Finite Group Databasebeta

← #29685607

Subgroups — #29685607

Order 15616.

1532 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×#16839899C211yesmaximal, characteristic
3C2×#16839853C211yesmaximal, characteristic, complemented
4C2×SD16×Dic61C211yesmaximal, characteristic, complemented
5#21448335C211yesmaximal, characteristic
6#21446177C211yesmaximal, characteristic, complemented
7#21446133C211yesmaximal, characteristic
8#21446090C211yesmaximal, characteristic, complemented
9#21446087C211yesmaximal, characteristic, complemented
10#21446013C211yesmaximal, characteristic, complemented
11#21445752C211yesmaximal, characteristic, complemented
12#103×Dic61C211yesmaximal, characteristic, complemented
13#21445638C211yesmaximal, characteristic, complemented
14#21445576C211yesmaximal, characteristic, complemented
15C61×#1880C211yesmaximal, characteristic, complemented
16C22×Q8×D61C2211yescharacteristic
17C22×#11758200C2211yescharacteristic
18C2×#14519748C2211yescharacteristic
19C2×Q8×Dic61C2211yescharacteristic
20C2×C4×Dic122—21no—
21C2×C4×Dic122C2211yescharacteristic
22C2×#14519742—21no—
23C2×#14519742C2211yescharacteristic
24C4×Q8×D61—24no—
25C4×Q8×D61—24no—
26C2×D4×Dic61C2211yescharacteristic
27C2×#14519737—21no—
28C2×C4⋊C4×D61—21no—
29C2×C4⋊C4×D61C2211yescharacteristic
30C2×C42×D61—21no—
31C2×C42×D61C2211yescharacteristic
32#16839899C418yescomplemented
33#16839853—24no—
34SD16×Dic61—24no—
35C2×#14519709C2211yescharacteristic
36C2×#14519708C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519702C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519701C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42C2×#14519698C2211yescharacteristic
43C2×#14519689C2211yescharacteristic
44C2×#14519689C2211yescharacteristic
45C2×C8×Dic61C2211yescharacteristic
46C2×C8×Dic61C2211yescharacteristic
47#16839660C2211yescharacteristic
48#16839656—21no—
49#16839638—21no—
50#16839619C2211yescharacteristic
51C4⋊C4×Dic61C2211yescharacteristic
52C22⋊C4×Dic61—21no—
53#16839525C2211yescharacteristic
54#16839524C2211yescharacteristic
55#16839524C2211yescharacteristic
56#16839517C2211yescharacteristic
57C22×SD16×C61C2211yescharacteristic
58C2×C4×Q8×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C61×#390C2211yescharacteristic
62C61×#340C2211yescharacteristic
63C61×#336C2211yescharacteristic
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×C22⋊D61—21no—
73C23×Dic61—21no—
74C22×C4×D61—21no—
75C22×C4×D61—21no—
76C22×C4×D61D411yescharacteristic
77C22×C4×D61D411yescharacteristic
78C22×C4×D61C2311yescharacteristic
79C2×#11758200—22no—
80C2×#11758200—22no—
81C2×#11758200C2×C414yescomplemented
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84#14519748—22no—
85#14519748C2×C414yes—
86Q8×Dic61—22no—
87Q8×Dic61D414yescomplemented
88C4×Dic122—28no—
89C4×Dic122—22no—
90C4×Dic122—22no—
91#14519742—28no—
92#14519742—22no—
93#14519742D414yescomplemented
94D4×Dic61—22no—
95D4×Dic61—22no—
96#14519737—44no—
97C2×C4⋊Dic61—21no—
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×C4⋊Dic61C2311yescharacteristic
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C4⋊C4×D61—28no—
106C4⋊C4×D61—22no—
107C4⋊C4×D61—22no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—21no—
