Finite Group Databasebeta

← C2×#21449247 #29848425

Subgroups — C2×#21449247 #29848425

Order 15616.

3526 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519755C211yesmaximal, characteristic, complemented
2C22×#14519755C211yesmaximal, characteristic, complemented
3C22×#14519739C211yesmaximal, characteristic
4C22×#14519734C211yesmaximal, characteristic, complemented
5#21449247C2116yesmaximal, direct product factor
6C2×#16839691C211yesmaximal, characteristic, complemented
7C2×#16839688C211yesmaximal, characteristic, complemented
8C2×#16839680C211yesmaximal, characteristic
9C2×#16839679C211yesmaximal, characteristic
10C2×#16839666C211yesmaximal, characteristic, complemented
11C2×#16839657C211yesmaximal, characteristic, complemented
12C2×#16839657C211yesmaximal, characteristic, complemented
13C2×#16839653C211yesmaximal, characteristic, complemented
14C2×#16839652C211yesmaximal, characteristic, complemented
15C2×#16839621C211yesmaximal, characteristic, complemented
16C2×C61×#389C211yesmaximal, characteristic, complemented
17C23×Dic122C2211yescharacteristic
18C23×D244C2211yescharacteristic
19C23×C4×D61C2211yescharacteristic
20C23×C4×D61C2211yescharacteristic
21C2×#14519755—28no—
22C2×#14519755—28no—
23C2×#14519755C2218yescomplemented
24C2×#14519755C2218yescomplemented
25C2×#14519739—28no—
26C2×#14519739C2218yes—
27C2×#14519734—28no—
28C2×#14519734C2218yescomplemented
29C22×#11758196C2211yescharacteristic
30C22×#11758196C2211yescharacteristic
31C22×#11758196C2211yescharacteristic
32C22×#11758196C2211yescharacteristic
33C22×#11758196C2211yescharacteristic
34C22×#11758196C2211yescharacteristic
35C22×#11758198C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C22×#11758198C2211yescharacteristic
38C22×#11758198C2211yescharacteristic
39C22×#11758198C2211yescharacteristic
40C22×#11758198C2211yescharacteristic
41C22×#11758198C2211yescharacteristic
42C22×#11758198C2211yescharacteristic
43C22×#11758198C2211yescharacteristic
44C22×#11758198C2211yescharacteristic
45C22×C4×Dic61C2211yescharacteristic
46C22×C4×Dic61C2211yescharacteristic
47#16839691C2218yescomplemented
48#16839688C2218yescomplemented
49#16839680C2218yes—
50#16839679C2218yes—
51#16839666C2218yescomplemented
52#16839657C2218yescomplemented
53#16839657C2218yescomplemented
54#16839653C2218yescomplemented
55#16839652C2218yescomplemented
56#16839621C2218yescomplemented
57C2×#14519684C2211yescharacteristic
58C2×#14519684C2211yescharacteristic
59C2×#14519684C2211yescharacteristic
60C2×#14519684C2211yescharacteristic
61C2×#14519684C2211yescharacteristic
62C2×#14519684C2211yescharacteristic
63C22×C4⋊C4×C61C2211yescharacteristic
64C22×C4⋊C4×C61C2211yescharacteristic
