Finite Group Databasebeta

← #29707520

Subgroups — #29707520

Order 15616.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840269C211yesmaximal, characteristic
2C2×#16839802C211yesmaximal, characteristic, complemented
3C2×#16839763C211yesmaximal, characteristic, complemented
4C2×#16839725C211yesmaximal, characteristic, complemented
5C2×#16839619C211yesmaximal, characteristic, complemented
6#21447020C212yesmaximal, complemented
7#21447013C212yesmaximal, complemented
8#21447006C212yesmaximal, complemented
9#21446999C212yesmaximal, complemented
10#21445539C211yesmaximal, characteristic, complemented
11C2×C61×#417C211yesmaximal, characteristic, complemented
12C23×C4×D61C2211yescharacteristic
13C22×#11758194C2211yescharacteristic
14#16840269—24no—
15#16840269—24no—
16C2×#14519758—21no—
17C2×#14519753C2211yescharacteristic
18C2×#14519753C2211yescharacteristic
19C2×#14519748C2211yescharacteristic
20C2×#14519748C2211yescharacteristic
21C2×#14519745—21no—
22C2×C4×C22⋊D61—21no—
23C2×C4×C22⋊D61—21no—
24C2×#14519736C2211yescharacteristic
25C22×C4⋊Dic61C2211yescharacteristic
26C22×#11758198—21no—
27#16839802—24no—
28C2×#14519710C2212yescomplemented
29C2×#14519708C2212yescomplemented
30#16839763—24no—
31C2×#14519701C2212yescomplemented
32C2×#14519698C2212yescomplemented
33#16839725—24no—
34C2×#14519689C2212yes—
35C2×#14519689C2212yes—
36#16839619—21no—
37#16839619—21no—
38#16839619C2212yes—
39#16839619C2212yes—
40C2×#14519684—21no—
41#16839525C2212yescomplemented
42#16839525C2212yescomplemented
43C22×#41×C61C2211yescharacteristic
44C22×M16×C61C2211yescharacteristic
45C22×C4⋊C4×C61C2211yescharacteristic
46C61×#417—24no—
47C2×#103×C61C2212yescomplemented
48C2×#102×C61C2212yescomplemented
49C24×D61D411yescharacteristic
50C22×C22⋊D61—21no—
51C22×C22⋊D61—21no—
52C23×Dic61—21no—
53C23×Dic61D411yescharacteristic
54C22×C4×D61—22no—
55C22×C4×D61—22no—
56C22×C4×D61—22no—
57C22×C4×D61—22no—
58C22×C4×D61—22no—
59C22×C4×D61—22no—
60C22×C4×D61D411yescharacteristic
61C22×C4×D61D411yescharacteristic
62C22×C4×D61C2311yescharacteristic
63C22×C4×D61C2311yescharacteristic
64C2×#11758194—22no—
65C2×#11758194—22no—
66C2×#11758194D414yescomplemented
67C22×#92418C2312yes—
68#14519758—28no—
69#14519753—22no—
70#14519753—22no—
71#14519753—22no—
72#14519753—22no—
73#14519748—22no—
74#14519748—22no—
75#14519748—22no—
76#14519748—22no—
77#14519745—28no—
78C4×C22⋊D61—28no—
79C4×C22⋊D61—28no—
80#14519736—22no—
81#14519736D414yes—
82C2×C4⋊Dic61—22no—
83C2×C4⋊Dic61—22no—
84C2×C4⋊Dic61—21no—
85C2×C4⋊Dic61C2312yes—
86C2×C4⋊Dic61C2311yescharacteristic
87C2×C4⋊Dic61C2311yescharacteristic
88C2×#11758196—21no—
89C2×#11758196—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×#11758198—21no—
94C2×#11758198—21no—
95C2×#11758198—22no—
96C2×#11758198—22no—
97C2×#11758198—44no—
98C2×C4×Dic61—21no—
99#14519710—24no—
