Finite Group Databasebeta

← #29685685

Subgroups — #29685685

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×#16839916C211yesmaximal, characteristic
3C2×#16839867C211yesmaximal, characteristic, complemented
4C4×#14519753C211yesmaximal, characteristic
5#21446162C211yesmaximal, characteristic, complemented
6#21446157C211yesmaximal, characteristic, complemented
7#21446123C211yesmaximal, characteristic
8#21446085C211yesmaximal, characteristic, complemented
9#21446084C211yesmaximal, characteristic, complemented
10#21446010C211yesmaximal, characteristic
11#21445752C211yesmaximal, characteristic
12#21445650C211yesmaximal, characteristic, complemented
13#21445649C211yesmaximal, characteristic, complemented
14#21445582C211yesmaximal, characteristic
15C2×C61×#441C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×#11758202C2211yescharacteristic
18C2×#14519753C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×C4×Dic122—21no—
21C2×C4×Dic122C2211yescharacteristic
22C2×#14519742—21no—
23C2×#14519742C2211yescharacteristic
24C4×Q8×D61—24no—
25C4×Q8×D61—24no—
26C2×C4⋊C4×D61—21no—
27C2×C4⋊C4×D61C2211yescharacteristic
28C2×C42×D61—21no—
29C2×C42×D61C2211yescharacteristic
30#16839916C418yescomplemented
31#16839867—24no—
32C2×#14519708C2211yescharacteristic
33C2×#14519702C2211yescharacteristic
34C2×#14519702C2211yescharacteristic
35C2×#14519701C2211yescharacteristic
36C2×#14519701C2211yescharacteristic
37C2×#14519701C2211yescharacteristic
38C2×#14519700C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519688C2211yescharacteristic
42#16839669C2211yescharacteristic
43#16839658C2211yescharacteristic
44#16839643—21no—
45#16839633—21no—
46#16839619C2211yescharacteristic
47C4×#11758196—21no—
48C4×C4⋊Dic61C2211yescharacteristic
49C4×#11758198—21no—
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839524C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C22×Q16×C61C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×C4×Q8×C61C2211yescharacteristic
59C61×#441—24no—
60C2×#106×C61C2211yescharacteristic
61C2×#103×C61C2211yescharacteristic
62C2×#103×C61C2211yescharacteristic
63C2×#97×C61C2211yescharacteristic
64C22×Dic122—21no—
65C22×Dic122C2311yescharacteristic
66C2×Q8×D61—22no—
67C2×Q8×D61—22no—
68C2×Q8×D61—22no—
69C2×Q8×D61—22no—
70C2×Q8×D61—22no—
71C2×Q8×D61C2×C414yes—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61D411yescharacteristic
75C22×C4×D61D411yescharacteristic
76C22×C4×D61C2311yescharacteristic
77C2×#11758202—22no—
78C2×#11758202—22no—
79C2×#11758202C2×C414yescomplemented
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82#14519753—22no—
83#14519753C2×C414yes—
84Q8×Dic61—22no—
85Q8×Dic61—22no—
86C4×Dic122—28no—
87C4×Dic122—22no—
88C4×Dic122D414yes—
89#14519742—28no—
90#14519742—22no—
91#14519742—22no—
92C2×C4⋊Dic61—21no—
93C2×C4⋊Dic61C2311yescharacteristic
94C2×C4⋊Dic61C2311yescharacteristic
95C2×C4⋊Dic61C2311yescharacteristic
96C2×#11758196—21no—
97C2×#11758196—21no—
98C2×#11758196—21no—
99C2×#11758196—21no—
100C2×#11758196—21no—
101C4⋊C4×D61—28no—
102C4⋊C4×D61—22no—
103C4⋊C4×D61—22no—
104C2×#11758198—21no—
105C2×#11758198—21no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61D411yescharacteristic
111C2×C4×Dic61D411yescharacteristic
112C2×C4×Dic61C2311yescharacteristic
113C42×D61—28no—
114C42×D61—22no—
115C42×D61—22no—
116#14519708—22no—
117#14519702—22no—
118#14519702C2×C414yescomplemented
119#14519701—22no—
120#14519701—22no—
121#14519701C2×C414yescomplemented
122#14519700—22no—
123#14519689—22no—
124#14519689C2×C414yes—
125#14519688—22no—
126#14519684—21no—
127#14519684—21no—
128#14519684—21no—
