Finite Group Databasebeta

← #29575579

Subgroups — #29575579

Order 15616.

1062 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊#92418C211yesmaximal, characteristic, complemented
2C2×#16839496C212yesmaximal, complemented
3#21444042C211yesmaximal, characteristic, complemented
4#21443697C212yesmaximal, complemented
5C61×#2847C211yesmaximal, characteristic
6C23×#92418—21no—
7C22×C22⋊Dic61—21no—
8C2×C22⋊#92418—24no—
9C2×C22⋊#92418—21no—
10C2×C22⋊#92418C2212yes—
11C2×#14519684—21no—
12C2×#14519684C2212yes—
13#16839496—24no—
14C24×C4×C61C2211yescharacteristic
15C2×#121×C61C411yescharacteristic, complemented
16C2×#121×C61C411yescharacteristic, complemented
17C2×#121×C61C2211yescharacteristic
18C2×#120×C61—21no—
19C61×#386—21no—
20C61×#386—21no—
21C61×#386—21no—
22C61×#380C411yescharacteristic, complemented
23C61×#380C411yescharacteristic, complemented
24C61×#380C2211yescharacteristic
25C23×Dic61—22no—
26C22×#92418—24no—
27C22×#92418—22no—
28C22×#92418—42no—
29C22×#92418—42no—
30C2×C22⋊Dic61—24no—
31C2×C22⋊Dic61—42no—
32C2×C22⋊Dic61—42no—
33C22⋊#92418—24no—
34C22⋊#92418—22no—
35C22⋊#92418D414yescomplemented
36#14519684—22no—
37#14519684—22no—
38#14519684—42no—
39C25×C61D411yescharacteristic
40C22×D4×C61—21no—
41C22×D4×C61—21no—
42C22×D4×C61—21no—
43C22×D4×C61C2×C411yescharacteristic
44C23×C4×C61—22no—
45C23×C4×C61—22no—
46C23×C4×C61—42no—
47C23×C4×C61—42no—
48C23×C4×C61C2×C411yescharacteristic
49C23×C4×C61C2×C411yescharacteristic
50C23×C4×C61D411yescharacteristic
51C23×C4×C61D411yescharacteristic
52C23×C4×C61D411yescharacteristic
53C23×C4×C61C2311yescharacteristic
54#121×C61—22no—
55#121×C61—22no—
56#121×C61—42no—
57#121×C61—42no—
58#120×C61—42no—
59#120×C61—42no—
60C2×C4⋊C4×C61C2×C411yescharacteristic
61C2×C4⋊C4×C61C2×C411yescharacteristic
62C2×C4⋊C4×C61C2×C411yescharacteristic
63C2×C22⋊C4×C61—21no—
64C2×C22⋊C4×C61—21no—
65C2×C22⋊C4×C61—21no—
66C2×C22⋊C4×C61—21no—
67C2×C22⋊C4×C61—21no—
68C2×C22⋊C4×C61—21no—
69#95×C61—21no—
70#95×C61—21no—
71#95×C61—21no—
72C24×C61—22no—
73C24×C61—22no—
74C24×C61—22no—
75C24×C61—22no—
76C24×C61—21no—
77C24×C61—41no—
78C24×C61—41no—
79C24×C61C22⋊C411yescharacteristic
80C24×C61C22⋊C411yescharacteristic
81C24×C61D812yes—
82C24×C61SD1612yes—
83C24×C61C2×D411yescharacteristic
84C2×D4×C61—22no—
85C2×D4×C61—41no—
86C2×D4×C61—41no—
87C2×D4×C61—42no—
88C2×D4×C61—42no—
89C2×D4×C61—42no—
90C2×D4×C61—42no—
91C2×D4×C61—42no—
92C2×D4×C61—42no—
93C2×D4×C61—42no—
94C2×D4×C61—41no—
95C2×D4×C61—41no—
96C2×D4×C61—42no—
97C22×C4×C61—22no—
98C22×C4×C61—22no—
99C22×C4×C61—21no—
100C22×C4×C61—21no—
101C22×C4×C61—22no—
102C22×C4×C61—22no—
103C22×C4×C61—22no—
104C22×C4×C61—22no—
105C22×C4×C61—22no—
106C22×C4×C61—22no—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—21no—
110C22×C4×C61—21no—
111C22×C4×C61—21no—
112C22×C4×C61—41no—
113C22×C4×C61—41no—
114C22×C4×C61—41no—
115C22×C4×C61—41no—
116C22×C4×C61—41no—
117C22×C4×C61—41no—
118C22×C4×C61—41no—
119C22×C4×C61—48no—
120C22×C4×C61—48no—
121C22×C4×C61C22⋊C411yescharacteristic
122C22×C4×C61C22⋊C411yescharacteristic