100#14519708—24no—
101#14519701—24no—
102#14519698—24no—
103#14519689—24no—
104#14519689—24no—
105#14519684—22no—
106#14519684—22no—
107C2×#41×C61—22no—
108C2×#41×C61—22no—
109C2×#41×C61—22no—
110C2×#41×C61—22no—
111C2×#41×C61—22no—
112C2×#41×C61D414yes—
113C22×Q8×C61C2311yescharacteristic
114C22×D4×C61—21no—
115C22×D4×C61C2311yescharacteristic
116C23×C4×C61—21no—
117C23×C4×C61—21no—
118C23×C4×C61C2311yescharacteristic
119C2×M16×C61—22no—
120C2×M16×C61—22no—
121C2×M16×C61—22no—
122C22×C8×C61C2312yes—
123C2×C4⋊C4×C61—22no—
124C2×C4⋊C4×C61—22no—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61C2312yes—
127#103×C61—24no—
128#102×C61—24no—
129C24×C61—21no—
130C24×C61C2×D411yescharacteristic
131C23×D61—22no—
132C23×D61—22no—
133C23×D61—22no—
134C23×D61—22no—
135C23×D61—22no—
136C23×D61—41no—
137C23×D61—41no—
138C23×D61C2×D411yescharacteristic
139C23×D61C2×D411yescharacteristic
140#41×C61—28no—
141#41×C61—28no—
142#41×C61—44no—
143#41×C61—44no—
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61C2×D412yes—
150C2×D4×C61—24no—
151C2×D4×C61—21no—
152C2×D4×C61—21no—
153C2×D4×C61—21no—
154C2×D4×C61—21no—
155C2×D4×C61—21no—
156C2×D4×C61—42no—
157C2×D4×C61—42no—
158C2×D4×C61C2×D412yes—
159C22×C4×C61—21no—
160C22×C4×C61—24no—
161C22×C4×C61—22no—
162C22×C4×C61—42no—
163C22×C4×C61—42no—
164C22×C4×C61—42no—
165C22×C4×C61—42no—
166C22×C4×C61—42no—
167C22×C4×C61C2×D411yescharacteristic
168C22×C4×C61C2×D412yes—
169C22×C4×C61C2×D412yes—
170C22×C4×C61C2×D412yes—
171C22×C4×C61#4112yes—
172C22×C4×C61#4112yes—
173C22×C4×C61#4112yes—
174C22×C4×C61C2411yescharacteristic
175C2×C22⋊D61—24no—
176C2×C22⋊D61—24no—
177C2×C22⋊D61—42no—
178C2×C22⋊D61—42no—
179C2×C22⋊D61—42no—
180C2×C22⋊D61—42no—
181C22×Dic61—22no—
182C22×Dic61—22no—
183C22×Dic61—22no—
184C22×Dic61—21no—
185C22×Dic61—21no—
186C22×Dic61—22no—
187C22×Dic61—42no—
188C22×Dic61—42no—
189C22×Dic61—42no—
190C22×Dic61C2×D411yescharacteristic
191C22×Dic61C2×D411yescharacteristic
192C2×C4×D61—22no—
193C2×C4×D61—22no—
194C2×C4×D61—22no—
195C2×C4×D61—22no—
196C2×C4×D61—22no—
197C2×C4×D61—22no—
198C2×C4×D61—21no—
199C2×C4×D61—21no—
200C2×C4×D61—21no—
201C2×C4×D61—21no—
202C2×C4×D61—21no—
203C2×C4×D61—21no—
204C2×C4×D61—21no—
205C2×C4×D61—21no—
206C2×C4×D61—21no—
207C2×C4×D61—21no—
208C2×C4×D61—21no—
209C2×C4×D61—21no—
210C2×C4×D61—44no—
211C2×C4×D61—44no—
212C2×C4×D61—44no—
213C2×C4×D61—44no—
214M16×C61—44no—
215C2×C8×C61—22no—
216C2×C8×C61—22no—
217C2×C8×C61—22no—
218C4⋊C4×C61—22no—
219C4⋊C4×C61—22no—
220C4⋊C4×C61—42no—
221C22⋊Dic61—24no—
222C22⋊Dic61—24no—
223C22⋊Dic61—24no—
224#11758198—24no—
225#11758198—24no—
226#11758198—44no—
227#11758198—44no—
228C4⋊Dic61—21no—
229C4⋊Dic61—21no—
230C4⋊Dic61—22no—
231C4⋊Dic61—22no—
232C4⋊Dic61—42no—
233C4⋊Dic61C2×D412yes—
234C4⋊Dic61C2×D412yes—
235#11758196—24no—
236#11758196—24no—
237C4×Dic61—24no—