65C22×C4⋊C4×C61C2211yescharacteristic
66C22×C4⋊C4×C61C2211yescharacteristic
67C22×C42×C61C2211yescharacteristic
68C61×#389C2218yescomplemented
69C2×#95×C61C2211yescharacteristic
70C2×#95×C61C2211yescharacteristic
71C24×D61C2311yescharacteristic
72C24×D61C2311yescharacteristic
73C22×Dic122—24no—
74C22×Dic122—24no—
75C22×Dic122—24no—
76C22×Dic122C2314yes—
77C22×D244—24no—
78C22×D244—24no—
79C22×D244—24no—
80C22×D244C2314yes—
81C23×Dic61C2311yescharacteristic
82C23×Dic61C2311yescharacteristic
83C23×Dic61C2311yescharacteristic
84C23×Dic61C2311yescharacteristic
85C23×Dic61C2311yescharacteristic
86C23×Dic61C2311yescharacteristic
87C22×C4×D61—24no—
88C22×C4×D61—24no—
89C22×C4×D61—24no—
90C22×C4×D61—24no—
91C22×C4×D61—24no—
92C22×C4×D61D418yes—
93C22×C4×D61C2314yes—
94C22×C4×D61C2314yes—
95#14519755—232no—
96#14519755—232no—
97#14519739—232no—
98#14519734—232no—
99C2×#11758196—24no—
100C2×#11758196—24no—
101C2×#11758196—24no—
102C2×#11758196—24no—
103C2×#11758196—24no—
104C2×#11758196D418yescomplemented
105C2×#11758196C2314yes—
106C2×#11758196C2314yes—
107C2×#11758196C2314yes—
108C2×#11758196C2314yes—
109C2×#11758196C2314yes—
110C2×#11758196C2314yes—
111C2×#11758198—24no—
112C2×#11758198—24no—
113C2×#11758198—24no—
114C2×#11758198—24no—
115C2×#11758198—24no—
116C2×#11758198—24no—
117C2×#11758198—24no—
118C2×#11758198—24no—
119C2×#11758198—24no—
120C2×#11758198—24no—
121C2×#11758198C2314yes—
122C2×#11758198C2314yes—
123C2×#11758198C2314yes—
124C2×#11758198C2314yes—
125C2×#11758198C2314yes—
126C2×#11758198C2314yes—
127C2×#11758198C2314yes—
128C2×#11758198C2314yes—
129C2×#11758198C2314yes—
130C2×#11758198C2314yes—
131C2×C4×Dic61—24no—
132C2×C4×Dic61—24no—
133C2×C4×Dic61C2314yes—
134C2×C4×Dic61C2314yes—
135#14519684C2314yes—
136#14519684C2314yes—
137#14519684C2314yes—
138#14519684C2314yes—
139#14519684C2314yes—
140#14519684C2314yes—
141C23×C4×C61C2311yescharacteristic
142C23×C4×C61C2311yescharacteristic
143C23×C4×C61C2311yescharacteristic
144C23×C4×C61C2311yescharacteristic
145C23×C4×C61C2311yescharacteristic
146C23×C4×C61C2311yescharacteristic
147C23×C4×C61C2311yescharacteristic
148C2×C4⋊C4×C61—24no—
149C2×C4⋊C4×C61—24no—
150C2×C4⋊C4×C61—24no—
151C2×C4⋊C4×C61—24no—
152C2×C4⋊C4×C61C2314yes—
153C2×C4⋊C4×C61C2314yes—
154C2×C4⋊C4×C61C2314yes—
155C2×C4⋊C4×C61C2314yes—
156C2×C42×C61—24no—
157C2×C42×C61C2314yes—
158#95×C61C2314yes—
159#95×C61C2314yes—
160C24×C61C2411yescharacteristic
161C23×D61—22no—
162C23×D61—22no—
163C23×D61—22no—
164C23×D61—22no—
165C23×D61—22no—
166C23×D61—22no—
167C23×D61—22no—
168C23×D61—22no—
169C23×D61—22no—
170C23×D61—22no—
171C23×D61—22no—
172C23×D61—22no—
