Finite Group Databasebeta

← C2×#21449321 #29848249

Subgroups — C2×#21449321 #29848249

Order 15616.

2702 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519755C211yesmaximal, characteristic
2C22×C4×Dic122C211yesmaximal, characteristic, complemented
3#21449321C2116yesmaximal, direct product factor
4C2×#16839703C211yesmaximal, characteristic, complemented
5C2×#16839701C211yesmaximal, characteristic, complemented
6C2×#16839691C211yesmaximal, characteristic
7C2×#16839689C211yesmaximal, characteristic
8C2×#16839666C211yesmaximal, characteristic, complemented
9C2×#16839657C211yesmaximal, characteristic, complemented
10C2×#16839653C211yesmaximal, characteristic
11C2×#16839652C211yesmaximal, characteristic
12C2×#16839644C211yesmaximal, characteristic, complemented
13C2×#16839626C211yesmaximal, characteristic, complemented
14C2×#16839621C211yesmaximal, characteristic
15C2×#16839609C211yesmaximal, characteristic
16C2×C61×#387C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×C4×D61C2211yescharacteristic
19C2×#14519755—28no—
20C2×#14519755C2218yes—
21C2×C4×Dic122—28no—
22C2×C4×Dic122C2218yescomplemented
23C22×C4⋊Dic61C2211yescharacteristic
24C22×#11758196C2211yescharacteristic
25C22×#11758196C2211yescharacteristic
26C22×#11758196C2211yescharacteristic
27C22×#11758196C2211yescharacteristic
28C22×#11758196C2211yescharacteristic
29C22×#11758196C2211yescharacteristic
30C22×#11758198C2211yescharacteristic
31C22×#11758198C2211yescharacteristic
32C22×#11758198C2211yescharacteristic
33C22×#11758198C2211yescharacteristic
34C22×#11758198C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37C22×C4×Dic61C2211yescharacteristic
38C22×C4×Dic61C2211yescharacteristic
39#16839703C2218yescomplemented
40#16839701C2218yescomplemented
41#16839691C2218yes—
42#16839689C2218yes—
43#16839666C2218yescomplemented
44#16839657C2218yescomplemented
45#16839653C2218yes—
46#16839652C2218yes—
47#16839644C2218yescomplemented
48#16839626C2218yescomplemented
49#16839621C2218yes—
50#16839609C2218yes—
51C2×#14519684C2211yescharacteristic
52C2×#14519684C2211yescharacteristic
53C2×#14519684C2211yescharacteristic
54C2×#14519684C2211yescharacteristic
55C2×#14519684C2211yescharacteristic
56C2×#14519684C2211yescharacteristic
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C22×C4⋊C4×C61C2211yescharacteristic
62C22×C4⋊C4×C61C2211yescharacteristic
63C22×C42×C61C2211yescharacteristic
64C61×#387C2218yescomplemented
65C2×#95×C61C2211yescharacteristic
66C2×#95×C61C2211yescharacteristic
67C2×#95×C61C2211yescharacteristic
68C2×#95×C61C2211yescharacteristic
69C24×D61C2311yescharacteristic
70C22×Dic122—24no—
71C22×Dic122—24no—
72C22×Dic122D418yes—
73C22×Dic122C2314yes—
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×D61C2314yes—
85#14519755—232no—
86C4×Dic122—232no—
87C2×C4⋊Dic61—24no—
88C2×C4⋊Dic61C2314yes—
89C2×#11758196—24no—
90C2×#11758196—24no—
91C2×#11758196—24no—
92C2×#11758196—24no—
93C2×#11758196—24no—
94C2×#11758196—24no—
95C2×#11758196C2314yes—
96C2×#11758196C2314yes—
97C2×#11758196C2314yes—
98C2×#11758196C2314yes—
99C2×#11758196C2314yes—
100C2×#11758196C2314yes—
101C2×#11758198—24no—
