Finite Group Databasebeta

← C2×#21457662 #30556373

Subgroups — C2×#21457662 #30556373

Order 15616.

2350 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840459C211yesmaximal, characteristic, complemented
2C2×#16840400C211yesmaximal, characteristic, complemented
3#21457662C2116yesmaximal, direct product factor
4C2×#16840118C211yesmaximal, characteristic, complemented
5C2×#16840096C211yesmaximal, characteristic, complemented
6C2×#16840087C211yesmaximal, characteristic, complemented
7C2×#16840064C211yesmaximal, characteristic, complemented
8C2×#16839996C211yesmaximal, characteristic, complemented
9C2×#16839988C211yesmaximal, characteristic, complemented
10C2×#16839979C211yesmaximal, characteristic, complemented
11C2×#16839894C211yesmaximal, characteristic, complemented
12C2×D8×Dic61C211yesmaximal, characteristic, complemented
13C2×#16839825C211yesmaximal, characteristic, complemented
14C2×#16839758C211yesmaximal, characteristic, complemented
15C2×#102×D61C211yesmaximal, characteristic, complemented
16C2×C61×#449C211yesmaximal, characteristic, complemented
17C22×D4×D61C2211yescharacteristic
18C22×#11758199C2211yescharacteristic
19C23×#92418C2211yescharacteristic, complemented
20C22×C8×D61C2211yescharacteristic
21#16840459—24no—
22#16840459C2218yescomplemented
23#16840400—24no—
24#16840400C2218yescomplemented
25C2×#14519770—21no—
26C2×#14519768C2211yescharacteristic, complemented
27C2×#14519766C2211yescharacteristic
28C2×#14519760—21no—
29C2×#14519758—21no—
30C2×#14519753C2211yescharacteristic
31C2×#14519751C2211yescharacteristic
32C2×#14519749—21no—
33C2×#14519748—21no—
34C2×#14519748C2211yescharacteristic
35C2×#14519745—21no—
36C2×D4×Dic61C2211yescharacteristic
37C2×D4×Dic61C2211yescharacteristic, complemented
38C2×C4×C22⋊D61C2211yescharacteristic
39C2×#14519737—21no—
40C2×#14519736C2211yescharacteristic, complemented
41C2×C4⋊C4×D61C2211yescharacteristic
42C22×#11758198—21no—
43#16840118C2218yescomplemented
44#16840096C2218yescomplemented
45#16840087C2218yescomplemented
46#16840064C2218yescomplemented
47#16839996C2218yescomplemented
48#16839988C2218yescomplemented
49#16839979C2218yescomplemented
50#16839894C2218yescomplemented
51D8×Dic61C2218yescomplemented
52#16839825C2218yescomplemented
53C2×#14519711C2211yescharacteristic, complemented
54C2×#14519710C2211yescharacteristic, complemented
55C2×#14519709C2211yescharacteristic, complemented
56C2×#14519706C2211yescharacteristic, complemented
57#16839758C2218yescomplemented
58C2×#14519701C2211yescharacteristic, complemented
59C2×#14519701C2211yescharacteristic, complemented
60C2×#14519699C2211yescharacteristic
61C2×#14519699C2211yescharacteristic
62C2×#14519698C2211yescharacteristic
63C2×#14519698C2211yescharacteristic
64C2×#14519698C2211yescharacteristic, complemented
65C2×#14519697C2211yescharacteristic
66#102×D61C2218yescomplemented
67C2×#14519689C2211yescharacteristic
68C2×C8×Dic61C2211yescharacteristic, complemented
