Finite Group Databasebeta

← #29684112

Subgroups — #29684112

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×#16840325C211yesmaximal, characteristic
2C2×#16839787C211yesmaximal, characteristic, complemented
3C2×#16839760C211yesmaximal, characteristic, complemented
4C2×#16839765C211yesmaximal, characteristic, complemented
5C2×#16839755C211yesmaximal, characteristic, complemented
6C2×#102×D61C211yesmaximal, characteristic, complemented
7#21448173C211yesmaximal, characteristic, complemented
8#21446751C211yesmaximal, characteristic, complemented
9#21446750C211yesmaximal, characteristic, complemented
10#21446750C211yesmaximal, characteristic, complemented
11#21446749C211yesmaximal, characteristic, complemented
12#21446747C211yesmaximal, characteristic, complemented
13#21446744C211yesmaximal, characteristic, complemented
14#21446744C211yesmaximal, characteristic, complemented
15C61×#1982C211yesmaximal, characteristic, complemented
16C22×#11758224C2211yescharacteristic
17C22×D4×D61C2211yescharacteristic
18C22×#11758189C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20#16840325—24no—
21#16840325C418yescomplemented
22C2×#14519773C2211yescharacteristic
23C2×#14519765C2211yescharacteristic
24C2×#14519764C2211yescharacteristic
25C2×#14519749—21no—
26C2×#14519749—21no—
27C2×#14519745—21no—
28C2×#14519745—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#16839760—24no—
38#16839755—24no—
39C2×#14519702C2211yescharacteristic, complemented
40C2×#14519702C2211yescharacteristic, complemented
41C2×#14519700C2211yescharacteristic, complemented
42C2×#14519700C2211yescharacteristic, complemented
43C2×#14519699C2211yescharacteristic
44C2×#14519699C2211yescharacteristic
45C2×#14519698C2211yescharacteristic
46C2×#14519698C2211yescharacteristic
47C2×#14519698C2211yescharacteristic, complemented
48C2×#14519698C2211yescharacteristic, complemented
49C2×#14519697C2211yescharacteristic
50C2×#14519697C2211yescharacteristic
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×#127×C61C2211yescharacteristic
60C2×C4⋊C8×C61C2211yescharacteristic, complemented
61C2×#102×C61C2211yescharacteristic
62C2×#102×C61C2211yescharacteristic
63C2×#102×C61C2211yescharacteristic, complemented
64C2×#102×C61C2211yescharacteristic, complemented
65C4×C4⋊C4×C61C2211yescharacteristic, complemented
66C24×D61—21no—
67C2×#11758224—22no—
68C2×#11758224—22no—
69C2×#11758224—22no—
70C2×#11758224—22no—
71C2×#11758224—22no—
72C2×#11758224C2×C414yes—
73C22×Dic122C2311yescharacteristic
74C22×D244C2311yescharacteristic
75C22×C22⋊D61—21no—
76C22×C22⋊D61—21no—
77C22×C22⋊D61—21no—
78C22×C22⋊D61—21no—
79C2×D4×D61—22no—
80C2×D4×D61—22no—
81C2×D4×D61—22no—
82C2×D4×D61—22no—
83C2×D4×D61—22no—
84C2×D4×D61C2×C414yes—
85C23×Dic61—21no—
86C22×C4×D61—21no—
87C22×C4×D61C2311yescharacteristic
88C2×#11758189—22no—
89C2×#11758189—22no—
90C2×#11758189—22no—
91C22×#92418C2311yescharacteristic
92C22×#92418C2311yescharacteristic
93C2×C8×D61—22no—
94C2×C8×D61—22no—
95C2×C8×D61—22no—
96#14519773—22no—
97#14519773C2×C414yescomplemented
