Finite Group Databasebeta

← C2×#21451971 #29846583

Subgroups — C2×#21451971 #29846583

Order 15616.

2786 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519759C211yesmaximal, characteristic
2C22×#14519755C211yesmaximal, characteristic, complemented
3#21451971C2116yesmaximal, direct product factor
4C2×#16839704C211yesmaximal, characteristic, complemented
5C2×#16839698C211yesmaximal, characteristic, complemented
6C2×#16839691C211yesmaximal, characteristic, complemented
7C2×#16839689C211yesmaximal, characteristic, complemented
8C2×#16839683C211yesmaximal, characteristic, complemented
9C2×#16839678C211yesmaximal, characteristic
10C2×#16839677C211yesmaximal, characteristic
11C2×#16839674C211yesmaximal, characteristic, complemented
12C2×#16839660C211yesmaximal, characteristic, complemented
13C2×#16839657C211yesmaximal, characteristic, complemented
14C2×#16839656C211yesmaximal, characteristic, complemented
15C2×C4×#11758198C211yesmaximal, characteristic, complemented
16C2×C61×#388C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×C22⋊D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C2×#14519759—28no—
21C2×#14519759C2218yes—
22C2×#14519755—28no—
23C2×#14519755C2218yescomplemented
24C22×C4⋊Dic61C2211yescharacteristic
25C22×C4⋊Dic61C2211yescharacteristic
26C22×C4⋊Dic61C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33C22×C22⋊Dic61C2211yescharacteristic
34C22×C22⋊Dic61C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×#11758198C2211yescharacteristic
40C22×C4×Dic61C2211yescharacteristic
41#16839704C2218yescomplemented
42#16839698C2218yescomplemented
43#16839691C2218yescomplemented
44#16839689C2218yescomplemented
45#16839683C2218yescomplemented
46#16839678C2218yes—
47#16839677C2218yes—
48#16839674C2218yescomplemented
49#16839660C2218yescomplemented
50#16839657C2218yescomplemented
51#16839656C2218yescomplemented
52C4×#11758198C2218yescomplemented
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C22⋊C4×C61C2211yescharacteristic
63C22×C22⋊C4×C61C2211yescharacteristic
64C22×C22⋊C4×C61C2211yescharacteristic
65C22×C42×C61C2211yescharacteristic
66C61×#388C2218yescomplemented
67C2×#95×C61C2211yescharacteristic
68C2×#95×C61C2211yescharacteristic
69C24×D61C2311yescharacteristic
70C22×Dic122—24no—
71C22×Dic122—42no—
72C22×Dic122—42no—
73C22×Dic122C2314yes—
74C22×C22⋊D61—24no—
75C22×C22⋊D61—42no—
76C22×C22⋊D61—42no—
77C22×C22⋊D61C2314yes—
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C22×C4×D61—42no—
86C22×C4×D61—42no—
87C22×C4×D61D418yes—
88C22×C4×D61C2314yes—
89#14519759—232no—
90#14519755—232no—
91C2×C4⋊Dic61—24no—
92C2×C4⋊Dic61—24no—
93C2×C4⋊Dic61—42no—
94C2×C4⋊Dic61C2314yes—
95C2×C4⋊Dic61C2314yes—
96C2×C4⋊Dic61C2314yes—
97C2×#11758196—24no—
98C2×#11758196—24no—
99C2×#11758196—24no—
100C2×#11758196—24no—
101C2×#11758196—42no—
102C2×#11758196C2314yes—
103C2×#11758196C2314yes—
104C2×#11758196C2314yes—
105C2×#11758196C2314yes—
106C2×#11758196C2314yes—
107C2×C22⋊Dic61—24no—
108C2×C22⋊Dic61—24no—
109C2×C22⋊Dic61—42no—
110C2×C22⋊Dic61C2314yes—
111C2×C22⋊Dic61C2314yes—
112C2×C22⋊Dic61C2314yes—
113C2×#11758198—24no—
