Finite Group Databasebeta

← #14677501

Subgroups — #14677501

Order 2816.

1530 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622598C211yesmaximal, characteristic
2C2×#10622598C211yesmaximal, characteristic
3C2×C4⋊C4×Dic11C211yesmaximal, characteristic
4C2×C4×C4⋊Dic11C211yesmaximal, characteristic
5#13066881C212yesmaximal
6#13066869C212yesmaximal
7#13066850C212yesmaximal
8#13066846C211yesmaximal, characteristic
9#13066845C211yesmaximal, characteristic
10#13066845C212yesmaximal
11C2×C11×#389C211yesmaximal, characteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2212yes—
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2211yescharacteristic
16C22×C4⋊Dic11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2212yes—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2212yes—
22C22×C4×Dic11C2211yescharacteristic
23C22×C4×Dic11C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C11×#389C418yescomplemented
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2211yescharacteristic
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36#10622598—24no—
37#10622598—24no—
38C4⋊C4×Dic11—24no—
39C4×C4⋊Dic11—24no—
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×Dic11C2312yes—
46C23×Dic11C2311yescharacteristic
47C23×Dic11C2311yescharacteristic
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C2×C11×C4⋊C4—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—42no—
54C2×C11×C4⋊C4—42no—
55C2×C11×C4⋊C4C2×C414yes—
56C2×C11×C4⋊C4C2×C418yes—
57C2×C11×C4⋊C4C2×C414yes—
58C2×C11×C4⋊C4D414yes—
59C2×C11×C4⋊C4Q814yes—
60C2×C42×C11—22no—
61C2×C42×C11—22no—
62C2×C42×C11C2×C414yes—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—22no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—24no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—22no—
74C2×C4⋊Dic11—24no—
75C2×C4⋊Dic11—24no—
76C2×C4⋊Dic11—42no—
77C2×C4⋊Dic11—42no—
78C2×C4⋊Dic11—42no—
79C2×C4⋊Dic11Q814yes—
80C2×C4⋊Dic11Q814yes—
81C2×C4×Dic11—22no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11—24no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—24no—
88C2×C4×Dic11—42no—
89C2×C4×Dic11D414yes—
90C11×#95C2×C418yes—
91C11⋊#95—24no—
92C11⋊#95—24no—
93C11⋊#95—24no—
94C11⋊#95—22no—
95C11⋊#95—22no—
96C11⋊#95—24no—
97C11⋊#95—42no—
98C11⋊#95—42no—
99C11⋊#95—42no—
100#14045—111nomaximal, Sylow
101C24×C11C2411yescharacteristic
102C22×C4×C11—21no—
103C22×C4×C11—22no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—21no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11C22×C414yes—
123C22×C4×C11C22×C412yes—
124C22×C4×C11C22×C414yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C22×C412yes—
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×Q814yes—
131C22×C4×C11C2×Q812yes—
132C22×C4×C11C2×Q812yes—
133C22×C4×C11C2×Q812yes—
134C22×C4×C11#4112yes—
135C22×C4×C11#4112yes—
136C22×C4×C11#4112yes—
137C22×Dic11—21no—
138C22×Dic11—21no—
139C22×Dic11—21no—
140C22×Dic11—22no—
141C22×Dic11—21no—
142C22×Dic11—21no—
143C22×Dic11—21no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—21no—
147C22×Dic11—22no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—21no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—21no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—21no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11C2×D412yes—
173C22×Dic11C2×D412yes—
174C22×Dic11C2×Q814yes—
175C22×Dic11C2×Q812yes—
176C22×Dic11C2×Q812yes—
177C22×Dic11#4112yes—
178C22×Dic11#4112yes—
179C11×C4⋊C4—28no—
180C11×C4⋊C4—48no—
181C11×C4⋊C4C4⋊C4116yescomplemented
182C42×C11—28no—
183C4⋊Dic11—28no—
184C4⋊Dic11—28no—
185C4⋊Dic11—28no—
186C4⋊Dic11—48no—
187C4⋊Dic11—48no—
