Finite Group Databasebeta

← C2×#21457781 #30556524

Subgroups — C2×#21457781 #30556524

Order 15616.

2514 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840413C211yesmaximal, characteristic, complemented
2C2×#16840400C211yesmaximal, characteristic, complemented
3#21457781C2116yesmaximal, direct product factor
4C2×#16840123C211yesmaximal, characteristic, complemented
5C2×#16840080C211yesmaximal, characteristic, complemented
6C2×#16840091C211yesmaximal, characteristic, complemented
7C2×#16840050C211yesmaximal, characteristic, complemented
8C2×#16840015C211yesmaximal, characteristic, complemented
9C2×#16839994C211yesmaximal, characteristic, complemented
10C2×#16839980C211yesmaximal, characteristic, complemented
11C2×#16839907C211yesmaximal, characteristic, complemented
12C2×#16839897C211yesmaximal, characteristic, complemented
13C2×#16839871C211yesmaximal, characteristic, complemented
14C2×#16839831C211yesmaximal, characteristic, complemented
15C2×#102×D61C211yesmaximal, characteristic, complemented
16C2×C61×#417C211yesmaximal, characteristic, complemented
17C22×#11758222—21no—
18C22×D4×D61C2211yescharacteristic
19C22×#11758201C2211yescharacteristic, complemented
20C22×D488C2211yescharacteristic
21C22×#11758199C2211yescharacteristic
22C22×C8×D61C2211yescharacteristic
23#16840413—24no—
24#16840413C2218yescomplemented
25#16840400—24no—
26#16840400C2218yescomplemented
27C2×#14519776C2211yescharacteristic, complemented
28C2×#14519766C2211yescharacteristic
29C2×#14519762—21no—
30C2×#14519760—21no—
31C2×#14519760—21no—
32C2×#14519755—21no—
33C2×#14519753C2211yescharacteristic
34C2×#14519752C2211yescharacteristic
35C2×#14519751C2211yescharacteristic
36C2×#14519751C2211yescharacteristic, complemented
37C2×#14519749—21no—
38C2×#14519745—21no—
39C2×D4×Dic61C2211yescharacteristic
40C2×#14519739C2211yescharacteristic, complemented
41C2×C4×C22⋊D61C2211yescharacteristic
42C2×C4⋊C4×D61C2211yescharacteristic
43C22×#11758198—21no—
44#16840123C2218yescomplemented
45#16840091C2218yescomplemented
46#16840080C2218yescomplemented
47#16840050C2218yescomplemented
48#16840015C2218yescomplemented
49#16839994C2218yescomplemented
50#16839980C2218yescomplemented
51#16839907C2218yescomplemented
52#16839897C2218yescomplemented
53#16839871C2218yescomplemented
54#16839831C2218yescomplemented
55C2×#14519709C2211yescharacteristic, complemented
56C2×#14519708C2211yescharacteristic, complemented
57C2×#14519708C2211yescharacteristic, complemented
58C2×#14519706C2211yescharacteristic, complemented
59C2×#14519701C2211yescharacteristic, complemented
60C2×#14519699C2211yescharacteristic
61C2×#14519699C2211yescharacteristic, complemented
62C2×#14519698C2211yescharacteristic
63C2×#14519697C2211yescharacteristic
64C2×#14519697C2211yescharacteristic
65#102×D61C2218yescomplemented
66C2×C22⋊#92418C2211yescharacteristic, complemented
67C2×#14519689C2211yescharacteristic
68C2×#14519687C2211yescharacteristic, complemented
69C22×#41×C61C2211yescharacteristic
70C22×M16×C61C2211yescharacteristic, complemented