69C22×#41×C61C2211yescharacteristic
70C22×SD16×C61C2211yescharacteristic, complemented
71C22×D8×C61C2211yescharacteristic
72C2×#121×C61C2211yescharacteristic, complemented
73C61×#449C2218yescomplemented
74C2×#103×C61C2211yescharacteristic, complemented
75C2×#102×C61C2211yescharacteristic
76C2×C22⋊C8×C61C2211yescharacteristic, complemented
77C24×D61—21no—
78C22×D244C2311yescharacteristic
79C22×C22⋊D61—21no—
80C22×C22⋊D61—21no—
81C22×C22⋊D61—21no—
82C22×C22⋊D61D411yescharacteristic
83C2×D4×D61—24no—
84C2×D4×D61—22no—
85C2×D4×D61—42no—
86C2×D4×D61C2314yes—
87C23×Dic61—21no—
88C23×Dic61—21no—
89C22×C4×D61—21no—
90C22×C4×D61C2311yescharacteristic
91C2×#11758199—42no—
92C2×#11758199C2314yes—
93C22×#92418—42no—
94C22×#92418C2311yescharacteristic
95C22×#92418C2311yescharacteristic
96C22×#92418C2314yescomplemented
97C2×C8×D61—42no—
98C2×C8×D61C2314yes—
99#14519770—28no—
100#14519768—22no—
101#14519768C2314yescomplemented
102#14519766—22no—
103#14519766C2314yes—
104#14519760—28no—
105#14519758—28no—
106#14519753—22no—
107#14519753C2314yes—
108#14519751—22no—
109#14519751C2314yes—
110#14519749—28no—
111#14519748—28no—
112#14519748—22no—
113#14519748C2314yes—
114#14519745—28no—
115D4×Dic61—22no—
116D4×Dic61—22no—
117D4×Dic61C2314yes—
118D4×Dic61C2314yescomplemented
119C4×C22⋊D61D414yes—
120C4×C22⋊D61C2314yes—
121#14519737—28no—
122#14519736—22no—
123#14519736C2314yescomplemented
124C2×C4⋊Dic61—21no—
125C2×C4⋊Dic61C2311yescharacteristic
126C2×C4⋊Dic61C2311yescharacteristic
127C2×C4⋊Dic61C2311yescharacteristic
128C2×#11758196—21no—
129C2×#11758196—21no—
130C2×#11758196—21no—
131C2×#11758196D411yescharacteristic
132C4⋊C4×D61—22no—
133C4⋊C4×D61C2314yes—
134C2×C22⋊Dic61—21no—
135C2×C22⋊Dic61—21no—
136C2×C22⋊Dic61—21no—
137C2×C22⋊Dic61—21no—
138C2×C22⋊Dic61D411yescharacteristic
139C2×#11758198—21no—
140C2×#11758198—21no—
141C2×#11758198—21no—
142C2×#11758198—21no—
143C2×#11758198—28no—
144C2×#11758198D411yescharacteristic
145C2×C4×Dic61—21no—
146C2×C4×Dic61C2311yescharacteristic
147#14519711C2314yescomplemented
148#14519710C2314yescomplemented
149#14519709C2314yescomplemented
150#14519706C2314yescomplemented
151#14519701C2314yescomplemented
152#14519701C2314yescomplemented
153#14519699C2314yes—
154#14519699C2314yes—
155#14519698C2314yes—
156#14519698C2314yes—
157#14519698C2314yescomplemented
158#14519697C2314yes—
159#14519689C2314yes—
160C8×Dic61C2314yescomplemented
161C2×#41×C61—22no—
162C2×#41×C61—24no—
163C2×#41×C61—42no—
164C2×#41×C61C2314yes—
165C22×Q8×C61C2311yescharacteristic
166C22×D4×C61—21no—
167C22×D4×C61—21no—
168C22×D4×C61C2311yescharacteristic
169C22×D4×C61C2311yescharacteristic
170C23×C4×C61—21no—
171C23×C4×C61C2311yescharacteristic
172C2×SD16×C61—42no—
173C2×SD16×C61C2314yescomplemented
174C2×D8×C61—24no—
175C2×D8×C61C2314yes—
176C22×C8×C61C2311yescharacteristic
177C22×C8×C61C2311yescharacteristic
178#121×C61—22no—
179#121×C61C2314yescomplemented
180C2×C4⋊C4×C61C2311yescharacteristic
181C2×C22⋊C4×C61—21no—
