Finite Group Databasebeta

← #29695552

Subgroups — #29695552

Order 15616.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840397C211yesmaximal, characteristic
2C2×#16839835C211yesmaximal, characteristic, complemented
3C2×#16839765C211yesmaximal, characteristic, complemented
4C2×#102×D61C211yesmaximal, characteristic, complemented
5#21448745C211yesmaximal, characteristic, complemented
6#21446747C211yesmaximal, characteristic, complemented
7#21446254C211yesmaximal, characteristic, complemented
8#21446244C211yesmaximal, characteristic, complemented
9#21446138C211yesmaximal, characteristic, complemented
10#21446133C211yesmaximal, characteristic, complemented
11#21445826C211yesmaximal, characteristic, complemented
12#21445748C211yesmaximal, characteristic, complemented
13#21445748C211yesmaximal, characteristic, complemented
14#21445645C211yesmaximal, characteristic, complemented
15C61×#1961C211yesmaximal, characteristic, complemented
16C22×D4×D61—21no—
17C22×D4×D61C2211yescharacteristic
18C22×D4×D61C2211yescharacteristic
19C22×#11758189C2211yescharacteristic, complemented
20C22×C8×D61C2211yescharacteristic, complemented
21#16840397—24no—
22#16840397C418yescomplemented
23C2×#14519748—21no—
24C2×#14519748C2211yescharacteristic
25C2×#14519748C2211yescharacteristic
26C2×#14519745—21no—
27C2×#14519745—21no—
28C2×C4×D244C2211yescharacteristic
29C2×C4×D244C2211yescharacteristic
30C2×#14519735C2211yescharacteristic, complemented
31C2×C4⋊C4×D61C2211yescharacteristic, complemented
32#16839835—24no—
33C2×C4⋊#92418C2211yescharacteristic, complemented
34#16839765—24no—
35C2×#14519699C2211yescharacteristic
36C2×#14519699C2211yescharacteristic
37C2×#14519698C2211yescharacteristic, complemented
38C2×#14519698C2211yescharacteristic, complemented
39C2×#14519698C2211yescharacteristic, complemented
40C2×#14519698C2211yescharacteristic, complemented
41C2×#14519697C2211yescharacteristic
42C2×#14519697C2211yescharacteristic
43#102×D61—24no—
44C2×#14519689C2211yescharacteristic, complemented
45C2×#14519689C2211yescharacteristic, complemented
46#16839651—21no—
47#16839645—21no—
48#16839640—21no—
49#16839619C2211yescharacteristic, complemented
50#16839619C2211yescharacteristic, complemented
51C4×C4⋊Dic61C2211yescharacteristic, complemented
52#16839609—21no—
53#16839525C2211yescharacteristic, complemented
54#16839525C2211yescharacteristic, complemented
55#16839524C2211yescharacteristic, complemented
56#16839524C2211yescharacteristic, complemented
57C2×#127×C61C2211yescharacteristic
58C2×#102×C61C2211yescharacteristic, complemented
59C2×#102×C61C2211yescharacteristic, complemented
60C2×#102×C61C2211yescharacteristic, complemented
61C2×#102×C61C2211yescharacteristic, complemented
62C2×#97×C61C2211yescharacteristic, complemented
63C61×#382C2211yescharacteristic, complemented
64C24×D61—21no—
65C24×D61—21no—
66C22×D244D411yescharacteristic
67C22×D244C2311yescharacteristic
68C22×C22⋊D61—21no—
69C22×C22⋊D61—21no—
70C22×C22⋊D61—21no—
71C22×C22⋊D61—21no—
72C2×D4×D61—28no—
