Finite Group Databasebeta

← #29602621

Subgroups — #29602621

Order 15616.

1486 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊Dic61C211yesmaximal, characteristic
2#21444079C212yesmaximal, complemented
3#21444066C212yesmaximal
4#21444056C212yesmaximal
5#21444045C212yesmaximal, complemented
6#21444045C211yesmaximal, characteristic, complemented
7#21444045C211yesmaximal, characteristic, complemented
8#21444044C211yesmaximal, characteristic, complemented
9#21444042C211yesmaximal, characteristic
10#95×Dic61C211yesmaximal, characteristic, complemented
11C61×C22⋊#95C211yesmaximal, characteristic
12C22×C22⋊Dic61C2212yes—
13C22×C22⋊Dic61C2211yescharacteristic
14C22×C22⋊Dic61C2211yescharacteristic
15C22×C4×Dic61C2212yes—
16C22×C4×Dic61C2211yescharacteristic
17C22×C4×Dic61C2211yescharacteristic
18C4×C22⋊Dic61C418yescomplemented
19C2×#14519684C2211yescharacteristic
20C2×#14519684C2212yes—
21C2×#14519684C2211yescharacteristic
22C2×#14519684C2212yes—
23C2×#14519684C2212yes—
24C2×#14519684C2212yes—
25C2×#14519684C2212yes—
26C2×#14519684C2212yes—
27C2×#14519684C2212yes—
28C2×#14519684C2212yes—
29C2×#14519684C2211yescharacteristic
30C2×#14519684C2211yescharacteristic
31C24×C4×C61C2211yescharacteristic
32C22×C22⋊C4×C61C2212yes—
33C2×#95×C61C2211yescharacteristic
34C2×#95×C61C2211yescharacteristic
35C2×#95×C61C2212yes—
36C23×Dic61C2312yes—
37C23×Dic61C2311yescharacteristic
38C23×Dic61C2311yescharacteristic
39C23×Dic61C2311yescharacteristic
40C23×Dic61C2312yes—
41C23×Dic61C2311yescharacteristic
42C2×C22⋊Dic61—22no—
43C2×C22⋊Dic61—22no—
44C2×C22⋊Dic61—22no—
45C2×C22⋊Dic61—22no—
46C2×C22⋊Dic61—24no—
47C2×C22⋊Dic61—24no—
48C2×C22⋊Dic61—42no—
49C2×C22⋊Dic61C2×C414yes—
50C2×C22⋊Dic61C2×C414yes—
51C2×C4×Dic61—24no—
52C2×C4×Dic61—24no—
53C2×C4×Dic61—42no—
54C2×C4×Dic61—42no—
55C2×C4×Dic61—42no—
56C2×C4×Dic61C2×C414yes—
57C2×C4×Dic61C2×C414yes—
58#14519684—24no—
59#14519684—24no—
60#14519684—22no—
61#14519684—22no—
62#14519684—24no—
63#14519684—24no—
64#14519684—42no—
65#14519684—42no—
66#14519684—42no—
67#14519684—42no—
68#14519684C2×C414yes—
69#14519684C2×C414yes—
70C25×C61C2311yescharacteristic
71C23×C4×C61—22no—
72C23×C4×C61—22no—
73C23×C4×C61—42no—
74C23×C4×C61—42no—
75C23×C4×C61C2×C414yes—
76C23×C4×C61C2312yes—
77C23×C4×C61C2311yescharacteristic
78C23×C4×C61C2312yes—
79C23×C4×C61C2311yescharacteristic
80C2×C22⋊C4×C61—24no—
81C2×C22⋊C4×C61—24no—
82C2×C22⋊C4×C61—42no—
83#95×C61—22no—
84#95×C61—22no—
85#95×C61—42no—
86C24×C61—22no—
87C24×C61—21no—
88C24×C61—21no—
89C24×C61—21no—
90C24×C61—21no—
91C24×C61—22no—
92C24×C61—22no—
93C24×C61—22no—
94C24×C61C22×C412yes—
95C24×C61#4112yes—
96C24×C61#4112yes—
97C24×C61C2411yescharacteristic