102C2×#11758198—24no—
103C2×#11758198—24no—
104C2×#11758198—24no—
105C2×#11758198—24no—
106C2×#11758198—24no—
107C2×#11758198C2314yes—
108C2×#11758198C2314yes—
109C2×#11758198C2314yes—
110C2×#11758198C2314yes—
111C2×#11758198C2314yes—
112C2×#11758198C2314yes—
113C2×C4×Dic61—24no—
114C2×C4×Dic61—24no—
115C2×C4×Dic61—24no—
116C2×C4×Dic61C2314yes—
117C2×C4×Dic61C2314yes—
118C2×C4×Dic61C2314yes—
119#14519684C2314yes—
120#14519684C2314yes—
121#14519684C2314yes—
122#14519684C2314yes—
123#14519684C2314yes—
124#14519684C2314yes—
125#14519684C2314yes—
126#14519684C2314yes—
127#14519684C2314yes—
128#14519684C2314yes—
129C23×C4×C61C2311yescharacteristic
130C23×C4×C61C2311yescharacteristic
131C23×C4×C61C2311yescharacteristic
132C23×C4×C61C2311yescharacteristic
133C23×C4×C61C2311yescharacteristic
134C23×C4×C61C2311yescharacteristic
135C23×C4×C61C2311yescharacteristic
136C2×C4⋊C4×C61—24no—
137C2×C4⋊C4×C61—24no—
138C2×C4⋊C4×C61C2314yes—
139C2×C4⋊C4×C61C2314yes—
140C2×C42×C61—24no—
141C2×C42×C61C2314yes—
142#95×C61C2314yes—
143#95×C61C2314yes—
144#95×C61C2314yes—
145#95×C61C2314yes—
146C24×C61C2411yescharacteristic
147C23×D61—22no—
148C23×D61—22no—
149C23×D61—22no—
150C23×D61—22no—
151C23×D61—22no—
152C23×D61—22no—
153C23×D61#4114yes—
154C23×D61C2412yes—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—22no—
159C22×C4×C61—22no—
160C22×C4×C61—22no—
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×C61C2×D414yes—
175C22×C4×C61#4114yes—
176C22×C4×C61C2412yes—
177C22×C4×C61C2412yes—
178C22×C4×C61C2412yes—
179C22×C4×C61C2412yes—
180C22×C4×C61C2412yes—
181C22×C4×C61C2412yes—
182C22×C4×C61C2412yes—
183C22×Dic61—22no—
184C22×Dic61—22no—
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×Dic61C2×D414yes—
201C22×Dic61C2×D414yes—
202C22×Dic61#4114yes—
203C22×Dic61#4114yes—
204C22×Dic61C2412yes—
205C22×Dic61C2412yes—
206C22×Dic61C2412yes—
207C22×Dic61C2412yes—
208C22×Dic61C2412yes—
209C22×Dic61C2412yes—
210C22×Dic61C2412yes—
211C2×C4×D61—28no—
212C2×C4×D61—28no—
213C2×C4×D61—28no—
214C2×C4×D61—416no—
215C2×Dic122—232no—
216C2×Dic122—28no—
217C2×Dic122—28no—
218C2×Dic122C2×D4116yes—
219C4⋊C4×C61—28no—
220C4⋊C4×C61—28no—
221C42×C61—28no—
222#11758198—28no—
223#11758198—28no—
224#11758198—28no—
225#11758198—28no—
226#11758198—28no—
227#11758198—28no—
228C4⋊Dic61—28no—
229#11758196—28no—
230#11758196—28no—
231#11758196—28no—
232#11758196—28no—
233#11758196—28no—
234#11758196—28no—
235C4×Dic61—28no—
236C4×Dic61—28no—
237C4×Dic61—28no—
238C23×C61C22×D412yes—
239C23×C61C2×#4112yes—
240C23×C61C2×#4112yes—
241C23×C61C2×#4112yes—
242C23×C61C2×#4112yes—
243C23×C612−1+412yes—
244C23×C612−1+412yes—
245C23×C61C2511yescharacteristic
246C22×D61—28no—
247C22×D61—28no—
248C22×D61—28no—
249C22×D61—22no—
250C22×D61—22no—
251C22×D61—22no—
252C22×D61—22no—
253C22×D61—22no—
254C22×D61—22no—
255C22×D61—44no—
256C22×D61—44no—
257C22×D61—44no—
258C22×D61—44no—
259C22×D61C2×#4114yes—
260C2×C4×C61—28no—
261C2×C4×C61—28no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—22no—
270C2×C4×C61—22no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—22no—
277C2×C4×C61—22no—
278C2×C4×C61—22no—
279C2×C4×C61—22no—
