Finite Group Databasebeta

← C2×#21450483 #29849028

Subgroups — C2×#21450483 #29849028

Order 15616.

2442 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450483C2116yesmaximal, direct product factor
2C2×#16839691C211yesmaximal, characteristic, complemented
3C2×#16839684C211yesmaximal, characteristic, complemented
4C2×#16839680C211yesmaximal, characteristic
5C2×#16839679C211yesmaximal, characteristic
6C2×#16839658C211yesmaximal, characteristic, complemented
7C2×#16839654C211yesmaximal, characteristic, complemented
8C2×#16839653C211yesmaximal, characteristic, complemented
9C2×#16839652C211yesmaximal, characteristic, complemented
10C2×#16839651C211yesmaximal, characteristic, complemented
11C2×#16839640C211yesmaximal, characteristic
12C2×#16839629C211yesmaximal, characteristic, complemented
13C2×#16839626C211yesmaximal, characteristic, complemented
14C2×C4×#11758198C211yesmaximal, characteristic, complemented
15C2×#16839609C211yesmaximal, characteristic, complemented
16C2×C61×#387C211yesmaximal, characteristic, complemented
17C23×D244C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×#11758196C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758198C2211yescharacteristic
24C22×#11758198C2211yescharacteristic
25C22×#11758198C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839691C2218yescomplemented
38#16839684C2218yescomplemented
39#16839680C2218yes—
40#16839679C2218yes—
41#16839658C2218yescomplemented
42#16839654C2218yescomplemented
43#16839653C2218yescomplemented
44#16839652C2218yescomplemented
45#16839651C2218yescomplemented
46#16839640C2218yes—
47#16839629C2218yescomplemented
48#16839626C2218yescomplemented
49C4×#11758198C2218yescomplemented
50#16839609C2218yescomplemented
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C22×C4⋊C4×C61C2211yescharacteristic
60C22×C4⋊C4×C61C2211yescharacteristic
61C22×C42×C61C2211yescharacteristic
62C61×#387C2218yescomplemented
63C2×#95×C61C2211yescharacteristic
64C2×#95×C61C2211yescharacteristic
65C2×#95×C61C2211yescharacteristic
66C2×#95×C61C2211yescharacteristic
67C24×D61C2311yescharacteristic
68C24×D61C2311yescharacteristic
69C22×D244—24no—
70C22×D244—42no—
71C22×D244—42no—
72C22×D244C2314yes—
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C22×C4×D61—24no—
80C22×C4×D61—24no—
81C22×C4×D61—42no—
82C22×C4×D61C2314yes—
83C2×C4⋊Dic61—24no—
84C2×C4⋊Dic61C2314yes—
85C2×#11758196—42no—
86C2×#11758196—42no—
87C2×#11758196—42no—
88C2×#11758196C2314yes—
89C2×#11758196C2314yes—
90C2×#11758196C2314yes—
91C2×#11758198—24no—
92C2×#11758198—24no—
93C2×#11758198—24no—
94C2×#11758198—24no—
95C2×#11758198—24no—
96C2×#11758198—24no—
97C2×#11758198—24no—
98C2×#11758198—24no—
99C2×#11758198—42no—
100C2×#11758198—42no—
101C2×#11758198—42no—
102C2×#11758198C2314yes—
103C2×#11758198C2314yes—
104C2×#11758198C2314yes—
105C2×#11758198C2314yes—
106C2×#11758198C2314yes—
107C2×#11758198C2314yes—
108C2×#11758198C2314yes—
109C2×#11758198C2314yes—
110C2×#11758198C2314yes—
111C2×#11758198C2314yes—
112C2×#11758198C2314yes—
113C2×C4×Dic61—24no—
114C2×C4×Dic61—24no—
115C2×C4×Dic61—42no—
116C2×C4×Dic61C2314yes—
117C2×C4×Dic61C2314yes—
