Finite Group Databasebeta

← C2×#21450047 #29848565

Subgroups — C2×#21450047 #29848565

Order 15616.

2898 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519772C211yesmaximal, characteristic, complemented
2C22×#14519736C211yesmaximal, characteristic, complemented
3#21450047C2116yesmaximal, direct product factor
4C2×#16839699C211yesmaximal, characteristic, complemented
5C2×#16839698C211yesmaximal, characteristic, complemented
6C2×#16839692C211yesmaximal, characteristic, complemented
7C2×#16839677C211yesmaximal, characteristic
8C2×#16839662C211yesmaximal, characteristic
9C2×#16839659C211yesmaximal, characteristic, complemented
10C2×#16839655C211yesmaximal, characteristic, complemented
11C2×#16839652C211yesmaximal, characteristic, complemented
12C2×#16839651C211yesmaximal, characteristic, complemented
13C2×#16839645C211yesmaximal, characteristic, complemented
14C2×#16839641C211yesmaximal, characteristic
15C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
16C2×C61×#385C211yesmaximal, characteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C2×#14519772—28no—
19C2×#14519772C2218yescomplemented
20C2×#14519736—28no—
21C2×#14519736C2218yescomplemented
22C22×C4⋊Dic61C2211yescharacteristic
23C22×C4⋊Dic61C2211yescharacteristic
24C22×C4⋊Dic61C2211yescharacteristic
25C22×C4⋊Dic61C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×C4×Dic61C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41C22×C4×Dic61C2211yescharacteristic
42C22×C4×Dic61C2211yescharacteristic
43#16839699C2218yescomplemented
44#16839698C2218yescomplemented
45#16839692C2218yescomplemented
46#16839677C2218yes—
47#16839662C2218yes—
48#16839659C2218yescomplemented
49#16839655C2218yescomplemented
50#16839652C2218yescomplemented
51#16839651C2218yescomplemented
52#16839645C2218yescomplemented
53#16839641C2218yes—
54C4⋊C4×Dic61C2218yescomplemented
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C24×C4×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×C4⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C22⋊C4×C61C2211yescharacteristic
66C61×#385C2218yescomplemented
67C2×#95×C61C2211yescharacteristic
68C2×#95×C61C2211yescharacteristic
69C24×D61C2311yescharacteristic
70C22×C22⋊D61—24no—
71C22×C22⋊D61—24no—
72C22×C22⋊D61—42no—
73C22×C22⋊D61C2314yes—
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81#14519772—232no—
82#14519736—232no—
83C2×C4⋊Dic61—24no—
84C2×C4⋊Dic61—24no—
85C2×C4⋊Dic61—42no—
86C2×C4⋊Dic61D418yescomplemented
87C2×C4⋊Dic61C2314yes—
88C2×C4⋊Dic61C2314yes—
89C2×C4⋊Dic61C2314yes—
90C2×C4⋊Dic61C2314yes—
91C2×#11758196—24no—
92C2×#11758196—24no—
93C2×#11758196—42no—
94C2×#11758196—42no—
95C2×#11758196C2314yes—
96C2×#11758196C2314yes—
97C2×#11758196C2314yes—
98C2×#11758196C2314yes—
99C2×C22⋊Dic61—24no—
100C2×C22⋊Dic61—24no—
101C2×C22⋊Dic61—42no—
102C2×C22⋊Dic61C2314yes—
