Finite Group Databasebeta

← #29684081

Subgroups — #29684081

Order 15616.

1706 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840308C211yesmaximal, characteristic
2C2×#16839785C211yesmaximal, characteristic, complemented
3C2×#16839764C211yesmaximal, characteristic, complemented
4C2×#16839763C211yesmaximal, characteristic, complemented
5C2×#16839761C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×Dic61C211yesmaximal, characteristic, complemented
7#21446750C212yesmaximal, complemented
8#21446748C212yesmaximal, complemented
9#21446744C212yesmaximal, complemented
10#21446740C212yesmaximal, complemented
11C2×C61×#417C211yesmaximal, characteristic, complemented
12C22×#11758222C2211yescharacteristic
13C22×#11758194C2211yescharacteristic
14#16840308—24no—
15#16840308C418yescomplemented
16C2×#14519775C2211yescharacteristic
17C2×#14519773C2211yescharacteristic
18C2×#14519766C2211yescharacteristic
19C2×#14519764C2211yescharacteristic
20C2×#14519749—21no—
21C2×#14519749—21no—
22C2×C4×C22⋊D61—21no—
23C2×C4×C22⋊D61—21no—
24C22×C4⋊Dic61C2211yescharacteristic
25C22×C4×Dic61—21no—
26C22×C4×Dic61C2211yescharacteristic
27#16839785—24no—
28C2×#14519706C2212yes—
29C2×#14519706C2212yes—
30#16839764—24no—
31#16839763—24no—
32#16839761—24no—
33C2×#14519702C2212yes—
34C2×#14519701C2212yes—
35C2×#14519700C2212yes—
36C2×#14519699C2212yes—
37C2×#14519698C2212yes—
38C2×#14519697C2212yes—
39C4⋊C4×Dic61—21no—
40C4⋊C4×Dic61—21no—
41C4⋊C4×Dic61C2212yes—
42C4⋊C4×Dic61C2212yes—
43C2×#14519684—21no—
44C22×#41×C61C2211yescharacteristic
45C22×M16×C61C2211yescharacteristic
46C22×C4⋊C4×C61C2211yescharacteristic
47C61×#417—24no—
48C2×#103×C61C2212yes—
49C2×#102×C61C2212yes—
50C2×#11758222—22no—
51C2×#11758222—22no—
52C2×#11758222—22no—
53C2×#11758222—22no—
54C2×#11758222—22no—
55C2×#11758222C2×C414yes—
56C22×Dic122C2311yescharacteristic
57C22×D244C2311yescharacteristic
58C22×C22⋊D61—21no—
59C22×C22⋊D61—21no—
60C22×C22⋊D61—21no—
61C23×Dic61—21no—
62C23×Dic61D411yescharacteristic
63C23×Dic61D411yescharacteristic
64C22×C4×D61—21no—
65C2×#11758194—22no—
66C2×#11758194—22no—
67C2×#11758194—22no—
68C22×#92418C2312yes—
69#14519775—22no—
70#14519775C2×C414yescomplemented
71#14519773—22no—
72#14519773C2×C414yescomplemented
73#14519766—22no—
74#14519766C2×C414yescomplemented
75#14519764—22no—
76#14519764C2×C414yescomplemented
77#14519749—28no—
78#14519749—28no—
79C4×C22⋊D61—28no—
80C4×C22⋊D61—28no—
81C2×C4⋊Dic61—21no—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61D414yescomplemented
84C2×C4⋊Dic61C2312yes—
85C2×#11758196—21no—
86C2×#11758196—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×#11758198—21no—
90C2×#11758198—21no—
91C2×C4×Dic61—22no—
92C2×C4×Dic61—22no—
93C2×C4×Dic61—44no—
94C2×C4×Dic61C2×C414yes—
