Finite Group Databasebeta

← #30620284

Subgroups — #30620284

Order 15616.

1424 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840792C212yesmaximal, complemented
2#21461993C212yesmaximal, complemented
3#21461799C212yesmaximal, complemented
4#21461795C212yesmaximal, complemented
5#21461711C211yesmaximal, characteristic, complemented
6#21461711C211yesmaximal, characteristic, complemented
7#21461676C211yesmaximal, characteristic, complemented
8#21461546C211yesmaximal, characteristic, complemented
9#21461483C211yesmaximal, characteristic, complemented
10#21461480C211yesmaximal, characteristic, complemented
11C2×C4×#11758226C211yesmaximal, characteristic
12C22×#11758213C2212yes—
13C22×D61⋊C8C2212yes—
14#16840792—28no—
15C2×#14519844C2212yes—
16C2×#14519834C2212yes—
17C2×#14519834C2212yes—
18C2×#14519834C2212yes—
19C2×#14519834C2212yes—
20C2×#14519832C2212yes—
21#16840628C2212yes—
22#16840628C2212yes—
23#16840628C2212yes—
24#16840628C2212yes—
25#16840628C2211yescharacteristic
26#16840628C2211yescharacteristic
27#16840628C2211yescharacteristic
28#16840628C2211yescharacteristic
29C22×#11758226C411yescharacteristic
30C4×#11758226—28no—
31C2×Q8×Dic61C2211yescharacteristic
32C2×C4×D244C411yescharacteristic
33C2×C4×D244C411yescharacteristic
34C2×C4×D244C411yescharacteristic
35C2×#14519739C2211yescharacteristic
36C2×#14519739C2211yescharacteristic
37C2×#14519739C2211yescharacteristic
38C2×#14519735C411yescharacteristic
39C2×#14519735C411yescharacteristic
40C2×#14519735C411yescharacteristic
41C2×C42×D61C2211yescharacteristic
42C2×C42×D61C2211yescharacteristic
43C2×C42×D61C2211yescharacteristic
44C2×C4×Q8×C61C411yescharacteristic
45C2×#11758213—24no—
46C2×#11758213—24no—
47C2×#11758213—42no—
48C2×D61⋊C8—24no—
49C2×D61⋊C8—24no—
50C2×D61⋊C8—42no—
51C22×#92420C2312yes—
52C22×#92420C2312yes—
53C22×#92420C2312yes—
54C22×#92420C2312yes—
55#14519844—24no—
56#14519834—24no—
57#14519834—24no—
58#14519834—24no—
59#14519834—42no—
60#14519832—24no—
61C2×#11758226—24no—
62C2×#11758226—24no—
63C2×#11758226—24no—
64C22×D244C2×C411yescharacteristic
65C22×D244C2×C411yescharacteristic
66C22×D244C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61C2×C411yescharacteristic
69C22×C4×D61C2×C411yescharacteristic
70C22×C4×D61C2×C411yescharacteristic
71C22×C4×D61C2×C411yescharacteristic
72C22×C4×D61C2×C411yescharacteristic
73C22×C4×D61C2311yescharacteristic
74C22×C4×D61C2311yescharacteristic
75C22×C4×D61C2311yescharacteristic
76Q8×Dic61—24no—
77C4×D244—24no—
78C4×D244—24no—
79C4×D244—24no—
80#14519739—24no—
81#14519739—24no—
82#14519739D418yes—
83#14519735—24no—
84#14519735—24no—
85#14519735—24no—
86C2×C4⋊Dic61C2×C411yescharacteristic
87C2×C4⋊Dic61C2×C411yescharacteristic
88C2×C4⋊Dic61C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×#11758198C2×C411yescharacteristic
93C2×#11758198C2×C411yescharacteristic
94C2×#11758198C2×C411yescharacteristic
95C2×C4×Dic61C2×C411yescharacteristic
96C2×C4×Dic61C2×C411yescharacteristic
97C2×C4×Dic61C2×C411yescharacteristic