173C23×D61C2×D414yes—
174C23×D61#4114yes—
175C23×D61C2412yes—
176C23×D61C2412yes—
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—22no—
187C22×C4×C61—22no—
188C22×C4×C61—22no—
189C22×C4×C61—22no—
190C22×C4×C61—22no—
191C22×C4×C61—22no—
192C22×C4×C61—22no—
193C22×C4×C61—22no—
194C22×C4×C61—22no—
195C22×C4×C61C2×D414yes—
196C22×C4×C61C2×D414yes—
197C22×C4×C61#4114yes—
198C22×C4×C61C2412yes—
199C22×C4×C61C2412yes—
200C22×C4×C61C2412yes—
201C22×C4×C61C2412yes—
202C22×C4×C61C2412yes—
203C22×C4×C61C2412yes—
204C22×C4×C61C2412yes—
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×Dic61C2×D414yes—
222C22×Dic61#4114yes—
223C22×Dic61C2412yes—
224C22×Dic61C2412yes—
225C22×Dic61C2412yes—
226C22×Dic61C2412yes—
227C22×Dic61C2412yes—
228C22×Dic61C2412yes—
229C2×D244—232no—
230C2×D244—28no—
231C2×D244—28no—
232C2×D244—28no—
233C2×C4×D61—232no—
234C2×C4×D61—28no—
235C2×C4×D61—28no—
236C2×C4×D61—28no—
237C2×C4×D61—28no—
238C2×C4×D61—28no—
239C2×C4×D61—416no—
240C2×C4×D61C2×D4116yes—
241C2×Dic122—28no—
242C2×Dic122—28no—
243C2×Dic122—28no—
244C2×Dic122—416no—
245C4⋊C4×C61—28no—
246C4⋊C4×C61—28no—
247C4⋊C4×C61—28no—
248C4⋊C4×C61—28no—
249C42×C61—28no—
250#11758198—28no—
251#11758198—28no—
252#11758198—28no—
253#11758198—28no—
254#11758198—28no—
255#11758198—28no—
256#11758198—28no—
257#11758198—28no—
258#11758198—28no—
259#11758198—28no—
260#11758196—28no—
261#11758196—28no—
262#11758196—28no—
263#11758196—28no—
264#11758196—28no—
265#11758196C2×D4116yescomplemented
266C4×Dic61—28no—
267C4×Dic61—28no—
268C23×C61C22×D412yes—
269C23×C61C22×D412yes—
270C23×C61C2×#4112yes—
271C23×C61C2×#4112yes—
272C23×C61C2×#4112yes—
273C23×C612−1+412yes—
274C23×C612−1+412yes—
275C23×C61C2511yescharacteristic
276C22×D61—28no—
277C22×D61—28no—
278C22×D61—28no—
279C22×D61—28no—
280C22×D61—28no—
281C22×D61—28no—
282C22×D61—22no—
283C22×D61—22no—
284C22×D61—22no—
285C22×D61—22no—
286C22×D61—22no—
287C22×D61—22no—
288C22×D61—22no—
289C22×D61—22no—
290C22×D61—22no—
291C22×D61—22no—
292C22×D61—22no—
293C22×D61—22no—
294C22×D61—44no—
295C22×D61—44no—
296C22×D61—44no—
297C22×D61—44no—
298C22×D61—44no—
299C22×D61—44no—
300C22×D61—44no—
301C22×D61—44no—
302C22×D61C22×D414yes—
303C22×D61C2×#4114yes—
304C2×C4×C61—28no—
305C2×C4×C61—28no—
306C2×C4×C61—28no—
307C2×C4×C61—22no—
308C2×C4×C61—22no—
309C2×C4×C61—22no—
310C2×C4×C61—22no—
311C2×C4×C61—22no—
312C2×C4×C61—22no—
313C2×C4×C61—22no—
314C2×C4×C61—22no—
315C2×C4×C61—22no—
316C2×C4×C61—22no—
317C2×C4×C61—22no—
318C2×C4×C61—22no—
319C2×C4×C61—22no—
320C2×C4×C61—22no—
321C2×C4×C61—22no—
322C2×C4×C61—22no—
323C2×C4×C61—22no—
324C2×C4×C61—22no—
325C2×C4×C61—44no—
326C2×C4×C61—44no—
327C2×C4×C61—44no—
