Finite Group Databasebeta

← C2×#21451148 #29850481

Subgroups — C2×#21451148 #29850481

Order 15616.

2550 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451148C2116yesmaximal, direct product factor
2C2×#16839691C211yesmaximal, characteristic, complemented
3C2×#16839689C211yesmaximal, characteristic, complemented
4C2×#16839679C211yesmaximal, characteristic
5C2×#16839651C211yesmaximal, characteristic, complemented
6C2×#16839651C211yesmaximal, characteristic, complemented
7C2×#16839647C211yesmaximal, characteristic, complemented
8C2×#16839643C211yesmaximal, characteristic, complemented
9C2×#16839640C211yesmaximal, characteristic
10C2×#16839640C211yesmaximal, characteristic
11C2×#16839633C211yesmaximal, characteristic, complemented
12C2×#16839629C211yesmaximal, characteristic, complemented
13C2×#16839619C211yesmaximal, characteristic, complemented
14C2×#16839609C211yesmaximal, characteristic, complemented
15C2×#16839609C211yesmaximal, characteristic, complemented
16C2×C61×#400C211yesmaximal, characteristic, complemented
17C23×D244C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
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×C4×Dic61C2211yescharacteristic
34C22×C4×Dic61C2211yescharacteristic
35C22×C4×Dic61C2211yescharacteristic
36#16839691C2218yescomplemented
37#16839689C2218yescomplemented
38#16839679C2218yes—
39#16839651C2218yescomplemented
40#16839651C2218yescomplemented
41#16839647C2218yescomplemented
42#16839643C2218yescomplemented
43#16839640C2218yes—
44#16839640C2218yes—
45#16839633C2218yescomplemented
46#16839629C2218yescomplemented
47#16839619C2218yescomplemented
48#16839609C2218yescomplemented
49#16839609C2218yescomplemented
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C22×C4⋊C4×C61C2211yescharacteristic
60C22×C4⋊C4×C61C2211yescharacteristic
61C61×#400C2218yescomplemented
62C2×#95×C61C2211yescharacteristic
63C2×#95×C61C2211yescharacteristic
64C2×#95×C61C2211yescharacteristic
65C2×#95×C61C2211yescharacteristic
66C2×#95×C61C2211yescharacteristic
67C24×D61C2311yescharacteristic
68C24×D61C2311yescharacteristic
69C22×D244—24no—
70C22×D244—24no—
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—24no—
82C22×C4×D61—42no—
83C22×C4×D61—42no—
84C22×C4×D61—42no—
85C22×C4×D61C2314yes—
86C22×C4×D61C2314yes—
87C2×C4⋊Dic61—24no—
88C2×C4⋊Dic61C2314yes—
89C2×#11758196—24no—
90C2×#11758196—42no—
91C2×#11758196C2314yes—
92C2×#11758196C2314yes—
93C2×#11758198—24no—
94C2×#11758198—24no—
95C2×#11758198—24no—
96C2×#11758198—24no—
97C2×#11758198—24no—
98C2×#11758198—24no—
99C2×#11758198—24no—
100C2×#11758198—42no—
101C2×#11758198—42no—
102C2×#11758198—42no—
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—42no—
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—
127#14519684C2314yes—
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C2×C4⋊C4×C61—42no—
136C2×C4⋊C4×C61—42no—
137C2×C4⋊C4×C61C2314yes—
138C2×C4⋊C4×C61C2314yes—
139#95×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#4114yes—
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—22no—
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—28no—
215C2×D244—44no—
216C2×D244—416no—
217C2×C4×D61—28no—
218C2×C4×D61—28no—
219C2×C4×D61—28no—
220C2×C4×D61—44no—
221C2×C4×D61—44no—
222C2×C4×D61—44no—
223C2×C4×D61—416no—
224C2×C4×D61—416no—
