Finite Group Databasebeta

← #29685686

Subgroups — #29685686

Order 15616.

1436 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D61C211yesmaximal, characteristic
2C2×#16839919C211yesmaximal, characteristic
3C2×#16839868C211yesmaximal, characteristic, complemented
4C2×#16839866C211yesmaximal, characteristic, complemented
5#21448349C211yesmaximal, characteristic
6#21446160C211yesmaximal, characteristic, complemented
7#21446159C211yesmaximal, characteristic, complemented
8#21446125C211yesmaximal, characteristic
9#21446086C211yesmaximal, characteristic, complemented
10#21446010C211yesmaximal, characteristic
11#21445752C211yesmaximal, characteristic
12#21445651C211yesmaximal, characteristic, complemented
13#21445648C211yesmaximal, characteristic, complemented
14#21445580C211yesmaximal, characteristic
15C61×#1865C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×Dic244C2211yescharacteristic
18C22×#11758202C2211yescharacteristic
19C2×#14519757C2211yescharacteristic
20C2×Q8×Dic61C2211yescharacteristic
21C2×C4×Dic122—21no—
22C2×C4×Dic122C2211yescharacteristic
23C2×#14519742—21no—
24C2×#14519742C2211yescharacteristic
25C2×#14519742C2211yescharacteristic
26C4×Q8×D61—24no—
27C4×Q8×D61—24no—
28C2×C4⋊C4×D61—21no—
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C42×D61—21no—
31C2×C42×D61C2211yescharacteristic
32#16839919C418yescomplemented
33#16839868—24no—
34#16839866—24no—
35C2×#14519708C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519700C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519689C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519687C2211yescharacteristic
45C2×#14519687C2211yescharacteristic
46#16839668C2211yescharacteristic
47#16839645—21no—
48#16839633—21no—
49#16839619C2211yescharacteristic
50C4⋊C4×Dic61—21no—
51C4⋊C4×Dic61C2211yescharacteristic
52#16839609—21no—
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839517C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×#106×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#103×C61C2211yescharacteristic
61C61×#389C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#336C2211yescharacteristic
64C22×Dic122—21no—
65C22×Dic122C2311yescharacteristic
66C22×Dic122C2311yescharacteristic
67C2×Q8×D61—22no—
68C2×Q8×D61—22no—
69C2×Q8×D61—22no—
70C2×Q8×D61—22no—
71C2×Q8×D61—22no—
72C2×Q8×D61C2×C414yes—
73C22×C4×D61—21no—
74C22×C4×D61—21no—
75C22×C4×D61D411yescharacteristic
76C22×C4×D61D411yescharacteristic
77C22×C4×D61C2311yescharacteristic
78C2×Dic244—22no—
79C2×Dic244—22no—
80C2×Dic244C2×C414yescomplemented
81C2×#11758202—22no—
82C2×#11758202—22no—
83C2×#11758202C2×C414yescomplemented
84C22×#92418C2311yescharacteristic
85C22×#92418C2311yescharacteristic
86#14519757—22no—
87#14519757C2×C414yes—
88Q8×Dic61—22no—
89Q8×Dic61D414yes—
90C4×Dic122—28no—
91C4×Dic122—22no—
92C4×Dic122—22no—
93#14519742—28no—
94#14519742—22no—
95#14519742—22no—
96#14519742—22no—
97#14519742D414yes—
98C2×C4⋊Dic61—21no—
99C2×C4⋊Dic61—21no—
100C2×C4⋊Dic61C2311yescharacteristic
101C2×C4⋊Dic61C2311yescharacteristic
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C4⋊C4×D61—28no—
107C4⋊C4×D61—22no—