98#14519765—22no—
99#14519765C2×C414yescomplemented
100#14519764—22no—
101#14519764C2×C414yescomplemented
102#14519749—28no—
103#14519749—28no—
104#14519745—28no—
105#14519745—28no—
106#14519735—22no—
107#14519735D414yescomplemented
108#14519734C2×C414yes—
109#14519734D414yes—
110C2×C4⋊Dic61C2311yescharacteristic
111C2×C4⋊Dic61C2311yescharacteristic
112C2×#11758196—21no—
113C2×#11758196D411yescharacteristic
114C2×#11758196D411yescharacteristic
115C4⋊C4×D61—22no—
116C4⋊C4×D61D414yescomplemented
117C2×C22⋊Dic61—21no—
118C2×C22⋊Dic61—21no—
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#14519702—22no—
133#14519702—22no—
134#14519700—22no—
135#14519700—22no—
136#14519699—22no—
137#14519699—22no—
138#14519698—22no—
139#14519698—22no—
140#14519698—22no—
141#14519698—22no—
142#14519697—22no—
143#14519697—22no—
144#14519684—21no—
145#14519684—21no—
146#14519684—21no—
147C22×D4×C61—21no—
148C22×D4×C61—21no—
149C22×D4×C61C2311yescharacteristic
150C22×D4×C61C2311yescharacteristic
151C22×C8×C61C2311yescharacteristic
152C22×C8×C61C2311yescharacteristic
153#127×C61—22no—
154#127×C61C2×C414yescomplemented
155C2×C4⋊C4×C61C2311yescharacteristic
156C2×C4⋊C4×C61C2311yescharacteristic
157C2×C42×C61—21no—
158C2×C42×C61C2311yescharacteristic
159C4⋊C8×C61—22no—
160#102×C61—22no—
161#102×C61—22no—
162#102×C61—22no—
163#102×C61—22no—
164#95×C61—21no—
165C24×C61—21no—
166C24×C61—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×D4×C61—24no—
177C2×D4×C61—24no—
178C2×D4×C61—21no—
179C2×D4×C61—21no—
180C2×D4×C61—21no—
181C2×D4×C61—21no—
182C2×D4×C61—21no—
183C2×D4×C61—21no—
184C2×D4×C61—21no—
185C2×D4×C61—21no—
186C2×D4×C61—21no—
187C2×D4×C61—21no—
188C2×D4×C61—81no—
189C2×D4×C61—81no—
190C2×D4×C61—81no—
191C2×D4×C61—81no—
192C2×D4×C61C22×C412yes—
193C2×D4×C61C22×C412yes—
194C22×C4×C61—21no—
195C22×C4×C61—21no—
196C22×C4×C61C2×D411yescharacteristic
197C22×C4×C61C2×D411yescharacteristic
198C22×C4×C61C2411yescharacteristic
199C2×C22⋊D61—24no—
200C2×C22⋊D61—24no—
201C2×C22⋊D61—24no—
202C2×C22⋊D61—24no—
203C2×C22⋊D61—42no—
204C2×C22⋊D61—42no—
205C2×C22⋊D61—42no—
206C2×C22⋊D61—42no—
207C2×C22⋊D61—81no—
208C2×C22⋊D61—81no—
209C2×C22⋊D61—81no—
210C2×C22⋊D61—81no—
211C22×Dic61—21no—
212C22×Dic61—21no—
213C22×Dic61—21no—
214C22×Dic61—24no—
215C22×Dic61—42no—
216C22×Dic61—42no—
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220#11758224—28no—
221#11758224—28no—
222#11758224—44no—
223#11758224—44no—
224D4×D61—28no—
225D4×D61—28no—
226D4×D61—44no—
227D4×D61—44no—
228C2×D244—21no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244C22×C412yes—
234C2×C4×D61—24no—
235C2×C4×D61—81no—
236C2×C4×D61—81no—
237C2×C4×D61C22×C412yes—
238C2×C4×D61C2×D412yes—
239C2×C4×D61C2×D412yes—
240C2×C4×D61C2×D412yes—
241C2×C4×D61#4112yes—
242C2×C4×D61#4112yes—
243C2×Dic122—21no—
244C2×Dic122—21no—
245C2×Dic122—21no—
246C2×Dic122—21no—
247C2×Dic122—21no—
248C2×Dic122C22×C412yes—
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—
259C42×C61—81no—
260C42×C61C22×C412yes—
261C42×C61C2×D412yes—