188C4⋊Dic11—44no—
189C4×Dic11—28no—
190C4×Dic11—48no—
191C4×Dic11—44no—
192C2×#389—111no—
193C2×#389—111no—
194C2×#389D1111yescharacteristic
195C2×C4×C4⋊C4—111no—
196C2×C4×C4⋊C4—111no—
197#1444—112no—
198#1441—112no—
199#1436—112no—
200C4⋊#95—111no—
201C4⋊#95—111no—
202C4⋊#95—112no—
203C23×C11C23×C411yescharacteristic
204C23×C11C22×D411yescharacteristic
205C23×C11C22×D411yescharacteristic
206C23×C11C22×Q811yescharacteristic
207C23×C11C22×Q811yescharacteristic
208C23×C11C22×Q811yescharacteristic
209C23×C11C2×#4111yescharacteristic
210C23×C11C2×#4111yescharacteristic
211C23×C11C2×#4111yescharacteristic
212C23×C11C2×#4111yescharacteristic
213C23×C11C2×#4111yescharacteristic
214C23×C11H(5,𝔽2)11yescharacteristic
215C23×C11H(5,𝔽2)11yescharacteristic
216C23×C11H(5,𝔽2)11yescharacteristic
217C23×C112−1+411yescharacteristic
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—42no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—41no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—42no—
244C2×C4×C11C2×C4⋊C418yes—
245C2×C4×C11C2×C4⋊C414yes—
246C2×C4×C11C4×D414yes—
247C2×C4×C11C4×Q814yes—
248C2×C4×C11C4×Q814yes—
249C2×C4×C11#12114yes—
250C2×C4×C11C22⋊Q814yes—
251C2×C4×C11#12514yes—
252C2×C4×C11C4⋊Q814yes—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—22no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—41no—
272C2×Dic11—41no—
273C2×Dic11—42no—
274C2×Dic11—41no—
275C2×Dic11—41no—
276C2×Dic11—42no—
277C2×Dic11—42no—
278C2×Dic11—41no—
279C2×Dic11—41no—
280C2×Dic11—41no—
281C2×Dic11—41no—
282C2×Dic11—42no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—42no—
288C2×Dic11—42no—
289C2×Dic11—42no—
290C2×Dic11—42no—
291C2×Dic11—42no—
292C2×Dic11—42no—
293C2×Dic11—42no—
294C2×Dic11C22⋊Q814yes—
295C22×C4⋊C4—111no—
296C22×C4⋊C4—111no—
297C22×C4⋊C4—111no—
298C22×C4⋊C4—111no—
299C22×C4⋊C4—112no—
300C22×C4⋊C4—112no—
301C22×C4⋊C4C2×D1111yescharacteristic
302C22×C4⋊C4C2×D1112yes—
303C22×C4⋊C4C2×D1111yescharacteristic
304C22×C42—111no—
305C22×C42—111no—
306C22×C42—112no—
307C22×C42C2×D1111yescharacteristic
308#389—224no—
309#389—224no—
310#389Dic1118yescomplemented
311C4×C4⋊C4—224no—
312C4×C4⋊C4—224no—
313C2×#95—111no—
314C2×#95—112no—
315C2×#95—112no—
316C2×#95—112no—
317C2×#95—111no—
318C2×#95—112no—
319C2×#95—112no—
320C2×#95—112no—
321C2×#95—112no—
322C2×#95C2×D1112yes—
323C22×C11C22×C4⋊C411yescharacteristic
324C22×C11C2×C4×D411yescharacteristic
325C22×C11C2×C4×Q811yescharacteristic
326C22×C11C2×C4×Q811yescharacteristic
327C22×C11C4×#4111yescharacteristic
328C22×C11#51811yescharacteristic
329C22×C11#52011yescharacteristic
330C22×C11C2×#12111yescharacteristic
331C22×C11C2×C22⋊Q811yescharacteristic
332C22×C11C2×C22⋊Q811yescharacteristic
333C22×C11#52511yescharacteristic
334C22×C11C2×#12511yescharacteristic
335C22×C11#52911yescharacteristic
336C22×C11C2×C4⋊Q811yescharacteristic
337C22×C11#53311yescharacteristic
338C22×C11#53511yescharacteristic
339C22×C11#53711yescharacteristic
340C22×C11#54011yescharacteristic
341C22×C11#54211yescharacteristic
342C22×C11#54611yescharacteristic
343C22×C11#54611yescharacteristic
344C22×C11D4×Q811yescharacteristic
345C22×C11#55011yescharacteristic
346C22×C11#55211yescharacteristic
347C22×C11#55311yescharacteristic
348C22×C11#55411yescharacteristic
349C22×C11#55411yescharacteristic
350C22×C11#55411yescharacteristic
351C22×C11#55411yescharacteristic
352C22×C11#55411yescharacteristic
353C22×C11#55511yescharacteristic
354C22×C11#55711yescharacteristic
355C22×C11#55711yescharacteristic
356C22×C11Q8211yescharacteristic
357C22×C11Q8211yescharacteristic
358C4×C11—28no—
359C4×C11—24no—
360C4×C11—42no—
361C4×C11—44no—