123C22×C4×C61C22×C411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D412yes—
126C22×C4×C61#4112yes—
127C22×Dic61—24no—
128C22×Dic61—42no—
129C22×Dic61—42no—
130C22×Dic61—42no—
131C22×Dic61—42no—
132C22×Dic61—42no—
133C22×Dic61—42no—
134C4⋊C4×C61—22no—
135C4⋊C4×C61—41no—
136C4⋊C4×C61—41no—
137C22⋊C4×C61—42no—
138C22⋊C4×C61—42no—
139C22⋊C4×C61—42no—
140C22⋊C4×C61—41no—
141C22⋊C4×C61—41no—
142C22⋊C4×C61—42no—
143C22⋊C4×C61—41no—
144C22⋊C4×C61—41no—
145C22⋊Dic61—48no—
146C2×#92418—24no—
147C2×#92418—48no—
148C2×#92418—42no—
149C2×#92418—42no—
150C23×C61—21no—
151C23×C61—21no—
152C23×C61—21no—
153C23×C61—21no—
154C23×C61—21no—
155C23×C61—21no—
156C23×C61—21no—
157C23×C61—21no—
158C23×C61—24no—
159C23×C61—24no—
160C23×C61—21no—
161C23×C61—21no—
162C23×C61—21no—
163C23×C61—21no—
164C23×C61—21no—
165C23×C61—21no—
166C23×C61—24no—
167C23×C61—24no—
168C23×C61—42no—
169C23×C61—42no—
170C23×C61—44no—
171C23×C61—44no—
172C23×C61—44no—
173C23×C61—44no—
174C23×C61—41no—
175C23×C61—41no—
176C23×C61—41no—
177C23×C61—41no—
178C23×C61—41no—
179C23×C61—41no—
180C23×C61—41no—
181C23×C61#9912yes—
182C23×C61#10212yes—
183C23×C61#10212yes—
184C23×C61#10412yes—
185C23×C61C2×C22⋊C411yescharacteristic
186C23×C61#12112yes—
187C23×C61C2×D811yescharacteristic
188C23×C61C2×SD1611yescharacteristic
189C23×C61#13512yes—
190D4×C61—82no—
191D4×C61—84no—
192D4×C61—84no—
193D4×C61—82no—
194D4×C61—82no—
195C2×C4×C61—24no—
196C2×C4×C61—24no—
197C2×C4×C61—21no—
198C2×C4×C61—21no—
199C2×C4×C61—21no—
200C2×C4×C61—21no—
201C2×C4×C61—21no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—42no—
207C2×C4×C61—42no—
208C2×C4×C61—44no—
209C2×C4×C61—44no—
210C2×C4×C61—44no—
211C2×C4×C61—42no—
212C2×C4×C61—42no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61#9912yes—
223C2×C4×C61C4×D412yes—
224C2×C4×C61#12011yescharacteristic
225C2×C4×C61#12311yescharacteristic
226C2×Dic61—44no—
227C2×Dic61—44no—
228C2×Dic61—44no—
229C2×Dic61—82no—
230C2×Dic61—82no—
231C2×Dic61—82no—
232C2×Dic61—82no—
233#92418—44no—
234#9113—611nomaximal, Sylow
235C22×C61—22no—
236C22×C61—22no—
237C22×C61—22no—
238C22×C61—22no—
239C22×C61—22no—
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—22no—
243C22×C61—22no—
244C22×C61—22no—
245C22×C61—22no—
246C22×C61—21no—
247C22×C61—22no—
248C22×C61—21no—
249C22×C61—22no—
250C22×C61—22no—
251C22×C61—22no—
252C22×C61—48no—
253C22×C61—48no—
254C22×C61—41no—
255C22×C61—41no—
256C22×C61—41no—
257C22×C61—41no—
258C22×C61—81no—
259C22×C61—81no—
260C22×C61—81no—
261C22×C61—81no—
262C22×C61—81no—
263C22×C61—81no—
264C22×C61—81no—
265C22×C61#32714yescomplemented
266C22×C61#38611yescharacteristic
267C22×C61C2×#9911yescharacteristic
268C22×C61C2×#9911yescharacteristic
269C22×C61C2×#10211yescharacteristic
270C22×C61#41611yescharacteristic
271C22×C61C2×#10411yescharacteristic
272C22×C61#42111yescharacteristic
273C22×C61#46512yes—
274C22×C61#46612yes—
275C4×C61—21no—
276C4×C61—22no—
277C4×C61—21no—
278C4×C61—22no—
279C4×C61—41no—
280C4×C61—81no—
281C4×C61—81no—
282C4×C61—81no—
283Dic61—84no—