95C2×C4×Dic61D411yescharacteristic
96C2×C4×Dic61D411yescharacteristic
97C2×C4×Dic61D414yes—
98C2×C4×Dic61C2311yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100#14519706—24no—
101#14519706—24no—
102#14519702—24no—
103#14519701—24no—
104#14519700—24no—
105#14519699—24no—
106#14519698—24no—
107#14519697—24no—
108#14519684—22no—
109#14519684—22no—
110C2×#41×C61—22no—
111C2×#41×C61—22no—
112C2×#41×C61—22no—
113C2×#41×C61—22no—
114C2×#41×C61—22no—
115C2×#41×C61C2×C414yes—
116C22×Q8×C61C2311yescharacteristic
117C22×D4×C61—21no—
118C22×D4×C61C2311yescharacteristic
119C23×C4×C61—21no—
120C23×C4×C61—21no—
121C23×C4×C61C2311yescharacteristic
122C2×M16×C61—22no—
123C2×M16×C61—22no—
124C2×M16×C61—22no—
125C22×C8×C61C2312yes—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—22no—
128C2×C4⋊C4×C61D414yescomplemented
129C2×C4⋊C4×C61C2312yes—
130#103×C61—24no—
131#102×C61—24no—
132C24×C61—21no—
133C24×C61C2×D411yescharacteristic
134C23×D61—21no—
135#41×C61—28no—
136#41×C61—28no—
137#41×C61—44no—
138#41×C61—44no—
139C2×Q8×C61—21no—
140C2×Q8×C61—21no—
141C2×Q8×C61—21no—
142C2×Q8×C61—21no—
143C2×Q8×C61—21no—
144C2×Q8×C61C22×C412yes—
145C2×D4×C61—24no—
146C2×D4×C61—21no—
147C2×D4×C61—21no—
148C2×D4×C61—21no—
149C2×D4×C61—21no—
150C2×D4×C61—21no—
151C2×D4×C61—42no—
152C2×D4×C61—42no—
153C2×D4×C61C22×C412yes—
154C22×C4×C61—24no—
155C22×C4×C61—22no—
156C22×C4×C61—21no—
157C22×C4×C61—24no—
158C22×C4×C61—42no—
159C22×C4×C61—42no—
160C22×C4×C61—42no—
161C22×C4×C61—42no—
162C22×C4×C61C22×C412yes—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D412yes—
165C22×C4×C61C2×D412yes—
166C22×C4×C61C2×D412yes—
167C22×C4×C61#4112yes—
168C22×C4×C61#4112yes—
169C22×C4×C61C2411yescharacteristic
170C2×C22⋊D61—24no—
171C2×C22⋊D61—24no—
172C2×C22⋊D61—24no—
173C2×C22⋊D61—42no—
174C2×C22⋊D61—42no—
175C2×C22⋊D61—42no—
176C2×C22⋊D61—42no—
177C2×C22⋊D61—42no—
178C2×C22⋊D61—42no—
179C22×Dic61—22no—
180C22×Dic61—22no—
181C22×Dic61—24no—
182C22×Dic61—21no—
183C22×Dic61—22no—
184C22×Dic61—41no—
185C22×Dic61—41no—
186C22×Dic61—42no—
187C22×Dic61—42no—
188C22×Dic61C22⋊C414yes—
189C22×Dic61C22⋊C414yes—
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C22×Dic61C2×D411yescharacteristic
193C22×Dic61C2×D411yescharacteristic
194#11758222—28no—
195#11758222—28no—
196#11758222—44no—
197#11758222—44no—
198C2×D244—21no—
199C2×D244—21no—
200C2×D244—21no—
201C2×D244—21no—
202C2×D244—21no—
203C2×D244C22×C412yes—
204C2×C4×D61—24no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×Dic122—21no—
208C2×Dic122—21no—
209C2×Dic122—21no—
210C2×Dic122—21no—
211C2×Dic122—21no—
212C2×Dic122C22×C412yes—
213M16×C61—44no—
214C2×C8×C61—22no—
215C2×C8×C61—22no—
216C2×C8×C61—22no—
217C4⋊C4×C61—24no—
218C4⋊C4×C61—22no—
219C4⋊C4×C61C2×D414yes—
220C22⋊Dic61—24no—
