Finite Group Databasebeta

← #29580221

Subgroups — #29580221

Order 15616.

968 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839900C211yesmaximal, characteristic, complemented
2C2×#16839674C211yesmaximal, characteristic, complemented
3#21445753C211yesmaximal, characteristic, complemented
4C2×#16839496C211yesmaximal, characteristic, complemented
5C2×#16839486C211yesmaximal, characteristic, complemented
6#21443697C211yesmaximal, characteristic, complemented
7C61×#2617C211yesmaximal, characteristic
8C23×Dic122C2211yescharacteristic
9C22×#11758200—21no—
10C22×C22⋊Dic61—21no—
11#16839900—22no—
12#16839900—22no—
13C2×#14519700—21no—
14C2×#14519700—22no—
15C2×C22⋊#92418C2211yescharacteristic
16C2×C22⋊#92418C2211yescharacteristic
17#16839674—22no—
18#16839674—22no—
19C2×#14519684—21no—
20C2×#14519684C2211yescharacteristic
21#16839496—22no—
22#16839486—22no—
23C2×#121×C61C2211yescharacteristic
24C2×#120×C61—21no—
25C22×C22⋊C4×C61C2211yescharacteristic
26C61×#397—21no—
27C61×#394—22no—
28C61×#392—21no—
29C61×#386—21no—
30C61×#380C2211yescharacteristic
31C22×Dic122—21no—
32C22×Dic122—21no—
33C22×Dic122—21no—
34C22×Dic122—21no—
35C22×Dic122—21no—
36C22×Dic122—44no—
37C22×Dic122D412yescomplemented
38C23×Dic61—21no—
39C23×Dic61—21no—
40C2×#11758200—24no—
41C2×#11758200—44no—
42C22×#92418—21no—
43C22×#92418—21no—
44C2×C22⋊Dic61—24no—
45C2×C22⋊Dic61—44no—
46#14519700—24no—
47#14519700—44no—
48C22⋊#92418—21no—
49C22⋊#92418—21no—
50C22⋊#92418—21no—
51C22⋊#92418D412yescomplemented
52#14519684—24no—
53#14519684—21no—
54#14519684D412yescomplemented
55C25×C61D411yescharacteristic
56C22×D4×C61—21no—
57C22×D4×C61—22no—
58C22×D4×C61D411yescharacteristic
59C23×C4×C61D411yescharacteristic
60C23×C4×C61C2311yescharacteristic
61#121×C61—21no—
62#121×C61—21no—
63#121×C61—21no—
64#121×C61—21no—
65#120×C61—42no—
66#120×C61—42no—
67C2×C4⋊C4×C61D411yescharacteristic
68C2×C4⋊C4×C61D412yes—
69C2×C22⋊C4×C61—22no—
70C2×C22⋊C4×C61—21no—
71C2×C22⋊C4×C61—21no—
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61—21no—
75C2×C22⋊C4×C61—21no—
76C2×C22⋊C4×C61—21no—
77C2×C22⋊C4×C61—21no—
78C2×C22⋊C4×C61—22no—
79#95×C61—22no—
80#95×C61—21no—
81C24×C61—21no—
82C24×C61—21no—
83C24×C61—21no—
84C24×C61—21no—
85C24×C61—21no—
86C24×C61—21no—
87C24×C61—21no—
88C24×C61—42no—
89C24×C61—42no—
90C24×C61SD1612yescomplemented
91C24×C61C2×D411yescharacteristic
92C2×D4×C61—21no—
93C2×D4×C61—21no—
94C2×D4×C61—42no—
95C2×D4×C61—44no—
96C2×D4×C61—41no—
97C2×D4×C61—41no—
98C2×D4×C61—41no—
99C2×D4×C61—41no—
100C2×D4×C61—41no—
101C2×D4×C61—41no—
102C2×D4×C61—82no—
103C2×D4×C61—82no—
104C22×C4×C61—21no—
105C22×C4×C61—21no—
106C22×C4×C61—22no—
107C22×C4×C61—21no—
108C22×C4×C61—21no—
109C22×C4×C61—42no—
110C22×C4×C61—42no—
111C22×C4×C61C2×D411yescharacteristic
112C22×C4×C61C2×D411yescharacteristic
113C22×C4×C61C2×D411yescharacteristic
114C22×C4×C61C2×D411yescharacteristic
115C22×C4×C61C2×D411yescharacteristic
116C22×C4×C61#4111yescharacteristic
117C22×Dic61—24no—
118C22×Dic61—22no—
119C22×Dic61—22no—
120C22×Dic61—42no—
121C22×Dic61—41no—
