Finite Group Databasebeta

← #29684114

Subgroups — #29684114

Order 15616.

1726 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840330C211yesmaximal, characteristic
2C2×#16839787C211yesmaximal, characteristic, complemented
3C2×#16839762C211yesmaximal, characteristic, complemented
4C2×#16839765C211yesmaximal, characteristic, complemented
5C2×#16839757C211yesmaximal, characteristic, complemented
6C2×#102×D61C211yesmaximal, characteristic, complemented
7#21448173C211yesmaximal, characteristic, complemented
8#21446752C211yesmaximal, characteristic, complemented
9#21446748C211yesmaximal, characteristic, complemented
10#21446748C211yesmaximal, characteristic, complemented
11#21446746C211yesmaximal, characteristic, complemented
12#21446745C211yesmaximal, characteristic, complemented
13#21446744C211yesmaximal, characteristic, complemented
14#21446744C211yesmaximal, characteristic, complemented
15C61×#1983C211yesmaximal, characteristic, complemented
16C22×#11758226C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840330—24no—
21#16840330C418yescomplemented
22C2×#14519774C2211yescharacteristic
23C2×#14519773C2211yescharacteristic
24C2×#14519766C2211yescharacteristic
25C2×#14519750—21no—
26C2×#14519750—21no—
27C2×#14519747—21no—
28C2×#14519747—21no—
29C2×#14519735C2211yescharacteristic
30C2×#14519734C2211yescharacteristic
31C2×C4⋊C4×D61C2211yescharacteristic
32#16839787—24no—
33C2×C4⋊#92418C2211yescharacteristic, complemented
34C2×#14519706C2211yescharacteristic, complemented
35C2×#14519706C2211yescharacteristic, complemented
36#16839765—24no—
37#16839762—24no—
38#16839757—24no—
39C2×#14519701C2211yescharacteristic, complemented
40C2×#14519701C2211yescharacteristic, complemented
41C2×#14519699C2211yescharacteristic
42C2×#14519699C2211yescharacteristic
43C2×#14519699C2211yescharacteristic, complemented
44C2×#14519699C2211yescharacteristic, complemented
45C2×#14519698C2211yescharacteristic
46C2×#14519698C2211yescharacteristic
47C2×#14519697C2211yescharacteristic
48C2×#14519697C2211yescharacteristic
49C2×#14519697C2211yescharacteristic, complemented
50C2×#14519697C2211yescharacteristic, complemented
51#102×D61—24no—
52C4⋊C4×Dic61C2211yescharacteristic, complemented
53C4⋊C4×Dic61C2211yescharacteristic, complemented
54C4×#11758196—21no—
55C4×C4⋊Dic61C2211yescharacteristic, complemented
56#16839613—21no—
57C4×#11758198—21no—
58#16839609—21no—
59C2×#124×C61C2211yescharacteristic
60C2×C4⋊C8×C61C2211yescharacteristic, complemented
61C2×#103×C61C2211yescharacteristic, complemented
62C2×#103×C61C2211yescharacteristic, complemented
63C2×#102×C61C2211yescharacteristic
64C2×#102×C61C2211yescharacteristic
65C4×C4⋊C4×C61C2211yescharacteristic, complemented
66C24×D61—21no—
67C2×#11758226—22no—
68C2×#11758226—22no—
69C2×#11758226—22no—
70C2×#11758226—22no—
71C2×#11758226—22no—
72C2×#11758226C2×C414yes—