129#14519684—21no—
130#14519684—21no—
131C22×Q8×C61C2311yescharacteristic
132C22×Q8×C61C2311yescharacteristic
133C2×Q16×C61—22no—
134C2×Q16×C61—22no—
135C2×Q16×C61C2×C414yescomplemented
136C22×C8×C61C2311yescharacteristic
137C22×C8×C61C2311yescharacteristic
138C4×Q8×C61—22no—
139C4×Q8×C61—22no—
140C4×Q8×C61—22no—
141C4×Q8×C61D414yes—
142C2×C4⋊C4×C61—21no—
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C42×C61—21no—
147C2×C42×C61—21no—
148C2×C42×C61C2311yescharacteristic
149#106×C61—22no—
150#103×C61—22no—
151#103×C61—22no—
152#97×C61—22no—
153C23×D61C2×D411yescharacteristic
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61—21no—
161C2×Q8×C61—21no—
162C2×Q8×C61C22×C412yes—
163C2×Q8×C61C22×C412yes—
164C2×Q8×C61C2×D412yes—
165C2×Q8×C61#4112yes—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61C2×D411yescharacteristic
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2411yescharacteristic
173C22×Dic61—21no—
174C22×Dic61—21no—
175C22×Dic61—21no—
176C22×Dic61—21no—
177C22×Dic61C2×D411yescharacteristic
178C22×Dic61C2×D411yescharacteristic
179C22×Dic61C2×D411yescharacteristic
180Q8×D61—28no—
181Q8×D61—28no—
182Q8×D61—28no—
183Q8×D61—28no—
184C2×C4×D61—24no—
185C2×C4×D61—24no—
186C2×C4×D61—24no—
187C2×C4×D61—22no—
188C2×C4×D61—22no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—21no—
193C2×C4×D61—22no—
194C2×C4×D61—24no—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—41no—
198C2×C4×D61—42no—
199C2×C4×D61—42no—
200C2×C4×D61C22×C412yes—
201C2×C4×D61#4112yes—
202C2×Dic122—24no—
203C2×Dic122—24no—
204C2×Dic122—21no—
205C2×Dic122—21no—
206C2×Dic122—21no—
207C2×Dic122—24no—
208C2×Dic122C22×C412yes—
209C2×Dic122C2×D412yes—
210C2×Dic122#4112yes—
211Q16×C61—28no—
212C2×C8×C61—21no—
213C2×C8×C61—21no—
214C2×C8×C61—21no—
215C2×C8×C61—21no—
216C2×C8×C61—21no—
217C2×C8×C61C22×C412yes—
218C4⋊C4×C61—24no—
219C4⋊C4×C61—21no—
220C4⋊C4×C61—21no—
221C4⋊C4×C61—21no—
222C4⋊C4×C61—42no—
223C4⋊C4×C61C2×D412yes—
224C42×C61—24no—
225C42×C61—42no—
226C42×C61C2×D412yes—
227C42×C61C2×D412yes—
228#11758202—28no—
229#11758198—24no—
230#11758198—42no—
231C4⋊Dic61—24no—
232C4⋊Dic61—21no—
233C4⋊Dic61—21no—
234C4⋊Dic61—21no—
235C4⋊Dic61—21no—
236C4⋊Dic61C22×C412yes—
237C4⋊Dic61C2×D412yes—
238#11758196—24no—
239#11758196—24no—
240#11758196—24no—
241#11758196—24no—
242#11758196—42no—
243C4×Dic61—24no—
244C4×Dic61—24no—
245C4×Dic61—24no—
246C4×Dic61—22no—
247C4×Dic61—22no—
248C4×Dic61—21no—
249C4×Dic61—21no—
250C4×Dic61—42no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418—21no—
256C2×#92418C22×C412yes—
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×C61—22no—
269Q8×C61—22no—
270Q8×C61—41no—
271Q8×C61—41no—
272Q8×C61C4×D414yes—
273C2×C4×C61—22no—
274C2×C4×C61—22no—
275C2×C4×C61—22no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—22no—
281C2×C4×C61—22no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—41no—
287C2×C4×C61—41no—
288C2×C4×C61—41no—
289C2×C4×C61#12012yes—
290C2×C4×C61#12012yes—
291C2×C4×C61C23×C411yescharacteristic
292C2×C4×C61C22×D411yescharacteristic
293C2×C4×C61C22×D411yescharacteristic
294C2×C4×C61C2×#4111yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×Dic61—22no—
298C2×Dic61—21no—
299C2×Dic61—21no—
300C2×Dic61—22no—
301C2×Dic61—21no—
302C2×Dic61—22no—
303C2×Dic61—21no—
304C2×Dic61—22no—
305C2×Dic61—21no—
306C2×Dic61—22no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—41no—
316C2×Dic61C4×D412yes—
317C2×Dic61#13712yes—
318C4×D61—28no—
319C4×D61—216no—
320C4×D61—22no—
321C4×D61—22no—
322C4×D61—22no—
323C4×D61—22no—
324C4×D61—44no—
325C4×D61—48no—
326Dic122—216no—
