Finite Group Databasebeta

← C2×#21449295 #29847717

Subgroups — C2×#21449295 #29847717

Order 15616.

3222 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519759C211yesmaximal, characteristic
2C22×C4×C22⋊D61C211yesmaximal, characteristic
3#21449295C2116yesmaximal, direct product factor
4C2×#16839703C211yesmaximal, characteristic, complemented
5C2×#16839695C211yesmaximal, characteristic, complemented
6C2×#16839690C211yesmaximal, characteristic, complemented
7C2×#16839687C211yesmaximal, characteristic, complemented
8C2×#16839648C211yesmaximal, characteristic, complemented
9C2×#16839645C211yesmaximal, characteristic, complemented
10C2×#16839638C211yesmaximal, characteristic
11C2×#16839633C211yesmaximal, characteristic, complemented
12C2×#16839625C211yesmaximal, characteristic, complemented
13C2×#16839624C211yesmaximal, characteristic, complemented
14C2×#16839619C211yesmaximal, characteristic, complemented
15C2×#95×D61C211yesmaximal, characteristic, complemented
16C2×C61×#385C211yesmaximal, characteristic, complemented
17C23×C22⋊D61C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519759—28no—
22C2×#14519759C2218yes—
23C2×C4×C22⋊D61—28no—
24C2×C4×C22⋊D61C2218yes—
25C22×C4⋊Dic61C2211yescharacteristic
26C22×C4⋊Dic61C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×C22⋊Dic61C2211yescharacteristic
31C22×C22⋊Dic61C2211yescharacteristic
32C22×C22⋊Dic61C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37#16839703C2218yescomplemented
38#16839695C2218yescomplemented
39#16839690C2218yescomplemented
40#16839687C2218yescomplemented
41#16839648C2218yescomplemented
42#16839645C2218yescomplemented
43#16839638C2218yes—
44#16839633C2218yescomplemented
45#16839625C2218yescomplemented
46#16839624C2218yescomplemented
47#16839619C2218yescomplemented
48C2×#14519684C2211yescharacteristic
49C2×#14519684C2211yescharacteristic
50C2×#14519684C2211yescharacteristic
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60#95×D61C2218yescomplemented
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⋊D61D418yes—
73C22×C22⋊D61C2314yes—
74C23×Dic61C2311yescharacteristic
75C23×Dic61C2311yescharacteristic
76C23×Dic61C2311yescharacteristic
77C23×Dic61C2311yescharacteristic
78C23×Dic61C2311yescharacteristic
79C23×Dic61C2311yescharacteristic
80C23×Dic61C2311yescharacteristic
81C22×C4×D61—24no—
82C22×C4×D61—24no—
83C22×C4×D61—24no—
84C22×C4×D61—24no—
85C22×C4×D61—24no—
86C22×C4×D61—24no—
87C22×C4×D61—24no—
88C22×C4×D61—42no—
89C22×C4×D61—42no—
90C22×C4×D61C2314yes—
91C22×C4×D61C2314yes—
92C22×C4×D61C2314yes—
93#14519759—232no—
94C4×C22⋊D61—232no—
95C2×C4⋊Dic61—24no—
96C2×C4⋊Dic61—24no—
97C2×C4⋊Dic61C2314yes—
98C2×C4⋊Dic61C2314yes—
99C2×#11758196—24no—
100C2×#11758196—24no—
101C2×#11758196—42no—
102C2×#11758196C2314yes—
103C2×#11758196C2314yes—
104C2×#11758196C2314yes—
105C2×C22⋊Dic61—24no—
106C2×C22⋊Dic61—24no—
107C2×C22⋊Dic61—42no—
108C2×C22⋊Dic61C2314yes—
109C2×C22⋊Dic61C2314yes—
110C2×C22⋊Dic61C2314yes—
111C2×#11758198—24no—
112C2×#11758198—24no—
113C2×#11758198—24no—
114C2×#11758198C2314yes—
115C2×#11758198C2314yes—