110C2×#11758198—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61—21no—
113C2×C4×Dic61—21no—
114C2×C4×Dic61—21no—
115C2×C4×Dic61D411yescharacteristic
116C2×C4×Dic61D411yescharacteristic
117C2×C4×Dic61C2311yescharacteristic
118C42×D61—28no—
119C42×D61—22no—
120C42×D61—22no—
121#14519709—22no—
122#14519708—22no—
123#14519702—22no—
124#14519702C2×C414yescomplemented
125#14519701—22no—
126#14519701C2×C414yescomplemented
127#14519700—22no—
128#14519698—22no—
129#14519689—22no—
130#14519689C2×C414yescomplemented
131C8×Dic61—22no—
132C8×Dic61—22no—
133#14519684—21no—
134#14519684—21no—
135#14519684—21no—
136C22×Q8×C61C2311yescharacteristic
137C22×D4×C61C2311yescharacteristic
138C2×SD16×C61—22no—
139C2×SD16×C61—22no—
140C2×SD16×C61C2×C414yescomplemented
141C22×C8×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C4×Q8×C61—22no—
144C4×Q8×C61—22no—
145C2×C4⋊C4×C61—21no—
146C2×C4⋊C4×C61C2311yescharacteristic
147C2×C4⋊C4×C61C2311yescharacteristic
148C2×C22⋊C4×C61—21no—
149C2×C22⋊C4×C61—21no—
150C2×C42×C61—21no—
151C2×C42×C61C2311yescharacteristic
152#103×C61—22no—
153#102×C61—22no—
154C24×C61—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—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61C22×C412yes—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61C2×D411yescharacteristic
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2411yescharacteristic
174C2×C22⋊D61—24no—
175C2×C22⋊D61—42no—
176C2×C22⋊D61—42no—
177C22×Dic61—21no—
178C22×Dic61—21no—
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—42no—
182C22×Dic61—42no—
183C22×Dic61—42no—
184C22×Dic61C2×D411yescharacteristic
185C22×Dic61C2×D411yescharacteristic
186C22×Dic61C2×D411yescharacteristic
187Q8×D61—28no—
188Q8×D61—28no—
189Q8×D61—28no—
190Q8×D61—28no—
191C2×C4×D61—24no—
192C2×C4×D61—24no—
193C2×C4×D61—24no—
194C2×C4×D61—21no—
195C2×C4×D61—21no—
196C2×C4×D61—21no—
197C2×C4×D61—21no—
198C2×C4×D61—22no—
199C2×C4×D61—22no—
200C2×C4×D61—24no—
201C2×C4×D61—22no—
202C2×C4×D61—22no—
203C2×C4×D61—41no—
204C2×C4×D61—42no—
205C2×C4×D61—42no—
206C2×C4×D61SD1614yescomplemented
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—
218SD16×C61—28no—
219C2×C8×C61—21no—
220C2×C8×C61—21no—
221C2×C8×C61—21no—
222C2×C8×C61—21no—
223C2×C8×C61—21no—
224C2×C8×C61C22×C412yes—
225C4⋊C4×C61—24no—
226C4⋊C4×C61—21no—
227C4⋊C4×C61—21no—
228C4⋊C4×C61—21no—
229C4⋊C4×C61C2×D412yes—
230C22⋊C4×C61—42no—
231C22⋊C4×C61—42no—
232C42×C61—24no—
233C42×C61—21no—
234C42×C61—21no—
235C22⋊Dic61—24no—
236C22⋊Dic61—42no—
237#11758200—28no—
238#11758198—42no—
239C4⋊Dic61—21no—
240C4⋊Dic61—21no—
241C4⋊Dic61—24no—
242C4⋊Dic61—21no—
243C4⋊Dic61—21no—
244C4⋊Dic61C22×C412yes—
245C4⋊Dic61C2×D412yes—
246#11758196—24no—
247#11758196—24no—
248#11758196—24no—
249#11758196—42no—
250C4×Dic61—24no—
251C4×Dic61—24no—
252C4×Dic61—24no—
253C4×Dic61—22no—
254C4×Dic61—22no—
255C4×Dic61—42no—
256C4×Dic61C2×D412yes—
257C4×Dic61C2×D412yes—
258C2×#92418—21no—
259C2×#92418—21no—
260C2×#92418—21no—
261C2×#92418—21no—
262C2×#92418—21no—
263C2×#92418C22×C412yes—
264C23×C61—22no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61—41no—
270C23×C61—41no—
271C23×C61C22×D411yescharacteristic
272C22×D61—21no—
273C22×D61—21no—
274C22×D61—21no—
275C22×D61—21no—
276C22×D61C4×D412yes—