71C22×C4⋊C4×C61C2211yescharacteristic, complemented
72C61×#417C2218yescomplemented
73C2×#103×C61C2211yescharacteristic, complemented
74C2×#103×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic
76C2×#102×C61C2211yescharacteristic
77C24×D61—21no—
78C2×#11758222—28no—
79C2×#11758222—48no—
80C22×Dic122—21no—
81C22×D244—21no—
82C22×D244C2311yescharacteristic
83C22×D244C2311yescharacteristic
84C22×C22⋊D61—21no—
85C22×C22⋊D61—21no—
86C22×C22⋊D61—21no—
87C22×C22⋊D61D411yescharacteristic
88C2×D4×D61—24no—
89C2×D4×D61—22no—
90C2×D4×D61—42no—
91C2×D4×D61C2314yes—
92C23×Dic61—21no—
93C22×C4×D61—21no—
94C22×C4×D61—21no—
95C22×C4×D61C2311yescharacteristic
96C2×#11758201—42no—
97C2×#11758201C2314yescomplemented
98C2×D488—42no—
99C2×D488C2314yes—
100C2×#11758199—24no—
101C2×#11758199C2314yes—
102C22×#92418C2311yescharacteristic
103C22×#92418C2311yescharacteristic
104C2×C8×D61—42no—
105C2×C8×D61C2314yes—
106#14519776—22no—
107#14519776C2314yescomplemented
108#14519766—22no—
109#14519766C2314yes—
110#14519762—28no—
111#14519760—28no—
112#14519760—28no—
113#14519755—28no—
114#14519753—22no—
115#14519753C2314yes—
116#14519752—22no—
117#14519752C2314yes—
118#14519751—22no—
119#14519751—22no—
120#14519751C2314yes—
121#14519751C2314yescomplemented
122#14519749—28no—
123#14519745—28no—
124D4×Dic61—22no—
125D4×Dic61C2314yes—
126#14519739—22no—
127#14519739C2314yescomplemented
128C4×C22⋊D61D414yes—
129C4×C22⋊D61C2314yes—
130C2×C4⋊Dic61C2311yescharacteristic
131C2×C4⋊Dic61C2311yescharacteristic
132C2×#11758196—21no—
133C2×#11758196—21no—
134C2×#11758196—21no—
135C2×#11758196D411yescharacteristic
136C4⋊C4×D61—22no—
137C4⋊C4×D61C2314yes—
138C2×C22⋊Dic61—21no—
139C2×C22⋊Dic61D411yescharacteristic
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—21no—
144C2×#11758198—21no—
145C2×#11758198—21no—
146C2×#11758198—21no—
147C2×#11758198—28no—
148C2×#11758198D411yescharacteristic
149C2×C4×Dic61C2311yescharacteristic
150#14519709C2314yescomplemented
151#14519708C2314yescomplemented
152#14519708C2314yescomplemented
153#14519706C2314yescomplemented
154#14519701C2314yescomplemented
155#14519699C2314yes—
156#14519699C2314yescomplemented
157#14519698C2314yes—
158#14519697C2314yes—
159#14519697C2314yes—
160C22⋊#92418C2314yescomplemented
161#14519689C2314yes—
162#14519687C2314yescomplemented
163C2×#41×C61—22no—
164C2×#41×C61—24no—
165C2×#41×C61—42no—
166C2×#41×C61C2314yes—
167C22×Q8×C61C2311yescharacteristic
168C22×D4×C61—21no—
169C22×D4×C61C2311yescharacteristic
170C23×C4×C61—21no—
171C23×C4×C61—21no—
172C23×C4×C61C2311yescharacteristic
173C2×M16×C61—42no—
174C2×M16×C61C2314yescomplemented
175C22×C8×C61C2311yescharacteristic
176C22×C8×C61C2311yescharacteristic
177C2×C4⋊C4×C61—21no—
178C2×C4⋊C4×C61—22no—
179C2×C4⋊C4×C61C2311yescharacteristic
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C4⋊C4×C61C2314yescomplemented
182#103×C61C2314yescomplemented
183#103×C61C2314yescomplemented
184#102×C61C2314yes—
185#102×C61C2314yes—
186C24×C61—21no—
187C24×C61C2×D411yescharacteristic
188C23×D61—21no—
