Finite Group Databasebeta

← C2×#21451341 #29850575

Subgroups — C2×#21451341 #29850575

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#21451341C2116yesmaximal, direct product factor
2C2×#16839701C211yesmaximal, characteristic, complemented
3C2×#16839690C211yesmaximal, characteristic, complemented
4C2×#16839687C211yesmaximal, characteristic, complemented
5C2×#16839665C211yesmaximal, characteristic
6C2×#16839655C211yesmaximal, characteristic, complemented
7C2×#16839650C211yesmaximal, characteristic, complemented
8C2×#16839650C211yesmaximal, characteristic, complemented
9C2×#16839650C211yesmaximal, characteristic, complemented
10C2×#16839649C211yesmaximal, characteristic, complemented
11C2×#16839647C211yesmaximal, characteristic, complemented
12C2×#16839642C211yesmaximal, characteristic
13C2×#16839637C211yesmaximal, characteristic, complemented
14C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
15C2×C22⋊C4×Dic61C211yesmaximal, characteristic, complemented
16C2×C61×#394C211yesmaximal, characteristic
17C24×Dic61C2211yescharacteristic
18C22×C4⋊Dic61C2211yescharacteristic
19C22×C4⋊Dic61C2211yescharacteristic
20C22×C4⋊Dic61C2211yescharacteristic
21C22×#11758196C2211yescharacteristic
22C22×#11758196C2211yescharacteristic
23C22×C22⋊Dic61C2211yescharacteristic
24C22×C22⋊Dic61C2211yescharacteristic
25C22×C22⋊Dic61C2211yescharacteristic
26C22×C22⋊Dic61C2211yescharacteristic
27C22×C22⋊Dic61C2211yescharacteristic
28C22×C22⋊Dic61C2211yescharacteristic
29C22×C22⋊Dic61C2211yescharacteristic
30C22×C4×Dic61C2211yescharacteristic
31C22×C4×Dic61C2211yescharacteristic
32C22×C4×Dic61C2211yescharacteristic
33C22×C4×Dic61C2211yescharacteristic
34#16839701C2218yescomplemented
35#16839690C2218yescomplemented
36#16839687C2218yescomplemented
37#16839665C2218yes—
38#16839655C2218yescomplemented
39#16839650C2218yescomplemented
40#16839650C2218yescomplemented
41#16839650C2218yescomplemented
42#16839649C2218yescomplemented
43#16839647C2218yescomplemented
44#16839642C2218yes—
45#16839637C2218yescomplemented
46C4⋊C4×Dic61C2218yescomplemented
47C22⋊C4×Dic61C2218yescomplemented
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C23×D4×C61C2211yescharacteristic
60C22×C4⋊C4×C61C2211yescharacteristic
61C22×C22⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C61×#394C2218yes—
66C2×#95×C61C2211yescharacteristic
67C23×Dic61—24no—
68C23×Dic61—42no—
69C23×Dic61—42no—
70C23×Dic61C2311yescharacteristic
71C23×Dic61C2311yescharacteristic
72C23×Dic61C2311yescharacteristic
73C23×Dic61C2311yescharacteristic
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2314yes—
79C2×C4⋊Dic61—24no—
80C2×C4⋊Dic61—24no—
81C2×C4⋊Dic61—42no—
82C2×C4⋊Dic61C2314yes—
83C2×C4⋊Dic61C2314yes—
84C2×C4⋊Dic61C2314yes—
85C2×#11758196—24no—
86C2×#11758196—42no—
87C2×#11758196C2314yes—
88C2×#11758196C2314yes—
89C2×C22⋊Dic61—24no—
90C2×C22⋊Dic61—24no—
91C2×C22⋊Dic61—24no—
