Finite Group Databasebeta

← #29584430

Subgroups — #29584430

Order 15616.

604 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451936C211yesmaximal, characteristic
2#21446014C211yesmaximal, characteristic
3#21446011C211yesmaximal, characteristic
4#21444084C211yesmaximal, characteristic
5#21443698C211yesmaximal, characteristic
6#21443661C211yesmaximal, characteristic
7C61×#1294C211yesmaximal, characteristic
8C2×#14519754—21no—
9C22×C4⋊Dic61—21no—
10C22×C4⋊Dic61C2211yescharacteristic
11C2×#14519709—21no—
12C2×#14519708—21no—
13C2×C22⋊#92418C2211yescharacteristic
14#16839696—21no—
15#16839695—21no—
16#16839683—21no—
17#16839682—21no—
18#16839622C2211yescharacteristic
19#16839620—21no—
20C2×#14519684—21no—
21C2×#14519684C2211yescharacteristic
22#16839525—21no—
23#16839524—21no—
24C2×C22⋊C8×C61C2211yescharacteristic
25C61×#380C2211yescharacteristic
26C2×#95×C61C2211yescharacteristic
27C22×Dic122—21no—
28C23×Dic61—21no—
29C23×Dic61D411yescharacteristic
30C23×Dic61D411yescharacteristic
31C22×#92418—21no—
32#14519754—42no—
33#14519754—42no—
34C2×C4⋊Dic61—21no—
35C2×C4⋊Dic61—21no—
36C2×C4⋊Dic61—21no—
37C2×C4⋊Dic61—42no—
38C2×C4⋊Dic61—42no—
39C2×C4⋊Dic61—42no—
40C2×C4⋊Dic61—42no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×C4⋊Dic61D411yescharacteristic
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×C22⋊Dic61—21no—
48#14519709—42no—
49#14519708—42no—
50C22⋊#92418—21no—
51C22⋊#92418Q812yescomplemented
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—42no—
58C23×C4×C61—21no—
59C23×C4×C61C2311yescharacteristic
60C22×C8×C61—21no—
61C2×C4⋊C4×C61D411yescharacteristic
62C2×C4⋊C4×C61D411yescharacteristic
63C2×C22⋊C4×C61—21no—
64C22⋊C8×C61—21no—
65C22⋊C8×C61Q812yescomplemented
66#95×C61—21no—
67#95×C61—21no—
68#95×C61Q812yescomplemented
69C24×C61C2×D411yescharacteristic
70C22×C4×C61—22no—
71C22×C4×C61—22no—
72C22×C4×C61—22no—
73C22×C4×C61—21no—
74C22×C4×C61—21no—
75C22×C4×C61—41no—
76C22×C4×C61—41no—
77C22×C4×C61—41no—
78C22×C4×C61—41no—
79C22×C4×C61—41no—
80C22×C4×C61—41no—
81C22×C4×C61C2×D411yescharacteristic
82C22×C4×C61C2×D411yescharacteristic
83C22×C4×C61C2×Q811yescharacteristic
84C22×C4×C61C2×Q811yescharacteristic
85C22×C4×C61C2×Q811yescharacteristic
86C22×C4×C61#4111yescharacteristic
87C22×Dic61—21no—
88C22×Dic61—21no—
89C22×Dic61—21no—
90C22×Dic61—21no—
91C22×Dic61—22no—
92C22×Dic61—21no—
93C22×Dic61—21no—
94C22×Dic61—41no—
95C22×Dic61—41no—
96C22×Dic61—41no—
97C22×Dic61—41no—
98C22×Dic61—41no—
99C22×Dic61—41no—
100C22×Dic61—41no—
101C22×Dic61—41no—
102C22×Dic61—41no—
103C22×Dic61—41no—
104C22×Dic61SD1612yes—
105C22×Dic61SD1612yes—
106C2×Dic122—42no—
107C2×Dic122—81no—
108C2×Dic122—81no—
109C2×C8×C61—22no—
110C2×C8×C61—41no—
111C2×C8×C61—41no—
112C4⋊C4×C61—41no—
113C4⋊C4×C61—41no—
114C22⋊C4×C61—41no—
115C22⋊C4×C61—41no—
116C22⋊Dic61—41no—
117C22⋊Dic61—41no—
118C4⋊Dic61—22no—
119C4⋊Dic61—22no—
120C4⋊Dic61—42no—
121C4⋊Dic61—41no—
122C4⋊Dic61—41no—
123C4⋊Dic61—48no—
124C4⋊Dic61—41no—
125C4⋊Dic61—41no—
126#11758196—42no—
127#11758196—42no—
128#11758196—81no—
129#11758196—81no—
130C2×#92418—22no—
131C2×#92418—41no—
132C2×#92418—41no—
133C23×C61—21no—
134C23×C61—21no—
135C23×C61—21no—
136C23×C61—21no—
137C23×C61#12011yescharacteristic
138C23×C61C22⋊Q811yescharacteristic
139C23×C61C4⋊Q811yescharacteristic
140C23×C61C2×SD1611yescharacteristic
141C23×C61C2×SD1611yescharacteristic
142C23×C61AGL(1,ℤ/8)11yescharacteristic
143C23×C61#13711yescharacteristic
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—24no—