284C22×C22⋊C8—611no—
285#2847D6111yescharacteristic
286C2×#327—612no—
287C22⋊#95—611no—
288#1294—612no—
289C2×C61—22no—
290C2×C61—24no—
291C2×C61—22no—
292C2×C61—42no—
293C2×C61—161no—
294C2×C61C2×#32711yescharacteristic
295C2×C61#150111yescharacteristic
296C2×C61#151611yescharacteristic
297C2×C61#151911yescharacteristic
298C2×C61#187111yescharacteristic
299C2×C61#189311yescharacteristic
300C2×C61#189811yescharacteristic
301C24×C4C2×D6111yescharacteristic
302C23×C8—1221no—
303C2×#121Dic6111yescharacteristic, complemented
304C2×#121Dic6111yescharacteristic, complemented
305C2×#121C2×D6111yescharacteristic
306C2×#120—21no—
307C22×C22⋊C4—1221no—
308C2×C22⋊C8—612no—
309C2×C22⋊C8—1224no—
310C2×C22⋊C8—1221no—
311#386—21no—
312#386—21no—
313#386—21no—
314#380Dic6111yescharacteristic, complemented
315#380Dic6111yescharacteristic, complemented
316#380C2×D6111yescharacteristic
317C2×#95—612no—
318C2×#95—1221no—
319#327—1224no—
320C61#911311yescharacteristic, complemented, Sylow
321C25C22⋊D6111yescharacteristic
322C22×D4—21no—
323C22×D4—21no—
324C22×D4—21no—
325C22×D4C2×Dic6111yescharacteristic
326C23×C4—22no—
327C23×C4—22no—
328C23×C4—42no—
329C23×C4—42no—
330C23×C4—1222no—
331C23×C4C2×Dic6111yescharacteristic
332C23×C4C2×Dic6111yescharacteristic
333C23×C4C22⋊D6111yescharacteristic
334C23×C4C22⋊D6111yescharacteristic
335C23×C4C22⋊D6111yescharacteristic
336C23×C4C22×D6111yescharacteristic
337C22×C8—1224no—
338C22×C8—1222no—
339C22×C8—2442no—
340C22×C8—2442no—
341#121—22no—
342#121—22no—
343#121—42no—
344#121—42no—
345#120—42no—
346#120—42no—
347C2×C4⋊C4C2×Dic6111yescharacteristic
348C2×C4⋊C4C2×Dic6111yescharacteristic
349C2×C4⋊C4C2×Dic6111yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—1224no—
357C2×C22⋊C4—2442no—
358C2×C22⋊C4—2442no—
359C22⋊C8—614no—
360C22⋊C8—1224no—
361C22⋊C8—1222no—
362#95—21no—
363#95—21no—
364#95—21no—
365#95—1222no—
366#95—1222no—
367#95—2442no—
368C24—22no—
369C24—22no—
370C24—22no—
371C24—22no—
372C24—21no—
373C24—41no—
374C24—41no—
375C24#1175819912yes—
376C24#1175820012yes—
377C24C22⋊Dic6111yescharacteristic
378C24C22⋊Dic6111yescharacteristic
379C24C2×C22⋊D6111yescharacteristic
380C2×D4—22no—
381C2×D4—41no—
382C2×D4—41no—
383C2×D4—42no—
384C2×D4—42no—
385C2×D4—42no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—42no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—42no—
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—41no—
409C22×C4—41no—
410C22×C4—41no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—41no—
415C22×C4—48no—
416C22×C4—48no—
417C22×C4—1224no—
418C22×C4—2442no—
419C22×C4—2442no—
420C22×C4—2442no—
421C22×C4—2442no—
422C22×C4—2442no—
423C22×C4—2442no—
424C22×C4C22⋊Dic6111yescharacteristic
425C22×C4C22⋊Dic6111yescharacteristic
426C22×C4D4×D6112yes—
427C22×C4#1175822412yes—
428C22×C4C22×Dic6111yescharacteristic
429C22×C4C2×C22⋊D6111yescharacteristic
430C2×C8—1224no—
431C2×C8—2448no—
432C2×C8—2442no—
433C2×C8—2442no—
434C4⋊C4—22no—
435C4⋊C4—41no—
436C4⋊C4—41no—
437C22⋊C4—42no—
438C22⋊C4—42no—