92C2×C22⋊Dic61—24no—
93C2×C22⋊Dic61—42no—
94C2×C22⋊Dic61—42no—
95C2×C22⋊Dic61—42no—
96C2×C22⋊Dic61C2314yes—
97C2×C22⋊Dic61C2314yes—
98C2×C22⋊Dic61C2314yes—
99C2×C22⋊Dic61C2314yes—
100C2×C22⋊Dic61C2314yes—
101C2×C22⋊Dic61C2314yes—
102C2×C22⋊Dic61C2314yes—
103C2×C4×Dic61—24no—
104C2×C4×Dic61—42no—
105C2×C4×Dic61—42no—
106C2×C4×Dic61—42no—
107C2×C4×Dic61C2314yes—
108C2×C4×Dic61C2314yes—
109C2×C4×Dic61C2314yes—
110C2×C4×Dic61C2314yes—
111#14519684C2314yes—
112#14519684C2314yes—
113#14519684C2314yes—
114#14519684C2314yes—
115#14519684C2314yes—
116#14519684C2314yes—
117#14519684C2314yes—
118#14519684C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122C25×C61C2311yescharacteristic
123C25×C61C2311yescharacteristic
124C22×D4×C61—24no—
125C22×D4×C61—24no—
126C22×D4×C61—42no—
127C22×D4×C61C2314yes—
128C23×C4×C61C2311yescharacteristic
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61—24no—
134C2×C4⋊C4×C61C2314yes—
135C2×C22⋊C4×C61—24no—
136C2×C22⋊C4×C61—24no—
137C2×C22⋊C4×C61—24no—
138C2×C22⋊C4×C61—42no—
139C2×C22⋊C4×C61C2314yes—
140C2×C22⋊C4×C61C2314yes—
141C2×C22⋊C4×C61C2314yes—
142C2×C22⋊C4×C61C2314yes—
143#95×C61C2314yes—
144C24×C61—22no—
145C24×C61—22no—
146C24×C61—22no—
147C24×C61—22no—
148C24×C61—22no—
149C24×C61—22no—
150C24×C61—22no—
151C24×C61—22no—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61—22no—
157C24×C61#4114yes—
158C24×C61C2412yes—
159C24×C61C2412yes—
160C24×C61C2411yescharacteristic
161C2×D4×C61—28no—
162C2×D4×C61—28no—
163C2×D4×C61—44no—
164C2×D4×C61—416no—
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×C61#4114yes—
180C22×C4×C61C2412yes—
181C22×C4×C61C2412yes—
182C22×C4×C61C2412yes—
183C22×C4×C61C2412yes—
184C22×C4×C61C2412yes—
185C22×Dic61—22no—
186C22×Dic61—22no—
187C22×Dic61—22no—
188C22×Dic61—22no—
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—28no—
208C22×Dic61—44no—
209C22×Dic61—44no—
210C22×Dic61—416no—
211C22×Dic61#4114yes—
212C22×Dic61#4114yes—
213C22×Dic61C2412yes—
214C22×Dic61C2412yes—
215C22×Dic61C2412yes—
216C22×Dic61C2412yes—
217C22×Dic61C2412yes—
218C22×Dic61C2412yes—
219C22×Dic61C2412yes—
220C22×Dic61C2412yes—
221C4⋊C4×C61—28no—
222C22⋊C4×C61—28no—
223C22⋊C4×C61—28no—
224C22⋊C4×C61—28no—
225C22⋊C4×C61—44no—
226C22⋊Dic61—28no—
227C22⋊Dic61—28no—
228C22⋊Dic61—28no—
229C22⋊Dic61—28no—
230C22⋊Dic61—44no—
231C22⋊Dic61—44no—
232C22⋊Dic61—44no—
233C4⋊Dic61—28no—
234C4⋊Dic61—28no—
235C4⋊Dic61—44no—
236#11758196—28no—
237#11758196—44no—
238C4×Dic61—28no—
239C4×Dic61—44no—
240C4×Dic61—44no—
241C4×Dic61—44no—
242C23×C61—28no—
243C23×C61—28no—
244C23×C61—28no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61—22no—
248C23×C61—22no—
249C23×C61—22no—
250C23×C61—22no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—22no—
254C23×C61—22no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61—44no—
259C23×C61—44no—
260C23×C61—44no—
261C23×C61—44no—
262C23×C61—44no—
263C23×C61—44no—