103C2×C22⋊Dic61C2314yes—
104C2×C22⋊Dic61C2314yes—
105C2×#11758198—24no—
106C2×#11758198—24no—
107C2×#11758198—24no—
108C2×#11758198—24no—
109C2×#11758198—24no—
110C2×#11758198—42no—
111C2×#11758198C2314yes—
112C2×#11758198C2314yes—
113C2×#11758198C2314yes—
114C2×#11758198C2314yes—
115C2×#11758198C2314yes—
116C2×#11758198C2314yes—
117C2×C4×Dic61—24no—
118C2×C4×Dic61—24no—
119C2×C4×Dic61—24no—
120C2×C4×Dic61—24no—
121C2×C4×Dic61C2314yes—
122C2×C4×Dic61C2314yes—
123C2×C4×Dic61C2314yes—
124C2×C4×Dic61C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131C25×C61C2311yescharacteristic
132C23×C4×C61—24no—
133C23×C4×C61—24no—
134C23×C4×C61—24no—
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2314yes—
139C23×C4×C61C2311yescharacteristic
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61—24no—
143C2×C4⋊C4×C61—24no—
144C2×C4⋊C4×C61C2314yes—
145C2×C4⋊C4×C61C2314yes—
146C2×C22⋊C4×C61—24no—
147C2×C22⋊C4×C61—24no—
148C2×C22⋊C4×C61C2314yes—
149C2×C22⋊C4×C61C2314yes—
150#95×C61C2314yes—
151#95×C61C2314yes—
152C24×C61—22no—
153C24×C61—22no—
154C24×C61—22no—
155C24×C61—22no—
156C24×C61—22no—
157C24×C61—22no—
158C24×C61#4114yes—
159C24×C61C2412yes—
160C24×C61C2411yescharacteristic
161C23×D61—22no—
162C23×D61—22no—
163C23×D61—22no—
164C23×D61—22no—
165C23×D61—22no—
166C23×D61—22no—
167C23×D61—22no—
168C23×D61C2412yes—
169C22×C4×C61—232no—
170C22×C4×C61—22no—
171C22×C4×C61—22no—
172C22×C4×C61—28no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—22no—
176C22×C4×C61—22no—
177C22×C4×C61—28no—
178C22×C4×C61—28no—
179C22×C4×C61—22no—
180C22×C4×C61—22no—
181C22×C4×C61—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61—22no—
186C22×C4×C61—22no—
187C22×C4×C61—22no—
188C22×C4×C61C2×D414yes—
189C22×C4×C61#4114yes—
190C22×C4×C61#4114yes—
191C22×C4×C61C2412yes—
192C22×C4×C61C2412yes—
193C22×C4×C61C2412yes—
194C22×C4×C61C2412yes—
195C22×C4×C61C2412yes—
196C22×C4×C61C2412yes—
197C2×C22⋊D61—28no—
198C2×C22⋊D61—28no—
199C2×C22⋊D61—44no—
200C2×C22⋊D61—416no—
201C22×Dic61—22no—
202C22×Dic61—22no—
203C22×Dic61—22no—
204C22×Dic61—22no—
205C22×Dic61—22no—
206C22×Dic61—22no—
207C22×Dic61—22no—
208C22×Dic61—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61—22no—
217C22×Dic61—22no—
218C22×Dic61—22no—
219C22×Dic61C2×D414yes—
220C22×Dic61C2×D414yes—
221C22×Dic61#4114yes—
222C22×Dic61C2412yes—
223C22×Dic61C2412yes—
224C22×Dic61C2412yes—
225C22×Dic61C2412yes—
226C22×Dic61C2412yes—
227C22×Dic61C2412yes—
228C22×Dic61C2412yes—
229C4⋊C4×C61—28no—
230C4⋊C4×C61—28no—
231C22⋊C4×C61—28no—
232C22⋊C4×C61—28no—
233C22⋊Dic61—28no—
234C22⋊Dic61—28no—
235C22⋊Dic61—44no—
236#11758198—28no—
237#11758198—28no—
238#11758198—28no—
239#11758198—28no—
240#11758198—28no—
241#11758198—44no—
242C4⋊Dic61—28no—
243C4⋊Dic61—28no—
244C4⋊Dic61—44no—
245C4⋊Dic61C2×D4116yescomplemented
246#11758196—28no—
247#11758196—28no—