328C2×C4×C61—44no—
329C2×C4×C61C22×D414yes—
330C2×C4×C61C22×D414yes—
331C2×C4×C61C2×#4114yes—
332C2×Dic61—28no—
333C2×Dic61—22no—
334C2×Dic61—22no—
335C2×Dic61—22no—
336C2×Dic61—22no—
337C2×Dic61—22no—
338C2×Dic61—22no—
339C2×Dic61—22no—
340C2×Dic61—22no—
341C2×Dic61—22no—
342C2×Dic61—22no—
343C2×Dic61—22no—
344C2×Dic61—22no—
345C2×Dic61—22no—
346C2×Dic61—22no—
347C2×Dic61—44no—
348C2×Dic61—44no—
349C2×Dic61—44no—
350C2×Dic61—44no—
351C2×Dic61#121116yes—
352C2×Dic61C22×D414yes—
353C2×Dic61C22×D414yes—
354C2×Dic61C22×D414yes—
355C2×Dic61C2×#4114yes—
356D244—232no—
357C4×D61—232no—
358C4×D61—416no—
359Dic122—416no—
360C2×#2415—611nomaximal, Sylow
361C22×C61C2×#12114yes—
362C22×C61#52514yes—
363C22×C61#53614yes—
364C22×C61#54714yes—
365C22×C61#54814yes—
366C22×C61#55214yes—
367C22×C61#55614yes—
368C22×C61C23×D411yescharacteristic
369C22×C61C23×D411yescharacteristic
370C22×C61C22×#4111yescharacteristic
371C22×C61C22×#4111yescharacteristic
372C22×C61C22×#4111yescharacteristic
373C22×C61C2×2−1+411yescharacteristic
374C22×C61C2×2−1+411yescharacteristic
375C2×D61—24no—
376C2×D61—24no—
377C2×D61—24no—
378C2×D61—24no—
379C2×D61—24no—
380C2×D61—24no—
381C2×D61—42no—
382C2×D61—416no—
383C2×D61—416no—
384C2×D61—42no—
385C2×D61—42no—
386C2×D61—42no—
387C2×D61—42no—
388C2×D61—42no—
389C2×D61—42no—
390C2×D61—42no—
391C4×C61—24no—
392C4×C61—24no—
393C4×C61—24no—
394C4×C61—42no—
395C4×C61—42no—
396C4×C61—42no—
397C4×C61—42no—
398Dic61—24no—
399Dic61—42no—
400Dic61—42no—
401Dic61—42no—
402Dic61—42no—
403Dic61C2×#12118yes—
404C22×C22⋊Q8—611no—
405C22×C22⋊Q8—611no—
406C22×C4×D4—611no—
407C22×#117—611no—
408#2415—6116no—
409C2×#397—611no—
410C2×#397—611no—
411C2×#394—611no—
412C2×#394—611no—
413C2×#391—611no—
414C2×#389—611no—
415C2×#389—611no—
416C2×#389D6111yescharacteristic, complemented
417C2×#388—611no—
418C2×#388—611no—
419C2×#380—611no—
420C2×C61#241518yescomplemented
421C2×C61C22×#12111yescharacteristic
422C2×C61C2×#52511yescharacteristic
423C2×C61C2×#53611yescharacteristic
424C2×C61C2×#54711yescharacteristic
425C2×C61C2×#54811yescharacteristic
426C2×C61C2×#55211yescharacteristic
427C2×C61C2×#55611yescharacteristic
428D61—44no—
429D61—44no—
430C23×Q8—611no—
431C23×D4—611no—
432C24×C4—611no—
433C24×C4—611no—
434C2×C22⋊Q8—618no—
435C2×C22⋊Q8—618no—
436C2×C22⋊Q8—1228no—
437C2×C22⋊Q8—1228no—
438C2×C4×D4—618no—
439C2×C4×D4—1228no—
440C2×#117—618no—
441C2×#117—1228no—
442C22×C4⋊C4—611no—
443C22×C4⋊C4—611no—
444C22×C4⋊C4—611no—
445C22×C4⋊C4—611no—
446C22×C4⋊C4—611no—
447C22×C4⋊C4—611no—
448C22×C4⋊C4C2×D6111yescharacteristic
449C22×C4⋊C4C2×D6111yescharacteristic
450C22×C4⋊C4C2×D6111yescharacteristic