98C22×C4×C61—22no—
99C22×C4×C61—22no—
100C22×C4×C61—22no—
101C22×C4×C61—22no—
102C22×C4×C61—21no—
103C22×C4×C61—21no—
104C22×C4×C61—22no—
105C22×C4×C61—22no—
106C22×C4×C61—22no—
107C22×C4×C61—22no—
108C22×C4×C61—22no—
109C22×C4×C61—22no—
110C22×C4×C61—28no—
111C22×C4×C61—22no—
112C22×C4×C61—22no—
113C22×C4×C61—22no—
114C22×C4×C61—22no—
115C22×C4×C61—22no—
116C22×C4×C61—22no—
117C22×C4×C61—22no—
118C22×C4×C61—44no—
119C22×C4×C61—44no—
120C22×C4×C61—48no—
121C22×C4×C61—48no—
122C22×C4×C61C22×C412yes—
123C22×C4×C61C22×C412yes—
124C22×C4×C61#4114yes—
125C22×C4×C61#4112yes—
126C22×C4×C61#4112yes—
127C22×Dic61—22no—
128C22×Dic61—22no—
129C22×Dic61—22no—
130C22×Dic61—22no—
131C22×Dic61—22no—
132C22×Dic61—22no—
133C22×Dic61—22no—
134C22×Dic61—22no—
135C22×Dic61—21no—
136C22×Dic61—21no—
137C22×Dic61—21no—
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C22×Dic61—22no—
142C22×Dic61—22no—
143C22×Dic61—22no—
144C22×Dic61—22no—
145C22×Dic61—22no—
146C22×Dic61—22no—
147C22×Dic61—22no—
148C22×Dic61—22no—
149C22×Dic61—22no—
150C22×Dic61—22no—
151C22×Dic61—22no—
152C22×Dic61—22no—
153C22×Dic61—22no—
154C22×Dic61C22×C412yes—
155C22×Dic61C22×C412yes—
156C22×Dic61C22×C412yes—
157C22×Dic61C22×C412yes—
158C22×Dic61#4114yes—
159C22×Dic61#4112yes—
160C22×Dic61#4112yes—
161C22⋊C4×C61—48no—
162C22⋊Dic61—28no—
163C22⋊Dic61—28no—
164C22⋊Dic61—48no—
165C4×Dic61—44no—
166C4×Dic61—44no—
167C4×Dic61—48no—
168C23×C61—22no—
169C23×C61—22no—
170C23×C61—22no—
171C23×C61—22no—
172C23×C61—22no—
173C23×C61—22no—
174C23×C61—22no—
175C23×C61—22no—
176C23×C61—22no—
177C23×C61—22no—
178C23×C61—24no—
179C23×C61—24no—
180C23×C61—24no—
181C23×C61—24no—
182C23×C61—42no—
183C23×C61—42no—
184C23×C61—42no—
185C23×C61—42no—
186C23×C61—42no—
187C23×C61—42no—
188C23×C61—42no—
189C23×C61—42no—
190C23×C61#11714yes—
191C23×C61C23×C411yescharacteristic
192C23×C61C2×#4111yescharacteristic
193C23×C61C2×#4111yescharacteristic
194C23×C61C2×#4111yescharacteristic
195C23×C61C2×#4111yescharacteristic
196C23×C61C2×#4111yescharacteristic
197C23×C61C2×#4111yescharacteristic
198C23×C61C2×#4112yes—
199C23×C61C2×#4112yes—
200C23×C61H(5,𝔽2)12yes—
201C23×C61H(5,𝔽2)12yes—
202C2×C4×C61—22no—
203C2×C4×C61—22no—
204C2×C4×C61—24no—
205C2×C4×C61—24no—
206C2×C4×C61—22no—
207C2×C4×C61—22no—
208C2×C4×C61—22no—
209C2×C4×C61—24no—
210C2×C4×C61—24no—
211C2×C4×C61—24no—
212C2×C4×C61—416no—
213C2×C4×C61—42no—
214C2×C4×C61—42no—
215C2×C4×C61—42no—
216C2×C4×C61—42no—
217C2×C4×C61—42no—
218C2×C4×C61—42no—
219C2×C4×C61—42no—
220C2×C4×C61—42no—
221C2×C4×C61—42no—
222C2×C4×C61—42no—
223C2×C4×C61—42no—
224C2×C4×C61—42no—
225C2×C4×C61—42no—
226C2×C4×C61#11714yes—
227C2×Dic61—22no—
228C2×Dic61—22no—
