Finite Group Databasebeta

← #14675957

Subgroups — #14675957

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×C22⋊D11C211yesmaximal, characteristic
2C2×#10622569C212yesmaximal
3C2×#10622602C212yesmaximal, complemented
4C2×D11×#95C211yesmaximal, characteristic, complemented
5#13066866C212yesmaximal, complemented
6#13066859C212yesmaximal, complemented
7Dic11⋊#95C211yesmaximal, characteristic, complemented
8#13066841C211yesmaximal, characteristic, complemented
9#13066839C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C211yesmaximal, characteristic, complemented
11C2×C11×#380C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C23×C4×D11C2212yes—
15C23×C4×D11C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C22⋊C4C2212yes—
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C2×C4×C22⋊D11—28no—
21C2×C4×C22⋊D11C418yescomplemented
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C11×#380—24no—
28C2×C11×#95C2211yescharacteristic
29C2×C11×#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38#10622602—28no—
39#10622569—28no—
40D11×#95—24no—
41C25×C11C2311yescharacteristic
42C24×D11C2311yescharacteristic
43C23×C4×C11—24no—
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—42no—
47C23×C4×C11C2×C414yescomplemented
48C23×C4×C11C2312yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—24no—
53C22×C22⋊D11—24no—
54C22×C22⋊D11C2×C414yes—
55C22×C22⋊D11D414yes—
56C22×C22⋊D11Q814yes—
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C22×C4×D11—24no—
63C22×C4×D11—24no—
64C22×C4×D11—24no—
65C22×C4×D11—22no—
66C22×C4×D11—22no—
67C22×C4×D11—24no—
68C22×C4×D11—24no—
69C22×C4×D11—24no—
70C22×C4×D11—42no—
71C22×C4×D11—42no—
72C22×C4×D11—42no—
73C22×C4×D11C2×C414yes—
74C2×C11×C4⋊C4—24no—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4—42no—
77C2×C11×C22⋊C4—24no—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4—42no—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11—24no—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11—42no—
84C2×C22⋊Dic11C2×C414yescomplemented
85C4×C22⋊D11—232no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4C2×C414yes—
90C2×(C2×D11)⋊C4D418yes—
91C2×Dic11⋊C4—24no—
92C2×Dic11⋊C4—24no—
93C2×Dic11⋊C4—24no—
94C2×Dic11⋊C4—42no—
95C2×Dic11⋊C4C2×C414yescomplemented
96C2×C4×Dic11—24no—
97C2×C4×Dic11C2×C414yescomplemented
98C11×#95—22no—
99C11×#95D414yescomplemented
100C11⋊#95—24no—
101C11⋊#95—22no—
102C11⋊#95—24no—
103C11⋊#95—22no—
104C11⋊#95—24no—
105C11⋊#95—24no—
106C11⋊#95—24no—
107C11⋊#95—42no—
108#13899—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11—21no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—21no—
114C24×C11—22no—
115C24×C11—21no—
116C24×C11—21no—
117C24×C11C22×C412yes—
118C24×C11C2×D412yes—
119C24×C11C2×Q812yes—
120C24×C11C2411yescharacteristic
121C23×D11—21no—
122C23×D11—21no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—21no—
126C23×D11—21no—
127C23×D11C22×C412yes—
128C23×D11C2×D414yes—
129C23×D11C2×D412yes—
130C23×D11C2×Q812yes—
131C23×D11#4114yes—
132C22×C4×C11—22no—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
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—22no—
143C22×C4×C11—28no—
144C22×C4×C11—28no—
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×C11—44no—
153C22×C4×C11—48no—
154C22×C4×C11—48no—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C22×C412yes—
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2×D414yes—
159C22×C4×C11C2×D412yes—
160C22×C4×C11#4112yes—
161C2×C22⋊D11—28no—
162C2×C22⋊D11—28no—
163C2×C22⋊D11—216no—
164C2×C22⋊D11—216no—
165C2×C22⋊D11C4⋊C4116yescomplemented
166C22×Dic11—22no—
