Finite Group Databasebeta

← #29700409

Subgroups — #29700409

Order 15616.

1190 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839863C211yesmaximal, characteristic, complemented
2C2×#16839763C211yesmaximal, characteristic, complemented
3#21448839C211yesmaximal, characteristic, complemented
4#21448660C211yesmaximal, characteristic, complemented
5#21446686C211yesmaximal, characteristic, complemented
6#21446518C211yesmaximal, characteristic, complemented
7#21446441C211yesmaximal, characteristic, complemented
8#21446258C211yesmaximal, characteristic, complemented
9#21446176C211yesmaximal, characteristic, complemented
10#21446169C211yesmaximal, characteristic, complemented
11#21446075C211yesmaximal, characteristic, complemented
12#21446009C211yesmaximal, characteristic, complemented
13#103×Dic61C211yesmaximal, characteristic, complemented
14#21445605C211yesmaximal, characteristic, complemented
15C2×C61×#449C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C2×Q8×Dic61C2211yescharacteristic
18C2×Q8×Dic61C2211yescharacteristic
19C2×D4×Dic61—21no—
20C2×D4×Dic61C2211yescharacteristic
21C22×C4⋊Dic61C2211yescharacteristic
22#16839863—24no—
23C2×#14519711C2211yescharacteristic
24C2×#14519711C2211yescharacteristic
25#16839763—24no—
26C2×#14519701C2211yescharacteristic
27C2×#14519701C2211yescharacteristic
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519687C2211yescharacteristic
33C2×C8×Dic61C2211yescharacteristic
34#16839665—21no—
35#16839665—21no—
36#16839665C2211yescharacteristic
37#16839665C2211yescharacteristic
38#16839665C2211yescharacteristic
39#16839661C2211yescharacteristic
40#16839655—21no—
41#16839642—21no—
42#16839637—21no—
43#16839622—21no—
44#16839622C2211yescharacteristic
45C4⋊C4×Dic61C2211yescharacteristic
46C4×C22⋊Dic61—21no—
47C4×C22⋊Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839516C2211yescharacteristic
53#16839516C2211yescharacteristic
54C22×#41×C61C2211yescharacteristic
55C22×SD16×C61C2211yescharacteristic
56C22×D8×C61C2211yescharacteristic
57C2×#121×C61C2211yescharacteristic
58C61×#449C418yescomplemented
59C2×#103×C61C2211yescharacteristic
60C2×#102×C61C2211yescharacteristic
61C2×C22⋊C8×C61C2211yescharacteristic
62C23×Dic61—21no—
63C23×Dic61—21no—
64C2×#11758194—22no—
65C2×#11758194—22no—
66C2×#11758194—41no—
67C22×#92418C2311yescharacteristic
68C22×#92418C2311yescharacteristic
69Q8×Dic61—22no—
70Q8×Dic61—22no—
71Q8×Dic61—41no—
72Q8×Dic61—41no—
73D4×Dic61—22no—
74D4×Dic61—41no—
75D4×Dic61—44no—
76C2×C4⋊Dic61—22no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61—21no—
80C2×C4⋊Dic61—21no—
81C2×C4⋊Dic61—41no—
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C22⋊Dic61—21no—
94C2×C22⋊Dic61D411yescharacteristic
95C2×C22⋊Dic61D411yescharacteristic
96C2×C4×Dic61—21no—
97C2×C4×Dic61—21no—
98C2×C4×Dic61—21no—
99C2×C4×Dic61C2311yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101#14519711—22no—
102#14519711—41no—
103#14519701—22no—
104#14519701D414yescomplemented
105#14519698—22no—
106#14519698—22no—
107#14519698—22no—
108#14519698—41no—
109#14519687—22no—
110C8×Dic61—41no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684D411yescharacteristic
115#14519684D411yescharacteristic
116C2×#41×C61—22no—
117C2×#41×C61—22no—
118C2×#41×C61—22no—
119C2×#41×C61—41no—
120C2×#41×C61—41no—
