Finite Group Databasebeta

← C2×#21451159 #29850490

Subgroups — C2×#21451159 #29850490

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#21451159C2116yesmaximal, direct product factor
2C2×#16839702C211yesmaximal, characteristic, complemented
3C2×#16839690C211yesmaximal, characteristic, complemented
4C2×#16839688C211yesmaximal, characteristic, complemented
5C2×#16839678C211yesmaximal, characteristic
6C2×#16839651C211yesmaximal, characteristic, complemented
7C2×#16839649C211yesmaximal, characteristic, complemented
8C2×#16839643C211yesmaximal, characteristic, complemented
9C2×#16839639C211yesmaximal, characteristic
10C2×#16839638C211yesmaximal, characteristic
11C2×#16839634C211yesmaximal, characteristic, complemented
12C2×#16839630C211yesmaximal, characteristic, complemented
13C2×#16839621C211yesmaximal, characteristic, complemented
14C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
15C2×C4×#11758198C211yesmaximal, characteristic, complemented
16C2×C61×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C24×Dic61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×#11758196C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×#11758198C2211yescharacteristic
27C22×#11758198C2211yescharacteristic
28C22×#11758198C2211yescharacteristic
29C22×#11758198C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33#16839702C2218yescomplemented
34#16839690C2218yescomplemented
35#16839688C2218yescomplemented
36#16839678C2218yes—
37#16839651C2218yescomplemented
38#16839649C2218yescomplemented
39#16839643C2218yescomplemented
40#16839639C2218yes—
41#16839638C2218yes—
42#16839634C2218yescomplemented
43#16839630C2218yescomplemented
44#16839621C2218yescomplemented
45C22⋊C4×Dic61C2218yescomplemented
46C4×#11758198C2218yescomplemented
47C2×#14519684C2211yescharacteristic
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C22×C4⋊C4×C61C2211yescharacteristic
60C22×C22⋊C4×C61C2211yescharacteristic
61C22×C22⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C42×C61C2211yescharacteristic
64C61×#388C2218yescomplemented
65C2×#95×C61C2211yescharacteristic
66C2×#95×C61C2211yescharacteristic
67C24×D61C2311yescharacteristic
68C22×C22⋊D61—24no—
69C22×C22⋊D61—24no—
70C22×C22⋊D61—42no—
71C22×C22⋊D61C2314yes—
72C23×Dic61—24no—
73C23×Dic61—42no—
74C23×Dic61—42no—
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2314yes—
83C22×C4×D61—24no—
84C22×C4×D61—24no—
85C22×C4×D61—42no—
86C22×C4×D61C2314yes—
87C2×C4⋊Dic61—42no—
88C2×C4⋊Dic61C2314yes—
89C2×#11758196—24no—
90C2×#11758196—24no—
91C2×#11758196—42no—
92C2×#11758196C2314yes—
93C2×#11758196C2314yes—
94C2×#11758196C2314yes—
95C2×C22⋊Dic61—24no—
96C2×C22⋊Dic61—24no—
97C2×C22⋊Dic61C2314yes—
98C2×C22⋊Dic61C2314yes—
99C2×#11758198—24no—
100C2×#11758198—24no—
101C2×#11758198—24no—
102C2×#11758198—42no—
103C2×#11758198—42no—
104C2×#11758198C2314yes—
105C2×#11758198C2314yes—
106C2×#11758198C2314yes—
107C2×#11758198C2314yes—
108C2×#11758198C2314yes—
109C2×C4×Dic61—42no—
110C2×C4×Dic61—42no—
111C2×C4×Dic61C2314yes—
112C2×C4×Dic61C2314yes—
113#14519684C2314yes—
114#14519684C2314yes—
115#14519684C2314yes—
116#14519684C2314yes—
117#14519684C2314yes—
118#14519684C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125C25×C61C2311yescharacteristic
126C23×C4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61—42no—
133C2×C4⋊C4×C61C2314yes—
