Finite Group Databasebeta

← #14676276

Subgroups — #14676276

Order 2816.

1794 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66940C211yesmaximal, characteristic
2C2×#10622542C211yesmaximal, characteristic
3C2×#10622587C211yesmaximal, characteristic
4C2×#10622598C211yesmaximal, characteristic
5#13066870C212yesmaximal
6#13066866C212yesmaximal
7#13066845C211yesmaximal, characteristic
8#13066845C212yesmaximal
9#13066840C212yesmaximal
10C4×C11⋊#95C211yesmaximal, characteristic
11C2×C11×#389C211yesmaximal, characteristic
12C23×Dic22C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C42×C11C2211yescharacteristic
17C22×C4⋊Dic11C2211yescharacteristic
18C22×C4⋊Dic11C2212yes—
19C22×Dic11⋊C4C2212yes—
20C22×C4×Dic11C2211yescharacteristic
21C22×C4×Dic11C2211yescharacteristic
22C22×C4×Dic11C2212yes—
23C2×#66940—24no—
24C2×#66940—24no—
25C2×#66940C418yescomplemented
26C11×#389—24no—
27C2×C11×#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2211yescharacteristic
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39#10622598—24no—
40#10622587—24no—
41#10622542—24no—
42C23×C4×C11C2312yes—
43C23×C4×C11C2311yescharacteristic
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2312yes—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2311yescharacteristic
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2312yes—
52C23×Dic11C2311yescharacteristic
53C22×Dic22—22no—
54C22×Dic22—22no—
55C22×Dic22—22no—
56C22×Dic22—22no—
57C22×Dic22C2×C414yes—
58C22×Dic22D414yes—
59C22×Dic22Q814yes—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—24no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4—42no—
66C2×C11×C4⋊C4C2×C414yes—
67C2×C11×C4⋊C4D414yes—
68C2×C11×C4⋊C4D414yes—
69C2×C42×C11—22no—
70C2×C42×C11—22no—
71C2×C42×C11—22no—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—24no—
74C2×C4⋊Dic11—22no—
75C2×C4⋊Dic11—22no—
76C2×C4⋊Dic11—24no—
77C2×C4⋊Dic11—42no—
78C2×Dic11⋊C4—24no—
79C2×Dic11⋊C4—24no—
80C2×Dic11⋊C4C2×C418yes—
81C2×C4×Dic11—24no—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—24no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11C2×C414yes—
89C2×C4×Dic11C2×C418yes—
90#66940—232no—
91C11×#95—24no—
92C11⋊#95—24no—
93C11⋊#95—22no—
94C11⋊#95—24no—
95C11⋊#95—24no—
96C11⋊#95—24no—
97C11⋊#95—24no—
98C11⋊#95—22no—
99C11⋊#95—22no—
100C11⋊#95—24no—
101C11⋊#95—42no—
102C11⋊#95Q814yescomplemented
103#13935—111nomaximal, Sylow
104C24×C11C2411yescharacteristic
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—21no—
110C22×C4×C11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—21no—
115C22×C4×C11—21no—
116C22×C4×C11—21no—
117C22×C4×C11—21no—
118C22×C4×C11—21no—
119C22×C4×C11—21no—
120C22×C4×C11—21no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11C22×C414yes—
129C22×C4×C11C22×C412yes—
130C22×C4×C11C2×D414yes—
131C22×C4×C11C2×D414yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×Q812yes—
136C22×C4×C11C2×Q812yes—
137C22×C4×C11#4112yes—