114C2×#11758198—24no—
115C2×#11758198—24no—
116C2×#11758198—24no—
117C2×#11758198—24no—
118C2×#11758198C2314yes—
119C2×#11758198C2314yes—
120C2×#11758198C2314yes—
121C2×#11758198C2314yes—
122C2×#11758198C2314yes—
123C2×C4×Dic61—42no—
124C2×C4×Dic61C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129#14519684C2314yes—
130#14519684C2314yes—
131#14519684C2314yes—
132#14519684C2314yes—
133C25×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2311yescharacteristic
140C2×C4⋊C4×C61—24no—
141C2×C4⋊C4×C61C2314yes—
142C2×C22⋊C4×C61—24no—
143C2×C22⋊C4×C61—24no—
144C2×C22⋊C4×C61—42no—
145C2×C22⋊C4×C61C2314yes—
146C2×C22⋊C4×C61C2314yes—
147C2×C22⋊C4×C61C2314yes—
148C2×C42×C61—42no—
149C2×C42×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—22no—
159C24×C61C2412yes—
160C24×C61C2411yescharacteristic
161C23×D61—22no—
162C23×D61—22no—
163C23×D61—22no—
164C23×D61—22no—
165C23×D61—22no—
166C23×D61—22no—
167C23×D61C2×D414yes—
168C23×D61C2412yes—
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—22no—
182C22×C4×C61—22no—
183C22×C4×C61—22no—
184C22×C4×C61—22no—
185C22×C4×C61C2×D414yes—
186C22×C4×C61#4114yes—
187C22×C4×C61C2412yes—
188C22×C4×C61C2412yes—
189C22×C4×C61C2412yes—
190C22×C4×C61C2412yes—
191C22×C4×C61C2412yes—
192C22×C4×C61C2412yes—
193C2×C22⋊D61—28no—
194C2×C22⋊D61—44no—
195C2×C22⋊D61—44no—
196C2×C22⋊D61—416no—
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—22no—
209C22×Dic61—22no—
210C22×Dic61—22no—
211C22×Dic61—22no—
212C22×Dic61—22no—
213C22×Dic61—22no—
214C22×Dic61—22no—
215C22×Dic61—22no—
216C22×Dic61C2×D414yes—
217C22×Dic61#4114yes—
218C22×Dic61C2412yes—
219C22×Dic61C2412yes—
220C22×Dic61C2412yes—
221C22×Dic61C2412yes—
222C22×Dic61C2412yes—
223C22×Dic61C2412yes—
224C22×Dic61C2412yes—
225C2×C4×D61—416no—
226C2×C4×D61—44no—
227C2×C4×D61—44no—
228C2×C4×D61C2×D4116yes—
229C2×Dic122—28no—
230C2×Dic122—44no—
231C2×Dic122—44no—
232C2×Dic122—416no—
233C4⋊C4×C61—28no—
234C22⋊C4×C61—28no—
235C22⋊C4×C61—28no—
236C22⋊C4×C61—44no—
237C42×C61—44no—
238C22⋊Dic61—28no—
239C22⋊Dic61—28no—
240C22⋊Dic61—44no—
241#11758198—28no—
242#11758198—28no—
243#11758198—28no—
244#11758198—28no—
245#11758198—28no—
246C4⋊Dic61—28no—
247C4⋊Dic61—28no—
248C4⋊Dic61—44no—
249#11758196—28no—
250#11758196—28no—
251#11758196—28no—
252#11758196—28no—
253#11758196—44no—
254C4×Dic61—44no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—22no—
258C23×C61—22no—
259C23×C61—22no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—44no—
263C23×C61—44no—
264C23×C61—44no—
265C23×C61—44no—
266C23×C61—44no—
267C23×C61—44no—
268C23×C61—44no—
269C23×C61C22×D412yes—
270C23×C61C2×#4112yes—
271C23×C61C2×#4112yes—
272C23×C61H(5,𝔽2)12yes—
273C23×C61H(5,𝔽2)12yes—
274C23×C612−1+412yes—
275C23×C612−1+412yes—
276C23×C61C2511yescharacteristic
277C22×D61—28no—
278C22×D61—28no—
279C22×D61—28no—
280C22×D61—22no—
281C22×D61—22no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—44no—
287C22×D61—44no—
288C22×D61—44no—
289C22×D61—44no—
290C22×D61C22×D414yes—
291C2×C4×C61—28no—
292C2×C4×C61—28no—
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—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×C61—44no—