118C2×C4×Dic61C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C2×C4⋊C4×C61—24no—
135C2×C4⋊C4×C61—42no—
136C2×C4⋊C4×C61C2314yes—
137C2×C4⋊C4×C61C2314yes—
138C2×C42×C61—42no—
139C2×C42×C61C2314yes—
140#95×C61C2314yes—
141#95×C61C2314yes—
142#95×C61C2314yes—
143#95×C61C2314yes—
144C24×C61C2411yescharacteristic
145C23×D61—22no—
146C23×D61—22no—
147C23×D61—22no—
148C23×D61—22no—
149C23×D61—22no—
150C23×D61—22no—
151C23×D61—22no—
152C23×D61—22no—
153C23×D61—22no—
154C23×D61—22no—
155C23×D61—22no—
156C23×D61—22no—
157C23×D61—22no—
158C23×D61#4114yes—
159C23×D61C2412yes—
160C23×D61C2412yes—
161C22×C4×C61—22no—
162C22×C4×C61—22no—
163C22×C4×C61—22no—
164C22×C4×C61—22no—
165C22×C4×C61—22no—
166C22×C4×C61—22no—
167C22×C4×C61—22no—
168C22×C4×C61—22no—
169C22×C4×C61—22no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—22no—
178C22×C4×C61—22no—
179C22×C4×C61—22no—
180C22×C4×C61#4114yes—
181C22×C4×C61#4114yes—
182C22×C4×C61C2412yes—
183C22×C4×C61C2412yes—
184C22×C4×C61C2412yes—
185C22×C4×C61C2412yes—
186C22×C4×C61C2412yes—
187C22×C4×C61C2412yes—
188C22×C4×C61C2412yes—
189C22×Dic61—22no—
190C22×Dic61—22no—
191C22×Dic61—22no—
192C22×Dic61—22no—
193C22×Dic61—22no—
194C22×Dic61—22no—
195C22×Dic61—22no—
196C22×Dic61—22no—
197C22×Dic61—22no—
198C22×Dic61—22no—
199C22×Dic61—22no—
200C22×Dic61—22no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61#4114yes—
206C22×Dic61#4114yes—
207C22×Dic61C2412yes—
208C22×Dic61C2412yes—
209C22×Dic61C2412yes—
210C22×Dic61C2412yes—
211C22×Dic61C2412yes—
212C22×Dic61C2412yes—
213C2×D244—28no—
214C2×D244—44no—
215C2×D244—44no—
216C2×D244—416no—
217C2×C4×D61—28no—
218C2×C4×D61—28no—
219C2×C4×D61—44no—
220C2×C4×D61—416no—
221C4⋊C4×C61—28no—
222C4⋊C4×C61—44no—
223C42×C61—44no—
224#11758198—28no—
225#11758198—28no—
226#11758198—28no—
227#11758198—28no—
228#11758198—28no—
229#11758198—28no—
230#11758198—28no—
231#11758198—28no—
232#11758198—44no—
233#11758198—44no—
234#11758198—44no—
235C4⋊Dic61—28no—
236#11758196—44no—
237#11758196—44no—
238#11758196—44no—
239C4×Dic61—28no—
240C4×Dic61—28no—
241C4×Dic61—44no—
242C23×C61C2×#4112yes—
243C23×C61C2×#4112yes—
244C23×C61C2×#4112yes—
245C23×C61C2×#4112yes—
246C23×C61C2×#4112yes—
247C23×C61H(5,𝔽2)12yes—
248C23×C61H(5,𝔽2)12yes—
249C23×C61C2511yescharacteristic
250C22×D61—28no—
251C22×D61—28no—
252C22×D61—28no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—22no—
258C22×D61—22no—
259C22×D61—22no—
260C22×D61—22no—
261C22×D61—22no—
262C22×D61—22no—
263C22×D61—22no—
264C22×D61—22no—
265C22×D61—22no—
266C22×D61—44no—
267C22×D61—44no—
268C22×D61—44no—
269C22×D61—44no—
270C22×D61—44no—
271C22×D61—44no—
272C22×D61—44no—
273C22×D61—44no—
274C22×D61—44no—
275C22×D61—44no—
276C22×D61—44no—
277C22×D61C2×#4114yes—
278C2×C4×C61—28no—
279C2×C4×C61—28no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—22no—
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—22no—
288C2×C4×C61—22no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—44no—
300C2×C4×C61—44no—
301C2×C4×C61—44no—
302C2×C4×C61—44no—
303C2×C4×C61—44no—
304C2×C4×C61C2×#4114yes—
305C2×C4×C61C2×#4114yes—
306C2×Dic61—28no—
307C2×Dic61—28no—
308C2×Dic61—22no—
309C2×Dic61—22no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—22no—