182#103×C61C2314yescomplemented
183#102×C61C2314yes—
184C22⋊C8×C61C2314yescomplemented
185C24×C61—21no—
186C24×C61—21no—
187C24×C61C2×D411yescharacteristic
188C23×D61—21no—
189C23×D61—24no—
190C23×D61—44no—
191C23×D61—44no—
192C23×D61—82no—
193C23×D61C2×D411yescharacteristic
194#41×C61—28no—
195#41×C61—44no—
196#41×C61—48no—
197C2×Q8×C61—21no—
198C2×Q8×C61—22no—
199C2×Q8×C61—22no—
200C2×Q8×C61C2412yes—
201C2×D4×C61—24no—
202C2×D4×C61—24no—
203C2×D4×C61—21no—
204C2×D4×C61—21no—
205C2×D4×C61—22no—
206C2×D4×C61—22no—
207C2×D4×C61—22no—
208C2×D4×C61—44no—
209C2×D4×C61—82no—
210C2×D4×C61#4114yes—
211C2×D4×C61C2412yes—
212C2×D4×C61C2412yes—
213C22×C4×C61—22no—
214C22×C4×C61—22no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—24no—
218C22×C4×C61—44no—
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D412yes—
221C22×C4×C61C2412yes—
222C22×C4×C61C2411yescharacteristic
223C2×C22⋊D61—24no—
224C2×C22⋊D61—24no—
225C2×C22⋊D61—24no—
226C2×C22⋊D61—24no—
227C2×C22⋊D61—44no—
228C2×C22⋊D61—44no—
229C2×C22⋊D61—82no—
230C2×C22⋊D61C2×D414yes—
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—24no—
235C22×Dic61—24no—
236C22×Dic61—82no—
237C22×Dic61—82no—
238C22×Dic61C2×D411yescharacteristic
239C22×Dic61C2×D411yescharacteristic
240C22×Dic61C2×D411yescharacteristic
241D4×D61—28no—
242D4×D61—44no—
243D4×D61—48no—
244C2×D244—22no—
245C2×D244—22no—
246C2×D244—21no—
247C2×D244C2412yes—
248C2×C4×D61—22no—
249C2×C4×D61—22no—
250C2×C4×D61—24no—
251C2×C4×D61—82no—
252C2×C4×D61C2×D412yes—
253C2×C4×D61C2412yes—
254SD16×C61—44no—
255D8×C61—28no—
256C2×C8×C61—22no—
257C2×C8×C61—22no—
258C2×C8×C61C2412yes—
259C2×C8×C61C2412yes—
260C4⋊C4×C61—21no—
261C4⋊C4×C61C2412yes—
262C22⋊C4×C61—24no—
263C22⋊Dic61—24no—
264C22⋊Dic61—24no—
265C22⋊Dic61—24no—
266C22⋊Dic61—24no—
267C22⋊Dic61C2×D414yes—
268#11758199—44no—
269#11758198—24no—
270#11758198—24no—
271#11758198—24no—
272#11758198—24no—
273#11758198C2×D414yes—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—24no—
278C4⋊Dic61C2412yes—
279C4⋊Dic61C2412yes—
280C4⋊Dic61C2412yes—
281#11758196—24no—
282#11758196—24no—
283#11758196—24no—
284#11758196C2×D414yes—
285C4×Dic61—24no—
286C4×Dic61C2×D412yes—
287C4×Dic61C2412yes—
288C2×#92418—22no—
289C2×#92418—22no—
290C2×#92418—44no—
291C2×#92418C2412yes—
292C2×#92418C2412yes—
293C8×D61—44no—
294C23×C61—24no—
295C23×C61—22no—
296C23×C61—22no—
297C23×C61—22no—
298C23×C61—22no—
299C23×C61—22no—
300C23×C61—42no—
301C23×C61—42no—
302C23×C61—42no—
303C23×C61—42no—
304C23×C61—42no—
305C23×C61C22×D412yes—
306C23×C61C22×D411yescharacteristic
307C22×D61—22no—
308C22×D61—22no—
309C22×D61—22no—
310C22×D61—48no—
311C22×D61—42no—
312C22×D61—42no—
313C22×D61—42no—
314C22×D61—48no—
315C22×D61—84no—
316C22×D61—816no—
317C22×D61#13514yes—
318C22×D61C22×D412yes—
319Q8×C61—22no—
320Q8×C61—22no—
321Q8×C61—42no—
322D4×C61—24no—
323D4×C61—22no—
324D4×C61—22no—
325D4×C61—22no—
326D4×C61—48no—
327D4×C61—42no—
328D4×C61—84no—
329D4×C61C2×#4114yes—