439C22⋊C4—42no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—42no—
443C22⋊C4—41no—
444C22⋊C4—41no—
445C22⋊C4—2448no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—24no—
457C23—24no—
458C23—24no—
459C23—24no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—42no—
465C23—42no—
466C23—44no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23#1451969212yes—
478C23#1451969812yes—
479C23#1451969812yes—
480C23#1451970412yes—
481C23C2×C22⋊Dic6111yescharacteristic
482C23#1451974912yes—
483C23C2×#1175819911yescharacteristic
484C23C2×#1175820011yescharacteristic
485C23#1451979712yes—
486D4—82no—
487D4—84no—
488D4—82no—
489D4—82no—
490D4—84no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—44no—
505C2×C4—44no—
506C2×C4—44no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—4882no—
519C2×C4—4882no—
520C2×C4—4882no—
521C2×C4—4882no—
522C2×C4—2444no—
523C2×C4—2444no—
524C2×C4—2444no—
525C2×C4#1451969212yes—
526C2×C4D4×Dic6112yes—
527C2×C4#1451974511yescharacteristic
528C2×C4#1451975811yescharacteristic
529C8—2444no—
530C22—22no—
531C22—22no—
532C22—21no—
533C22—22no—
534C22—21no—
535C22—22no—
536C22—22no—
537C22—22no—
538C22—21no—
539C22—21no—
540C22—22no—
541C22—22no—
542C22—22no—
543C22—22no—
544C22—22no—
545C22—22no—
546C22—22no—
547C22—48no—
548C22—48no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—41no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22#1683949614yescomplemented
561C22#1683964211yescharacteristic
562C22C2×#1451969211yescharacteristic
563C22C2×#1451969211yescharacteristic
564C22C2×#1451969811yescharacteristic
565C22#1683975811yescharacteristic
566C22C2×#1451970411yescharacteristic
567C22#1683977911yescharacteristic
568C22#1683998912yes—
569C22#1683999612yes—
570C4—21no—
571C4—22no—
572C4—21no—
573C4—22no—
574C4—41no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—4884no—
579C2—22no—
580C2—22no—
581C2—24no—
582C2—42no—
583C2—161no—
584C2C2×#1683949611yescharacteristic
585C2#2144431011yescharacteristic
586C2#2144437511yescharacteristic
587C2#2144438711yescharacteristic
588C2#2144612211yescharacteristic
589C2#2144624811yescharacteristic
590C2#2144627311yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic61
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
Fitting, prime radicalC61×#2847C2
socleC23×C61C2×C22⋊C4
cosocleC23×C4×C61C23
hypercenter#2847D61
hypocenterC61#9113
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2847

Complements

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

NH ≅ G/Ntype
1. C22×C22⋊#92418C2semidirect
2. C2×#16839496C2semidirect
3. #21444042C2semidirect
4. #21443697C2semidirect
15. C2×#121×C61C4semidirect
16. C2×#121×C61C4semidirect
22. C61×#380C4semidirect
23. C61×#380C4semidirect
35. C22⋊#92418D4semidirect
265. C22×C61#327semidirect
303. C2×#121Dic61semidirect
304. C2×#121Dic61semidirect
314. #380Dic61semidirect
315. #380Dic61semidirect
320. C61#9113semidirect
560. C22#16839496semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊#924182
C2×#168394962
#214440422
#214436972
C61×#28472
#911361