149C2×C4×C61—41no—
150C2×C4×C61—41no—
151C2×C4×C61—41no—
152C2×C4×C61—41no—
153C2×C4×C61—42no—
154C2×C4×C61—42no—
155C2×C4×C61—42no—
156C2×C4×C61—42no—
157C2×C4×C61—42no—
158C2×C4×C61—42no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—41no—
163C2×C4×C61—41no—
164C2×C4×C61—41no—
165C2×C4×C61C22⋊Q811yescharacteristic
166C2×C4×C61C22⋊Q811yescharacteristic
167C2×C4×C61C4⋊Q811yescharacteristic
168C2×C4×C61C4⋊Q811yescharacteristic
169C2×Dic61—22no—
170C2×Dic61—22no—
171C2×Dic61—41no—
172C2×Dic61—41no—
173C2×Dic61—41no—
174C2×Dic61—41no—
175C2×Dic61—42no—
176C2×Dic61—42no—
177C2×Dic61—42no—
178C2×Dic61—42no—
179C2×Dic61—41no—
180C2×Dic61—41no—
181C2×Dic61—41no—
182C2×Dic61—41no—
183C2×Dic61—41no—
184C2×Dic61—42no—
185C2×Dic61—41no—
186C2×Dic61—81no—
187C2×Dic61—81no—
188C2×Dic61—81no—
189C2×Dic61—81no—
190C2×Dic61—81no—
191C2×Dic61—81no—
192Dic122—84no—
193C8×C61—42no—
194#92418—42no—
195#10570—611nomaximal, Sylow
196C22×C61—21no—
197C22×C61—21no—
198C22×C61—21no—
199C22×C61—21no—
200C22×C61—21no—
201C22×C61—21no—
202C22×C61—21no—
203C22×C61—21no—
204C22×C61—21no—
205C22×C61—21no—
206C22×C61—21no—
207C22×C61—21no—
208C22×C61#39511yescharacteristic
209C22×C61#44811yescharacteristic
210C22×C61#45011yescharacteristic
211C22×C61#45311yescharacteristic
212C22×C61#45611yescharacteristic
213C22×C61B(4,𝔽2)11yescharacteristic
214C22×C61#45811yescharacteristic
215C22×C61#47511yescharacteristic
216C22×C61#47611yescharacteristic
217C22×C61#49811yescharacteristic
218C22×C61#50111yescharacteristic
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—21no—
222C4×C61—21no—
223C4×C61—44no—
224C4×C61—81no—
225C4×C61—81no—
226Dic61—42no—
227Dic61—42no—
228Dic61—82no—
229Dic61—81no—
230Dic61—81no—
231#2659—611no—
232#1853—611no—
233#1853—611no—
234#1444—611no—
235#1294—611no—
236#1294D6111yescharacteristic
237#1280—611no—
238C2×C61—21no—
239C2×C61—21no—
240C2×C61—21no—
241C2×C61—21no—
242C2×C61#159611yescharacteristic
243C2×C61#160411yescharacteristic
244C2×C61#161111yescharacteristic
245C2×C61#161311yescharacteristic
246C2×C61#205811yescharacteristic
247C2×C61#206011yescharacteristic
248C2×C61#206211yescharacteristic
249C2×C22⋊Q8—1221no—
250C22×C4⋊C4—611no—
251C22×C4⋊C4—1221no—
252C2×#106—1221no—
253C2×#106—1221no—
254C2×C22⋊C8—611no—
255C2×C22⋊C8C2×D6111yescharacteristic
256#398—1221no—
257#398—1221no—
258#395—1221no—
259#395—1221no—
260#380—611no—
261#380—1221no—
262#380C2×D6111yescharacteristic
263C2×#95—611no—
264C2×#95—1221no—
265C2×#95C2×D6111yescharacteristic
266#340—1221no—
267#340—1221no—
268C61#1057011yescharacteristic, complemented, Sylow
269C22×Q8—1221no—
270C23×C4—21no—
271C23×C4—611no—
272C23×C4—611no—
273C23×C4—1221no—
274C23×C4C22×D6111yescharacteristic
275C22×C8—21no—
276C22×C8—1221no—
277C22⋊Q8—2442no—
278C22⋊Q8—2442no—
279C2×C4⋊C4—611no—
280C2×C4⋊C4—611no—
281C2×C4⋊C4—1221no—
282C2×C4⋊C4—1221no—
283C2×C4⋊C4—1221no—
284C2×C4⋊C4—1221no—
285C2×C4⋊C4—1221no—
286C2×C4⋊C4—1221no—
287C2×C4⋊C4—1221no—
288C2×C4⋊C4—2442no—
289C2×C4⋊C4—2442no—
290C2×C4⋊C4—2442no—
291C2×C4⋊C4—2442no—
292C2×C4⋊C4D24411yescharacteristic
293C2×C4⋊C4D24411yescharacteristic
294C2×C22⋊C4—21no—
295C2×C22⋊C4—1221no—
296#106—2442no—
297#106—2442no—
298C22⋊C8—21no—
299C22⋊C8—612no—
300C22⋊C8—1221no—
301C22⋊C8Dic12212yescomplemented
302#95—21no—
303#95—21no—
304#95—1221no—
305#95—1221no—
306#95—1221no—
307#95—1221no—
308#95—1221no—
309#95—2442no—
310#95Dic12212yescomplemented
311C24D4×D6111yescharacteristic
312C2×Q8—4881no—
313C2×Q8—4881no—
