Finite Group Databasebeta

← C2×#21455361 #30546941

Subgroups — C2×#21455361 #30546941

Order 15616.

2934 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519804C211yesmaximal, characteristic, complemented
2C22×#14519800C211yesmaximal, characteristic, complemented
3C2×#16840330C211yesmaximal, characteristic, complemented
4C2×#16840244C211yesmaximal, characteristic, complemented
5#21455361C2116yesmaximal, direct product factor
6C2×#16839986C211yesmaximal, characteristic, complemented
7C2×#16839962C211yesmaximal, characteristic, complemented
8C2×#16839960C211yesmaximal, characteristic, complemented
9C2×#16839980C211yesmaximal, characteristic, complemented
10C2×#16839974C211yesmaximal, characteristic, complemented
11C2×#16839958C211yesmaximal, characteristic, complemented
12C2×#16839956C211yesmaximal, characteristic, complemented
13C2×#16839787C211yesmaximal, characteristic, complemented
14C2×#16839762C211yesmaximal, characteristic, complemented
15C2×#102×D61C211yesmaximal, characteristic, complemented
16C2×C61×#464C211yesmaximal, characteristic, complemented
17C22×#11758226C2211yescharacteristic
18C22×#11758226C2211yescharacteristic
19C22×D4×D61C2211yescharacteristic
20C2×#14519804—28no—
21C2×#14519804C2218yescomplemented
22C2×#14519800—28no—
23C2×#14519800C2218yescomplemented
24C22×#11758201C2211yescharacteristic
25C22×#11758201C2211yescharacteristic, complemented
26C22×#11758201C2211yescharacteristic, complemented
27C22×D488C2211yescharacteristic
28C22×D488C2211yescharacteristic, complemented
29C22×#11758199C2211yescharacteristic
30C22×#11758189C2211yescharacteristic
31C22×C8×D61C2211yescharacteristic
32#16840330—24no—
33#16840330C2218yescomplemented
34C2×#14519774C2211yescharacteristic
35C2×#14519773C2211yescharacteristic
36C2×#14519766C2211yescharacteristic
37C2×#14519750—21no—
38C2×#14519750—21no—
39C2×#14519747—21no—
40C2×#14519747—21no—
41#16840244—24no—
42#16840244C2218yescomplemented
43C2×Q8×Dic61C2211yescharacteristic, complemented
44C2×C4×D244—21no—
45C2×C4×D244C2211yescharacteristic, complemented
46C2×#14519739—21no—
47C2×#14519739C2211yescharacteristic, complemented
48C2×#14519734—21no—
49C2×#14519734C2211yescharacteristic
50C2×C4⋊C4×D61—21no—
51C2×C4⋊C4×D61C2211yescharacteristic
52#16839986C2218yescomplemented
53#16839980C2218yescomplemented
54#16839974C2218yescomplemented
55#16839962C2218yescomplemented
56#16839960C2218yescomplemented
57#16839958C2218yescomplemented
58#16839956C2218yescomplemented
59#16839787C2218yescomplemented
60C2×C4⋊#92418C2211yescharacteristic, complemented
61C2×#14519706C2211yescharacteristic, complemented
62C2×#14519706C2211yescharacteristic, complemented
63#16839762C2218yescomplemented
64C2×#14519701C2211yescharacteristic, complemented