122C22×Dic61—41no—
123C22×Dic61—42no—
124C22×Dic61—42no—
125C22×Dic61—41no—
126C22×Dic61—41no—
127C2×Dic122—24no—
128C2×Dic122—24no—
129C2×Dic122—22no—
130C2×Dic122—22no—
131C2×Dic122—44no—
132C2×Dic122—44no—
133C2×Dic122—44no—
134C2×Dic122—44no—
135C2×Dic122—42no—
136C2×Dic122—42no—
137C2×Dic122—41no—
138C2×Dic122—41no—
139C4⋊C4×C61—21no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61—42no—
142C22⋊C4×C61—44no—
143C22⋊C4×C61—41no—
144C22⋊C4×C61—41no—
145C22⋊C4×C61—41no—
146C22⋊C4×C61—41no—
147C22⋊C4×C61—41no—
148C22⋊C4×C61—41no—
149C22⋊C4×C61—41no—
150C22⋊C4×C61—41no—
151C22⋊C4×C61—82no—
152C22⋊Dic61—48no—
153#11758200—48no—
154C2×#92418—22no—
155C2×#92418—42no—
156C2×#92418—42no—
157C2×#92418—41no—
158C23×C61—22no—
159C23×C61—22no—
160C23×C61—22no—
161C23×C61—22no—
162C23×C61—22no—
163C23×C61—44no—
164C23×C61—42no—
165C23×C61—44no—
166C23×C61—42no—
167C23×C61—41no—
168C23×C61—41no—
169C23×C61—41no—
170C23×C61—42no—
171C23×C61—42no—
172C23×C61—41no—
173C23×C61—41no—
174C23×C61—41no—
175C23×C61—41no—
176C23×C61—42no—
177C23×C61—42no—
178C23×C61—82no—
179C23×C61—82no—
180C23×C61—81no—
181C23×C61—81no—
182C23×C61#12011yescharacteristic
183C23×C61#12011yescharacteristic
184C23×C61#12111yescharacteristic
185C23×C61C2×SD1611yescharacteristic
186C23×C61#13511yescharacteristic
187C23×C61AGL(1,ℤ/8)11yescharacteristic
188C23×C61#13711yescharacteristic
189D4×C61—42no—
190D4×C61—81no—
191D4×C61—88no—
192D4×C61—81no—
193D4×C61—81no—
194D4×C61—81no—
195D4×C61—81no—
196C2×C4×C61—22no—
197C2×C4×C61—22no—
198C2×C4×C61—41no—
199C2×C4×C61—41no—
200C2×C4×C61—41no—
201C2×C4×C61—41no—
202C2×C4×C61—42no—
203C2×C4×C61—41no—
204C2×C4×C61—41no—
205C2×C4×C61—42no—
206C2×C4×C61—41no—
207C2×C4×C61—41no—
208C2×C4×C61—42no—
209C2×C4×C61—42no—
210C2×C4×C61—42no—
211C2×C4×C61—81no—
212C2×C4×C61#12011yescharacteristic
213C2×C4×C61#12111yescharacteristic
214C2×C4×C61#12111yescharacteristic
215C2×C4×C61#12711yescharacteristic
216C2×Dic61—24no—
217C2×Dic61—42no—
218C2×Dic61—44no—
219C2×Dic61—42no—
220C2×Dic61—44no—
221C2×Dic61—42no—
222C2×Dic61—42no—
223C2×Dic61—42no—
224C2×Dic61—82no—
225C2×Dic61—82no—
226Dic122—24no—
227Dic122—24no—
228Dic122—42no—
229Dic122—44no—
230Dic122—42no—
231Dic122—44no—
232#92418—42no—
233#92418—81no—
234#9916—611nomaximal, Sylow
235C22×C61—22no—
236C22×C61—22no—
237C22×C61—22no—
238C22×C61—22no—
239C22×C61—21no—
240C22×C61—21no—
241C22×C61—21no—
242C22×C61—21no—
243C22×C61—44no—
244C22×C61—44no—
245C22×C61—42no—
246C22×C61—82no—
247C22×C61—82no—
248C22×C61—82no—
249C22×C61—82no—
250C22×C61—81no—
251C22×C61—81no—
252C22×C61—82no—
253C22×C61—82no—
254C22×C61—81no—
255C22×C61—81no—
256C22×C61—81no—
257C22×C61#39211yescharacteristic
258C22×C61#44811yescharacteristic
259C22×C61#44911yescharacteristic
260C22×C61#45011yescharacteristic
261C22×C61#45211yescharacteristic
262C22×C61#45512yes—
263C22×C61B(4,𝔽2)12yes—
264C22×C61#46511yescharacteristic
265C22×C61#46811yescharacteristic
266C4×C61—21no—
267C4×C61—21no—
268C4×C61—21no—
269C4×C61—21no—
270C4×C61—82no—
271C4×C61—81no—
272C4×C61—81no—
273Dic61—44no—