138C22×C4×C11#4112yes—
139C22×C4×C11#4112yes—
140C22×Dic11—21no—
141C22×Dic11—21no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—21no—
145C22×Dic11—21no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—21no—
155C22×Dic11—21no—
156C22×Dic11—21no—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—22no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—21no—
164C22×Dic11—21no—
165C22×Dic11—22no—
166C22×Dic11—21no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—22no—
173C22×Dic11C22×C412yes—
174C22×Dic11C22×C414yes—
175C22×Dic11C22×C412yes—
176C22×Dic11C2×D414yes—
177C22×Dic11C2×Q812yes—
178C22×Dic11C2×Q814yes—
179C22×Dic11C2×Q812yes—
180C22×Dic11#4112yes—
181C22×Dic11#4112yes—
182C2×Dic22—28no—
183C2×Dic22—28no—
184C2×Dic22—28no—
185C2×Dic22—28no—
186C2×Dic22—28no—
187C2×Dic22—28no—
188C2×Dic22C4⋊C4116yescomplemented
189C11×C4⋊C4—48no—
190C11×C4⋊C4—44no—
191C11×C4⋊C4C22⋊C4116yes—
192C42×C11—44no—
193C4⋊Dic11—48no—
194C4⋊Dic11—44no—
195Dic11⋊C4—216no—
196C4×Dic11—216no—
197C4×Dic11—28no—
198C4×Dic11—44no—
199C22×C4×Q8—111no—
200C2×#391—111no—
201C2×#391—111no—
202C2×#389—111no—
203C2×#389D1111yescharacteristic
204#1441—112no—
205#1441—112no—
206C4⋊#95—111no—
207C4⋊#95—112no—
208#1434—112no—
209C4×#95—111no—
210C23×C11C23×C411yescharacteristic
211C23×C11C22×D411yescharacteristic
212C23×C11C22×D411yescharacteristic
213C23×C11C22×D411yescharacteristic
214C23×C11C22×Q811yescharacteristic
215C23×C11C22×Q811yescharacteristic
216C23×C11C2×#4111yescharacteristic
217C23×C11C2×#4111yescharacteristic
218C23×C11C2×#4111yescharacteristic
219C23×C11C2×#4111yescharacteristic
220C23×C11C2×#4111yescharacteristic
221C23×C11H(5,𝔽2)11yescharacteristic
222C23×C112−1+411yescharacteristic
223C23×C112−1+411yescharacteristic
224C23×C112−1+411yescharacteristic
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—22no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—41no—
240C2×C4×C11—41no—
241C2×C4×C11—41no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—41no—
245C2×C4×C11—42no—
246C2×C4×C11—42no—
247C2×C4×C11—42no—
248C2×C4×C11—42no—
249C2×C4×C11—42no—
250C2×C4×C11—42no—
251C2×C4×C11—42no—
252C2×C4×C11C2×C22⋊C418yes—
253C2×C4×C11C2×C22⋊C414yes—
254C2×C4×C11C2×C4⋊C414yes—
255C2×C4×C11#11714yes—
256C2×C4×C11#12114yes—
257C2×C4×C11#12114yes—
258C2×C4×C11C22⋊Q814yes—
259C2×C4×C11C22⋊Q814yes—
260C2×Dic11—22no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—22no—
280C2×Dic11—22no—
281C2×Dic11—41no—
282C2×Dic11—41no—
283C2×Dic11—41no—
284C2×Dic11—41no—
285C2×Dic11—41no—
286C2×Dic11—41no—
287C2×Dic11—41no—
288C2×Dic11—41no—
289C2×Dic11—41no—
290C2×Dic11—41no—
291C2×Dic11—41no—
292C2×Dic11—41no—
293C2×Dic11—42no—
294C2×Dic11—42no—
295C2×Dic11—42no—
296C2×Dic11—42no—
297C2×Dic11—42no—
298C2×Dic11—42no—
299C2×Dic11—42no—
300C2×Dic11C2×C4⋊C418yes—
301C2×Dic11C4×Q814yes—
302Dic22—232no—
303C23×Q8—111no—
304C2×C4×Q8—118no—
305C2×C4×Q8—224no—
306C2×C4×Q8—224no—
307C22×C4⋊C4—112no—