73C22×D244—21no—
74C22×D244—21no—
75C22×D244—21no—
76C22×D244C2311yescharacteristic
77C22×D244C2311yescharacteristic
78C22×C22⋊D61—21no—
79C22×C22⋊D61—21no—
80C22×C22⋊D61—21no—
81C2×D4×D61—22no—
82C2×D4×D61—22no—
83C2×D4×D61—22no—
84C2×D4×D61—22no—
85C2×D4×D61—22no—
86C2×D4×D61C2×C414yes—
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61C2311yescharacteristic
90C2×#11758189—22no—
91C2×#11758189—22no—
92C2×#11758189—22no—
93C22×#92418C2311yescharacteristic
94C22×#92418C2311yescharacteristic
95C2×C8×D61—22no—
96C2×C8×D61—22no—
97C2×C8×D61—22no—
98#14519774—22no—
99#14519774C2×C414yescomplemented
100#14519773—22no—
101#14519773C2×C414yescomplemented
102#14519766—22no—
103#14519766C2×C414yescomplemented
104#14519750—28no—
105#14519750—28no—
106#14519747—28no—
107#14519747—28no—
108#14519735—22no—
109#14519735D414yescomplemented
110#14519734C2×C414yes—
111#14519734D414yes—
112C2×C4⋊Dic61C2311yescharacteristic
113C2×C4⋊Dic61C2311yescharacteristic
114C2×#11758196—21no—
115C2×#11758196D411yescharacteristic
116C2×#11758196D411yescharacteristic
117C4⋊C4×D61—22no—
118C4⋊C4×D61D414yescomplemented
119C2×#11758198—21no—
120C2×#11758198—21no—
121C2×#11758198—21no—
122C2×#11758198D411yescharacteristic
123C2×#11758198D411yescharacteristic
124C2×C4×Dic61—21no—
125C2×C4×Dic61—21no—
126C2×C4×Dic61—21no—
127C2×C4×Dic61—21no—
128C2×C4×Dic61C2311yescharacteristic
129C4⋊#92418—22no—
130#14519706—22no—
131#14519706—22no—
132#14519701—22no—
133#14519701—22no—
134#14519699—22no—
135#14519699—22no—
136#14519699—22no—
137#14519699—22no—
138#14519698—22no—
139#14519698—22no—
140#14519697—22no—
141#14519697—22no—
142#14519697—22no—
143#14519697—22no—
144#14519684—21no—
145#14519684—21no—
146#14519684—21no—
147C22×Q8×C61C2311yescharacteristic
148C22×D4×C61C2311yescharacteristic
149C22×C8×C61C2311yescharacteristic
150C22×C8×C61C2311yescharacteristic
151#124×C61—22no—
152#124×C61C2×C414yescomplemented
153C2×C4⋊C4×C61C2311yescharacteristic
154C2×C4⋊C4×C61C2311yescharacteristic
155C2×C22⋊C4×C61—21no—
156C2×C22⋊C4×C61—21no—
157C2×C42×C61—21no—
158C2×C42×C61C2311yescharacteristic
159C4⋊C8×C61—22no—
160#103×C61—22no—
161#103×C61—22no—
162#102×C61—22no—
163#102×C61—22no—
164#95×C61—21no—
165C24×C61—21no—
166C23×D61—21no—
167C23×D61—21no—
168C23×D61—24no—
169C23×D61—42no—
170C23×D61—42no—
171C23×D61—81no—
172C23×D61—81no—
173C23×D61—81no—
174C23×D61—81no—
175C23×D61C2×D411yescharacteristic
176C2×Q8×C61—21no—
177C2×Q8×C61—21no—
178C2×Q8×C61—21no—
179C2×Q8×C61—21no—
180C2×Q8×C61—21no—
181C2×Q8×C61C22×C412yes—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61C22×C412yes—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61C2×D411yescharacteristic
192C22×C4×C61C2×D411yescharacteristic
193C22×C4×C61C2411yescharacteristic
194C2×C22⋊D61—24no—
195C2×C22⋊D61—24no—
196C2×C22⋊D61—24no—
197C2×C22⋊D61—42no—
198C2×C22⋊D61—42no—