451C22×C4⋊C4C2×D6111yescharacteristic
452C22×C22⋊C4—611no—
453C22×C22⋊C4—611no—
454C22×C22⋊C4—611no—
455C22×C22⋊C4—611no—
456C22×C22⋊C4—611no—
457C22×C22⋊C4—611no—
458C22×C22⋊C4—611no—
459C22×C22⋊C4—611no—
460C22×C22⋊C4—611no—
461C22×C22⋊C4—611no—
462C22×C42—611no—
463C22×C42—611no—
464C22×C42C2×D6111yescharacteristic
465#397—618no—
466#397—618no—
467#394—618no—
468#394—618no—
469#391—618no—
470#389—618no—
471#389—618no—
472#389C2×D6118yescomplemented
473#388—618no—
474#388—618no—
475#380—618no—
476C2×#95—611no—
477C2×#95—611no—
478C2×#95—611no—
479C2×#95—611no—
480C2×#95—611no—
481C2×#95—611no—
482C2×#95C2×D6111yescharacteristic
483C2×#95C2×D6111yescharacteristic
484C61C2×#241511yescharacteristic, complemented, Sylow
485C25—611no—
486C25—611no—
487C22×Q8—614no—
488C22×Q8—1224no—
489C22×Q8—1224no—
490C22×Q8—1224no—
491C22×D4—614no—
492C22×D4—1224no—
493C22×D4—1224no—
494C22×D4—1224no—
495C23×C4—611no—
496C23×C4—611no—
497C23×C4—618no—
498C23×C4—614no—
499C23×C4—611no—
500C23×C4—611no—
501C23×C4—611no—
502C23×C4—611no—
503C23×C4—614no—
504C23×C4—1224no—
505C23×C4—1224no—
506C23×C4—1224no—
507C23×C4—1224no—
508C23×C4—1224no—
509C23×C4C22×D6111yescharacteristic
510C23×C4C22×D6111yescharacteristic
511C23×C4C22×D6111yescharacteristic
512C23×C4C22×D6111yescharacteristic
513C23×C4C22×D6111yescharacteristic
514C23×C4C22×D6111yescharacteristic
515C23×C4C22×D6111yescharacteristic
516C22⋊Q8—12232no—
517C22⋊Q8—12232no—
518C4×D4—12232no—
519#117—12232no—
520C2×C4⋊C4—24no—
521C2×C4⋊C4—24no—
522C2×C4⋊C4—24no—
523C2×C4⋊C4—24no—
524C2×C4⋊C4—618no—
525C2×C4⋊C4—614no—
526C2×C4⋊C4—614no—
527C2×C4⋊C4—614no—
528C2×C4⋊C4—614no—
529C2×C4⋊C4—614no—
530C2×C4⋊C4—614no—
531C2×C4⋊C4—1224no—
532C2×C4⋊C4—1224no—
533C2×C4⋊C4—1224no—
534C2×C4⋊C4—1224no—
535C2×C4⋊C4—1224no—
536C2×C4⋊C4C22×D6114yes—
537C2×C4⋊C4C22×D6114yes—
538C2×C4⋊C4C22×D6114yes—
539C2×C4⋊C4C22×D6114yes—
540C2×C22⋊C4—614no—
541C2×C22⋊C4—614no—
542C2×C22⋊C4—614no—
543C2×C22⋊C4—614no—
544C2×C22⋊C4—614no—
545C2×C22⋊C4—614no—
546C2×C22⋊C4—614no—
547C2×C22⋊C4—614no—
548C2×C22⋊C4—614no—
549C2×C22⋊C4—614no—
550C2×C22⋊C4—1224no—
551C2×C22⋊C4—1224no—
552C2×C22⋊C4—1224no—
553C2×C22⋊C4—1224no—
554C2×C22⋊C4—1224no—
555C2×C22⋊C4—1224no—
556C2×C22⋊C4—1224no—
557C2×C22⋊C4—1224no—
558C2×C22⋊C4—1224no—
559C2×C22⋊C4—1224no—
560C2×C42—24no—
561C2×C42—614no—
562C2×C42—614no—
563C2×C42—1224no—
564C2×C42—1224no—
565C2×C42C22×D6114yes—
566#95—614no—
567#95—614no—
568#95—614no—
569#95—614no—
570#95—614no—
571#95—614no—
572#95C22×D6114yes—
573#95C22×D6114yes—
574C24—614no—
575C24—614no—
576C24—612no—
577C24—612no—
578C24—1222no—
579C24—1222no—
580C24—1222no—
581C24—1222no—
582C24—1222no—
583C24—1222no—