65C2×#14519699C2211yescharacteristic
66C2×#14519699C2211yescharacteristic, complemented
67C2×#14519698C2211yescharacteristic
68C2×#14519697C2211yescharacteristic
69C2×#14519697C2211yescharacteristic, complemented
70#102×D61C2218yescomplemented
71C22×Q16×C61C2211yescharacteristic, complemented
72C22×SD16×C61C2211yescharacteristic
73C2×#124×C61C2211yescharacteristic
74C2×C4×Q8×C61C2211yescharacteristic, complemented
75C61×#464C2218yescomplemented
76C2×C4⋊C8×C61C2211yescharacteristic, complemented
77C2×#103×C61C2211yescharacteristic, complemented
78C2×#102×C61C2211yescharacteristic
79C24×D61—21no—
80C2×#11758226—22no—
81C2×#11758226—22no—
82C2×#11758226—24no—
83C2×#11758226—24no—
84C2×#11758226—24no—
85C2×#11758226D418yescomplemented
86C2×#11758226C2314yes—
87C2×#11758226C2314yes—
88C22×D244—21no—
89C22×D244—21no—
90C22×D244—21no—
91C22×D244—21no—
92C22×D244C2311yescharacteristic
93C22×D244C2311yescharacteristic
94C22×D244C2311yescharacteristic
95C22×C22⋊D61—21no—
96C22×C22⋊D61—21no—
97C22×C22⋊D61—21no—
98C2×D4×D61—24no—
99C2×D4×D61—22no—
100C2×D4×D61—24no—
101C2×D4×D61C2314yes—
102C22×C4×D61—21no—
103C22×C4×D61—21no—
104C22×C4×D61—21no—
105C22×C4×D61—21no—
106C22×C4×D61—21no—
107C22×C4×D61C2311yescharacteristic
108#14519804—232no—
109#14519800—232no—
110C2×#11758201—24no—
111C2×#11758201—24no—
112C2×#11758201—24no—
113C2×#11758201C2314yes—
114C2×#11758201C2314yescomplemented
115C2×#11758201C2314yescomplemented
116C2×D488—24no—
117C2×D488—24no—
118C2×D488C2314yes—
119C2×D488C2314yescomplemented
120C2×#11758199—24no—
121C2×#11758199C2314yes—
122C2×#11758189—24no—
123C2×#11758189C2314yes—
124C22×#92418C2311yescharacteristic
125C22×#92418C2311yescharacteristic
126C2×C8×D61—24no—
127C2×C8×D61C2314yes—
128#14519774—22no—
129#14519774C2314yes—
130#14519773—22no—
131#14519773C2314yes—
132#14519766—22no—
133#14519766C2314yes—
134#14519750—28no—
135#14519750—28no—
136#14519747—28no—
137#14519747—28no—
138Q8×Dic61—22no—
139Q8×Dic61C2314yescomplemented
140C4×D244—22no—
141C4×D244—28no—
142C4×D244C2314yescomplemented
143#14519739—28no—
144#14519739—22no—
145#14519739C2314yescomplemented
146#14519734—28no—
147#14519734D414yes—
148#14519734C2314yes—
149C2×C4⋊Dic61—21no—
150C2×C4⋊Dic61C2311yescharacteristic
151C2×#11758196—21no—
152C2×#11758196D411yescharacteristic
153C2×#11758196D411yescharacteristic
154C4⋊C4×D61—22no—
155C4⋊C4×D61—28no—
156C4⋊C4×D61C2314yes—
157C2×#11758198—21no—
158C2×#11758198—21no—
159C2×#11758198—21no—
160C2×#11758198—21no—
161C2×#11758198D411yescharacteristic
162C2×#11758198D411yescharacteristic
163C2×C4×Dic61—21no—
164C2×C4×Dic61C2311yescharacteristic
165C4⋊#92418C2314yescomplemented
166#14519706C2314yescomplemented
167#14519706C2314yescomplemented
168#14519701C2314yescomplemented