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—48no—
337C2×C4×C61—42no—
338C2×C4×C61—42no—
339C2×C4×C61C22×D412yes—
340C2×C4×C61C22×D411yescharacteristic
341C2×C4×C61C2×#4112yes—
342C2×C4×C61H(5,𝔽2)12yes—
343C2×C4×C61C2511yescharacteristic
344C22⋊D61—28no—
345C22⋊D61—48no—
346C22⋊D61—48no—
347C22⋊D61—84no—
348C2×Dic61—22no—
349C2×Dic61—22no—
350C2×Dic61—22no—
351C2×Dic61—22no—
352C2×Dic61—22no—
353C2×Dic61—22no—
354C2×Dic61—42no—
355C2×Dic61—42no—
356C2×Dic61—42no—
357C2×Dic61—84no—
358C2×Dic61—84no—
359C2×Dic61C22×D412yes—
360C2×Dic61C22×D412yes—
361C2×Dic61C22×D412yes—
362D244—22no—
363D244—22no—
364D244—42no—
365C4×D61—24no—
366C4×D61—22no—
367C4×D61—22no—
368C4×D61—84no—
369C8×C61—22no—
370C8×C61—22no—
371#92418—22no—
372#92418—22no—
373C2×#3297—611nomaximal, Sylow
374C22×C61—24no—
375C22×C61—22no—
376C22×C61—22no—
377C22×C61—22no—
378C22×C61—48no—
379C22×C61—44no—
380C22×C61—42no—
381C22×C61—42no—
382C22×C61—42no—
383C22×C61—42no—
384C22×C61—42no—
385C22×C61—84no—
386C22×C61#54612yes—
387C22×C61C2×#13512yes—
388C22×C61#57612yes—
389C22×C61C23×D411yescharacteristic
390C2×D61—22no—
391C2×D61—28no—
392C2×D61—22no—
393C2×D61—42no—
394C2×D61—42no—
395C2×D61—42no—
396C2×D61—816no—
397C2×D61—84no—
398C2×D61C2×#13514yes—
399C4×C61—22no—
400C4×C61—42no—
401C4×C61—42no—
402C4×C61#54612yes—
403C4×C61C22×#4111yescharacteristic
404C4×C61C2×H(5,𝔽2)11yescharacteristic
405Dic61—22no—
406Dic61—22no—
407Dic61—22no—
408Dic61—42no—
409Dic61—42no—
410Dic61—42no—
411C2×#553—611no—
412C2×#546—611no—
413#3297—6116no—
414C2×#488—611no—
415C2×#484—611no—
416C2×#482—611no—
417C2×#478—611no—
418C2×#466—611no—
419C2×#465—611no—
420C2×#463—611no—
421C2×#449D6111yescharacteristic, complemented
422C2×#447—611no—
423C2×C4×D8—611no—
424C2×C8×D4—611no—
425C2×#416—611no—
426C22×#102—611no—
427C2×C61—44no—
428C2×C61—42no—
429C2×C61—82no—
430C2×C61#329714yescomplemented
431C2×C61C2×#54611yescharacteristic
432C2×C61C22×#13511yescharacteristic
433C2×C61C2×#57611yescharacteristic
434D61—24no—
435D61—82no—
436C22×#41C2×D6111yescharacteristic
437C23×D4—611no—
438C22×SD16C2×D6111yescharacteristic, complemented
439C22×D8—611no—
440C22×D8C2×D6111yescharacteristic
441C23×C8—611no—
442C23×C8—611no—
443#553—618no—
444#553—1224no—
445#546—618no—
446#546—1224no—
447C2×#126—1221no—
448C2×#125—611no—
449C2×#124—611no—
450C2×#123—1221no—
451C2×#123—1221no—
452C2×C22⋊Q8—611no—
453C2×#121—611no—
454C2×#121—611no—
455C2×#121—1221no—
456C2×#121—1221no—
457C2×#121C2×D6111yescharacteristic, complemented
458C2×#120—1221no—
459C2×C4×D4—611no—
460C2×C4×D4—611no—
461C2×C4×D4—611no—
462C2×C4×D4—1221no—
463C2×#117—611no—
464C22×C4⋊C4—611no—
465C22×C22⋊C4—1221no—
466#488—618no—
467#484—618no—
468#482—618no—
469#478—618no—
470#466—618no—
471#465—618no—
472#463—618no—
473#449C2×D6118yescomplemented
474#447—618no—
475C4×D8—618no—
476C8×D4—618no—
477C2×#107—611no—
478C2×#107—611no—
479C2×#106—611no—
480C2×C4⋊C8—611no—
481#416—618no—
482C2×#103—611no—