73C2×D4×D61—22no—
74C2×D4×D61—22no—
75C2×D4×D61—22no—
76C2×D4×D61—22no—
77C2×D4×D61—22no—
78C2×D4×D61—22no—
79C2×D4×D61—41no—
80C2×D4×D61—41no—
81C2×D4×D61—41no—
82C2×D4×D61—41no—
83C2×D4×D61—44no—
84C2×D4×D61—44no—
85C2×D4×D61C2×C414yes—
86C2×D4×D61C2×C414yescomplemented
87C22×C4×D61—21no—
88C22×C4×D61—21no—
89C22×C4×D61C2311yescharacteristic
90C22×C4×D61C2311yescharacteristic
91C2×#11758189—22no—
92C2×#11758189—22no—
93C2×#11758189—41no—
94C22×#92418C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96C2×C8×D61—22no—
97C2×C8×D61—22no—
98C2×C8×D61—41no—
99#14519748—22no—
100#14519748—22no—
101#14519748—28no—
102#14519748C2×C414yes—
103#14519748C2×C414yescomplemented
104#14519745—28no—
105#14519745—28no—
106C4×D244—22no—
107C4×D244C2×C414yes—
108C4×D244C2×C414yescomplemented
109C4×D244D414yes—
110#14519735—22no—
111#14519735—41no—
112C2×C4⋊Dic61D411yescharacteristic
113C2×C4⋊Dic61C2311yescharacteristic
114C2×C4⋊Dic61C2311yescharacteristic
115C2×C4⋊Dic61C2311yescharacteristic
116C2×#11758196—21no—
117C4⋊C4×D61—22no—
118C4⋊C4×D61—41no—
119C2×C22⋊Dic61—21no—
120C2×C22⋊Dic61—21no—
121C2×#11758198—21no—
122C2×#11758198—21no—
123C2×#11758198—21no—
124C2×#11758198—21no—
125C2×#11758198D411yescharacteristic
126C2×#11758198D411yescharacteristic
127C2×C4×Dic61—21no—
128C2×C4×Dic61—21no—
129C4⋊#92418—22no—
130#14519699—22no—
131#14519699D414yescomplemented
132#14519698—22no—
133#14519698—22no—
134#14519698—41no—
135#14519698—41no—
136#14519697—22no—
137#14519697—22no—
138#14519689—22no—
139#14519689—22no—
140#14519684—21no—
141#14519684—21no—
142#14519684—21no—
143C22×D4×C61—21no—
144C22×D4×C61—21no—
145C22×D4×C61C2311yescharacteristic
146C22×D4×C61C2311yescharacteristic
147C22×C8×C61C2311yescharacteristic
148C22×C8×C61C2311yescharacteristic
149#127×C61—22no—
150#127×C61C2×C414yescomplemented
151C2×C4⋊C4×C61C2311yescharacteristic
152C2×C4⋊C4×C61C2311yescharacteristic
153C2×C42×C61C2311yescharacteristic
154#102×C61—22no—
155#102×C61—22no—
156#102×C61—41no—
157#102×C61—41no—
158#97×C61—22no—
159#95×C61—21no—
160#95×C61—21no—
161C24×C61—21no—
162C24×C61—21no—
163C23×D61—21no—
164C23×D61—24no—
165C23×D61—24no—
166C23×D61—42no—
167C23×D61—42no—
168C23×D61—42no—
169C23×D61—42no—
170C23×D61—42no—
171C23×D61—42no—
172C23×D61—42no—
173C23×D61—42no—
174C23×D61—81no—
175C23×D61—81no—
176C23×D61—81no—
177C23×D61—81no—
178C23×D61C2×D411yescharacteristic
179C23×D61C2×D411yescharacteristic
180C2×D4×C61—24no—
181C2×D4×C61—24no—
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—21no—
189C2×D4×C61—21no—
190C2×D4×C61—21no—
191C2×D4×C61—21no—
192C2×D4×C61—42no—
193C2×D4×C61—42no—
194C2×D4×C61—81no—
195C2×D4×C61—81no—
196C2×D4×C61C22×C412yes—
197C2×D4×C61C22×C412yes—
198C22×C4×C61—21no—
199C22×C4×C61—21no—
200C22×C4×C61C2×D411yescharacteristic
201C22×C4×C61C2×D411yescharacteristic
202C22×C4×C61C2411yescharacteristic
203C2×C22⋊D61—24no—
204C2×C22⋊D61—24no—
205C2×C22⋊D61—24no—
206C2×C22⋊D61—24no—
207C2×C22⋊D61—42no—
208C2×C22⋊D61—42no—
209C2×C22⋊D61—42no—
210C2×C22⋊D61—42no—