262C22⋊Dic61—24no—
263C22⋊Dic61—24no—
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—22no—
292C23×C61—41no—
293C23×C61—41no—
294C23×C61—41no—
295C23×C61—41no—
296C23×C61—41no—
297C23×C61—41no—
298C23×C61—41no—
299C23×C61—41no—
300C23×C61—41no—
301C23×C61—41no—
302C23×C61—41no—
303C23×C61—41no—
304C23×C61C22×D411yescharacteristic
305C22×D61—21no—
306C22×D61—21no—
307C22×D61—21no—
308C22×D61—21no—
309C22×D61—22no—
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—
326D4×C61—22no—
327D4×C61—22no—
328D4×C61—22no—
329D4×C61—22no—
330D4×C61—41no—
331D4×C61—41no—
332D4×C61—41no—
333D4×C61—41no—
334D4×C61—84no—
335D4×C61—84no—
336C2×C4×C61—21no—
337C2×C4×C61—21no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61C2×C22⋊C412yes—
347C2×C4×C61C2×C22⋊C412yes—
348C2×C4×C61C23×C411yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C2×#4111yescharacteristic
353C2×C4×C61C2×#4111yescharacteristic
354C22⋊D61—48no—
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—22no—
365C2×Dic61—41no—
366C2×Dic61—41no—
367C2×Dic61—41no—
368C2×Dic61—41no—
369C2×Dic61—41no—
370C2×Dic61—41no—
371C2×Dic61—48no—
372C2×Dic61C2×C22⋊C412yes—
373C2×Dic61C2×C22⋊C412yes—
374C2×Dic61C2×C22⋊C412yes—
375C2×Dic61#12112yes—
376C2×Dic61#12112yes—
377D244—22no—
378D244—22no—
379D244—41no—
380D244—41no—
381C4×D61—84no—
382C4×D61C4×D414yes—
383C4×D61C4×D414yes—
384C4×D61#12414yes—
385C4×D61#12714yes—
386Dic122—22no—
387Dic122—22no—
388Dic122—41no—
389Dic122—41no—
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—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—81no—
402C22×C61—81no—
403C22×C61—81no—
404C22×C61—81no—
405C22×C61—81no—
406C22×C61—81no—
407C22×C61—81no—
408C22×C61—81no—
409C22×C61C22×C22⋊C411yescharacteristic
410C22×C61C2×#12111yescharacteristic
411C22×C61C2×#12111yescharacteristic
412C22×C61#57611yescharacteristic
413C22×C61#57611yescharacteristic
414C22×C61#57711yescharacteristic
415C22×C61#57711yescharacteristic
416C2×D61—22no—
417C2×D61—22no—
418C2×D61—22no—
419C2×D61—22no—
420C2×D61—22no—
421C2×D61—22no—
422C2×D61—42no—
423C2×D61—42no—
424C2×D61—42no—
425C2×D61—816no—
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×C61C2×C4×D411yescharacteristic
436C4×C61C2×C4×D411yescharacteristic
437C4×C61C2×#12411yescharacteristic
438C4×C61C2×#12711yescharacteristic
439Dic61—22no—
440Dic61—22no—
441Dic61—42no—
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#1983—611no—
456#1982—611no—
457#1982—611no—
458#1982—611no—
459#1982D6111yescharacteristic, complemented
460C2×C61—82no—
461C2×C61—82no—
462C2×C61C2×#39011yescharacteristic
463C2×C61#289711yescharacteristic
464C2×C61#289711yescharacteristic
465C2×C61#304111yescharacteristic
466C2×C61#304311yescharacteristic
467C2×C61#304511yescharacteristic
468C2×C61#304511yescharacteristic
469D61—24no—
470D61—82no—
471C22×#41—611no—
472C23×D4—611no—
473C22×M16—611no—
474C23×C8—611no—
475#535—618no—
476#535—1224no—
477C2×#127—611no—
478C2×#127C2×D6111yescharacteristic
479C2×#124—611no—
480C2×#124—611no—
