Finite Group Databasebeta

← C2×#21455308 #30546872

Subgroups — C2×#21455308 #30546872

Order 15616.

2918 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519806C211yesmaximal, characteristic, complemented
2C22×#14519801C211yesmaximal, characteristic
3C2×#124×D61C211yesmaximal, characteristic, complemented
4C2×C4×#11758224C211yesmaximal, characteristic, complemented
5#21455308C2116yesmaximal, direct product factor
6C2×#16839987C211yesmaximal, characteristic, complemented
7C2×#16839985C211yesmaximal, characteristic, complemented
8C2×#16839983C211yesmaximal, characteristic, complemented
9C2×#16839981C211yesmaximal, characteristic, complemented
10C2×#16839979C211yesmaximal, characteristic, complemented
11C2×#16839977C211yesmaximal, characteristic, complemented
12C2×#16839975C211yesmaximal, characteristic, complemented
13C2×#16839784C211yesmaximal, characteristic, complemented
14C2×#16839769C211yesmaximal, characteristic, complemented
15C2×#16839765C211yesmaximal, characteristic, complemented
16C2×C61×#463C211yesmaximal, characteristic, complemented
17C22×#11758224C2211yescharacteristic
18C22×Q8×D61C2211yescharacteristic
19C22×D4×D61C2211yescharacteristic
20C2×#14519806—28no—
21C2×#14519806C2218yescomplemented
22C2×#14519801—28no—
23C2×#14519801C2218yes—
24C22×Dic244C2211yescharacteristic, complemented
25C22×#11758202C2211yescharacteristic, complemented
26C22×#11758190C2211yescharacteristic
27C22×#11758200C2211yescharacteristic
28C22×#11758200C2211yescharacteristic, complemented
29C22×#11758199C2211yescharacteristic
30C22×#11758189C2211yescharacteristic
31C22×#11758189C2211yescharacteristic
32C2×#14519766C2211yescharacteristic
33C2×#14519765C2211yescharacteristic
34C2×#14519764C2211yescharacteristic
35C2×#14519763—21no—
36C2×#14519763—21no—
37#124×D61—24no—
38#124×D61C2218yescomplemented
39C4×#11758224—24no—
40C4×#11758224C2218yescomplemented
41C2×C4×Dic122C2211yescharacteristic, complemented
42C2×#14519742C2211yescharacteristic, complemented
43C2×D4×Dic61C2211yescharacteristic, complemented
44C2×C4×C22⋊D61—21no—
45C2×#14519737—21no—
46C2×#14519735C2211yescharacteristic
47C2×#14519733—21no—
48C2×C22⋊C4×D61—21no—
49C2×C22⋊C4×D61—21no—
50C22×C4×Dic61—21no—
51C2×C42×D61C2211yescharacteristic
52#16839987C2218yescomplemented
53#16839985C2218yescomplemented
54#16839983C2218yescomplemented
55#16839981C2218yescomplemented
56#16839979C2218yescomplemented
57#16839977C2218yescomplemented
58#16839975C2218yescomplemented
59#16839784C2218yescomplemented
60C2×C4⋊#92418C2211yescharacteristic, complemented
61C2×#14519706C2211yescharacteristic, complemented
62C2×#14519706C2211yescharacteristic, complemented
63#16839769C2218yescomplemented
64#16839765C2218yescomplemented