211C2×C22⋊D61—42no—
212C2×C22⋊D61—42no—
213C2×C22⋊D61—42no—
214C2×C22⋊D61—42no—
215C22×Dic61—21no—
216C22×Dic61—21no—
217C22×Dic61—21no—
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220D4×D61—28no—
221D4×D61—28no—
222D4×D61—44no—
223D4×D61—44no—
224D4×D61—44no—
225D4×D61—44no—
226D4×D61—44no—
227D4×D61—44no—
228D4×D61—432no—
229C2×D244—22no—
230C2×D244—22no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244C22⋊C414yes—
235C2×D244C22×C412yes—
236C2×D244C2×D412yes—
237C2×D244#4112yes—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—24no—
247C2×C4×D61—42no—
248C2×C4×D61—42no—
249C2×C4×D61—42no—
250C2×C4×D61—42no—
251C2×C4×D61—81no—
252C2×C4×D61C22×C412yes—
253C2×C4×D61C22×C412yes—
254C2×C4×D61C2×D412yes—
255C2×C4×D61C2×D412yes—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C2×C8×C61—21no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61C2×D412yescomplemented
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C42×C61C22×C412yes—
267C42×C61C2×D412yes—
268C22⋊Dic61—24no—
269C22⋊Dic61—24no—
270#11758198—24no—
271#11758198—42no—
272#11758198—42no—
273#11758198—81no—
274#11758198C22⋊C414yes—
275#11758198C22⋊C414yes—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61C22⋊C414yes—
281C4⋊Dic61C22×C412yes—
282C4⋊Dic61C2×D412yescomplemented
283#11758196—42no—
284C4×Dic61—42no—
285C4×Dic61—81no—
286C2×#92418—21no—
287C2×#92418—21no—
288C2×#92418—21no—
289C2×#92418—21no—
290C2×#92418—21no—
291C2×#92418—21no—
292#11758189—44no—
293C8×D61—44no—
294C23×C61—22no—
295C23×C61—22no—
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×C61—41no—
305C23×C61—41no—
306C23×C61—41no—
307C23×C61—41no—
308C23×C61C22×D411yescharacteristic
309C22×D61—21no—
310C22×D61—21no—
311C22×D61—21no—
312C22×D61—21no—
313C22×D61—22no—
314C22×D61—21no—
315C22×D61—22no—
316C22×D61—21no—
317C22×D61—22no—
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—21no—
321C22×D61—21no—
322C22×D61—48no—
323C22×D61—48no—
324C22×D61—48no—
325C22×D61—41no—
326C22×D61—41no—
327C22×D61—41no—
328C22×D61—41no—
329C22×D61—48no—
330C22×D61—84no—
331C22×D61—84no—
332C22×D61—84no—
333C22×D61—84no—
334C22×D61—84no—
335C22×D61—84no—
336C22×D61—84no—
337C22×D61—84no—
338C22×D61—84no—
339C22×D61—84no—
340C22×D61C2×C22⋊C412yes—
341C22×D61C2×C22⋊C412yes—
342C22×D61AGL(1,ℤ/8)12yes—
343C22×D61AGL(1,ℤ/8)12yes—
344D4×C61—22no—
345D4×C61—22no—
346D4×C61—22no—
347D4×C61—22no—
348D4×C61—48no—
349D4×C61—41no—
350D4×C61—41no—
351D4×C61—41no—
352D4×C61—41no—
353D4×C61—84no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—21no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61C2×C22⋊C412yes—
365C2×C4×C61C2×C22⋊C412yes—
366C2×C4×C61C23×C411yescharacteristic
367C2×C4×C61C22×D411yescharacteristic
368C2×C4×C61C22×D411yescharacteristic
369C2×C4×C61C2×#4111yescharacteristic
370C2×C4×C61H(5,𝔽2)11yescharacteristic
371C2×C4×C61H(5,𝔽2)11yescharacteristic
372C22⋊D61—48no—
373C22⋊D61—48no—
374C22⋊D61—48no—
375C22⋊D61—48no—
376C2×Dic61—21no—
377C2×Dic61—21no—
378C2×Dic61—21no—
379C2×Dic61—21no—