169#14519699C2314yes—
170#14519699C2314yescomplemented
171#14519698C2314yes—
172#14519697C2314yes—
173#14519697C2314yescomplemented
174C22×Q8×C61C2311yescharacteristic
175C22×Q8×C61C2311yescharacteristic
176C22×D4×C61C2311yescharacteristic
177C2×Q16×C61—24no—
178C2×Q16×C61C2314yescomplemented
179C2×SD16×C61—24no—
180C2×SD16×C61C2314yes—
181C22×C8×C61C2311yescharacteristic
182C22×C8×C61C2311yescharacteristic
183#124×C61—22no—
184#124×C61C2314yes—
185C4×Q8×C61—22no—
186C4×Q8×C61C2314yescomplemented
187C2×C4⋊C4×C61—21no—
188C2×C4⋊C4×C61C2311yescharacteristic
189C2×C22⋊C4×C61—21no—
190C2×C22⋊C4×C61—21no—
191C2×C42×C61—21no—
192C2×C42×C61C2311yescharacteristic
193C4⋊C8×C61C2314yescomplemented
194#103×C61C2314yescomplemented
195#102×C61C2314yes—
196C24×C61—21no—
197C23×D61—21no—
198C23×D61—21no—
199C23×D61—21no—
200C23×D61—24no—
201C23×D61—44no—
202C23×D61—82no—
203C23×D61—82no—
204C23×D61C2×D411yescharacteristic
205C2×Q8×C61—21no—
206C2×Q8×C61—21no—
207C2×Q8×C61—22no—
208C2×Q8×C61—22no—
209C2×Q8×C61—22no—
210C2×Q8×C61C2×D414yes—
211C2×Q8×C61C2412yes—
212C2×Q8×C61C2412yes—
213C2×D4×C61—22no—
214C2×D4×C61—21no—
215C2×D4×C61—22no—
216C2×D4×C61C2412yes—
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2411yescharacteristic
223C2×C22⋊D61—24no—
224C2×C22⋊D61—24no—
225C2×C22⋊D61—24no—
226C2×C22⋊D61—44no—
227C2×C22⋊D61—82no—
228C2×C22⋊D61—82no—
229C22×Dic61—21no—
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233#11758226—216no—
234#11758226—28no—
235#11758226—28no—
236#11758226—28no—
237#11758226—48no—
238#11758226C2×D4116yescomplemented
239D4×D61—28no—
240D4×D61—28no—
241D4×D61—48no—
242C2×D244—28no—
243C2×D244—24no—
244C2×D244—21no—
245C2×D244—22no—
246C2×D244—22no—
247C2×D244—22no—
248C2×D244—22no—
249C2×D244—22no—
250C2×D244—24no—
251C2×D244—21no—
252C2×D244—21no—
253C2×D244—24no—
254C2×D244—24no—
255C2×D244—44no—
256C2×D244—82no—
257C2×D244—82no—
258C2×D244C2×D414yes—
259C2×D244C2412yes—
260C2×D244C2412yes—
261C2×D244C2412yes—
262C2×C4×D61—28no—
263C2×C4×D61—24no—
264C2×C4×D61—24no—
265C2×C4×D61—24no—
266C2×C4×D61—24no—
267C2×C4×D61—24no—
268C2×C4×D61—44no—
269C2×C4×D61—82no—
270C2×C4×D61—82no—
271C2×C4×D61—82no—
272C2×C4×D61C2×D412yes—
273C2×C4×D61C2×D414yes—
274C2×C4×D61#4114yes—
275C2×C4×D61C2412yes—
276Q16×C61—28no—
277SD16×C61—28no—
278C2×C8×C61—22no—
279C2×C8×C61—22no—
280C2×C8×C61C2412yes—
281C2×C8×C61C2412yes—
282C4⋊C4×C61—24no—
283C4⋊C4×C61—21no—
284C4⋊C4×C61C2412yes—
285C22⋊C4×C61—24no—
286C22⋊C4×C61—24no—
287C42×C61—24no—
288C42×C61C2×D412yes—
289C42×C61C2412yes—
290#11758201—28no—
291#11758201—28no—
292#11758201—28no—
293#11758199—28no—
294#11758198—24no—
295#11758198—24no—
296#11758198—24no—
297#11758198—24no—
298#11758198C2×D414yes—
299#11758198C2×D414yes—