248#11758196—44no—
249#11758196—44no—
250C4×Dic61—28no—
251C4×Dic61—28no—
252C4×Dic61—28no—
253C4×Dic61—28no—
254C23×C61—28no—
255C23×C61—28no—
256C23×C61—28no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—44no—
264C23×C61—44no—
265C23×C61—44no—
266C23×C61—44no—
267C23×C61C22×D412yes—
268C23×C61C2×#4114yes—
269C23×C61C2×#4112yes—
270C23×C61C2×#4112yes—
271C23×C61C2×#4112yes—
272C23×C61C2×#4112yes—
273C23×C61H(5,𝔽2)12yes—
274C23×C612−1+412yes—
275C23×C61C2511yescharacteristic
276C22×D61—22no—
277C22×D61—22no—
278C22×D61—22no—
279C22×D61—22no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—44no—
284C22×D61—44no—
285C22×D61—44no—
286C22×D61—44no—
287C22×D61—44no—
288C22×D61—44no—
289C22×D61—44no—
290C2×C4×C61—232no—
291C2×C4×C61—28no—
292C2×C4×C61—28no—
293C2×C4×C61—28no—
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—22no—
301C2×C4×C61—22no—
302C2×C4×C61—22no—
303C2×C4×C61—22no—
304C2×C4×C61—22no—
305C2×C4×C61—22no—
306C2×C4×C61—22no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—44no—
310C2×C4×C61—44no—
311C2×C4×C61—44no—
312C2×C4×C61C22×D414yes—
313C2×C4×C61C2×#4114yes—
314C2×C4×C61C2×#4114yes—
315C22⋊D61—416no—
316C2×Dic61—28no—
317C2×Dic61—28no—
318C2×Dic61—28no—
319C2×Dic61—22no—
320C2×Dic61—22no—
321C2×Dic61—22no—
322C2×Dic61—22no—
323C2×Dic61—22no—
324C2×Dic61—22no—
325C2×Dic61—22no—
326C2×Dic61—22no—
327C2×Dic61—22no—
328C2×Dic61—22no—
329C2×Dic61—22no—
330C2×Dic61—22no—
331C2×Dic61—22no—
332C2×Dic61—22no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—44no—
338C2×Dic61—44no—
339C2×Dic61—44no—
340C2×Dic61—44no—
341C2×Dic61C22×D414yes—
342C2×Dic61C22×D414yes—
343C2×Dic61C2×#4114yes—
344C2×#2479—611nomaximal, Sylow
345C22×C61—24no—
346C22×C61—24no—
347C22×C61—24no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—416no—
353C22×C61#52514yes—
354C22×C61#52914yes—
355C22×C61#54214yes—
356C22×C61#54714yes—
357C22×C61#55014yes—
358C22×C61#55114yes—
359C22×C61#55214yes—
360C22×C61C23×D411yescharacteristic
361C22×C61C22×#4111yescharacteristic
362C22×C61C22×#4111yescharacteristic
363C22×C61C22×#4111yescharacteristic
364C22×C61C22×#4111yescharacteristic
365C22×C61C2×H(5,𝔽2)11yescharacteristic
366C22×C61C2×2−1+411yescharacteristic
367C2×D61—42no—
368C2×D61—42no—
369C2×D61—42no—
370C2×D61—42no—
371C2×D61—42no—
372C2×D61—42no—
373C2×D61—42no—
374C2×D61—88no—
375C4×C61—24no—
376C4×C61—24no—
377C4×C61—24no—
378C4×C61—42no—
379C4×C61—42no—
380C4×C61—42no—
381Dic61—24no—
382Dic61—24no—
383Dic61—24no—
384Dic61—42no—
385Dic61—42no—
386Dic61—42no—
387Dic61—42no—
388C22×#126—611no—
389C22×#117—611no—
390#2479—6116no—
391C2×#399—611no—
392C2×#399—611no—
393C2×#398—611no—
394C2×#394—611no—
395C2×#390—611no—
396C2×#389—611no—
397C2×#388—611no—
398C2×#388—611no—
399C2×#388—611no—
400C2×#387—611no—
401C2×#386—611no—
402C2×#385D6111yescharacteristic, complemented