380C2×Dic61—22no—
381C2×Dic61—22no—
382C2×Dic61—41no—
383C2×Dic61—41no—
384C2×Dic61—41no—
385C2×Dic61—41no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—41no—
389C2×Dic61C2×C22⋊C412yes—
390C2×Dic61C2×C22⋊C412yes—
391D244—28no—
392D244—22no—
393D244—22no—
394D244—22no—
395D244C4×D414yes—
396C4×D61—22no—
397C4×D61—22no—
398C4×D61—22no—
399C4×D61—22no—
400C4×D61—22no—
401C4×D61—22no—
402C4×D61—22no—
403C4×D61—22no—
404C4×D61—48no—
405C4×D61—84no—
406C8×C61—22no—
407C8×C61—41no—
408#92418—41no—
409#92418—41no—
410#22423—611nomaximal, Sylow
411C22×C61—42no—
412C22×C61—42no—
413C22×C61—42no—
414C22×C61—42no—
415C22×C61—42no—
416C22×C61—42no—
417C22×C61—81no—
418C22×C61—81no—
419C22×C61—81no—
420C22×C61—81no—
421C22×C61—81no—
422C22×C61—81no—
423C22×C61—81no—
424C22×C61—81no—
425C22×C61C22×C22⋊C411yescharacteristic
426C22×C61D4211yescharacteristic
427C22×C61#54611yescharacteristic
428C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
430C22×C61#57611yescharacteristic
431C22×C61#57711yescharacteristic
432C2×D61—22no—
433C2×D61—22no—
434C2×D61—22no—
435C2×D61—22no—
436C2×D61—22no—
437C2×D61—22no—
438C2×D61—22no—
439C2×D61—24no—
440C2×D61—22no—
441C2×D61—22no—
442C2×D61—42no—
443C2×D61—42no—
444C2×D61—41no—
445C2×D61—42no—
446C2×D61—41no—
447C2×D61—42no—
448C2×D61—41no—
449C2×D61—42no—
450C2×D61—41no—
451C2×D61—42no—
452C2×D61—816no—
453C2×D61—816no—
454C2×D61#41814yescomplemented
455C4×C61—22no—
456C4×C61—22no—
457C4×C61—81no—
458C4×C61—81no—
459C4×C61C2×C4×D411yescharacteristic
460C4×C61#51811yescharacteristic
461C4×C61D4211yescharacteristic
462C4×C61#54611yescharacteristic
463Dic61—22no—
464Dic61—22no—
465Dic61—42no—
466Dic61—42no—
467Dic61—81no—
468C2×D42—611no—
469C2×#435—611no—
470C2×#418—611no—
471C22×#102—611no—
472#2352—611no—
473#1982—611no—
474#1961D6111yescharacteristic, complemented
475#1895—611no—
476#1893—611no—
477#1875—611no—
478#1874—611no—
479#1804—611no—
480#1786—611no—
481#1786—611no—
482#1762—611no—
483C2×C61—82no—
484C2×C61—82no—
485C2×C61D4×C22⋊C411yescharacteristic
486C2×C61C2×#41811yescharacteristic
487C2×C61#289711yescharacteristic
488C2×C61#326411yescharacteristic
489C2×C61#326511yescharacteristic
490C2×C61#331011yescharacteristic
491C2×C61#331811yescharacteristic
492D61—24no—
493D61—42no—
494D61—44no—
495C23×D4—611no—
496C23×D4—611no—
497C23×D4—1221no—
498C22×M16—611no—
499C23×C8—611no—
500D42—618no—
501D42—1224no—
502C2×#127C2×D6111yescharacteristic
503C2×#121—611no—
504C2×#121—611no—
505C2×#121—1221no—
506C2×#120—1221no—
507C2×#120—1221no—
508C2×C4×D4—611no—
509C2×C4×D4—611no—
510C2×#117—611no—
511C22×C4⋊C4—611no—
512#435—1224no—
513C2×C4⋊C8—611no—
514#418—1224no—
515C2×#102—611no—
516C2×#102—611no—
517C2×#102—611no—
518C2×#102—611no—
519C2×#102—611no—
520C2×#102—611no—
521C2×#102—611no—
522C2×#102—611no—
523C2×#102—1224no—
524C2×#102C2×D6111yescharacteristic, complemented
525C2×#102C2×D6111yescharacteristic, complemented
526C2×#102C2×D6111yescharacteristic, complemented
527C2×#102C2×D6111yescharacteristic, complemented