300C4⋊Dic61—21no—
301C4⋊Dic61—24no—
302C4⋊Dic61C2412yes—
303#11758196—24no—
304#11758196C2×D414yes—
305#11758196C2×D414yes—
306C4×Dic61—24no—
307C4×Dic61C2×D412yes—
308C4×Dic61C2412yes—
309C2×#92418—22no—
310C2×#92418—22no—
311C2×#92418C2412yes—
312C2×#92418C2412yes—
313D488—28no—
314D488—28no—
315#11758189—28no—
316C8×D61—28no—
317C23×C61—22no—
318C23×C61—42no—
319C23×C61—42no—
320C23×C61—42no—
321C23×C61C22×D411yescharacteristic
322C22×D61—22no—
323C22×D61—22no—
324C22×D61—24no—
325C22×D61—22no—
326C22×D61—22no—
327C22×D61—22no—
328C22×D61—42no—
329C22×D61—42no—
330C22×D61—42no—
331C22×D61—42no—
332C22×D61—42no—
333C22×D61—42no—
334C22×D61—42no—
335C22×D61—42no—
336C22×D61—48no—
337C22×D61—84no—
338C22×D61—84no—
339C22×D61—816no—
340C22×D61#12114yes—
341C22×D61C22×D412yes—
342Q8×C61—24no—
343Q8×C61—22no—
344Q8×C61—22no—
345Q8×C61—22no—
346Q8×C61—42no—
347Q8×C61C22×D414yes—
348D4×C61—22no—
349D4×C61—22no—
350D4×C61—42no—
351C2×C4×C61—24no—
352C2×C4×C61—22no—
353C2×C4×C61—22no—
354C2×C4×C61—22no—
355C2×C4×C61—22no—
356C2×C4×C61—22no—
357C2×C4×C61—42no—
358C2×C4×C61—42no—
359C2×C4×C61C22×D412yes—
360C2×C4×C61C22×D412yes—
361C2×C4×C61C22×D411yescharacteristic
362C2×C4×C61C22×D412yes—
363C2×C4×C61C2×#4112yes—
364C2×C4×C61C2511yescharacteristic
365C22⋊D61—48no—
366C22⋊D61—84no—
367C22⋊D61—84no—
368C2×Dic61—22no—
369C2×Dic61—22no—
370C2×Dic61—22no—
371C2×Dic61—42no—
372C2×Dic61#12114yes—
373C2×Dic61C22×D412yes—
374C2×Dic61C22×D412yes—
375C2×Dic61C22×D412yes—
376D244—216no—
377D244—24no—
378D244—22no—
379D244—22no—
380D244—22no—
381D244—22no—
382D244—22no—
383D244—48no—
384D244—42no—
385D244—42no—
386D244—84no—
387D244—84no—
388D244C22×D414yes—
389C4×D61—216no—
390C4×D61—48no—
391C4×D61—84no—
392C4×D61—84no—
393C4×D61—84no—
394C4×D61#12118yes—
395C4×D61C22×D414yes—
396C4×D61C2×#4114yes—
397C8×C61—22no—
398C8×C61—22no—
399#92418—22no—
400#92418—22no—
401C2×#3045—611nomaximal, Sylow
402C22×C61—42no—
403C22×C61—42no—
404C22×C61—42no—
405C22×C61—84no—
406C22×C61C2×#12112yes—
407C22×C61#57612yes—
408C22×C61#57712yes—
409C22×C61C23×D411yescharacteristic
410C2×D61—28no—
411C2×D61—22no—
412C2×D61—22no—
413C2×D61—24no—
414C2×D61—48no—
415C2×D61—42no—
416C2×D61—42no—
417C2×D61—42no—
418C2×D61—42no—
419C2×D61—42no—
420C2×D61—42no—
421C2×D61—42no—
422C2×D61—42no—
423C2×D61—816no—
424C2×D61—84no—
425C2×D61—84no—
426C2×D61C2×#12114yes—
427C4×C61—24no—
428C4×C61—22no—
429C4×C61—22no—
430C4×C61—42no—
431C4×C61—42no—
432C4×C61C2×#12112yes—
433C4×C61C23×D411yescharacteristic
434C4×C61C22×#4111yescharacteristic
435Dic61—22no—
436Dic61—22no—
437Dic61—42no—
438Dic61C2×#12114yes—
439C22×AGL(1,ℤ/8)—611no—
440C22×#135—611no—
441C2×#535—611no—
442C2×#520—611no—
443#3045—6116no—
444C2×#464—611no—