313C2×Dic61—22no—
314C2×Dic61—22no—
315C2×Dic61—22no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—22no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—44no—
325C2×Dic61—44no—
326C2×Dic61—44no—
327C2×Dic61—44no—
328C2×Dic61C2×#4114yes—
329C2×Dic61C2×#4114yes—
330D244—416no—
331C4×D61—416no—
332C2×#2518—611nomaximal, Sylow
333C22×C61#52914yes—
334C22×C61#52914yes—
335C22×C61#53814yes—
336C22×C61#55114yes—
337C22×C61#55314yes—
338C22×C61#55314yes—
339C22×C61#55514yes—
340C22×C61C22×#4111yescharacteristic
341C22×C61C22×#4111yescharacteristic
342C22×C61C22×#4111yescharacteristic
343C22×C61C22×#4111yescharacteristic
344C22×C61C22×#4111yescharacteristic
345C22×C61C2×H(5,𝔽2)11yescharacteristic
346C22×C61C2×H(5,𝔽2)11yescharacteristic
347C2×D61—24no—
348C2×D61—24no—
349C2×D61—24no—
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—42no—
354C2×D61—416no—
355C2×D61—42no—
356C2×D61—42no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—88no—
363C4×C61—24no—
364C4×C61—24no—
365C4×C61—42no—
366C4×C61—42no—
367C4×C61—42no—
368C4×C61—42no—
369C4×C61—42no—
370Dic61—24no—
371Dic61—24no—
372Dic61—42no—
373Dic61—42no—
374Dic61—42no—
375Dic61—42no—
376#2518—6116no—
377C2×#397—611no—
378C2×#396—611no—
379C2×#394—611no—
380C2×#394—611no—
381C2×#389—611no—
382C2×#388—611no—
383C2×#388—611no—
384C2×#388—611no—
385C2×#388—611no—
386C2×#387D6111yescharacteristic, complemented
387C2×#386—611no—
388C2×#383—611no—
389C2×#382—611no—
390C2×C4×C22⋊C4—611no—
391C2×C4×C22⋊C4—611no—
392C2×C61#251818yescomplemented
393C2×C61C2×#52911yescharacteristic
394C2×C61C2×#52911yescharacteristic
395C2×C61C2×#53811yescharacteristic
396C2×C61C2×#55111yescharacteristic
397C2×C61C2×#55311yescharacteristic
398C2×C61C2×#55311yescharacteristic
399C2×C61C2×#55511yescharacteristic
400D61—44no—
401D61—82no—
402C23×D4—611no—
403C24×C4—611no—
404C22×C4⋊C4—611no—
405C22×C4⋊C4—611no—
406C22×C4⋊C4—611no—
407C22×C4⋊C4—611no—
408C22×C4⋊C4C2×D6111yescharacteristic
409C22×C4⋊C4C2×D6111yescharacteristic
410C22×C22⋊C4—611no—
411C22×C22⋊C4—611no—
412C22×C22⋊C4—611no—
413C22×C22⋊C4—611no—
414C22×C22⋊C4—611no—
415C22×C22⋊C4—611no—
416C22×C22⋊C4—611no—
417C22×C22⋊C4—611no—
418C22×C22⋊C4—611no—
419C22×C22⋊C4—611no—
420C22×C22⋊C4—611no—
421C22×C42—611no—
422C22×C42—611no—
423C22×C42—611no—
424C22×C42C2×D6111yescharacteristic
425#397—618no—
426#396—618no—
427#394—618no—
428#394—618no—
429#389—618no—
430#388—618no—
431#388—618no—
432#388—618no—
433#388—618no—
434#387C2×D6118yescomplemented
435#386—618no—
436#383—618no—
437#382—618no—
438C4×C22⋊C4—618no—
439C4×C22⋊C4—618no—
440C2×#95—611no—
441C2×#95—611no—
442C2×#95—611no—
443C2×#95—611no—
444C2×#95—611no—
445C2×#95—611no—
446C2×#95—611no—
447C2×#95—611no—
448C2×#95C2×D6111yescharacteristic
449C2×#95C2×D6111yescharacteristic
450C2×#95C2×D6111yescharacteristic
451C2×#95C2×D6111yescharacteristic
452C61C2×#251811yescharacteristic, complemented, Sylow
453C25—611no—
454C25—611no—
455C22×D4—614no—
456C22×D4—1224no—
457C22×D4—2442no—
458C22×D4—2442no—
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—614no—
466C23×C4—1224no—
467C23×C4—1224no—
468C23×C4—2442no—
469C23×C4C22×D6111yescharacteristic