116C2×#11758198C2314yes—
117C2×C4×Dic61—24no—
118C2×C4×Dic61C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
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—42no—
135C23×C4×C61C2311yescharacteristic
136C23×C4×C61C2311yescharacteristic
137C23×C4×C61C2311yescharacteristic
138C23×C4×C61C2311yescharacteristic
139C23×C4×C61C2314yes—
140C23×C4×C61C2311yescharacteristic
141C23×C4×C61C2311yescharacteristic
142C2×C4⋊C4×C61—24no—
143C2×C4⋊C4×C61—42no—
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×C61C2×D414yes—
159C24×C61C2412yes—
160C24×C61C2411yescharacteristic
161C23×D61—22no—
162C23×D61—22no—
163C23×D61—22no—
164C23×D61—22no—
165C23×D61C2×D414yes—
166C23×D61#4114yes—
167C23×D61#4114yes—
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—28no—
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×C61—22no—
186C22×C4×C61—28no—
187C22×C4×C61—44no—
188C22×C4×C61—416no—
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—232no—
198C2×C22⋊D61—28no—
199C2×C22⋊D61—28no—
200C2×C22⋊D61C2×D4116yes—
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×Dic61—22no—
220C22×Dic61—22no—
221C22×Dic61C2×D414yes—
222C22×Dic61C2412yes—
223C22×Dic61C2412yes—
224C22×Dic61C2412yes—
225C22×Dic61C2412yes—
226C22×Dic61C2412yes—
227C22×Dic61C2412yes—
228C22×Dic61C2412yes—
229C2×C4×D61—28no—
230C2×C4×D61—28no—
231C2×C4×D61—28no—
232C2×C4×D61—28no—
233C2×C4×D61—28no—
234C2×C4×D61—28no—
235C2×C4×D61—28no—
236C2×C4×D61—44no—
237C2×C4×D61—44no—
238C2×C4×D61—416no—
239C2×C4×D61—416no—
240C2×C4×D61—416no—
241C4⋊C4×C61—28no—
242C4⋊C4×C61—44no—
243C22⋊C4×C61—28no—
244C22⋊C4×C61—28no—
245C22⋊Dic61—28no—
246C22⋊Dic61—28no—
247C22⋊Dic61—44no—
248#11758198—28no—
249#11758198—28no—
250#11758198—28no—
251C4⋊Dic61—28no—
252C4⋊Dic61—28no—
253#11758196—28no—
254#11758196—28no—
255#11758196—44no—
256C4×Dic61—28no—
257C23×C61—28no—
258C23×C61—28no—
259C23×C61—28no—
260C23×C61—22no—
261C23×C61—22no—
262C23×C61—22no—
263C23×C61—22no—
264C23×C61—22no—
265C23×C61—22no—
266C23×C61—44no—
267C23×C61—44no—
268C23×C61—44no—
269C23×C61—44no—
270C23×C61C22×D414yes—
271C23×C61C22×D412yes—
272C23×C61C2×#4112yes—
273C23×C61C2×#4112yes—
274C23×C61C2×#4112yes—
275C23×C61C2×#4112yes—
276C23×C61H(5,𝔽2)12yes—
277C23×C612−1+412yes—
278C23×C61C2511yescharacteristic
279C22×D61—28no—
280C22×D61—28no—
281C22×D61—28no—
282C22×D61—28no—
283C22×D61—28no—
284C22×D61—28no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61#123116yes—
290C22×D61C22×D414yes—
291C22×D61C2×#4114yes—
292C22×D61C2×#4114yes—
293C2×C4×C61—28no—
294C2×C4×C61—28no—
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—22no—
310C2×C4×C61—22no—
311C2×C4×C61—416no—
312C2×C4×C61—44no—
313C2×C4×C61—44no—
314C2×C4×C61—44no—
315C2×C4×C61—44no—
316C2×C4×C61C2×#4114yes—
317C2×C4×C61C2×#4114yes—
318C22⋊D61—232no—
319C2×Dic61—28no—
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—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—44no—
341C2×Dic61—44no—
342C2×Dic61—44no—
343C2×Dic61—44no—
344C2×Dic61—44no—
345C2×Dic61—44no—
346C2×Dic61C22×D414yes—
347C4×D61—416no—
348C4×D61—416no—
349C4×D61—416no—
