Finite Group Databasebeta

← #29685680

Subgroups — #29685680

Order 15616.

1520 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D61C211yesmaximal, characteristic, complemented
2C2×#16839902C211yesmaximal, characteristic
3C2×#16839864C211yesmaximal, characteristic, complemented
4C2×#16839860C211yesmaximal, characteristic, complemented
5C4×#14519752C211yesmaximal, characteristic
6#21446175C211yesmaximal, characteristic, complemented
7#21446172C211yesmaximal, characteristic, complemented
8#21446135C211yesmaximal, characteristic
9#21446075C211yesmaximal, characteristic, complemented
10#21446074C211yesmaximal, characteristic, complemented
11#21446008C211yesmaximal, characteristic, complemented
12#21445752C211yesmaximal, characteristic, complemented
13#21445652C211yesmaximal, characteristic, complemented
14#21445582C211yesmaximal, characteristic, complemented
15C61×#1763C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×#11758190C2211yescharacteristic
18C22×#11758201C2211yescharacteristic
19C2×#14519752C2211yescharacteristic
20C2×Q8×Dic61C2211yescharacteristic
21C2×C4×Dic122—21no—
22C2×C4×Dic122C2211yescharacteristic
23C2×#14519742—21no—
24C2×#14519742C2211yescharacteristic
25C4×Q8×D61—24no—
26C4×Q8×D61—24no—
27C2×C4×D244—21no—
28C2×C4×D244C2211yescharacteristic
29C2×C4⋊C4×D61—21no—
30C2×C4⋊C4×D61C2211yescharacteristic
31C2×C42×D61—21no—
32C2×C42×D61C2211yescharacteristic
33#16839902C418yescomplemented
34#16839864—24no—
35#16839860—24no—
36C2×#14519711C2211yescharacteristic
37C2×#14519710C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519700C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519699C2211yescharacteristic
43C2×#14519697C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×#14519689C2211yescharacteristic
46C2×#14519688C2211yescharacteristic
47#16839663C2211yescharacteristic
48#16839661C2211yescharacteristic
49#16839654—21no—
50#16839640—21no—
51#16839619C2211yescharacteristic
52C4×#11758198—21no—
53#16839524C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839516C2211yescharacteristic
56#16839516C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#97×C61C2211yescharacteristic
61C4×C4⋊C4×C61C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#340C2211yescharacteristic
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×C414yescomplemented
72C22×D244—21no—
73C22×D244C2311yescharacteristic
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61—21no—
77C22×C4×D61D411yescharacteristic
78C22×C4×D61D411yescharacteristic
79C22×C4×D61C2311yescharacteristic
80C2×#11758190—22no—
81C2×#11758190—22no—
82C2×#11758190C2×C414yescomplemented
83C2×#11758201—22no—
84C2×#11758201—22no—
85C2×#11758201C2×C414yescomplemented
86C22×#92418C2311yescharacteristic
87C22×#92418C2311yescharacteristic
88#14519752—22no—
89#14519752C2×C414yes—
90Q8×Dic61—22no—
91Q8×Dic61—22no—
92C4×Dic122—28no—
93C4×Dic122—22no—
94C4×Dic122D414yescomplemented
95#14519742—28no—
96#14519742—22no—
97#14519742—22no—
98C4×D244—22no—
99C4×D244—22no—
100C4×D244—44no—
101C2×C4⋊Dic61—21no—
102C2×C4⋊Dic61—21no—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×C4⋊Dic61C2311yescharacteristic
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758196—21no—
108C4⋊C4×D61—28no—
109C4⋊C4×D61—22no—
110C4⋊C4×D61—22no—
111C2×#11758198—21no—
112C2×#11758198—21no—
113C2×#11758198—21no—
114C2×#11758198—21no—
115C2×#11758198—21no—