221C22⋊Dic61—24no—
222#11758198—24no—
223#11758198—24no—
224C4⋊Dic61—24no—
225C4⋊Dic61—22no—
226C4⋊Dic61C2×D414yes—
227#11758196—24no—
228#11758196—24no—
229C4×Dic61—44no—
230C4×Dic61—44no—
231C4×Dic61C22⋊C414yes—
232C4×Dic61C22⋊C414yes—
233C4×Dic61C22×C412yes—
234C4×Dic61C22×C412yes—
235C4×Dic61C2×D412yes—
236C4×Dic61C2×D412yes—
237#11758194—44no—
238C2×#92418—22no—
239C2×#92418—22no—
240C2×#92418—22no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—22no—
246C23×C61—41no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61C2×C22⋊C412yes—
253C23×C61#12112yes—
254C23×C61#12112yes—
255C23×C61C22×D411yescharacteristic
256C22×D61—22no—
257C22×D61—41no—
258C22×D61—41no—
259C22×D61—41no—
260C22×D61—41no—
261C22×D61—41no—
262C22×D61—41no—
263Q8×C61—22no—
264Q8×C61—22no—
265Q8×C61—41no—
266Q8×C61—41no—
267D4×C61—22no—
268D4×C61—22no—
269D4×C61—48no—
270D4×C61—41no—
271D4×C61—41no—
272C2×C4×C61—22no—
273C2×C4×C61—24no—
274C2×C4×C61—48no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—42no—
278C2×C4×C61—42no—
279C2×C4×C61—48no—
280C2×C4×C61C2×C22⋊C412yes—
281C2×C4×C61C4×D414yes—
282C2×C4×C61C4×D414yes—
283C2×C4×C61#12112yes—
284C2×C4×C61#12112yes—
285C2×C4×C61#12414yes—
286C2×C4×C61#12714yes—
287C2×C4×C61C23×C411yescharacteristic
288C2×C4×C61C22×D411yescharacteristic
289C2×C4×C61C22×D411yescharacteristic
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C22⋊D61—48no—
294C22⋊D61—48no—
295C22⋊D61—48no—
296C2×Dic61—21no—
297C2×Dic61—21no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—28no—
303C2×Dic61—22no—
304C2×Dic61—24no—
305C2×Dic61—44no—
306C2×Dic61—48no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—42no—
310C2×Dic61—42no—
311C2×Dic61C2×C22⋊C412yes—
312C2×Dic61C2×C22⋊C412yes—
313C2×Dic61C2×C22⋊C412yes—
314C2×Dic61C2×C22⋊C412yes—
315C2×Dic61AGL(1,ℤ/8)12yes—
316C2×Dic61#13712yes—
317D244—22no—
318D244—22no—
319D244—41no—
320D244—41no—
321C4×D61—48no—
322Dic122—22no—
323Dic122—22no—
324Dic122—41no—
325Dic122—41no—
326C8×C61—42no—
327#92418—42no—
328#21258—611nomaximal, Sylow
329C22×C61—22no—
330C22×C61—22no—
331C22×C61—22no—
332C22×C61—22no—
333C22×C61—22no—
334C22×C61—22no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—81no—
339C22×C61—81no—
340C22×C61—81no—
341C22×C61—81no—
342C22×C61#39014yes—
343C22×C61C22×C22⋊C411yescharacteristic
344C22×C61C2×#12111yescharacteristic
345C22×C61C2×#12111yescharacteristic
346C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
347C22×C61C2×#13711yescharacteristic
348C22×C61#57511yescharacteristic
349C22×C61#57511yescharacteristic
350C2×D61—42no—
351C2×D61—42no—
352C2×D61—42no—
353C2×D61—81no—
354C2×D61—81no—
355C2×D61—81no—
356C2×D61—81no—
357C4×C61—44no—
358C4×C61—42no—
359C4×C61#39014yes—
360C4×C61C2×C4×D411yescharacteristic