238#11758194—28no—
239C2×#92418—22no—
240C2×#92418—22no—
241C2×#92418C2×D414yes—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—22no—
247C23×C61—41no—
248C23×C61—41no—
249C23×C61—41no—
250C23×C61—41no—
251C23×C61—41no—
252C23×C61—41no—
253C23×C61#12012yes—
254C23×C61#12112yes—
255C23×C61#12312yes—
256C23×C61C22×D411yescharacteristic
257C22×D61—28no—
258C22×D61—21no—
259C22×D61—21no—
260C22×D61—21no—
261C22×D61—21no—
262C22×D61—21no—
263C22×D61—21no—
264C22×D61—21no—
265C22×D61—21no—
266C22×D61—21no—
267C22×D61—21no—
268C22×D61—21no—
269C22×D61—21no—
270C22×D61—44no—
271C22×D61—44no—
272C22×D61—44no—
273C22×D61—44no—
274C22×D61—44no—
275C22×D61—44no—
276C22×D61AGL(1,ℤ/8)12yes—
277C22×D61#13712yes—
278Q8×C61—22no—
279Q8×C61—22no—
280Q8×C61—41no—
281Q8×C61—41no—
282D4×C61—22no—
283D4×C61—22no—
284D4×C61—48no—
285D4×C61—41no—
286D4×C61—41no—
287C2×C4×C61—22no—
288C2×C4×C61—41no—
289C2×C4×C61—41no—
290C2×C4×C61—48no—
291C2×C4×C61—42no—
292C2×C4×C61—42no—
293C2×C4×C61—42no—
294C2×C4×C61—84no—
295C2×C4×C61#12012yes—
296C2×C4×C61#12114yes—
297C2×C4×C61#12114yes—
298C2×C4×C61#12112yes—
299C2×C4×C61#12314yes—
300C2×C4×C61#12312yes—
301C2×C4×C61#12414yes—
302C2×C4×C61C22×D411yescharacteristic
303C2×C4×C61C22×D411yescharacteristic
304C2×C4×C61C22×D411yescharacteristic
305C2×C4×C61C2×#4111yescharacteristic
306C2×C4×C61C2×#4111yescharacteristic
307C2×C4×C61C2×#4111yescharacteristic
308C22⋊D61—48no—
309C22⋊D61—48no—
310C2×Dic61—22no—
311C2×Dic61—22no—
312C2×Dic61—21no—
313C2×Dic61—21no—
314C2×Dic61—21no—
315C2×Dic61—21no—
316C2×Dic61—21no—
317C2×Dic61—21no—
318C2×Dic61—41no—
319C2×Dic61—41no—
320C2×Dic61—41no—
321C2×Dic61—41no—
322C2×Dic61—44no—
323C2×Dic61—42no—
324C2×Dic61—42no—
325C2×Dic61—42no—
326C2×Dic61—84no—
327C4×D61—41no—
328C4×D61—41no—
329C4×D61—41no—
330C4×D61—41no—
331C4×D61—41no—
332C4×D61—41no—
333C4×D61—41no—
334C4×D61—41no—
335C4×D61—44no—
336C4×D61—44no—
337C8×C61—42no—
338#92418—24no—
339#23482—611nomaximal, Sylow
340C22×C61—22no—
341C22×C61—22no—
342C22×C61—22no—
343C22×C61—22no—
344C22×C61—22no—
345C22×C61—22no—
346C22×C61—42no—
347C22×C61—42no—
348C22×C61—42no—
349C22×C61—81no—
350C22×C61—81no—
351C22×C61—81no—
352C22×C61—81no—
353C22×C61#39414yes—
354C22×C61C2×#12011yescharacteristic
355C22×C61C2×#12111yescharacteristic
356C22×C61C2×#12311yescharacteristic
357C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
358C22×C61C2×#13711yescharacteristic
359C22×C61#57511yescharacteristic
360C22×C61#57511yescharacteristic
361C2×D61—22no—
362C2×D61—22no—
363C2×D61—22no—
364C2×D61—22no—
365C2×D61—22no—
366C2×D61—22no—
367C2×D61—416no—
368C2×D61—41no—
369C2×D61—41no—
370C2×D61—41no—
371C2×D61—41no—
372C2×D61—41no—
373C2×D61—41no—
374C2×D61—41no—
375C2×D61—41no—
376C4×C61—42no—
377C4×C61—82no—
378C4×C61#39414yes—
379C4×C61C2×#12111yescharacteristic
380C4×C61C2×#12111yescharacteristic