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×#103—611no—
499C2×#103—611no—
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—1224no—
509C2×#102C2×D6111yescharacteristic
510C2×#102C2×D6111yescharacteristic
511C2×#102C2×D6111yescharacteristic, complemented
512C2×#102C2×D6111yescharacteristic, complemented
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×Q8—611no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—614no—
533C22×D4—611no—
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×D4C22×D6111yescharacteristic
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—22no—
559#127—614no—
560#127—1222no—
561#127C4×D6114yescomplemented
562#124—614no—
563#124—614no—
564#124—1222no—
565#124—1222no—
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—611no—
584C2×C22⋊C4—611no—
585C2×C22⋊C4—1221no—
586C2×C22⋊C4—1221no—
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—1222no—
602#103—1222no—
603#103—1222no—
604#103—1222no—
605#102—22no—
606#102—22no—
607#102—22no—
608#102—22no—
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—21no—
623C24—611no—
624C24—1224no—
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—612no—
637C2×Q8—1221no—
638C2×Q8—1221no—
639C2×Q8—1221no—
640C2×Q8—1221no—
641C2×Q8—1221no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—81no—
655C2×D4—81no—
656C2×D4—81no—
657C2×D4—81no—
658C2×D4—612no—
659C2×D4—1228no—
660C2×D4—1228no—
661C2×D4—1224no—
662C2×D4—1224no—
663C2×D4—1224no—
664C2×D4—1224no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1221no—
668C2×D4—1221no—
669C2×D4—1221no—
670C2×D4—4881no—
671C2×D4—4881no—
672C2×D4—4881no—
673C2×D4—4881no—
674C2×D4—2444no—
675C2×D4—2444no—
676C2×D4—2442no—
677C2×D4—2442no—
678C2×D4—2442no—
679C2×D4—2442no—
680C2×D4C2×C4×D6112yes—
681C2×D4C2×C4×D6112yes—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—611no—
685C22×C4—612no—
686C22×C4—612no—
687C22×C4—612no—
688C22×C4—612no—
689C22×C4—612no—
690C22×C4—612no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—1224no—
694C22×C4—1224no—
695C22×C4—1221no—
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—614no—
731C22⋊C4—614no—
732C22⋊C4—1224no—
733C22⋊C4—1224no—
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—22no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—612no—
761C23—612no—
762C23—612no—
763C23—1221no—
764C23—1221no—
765C23—1221no—
766C23—1221no—
767C23—1222no—
768C23—4884no—
769C23—4884no—
770C23—4884no—
771C23—4884no—
772C23—4884no—
773C23—4884no—
774C23—2448no—
775C23—2441no—
776C23—2441no—
777C23—2441no—
778C23—2441no—
779C23—2441no—
780C23—2441no—
781C23C2×D4×D6111yescharacteristic
782Q8—1222no—
783Q8—1222no—
784Q8—2441no—
785Q8—2441no—
786D4—22no—
787D4—22no—
788D4—22no—
789D4—22no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—84no—
795D4—84no—
796D4—1222no—
797D4—1222no—
798D4—4884no—
799D4—4884no—
800D4—2448no—
801D4—2448no—
802D4—2441no—
803D4—2441no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—612no—
815C2×C4—612no—
816C2×C4—612no—
817C2×C4—614no—
818C2×C4—614no—
819C2×C4—614no—