116C2×C4×Dic61—21no—
117C2×C4×Dic61—21no—
118C2×C4×Dic61—21no—
119C2×C4×Dic61D411yescharacteristic
120C2×C4×Dic61D411yescharacteristic
121C2×C4×Dic61C2311yescharacteristic
122C42×D61—28no—
123C42×D61—22no—
124C42×D61—22no—
125#14519711—22no—
126#14519710—22no—
127#14519702—22no—
128#14519701—22no—
129#14519700—22no—
130#14519700C2×C414yescomplemented
131#14519699—22no—
132#14519697—22no—
133#14519689—22no—
134#14519689C2×C414yescomplemented
135#14519688—22no—
136#14519684—21no—
137#14519684—21no—
138C22×Q8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C4×Q8×C61—22no—
142C4×Q8×C61D414yescomplemented
143C2×C4⋊C4×C61—21no—
144C2×C4⋊C4×C61C2311yescharacteristic
145C2×C4⋊C4×C61C2311yescharacteristic
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C42×C61—21no—
148C2×C42×C61—21no—
149C2×C42×C61C2311yescharacteristic
150#103×C61—22no—
151#103×C61C2×C414yescomplemented
152#97×C61—22no—
153#95×C61—21no—
154C23×D61—21no—
155C23×D61C2×D411yescharacteristic
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61C22×C412yes—
160C2×Q8×C61C2×D412yes—
161C2×Q8×C61#4112yes—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2411yescharacteristic
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175Q8×D61—28no—
176Q8×D61—28no—
177Q8×D61—28no—
178Q8×D61—28no—
179C2×D244—21no—
180C2×D244—21no—
181C2×D244—21no—
182C2×D244—21no—
183C2×D244—24no—
184C2×D244—21no—
185C2×D244—42no—
186C2×D244—42no—
187C2×D244C22×C412yes—
188C2×C4×D61—24no—
189C2×C4×D61—24no—
190C2×C4×D61—24no—
191C2×C4×D61—22no—
192C2×C4×D61—22no—
193C2×C4×D61—21no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—22no—
198C2×C4×D61—24no—
199C2×C4×D61—22no—
200C2×C4×D61—22no—
201C2×C4×D61—41no—
202C2×C4×D61—42no—
203C2×C4×D61—42no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61—42no—
207C2×C4×D61C22×C412yes—
208C2×C4×D61#4112yes—
209C2×Dic122—24no—
210C2×Dic122—24no—
211C2×Dic122—21no—
212C2×Dic122—21no—
213C2×Dic122—21no—
214C2×Dic122—24no—
215C2×Dic122C22×C412yes—
216C2×Dic122C2×D412yes—
217C2×Dic122#4112yes—
218C2×C8×C61—21no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61C22×C412yes—
224C4⋊C4×C61—24no—
225C4⋊C4×C61—21no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61C22×C412yes—
230C4⋊C4×C61C2×D412yes—
231C42×C61—24no—
232C42×C61—42no—
233C42×C61C2×D412yes—
234C42×C61C2×D412yes—
235#11758201—28no—
236#11758198—24no—
237#11758198—42no—
238#11758198—42no—
239#11758198—42no—
240#11758198—42no—
241C4⋊Dic61—24no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61—21no—
245C4⋊Dic61—42no—
246C4⋊Dic61C2×D412yes—
247#11758196—24no—
248#11758196—24no—
249#11758196—24no—
250C4×Dic61—24no—
251C4×Dic61—24no—
252C4×Dic61—24no—
253C4×Dic61—22no—
254C4×Dic61—22no—
255C4×Dic61—21no—
256C4×Dic61—21no—
257C2×#92418—21no—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418C22×C412yes—
263#11758190—28no—
264C23×C61C22×D411yescharacteristic
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—22no—
270C22×D61—41no—
271C22×D61—41no—
272C22×D61—41no—
273C22×D61—41no—
274C22×D61—41no—
275C22×D61—41no—
276C22×D61C4×D412yes—
277C22×D61AGL(1,ℤ/8)12yes—
278C22×D61#13712yes—
279Q8×C61—22no—
280Q8×C61—22no—
281Q8×C61—22no—
282Q8×C61C4×D414yescomplemented
283C2×C4×C61—22no—
284C2×C4×C61—22no—
285C2×C4×C61—22no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—41no—
293C2×C4×C61—41no—
294C2×C4×C61—41no—