528C2×C22⋊C8—611no—
529C2×C22⋊C8—611no—
530C2×#97C2×D6111yescharacteristic, complemented
531#388—1221no—
532#387—1221no—
533#386—1221no—
534#382C2×D6111yescharacteristic, complemented
535#380—611no—
536#380—611no—
537C4×C4⋊C4—611no—
538C4×C22⋊C4—1221no—
539#340—611no—
540#340—611no—
541#340—611no—
542#340—611no—
543C61#2242311yescharacteristic, complemented, Sylow
544C25—1221no—
545C25—1221no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—614no—
549C22×D4—614no—
550C22×D4—611no—
551C22×D4—611no—
552C22×D4—1222no—
553C22×D4—1222no—
554C22×D4—1221no—
555C22×D4—1221no—
556C22×D4—1222no—
557C22×D4—1222no—
558C22×D4—1222no—
559C22×D4—1222no—
560C22×D4—1228no—
561C22×D4—1221no—
562C22×D4—1221no—
563C22×D4—2441no—
564C22×D4—2441no—
565C22×D4—2441no—
566C22×D4—2441no—
567C22×D4—2444no—
568C22×D4—2444no—
569C22×D4C22×D6111yescharacteristic
570C22×D4C22×D6111yescharacteristic
571C23×C4—611no—
572C23×C4—611no—
573C23×C4—1221no—
574C23×C4—1221no—
575C2×M16—1222no—
576C2×M16—1222no—
577C2×M16—2441no—
578C22×C8—611no—
579C22×C8—611no—
580C22×C8—1222no—
581C22×C8—1222no—
582C22×C8—2441no—
583C22×C8C22×D6111yescharacteristic
584C22×C8C22×D6111yescharacteristic
585#127—22no—
586#127C4×D6114yescomplemented
587#121—614no—
588#121—614no—
589#121—1228no—
590#121—1222no—
591#121—1222no—
592#120—1228no—
593#120—1228no—
594C4×D4—614no—
595C4×D4—614no—
596C4×D4—614no—
597C4×D4—1222no—
598#117—1222no—
599#117—2441no—
600C2×C4⋊C4—611no—
601C2×C4⋊C4—611no—
602C2×C4⋊C4—611no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—1222no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4—2441no—
607C2×C4⋊C4C22×D6111yescharacteristic
608C2×C4⋊C4C22×D6111yescharacteristic
609C2×C22⋊C4—611no—
610C2×C22⋊C4—611no—
611C2×C22⋊C4—1221no—
612C2×C22⋊C4—1221no—
613C2×C22⋊C4—1221no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4—1221no—
616C2×C22⋊C4—1221no—
617C2×C42—1221no—
618C2×C42—1221no—
619C2×C42C22×D6111yescharacteristic
620C4⋊C8—1222no—
621#102—22no—
622#102—22no—
623#102—41no—
624#102—41no—
625#102—614no—
626#102—1222no—
627#102—1222no—
628#102—1222no—
629#102—1222no—
630#102—1222no—
631#102—2441no—
632#102—2441no—
633C22⋊C8—1222no—
634C22⋊C8—1222no—
635#97—22no—
636#95—21no—
637#95—21no—
638#95—1221no—
639#95—1221no—
640#95—1221no—
641C24—21no—
642C24—21no—
643C24—611no—
644C24—611no—
645C24—1224no—
646C24—1224no—
647C24—1221no—
648C24—4881no—
649C24—4881no—
650C24—4881no—
651C24—4881no—
652C24—2442no—
653C24—2442no—
654C24—2442no—
655C24—2442no—
656C24—2442no—
657C24—2442no—
658C24—2442no—
659C24—2442no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4—612no—
677C2×D4—612no—
678C2×D4—612no—
679C2×D4—614no—
680C2×D4—1222no—
681C2×D4—1222no—
682C2×D4—1224no—
683C2×D4—1224no—
684C2×D4—1228no—
685C2×D4—1228no—
686C2×D4—1224no—
687C2×D4—1224no—
688C2×D4—1221no—
689C2×D4—1221no—
690C2×D4—1221no—
691C2×D4—2444no—
692C2×D4—2444no—
693C2×D4—2444no—
694C2×D4—2444no—
695C2×D4—2444no—
696C2×D4—2444no—
697C2×D4—2442no—
698C2×D4—2442no—
699C2×D4—2442no—
700C2×D4—2442no—