65C2×#14519702C2211yescharacteristic, complemented
66C2×#14519701C2211yescharacteristic, complemented
67C2×#14519700C2211yescharacteristic, complemented
68C2×#14519699C2211yescharacteristic
69C2×#14519698C2211yescharacteristic
70C2×#14519697C2211yescharacteristic
71C22×SD16×C61C2211yescharacteristic, complemented
72C22×D8×C61C2211yescharacteristic
73C2×#124×C61C2211yescharacteristic
74C2×C4×D4×C61C2211yescharacteristic, complemented
75C61×#463C2218yescomplemented
76C2×C4⋊C8×C61C2211yescharacteristic, complemented
77C2×#103×C61C2211yescharacteristic, complemented
78C2×#102×C61C2211yescharacteristic
79C24×D61—21no—
80C2×#11758224—22no—
81C2×#11758224—24no—
82C2×#11758224D418yes—
83C2×#11758224C2314yes—
84C22×Dic122—21no—
85C22×Dic122C2311yescharacteristic
86C22×Dic122C2311yescharacteristic
87C2×Q8×D61—22no—
88C2×Q8×D61—24no—
89C2×Q8×D61—24no—
90C2×Q8×D61C2314yes—
91C22×D244C2311yescharacteristic
92C22×C22⋊D61—21no—
93C22×C22⋊D61—21no—
94C2×D4×D61—24no—
95C2×D4×D61—22no—
96C2×D4×D61—24no—
97C2×D4×D61C2314yes—
98C23×Dic61—21no—
99C23×Dic61—21no—
100C22×C4×D61—21no—
101C22×C4×D61D411yescharacteristic
102C22×C4×D61D411yescharacteristic
103C22×C4×D61C2311yescharacteristic
104#14519806—232no—
105#14519801—232no—
106C2×Dic244—24no—
107C2×Dic244C2314yescomplemented
108C2×#11758202—24no—
109C2×#11758202C2314yescomplemented
110C2×#11758190—24no—
111C2×#11758190C2314yes—
112C2×#11758200—24no—
113C2×#11758200—24no—
114C2×#11758200C2314yes—
115C2×#11758200C2314yescomplemented
116C2×#11758199—24no—
117C2×#11758199C2314yes—
118C2×#11758189—24no—
119C2×#11758189—24no—
120C2×#11758189C2314yes—
121C2×#11758189C2314yes—
122C22×#92418C2311yescharacteristic
123C22×#92418C2311yescharacteristic
124#14519766—22no—
125#14519766C2314yes—
126#14519765—22no—
127#14519765C2314yes—
128#14519764—22no—
129#14519764C2314yes—
130#14519763—28no—
131#14519763—28no—
132C4×Dic122—22no—
133C4×Dic122C2314yescomplemented
134#14519742—22no—
135#14519742C2314yescomplemented
136D4×Dic61—22no—
137D4×Dic61C2314yescomplemented
138C4×C22⋊D61—28no—
139#14519737—28no—
140#14519735—22no—
141#14519735C2314yes—
142#14519733—28no—
143C2×C4⋊Dic61C2311yescharacteristic
144C2×#11758196—21no—
145C2×#11758196—21no—
146C2×C22⋊Dic61—21no—
147C2×C22⋊Dic61—21no—
148C2×C22⋊Dic61—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×#11758198—21no—
152C2×#11758198—21no—
153C2×#11758198—21no—
154C22⋊C4×D61—28no—
155C22⋊C4×D61—28no—
156C2×C4×Dic61—21no—
157C2×C4×Dic61—21no—
158C2×C4×Dic61—21no—
159C2×C4×Dic61—28no—
160C2×C4×Dic61D411yescharacteristic
161C2×C4×Dic61D411yescharacteristic
162C2×C4×Dic61C2311yescharacteristic
163C42×D61D414yes—
164C42×D61C2314yes—
165C4⋊#92418C2314yescomplemented