381C4×C61C2×#12311yescharacteristic
382C4×C61C2×#12411yescharacteristic
383Dic61—41no—
384Dic61—41no—
385Dic61—42no—
386Dic61—42no—
387Dic61—82no—
388C2×#525—611no—
389C2×#428—611no—
390C2×#417—611no—
391C2×#417D6111yescharacteristic, complemented
392C2×#407—611no—
393C2×#380—611no—
394#2036—612no—
395#2035—612no—
396#2034—612no—
397#2033—612no—
398#1736—611no—
399C2×C61—24no—
400C2×C61—82no—
401C2×C61C2×#39411yescharacteristic
402C2×C61#300611yescharacteristic
403C2×C61#300711yescharacteristic
404C2×C61#305511yescharacteristic
405C2×C61#305611yescharacteristic
406C2×C61#309211yescharacteristic
407C2×C61#309311yescharacteristic
408D61—42no—
409D61—42no—
410C22×#41C2×D6111yescharacteristic
411C24×C4—611no—
412C22×M16—611no—
413C22×M16C2×D6111yescharacteristic
414#525—1224no—
415#525—1224no—
416C2×#123—1221no—
417C2×C22⋊Q8—611no—
418C2×C22⋊Q8—611no—
419C2×#121—611no—
420C2×#121—611no—
421C2×#120—1221no—
422C2×C4×D4—1221no—
423C2×C4×D4—1221no—
424C2×#117—611no—
425C22×C4⋊C4—611no—
426C22×C4⋊C4C2×D6111yescharacteristic
427C22×C22⋊C4—1221no—
428#428—1224no—
429C2×#107—612no—
430C2×#106—612no—
431#417—24no—
432#417—1224no—
433C2×#103—612no—
434C2×#103C2×D6112yescomplemented
435C2×#102—612no—
436C2×#102C2×D6112yescomplemented
437#407—1224no—
438C2×C22⋊C8—612no—
439C2×C22⋊C8—612no—
440#380—612no—
441#380—612no—
442#380—1221no—
443#380—1221no—
444C2×#95—1221no—
445#340—612no—
446#340—612no—
447C61#2348211yescharacteristic, complemented, Sylow
448C25—611no—
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41C22⋊D6114yes—
455C22×Q8C22×D6111yescharacteristic
456C22×D4—21no—
457C22×D4—1221no—
458C22×D4—1221no—
459C22×D4C22×D6111yescharacteristic
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—611no—
463C23×C4—611no—
464C23×C4—611no—
465C23×C4—611no—
466C23×C4—611no—
467C23×C4—1222no—
468C23×C4—1222no—
469C23×C4—1222no—
470C23×C4—1222no—
471C23×C4—1222no—
472C23×C4—1222no—
473C23×C4—1221no—
474C23×C4C22×D6111yescharacteristic
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—614no—
479C2×M16—1222no—
480C2×M16—1222no—
481C22×C8—612no—
482C22×C8C22×D6112yes—
483#123—1228no—
484C22⋊Q8—1222no—
485C22⋊Q8—1222no—
486C22⋊Q8—1222no—
487C22⋊Q8—1222no—
488#121—1222no—
489#121—1222no—
490#121—1222no—
491#121—1222no—
492#120—1228no—
493C4×D4—1228no—
494C4×D4—1228no—
495#117—614no—
496#117—1222no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—611no—
501C2×C4⋊C4—611no—
502C2×C4⋊C4—612no—
503C2×C4⋊C4—1221no—
504C2×C4⋊C4—1221no—
505C2×C4⋊C4—1222no—
506C2×C4⋊C4—1222no—
507C2×C4⋊C4—1221no—
508C2×C4⋊C4C22×D6112yes—
509C2×C22⋊C4—1221no—
510C2×C22⋊C4—1221no—
511C2×C22⋊C4—1221no—
512C2×C22⋊C4—1221no—
513C2×C22⋊C4—1221no—
514C2×C22⋊C4—1222no—
515C2×C22⋊C4—1222no—
516C2×C22⋊C4—2444no—
517C2×C42—1221no—
518#107—1224no—
519#106—1224no—
520#103—24no—
521#103—1224no—
522#102—24no—