350C2×#2419—611nomaximal, Sylow
351C22×C61—24no—
352C22×C61—24no—
353C22×C61—24no—
354C22×C61—42no—
355C22×C61—416no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—42no—
359C22×C61C2×#12314yes—
360C22×C61#52914yes—
361C22×C61#53914yes—
362C22×C61#54614yes—
363C22×C61#54714yes—
364C22×C61#55114yes—
365C22×C61#55214yes—
366C22×C61C23×D411yescharacteristic
367C22×C61C22×#4111yescharacteristic
368C22×C61C22×#4111yescharacteristic
369C22×C61C22×#4111yescharacteristic
370C22×C61C22×#4111yescharacteristic
371C22×C61C2×H(5,𝔽2)11yescharacteristic
372C22×C61C2×2−1+411yescharacteristic
373C2×D61—24no—
374C2×D61—232no—
375C2×D61—24no—
376C2×D61—24no—
377C2×D61—24no—
378C2×D61—24no—
379C2×D61—24no—
380C2×D61C2×#12318yes—
381C4×C61—24no—
382C4×C61—24no—
383C4×C61—42no—
384C4×C61—42no—
385C4×C61—42no—
386C4×C61—42no—
387Dic61—24no—
388Dic61—42no—
389Dic61—42no—
390Dic61—42no—
391Dic61—42no—
392Dic61—42no—
393Dic61—42no—
394C22×#123—611no—
395C22×C4×D4—611no—
396#2419—6116no—
397C2×#400—611no—
398C2×#398—611no—
399C2×#397—611no—
400C2×#397—611no—
401C2×#387—611no—
402C2×#387—611no—
403C2×#386—611no—
404C2×#385—611no—
405C2×#385D6111yescharacteristic, complemented
406C2×#381—611no—
407C2×#381—611no—
408C2×#380—611no—
409C22×#95—611no—
410C2×C61—44no—
411C2×C61#241918yescomplemented
412C2×C61C22×#12311yescharacteristic
413C2×C61C2×#52911yescharacteristic
414C2×C61C2×#53911yescharacteristic
415C2×C61C2×#54611yescharacteristic
416C2×C61C2×#54711yescharacteristic
417C2×C61C2×#55111yescharacteristic
418C2×C61C2×#55211yescharacteristic
419D61—28no—
420C23×D4—611no—
421C24×C4—611no—
422C24×C4—611no—
423C24×C4—611no—
424C24×C4C2×D6111yescharacteristic
425C2×#123—618no—
426C2×#123—1228no—
427C2×C4×D4—618no—
428C2×C4×D4—1228no—
429C22×C4⋊C4—611no—
430C22×C4⋊C4—611no—
431C22×C4⋊C4—611no—
432C22×C4⋊C4—611no—
433C22×C4⋊C4—611no—
434C22×C4⋊C4C2×D6111yescharacteristic
435C22×C4⋊C4C2×D6111yescharacteristic
436C22×C22⋊C4—611no—
437C22×C22⋊C4—611no—
438C22×C22⋊C4—611no—
439C22×C22⋊C4—611no—
440C22×C22⋊C4—611no—
441C22×C22⋊C4—611no—
442C22×C22⋊C4C2×D6111yescharacteristic
443C22×C22⋊C4C2×D6111yescharacteristic
444C22×C42—611no—
445#400—618no—
446#398—618no—
447#397—618no—
448#397—618no—
449#387—618no—
450#387—618no—
451#386—618no—
452#385—618no—
453#385C2×D6118yescomplemented
454#381—618no—
455#381—618no—
456#380—618no—
457C2×#95—611no—
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×#95—611no—
467C2×#95—611no—
468C2×#95—611no—
469C2×#95—618no—
470C2×#95C2×D6111yescharacteristic
471C2×#95C2×D6111yescharacteristic
472C61C2×#241911yescharacteristic, complemented, Sylow
473C25—611no—
474C25C22×D6111yescharacteristic
475C22×D4—618no—
476C22×D4—614no—
477C22×D4—1224no—
478C22×D4—1224no—
479C23×C4—24no—
480C23×C4—24no—
481C23×C4—42no—
482C23×C4—611no—
483C23×C4—611no—
484C23×C4—611no—
485C23×C4—611no—
486C23×C4—611no—
487C23×C4—611no—
488C23×C4—611no—
489C23×C4—614no—
490C23×C4—614no—
491C23×C4—614no—
492C23×C4—1224no—
493C23×C4—1224no—
494C23×C4—1224no—
495C23×C4—1224no—
496C23×C4—1224no—
497C23×C4—1224no—
498C23×C4—1224no—
499C23×C4—2442no—