134C2×C22⋊C4×C61—24no—
135C2×C22⋊C4×C61—24no—
136C2×C22⋊C4×C61—42no—
137C2×C22⋊C4×C61C2314yes—
138C2×C22⋊C4×C61C2314yes—
139C2×C22⋊C4×C61C2314yes—
140C2×C42×C61—24no—
141C2×C42×C61C2314yes—
142#95×C61C2314yes—
143#95×C61C2314yes—
144C24×C61—22no—
145C24×C61—22no—
146C24×C61—22no—
147C24×C61—22no—
148C24×C61—22no—
149C24×C61—22no—
150C24×C61#4114yes—
151C24×C61C2412yes—
152C24×C61C2411yescharacteristic
153C23×D61—22no—
154C23×D61—22no—
155C23×D61—22no—
156C23×D61—22no—
157C23×D61—22no—
158C23×D61—22no—
159C23×D61#4114yes—
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#4114yes—
179C22×C4×C61C2412yes—
180C22×C4×C61C2412yes—
181C22×C4×C61C2412yes—
182C22×C4×C61C2412yes—
183C22×C4×C61C2412yes—
184C22×C4×C61C2412yes—
185C2×C22⋊D61—28no—
186C2×C22⋊D61—28no—
187C2×C22⋊D61—44no—
188C2×C22⋊D61—416no—
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—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—28no—
209C22×Dic61—44no—
210C22×Dic61—44no—
211C22×Dic61—416no—
212C22×Dic61#4114yes—
213C22×Dic61#4114yes—
214C22×Dic61C2412yes—
215C22×Dic61C2412yes—
216C22×Dic61C2412yes—
217C22×Dic61C2412yes—
218C22×Dic61C2412yes—
219C22×Dic61C2412yes—
220C22×Dic61C2412yes—
221C2×C4×D61—28no—
222C2×C4×D61—28no—
223C2×C4×D61—44no—
224C2×C4×D61—416no—
225C4⋊C4×C61—44no—
226C22⋊C4×C61—28no—
227C22⋊C4×C61—28no—
228C22⋊C4×C61—44no—
229C42×C61—28no—
230C22⋊Dic61—28no—
231C22⋊Dic61—28no—
232#11758198—28no—
233#11758198—28no—
234#11758198—28no—
235#11758198—44no—
236#11758198—44no—
237C4⋊Dic61—44no—
238#11758196—28no—
239#11758196—28no—
240#11758196—44no—
241C4×Dic61—44no—
242C4×Dic61—44no—
243C23×C61—28no—
244C23×C61—28no—
245C23×C61—28no—
246C23×C61—22no—
247C23×C61—22no—
248C23×C61—22no—
249C23×C61—22no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—44no—
253C23×C61—44no—
254C23×C61—44no—
255C23×C61—44no—
256C23×C61C2×#4114yes—
257C23×C61C2×#4112yes—
258C23×C61C2×#4112yes—
259C23×C61C2×#4112yes—
260C23×C61C2×#4112yes—
261C23×C61C2×#4112yes—
262C23×C61H(5,𝔽2)12yes—
263C23×C61H(5,𝔽2)12yes—
264C23×C61C2511yescharacteristic
265C22×D61—28no—
266C22×D61—28no—
267C22×D61—28no—
268C22×D61—22no—
269C22×D61—22no—
270C22×D61—22no—
271C22×D61—22no—
272C22×D61—22no—
273C22×D61—22no—
274C22×D61—44no—
275C22×D61—44no—
276C22×D61—44no—
277C22×D61—44no—
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—44no—
298C2×C4×C61—44no—
299C2×C4×C61—44no—
300C2×C4×C61—44no—
301C2×C4×C61—44no—
302C2×C4×C61C2×#4114yes—
303C22⋊D61—416no—
304C2×Dic61—28no—
305C2×Dic61—28no—
306C2×Dic61—22no—
307C2×Dic61—22no—
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—22no—
325C2×Dic61—416no—
326C2×Dic61—44no—
327C2×Dic61—44no—
328C2×Dic61—44no—
329C2×Dic61—44no—
330C2×Dic61—44no—
331C2×Dic61C2×#4114yes—
332C2×Dic61C2×#4114yes—
333C4×D61—416no—
334C2×#2578—611nomaximal, Sylow
335C22×C61—24no—
336C22×C61—24no—
337C22×C61—24no—
338C22×C61—416no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61#52914yes—
344C22×C61#52914yes—
345C22×C61#53814yes—
346C22×C61#55114yes—
347C22×C61#55114yes—
348C22×C61#55314yes—
349C22×C61#55314yes—
350C22×C61C22×#4111yescharacteristic
351C22×C61C22×#4111yescharacteristic
352C22×C61C22×#4111yescharacteristic
353C22×C61C22×#4111yescharacteristic
354C22×C61C22×#4111yescharacteristic
355C22×C61C2×H(5,𝔽2)11yescharacteristic
356C22×C61C2×H(5,𝔽2)11yescharacteristic
357C2×D61—24no—
358C2×D61—24no—