121C2×#41×C61C2×C414yescomplemented
122C22×Q8×C61C2311yescharacteristic
123C22×D4×C61—21no—
124C22×D4×C61—21no—
125C22×D4×C61C2311yescharacteristic
126C22×D4×C61C2311yescharacteristic
127C23×C4×C61—21no—
128C23×C4×C61C2311yescharacteristic
129C2×SD16×C61—22no—
130C2×SD16×C61—22no—
131C2×SD16×C61C2×C414yescomplemented
132C2×D8×C61—41no—
133C2×D8×C61—41no—
134C2×D8×C61C2×C414yescomplemented
135C22×C8×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137#121×C61—22no—
138#121×C61C2×C414yes—
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—21no—
141#103×C61C2×C414yescomplemented
142#102×C61C2×C414yescomplemented
143C22⋊C8×C61C2×C414yescomplemented
144C24×C61—21no—
145C24×C61—21no—
146C24×C61C2×D411yescharacteristic
147#41×C61—28no—
148#41×C61—44no—
149#41×C61—44no—
150#41×C61—44no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61C22×C412yes—
155C2×Q8×C61C2×D412yes—
156C2×Q8×C61#4112yes—
157C2×D4×C61—24no—
158C2×D4×C61—24no—
159C2×D4×C61—21no—
160C2×D4×C61—21no—
161C2×D4×C61—21no—
162C2×D4×C61—21no—
163C2×D4×C61—21no—
164C2×D4×C61—21no—
165C2×D4×C61—21no—
166C2×D4×C61—21no—
167C2×D4×C61—21no—
168C2×D4×C61—21no—
169C2×D4×C61—42no—
170C2×D4×C61—42no—
171C2×D4×C61—42no—
172C2×D4×C61—42no—
173C2×D4×C61C22×C412yes—
174C2×D4×C61C22×C412yes—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—24no—
182C22×C4×C61—42no—
183C22×C4×C61—42no—
184C22×C4×C61C22×C412yes—
185C22×C4×C61C2×D411yescharacteristic
186C22×C4×C61#4112yes—
187C22×C4×C61C2411yescharacteristic
188C22×Dic61—21no—
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—42no—
193C22×Dic61—42no—
194C22×Dic61—42no—
195C22×Dic61—42no—
196C22×Dic61—81no—
197C22×Dic61—81no—
198C22×Dic61C2×D411yescharacteristic
199C22×Dic61C2×D411yescharacteristic
200C22×Dic61C2×D411yescharacteristic
201C22×Dic61C2×D411yescharacteristic
202SD16×C61—28no—
203D8×C61—44no—
204C2×C8×C61—21no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61C22×C412yes—
209C2×C8×C61C22×C412yes—
210C4⋊C4×C61—21no—
211C4⋊C4×C61C22×C412yes—
212C22⋊C4×C61—24no—
213C22⋊Dic61—22no—
214C22⋊Dic61—41no—
215C22⋊Dic61—42no—
216C22⋊Dic61—42no—
217C22⋊Dic61—42no—
218C22⋊Dic61—42no—
219C22⋊Dic61—81no—
220C22⋊Dic61—81no—
221C22⋊Dic61—81no—
222C22⋊Dic61—81no—
223C4⋊Dic61—21no—
224C4⋊Dic61—21no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—42no—
231C4⋊Dic61—42no—
232C4⋊Dic61—42no—
233C4⋊Dic61—42no—
234C4⋊Dic61C2×D412yes—
235C4×Dic61—21no—
236C4×Dic61—21no—
237C4×Dic61—21no—
238C4×Dic61—21no—
239C4×Dic61—42no—
240C4×Dic61—42no—
241C4×Dic61—42no—
242#11758194—44no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418C2×D412yes—
249C23×C61—21no—
250C23×C61—21no—
251C23×C61—21no—
252C23×C61—21no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—22no—
256C23×C61—22no—
257C23×C61—41no—
258C23×C61—41no—
259C23×C61—41no—
260C23×C61—41no—
261C23×C61—41no—
262C23×C61—41no—
263C23×C61—41no—
264C23×C61—41no—
265C23×C61—41no—
266C23×C61—41no—
267C23×C61—41no—
268C23×C61—41no—
269C23×C61C4×D412yes—
270C23×C61C22×D411yescharacteristic
271Q8×C61—22no—
272Q8×C61—22no—
273Q8×C61—22no—
274Q8×C61C4×D414yescomplemented
275D4×C61—22no—
276D4×C61—22no—
277D4×C61—22no—
278D4×C61—22no—
279D4×C61—48no—
280D4×C61—48no—
281D4×C61—41no—
282D4×C61—41no—
283D4×C61—41no—
284D4×C61—41no—
285C2×C4×C61—22no—
286C2×C4×C61—22no—