483C2×#103—611no—
484C2×#103C2×D6111yescharacteristic, complemented
485C2×#102—611no—
486C2×#102—611no—
487C2×#102—611no—
488C2×#102—611no—
489C2×#102—611no—
490C2×#102—611no—
491C2×#102—618no—
492C2×#102C2×D6111yescharacteristic
493C2×C22⋊C8—611no—
494C2×C22⋊C8C2×D6111yescharacteristic, complemented
495C2×C4×C8—611no—
496C61C2×#329711yescharacteristic, complemented, Sylow
497C25—1221no—
498C2×#41—22no—
499C2×#41—24no—
500C2×#41—42no—
501C2×#41C22×D6114yes—
502C22×Q8C22×D6111yescharacteristic
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—611no—
506C22×D4—614no—
507C22×D4—611no—
508C22×D4—1222no—
509C22×D4—1221no—
510C22×D4—1224no—
511C22×D4—1221no—
512C22×D4—1221no—
513C22×D4—2442no—
514C22×D4C22×D6111yescharacteristic
515C22×D4C22×D6111yescharacteristic
516C23×C4—21no—
517C23×C4—611no—
518C23×C4—1221no—
519C23×C4—1221no—
520C23×C4—1221no—
521C23×C4C22×D6111yescharacteristic
522C2×SD16—42no—
523C2×SD16C22×D6114yescomplemented
524C2×D8—24no—
525C2×D8—614no—
526C2×D8—2442no—
527C2×D8C22×D6114yes—
528C22×C8—611no—
529C22×C8—611no—
530C22×C8—614no—
531C22×C8—614no—
532C22×C8—2442no—
533C22×C8—2442no—
534C22×C8C22×D6111yescharacteristic
535C22×C8C22×D6111yescharacteristic
536#126—1228no—
537#125—614no—
538#125—1222no—
539#124—614no—
540#124—1222no—
541#123—1228no—
542#123—1228no—
543C22⋊Q8—614no—
544C22⋊Q8—1222no—
545#121—22no—
546#121—614no—
547#121—614no—
548#121—1228no—
549#121—1222no—
550#121—1228no—
551#121—1222no—
552#121C22×D6114yescomplemented
553#120—1228no—
554C4×D4—614no—
555C4×D4—614no—
556C4×D4—614no—
557C4×D4—614no—
558C4×D4—1222no—
559C4×D4—1222no—
560C4×D4—1228no—
561#117—614no—
562#117—1222no—
563C2×C4⋊C4—611no—
564C2×C4⋊C4—611no—
565C2×C4⋊C4—611no—
566C2×C4⋊C4—611no—
567C2×C4⋊C4—614no—
568C2×C4⋊C4—1222no—
569C2×C4⋊C4—1221no—
570C2×C4⋊C4—1221no—
571C2×C4⋊C4—1221no—
572C2×C4⋊C4—1221no—
573C2×C4⋊C4C22×D6111yescharacteristic
574C2×C22⋊C4—21no—
575C2×C22⋊C4—611no—
576C2×C22⋊C4—611no—
577C2×C22⋊C4—1228no—
578C2×C22⋊C4—1221no—
579C2×C22⋊C4—1221no—
580C2×C22⋊C4—1221no—
581C2×C22⋊C4—1221no—
582C2×C22⋊C4—1221no—
583C2×C22⋊C4—1221no—
584C2×C22⋊C4—1221no—
585C2×C22⋊C4—1221no—
586C2×C42—611no—
587C2×C42—1221no—
588#107—614no—
589#107—614no—
590#106—614no—
591C4⋊C8—614no—
592#103—614no—
593#103—614no—
594#103C22×D6114yescomplemented
595#102—614no—
596#102—614no—
597#102—614no—
598#102—614no—
599#102—614no—
600#102—614no—
601#102C22×D6114yes—
602C22⋊C8—614no—
603C22⋊C8C22×D6114yescomplemented
604C4×C8—614no—
605C24—21no—
606C24—21no—
607C24—611no—
608C24—1224no—
609C24—1221no—
610C24—4882no—
611C24—2444no—
612C24—2444no—
613C24D4×D6111yescharacteristic
614#41—28no—
615#41—44no—
616#41—48no—
617C2×Q8—21no—
618C2×Q8—22no—
619C2×Q8—22no—
620C2×Q8C23×D6112yes—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—614no—
631C2×D4—612no—
632C2×D4—1224no—
633C2×D4—1224no—
634C2×D4—1228no—
635C2×D4—1224no—
636C2×D4—1224no—
637C2×D4—1221no—
638C2×D4—1222no—
639C2×D4—1222no—
640C2×D4—4882no—