523#102—1224no—
524C22⋊C8—1224no—
525C22⋊C8—1224no—
526#95—1222no—
527#95—1222no—
528C24—21no—
529C24—611no—
530C24—611no—
531C24—1222no—
532C24—1222no—
533C24—1222no—
534C24—1222no—
535C24—1222no—
536C24—2441no—
537C24—2441no—
538C24D4×D6111yescharacteristic
539#41—28no—
540#41—28no—
541#41—44no—
542#41—44no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×C22⋊D6112yes—
549C2×D4—24no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—42no—
556C2×D4—42no—
557C2×D4—1224no—
558C2×D4—1224no—
559C2×D4—2442no—
560C2×D4—2442no—
561C2×D4—2442no—
562C2×D4—2442no—
563C2×D4C2×C22⋊D6112yes—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—22no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—611no—
573C22×C4—611no—
574C22×C4—1221no—
575C22×C4—1221no—
576C22×C4—1222no—
577C22×C4—1222no—
578C22×C4—1222no—
579C22×C4—1221no—
580C22×C4—1221no—
581C22×C4—1221no—
582C22×C4—1221no—
583C22×C4—1221no—
584C22×C4—1221no—
585C22×C4—1221no—
586C22×C4—1221no—
587C22×C4—1221no—
588C22×C4—1221no—
589C22×C4—1221no—
590C22×C4—1221no—
591C22×C4—1222no—
592C22×C4—1222no—
593C22×C4—1222no—
594C22×C4—1222no—
595C22×C4—1222no—
596C22×C4—1222no—
597C22×C4—1222no—
598C22×C4—2442no—
599C22×C4—2442no—
600C22×C4—2442no—
601C22×C4—2444no—
602C22×C4—2444no—
603C22×C4—2444no—
604C22×C4—2444no—
605C22×C4#1175822212yes—
606C22×C4#1175822212yes—
607C22×C4D4×D6112yes—
608C22×C4D4×D6112yes—
609C22×C4D4×D6111yescharacteristic
610C22×C4#1175822412yes—
611C22×C4C2×C22⋊D6112yes—
612C22×C4C23×D6111yescharacteristic
613M16—44no—
614M16—1228no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—614no—
619C2×C8—1222no—
620C2×C8—1222no—
621C4⋊C4—22no—
622C4⋊C4—22no—
623C4⋊C4—42no—
624C4⋊C4—612no—
625C4⋊C4—612no—
626C4⋊C4—1224no—
627C4⋊C4—1224no—
628C4⋊C4—1221no—
629C4⋊C4—1221no—
630C4⋊C4—1222no—
631C4⋊C4—1222no—
632C4⋊C4—2442no—
633C22⋊C4—1224no—
634C22⋊C4—1224no—
635C22⋊C4—1224no—
636C22⋊C4—1224no—
637C22⋊C4—1224no—
638C22⋊C4—2444no—
639C22⋊C4—2444no—
640C42—1224no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—22no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—612no—
653C23—612no—
654C23—1228no—
655C23—1221no—
656C23—1221no—
657C23—1221no—
658C23—1221no—
659C23—1221no—
660C23—1221no—
661C23—1221no—
662C23—1221no—
663C23—1221no—
664C23—1221no—
665C23—1221no—
666C23—1221no—
667C23—2444no—
668C23—2444no—
669C23—2444no—
670C23—2444no—
671C23—2444no—
672C23—2444no—
673C23#1451974512yes—
674C23#1451975012yes—
675C23#1451975912yes—
676C23C2×D4×D6111yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—41no—
685D4—41no—
686D4—2448no—
687D4—2448no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—48no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—84no—
696C2×C4—1222no—
697C2×C4—1222no—
698C2×C4—1221no—
699C2×C4—1221no—
700C2×C4—1221no—
701C2×C4—1221no—
702C2×C4—1221no—
703C2×C4—1221no—