264C23×C61—44no—
265C23×C61—44no—
266C23×C61—44no—
267C23×C61—44no—
268C23×C61—44no—
269C23×C61C2×#4114yes—
270C23×C61C2×#4112yes—
271C23×C61C2×#4112yes—
272C23×C61C2×#4112yes—
273C23×C61C2×#4112yes—
274C23×C61C2×#4112yes—
275C23×C61H(5,𝔽2)12yes—
276C23×C61H(5,𝔽2)12yes—
277C23×C61C2511yescharacteristic
278D4×C61—416no—
279C2×C4×C61—28no—
280C2×C4×C61—28no—
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—44no—
295C2×C4×C61—44no—
296C2×C4×C61—44no—
297C2×C4×C61C2×#4114yes—
298C2×C4×C61C2×#4114yes—
299C2×Dic61—28no—
300C2×Dic61—28no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
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—416no—
324C2×Dic61—44no—
325C2×Dic61—44no—
326C2×Dic61—44no—
327C2×Dic61—44no—
328C2×Dic61—44no—
329C2×Dic61—44no—
330C2×Dic61C2×#4114yes—
331C2×Dic61C2×#4114yes—
332C2×#2595—611nomaximal, Sylow
333C22×C61—24no—
334C22×C61—24no—
335C22×C61—24no—
336C22×C61—416no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61—42no—
342C22×C61—42no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—88no—
349C22×C61#52914yes—
350C22×C61#52914yes—
351C22×C61#53814yes—
352C22×C61#55114yes—
353C22×C61#55314yes—
354C22×C61#55314yes—
355C22×C61#55914yes—
356C22×C61C22×#4111yescharacteristic
357C22×C61C22×#4111yescharacteristic
358C22×C61C22×#4111yescharacteristic
359C22×C61C22×#4111yescharacteristic
360C22×C61C22×#4111yescharacteristic
361C22×C61C2×H(5,𝔽2)11yescharacteristic
362C22×C61C2×H(5,𝔽2)11yescharacteristic
363C4×C61—24no—
364C4×C61—24no—
365C4×C61—42no—
366C4×C61—42no—
367C4×C61—42no—
368Dic61—24no—
369Dic61—24no—
370Dic61—42no—
371Dic61—42no—
372Dic61—42no—
373Dic61—42no—
374Dic61—42no—
375Dic61—42no—
376#2595—6116no—
377C2×#400—611no—
378C2×#397—611no—
379C2×#397—611no—
380C2×#394D6111yescharacteristic
381C2×#390—611no—
382C2×#388—611no—
383C2×#388—611no—
384C2×#388—611no—
385C2×#388—611no—
386C2×#387—611no—
387C2×#387—611no—
388C2×#386—611no—
389C2×#385—611no—
390C2×C4×C4⋊C4—611no—
391C2×C4×C22⋊C4—611no—
392C2×C61—44no—
393C2×C61—82no—
394C2×C61#259518yescomplemented
395C2×C61C2×#52911yescharacteristic
396C2×C61C2×#52911yescharacteristic
397C2×C61C2×#53811yescharacteristic
398C2×C61C2×#55111yescharacteristic
399C2×C61C2×#55311yescharacteristic
400C2×C61C2×#55311yescharacteristic
401C2×C61C2×#55911yescharacteristic
402C23×D4C2×D6111yescharacteristic
403C24×C4—611no—
404C22×C4⋊C4—611no—
405C22×C4⋊C4—611no—
406C22×C4⋊C4—611no—
407C22×C4⋊C4—611no—
408C22×C4⋊C4—611no—
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⋊C4C2×D6111yescharacteristic
418C22×C22⋊C4C2×D6111yescharacteristic
419C22×C22⋊C4C2×D6111yescharacteristic
420C22×C22⋊C4C2×D6111yescharacteristic
421C22×C42—611no—
422C22×C42—611no—
423C22×C42—611no—
424C22×C42—611no—
425#400—618no—
426#397—618no—
427#397—618no—
428#394C2×D6118yes—
429#390—618no—
430#388—618no—
431#388—618no—
432#388—618no—
433#388—618no—
434#387—618no—
