Finite Group Databasebeta

← #29700424

Subgroups — #29700424

Order 15616.

1274 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×#16839863C211yesmaximal, characteristic, complemented
2C2×#16839767C211yesmaximal, characteristic
3#21448850C211yesmaximal, characteristic, complemented
4D4×C22⋊Dic61C211yesmaximal, characteristic
5#21446675C211yesmaximal, characteristic, complemented
6#21446518C211yesmaximal, characteristic, complemented
7#21446441C211yesmaximal, characteristic, complemented
8#21446253C211yesmaximal, characteristic, complemented
9#21446176C211yesmaximal, characteristic, complemented
10#21446155C211yesmaximal, characteristic, complemented
11#21446082C211yesmaximal, characteristic, complemented
12#21446020C211yesmaximal, characteristic, complemented
13#102×Dic61C211yesmaximal, characteristic, complemented
14#21445605C211yesmaximal, characteristic, complemented
15C2×C61×#450C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C2×Q8×Dic61C2211yescharacteristic, complemented
18C2×D4×Dic61C2211yescharacteristic
19C2×D4×Dic61C2211yescharacteristic
20C2×#14519736C2211yescharacteristic
21C22×C22⋊Dic61—21no—
22#16839863—24no—
23C2×#14519711C2211yescharacteristic, complemented
24C2×#14519709C2211yescharacteristic, complemented
25#16839767—24no—
26C2×#14519701C2211yescharacteristic, complemented
27C2×#14519701C2211yescharacteristic, complemented
28C2×#14519698C2211yescharacteristic
29C2×#14519698C2211yescharacteristic
30C2×#14519698C2211yescharacteristic
31C2×#14519698C2211yescharacteristic
32C2×#14519687C2211yescharacteristic, complemented
33C2×C8×Dic61C2211yescharacteristic, complemented
34#16839669C2211yescharacteristic, complemented
35#16839665C2211yescharacteristic
36#16839665C2211yescharacteristic
37#16839661C2211yescharacteristic, complemented
38#16839655—21no—
39#16839655—21no—
40#16839648—21no—
41#16839642—21no—
42#16839642—21no—
43#16839622C2211yescharacteristic
44#16839618—21no—
45C4⋊C4×Dic61—21no—
46C4⋊C4×Dic61C2211yescharacteristic, complemented
47C4×C22⋊Dic61C2211yescharacteristic
48#16839525C2211yescharacteristic, complemented
49#16839525C2211yescharacteristic, complemented
50#16839524C2211yescharacteristic, complemented
51#16839524C2211yescharacteristic, complemented
52#16839516C2211yescharacteristic, complemented
53#16839516C2211yescharacteristic, complemented
54C23×D4×C61C2211yescharacteristic
55C22×SD16×C61C2211yescharacteristic
56C22×SD16×C61C2211yescharacteristic
57C2×C22⋊Q8×C61C2211yescharacteristic
58C61×#450C418yescomplemented
59C2×#102×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—41no—
71D4×Dic61—22no—
72D4×Dic61—22no—
73D4×Dic61—41no—
74D4×Dic61—41no—
75#14519736—22no—
76#14519736—41no—
77C2×C4⋊Dic61—21no—
78C2×C4⋊Dic61—21no—
79C2×C4⋊Dic61C2311yescharacteristic
80C2×C4⋊Dic61C2311yescharacteristic
81C2×C4⋊Dic61C2311yescharacteristic
82C2×C4⋊Dic61C2311yescharacteristic
