Finite Group Databasebeta

← #30615182

Subgroups — #30615182

Order 15616.

1490 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462295C212yesmaximal, complemented
2#21461715C212yesmaximal, complemented
3#21461682C212yesmaximal, complemented
4#21461680C212yesmaximal, complemented
5#21461647C212yesmaximal
6C4×#14519836C212yesmaximal, complemented
7#21461564C212yesmaximal, complemented
8C2×#16840236C211yesmaximal, characteristic
9C2×#14519836C2214yes—
10C2×#14519836C2214yes—
11#16840712—28no—
12#16840704C2214yescomplemented
13#16840703C2214yes—
14C4×C22⋊#6923C2214yescomplemented
15#16840640C2214yescomplemented
16#16840640C2214yescomplemented
17C23×D244C2211yescharacteristic
18#16840236—28no—
19C2×C4×D244C411yescharacteristic, complemented
20C2×C4×D244C411yescharacteristic, complemented
21C2×C4×D244C2211yescharacteristic
22C2×C4×D244C2211yescharacteristic
23C2×#14519739C411yescharacteristic, complemented
24C2×#14519739C411yescharacteristic, complemented
25C2×#14519739C2211yescharacteristic
26C2×#14519739C2211yescharacteristic
27C2×#14519736C411yescharacteristic, complemented
28C2×C22⋊C4×D61C411yescharacteristic, complemented
29C2×C22⋊C4×D61C411yescharacteristic, complemented
30C2×C22⋊C4×D61C2211yescharacteristic
31C2×C22⋊C4×D61C2211yescharacteristic
32C2×#117×C61C411yescharacteristic, complemented
33C2×C4⋊#6923—24no—
34C2×C22⋊#6923—24no—
35C2×C22⋊#6923—24no—
36C2×C22⋊#6923C2318yes—
37C2×C4×#6923—24no—
38#14519836—28no—
39#14519836—28no—
40(C2×#6923)⋊C4—24no—
41(C2×#6923)⋊C4—24no—
42C24×D61C2×C411yescharacteristic
43C24×D61C2311yescharacteristic
44C22×D244—24no—
45C22×D244—24no—
46C22×D244—24no—
47C22×D244C2×C411yescharacteristic
48C22×D244C2×C411yescharacteristic
49C22×D244C2311yescharacteristic
50C22×D244C2311yescharacteristic
51C22×C4×D61C2×C411yescharacteristic
52C22×C4×D61C2×C411yescharacteristic
53C22×C4×D61C2×C411yescharacteristic
54C22×C4×D61C2×C411yescharacteristic
55C22×C4×D61C2×C411yescharacteristic
56C22×C4×D61C2×C411yescharacteristic
57C22×C4×D61C2311yescharacteristic
58C22×C4×D61C2311yescharacteristic
59C4×D244—24no—
60C4×D244—24no—
61C4×D244—24no—
62C4×D244—24no—
63#14519739—24no—
64#14519739—24no—
65#14519739—24no—
66#14519739—24no—
67#14519736—24no—
68C2×C4⋊Dic61C2×C411yescharacteristic
69C2×C4⋊Dic61C2×C411yescharacteristic
70C2×C22⋊Dic61C2×C411yescharacteristic
71C2×C22⋊Dic61C2×C411yescharacteristic
72C2×#11758198C2×C411yescharacteristic
73C2×#11758198C2×C411yescharacteristic
74C2×#11758198C2×C411yescharacteristic
75C2×#11758198C2×C411yescharacteristic
76C2×#11758198C2×C411yescharacteristic
77C2×#11758198C2×C411yescharacteristic
78C2×#11758198C2311yescharacteristic
79C2×#11758198C2311yescharacteristic
80C22⋊C4×D61—24no—
81C22⋊C4×D61—24no—