189C23×D61—21no—
190C23×D61—24no—
191C23×D61—44no—
192C23×D61—44no—
193C23×D61—82no—
194C23×D61C2×D411yescharacteristic
195#41×C61—28no—
196#41×C61—44no—
197#41×C61—48no—
198C2×Q8×C61—21no—
199C2×Q8×C61—22no—
200C2×Q8×C61—22no—
201C2×Q8×C61C2412yes—
202C2×D4×C61—24no—
203C2×D4×C61—21no—
204C2×D4×C61—22no—
205C2×D4×C61—44no—
206C2×D4×C61#4114yescomplemented
207C2×D4×C61C2412yes—
208C22×C4×C61—22no—
209C22×C4×C61—22no—
210C22×C4×C61—21no—
211C22×C4×C61—21no—
212C22×C4×C61—24no—
213C22×C4×C61—21no—
214C22×C4×C61—24no—
215C22×C4×C61—44no—
216C22×C4×C61—44no—
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D412yes—
219C22×C4×C61C2412yes—
220C22×C4×C61C2411yescharacteristic
221C2×C22⋊D61—24no—
222C2×C22⋊D61—24no—
223C2×C22⋊D61—24no—
224C2×C22⋊D61—24no—
225C2×C22⋊D61—44no—
226C2×C22⋊D61—44no—
227C2×C22⋊D61—82no—
228C2×C22⋊D61C2×D414yes—
229C22×Dic61—21no—
230C22×Dic61—21no—
231C22×Dic61—24no—
232C22×Dic61—82no—
233C22×Dic61C2×D411yescharacteristic
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D411yescharacteristic
236D4×D61—28no—
237D4×D61—44no—
238D4×D61—48no—
239#11758222—432no—
240C2×D244—22no—
241C2×D244—22no—
242C2×D244—22no—
243C2×D244—22no—
244C2×D244—24no—
245C2×D244—21no—
246C2×D244—21no—
247C2×D244—44no—
248C2×D244C2412yes—
249C2×D244C2412yes—
250C2×C4×D61—22no—
251C2×C4×D61—22no—
252C2×C4×D61—24no—
253C2×C4×D61—24no—
254C2×C4×D61—44no—
255C2×C4×D61—44no—
256C2×C4×D61C2×D412yes—
257C2×C4×D61C2412yes—
258C2×Dic122—24no—
259C2×Dic122—44no—
260M16×C61—44no—
261C2×C8×C61—22no—
262C2×C8×C61—22no—
263C2×C8×C61C2412yes—
264C2×C8×C61C2412yes—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—24no—
268C4⋊C4×C61C2412yes—
269C4⋊C4×C61C2412yes—
270C22⋊Dic61—24no—
271C22⋊Dic61C2×D414yes—
272#11758201—44no—
273#11758199—28no—
274#11758198—24no—
275#11758198—24no—
276#11758198—24no—
277#11758198—24no—
278#11758198—24no—
279#11758198—24no—
280#11758198—24no—
281#11758198C2×D414yes—
282C4⋊Dic61—21no—
283C4⋊Dic61—21no—
284C4⋊Dic61C2412yes—
285C4⋊Dic61C2412yes—
286#11758196—24no—
287#11758196—24no—
288#11758196—24no—
289#11758196C2×D414yes—
290C4×Dic61C2×D412yes—
291C4×Dic61C2412yes—
292C2×#92418—22no—
293C2×#92418—22no—
294C2×#92418C2412yes—
295C2×#92418C2412yes—
296D488—44no—
297C8×D61—44no—
298C23×C61—24no—
299C23×C61—22no—
300C23×C61—22no—
301C23×C61—22no—
302C23×C61—22no—
303C23×C61—42no—
304C23×C61—42no—
305C23×C61C22×D412yes—
306C23×C61C22×D411yescharacteristic
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—22no—
311C22×D61—48no—
312C22×D61—42no—
313C22×D61—42no—
314C22×D61—42no—
315C22×D61—42no—
316C22×D61—42no—
317C22×D61—42no—
318C22×D61—48no—
319C22×D61—84no—
320C22×D61—816no—
321C22×D61AGL(1,ℤ/8)14yes—
322C22×D61C22×D412yes—
323Q8×C61—22no—
324Q8×C61—22no—
325Q8×C61—42no—
326D4×C61—24no—
327D4×C61—22no—
328D4×C61—48no—
329D4×C61C2×#4114yescomplemented
330C2×C4×C61—22no—
331C2×C4×C61—24no—
332C2×C4×C61—22no—
333C2×C4×C61—22no—
334C2×C4×C61—22no—
335C2×C4×C61—22no—
336C2×C4×C61—22no—
337C2×C4×C61—48no—
338C2×C4×C61—48no—
339C2×C4×C61—42no—
340C2×C4×C61—42no—