83C2×C22⋊Dic61—21no—
84C2×C22⋊Dic61—21no—
85C2×C22⋊Dic61—21no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—44no—
92C2×C22⋊Dic61D411yescharacteristic
93C2×C22⋊Dic61D411yescharacteristic
94C2×C4×Dic61—21no—
95C2×C4×Dic61—21no—
96C2×C4×Dic61—21no—
97C2×C4×Dic61C2311yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99#14519711—22no—
100#14519709—41no—
101#14519701—22no—
102#14519701—41no—
103#14519698—22no—
104#14519698—22no—
105#14519698—22no—
106#14519698D414yes—
107#14519687—22no—
108C8×Dic61—41no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113#14519684—21no—
114#14519684D411yescharacteristic
115#14519684D411yescharacteristic
116C25×C61—21no—
117C22×Q8×C61C2311yescharacteristic
118C22×D4×C61—22no—
119C22×D4×C61—22no—
120C22×D4×C61—21no—
121C22×D4×C61—22no—
122C22×D4×C61—41no—
123C22×D4×C61—41no—
124C22×D4×C61C2×C414yes—
125C22×D4×C61C2311yescharacteristic
126C22×D4×C61C2311yescharacteristic
127C23×C4×C61C2311yescharacteristic
128C2×SD16×C61—22no—
129C2×SD16×C61—22no—
130C2×SD16×C61—41no—
131C2×SD16×C61—41no—
132C2×SD16×C61C2×C414yes—
133C2×SD16×C61C2×C414yescomplemented
134C22×C8×C61C2311yescharacteristic
135C22×C8×C61C2311yescharacteristic
136C22⋊Q8×C61—22no—
137C22⋊Q8×C61C2×C414yescomplemented
138C2×C4⋊C4×C61—21no—
139C2×C4⋊C4×C61C2311yescharacteristic
140C2×C22⋊C4×C61—21no—
141#102×C61C2×C414yes—
142#102×C61C2×C414yescomplemented
143C22⋊C8×C61C2×C414yescomplemented
144C24×C61—21no—
145C24×C61—21no—
146C24×C61—24no—
147C24×C61—42no—
148C24×C61—42no—
149C24×C61—42no—
150C24×C61—42no—
151C24×C61—81no—
152C24×C61—81no—
153C24×C61C2×D411yescharacteristic
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61C22×C412yes—
160C2×D4×C61—28no—
161C2×D4×C61—24no—
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—21no—
170C2×D4×C61—44no—
171C2×D4×C61—44no—
172C2×D4×C61—44no—
173C2×D4×C61—42no—
174C2×D4×C61—42no—
175C2×D4×C61C22×C412yes—
176C2×D4×C61C22×C412yes—
177C2×D4×C61C2×D412yes—
178C2×D4×C61#4112yes—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61C22×C412yes—
186C22×C4×C61C2×D411yescharacteristic
187C22×C4×C61#4112yes—
188C22×C4×C61C2411yescharacteristic
189C22×Dic61—21no—
190C22×Dic61—21no—
191C22×Dic61—21no—
192C22×Dic61—21no—
193C22×Dic61—42no—
194C22×Dic61—42no—
195C22×Dic61—42no—
196C22×Dic61—42no—
197C22×Dic61—81no—
198C22×Dic61—81no—
199C22×Dic61C2×D411yescharacteristic
200C22×Dic61C2×D411yescharacteristic
201C22×Dic61C2×D411yescharacteristic
202C22×Dic61C2×D411yescharacteristic
203SD16×C61—28no—
204SD16×C61—44no—
205C2×C8×C61—21no—
206C2×C8×C61—21no—
207C2×C8×C61—21no—
208C2×C8×C61—21no—
209C2×C8×C61C22×C412yes—
210C2×C8×C61C22×C412yes—
211C4⋊C4×C61—24no—
212C4⋊C4×C61—21no—
213C4⋊C4×C61C22×C412yes—
214C22⋊C4×C61—24no—
215C22⋊Dic61—22no—
216C22⋊Dic61—41no—
217C22⋊Dic61—42no—
218C22⋊Dic61—42no—
219C22⋊Dic61—42no—
220C22⋊Dic61—42no—
221C22⋊Dic61—42no—
222C22⋊Dic61—42no—