287C2×C4×C61—21no—
288C2×C4×C61—22no—
289C2×C4×C61—21no—
290C2×C4×C61—22no—
291C2×C4×C61—22no—
292C2×C4×C61—22no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—48no—
296C2×C4×C61—41no—
297C2×C4×C61—41no—
298C2×C4×C61C4×D412yes—
299C2×C4×C61C23×C411yescharacteristic
300C2×C4×C61C22×D411yescharacteristic
301C2×C4×C61C2×#4111yescharacteristic
302C2×C4×C61C2×#4111yescharacteristic
303C2×C4×C61H(5,𝔽2)11yescharacteristic
304C2×C4×C61H(5,𝔽2)11yescharacteristic
305C2×Dic61—21no—
306C2×Dic61—21no—
307C2×Dic61—21no—
308C2×Dic61—21no—
309C2×Dic61—22no—
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—41no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—84no—
329C2×Dic61—84no—
330C2×Dic61AGL(1,ℤ/8)12yes—
331C8×C61—22no—
332C8×C61—22no—
333#92418—22no—
334#92418—41no—
335#22863—611nomaximal, Sylow
336C22×C61—22no—
337C22×C61—22no—
338C22×C61—22no—
339C22×C61—41no—
340C22×C61—41no—
341C22×C61—41no—
342C22×C61—41no—
343C22×C61—42no—
344C22×C61—42no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61—81no—
353C22×C61—81no—
354C22×C61—81no—
355C22×C61—81no—
356C22×C61—81no—
357C22×C61C2×C4×D411yescharacteristic
358C22×C61D4211yescharacteristic
359C22×C61#54611yescharacteristic
360C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
361C22×C61#57511yescharacteristic
362C22×C61#57611yescharacteristic
363C22×C61#57811yescharacteristic
364C4×C61—22no—
365C4×C61—24no—
366C4×C61—42no—
367C4×C61C2×C4×D411yescharacteristic
368C4×C61#51811yescharacteristic
369C4×C61#54611yescharacteristic
370C4×C61#55111yescharacteristic
371Dic61—22no—
372Dic61—41no—
373Dic61—42no—
374Dic61—41no—
375Dic61—41no—
376Dic61—81no—
377Dic61—81no—
378Dic61—81no—
379C2×#449D6111yescharacteristic
380C2×#440—611no—
381C2×#417—611no—
382#2361—611no—
383#2341—611no—
384#1970—611no—
385#1936—611no—
386#1925—611no—
387#1895—611no—
388#1880—611no—
389#1879—611no—
390#1863—611no—
391#1852—611no—
392C4×#103—611no—
393#1753—611no—
394C2×C61—42no—
395C2×C61—82no—
396C2×C61—82no—
397C2×C61#235811yescharacteristic
398C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
399C2×C61#295111yescharacteristic
400C2×C61#327411yescharacteristic
401C2×C61#327711yescharacteristic
402C2×C61#330811yescharacteristic
403C2×C61#330911yescharacteristic
404C22×#41C2×D6111yescharacteristic
405C22×SD16C2×D6111yescharacteristic
406C22×D8C2×D6111yescharacteristic
407C22×M16—611no—
408C2×#121C2×D6111yescharacteristic
409C2×C4×Q8—611no—
410C2×C4×Q8—611no—
411C2×C4×D4—611no—
412C2×C4×D4—1221no—
413C22×C4⋊C4—611no—
414#449Dic6118yescomplemented
415#440—1224no—
416C2×#107—611no—
417C2×#107—611no—
418#417—1224no—
419C2×#103—611no—
420C2×#103—611no—
421C2×#103C2×D6111yescharacteristic
422C2×#102—611no—
423C2×#102—611no—
424C2×#102—611no—
425C2×#102—611no—
426C2×#102C2×D6111yescharacteristic
427C2×C22⋊C8C2×D6111yescharacteristic
428C2×#97—611no—
429C2×C4×C8—611no—
430#390—611no—
431#390—611no—
432#390—611no—
433#390—1221no—
434#390—1221no—
435#389—611no—
436#388—1221no—
437#386—1221no—
438#385—1221no—
439#380—611no—
440#380—1221no—
441C4×C4⋊C4—611no—
442C4×C22⋊C4—611no—
443C4×C22⋊C4—1221no—
444#340—611no—
445#340—611no—
446#340—611no—
447#340—611no—
448#336—611no—
449#336—611no—
450C61#2286311yescharacteristic, complemented, Sylow
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—41no—
455C2×#41—41no—