229C2×Dic61—24no—
230C2×Dic61—24no—
231C2×Dic61—22no—
232C2×Dic61—22no—
233C2×Dic61—22no—
234C2×Dic61—22no—
235C2×Dic61—22no—
236C2×Dic61—22no—
237C2×Dic61—22no—
238C2×Dic61—22no—
239C2×Dic61—22no—
240C2×Dic61—24no—
241C2×Dic61—24no—
242C2×Dic61—24no—
243C2×Dic61—42no—
244C2×Dic61—42no—
245C2×Dic61—42no—
246C2×Dic61—42no—
247C2×Dic61—42no—
248C2×Dic61—42no—
249C2×Dic61—42no—
250C2×Dic61—42no—
251C2×Dic61—42no—
252C2×Dic61—42no—
253C2×Dic61—42no—
254C2×Dic61—42no—
255C2×Dic61—42no—
256C2×Dic61—42no—
257C2×Dic61—42no—
258C2×Dic61—42no—
259C2×Dic61—42no—
260C2×Dic61#11714yes—
261#13947—611nomaximal, Sylow
262C22×C61—24no—
263C22×C61—24no—
264C22×C61—24no—
265C22×C61—42no—
266C22×C61—44no—
267C22×C61—44no—
268C22×C61—44no—
269C22×C61—44no—
270C22×C61—42no—
271C22×C61—42no—
272C22×C61—42no—
273C22×C61C2×#11711yescharacteristic
274C22×C61C2×#11711yescharacteristic
275C22×C61C2×#11711yescharacteristic
276C22×C61C4×#4111yescharacteristic
277C22×C61C4×#4111yescharacteristic
278C22×C61#51811yescharacteristic
279C22×C61#51811yescharacteristic
280C22×C61#52912yes—
281C22×C61#52911yescharacteristic
282C22×C61#52911yescharacteristic
283C22×C61#52912yes—
284C22×C61#52911yescharacteristic
285C22×C61#52911yescharacteristic
286C22×C61#53812yes—
287C22×C61#53812yes—
288C22×C61#55112yes—
289C22×C61#55112yes—
290C22×C61#55112yes—
291C22×C61#55312yes—
292C22×C61#55312yes—
293C22×C61#55312yes—
294C22×C61#55312yes—
295C22×C61#55912yes—
296C4×C61—24no—
297C4×C61—42no—
298C4×C61—44no—
299C4×C61—82no—
300Dic61—24no—
301Dic61—44no—
302Dic61—42no—
303Dic61—42no—
304Dic61—42no—
305Dic61—82no—
306C2×C4×C22⋊C4—611no—
307#1443—612no—
308#1440—612no—
309#1437—612no—
310#1434—611no—
311#1434—612no—
312#1434—611no—
313#1434—611no—
314C22⋊#95—611no—
315C22⋊#95D6111yescharacteristic
316C4×#95—611no—
317C2×C61—44no—
318C2×C61#228311yescharacteristic
319C2×C61#229811yescharacteristic
320C2×C61#231211yescharacteristic
321C2×C61#235311yescharacteristic
322C2×C61#235311yescharacteristic
323C2×C61#235311yescharacteristic
324C2×C61#235711yescharacteristic
325C2×C61#257612yes—
326C2×C61#257812yes—
327C2×C61#259512yes—
328C2×C61#259712yes—
329C24×C4C2×D6111yescharacteristic
330C22×C22⋊C4—611no—
331C22×C22⋊C4—611no—
332C22×C22⋊C4—612no—
333C22×C22⋊C4C2×D6112yes—
334C22×C42—611no—
335C22×C42—611no—
336C22×C42—612no—
337C4×C22⋊C4—618no—
338C2×#95—611no—
339C2×#95—611no—
340C2×#95—611no—
341C2×#95—612no—
342C2×#95—611no—
343C2×#95—612no—
344C2×#95—612no—
345C2×#95—612no—
346C2×#95—612no—
347C2×#95—612no—
348C2×#95—612no—
349C2×#95—612no—
350C2×#95C2×D6111yescharacteristic
351C2×#95C2×D6111yescharacteristic
352C2×#95C2×D6112yes—