223C22⋊Dic61—81no—
224C22⋊Dic61—81no—
225C4⋊Dic61—21no—
226C4⋊Dic61—21no—
227C4⋊Dic61—21no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—21no—
231C4⋊Dic61—21no—
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—22no—
250C23×C61—21no—
251C23×C61—22no—
252C23×C61—22no—
253C23×C61—21no—
254C23×C61—21no—
255C23×C61—21no—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—22no—
259C23×C61—48no—
260C23×C61—48no—
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×C61—41no—
270C23×C61—41no—
271C23×C61—84no—
272C23×C61—84no—
273C23×C61—84no—
274C23×C61—84no—
275C23×C61—84no—
276C23×C61C4×D412yes—
277C23×C61C22×D411yescharacteristic
278Q8×C61—22no—
279Q8×C61—22no—
280Q8×C61—41no—
281Q8×C61—41no—
282D4×C61—22no—
283D4×C61—22no—
284D4×C61—22no—
285D4×C61—22no—
286D4×C61—22no—
287D4×C61—48no—
288D4×C61—41no—
289D4×C61—41no—
290D4×C61C4×D414yes—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—22no—
294C2×C4×C61—22no—
295C2×C4×C61—22no—
296C2×C4×C61—22no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—41no—
300C2×C4×C61—41no—
301C2×C4×C61—41no—
302C2×C4×C61—41no—
303C2×C4×C61C4×D412yes—
304C2×C4×C61C23×C411yescharacteristic
305C2×C4×C61C22×D411yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C2×C4×C61H(5,𝔽2)11yescharacteristic
309C2×C4×C61H(5,𝔽2)11yescharacteristic
310C2×Dic61—21no—
311C2×Dic61—21no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—22no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—21no—
319C2×Dic61—21no—
320C2×Dic61—21no—
321C2×Dic61—21no—
322C2×Dic61—41no—
323C2×Dic61—41no—
324C2×Dic61—41no—
325C2×Dic61—41no—
326C2×Dic61—41no—
327C2×Dic61—41no—
328C2×Dic61—41no—
329C2×Dic61—41no—
330C2×Dic61—41no—
331C2×Dic61—41no—
332C2×Dic61—41no—
333C2×Dic61—84no—
334C2×Dic61—84no—
335C2×Dic61AGL(1,ℤ/8)12yes—
336C8×C61—22no—
337C8×C61—22no—
338#92418—22no—
339#92418—41no—
340#22864—611nomaximal, Sylow
341C22×C61—22no—
342C22×C61—24no—
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—42no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—41no—
349C22×C61—41no—
350C22×C61—42no—
351C22×C61—42no—
352C22×C61—41no—
353C22×C61—41no—
354C22×C61—42no—
355C22×C61—42no—
356C22×C61—42no—
357C22×C61—42no—
358C22×C61—816no—
359C22×C61—81no—
360C22×C61—81no—
361C22×C61—81no—
362C22×C61—81no—
363C22×C61C2×C4×D411yescharacteristic
364C22×C61D4211yescharacteristic
365C22×C61#54611yescharacteristic
366C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C61#57511yescharacteristic
368C22×C61#57711yescharacteristic
369C22×C61#57711yescharacteristic
370C4×C61—22no—
371C4×C61—42no—
372C4×C61—42no—
373C4×C61C2×C4×D411yescharacteristic
374C4×C61#51811yescharacteristic
375C4×C61#54611yescharacteristic
376C4×C61#55111yescharacteristic
377Dic61—22no—
378Dic61—41no—
379Dic61—42no—
380Dic61—41no—
381Dic61—41no—
382Dic61—81no—
383Dic61—81no—
384Dic61—81no—
385C2×#450D6111yescharacteristic