435#387—618no—
436#386—618no—
437#385—618no—
438C4×C4⋊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×#95C2×D6111yescharacteristic
452C61C2×#259511yescharacteristic, complemented, Sylow
453C25C22×D6111yescharacteristic
454C25C22×D6111yescharacteristic
455C22×D4—24no—
456C22×D4—24no—
457C22×D4—42no—
458C22×D4C22×D6114yes—
459C23×C4—611no—
460C23×C4—611no—
461C23×C4—611no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—614no—
468C23×C4—1224no—
469C23×C4—2442no—
470C23×C4—2442no—
471C23×C4C22×D6111yescharacteristic
472C23×C4C22×D6111yescharacteristic
473C23×C4C22×D6111yescharacteristic
474C23×C4C22×D6111yescharacteristic
475C23×C4C22×D6111yescharacteristic
476C2×C4⋊C4—24no—
477C2×C4⋊C4—614no—
478C2×C4⋊C4—614no—
479C2×C4⋊C4—614no—
480C2×C4⋊C4—614no—
481C2×C4⋊C4—614no—
482C2×C4⋊C4—1224no—
483C2×C4⋊C4—1224no—
484C2×C4⋊C4—1224no—
485C2×C4⋊C4—2442no—
486C2×C4⋊C4—2442no—
487C2×C4⋊C4C22×D6114yes—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—42no—
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—2442no—
504C2×C22⋊C4—2442no—
505C2×C22⋊C4—2442no—
506C2×C22⋊C4C22×D6114yes—
507C2×C22⋊C4C22×D6114yes—
508C2×C22⋊C4C22×D6114yes—
509C2×C22⋊C4C22×D6114yes—
510C2×C42—614no—
511C2×C42—614no—
512C2×C42—614no—
513C2×C42—614no—
514C2×C42—1224no—
515C2×C42—2442no—
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#95—614no—
528#95—614no—
529#95C22×D6114yes—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24#1175822414yes—
544C24C23×D6112yes—
545C24C23×D6112yes—
546C24C23×D6111yescharacteristic
547C2×D4—28no—
548C2×D4—28no—
549C2×D4—44no—
550C2×D4—416no—
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—614no—
565C22×C4—614no—
566C22×C4—612no—
567C22×C4—612no—
568C22×C4—612no—
569C22×C4—612no—
570C22×C4—612no—
571C22×C4—612no—
572C22×C4—612no—
573C22×C4—612no—
574C22×C4—1228no—
575C22×C4—1222no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
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—1222no—
596C22×C4—1222no—
597C22×C4—2444no—
598C22×C4—2444no—
599C22×C4—24416no—
600C22×C4#1175822414yes—
601C22×C4#1175822414yes—
602C22×C4C23×D6112yes—
603C22×C4C23×D6112yes—
604C22×C4C23×D6112yes—
605C22×C4C23×D6112yes—
606C22×C4C23×D6112yes—
607C4⋊C4—28no—
608C4⋊C4—1228no—
609C4⋊C4—1228no—
610C4⋊C4—1228no—
611C4⋊C4—2444no—
612C4⋊C4—2444no—
613C22⋊C4—28no—
614C22⋊C4—28no—
615C22⋊C4—28no—
616C22⋊C4—44no—
617C22⋊C4—1228no—
618C22⋊C4—1228no—
619C22⋊C4—1228no—
620C22⋊C4—1228no—
621C22⋊C4—2444no—
622C22⋊C4—2444no—
623C22⋊C4—2444no—
624C42—1228no—
625C42—2444no—
626C42—2444no—
627C42—2444no—
628C23—28no—
629C23—28no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—28no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23—44no—
654C23—44no—
655C23#41×D6112yes—
656C23#41×D6112yes—
657C23C2×#1175822414yes—
658C23C2×#1175822412yes—
659C23C2×#1175822412yes—
660C23C2×#1175822412yes—
661C23#1451982212yes—
662C23#1451982312yes—