277C22×D61C2×SD1612yes—
278C22×D61#13512yes—
279Q8×C61—22no—
280Q8×C61—22no—
281Q8×C61—22no—
282Q8×C61C4×D414yescomplemented
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—41no—
286D4×C61—41no—
287C2×C4×C61—22no—
288C2×C4×C61—21no—
289C2×C4×C61—22no—
290C2×C4×C61—22no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—22no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61—41no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61C2×SD1612yes—
302C2×C4×C61C23×C411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C22⋊D61—48no—
309C2×Dic61—22no—
310C2×Dic61—21no—
311C2×Dic61—22no—
312C2×Dic61—21no—
313C2×Dic61—22no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—22no—
317C2×Dic61—22no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—84no—
326C2×Dic61C4×D412yes—
327C2×Dic61#12012yes—
328C2×Dic61#12012yes—
329C2×Dic61C2×SD1612yes—
330C2×Dic61#13712yes—
331C4×D61—216no—
332C4×D61—22no—
333C4×D61—22no—
334C4×D61—22no—
335C4×D61—22no—
336C4×D61—28no—
337C4×D61—44no—
338C4×D61—48no—
339Dic122—216no—
340Dic122—22no—
341Dic122—22no—
342Dic122—22no—
343Dic122C4×D414yescomplemented
344C8×C61—22no—
345C8×C61—41no—
346#92418—22no—
347#92418—41no—
348C4×#448—611nomaximal, Sylow
349C22×C61—42no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—81no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61—81no—
356C22×C61C2×C4×D411yescharacteristic
357C22×C61C2×#12011yescharacteristic
358C22×C61#52511yescharacteristic
359C22×C61C22×SD1611yescharacteristic
360C22×C61C2×#13511yescharacteristic
361C22×C61C2×#13711yescharacteristic
362C22×C61#57511yescharacteristic
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—22no—
368C2×D61—22no—
369C2×D61C4×SD1614yescomplemented
370C4×C61—22no—
371C4×C61—24no—
372C4×C61—41no—
373C4×C61—42no—
374C4×C61—81no—
375C4×C61C2×C4×D411yescharacteristic
376C4×C61C2×C4×D411yescharacteristic
377C4×C61#52511yescharacteristic
378C4×C61#52511yescharacteristic
379Dic61—22no—
380Dic61—22no—
381Dic61—24no—
382Dic61—42no—
383Dic61—42no—
384Dic61—81no—
385Dic61#44814yescomplemented
386C22×C4×Q8—611no—
387C2×#448—611no—
388C2×C4×SD16—611no—
389C2×C4×SD16—611no—
390C4×#121—611no—
391#1880—611no—
392#1880D6111yescharacteristic, complemented
393#1874—611no—
394#1865—611no—
395#1865—611no—
396#1853—611no—
397#1787—611no—
398C4×#103—611no—
399C4×#103—611no—
400C4×C22⋊C8—611no—
401C2×C61—82no—
402C2×C61C4×#12011yescharacteristic
403C2×C61C2×C4×SD1611yescharacteristic
404C2×C61C4×#13711yescharacteristic
405C2×C61C2×#44811yescharacteristic
406C2×C61#300211yescharacteristic
407C2×C61#310311yescharacteristic
408C2×C61#310811yescharacteristic
409D61—24no—
410C23×Q8—611no—
411C22×SD16—611no—
412C22×SD16C2×D6111yescharacteristic
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—
429C4×SD16—1224no—
430C4×SD16—1224no—
431C2×#106—611no—
432C2×#106—611no—
433C2×#103—611no—
434C2×#103—611no—
435C2×#103—611no—
436C2×#103—611no—
437C2×#103—611no—
438C2×#103C2×D6111yescharacteristic
439C2×#102—611no—
440C2×#102C2×D6111yescharacteristic
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C4×C8—611no—
444C2×C4×C8—611no—
445#390C2×D6111yescharacteristic
446#389—611no—
447#388—1221no—
448#386—1221no—
449#380—611no—
450C4×C4⋊C4—611no—
451C4×C22⋊C4—1221no—
452#340—611no—