166#14519706C2314yescomplemented
167#14519706C2314yescomplemented
168#14519702C2314yescomplemented
169#14519701C2314yescomplemented
170#14519700C2314yescomplemented
171#14519699C2314yes—
172#14519698C2314yes—
173#14519697C2314yes—
174C22×Q8×C61C2311yescharacteristic
175C22×D4×C61C2311yescharacteristic
176C22×D4×C61C2311yescharacteristic
177C23×C4×C61—21no—
178C2×SD16×C61—24no—
179C2×SD16×C61C2314yescomplemented
180C2×D8×C61—24no—
181C2×D8×C61C2314yes—
182C22×C8×C61C2311yescharacteristic
183C22×C8×C61C2311yescharacteristic
184#124×C61—22no—
185#124×C61C2314yes—
186C4×D4×C61—22no—
187C4×D4×C61C2314yescomplemented
188C2×C4⋊C4×C61C2311yescharacteristic
189C2×C22⋊C4×C61—21no—
190C2×C22⋊C4×C61—21no—
191C2×C22⋊C4×C61—21no—
192C2×C42×C61C2311yescharacteristic
193C4⋊C8×C61C2314yescomplemented
194#103×C61C2314yescomplemented
195#102×C61C2314yes—
196C24×C61—21no—
197C24×C61—21no—
198C23×D61—21no—
199C23×D61—24no—
200C23×D61—44no—
201C23×D61—44no—
202C23×D61—44no—
203C23×D61C2×D411yescharacteristic
204C2×Q8×C61—21no—
205C2×Q8×C61—22no—
206C2×Q8×C61—22no—
207C2×Q8×C61C2412yes—
208C2×D4×C61—21no—
209C2×D4×C61—22no—
210C2×D4×C61—21no—
211C2×D4×C61—22no—
212C2×D4×C61—22no—
213C2×D4×C61C2×D414yes—
214C2×D4×C61C2412yes—
215C2×D4×C61C2412yes—
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61—24no—
219C22×C4×C61—44no—
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2411yescharacteristic
223C2×C22⋊D61—28no—
224C2×C22⋊D61—24no—
225C2×C22⋊D61—24no—
226C2×C22⋊D61—44no—
227C22×Dic61—21no—
228C22×Dic61—28no—
229C22×Dic61—24no—
230C22×Dic61—21no—
231C22×Dic61—21no—
232C22×Dic61—24no—
233C22×Dic61—44no—
234C22×Dic61C2×D411yescharacteristic
235C22×Dic61C2×D411yescharacteristic
236C22×Dic61C2×D411yescharacteristic
237Q8×D61—28no—
238Q8×D61—28no—
239Q8×D61—48no—
240#11758224—216no—
241#11758224—28no—
242#11758224C2×D4116yes—
243D4×D61—28no—
244D4×D61—28no—
245D4×D61—48no—
246C2×D244—22no—
247C2×D244—22no—
248C2×D244—21no—
249C2×D244C2412yes—
250C2×C4×D61—24no—
251C2×C4×D61—42no—
252C2×C4×D61—42no—
253C2×C4×D61—44no—
254C2×C4×D61C2×D414yes—
255C2×C4×D61C2×D414yes—
256C2×C4×D61C2×D412yes—
257C2×C4×D61C2×D414yes—
258C2×C4×D61#4114yes—
259C2×C4×D61C2412yes—
260C2×Dic122—21no—
261C2×Dic122—22no—
262C2×Dic122—22no—
263C2×Dic122—22no—
264C2×Dic122—21no—
265C2×Dic122—24no—
266C2×Dic122—44no—
267C2×Dic122C2×D414yes—
268C2×Dic122C2412yes—
269C2×Dic122C2412yes—
270SD16×C61—28no—
271D8×C61—28no—
272C2×C8×C61—22no—
273C2×C8×C61—22no—
274C2×C8×C61C2412yes—
275C2×C8×C61C2412yes—
276C4⋊C4×C61—21no—
277C4⋊C4×C61C2412yes—
278C22⋊C4×C61—24no—
279C22⋊C4×C61—24no—
280C22⋊C4×C61—24no—
281C42×C61C2×D412yes—
282C42×C61C2412yes—
283C22⋊Dic61—24no—
284C22⋊Dic61—24no—
285C22⋊Dic61—24no—
286#11758202—28no—