199C2×C22⋊D61—81no—
200C2×C22⋊D61—81no—
201C2×C22⋊D61—81no—
202C2×C22⋊D61—81no—
203C22×Dic61—21no—
204C22×Dic61—21no—
205C22×Dic61C2×D411yescharacteristic
206C22×Dic61C2×D411yescharacteristic
207C22×Dic61C2×D411yescharacteristic
208#11758226—28no—
209#11758226—28no—
210#11758226—44no—
211#11758226—44no—
212D4×D61—28no—
213D4×D61—28no—
214D4×D61—44no—
215D4×D61—44no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244—21no—
224C2×D244—24no—
225C2×D244—21no—
226C2×D244—21no—
227C2×D244—24no—
228C2×D244—24no—
229C2×D244—42no—
230C2×D244—42no—
231C2×D244—81no—
232C2×D244—81no—
233C2×D244—81no—
234C2×D244—81no—
235C2×D244C22×C412yes—
236C2×D244C22×C412yes—
237C2×C4×D61—24no—
238C2×C4×D61—24no—
239C2×C4×D61—42no—
240C2×C4×D61—42no—
241C2×C4×D61—81no—
242C2×C4×D61—81no—
243C2×C4×D61C22×C412yes—
244C2×C4×D61C2×D412yes—
245C2×C4×D61C2×D412yes—
246C2×C4×D61C2×D412yes—
247C2×C4×D61#4112yes—
248C2×C4×D61#4112yes—
249C2×C8×C61—21no—
250C2×C8×C61—21no—
251C2×C8×C61—21no—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61C2×D412yes—
258C4⋊C4×C61C2×D412yes—
259C22⋊C4×C61—24no—
260C22⋊C4×C61—24no—
261C42×C61—81no—
262C42×C61C22×C412yes—
263C42×C61C2×D412yes—
264#11758198—24no—
265#11758198—24no—
266#11758198—24no—
267#11758198C22⋊C414yes—
268#11758198C22⋊C414yes—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61C2×D412yes—
272C4⋊Dic61C2×D412yes—
273#11758196—24no—
274#11758196C22⋊C414yes—
275#11758196C22⋊C414yes—
276C4×Dic61—24no—
277C4×Dic61—81no—
278C4×Dic61—81no—
279C4×Dic61—81no—
280C4×Dic61C22×C412yes—
281C4×Dic61C2×D412yes—
282C2×#92418—21no—
283C2×#92418—21no—
284C2×#92418—21no—
285C2×#92418—21no—
286C2×#92418—21no—
287C2×#92418—21no—
288#11758189—44no—
289C8×D61—44no—
290C23×C61—22no—
291C23×C61—41no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61C22×D411yescharacteristic
298C22×D61—21no—
299C22×D61—21no—
300C22×D61—21no—
301C22×D61—21no—
302C22×D61—22no—
303C22×D61—22no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61—41no—
315C22×D61—41no—
316C22×D61—48no—
317C22×D61—84no—
318C22×D61—84no—
319C22×D61—84no—
320C22×D61—84no—
321C22×D61—84no—
322C22×D61—84no—
323C22×D61C2×C22⋊C412yes—
324C22×D61#12112yes—
325C22×D61#12112yes—
326Q8×C61—22no—
327Q8×C61—22no—
328Q8×C61—41no—
329Q8×C61—41no—
330D4×C61—22no—
331D4×C61—22no—
332D4×C61—41no—
333D4×C61—41no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—22no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61C2×C22⋊C412yes—
348C2×C4×C61C2×C22⋊C412yes—
349C2×C4×C61C23×C411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C2×#4111yescharacteristic
354C2×C4×C61C2×#4111yescharacteristic
355C22⋊D61—48no—
356C22⋊D61—84no—
357C22⋊D61—84no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—22no—
363C2×Dic61—22no—
364C2×Dic61—41no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61C2×C22⋊C412yes—
369C2×Dic61C2×C22⋊C412yes—