98C2×C4×Dic61C2311yescharacteristic
99C2×C4×Dic61C2311yescharacteristic
100C2×C4×Dic61C2311yescharacteristic
101C2×C4×Dic61C2311yescharacteristic
102C42×D61—24no—
103C42×D61—24no—
104C42×D61—24no—
105C22×Q8×C61C2×C411yescharacteristic
106C4×Q8×C61—24no—
107C2×C4⋊C4×C61C2×C411yescharacteristic
108C2×C4⋊C4×C61C2×C411yescharacteristic
109C2×C4⋊C4×C61C2×C411yescharacteristic
110C2×C42×C61C2×C411yescharacteristic
111C2×C42×C61C2×C411yescharacteristic
112C2×C42×C61C2×C411yescharacteristic
113C23×D61C22×C411yescharacteristic
114C23×D61C22×C411yescharacteristic
115C23×D61C22×C411yescharacteristic
116C2×Q8×C61—22no—
117C2×Q8×C61—22no—
118C2×Q8×C61—22no—
119C22×C4×C61C22×C411yescharacteristic
120C22×C4×C61C22×C411yescharacteristic
121C22×C4×C61C22×C411yescharacteristic
122C22×C4×C61C22×C411yescharacteristic
123C22×C4×C61C22×C411yescharacteristic
124C22×C4×C61C22×C411yescharacteristic
125C22×C4×C61C22×C411yescharacteristic
126C22×Dic61C22×C411yescharacteristic
127C22×Dic61C22×C411yescharacteristic
128C22×Dic61C22×C411yescharacteristic
129C22×Dic61C22×C411yescharacteristic
130C22×Dic61C2411yescharacteristic
131#11758226—232no—
132C2×D244—22no—
133C2×D244—22no—
134C2×D244—22no—
135C2×D244—22no—
136C2×D244—22no—
137C2×D244—22no—
138C2×D244—22no—
139C2×D244C22⋊C414yes—
140C2×D244M1614yescomplemented
141C2×C4×D61—22no—
142C2×C4×D61—22no—
143C2×C4×D61—22no—
144C2×C4×D61—22no—
145C2×C4×D61—22no—
146C2×C4×D61—22no—
147C2×C4×D61—22no—
148C2×C4×D61—22no—
149C2×C4×D61—22no—
150C2×C4×D61—22no—
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×C4×D61—22no—
156C2×C4×D61—22no—
157C2×C4×D61—22no—
158C2×C4×D61—22no—
159C2×C4×D61—22no—
160C2×C4×D61—22no—
161C2×C4×D61—22no—
162C2×C4×D61—22no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—41no—
166C2×C4×D61—41no—
167C2×C4×D61—41no—
168C2×C4×D61M1614yescomplemented
169C2×C4×D61C2×D414yes—
170C2×C4×D61C2×D414yes—
171C2×#92420—22no—
172C2×#92420—22no—
173C2×#92420—22no—
174C2×#92420—22no—
175C2×#92420—22no—
176C2×#92420—22no—
177C2×#92420—22no—
178C2×#92420—22no—
179C2×#92420—22no—
180C2×#92420—22no—
181C2×#92420—22no—
182C2×#92420#4114yescomplemented
183#11758213—48no—
184D61⋊C8—48no—
185C4⋊C4×C61—22no—
186C4⋊C4×C61—22no—
187C4⋊C4×C61C22⋊C414yes—
188C42×C61—22no—
189C42×C61—22no—
190C42×C61—22no—
191#11758198—22no—
192#11758198—22no—
193#11758198—22no—
194#11758198—22no—
195#11758198C22⋊C414yes—
196#11758198C22⋊C414yes—
197C4⋊Dic61—22no—
198C4⋊Dic61—22no—
199C4⋊Dic61—22no—
200C4×Dic61—22no—
201C4×Dic61—22no—
202C4×Dic61—22no—
203C4×Dic61—22no—
204C4×Dic61—22no—
205C4×Dic61—22no—
206C4×Dic61C2×D414yes—
207C23×C61C23×C411yescharacteristic
208C22×D61—21no—
209C22×D61—21no—
210C22×D61—21no—
211C22×D61—21no—
212C22×D61—21no—
213C22×D61—21no—
214C22×D61—21no—
215C22×D61—21no—
216C22×D61—21no—
217C22×D61—21no—
218C22×D61—21no—
219C22×D61—21no—
220C22×D61—21no—
221C22×D61—21no—
222C22×D61—21no—
223C22×D61—21no—
224C22×D61C2×C22⋊C412yes—
225C22×D61C2×C22⋊C412yes—
226C22×D61C2×M1612yes—