313C2×C4×C61C22×D414yes—
314C2×C4×C61C2×#4114yes—
315C22⋊D61—416no—
316C2×Dic61—28no—
317C2×Dic61—28no—
318C2×Dic61—22no—
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×Dic61—44no—
342C2×Dic61C22×D414yes—
343C2×Dic61C2×#4114yes—
344C4×D61—416no—
345Dic122—416no—
346C2×#2663—611nomaximal, Sylow
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—42no—
353C22×C61—42no—
354C22×C61—88no—
355C22×C61#53214yes—
356C22×C61#53414yes—
357C22×C61#53614yes—
358C22×C61#53914yes—
359C22×C61#53914yes—
360C22×C61#54214yes—
361C22×C61#54214yes—
362C22×C61C23×D411yescharacteristic
363C22×C61C22×#4111yescharacteristic
364C22×C61C22×#4111yescharacteristic
365C22×C61C2×H(5,𝔽2)11yescharacteristic
366C22×C61C2×H(5,𝔽2)11yescharacteristic
367C22×C61C2×2−1+411yescharacteristic
368C22×C61C2×2−1+411yescharacteristic
369C2×D61—24no—
370C2×D61—24no—
371C2×D61—24no—
372C2×D61—416no—
373C2×D61—42no—
374C2×D61—42no—
375C2×D61—42no—
376C2×D61—42no—
377C4×C61—24no—
378C4×C61—24no—
379C4×C61—42no—
380C4×C61—42no—
381C4×C61—42no—
382C4×C61—42no—
383Dic61—24no—
384Dic61—24no—
385Dic61—42no—
386Dic61—42no—
387Dic61—42no—
388Dic61—42no—
389Dic61—42no—
390C22×#123—611no—
391C22×C22⋊Q8—611no—
392#2663—6116no—
393C2×#400—611no—
394C2×#399—611no—
395C2×#397—611no—
396C2×#397—611no—
397C2×#395—611no—
398C2×#394—611no—
399C2×#394—611no—
400C2×#393—611no—
401C2×#389—611no—
402C2×#389—611no—
403C2×#388—611no—
404C2×#388D6111yescharacteristic, complemented
405C2×C4×C22⋊C4—611no—
406C2×C61—82no—
407C2×C61#266318yescomplemented
408C2×C61C2×#53211yescharacteristic
409C2×C61C2×#53411yescharacteristic
410C2×C61C2×#53611yescharacteristic
411C2×C61C2×#53911yescharacteristic
412C2×C61C2×#53911yescharacteristic
413C2×C61C2×#54211yescharacteristic
414C2×C61C2×#54211yescharacteristic
415D61—44no—
416C23×Q8—611no—
417C23×D4—611no—
418C24×C4—611no—
419C2×#123—618no—
420C2×#123—1228no—
421C2×C22⋊Q8—618no—
422C2×C22⋊Q8—1228no—
423C22×C4⋊C4—611no—
424C22×C4⋊C4—611no—
425C22×C4⋊C4—611no—
426C22×C4⋊C4—611no—
427C22×C4⋊C4—611no—
428C22×C4⋊C4—611no—
429C22×C4⋊C4—611no—
430C22×C4⋊C4—611no—
431C22×C4⋊C4C2×D6111yescharacteristic
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⋊C4—611no—
440C22×C22⋊C4C2×D6111yescharacteristic
441C22×C22⋊C4C2×D6111yescharacteristic
442C22×C22⋊C4C2×D6111yescharacteristic
443C22×C42—611no—
444C22×C42C2×D6111yescharacteristic
445#400—618no—
446#399—618no—
447#397—618no—
448#397—618no—
449#395—618no—
450#394—618no—
451#394—618no—
452#393—618no—
453#389—618no—
454#389—618no—
455#388—618no—
456#388C2×D6118yescomplemented
457C4×C22⋊C4—618no—
458C2×#95—611no—
459C2×#95—611no—
460C2×#95—611no—
461C2×#95—611no—
462C2×#95—611no—
463C2×#95—611no—
464C2×#95—611no—
465C2×#95—611no—
466C2×#95C2×D6111yescharacteristic
467C2×#95C2×D6111yescharacteristic
468C61C2×#266311yescharacteristic, complemented, Sylow
469C25—611no—
470C25C22×D6111yescharacteristic
471C22×Q8—614no—
472C22×Q8—1224no—
473C22×Q8—2442no—
474C22×Q8—2442no—
475C22×D4—614no—
476C22×D4—1224no—
477C22×D4—2442no—
478C22×D4—2442no—
479C23×C4—611no—
480C23×C4—611no—
481C23×C4—618no—