370C2×Dic61C2×C22⋊C412yes—
371C2×Dic61#12112yes—
372C2×Dic61#12112yes—
373D244—22no—
374D244—22no—
375D244—22no—
376D244—22no—
377D244—48no—
378D244—41no—
379D244—41no—
380D244—41no—
381D244—41no—
382D244—84no—
383D244—84no—
384C4×D61—48no—
385C4×D61—84no—
386C4×D61C4×D414yes—
387C4×D61C4×D414yes—
388C4×D61#12414yes—
389C4×D61#12714yes—
390C8×C61—41no—
391C8×C61—41no—
392#92418—41no—
393#92418—41no—
394#21263—611nomaximal, Sylow
395C22×C61—42no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—81no—
399C22×C61—81no—
400C22×C61—81no—
401C22×C61—81no—
402C22×C61C22×C22⋊C411yescharacteristic
403C22×C61C2×#12111yescharacteristic
404C22×C61C2×#12111yescharacteristic
405C22×C61#57611yescharacteristic
406C22×C61#57611yescharacteristic
407C22×C61#57711yescharacteristic
408C22×C61#57711yescharacteristic
409C2×D61—22no—
410C2×D61—22no—
411C2×D61—22no—
412C2×D61—22no—
413C2×D61—22no—
414C2×D61—22no—
415C2×D61—42no—
416C2×D61—42no—
417C2×D61—42no—
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—816no—
422C2×D61—81no—
423C2×D61—81no—
424C2×D61—81no—
425C2×D61—81no—
426C2×D61—81no—
427C2×D61—81no—
428C2×D61—81no—
429C2×D61—81no—
430C2×D61#39014yes—
431C4×C61—22no—
432C4×C61—22no—
433C4×C61—42no—
434C4×C61—42no—
435C4×C61—42no—
436C4×C61C2×C4×D411yescharacteristic
437C4×C61C2×C4×D411yescharacteristic
438C4×C61C2×#12411yescharacteristic
439C4×C61C2×#12711yescharacteristic
440Dic61—22no—
441Dic61—22no—
442Dic61—42no—
443Dic61—42no—
444Dic61#39014yes—
445C2×#535—611no—
446C2×#424—611no—
447C2×#417—611no—
448C2×#418—611no—
449C2×#416—611no—
450C22×#102—611no—
451#2274—611no—
452#1983—611no—
453#1983—611no—
454#1983—611no—
455#1983D6111yescharacteristic, complemented
456#1982—611no—
457#1982—611no—
458#1982—611no—
459#1982—611no—
460C2×C61—82no—
461C2×C61C2×#39011yescharacteristic
462C2×C61#289711yescharacteristic
463C2×C61#289711yescharacteristic
464C2×C61#304111yescharacteristic
465C2×C61#304311yescharacteristic
466C2×C61#304511yescharacteristic
467C2×C61#304511yescharacteristic
468D61—24no—
469D61—82no—
470D61—82no—
471C22×#41—611no—
472C23×D4—611no—
473C22×M16—611no—
474C23×C8—611no—
475#535—618no—
476#535—1224no—
477C2×#127—611no—
478C2×#127—611no—
479C2×#124—611no—
480C2×#124C2×D6111yescharacteristic
481C2×#121—1221no—
482C2×#121—1221no—
483C2×#120—1221no—
484C2×#120—1221no—
485C2×#117—611no—
486C2×#117—611no—
487C22×C4⋊C4—611no—
488#424—1224no—
489C2×C4⋊C8—611no—
490C2×C4⋊C8—611no—
491C2×C4⋊C8—611no—
492C2×C4⋊C8C2×D6111yescharacteristic, complemented
493#418—1224no—
494#417—1224no—
495#416—1224no—
496C2×#103—611no—
497C2×#103—611no—
498C2×#103C2×D6111yescharacteristic, complemented
499C2×#103C2×D6111yescharacteristic, complemented
500C2×#102—611no—
501C2×#102—611no—
502C2×#102—611no—
503C2×#102—611no—
504C2×#102—611no—
505C2×#102—611no—
506C2×#102—611no—
507C2×#102—611no—
508C2×#102—611no—
509C2×#102—611no—