470C23×C4C22×D6111yescharacteristic
471C23×C4C22×D6111yescharacteristic
472C23×C4C22×D6111yescharacteristic
473C23×C4C22×D6111yescharacteristic
474C23×C4C22×D6111yescharacteristic
475C23×C4C22×D6111yescharacteristic
476C2×C4⋊C4—24no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—614no—
479C2×C4⋊C4—614no—
480C2×C4⋊C4—614no—
481C2×C4⋊C4—614no—
482C2×C4⋊C4—1224no—
483C2×C4⋊C4—2442no—
484C2×C4⋊C4—2442no—
485C2×C4⋊C4—2442no—
486C2×C4⋊C4C22×D6114yes—
487C2×C4⋊C4C22×D6114yes—
488C2×C22⋊C4—614no—
489C2×C22⋊C4—614no—
490C2×C22⋊C4—614no—
491C2×C22⋊C4—614no—
492C2×C22⋊C4—614no—
493C2×C22⋊C4—614no—
494C2×C22⋊C4—614no—
495C2×C22⋊C4—614no—
496C2×C22⋊C4—614no—
497C2×C22⋊C4—614no—
498C2×C22⋊C4—614no—
499C2×C22⋊C4—1224no—
500C2×C22⋊C4—1224no—
501C2×C22⋊C4—1224no—
502C2×C22⋊C4—1224no—
503C2×C22⋊C4—1224no—
504C2×C22⋊C4—1224no—
505C2×C22⋊C4—1224no—
506C2×C22⋊C4—1224no—
507C2×C22⋊C4—2442no—
508C2×C22⋊C4—2442no—
509C2×C22⋊C4—2442no—
510C2×C42—42no—
511C2×C42—614no—
512C2×C42—614no—
513C2×C42—614no—
514C2×C42—1224no—
515C2×C42—1224no—
516C2×C42—2442no—
517C2×C42C22×D6114yes—
518#95—614no—
519#95—614no—
520#95—614no—
521#95—614no—
522#95—614no—
523#95—614no—
524#95—614no—
525#95—614no—
526#95C22×D6114yes—
527#95C22×D6114yes—
528#95C22×D6114yes—
529#95C22×D6114yes—
530C24—614no—
531C24—612no—
532C24—612no—
533C24—1222no—
534C24—1222no—
535C24—1222no—
536C24—1222no—
537C24—1222no—
538C24—1222no—
539C24—1222no—
540C24—1222no—
541C24—1222no—
542C24—1222no—
543C24—1222no—
544C24—1222no—
545C24—1222no—
546C24C23×D6111yescharacteristic
547C2×D4—1228no—
548C2×D4—2444no—
549C2×D4—2444no—
550C2×D4—24416no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—614no—
571C22×C4—614no—
572C22×C4—612no—
573C22×C4—612no—
574C22×C4—612no—
575C22×C4—612no—
576C22×C4—612no—
577C22×C4—612no—
578C22×C4—1228no—
579C22×C4—1222no—
580C22×C4—1222no—
581C22×C4—1222no—
582C22×C4—1222no—
583C22×C4—1222no—
584C22×C4—1222no—
585C22×C4—1222no—
586C22×C4—1222no—
587C22×C4—1222no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1228no—
596C22×C4—2444no—
597C22×C4—24416no—
598C22×C4#1175822214yes—
599C22×C4#1175822614yes—
600C22×C4C23×D6112yes—
601C22×C4C23×D6112yes—
602C22×C4C23×D6112yes—
603C22×C4C23×D6112yes—
604C22×C4C23×D6112yes—
605C22×C4C23×D6112yes—
606C22×C4C23×D6112yes—
607C4⋊C4—28no—
608C4⋊C4—44no—
609C4⋊C4—1228no—
610C4⋊C4—2444no—
611C4⋊C4—2444no—
612C4⋊C4—2444no—
613C22⋊C4—1228no—
614C22⋊C4—1228no—
615C22⋊C4—1228no—
616C22⋊C4—1228no—
617C22⋊C4—1228no—
618C22⋊C4—1228no—
619C22⋊C4—1228no—
620C22⋊C4—1228no—
621C22⋊C4—2444no—
622C22⋊C4—2444no—
623C22⋊C4—2444no—
624C42—44no—
625C42—1228no—
626C42—1228no—
627C42—2444no—
628C23—614no—
629C23—1228no—
630C23—1228no—
631C23—1222no—
632C23—1222no—
633C23—1222no—
634C23—1222no—
635C23—1222no—
636C23—1222no—
637C23—1228no—
638C23—1222no—
639C23—1222no—
640C23—1222no—
641C23—1222no—
642C23—1222no—
643C23—1222no—
644C23—1222no—
645C23—2444no—
646C23—2444no—
647C23—2444no—
648C23—2444no—
649C23—2444no—
650C23—2444no—
651C23—2444no—
652C23—2444no—
653C23—2444no—
654C23—2444no—
655C23—2444no—
656C23#41×D6112yes—
657C23#41×D6112yes—
658C23#41×D6112yes—
659C23C2×#1175822212yes—
660C23C2×#1175822612yes—