663C23C24×D6111yescharacteristic
664D4—416no—
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—44no—
681C2×C4—44no—
682C2×C4—44no—
683C2×C4—614no—
684C2×C4—614no—
685C2×C4—1228no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—1228no—
691C2×C4—1222no—
692C2×C4—1222no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1222no—
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—24416no—
710C2×C4—2444no—
711C2×C4—2444no—
712C2×C4—2444no—
713C2×C4—2444no—
714C2×C4—2444no—
715C2×C4—2444no—
716C2×C4C2×#1175822414yes—
717C2×C4C2×#1175822414yes—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—416no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—42no—
733C22—88no—
734C22#1684028914yes—
735C22#1684029314yes—
736C22#1684034814yes—
737C22#1684044314yes—
738C22#1684045914yes—
739C22#1684046414yes—
740C22#1684049414yes—
741C22C2×#41×D6111yescharacteristic
742C22C2×#41×D6111yescharacteristic
743C22C22×#1175822411yescharacteristic
744C22C22×#1175822411yescharacteristic
745C22C22×#1175822411yescharacteristic
746C22C2×#1451982211yescharacteristic
747C22C2×#1451982311yescharacteristic
748C4—24no—
749C4—24no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—1224no—
754C4—1224no—
755C4—2442no—
756C4—2442no—
757C4—2442no—
758C4—2442no—
759C4—2442no—
760C4—2442no—
761C2—44no—
762C2—82no—
763C2#2145134118yesdirect product factor
764C2C2×#1684028911yescharacteristic
765C2C2×#1684029311yescharacteristic
766C2C2×#1684034811yescharacteristic
767C2C2×#1684044311yescharacteristic
768C2C2×#1684045911yescharacteristic
769C2C2×#1684046411yescharacteristic
770C2C2×#1684049411yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#394C2
socleC24×C61C24
prime radicalC23×D4×C61C22
hypercenterC2×#394D61
hypocenterC61C2×#2595
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #21451341C2direct (N × H)
2. C2×#16839701C2semidirect
3. C2×#16839690C2semidirect
4. C2×#16839687C2semidirect
6. C2×#16839655C2semidirect
7. C2×#16839650C2semidirect
8. C2×#16839650C2semidirect
9. C2×#16839650C2semidirect
10. C2×#16839649C2semidirect
11. C2×#16839647C2semidirect
13. C2×#16839637C2semidirect
14. C2×C4⋊C4×Dic61C2semidirect
15. C2×C22⋊C4×Dic61C2semidirect
34. #16839701C22semidirect
35. #16839690C22semidirect
36. #16839687C22semidirect
38. #16839655C22semidirect
39. #16839650C22semidirect
40. #16839650C22semidirect
41. #16839650C22semidirect
42. #16839649C22semidirect
43. #16839647C22semidirect
45. #16839637C22semidirect
46. C4⋊C4×Dic61C22semidirect
47. C22⋊C4×Dic61C22semidirect
394. C2×C61#2595semidirect
452. C61C2×#2595semidirect
763. C2#21451341direct (N × H)

Maximal subgroups

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

subgroupindex
#214513412
C2×#168397012
C2×#168396902
C2×#168396872
C2×#168396652
C2×#168396552
C2×#168396502
C2×#168396492
C2×#168396472
C2×#168396422
C2×#168396372
C2×C4⋊C4×Dic612
C2×C22⋊C4×Dic612
C2×C61×#3942
C2×#259561