386C2×#440—611no—
387C2×#418—611no—
388#2362—611no—
389D4×C22⋊C4—611no—
390#1968—611no—
391#1936—611no—
392#1925—611no—
393#1894—611no—
394#1880—611no—
395#1877—611no—
396#1864—611no—
397#1854—611no—
398C4×#102—611no—
399#1753—611no—
400C2×C61—42no—
401C2×C61—44no—
402C2×C61—82no—
403C2×C61#235811yescharacteristic
404C2×C61C4×AGL(1,ℤ/8)11yescharacteristic
405C2×C61#294911yescharacteristic
406C2×C61#327211yescharacteristic
407C2×C61#327511yescharacteristic
408C2×C61#331011yescharacteristic
409C2×C61#331111yescharacteristic
410C23×D4C2×D6111yescharacteristic
411C22×SD16C2×D6111yescharacteristic
412C22×SD16C2×D6111yescharacteristic
413C22×M16—611no—
414C2×C22⋊Q8C2×D6111yescharacteristic
415C2×C4×Q8—611no—
416C2×C4×D4—611no—
417C2×C4×D4—611no—
418C2×#117—611no—
419C22×C22⋊C4—1221no—
420#450Dic6118yescomplemented
421#440—1224no—
422C2×#107—611no—
423C2×#106—611no—
424#418—1224no—
425C2×#103—611no—
426C2×#103—611no—
427C2×#102—611no—
428C2×#102—611no—
429C2×#102—611no—
430C2×#102—611no—
431C2×#102C2×D6111yescharacteristic
432C2×#102C2×D6111yescharacteristic
433C2×C22⋊C8C2×D6111yescharacteristic
434C2×#97—611no—
435C2×C4×C8—611no—
436#391—611no—
437#390—611no—
438#390—611no—
439#389—611no—
440#388—1221no—
441#388—1221no—
442#387—1221no—
443#386—1221no—
444#386—1221no—
445#380—611no—
446#379—1221no—
447C4×C4⋊C4—611no—
448C4×C4⋊C4—1221no—
449C4×C22⋊C4—611no—
450#340—611no—
451#340—611no—
452#340—611no—
453#340—611no—
454#336—611no—
455#336—611no—
456C61#2286411yescharacteristic, complemented, Sylow
457C25—21no—
458C22×Q8C22×D6111yescharacteristic
459C22×D4—22no—
460C22×D4—22no—
461C22×D4—21no—
462C22×D4—22no—
463C22×D4—41no—
464C22×D4—41no—
465C22×D4C2×Dic6114yes—
466C22×D4C22×D6111yescharacteristic
467C22×D4C22×D6111yescharacteristic
468C23×C4—1221no—
469C23×C4—1221no—
470C23×C4C22×D6111yescharacteristic
471C2×SD16—22no—
472C2×SD16—22no—
473C2×SD16—41no—
474C2×SD16—41no—
475C2×SD16C2×Dic6114yes—
476C2×SD16C2×Dic6114yescomplemented
477C2×M16—1222no—
478C2×M16—1222no—
479C2×M16—2441no—
480C22×C8—611no—
481C22×C8—611no—
482C22×C8C22×D6111yescharacteristic
483C22×C8C22×D6111yescharacteristic
484C22⋊Q8—22no—
485C22⋊Q8C2×Dic6114yescomplemented
486C4×Q8—1222no—
487C4×Q8—2441no—
488C4×D4—1222no—
489C4×D4—1222no—
490C4×D4—2441no—
491C4×D4—2441no—
492#117—1222no—
493#117—2441no—
494C2×C4⋊C4—21no—
495C2×C4⋊C4—611no—
496C2×C4⋊C4—611no—
497C2×C4⋊C4—611no—
498C2×C4⋊C4—611no—
499C2×C4⋊C4—1221no—
500C2×C4⋊C4—1221no—
501C2×C4⋊C4C22×D6111yescharacteristic
502C2×C22⋊C4—21no—
503C2×C22⋊C4—611no—
504C2×C22⋊C4—611no—
505C2×C22⋊C4—1221no—
506C2×C22⋊C4—1221no—
507C2×C22⋊C4—1221no—
508C2×C22⋊C4—1221no—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—2444no—
514C2×C42—611no—
515C2×C42—611no—
516C2×C42—1221no—
517C2×C42—1221no—
518C2×C42—1221no—
519#107—1222no—
520#106—2441no—
521#103—1222no—
522#103—2441no—
523#102—614no—