445C2×#464D6111yescharacteristic, complemented
446C2×#460—611no—
447C2×#460—611no—
448C2×#463—611no—
449C2×#463—611no—
450C2×#459—611no—
451C2×#459—611no—
452C2×#424—611no—
453C2×#417—611no—
454C22×#102—611no—
455C2×C61—82no—
456C2×C61#304514yescomplemented
457C2×C61C22×#12111yescharacteristic
458C2×C61C2×#57611yescharacteristic
459C2×C61C2×#57711yescharacteristic
460D61—24no—
461D61—44no—
462D61—82no—
463D61—82no—
464C22×#41—611no—
465C22×#41—611no—
466C23×D4—611no—
467C2×AGL(1,ℤ/8)—618no—
468C2×AGL(1,ℤ/8)—1228no—
469C2×#135—618no—
470C2×#135—1228no—
471C22×Q16C2×D6111yescharacteristic, complemented
472C22×SD16—611no—
473C22×SD16—611no—
474C22×SD16—611no—
475C22×SD16C2×D6111yescharacteristic
476C22×D8—611no—
477C22×D8—611no—
478C22×D8—611no—
479C22×M16—611no—
480C23×C8—611no—
481#535—618no—
482#535—1224no—
483C2×#127—611no—
484C2×#127—611no—
485C2×#124—611no—
486C2×#124C2×D6111yescharacteristic
487C2×#121—1221no—
488C2×#121—1221no—
489C2×#120—1221no—
490C2×#120—1221no—
491#520—618no—
492#520—1224no—
493C2×C4×Q8—611no—
494C2×C4×Q8C2×D6111yescharacteristic, complemented
495C2×C4×D4—611no—
496C2×C4×D4—611no—
497C2×C4×D4—1221no—
498C2×C4×D4—1221no—
499C2×#117—611no—
500C2×#117—1221no—
501C22×C4⋊C4—611no—
502C22×C4⋊C4—1221no—
503#464—618no—
504#464C2×D6118yescomplemented
505#463—618no—
506#463—618no—
507#460—618no—
508#460—618no—
509#459—618no—
510#459—618no—
511#424—618no—
512C2×C4⋊C8—611no—
513C2×C4⋊C8—611no—
514C2×C4⋊C8—611no—
515C2×C4⋊C8C2×D6111yescharacteristic, complemented
516#417—618no—
517C2×#103—611no—
518C2×#103C2×D6111yescharacteristic, complemented
519C2×#102—611no—
520C2×#102—611no—
521C2×#102—611no—
522C2×#102—611no—
523C2×#102—611no—
524C2×#102—618no—
525C2×#102C2×D6111yescharacteristic
526C61C2×#304511yescharacteristic, complemented, Sylow
527C25—1221no—
528C2×#41—618no—
529C2×#41—614no—
530C2×#41—614no—
531C2×#41—1222no—
532C2×#41—1224no—
533C2×#41—1222no—
534C2×#41—1224no—
535C2×#41—1224no—
536C22×Q8C22×D6111yescharacteristic
537C22×Q8C22×D6111yescharacteristic
538C22×D4—614no—
539C22×D4—611no—
540C22×D4—611no—
541C22×D4—611no—
542C22×D4—1221no—
543C22×D4—1221no—
544C22×D4—1224no—
545C22×D4—1224no—
546C22×D4—1222no—
547C22×D4—1221no—
548C22×D4—1221no—
549C22×D4—1221no—
550C22×D4—1221no—
551C22×D4—1221no—
552C22×D4C22×D6111yescharacteristic
553C23×C4—611no—
554C23×C4—1221no—
555C23×C4—1221no—
556C23×C4—1221no—
557C23×C4—1221no—
558C23×C4—1221no—
559AGL(1,ℤ/8)—12232no—
560#135—12232no—
561C2×Q16—24no—
562C2×Q16C22×D6114yescomplemented
563C2×SD16—24no—
564C2×SD16—614no—
565C2×SD16—614no—
566C2×SD16—614no—
567C2×SD16—1224no—
568C2×SD16—1224no—
569C2×SD16—1224no—
570C2×SD16C22×D6114yes—
571C2×D8—614no—
572C2×D8—614no—
573C2×D8—614no—
574C2×D8—1224no—
575C2×D8—1224no—
576C2×D8—1224no—