82C22⋊C4×D61—24no—
83C22⋊C4×D61D418yes—
84C2×C4×Dic61C2×C411yescharacteristic
85C2×C4×Dic61C2×C411yescharacteristic
86C23×C4×C61C2×C411yescharacteristic
87#117×C61—24no—
88C2×C4⋊C4×C61C2×C411yescharacteristic
89C2×C4⋊C4×C61C2×C411yescharacteristic
90C2×C22⋊C4×C61C2×C411yescharacteristic
91C2×C22⋊C4×C61C2×C411yescharacteristic
92C2×C42×C61C2×C411yescharacteristic
93C2×C42×C61C2×C411yescharacteristic
94C24×C61C22×C411yescharacteristic
95C23×D61—22no—
96C23×D61—22no—
97C23×D61—22no—
98C23×D61—22no—
99C23×D61—22no—
100C23×D61—81no—
101C23×D61—81no—
102C23×D61—81no—
103C23×D61—81no—
104C23×D61C22×C411yescharacteristic
105C23×D61C22×C411yescharacteristic
106C23×D61C22×C411yescharacteristic
107C23×D61C2×D414yes—
108C23×D61C2411yescharacteristic
109C22×#6923—28no—
110C22×C4×C61—22no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61C22×C411yescharacteristic
114C22×C4×C61C22×C411yescharacteristic
115C22×C4×C61C22×C411yescharacteristic
116C22×C4×C61C22×C411yescharacteristic
117C22×C4×C61C22×C411yescharacteristic
118C22×C4×C61C22×C411yescharacteristic
119C22×Dic61C22×C411yescharacteristic
120C22×Dic61C22×C411yescharacteristic
121C22×Dic61C22×C411yescharacteristic
122C22×Dic61C22×C411yescharacteristic
123C2×D244—232no—
124C2×D244—22no—
125C2×D244—22no—
126C2×D244—22no—
127C2×D244—22no—
128C2×D244—22no—
129C2×D244—22no—
130C2×D244—22no—
131C2×D244—22no—
132C2×D244—22no—
133C2×D244—22no—
134C2×D244#4114yes—
135C2×D244#4114yes—
136C2×C4×D61—22no—
137C2×C4×D61—22no—
138C2×C4×D61—22no—
139C2×C4×D61—22no—
140C2×C4×D61—22no—
141C2×C4×D61—22no—
142C2×C4×D61—81no—
143C2×C4×D61—81no—
144C2×C4×D61—81no—
145C2×C4×D61—81no—
146C2×C4×D61—81no—
147C2×C4×D61—81no—
148C2×C4×D61—81no—
149C2×C4×D61—81no—
150C2×C4×D61C2×D414yes—
151C2×C4×D61C2×D414yes—
152C22⋊#6923—28no—
153C22⋊#6923—28no—
154C22⋊#6923—84no—
155C22⋊#6923—84no—
156C4⋊#6923—84no—
157C4×#6923—84no—
158C4⋊C4×C61—22no—
159C4⋊C4×C61—22no—
160C22⋊C4×C61—22no—
161C22⋊C4×C61C22⋊C414yes—
162C42×C61—22no—
163C42×C61—22no—
164C22⋊Dic61—22no—
165C22⋊Dic61C22⋊C414yes—
166#11758198—22no—
167#11758198—22no—
168#11758198—22no—
169#11758198—22no—
170#11758198—22no—
171#11758198—22no—
172#11758198C22⋊C414yes—
173#11758198C22⋊C414yes—
174C4⋊Dic61—22no—
175C4⋊Dic61—22no—
176C4×Dic61—22no—
177C4×Dic61—22no—
178C23×C61—21no—
179C23×C61—21no—
180C23×C61—41no—
181C23×C61—41no—
182C23×C61C2×C22⋊C412yes—
183C23×C61C23×C411yescharacteristic
184C22×D61—21no—
185C22×D61—21no—
186C22×D61—21no—
187C22×D61—21no—
188C22×D61—21no—
189C22×D61—21no—
190C22×D61—28no—
191C22×D61—28no—
192C22×D61—41no—
193C22×D61—41no—
194C22×D61—41no—
195C22×D61—41no—
196C22×D61—44no—
197C22×D61—44no—
198C22×D61—41no—
199C22×D61—41no—
200C22×D61—41no—
201C22×D61—41no—