341C2×C4×C61—42no—
342C2×C4×C61C22×D412yes—
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C2×#4112yes—
345C2×C4×C61H(5,𝔽2)12yes—
346C2×C4×C61C2511yescharacteristic
347C22⋊D61—28no—
348C22⋊D61—48no—
349C22⋊D61—48no—
350C22⋊D61—84no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—22no—
355C2×Dic61—22no—
356C2×Dic61—42no—
357C2×Dic61—42no—
358C2×Dic61—84no—
359C2×Dic61C22×D412yes—
360C2×Dic61C22×D412yes—
361C2×Dic61C22×D412yes—
362D244—22no—
363D244—22no—
364D244—22no—
365D244—22no—
366D244—48no—
367D244—42no—
368D244—42no—
369C4×D61—24no—
370C4×D61—22no—
371C4×D61—22no—
372C4×D61—48no—
373C4×D61—48no—
374Dic122—48no—
375C8×C61—22no—
376C8×C61—22no—
377#92418—22no—
378#92418—22no—
379C2×#3306—611nomaximal, Sylow
380C22×C61—24no—
381C22×C61—22no—
382C22×C61—22no—
383C22×C61—22no—
384C22×C61—48no—
385C22×C61—44no—
386C22×C61—42no—
387C22×C61—42no—
388C22×C61#54612yes—
389C22×C61C2×AGL(1,ℤ/8)12yes—
390C22×C61#57712yes—
391C22×C61C23×D411yescharacteristic
392C2×D61—22no—
393C2×D61—28no—
394C2×D61—22no—
395C2×D61—42no—
396C2×D61—42no—
397C2×D61—42no—
398C2×D61—42no—
399C2×D61—42no—
400C2×D61—42no—
401C2×D61—816no—
402C2×D61—84no—
403C2×D61—84no—
404C2×D61C2×AGL(1,ℤ/8)14yes—
405C4×C61—22no—
406C4×C61—42no—
407C4×C61—42no—
408C4×C61—42no—
409C4×C61#54612yes—
410C4×C61C22×#4111yescharacteristic
411C4×C61C2×H(5,𝔽2)11yescharacteristic
412Dic61—22no—
413Dic61—22no—
414Dic61—22no—
415Dic61—42no—
416Dic61—42no—
417C2×#547—611no—
418C2×#546—611no—
419#3306—6116no—
420C2×#489—611no—
421C2×#481—611no—
422C2×#483—611no—
423C2×#476—611no—
424C2×#469—611no—
425C2×#465—611no—
426C2×#463—611no—
427C2×#449—611no—
428C2×#447—611no—
429C2×#442—611no—
430C2×#435—611no—
431C2×#417D6111yescharacteristic, complemented
432C22×#102—611no—
433C2×C61—44no—
434C2×C61—42no—
435C2×C61#330614yescomplemented
436C2×C61C2×#54611yescharacteristic
437C2×C61C22×AGL(1,ℤ/8)11yescharacteristic
438C2×C61C2×#57711yescharacteristic
439D61—24no—
440D61—82no—
441D61—82no—
442C22×#41—1221no—
443C22×#41C2×D6111yescharacteristic
444C23×D4—611no—
445C22×SD16—611no—
446C22×D8—611no—
447C22×D8—611no—
448C22×M16C2×D6111yescharacteristic, complemented
449C23×C8—611no—
450#547—618no—
451#547—1224no—
452#546—618no—
453#546—1224no—
454C2×C4⋊Q8—611no—
455C2×#124—611no—
456C2×#123—1221no—
457C2×#123—1221no—
458C2×#123—1221no—
459C2×C22⋊Q8—611no—
460C2×C22⋊Q8—1221no—
461C2×#121—611no—
462C2×#121—611no—
463C2×#121—611no—
464C2×#121—1221no—
465C2×#120—1221no—
466C2×C4×D4—611no—
467C2×C4×D4—611no—
468C2×C4×D4—611no—
469C22×C4⋊C4—611no—
470C22×C4⋊C4C2×D6111yescharacteristic, complemented
471C22×C22⋊C4—1221no—
472#489—618no—
473#483—618no—
474#481—618no—
475#476—618no—
476#469—618no—
477#465—618no—
478#463—618no—
479#449—618no—
480#447—618no—
481#442—618no—
482#435—618no—
483C2×#106—611no—
484C2×#106—611no—
485C2×#106—611no—
486C2×C4⋊C8—611no—
487#417C2×D6118yescomplemented
488C2×#103—611no—
489C2×#103C2×D6111yescharacteristic, complemented
490C2×#103C2×D6111yescharacteristic, complemented
491C2×#102—611no—
492C2×#102—611no—