584C24—1222no—
585C24—1222no—
586C24—1222no—
587C24—1222no—
588C24—1222no—
589C24—1222no—
590C24C23×D6111yescharacteristic
591C2×Q8—1228no—
592C2×Q8—1228no—
593C2×Q8—1228no—
594C2×Q8—24416no—
595C2×D4—1228no—
596C2×D4—1228no—
597C2×D4—12232no—
598C2×D4—1228no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—614no—
618C22×C4—614no—
619C22×C4—614no—
620C22×C4—612no—
621C22×C4—614no—
622C22×C4—612no—
623C22×C4—6116no—
624C22×C4—612no—
625C22×C4—612no—
626C22×C4—612no—
627C22×C4—612no—
628C22×C4—1228no—
629C22×C4—12232no—
630C22×C4—1228no—
631C22×C4—1228no—
632C22×C4—1228no—
633C22×C4—1228no—
634C22×C4—1222no—
635C22×C4—1222no—
636C22×C4—1222no—
637C22×C4—1222no—
638C22×C4—1222no—
639C22×C4—1222no—
640C22×C4—1222no—
641C22×C4—1222no—
642C22×C4—1222no—
643C22×C4—1222no—
644C22×C4—1222no—
645C22×C4—1222no—
646C22×C4—1222no—
647C22×C4—1222no—
648C22×C4—24416no—
649C22×C4#1175822214yes—
650C22×C4D4×D6114yes—
651C22×C4D4×D6114yes—
652C22×C4C23×D6112yes—
653C22×C4C23×D6112yes—
654C22×C4C23×D6112yes—
655C22×C4C23×D6112yes—
656C22×C4C23×D6112yes—
657C22×C4C23×D6112yes—
658C22×C4C23×D6112yes—
659C4⋊C4—28no—
660C4⋊C4—28no—
661C4⋊C4—28no—
662C4⋊C4—28no—
663C4⋊C4—6116no—
664C4⋊C4—1228no—
665C4⋊C4—1228no—
666C4⋊C4—1228no—
667C4⋊C4—1228no—
668C4⋊C4—1228no—
669C22⋊C4—1228no—
670C22⋊C4—1228no—
671C22⋊C4—1228no—
672C22⋊C4—1228no—
673C22⋊C4—1228no—
674C22⋊C4—1228no—
675C22⋊C4—1228no—
676C22⋊C4—1228no—
677C22⋊C4—1228no—
678C22⋊C4—1228no—
679C42—28no—
680C42—1228no—
681C42—1228no—
682C23—614no—
683C23—614no—
684C23—1228no—
685C23—1228no—
686C23—1228no—
687C23—1222no—
688C23—1222no—
689C23—1222no—
690C23—1222no—
691C23—1222no—
692C23—1222no—
693C23—1222no—
694C23—1222no—
695C23—1228no—
696C23—1222no—
697C23—1222no—
698C23—1222no—
699C23—1222no—
700C23—1228no—
701C23—1228no—
702C23—2444no—
703C23—2444no—
704C23—2444no—
705C23—2444no—
706C23—2444no—
707C23—2444no—
708C23—2444no—
709C23—2444no—
710C23C2×D4×D6112yes—
711C23C2×D4×D6112yes—
712C23#41×D6112yes—
713C23#41×D6112yes—
714C23C2×#1175822212yes—
715C23#1451982512yes—
716C23#1451982512yes—
717C23C24×D6111yescharacteristic
718Q8—24416no—
719D4—12232no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—28no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—44no—
742C2×C4—44no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—6116no—
746C2×C4—614no—
747C2×C4—614no—
748C2×C4—614no—
749C2×C4—614no—
750C2×C4—12232no—
751C2×C4—1222no—
752C2×C4—1222no—
753C2×C4—1228no—
754C2×C4—1222no—
755C2×C4—1222no—
756C2×C4—1222no—
757C2×C4—1222no—
758C2×C4—1222no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1222no—
762C2×C4—1222no—
763C2×C4—1222no—
764C2×C4—1222no—
