Finite Group Databasebeta

← #30615200

Subgroups — #30615200

Order 15616.

1294 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462495C212yesmaximal, complemented
2#21461721C212yesmaximal, complemented
3#21461685C212yesmaximal, complemented
4#21461683C212yesmaximal, complemented
5#21461656C212yesmaximal
6#21461572C212yesmaximal, complemented
7#21461569C212yesmaximal, complemented
8C2×C4×#11758224C211yesmaximal, characteristic
9#16840783—22no—
10#16840782—22no—
11#16840779—22no—
12#16840778—22no—
13#16840765C2214yes—
14C2×#14519838C2214yes—
15C2×#14519837C2214yes—
16#16840732C2214yes—
17C4×#11758217C2214yes—
18#16840642C2214yes—
19#16840642C2214yes—
20C22×#11758224C2211yescharacteristic
21C4×#11758224—22no—
22C4×#11758224—22no—
23C4×#11758224—22no—
24C4×#11758224—22no—
25C2×C4×Dic122C2211yescharacteristic
26C2×#14519742C2211yescharacteristic
27C2×D4×Dic61C411yescharacteristic
28C2×C4×C22⋊D61C411yescharacteristic
29C2×C4×C22⋊D61C2211yescharacteristic
30C2×#14519737C411yescharacteristic
31C2×#14519737C2211yescharacteristic
32C2×#14519735C411yescharacteristic
33C2×#14519733C411yescharacteristic
34C2×#14519733C2211yescharacteristic
35C22×C4×Dic61C411yescharacteristic
36C22×C4×Dic61C2211yescharacteristic
37C2×C42×D61C411yescharacteristic
38C2×C4×D4×C61C411yescharacteristic
39C2×#11758217C2318yes—
40#14519844—24no—
41C4⋊#92420—24no—
42#14519838—28no—
43#14519837—28no—
44C22⋊#92420—24no—
45C22⋊#92420—24no—
46#14519832—24no—
47C4×#92420—24no—
48C2×#11758224—24no—
49C2×#11758224—22no—
50C2×#11758224—22no—
51C2×#11758224—24no—
52C22×Dic122C2311yescharacteristic
53C22×C22⋊D61C2×C411yescharacteristic
54C22×C22⋊D61C2311yescharacteristic
55C23×Dic61C2×C411yescharacteristic
56C23×Dic61C2×C411yescharacteristic
57C23×Dic61C2×C411yescharacteristic
58C23×Dic61C2311yescharacteristic
59C22×C4×D61C2×C411yescharacteristic
60C22×C4×D61C2×C411yescharacteristic
61C22×C4×D61C2×C411yescharacteristic
62C4×Dic122—22no—
63C4×Dic122—22no—
64#14519742—22no—
65#14519742—22no—
66D4×Dic61—22no—
67D4×Dic61—22no—
68C4×C22⋊D61—22no—
69C4×C22⋊D61—22no—
70C4×C22⋊D61—22no—
71C4×C22⋊D61—22no—
72#14519737—22no—
73#14519737—22no—
74#14519737—22no—
75#14519737—22no—
76#14519735—22no—
77#14519735—22no—
78#14519733—22no—
79#14519733—22no—
80#14519733—22no—
81#14519733—22no—
82C2×C4⋊Dic61C2×C411yescharacteristic
83C2×#11758196C2×C411yescharacteristic
84C2×#11758196C2×C411yescharacteristic
85C2×#11758196C2311yescharacteristic
86C2×#11758196C2311yescharacteristic
87C2×C22⋊Dic61C2×C411yescharacteristic
88C2×C22⋊Dic61C2×C411yescharacteristic
89C2×#11758198C2×C411yescharacteristic
90C2×#11758198C2×C411yescharacteristic
91C2×C4×Dic61—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61—21no—
94C2×C4×Dic61—21no—
95C2×C4×Dic61C2×C411yescharacteristic
96C2×C4×Dic61C2×C411yescharacteristic
97C2×C4×Dic61C2×C411yescharacteristic
98C2×C4×Dic61C2×C411yescharacteristic