577C2×M16—614no—
578C2×M16—1224no—
579C22×C8—611no—
580C22×C8—611no—
581C22×C8—614no—
582C22×C8—1224no—
583C22×C8C22×D6111yescharacteristic
584C22×C8C22×D6111yescharacteristic
585#127—614no—
586#127—614no—
587#127—1222no—
588#127—1222no—
589#124—22no—
590#124—614no—
591#124—1222no—
592#124C22×D6114yes—
593#121—1228no—
594#121—1228no—
595#120—1228no—
596#120—1228no—
597C4×Q8—22no—
598C4×Q8—614no—
599C4×Q8—1222no—
600C4×Q8C22×D6114yescomplemented
601C4×D4—614no—
602C4×D4—614no—
603C4×D4—1228no—
604C4×D4—1222no—
605C4×D4—1228no—
606C4×D4—1222no—
607#117—614no—
608#117—614no—
609#117—1228no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—611no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—611no—
614C2×C4⋊C4—614no—
615C2×C4⋊C4—1228no—
616C2×C4⋊C4—1222no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4—1221no—
619C2×C4⋊C4C22×D6111yescharacteristic
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—611no—
623C2×C22⋊C4—611no—
624C2×C22⋊C4—1221no—
625C2×C22⋊C4—1221no—
626C2×C22⋊C4—1221no—
627C2×C22⋊C4—1221no—
628C2×C42—21no—
629C2×C42—611no—
630C2×C42—1221no—
631C2×C42C22×D6111yescharacteristic
632C4⋊C8—614no—
633C4⋊C8—614no—
634C4⋊C8—614no—
635C4⋊C8C22×D6114yescomplemented
636#103—614no—
637#103C22×D6114yescomplemented
638#102—614no—
639#102—614no—
640#102—614no—
641#102—614no—
642#102—614no—
643#102C22×D6114yes—
644C24—21no—
645C24—611no—
646C24—1224no—
647C24—1221no—
648C24—1221no—
649C24—1221no—
650C24—4882no—
651C24—4882no—
652C24—2444no—
653#41—6116no—
654#41—12216no—
655#41—1228no—
656#41—1228no—
657#41—1228no—
658#41—2448no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—22no—
662C2×Q8—22no—
663C2×Q8—22no—
664C2×Q8D4×D6114yes—
665C2×Q8C23×D6112yes—
666C2×Q8C23×D6112yes—
667C2×D4—22no—
668C2×D4—21no—
669C2×D4—22no—
670C2×D4—614no—
671C2×D4—612no—
672C2×D4—612no—
673C2×D4—612no—
674C2×D4—1224no—
675C2×D4—1228no—
676C2×D4—1224no—
677C2×D4—1228no—
678C2×D4—1228no—
679C2×D4—1224no—
680C2×D4—1224no—
681C2×D4—1224no—
682C2×D4—1221no—
683C2×D4—1222no—
684C2×D4—1222no—
685C2×D4—1224no—
686C2×D4—1224no—
687C2×D4—1221no—
688C2×D4—1221no—
689C2×D4—1222no—
690C2×D4—1222no—
691C2×D4—1222no—
692C2×D4—4882no—
693C2×D4—4882no—
694C2×D4—4882no—
695C2×D4—4882no—
696C2×D4—2444no—
697C2×D4—2448no—
698C2×D4—2444no—
699C2×D4C23×D6112yes—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—611no—
704C22×C4—612no—
705C22×C4—614no—
706C22×C4—614no—
707C22×C4—612no—
708C22×C4—611no—
709C22×C4—611no—
710C22×C4—1224no—
711C22×C4—1228no—
712C22×C4—1224no—
713C22×C4—1224no—
714C22×C4—1224no—
715C22×C4—1221no—
716C22×C4—1224no—
717C22×C4—4882no—
718C22×C4—4882no—
719C22×C4—4882no—
720C22×C4—2444no—
721C22×C4D4×D6111yescharacteristic
722C22×C4D4×D6111yescharacteristic