453#340—611no—
454#340—611no—
455#340C2×D6111yescharacteristic
456#336—611no—
457#336C2×D6111yescharacteristic
458C61C4×#44811yescharacteristic, 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—1221no—
469C22×D4C22×D6111yescharacteristic
470C23×C4—611no—
471C23×C4—611no—
472C23×C4—611no—
473C23×C4—1221no—
474C23×C4—1221no—
475C23×C4—1221no—
476C2×SD16—22no—
477C2×SD16—22no—
478C2×SD16—614no—
479C2×SD16—1222no—
480C2×SD16—1222no—
481C2×SD16C4×D6114yescomplemented
482C22×C8—611no—
483C22×C8—611no—
484C22×C8C22×D6111yescharacteristic
485C22×C8C22×D6111yescharacteristic
486#121—614no—
487#121—1222no—
488C4×Q8—22no—
489C4×Q8—22no—
490C4×Q8—614no—
491C4×Q8—614no—
492C4×Q8—1222no—
493C4×Q8—1222no—
494C4×Q8—1228no—
495C4×Q8—1222no—
496C4×Q8—1222no—
497C4×Q8—1228no—
498C4×D4—1222no—
499C4×D4—1222no—
500C4×D4—2444no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—611no—
503C2×C4⋊C4—611no—
504C2×C4⋊C4—611no—
505C2×C4⋊C4—1222no—
506C2×C4⋊C4—1228no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4—1221no—
509C2×C4⋊C4—1221no—
510C2×C4⋊C4—1221no—
511C2×C4⋊C4—1222no—
512C2×C4⋊C4—1221no—
513C2×C4⋊C4C22×D6111yescharacteristic
514C2×C4⋊C4C22×D6111yescharacteristic
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—1221no—
518C2×C22⋊C4—1221no—
519C2×C22⋊C4—1221no—
520C2×C42—21no—
521C2×C42—611no—
522C2×C42—611no—
523C2×C42—611no—
524C2×C42—1222no—
525C2×C42—1222no—
526C2×C42—1228no—
527C2×C42—1221no—
528C2×C42—1221no—
529C2×C42—1221no—
530C2×C42—1221no—
531C2×C42C22×D6111yescharacteristic
532#106—1222no—
533#106—1222no—
534#103—22no—
535#103—614no—
536#103—614no—
537#103—1222no—
538#103—1222no—
539#103—1222no—
540#102—22no—
541#102—1222no—
542C22⋊C8—614no—
543C22⋊C8—1222no—
544C4×C8—1222no—
545C4×C8—1222no—
546#95—1221no—
547#95—1221no—
548#95—1221no—
549C24—21no—
550C24—611no—
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×Q8D4×D6112yes—
569C2×Q8#1175822412yes—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—1224no—
576C2×D4—2442no—
577C2×D4—2442no—
578C2×D4C2×C4×D6112yes—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—611no—
585C22×C4—612no—
586C22×C4—612no—
587C22×C4—614no—
588C22×C4—1222no—
589C22×C4—1222no—
590C22×C4—1222no—
591C22×C4—1224no—
592C22×C4—1224no—
593C22×C4—1224no—
594C22×C4—1222no—
595C22×C4—1224no—
596C22×C4—1221no—
597C22×C4—1221no—
598C22×C4—1221no—
599C22×C4—1221no—
600C22×C4—1221no—
601C22×C4—1221no—
602C22×C4—1221no—
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—28no—
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—24no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—612no—
632C4⋊C4—612no—
633C4⋊C4—1224no—
634C4⋊C4—1224no—
635C4⋊C4—1224no—
636C4⋊C4—1224no—
637C4⋊C4—1221no—
638C4⋊C4—1221no—
639C4⋊C4—1221no—
640C4⋊C4—1221no—
641C4⋊C4—2442no—
642C4⋊C4D4×D6112yes—
643C22⋊C4—42no—
644C22⋊C4—42no—
645C22⋊C4—1224no—
646C22⋊C4—2442no—
647C22⋊C4—2442no—
648C42—24no—
649C42—21no—
650C42—21no—
651C42—612no—
652C42—612no—
653C42—1222no—
654C42—1222no—
655C42—1224no—
656C42—1224no—
657C42—1224no—
658C42—2442no—
659C23—22no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—612no—
667C23—612no—
668C23—612no—
669C23—1221no—
670C23—1221no—
671C23—1221no—
672C23—1221no—
673C23C2×D4×D6111yescharacteristic
674Q8—22no—
