Finite Group Databasebeta

← #29680102

Subgroups — #29680102

Order 15616.

1438 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840234C211yesmaximal, characteristic
2C2×#16839822C211yesmaximal, characteristic, complemented
3#21448429C211yesmaximal, characteristic, complemented
4#21445913C211yesmaximal, characteristic, complemented
5#21445912C211yesmaximal, characteristic, complemented
6#21445826C211yesmaximal, characteristic, complemented
7#21445820C211yesmaximal, characteristic, complemented
8#21445819C211yesmaximal, characteristic, complemented
9#21445748C211yesmaximal, characteristic
10#21445748C211yesmaximal, characteristic
11#21445646C211yesmaximal, characteristic, complemented
12#21445643C211yesmaximal, characteristic, complemented
13#102×Dic61C211yesmaximal, characteristic, complemented
14#21445633C211yesmaximal, characteristic, complemented
15C61×#1804C211yesmaximal, characteristic, complemented
16C22×D4×D61C2211yescharacteristic
17#16840234—24no—
18#16840234C418yescomplemented
19C2×C4×D244C2211yescharacteristic
20C2×D4×Dic61C2211yescharacteristic
21C2×#14519739C2211yescharacteristic
22C2×C4×C22⋊D61—21no—
23C2×#14519737—21no—
24C2×#14519735C2211yescharacteristic
25C2×#14519734C2211yescharacteristic
26C22×#11758198—21no—
27C2×C22⋊C4×D61—21no—
28#16839822—24no—
29C2×C4⋊#92418C2211yescharacteristic, complemented
30C2×#14519699C2211yescharacteristic
31C2×#14519699C2211yescharacteristic
32C2×#14519698C2211yescharacteristic
33C2×#14519698C2211yescharacteristic
34C2×#14519697C2211yescharacteristic
35C2×#14519697C2211yescharacteristic
36C2×#14519689C2211yescharacteristic
37C2×#14519689C2211yescharacteristic
38C2×#14519687C2211yescharacteristic, complemented
39C2×C8×Dic61C2211yescharacteristic, complemented
40#16839654—21no—
41#16839654—21no—
42#16839649—21no—
43#16839649—21no—
44#16839632C2211yescharacteristic, complemented
45#16839619C2211yescharacteristic
46#16839619C2211yescharacteristic
47C4⋊C4×Dic61C2211yescharacteristic, complemented
48C4⋊C4×Dic61C2211yescharacteristic, complemented
49#16839525C2211yescharacteristic, complemented
50#16839525C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839524C2211yescharacteristic, complemented
53#16839524C2211yescharacteristic, complemented
54#16839524C2211yescharacteristic, complemented
55C2×C4×D4×C61C2211yescharacteristic
56C2×C4⋊C8×C61C2211yescharacteristic, complemented
57C2×#102×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic
59C61×#382C2211yescharacteristic, complemented
60C61×#340C2211yescharacteristic, complemented
61C61×#340C2211yescharacteristic, complemented
62C24×D61—21no—
63C22×D244C2311yescharacteristic
64C22×C22⋊D61—21no—
65C2×D4×D61—22no—
66C2×D4×D61—22no—
67C2×D4×D61—22no—
68C2×D4×D61—22no—
69C2×D4×D61—22no—
70C2×D4×D61C2×C414yes—
71C23×Dic61—21no—
72C22×C4×D61—21no—
73C22×C4×D61—21no—
74C22×C4×D61C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C4×D244—22no—
