Finite Group Databasebeta

← #29583007

Subgroups — #29583007

Order 15616.

640 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451792C211yesmaximal, characteristic
2#21445755C211yesmaximal, characteristic
3#21445753C211yesmaximal, characteristic
4#21444089C211yesmaximal, characteristic
5#21443698C211yesmaximal, characteristic
6#21443661C211yesmaximal, characteristic
7C61×#1294C211yesmaximal, characteristic
8C23×Dic122C2211yescharacteristic
9C2×#14519702—21no—
10C2×#14519702—21no—
11C2×#14519700—21no—
12C2×#14519700—21no—
13C2×C22⋊#92418C2211yescharacteristic
14#16839704—21no—
15#16839701—21no—
16#16839695—21no—
17#16839694—21no—
18#16839637—21no—
19#16839634—21no—
20#16839622C2211yescharacteristic
21C2×#14519684—21no—
22C2×#14519684—21no—
23C2×#14519684C2211yescharacteristic
24C2×C22⋊C8×C61C2211yescharacteristic
25C61×#380C2211yescharacteristic
26C2×#95×C61C2211yescharacteristic
27C22×Dic122—21no—
28C22×Dic122—21no—
29C22×Dic122—21no—
30C22×Dic122—21no—
31C22×Dic122—21no—
32C22×Dic122—42no—
33C22×Dic122—42no—
34C22×Dic122Q812yes—
35C23×Dic61—21no—
36C23×Dic61D411yescharacteristic
37C23×Dic61D411yescharacteristic
38C22×#92418—21no—
39C2×C4⋊Dic61—21no—
40C2×C4⋊Dic61—21no—
41C2×C4⋊Dic61D411yescharacteristic
42C2×C4⋊Dic61D411yescharacteristic
43C2×#11758196—21no—
44C2×#11758196—21no—
45C2×C22⋊Dic61—21no—
46#14519702—42no—
47#14519702—42no—
48#14519700—42no—
49#14519700—42no—
50C22⋊#92418—21no—
51C22⋊#92418—21no—
52#14519684—21no—
53#14519684—21no—
54#14519684—21no—
55#14519684—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684—42no—
60#14519684—42no—
61C23×C4×C61—21no—
62C23×C4×C61C2311yescharacteristic
63C22×C8×C61—21no—
64C2×C4⋊C4×C61D411yescharacteristic
65C2×C4⋊C4×C61D411yescharacteristic
66C2×C22⋊C4×C61—21no—
67C22⋊C8×C61—21no—
68C22⋊C8×C61—21no—
69#95×C61—21no—
70#95×C61—21no—
71#95×C61—21no—
72C24×C61C2×D411yescharacteristic
73C22×C4×C61—22no—
74C22×C4×C61—21no—
75C22×C4×C61—21no—
76C22×C4×C61—41no—
77C22×C4×C61—41no—
78C22×C4×C61—41no—
79C22×C4×C61—41no—
80C22×C4×C61—41no—
81C22×C4×C61—41no—
82C22×C4×C61—41no—
83C22×C4×C61—41no—
84C22×C4×C61C2×D411yescharacteristic
85C22×C4×C61C2×D411yescharacteristic
86C22×C4×C61C2×Q811yescharacteristic
87C22×C4×C61#4111yescharacteristic
88C22×C4×C61#4111yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C22×Dic61—22no—
91C22×Dic61—22no—
92C22×Dic61—22no—
93C22×Dic61—21no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96C22×Dic61—21no—
97C22×Dic61—21no—
98C22×Dic61—21no—
99C22×Dic61—21no—
100C22×Dic61—21no—
101C22×Dic61—41no—
102C22×Dic61—41no—
103C22×Dic61—41no—
104C22×Dic61—41no—
105C22×Dic61—41no—
106C22×Dic61—41no—
107C22×Dic61—41no—
108C22×Dic61—41no—
109C2×Dic122—22no—
110C2×Dic122—22no—
111C2×Dic122—22no—
112C2×Dic122—22no—
113C2×Dic122—22no—
114C2×Dic122—22no—
115C2×Dic122—44no—
116C2×Dic122—44no—
117C2×Dic122—44no—
118C2×Dic122—44no—
119C2×Dic122—41no—
120C2×Dic122—41no—
121C2×Dic122—41no—
122C2×Dic122—41no—
123C2×Dic122—41no—
124C2×Dic122—41no—
125C2×C8×C61—41no—
126C2×C8×C61—41no—
127C2×C8×C61—41no—
128C4⋊C4×C61—41no—
129C4⋊C4×C61—41no—
130C22⋊C4×C61—41no—
131C22⋊C4×C61—41no—
132C22⋊Dic61—41no—
133C22⋊Dic61—41no—
134C4⋊Dic61—41no—
135C4⋊Dic61—41no—
136C4⋊Dic61—81no—
137C4⋊Dic61—81no—
138#11758196—81no—
139#11758196—81no—
140C2×#92418—41no—
141C2×#92418—41no—
142C2×#92418—41no—
143C23×C61—21no—
144C23×C61—21no—
145C23×C61—21no—
146C23×C61—21no—
147C23×C61#12011yescharacteristic
148C23×C61C22⋊Q811yescharacteristic
149C23×C61#12411yescharacteristic
150C23×C61#13511yescharacteristic
151C23×C61#13511yescharacteristic
152C23×C61#13711yescharacteristic