482C23×C4—614no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—2442no—
489C23×C4—2442no—
490C23×C4C22×D6111yescharacteristic
491C23×C4C22×D6111yescharacteristic
492C23×C4C22×D6111yescharacteristic
493C23×C4C22×D6111yescharacteristic
494C23×C4C22×D6111yescharacteristic
495C23×C4C22×D6111yescharacteristic
496#123—12232no—
497C22⋊Q8—12232no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—614no—
500C2×C4⋊C4—614no—
501C2×C4⋊C4—614no—
502C2×C4⋊C4—614no—
503C2×C4⋊C4—614no—
504C2×C4⋊C4—614no—
505C2×C4⋊C4—614no—
506C2×C4⋊C4—614no—
507C2×C4⋊C4—1224no—
508C2×C4⋊C4—1224no—
509C2×C4⋊C4—1224no—
510C2×C4⋊C4—1224no—
511C2×C4⋊C4—1224no—
512C2×C4⋊C4—1224no—
513C2×C4⋊C4—2442no—
514C2×C4⋊C4—2442no—
515C2×C4⋊C4C22×D6114yes—
516C2×C22⋊C4—24no—
517C2×C22⋊C4—24no—
518C2×C22⋊C4—42no—
519C2×C22⋊C4—614no—
520C2×C22⋊C4—614no—
521C2×C22⋊C4—614no—
522C2×C22⋊C4—614no—
523C2×C22⋊C4—614no—
524C2×C22⋊C4—614no—
525C2×C22⋊C4—614no—
526C2×C22⋊C4—614no—
527C2×C22⋊C4—1224no—
528C2×C22⋊C4—1224no—
529C2×C22⋊C4—1224no—
530C2×C22⋊C4—1224no—
531C2×C22⋊C4—1224no—
532C2×C22⋊C4—1224no—
533C2×C22⋊C4—1224no—
534C2×C22⋊C4—2442no—
535C2×C22⋊C4C22×D6114yes—
536C2×C22⋊C4C22×D6114yes—
537C2×C22⋊C4C22×D6114yes—
538C2×C42—42no—
539C2×C42—614no—
540C2×C42—2442no—
541C2×C42C22×D6114yes—
542#95—614no—
543#95—614no—
544#95—614no—
545#95—614no—
546#95—614no—
547#95—614no—
548#95—614no—
549#95—614no—
550#95C22×D6114yes—
551#95C22×D6114yes—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—614no—
560C24—612no—
561C24—1222no—
562C24—1222no—
563C24—1222no—
564C24—1222no—
565C24—1222no—
566C24—1222no—
567C24C23×D6112yes—
568C24C23×D6111yescharacteristic
569C2×Q8—1228no—
570C2×Q8—2444no—
571C2×Q8—2444no—
572C2×Q8—24416no—
573C2×D4—1228no—
574C2×D4—2444no—
575C2×D4—2444no—
576C2×D4—24416no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
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—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—614no—
594C22×C4—614no—
595C22×C4—612no—
596C22×C4—612no—
597C22×C4—6116no—
598C22×C4—612no—
599C22×C4—612no—
600C22×C4—612no—
601C22×C4—612no—
602C22×C4—612no—
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—1222no—
619C22×C4—1222no—
620C22×C4—1222no—
621C22×C4—1222no—
622C22×C4—24416no—
623C22×C4—2444no—
624C22×C4—2444no—
625C22×C4#1175822214yes—
626C22×C4D4×D6114yes—
627C22×C4C23×D6112yes—
628C22×C4C23×D6112yes—
629C22×C4C23×D6112yes—
630C22×C4C23×D6112yes—
631C22×C4C23×D6112yes—
632C22×C4C23×D6112yes—
633C4⋊C4—28no—
634C4⋊C4—1228no—
635C4⋊C4—1228no—
636C4⋊C4—1228no—
637C4⋊C4—1228no—
638C4⋊C4—1228no—
639C4⋊C4—1228no—
640C4⋊C4—2444no—
641C4⋊C4—2444no—
642C22⋊C4—28no—
643C22⋊C4—28no—
644C22⋊C4—44no—
645C22⋊C4—1228no—
646C22⋊C4—1228no—
647C22⋊C4—1228no—
648C22⋊C4—1228no—
649C22⋊C4—1228no—
650C22⋊C4—1228no—
651C22⋊C4—1228no—
652C22⋊C4—2444no—
653C42—44no—
654C42—2444no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—614no—
670C23—1228no—
671C23—1228no—
672C23—1222no—
673C23—1228no—
674C23—1222no—
675C23—1222no—
676C23—1222no—
677C23—1222no—
678C23—1222no—
679C23—2444no—
680C23—2444no—
681C23—2444no—
682C23—2444no—