227C22×D61C2×M1612yes—
228C22×D61C2×M1612yes—
229Q8×C61—28no—
230C2×C4×C61—21no—
231C2×C4×C61—21no—
232C2×C4×C61—21no—
233C2×C4×C61—21no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—21no—
237C2×C4×C61—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—21no—
244C2×C4×C61—21no—
245C2×C4×C61C2×C22⋊C412yes—
246C2×C4×C61C2×C22⋊C412yes—
247C2×C4×C61C2×C22⋊C412yes—
248C2×C4×C61C2×M1612yes—
249C2×C4×C61C2×M1612yes—
250C2×C4×C61#13112yes—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—21no—
259C2×Dic61—21no—
260C2×Dic61—21no—
261C2×Dic61C2×C22⋊C412yes—
262C2×Dic61C2×M1612yes—
263C2×Dic61C22×D412yes—
264C2×Dic61C2×#4112yes—
265C2×Dic61H(5,𝔽2)11yescharacteristic
266C2×Dic612−1+411yescharacteristic
267D244—28no—
268D244—28no—
269D244—28no—
270C4×D61—28no—
271C4×D61—28no—
272C4×D61—28no—
273C4×D61—24no—
274C4×D61—24no—
275C4×D61—24no—
276C4×D61—24no—
277C4×D61—44no—
278C4×D61—44no—
279C4×D61—44no—
280C4×D61—42no—
281C4×D61—42no—
282#92420—24no—
283#92420—42no—
284#92420—42no—
285#92420—42no—
286#22471—611nomaximal, Sylow
287C22×C61C22×C22⋊C411yescharacteristic
288C22×C61C4×#4111yescharacteristic
289C22×C61#52011yescharacteristic
290C22×C61C22×M1611yescharacteristic
291C22×C61C22×M1611yescharacteristic
292C22×C61C2×#13111yescharacteristic
293C22×C61#56811yescharacteristic
294C2×D61—22no—
295C2×D61—22no—
296C2×D61—22no—
297C2×D61—22no—
298C2×D61—22no—
299C2×D61—22no—
300C2×D61—22no—
301C2×D61—22no—
302C2×D61—22no—
303C2×D61—22no—
304C2×D61—22no—
305C2×D61—22no—
306C2×D61—41no—
307C2×D61—41no—
308C2×D61—41no—
309C2×D61—41no—
310C2×D61—41no—
311C2×D61—41no—
312C2×D61—41no—
313C2×D61—41no—
314C2×D61#40714yes—
315C4×C61—22no—
316C4×C61—22no—
317C4×C61—22no—
318C4×C61—22no—
319C4×C61—22no—
320C4×C61—22no—
321C4×C61—41no—
322Dic61—22no—
323Dic61—22no—
324Dic61—41no—
325Dic61—41no—
326Dic61#54612yes—
327Dic61#54712yes—
328C2×C4×#41—611no—
329C2×#435—612no—
330#1985—612no—
331#1870—612no—
332#1869—612no—
333#1817—611no—
334#1817—611no—
335#1797—611no—
336#1749—611no—
337#1728—611no—
338C2×#336—611no—
339C2×C61#233911yescharacteristic
340C2×C61C2×#40711yescharacteristic
341C2×C61#288011yescharacteristic
342C2×C61#296511yescharacteristic
343C2×C61#297011yescharacteristic
344C2×C61#298911yescharacteristic
345C2×C61#299011yescharacteristic
346D61—24no—
347D61—42no—
348D61—42no—
349C22×#41—611no—
350C22×M16—612no—
351C23×C8—612no—
352C4×#41—1228no—
353C2×C4×Q8—611no—
354C2×C4×Q8#692311yescharacteristic
355C2×C4×D4—611no—
356C2×C4×D4—611no—
357C2×C4×D4—611no—
358C2×C4×D4—611no—
359C2×C4×D4—611no—
360C2×C4×D4—611no—
361C2×#117—611no—
362C2×#117—611no—
363C2×#117—611no—
364C22×C42—611no—
365C22×C42—611no—
366C22×C42—611no—
367#435—1228no—
368C2×C4⋊C8—612no—
369C2×C22⋊C8—612no—
370C2×C22⋊C8—612no—
371C2×C22⋊C8—612no—
372C2×C22⋊C8—612no—
373C2×#97—612no—
374#336—611no—
375#336—611no—
376#336—611no—
377#336—612no—
378#336—612no—
379#336—612no—
380#336—612no—
381#336—611no—
382C61#2247111yescharacteristic, complemented, Sylow
383C2×#41—1224no—