167C22×Dic11—21no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—21no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—21no—
187C22×Dic11—22no—
188C22×Dic11C22×C412yes—
189C22×Dic11C22×C412yes—
190C22×Dic11C22×C412yes—
191C22×Dic11C2×D414yes—
192C22×Dic11C2×D412yes—
193C22×Dic11C2×Q812yes—
194C22×Dic11#4114yes—
195C2×C4×D11—216no—
196C2×C4×D11—28no—
197C2×C4×D11—28no—
198C2×C4×D11—44no—
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—
208C11×C22⋊C4—48no—
209C22⋊Dic11—28no—
210C22⋊Dic11—48no—
211(C2×D11)⋊C4—48no—
212(C2×D11)⋊C4C22⋊C4116yescomplemented
213Dic11⋊C4—28no—
214Dic11⋊C4—48no—
215C4×Dic11—28no—
216C22×C4×D4—111no—
217C2×#386—112no—
218C2×#385—112no—
219C2×#380D1111yescharacteristic, complemented
220C22×#95—111no—
221#1441—112no—
222#1439—112no—
223C4⋊#95—111no—
224#1434—111no—
225C22⋊#95—111no—
226C22⋊#95—111no—
227C23×C11—22no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—22no—
231C23×C11—22no—
232C23×C11—22no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—22no—
236C23×C11—24no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—24no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11—42no—
245C23×C11—42no—
246C23×C11—42no—
247C23×C11—42no—
248C23×C11—42no—
249C23×C11C2×C4⋊C414yes—
250C23×C11C23×C411yescharacteristic
251C23×C11C22×D412yes—
252C23×C11C22×D411yescharacteristic
253C23×C11C22×D411yescharacteristic
254C23×C11C22×Q811yescharacteristic
255C23×C11C2×#4111yescharacteristic
256C23×C11C2×#4112yes—
257C23×C11C2×#4112yes—
258C23×C11H(5,𝔽2)12yes—
259C23×C11H(5,𝔽2)11yescharacteristic
260C23×C112−1+411yescharacteristic
261C22×D11—22no—
262C22×D11—22no—
263C22×D11—22no—
264C22×D11—22no—
265C22×D11—24no—
266C22×D11—24no—
267C22×D11—24no—
268C22×D11—24no—
269C22×D11—24no—
270C22×D11—22no—
271C22×D11—24no—
272C22×D11—24no—
273C22×D11—24no—
274C22×D11—22no—
275C22×D11—24no—
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—24no—
279C22×D11C2×C22⋊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—24no—
289C2×C4×C11—24no—
290C2×C4×C11—24no—
291C2×C4×C11—24no—
292C2×C4×C11—24no—
293C2×C4×C11—24no—
294C2×C4×C11—24no—
295C2×C4×C11—416no—
296C2×C4×C11—42no—
297C2×C4×C11—42no—
298C2×C4×C11—42no—
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×C11C2×C22⋊C414yes—
308C2×C4×C11C4×D414yes—
309C22⋊D11—232no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—24no—
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×Dic11—42no—
337C2×Dic11C2×C22⋊C414yes—
338C2×Dic11C2×C4⋊C414yes—
339C4×D11—416no—
340C4×D11—432no—
341C23×D4—111no—
342C24×C4—111no—
343C24×C4—112no—
344C24×C4C2×D1111yescharacteristic
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⋊C4C2×D1112yes—
355C22×C42—111no—
356#386—228no—
357#385—228no—
358#380—24no—
359C2×#95—111no—
360C2×#95—111no—
361C2×#95—112no—
362C2×#95—112no—
363C2×#95—112no—
364C2×#95—112no—
365C2×#95—112no—
366C2×#95—112no—
367C2×#95—224no—
368C2×#95C2×D1111yescharacteristic
369C2×#95C2×D1111yescharacteristic
370C22×C11—24no—
371C22×C11—24no—
372C22×C11—24no—
373C22×C11—42no—
374C22×C11—42no—
375C22×C11—42no—
376C22×C11—44no—
377C22×C11—44no—
378C22×C11—44no—
379C22×C11—44no—
380C22×C11—42no—
381C22×C11C22×C22⋊C411yescharacteristic
382C22×C11C22×C4⋊C411yescharacteristic
383C22×C11C2×#11711yescharacteristic
384C22×C11C2×C4×D411yescharacteristic
385C22×C11C4×#4111yescharacteristic
386C22×C11#51811yescharacteristic
387C22×C11#52011yescharacteristic
388C22×C11C2×#12112yes—
389C22×C11C2×C22⋊Q812yes—
390C22×C11#52512yes—
391C22×C11#52912yes—
392C22×C11#53812yes—
393C22×C11#53912yes—
394C22×C11D4212yes—
395C22×C11D4211yescharacteristic
396C22×C11#54612yes—
397C22×C11#54612yes—
398C22×C11#54612yes—