361C4×C61C2×C4×D411yescharacteristic
362C4×C61C2×#12411yescharacteristic
363C4×C61C2×#12711yescharacteristic
364Dic61—22no—
365Dic61—22no—
366Dic61—22no—
367Dic61—44no—
368Dic61—42no—
369Dic61#41714yescomplemented
370C2×#532—611no—
371C2×#423—611no—
372C2×#417—611no—
373C2×#417—611no—
374C2×#417—611no—
375C2×#417D6111yescharacteristic, complemented
376C2×C4×C4⋊C4—611no—
377#1983—612no—
378#1983—612no—
379#1982—612no—
380#1981—612no—
381C2×C61—24no—
382C2×C61—82no—
383C2×C61C2×#39011yescharacteristic
384C2×C61C2×#41711yescharacteristic
385C2×C61#289611yescharacteristic
386C2×C61#303611yescharacteristic
387C2×C61#303611yescharacteristic
388C2×C61#303711yescharacteristic
389C2×C61#303711yescharacteristic
390D61—82no—
391C22×#41—611no—
392C22×#41C2×D6111yescharacteristic
393C22×M16—611no—
394C22×M16C2×D6111yescharacteristic
395#532—618no—
396#532—1224no—
397C2×C4⋊Q8—611no—
398C2×#127—611no—
399C2×#124—611no—
400C2×#124—611no—
401C2×#121—1221no—
402C2×#121—1221no—
403C2×C4×D4—1221no—
404C2×C4×D4—1221no—
405C22×C4⋊C4—611no—
406C22×C4⋊C4C2×D6111yescharacteristic
407C22×C42—611no—
408C22×C42—1221no—
409#423—1224no—
410C2×C4⋊C8—612no—
411C2×C4⋊C8—612no—
412#417—24no—
413#417—1224no—
414#417—1224no—
415#417—1224no—
416C2×#103—612no—
417C2×#103—612no—
418C2×#103—612no—
419C2×#103C2×D6112yes—
420C2×#102—612no—
421C2×#102—612no—
422C2×#102—612no—
423C2×#102C2×D6112yes—
424C4×C4⋊C4—612no—
425C4×C4⋊C4—612no—
426C4×C4⋊C4—1221no—
427C4×C4⋊C4—1221no—
428C2×#95—1221no—
429C61#2125811yescharacteristic, complemented, Sylow
430C2×#41—22no—
431C2×#41—22no—
432C2×#41—22no—
433C2×#41—22no—
434C2×#41—22no—
435C2×#41—614no—
436C2×#41—1222no—
437C2×#41—1222no—
438C2×#41—1222no—
439C2×#41—1222no—
440C2×#41—1222no—
441C2×#41C4×D6114yes—
442C22×Q8—611no—
443C22×Q8C22×D6111yescharacteristic
444C22×D4—21no—
445C22×D4—611no—
446C22×D4—1221no—
447C22×D4—1221no—
448C22×D4—1221no—
449C22×D4C22×D6111yescharacteristic
450C23×C4—21no—
451C23×C4—21no—
452C23×C4—611no—
453C23×C4—611no—
454C23×C4—1221no—
455C23×C4—1221no—
456C23×C4C22×D6111yescharacteristic
457C2×M16—22no—
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—1222no—
461C2×M16—1222no—
462C2×M16—1222no—
463C22×C8—612no—
464C22×C8C22×D6112yes—
465C4⋊Q8—614no—
466C4⋊Q8—1222no—
467#127—614no—
468#127—1222no—
469#124—614no—
470#124—614no—
471#124—1222no—
472#124—1222no—
473#121—1228no—
474#121—1228no—
475C4×D4—1228no—
476C4×D4—1228no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—614no—
480C2×C4⋊C4—612no—
481C2×C4⋊C4—1221no—
482C2×C4⋊C4—1221no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4C22⋊D6114yescomplemented
486C2×C4⋊C4C22×D6112yes—
487C2×C22⋊C4—1221no—
488C2×C22⋊C4—1221no—
489C2×C22⋊C4—1221no—
490C2×C22⋊C4—1221no—
491C2×C42—614no—
492C2×C42—611no—
493C2×C42—611no—