362C4×C11#38918yes—
363Dic11—24no—
364Dic11—42no—
365Dic11—42no—
366Dic11—42no—
367Dic11—44no—
368Dic11—82no—
369C23×C4—111no—
370C23×C4—111no—
371C23×C4—111no—
372C23×C4—111no—
373C23×C4—112no—
374C23×C4—112no—
375C23×C4C22×D1112yes—
376C23×C4C22×D1111yescharacteristic
377C23×C4C22×D1112yes—
378C23×C4C22×D1111yescharacteristic
379C23×C4C22×D1111yescharacteristic
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—42no—
383C2×C4⋊C4—42no—
384C2×C4⋊C4—114no—
385C2×C4⋊C4—114no—
386C2×C4⋊C4—222no—
387C2×C4⋊C4—222no—
388C2×C4⋊C4—222no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4—224no—
394C2×C4⋊C4—224no—
395C2×C4⋊C4—224no—
396C2×C4⋊C4—222no—
397C2×C4⋊C4—222no—
398C2×C4⋊C4—222no—
399C2×C4⋊C4—442no—
400C2×C4⋊C4—442no—
401C2×C4⋊C4—442no—
402C2×C4⋊C4Dic2214yes—
403C2×C4⋊C4D4414yes—
404C2×C4⋊C4C2×Dic1114yes—
405C2×C4⋊C4C2×Dic1118yes—
406C2×C4⋊C4C2×Dic1114yes—
407C2×C42—22no—
408C2×C42—22no—
409C2×C42—114no—
410C2×C42—222no—
411C2×C42—222no—
412C2×C42—224no—
413C2×C42—224no—
414C2×C42—222no—
415C2×C42—222no—
416C2×C42—222no—
417C2×C42—442no—
418C2×C42C2×Dic1114yes—
419#95—222no—
420#95—222no—
421#95—224no—
422#95—224no—
423#95—224no—
424#95—224no—
425#95—442no—
426#95—442no—
427#95—442no—
428#95C2×Dic1118yes—
429C2×C11C2×#38911yescharacteristic
430C2×C11C4×C22⋊Q811yescharacteristic
431C2×C11#232411yescharacteristic
432C2×C11#234911yescharacteristic
433C2×C11Q8×C4⋊C411yescharacteristic
434C2×C11#236911yescharacteristic
435C2×C11#237011yescharacteristic
436C2×C11#241411yescharacteristic
437C2×C11#241711yescharacteristic
438C2×C11#245111yescharacteristic
439C2×C11#245411yescharacteristic
440C2×C11#250711yescharacteristic
441C2×C11#250811yescharacteristic
442C2×C11#256711yescharacteristic
443C2×C11#258411yescharacteristic
444C24C23×D1111yescharacteristic
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—21no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—21no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—112no—
466C22×C4—112no—
467C22×C4—112no—
468C22×C4—112no—
469C22×C4—114no—
470C22×C4—112no—
471C22×C4—112no—
472C22×C4—221no—
473C22×C4—221no—
474C22×C4—221no—
475C22×C4—221no—
476C22×C4—221no—
477C22×C4—221no—
478C22×C4—222no—
479C22×C4—221no—
480C22×C4—221no—
481C22×C4—221no—
482C22×C4—222no—
483C22×C4—221no—
484C22×C4—222no—
485C22×C4—221no—
486C22×C4—221no—
487C22×C4—222no—
488C22×C4—221no—
489C22×C4—221no—
490C22×C4—221no—
491C22×C4—221no—
492C22×C4—221no—
493C22×C4—222no—
494C22×C4—221no—
495C22×C4—221no—
496C22×C4—222no—
497C22×C4—221no—
498C22×C4—221no—
499C22×C4—221no—
500C22×C4—222no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4C2×Dic2214yes—
508C22×C4C2×Dic2212yes—
509C22×C4C2×D4414yes—
510C22×C4C2×D4412yes—
511C22×C4D4×D1112yes—
512C22×C4#434112yes—
513C22×C4Q8×D1112yes—
514C22×C4Q8×D1112yes—
515C22×C4#434312yes—
516C22×C4#434312yes—
517C22×C4C22×Dic1114yes—
518C22×C4C22×Dic1112yes—
519C22×C4C22×Dic1114yes—
520C22×C4C22×Dic1112yes—
521C22×C4C22×Dic1112yes—
522C4⋊C4—28no—
523C4⋊C4—48no—
524C4⋊C4—228no—
525C4⋊C4—228no—
526C4⋊C4—228no—
527C4⋊C4—448no—
528C4⋊C4—448no—
529C4⋊C4—444no—
530C4⋊C4C4⋊Dic11116yescomplemented
531C42—28no—
532C42—228no—
533C42—448no—
534C42—444no—
535C11#1404511yescharacteristic, complemented, Sylow
536C23C22×Dic2211yescharacteristic
537C23C22×D4411yescharacteristic
538C23C2×D4×D1111yescharacteristic
539C23C2×#434111yescharacteristic
540C23#6703711yescharacteristic
541C23#6703711yescharacteristic
542C23C2×Q8×D1111yescharacteristic
543C23C2×Q8×D1111yescharacteristic
544C23C2×#434311yescharacteristic
545C23C2×#434311yescharacteristic
546C23#41×D1111yescharacteristic