99C2×C4×Dic61C2×C411yescharacteristic
100C2×C4×Dic61C2×C411yescharacteristic
101C2×C4×Dic61C2×C411yescharacteristic
102C2×C4×Dic61D412yes—
103C2×C4×Dic61D412yes—
104C2×C4×Dic61D412yes—
105C2×C4×Dic61D412yes—
106C2×C4×Dic61C2311yescharacteristic
107C2×C4×Dic61C2311yescharacteristic
108C42×D61—21no—
109C42×D61—21no—
110C42×D61—21no—
111C42×D61—21no—
112C22×D4×C61C2×C411yescharacteristic
113C23×C4×C61C2×C411yescharacteristic
114C23×C4×C61C2×C411yescharacteristic
115C4×D4×C61—22no—
116C4×D4×C61—22no—
117C2×C4⋊C4×C61C2×C411yescharacteristic
118C2×C22⋊C4×C61C2×C411yescharacteristic
119C2×C22⋊C4×C61C2×C411yescharacteristic
120C2×C42×C61C2×C411yescharacteristic
121C24×C61C22×C411yescharacteristic
122C24×C61C22×C411yescharacteristic
123C23×D61C22×C411yescharacteristic
124C2×D4×C61—22no—
125C2×D4×C61—22no—
126C2×D4×C61—22no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—42no—
130C22×C4×C61—42no—
131C22×C4×C61C22⋊C412yes—
132C22×C4×C61C22⋊C412yes—
133C22×C4×C61C22×C411yescharacteristic
134C22×C4×C61C22×C411yescharacteristic
135C22×C4×C61C22×C411yescharacteristic
136C22×C4×C61C22×C411yescharacteristic
137C22×C4×C61C22×C411yescharacteristic
138C2×C22⋊D61—22no—
139C2×C22⋊D61—22no—
140C2×C22⋊D61—22no—
141C2×C22⋊D61—22no—
142C2×C22⋊D61—22no—
143C2×C22⋊D61#4114yes—
144C22×Dic61—22no—
145C22×Dic61—21no—
146C22×Dic61—21no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—21no—
151C22×Dic61—21no—
152C22×Dic61—42no—
153C22×Dic61—42no—
154C22×Dic61C22⋊C412yes—
155C22×Dic61C22⋊C412yes—
156C22×Dic61C22×C411yescharacteristic
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159C22×Dic61C22×C411yescharacteristic
160C22×Dic61C22×C411yescharacteristic
161C22×Dic61C22×C411yescharacteristic
162C22×Dic61C2×D412yes—
163C22×Dic61C2×D412yes—
164C22×Dic61C2411yescharacteristic
165#11758224—216no—
166#11758224—216no—
167C2×C4×D61—22no—
168C2×C4×D61—22no—
169C2×C4×D61—21no—
170C2×C4×D61—21no—
171C2×C4×D61—21no—
172C2×C4×D61—21no—
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—42no—
176C2×C4×D61—42no—
177C2×Dic122—22no—
178C2×Dic122—22no—
179C2×Dic122#4114yes—
180#11758217—28no—
181#11758217—28no—
182C2×#92420—28no—
183C4⋊C4×C61—22no—
184C22⋊C4×C61—22no—
185C22⋊C4×C61—22no—
186C42×C61—21no—
187C42×C61—21no—
188C22⋊Dic61—22no—
189C22⋊Dic61—22no—
190#11758198—22no—
191#11758198—22no—
192C4⋊Dic61—22no—
193#11758196—22no—
194#11758196—22no—
195#11758196—22no—
196#11758196—22no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61—21no—
202C4×Dic61—21no—
203C4×Dic61—21no—
204C4×Dic61—21no—
205C4×Dic61—21no—
206C4×Dic61—21no—
207C4×Dic61C22⋊C411yescharacteristic
208C4×Dic61C22⋊C411yescharacteristic
209C4×Dic61C22⋊C411yescharacteristic
210C4×Dic61C22⋊C411yescharacteristic
211C4×Dic61C22⋊C412yes—
212C4×Dic61C22⋊C412yes—
213C4×Dic61C2×D412yes—
214C4×Dic61C2×D412yes—
215C4×Dic61C2×D412yes—
216C4×Dic61C2×D412yes—
217C23×C61—21no—
218C23×C61—21no—
219C23×C61—21no—