280C2×C4×C61—22no—
281C2×C4×C61—44no—
282C2×C4×C61—44no—
283C2×C4×C61—44no—
284C2×C4×C61—44no—
285C2×C4×C61—44no—
286C2×C4×C61C22×D414yes—
287C2×C4×C61C2×#4114yes—
288C2×Dic61—28no—
289C2×Dic61—22no—
290C2×Dic61—22no—
291C2×Dic61—22no—
292C2×Dic61—22no—
293C2×Dic61—22no—
294C2×Dic61—22no—
295C2×Dic61—22no—
296C2×Dic61—22no—
297C2×Dic61—22no—
298C2×Dic61—22no—
299C2×Dic61—22no—
300C2×Dic61—22no—
301C2×Dic61—22no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—22no—
305C2×Dic61—22no—
306C2×Dic61—44no—
307C2×Dic61—44no—
308C2×Dic61—44no—
309C2×Dic61—44no—
310C2×Dic61—44no—
311C2×Dic61#123116yes—
312C2×Dic61C22×D414yes—
313C2×Dic61C22×D414yes—
314C2×Dic61C2×#4114yes—
315C2×Dic61C2×#4114yes—
316C4×D61—416no—
317Dic122—232no—
318C2×#2421—611nomaximal, Sylow
319C22×C61C2×#12314yes—
320C22×C61#52914yes—
321C22×C61#54114yes—
322C22×C61#54814yes—
323C22×C61#54814yes—
324C22×C61#55214yes—
325C22×C61#55614yes—
326C22×C61C23×D411yescharacteristic
327C22×C61C22×#4111yescharacteristic
328C22×C61C22×#4111yescharacteristic
329C22×C61C22×#4111yescharacteristic
330C22×C61C22×#4111yescharacteristic
331C22×C61C2×2−1+411yescharacteristic
332C22×C61C2×2−1+411yescharacteristic
333C2×D61—24no—
334C2×D61—24no—
335C2×D61—24no—
336C2×D61—42no—
337C2×D61—416no—
338C2×D61—42no—
339C2×D61—42no—
340C2×D61—42no—
341C4×C61—24no—
342C4×C61—24no—
343C4×C61—42no—
344C4×C61—42no—
345C4×C61—42no—
346C4×C61—42no—
347C4×C61—42no—
348Dic61—24no—
349Dic61—42no—
350Dic61—42no—
351Dic61—42no—
352Dic61—42no—
353Dic61—42no—
354Dic61C2×#12318yes—
355C22×C22⋊Q8—611no—
356C22×C4×Q8—611no—
357#2421—6116no—
358C2×#400—611no—
359C2×#400—611no—
360C2×#397—611no—
361C2×#397—611no—
362C2×#391—611no—
363C2×#389—611no—
364C2×#388—611no—
365C2×#388—611no—
366C2×#387—611no—
367C2×#387D6111yescharacteristic, complemented
368C2×#382—611no—
369C2×#380—611no—
370C2×C4×C22⋊C4—611no—
371C2×C61#242118yescomplemented
372C2×C61C22×#12311yescharacteristic
373C2×C61C2×#52911yescharacteristic
374C2×C61C2×#54111yescharacteristic
375C2×C61C2×#54811yescharacteristic
376C2×C61C2×#54811yescharacteristic
377C2×C61C2×#55211yescharacteristic
378C2×C61C2×#55611yescharacteristic
379D61—44no—
380C23×Q8—611no—
381C24×C4—611no—
382C2×C22⋊Q8—618no—
383C2×C22⋊Q8—1228no—
384C2×C4×Q8—618no—
385C2×C4×Q8—1228no—
386C22×C4⋊C4—611no—
387C22×C4⋊C4—611no—
388C22×C4⋊C4—611no—
389C22×C4⋊C4—611no—
390C22×C4⋊C4—611no—
391C22×C4⋊C4—611no—
392C22×C4⋊C4—611no—
393C22×C4⋊C4C2×D6111yescharacteristic
394C22×C4⋊C4C2×D6111yescharacteristic
395C22×C22⋊C4—611no—
396C22×C22⋊C4—611no—
397C22×C22⋊C4—611no—
398C22×C22⋊C4—611no—
399C22×C22⋊C4—611no—
400C22×C22⋊C4—611no—
401C22×C42—611no—
402C22×C42—611no—
403C22×C42—611no—
404C22×C42C2×D6111yescharacteristic
405#400—618no—
406#400—618no—
407#397—618no—
408#397—618no—
409#391—618no—
410#389—618no—
411#388—618no—
412#388—618no—
413#387—618no—
414#387C2×D6118yescomplemented
415#382—618no—
416#380—618no—
417C4×C22⋊C4—618no—
418C2×#95—611no—
419C2×#95—611no—
420C2×#95—611no—
421C2×#95—611no—
422C2×#95—611no—
423C2×#95—611no—
424C2×#95—611no—
425C2×#95—611no—
426C2×#95—611no—
427C2×#95—611no—