384C2×#41—1224no—
385C2×#41—1224no—
386C22×Q8C2×#692311yescharacteristic
387C22×D4—611no—
388C22×D4—611no—
389C22×D4—611no—
390C23×C4—611no—
391C23×C4—611no—
392C23×C4—611no—
393C23×C4—611no—
394C23×C4—611no—
395C23×C4—611no—
396C23×C4—611no—
397C23×C4—611no—
398C23×C4—611no—
399C2×M16—1224no—
400C2×M16—1224no—
401C2×M16—2442no—
402C22×C8—612no—
403C22×C8—612no—
404C22×C8—612no—
405C22×C8—612no—
406C22×C8—1224no—
407C22×C8—1224no—
408C22×C8—2442no—
409C4×Q8—24no—
410C4×Q8—1224no—
411C4×D4—618no—
412C4×D4—1224no—
413C4×D4—1224no—
414C4×D4—1224no—
415C4×D4—1224no—
416C4×D4—1224no—
417#117—1224no—
418#117—1224no—
419#117—1224no—
420C2×C4⋊C4—611no—
421C2×C4⋊C4—611no—
422C2×C4⋊C4—611no—
423C2×C4⋊C4C2×#692311yescharacteristic
424C2×C4⋊C4C2×#692311yescharacteristic
425C2×C4⋊C4C2×#692311yescharacteristic
426C2×C22⋊C4—611no—
427C2×C22⋊C4—611no—
428C2×C22⋊C4—611no—
429C2×C22⋊C4—611no—
430C2×C22⋊C4—611no—
431C2×C22⋊C4—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—611no—
436C2×C42—611no—
437C2×C42—611no—
438C2×C42—611no—
439C2×C42—1224no—
440C2×C42—1224no—
441C2×C42—1224no—
442C2×C42C2×#692311yescharacteristic
443C2×C42C2×#692311yescharacteristic
444C2×C42C2×#692311yescharacteristic
445C4⋊C8—1224no—
446C22⋊C8—1224no—
447C22⋊C8—1224no—
448C22⋊C8—1224no—
449C22⋊C8—2442no—
450#97—1224no—
451C24—611no—
452C24—611no—
453C24—611no—
454#41—12232no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×D4—614no—
459C2×D4—614no—
460C2×D4—1222no—
461C2×D4—1222no—
462C2×D4—1222no—
463C2×D4—1222no—
464C2×D4—1222no—
465C2×D4—1222no—
466C2×D4—1222no—
467C22×C4—611no—
468C22×C4—611no—
469C22×C4—611no—
470C22×C4—614no—
471C22×C4—614no—
472C22×C4—614no—
473C22×C4—611no—
474C22×C4—611no—
475C22×C4—1222no—
476C22×C4—1221no—
477C22×C4—1222no—
478C22×C4—1221no—
479C22×C4—1221no—
480C22×C4—1221no—
481C22×C4—1222no—
482C22×C4—1222no—
483C22×C4—1222no—
484C22×C4—1221no—
485C22×C4—1222no—
486C22×C4—1222no—
487C22×C4—1221no—
488C22×C4—1222no—
489C22×C4—1222no—
490C22×C4—1222no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1222no—
495C22×C4—1222no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1222no—
499C22×C4—2441no—
500C22×C4—2441no—
501C22×C4—2441no—
502C22×C4C22×#692311yescharacteristic
503C22×C4C22×#692311yescharacteristic
504C22×C4C22×#692311yescharacteristic
505C22×C4C22×#692311yescharacteristic
506C22×C4C22×#692311yescharacteristic
507C22×C4C22×#692311yescharacteristic
508C22×C4C22×#692311yescharacteristic
509M16—2448no—
510C2×C8—614no—
511C2×C8—1222no—
512C2×C8—1222no—
513C2×C8—1222no—
514C2×C8—1222no—
515C2×C8—1222no—
516C2×C8—1222no—
517C2×C8—1222no—
518C2×C8—1222no—
519C2×C8—1222no—
520C2×C8—1222no—
521C2×C8—1222no—
522C2×C8—2448no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—1222no—
526C4⋊C4—1222no—
527C4⋊C4—1222no—
528C4⋊C4C22⋊#692314yes—
529C22⋊C4—614no—
530C22⋊C4—614no—
531C22⋊C4—1222no—
532C22⋊C4—1222no—
533C22⋊C4—1222no—
534C22⋊C4—1222no—
535C42—22no—
536C42—22no—
537C42—22no—
538C42—614no—
539C42—1222no—
540C42—1222no—