295C2×C4×C61—41no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61#12012yes—
300C2×C4×C61#12012yes—
301C2×C4×C61C23×C411yescharacteristic
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C2×#4111yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×Dic61—22no—
308C2×Dic61—21no—
309C2×Dic61—21no—
310C2×Dic61—22no—
311C2×Dic61—21no—
312C2×Dic61—22no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—22no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61C4×D412yes—
324C2×Dic61#13712yes—
325D244—22no—
326D244—22no—
327D244—48no—
328D244—41no—
329D244—41no—
330C4×D61—28no—
331C4×D61—216no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—44no—
337C4×D61—48no—
338C4×D61—84no—
339Dic122—216no—
340Dic122—22no—
341Dic122—22no—
342Dic122—22no—
343Dic122C4×D414yescomplemented
344C8×C61—22no—
345C8×C61—41no—
346#92418—22no—
347#92418—41no—
348#21454—611nomaximal, Sylow
349C22×C61C2×C4×D411yescharacteristic
350C22×C61C2×#12011yescharacteristic
351C22×C61#52511yescharacteristic
352C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C61C2×#13711yescharacteristic
354C22×C61C2×#13711yescharacteristic
355C22×C61#57511yescharacteristic
356C2×D61—22no—
357C2×D61—22no—
358C2×D61—22no—
359C2×D61—22no—
360C2×D61—22no—
361C2×D61—22no—
362C2×D61—42no—
363C2×D61—42no—
364C2×D61—42no—
365C2×D61—81no—
366C2×D61—81no—
367C2×D61—81no—
368C2×D61—81no—
369C2×D61#44014yescomplemented
370C4×C61—22no—
371C4×C61—22no—
372C4×C61—24no—
373C4×C61—42no—
374C4×C61—42no—
375C4×C61—81no—
376C4×C61C2×C4×D411yescharacteristic
377C4×C61C2×C4×D411yescharacteristic
378C4×C61#52511yescharacteristic
379C4×C61#52511yescharacteristic
380Dic61—22no—
381Dic61—22no—
382Dic61—24no—
383Dic61—41no—
384Dic61—42no—
385Dic61—81no—
386C22×C4×Q8—611no—
387C2×#448—611no—
388C2×#440—611no—
389C2×#440—611no—
390C4×#121—611no—
391#1880—611no—
392#1880—611no—
393#1874—611no—
394#1863—611no—
395#1863—611no—
396#1852—611no—
397#1787—611no—
398#1763—611no—
399#1763D6111yescharacteristic, complemented
400#1749—611no—
401C2×C61C4×#12011yescharacteristic
402C2×C61C2×#44011yescharacteristic
403C2×C61C4×#13711yescharacteristic
404C2×C61#300411yescharacteristic
405C2×C61#300611yescharacteristic
406C2×C61#311211yescharacteristic
407C2×C61#311711yescharacteristic
408D61—24no—
409D61—82no—
410C23×Q8—611no—
411C22×SD16—611no—
412C22×SD16—611no—
413C2×#121—611no—
414C2×C4×Q8—611no—
415C2×C4×Q8—611no—
416C2×C4×Q8—611no—
417C2×C4×Q8—1221no—
418C2×C4×Q8—1221no—
419C2×C4×Q8—1224no—
420C2×C4×Q8—1224no—
421C2×C4×Q8C2×D6111yescharacteristic
422C2×C4×D4—611no—
423C2×C4×D4—1221no—
424C22×C4⋊C4—611no—
425C22×C4⋊C4—1221no—
426C22×C42—611no—
427C22×C42—1221no—
428#448—618no—
429#440—1224no—
430#440—1224no—
431C2×#107—611no—
432C2×#107—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#103—611no—
437C2×#103C2×D6111yescharacteristic
438C2×#103C2×D6111yescharacteristic
439C2×#102—611no—
440C2×#102—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×#97—611no—
444C2×#97C2×D6111yescharacteristic
445#390—611no—
446#389—611no—
447#388—1221no—
448#386—1221no—
449#380—611no—
450C4×C4⋊C4C2×D6111yescharacteristic
451C4×C22⋊C4—1221no—
452#340—611no—
453#340—611no—
454#340C2×D6111yescharacteristic
455#340C2×D6111yescharacteristic
456#336—611no—
457#336—611no—
458C61#2145411yescharacteristic, complemented, Sylow
459C22×Q8—614no—
460C22×Q8—611no—
461C22×Q8—1221no—
462C22×Q8—1222no—
463C22×Q8—1222no—
464C22×Q8—1222no—
