#1062322511yescharacteristic
768C22#1062322611yescharacteristic
769C22#1062323612yes—
770C22#1062324012yes—
771C4—24no—
772C4—24no—
773C4—24no—
774C4—44no—
775C4—44no—
776C4—224no—
777C4—228no—
778C4—444no—
779C4—442no—
780C2—228no—
781C2—444no—
782C2C4×C22⋊C4×D1111yescharacteristic
783C2C4×#6694611yescharacteristic
784C2#1307097811yescharacteristic
785C2#1307143611yescharacteristic
786C2#1307144011yescharacteristic
787C2#1307154211yescharacteristic
788C2#1307154911yescharacteristic
789C2#1307159412yes—
790C2#1307161512yes—
791C2#1307162912yes—
792C2#1307166212yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC22×C11C22×C42
FittingC11×#1434C2
socle, cosocleC24×C11C24
prime radicalC23×D44C22
hypercenter#1434D11
hypocenterC11#13813
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
3. C2×#10622279C2semidirect
4. C2×#10622279C2semidirect
5. C2×D11×#95C2semidirect
6. #13066852C2semidirect
7. #13066850C2semidirect
8. (C2×D11)⋊#95C2semidirect
9. (C2×D11)⋊#95C2semidirect
10. C4×C11⋊#95C2semidirect
11. C11×#1434C2semidirect
26. C2×C4×D44C4semidirect
39. #10622278C4semidirect
72. C22×C4×D11C2×C4semidirect
73. C22×C4×D11C2×C4semidirect
75. C2×C42×C11C2×C4semidirect
84. C2×(C2×D11)⋊C4C2×C4semidirect
85. C2×(C2×D11)⋊C4C2×C4semidirect
86. C2×(C2×D11)⋊C4C2×C4semidirect
87. C2×(C2×D11)⋊C4C2×C4semidirect
90. C2×C4⋊Dic11C2×C4semidirect
101. C11×#95C2×C4semidirect
106. C11⋊#95C2×C4semidirect
107. C11⋊#95D4semidirect
189. C2×D44C42semidirect
212. (C2×D11)⋊C4C22⋊C4semidirect
223. #1434D11semidirect
336. C2×Dic11C4×D4semidirect
414. C2×D11C4×C22⋊C4semidirect
480. C2×C42C4×D11semidirect
490. #95C4×D11semidirect
611. C11#13813semidirect

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×#106222792
C2×D11×#952
#130668522
#130668502
(C2×D11)⋊#952
C4×C11⋊#952
C11×#14342
#1381311