641C2×D4—2444no—
642C2×D4—2448no—
643C2×D4—2444no—
644C2×D4—2444no—
645C2×D4#1175822414yes—
646C2×D4C23×D6112yes—
647C2×D4C23×D6112yes—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—24no—
653C22×C4—44no—
654C22×C4—611no—
655C22×C4—611no—
656C22×C4—611no—
657C22×C4—612no—
658C22×C4—612no—
659C22×C4—1224no—
660C22×C4—1224no—
661C22×C4—1224no—
662C22×C4—1222no—
663C22×C4—1222no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4—4882no—
668C22×C4—4882no—
669C22×C4—4882no—
670C22×C4D4×D6112yes—
671C22×C4D4×D6111yescharacteristic
672C22×C4C23×D6112yes—
673C22×C4C23×D6111yescharacteristic
674SD16—44no—
675D8—28no—
676D8—2444no—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—612no—
680C2×C8—612no—
681C2×C8—1222no—
682C2×C8—1222no—
683C2×C8—2444no—
684C2×C8—2444no—
685C2×C8C23×D6112yes—
686C2×C8C23×D6112yes—
687C4⋊C4—21no—
688C4⋊C4—614no—
689C4⋊C4—612no—
690C4⋊C4—612no—
691C4⋊C4—612no—
692C4⋊C4—1224no—
693C4⋊C4—1224no—
694C4⋊C4—1224no—
695C4⋊C4—1224no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4C23×D6112yes—
700C22⋊C4—24no—
701C22⋊C4—614no—
702C22⋊C4—614no—
703C22⋊C4—1224no—
704C22⋊C4—1224no—
705C22⋊C4—1224no—
706C22⋊C4—1224no—
707C22⋊C4—1224no—
708C22⋊C4—1224no—
709C22⋊C4—1224no—
710C22⋊C4—1224no—
711C42—612no—
712C42—612no—
713C42—1224no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—24no—
719C23—22no—
720C23—42no—
721C23—42no—
722C23—42no—
723C23—42no—
724C23—42no—
725C23—614no—
726C23—612no—
727C23—1222no—
728C23—1222no—
729C23—1222no—
730C23—48816no—
731C23—4884no—
732C23—2448no—
733C23—2448no—
734C23—2442no—
735C23—2442no—
736C23—2442no—
737C23C2×D4×D6112yes—
738C23C2×D4×D6111yescharacteristic
739Q8—22no—
740Q8—22no—
741Q8—42no—
742D4—22no—
743D4—22no—
744D4—22no—
745D4—24no—
746D4—48no—
747D4—42no—
748D4—84no—
749D4—1228no—
750D4—1222no—
751D4—1222no—
752D4—4884no—
753D4—2448no—
754D4—2448no—
755D4—2442no—
756D4C2×#1175822414yes—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—48no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—612no—
767C2×C4—612no—
768C2×C4—612no—
769C2×C4—1222no—
770C2×C4—1222no—
771C2×C4—1222no—
772C2×C4—1222no—
773C2×C4—1222no—
774C2×C4—1224no—
775C2×C4—1222no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—4884no—
779C2×C4—4884no—
780C2×C4—4884no—
781C2×C4—2442no—
782C2×C4—2442no—
783C2×C4—2442no—
784C2×C4C2×D4×D6112yes—
785C2×C4C2×D4×D6111yescharacteristic
786C2×C4C2×#1175822412yes—
787C2×C4#1451982212yes—
788C2×C4C24×D6111yescharacteristic
789C8—22no—
790C8—22no—
791C8—1222no—
792C8—1222no—
793C22—22no—
794C22—24no—
795C22—22no—
796C22—22no—
797C22—42no—
798C22—42no—
799C22—44no—
800C22—48no—
801C22—42no—
802C22—42no—
803C22—42no—
804C22—84no—
805C22—614no—
806C22—1222no—
807C22—1222no—
808C22—1228no—
809C22—48816no—
810C22—4884no—
811C22—2442no—
812C22—2442no—
813C22—2442no—
814C22#1684039912yes—
815C22#135×D6112yes—
816C22#1684056612yes—
817C22C22×D4×D6111yescharacteristic
818C4—22no—
819C4—42no—
820C4—42no—
821C4—1222no—