456C2×#41C2×Dic6114yescomplemented
457C22×Q8C22×D6111yescharacteristic
458C22×D4—21no—
459C22×D4—21no—
460C22×D4C22×D6111yescharacteristic
461C22×D4C22×D6111yescharacteristic
462C23×C4—21no—
463C23×C4—1221no—
464C23×C4—1221no—
465C23×C4C22×D6111yescharacteristic
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16C2×Dic6114yescomplemented
469C2×D8—41no—
470C2×D8—41no—
471C2×D8C2×Dic6114yescomplemented
472C2×M16—1222no—
473C2×M16—1222no—
474C2×M16—2441no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8C22×D6111yescharacteristic
478C22×C8C22×D6111yescharacteristic
479#121—22no—
480#121C2×Dic6114yes—
481C4×Q8—1222no—
482C4×Q8—1222no—
483C4×Q8—2441no—
484C4×Q8—2441no—
485C4×D4—1222no—
486C4×D4—2441no—
487C4×D4—2444no—
488C2×C4⋊C4—611no—
489C2×C4⋊C4—611no—
490C2×C4⋊C4—611no—
491C2×C4⋊C4—611no—
492C2×C4⋊C4—1222no—
493C2×C4⋊C4—1221no—
494C2×C4⋊C4—1221no—
495C2×C4⋊C4—1221no—
496C2×C4⋊C4—1221no—
497C2×C4⋊C4—2441no—
498C2×C4⋊C4C22×D6111yescharacteristic
499C2×C22⋊C4—21no—
500C2×C22⋊C4—611no—
501C2×C22⋊C4—611no—
502C2×C22⋊C4—1221no—
503C2×C22⋊C4—1221no—
504C2×C22⋊C4—1221no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C42—611no—
511C2×C42—611no—
512C2×C42—1221no—
513C2×C42—1221no—
514C2×C42—1221no—
515#107—1222no—
516#107—2441no—
517#103—614no—
518#103—1222no—
519#103C2×Dic6114yescomplemented
520#102—1222no—
521#102—1222no—
522#102—1222no—
523#102—2441no—
524#102C2×Dic6114yescomplemented
525C22⋊C8C2×Dic6114yescomplemented
526#97—1222no—
527C4×C8—2441no—
528#95—611no—
529#95—611no—
530#95—1221no—
531#95—1221no—
532#95—1221no—
533C24—21no—
534C24—21no—
535C24D4×D6111yescharacteristic
536#41—28no—
537#41—44no—
538#41—44no—
539#41—44no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8D4×D6112yes—
544C2×Q8#1175822412yes—
545C2×Q8C22×Dic6112yes—
546C2×D4—24no—
547C2×D4—24no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4C22×Dic6112yes—
563C2×D4C22×Dic6112yes—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—24no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—611no—
574C22×C4—611no—
575C22×C4—611no—
576C22×C4—611no—
577C22×C4—1221no—
578C22×C4—1221no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—4881no—
582C22×C4—4881no—
583C22×C4—2442no—
584C22×C4—2442no—
585C22×C4—2442no—
586C22×C4—2442no—
587C22×C4D4×D6111yescharacteristic
588C22×C4#1175822412yes—
589C22×C4C22×Dic6112yes—
590C22×C4C23×D6111yescharacteristic
591SD16—28no—
592D8—44no—
593M16—2444no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—612no—
599C2×C8—1221no—
600C2×C8—1221no—
601C2×C8—1221no—
602C2×C8—1221no—
603C2×C8—1221no—
604C2×C8C22×Dic6112yes—
605C2×C8C22×Dic6112yes—
606C4⋊C4—21no—
607C4⋊C4—612no—
608C4⋊C4—1221no—
609C4⋊C4—1221no—
610C4⋊C4—1221no—
611C4⋊C4—1221no—
612C4⋊C4—1221no—
613C4⋊C4—1221no—
614C4⋊C4—1221no—
615C4⋊C4—2442no—
616C4⋊C4—2442no—
617C4⋊C4—2442no—
618C4⋊C4—2442no—
619C4⋊C4C22×Dic6112yes—
620C22⋊C4—24no—
621C22⋊C4—1222no—
622C22⋊C4—4881no—
623C22⋊C4—4881no—
624C22⋊C4—4881no—
625C22⋊C4—4881no—
626C22⋊C4—2442no—
627C22⋊C4—2442no—
628C22⋊C4—2441no—
629C22⋊C4—2442no—
630C22⋊C4—2442no—
631C42—1221no—
632C42—1221no—
633C42—1221no—
634C42—1221no—
635C42—2442no—
636C42—2442no—
637C42—2442no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—22no—
645C23—22no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23D4×Dic6112yes—