403C2×C4×C4⋊C4—611no—
404C2×C61—44no—
405C2×C61#247918yescomplemented
406C2×C61C2×#52511yescharacteristic
407C2×C61C2×#52911yescharacteristic
408C2×C61C2×#54211yescharacteristic
409C2×C61C2×#54711yescharacteristic
410C2×C61C2×#55011yescharacteristic
411C2×C61C2×#55111yescharacteristic
412C2×C61C2×#55211yescharacteristic
413D61—82no—
414C23×D4—611no—
415C24×C4C2×D6111yescharacteristic
416C2×#126—618no—
417C2×#126—1228no—
418C2×#117—618no—
419C2×#117—1228no—
420C22×C4⋊C4—611no—
421C22×C4⋊C4—611no—
422C22×C4⋊C4—611no—
423C22×C4⋊C4—611no—
424C22×C4⋊C4—611no—
425C22×C4⋊C4—611no—
426C22×C4⋊C4—611no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4C2×D6111yescharacteristic
429C22×C4⋊C4C2×D6111yescharacteristic
430C22×C22⋊C4—611no—
431C22×C22⋊C4—611no—
432C22×C22⋊C4—611no—
433C22×C22⋊C4—611no—
434C22×C22⋊C4—611no—
435C22×C22⋊C4—611no—
436C22×C22⋊C4—611no—
437C22×C22⋊C4—611no—
438C22×C22⋊C4—611no—
439C22×C22⋊C4C2×D6111yescharacteristic
440C22×C22⋊C4C2×D6111yescharacteristic
441C22×C42—611no—
442C22×C42—611no—
443C22×C42—611no—
444C22×C42—611no—
445#399—618no—
446#399—618no—
447#398—618no—
448#394—618no—
449#390—618no—
450#389—618no—
451#388—618no—
452#388—618no—
453#388—618no—
454#387—618no—
455#386—618no—
456#385C2×D6118yescomplemented
457C4×C4⋊C4—618no—
458C2×#95—611no—
459C2×#95—611no—
460C2×#95—611no—
461C2×#95—611no—
462C2×#95—611no—
463C2×#95—611no—
464C2×#95C2×D6111yescharacteristic
465C2×#95C2×D6111yescharacteristic
466C61C2×#247911yescharacteristic, complemented, Sylow
467C25—611no—
468C25C22×D6111yescharacteristic
469C22×D4—614no—
470C22×D4—1224no—
471C22×D4—1224no—
472C22×D4—2442no—
473C23×C4—24no—
474C23×C4—24no—
475C23×C4—24no—
476C23×C4—611no—
477C23×C4—611no—
478C23×C4—611no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—611no—
482C23×C4—611no—
483C23×C4C22×D6114yes—
484C23×C4C22×D6111yescharacteristic
485C23×C4C22×D6111yescharacteristic
486C23×C4C22×D6111yescharacteristic
487C23×C4C22×D6111yescharacteristic
488C23×C4C22×D6111yescharacteristic
489C23×C4C22×D6111yescharacteristic
490#126—12232no—
491#117—12232no—
492C2×C4⋊C4—24no—
493C2×C4⋊C4—24no—
494C2×C4⋊C4—618no—
495C2×C4⋊C4—614no—
496C2×C4⋊C4—614no—
497C2×C4⋊C4—614no—
498C2×C4⋊C4—614no—
499C2×C4⋊C4—614no—
500C2×C4⋊C4—614no—
501C2×C4⋊C4—614no—
502C2×C4⋊C4—614no—
503C2×C4⋊C4—1224no—
504C2×C4⋊C4—1224no—
505C2×C4⋊C4—1224no—
506C2×C4⋊C4—1224no—
507C2×C4⋊C4—2442no—
508C2×C4⋊C4—2442no—
509C2×C4⋊C4—2442no—
510C2×C4⋊C4C22×D6114yes—
511C2×C4⋊C4C22×D6114yes—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—614no—
515C2×C22⋊C4—614no—
516C2×C22⋊C4—614no—
517C2×C22⋊C4—614no—
518C2×C22⋊C4—614no—
519C2×C22⋊C4—614no—
520C2×C22⋊C4—614no—
521C2×C22⋊C4—614no—
522C2×C22⋊C4—614no—
523C2×C22⋊C4—1224no—
524C2×C22⋊C4—1224no—
525C2×C22⋊C4—1224no—
526C2×C22⋊C4—1224no—
527C2×C22⋊C4—1224no—
528C2×C22⋊C4—1224no—