202C22×D61—82no—
203C22×D61—82no—
204C22×D61—84no—
205C22×D61—84no—
206C22×D61—84no—
207C22×D61—84no—
208C22×D61C2×C22⋊C412yes—
209C22×D61#11712yes—
210C22×D61#11712yes—
211C22×D61C22×D412yes—
212C22×D61C2×#4112yes—
213C22×D61C2×#4112yes—
214C2×#6923—48no—
215C2×#6923—48no—
216C2×#6923—48no—
217C2×C4×C61—28no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61C2×C22⋊C412yes—
229C2×C4×C61C2×C22⋊C412yes—
230C2×C4×C61#11712yes—
231C2×C4×C61#11712yes—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61C2×C22⋊C412yes—
239C2×Dic61C2×C22⋊C412yes—
240D244—28no—
241D244—28no—
242D244—28no—
243D244—28no—
244C4×D61—44no—
245C4×D61—44no—
246C4×D61—82no—
247C4×D61—82no—
248C4×D61—82no—
249C4×D61—82no—
250C4×D61—82no—
251C4×D61—82no—
252#20724—611nomaximal, Sylow
253C22×C61—21no—
254C22×C61—21no—
255C22×C61—22no—
256C22×C61—22no—
257C22×C61—22no—
258C22×C61—42no—
259C22×C61—42no—
260C22×C61C22×C22⋊C411yescharacteristic
261C22×C61C2×#11711yescharacteristic
262C22×C61C2×#11711yescharacteristic
263C2×D61—22no—
264C2×D61—22no—
265C2×D61—22no—
266C2×D61—22no—
267C2×D61—22no—
268C2×D61—22no—
269C2×D61—22no—
270C2×D61—42no—
271C2×D61—42no—
272C2×D61—42no—
273C2×D61—42no—
274C2×D61—42no—
275C2×D61—42no—
276C2×D61—41no—
277C2×D61—41no—
278C2×D61—41no—
279C2×D61—41no—
280C2×D61—42no—
281C2×D61—42no—
282C2×D61—88no—
283C2×D61—88no—
284C2×D61#52514yes—
285#6923—88no—
286C4×C61—22no—
287C4×C61—22no—
288C4×C61—22no—
289C4×C61—22no—
290C4×C61—41no—
291C4×C61—41no—
292Dic61—22no—
293Dic61—22no—
294Dic61—41no—
295Dic61—41no—
296C2×#518—611no—
297#2312—612no—
298#1819—612no—
299#1799—612no—
300#1799—612no—
301#1781—612no—
302C4×#99—612no—
303C4×#99—612no—
304C2×C61—21no—
305C2×C61—21no—
306C2×C61—42no—
307C2×C61#228011yescharacteristic
308C2×C61#288311yescharacteristic
309C2×C61#288311yescharacteristic
310D61—24no—
311D61—42no—
312D61—42no—
313D61—42no—
314C23×D4—611no—
315#518—1228no—
316C2×C4×D4—611no—
317C2×C4×D4—611no—
318C2×C4×D4—611no—
319C2×C4×D4—611no—
320C2×C4×D4—611no—
321C2×C4×D4—611no—
322C2×C4×D4—611no—
323C2×C4×D4—611no—
324C2×#117—611no—
325C2×#117#692311yescharacteristic, complemented
326C22×C22⋊C4—611no—
327C22×C22⋊C4—611no—
328C22×C22⋊C4—611no—
329C22×C22⋊C4—611no—
330C2×#99—614no—
331C2×#99—614no—
332#388—1228no—
333#380—614no—
334#379—614no—
335C4×C22⋊C4—614no—
336#342—614no—
337#342—614no—
338C61#2072411yescharacteristic, complemented, Sylow
339C25—611no—
340C25—611no—
341C22×D4—611no—
342C22×D4—611no—
343C22×D4—611no—
344C22×D4—611no—
345C22×D4—1224no—
346C22×D4—1224no—
347C22×D4—1224no—
348C23×C4—611no—
349C23×C4—611no—
350C23×C4—611no—
351C23×C4—611no—
352C23×C4—611no—
353C23×C4—611no—
354C23×C4—611no—
355C23×C4—611no—
356C23×C4C2×#692311yescharacteristic
357C4×D4—1224no—