78C4×D244C2×C414yes—
79D4×Dic61—22no—
80D4×Dic61C2×C414yes—
81#14519739—22no—
82#14519739C2×C414yes—
83C4×C22⋊D61—28no—
84#14519737—28no—
85#14519735—22no—
86#14519735C2×C414yes—
87#14519734C2×C414yes—
88#14519734D414yes—
89C2×C4⋊Dic61—21no—
90C2×C4⋊Dic61—21no—
91C2×C4⋊Dic61C2311yescharacteristic
92C2×C4⋊Dic61C2311yescharacteristic
93C2×C4⋊Dic61C2311yescharacteristic
94C2×#11758196D411yescharacteristic
95C2×#11758196D411yescharacteristic
96C2×C22⋊Dic61—21no—
97C2×#11758198—21no—
98C2×#11758198—21no—
99C2×#11758198—21no—
100C2×#11758198—28no—
101C2×#11758198—21no—
102C2×#11758198—21no—
103C2×#11758198D411yescharacteristic
104C2×#11758198D411yescharacteristic
105C22⋊C4×D61—28no—
106C2×C4×Dic61—21no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—21no—
109C2×C4×Dic61C2311yescharacteristic
110C4⋊#92418—22no—
111#14519699—22no—
112#14519699—22no—
113#14519698—22no—
114#14519698—22no—
115#14519697—22no—
116#14519697—22no—
117#14519689—22no—
118#14519689—22no—
119#14519687—22no—
120C8×Dic61—22no—
121#14519684—21no—
122#14519684—21no—
123#14519684—21no—
124#14519684—21no—
125C22×D4×C61C2311yescharacteristic
126C23×C4×C61—21no—
127C22×C8×C61C2311yescharacteristic
128C22×C8×C61C2311yescharacteristic
129C4×D4×C61—22no—
130C4×D4×C61C2×C414yes—
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—21no—
135C2×C42×C61C2311yescharacteristic
136C4⋊C8×C61—22no—
137#102×C61—22no—
138#102×C61—22no—
139#95×C61—21no—
140#95×C61—21no—
141C24×C61—21no—
142C23×D61—21no—
143C23×D61—24no—
144C23×D61—24no—
145C23×D61—24no—
146C23×D61—81no—
147C23×D61—81no—
148C23×D61—81no—
149C23×D61—81no—
150C23×D61C2×D411yescharacteristic
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61C22×C412yes—
155C2×D4×C61#4112yes—
156C2×D4×C61#4112yes—
157C22×C4×C61—21no—
158C22×C4×C61—24no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—81no—
162C22×C4×C61—81no—
163C22×C4×C61C2×D411yescharacteristic
164C22×C4×C61C2×D411yescharacteristic
165C22×C4×C61C2411yescharacteristic
166C2×C22⋊D61—24no—
167C2×C22⋊D61—24no—
168C2×C22⋊D61—24no—
169C22×Dic61—21no—
170C22×Dic61—24no—
171C22×Dic61—21no—
172C22×Dic61—21no—
173C22×Dic61—81no—
174C22×Dic61—81no—
175C22×Dic61C2×D411yescharacteristic
176C22×Dic61C2×D411yescharacteristic
177C22×Dic61C2×D411yescharacteristic
178D4×D61—28no—
179D4×D61—28no—
180D4×D61—28no—
181D4×D61—28no—
182C2×D244—21no—
183C2×D244—21no—
184C2×D244—21no—
185C2×D244C22×C412yes—
186C2×D244#4112yes—
187C2×D244#4112yes—
188C2×C4×D61—21no—
189C2×C4×D61—21no—
190C2×C4×D61—21no—
191C2×C4×D61—21no—
192C2×C4×D61—24no—
193C2×C4×D61—24no—
194C2×C4×D61—81no—
195C2×C4×D61—81no—
196C2×C4×D61—81no—
197C2×C4×D61—81no—
198C2×C4×D61C22×C412yes—
199C2×C4×D61C2×D412yes—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61—21no—
203C2×C8×C61—21no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61—21no—
208C4⋊C4×C61—21no—
209C4⋊C4×C61—21no—
210C4⋊C4×C61—21no—