529C2×C22⋊C4—1224no—
530C2×C22⋊C4—2442no—
531C2×C22⋊C4—2442no—
532C2×C22⋊C4C22×D6114yes—
533C2×C22⋊C4C22×D6114yes—
534C2×C42—614no—
535C2×C42—614no—
536C2×C42—614no—
537C2×C42—614no—
538C2×C42—1224no—
539C2×C42—1224no—
540C2×C42—1224no—
541C2×C42—1224no—
542#95—614no—
543#95—614no—
544#95—614no—
545#95—614no—
546#95—614no—
547#95—614no—
548#95C22×D6114yes—
549#95C22×D6114yes—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—612no—
557C24—1222no—
558C24—1222no—
559C24—1222no—
560C24—1222no—
561C24—1222no—
562C24—1222no—
563C24—1222no—
564C24#1175822414yes—
565C24C23×D6112yes—
566C24C23×D6111yescharacteristic
567C2×D4—1228no—
568C2×D4—1228no—
569C2×D4—2444no—
570C2×D4—24416no—
571C22×C4—232no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—28no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—614no—
591C22×C4—614no—
592C22×C4—614no—
593C22×C4—612no—
594C22×C4—612no—
595C22×C4—612no—
596C22×C4—612no—
597C22×C4—612no—
598C22×C4—612no—
599C22×C4—612no—
600C22×C4—1222no—
601C22×C4—1222no—
602C22×C4—1222no—
603C22×C4—1222no—
604C22×C4—1222no—
605C22×C4—1222no—
606C22×C4—1222no—
607C22×C4—1222no—
608C22×C4—1222no—
609C22×C4—1222no—
610C22×C4—1222no—
611C22×C4—1222no—
612C22×C4—1222no—
613C22×C4—1222no—
614C22×C4—1222no—
615C22×C4—1222no—
616C22×C4—1222no—
617C22×C4—1222no—
618C22×C4#1175822214yes—
619C22×C4D4×D6114yes—
620C22×C4#1175822414yes—
621C22×C4C23×D6112yes—
622C22×C4C23×D6112yes—
623C22×C4C23×D6112yes—
624C22×C4C23×D6112yes—
625C22×C4C23×D6112yes—
626C22×C4C23×D6112yes—
627C4⋊C4—28no—
628C4⋊C4—28no—
629C4⋊C4—6116no—
630C4⋊C4—1228no—
631C4⋊C4—1228no—
632C4⋊C4—1228no—
633C4⋊C4—1228no—
634C4⋊C4—2444no—
635C4⋊C4—2444no—
636C4⋊C4—2444no—
637C22⋊C4—28no—
638C22⋊C4—28no—
639C22⋊C4—1228no—
640C22⋊C4—1228no—
641C22⋊C4—1228no—
642C22⋊C4—1228no—
643C22⋊C4—1228no—
644C22⋊C4—1228no—
645C22⋊C4—1228no—
646C22⋊C4—2444no—
647C22⋊C4—2444no—
648C42—1228no—
649C42—1228no—
650C42—1228no—
651C42—1228no—
652C23—28no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—28no—
660C23—28no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—1222no—
666C23—1222no—
667C23—1222no—
668C23—1222no—
669C23—1222no—
670C23—1222no—
671C23—1222no—
672C23—2444no—
673C23—2444no—
674C23—2444no—
675C23—2444no—
676C23—2444no—
677C23—2444no—
678C23—2444no—
679C23C2×D4×D6112yes—
680C23#41×D6112yes—
681C23C2×#1175822414yes—
682C23C2×#1175822412yes—
683C23C2×#1175822412yes—
684C23C2×#1175822212yes—
685C23#1451982312yes—
686C23#1451982512yes—
687C23C24×D6111yescharacteristic
688D4—24416no—
689C2×C4—232no—
690C2×C4—28no—
691C2×C4—28no—
692C2×C4—28no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—44no—
709C2×C4—44no—
710C2×C4—44no—
711C2×C4—614no—
712C2×C4—614no—
713C2×C4—614no—
714C2×C4—1222no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1228no—
721C2×C4—1228no—
722C2×C4—1228no—
723C2×C4—1222no—