493C2×#102—611no—
494C2×#102—611no—
495C2×#102—611no—
496C2×#102—618no—
497C2×#102C2×D6111yescharacteristic
498C2×#102C2×D6111yescharacteristic
499C2×C22⋊C8—611no—
500C2×C22⋊C8—611no—
501C2×#97—611no—
502C61C2×#330611yescharacteristic, complemented, Sylow
503C25—1221no—
504C2×#41—22no—
505C2×#41—24no—
506C2×#41—42no—
507C2×#41—1228no—
508C2×#41—2448no—
509C2×#41C22×D6114yes—
510C22×Q8—1221no—
511C22×Q8C22×D6111yescharacteristic
512C22×D4—21no—
513C22×D4—611no—
514C22×D4—614no—
515C22×D4—611no—
516C22×D4—611no—
517C22×D4—1221no—
518C22×D4—1222no—
519C22×D4—1221no—
520C22×D4—1224no—
521C22×D4—1221no—
522C22×D4—1221no—
523C22×D4—2442no—
524C22×D4C22×D6111yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—611no—
528C23×C4—1221no—
529C23×C4—1221no—
530C23×C4—1221no—
531C23×C4C22×D6111yescharacteristic
532C2×SD16—614no—
533C2×SD16—2442no—
534C2×D8—614no—
535C2×D8—614no—
536C2×D8—1224no—
537C2×D8—2442no—
538C2×M16—42no—
539C2×M16C22×D6114yescomplemented
540C22×C8—611no—
541C22×C8—611no—
542C22×C8—614no—
543C22×C8—2442no—
544C22×C8C22×D6111yescharacteristic
545C22×C8C22×D6111yescharacteristic
546C4⋊Q8—614no—
547C4⋊Q8—1222no—
548#124—614no—
549#124—1222no—
550#123—1228no—
551#123—1228no—
552#123—1228no—
553C22⋊Q8—614no—
554C22⋊Q8—1228no—
555C22⋊Q8—1222no—
556#121—614no—
557#121—614no—
558#121—614no—
559#121—1228no—
560#121—1222no—
561#121—1222no—
562#121—1222no—
563#120—1228no—
564C4×D4—614no—
565C4×D4—614no—
566C4×D4—614no—
567C4×D4—614no—
568C4×D4—1222no—
569C4×D4—1222no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—611no—
573C2×C4⋊C4—611no—
574C2×C4⋊C4—611no—
575C2×C4⋊C4—614no—
576C2×C4⋊C4—1222no—
577C2×C4⋊C4—1221no—
578C2×C4⋊C4—1221no—
579C2×C4⋊C4—1221no—
580C2×C4⋊C4C22×D6111yescharacteristic
581C2×C4⋊C4C22×D6111yescharacteristic
582C2×C4⋊C4C22×D6114yescomplemented
583C2×C22⋊C4—611no—
584C2×C22⋊C4—611no—
585C2×C22⋊C4—1228no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C22⋊C4—1221no—
592C2×C22⋊C4—1221no—
593C2×C22⋊C4—1221no—
594C2×C42—611no—
595#106—614no—
596#106—614no—
597#106—614no—
598C4⋊C8—614no—
599#103—614no—
600#103C22×D6114yescomplemented
601#103C22×D6114yescomplemented
602#102—614no—
603#102—614no—
604#102—614no—
605#102—614no—
606#102—614no—
607#102C22×D6114yes—
608#102C22×D6114yes—
609C22⋊C8—614no—
610C22⋊C8—614no—
611#97—614no—
612C24—21no—
613C24—611no—
614C24—1224no—
615C24—1221no—
616C24—1221no—
617C24—4882no—
618C24—2444no—
619C24—2444no—
620C24D4×D6111yescharacteristic
621#41—28no—
622#41—44no—
623#41—48no—
624#41—24432no—
625C2×Q8—21no—
626C2×Q8—22no—
627C2×Q8—22no—
628C2×Q8—1224no—
629C2×Q8—2444no—
630C2×Q8C23×D6112yes—
631C2×D4—24no—
632C2×D4—21no—
633C2×D4—22no—
634C2×D4—44no—
635C2×D4—614no—
636C2×D4—612no—
637C2×D4—612no—
638C2×D4—1224no—
639C2×D4—1224no—
640C2×D4—1224no—
641C2×D4—1228no—
642C2×D4—1224no—
643C2×D4—1224no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1222no—
647C2×D4—1222no—
648C2×D4—1222no—
649C2×D4—1222no—
650C2×D4—4882no—
651C2×D4—2444no—
652C2×D4—2444no—
653C2×D4—2448no—
654C2×D4—2444no—
655C2×D4—2444no—