211C4⋊C4×C61C22×C412yes—
212C22⋊C4×C61—24no—
213C42×C61C22×C412yes—
214C42×C61C2×D412yes—
215C22⋊Dic61—24no—
216#11758198—24no—
217#11758198—24no—
218#11758198—24no—
219#11758198—81no—
220#11758198—81no—
221#11758198C22⋊C414yes—
222#11758198C22⋊C414yes—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—81no—
229C4⋊Dic61—81no—
230C4⋊Dic61C22×C412yes—
231#11758196C22⋊C414yes—
232#11758196C22⋊C414yes—
233C4×Dic61—24no—
234C4×Dic61—81no—
235C4×Dic61—81no—
236C4×Dic61C22×C412yes—
237C4×Dic61C2×D412yes—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C23×C61—22no—
245C23×C61—22no—
246C23×C61—22no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61C22×D411yescharacteristic
252C22×D61—22no—
253C22×D61—21no—
254C22×D61—21no—
255C22×D61—22no—
256C22×D61—22no—
257C22×D61—21no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—216no—
262C22×D61—41no—
263C22×D61—41no—
264C22×D61—41no—
265C22×D61—41no—
266C22×D61—84no—
267C22×D61—84no—
268C22×D61—84no—
269C22×D61—84no—
270C22×D61—84no—
271C22×D61—84no—
272C22×D61C2×C22⋊C412yes—
273D4×C61—22no—
274D4×C61—22no—
275D4×C61—22no—
276D4×C61#11714yes—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
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—41no—
290C2×C4×C61—84no—
291C2×C4×C61C2×C22⋊C412yes—
292C2×C4×C61C2×C22⋊C412yes—
293C2×C4×C61C23×C411yescharacteristic
294C2×C4×C61C22×D411yescharacteristic
295C2×C4×C61C2×#4111yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61C2×#4111yescharacteristic
298C2×C4×C61C2×#4111yescharacteristic
299C22⋊D61—216no—
300C2×Dic61—21no—
301C2×Dic61—21no—
302C2×Dic61—21no—
303C2×Dic61—21no—
304C2×Dic61—21no—
305C2×Dic61—21no—
306C2×Dic61—22no—
307C2×Dic61—41no—
308C2×Dic61—41no—
309C2×Dic61—41no—
310C2×Dic61—41no—
311C2×Dic61—41no—
312C2×Dic61—41no—
313C2×Dic61—41no—
314C2×Dic61—41no—
315C2×Dic61—84no—
316C2×Dic61C2×C22⋊C412yes—
317C2×Dic61C2×C22⋊C412yes—
318C2×Dic61C2×C22⋊C412yes—
319D244—22no—
320D244—22no—
321D244—22no—
322D244#11714yes—
323C4×D61—22no—
324C4×D61—22no—
325C4×D61—22no—
326C4×D61—22no—
327C4×D61—84no—
328C4×D61—84no—
329C8×C61—41no—
330C8×C61—41no—
331#92418—41no—
332#92418—41no—
333#20744—611nomaximal, Sylow
334C22×C61—24no—
335C22×C61—42no—
336C22×C61—42no—
337C22×C61—42no—
338C22×C61—42no—
339C22×C61—42no—
340C22×C61—42no—
341C22×C61C22×C22⋊C411yescharacteristic
342C22×C61#52511yescharacteristic
343C22×C61#52511yescharacteristic
344C22×C61#57611yescharacteristic
345C22×C61#57611yescharacteristic
346C22×C61#57711yescharacteristic
347C22×C61#57711yescharacteristic
348C2×D61—22no—
349C2×D61—22no—
350C2×D61—22no—
351C2×D61—24no—
352C2×D61—41no—
353C2×D61—41no—
354C2×D61—42no—
355C2×D61—42no—
356C2×D61—41no—
357C2×D61—42no—
358C2×D61—41no—
359C2×D61—42no—
360C2×D61—42no—
361C2×D61—42no—
362C2×D61—816no—
363C4×C61—22no—
364C4×C61—22no—
365C4×C61—42no—
366C4×C61—81no—
367C4×C61—81no—
368C4×C61C2×#11711yescharacteristic
369C4×C61C2×#11711yescharacteristic