765C2×C4—1222no—
766C2×C4—24416no—
767C2×C4—2444no—
768C2×C4—2444no—
769C2×C4—2444no—
770C2×C4—2444no—
771C2×C4C2×D4×D6114yes—
772C2×C4C2×D4×D6114yes—
773C2×C4C2×#1175822214yes—
774C22—1224no—
775C22—1224no—
776C22—1224no—
777C22—1224no—
778C22—1224no—
779C22—1224no—
780C22—24416no—
781C22—24416no—
782C22—2442no—
783C22—2442no—
784C22—2442no—
785C22—2442no—
786C22—2442no—
787C22—2442no—
788C22—2442no—
789C22—2442no—
790C22#121×D6114yes—
791C22#1684027114yes—
792C22#1684033714yes—
793C22#1684041314yes—
794C22#1684042214yes—
795C22#1684044414yes—
796C22#1684048414yes—
797C22C22×D4×D6111yescharacteristic
798C22C22×D4×D6111yescharacteristic
799C22C2×#41×D6111yescharacteristic
800C22C2×#41×D6111yescharacteristic
801C22C22×#1175822211yescharacteristic
802C22C2×#1451982511yescharacteristic
803C22C2×#1451982511yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—618no—
812C4—1224no—
813C4—2442no—
814C4—2442no—
815C4—2442no—
816C4—2442no—
817C2—2444no—
818C2—2444no—
819C2#2144924718yesdirect product factor
820C2C2×#121×D6111yescharacteristic
821C2C2×#1684027111yescharacteristic
822C2C2×#1684033711yescharacteristic
823C2C2×#1684041311yescharacteristic
824C2C2×#1684042211yescharacteristic
825C2C2×#1684044411yescharacteristic
826C2C2×#1684048411yescharacteristic
subgroupG/H
centerC24C23×D61
commutator, cosocleC23×C61C25
FrattiniC23C24×D61
FittingC2×C61×#389C2
socleC24×C61C24
prime radicalC23×D244C22
hypercenterC2×#389D61
hypocenterC61C2×#2415
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#14519755C2semidirect
2. C22×#14519755C2semidirect
4. C22×#14519734C2semidirect
5. #21449247C2direct (N × H)
6. C2×#16839691C2semidirect
7. C2×#16839688C2semidirect
10. C2×#16839666C2semidirect
11. C2×#16839657C2semidirect
12. C2×#16839657C2semidirect
13. C2×#16839653C2semidirect
14. C2×#16839652C2semidirect
15. C2×#16839621C2semidirect
16. C2×C61×#389C2semidirect
23. C2×#14519755C22semidirect
24. C2×#14519755C22semidirect
28. C2×#14519734C22semidirect
47. #16839691C22semidirect
48. #16839688C22semidirect
51. #16839666C22semidirect
52. #16839657C22semidirect
53. #16839657C22semidirect
54. #16839653C22semidirect
55. #16839652C22semidirect
56. #16839621C22semidirect
68. C61×#389C22semidirect
104. C2×#11758196D4semidirect
265. #11758196C2×D4semidirect
416. C2×#389D61semidirect
420. C2×C61#2415semidirect
472. #389C2×D61semidirect
484. C61C2×#2415semidirect
819. C2#21449247direct (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×#145197392
C22×#145197342
#214492472
C2×#168396912
C2×#168396882
C2×#168396802
C2×#168396792
C2×#168396662
C2×#168396572
C2×#168396532
C2×#168396522
C2×#168396212
C2×C61×#3892
C2×#241561