428C2×#95C2×D6111yescharacteristic
429C2×#95C2×D6111yescharacteristic
430C2×#95C2×D6111yescharacteristic
431C2×#95C2×D6111yescharacteristic
432C61C2×#242111yescharacteristic, complemented, Sylow
433C25—611no—
434C22×Q8—618no—
435C22×Q8—614no—
436C22×Q8—1224no—
437C22×Q8—1224no—
438C23×C4—611no—
439C23×C4—611no—
440C23×C4—611no—
441C23×C4—611no—
442C23×C4—611no—
443C23×C4—611no—
444C23×C4—611no—
445C23×C4—614no—
446C23×C4—1224no—
447C23×C4—1224no—
448C23×C4—1224no—
449C23×C4C22×D6111yescharacteristic
450C23×C4C22×D6111yescharacteristic
451C23×C4C22×D6111yescharacteristic
452C23×C4C22×D6111yescharacteristic
453C23×C4C22×D6111yescharacteristic
454C23×C4C22×D6111yescharacteristic
455C23×C4C22×D6111yescharacteristic
456C22⋊Q8—12232no—
457C4×Q8—12232no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—24no—
460C2×C4⋊C4—614no—
461C2×C4⋊C4—614no—
462C2×C4⋊C4—614no—
463C2×C4⋊C4—614no—
464C2×C4⋊C4—614no—
465C2×C4⋊C4—614no—
466C2×C4⋊C4—614no—
467C2×C4⋊C4—1224no—
468C2×C4⋊C4—1224no—
469C2×C4⋊C4—1224no—
470C2×C4⋊C4—1224no—
471C2×C4⋊C4—1224no—
472C2×C4⋊C4—1224no—
473C2×C4⋊C4—1224no—
474C2×C4⋊C4C22×D6114yes—
475C2×C4⋊C4C22×D6114yes—
476C2×C22⋊C4—614no—
477C2×C22⋊C4—614no—
478C2×C22⋊C4—614no—
479C2×C22⋊C4—614no—
480C2×C22⋊C4—614no—
481C2×C22⋊C4—614no—
482C2×C22⋊C4—1224no—
483C2×C22⋊C4—1224no—
484C2×C22⋊C4—1224no—
485C2×C22⋊C4—1224no—
486C2×C22⋊C4—1224no—
487C2×C22⋊C4—1224no—
488C2×C42—24no—
489C2×C42—614no—
490C2×C42—614no—
491C2×C42—614no—
492C2×C42—1224no—
493C2×C42—1224no—
494C2×C42—1224no—
495C2×C42C22×D6114yes—
496#95—614no—
497#95—614no—
498#95—614no—
499#95—614no—
500#95—614no—
501#95—614no—
502#95—614no—
503#95—614no—
504#95—614no—
505#95—614no—
506#95C22×D6114yes—
507#95C22×D6114yes—
508#95C22×D6114yes—
509#95C22×D6114yes—
510C24—614no—
511C24—612no—
512C24—1222no—
513C24—1222no—
514C24—1222no—
515C24—1222no—
516C24—1222no—
517C24—1222no—
518C24C23×D6111yescharacteristic
519C2×Q8—6116no—
520C2×Q8—12232no—
521C2×Q8—1228no—
522C2×Q8—1228no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—614no—
543C22×C4—614no—
544C22×C4—614no—
545C22×C4—612no—
546C22×C4—614no—
547C22×C4—612no—
548C22×C4—612no—
549C22×C4—612no—
550C22×C4—612no—
551C22×C4—612no—
552C22×C4—612no—
553C22×C4—1228no—
554C22×C4—1228no—
555C22×C4—1228no—
556C22×C4—1222no—
557C22×C4—1222no—
558C22×C4—1222no—
559C22×C4—1222no—
560C22×C4—1222no—
561C22×C4—1222no—
562C22×C4—1222no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1222no—
567C22×C4—1222no—
568C22×C4—1222no—
569C22×C4—1222no—
570C22×C4—1222no—
571C22×C4—1222no—
572C22×C4—1222no—
573C22×C4—24416no—
574C22×C4#1175822214yes—
575C22×C4D4×D6114yes—
576C22×C4C23×D6112yes—
577C22×C4C23×D6112yes—
578C22×C4C23×D6112yes—
579C22×C4C23×D6112yes—
580C22×C4C23×D6112yes—
581C22×C4C23×D6112yes—
582C22×C4C23×D6112yes—
583C4⋊C4—28no—
584C4⋊C4—28no—
585C4⋊C4—1228no—
586C4⋊C4—1228no—
587C4⋊C4—1228no—
588C4⋊C4—1228no—
589C4⋊C4—1228no—
590C4⋊C4—1228no—
591C4⋊C4—1228no—
592C22⋊C4—1228no—
593C22⋊C4—1228no—
594C22⋊C4—1228no—
595C22⋊C4—1228no—
596C22⋊C4—1228no—
597C22⋊C4—1228no—
598C42—28no—
599C42—1228no—
600C42—1228no—
601C42—1228no—
602C23—614no—
603C23—1228no—
604C23—1228no—