370C4×C61#52511yescharacteristic
371C4×C61#52511yescharacteristic
372Dic61—22no—
373Dic61—22no—
374Dic61—22no—
375Dic61—42no—
376Dic61—81no—
377Dic61—81no—
378C2×#518—611no—
379C2×#433—611no—
380#2314—611no—
381#1825—611no—
382#1825—611no—
383#1804—611no—
384#1804D6111yescharacteristic, complemented
385#1802—611no—
386#1802—611no—
387#1786—611no—
388#1786—611no—
389#1762—611no—
390#1762—611no—
391C4×#102—611no—
392C4×#102—611no—
393C2×C61—44no—
394C2×C61#228011yescharacteristic
395C2×C61#289711yescharacteristic
396C2×C61#289711yescharacteristic
397C2×C61#311811yescharacteristic
398C2×C61#311811yescharacteristic
399C2×C61#312211yescharacteristic
400C2×C61#312311yescharacteristic
401D61—42no—
402D61—44no—
403C23×D4—611no—
404#518—618no—
405#518—1224no—
406C2×C4×D4—611no—
407C2×C4×D4—611no—
408C2×C4×D4—611no—
409C2×C4×D4—1221no—
410C2×C4×D4—1221no—
411C2×C4×D4C2×D6111yescharacteristic
412C2×#117—611no—
413C2×#117—611no—
414C22×C22⋊C4—1221no—
415C22×C22⋊C4—1221no—
416#433—1224no—
417C2×C4⋊C8—611no—
418C2×C4⋊C8C2×D6111yescharacteristic, complemented
419C2×#102—611no—
420C2×#102—611no—
421C2×#102—611no—
422C2×#102—611no—
423C2×#102—611no—
424C2×#102—611no—
425C2×#102C2×D6111yescharacteristic
426C2×#102C2×D6111yescharacteristic
427C2×C22⋊C8—611no—
428C2×C22⋊C8—611no—
429C2×#97—611no—
430C2×C4×C8—611no—
431#388—1221no—
432#388—1221no—
433#387—1221no—
434#387—1221no—
435#384—611no—
436#382C2×D6111yescharacteristic, complemented
437#380—611no—
438#380—611no—
439C4×C4⋊C4—611no—
440C4×C4⋊C4—611no—
441#340—611no—
442#340—611no—
443#340—611no—
444#340—611no—
445#340—611no—
446#340—611no—
447#340C2×D6111yescharacteristic, complemented
448#340C2×D6111yescharacteristic, complemented
449C61#2074411yescharacteristic, complemented, Sylow
450C25—1221no—
451C22×D4—614no—
452C22×D4—611no—
453C22×D4—1222no—
454C22×D4—1221no—
455C22×D4—1222no—
456C22×D4—1222no—
457C22×D4—1222no—
458C22×D4—1222no—
459C22×D4C22×D6111yescharacteristic
460C23×C4—21no—
461C23×C4—611no—
462C23×C4—1221no—
463C23×C4—1221no—
464C23×C4—1221no—
465C22×C8—611no—
466C22×C8—611no—
467C22×C8C22×D6111yescharacteristic
468C22×C8C22×D6111yescharacteristic
469C4×D4—22no—
470C4×D4—614no—
471C4×D4—614no—
472C4×D4—614no—
473C4×D4—1222no—
474C4×D4—1222no—
475C4×D4—1228no—
476C4×D4—1228no—
477C4×D4—1222no—
478C4×D4C4×D6114yes—
479#117—614no—
480#117—614no—
481#117—614no—
482#117—1222no—
483C2×C4⋊C4—611no—
484C2×C4⋊C4—611no—
485C2×C4⋊C4—611no—
486C2×C4⋊C4—611no—
487C2×C4⋊C4—611no—
488C2×C4⋊C4—1221no—
489C2×C4⋊C4—1221no—
490C2×C4⋊C4C22×D6111yescharacteristic
491C2×C4⋊C4C22×D6111yescharacteristic
492C2×C4⋊C4C22×D6111yescharacteristic
493C2×C22⋊C4—21no—
494C2×C22⋊C4—611no—
495C2×C22⋊C4—611no—
496C2×C22⋊C4—1228no—
497C2×C22⋊C4—1228no—
498C2×C22⋊C4—1221no—
499C2×C22⋊C4—1221no—
500C2×C22⋊C4—1221no—
501C2×C22⋊C4—1221no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C42—611no—
505C2×C42—1221no—