701C2×D4—24432no—
702C2×D4—2442no—
703C2×D4—2442no—
704C2×D4—2442no—
705C2×D4—2442no—
706C2×D4C2×C4×D6112yes—
707C2×D4C2×C4×D6112yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—612no—
713C22×C4—612no—
714C22×C4—612no—
715C22×C4—612no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—1221no—
726C22×C4—1224no—
727C22×C4—1221no—
728C22×C4—4881no—
729C22×C4—2442no—
730C22×C4—2442no—
731C22×C4—2442no—
732C22×C4—2442no—
733C22×C4D4×D6111yescharacteristic
734C22×C4D4×D6111yescharacteristic
735C22×C4C23×D6111yescharacteristic
736M16—2444no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—1221no—
743C2×C8—1221no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—1221no—
748C2×C8—2444no—
749C2×C8D4×D6112yescomplemented
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—614no—
755C4⋊C4—612no—
756C4⋊C4—612no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—2442no—
762C22⋊C4—614no—
763C22⋊C4—614no—
764C22⋊C4—1224no—
765C22⋊C4—1224no—
766C22⋊C4—1224no—
767C22⋊C4—4881no—
768C22⋊C4—2442no—
769C22⋊C4—2442no—
770C42—4881no—
771C42—2442no—
772C42C2×C4×D6112yes—
773C42D4×D6112yes—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—612no—
789C23—612no—
790C23—612no—
791C23—612no—
792C23—1221no—
793C23—1221no—
794C23—1221no—
795C23—1221no—
796C23—1222no—
797C23—1221no—
798C23—1221no—
799C23—1221no—
800C23—1221no—
801C23—1221no—
802C23—1222no—
803C23—1221no—
804C23—1222no—
805C23—4884no—
806C23—4884no—
807C23—4884no—
808C23—4884no—
809C23—4884no—
810C23—4884no—
811C23—4884no—
812C23—4884no—
813C23—4884no—
814C23—4884no—
815C23—2448no—
816C23—2448no—
817C23—2448no—
818C23—2448no—
819C23—2441no—
820C23—2441no—
821C23—2441no—
822C23—2441no—
823C23C2×D4×D6111yescharacteristic
824D4—22no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—48no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—84no—
834D4—614no—
835D4—1228no—
836D4—1222no—
837D4—1222no—
838D4—1222no—
839D4—2448no—
840D4—2448no—
841D4—2448no—
842D4—2448no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—612no—
854C2×C4—612no—
855C2×C4—1221no—
856C2×C4—1221no—
857C2×C4—1221no—
858C2×C4—1221no—
859C2×C4—1222no—
860C2×C4—1222no—
861C2×C4—1222no—
862C2×C4—1222no—
863C2×C4—1222no—
864C2×C4—1222no—
865C2×C4—1222no—
866C2×C4—1222no—
867C2×C4—1222no—
868C2×C4—1222no—
869C2×C4—4884no—
870C2×C4—2448no—
871C2×C4—2441no—
872C2×C4—2441no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2441no—
878C2×C4C22⋊C4×D6112yes—
879C2×C4C22⋊C4×D6112yes—
880C2×C4C22×C4×D6111yescharacteristic
881C2×C4C2×D4×D6111yescharacteristic
882C2×C4C2×D4×D6111yescharacteristic
883C2×C4#41×D6111yescharacteristic
884C2×C4#1451982211yescharacteristic
885C2×C4#1451982311yescharacteristic
886C8—22no—
887C8—41no—
888C8—2441no—
889C8—2441no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—81no—
897C22—81no—
898C22—81no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—614no—
905C22—1222no—
906C22—1222no—
907C22—1222no—
908C22—1222no—
909C22—1222no—
910C22—1222no—
911C22—1222no—
912C22—1222no—
913C22—1224no—