541C42—1222no—
542C42—1222no—
543C42—1222no—
544C42—1222no—
545C23—612no—
546C23—612no—
547C23—612no—
548C23—612no—
549C23—612no—
550C23—1221no—
551C23—1221no—
552C23—1221no—
553C23—1221no—
554C23—1221no—
555C23—1221no—
556C23—1221no—
557C23—1221no—
558C23—1221no—
559C23—1221no—
560C23—1221no—
561C23—1221no—
562C23—1221no—
563C23—1221no—
564C23—1221no—
565C23—1221no—
566C23C23×#692311yescharacteristic
567Q8—28no—
568D4—1228no—
569D4—1228no—
570D4—1228no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—612no—
587C2×C4—612no—
588C2×C4—611no—
589C2×C4—611no—
590C2×C4—612no—
591C2×C4—612no—
592C2×C4—1224no—
593C2×C4—1224no—
594C2×C4—1224no—
595C2×C4—1224no—
596C2×C4—1228no—
597C2×C4—1228no—
598C2×C4—1228no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—1221no—
604C2×C4—1221no—
605C2×C4—1221no—
606C2×C4—1221no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—2444no—
610C2×C4—2444no—
611C2×C4—2444no—
612C2×C4—2442no—
613C2×C4—2442no—
614C2×C4C2×C22⋊#692312yes—
615C2×C4C2×C22⋊#692312yes—
616C2×C4C2×C22⋊#692312yes—
617C2×C4D61⋊M1612yes—
618C2×C4D61⋊M1612yes—
619C2×C4#1451986512yes—
620C8—1224no—
621C8—2442no—
622C8—2442no—
623C8—2442no—
624C22—614no—
625C22—1222no—
626C22—1222no—
627C22—1222no—
628C22—1222no—
629C22—1222no—
630C22—1222no—
631C22—1222no—
632C22—1222no—
633C22—1222no—
634C22—1222no—
635C22—1222no—
636C22—1222no—
637C22—2441no—
638C22—2441no—
639C22—2441no—
640C22—2441no—
641C22—2441no—
642C22—2441no—
643C22—2441no—
644C22—2441no—
645C22C22×C22⋊#692311yescharacteristic
646C22#41×#692311yescharacteristic
647C22#1684083111yescharacteristic
648C22C2×D61⋊M1611yescharacteristic
649C22C2×D61⋊M1611yescharacteristic
650C22C2×#1451986511yescharacteristic
651C22#1684084211yescharacteristic
652C4—22no—
653C4—22no—
654C4—22no—
655C4—22no—
656C4—22no—
657C4—22no—
658C4—41no—
659C4—612no—
660C4—612no—
661C4—1222no—
662C4—1222no—
663C4—2441no—
664C4—2441no—
665C2—1224no—
666C2—2442no—
667C2—2442no—
668C2#2146232211yescharacteristic
669C2D61⋊#40711yescharacteristic
670C2#2146240811yescharacteristic
671C2#2146262711yescharacteristic
672C2#2146266111yescharacteristic
673C2#2146274311yescharacteristic
674C2#2146274911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6923
commutator, socleC23×C61C23×C4
FittingC2×C4×Q8×C61C4
prime radicalC22×#11758226C4
cosocleC22×Dic61C24
hypercenterC2×C4×Q8#6923
hypocenterC61#22471
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#16840792C2semidirect
2. #21461993C2semidirect
3. #21461799C2semidirect
4. #21461795C2semidirect
5. #21461711C2semidirect
6. #21461711C2semidirect
7. #21461676C2semidirect
8. #21461546C2semidirect
9. #21461483C2semidirect
10. #21461480C2semidirect
140. C2×D244M16semidirect
168. C2×C4×D61M16semidirect
182. C2×#92420#41semidirect
382. C61#22471semidirect

Maximal subgroups

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

subgroupindex
C2×#168407922
#214619932
#214617992
#214617952
#214617112
#214616762
#214615462
#214614832
#214614802
C2×C4×#117582262
#2247161