661C23#1451982212yes—
662C23#1451982312yes—
663C23C24×D6111yescharacteristic
664D4—24416no—
665C2×C4—28no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—28no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—614no—
692C2×C4—614no—
693C2×C4—1228no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1228no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1222no—
702C2×C4—1222no—
703C2×C4—1222no—
704C2×C4—1222no—
705C2×C4—1222no—
706C2×C4—1222no—
707C2×C4—1222no—
708C2×C4—1222no—
709C2×C4—1222no—
710C2×C4—1222no—
711C2×C4—24416no—
712C2×C4—2444no—
713C2×C4—2444no—
714C2×C4—2444no—
715C2×C4—2444no—
716C2×C4C2×#1175822214yes—
717C2×C4C2×#1175822614yes—
718C22—1224no—
719C22—1224no—
720C22—1224no—
721C22—4888no—
722C22—2442no—
723C22—2442no—
724C22—2442no—
725C22—2442no—
726C22—2442no—
727C22—2442no—
728C22—2442no—
729C22—2442no—
730C22—2442no—
731C22—2442no—
732C22—2442no—
733C22—24416no—
734C22#1684029514yes—
735C22#1684029914yes—
736C22#1684034814yes—
737C22#1684043914yes—
738C22#1684046114yes—
739C22#1684046514yes—
740C22#1684047514yes—
741C22C2×#41×D6111yescharacteristic
742C22C2×#41×D6111yescharacteristic
743C22C2×#41×D6111yescharacteristic
744C22C22×#1175822211yescharacteristic
745C22C22×#1175822611yescharacteristic
746C22C2×#1451982211yescharacteristic
747C22C2×#1451982311yescharacteristic
748C4—24no—
749C4—24no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—1224no—
756C4—1224no—
757C4—2442no—
758C4—2442no—
759C4—2442no—
760C4—2442no—
761C2—4882no—
762C2—2444no—
763C2#2145048318yesdirect product factor
764C2C2×#1684029511yescharacteristic
765C2C2×#1684029911yescharacteristic
766C2C2×#1684034811yescharacteristic
767C2C2×#1684043911yescharacteristic
768C2C2×#1684046111yescharacteristic
769C2C2×#1684046511yescharacteristic
770C2C2×#1684047511yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#387C2
socleC24×C61C24
prime radicalC23×D244C22
hypercenterC2×#387D61
hypocenterC61C2×#2518
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. #21450483C2direct (N × H)
2. C2×#16839691C2semidirect
3. C2×#16839684C2semidirect
6. C2×#16839658C2semidirect
7. C2×#16839654C2semidirect
8. C2×#16839653C2semidirect
9. C2×#16839652C2semidirect
10. C2×#16839651C2semidirect
12. C2×#16839629C2semidirect
13. C2×#16839626C2semidirect
14. C2×C4×#11758198C2semidirect
15. C2×#16839609C2semidirect
16. C2×C61×#387C2semidirect
37. #16839691C22semidirect
38. #16839684C22semidirect
41. #16839658C22semidirect
42. #16839654C22semidirect
43. #16839653C22semidirect
44. #16839652C22semidirect
45. #16839651C22semidirect
47. #16839629C22semidirect
48. #16839626C22semidirect
49. C4×#11758198C22semidirect
50. #16839609C22semidirect
62. C61×#387C22semidirect
386. C2×#387D61semidirect
392. C2×C61#2518semidirect
434. #387C2×D61semidirect
452. C61C2×#2518semidirect
763. C2#21450483direct (N × H)

Maximal subgroups

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

subgroupindex
#214504832
C2×#168396912
C2×#168396842
C2×#168396802
C2×#168396792
C2×#168396582
C2×#168396542
C2×#168396532
C2×#168396522
C2×#168396512
C2×#168396402
C2×#168396292
C2×#168396262
C2×C4×#117581982
C2×#168396092
C2×C61×#3872
C2×#251861