220C23×C61—21no—
221C23×C61—41no—
222C23×C61—41no—
223C23×C61—41no—
224C23×C61—41no—
225C23×C61C2×C22⋊C412yes—
226C23×C61#11712yes—
227C23×C61C23×C411yescharacteristic
228C22×D61—21no—
229C22×D61—21no—
230C22×D61—41no—
231C22×D61—41no—
232C22×D61#11712yes—
233D4×C61—28no—
234C2×C4×C61—21no—
235C2×C4×C61—21no—
236C2×C4×C61—22no—
237C2×C4×C61—24no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—42no—
241C2×C4×C61—41no—
242C2×C4×C61—42no—
243C2×C4×C61—42no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61C2×C22⋊C411yescharacteristic
247C2×C4×C61C2×C22⋊C412yes—
248C2×C4×C61C2×C22⋊C411yescharacteristic
249C2×C4×C61#11712yes—
250C22⋊D61—28no—
251C22⋊D61—28no—
252C2×Dic61—24no—
253C2×Dic61—24no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—24no—
259C2×Dic61—24no—
260C2×Dic61—22no—
261C2×Dic61—24no—
262C2×Dic61—21no—
263C2×Dic61—21no—
264C2×Dic61—42no—
265C2×Dic61—41no—
266C2×Dic61—42no—
267C2×Dic61—42no—
268C2×Dic61—41no—
269C2×Dic61—41no—
270C2×Dic61C2×C22⋊C411yescharacteristic
271C2×Dic61C2×C22⋊C411yescharacteristic
272C2×Dic61C2×C22⋊C411yescharacteristic
273C2×Dic61C2×C22⋊C412yes—
274C2×Dic61C2×C22⋊C411yescharacteristic
275C2×Dic61#11712yes—
276C2×Dic61C22×D412yes—
277C2×Dic61C2×#4112yes—
278C2×Dic61C2×#4112yes—
279C4×D61—24no—
280C4×D61—24no—
281C4×D61—42no—
282C4×D61—42no—
283C4×D61—42no—
284C4×D61—42no—
285Dic122—28no—
286#92420—48no—
287#20728—611nomaximal, Sylow
288C22×C61—21no—
289C22×C61—21no—
290C22×C61—22no—
291C22×C61—22no—
292C22×C61—22no—
293C22×C61—22no—
294C22×C61—42no—
295C22×C61—42no—
296C22×C61—42no—
297C22×C61—42no—
298C22×C61—41no—
299C22×C61—41no—
300C22×C61C22×C22⋊C411yescharacteristic
301C22×C61C2×#11711yescharacteristic
302C22×C61C2×#11711yescharacteristic
303C2×D61—22no—
304C2×D61—42no—
305C2×D61—41no—
306C2×D61—41no—
307C2×D61—42no—
308C4×C61—21no—
309C4×C61—22no—
310C4×C61—22no—
311C4×C61—41no—
312C4×C61—41no—
313C4×C61#41312yes—
314Dic61—21no—
315Dic61—22no—
316Dic61—22no—
317Dic61—21no—
318Dic61—21no—
319Dic61—41no—
320Dic61—41no—
321Dic61#41312yes—
322Dic61#52514yes—
323C2×C4×#41—611no—
324#2920—612no—
325#1822—612no—
326#1801—612no—
327#1800—612no—
328#1785—612no—
329C4×#101—612no—
330C4×#100—612no—
331C2×C61—21no—
332C2×C61—21no—
333C2×C61—42no—
334C2×C61—42no—
335C2×C61#228011yescharacteristic
336C2×C61C2×#41311yescharacteristic
337C2×C61C2×#41311yescharacteristic
338D61—42no—
339C22×#41—611no—
340C4×#41—1222no—
341C4×#41—1222no—
342C4×#41—1222no—
343C4×#41—1222no—
344C2×C4×Q8—611no—
345C2×C4×Q8—611no—
346C2×C4×D4—611no—
347C2×C4×D4—611no—
348C2×C4×D4—611no—
349C2×C4×D4—611no—
350C2×C4×D4—611no—
351C2×C4×D4#692311yescharacteristic
352C2×#117—611no—
353C2×#117—611no—
354C2×#117—611no—
355C22×C42—611no—
356C22×C42—611no—
357C22×C42—611no—
358#432—1222no—
359#432—1222no—
360#431—1222no—
361#431—1222no—
362#423—614no—
363C2×#101—614no—
364C2×#100—614no—
365#407—614no—
366C4×M16—614no—
367#343—614no—