399C22×C11#54711yescharacteristic
400C22×C11#54712yes—
401C22×C11D4×Q811yescharacteristic
402C22×C11#55411yescharacteristic
403C22×C11#55412yes—
404C2×D11—24no—
405C2×D11—24no—
406C2×D11—24no—
407C2×D11—24no—
408C2×D11—24no—
409C2×D11—28no—
410C2×D11—28no—
411C2×D11—28no—
412C2×D11—28no—
413C2×D11—24no—
414C2×D11#38018yescomplemented
415C4×C11—24no—
416C4×C11—24no—
417C4×C11—44no—
418C4×C11—82no—
419Dic11—24no—
420Dic11—24no—
421Dic11—42no—
422Dic11—44no—
423Dic11—82no—
424C25—111no—
425C25C22×D1111yescharacteristic
426C22×D4—114no—
427C22×D4—114no—
428C22×D4—114no—
429C22×D4—224no—
430C22×D4—224no—
431C23×C4—22no—
432C23×C4—24no—
433C23×C4—22no—
434C23×C4—42no—
435C23×C4—111no—
436C23×C4—111no—
437C23×C4—111no—
438C23×C4—112no—
439C23×C4—114no—
440C23×C4—112no—
441C23×C4—224no—
442C23×C4—224no—
443C23×C4—224no—
444C23×C4—224no—
445C23×C4—224no—
446C23×C4—222no—
447C23×C4—224no—
448C23×C4—222no—
449C23×C4—442no—
450C23×C4—442no—
451C23×C4—442no—
452C23×C4C4×D1114yescomplemented
453C23×C4C22×D1112yes—
454C23×C4C22×D1112yes—
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—24no—
467C2×C22⋊C4—24no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—114no—
470C2×C22⋊C4—118no—
471C2×C22⋊C4—114no—
472C2×C22⋊C4—224no—
473C2×C22⋊C4—224no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—224no—
477C2×C22⋊C4—224no—
478C2×C22⋊C4—442no—
479C2×C42—114no—
480C2×C42—224no—
481#95—22no—
482#95—224no—
483#95—224no—
484#95—224no—
485#95—222no—
486#95—224no—
487#95—224no—
488#95—222no—
489#95—442no—
490#95C22⋊D1114yescomplemented
491C2×C11—44no—
492C2×C11C2×#38011yescharacteristic
493C2×C11#229011yescharacteristic
494C2×C11#231811yescharacteristic
495C2×C11D4×C22⋊C411yescharacteristic
496C2×C11#233911yescharacteristic
497C2×C11D4×C4⋊C411yescharacteristic
498C2×C11#234911yescharacteristic
499C2×C11#242412yes—
500C2×C11#242512yes—
501C2×C11#244912yes—
502C2×C11#245012yes—
503D11—28no—
504C24—21no—
505C24—22no—
506C24—21no—
507C24—22no—
508C24—21no—
509C24—22no—
510C24—22no—
511C24—21no—
512C24—112no—
513C24—114no—
514C24—112no—
515C24—112no—
516C24—114no—
517C24—221no—
518C24—222no—
519C24—221no—
520C24—221no—
521C24—222no—
522C24—221no—
523C24C2×C4×D1112yes—
524C24D4×D1112yes—
525C24Q8×D1112yes—
526C24C23×D1111yescharacteristic
527C2×D4—1116no—
528C2×D4—228no—
529C2×D4—228no—
530C2×D4—2216no—
531C2×D4—2216no—
532C22×C4—21no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—21no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—28no—
544C22×C4—28no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—44no—
553C22×C4—48no—
554C22×C4—48no—
555C22×C4—112no—
556C22×C4—112no—
557C22×C4—112no—
558C22×C4—114no—
559C22×C4—112no—
560C22×C4—112no—
561C22×C4—114no—
562C22×C4—228no—
563C22×C4—2216no—
564C22×C4—222no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—222no—
568C22×C4—222no—
569C22×C4—221no—
570C22×C4—222no—
571C22×C4—222no—
572C22×C4—222no—
573C22×C4—222no—
574C22×C4—222no—
575C22×C4—222no—
576C22×C4—222no—
577C22×C4—221no—
578C22×C4—222no—
579C22×C4—228no—
580C22×C4—222no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—444no—
588C22×C4—448no—
589C22×C4—448no—
590C22×C4—448no—
591C22×C4—448no—
592C22×C4—448no—
593C22×C4—448no—
594C22×C4—448no—
595C22×C4—448no—
596C22×C4C2×C4×D1112yes—
597C22×C4C2×C4×D1112yes—
598C22×C4#433912yes—
599C22×C4D4×D1114yes—
600C22×C4C2×C22⋊D1114yes—
601C22×C4C2×C22⋊D1112yes—
602C4⋊C4—48no—
603C4⋊C4—228no—
604C4⋊C4—448no—
605C22⋊C4—48no—
606C22⋊C4—1116no—
607C22⋊C4—228no—
608C22⋊C4—448no—
609C22⋊C4—448no—
610C42—228no—
611C11#1389911yescharacteristic, complemented, Sylow