494C2×C42—614no—
495C2×C42—611no—
496C2×C42—611no—
497C2×C42—1222no—
498C2×C42—1222no—
499C2×C42—2444no—
500C4⋊C8—1224no—
501C4⋊C8—1224no—
502#103—24no—
503#103—1224no—
504#103—1224no—
505#103—1224no—
506#102—24no—
507#102—1224no—
508#102—1224no—
509#102—1224no—
510#95—1222no—
511#95—1222no—
512C24—21no—
513C24—1221no—
514C24D4×D6111yescharacteristic
515#41—28no—
516#41—28no—
517#41—44no—
518#41—44no—
519#41—1228no—
520#41—1228no—
521#41—2444no—
522#41—2444no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—612no—
529C2×Q8—1221no—
530C2×Q8—1221no—
531C2×Q8—1221no—
532C2×Q8—1221no—
533C2×Q8—1221no—
534C2×Q8C2×C4×D6112yes—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—42no—
542C2×D4—42no—
543C2×D4—612no—
544C2×D4—1224no—
545C2×D4—1224no—
546C2×D4—1224no—
547C2×D4—1221no—
548C2×D4—1221no—
549C2×D4—1221no—
550C2×D4—1221no—
551C2×D4—1221no—
552C2×D4—2442no—
553C2×D4—2442no—
554C2×D4—2442no—
555C2×D4—2442no—
556C2×D4—2442no—
557C2×D4—2442no—
558C2×D4C2×C4×D6112yes—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—611no—
568C22×C4—611no—
569C22×C4—611no—
570C22×C4—611no—
571C22×C4—614no—
572C22×C4—614no—
573C22×C4—1222no—
574C22×C4—1222no—
575C22×C4—1222no—
576C22×C4—1221no—
577C22×C4—1224no—
578C22×C4—1224no—
579C22×C4—2441no—
580C22×C4—2441no—
581C22×C4—2442no—
582C22×C4—2442no—
583C22×C4—2442no—
584C22×C4—2442no—
585C22×C4C2×C4×D6112yes—
586C22×C4#1175822212yes—
587C22×C4D4×D6112yes—
588C22×C4D4×D6112yes—
589C22×C4D4×D6111yescharacteristic
590C22×C4#1175822412yes—
591C22×C4C2×C22⋊D6112yes—
592C22×C4C23×D6111yescharacteristic
593M16—44no—
594M16—2444no—
595C2×C8—22no—
596C2×C8—22no—
597C2×C8—22no—
598C2×C8—1222no—
599C2×C8—1222no—
600C2×C8—1222no—
601C4⋊C4—22no—
602C4⋊C4—24no—
603C4⋊C4—614no—
604C4⋊C4—1224no—
605C4⋊C4—1224no—
606C4⋊C4—1222no—
607C4⋊C4—1224no—
608C4⋊C4C2×C22⋊D6114yes—
609C22⋊C4—1224no—
610C22⋊C4—1224no—
611C22⋊C4—1224no—
612C22⋊C4—1224no—
613C42—612no—
614C42—612no—
615C42—612no—
616C42—612no—
617C42—614no—
618C42—614no—
619C42—2444no—
620C42—2444no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—22no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—1222no—
633C23—2441no—
634C23—2441no—
635C23—2441no—
636C23—2441no—
637C23—2441no—
638C23—2441no—
639C23C22⋊C4×D6112yes—
640C23#1451974912yes—
641C23#1451975012yes—
642C23C2×D4×D6111yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—41no—
646Q8—41no—
647Q8—1222no—
648Q8—1222no—
649Q8—2441no—
650Q8—2441no—
651D4—22no—
652D4—22no—
653D4—48no—
654D4—41no—
655D4—41no—
656D4—1222no—
657D4—1222no—
658D4—2448no—
659D4—2448no—
660D4—2448no—
661D4—2441no—
662D4—2441no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—48no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—48no—
671C2×C4—612no—
672C2×C4—612no—
673C2×C4—612no—