820C2×C4—614no—
821C2×C4—612no—
822C2×C4—612no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1222no—
828C2×C4—1222no—
829C2×C4—1222no—
830C2×C4—4884no—
831C2×C4—2448no—
832C2×C4—2441no—
833C2×C4—2441no—
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—42no—
854C22—42no—
855C22—42no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—614no—
865C22—1222no—
866C22—1222no—
867C22—1222no—
868C22—1222no—
869C22—1222no—
870C22—1222no—
871C22—48816no—
872C22—4881no—
873C22—4881no—
874C22—4881no—
875C22—4881no—
876C22—2442no—
877C22—2442no—
878C22—2442no—
879C22C2×C22⋊C4×D6111yescharacteristic
880C22#121×D6111yescharacteristic
881C22#121×D6111yescharacteristic
882C22#1684056311yescharacteristic
883C22#1684056611yescharacteristic
884C22#1684056811yescharacteristic
885C22#1684057211yescharacteristic
886C4—22no—
887C4—22no—
888C4—42no—
889C4—42no—
890C4—614no—
891C4—1222no—
892C4—1222no—
893C4—2442no—
894C4—2442no—
895C4—2442no—
896C4C4×D4×D6111yescharacteristic
897C4C4×D4×D6111yescharacteristic
898C4#124×D6111yescharacteristic
899C4#127×D6111yescharacteristic
900C2—82no—
901C2—82no—
902C2—1224no—
903C2—4882no—
904C2#390×D6111yescharacteristic
905C2#2145434011yescharacteristic
906C2#2145434411yescharacteristic
907C2#2145531711yescharacteristic
908C2#2145533511yescharacteristic
909C2#2145535311yescharacteristic
910C2#2145535511yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1982C2
socleC23×C61C22×D4
prime radicalC2×#16840325C2
cosocleC22×C4×C61C24
hypercenter#1982D61
hypocenterC61#21263
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
2. C2×#16839787C2semidirect
3. C2×#16839760C2semidirect
4. C2×#16839765C2semidirect
5. C2×#16839755C2semidirect
6. C2×#102×D61C2semidirect
7. #21448173C2semidirect
8. #21446751C2semidirect
9. #21446750C2semidirect
10. #21446750C2semidirect
11. #21446749C2semidirect
12. #21446747C2semidirect
13. #21446744C2semidirect
14. #21446744C2semidirect
15. C61×#1982C2semidirect
21. #16840325C4semidirect
33. C2×C4⋊#92418C22semidirect
34. C2×#14519706C22semidirect
35. C2×#14519706C22semidirect
39. C2×#14519702C22semidirect
40. C2×#14519702C22semidirect
41. C2×#14519700C22semidirect
42. C2×#14519700C22semidirect
47. C2×#14519698C22semidirect
48. C2×#14519698C22semidirect
52. C4⋊C4×Dic61C22semidirect
53. C4⋊C4×Dic61C22semidirect
55. C4×C4⋊Dic61C22semidirect
60. C2×C4⋊C8×C61C22semidirect
63. C2×#102×C61C22semidirect
64. C2×#102×C61C22semidirect
65. C4×C4⋊C4×C61C22semidirect
97. #14519773C2×C4semidirect
99. #14519765C2×C4semidirect
101. #14519764C2×C4semidirect
107. #14519735D4semidirect
116. C4⋊C4×D61D4semidirect
154. #127×C61C2×C4semidirect
459. #1982D61semidirect
492. C2×C4⋊C8C2×D61semidirect
511. C2×#102C2×D61semidirect
512. C2×#102C2×D61semidirect
518. C4×C4⋊C4C2×D61semidirect
521. C61#21263semidirect
561. #127C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403252
C2×#168397872
C2×#168397602
C2×#168397652
C2×#168397552
C2×#102×D612
#214481732
#214467512
#214467502
#214467492
#214467472
#214467442
C61×#19822
#2126361