510C2×#102—1224no—
511C2×#102C2×D6111yescharacteristic
512C2×#102C2×D6111yescharacteristic
513C4×C4⋊C4—611no—
514C4×C4⋊C4—611no—
515C4×C4⋊C4—611no—
516C4×C4⋊C4—1221no—
517C4×C4⋊C4—1221no—
518C4×C4⋊C4C2×D6111yescharacteristic, complemented
519C4×C22⋊C4—1221no—
520C4×C22⋊C4—1221no—
521C61#2126311yescharacteristic, complemented, Sylow
522C25—1221no—
523C2×#41—614no—
524C2×#41—1222no—
525C2×#41—1222no—
526C2×#41—1222no—
527C2×#41—1222no—
528C2×#41—1222no—
529C22×Q8C22×D6111yescharacteristic
530C22×D4—614no—
531C22×D4—611no—
532C22×D4—611no—
533C22×D4—1221no—
534C22×D4—1222no—
535C22×D4—1222no—
536C22×D4—1222no—
537C22×D4—1222no—
538C22×D4—1222no—
539C22×D4—1221no—
540C22×D4—1221no—
541C22×D4—1221no—
542C22×D4—1221no—
543C22×D4—1221no—
544C22×D4C22×D6111yescharacteristic
545C23×C4—611no—
546C23×C4—1221no—
547C23×C4—1221no—
548C2×M16—1222no—
549C2×M16—1222no—
550C2×M16—1222no—
551C22×C8—611no—
552C22×C8—611no—
553C22×C8—1222no—
554C22×C8—1222no—
555C22×C8—1222no—
556C22×C8C22×D6111yescharacteristic
557C22×C8C22×D6111yescharacteristic
558#127—614no—
559#127—614no—
560#127—1222no—
561#127—1222no—
562#124—22no—
563#124—614no—
564#124—1222no—
565#124C4×D6114yescomplemented
566#121—1228no—
567#121—1228no—
568#120—1228no—
569#120—1228no—
570#117—614no—
571#117—614no—
572#117—614no—
573#117—1222no—
574C2×C4⋊C4—611no—
575C2×C4⋊C4—611no—
576C2×C4⋊C4—611no—
577C2×C4⋊C4—611no—
578C2×C4⋊C4—614no—
579C2×C4⋊C4—1222no—
580C2×C4⋊C4—1221no—
581C2×C4⋊C4C22×D6111yescharacteristic
582C2×C4⋊C4C22×D6111yescharacteristic
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—611no—
586C2×C22⋊C4—611no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C42—21no—
591C2×C42—611no—
592C2×C42—1221no—
593C2×C42—1221no—
594C2×C42—1221no—
595C2×C42—1221no—
596C2×C42C22×D6111yescharacteristic
597C4⋊C8—22no—
598C4⋊C8—1222no—
599C4⋊C8—1222no—
600C4⋊C8—1222no—
601#103—22no—
602#103—22no—
603#103—1222no—
604#103—1222no—
605#102—22no—
606#102—22no—
607#102—1222no—
608#102—1222no—
609#102—1222no—
610#102—1222no—
611#102—1222no—
612#102—1222no—
613#102—1222no—
614#102—1222no—
615#102—1222no—
616#102—1222no—
617#95—21no—
618#95—1221no—
619#95—1221no—
620#95—1221no—
621C24—21no—
622C24—611no—
623C24—1224no—
624C24—1221no—
625C24—1221no—
626C24—4881no—
627C24—4881no—
628C24—4881no—
629C24—4881no—
630C24—2442no—
631C24—2442no—
632#41—1228no—
633#41—1228no—
634#41—2444no—
635#41—2444no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8C2×C4×D6112yes—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—612no—
648C2×D4—612no—
649C2×D4—1224no—
650C2×D4—1228no—
651C2×D4—1228no—
652C2×D4—1224no—
653C2×D4—1224no—
654C2×D4—1224no—
655C2×D4—1221no—
656C2×D4—1221no—
657C2×D4—1221no—
658C2×D4—1221no—
659C2×D4—1221no—
660C2×D4—1221no—
661C2×D4—1221no—
662C2×D4—1221no—
663C2×D4—1221no—
664C2×D4—1221no—
665C2×D4—1224no—
666C2×D4—1224no—
667C2×D4—4881no—