368#343—614no—
369C61#2072811yescharacteristic, complemented, Sylow
370C2×#41—1222no—
371C2×#41—1222no—
372C2×#41—1224no—
373C2×#41—1224no—
374C22×Q8—611no—
375C22×D4—611no—
376C22×D4—611no—
377C22×D4C2×#692311yescharacteristic
378C23×C4—611no—
379C23×C4—611no—
380C23×C4—611no—
381C23×C4—611no—
382C23×C4—611no—
383C23×C4—611no—
384C23×C4—611no—
385C23×C4C2×#692311yescharacteristic
386C23×C4C2×#692311yescharacteristic
387C2×M16—618no—
388C4×Q8—1222no—
389C4×Q8—1222no—
390C4×Q8—1222no—
391C4×Q8—1222no—
392C4×D4—22no—
393C4×D4—22no—
394C4×D4—1222no—
395C4×D4—1222no—
396C4×D4—1222no—
397C4×D4—1222no—
398C4×D4—1222no—
399C4×D4—1222no—
400C4×D4—1222no—
401C4×D4—1222no—
402C4×D4—1222no—
403C4×D4—1222no—
404#117—1222no—
405#117—1222no—
406#117—1222no—
407#117—1222no—
408#117—1222no—
409#117—1222no—
410C2×C4⋊C4—611no—
411C2×C4⋊C4—611no—
412C2×C4⋊C4—611no—
413C2×C4⋊C4—611no—
414C2×C4⋊C4—611no—
415C2×C4⋊C4C2×#692311yescharacteristic
416C2×C22⋊C4—611no—
417C2×C22⋊C4—611no—
418C2×C22⋊C4—611no—
419C2×C22⋊C4—611no—
420C2×C22⋊C4C2×#692311yescharacteristic
421C2×C22⋊C4C2×#692311yescharacteristic
422C2×C42—612no—
423C2×C42—612no—
424C2×C42—612no—
425C2×C42—612no—
426C2×C42—611no—
427C2×C42—611no—
428C2×C42—611no—
429C2×C42—611no—
430C2×C42—611no—
431C2×C42—611no—
432C2×C42—611no—
433C2×C42—611no—
434C2×C42—611no—
435C2×C42—1221no—
436C2×C42—1221no—
437C2×C42—1221no—
438C2×C42—1221no—
439C2×C42—1221no—
440C2×C42—1221no—
441C2×C42—1221no—
442C2×C42—1221no—
443C2×C42C2×#692311yescharacteristic
444C4⋊C8—1224no—
445C4⋊C8—1224no—
446#101—1228no—
447#100—1228no—
448C22⋊C8—1224no—
449C22⋊C8—1224no—
450#97—1224no—
451C4×C8—1224no—
452C24—611no—
453C24C22×#692311yescharacteristic
454C24C22×#692311yescharacteristic
455#41—12216no—
456#41—12216no—
457C2×Q8—614no—
458C2×Q8—1222no—
459C2×Q8—1222no—
460C2×D4—22no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—614no—
464C2×D4—1222no—
465C2×D4—1222no—
466C2×D4—1222no—
467C2×D4—1222no—
468C2×D4—1222no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—611no—
474C22×C4—612no—
475C22×C4—612no—
476C22×C4—612no—
477C22×C4—611no—
478C22×C4—611no—
479C22×C4—611no—
480C22×C4—612no—
481C22×C4—611no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—1221no—
488C22×C4—1222no—
489C22×C4—1221no—
490C22×C4—1221no—
491C22×C4—1222no—
492C22×C4—1222no—
493C22×C4—1222no—
494C22×C4—1221no—
495C22×C4—1221no—
496C22×C4—1222no—
497C22×C4—1222no—
498C22×C4—1221no—
499C22×C4—1221no—
500C22×C4—2442no—
501C22×C4—2442no—
502C22×C4—2442no—
503C22×C4—2442no—
504C22×C4C22⋊#692312yes—
505C22×C4C22⋊#692312yes—
506C22×C4C22×#692311yescharacteristic
507C22×C4C22×#692311yescharacteristic
508C22×C4C22×#692311yescharacteristic
509C22×C4C22×#692311yescharacteristic
510C22×C4C22×#692311yescharacteristic
511M16—1228no—
512M16—1228no—
513C2×C8—1228no—
514C4⋊C4—22no—
515C4⋊C4—1222no—
516C4⋊C4—1222no—
517C4⋊C4—1222no—
518C4⋊C4—1222no—