225C4⋊C4×C61—44no—
226C4⋊C4×C61—44no—
227#11758198—28no—
228#11758198—28no—
229#11758198—28no—
230#11758198—28no—
231#11758198—28no—
232#11758198—28no—
233#11758198—28no—
234#11758198—44no—
235#11758198—44no—
236#11758198—44no—
237C4⋊Dic61—28no—
238#11758196—28no—
239#11758196—44no—
240C4×Dic61—28no—
241C4×Dic61—44no—
242C4×Dic61—44no—
243C23×C61C2×#4112yes—
244C23×C61C2×#4112yes—
245C23×C61C2×#4112yes—
246C23×C61C2×#4112yes—
247C23×C61C2×#4112yes—
248C23×C61H(5,𝔽2)12yes—
249C23×C61H(5,𝔽2)12yes—
250C23×C61C2511yescharacteristic
251C22×D61—28no—
252C22×D61—28no—
253C22×D61—28no—
254C22×D61—28no—
255C22×D61—28no—
256C22×D61—28no—
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—22no—
267C22×D61—22no—
268C22×D61—22no—
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—
278C22×D61C2×#4114yes—
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—22no—
300C2×C4×C61—44no—
301C2×C4×C61—44no—
302C2×C4×C61—44no—
303C2×C4×C61—44no—
304C2×C4×C61—44no—
305C2×C4×C61—44no—
306C2×C4×C61C2×#4114yes—
307C2×Dic61—28no—
308C2×Dic61—28no—
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—22no—
325C2×Dic61—44no—
326C2×Dic61—44no—
327C2×Dic61—44no—
328C2×Dic61—44no—
329C2×Dic61C2×#4114yes—
330C2×Dic61C2×#4114yes—
331D244—416no—
332C4×D61—416no—
333C4×D61—416no—
334C2×#2578—611nomaximal, Sylow
335C22×C61#52914yes—
336C22×C61#52914yes—
337C22×C61#53814yes—
338C22×C61#55114yes—
339C22×C61#55114yes—
340C22×C61#55314yes—
341C22×C61#55314yes—
342C22×C61C22×#4111yescharacteristic
343C22×C61C22×#4111yescharacteristic
344C22×C61C22×#4111yescharacteristic
345C22×C61C22×#4111yescharacteristic
346C22×C61C22×#4111yescharacteristic
347C22×C61C2×H(5,𝔽2)11yescharacteristic
348C22×C61C2×H(5,𝔽2)11yescharacteristic
349C2×D61—24no—
350C2×D61—24no—
351C2×D61—24no—
352C2×D61—24no—
353C2×D61—24no—
354C2×D61—24no—
355C2×D61—416no—
356C2×D61—416no—
357C2×D61—42no—
358C2×D61—42no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C4×C61—24no—
366C4×C61—42no—
367C4×C61—42no—
368C4×C61—42no—
369C4×C61—42no—
370C4×C61—42no—
371C4×C61—42no—
372Dic61—24no—
373Dic61—24no—
374Dic61—42no—
375Dic61—42no—
376Dic61—42no—
377Dic61—42no—
378#2578—6116no—
379C2×#400D6111yescharacteristic, complemented
380C2×#397—611no—
381C2×#397—611no—
382C2×#394—611no—
383C2×#388—611no—
384C2×#388—611no—
385C2×#387—611no—
386C2×#387—611no—
387C2×#386—611no—
388C2×#386—611no—
389C2×#385—611no—
390C2×#383—611no—
391C2×#380—611no—
392C2×C4×C22⋊C4—611no—
393C2×C4×C22⋊C4—611no—
394C2×C61#257818yescomplemented
395C2×C61C2×#52911yescharacteristic
396C2×C61C2×#52911yescharacteristic
397C2×C61C2×#53811yescharacteristic
398C2×C61C2×#55111yescharacteristic
399C2×C61C2×#55111yescharacteristic
400C2×C61C2×#55311yescharacteristic
401C2×C61C2×#55311yescharacteristic
402D61—44no—
403D61—44no—
404C23×D4—611no—
405C24×C4—611no—
406C24×C4—611no—
407C22×C4⋊C4—611no—
408C22×C4⋊C4—611no—
409C22×C4⋊C4—611no—
410C22×C4⋊C4C2×D6111yescharacteristic
411C22×C4⋊C4C2×D6111yescharacteristic
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×C22⋊C4—611no—
422C22×C42—611no—
423C22×C42—611no—
424C22×C42—611no—
425#400C2×D6118yescomplemented
426#397—618no—
427#397—618no—
428#394—618no—
429#388—618no—
430#388—618no—
431#387—618no—
432#387—618no—
433#386—618no—
434#386—618no—
435#385—618no—