675Q8—22no—
676Q8—22no—
677Q8—614no—
678Q8—12216no—
679Q8—1222no—
680Q8—1222no—
681Q8—1222no—
682Q8#1451973714yescomplemented
683D4—22no—
684D4—22no—
685D4—41no—
686D4—41no—
687D4—2448no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—612no—
703C2×C4—612no—
704C2×C4—612no—
705C2×C4—612no—
706C2×C4—612no—
707C2×C4—1228no—
708C2×C4—12216no—
709C2×C4—1222no—
710C2×C4—1221no—
711C2×C4—1222no—
712C2×C4—1221no—
713C2×C4—1222no—
714C2×C4—1221no—
715C2×C4—1221no—
716C2×C4—1222no—
717C2×C4—1222no—
718C2×C4—1222no—
719C2×C4—1222no—
720C2×C4—1222no—
721C2×C4—1222no—
722C2×C4—4884no—
723C2×C4—2444no—
724C2×C4—2448no—
725C2×C4—2441no—
726C2×C4—2441no—
727C2×C4—2441no—
728C2×C4—2441no—
729C2×C4—2441no—
730C2×C4—2441no—
731C2×C4—2441no—
732C2×C4SD16×D6112yes—
733C2×C4C22×C4×D6111yescharacteristic
734C2×C4C2×D4×D6111yescharacteristic
735C2×C4C2×D4×D6111yescharacteristic
736C2×C4#41×D6111yescharacteristic
737C2×C4#41×D6111yescharacteristic
738C2×C4C2×#1175822411yescharacteristic
739C8—22no—
740C8—41no—
741C8—1222no—
742C8—2441no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—614no—
751C22—1222no—
752C22—1222no—
753C22—1222no—
754C22—1222no—
755C22—1222no—
756C22—1222no—
757C22C4×D4×D6111yescharacteristic
758C22#120×D6111yescharacteristic
759C22#1684027211yescharacteristic
760C22C2×SD16×D6111yescharacteristic
761C22#135×D6111yescharacteristic
762C22#137×D6111yescharacteristic
763C22#1684055811yescharacteristic
764C4—24no—
765C4—22no—
766C4—41no—
767C4—42no—
768C4—81no—
769C4—614no—
770C4—1222no—
771C4—1224no—
772C4—1222no—
773C4—4881no—
774C4—2442no—
775C4—2442no—
776C4C4×D4×D6111yescharacteristic
777C4C2×#1451973711yescharacteristic
778C4#1684027011yescharacteristic
779C4#1684027211yescharacteristic
780C2—82no—
781C2—1224no—
782C2#2144832411yescharacteristic
783C2C4×SD16×D6111yescharacteristic
784C2#2145464111yescharacteristic
785C2#448×D6111yescharacteristic
786C2#2145503411yescharacteristic
787C2#2145584911yescharacteristic
788C2#2145589811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1880C2
socleC23×C61C22×D4
prime radicalC2×#14519748C22
cosocleC22×C4×C61C24
hypercenter#1880D61
hypocenterC61C4×#448
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×D61C2semidirect
3. C2×#16839853C2semidirect
4. C2×SD16×Dic61C2semidirect
6. #21446177C2semidirect
8. #21446090C2semidirect
9. #21446087C2semidirect
10. #21446013C2semidirect
11. #21445752C2semidirect
12. #103×Dic61C2semidirect
13. #21445638C2semidirect
14. #21445576C2semidirect
15. C61×#1880C2semidirect
32. #16839899C4semidirect
71. C2×Q8×D61C2×C4semidirect
81. C2×#11758200C2×C4semidirect
87. Q8×Dic61D4semidirect
93. #14519742D4semidirect
124. #14519702C2×C4semidirect
126. #14519701C2×C4semidirect
130. #14519689C2×C4semidirect
140. C2×SD16×C61C2×C4semidirect
206. C2×C4×D61SD16semidirect
282. Q8×C61C4×D4semidirect
343. Dic122C4×D4semidirect
369. C2×D61C4×SD16semidirect
385. Dic61#448semidirect
392. #1880D61semidirect
458. C61C4×#448semidirect
481. C2×SD16C4×D61semidirect
682. Q8#14519737semidirect

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×#168398992
C2×#168398532
C2×SD16×Dic612
#214483352
#214461772
#214461332
#214460902
#214460872
#214460132
#214457522
#103×Dic612
#214456382
#214455762
C61×#18802
C4×#44861