659C23C2×D4×D6111yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—22no—
663Q8D4×Dic6114yescomplemented
664D4—22no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—48no—
669D4—48no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—22no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—48no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—612no—
688C2×C4—1221no—
689C2×C4—1221no—
690C2×C4—1221no—
691C2×C4—1221no—
692C2×C4—1221no—
693C2×C4—1221no—
694C2×C4—1221no—
695C2×C4—1221no—
696C2×C4—1221no—
697C2×C4—1221no—
698C2×C4—1222no—
699C2×C4—1221no—
700C2×C4—4884no—
701C2×C4—4884no—
702C2×C4—2441no—
703C2×C4—2441no—
704C2×C4—2441no—
705C2×C4—2441no—
706C2×C4—2441no—
707C2×C4—2441no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2441no—
713C2×C4D4×Dic6112yes—
714C2×C4C23×Dic6111yescharacteristic
715C2×C4C2×D4×D6111yescharacteristic
716C2×C4C2×#1175822411yescharacteristic
717C2×C4C2×#1175822411yescharacteristic
718C2×C4#1451982211yescharacteristic
719C2×C4#1451982211yescharacteristic
720C8—22no—
721C8—22no—
722C8—1222no—
723C8—2441no—
724C22—22no—
725C22—22no—
726C22—22no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22C2×D4×Dic6111yescharacteristic
746C22#1684039411yescharacteristic
747C22#1684039911yescharacteristic
748C22AGL(1,ℤ/8)×D6111yescharacteristic
749C22#1684055811yescharacteristic
750C22#1684056411yescharacteristic
751C22#1684057611yescharacteristic
752C4—22no—
753C4—24no—
754C4—42no—
755C4—1222no—
756C4—4881no—
757C4—4881no—
758C4—4881no—
759C4—2441no—
760C4—2442no—
761C4—2441no—
762C4—2441no—
763C4C2×D4×Dic6111yescharacteristic
764C4#1684023711yescharacteristic
765C4#1684039911yescharacteristic
766C4#1684044311yescharacteristic
767C2—42no—
768C2—82no—
769C2—82no—
770C2#2144880311yescharacteristic
771C2AGL(1,ℤ/8)×Dic6111yescharacteristic
772C2#2145469511yescharacteristic
773C2#2145743211yescharacteristic
774C2#2145746911yescharacteristic
775C2#2145780311yescharacteristic
776C2#2145781811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
Fitting, prime radicalC2×C61×#449C2
socleC23×C61C22×D4
cosocleC22×C4×C61C24
hypercenterC2×#449D61
hypocenterC61#22863
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#16839863C2semidirect
2. C2×#16839763C2semidirect
3. #21448839C2semidirect
4. #21448660C2semidirect
5. #21446686C2semidirect
6. #21446518C2semidirect
7. #21446441C2semidirect
8. #21446258C2semidirect
9. #21446176C2semidirect
10. #21446169C2semidirect
11. #21446075C2semidirect
12. #21446009C2semidirect
13. #103×Dic61C2semidirect
14. #21445605C2semidirect
58. C61×#449C4semidirect
104. #14519701D4semidirect
121. C2×#41×C61C2×C4semidirect
131. C2×SD16×C61C2×C4semidirect
134. C2×D8×C61C2×C4semidirect
141. #103×C61C2×C4semidirect
142. #102×C61C2×C4semidirect
143. C22⋊C8×C61C2×C4semidirect
274. Q8×C61C4×D4semidirect
414. #449Dic61semidirect
450. C61#22863semidirect
456. C2×#41C2×Dic61semidirect
468. C2×SD16C2×Dic61semidirect
471. C2×D8C2×Dic61semidirect
519. #103C2×Dic61semidirect
524. #102C2×Dic61semidirect
525. C22⋊C8C2×Dic61semidirect
663. Q8D4×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398632
C2×#168397632
#214488392
#214486602
#214466862
#214465182
#214464412
#214462582
#214461762
#214461692
#214460752
#214460092
#103×Dic612
#214456052
C2×C61×#4492
#2286361