822C4—1222no—
823C4—1222no—
824C4—2442no—
825C4—2442no—
826C4—2442no—
827C4#1684039912yes—
828C4C22×#1175822411yescharacteristic
829C4C2×#1451982211yescharacteristic
830C2—42no—
831C2—44no—
832C2—82no—
833C2—1224no—
834C2—4882no—
835C2#2145766214yesdirect product factor
836C2C2×#1684039911yescharacteristic
837C2C2×#135×D6111yescharacteristic
838C2C2×#1684056611yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#449C2
socleC23×C61C22×D4
hypercenterC2×#449D61
hypocenterC61C2×#3297
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#16840459C2semidirect
2. C2×#16840400C2semidirect
3. #21457662C2direct (N × H)
4. C2×#16840118C2semidirect
5. C2×#16840096C2semidirect
6. C2×#16840087C2semidirect
7. C2×#16840064C2semidirect
8. C2×#16839996C2semidirect
9. C2×#16839988C2semidirect
10. C2×#16839979C2semidirect
11. C2×#16839894C2semidirect
12. C2×D8×Dic61C2semidirect
13. C2×#16839825C2semidirect
14. C2×#16839758C2semidirect
15. C2×#102×D61C2semidirect
16. C2×C61×#449C2semidirect
19. C23×#92418C22semidirect
22. #16840459C22semidirect
24. #16840400C22semidirect
26. C2×#14519768C22semidirect
37. C2×D4×Dic61C22semidirect
40. C2×#14519736C22semidirect
43. #16840118C22semidirect
44. #16840096C22semidirect
45. #16840087C22semidirect
46. #16840064C22semidirect
47. #16839996C22semidirect
48. #16839988C22semidirect
49. #16839979C22semidirect
50. #16839894C22semidirect
51. D8×Dic61C22semidirect
52. #16839825C22semidirect
53. C2×#14519711C22semidirect
54. C2×#14519710C22semidirect
55. C2×#14519709C22semidirect
56. C2×#14519706C22semidirect
57. #16839758C22semidirect
58. C2×#14519701C22semidirect
59. C2×#14519701C22semidirect
64. C2×#14519698C22semidirect
66. #102×D61C22semidirect
68. C2×C8×Dic61C22semidirect
70. C22×SD16×C61C22semidirect
72. C2×#121×C61C22semidirect
73. C61×#449C22semidirect
74. C2×#103×C61C22semidirect
76. C2×C22⋊C8×C61C22semidirect
96. C22×#92418C23semidirect
101. #14519768C23semidirect
118. D4×Dic61C23semidirect
123. #14519736C23semidirect
147. #14519711C23semidirect
148. #14519710C23semidirect
149. #14519709C23semidirect
150. #14519706C23semidirect
151. #14519701C23semidirect
152. #14519701C23semidirect
157. #14519698C23semidirect
160. C8×Dic61C23semidirect
173. C2×SD16×C61C23semidirect
179. #121×C61C23semidirect
182. #103×C61C23semidirect
184. C22⋊C8×C61C23semidirect
421. C2×#449D61semidirect
430. C2×C61#3297semidirect
438. C22×SD16C2×D61semidirect
457. C2×#121C2×D61semidirect
473. #449C2×D61semidirect
484. C2×#103C2×D61semidirect
494. C2×C22⋊C8C2×D61semidirect
496. C61C2×#3297semidirect
523. C2×SD16C22×D61semidirect
552. #121C22×D61semidirect
594. #103C22×D61semidirect
603. C22⋊C8C22×D61semidirect
835. C2#21457662direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168404592
C2×#168404002
#214576622
C2×#168401182
C2×#168400962
C2×#168400872
C2×#168400642
C2×#168399962
C2×#168399882
C2×#168399792
C2×#168398942
C2×D8×Dic612
C2×#168398252
C2×#168397582
C2×#102×D612
C2×C61×#4492
C2×#329761