358C4×D4—1224no—
359C4×D4—1224no—
360C4×D4—1224no—
361C4×D4—1224no—
362C4×D4—1224no—
363C4×D4—1224no—
364C4×D4—1224no—
365#117—24no—
366#117—1224no—
367C2×C4⋊C4—611no—
368C2×C4⋊C4—611no—
369C2×C4⋊C4—1224no—
370C2×C4⋊C4C2×#692311yescharacteristic
371C2×C4⋊C4C2×#692311yescharacteristic
372C2×C22⋊C4—611no—
373C2×C22⋊C4—611no—
374C2×C22⋊C4—611no—
375C2×C22⋊C4—618no—
376C2×C22⋊C4—611no—
377C2×C22⋊C4—611no—
378C2×C22⋊C4—611no—
379C2×C22⋊C4—611no—
380C2×C22⋊C4—611no—
381C2×C22⋊C4—611no—
382C2×C22⋊C4—611no—
383C2×C22⋊C4—618no—
384C2×C22⋊C4—1224no—
385C2×C22⋊C4—1224no—
386C2×C22⋊C4—1224no—
387C2×C22⋊C4—1224no—
388C2×C22⋊C4—1224no—
389C2×C22⋊C4C2×#692311yescharacteristic
390C2×C22⋊C4C2×#692311yescharacteristic
391C2×C42—611no—
392C2×C42—611no—
393C2×C42—1224no—
394C2×C42C2×#692311yescharacteristic
395C2×C42C2×#692311yescharacteristic
396#99—1228no—
397#99—1228no—
398#95—1224no—
399#95—1224no—
400C24—611no—
401C24—614no—
402C24—611no—
403C24—611no—
404C24—611no—
405C24—1222no—
406C24—1222no—
407C24—1222no—
408C24—1222no—
409C24—1222no—
410C24—4881no—
411C24—4881no—
412C24—4881no—
413C24—4881no—
414C24C22×#692311yescharacteristic
415C2×D4—614no—
416C2×D4—614no—
417C2×D4—1222no—
418C2×D4—1222no—
419C2×D4—1222no—
420C2×D4—1222no—
421C2×D4—1222no—
422C2×D4—1222no—
423C2×D4—1222no—
424C2×D4—1222no—
425C2×D4—12232no—
426C2×D4—1222no—
427C2×D4—1222no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—614no—
434C22×C4—614no—
435C22×C4—611no—
436C22×C4—611no—
437C22×C4—1222no—
438C22×C4—1222no—
439C22×C4—1222no—
440C22×C4—1222no—
441C22×C4—1222no—
442C22×C4—1222no—
443C22×C4—1228no—
444C22×C4—4881no—
445C22×C4—4881no—
446C22×C4—4881no—
447C22×C4—4881no—
448C22×C4—4881no—
449C22×C4—4881no—
450C22×C4—4881no—
451C22×C4—4881no—
452C22×C4C22×#692311yescharacteristic
453C22×C4C22×#692311yescharacteristic
454C22×C4C22×#692311yescharacteristic
455C22×C4C22×#692311yescharacteristic
456C22×C4C22×#692311yescharacteristic
457C22×C4C22×#692311yescharacteristic
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—1222no—
461C4⋊C4—1222no—
462C4⋊C4—4884no—
463C22⋊C4—22no—
464C22⋊C4—614no—
465C22⋊C4—614no—
466C22⋊C4—614no—
467C22⋊C4—1222no—
468C22⋊C4—1222no—
469C22⋊C4—1222no—
470C22⋊C4—1222no—
471C22⋊C4—1222no—
472C22⋊C4—1222no—
473C22⋊C4—1222no—
474C22⋊C4—1228no—
475C22⋊C4—1228no—
476C22⋊C4—4884no—
477C22⋊C4—4884no—
478C22⋊C4C22⋊#692314yes—
479C42—22no—
480C42—22no—
481C42—1222no—
482C42—1222no—
483C42—4884no—
484C23—21no—
485C23—21no—
486C23—41no—
487C23—41no—
488C23—612no—
489C23—612no—
490C23—612no—
491C23—612no—
492C23—612no—
493C23—612no—
494C23—1228no—
495C23—1228no—
496C23—1221no—
497C23—1221no—
498C23—1221no—
499C23—1221no—
500C23—1221no—
501C23—1221no—
502C23—4882no—
503C23—4882no—