287#11758200—28no—
288#11758200—28no—
289#11758199—28no—
290#11758198—24no—
291#11758198—24no—
292#11758198—24no—
293#11758198—24no—
294#11758198—24no—
295C4⋊Dic61—21no—
296C4⋊Dic61C2412yes—
297#11758196—24no—
298#11758196—24no—
299C4×Dic61—24no—
300C4×Dic61—24no—
301C4×Dic61—24no—
302C4×Dic61C2×D412yes—
303C4×Dic61C2×D414yes—
304C4×Dic61C2×D414yes—
305C4×Dic61C2412yes—
306C2×#92418—22no—
307C2×#92418—22no—
308C2×#92418C2412yes—
309C2×#92418C2412yes—
310Dic244—28no—
311#11758190—28no—
312#11758189—28no—
313#11758189—28no—
314C23×C61—24no—
315C23×C61—22no—
316C23×C61—22no—
317C23×C61—42no—
318C23×C61—42no—
319C23×C61—42no—
320C23×C61—42no—
321C23×C61—42no—
322C23×C61C22×D411yescharacteristic
323C22×D61—22no—
324C22×D61—22no—
325C22×D61—22no—
326C22×D61—48no—
327C22×D61—48no—
328C22×D61—42no—
329C22×D61—42no—
330C22×D61—42no—
331C22×D61—48no—
332C22×D61—816no—
333C22×D61#12114yes—
334C22×D61C22×D412yes—
335Q8×C61—22no—
336Q8×C61—22no—
337Q8×C61—42no—
338D4×C61—24no—
339D4×C61—22no—
340D4×C61—22no—
341D4×C61—22no—
342D4×C61—42no—
343D4×C61C22×D414yes—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—48no—
349C2×C4×C61—42no—
350C2×C4×C61—42no—
351C2×C4×C61C22×D412yes—
352C2×C4×C61C22×D412yes—
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D412yes—
355C2×C4×C61C2×#4112yes—
356C2×C4×C61C2511yescharacteristic
357C22⋊D61—216no—
358C22⋊D61—48no—
359C2×Dic61—24no—
360C2×Dic61—22no—
361C2×Dic61—22no—
362C2×Dic61—22no—
363C2×Dic61—216no—
364C2×Dic61—22no—
365C2×Dic61—22no—
366C2×Dic61—48no—
367C2×Dic61—42no—
368C2×Dic61—42no—
369C2×Dic61#12114yes—
370C2×Dic61C22×D412yes—
371C2×Dic61C22×D412yes—
372C2×Dic61C22×D412yes—
373D244—22no—
374D244—22no—
375D244—42no—
376C4×D61—44no—
377C4×D61—44no—
378C4×D61—48no—
379C4×D61#12118yes—
380C4×D61C22×D414yes—
381C4×D61C2×#4114yes—
382Dic122—24no—
383Dic122—22no—
384Dic122—22no—
385Dic122—22no—
386Dic122—42no—
387Dic122—48no—
388Dic122C22×D414yes—
389C8×C61—22no—
390C8×C61—22no—
391#92418—22no—
392#92418—22no—
393C2×#3040—611nomaximal, Sylow
394C22×C61—24no—
395C22×C61—48no—
396C22×C61—42no—
397C22×C61—42no—
398C22×C61—42no—
399C22×C61—42no—
400C22×C61—42no—
401C22×C61—84no—
402C22×C61C2×#12112yes—
403C22×C61#57512yes—
404C22×C61#57512yes—
405C22×C61C23×D411yescharacteristic
406C2×D61—28no—
407C2×D61—22no—
408C2×D61—22no—
409C2×D61—42no—
410C2×D61—42no—
411C2×D61—42no—
412C2×D61—816no—
413C2×D61—84no—
414C2×D61C2×#12114yes—
415C4×C61—22no—
416C4×C61—22no—
417C4×C61—42no—
418C4×C61—42no—
419C4×C61C2×#12112yes—
420C4×C61C23×D411yescharacteristic
421C4×C61C22×#4111yescharacteristic
422Dic61—24no—
423Dic61—22no—
424Dic61—22no—
425Dic61—42no—
426Dic61—42no—
427Dic61C2×#12114yes—
428C22×#137—611no—