500C23×C4—2442no—
501C23×C4C22×D6111yescharacteristic
502C23×C4C22×D6111yescharacteristic
503C23×C4C22×D6111yescharacteristic
504C23×C4C22×D6111yescharacteristic
505C23×C4C22×D6114yes—
506C23×C4C22×D6111yescharacteristic
507C23×C4C22×D6111yescharacteristic
508#123—12232no—
509C4×D4—12232no—
510C2×C4⋊C4—24no—
511C2×C4⋊C4—42no—
512C2×C4⋊C4—614no—
513C2×C4⋊C4—614no—
514C2×C4⋊C4—614no—
515C2×C4⋊C4—614no—
516C2×C4⋊C4—614no—
517C2×C4⋊C4—1224no—
518C2×C4⋊C4—1224no—
519C2×C4⋊C4—1224no—
520C2×C4⋊C4—1224no—
521C2×C4⋊C4—2442no—
522C2×C4⋊C4C22×D6114yes—
523C2×C4⋊C4C22×D6114yes—
524C2×C22⋊C4—24no—
525C2×C22⋊C4—24no—
526C2×C22⋊C4—614no—
527C2×C22⋊C4—614no—
528C2×C22⋊C4—614no—
529C2×C22⋊C4—614no—
530C2×C22⋊C4—614no—
531C2×C22⋊C4—614no—
532C2×C22⋊C4—1224no—
533C2×C22⋊C4—1224no—
534C2×C22⋊C4—1224no—
535C2×C22⋊C4—1224no—
536C2×C22⋊C4—1224no—
537C2×C22⋊C4—2442no—
538C2×C22⋊C4C22×D6114yes—
539C2×C22⋊C4C22×D6114yes—
540C2×C42—614no—
541C2×C42—1224no—
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#95—614no—
551#95—614no—
552#95—614no—
553#95—614no—
554#95C22×D6114yes—
555#95C22×D6114yes—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—22no—
560C24—22no—
561C24—22no—
562C24—614no—
563C24—614no—
564C24—614no—
565C24—612no—
566C24—1222no—
567C24—1222no—
568C24—1222no—
569C24—1222no—
570C24D4×D6114yes—
571C24C23×D6112yes—
572C24C23×D6111yescharacteristic
573C2×D4—6116no—
574C2×D4—12232no—
575C2×D4—1228no—
576C2×D4—1228no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—28no—
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—22no—
594C22×C4—28no—
595C22×C4—44no—
596C22×C4—416no—
597C22×C4—614no—
598C22×C4—612no—
599C22×C4—612no—
600C22×C4—612no—
601C22×C4—612no—
602C22×C4—612no—
603C22×C4—612no—
604C22×C4—612no—
605C22×C4—1228no—
606C22×C4—1228no—
607C22×C4—1228no—
608C22×C4—1228no—
609C22×C4—1228no—
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—1222no—
623C22×C4—1222no—
624C22×C4—1222no—
625C22×C4—1222no—
626C22×C4—1222no—
627C22×C4—1222no—
628C22×C4—1222no—
629C22×C4—1222no—
630C22×C4—1228no—
631C22×C4—1228no—
632C22×C4—2444no—
633C22×C4—2444no—
634C22×C4—24416no—
635C22×C4—24416no—
636C22×C4—24416no—
637C22×C4#1175822214yes—
638C22×C4#1175822414yes—
639C22×C4C23×D6112yes—
640C22×C4C23×D6112yes—
641C22×C4C23×D6112yes—
642C22×C4C23×D6112yes—
643C22×C4C23×D6112yes—
644C22×C4C23×D6112yes—
645C4⋊C4—28no—
646C4⋊C4—44no—
647C4⋊C4—1228no—
648C4⋊C4—1228no—
649C4⋊C4—1228no—
650C4⋊C4—1228no—
651C4⋊C4—2444no—
652C22⋊C4—28no—
653C22⋊C4—28no—
654C22⋊C4—1228no—
655C22⋊C4—1228no—
656C22⋊C4—1228no—
657C22⋊C4—1228no—
658C22⋊C4—1228no—
659C22⋊C4—2444no—
660C42—1228no—
661C23—28no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—28no—
669C23—28no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—6116no—
675C23—614no—
676C23—614no—
677C23—614no—
678C23—1228no—
679C23—1222no—
680C23—1222no—
681C23—1222no—
682C23—1222no—
683C23—1228no—
684C23—1228no—
685C23—1228no—
686C23—1228no—
687C23—1228no—
688C23C2×D4×D6114yes—
689C23C2×D4×D6112yes—
690C23#41×D6112yes—
691C23#41×D6112yes—
692C23C2×#1175822412yes—
693C23C2×#1175822212yes—