519C4⋊C4—1222no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—1222no—
523C22⋊C4—1222no—
524C22⋊C4—1222no—
525C22⋊C4—1222no—
526C42—21no—
527C42—21no—
528C42—612no—
529C42—612no—
530C42—612no—
531C42—612no—
532C42—611no—
533C42—611no—
534C42—611no—
535C42—611no—
536C42—612no—
537C42—612no—
538C42—1221no—
539C42—1221no—
540C42—1221no—
541C42—1221no—
542C42—1221no—
543C42—1221no—
544C42—1221no—
545C42—1221no—
546C42—1221no—
547C42—1221no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—612no—
557C23—1221no—
558C23—1221no—
559C23—2441no—
560C23—2441no—
561C23C2×C22⋊#692312yes—
562C23#1451985612yes—
563C23C23×#692311yescharacteristic
564Q8—1228no—
565D4—28no—
566D4—1228no—
567D4—1228no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—42no—
575C2×C4—41no—
576C2×C4—42no—
577C2×C4—42no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—611no—
581C2×C4—612no—
582C2×C4—612no—
583C2×C4—612no—
584C2×C4—611no—
585C2×C4—611no—
586C2×C4—611no—
587C2×C4—612no—
588C2×C4—612no—
589C2×C4—1224no—
590C2×C4—1224no—
591C2×C4—1224no—
592C2×C4—1224no—
593C2×C4—1224no—
594C2×C4—1222no—
595C2×C4—1224no—
596C2×C4—1224no—
597C2×C4—1221no—
598C2×C4—1221no—
599C2×C4—1221no—
600C2×C4—1221no—
601C2×C4—1221no—
602C2×C4—1221no—
603C2×C4—2442no—
604C2×C4—2442no—
605C2×C4—2442no—
606C2×C4—2442no—
607C2×C4—2441no—
608C2×C4—2442no—
609C2×C4—2442no—
610C2×C4—2442no—
611C2×C4—2441no—
612C2×C4—2441no—
613C2×C4C2×C22⋊#692311yescharacteristic
614C2×C4C2×C22⋊#692312yes—
615C2×C4C2×C22⋊#692311yescharacteristic
616C2×C4#1451985612yes—
617C8—2448no—
618C22—21no—
619C22—21no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—42no—
625C22—42no—
626C22—42no—
627C22—42no—
628C22—41no—
629C22—41no—
630C22—1222no—
631C22—2442no—
632C22—2442no—
633C22—2441no—
634C22—2441no—
635C22C22×C22⋊#692311yescharacteristic
636C22C2×#1451985611yescharacteristic
637C22C2×#1451985611yescharacteristic
638C4—21no—
639C4—22no—
640C4—22no—
641C4—41no—
642C4—41no—
643C4—612no—
644C4—614no—
645C4—1222no—
646C4—1221no—
647C4—1221no—
648C4—1221no—
649C4—1222no—
650C4—2441no—
651C4—2441no—
652C4#1684074912yes—
653C2—21no—
654C2—21no—
655C2—42no—
656C2—42no—
657C2—2442no—
658C2#2146226311yescharacteristic
659C2D61⋊#41311yescharacteristic
660C2C2×#1684074911yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC23×C61C23×C4
FrattiniC23C23×#6923
FittingC2×C4×D4×C61C4
socleC22×C61C22×C22⋊C4
prime radicalC22×#11758224C22
cosocleC22×Dic61C24
hypercenterC2×C4×D4#6923
hypocenterC61#20728
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #21462495C2semidirect
2. #21461721C2semidirect
3. #21461685C2semidirect
4. #21461683C2semidirect
6. #21461572C2semidirect
7. #21461569C2semidirect
369. C61#20728semidirect

Maximal subgroups

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

subgroupindex
#214624952
#214617212
#214616852
#214616832
#214616562
#214615722
#214615692
C2×C4×#117582242
#2072861