504C23—4884no—
505C23—4884no—
506C23—4884no—
507C23—4884no—
508C23—2444no—
509C23—2444no—
510C23—2441no—
511C23—2441no—
512C23—2441no—
513C23—2441no—
514C23—2441no—
515C23—2441no—
516C23—2441no—
517C23—2441no—
518C23C2×C22⋊#692312yes—
519C23C23×#692311yescharacteristic
520D4—1228no—
521D4—1228no—
522D4—1228no—
523D4—1228no—
524C2×C4—28no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—612no—
536C2×C4—612no—
537C2×C4—1221no—
538C2×C4—1221no—
539C2×C4—4882no—
540C2×C4—4882no—
541C2×C4—4882no—
542C2×C4—4882no—
543C2×C4—4882no—
544C2×C4—4882no—
545C2×C4—2444no—
546C2×C4—2444no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2448no—
550C2×C4—2448no—
551C2×C4—2448no—
552C2×C4—2441no—
553C2×C4—2441no—
554C2×C4C2×C22⋊#692312yes—
555C2×C4C2×C22⋊#692312yes—
556C2×C4#1451985612yes—
557C2×C4#1451985612yes—
558C22—21no—
559C22—21no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—42no—
564C22—42no—
565C22—614no—
566C22—1222no—
567C22—1222no—
568C22—1222no—
569C22—1222no—
570C22—1222no—
571C22—1222no—
572C22—1222no—
573C22—4888no—
574C22—4888no—
575C22—2442no—
576C22—2442no—
577C22—2442no—
578C22—2442no—
579C22—2442no—
580C22—2442no—
581C22—2442no—
582C22—2442no—
583C22—2441no—
584C22—2441no—
585C22—2441no—
586C22—2441no—
587C22C22×C22⋊#692311yescharacteristic
588C22C2×#1451985611yescharacteristic
589C22C2×#1451985611yescharacteristic
590C4—22no—
591C4—22no—
592C4—22no—
593C4—22no—
594C4—41no—
595C4—41no—
596C4—1222no—
597C4—1222no—
598C4—4888no—
599C4—2441no—
600C4—2441no—
601C2—21no—
602C2—21no—
603C2—42no—
604C2—1224no—
605C2—2442no—
606C2—2442no—
607C2—2442no—
608C2#2146226311yescharacteristic
609C2#2146241911yescharacteristic
610C2#2146241911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×#117×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC23×D244C22
cosocleC23×D61C24
hypercenterC2×#117#6923
hypocenterC61#20724
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C22⋊C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. #21462295C2semidirect
2. #21461715C2semidirect
3. #21461682C2semidirect
4. #21461680C2semidirect
6. C4×#14519836C2semidirect
7. #21461564C2semidirect
12. #16840704C22semidirect
14. C4×C22⋊#6923C22semidirect
15. #16840640C22semidirect
16. #16840640C22semidirect
19. C2×C4×D244C4semidirect
20. C2×C4×D244C4semidirect
23. C2×#14519739C4semidirect
24. C2×#14519739C4semidirect
27. C2×#14519736C4semidirect
28. C2×C22⋊C4×D61C4semidirect
29. C2×C22⋊C4×D61C4semidirect
32. C2×#117×C61C4semidirect
325. C2×#117#6923semidirect
338. C61#20724semidirect

Maximal subgroups

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

subgroupindex
#214622952
#214617152
#214616822
#214616802
#214616472
C4×#145198362
#214615642
C2×#168402362
#2072461