327Dic122—22no—
328Dic122—22no—
329Dic122—22no—
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—22no—
352C4×C61—24no—
353C4×C61—42no—
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—24no—
363Dic61—42no—
364Dic61—41no—
365Dic61—42no—
366Dic61—81no—
367C22×C4×Q8—611no—
368C2×#451—611no—
369C2×#441—611no—
370C2×#441D6111yescharacteristic, complemented
371C4×C22⋊Q8—611no—
372#1878—611no—
373#1878—611no—
374#1872—611no—
375#1865—611no—
376#1865—611no—
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×Q16C2×D6111yescharacteristic
393C2×C22⋊Q8—611no—
394C2×C4×Q8—611no—
395C2×C4×Q8—611no—
396C2×C4×Q8—611no—
397C2×C4×Q8—1221no—
398C2×C4×Q8—1221no—
399C2×C4×Q8—1224no—
400C2×C4×Q8—1224no—
401C2×C4×Q8C2×D6111yescharacteristic
402C2×C4×Q8C2×D6111yescharacteristic
403C22×C4⋊C4—611no—
404C22×C4⋊C4—1221no—
405C22×C42—611no—
406C22×C42—1221no—
407#451—618no—
408#441—24no—
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×#97C2×D6111yescharacteristic
424#391—611no—
425#389—611no—
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#340—611no—
436#336—611no—
437#336—611no—
438C61#2145511yescharacteristic, complemented, Sylow
439C22×Q8—614no—
440C22×Q8—611no—
441C22×Q8—1221no—
442C22×Q8—1222no—
443C22×Q8—1222no—
444C22×Q8—1222no—
445C22×Q8—1222no—
446C22×Q8—1222no—
447C22×Q8C22×D6111yescharacteristic
448C22×Q8C22×D6111yescharacteristic
449C23×C4—611no—
450C23×C4—611no—
451C23×C4—611no—
452C23×C4—1221no—
453C23×C4—1221no—
454C2×Q16—22no—
455C2×Q16—22no—
456C2×Q16—614no—
457C2×Q16—1222no—
458C2×Q16—1222no—
459C2×Q16C4×D6114yescomplemented
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—22no—
469C4×Q8—614no—
470C4×Q8—1228no—
471C4×Q8—1222no—
472C4×Q8—1228no—
473C4×Q8—1222no—
474C4×Q8—1222no—
475C4×Q8—1222no—
476C4×Q8—1222no—
477C4×Q8C22⋊D6114yes—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—611no—
481C2×C4⋊C4—611no—
482C2×C4⋊C4—611no—
483C2×C4⋊C4—1222no—
484C2×C4⋊C4—1228no—
485C2×C4⋊C4—1221no—
486C2×C4⋊C4—1221no—
487C2×C4⋊C4—1221no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4—1222no—
491C2×C4⋊C4—1221no—
492C2×C4⋊C4C22×D6111yescharacteristic
493C2×C4⋊C4C22×D6111yescharacteristic
494C2×C22⋊C4—1221no—
495C2×C22⋊C4—1221no—
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—611no—
499C2×C42—611no—
500C2×C42—611no—
501C2×C42—1228no—
502C2×C42—1221no—
503C2×C42—1221no—
504C2×C42—1221no—
505C2×C42—1222no—
506C2×C42—1222no—
507C2×C42—1221no—
508C2×C42C22×D6111yescharacteristic
509#106—22no—
510#106—1222no—
511#103—22no—
512#103—22no—
513#103—614no—
514#103—614no—
515#103—1222no—
516#103—1222no—
517#103—1222no—
518#103—1222no—
519C22⋊C8—614no—
520C22⋊C8—1222no—
521#97—22no—
522#97—1222no—
523#95—1221no—
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—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—612no—
538C2×Q8—612no—
539C2×Q8—612no—
540C2×Q8—1224no—
541C2×Q8—1224no—
542C2×Q8—1224no—
543C2×Q8—1228no—
544C2×Q8—1228no—
545C2×Q8—1228no—
546C2×Q8—1228no—
547C2×Q8—1221no—
548C2×Q8—1221no—
549C2×Q8—1221no—
550C2×Q8C2×C4×D6112yes—
551C2×Q8C2×C4×D6112yes—
552C2×Q8#1175822212yes—
553C2×Q8C2×C22⋊D6112yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—611no—
559C22×C4—611no—
560C22×C4—612no—
561C22×C4—612no—
562C22×C4—611no—
563C22×C4—1222no—
564C22×C4—1222no—
565C22×C4—1224no—
566C22×C4—1224no—
567C22×C4—1224no—
568C22×C4—1222no—
569C22×C4—1224no—
570C22×C4—1221no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1222no—
576C22×C4—1221no—
577C22×C4—1221no—
578C22×C4—1222no—
579C22×C4—1221no—
580C22×C4—2441no—
581C22×C4—2442no—
582C22×C4—2442no—
583C22×C4D4×D6111yescharacteristic