429C22×AGL(1,ℤ/8)—611no—
430C22×#124—611no—
431C2×C4×#41—611no—
432#3040—6116no—
433C2×#464—611no—
434C2×#464—611no—
435C2×#464—611no—
436C2×#464—611no—
437C2×#463—611no—
438C2×#463—611no—
439C2×#463—611no—
440C2×#463D6111yescharacteristic, complemented
441C2×#423—611no—
442C2×#419—611no—
443C2×#418—611no—
444C2×C61—44no—
445C2×C61—82no—
446C2×C61#304014yescomplemented
447C2×C61C22×#12111yescharacteristic
448C2×C61C2×#57511yescharacteristic
449C2×C61C2×#57511yescharacteristic
450D61—24no—
451D61—82no—
452C22×#41—611no—
453C23×Q8—611no—
454C23×D4—611no—
455C2×#137—618no—
456C2×#137—1228no—
457C2×AGL(1,ℤ/8)—618no—
458C2×AGL(1,ℤ/8)—1228no—
459C22×Q16—611no—
460C22×Q16—611no—
461C22×SD16—611no—
462C22×SD16—611no—
463C22×SD16—611no—
464C22×SD16C2×D6111yescharacteristic, complemented
465C22×D8—611no—
466C22×D8C2×D6111yescharacteristic
467C22×M16—611no—
468C22×M16—611no—
469C2×#124—611no—
470C2×#124—611no—
471C2×#124—618no—
472C2×#124—611no—
473C2×#124—1221no—
474C2×#124—1221no—
475C2×#124—1224no—
476C2×#124C2×D6111yescharacteristic
477C4×#41—618no—
478C4×#41—1224no—
479C2×C4×Q8—611no—
480C2×C4×Q8—611no—
481C2×C4×D4—611no—
482C2×C4×D4—1221no—
483C2×C4×D4—1221no—
484C2×C4×D4C2×D6111yescharacteristic, complemented
485C2×#117—611no—
486C2×#117—1221no—
487C22×C22⋊C4—1221no—
488C22×C22⋊C4—1221no—
489C22×C42—611no—
490C22×C42—1221no—
491#464—618no—
492#464—618no—
493#464—618no—
494#464—618no—
495#463—618no—
496#463—618no—
497#463—618no—
498#463C2×D6118yescomplemented
499#423—618no—
500C2×C4⋊C8—611no—
501C2×C4⋊C8—611no—
502C2×C4⋊C8—611no—
503C2×C4⋊C8C2×D6111yescharacteristic, complemented
504#419—618no—
505#418—618no—
506C2×#103—611no—
507C2×#103—611no—
508C2×#103—611no—
509C2×#103C2×D6111yescharacteristic, complemented
510C2×#102—611no—
511C2×#102—611no—
512C2×#102—611no—
513C2×#102C2×D6111yescharacteristic
514C61C2×#304011yescharacteristic, complemented, Sylow
515C25—1221no—
516C2×#41—618no—
517C2×#41—614no—
518C2×#41—1222no—
519C2×#41—1224no—
520C22×Q8—614no—
521C22×Q8—611no—
522C22×Q8—611no—
523C22×Q8—1221no—
524C22×Q8—1222no—
525C22×Q8—1224no—
526C22×Q8—1224no—
527C22×Q8C22×D6111yescharacteristic
528C22×D4—614no—
529C22×D4—611no—
530C22×D4—1224no—
531C22×D4—1224no—
532C22×D4—1222no—
533C22×D4—1221no—
534C22×D4—1221no—
535C22×D4C22×D6111yescharacteristic
536C22×D4C22×D6111yescharacteristic
537C23×C4—21no—
538C23×C4—611no—
539C23×C4—611no—
540C23×C4—611no—
541C23×C4—1221no—
542C23×C4—1221no—
543C23×C4—1221no—
544#137—12232no—
545AGL(1,ℤ/8)—12232no—
546C2×Q16—614no—
547C2×Q16—614no—
548C2×Q16—1224no—
549C2×Q16—1224no—
550C2×SD16—24no—
551C2×SD16—614no—
552C2×SD16—614no—
553C2×SD16—614no—
554C2×SD16—1224no—
555C2×SD16—1224no—
556C2×SD16—1224no—
557C2×SD16C22×D6114yescomplemented