436#383—618no—
437#380—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×#95—611no—
449C2×#95C2×D6111yescharacteristic
450C2×#95C2×D6111yescharacteristic
451C2×#95C2×D6111yescharacteristic
452C2×#95C2×D6111yescharacteristic
453C2×#95C2×D6111yescharacteristic
454C61C2×#257811yescharacteristic, complemented, Sylow
455C25—611no—
456C25—611no—
457C22×D4—614no—
458C22×D4—1224no—
459C22×D4—1224no—
460C22×D4—2442no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—614no—
468C23×C4—614no—
469C23×C4—1224no—
470C23×C4—1224no—
471C23×C4—1224no—
472C23×C4—2442no—
473C23×C4—2442no—
474C23×C4—2442no—
475C23×C4C22×D6111yescharacteristic
476C23×C4C22×D6111yescharacteristic
477C23×C4C22×D6111yescharacteristic
478C23×C4C22×D6111yescharacteristic
479C23×C4C22×D6111yescharacteristic
480C23×C4C22×D6111yescharacteristic
481C23×C4C22×D6111yescharacteristic
482C2×C4⋊C4—42no—
483C2×C4⋊C4—42no—
484C2×C4⋊C4—614no—
485C2×C4⋊C4—614no—
486C2×C4⋊C4—614no—
487C2×C4⋊C4—1224no—
488C2×C4⋊C4—1224no—
489C2×C4⋊C4—2442no—
490C2×C4⋊C4C22×D6114yes—
491C2×C4⋊C4C22×D6114yes—
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—614no—
500C2×C22⋊C4—614no—
501C2×C22⋊C4—614no—
502C2×C22⋊C4—1224no—
503C2×C22⋊C4—1224no—
504C2×C22⋊C4—1224no—
505C2×C22⋊C4—1224no—
506C2×C22⋊C4—1224no—
507C2×C22⋊C4—1224no—
508C2×C22⋊C4—1224no—
509C2×C22⋊C4—2442no—
510C2×C22⋊C4—2442no—
511C2×C22⋊C4—2442no—
512C2×C42—614no—
513C2×C42—614no—
514C2×C42—614no—
515C2×C42—1224no—
516C2×C42—2442no—
517C2×C42—2442no—
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#95—614no—
527#95C22×D6114yes—
528#95C22×D6114yes—
529#95C22×D6114yes—
530#95C22×D6114yes—
531#95C22×D6114yes—
532C24—614no—
533C24—614no—
534C24—612no—
535C24—612no—
536C24—1222no—
537C24—1222no—
538C24—1222no—
539C24—1222no—
540C24—1222no—
541C24—1222no—
542C24—1222no—
543C24—1222no—
544C24—1222no—
545C24—1222no—
546C24—1222no—
547C24—1222no—
548C24C23×D6111yescharacteristic
549C2×D4—1228no—
550C2×D4—1228no—
551C2×D4—2444no—
552C2×D4—24416no—
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—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—614no—
574C22×C4—614no—
575C22×C4—612no—
576C22×C4—612no—
577C22×C4—612no—
578C22×C4—612no—
579C22×C4—612no—
580C22×C4—612no—
581C22×C4—1228no—
582C22×C4—1228no—
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—1222no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1228no—
600C22×C4—2444no—
601C22×C4—2444no—
602C22×C4—2444no—
603C22×C4—24416no—
604C22×C4—24416no—
605C22×C4#1175822614yes—
606C22×C4C23×D6112yes—
607C22×C4C23×D6112yes—
608C22×C4C23×D6112yes—
609C22×C4C23×D6112yes—
610C22×C4C23×D6112yes—
611C22×C4C23×D6112yes—
612C22×C4C23×D6112yes—
613C4⋊C4—44no—
614C4⋊C4—44no—
615C4⋊C4—1228no—
616C4⋊C4—1228no—
617C4⋊C4—2444no—
618C22⋊C4—1228no—
619C22⋊C4—1228no—
620C22⋊C4—1228no—
621C22⋊C4—1228no—
622C22⋊C4—1228no—
623C22⋊C4—1228no—
624C22⋊C4—1228no—
625C22⋊C4—2444no—
626C22⋊C4—2444no—
627C22⋊C4—2444no—
628C42—1228no—
629C42—2444no—
630C42—2444no—
631C23—614no—
632C23—614no—
633C23—1228no—
634C23—1228no—
635C23—1228no—
636C23—1228no—
637C23—1222no—
638C23—1222no—
639C23—1222no—
640C23—1222no—
641C23—1222no—
642C23—1222no—
643C23—1222no—
644C23—1222no—
645C23—1222no—
646C23—1222no—
647C23—1222no—
648C23—1222no—
649C23—1228no—
650C23—1228no—
651C23—2444no—
652C23—2444no—