353C61#1394711yescharacteristic, complemented, Sylow
354C25C22×D6111yescharacteristic
355C23×C4—22no—
356C23×C4—22no—
357C23×C4—42no—
358C23×C4—42no—
359C23×C4—611no—
360C23×C4—611no—
361C23×C4—611no—
362C23×C4—611no—
363C23×C4—612no—
364C23×C4—612no—
365C23×C4C4×D6114yes—
366C23×C4C22×D6112yes—
367C23×C4C22×D6111yescharacteristic
368C23×C4C22×D6112yes—
369C23×C4C22×D6111yescharacteristic
370C2×C22⋊C4—24no—
371C2×C22⋊C4—24no—
372C2×C22⋊C4—42no—
373C2×C22⋊C4—614no—
374C2×C22⋊C4—614no—
375C2×C22⋊C4—1222no—
376C2×C22⋊C4—1222no—
377C2×C22⋊C4—1222no—
378C2×C22⋊C4—1222no—
379C2×C22⋊C4—1224no—
380C2×C22⋊C4—1224no—
381C2×C22⋊C4—2442no—
382C2×C42—614no—
383C2×C42—614no—
384C2×C42—1224no—
385C2×C42—1224no—
386C2×C42—2442no—
387C2×C42—2442no—
388C2×C42—2442no—
389#95—22no—
390#95—22no—
391#95—42no—
392#95—614no—
393#95—614no—
394#95—1224no—
395#95—1224no—
396#95—1224no—
397#95—1224no—
398#95—1222no—
399#95—1222no—
400#95—2442no—
401#95—2442no—
402#95—2442no—
403#95—2442no—
404C24—22no—
405C24—21no—
406C24—21no—
407C24—21no—
408C24—21no—
409C24—22no—
410C24—22no—
411C24—22no—
412C24C2×C4×D6112yes—
413C24#1175822412yes—
414C24#1175822612yes—
415C24C23×D6111yescharacteristic
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—28no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—44no—
437C22×C4—44no—
438C22×C4—48no—
439C22×C4—48no—
440C22×C4—612no—
441C22×C4—612no—
442C22×C4—612no—
443C22×C4—612no—
444C22×C4—612no—
445C22×C4—612no—
446C22×C4—614no—
447C22×C4—1222no—
448C22×C4—1222no—
449C22×C4—1222no—
450C22×C4—1222no—
451C22×C4—1221no—
452C22×C4—1221no—
453C22×C4—1222no—
454C22×C4—1221no—
455C22×C4—1221no—
456C22×C4—1222no—
457C22×C4—1222no—
458C22×C4—1222no—
459C22×C4—1221no—
460C22×C4—1221no—
461C22×C4—1222no—
462C22×C4—1222no—
463C22×C4—1222no—
464C22×C4—1222no—
465C22×C4—1222no—
466C22×C4—1222no—
467C22×C4—1222no—
468C22×C4—1222no—
469C22×C4—1222no—
470C22×C4—1222no—
471C22×C4—1222no—
472C22×C4—1222no—
473C22×C4—1222no—
474C22×C4C2×C4×D6112yes—
475C22×C4C2×C4×D6112yes—
476C22×C4#1175822214yes—
477C22×C4#1175822412yes—
478C22×C4#1175822412yes—
479C22⋊C4—48no—
480C22⋊C4—1228no—
481C22⋊C4—1228no—
482C22⋊C4—2448no—
483C42—2444no—
484C42—2444no—
485C42—2448no—
486C23—24no—
487C23—24no—
488C23—22no—
489C23—22no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—22no—
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—24no—
499C23—24no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23#1451973514yes—
509C23C22×C4×D6111yescharacteristic
510C23#41×D6112yes—
511C23#41×D6111yescharacteristic
512C23#41×D6111yescharacteristic
513C23C2×#1175822411yescharacteristic
514C23C2×#1175822411yescharacteristic
515C23C2×#1175822411yescharacteristic