605C23—1222no—
606C23—1222no—
607C23—1222no—
608C23—1222no—
609C23—1222no—
610C23—1222no—
611C23—1228no—
612C23—2444no—
613C23—2444no—
614C23—2444no—
615C23—2444no—
616C23C2×D4×D6112yes—
617C23#41×D6112yes—
618C23#41×D6112yes—
619C23#41×D6112yes—
620C23C2×#1175822212yes—
621C23#1451982412yes—
622C23#1451982512yes—
623C23C24×D6111yescharacteristic
624Q8—12232no—
625C2×C4—28no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—28no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—44no—
651C2×C4—6116no—
652C2×C4—614no—
653C2×C4—614no—
654C2×C4—614no—
655C2×C4—614no—
656C2×C4—1228no—
657C2×C4—1222no—
658C2×C4—1222no—
659C2×C4—1222no—
660C2×C4—1222no—
661C2×C4—1222no—
662C2×C4—1222no—
663C2×C4—1222no—
664C2×C4—1222no—
665C2×C4—1222no—
666C2×C4—1222no—
667C2×C4—1222no—
668C2×C4—1222no—
669C2×C4—1222no—
670C2×C4—1222no—
671C2×C4—1222no—
672C2×C4—1222no—
673C2×C4—1222no—
674C2×C4—24416no—
675C2×C4—2444no—
676C2×C4—2444no—
677C2×C4—2444no—
678C2×C4—2444no—
679C2×C4—2444no—
680C2×C4C2×D4×D6114yes—
681C2×C4C2×#1175822214yes—
682C22—1224no—
683C22—1224no—
684C22—1224no—
685C22—2442no—
686C22—24416no—
687C22—2442no—
688C22—2442no—
689C22—2442no—
690C22#123×D6114yes—
691C22#1684029014yes—
692C22#1684037114yes—
693C22#1684042114yes—
694C22#1684042214yes—
695C22#1684044814yes—
696C22#1684048414yes—
697C22C22×D4×D6111yescharacteristic
698C22C2×#41×D6111yescharacteristic
699C22C2×#41×D6111yescharacteristic
700C22C2×#41×D6111yescharacteristic
701C22C22×#1175822211yescharacteristic
702C22C2×#1451982411yescharacteristic
703C22C2×#1451982511yescharacteristic
704C4—24no—
705C4—24no—
706C4—42no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—618no—
712C4—1224no—
713C4—2442no—
714C4—2442no—
715C4—2442no—
716C4—2442no—
717C4—2442no—
718C2—2444no—
719C2#2144932118yesdirect product factor
720C2C2×#123×D6111yescharacteristic
721C2C2×#1684029011yescharacteristic
722C2C2×#1684037111yescharacteristic
723C2C2×#1684042111yescharacteristic
724C2C2×#1684042211yescharacteristic
725C2C2×#1684044811yescharacteristic
726C2C2×#1684048411yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#387C2
socleC24×C61C24
prime radicalC24×D61C23
hypercenterC2×#387D61
hypocenterC61C2×#2421
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic122C2semidirect
3. #21449321C2direct (N × H)
4. C2×#16839703C2semidirect
5. C2×#16839701C2semidirect
8. C2×#16839666C2semidirect
9. C2×#16839657C2semidirect
12. C2×#16839644C2semidirect
13. C2×#16839626C2semidirect
16. C2×C61×#387C2semidirect
22. C2×C4×Dic122C22semidirect
39. #16839703C22semidirect
40. #16839701C22semidirect
43. #16839666C22semidirect
44. #16839657C22semidirect
47. #16839644C22semidirect
48. #16839626C22semidirect
64. C61×#387C22semidirect
367. C2×#387D61semidirect
371. C2×C61#2421semidirect
414. #387C2×D61semidirect
432. C61C2×#2421semidirect
719. C2#21449321direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145197552
C22×C4×Dic1222
#214493212
C2×#168397032
C2×#168397012
C2×#168396912
C2×#168396892
C2×#168396662
C2×#168396572
C2×#168396532
C2×#168396522
C2×#168396442
C2×#168396262
C2×#168396212
C2×#168396092
C2×C61×#3872
C2×#242161