694C23#1451982212yes—
695C23#1451982512yes—
696C23C24×D6111yescharacteristic
697D4—12232no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—28no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—416no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—44no—
720C2×C4—44no—
721C2×C4—614no—
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—1222no—
739C2×C4—1222no—
740C2×C4—1222no—
741C2×C4—1222no—
742C2×C4—1222no—
743C2×C4—24416no—
744C2×C4—24416no—
745C2×C4—24416no—
746C2×C4—2444no—
747C2×C4—2444no—
748C2×C4—2444no—
749C2×C4—2444no—
750C2×C4—2444no—
751C2×C4—2444no—
752C2×C4C2×#1175822414yes—
753C2×C4C2×#1175822214yes—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—416no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—618no—
763C22—1224no—
764C22—1224no—
765C22—12232no—
766C22—1224no—
767C22—1224no—
768C22—1224no—
769C22—1224no—
770C22#123×D6114yes—
771C22#1684029414yes—
772C22#1684035814yes—
773C22#1684039914yes—
774C22#1684041314yes—
775C22#1684044114yes—
776C22#1684044614yes—
777C22C22×D4×D6111yescharacteristic
778C22C2×#41×D6111yescharacteristic
779C22C2×#41×D6111yescharacteristic
780C22C22×#1175822411yescharacteristic
781C22C22×#1175822211yescharacteristic
782C22C2×#1451982211yescharacteristic
783C22C2×#1451982511yescharacteristic
784C4—24no—
785C4—24no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—42no—
790C4—1224no—
791C4—2442no—
792C4—2442no—
793C4—2442no—
794C4—2442no—
795C4—2442no—
796C4—2442no—
797C2—44no—
798C2—1228no—
799C2#2144929518yesdirect product factor
800C2C2×#123×D6111yescharacteristic
801C2C2×#1684029411yescharacteristic
802C2C2×#1684035811yescharacteristic
803C2C2×#1684039911yescharacteristic
804C2C2×#1684041311yescharacteristic
805C2C2×#1684044111yescharacteristic
806C2C2×#1684044611yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#385C2
socleC24×C61C24
prime radicalC23×C22⋊D61C22
hypercenterC2×#385D61
hypocenterC61C2×#2419
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
3. #21449295C2direct (N × H)
4. C2×#16839703C2semidirect
5. C2×#16839695C2semidirect
6. C2×#16839690C2semidirect
7. C2×#16839687C2semidirect
8. C2×#16839648C2semidirect
9. C2×#16839645C2semidirect
11. C2×#16839633C2semidirect
12. C2×#16839625C2semidirect
13. C2×#16839624C2semidirect
14. C2×#16839619C2semidirect
15. C2×#95×D61C2semidirect
16. C2×C61×#385C2semidirect
37. #16839703C22semidirect
38. #16839695C22semidirect
39. #16839690C22semidirect
40. #16839687C22semidirect
41. #16839648C22semidirect
42. #16839645C22semidirect
44. #16839633C22semidirect
45. #16839625C22semidirect
46. #16839624C22semidirect
47. #16839619C22semidirect
60. #95×D61C22semidirect
66. C61×#385C22semidirect
405. C2×#385D61semidirect
411. C2×C61#2419semidirect
453. #385C2×D61semidirect
472. C61C2×#2419semidirect
799. C2#21449295direct (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×C4×C22⋊D612
#214492952
C2×#168397032
C2×#168396952
C2×#168396902
C2×#168396872
C2×#168396482
C2×#168396452
C2×#168396382
C2×#168396332
C2×#168396252
C2×#168396242
C2×#168396192
C2×#95×D612
C2×C61×#3852
C2×#241961