274Dic61—82no—
275C2×#448—611no—
276#2617D6111yescharacteristic
277C2×#393—611no—
278#1787—611no—
279C2×#327—611no—
280C2×#323—611no—
281#1294—611no—
282C2×C61—21no—
283C2×C61—21no—
284C2×C61—21no—
285C2×C61—21no—
286C2×C61—82no—
287C2×C61—161no—
288C2×C61#160112yes—
289C2×C61#160612yes—
290C2×C61#200011yescharacteristic
291C2×C61#200411yescharacteristic
292C2×C61#202111yescharacteristic
293C23×Q8—611no—
294C22×SD16—1221no—
295C2×#121C2×D6111yescharacteristic
296C2×#120—21no—
297C22×C22⋊C4—1221no—
298C22×C22⋊C4C2×D6111yescharacteristic
299#448—1222no—
300#448—1222no—
301C2×#103—1221no—
302C2×#103—1222no—
303C2×C22⋊C8—611no—
304C2×C22⋊C8—611no—
305#397—21no—
306#394—22no—
307#393—1222no—
308#393—1222no—
309#392—21no—
310#386—21no—
311#380C2×D6111yescharacteristic
312C2×#95—611no—
313C2×#95—1221no—
314#327—1222no—
315#323—1222no—
316C61#991611yescharacteristic, complemented, Sylow
317C25C22⋊D6111yescharacteristic
318C22×Q8—612no—
319C22×Q8—1221no—
320C22×Q8—1221no—
321C22×Q8—1221no—
322C22×Q8—1221no—
323C22×Q8—1221no—
324C22×Q8—2444no—
325C22×D4—21no—
326C22×D4—22no—
327C22×D4C22⋊D6111yescharacteristic
328C23×C4—1221no—
329C23×C4—1221no—
330C23×C4C22⋊D6111yescharacteristic
331C23×C4C22×D6111yescharacteristic
332C2×SD16—1224no—
333C2×SD16—2444no—
334C22×C8—1221no—
335C22×C8—1221no—
336#121—21no—
337#121—21no—
338#121—21no—
339#121—21no—
340#120—42no—
341#120—42no—
342C2×C4⋊C4C22⋊D6111yescharacteristic
343C2×C4⋊C4C22⋊D6112yes—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—21no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—21no—
348C2×C22⋊C4—21no—
349C2×C22⋊C4—21no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—22no—
354C2×C22⋊C4—1224no—
355C2×C22⋊C4—2444no—
356#103—1224no—
357#103—2444no—
358C22⋊C8—612no—
359C22⋊C8—1221no—
360C22⋊C8—1221no—
361C22⋊C8—1221no—
362#95—22no—
363#95—21no—
364#95—612no—
365#95—1224no—
366#95—1221no—
367C24—21no—
368C24—21no—
369C24—21no—
370C24—21no—
371C24—21no—
372C24—21no—
373C24—21no—
374C24—42no—
375C24—42no—
376C24#1175820012yescomplemented
377C24C2×C22⋊D6111yescharacteristic
378C2×Q8—1224no—
379C2×Q8—1224no—
380C2×Q8—1222no—
381C2×Q8—1222no—
382C2×Q8—2442no—
383C2×Q8—2442no—
384C2×Q8—2444no—
385C2×Q8—2444no—
386C2×Q8—2444no—
387C2×Q8—2444no—
388C2×Q8—2441no—
389C2×Q8—2441no—
390C2×D4—21no—
391C2×D4—21no—
392C2×D4—42no—
393C2×D4—44no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—41no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—82no—
401C2×D4—82no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4—1224no—
410C22×C4—1222no—
411C22×C4—1222no—
412C22×C4—2442no—
413C22×C4—2442no—
414C22×C4—2441no—
415C22×C4—2441no—
416C22×C4—2442no—
417C22×C4—2441no—
418C22×C4—2441no—
419C22×C4D4×D6111yescharacteristic
420C22×C4D4×D6111yescharacteristic
421C22×C4D4×D6111yescharacteristic
422C22×C4#1175822411yescharacteristic
423C22×C4C2×C22⋊D6111yescharacteristic
424C22×C4C2×C22⋊D6111yescharacteristic
425SD16—2448no—
426C2×C8—1222no—
427C2×C8—2442no—
428C2×C8—2441no—
429C2×C8—2442no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—42no—