308C22×C4⋊C4—111no—
309C22×C4⋊C4—112no—
310C22×C4⋊C4C2×D1111yescharacteristic
311C22×C4⋊C4C2×D1112yes—
312C22×C4⋊C4C2×D1111yescharacteristic
313C22×C42—111no—
314C22×C42—112no—
315C22×C42—111no—
316C22×C42C2×D1111yescharacteristic
317#391—224no—
318#391—224no—
319#389—24no—
320#389—224no—
321C2×#95—111no—
322C2×#95—111no—
323C2×#95—111no—
324C2×#95—111no—
325C2×#95—112no—
326C2×#95—112no—
327C2×#95—112no—
328C2×#95—112no—
329C2×#95—112no—
330C2×#95—112no—
331C2×#95—112no—
332C2×#95C2×D1112yes—
333C22×C11C22×C22⋊C411yescharacteristic
334C22×C11C22×C4⋊C411yescharacteristic
335C22×C11C2×#11711yescharacteristic
336C22×C11C2×C4×Q811yescharacteristic
337C22×C11C4×#4111yescharacteristic
338C22×C11#51911yescharacteristic
339C22×C11#52011yescharacteristic
340C22×C11C2×#12111yescharacteristic
341C22×C11C2×#12111yescharacteristic
342C22×C11C2×C22⋊Q811yescharacteristic
343C22×C11C2×C22⋊Q811yescharacteristic
344C22×C11#52911yescharacteristic
345C22×C11#52911yescharacteristic
346C22×C11#53311yescharacteristic
347C22×C11#53311yescharacteristic
348C22×C11#54111yescharacteristic
349C22×C11#54111yescharacteristic
350C22×C11#54211yescharacteristic
351C22×C11#54211yescharacteristic
352C22×C11#54611yescharacteristic
353C22×C11#54611yescharacteristic
354C22×C11#54711yescharacteristic
355C22×C11#54711yescharacteristic
356C22×C11#54811yescharacteristic
357C22×C11#54811yescharacteristic
358C22×C11#54811yescharacteristic
359C22×C11#54811yescharacteristic
360C22×C11D4×Q811yescharacteristic
361C22×C11D4×Q811yescharacteristic
362C22×C11D4×Q811yescharacteristic
363C22×C11#55011yescharacteristic
364C22×C11#55711yescharacteristic
365C22×C11#55711yescharacteristic
366C22×C11#55711yescharacteristic
367C22×C11Q8211yescharacteristic
368C4×C11—28no—
369C4×C11—42no—
370C4×C11—42no—
371C4×C11—82no—
372C4×C11#38018yes—
373Dic11—24no—
374Dic11—28no—
375Dic11—42no—
376Dic11—42no—
377Dic11—42no—
378Dic11—82no—
379C22×Q8—114no—
380C22×Q8—114no—
381C22×Q8—114no—
382C22×Q8—222no—
383C22×Q8—222no—
384C22×Q8—222no—
385C22×Q8—222no—
386C23×C4—112no—
387C23×C4—111no—
388C23×C4—111no—
389C23×C4—111no—
390C23×C4—111no—
391C23×C4—112no—
392C23×C4C22×D1112yes—
393C23×C4C22×D1111yescharacteristic
394C23×C4C22×D1111yescharacteristic
395C23×C4C22×D1112yes—
396C23×C4C22×D1111yescharacteristic
397C4×Q8—2232no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—24no—
400C2×C4⋊C4—22no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—22no—
403C2×C4⋊C4—42no—
404C2×C4⋊C4—118no—
405C2×C4⋊C4—224no—
406C2×C4⋊C4—224no—
407C2×C4⋊C4—224no—
408C2×C4⋊C4—224no—
409C2×C4⋊C4—222no—
410C2×C4⋊C4—222no—
411C2×C4⋊C4—222no—
412C2×C4⋊C4—442no—
413C2×C4⋊C4C4×D1114yes—
414C2×C4⋊C4D4414yes—
415C2×C4⋊C4C22⋊D1114yes—
416C2×C42—22no—
417C2×C42—22no—
418C2×C42—22no—
419C2×C42—118no—
420C2×C42—114no—
421C2×C42—224no—
422C2×C42—222no—
423C2×C42—224no—
424C2×C42—222no—
425C2×C42—222no—
426C2×C42—222no—
427C2×C42—222no—
428#95—24no—
429#95—114no—