558C2×D8—24no—
559C2×D8—614no—
560C2×D8—1224no—
561C2×D8C22×D6114yes—
562C2×M16—614no—
563C2×M16—614no—
564C2×M16—1224no—
565C2×M16—1224no—
566C22×C8—611no—
567C22×C8—611no—
568C22×C8C22×D6111yescharacteristic
569C22×C8C22×D6111yescharacteristic
570#124—22no—
571#124—614no—
572#124—614no—
573#124—614no—
574#124—1228no—
575#124—1228no—
576#124—1222no—
577#124—1222no—
578#124—1222no—
579#124C22×D6114yes—
580C4×Q8—614no—
581C4×Q8—614no—
582C4×Q8—1222no—
583C4×Q8—1222no—
584C4×D4—22no—
585C4×D4—614no—
586C4×D4—1222no—
587C4×D4—1228no—
588C4×D4—1228no—
589C4×D4C22×D6114yescomplemented
590#117—614no—
591#117—1228no—
592#117—1222no—
593C2×C4⋊C4—611no—
594C2×C4⋊C4—1221no—
595C2×C4⋊C4—1221no—
596C2×C4⋊C4C22×D6111yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—1228no—
601C2×C22⋊C4—1228no—
602C2×C22⋊C4—1221no—
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4—1221no—
606C2×C22⋊C4—1221no—
607C2×C22⋊C4—1221no—
608C2×C22⋊C4—1221no—
609C2×C22⋊C4—1221no—
610C2×C42—611no—
611C2×C42—611no—
612C2×C42—611no—
613C2×C42—614no—
614C2×C42—614no—
615C2×C42—1228no—
616C2×C42—1221no—
617C2×C42—1221no—
618C2×C42—1221no—
619C2×C42C22×D6111yescharacteristic
620C4⋊C8—614no—
621C4⋊C8—614no—
622C4⋊C8—614no—
623C4⋊C8C22×D6114yescomplemented
624#103—614no—
625#103—614no—
626#103—614no—
627#103C22×D6114yescomplemented
628#102—614no—
629#102—614no—
630#102—614no—
631#102C22×D6114yes—
632C24—21no—
633C24—21no—
634C24—611no—
635C24—1224no—
636C24—1221no—
637C24—2444no—
638C24—2444no—
639C24—2444no—
640#41—6116no—
641#41—12216no—
642#41—1228no—
643C2×Q8—21no—
644C2×Q8—22no—
645C2×Q8—22no—
646C2×Q8—614no—
647C2×Q8—612no—
648C2×Q8—612no—
649C2×Q8—1224no—
650C2×Q8—1228no—
651C2×Q8—1228no—
652C2×Q8—1221no—
653C2×Q8—1221no—
654C2×Q8—1222no—
655C2×Q8—1222no—
656C2×Q8—1222no—
657C2×Q8—2444no—
658C2×Q8—2448no—
659C2×Q8C23×D6112yes—
660C2×D4—21no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—612no—
666C2×D4—1228no—
667C2×D4—1228no—
668C2×D4—1224no—
669C2×D4—1224no—
670C2×D4—1228no—
671C2×D4—1222no—
672C2×D4—1221no—
673C2×D4—1222no—
674C2×D4—2448no—
675C2×D4—2444no—
676C2×D4D4×D6114yes—
677C2×D4C23×D6112yes—
678C2×D4C23×D6112yes—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—24no—
682C22×C4—44no—
683C22×C4—611no—
684C22×C4—612no—
685C22×C4—614no—
686C22×C4—614no—
687C22×C4—612no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—614no—
691C22×C4—614no—
692C22×C4—1224no—
693C22×C4—1224no—
694C22×C4—1228no—
695C22×C4—1224no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4—2442no—
700C22×C4—2442no—
701C22×C4—2444no—
702C22×C4—2444no—
703C22×C4D4×D6111yescharacteristic
704C22×C4D4×D6111yescharacteristic
705C22×C4C23×D6111yescharacteristic
706Q16—1228no—