359C2×D61—24no—
360C2×D61—416no—
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—
371Dic61—24no—
372Dic61—24no—
373Dic61—42no—
374Dic61—42no—
375Dic61—42no—
376Dic61—42no—
377Dic61—42no—
378#2578—6116no—
379C2×#400—611no—
380C2×#397—611no—
381C2×#397—611no—
382C2×#394—611no—
383C2×#388—611no—
384C2×#388D6111yescharacteristic, complemented
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—44no—
395C2×C61#257818yescomplemented
396C2×C61C2×#52911yescharacteristic
397C2×C61C2×#52911yescharacteristic
398C2×C61C2×#53811yescharacteristic
399C2×C61C2×#55111yescharacteristic
400C2×C61C2×#55111yescharacteristic
401C2×C61C2×#55311yescharacteristic
402C2×C61C2×#55311yescharacteristic
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⋊C4—611no—
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⋊C4C2×D6111yescharacteristic
420C22×C22⋊C4C2×D6111yescharacteristic
421C22×C22⋊C4C2×D6111yescharacteristic
422C22×C42—611no—
423C22×C42—611no—
424C22×C42C2×D6111yescharacteristic
425#400—618no—
426#397—618no—
427#397—618no—
428#394—618no—
429#388—618no—
430#388C2×D6118yescomplemented
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×#95—611no—
450C2×#95—611no—
451C2×#95—611no—
452C2×#95C2×D6111yescharacteristic
453C2×#95C2×D6111yescharacteristic
454C61C2×#257811yescharacteristic, complemented, Sylow
455C25—611no—
456C25C22×D6111yescharacteristic
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—611no—
468C23×C4—614no—
469C23×C4—614no—
470C23×C4—1224no—
471C23×C4—1224no—
472C23×C4—1224no—
473C23×C4—2442no—
474C23×C4—2442no—
475C23×C4—2442no—
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—614no—
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⋊C4—2442no—
491C2×C4⋊C4C22×D6114yes—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—42no—
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—2442no—
508C2×C22⋊C4—2442no—
509C2×C22⋊C4C22×D6114yes—
510C2×C22⋊C4C22×D6114yes—
511C2×C22⋊C4C22×D6114yes—
512C2×C42—24no—
513C2×C42—614no—
514C2×C42—614no—
515C2×C42—2442no—
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#95—614no—
527#95—614no—
528#95—614no—
529#95—614no—
530#95C22×D6114yes—
531#95C22×D6114yes—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—614no—
539C24—612no—
540C24—1222no—
541C24—1222no—
542C24—1222no—
543C24—1222no—
544C24—1222no—
545C24—1222no—
546C24#1175822214yes—
547C24C23×D6112yes—
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—614no—
571C22×C4—614no—
572C22×C4—612no—
573C22×C4—612no—
574C22×C4—612no—
575C22×C4—612no—
576C22×C4—612no—
577C22×C4—612no—
578C22×C4—612no—
579C22×C4—1228no—
580C22×C4—1228no—
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—1222no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—1222no—
599C22×C4—1222no—
600C22×C4—1228no—
601C22×C4—2444no—
602C22×C4—24416no—
603C22×C4—2444no—
604C22×C4—2444no—
605C22×C4—24416no—
606C22×C4#1175822414yes—
607C22×C4C23×D6112yes—
608C22×C4C23×D6112yes—
609C22×C4C23×D6112yes—
610C22×C4C23×D6112yes—
611C22×C4C23×D6112yes—
612C22×C4C23×D6112yes—
613C4⋊C4—44no—
614C4⋊C4—1228no—
615C4⋊C4—1228no—
616C4⋊C4—2444no—
617C4⋊C4—2444no—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—44no—
621C22⋊C4—1228no—
622C22⋊C4—1228no—
623C22⋊C4—1228no—
624C22⋊C4—1228no—
625C22⋊C4—1228no—
626C22⋊C4—2444no—
627C22⋊C4—2444no—
628C42—28no—
629C42—2444no—
630C42—2444no—
631C23—28no—