723C22×C4C23×D6111yescharacteristic
724Q16—28no—
725SD16—28no—
726SD16—1228no—
727SD16—1228no—
728SD16—1228no—
729D8—1228no—
730D8—1228no—
731D8—1228no—
732M16—1228no—
733C2×C8—22no—
734C2×C8—22no—
735C2×C8—612no—
736C2×C8—612no—
737C2×C8—1228no—
738C2×C8—1222no—
739C2×C8—1222no—
740C2×C8C23×D6112yes—
741C2×C8C23×D6112yes—
742C4⋊C4—24no—
743C4⋊C4—21no—
744C4⋊C4—614no—
745C4⋊C4—614no—
746C4⋊C4—612no—
747C4⋊C4—1224no—
748C4⋊C4—1224no—
749C4⋊C4—1221no—
750C4⋊C4C23×D6112yes—
751C22⋊C4—24no—
752C22⋊C4—24no—
753C22⋊C4—614no—
754C22⋊C4—614no—
755C22⋊C4—1224no—
756C22⋊C4—1224no—
757C22⋊C4—1224no—
758C22⋊C4—1224no—
759C42—24no—
760C42—612no—
761C42—612no—
762C42—1224no—
763C42D4×D6112yes—
764C42C23×D6112yes—
765C23—22no—
766C23—42no—
767C23—42no—
768C23—42no—
769C23—614no—
770C23—612no—
771C23—1222no—
772C23—1222no—
773C23—1224no—
774C23—1222no—
775C23—1222no—
776C23—1222no—
777C23—4884no—
778C23—4884no—
779C23—48816no—
780C23—2448no—
781C23—2442no—
782C23—2442no—
783C23—2442no—
784C23—2442no—
785C23—2442no—
786C23—2442no—
787C23—2442no—
788C23—2442no—
789C23C2×D4×D6111yescharacteristic
790Q8—24no—
791Q8—22no—
792Q8—22no—
793Q8—22no—
794Q8—42no—
795Q8C2×D4×D6114yes—
796D4—22no—
797D4—22no—
798D4—42no—
799D4—614no—
800D4—12216no—
801D4—1224no—
802D4—1222no—
803D4—1222no—
804D4—1222no—
805D4—1222no—
806D4—1222no—
807D4—4884no—
808D4—4884no—
809D4—4884no—
810D4—4884no—
811D4—2448no—
812D4—2448no—
813D4—2442no—
814D4—2442no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—42no—
822C2×C4—42no—
823C2×C4—614no—
824C2×C4—612no—
825C2×C4—618no—
826C2×C4—614no—
827C2×C4—614no—
828C2×C4—612no—
829C2×C4—612no—
830C2×C4—12216no—
831C2×C4—1222no—
832C2×C4—1222no—
833C2×C4—1222no—
834C2×C4—4884no—
835C2×C4—4884no—
836C2×C4—4884no—
837C2×C4—2448no—
838C2×C4—2442no—
839C2×C4C2×D4×D6112yes—
840C2×C4C2×D4×D6112yes—
841C2×C4C2×D4×D6111yescharacteristic
842C2×C4C2×D4×D6112yes—
843C2×C4#41×D6112yes—
844C2×C4C24×D6111yescharacteristic
845C8—22no—
846C8—22no—
847C8—1222no—
848C8—1222no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—84no—
853C22—614no—
854C22—1228no—
855C22—1222no—
856C22—1222no—
857C22—1224no—
858C22—48816no—
859C22—4884no—
860C22—4884no—
861C22—2442no—
862C22—2442no—
863C22—2442no—
864C22—2442no—
865C22—2442no—
866C22—2442no—
867C22—2448no—
868C22—2442no—
869C22—2442no—
870C22#121×D6112yes—
871C22#1684056412yes—
872C22#1684057112yes—
873C22C22×D4×D6111yescharacteristic
874C4—22no—
875C4—24no—
876C4—22no—
877C4—42no—
878C4—42no—
879C4—614no—
880C4—1222no—
881C4—1222no—
882C4—2442no—
883C4#121×D6112yes—
884C4C22×D4×D6111yescharacteristic
885C4C2×#41×D6111yescharacteristic
886C2—82no—
887C2—1224no—
888C2—4882no—
889C2—4882no—
890C2—2444no—
891C2#2145536114yesdirect product factor