653C23—2444no—
654C23—2444no—
655C23—2444no—
656C23—2444no—
657C23—2444no—
658C23—2444no—
659C23#41×D6112yes—
660C23#41×D6112yes—
661C23#41×D6112yes—
662C23#41×D6112yes—
663C23C2×#1175822612yes—
664C23#1451982212yes—
665C23#1451982312yes—
666C23C24×D6111yescharacteristic
667D4—24416no—
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—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—44no—
692C2×C4—44no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—614no—
696C2×C4—614no—
697C2×C4—1222no—
698C2×C4—1222no—
699C2×C4—1222no—
700C2×C4—1222no—
701C2×C4—1228no—
702C2×C4—1228no—
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—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—1222no—
715C2×C4—24416no—
716C2×C4—24416no—
717C2×C4—2444no—
718C2×C4—2444no—
719C2×C4—2444no—
720C2×C4—2444no—
721C2×C4C2×#1175822614yes—
722C22—1224no—
723C22—1224no—
724C22—1224no—
725C22—1224no—
726C22—1224no—
727C22—1224no—
728C22—2442no—
729C22—2442no—
730C22—24416no—
731C22—24416no—
732C22—2442no—
733C22—2442no—
734C22—2442no—
735C22—2442no—
736C22—2442no—
737C22—2442no—
738C22#1684029514yes—
739C22#1684029714yes—
740C22#1684034814yes—
741C22#1684043914yes—
742C22#1684044214yes—
743C22#1684046314yes—
744C22#1684046514yes—
745C22C2×#41×D6111yescharacteristic
746C22C2×#41×D6111yescharacteristic
747C22C2×#41×D6111yescharacteristic
748C22C2×#41×D6111yescharacteristic
749C22C22×#1175822611yescharacteristic
750C22C2×#1451982211yescharacteristic
751C22C2×#1451982311yescharacteristic
752C4—24no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—42no—
759C4—1224no—
760C4—1224no—
761C4—2442no—
762C4—2442no—
763C4—2442no—
764C4—2442no—
765C2—2444no—
766C2—2444no—
767C2#2145114818yesdirect product factor
768C2C2×#1684029511yescharacteristic
769C2C2×#1684029711yescharacteristic
770C2C2×#1684034811yescharacteristic
771C2C2×#1684043911yescharacteristic
772C2C2×#1684044211yescharacteristic
773C2C2×#1684046311yescharacteristic
774C2C2×#1684046511yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#400C2
socleC24×C61C24
prime radicalC23×D244C22
hypercenterC2×#400D61
hypocenterC61C2×#2578
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. #21451148C2direct (N × H)
2. C2×#16839691C2semidirect
3. C2×#16839689C2semidirect
5. C2×#16839651C2semidirect
6. C2×#16839651C2semidirect
7. C2×#16839647C2semidirect
8. C2×#16839643C2semidirect
11. C2×#16839633C2semidirect
12. C2×#16839629C2semidirect
13. C2×#16839619C2semidirect
14. C2×#16839609C2semidirect
15. C2×#16839609C2semidirect
16. C2×C61×#400C2semidirect
36. #16839691C22semidirect
37. #16839689C22semidirect
39. #16839651C22semidirect
40. #16839651C22semidirect
41. #16839647C22semidirect
42. #16839643C22semidirect
45. #16839633C22semidirect
46. #16839629C22semidirect
47. #16839619C22semidirect
48. #16839609C22semidirect
49. #16839609C22semidirect
61. C61×#400C22semidirect
379. C2×#400D61semidirect
394. C2×C61#2578semidirect
425. #400C2×D61semidirect
454. C61C2×#2578semidirect
767. C2#21451148direct (N × H)

Maximal subgroups

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

subgroupindex
#214511482
C2×#168396912
C2×#168396892
C2×#168396792
C2×#168396512
C2×#168396472
C2×#168396432
C2×#168396402
C2×#168396332
C2×#168396292
C2×#168396192
C2×#168396092
C2×C61×#4002
C2×#257861