584C22×C4D4×D6111yescharacteristic
585C22×C4C23×D6111yescharacteristic
586Q16—28no—
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—21no—
601C4⋊C4—24no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—42no—
605C4⋊C4—612no—
606C4⋊C4—612no—
607C4⋊C4—1224no—
608C4⋊C4—1224no—
609C4⋊C4—1224no—
610C4⋊C4—1224no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1224no—
614C4⋊C4—1221no—
615C4⋊C4—1221no—
616C4⋊C4—2442no—
617C4⋊C4C2×C22⋊D6112yes—
618C22⋊C4—1224no—
619C22⋊C4—2442no—
620C42—24no—
621C42—42no—
622C42—1224no—
623C42—1224no—
624C42—1221no—
625C42—1221no—
626C42—1222no—
627C42—1222no—
628C42—1224no—
629C42—2442no—
630C42D4×D6112yes—
631C42C2×C22⋊D6112yes—
632C23—612no—
633C23—612no—
634C23—612no—
635C23—1221no—
636C23—1221no—
637C23—1221no—
638C23—1221no—
639C23C2×D4×D6111yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—22no—
645Q8—41no—
646Q8—41no—
647Q8—614no—
648Q8—12216no—
649Q8—1222no—
650Q8—1222no—
651Q8—1222no—
652Q8C4×C22⋊D6114yes—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—612no—
670C2×C4—612no—
671C2×C4—1228no—
672C2×C4—12216no—
673C2×C4—1222no—
674C2×C4—1221no—
675C2×C4—1221no—
676C2×C4—1222no—
677C2×C4—1221no—
678C2×C4—1222no—
679C2×C4—1221no—
680C2×C4—1222no—
681C2×C4—1222no—
682C2×C4—1222no—
683C2×C4—1222no—
684C2×C4—1222no—
685C2×C4—1222no—
686C2×C4—1221no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—2444no—
690C2×C4—2448no—
691C2×C4—2441no—
692C2×C4—2441no—
693C2×C4—2441no—
694C2×C4—2441no—
695C2×C4—2441no—
696C2×C4—2441no—
697C2×C4—2441no—
698C2×C4#1451974512yes—
699C2×C4#1451974512yes—
700C2×C4C22×C4×D6111yescharacteristic
701C2×C4C2×D4×D6111yescharacteristic
702C2×C4C22×C22⋊D6111yescharacteristic
703C2×C4#41×D6111yescharacteristic
704C2×C4#41×D6111yescharacteristic
705C2×C4C2×#1175822211yescharacteristic
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
718C22C2×#1451974511yescharacteristic
719C22#1684027111yescharacteristic
720C22#137×D6111yescharacteristic
721C22#137×D6111yescharacteristic
722C22#137×D6111yescharacteristic
723C22#1684056111yescharacteristic
724C4—24no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—42no—
729C4—81no—
730C4—1222no—
731C4—1224no—
732C4—1222no—
733C4—4881no—
734C4—2442no—
735C4—2441no—
736C4—2442no—
737C4C4×D4×D6111yescharacteristic
738C4C2×C4×C22⋊D6111yescharacteristic
739C4#1684026911yescharacteristic
740C4#1684027111yescharacteristic
741C2—1224no—
742C2C4×#1451974511yescharacteristic
743C2#441×D6111yescharacteristic
744C2#2145463511yescharacteristic
745C2#2145505111yescharacteristic
746C2#2145507511yescharacteristic
747C2#2145594711yescharacteristic
748C2#2145599411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#441C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
cosocleC22×C4×C61C24
hypercenterC2×#441D61
hypocenterC61#21455
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#441

Complements

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

NH ≅ G/Ntype
3. C2×#16839867C2semidirect
5. #21446162C2semidirect
6. #21446157C2semidirect
8. #21446085C2semidirect
9. #21446084C2semidirect
12. #21445650C2semidirect
13. #21445649C2semidirect
15. C2×C61×#441C2semidirect
30. #16839916C4semidirect
79. C2×#11758202C2×C4semidirect
118. #14519702C2×C4semidirect
121. #14519701C2×C4semidirect
135. C2×Q16×C61C2×C4semidirect
349. C2×D61#441semidirect
370. C2×#441D61semidirect
438. C61#21455semidirect
459. C2×Q16C4×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×#168399162
C2×#168398672
C4×#145197532
#214461622
#214461572
#214461232
#214460852
#214460842
#214460102
#214457522
#214456502
#214456492
#214455822
C2×C61×#4412
#2145561