724C2×C4—1222no—
725C2×C4—1222no—
726C2×C4—1222no—
727C2×C4—1222no—
728C2×C4—1222no—
729C2×C4—1222no—
730C2×C4—1222no—
731C2×C4—1222no—
732C2×C4—1222no—
733C2×C4—1222no—
734C2×C4—1222no—
735C2×C4—2444no—
736C2×C4—2444no—
737C2×C4—2444no—
738C2×C4—2444no—
739C2×C4C2×D4×D6114yes—
740C2×C4C2×#1175822414yes—
741C2×C4C2×#1175822214yes—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—416no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—4888no—
751C22—2442no—
752C22—2442no—
753C22—2442no—
754C22—2442no—
755C22—2442no—
756C22—2442no—
757C22—2442no—
758C22#1684026814yes—
759C22#1684029214yes—
760C22#1684038514yes—
761C22#1684041414yes—
762C22#1684043314yes—
763C22#1684043514yes—
764C22#1684044714yes—
765C22C22×D4×D6111yescharacteristic
766C22C2×#41×D6111yescharacteristic
767C22C22×#1175822411yescharacteristic
768C22C22×#1175822411yescharacteristic
769C22C22×#1175822211yescharacteristic
770C22C2×#1451982311yescharacteristic
771C22C2×#1451982511yescharacteristic
772C4—24no—
773C4—24no—
774C4—24no—
775C4—42no—
776C4—42no—
777C4—42no—
778C4—1224no—
779C4—1224no—
780C4—1224no—
781C4—2442no—
782C4—2442no—
783C4—2442no—
784C4—2442no—
785C2—44no—
786C2—4882no—
787C2#2145004718yesdirect product factor
788C2C2×#1684026811yescharacteristic
789C2C2×#1684029211yescharacteristic
790C2C2×#1684038511yescharacteristic
791C2C2×#1684041411yescharacteristic
792C2C2×#1684043311yescharacteristic
793C2C2×#1684043511yescharacteristic
794C2C2×#1684044711yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#385C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#385D61
hypocenterC61C2×#2479
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#14519772C2semidirect
2. C22×#14519736C2semidirect
3. #21450047C2direct (N × H)
4. C2×#16839699C2semidirect
5. C2×#16839698C2semidirect
6. C2×#16839692C2semidirect
9. C2×#16839659C2semidirect
10. C2×#16839655C2semidirect
11. C2×#16839652C2semidirect
12. C2×#16839651C2semidirect
13. C2×#16839645C2semidirect
15. C2×C4⋊C4×Dic61C2semidirect
16. C2×C61×#385C2semidirect
19. C2×#14519772C22semidirect
21. C2×#14519736C22semidirect
43. #16839699C22semidirect
44. #16839698C22semidirect
45. #16839692C22semidirect
48. #16839659C22semidirect
49. #16839655C22semidirect
50. #16839652C22semidirect
51. #16839651C22semidirect
52. #16839645C22semidirect
54. C4⋊C4×Dic61C22semidirect
66. C61×#385C22semidirect
86. C2×C4⋊Dic61D4semidirect
245. C4⋊Dic61C2×D4semidirect
402. C2×#385D61semidirect
405. C2×C61#2479semidirect
456. #385C2×D61semidirect
466. C61C2×#2479semidirect
787. C2#21450047direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197722
C22×#145197362
#214500472
C2×#168396992
C2×#168396982
C2×#168396922
C2×#168396772
C2×#168396622
C2×#168396592
C2×#168396552
C2×#168396522
C2×#168396512
C2×#168396452
C2×#168396412
C2×C4⋊C4×Dic612
C2×C61×#3852
C2×#247961