430#95—222no—
431#95—222no—
432#95—224no—
433#95—224no—
434#95—224no—
435#95—224no—
436#95—224no—
437#95—224no—
438#95—222no—
439#95—442no—
440C2×C11C2×#38011yescharacteristic
441C2×C11#229511yescharacteristic
442C2×C11#232011yescharacteristic
443C2×C11#233911yescharacteristic
444C2×C11Q8×C22⋊C411yescharacteristic
445C2×C11Q8×C4⋊C411yescharacteristic
446C2×C11#235111yescharacteristic
447C2×C11#242611yescharacteristic
448C2×C11#242611yescharacteristic
449C2×C11#242911yescharacteristic
450C2×C11#242911yescharacteristic
451C2×C11#245111yescharacteristic
452C2×C11#245111yescharacteristic
453C2×C11#245311yescharacteristic
454C2×C11#245311yescharacteristic
455C24C23×D1111yescharacteristic
456C2×Q8—1116no—
457C2×Q8—228no—
458C2×Q8—228no—
459C2×Q8—228no—
460C2×Q8—228no—
461C2×Q8—228no—
462C2×Q8—228no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—112no—
487C22×C4—114no—
488C22×C4—114no—
489C22×C4—112no—
490C22×C4—114no—
491C22×C4—112no—
492C22×C4—112no—
493C22×C4—112no—
494C22×C4—112no—
495C22×C4—221no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—221no—
500C22×C4—221no—
501C22×C4—221no—
502C22×C4—222no—
503C22×C4—221no—
504C22×C4—221no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—221no—
508C22×C4—221no—
509C22×C4—221no—
510C22×C4—221no—
511C22×C4—221no—
512C22×C4—221no—
513C22×C4—221no—
514C22×C4—221no—
515C22×C4—221no—
516C22×C4—221no—
517C22×C4—221no—
518C22×C4—221no—
519C22×C4—221no—
520C22×C4—221no—
521C22×C4—222no—
522C22×C4—222no—
523C22×C4—222no—
524C22×C4—222no—
525C22×C4—222no—
526C22×C4—222no—
527C22×C4—222no—
528C22×C4C2×C4×D1114yes—
529C22×C4C2×C4×D1112yes—
530C22×C4C2×D4414yes—
531C22×C4C2×D4412yes—
532C22×C4D4×D1112yes—
533C22×C4#434112yes—
534C22×C4#434112yes—
535C22×C4Q8×D1112yes—
536C22×C4Q8×D1112yes—
537C22×C4#434312yes—
538C22×C4C2×C22⋊D1114yes—
539C22×C4C2×C22⋊D1112yes—
540C4⋊C4—48no—
541C4⋊C4—44no—
542C4⋊C4—2216no—
543C4⋊C4—448no—
544C4⋊C4—444no—
545C4⋊C4(C2×D11)⋊C4116yes—
546C42—44no—
547C42—2216no—
548C42—228no—
549C42—444no—
550C11#1393511yescharacteristic, complemented, Sylow
551C23C22×C4×D1111yescharacteristic
552C23C22×D4411yescharacteristic
553C23C2×D4×D1111yescharacteristic
554C23C2×#434111yescharacteristic
555C23C2×#434111yescharacteristic
556C23#6703711yescharacteristic
557C23C2×Q8×D1111yescharacteristic
558C23C2×Q8×D1111yescharacteristic
559C23C2×#434311yescharacteristic
560C23#6704011yescharacteristic
561C23#41×D1111yescharacteristic
562C23#41×D1111yescharacteristic
563C23#6704311yescharacteristic
564C23#6704311yescharacteristic
565C23C22×C22⋊D1111yescharacteristic
566Q8—2232no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—118no—
595C2×C4—114no—
596C2×C4—224no—
597C2×C4—224no—
598C2×C4—224no—
599C2×C4—222no—
600C2×C4—224no—
601C2×C4—224no—
602C2×C4—224no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—222no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—222no—
612C2×C4—222no—
613C2×C4—222no—
614C2×C4—222no—