656C2×D4#1175822214yescomplemented
657C2×D4C23×D6112yes—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—24no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—24no—
665C22×C4—44no—
666C22×C4—44no—
667C22×C4—611no—
668C22×C4—611no—
669C22×C4—611no—
670C22×C4—612no—
671C22×C4—612no—
672C22×C4—1224no—
673C22×C4—1224no—
674C22×C4—1224no—
675C22×C4—1222no—
676C22×C4—1222no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—4882no—
680C22×C4—2444no—
681C22×C4—2444no—
682C22×C4D4×D6112yes—
683C22×C4D4×D6111yescharacteristic
684C22×C4C23×D6112yes—
685C22×C4C23×D6111yescharacteristic
686SD16—2444no—
687D8—1228no—
688D8—2444no—
689M16—44no—
690C2×C8—22no—
691C2×C8—22no—
692C2×C8—612no—
693C2×C8—612no—
694C2×C8—1222no—
695C2×C8—1222no—
696C2×C8—2444no—
697C2×C8C23×D6112yes—
698C2×C8C23×D6112yes—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—24no—
702C4⋊C4—614no—
703C4⋊C4—612no—
704C4⋊C4—612no—
705C4⋊C4—1224no—
706C4⋊C4—1224no—
707C4⋊C4—1224no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4C23×D6112yes—
711C4⋊C4C23×D6112yes—
712C22⋊C4—614no—
713C22⋊C4—614no—
714C22⋊C4—1224no—
715C22⋊C4—1224no—
716C22⋊C4—1224no—
717C22⋊C4—1224no—
718C22⋊C4—1224no—
719C22⋊C4—1224no—
720C22⋊C4—1224no—
721C22⋊C4—1224no—
722C42—612no—
723C42—612no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—24no—
729C23—42no—
730C23—42no—
731C23—614no—
732C23—612no—
733C23—1222no—
734C23—1222no—
735C23—1222no—
736C23—1222no—
737C23—48816no—
738C23—4884no—
739C23—2448no—
740C23—2448no—
741C23—2442no—
742C23—2442no—
743C23—2442no—
744C23—2442no—
745C23—2442no—
746C23—2442no—
747C23C2×D4×D6112yes—
748C23C2×D4×D6111yescharacteristic
749Q8—22no—
750Q8—22no—
751Q8—42no—
752Q8—2448no—
753D4—22no—
754D4—24no—
755D4—48no—
756D4—1228no—
757D4—1222no—
758D4—1222no—
759D4—1222no—
760D4—1222no—
761D4—4884no—
762D4—2448no—
763D4—2448no—
764D4—2448no—
765D4—2442no—
766D4—2442no—
767D4C2×#1175822214yescomplemented
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—48no—
776C2×C4—48no—
777C2×C4—42no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—612no—
781C2×C4—612no—
782C2×C4—612no—
783C2×C4—1222no—
784C2×C4—1222no—
785C2×C4—1222no—
786C2×C4—1222no—
787C2×C4—1222no—
788C2×C4—1224no—
789C2×C4—1222no—
790C2×C4—1222no—
791C2×C4—4884no—
792C2×C4—2448no—
793C2×C4—2448no—
794C2×C4—2442no—
795C2×C4—2442no—
796C2×C4C2×D4×D6112yes—
797C2×C4C2×D4×D6111yescharacteristic
798C2×C4C2×#1175822212yes—
799C2×C4#1451982212yes—
800C2×C4C24×D6111yescharacteristic
801C8—22no—
802C8—22no—
803C8—1222no—
804C8—1222no—
805C22—22no—
806C22—24no—
807C22—22no—
808C22—22no—
809C22—42no—
810C22—42no—
811C22—44no—
812C22—48no—
813C22—614no—
814C22—1222no—
815C22—1222no—
816C22—1228no—
817C22—48816no—
818C22—4884no—
819C22—4884no—
820C22—2442no—
821C22—2442no—
822C22—2442no—
823C22—2442no—
824C22—2442no—
825C22—2442no—
826C22#1684040212yes—
827C22AGL(1,ℤ/8)×D6112yes—
828C22#1684057112yes—
829C22C22×D4×D6111yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—1222no—
835C4—1222no—
836C4—1222no—
837C4—2442no—