707Q16—1228no—
708SD16—28no—
709SD16—1228no—
710SD16—1228no—
711SD16—1228no—
712D8—28no—
713D8—1228no—
714M16—1228no—
715M16—1228no—
716C2×C8—22no—
717C2×C8—22no—
718C2×C8—612no—
719C2×C8—612no—
720C2×C8—1222no—
721C2×C8—1222no—
722C2×C8C23×D6112yes—
723C2×C8C23×D6112yes—
724C4⋊C4—21no—
725C4⋊C4—612no—
726C4⋊C4—1224no—
727C4⋊C4—1221no—
728C4⋊C4—1224no—
729C4⋊C4C23×D6112yes—
730C22⋊C4—24no—
731C22⋊C4—24no—
732C22⋊C4—24no—
733C22⋊C4—1224no—
734C22⋊C4—1224no—
735C22⋊C4—1224no—
736C22⋊C4—1224no—
737C22⋊C4—1224no—
738C22⋊C4—1224no—
739C22⋊C4—1224no—
740C22⋊C4—1224no—
741C42—614no—
742C42—614no—
743C42—612no—
744C42—612no—
745C42—1224no—
746C42—1224no—
747C42—1224no—
748C42D4×D6112yes—
749C42C23×D6112yes—
750C23—24no—
751C23—22no—
752C23—22no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—42no—
757C23—42no—
758C23—614no—
759C23—612no—
760C23—1222no—
761C23—1222no—
762C23—1222no—
763C23—48816no—
764C23—2448no—
765C23—2448no—
766C23—2448no—
767C23—2442no—
768C23—2442no—
769C23—2442no—
770C23C2×D4×D6111yescharacteristic
771Q8—22no—
772Q8—22no—
773Q8—42no—
774Q8—614no—
775Q8—1224no—
776Q8—1222no—
777Q8—1222no—
778Q8—1222no—
779Q8—2448no—
780Q8—2442no—
781D4—24no—
782D4—22no—
783D4—22no—
784D4—22no—
785D4—42no—
786D4—12216no—
787D4—1222no—
788D4—1222no—
789D4—2448no—
790D4—2442no—
791D4C2×D4×D6114yes—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—48no—
797C2×C4—42no—
798C2×C4—42no—
799C2×C4—614no—
800C2×C4—612no—
801C2×C4—618no—
802C2×C4—614no—
803C2×C4—614no—
804C2×C4—612no—
805C2×C4—612no—
806C2×C4—12216no—
807C2×C4—1224no—
808C2×C4—1222no—
809C2×C4—1222no—
810C2×C4—1222no—
811C2×C4—1222no—
812C2×C4—1222no—
813C2×C4—2444no—
814C2×C4—2444no—
815C2×C4—2448no—
816C2×C4—2448no—
817C2×C4—2442no—
818C2×C4—2442no—
819C2×C4C2×D4×D6112yes—
820C2×C4C2×D4×D6112yes—
821C2×C4C2×D4×D6111yescharacteristic
822C2×C4C2×D4×D6112yes—
823C2×C4#41×D6112yes—
824C2×C4C24×D6111yescharacteristic
825C8—22no—
826C8—22no—
827C8—1222no—
828C8—1222no—
829C22—24no—
830C22—42no—
831C22—42no—
832C22—48no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—84no—
837C22—614no—
838C22—1222no—
839C22—1222no—
840C22—1228no—
841C22—48816no—
842C22—4884no—
843C22—2442no—
844C22—2442no—
845C22—2442no—
846C22#121×D6112yes—
847C22#1684055812yes—
848C22#1684055912yes—
849C22C22×D4×D6111yescharacteristic
850C4—22no—
851C4—22no—
852C4—42no—
853C4—42no—
854C4—614no—
855C4—1222no—
856C4—1222no—
857C4—1224no—
858C4—2442no—
859C4—2442no—
860C4#121×D6112yes—
861C4C22×D4×D6111yescharacteristic
862C4C2×#41×D6111yescharacteristic
863C2—44no—
864C2—82no—
865C2—1224no—
866C2—4882no—
867C2#2145530814yesdirect product factor
868C2C2×#121×D6111yescharacteristic
869C2C2×#1684055811yescharacteristic