704C2×C4—4884no—
705C2×C4—2442no—
706C2×C4—2442no—
707C2×C4—2442no—
708C2×C4—2441no—
709C2×C4—2441no—
710C2×C4—2441no—
711C2×C4—2441no—
712C2×C4—2444no—
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—2444no—
722C2×C4—2444no—
723C2×C4#1451974512yes—
724C2×C4#1451974914yes—
725C2×C4#1451975014yes—
726C2×C4#1451975012yes—
727C2×C4#1451975912yes—
728C2×C4#1451976014yes—
729C2×C4#1451976314yes—
730C2×C4C2×D4×D6111yescharacteristic
731C2×C4C2×D4×D6111yescharacteristic
732C2×C4C22×C22⋊D6111yescharacteristic
733C2×C4C2×#1175822411yescharacteristic
734C2×C4C2×#1175822211yescharacteristic
735C2×C4C2×#1175822211yescharacteristic
736C8—42no—
737C8—1224no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—1222no—
752C22—1222no—
753C22—1222no—
754C22—1222no—
755C22—1222no—
756C22—1222no—
757C22—24416no—
758C22—2441no—
759C22—2441no—
760C22—2441no—
761C22—2441no—
762C22—2441no—
763C22—2441no—
764C22—2441no—
765C22—2441no—
766C22#1683967714yes—
767C22C2×#1451974511yescharacteristic
768C22C2×#1451975011yescharacteristic
769C22C2×#1451975911yescharacteristic
770C22AGL(1,ℤ/8)×D6111yescharacteristic
771C22#137×D6111yescharacteristic
772C22#1684055811yescharacteristic
773C22#1684056111yescharacteristic
774C4—42no—
775C4—82no—
776C4—4882no—
777C4—2441no—
778C4—2441no—
779C4—2442no—
780C4—2442no—
781C4#1683967714yes—
782C4C2×#1451974911yescharacteristic
783C4C2×#1451975011yescharacteristic
784C4C2×#1451976011yescharacteristic
785C4C2×#1451976311yescharacteristic
786C2—24no—
787C2—82no—
788C2—2442no—
789C2—2442no—
790C2C2×#1683967711yescharacteristic
791C2#2145506711yescharacteristic
792C2#2145507511yescharacteristic
793C2#2145544111yescharacteristic
794C2#2145545211yescharacteristic
795C2#2145574011yescharacteristic
796C2#2145574911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC2×C61×#417C2
socleC23×C61C22×D4
prime radicalC2×#16840269C2
hypercenterC2×#417D61
hypocenterC61#23482
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
2. C2×#16839802C2semidirect
3. C2×#16839763C2semidirect
4. C2×#16839725C2semidirect
5. C2×#16839619C2semidirect
6. #21447020C2semidirect
7. #21447013C2semidirect
8. #21447006C2semidirect
9. #21446999C2semidirect
10. #21445539C2semidirect
11. C2×C61×#417C2semidirect
28. C2×#14519710C22semidirect
29. C2×#14519708C22semidirect
31. C2×#14519701C22semidirect
32. C2×#14519698C22semidirect
41. #16839525C22semidirect
42. #16839525C22semidirect
47. C2×#103×C61C22semidirect
48. C2×#102×C61C22semidirect
66. C2×#11758194D4semidirect
391. C2×#417D61semidirect
434. C2×#103C2×D61semidirect
436. C2×#102C2×D61semidirect
447. C61#23482semidirect

Maximal subgroups

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

subgroupindex
C2×#168402692
C2×#168398022
C2×#168397632
C2×#168397252
C2×#168396192
#214470202
#214470132
#214470062
#214469992
#214455392
C2×C61×#4172
#2348261