668C2×D4—4881no—
669C2×D4—4881no—
670C2×D4—4881no—
671C2×D4—4881no—
672C2×D4—4881no—
673C2×D4—4881no—
674C2×D4—4881no—
675C2×D4—2442no—
676C2×D4—2442no—
677C2×D4—2444no—
678C2×D4—2444no—
679C2×D4—2442no—
680C2×D4—2442no—
681C2×D4C2×C4×D6112yes—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—611no—
686C22×C4—612no—
687C22×C4—612no—
688C22×C4—612no—
689C22×C4—612no—
690C22×C4—612no—
691C22×C4—612no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—1224no—
695C22×C4—1224no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—4881no—
699C22×C4—4881no—
700C22×C4—2442no—
701C22×C4—2442no—
702C22×C4D4×D6111yescharacteristic
703C22×C4D4×D6111yescharacteristic
704C22×C4C23×D6111yescharacteristic
705M16—2444no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—2444no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—614no—
722C4⋊C4—614no—
723C4⋊C4—612no—
724C4⋊C4—612no—
725C4⋊C4—1224no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4D4×D6112yes—
729C4⋊C4D4×D6112yes—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—614no—
733C22⋊C4—614no—
734C22⋊C4—1224no—
735C22⋊C4—1224no—
736C22⋊C4—1224no—
737C42—81no—
738C42—612no—
739C42—612no—
740C42—1224no—
741C42—4881no—
742C42—4881no—
743C42—4881no—
744C42C2×C4×D6112yes—
745C42D4×D6112yes—
746C23—22no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—612no—
754C23—612no—
755C23—612no—
756C23—1221no—
757C23—1221no—
758C23—1221no—
759C23—1221no—
760C23—1222no—
761C23—1222no—
762C23—4884no—
763C23—4884no—
764C23—4884no—
765C23—4884no—
766C23—4884no—
767C23—4884no—
768C23—2448no—
769C23—2441no—
770C23—2441no—
771C23—2441no—
772C23—2441no—
773C23—2441no—
774C23—2441no—
775C23—2441no—
776C23—2441no—
777C23—2441no—
778C23—2441no—
779C23—2441no—
780C23—2441no—
781C23C2×D4×D6111yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—41no—
785Q8—41no—
786D4—22no—
787D4—22no—
788D4—41no—
789D4—41no—
790D4—1222no—
791D4—1222no—
792D4—1222no—
793D4—1222no—
794D4—4884no—
795D4—4884no—
796D4—4884no—
797D4—4884no—
798D4—2448no—
799D4—2448no—
800D4—2441no—
801D4—2441no—
802D4—2441no—
803D4—2441no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—612no—
818C2×C4—612no—
819C2×C4—612no—
820C2×C4—614no—
821C2×C4—614no—
822C2×C4—614no—
823C2×C4—614no—
824C2×C4—612no—
825C2×C4—612no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—1221no—
830C2×C4—1222no—
831C2×C4—1222no—
832C2×C4—4884no—
833C2×C4—2448no—
834C2×C4—2441no—
835C2×C4—2441no—
836C2×C4—2441no—
837C2×C4—2441no—
838C2×C4C22⋊C4×D6112yes—
839C2×C4C22⋊C4×D6112yes—
840C2×C4C22×C4×D6111yescharacteristic
841C2×C4C2×D4×D6111yescharacteristic
842C2×C4C2×D4×D6111yescharacteristic
843C2×C4C2×D4×D6111yescharacteristic
844C2×C4#41×D6111yescharacteristic
845C2×C4#41×D6111yescharacteristic
846C8—41no—
847C8—41no—
848C8—2441no—
849C8—2441no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—614no—