108C4⋊C4×D61—22no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61—21no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61—21no—
116C2×C4×Dic61D411yescharacteristic
117C2×C4×Dic61D411yescharacteristic
118C2×C4×Dic61C2311yescharacteristic
119C42×D61—28no—
120C42×D61—22no—
121C42×D61—22no—
122#14519708—22no—
123#14519702—22no—
124#14519702—22no—
125#14519701—22no—
126#14519700—22no—
127#14519700—22no—
128#14519700C2×C414yescomplemented
129#14519689—22no—
130#14519689C2×C414yes—
131#14519687—22no—
132#14519687—22no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136#14519684—21no—
137C22×Q8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C4×Q8×C61—22no—
141C4×Q8×C61—22no—
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C42×C61—21no—
148C2×C42×C61C2311yescharacteristic
149#106×C61—22no—
150#103×C61—22no—
151#103×C61C2×C414yescomplemented
152#95×C61—21no—
153C23×D61C2×D411yescharacteristic
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61C22×C412yes—
158C2×Q8×C61C2×D412yes—
159C2×Q8×C61#4112yes—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2411yescharacteristic
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61C2×D411yescharacteristic
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174Q8×D61—28no—
175Q8×D61—28no—
176Q8×D61—28no—
177Q8×D61—28no—
178C2×C4×D61—24no—
179C2×C4×D61—24no—
180C2×C4×D61—24no—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—21no—
184C2×C4×D61—21no—
185C2×C4×D61—21no—
186C2×C4×D61—21no—
187C2×C4×D61—22no—
188C2×C4×D61—24no—
189C2×C4×D61—22no—
190C2×C4×D61—22no—
191C2×C4×D61—41no—
192C2×C4×D61—42no—
193C2×C4×D61—42no—
194C2×C4×D61C22×C412yes—
195C2×C4×D61#4112yes—
196C2×Dic122—24no—
197C2×Dic122—24no—
198C2×Dic122—21no—
199C2×Dic122—21no—
200C2×Dic122—21no—
201C2×Dic122—24no—
202C2×Dic122—21no—
203C2×Dic122—21no—
204C2×Dic122—21no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122C22×C412yes—
208C2×Dic122C22×C412yes—
209C2×Dic122C2×D412yes—
210C2×Dic122#4112yes—
211C2×C8×C61—21no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61C22×C412yes—
217C4⋊C4×C61—24no—
218C4⋊C4×C61—21no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—42no—
223C4⋊C4×C61C22×C412yes—
224C4⋊C4×C61C2×D412yes—
225C42×C61—24no—
226C42×C61—21no—
227C42×C61—21no—
228#11758202—28no—
229#11758198—24no—
230#11758198—42no—
231C4⋊Dic61—21no—
232C4⋊Dic61—24no—
233C4⋊Dic61—24no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61C2×D412yes—
237#11758196—24no—
238#11758196—24no—
239#11758196—24no—
240#11758196—42no—
241C4×Dic61—24no—
242C4×Dic61—24no—
243C4×Dic61—24no—
244C4×Dic61—22no—
245C4×Dic61—22no—
246C4×Dic61—42no—
247C4×Dic61—42no—
248C4×Dic61C2×D412yes—
249C4×Dic61C2×D412yes—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418C22×C412yes—
256Dic244—28no—
257C23×C61C22×D411yescharacteristic
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61C4×D412yes—
263C22×D61#13712yes—
264C22×D61#13712yes—
265Q8×C61—22no—
266Q8×C61—22no—
267Q8×C61—22no—
268Q8×C61C4×D414yes—
269C2×C4×C61—22no—
270C2×C4×C61—21no—
271C2×C4×C61—22no—
272C2×C4×C61—22no—
273C2×C4×C61—21no—
274C2×C4×C61—22no—
275C2×C4×C61—21no—