465C22×Q8—1222no—
466C22×Q8—1222no—
467C22×Q8C22×D6111yescharacteristic
468C22×D4—611no—
469C22×D4—1221no—
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—1221no—
474C23×C4—1221no—
475C23×C4—1221no—
476C2×SD16—614no—
477C2×SD16—614no—
478C2×SD16—1222no—
479C2×SD16—1222no—
480C2×SD16—1222no—
481C2×SD16—1222no—
482C22×C8—611no—
483C22×C8—611no—
484C22×C8C22×D6111yescharacteristic
485C22×C8C22×D6111yescharacteristic
486#121—614no—
487#121—1222no—
488C4×Q8—22no—
489C4×Q8—614no—
490C4×Q8—1228no—
491C4×Q8—1222no—
492C4×Q8—1228no—
493C4×Q8—1222no—
494C4×Q8—1222no—
495C4×Q8—1222no—
496C4×Q8—1222no—
497C4×Q8D24414yescomplemented
498C4×D4—1222no—
499C4×D4—1222no—
500C4×D4—2444no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—1222no—
505C2×C4⋊C4—1228no—
506C2×C4⋊C4—1221no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1222no—
511C2×C4⋊C4—1221no—
512C2×C4⋊C4C22×D6111yescharacteristic
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—1221no—
516C2×C22⋊C4—1221no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C42—21no—
521C2×C42—21no—
522C2×C42—611no—
523C2×C42—611no—
524C2×C42—611no—
525C2×C42—1228no—
526C2×C42—1221no—
527C2×C42—1221no—
528C2×C42—1221no—
529C2×C42—1222no—
530C2×C42—1222no—
531C2×C42C22×D6111yescharacteristic
532#107—1222no—
533#107—1222no—
534#103—22no—
535#103—614no—
536#103—1222no—
537#103—1222no—
538#103—1222no—
539#103C4×D6114yescomplemented
540#102—1222no—
541#102—1222no—
542C22⋊C8—614no—
543C22⋊C8—1222no—
544#97—22no—
545#97—1222no—
546#95—21no—
547#95—1221no—
548#95—1221no—
549C24—611no—
550C24—1221no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—612no—
555C2×Q8—612no—
556C2×Q8—612no—
557C2×Q8—1224no—
558C2×Q8—1224no—
559C2×Q8—1224no—
560C2×Q8—1228no—
561C2×Q8—1228no—
562C2×Q8—1228no—
563C2×Q8—1228no—
564C2×Q8—1221no—
565C2×Q8—1221no—
566C2×Q8—1221no—
567C2×Q8C2×C4×D6112yes—
568C2×Q8C2×D24412yes—
569C2×Q8#1175822212yes—
570C2×D4—612no—
571C2×D4—1224no—
572C2×D4—1221no—
573C2×D4—1221no—
574C2×D4—1221no—
575C2×D4—1221no—
576C2×D4—1221no—
577C2×D4—2442no—
578C2×D4—2442no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—611no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1224no—
591C22×C4—1224no—
592C22×C4—1224no—
593C22×C4—1222no—
594C22×C4—1224no—
595C22×C4—1221no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1222no—
601C22×C4—1221no—
602C22×C4—1222no—
603C22×C4—1221no—
604C22×C4—2441no—
605C22×C4—2442no—
606C22×C4—2442no—
607C22×C4—2442no—
608C22×C4—2442no—
609C22×C4—2442no—
610C22×C4D4×D6111yescharacteristic
611C22×C4D4×D6111yescharacteristic
612C22×C4C23×D6111yescharacteristic
613SD16—1228no—
614SD16—1228no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—612no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8C2×C4×D6112yes—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—24no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—612no—
633C4⋊C4—1224no—
634C4⋊C4—1224no—
635C4⋊C4—1224no—
636C4⋊C4—1221no—
637C4⋊C4—1224no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—2442no—
641C4⋊C4C2×C4×D6112yes—
642C4⋊C4C2×D24412yes—
643C22⋊C4—1224no—
644C22⋊C4—2442no—
645C22⋊C4—2442no—
646C22⋊C4—2442no—
647C22⋊C4—2442no—
648C42—24no—
649C42—42no—
650C42—1224no—
651C42—1224no—
652C42—1221no—
653C42—1221no—
654C42—1222no—
655C42—1222no—
656C42—1224no—
657C42C2×D24412yes—
658C42D4×D6112yes—
659C23—612no—
660C23—612no—
661C23—612no—
662C23—1221no—