632C23—28no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—28no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—614no—
645C23—1228no—
646C23—1228no—
647C23—1222no—
648C23—1222no—
649C23—1222no—
650C23—1222no—
651C23—1222no—
652C23—1222no—
653C23—1228no—
654C23—2444no—
655C23—2444no—
656C23—2444no—
657C23—2444no—
658C23#41×D6112yes—
659C23#41×D6112yes—
660C23#41×D6112yes—
661C23C2×#1175822412yes—
662C23C2×#1175822214yes—
663C23C2×#1175822212yes—
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—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—44no—
691C2×C4—614no—
692C2×C4—614no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1228no—
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—1222no—
712C2×C4—1222no—
713C2×C4—1222no—
714C2×C4—24416no—
715C2×C4—24416no—
716C2×C4—2444no—
717C2×C4—2444no—
718C2×C4—2444no—
719C2×C4—2444no—
720C2×C4—2444no—
721C2×C4C2×#1175822414yes—
722C22—24no—
723C22—24no—
724C22—24no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—416no—
729C22—42no—
730C22—1224no—
731C22—1224no—
732C22—1224no—
733C22—2442no—
734C22—2442no—
735C22—2442no—
736C22—24416no—
737C22—2442no—
738C22#1684029214yes—
739C22#1684029514yes—
740C22#1684034614yes—
741C22#1684043514yes—
742C22#1684043614yes—
743C22#1684045914yes—
744C22#1684046114yes—
745C22C2×#41×D6111yescharacteristic
746C22C2×#41×D6111yescharacteristic
747C22C2×#41×D6111yescharacteristic
748C22C22×#1175822411yescharacteristic
749C22C22×#1175822211yescharacteristic
750C22C2×#1451982211yescharacteristic
751C22C2×#1451982311yescharacteristic
752C4—24no—
753C4—42no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—1224no—
759C4—1224no—
760C4—2442no—
761C4—2442no—
762C4—2442no—
763C4—2442no—
764C4—2442no—
765C2—44no—
766C2—2444no—
767C2#2145115918yesdirect product factor
768C2C2×#1684029211yescharacteristic
769C2C2×#1684029511yescharacteristic
770C2C2×#1684034611yescharacteristic
771C2C2×#1684043511yescharacteristic
772C2C2×#1684043611yescharacteristic
773C2C2×#1684045911yescharacteristic
774C2C2×#1684046111yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#388D61
hypocenterC61C2×#2578
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
1. #21451159C2direct (N × H)
2. C2×#16839702C2semidirect
3. C2×#16839690C2semidirect
4. C2×#16839688C2semidirect
6. C2×#16839651C2semidirect
7. C2×#16839649C2semidirect
8. C2×#16839643C2semidirect
11. C2×#16839634C2semidirect
12. C2×#16839630C2semidirect
13. C2×#16839621C2semidirect
14. C2×C22⋊C4×Dic61C2semidirect
15. C2×C4×#11758198C2semidirect
16. C2×C61×#388C2semidirect
33. #16839702C22semidirect
34. #16839690C22semidirect
35. #16839688C22semidirect
37. #16839651C22semidirect
38. #16839649C22semidirect
39. #16839643C22semidirect
42. #16839634C22semidirect
43. #16839630C22semidirect
44. #16839621C22semidirect
45. C22⋊C4×Dic61C22semidirect
46. C4×#11758198C22semidirect
64. C61×#388C22semidirect
384. C2×#388D61semidirect
395. C2×C61#2578semidirect
430. #388C2×D61semidirect
454. C61C2×#2578semidirect
767. C2#21451159direct (N × H)

Maximal subgroups

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

subgroupindex
#214511592
C2×#168397022
C2×#168396902
C2×#168396882
C2×#168396782
C2×#168396512
C2×#168396492
C2×#168396432
C2×#168396392
C2×#168396382
C2×#168396342
C2×#168396302
C2×#168396212
C2×C22⋊C4×Dic612
C2×C4×#117581982
C2×C61×#3882
C2×#257861