276C2×C4×C61—22no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61#13712yes—
287C2×C4×C61C23×C411yescharacteristic
288C2×C4×C61C22×D411yescharacteristic
289C2×C4×C61C22×D411yescharacteristic
290C2×C4×C61C2×#4111yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×Dic61—22no—
294C2×Dic61—21no—
295C2×Dic61—22no—
296C2×Dic61—21no—
297C2×Dic61—22no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—22no—
303C2×Dic61—22no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61C4×D412yes—
312C2×Dic61#12012yes—
313C2×Dic61#12012yes—
314C4×D61—28no—
315C4×D61—216no—
316C4×D61—22no—
317C4×D61—22no—
318C4×D61—22no—
319C4×D61—22no—
320C4×D61—44no—
321C4×D61—48no—
322Dic122—216no—
323Dic122—22no—
324Dic122—22no—
325Dic122—22no—
326Dic122—22no—
327Dic122—22no—
328Dic122—41no—
329Dic122—41no—
330Dic122C4×D414yes—
331C8×C61—22no—
332C8×C61—41no—
333#92418—22no—
334#92418—41no—
335#21455—611nomaximal, Sylow
336C22×C61C2×C4×D411yescharacteristic
337C22×C61C2×#12011yescharacteristic
338C22×C61#52511yescharacteristic
339C22×C61C2×#13711yescharacteristic
340C22×C61C2×#13711yescharacteristic
341C22×C61C2×#13711yescharacteristic
342C22×C61#57511yescharacteristic
343C2×D61—22no—
344C2×D61—22no—
345C2×D61—22no—
346C2×D61—22no—
347C2×D61—22no—
348C2×D61—22no—
349C2×D61#44114yescomplemented
350C4×C61—22no—
351C4×C61—24no—
352C4×C61—42no—
353C4×C61—41no—
354C4×C61—42no—
355C4×C61—81no—
356C4×C61C2×C4×D411yescharacteristic
357C4×C61C2×C4×D411yescharacteristic
358C4×C61#52511yescharacteristic
359C4×C61#52511yescharacteristic
360Dic61—22no—
361Dic61—22no—
362Dic61—22no—
363Dic61—24no—
364Dic61—42no—
365Dic61—42no—
366Dic61—81no—
367C22×C4×Q8—611no—
368C2×#451—611no—
369C2×#441—611no—
370C2×#441—611no—
371C4×C22⋊Q8—611no—
372#1878—611no—
373#1878—611no—
374#1872—611no—
375#1865—611no—
376#1865D6111yescharacteristic, complemented
377#1853—611no—
378#1787—611no—
379#1763—611no—
380#1763—611no—
381#1749—611no—
382C2×C61C4×#12011yescharacteristic
383C2×C61C2×#44111yescharacteristic
384C2×C61C4×#13711yescharacteristic
385C2×C61#300411yescharacteristic
386C2×C61#300711yescharacteristic
387C2×C61#311311yescharacteristic
388C2×C61#311711yescharacteristic
389D61—24no—
390C23×Q8—611no—
391C22×Q16—611no—
392C22×Q16—611no—
393C2×C22⋊Q8—611no—
394C2×C4×Q8—611no—
395C2×C4×Q8—611no—
396C2×C4×Q8—611no—
397C2×C4×Q8—611no—
398C2×C4×Q8—1221no—
399C2×C4×Q8—1221no—
400C2×C4×Q8—1224no—
401C2×C4×Q8—1224no—
402C2×C4×Q8C2×D6111yescharacteristic
403C22×C4⋊C4—611no—
404C22×C4⋊C4—1221no—
405C22×C42—611no—
406C22×C42—1221no—
407#451—618no—
408#441—1224no—
409#441—1224no—
410C2×#106—611no—
411C2×#106C2×D6111yescharacteristic
412C2×#103—611no—
413C2×#103—611no—
414C2×#103—611no—
415C2×#103—611no—
416C2×#103—611no—
417C2×#103—611no—
418C2×#103C2×D6111yescharacteristic
419C2×#103C2×D6111yescharacteristic
420C2×C22⋊C8—611no—
421C2×C22⋊C8—611no—
422C2×#97—611no—
423C2×#97—611no—
424#391—611no—
425#389C2×D6111yescharacteristic
426#387—1221no—
427#385—1221no—
428#380—611no—
429C4×C4⋊C4—611no—
430C4×C4⋊C4—1221no—
431C4×C22⋊C4—1221no—
432#340—611no—
433#340—611no—
434#340—611no—
435#340C2×D6111yescharacteristic
436#336—611no—