153C23×C61#13711yescharacteristic
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61—21no—
158C2×C4×C61—41no—
159C2×C4×C61—41no—
160C2×C4×C61—41no—
161C2×C4×C61—41no—
162C2×C4×C61—42no—
163C2×C4×C61—42no—
164C2×C4×C61—42no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—41no—
169C2×C4×C61—41no—
170C2×C4×C61—41no—
171C2×C4×C61—81no—
172C2×C4×C61—81no—
173C2×C4×C61—81no—
174C2×C4×C61—81no—
175C2×C4×C61C22⋊Q811yescharacteristic
176C2×C4×C61C22⋊Q811yescharacteristic
177C2×C4×C61#12411yescharacteristic
178C2×C4×C61#12411yescharacteristic
179C2×Dic61—24no—
180C2×Dic61—42no—
181C2×Dic61—42no—
182C2×Dic61—42no—
183C2×Dic61—42no—
184C2×Dic61—42no—
185C2×Dic61—42no—
186C2×Dic61—42no—
187C2×Dic61—42no—
188C2×Dic61—41no—
189C2×Dic61—41no—
190C2×Dic61—41no—
191C2×Dic61—41no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—41no—
196C2×Dic61—41no—
197C2×Dic61—41no—
198C2×Dic61—41no—
199C2×Dic61—41no—
200C2×Dic61—81no—
201C2×Dic61—81no—
202Dic122—24no—
203Dic122—24no—
204Dic122—42no—
205Dic122—42no—
206Dic122—42no—
207Dic122—42no—
208Dic122—42no—
209Dic122—42no—
210C8×C61—81no—
211#92418—81no—
212#10345—611nomaximal, Sylow
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—21no—
216C22×C61—21no—
217C22×C61—21no—
218C22×C61—21no—
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61#39311yescharacteristic
226C22×C61#45211yescharacteristic
227C22×C61#45211yescharacteristic
228C22×C61#45511yescharacteristic
229C22×C61#45611yescharacteristic
230C22×C61B(4,𝔽2)11yescharacteristic
231C22×C61B(4,𝔽2)11yescharacteristic
232C22×C61#47911yescharacteristic
233C22×C61#47911yescharacteristic
234C22×C61#48811yescharacteristic
235C22×C61#49111yescharacteristic
236C4×C61—21no—
237C4×C61—21no—
238C4×C61—21no—
239C4×C61—21no—
240C4×C61—82no—
241C4×C61—81no—
242C4×C61—81no—
243Dic61—44no—
244Dic61—81no—
245Dic61—81no—
246Dic61—81no—
247Dic61—81no—
248#2646—611no—
249#1787—611no—
250#1787—611no—
251#1446—611no—
252#1294—611no—
253#1294D6111yescharacteristic
254#1280—611no—
255C2×C61—21no—
256C2×C61—21no—
257C2×C61—21no—
258C2×C61—21no—
259C2×C61#160311yescharacteristic
260C2×C61#160311yescharacteristic
261C2×C61#160611yescharacteristic
262C2×C61#160611yescharacteristic
263C2×C61#202611yescharacteristic
264C2×C61#202811yescharacteristic
265C2×C61#202911yescharacteristic
266C23×Q8—611no—
267C2×#103—1221no—
268C2×#103—1221no—
269C2×#103—1221no—
270C2×#103—1221no—
271C2×C22⋊C8—611no—
272C2×C22⋊C8C2×D6111yescharacteristic
273#400—1221no—
274#400—1221no—
275#398—1221no—
276#398—1221no—
277#385—1221no—
278#385—1221no—
279#380—611no—
280#380C2×D6111yescharacteristic
281C2×#95—611no—
282C2×#95—1221no—
283C2×#95—1221no—
284C2×#95C2×D6111yescharacteristic
285C61#1034511yescharacteristic, complemented, Sylow
286C22×Q8—612no—
287C22×Q8—1221no—
288C22×Q8—1221no—
289C22×Q8—1221no—
290C22×Q8—1221no—
291C22×Q8—1221no—
292C22×Q8—2442no—
293C22×Q8—2442no—
294C23×C4—21no—
295C23×C4—611no—
296C23×C4—611no—
297C23×C4—1221no—
298C23×C4C22×D6111yescharacteristic
299C22×C8—21no—
300C22×C8—1221no—
301C2×C4⋊C4—611no—
302C2×C4⋊C4—611no—
303C2×C4⋊C4—1221no—
304C2×C4⋊C4—1221no—
305C2×C4⋊C4—1221no—
306C2×C4⋊C4—1221no—
307C2×C4⋊C4D24411yescharacteristic
308C2×C4⋊C4D24411yescharacteristic
309C2×C22⋊C4—21no—
310C2×C22⋊C4—1221no—
311#103—2442no—
312#103—2442no—
313#103—2442no—
314#103—2442no—
315C22⋊C8—21no—
316C22⋊C8—21no—
317C22⋊C8—1221no—
318C22⋊C8—1221no—
319#95—21no—
320#95—21no—
321#95—21no—
322#95—1221no—
323#95—1221no—
324#95—1221no—
325#95—1221no—
326#95—1221no—
327#95—1221no—
328#95—1221no—
329#95—2442no—
330#95—2442no—
331C24D4×D6111yescharacteristic