858C22—1222no—
859C22—1222no—
860C22—1222no—
861C22—1222no—
862C22—1222no—
863C22—1222no—
864C22—48816no—
865C22—4881no—
866C22—4881no—
867C22—4881no—
868C22—4881no—
869C22—4881no—
870C22—4881no—
871C22—4881no—
872C22—4881no—
873C22—2442no—
874C22—2442no—
875C22—2442no—
876C22—2442no—
877C22—2442no—
878C22—2442no—
879C22C2×C22⋊C4×D6111yescharacteristic
880C22#121×D6111yescharacteristic
881C22#121×D6111yescharacteristic
882C22#1684056411yescharacteristic
883C22#1684056611yescharacteristic
884C22#1684056911yescharacteristic
885C22#1684057111yescharacteristic
886C4—22no—
887C4—22no—
888C4—42no—
889C4—42no—
890C4—42no—
891C4—614no—
892C4—1222no—
893C4—1222no—
894C4—2442no—
895C4—2442no—
896C4C4×D4×D6111yescharacteristic
897C4C4×D4×D6111yescharacteristic
898C4#124×D6111yescharacteristic
899C4#127×D6111yescharacteristic
900C2—82no—
901C2—1224no—
902C2—4882no—
903C2—4882no—
904C2#390×D6111yescharacteristic
905C2#2145434111yescharacteristic
906C2#2145434311yescharacteristic
907C2#2145532011yescharacteristic
908C2#2145533811yescharacteristic
909C2#2145535911yescharacteristic
910C2#2145536111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1983C2
socleC23×C61C22×D4
prime radicalC2×#16840330C2
cosocleC22×C4×C61C24
hypercenter#1983D61
hypocenterC61#21263
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1983

Complements

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

NH ≅ G/Ntype
2. C2×#16839787C2semidirect
3. C2×#16839762C2semidirect
4. C2×#16839765C2semidirect
5. C2×#16839757C2semidirect
6. C2×#102×D61C2semidirect
7. #21448173C2semidirect
8. #21446752C2semidirect
9. #21446748C2semidirect
10. #21446748C2semidirect
11. #21446746C2semidirect
12. #21446745C2semidirect
13. #21446744C2semidirect
14. #21446744C2semidirect
15. C61×#1983C2semidirect
21. #16840330C4semidirect
33. C2×C4⋊#92418C22semidirect
34. C2×#14519706C22semidirect
35. C2×#14519706C22semidirect
39. C2×#14519701C22semidirect
40. C2×#14519701C22semidirect
43. C2×#14519699C22semidirect
44. C2×#14519699C22semidirect
49. C2×#14519697C22semidirect
50. C2×#14519697C22semidirect
52. C4⋊C4×Dic61C22semidirect
53. C4⋊C4×Dic61C22semidirect
55. C4×C4⋊Dic61C22semidirect
60. C2×C4⋊C8×C61C22semidirect
61. C2×#103×C61C22semidirect
62. C2×#103×C61C22semidirect
65. C4×C4⋊C4×C61C22semidirect
99. #14519774C2×C4semidirect
101. #14519773C2×C4semidirect
103. #14519766C2×C4semidirect
109. #14519735D4semidirect
118. C4⋊C4×D61D4semidirect
152. #124×C61C2×C4semidirect
455. #1983D61semidirect
492. C2×C4⋊C8C2×D61semidirect
498. C2×#103C2×D61semidirect
499. C2×#103C2×D61semidirect
518. C4×C4⋊C4C2×D61semidirect
521. C61#21263semidirect
565. #124C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403302
C2×#168397872
C2×#168397622
C2×#168397652
C2×#168397572
C2×#102×D612
#214481732
#214467522
#214467482
#214467462
#214467452
#214467442
C61×#19832
#2126361