524#102—1222no—
525#102—1222no—
526#102—1222no—
527#102C2×Dic6114yes—
528#102C2×Dic6114yescomplemented
529C22⋊C8C2×Dic6114yescomplemented
530#97—1222no—
531C4×C8—2441no—
532#95—611no—
533#95—611no—
534#95—1221no—
535#95—1221no—
536#95—1221no—
537#95—1221no—
538#95—1221no—
539C24—21no—
540C24—21no—
541C24—24no—
542C24—42no—
543C24—42no—
544C24—42no—
545C24—42no—
546C24—81no—
547C24—81no—
548C24D4×D6111yescharacteristic
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8C22×Dic6112yes—
555C2×D4—28no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—24no—
565C2×D4—44no—
566C2×D4—44no—
567C2×D4—44no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4D4×D6112yes—
571C2×D4#1175822412yes—
572C2×D4C22×Dic6112yes—
573C2×D4C22×Dic6112yes—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—611no—
581C22×C4—611no—
582C22×C4—611no—
583C22×C4—611no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—4881no—
589C22×C4—4881no—
590C22×C4—2442no—
591C22×C4—2442no—
592C22×C4—2442no—
593C22×C4—2442no—
594C22×C4D4×D6111yescharacteristic
595C22×C4#1175822412yes—
596C22×C4C22×Dic6112yes—
597C22×C4C23×D6111yescharacteristic
598SD16—28no—
599SD16—44no—
600M16—2444no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—612no—
606C2×C8—1221no—
607C2×C8—1221no—
608C2×C8—1221no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8C22×Dic6112yes—
612C2×C8C22×Dic6112yes—
613C4⋊C4—21no—
614C4⋊C4—24no—
615C4⋊C4—612no—
616C4⋊C4—1221no—
617C4⋊C4—1221no—
618C4⋊C4—1221no—
619C4⋊C4—1221no—
620C4⋊C4—1221no—
621C4⋊C4—1221no—
622C4⋊C4—1221no—
623C4⋊C4—2442no—
624C4⋊C4—2442no—
625C4⋊C4C22×Dic6112yes—
626C22⋊C4—24no—
627C22⋊C4—1222no—
628C22⋊C4—4881no—
629C22⋊C4—4881no—
630C22⋊C4—2442no—
631C22⋊C4—2441no—
632C22⋊C4—2442no—
633C22⋊C4—2442no—
634C22⋊C4—2442no—
635C22⋊C4—2442no—
636C22⋊C4—2442no—
637C42—1221no—
638C42—1221no—
639C42—1221no—
640C42—1221no—
641C42—2442no—
642C42—2442no—
643C42—2442no—
644C23—22no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—22no—
652C23—21no—
653C23—22no—
654C23—48no—
655C23—48no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—84no—
667C23—84no—
668C23—84no—
669C23—84no—
670C23—84no—
671C23D4×Dic6112yes—
672C23C2×D4×D6111yescharacteristic
673Q8—22no—
674Q8—22no—
675Q8—41no—
676Q8—41no—
677D4—22no—
678D4—22no—
679D4—22no—
680D4—22no—
681D4—22no—
682D4—48no—
683D4—41no—
684D4—41no—
685D4D4×Dic6114yes—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—612no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—1221no—
705C2×C4—1221no—
706C2×C4—1221no—
707C2×C4—1221no—
708C2×C4—1221no—
709C2×C4—1222no—
710C2×C4—1221no—
711C2×C4—4884no—
712C2×C4—4884no—
713C2×C4—2441no—
714C2×C4—2441no—
715C2×C4—2441no—
716C2×C4—2441no—
717C2×C4—2441no—
718C2×C4—2441no—
719C2×C4—2441no—
720C2×C4—2441no—
721C2×C4—2441no—
722C2×C4—2441no—
723C2×C4—2441no—
724C2×C4D4×Dic6112yes—
725C2×C4C23×Dic6111yescharacteristic