674C2×C4—612no—
675C2×C4—612no—
676C2×C4—612no—
677C2×C4—1228no—
678C2×C4—1221no—
679C2×C4—1221no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1222no—
685C2×C4—1224no—
686C2×C4—2444no—
687C2×C4—2448no—
688C2×C4—2441no—
689C2×C4—2441no—
690C2×C4—2442no—
691C2×C4—2442no—
692C2×C4—2448no—
693C2×C4C22⋊C4×D6112yes—
694C2×C4#1451973714yes—
695C2×C4C4×C22⋊D6114yes—
696C2×C4#1451974912yes—
697C2×C4#1451975012yes—
698C2×C4#1451976314yes—
699C2×C4#1451977314yes—
700C2×C4C22×C4×D6111yescharacteristic
701C2×C4C2×D4×D6111yescharacteristic
702C2×C4C2×D4×D6111yescharacteristic
703C2×C4C22×C22⋊D6111yescharacteristic
704C2×C4C2×#1175822411yescharacteristic
705C2×C4C2×#1175822211yescharacteristic
706C8—42no—
707C8—2442no—
708C22—22no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—22no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—4881no—
722C22—4881no—
723C22—4881no—
724C22—4881no—
725C22—2442no—
726C22—2442no—
727C22—2442no—
728C22#1683966214yes—
729C22C2×C22⋊C4×D6111yescharacteristic
730C22C2×#1451974911yescharacteristic
731C22C2×#1451975011yescharacteristic
732C22AGL(1,ℤ/8)×D6111yescharacteristic
733C22#137×D6111yescharacteristic
734C22#1684055811yescharacteristic
735C22#1684056111yescharacteristic
736C4—42no—
737C4—44no—
738C4—614no—
739C4—1222no—
740C4—1222no—
741C4—1222no—
742C4—2442no—
743C4—2444no—
744C4#1683966214yes—
745C4C2×#1451973711yescharacteristic
746C4C2×C4×C22⋊D6111yescharacteristic
747C4C2×#1451976311yescharacteristic
748C4C2×#1451977311yescharacteristic
749C2—24no—
750C2—82no—
751C2—4882no—
752C2C2×#1683966211yescharacteristic
753C2#417×D6111yescharacteristic
754C2#2145433511yescharacteristic
755C2#2145528011yescharacteristic
756C2#2145528211yescharacteristic
757C2#2145528811yescharacteristic
758C2#2145529011yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#417C2
socleC23×C61C22×D4
prime radicalC2×#16840308C2
cosocleC22×C4×C61C24
hypercenterC2×#417D61
hypocenterC61#21258
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#16839785C2semidirect
3. C2×#16839764C2semidirect
4. C2×#16839763C2semidirect
5. C2×#16839761C2semidirect
6. C2×C4⋊C4×Dic61C2semidirect
7. #21446750C2semidirect
8. #21446748C2semidirect
9. #21446744C2semidirect
10. #21446740C2semidirect
11. C2×C61×#417C2semidirect
15. #16840308C4semidirect
70. #14519775C2×C4semidirect
72. #14519773C2×C4semidirect
74. #14519766C2×C4semidirect
76. #14519764C2×C4semidirect
83. C2×C4⋊Dic61D4semidirect
128. C2×C4⋊C4×C61D4semidirect
369. Dic61#417semidirect
375. C2×#417D61semidirect
429. C61#21258semidirect
485. C2×C4⋊C4C22⋊D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403082
C2×#168397852
C2×#168397642
C2×#168397632
C2×#168397612
C2×C4⋊C4×Dic612
#214467502
#214467482
#214467442
#214467402
C2×C61×#4172
#2125861