838C4—2442no—
839C4#1684040212yes—
840C4C22×#1175822211yescharacteristic
841C4C2×#1451982211yescharacteristic
842C2—42no—
843C2—44no—
844C2—1224no—
845C2—4882no—
846C2—4882no—
847C2#2145778114yesdirect product factor
848C2C2×#1684040211yescharacteristic
849C2C2×AGL(1,ℤ/8)×D6111yescharacteristic
850C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#417C2
socleC23×C61C22×D4
hypercenterC2×#417D61
hypocenterC61C2×#3306
LCSG ▷ C2×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
1. C2×#16840413C2semidirect
2. C2×#16840400C2semidirect
3. #21457781C2direct (N × H)
4. C2×#16840123C2semidirect
5. C2×#16840080C2semidirect
6. C2×#16840091C2semidirect
7. C2×#16840050C2semidirect
8. C2×#16840015C2semidirect
9. C2×#16839994C2semidirect
10. C2×#16839980C2semidirect
11. C2×#16839907C2semidirect
12. C2×#16839897C2semidirect
13. C2×#16839871C2semidirect
14. C2×#16839831C2semidirect
15. C2×#102×D61C2semidirect
16. C2×C61×#417C2semidirect
19. C22×#11758201C22semidirect
24. #16840413C22semidirect
26. #16840400C22semidirect
27. C2×#14519776C22semidirect
36. C2×#14519751C22semidirect
40. C2×#14519739C22semidirect
44. #16840123C22semidirect
45. #16840091C22semidirect
46. #16840080C22semidirect
47. #16840050C22semidirect
48. #16840015C22semidirect
49. #16839994C22semidirect
50. #16839980C22semidirect
51. #16839907C22semidirect
52. #16839897C22semidirect
53. #16839871C22semidirect
54. #16839831C22semidirect
55. C2×#14519709C22semidirect
56. C2×#14519708C22semidirect
57. C2×#14519708C22semidirect
58. C2×#14519706C22semidirect
59. C2×#14519701C22semidirect
61. C2×#14519699C22semidirect
65. #102×D61C22semidirect
66. C2×C22⋊#92418C22semidirect
68. C2×#14519687C22semidirect
70. C22×M16×C61C22semidirect
71. C22×C4⋊C4×C61C22semidirect
72. C61×#417C22semidirect
73. C2×#103×C61C22semidirect
74. C2×#103×C61C22semidirect
97. C2×#11758201C23semidirect
107. #14519776C23semidirect
121. #14519751C23semidirect
127. #14519739C23semidirect
150. #14519709C23semidirect
151. #14519708C23semidirect
152. #14519708C23semidirect
153. #14519706C23semidirect
154. #14519701C23semidirect
156. #14519699C23semidirect
160. C22⋊#92418C23semidirect
162. #14519687C23semidirect
174. C2×M16×C61C23semidirect
181. C2×C4⋊C4×C61C23semidirect
182. #103×C61C23semidirect
183. #103×C61C23semidirect
206. C2×D4×C61#41semidirect
329. D4×C61C2×#41semidirect
431. C2×#417D61semidirect
435. C2×C61#3306semidirect
448. C22×M16C2×D61semidirect
470. C22×C4⋊C4C2×D61semidirect
487. #417C2×D61semidirect
489. C2×#103C2×D61semidirect
490. C2×#103C2×D61semidirect
502. C61C2×#3306semidirect
539. C2×M16C22×D61semidirect
582. C2×C4⋊C4C22×D61semidirect
600. #103C22×D61semidirect
601. #103C22×D61semidirect
656. C2×D4#11758222semidirect
767. D4C2×#11758222semidirect
847. C2#21457781direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404132
C2×#168404002
#214577812
C2×#168401232
C2×#168400802
C2×#168400912
C2×#168400502
C2×#168400152
C2×#168399942
C2×#168399802
C2×#168399072
C2×#168398972
C2×#168398712
C2×#168398312
C2×#102×D612
C2×C61×#4172
C2×#330661