506C2×C42—1221no—
507C2×C42—1221no—
508C2×C42C22×D6111yescharacteristic
509C4⋊C8—22no—
510C4⋊C8—1222no—
511#102—22no—
512#102—22no—
513#102—1222no—
514#102—1222no—
515#102—1222no—
516#102—1222no—
517#102—1222no—
518#102—1222no—
519C22⋊C8—1222no—
520C22⋊C8—1222no—
521#97—1222no—
522C4×C8—1222no—
523#95—21no—
524#95—21no—
525#95—1221no—
526#95—1221no—
527#95—1221no—
528#95—1221no—
529C24—21no—
530C24—611no—
531C24—1224no—
532C24—1224no—
533C24—1224no—
534C24—1221no—
535C24—4881no—
536C24—4881no—
537C24—4881no—
538C24—4881no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—612no—
543C2×D4—612no—
544C2×D4—612no—
545C2×D4—1224no—
546C2×D4—1228no—
547C2×D4—1228no—
548C2×D4—1228no—
549C2×D4—1224no—
550C2×D4—1224no—
551C2×D4—1228no—
552C2×D4—1221no—
553C2×D4—1221no—
554C2×D4—1221no—
555C2×D4C2×C4×D6112yes—
556C2×D4#1175822412yes—
557C2×D4#1175822612yes—
558C22×C4—21no—
559C22×C4—24no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—81no—
563C22×C4—81no—
564C22×C4—611no—
565C22×C4—611no—
566C22×C4—611no—
567C22×C4—612no—
568C22×C4—612no—
569C22×C4—1224no—
570C22×C4—1224no—
571C22×C4—1221no—
572C22×C4—1221no—
573C22×C4—1221no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1224no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—4881no—
580C22×C4—4881no—
581C22×C4—4881no—
582C22×C4—4881no—
583C22×C4—4881no—
584C22×C4—4881no—
585C22×C4D4×D6111yescharacteristic
586C22×C4D4×D6111yescharacteristic
587C22×C4C23×D6111yescharacteristic
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—1221no—
595C2×C8—1221no—
596C2×C8—1221no—
597C2×C8—1221no—
598C2×C8—1221no—
599C2×C8—1221no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—614no—
606C4⋊C4—614no—
607C4⋊C4—612no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—4881no—
614C4⋊C4—4881no—
615C4⋊C4C2×C4×D6112yes—
616C22⋊C4—24no—
617C22⋊C4—614no—
618C22⋊C4—614no—
619C22⋊C4—1224no—
620C22⋊C4—1224no—
621C22⋊C4—1224no—
622C22⋊C4—1224no—
623C22⋊C4—4881no—
624C22⋊C4—4881no—
625C42—612no—
626C42—612no—
627C42—1224no—
628C42—4881no—
629C42—4881no—
630C42C2×C4×D6112yes—
631C42D4×D6112yes—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—612no—
640C23—12216no—
641C23—1222no—
642C23—1221no—
643C23—1222no—
644C23—1221no—
645C23—1222no—
646C23—1221no—
647C23—1221no—
648C23—1221no—
649C23—1221no—
650C23—4884no—
651C23—4884no—
652C23—4884no—
653C23—4884no—
654C23—4884no—
655C23—4884no—
656C23—2441no—
657C23—2441no—
658C23—2441no—
659C23—2441no—
660C23C2×D4×D6111yescharacteristic
661D4—22no—
662D4—22no—
663D4—22no—
664D4—614no—
665D4—12216no—
666D4—1222no—
667D4—1222no—
668D4—1222no—
669D4#1451973514yes—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—84no—
684C2×C4—612no—
685C2×C4—612no—
686C2×C4—612no—
687C2×C4—1221no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1222no—
694C2×C4—1222no—
695C2×C4—1222no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—4884no—
699C2×C4—4884no—