726C2×C4C2×D4×D6111yescharacteristic
727C2×C4C2×#1175822411yescharacteristic
728C2×C4C2×#1175822411yescharacteristic
729C2×C4#1451982211yescharacteristic
730C2×C4#1451982211yescharacteristic
731C8—22no—
732C8—22no—
733C8—1222no—
734C8—2441no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—24no—
739C22—42no—
740C22—41no—
741C22—42no—
742C22—41no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—41no—
747C22—41no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—816no—
753C22—81no—
754C22—81no—
755C22—81no—
756C22—81no—
757C22C2×D4×Dic6111yescharacteristic
758C22#1684039411yescharacteristic
759C22#1684039911yescharacteristic
760C22AGL(1,ℤ/8)×D6111yescharacteristic
761C22#1684055811yescharacteristic
762C22#1684056811yescharacteristic
763C22#1684056811yescharacteristic
764C4—22no—
765C4—42no—
766C4—42no—
767C4—1222no—
768C4—4881no—
769C4—4881no—
770C4—4881no—
771C4—2441no—
772C4—2442no—
773C4—2441no—
774C4—2441no—
775C4C2×D4×Dic6111yescharacteristic
776C4#1684023711yescharacteristic
777C4#1684039911yescharacteristic
778C4#1684044311yescharacteristic
779C2—42no—
780C2—44no—
781C2—82no—
782C2#2144880311yescharacteristic
783C2AGL(1,ℤ/8)×Dic6111yescharacteristic
784C2#2145467911yescharacteristic
785C2#2145741711yescharacteristic
786C2#2145745411yescharacteristic
787C2#2145783311yescharacteristic
788C2#2145784811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#450C2
socleC23×C61C22×D4
prime radicalC23×D4×C61C22
cosocleC22×C4×C61C24
hypercenterC2×#450D61
hypocenterC61#22864
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×#16839863C2semidirect
3. #21448850C2semidirect
5. #21446675C2semidirect
6. #21446518C2semidirect
7. #21446441C2semidirect
8. #21446253C2semidirect
9. #21446176C2semidirect
10. #21446155C2semidirect
11. #21446082C2semidirect
12. #21446020C2semidirect
13. #102×Dic61C2semidirect
14. #21445605C2semidirect
17. C2×Q8×Dic61C22semidirect
23. C2×#14519711C22semidirect
24. C2×#14519709C22semidirect
26. C2×#14519701C22semidirect
27. C2×#14519701C22semidirect
32. C2×#14519687C22semidirect
33. C2×C8×Dic61C22semidirect
34. #16839669C22semidirect
37. #16839661C22semidirect
46. C4⋊C4×Dic61C22semidirect
48. #16839525C22semidirect
49. #16839525C22semidirect
50. #16839524C22semidirect
51. #16839524C22semidirect
52. #16839516C22semidirect
53. #16839516C22semidirect
58. C61×#450C4semidirect
133. C2×SD16×C61C2×C4semidirect
137. C22⋊Q8×C61C2×C4semidirect
142. #102×C61C2×C4semidirect
143. C22⋊C8×C61C2×C4semidirect
420. #450Dic61semidirect
456. C61#22864semidirect
476. C2×SD16C2×Dic61semidirect
485. C22⋊Q8C2×Dic61semidirect
528. #102C2×Dic61semidirect
529. C22⋊C8C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
C2×#168398632
C2×#168397672
#214488502
D4×C22⋊Dic612
#214466752
#214465182
#214464412
#214462532
#214461762
#214461552
#214460822
#214460202
#102×Dic612
#214456052
C2×C61×#4502
#2286461