332C2×Q8—1222no—
333C2×Q8—1222no—
334C2×Q8—1222no—
335C2×Q8—1222no—
336C2×Q8—1222no—
337C2×Q8—1222no—
338C2×Q8—2441no—
339C2×Q8—2441no—
340C2×Q8—2441no—
341C2×Q8—2441no—
342C2×Q8—2444no—
343C2×Q8—2444no—
344C2×Q8—2444no—
345C2×Q8—2444no—
346C2×Q8—2441no—
347C2×Q8—2441no—
348C22×C4—22no—
349C22×C4—21no—
350C22×C4—21no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—1222no—
360C22×C4—1222no—
361C22×C4—1222no—
362C22×C4—1221no—
363C22×C4—1221no—
364C22×C4—1221no—
365C22×C4—1221no—
366C22×C4—1221no—
367C22×C4—1221no—
368C22×C4—1221no—
369C22×C4—1221no—
370C22×C4—2441no—
371C22×C4—2441no—
372C22×C4—2441no—
373C22×C4—2441no—
374C22×C4—2441no—
375C22×C4—2441no—
376C22×C4—2441no—
377C22×C4—2441no—
378C22×C4C2×D24411yescharacteristic
379C22×C4#1175822211yescharacteristic
380C22×C4#1175822211yescharacteristic
381C22×C4D4×D6111yescharacteristic
382C22×C4#1175822411yescharacteristic
383C22×C4Q8×D6111yescharacteristic
384C2×C8—41no—
385C2×C8—41no—
386C2×C8—41no—
387C2×C8—2441no—
388C2×C8—2441no—
389C2×C8—2441no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—4881no—
393C4⋊C4—4881no—
394C4⋊C4—4881no—
395C4⋊C4—4881no—
396C4⋊C4—2441no—
397C4⋊C4—2441no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—2441no—
401C22⋊C4—2441no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23#1451974711yescharacteristic
407C23#1451975511yescharacteristic
408C23#1451976311yescharacteristic
409C23#1451979611yescharacteristic
410C23#1451979811yescharacteristic
411C23#1451980611yescharacteristic
412C23#1451980911yescharacteristic
413Q8—1224no—
414Q8—1224no—
415Q8—2442no—
416Q8—2442no—
417Q8—2442no—
418Q8—2442no—
419Q8—2442no—
420Q8—2442no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—81no—
439C2×C4—81no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—1224no—
443C2×C4—4881no—
444C2×C4—4881no—
445C2×C4—2442no—
446C2×C4—2442no—
447C2×C4—2441no—
448C2×C4—2441no—
449C2×C4—2441no—
450C2×C4—2441no—
451C2×C4—2441no—
452C2×C4—2441no—
453C2×C4—2441no—
454C2×C4—2441no—
455C2×C4—2441no—
456C2×C4—2441no—
457C2×C4—2441no—
458C2×C4—2441no—
459C2×C4—2442no—
460C2×C4—2442no—
461C2×C4—2442no—
462C2×C4—2442no—
463C2×C4—2442no—
464C2×C4—2442no—
465C2×C4#1451975511yescharacteristic
466C2×C4#1451975711yescharacteristic
467C2×C4#1451976311yescharacteristic
468C2×C4#1451976511yescharacteristic
469C8—81no—
470C8—4881no—
471C22—21no—
472C22—21no—
473C22—21no—
474C22—21no—
475C22—21no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22#1683967511yescharacteristic
484C22#1683992511yescharacteristic
485C22#1683992711yescharacteristic
486C22#1683994111yescharacteristic
487C22#1683994611yescharacteristic
488C22#1683995011yescharacteristic
489C22#1683995011yescharacteristic
490C22#1684006811yescharacteristic
491C22#1684007211yescharacteristic
492C22#1684011511yescharacteristic
493C22#1684012911yescharacteristic
494C4—21no—
495C4—21no—
496C4—21no—
497C4—21no—
498C4—82no—
499C4—81no—
500C4—81no—
501C4—4881no—
502C4—4881no—
503C4—4881no—
504C4—4881no—
505C4—2444no—
506C2—21no—
507C2—21no—
508C2—21no—
509C2—21no—
510C2#2144478311yescharacteristic
511C2#2144478511yescharacteristic
512C2#2144480011yescharacteristic
513C2#2144480211yescharacteristic
514C2#2144696911yescharacteristic
515C2#2144697911yescharacteristic
516C2#2144698411yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenter#1294D61
hypocenterC61#10345
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
285. C61#10345semidirect

Maximal subgroups

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

subgroupindex
#214517922
#214457552
#214457532
#214440892
#214436982
#214436612
C61×#12942
#1034561