663C23—1221no—
664C23—1221no—
665C23—1221no—
666C23—1222no—
667C23—2441no—
668C23—2441no—
669C23—2441no—
670C23—2441no—
671C23—2441no—
672C23—2441no—
673C23C2×D4×D6111yescharacteristic
674Q8—22no—
675Q8—22no—
676Q8—22no—
677Q8—614no—
678Q8—12216no—
679Q8—1222no—
680Q8—1222no—
681Q8—1222no—
682Q8C4×D24414yescomplemented
683D4—1222no—
684D4—1222no—
685D4—2448no—
686D4—2441no—
687D4—2441no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—612no—
705C2×C4—612no—
706C2×C4—1228no—
707C2×C4—12216no—
708C2×C4—1222no—
709C2×C4—1221no—
710C2×C4—1221no—
711C2×C4—1222no—
712C2×C4—1221no—
713C2×C4—1222no—
714C2×C4—1221no—
715C2×C4—1222no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1221no—
721C2×C4—1221no—
722C2×C4—1221no—
723C2×C4—4884no—
724C2×C4—2444no—
725C2×C4—2448no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4#1451974712yes—
732C2×C4#1451974712yes—
733C2×C4C22×C4×D6111yescharacteristic
734C2×C4C2×D4×D6111yescharacteristic
735C2×C4C22×D24411yescharacteristic
736C2×C4#41×D6111yescharacteristic
737C2×C4#41×D6111yescharacteristic
738C2×C4C2×#1175822211yescharacteristic
739C8—22no—
740C8—41no—
741C8—1222no—
742C8—2441no—
743C22—614no—
744C22—1222no—
745C22—1222no—
746C22—1222no—
747C22—1222no—
748C22—1222no—
749C22—1222no—
750C22—4881no—
751C22—4881no—
752C22—4881no—
753C22—4881no—
754C22—2442no—
755C22—2442no—
756C22—2442no—
757C22C4×D4×D6111yescharacteristic
758C22C2×#1451974711yescharacteristic
759C22#1684027111yescharacteristic
760C22AGL(1,ℤ/8)×D6111yescharacteristic
761C22#137×D6111yescharacteristic
762C22#137×D6111yescharacteristic
763C22#1684056111yescharacteristic
764C4—24no—
765C4—22no—
766C4—22no—
767C4—42no—
768C4—42no—
769C4—81no—
770C4—1222no—
771C4—1224no—
772C4—1222no—
773C4—4881no—
774C4—2441no—
775C4—2442no—
776C4C4×D4×D6111yescharacteristic
777C4C2×C4×D24411yescharacteristic
778C4#1684027111yescharacteristic
779C4#1684027411yescharacteristic
780C2—1224no—
781C2—4882no—
782C2C4×#1451974711yescharacteristic
783C2#440×D6111yescharacteristic
784C2#2145463511yescharacteristic
785C2#2145505511yescharacteristic
786C2#2145507211yescharacteristic
787C2#2145593911yescharacteristic
788C2#2145599411yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1763C2
socleC23×C61C22×D4
prime radicalC2×#14519752C22
cosocleC22×C4×C61C24
hypercenter#1763D61
hypocenterC61#21454
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×D61C2semidirect
3. C2×#16839864C2semidirect
4. C2×#16839860C2semidirect
6. #21446175C2semidirect
7. #21446172C2semidirect
9. #21446075C2semidirect
10. #21446074C2semidirect
11. #21446008C2semidirect
12. #21445752C2semidirect
13. #21445652C2semidirect
14. #21445582C2semidirect
15. C61×#1763C2semidirect
33. #16839902C4semidirect
71. C2×Q8×D61C2×C4semidirect
82. C2×#11758190C2×C4semidirect
85. C2×#11758201C2×C4semidirect
94. C4×Dic122D4semidirect
130. #14519700C2×C4semidirect
134. #14519689C2×C4semidirect
142. C4×Q8×C61D4semidirect
151. #103×C61C2×C4semidirect
282. Q8×C61C4×D4semidirect
343. Dic122C4×D4semidirect
369. C2×D61#440semidirect
399. #1763D61semidirect
458. C61#21454semidirect
497. C4×Q8D244semidirect
539. #103C4×D61semidirect
682. Q8C4×D244semidirect

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×#168399022
C2×#168398642
C2×#168398602
C4×#145197522
#214461752
#214461722
#214461352
#214460752
#214460742
#214460082
#214457522
#214456522
#214455822
C61×#17632
#2145461