433C22⋊C4—44no—
434C22⋊C4—41no—
435C22⋊C4—41no—
436C22⋊C4—41no—
437C22⋊C4—41no—
438C22⋊C4—41no—
439C22⋊C4—41no—
440C22⋊C4—41no—
441C22⋊C4—41no—
442C22⋊C4—82no—
443C22⋊C4—2448no—
444C23—22no—
445C23—22no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—44no—
450C23—42no—
451C23—42no—
452C23—44no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—41no—
457C23—41no—
458C23—41no—
459C23—42no—
460C23—42no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—82no—
465C23—81no—
466C23—81no—
467C23—82no—
468C23#1451974511yescharacteristic
469C23#1451974611yescharacteristic
470C23#1451974911yescharacteristic
471C23C2×#1175820011yescharacteristic
472C23#1451979711yescharacteristic
473C23#1451980311yescharacteristic
474C23#1451980711yescharacteristic
475Q8—1224no—
476Q8—1224no—
477Q8—2444no—
478Q8—2442no—
479Q8—2442no—
480Q8—2444no—
481D4—42no—
482D4—81no—
483D4—88no—
484D4—81no—
485D4—81no—
486D4—81no—
487D4—81no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—81no—
504C2×C4—1224no—
505C2×C4—4882no—
506C2×C4—4882no—
507C2×C4—2442no—
508C2×C4—2442no—
509C2×C4—2442no—
510C2×C4—2442no—
511C2×C4—2444no—
512C2×C4—2444no—
513C2×C4—2442no—
514C2×C4#1451974511yescharacteristic
515C2×C4#1451974811yescharacteristic
516C2×C4#1451974911yescharacteristic
517C2×C4#1451977311yescharacteristic
518C8—4881no—
519C8—2442no—
520C22—21no—
521C22—21no—
522C22—22no—
523C22—22no—
524C22—21no—
525C22—21no—
526C22—22no—
527C22—22no—
528C22—44no—
529C22—44no—
530C22—42no—
531C22—82no—
532C22—82no—
533C22—82no—
534C22—81no—
535C22—81no—
536C22—82no—
537C22—81no—
538C22—82no—
539C22—81no—
540C22—81no—
541C22—82no—
542C22#1683967011yescharacteristic
543C22#1683990011yescharacteristic
544C22#1683990511yescharacteristic
545C22#1683991311yescharacteristic
546C22#1683992411yescharacteristic
547C22#1683994012yes—
548C22#1683994912yes—
549C22#1683998911yescharacteristic
550C22#1684000611yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—82no—
556C4—81no—
557C4—81no—
558C4—4882no—
559C4—2444no—
560C2—21no—
561C2—21no—
562C2—21no—
563C2—21no—
564C2—82no—
565C2—161no—
566C2#2144477112yes—
567C2#2144479912yes—
568C2#2144682211yescharacteristic
569C2#2144684611yescharacteristic
570C2#2144694311yescharacteristic
subgroupG/H
centerC23#14519746
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
Fitting, prime radicalC61×#2617C2
socleC23×C61#120
hypercenter#2617D61
hypocenterC61#9916
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2617

Complements

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

NH ≅ G/Ntype
1. C2×#16839900C2semidirect
2. C2×#16839674C2semidirect
3. #21445753C2semidirect
4. C2×#16839496C2semidirect
5. C2×#16839486C2semidirect
6. #21443697C2semidirect
37. C22×Dic122D4semidirect
51. C22⋊#92418D4semidirect
54. #14519684D4semidirect
90. C24×C61SD16semidirect
316. C61#9916semidirect
376. C24#11758200semidirect

Maximal subgroups

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

subgroupindex
C2×#168399002
C2×#168396742
#214457532
C2×#168394962
C2×#168394862
#214436972
C61×#26172
#991661