914C22—1222no—
915C22—48816no—
916C22—48816no—
917C22—2442no—
918C22—2441no—
919C22—2442no—
920C22—2441no—
921C22—2442no—
922C22—2441no—
923C22—2442no—
924C22—2441no—
925C22—2442no—
926C22—2442no—
927C22C2×C22⋊C4×D6111yescharacteristic
928C22#1684039711yescharacteristic
929C22#1684040511yescharacteristic
930C22AGL(1,ℤ/8)×D6111yescharacteristic
931C22AGL(1,ℤ/8)×D6111yescharacteristic
932C22#1684056611yescharacteristic
933C22#1684057211yescharacteristic
934C4—22no—
935C4—22no—
936C4—81no—
937C4—81no—
938C4—1222no—
939C4—1222no—
940C4—4881no—
941C4—2442no—
942C4—2442no—
943C4C4×D4×D6111yescharacteristic
944C4#1684023411yescharacteristic
945C4#1684039611yescharacteristic
946C4#1684040911yescharacteristic
947C2—82no—
948C2—82no—
949C2—1224no—
950C2—2442no—
951C2—2444no—
952C2#2144864011yescharacteristic
953C2#418×D6111yescharacteristic
954C2#2145434411yescharacteristic
955C2#2145729811yescharacteristic
956C2#2145731311yescharacteristic
957C2#2145783911yescharacteristic
958C2#2145795911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1961C2
socleC23×C61C22×D4
prime radicalC2×#16840397C2
cosocleC22×C4×C61C24
hypercenter#1961D61
hypocenterC61#22423
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
2. C2×#16839835C2semidirect
3. C2×#16839765C2semidirect
4. C2×#102×D61C2semidirect
5. #21448745C2semidirect
6. #21446747C2semidirect
7. #21446254C2semidirect
8. #21446244C2semidirect
9. #21446138C2semidirect
10. #21446133C2semidirect
11. #21445826C2semidirect
12. #21445748C2semidirect
13. #21445748C2semidirect
14. #21445645C2semidirect
15. C61×#1961C2semidirect
19. C22×#11758189C22semidirect
20. C22×C8×D61C22semidirect
22. #16840397C4semidirect
30. C2×#14519735C22semidirect
31. C2×C4⋊C4×D61C22semidirect
33. C2×C4⋊#92418C22semidirect
37. C2×#14519698C22semidirect
38. C2×#14519698C22semidirect
39. C2×#14519698C22semidirect
40. C2×#14519698C22semidirect
44. C2×#14519689C22semidirect
45. C2×#14519689C22semidirect
49. #16839619C22semidirect
50. #16839619C22semidirect
51. C4×C4⋊Dic61C22semidirect
53. #16839525C22semidirect
54. #16839525C22semidirect
55. #16839524C22semidirect
56. #16839524C22semidirect
58. C2×#102×C61C22semidirect
59. C2×#102×C61C22semidirect
60. C2×#102×C61C22semidirect
61. C2×#102×C61C22semidirect
62. C2×#97×C61C22semidirect
63. C61×#382C22semidirect
86. C2×D4×D61C2×C4semidirect
103. #14519748C2×C4semidirect
108. C4×D244C2×C4semidirect
131. #14519699D4semidirect
150. #127×C61C2×C4semidirect
261. C2×C8×C61C2×D4semidirect
282. C4⋊Dic61C2×D4semidirect
454. C2×D61#418semidirect
474. #1961D61semidirect
524. C2×#102C2×D61semidirect
525. C2×#102C2×D61semidirect
526. C2×#102C2×D61semidirect
527. C2×#102C2×D61semidirect
530. C2×#97C2×D61semidirect
534. #382C2×D61semidirect
543. C61#22423semidirect
586. #127C4×D61semidirect
749. C2×C8D4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168403972
C2×#168398352
C2×#168397652
C2×#102×D612
#214487452
#214467472
#214462542
#214462442
#214461382
#214461332
#214458262
#214457482
#214456452
C61×#19612
#2242361