615C2×C4—222no—
616C2×C4—222no—
617C2×C4—441no—
618C2×C4—441no—
619C2×C4—441no—
620C2×C4—441no—
621C2×C4—441no—
622C2×C4—441no—
623C2×C4—441no—
624C2×C4—441no—
625C2×C4—441no—
626C2×C4—441no—
627C2×C4—441no—
628C2×C4—441no—
629C2×C4—442no—
630C2×C4—442no—
631C2×C4—442no—
632C2×C4—442no—
633C2×C4—442no—
634C2×C4—442no—
635C2×C4—442no—
636C2×C4C4⋊C4×D1114yes—
637C2×C4#6694514yes—
638C2×C4#6694814yes—
639C2×C4#6695014yes—
640C2×C4C2×(C2×D11)⋊C418yes—
641C2×C4C2×(C2×D11)⋊C414yes—
642C2×C4#6699114yes—
643C2×C4#6699914yes—
644C22C2×C4⋊C4×D1111yescharacteristic
645C22C2×#6694511yescharacteristic
646C22C2×#6694811yescharacteristic
647C22C2×#6695011yescharacteristic
648C22C4×#434111yescharacteristic
649C22#1062307711yescharacteristic
650C22#1062308511yescharacteristic
651C22#1062308611yescharacteristic
652C22C4×Q8×D1111yescharacteristic
653C22#1062310311yescharacteristic
654C22Q8×D4411yescharacteristic
655C22#1062310711yescharacteristic
656C22#1062312911yescharacteristic
657C22#1062313011yescharacteristic
658C22#1062313111yescharacteristic
659C22#1062313411yescharacteristic
660C22#1062315311yescharacteristic
661C22#1062315611yescharacteristic
662C22#1062316311yescharacteristic
663C22#1062316411yescharacteristic
664C22#1062321611yescharacteristic
665C22#1062321611yescharacteristic
666C22#1062322211yescharacteristic
667C22#1062322811yescharacteristic
668C22#1062325211yescharacteristic
669C22#1062325311yescharacteristic
670C22#1062325911yescharacteristic
671C22#1062326411yescharacteristic
672C22C22×(C2×D11)⋊C411yescharacteristic
673C22C2×#6699111yescharacteristic
674C22#1062333711yescharacteristic
675C22C2×#6699911yescharacteristic
676C22Q8×C22⋊D1111yescharacteristic
677C22#1062335511yescharacteristic
678C22#1062336211yescharacteristic
679C4—28no—
680C4—42no—
681C4—42no—
682C4—82no—
683C4—224no—
684C4—228no—
685C4—442no—
686C4—442no—
687C4—442no—
688C4—882no—
689C4#1062260018yes—
690C2C2×#1062260011yescharacteristic
691C2#1307108711yescharacteristic
692C2#1307126311yescharacteristic
693C2#1307144111yescharacteristic
694C2Q8×(C2×D11)⋊C411yescharacteristic
695C2#1307153011yescharacteristic
696C2#1307153511yescharacteristic
697C2#1307217811yescharacteristic
698C2#1307218011yescharacteristic
699C2#1307221111yescharacteristic
700C2#1307221311yescharacteristic
701C2#1307245111yescharacteristic
702C2#1307245311yescharacteristic
703C2#1307247311yescharacteristic
704C2#1307247511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#389C2
socle, prime radical, cosocleC24×C11C24
hypercenterC2×#389D11
hypocenterC11#13935
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
25. C2×#66940C4semidirect
102. C11⋊#95Q8semidirect
188. C2×Dic22C4⋊C4semidirect
550. C11#13935semidirect

Maximal subgroups

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

subgroupindex
C22×#669402
C2×#106225422
C2×#106225872
C2×#106225982
#130668702
#130668662
#130668452
#130668402
C4×C11⋊#952
C2×C11×#3892
#1393511