437#336C2×D6111yescharacteristic
438C61#2145511yescharacteristic, complemented, Sylow
439C22×Q8—614no—
440C22×Q8—611no—
441C22×Q8—611no—
442C22×Q8—1221no—
443C22×Q8—1222no—
444C22×Q8—1222no—
445C22×Q8—1222no—
446C22×Q8—1222no—
447C22×Q8—1222no—
448C22×Q8C22×D6111yescharacteristic
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—1221no—
453C23×C4—1221no—
454C2×Q16—614no—
455C2×Q16—614no—
456C2×Q16—1222no—
457C2×Q16—1222no—
458C2×Q16—1222no—
459C2×Q16—1222no—
460C22×C8—611no—
461C22×C8—611no—
462C22×C8C22×D6111yescharacteristic
463C22×C8C22×D6111yescharacteristic
464C22⋊Q8—614no—
465C22⋊Q8—1222no—
466C4×Q8—22no—
467C4×Q8—22no—
468C4×Q8—614no—
469C4×Q8—614no—
470C4×Q8—1222no—
471C4×Q8—1222no—
472C4×Q8—1228no—
473C4×Q8—1222no—
474C4×Q8—1222no—
475C4×Q8—1222no—
476C4×Q8—1222no—
477C4×Q8—1228no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—1222no—
483C2×C4⋊C4—1228no—
484C2×C4⋊C4—1221no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1222no—
490C2×C4⋊C4—1221no—
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C4⋊C4C22×D6111yescharacteristic
493C2×C4⋊C4C22×D6111yescharacteristic
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C42—21no—
497C2×C42—611no—
498C2×C42—611no—
499C2×C42—611no—
500C2×C42—1222no—
501C2×C42—1222no—
502C2×C42—1228no—
503C2×C42—1221no—
504C2×C42—1221no—
505C2×C42—1221no—
506C2×C42—1221no—
507C2×C42—1221no—
508C2×C42C22×D6111yescharacteristic
509#106—22no—
510#106—1222no—
511#103—22no—
512#103—614no—
513#103—1222no—
514#103—1222no—
515#103—1222no—
516#103—1222no—
517#103—1222no—
518#103C4×D6114yescomplemented
519C22⋊C8—614no—
520C22⋊C8—1222no—
521#97—1222no—
522#97—1222no—
523#95—21no—
524#95—1221no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528C24—611no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—612no—
533C2×Q8—612no—
534C2×Q8—612no—
535C2×Q8—612no—
536C2×Q8—1224no—
537C2×Q8—1224no—
538C2×Q8—1224no—
539C2×Q8—1228no—
540C2×Q8—1228no—
541C2×Q8—1228no—
542C2×Q8—1228no—
543C2×Q8—1221no—
544C2×Q8—1221no—
545C2×Q8—1221no—
546C2×Q8—1221no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8—1221no—
551C2×Q8C2×C4×D6112yes—
552C2×Q8D4×D6112yes—
553C2×Q8#1175822612yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—611no—
561C22×C4—612no—
562C22×C4—612no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—1222no—
566C22×C4—1224no—
567C22×C4—1224no—
568C22×C4—1224no—
569C22×C4—1222no—
570C22×C4—1224no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1222no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—2441no—
581C22×C4—2442no—
582C22×C4—2442no—
583C22×C4D4×D6111yescharacteristic
584C22×C4D4×D6111yescharacteristic
585C22×C4C23×D6111yescharacteristic
586Q16—1228no—
587Q16—1228no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—612no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8C2×C4×D6112yes—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—42no—
606C4⋊C4—612no—
607C4⋊C4—1224no—
608C4⋊C4—1224no—
609C4⋊C4—1224no—
610C4⋊C4—1224no—
611C4⋊C4—1224no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—2442no—
616C4⋊C4C2×C4×D6112yes—
617C4⋊C4D4×D6112yes—
618C22⋊C4—1224no—
619C22⋊C4—2442no—