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—42no—
627C23—42no—
628C23—42no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—114no—
635C23—114no—
636C23—114no—
637C23—118no—
638C23—118no—
639C23—222no—
640C23—224no—
641C23—222no—
642C23—222no—
643C23—222no—
644C23—222no—
645C23—224no—
646C23—222no—
647C23—222no—
648C23—224no—
649C23—222no—
650C23—224no—
651C23—224no—
652C23—224no—
653C23—224no—
654C23—224no—
655C23—224no—
656C23—224no—
657C23C4⋊C4×D1114yes—
658C23C22×C4×D1111yescharacteristic
659C23C2×#433911yescharacteristic
660C23C2×D4×D1112yes—
661C23C2×D4×D1111yescharacteristic
662C23#6703712yes—
663C23#6703711yescharacteristic
664C23C2×Q8×D1111yescharacteristic
665C23#6704011yescharacteristic
666C23#41×D1112yes—
667C23#41×D1112yes—
668C23C22×C22⋊D1111yescharacteristic
669D4—2232no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—416no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
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—114no—
694C2×C4—114no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—224no—
700C2×C4—224no—
701C2×C4—224no—
702C2×C4—224no—
703C2×C4—222no—
704C2×C4—222no—
705C2×C4—222no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—224no—
709C2×C4—4416no—
710C2×C4—4432no—
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×C4—442no—
724C2×C4C22⋊C4×D1114yes—
725C2×C4C4×C22⋊D1114yes—
726C22—24no—
727C22—24no—
728C22—24no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—118no—
738C22—228no—
739C22—228no—
740C22—228no—
741C22—228no—
742C22—224no—
743C22—224no—
744C22—224no—
745C22—224no—
746C22—224no—
747C22—224no—
748C22C2×C22⋊C4×D1111yescharacteristic
749C22#1062301711yescharacteristic
750C22#1062302112yes—
751C22C2×C4⋊C4×D1111yescharacteristic
752C22#1062303511yescharacteristic
753C22#1062303811yescharacteristic
754C22#1062304211yescharacteristic
755C22D11×#11711yescharacteristic
756C22#1062305311yescharacteristic
757C22#1062305912yes—
758C22D11×#12112yes—
759C22#1062314112yes—
760C22#1062314312yes—
761C22#1062314412yes—
762C22D11×C22⋊Q812yes—
763C22#1062316212yes—
764C22#1062316712yes—
765C22#1062316912yes—
766C22C2×C4×C22⋊D1111yescharacteristic
767C22D4×C22⋊D1111yescharacteristic
768C22D4×C22⋊D1112yes—
769C22Q8×C22⋊D1111yescharacteristic
770C22#1062335912yes—
771C4—24no—
772C4—24no—
773C4—44no—
774C4—82no—
775C4—224no—
776C4—224no—
777C4—444no—
778C4—442no—
779C4—882no—
780C2—44no—
781C2—228no—
782C2D11×#38011yescharacteristic
783C2#1307105311yescharacteristic
784C2#1307125111yescharacteristic
785C2C22⋊C4×C22⋊D1111yescharacteristic
786C2#1307144411yescharacteristic
787C2C4⋊C4×C22⋊D1111yescharacteristic
788C2#1307152011yescharacteristic
789C2#1307214912yes—
790C2#1307216412yes—
791C2#1307242212yes—
792C2#1307244712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#380D11
hypocenterC11#13899
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
3. C2×#10622602C2semidirect
4. C2×D11×#95C2semidirect
5. #13066866C2semidirect
6. #13066859C2semidirect
7. Dic11⋊#95C2semidirect
8. #13066841C2semidirect
9. #13066839C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C2×C11×#380C2semidirect
21. C2×C4×C22⋊D11C4semidirect
47. C23×C4×C11C2×C4semidirect
84. C2×C22⋊Dic11C2×C4semidirect
95. C2×Dic11⋊C4C2×C4semidirect
97. C2×C4×Dic11C2×C4semidirect
99. C11×#95D4semidirect
165. C2×C22⋊D11C4⋊C4semidirect
212. (C2×D11)⋊C4C22⋊C4semidirect
219. C2×#380D11semidirect
414. C2×D11#380semidirect
452. C23×C4C4×D11semidirect
490. #95C22⋊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×C22⋊D112
C2×#106225692
C2×#106226022
C2×D11×#952
#130668662
#130668592
Dic11⋊#952
#130668412
#130668392
(C2×D11)⋊#952
C2×C11×#3802
#1389911