870C2C2×#1684055911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#463C2
socleC23×C61C22×D4
prime radicalC22×#14519801C2
hypercenterC2×#463D61
hypocenterC61C2×#3040
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#463

Complements

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

NH ≅ G/Ntype
1. C22×#14519806C2semidirect
3. C2×#124×D61C2semidirect
4. C2×C4×#11758224C2semidirect
5. #21455308C2direct (N × H)
6. C2×#16839987C2semidirect
7. C2×#16839985C2semidirect
8. C2×#16839983C2semidirect
9. C2×#16839981C2semidirect
10. C2×#16839979C2semidirect
11. C2×#16839977C2semidirect
12. C2×#16839975C2semidirect
13. C2×#16839784C2semidirect
14. C2×#16839769C2semidirect
15. C2×#16839765C2semidirect
16. C2×C61×#463C2semidirect
21. C2×#14519806C22semidirect
24. C22×Dic244C22semidirect
25. C22×#11758202C22semidirect
28. C22×#11758200C22semidirect
38. #124×D61C22semidirect
40. C4×#11758224C22semidirect
41. C2×C4×Dic122C22semidirect
42. C2×#14519742C22semidirect
43. C2×D4×Dic61C22semidirect
52. #16839987C22semidirect
53. #16839985C22semidirect
54. #16839983C22semidirect
55. #16839981C22semidirect
56. #16839979C22semidirect
57. #16839977C22semidirect
58. #16839975C22semidirect
59. #16839784C22semidirect
60. C2×C4⋊#92418C22semidirect
61. C2×#14519706C22semidirect
62. C2×#14519706C22semidirect
63. #16839769C22semidirect
64. #16839765C22semidirect
65. C2×#14519702C22semidirect
66. C2×#14519701C22semidirect
67. C2×#14519700C22semidirect
71. C22×SD16×C61C22semidirect
74. C2×C4×D4×C61C22semidirect
75. C61×#463C22semidirect
76. C2×C4⋊C8×C61C22semidirect
77. C2×#103×C61C22semidirect
107. C2×Dic244C23semidirect
109. C2×#11758202C23semidirect
115. C2×#11758200C23semidirect
133. C4×Dic122C23semidirect
135. #14519742C23semidirect
137. D4×Dic61C23semidirect
165. C4⋊#92418C23semidirect
166. #14519706C23semidirect
167. #14519706C23semidirect
168. #14519702C23semidirect
169. #14519701C23semidirect
170. #14519700C23semidirect
179. C2×SD16×C61C23semidirect
187. C4×D4×C61C23semidirect
193. C4⋊C8×C61C23semidirect
194. #103×C61C23semidirect
440. C2×#463D61semidirect
446. C2×C61#3040semidirect
464. C22×SD16C2×D61semidirect
484. C2×C4×D4C2×D61semidirect
498. #463C2×D61semidirect
503. C2×C4⋊C8C2×D61semidirect
509. C2×#103C2×D61semidirect
514. C61C2×#3040semidirect
557. C2×SD16C22×D61semidirect
589. C4×D4C22×D61semidirect
623. C4⋊C8C22×D61semidirect
627. #103C22×D61semidirect
867. C2#21455308direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145198062
C22×#145198012
C2×#124×D612
C2×C4×#117582242
#214553082
C2×#168399872
C2×#168399852
C2×#168399832
C2×#168399812
C2×#168399792
C2×#168399772
C2×#168399752
C2×#168397842
C2×#168397692
C2×#168397652
C2×C61×#4632
C2×#304061