620C42—24no—
621C42—21no—
622C42—21no—
623C42—612no—
624C42—612no—
625C42—1222no—
626C42—1222no—
627C42—1224no—
628C42—1224no—
629C42—1224no—
630C42—2442no—
631C42—2442no—
632C23—612no—
633C23—612no—
634C23—612no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23C2×D4×D6111yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—614no—
644Q8—12216no—
645Q8—1222no—
646Q8—1222no—
647Q8—1222no—
648Q8—1222no—
649Q8—1222no—
650Q8—2441no—
651Q8—2441no—
652Q8#1451973914yes—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—612no—
671C2×C4—612no—
672C2×C4—612no—
673C2×C4—1228no—
674C2×C4—12216no—
675C2×C4—1222no—
676C2×C4—1221no—
677C2×C4—1222no—
678C2×C4—1221no—
679C2×C4—1222no—
680C2×C4—1221no—
681C2×C4—1221no—
682C2×C4—1221no—
683C2×C4—1221no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1222no—
687C2×C4—1222no—
688C2×C4—1222no—
689C2×C4—1222no—
690C2×C4—2444no—
691C2×C4—2448no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4—2441no—
699C2×C4#1451980612yes—
700C2×C4C22×C4×D6111yescharacteristic
701C2×C4C2×D4×D6111yescharacteristic
702C2×C4C2×D4×D6111yescharacteristic
703C2×C4#41×D6111yescharacteristic
704C2×C4#41×D6111yescharacteristic
705C2×C4C2×#1175822611yescharacteristic
706C8—22no—
707C8—41no—
708C8—1222no—
709C8—2441no—
710C22—614no—
711C22—1222no—
712C22—1222no—
713C22—1222no—
714C22—1222no—
715C22—1222no—
716C22—1222no—
717C22C4×D4×D6111yescharacteristic
718C22#120×D6111yescharacteristic
719C22#1684027511yescharacteristic
720C22#137×D6111yescharacteristic
721C22#137×D6111yescharacteristic
722C22C2×#1451980611yescharacteristic
723C22#1684055911yescharacteristic
724C4—24no—
725C4—22no—
726C4—42no—
727C4—41no—
728C4—42no—
729C4—81no—
730C4—1222no—
731C4—1224no—
732C4—1222no—
733C4—1222no—
734C4—4881no—
735C4—2442no—
736C4—2442no—
737C4C4×D4×D6111yescharacteristic
738C4C2×#1451973911yescharacteristic
739C4#1684027011yescharacteristic
740C4#1684027511yescharacteristic
741C2—1224no—
742C2#2144832011yescharacteristic
743C2#441×D6111yescharacteristic
744C2C4×#1451980611yescharacteristic
745C2#2145505011yescharacteristic
746C2#2145507611yescharacteristic
747C2#2145595111yescharacteristic
748C2#2145599511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1865C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenter#1865D61
hypocenterC61#21455
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1865

Complements

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

NH ≅ G/Ntype
3. C2×#16839868C2semidirect
4. C2×#16839866C2semidirect
6. #21446160C2semidirect
7. #21446159C2semidirect
9. #21446086C2semidirect
12. #21445651C2semidirect
13. #21445648C2semidirect
15. C61×#1865C2semidirect
32. #16839919C4semidirect
80. C2×Dic244C2×C4semidirect
83. C2×#11758202C2×C4semidirect
128. #14519700C2×C4semidirect
151. #103×C61C2×C4semidirect
349. C2×D61#441semidirect
376. #1865D61semidirect
438. C61#21455semidirect
518. #103C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D612
C2×#168399192
C2×#168398682
C2×#168398662
#214483492
#214461602
#214461592
#214461252
#214460862
#214460102
#214457522
#214456512
#214456482
#214455802
C61×#18652
#2145561