314C2×Q8—2442no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—41no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—41no—
326C22×C4—612no—
327C22×C4—612no—
328C22×C4—1221no—
329C22×C4—1221no—
330C22×C4—1221no—
331C22×C4—1221no—
332C22×C4—1222no—
333C22×C4—1221no—
334C22×C4—1221no—
335C22×C4—2441no—
336C22×C4—2441no—
337C22×C4—2441no—
338C22×C4—2441no—
339C22×C4—2441no—
340C22×C4—2441no—
341C22×C4—2441no—
342C22×C4—2441no—
343C22×C4—2441no—
344C22×C4—2441no—
345C22×C4C2×Dic12211yescharacteristic
346C22×C4C2×Dic12211yescharacteristic
347C22×C4C2×D24411yescharacteristic
348C22×C4D4×D6111yescharacteristic
349C22×C4#1175822411yescharacteristic
350C22×C4Q8×D6111yescharacteristic
351C2×C8—22no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—1222no—
355C2×C8—2441no—
356C2×C8—2441no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4—1222no—
360C4⋊C4—1222no—
361C4⋊C4—4881no—
362C4⋊C4—4881no—
363C4⋊C4—2441no—
364C4⋊C4—2441no—
365C4⋊C4—2441no—
366C4⋊C4—2441no—
367C4⋊C4—2442no—
368C4⋊C4—2442no—
369C4⋊C4—2442no—
370C4⋊C4—2448no—
371C22⋊C4—41no—
372C22⋊C4—41no—
373C22⋊C4—2441no—
374C22⋊C4—2441no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23#1451974711yescharacteristic
380C23#1451975411yescharacteristic
381C23#1451977611yescharacteristic
382C23SD16×D6111yescharacteristic
383C23SD16×D6111yescharacteristic
384C23#1451980111yescharacteristic
385C23#1451980911yescharacteristic
386Q8—4884no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—24no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—1222no—
409C2×C4—1222no—
410C2×C4—4881no—
411C2×C4—4881no—
412C2×C4—4881no—
413C2×C4—4881no—
414C2×C4—4881no—
415C2×C4—4881no—
416C2×C4—2442no—
417C2×C4—2442no—
418C2×C4—2441no—
419C2×C4—2442no—
420C2×C4—2441no—
421C2×C4—2441no—
422C2×C4—2441no—
423C2×C4—2441no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4—2441no—
427C2×C4—2441no—
428C2×C4—2441no—
429C2×C4—2442no—
430C2×C4—2442no—
431C2×C4#1451975411yescharacteristic
432C2×C4#1451975711yescharacteristic
433C2×C4#1451977611yescharacteristic
434C2×C4#1451977711yescharacteristic
435C8—42no—
436C8—2442no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22#1683968311yescharacteristic
450C22#1683990211yescharacteristic
451C22#1683991411yescharacteristic
452C22#1683993111yescharacteristic
453C22#1683994611yescharacteristic
454C22#1683995011yescharacteristic
455C22#1683995311yescharacteristic
456C22#1684004511yescharacteristic
457C22#1684005011yescharacteristic
458C22#1684015911yescharacteristic
459C22#1684017011yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—44no—
465C4—81no—
466C4—81no—
467C4—4882no—
468C4—4881no—
469C4—4881no—
470C4—2442no—
471C4—2442no—
472C2—21no—
473C2—21no—
474C2—21no—
475C2—21no—
476C2#2144474311yescharacteristic
477C2#2144478911yescharacteristic
478C2#2144482811yescharacteristic
479C2#2144484011yescharacteristic
480C2#2144715111yescharacteristic
481C2#2144716311yescharacteristic
482C2#2144717311yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenter#1294D61
hypocenterC61#10570
LCSG ▷ C23×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1294

Complements

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

NH ≅ G/Ntype
51. C22⋊#92418Q8semidirect
65. C22⋊C8×C61Q8semidirect
68. #95×C61Q8semidirect
268. C61#10570semidirect
301. C22⋊C8Dic122semidirect
310. #95Dic122semidirect

Maximal subgroups

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

subgroupindex
#214519362
#214460142
#214460112
#214440842
#214436982
#214436612
C61×#12942
#1057061