892C2C2×#121×D6111yescharacteristic
893C2C2×#1684056411yescharacteristic
894C2C2×#1684057111yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#464C2
socleC23×C61C22×D4
hypercenterC2×#464D61
hypocenterC61C2×#3045
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C22×#14519804C2semidirect
2. C22×#14519800C2semidirect
3. C2×#16840330C2semidirect
4. C2×#16840244C2semidirect
5. #21455361C2direct (N × H)
6. C2×#16839986C2semidirect
7. C2×#16839962C2semidirect
8. C2×#16839960C2semidirect
9. C2×#16839980C2semidirect
10. C2×#16839974C2semidirect
11. C2×#16839958C2semidirect
12. C2×#16839956C2semidirect
13. C2×#16839787C2semidirect
14. C2×#16839762C2semidirect
15. C2×#102×D61C2semidirect
16. C2×C61×#464C2semidirect
21. C2×#14519804C22semidirect
23. C2×#14519800C22semidirect
25. C22×#11758201C22semidirect
26. C22×#11758201C22semidirect
28. C22×D488C22semidirect
33. #16840330C22semidirect
42. #16840244C22semidirect
43. C2×Q8×Dic61C22semidirect
45. C2×C4×D244C22semidirect
47. C2×#14519739C22semidirect
52. #16839986C22semidirect
53. #16839980C22semidirect
54. #16839974C22semidirect
55. #16839962C22semidirect
56. #16839960C22semidirect
57. #16839958C22semidirect
58. #16839956C22semidirect
59. #16839787C22semidirect
60. C2×C4⋊#92418C22semidirect
61. C2×#14519706C22semidirect
62. C2×#14519706C22semidirect
63. #16839762C22semidirect
64. C2×#14519701C22semidirect
66. C2×#14519699C22semidirect
69. C2×#14519697C22semidirect
70. #102×D61C22semidirect
71. C22×Q16×C61C22semidirect
74. C2×C4×Q8×C61C22semidirect
75. C61×#464C22semidirect
76. C2×C4⋊C8×C61C22semidirect
77. C2×#103×C61C22semidirect
85. C2×#11758226D4semidirect
114. C2×#11758201C23semidirect
115. C2×#11758201C23semidirect
119. C2×D488C23semidirect
139. Q8×Dic61C23semidirect
142. C4×D244C23semidirect
145. #14519739C23semidirect
165. C4⋊#92418C23semidirect
166. #14519706C23semidirect
167. #14519706C23semidirect
168. #14519701C23semidirect
170. #14519699C23semidirect
173. #14519697C23semidirect
178. C2×Q16×C61C23semidirect
186. C4×Q8×C61C23semidirect
193. C4⋊C8×C61C23semidirect
194. #103×C61C23semidirect
238. #11758226C2×D4semidirect
445. C2×#464D61semidirect
456. C2×C61#3045semidirect
471. C22×Q16C2×D61semidirect
494. C2×C4×Q8C2×D61semidirect
504. #464C2×D61semidirect
515. C2×C4⋊C8C2×D61semidirect
518. C2×#103C2×D61semidirect
526. C61C2×#3045semidirect
562. C2×Q16C22×D61semidirect
600. C4×Q8C22×D61semidirect
635. C4⋊C8C22×D61semidirect
637. #103C22×D61semidirect
891. C2#21455361direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198042
C22×#145198002
C2×#168403302
C2×#168402442
#214553612
C2×#168399862
C2×#168399622
C2×#168399602
C2×#168399802
C2×#168399742
C2×#168399582
C2×#168399562
C2×#168397872
C2×#168397622
C2×#102×D612
C2×C61×#4642
C2×#304561