516C23C2×#1175822212yes—
517C23C2×#1175822611yescharacteristic
518C23#1451982212yes—
519C23#1451982212yes—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—416no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—614no—
545C2×C4—1224no—
546C2×C4—1222no—
547C2×C4—1222no—
548C2×C4—1224no—
549C2×C4—1222no—
550C2×C4—1222no—
551C2×C4—1222no—
552C2×C4—1222no—
553C2×C4—1222no—
554C2×C4—1222no—
555C2×C4—1222no—
556C2×C4—1222no—
557C2×C4—1222no—
558C2×C4—1224no—
559C2×C4—1224no—
560C2×C4—1224no—
561C2×C4—2442no—
562C2×C4—2442no—
563C2×C4—2442no—
564C2×C4—2442no—
565C2×C4—2442no—
566C2×C4—2442no—
567C2×C4—2442no—
568C2×C4—2442no—
569C2×C4—2442no—
570C2×C4—2442no—
571C2×C4—2442no—
572C2×C4—2442no—
573C2×C4—2442no—
574C2×C4—2442no—
575C2×C4—2442no—
576C2×C4—2442no—
577C2×C4—2442no—
578C2×C4#1451973314yes—
579C22—24no—
580C22—24no—
581C22—24no—
582C22—42no—
583C22—44no—
584C22—42no—
585C22—44no—
586C22—44no—
587C22—42no—
588C22—44no—
589C22—42no—
590C22#117×D6111yescharacteristic
591C22C2×#1451973311yescharacteristic
592C22C2×#1451973511yescharacteristic
593C22#1684023011yescharacteristic
594C22C4×#1175822211yescharacteristic
595C22#1684023511yescharacteristic
596C22#1684023511yescharacteristic
597C22#1684029212yes—
598C22#1684029311yescharacteristic
599C22#1684029311yescharacteristic
600C22#1684029412yes—
601C22#1684029811yescharacteristic
602C22#1684029811yescharacteristic
603C22#1684034712yes—
604C22#1684034712yes—
605C22#1684043812yes—
606C22#1684043912yes—
607C22#1684044012yes—
608C22#1684045512yes—
609C22#1684045712yes—
610C22#1684046012yes—
611C22#1684046112yes—
612C22#1684049512yes—
613C4—24no—
614C4—44no—
615C4—42no—
616C4—82no—
617C4—1224no—
618C4—4882no—
619C4—2442no—
620C4—2442no—
621C4—2442no—
622C4—2444no—
623C2—44no—
624C2#2144821411yescharacteristic
625C2#2144831511yescharacteristic
626C2#2144841511yescharacteristic
627C2#2144875511yescharacteristic
628C2#2144875611yescharacteristic
629C2#2144876111yescharacteristic
630C2#2144879311yescharacteristic
631C2#2145112212yes—
632C2#2145115012yes—
633C2#2145133912yes—
634C2#2145136712yes—
subgroupG/H
center, FrattiniC24C23×D61
commutatorC23×C61C23×C4
FittingC61×C22⋊#95C2
socle, cosocleC24×C61C24
prime radicalC25×C61C23
hypercenterC22⋊#95D61
hypocenterC61#13947
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
2. #21444079C2semidirect
5. #21444045C2semidirect
6. #21444045C2semidirect
7. #21444045C2semidirect
8. #21444044C2semidirect
10. #95×Dic61C2semidirect
18. C4×C22⋊Dic61C4semidirect
353. C61#13947semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊Dic612
#214440792
#214440662
#214440562
#214440452
#214440442
#214440422
#95×Dic612
C61×C22⋊#952
#1394761