547C23#41×D1111yescharacteristic
548C23#6704211yescharacteristic
549C23#6704311yescharacteristic
550C23C23×Dic1111yescharacteristic
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—24no—
567C2×C4—22no—
568C2×C4—24no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—42no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—114no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—222no—
584C2×C4—224no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—224no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—222no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—224no—
595C2×C4—222no—
596C2×C4—441no—
597C2×C4—441no—
598C2×C4—441no—
599C2×C4—441no—
600C2×C4—442no—
601C2×C4—441no—
602C2×C4—441no—
603C2×C4—442no—
604C2×C4—441no—
605C2×C4—441no—
606C2×C4—441no—
607C2×C4—441no—
608C2×C4—442no—
609C2×C4—442no—
610C2×C4—441no—
611C2×C4—441no—
612C2×C4—442no—
613C2×C4—442no—
614C2×C4—442no—
615C2×C4—442no—
616C2×C4—442no—
617C2×C4—442no—
618C2×C4—442no—
619C2×C4#6694114yes—
620C2×C4#6694314yes—
621C2×C4#6694814yes—
622C2×C4#6695014yes—
623C2×C4C2×C4⋊Dic1118yes—
624C2×C4C2×C4⋊Dic1114yes—
625C2×C4D4×Dic1114yes—
626C2×C4Q8×Dic1114yes—
627C2×C4Q8×Dic1114yes—
628C22C2×#6694111yescharacteristic
629C22C2×#6694311yescharacteristic
630C22C2×#6694811yescharacteristic
631C22C2×#6695011yescharacteristic
632C22#1062307011yescharacteristic
633C22#1062307011yescharacteristic
634C22#1062308511yescharacteristic
635C22#1062308511yescharacteristic
636C22Q8×Dic2211yescharacteristic
637C22#1062310111yescharacteristic
638C22Q8×D4411yescharacteristic
639C22#1062310811yescharacteristic
640C22#1062313411yescharacteristic
641C22#1062313811yescharacteristic
642C22#1062313911yescharacteristic
643C22#1062315011yescharacteristic
644C22#1062315311yescharacteristic
645C22#1062315511yescharacteristic
646C22D11×C22⋊Q811yescharacteristic
647C22#1062315811yescharacteristic
648C22#1062321611yescharacteristic
649C22#1062322111yescharacteristic
650C22#1062322511yescharacteristic
651C22#1062322611yescharacteristic
652C22#1062325311yescharacteristic
653C22#1062326111yescharacteristic
654C22#1062326111yescharacteristic
655C22#1062326511yescharacteristic
656C22C22×C4⋊Dic1111yescharacteristic
657C22C2×D4×Dic1111yescharacteristic
658C22#1062332911yescharacteristic
659C22C2×Q8×Dic1111yescharacteristic
660C22C2×Q8×Dic1111yescharacteristic
661C22#41×Dic1111yescharacteristic
662C22#1062335811yescharacteristic
663C4—24no—
664C4—28no—
665C4—42no—
666C4—44no—
667C4—224no—
668C4—444no—
669C4—442no—
670C4—442no—
671C4—442no—
672C4—882no—
673C4#1062259818yes—
674C2C2×#1062259811yescharacteristic
675C2C22⋊Q8×Dic1111yescharacteristic
676C2#1307131111yescharacteristic
677C2#1307152611yescharacteristic
678C2Q8×C4⋊Dic1111yescharacteristic
679C2#1307170611yescharacteristic
680C2#1307171611yescharacteristic
681C2#1307203211yescharacteristic
682C2#1307206511yescharacteristic
683C2#1307245311yescharacteristic
684C2#1307248611yescharacteristic
685C2#1307314611yescharacteristic
686C2#1307315711yescharacteristic
687C2#1307382311yescharacteristic
688C2#1307400311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#389C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#389D11
hypocenterC11#14045
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
25. C11×#389C4semidirect
181. C11×C4⋊C4C4⋊C4semidirect
310. #389Dic11semidirect
530. C4⋊C4C4⋊Dic11semidirect
535. C11#14045semidirect

Maximal subgroups

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

subgroupindex
C2×#106225982
C2×C4⋊C4×Dic112
C2×C4×C4⋊Dic112
#130668812
#130668692
#130668502
#130668462
#130668452
C2×C11×#3892
#1404511