683C23C2×D4×D6112yes—
684C23#41×D6112yes—
685C23C2×#1175822212yes—
686C23#1451982212yes—
687C23#1451982312yes—
688C23#1451982412yes—
689C23#1451982412yes—
690C23C24×D6111yescharacteristic
691Q8—24416no—
692D4—24416no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—28no—
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—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—614no—
716C2×C4—614no—
717C2×C4—1228no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
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—1222no—
736C2×C4—1222no—
737C2×C4—1222no—
738C2×C4—24416no—
739C2×C4—2444no—
740C2×C4—2444no—
741C2×C4—2444no—
742C2×C4—2444no—
743C2×C4—2444no—
744C2×C4C2×D4×D6114yes—
745C2×C4C2×#1175822214yes—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—88no—
754C22—1224no—
755C22—1224no—
756C22—1224no—
757C22—24416no—
758C22—2442no—
759C22—2442no—
760C22—2442no—
761C22—2442no—
762C22#1684030914yes—
763C22#1684032014yes—
764C22#1684033214yes—
765C22#1684035314yes—
766C22#1684035414yes—
767C22#1684038014yes—
768C22#1684038314yes—
769C22C22×D4×D6111yescharacteristic
770C22C2×#41×D6111yescharacteristic
771C22C22×#1175822211yescharacteristic
772C22C2×#1451982211yescharacteristic
773C22C2×#1451982311yescharacteristic
774C22C2×#1451982411yescharacteristic
775C22C2×#1451982411yescharacteristic
776C4—24no—
777C4—24no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—1224no—
783C4—1224no—
784C4—2442no—
785C4—2442no—
786C4—2442no—
787C4—2442no—
788C4—2442no—
789C2—82no—
790C2—2444no—
791C2#2145197118yesdirect product factor
792C2C2×#1684030911yescharacteristic
793C2C2×#1684032011yescharacteristic
794C2C2×#1684033211yescharacteristic
795C2C2×#1684035311yescharacteristic
796C2C2×#1684035411yescharacteristic
797C2C2×#1684038011yescharacteristic
798C2C2×#1684038311yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#388C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#388D61
hypocenterC61C2×#2663
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#14519755C2semidirect
3. #21451971C2direct (N × H)
4. C2×#16839704C2semidirect
5. C2×#16839698C2semidirect
6. C2×#16839691C2semidirect
7. C2×#16839689C2semidirect
8. C2×#16839683C2semidirect
11. C2×#16839674C2semidirect
12. C2×#16839660C2semidirect
13. C2×#16839657C2semidirect
14. C2×#16839656C2semidirect
15. C2×C4×#11758198C2semidirect
16. C2×C61×#388C2semidirect
23. C2×#14519755C22semidirect
41. #16839704C22semidirect
42. #16839698C22semidirect
43. #16839691C22semidirect
44. #16839689C22semidirect
45. #16839683C22semidirect
48. #16839674C22semidirect
49. #16839660C22semidirect
50. #16839657C22semidirect
51. #16839656C22semidirect
52. C4×#11758198C22semidirect
66. C61×#388C22semidirect
404. C2×#388D61semidirect
407. C2×C61#2663semidirect
456. #388C2×D61semidirect
468. C61C2×#2663semidirect
791. C2#21451971direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197592
C22×#145197552
#214519712
C2×#168397042
C2×#168396982
C2×#168396912
C2×#168396892
C2×#168396832
C2×#168396782
C2×#168396772
C2×#168396742
C2×#168396602
C2×#168396572
C2×#168396562
C2×C4×#117581982
C2×C61×#3882
C2×#266361