700C2×C4—4884no—
701C2×C4—2441no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4C22⋊C4×D6112yes—
710C2×C4C22⋊C4×D6112yes—
711C2×C4C22×C4×D6111yescharacteristic
712C2×C4C2×D4×D6111yescharacteristic
713C2×C4#41×D6111yescharacteristic
714C2×C4#41×D6111yescharacteristic
715C2×C4C2×#1175822411yescharacteristic
716C2×C4C2×#1175822611yescharacteristic
717C8—41no—
718C8—41no—
719C8—2441no—
720C8—2441no—
721C22—24no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—1222no—
729C22—1222no—
730C22—1222no—
731C22—1224no—
732C22—48816no—
733C22—2442no—
734C22—2442no—
735C22—2441no—
736C22—2442no—
737C22—2441no—
738C22—2442no—
739C22—2441no—
740C22—2442no—
741C22—2441no—
742C22—2442no—
743C22C2×C22⋊C4×D6111yescharacteristic
744C22#1684027211yescharacteristic
745C22#1684027511yescharacteristic
746C22#1684056411yescharacteristic
747C22#1684056611yescharacteristic
748C22#1684056911yescharacteristic
749C22#1684057211yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—81no—
754C4—81no—
755C4—1222no—
756C4—1222no—
757C4—1222no—
758C4—4881no—
759C4—4881no—
760C4—2442no—
761C4#117×D6111yescharacteristic
762C4C2×#1451973511yescharacteristic
763C4#1684027211yescharacteristic
764C4#1684027511yescharacteristic
765C2—44no—
766C2—2442no—
767C2—2444no—
768C2#2144820111yescharacteristic
769C2#2145434111yescharacteristic
770C2#2145434411yescharacteristic
771C2#2145600011yescharacteristic
772C2#2145600211yescharacteristic
773C2#2145606411yescharacteristic
774C2#2145607311yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1804C2
socleC23×C61C22×D4
prime radicalC22×D4×D61C22
cosocleC22×C4×C61C24
hypercenter#1804D61
hypocenterC61#20744
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. C2×#16839822C2semidirect
3. #21448429C2semidirect
4. #21445913C2semidirect
5. #21445912C2semidirect
6. #21445826C2semidirect
7. #21445820C2semidirect
8. #21445819C2semidirect
11. #21445646C2semidirect
12. #21445643C2semidirect
13. #102×Dic61C2semidirect
14. #21445633C2semidirect
15. C61×#1804C2semidirect
18. #16840234C4semidirect
29. C2×C4⋊#92418C22semidirect
38. C2×#14519687C22semidirect
39. C2×C8×Dic61C22semidirect
44. #16839632C22semidirect
47. C4⋊C4×Dic61C22semidirect
48. C4⋊C4×Dic61C22semidirect
49. #16839525C22semidirect
50. #16839525C22semidirect
51. #16839524C22semidirect
52. #16839524C22semidirect
53. #16839524C22semidirect
54. #16839524C22semidirect
56. C2×C4⋊C8×C61C22semidirect
59. C61×#382C22semidirect
60. C61×#340C22semidirect
61. C61×#340C22semidirect
384. #1804D61semidirect
418. C2×C4⋊C8C2×D61semidirect
436. #382C2×D61semidirect
447. #340C2×D61semidirect
448. #340C2×D61semidirect
449. C61#20744semidirect

Maximal subgroups

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

subgroupindex
C2×#168402342
C2×#168398222
#214484292
#214459132
#214459122
#214458262
#214458202
#214458192
#214457482
#214456462
#214456432
#102×Dic612
#214456332
C61×#18042
#2074461