Finite Group Databasebeta

← #29582987

Subgroups — #29582987

Order 15616.

684 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21451936C211yesmaximal, characteristic
2#21445755C211yesmaximal, characteristic
3#21445753C211yesmaximal, characteristic
4#21444089C211yesmaximal, characteristic
5#21443698C211yesmaximal, characteristic
6#21443661C211yesmaximal, characteristic
7C61×#1294C211yesmaximal, characteristic
8C23×Dic122C2211yescharacteristic
9C2×#14519754—21no—
10C2×#14519702—21no—
11C2×#14519702—21no—
12C2×#14519700—21no—
13C2×#14519700—21no—
14C2×C22⋊#92418C2211yescharacteristic
15#16839696—21no—
16#16839695—21no—
17#16839683—21no—
18#16839682—21no—
19#16839622C2211yescharacteristic
20#16839620—21no—
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—21no—
33C22×Dic122—42no—
34C22×Dic122—42no—
35C22×Dic122Q812yescomplemented
36C23×Dic61—21no—
37C23×Dic61D411yescharacteristic
38C23×Dic61D411yescharacteristic
39C22×#92418—21no—
40#14519754—42no—
41#14519754—42no—
42C2×C4⋊Dic61—21no—
43C2×C4⋊Dic61D411yescharacteristic
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758196—21no—
46C2×#11758196—21no—
47C2×#11758196—21no—
48C2×#11758196—21no—
49C2×C22⋊Dic61—21no—
50#14519702—42no—
51#14519702—42no—
52#14519700—42no—
53#14519700—42no—
54C22⋊#92418—21no—
55C22⋊#92418—21no—
56#14519684—21no—
57#14519684—21no—
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684—42no—
62#14519684—42no—
63C23×C4×C61—21no—
64C23×C4×C61C2311yescharacteristic
65C22×C8×C61—21no—
66C2×C4⋊C4×C61D411yescharacteristic
67C2×C4⋊C4×C61D411yescharacteristic
68C2×C22⋊C4×C61—21no—
69C22⋊C8×C61—21no—
70C22⋊C8×C61—21no—
71#95×C61—21no—
72#95×C61—21no—
73#95×C61—21no—
74C24×C61C2×D411yescharacteristic
75C22×C4×C61—22no—
76C22×C4×C61—21no—
77C22×C4×C61—21no—
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×C61—41no—
85C22×C4×C61—41no—
86C22×C4×C61C2×D411yescharacteristic
87C22×C4×C61C2×D411yescharacteristic
88C22×C4×C61C2×Q811yescharacteristic
89C22×C4×C61#4111yescharacteristic
90C22×C4×C61#4111yescharacteristic
91C22×C4×C61#4111yescharacteristic
92C22×Dic61—22no—
93C22×Dic61—22no—
94C22×Dic61—21no—
95C22×Dic61—21no—
96C22×Dic61—22no—
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—
109C22×Dic61SD1612yes—
110C22×Dic61Q1612yes—
111C2×Dic122—22no—
112C2×Dic122—22no—
113C2×Dic122—22no—
114C2×Dic122—22no—
115C2×Dic122—22no—
116C2×Dic122—22no—
117C2×Dic122—44no—
118C2×Dic122—44no—
119C2×Dic122—44no—
120C2×Dic122—44no—
121C2×Dic122—41no—
122C2×Dic122—41no—
123C2×Dic122—41no—
124C2×Dic122—41no—
125C2×Dic122—41no—
126C2×Dic122—41no—
127C2×Dic122—42no—
128C2×Dic122—81no—
129C2×Dic122—81no—
130C2×C8×C61—41no—
131C2×C8×C61—41no—
132C2×C8×C61—41no—
133C4⋊C4×C61—41no—
134C4⋊C4×C61—41no—
135C22⋊C4×C61—41no—
136C22⋊C4×C61—41no—
137C22⋊Dic61—41no—
138C22⋊Dic61—41no—
139C4⋊Dic61—42no—
140C4⋊Dic61—41no—
141C4⋊Dic61—41no—
142#11758196—42no—
143#11758196—42no—
144#11758196—81no—
145#11758196—81no—
146C2×#92418—41no—
147C2×#92418—41no—
148C2×#92418—41no—
149C23×C61—21no—
150C23×C61—21no—
151C23×C61—21no—
152C23×C61—21no—
153C23×C61#12011yescharacteristic
154C23×C61C22⋊Q811yescharacteristic
155C23×C61#12411yescharacteristic
156C23×C61C2×SD1611yescharacteristic
157C23×C61C2×Q1611yescharacteristic
158C23×C61AGL(1,ℤ/8)11yescharacteristic
159C23×C61#13711yescharacteristic
160C2×C4×C61—21no—
161C2×C4×C61—21no—
162C2×C4×C61—21no—
163C2×C4×C61—21no—
164C2×C4×C61—41no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—41no—
168C2×C4×C61—42no—
169C2×C4×C61—42no—
170C2×C4×C61—42no—
171C2×C4×C61—41no—
172C2×C4×C61—41no—
173C2×C4×C61—41no—
174C2×C4×C61—41no—
175C2×C4×C61—41no—
176C2×C4×C61—41no—
177C2×C4×C61—81no—
178C2×C4×C61—81no—
179C2×C4×C61—81no—
180C2×C4×C61—81no—
181C2×C4×C61C22⋊Q811yescharacteristic
182C2×C4×C61C22⋊Q811yescharacteristic
183C2×C4×C61#12411yescharacteristic
184C2×C4×C61#12411yescharacteristic
185C2×Dic61—24no—
186C2×Dic61—22no—
187C2×Dic61—22no—
188C2×Dic61—42no—
189C2×Dic61—42no—
190C2×Dic61—42no—
191C2×Dic61—42no—
192C2×Dic61—41no—
193C2×Dic61—41no—
194C2×Dic61—41no—
195C2×Dic61—42no—
196C2×Dic61—42no—
197C2×Dic61—41no—
198C2×Dic61—42no—
199C2×Dic61—42no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—41no—
203C2×Dic61—41no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—81no—
207C2×Dic61—81no—
208Dic122—24no—
209Dic122—24no—
210Dic122—42no—
211Dic122—42no—
212Dic122—42no—
213Dic122—42no—
214Dic122—42no—
215Dic122—42no—
216Dic122—84no—
217C8×C61—81no—
218#92418—81no—
219#10341—611nomaximal, Sylow
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—21no—
226C22×C61—21no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—21no—
230C22×C61—21no—
231C22×C61—21no—
232C22×C61#39311yescharacteristic
233C22×C61#45011yescharacteristic
234C22×C61#45111yescharacteristic
235C22×C61#45511yescharacteristic
236C22×C61#45611yescharacteristic
237C22×C61B(4,𝔽2)11yescharacteristic
238C22×C61B(4,𝔽2)11yescharacteristic
239C22×C61#47511yescharacteristic
240C22×C61#47711yescharacteristic
241C22×C61#48711yescharacteristic
242C22×C61#48911yescharacteristic
243C4×C61—21no—
244C4×C61—21no—
245C4×C61—21no—
246C4×C61—21no—
247C4×C61—82no—
248C4×C61—81no—
249C4×C61—81no—
250Dic61—42no—
251Dic61—42no—
252Dic61—44no—
253Dic61—81no—
254Dic61—81no—
255#2659—611no—
256#1787—611no—
257#1787—611no—
258#1446—611no—
259#1294—611no—
260#1294D6111yescharacteristic
261#1280—611no—
262C2×C61—21no—
263C2×C61—21no—
264C2×C61—21no—
265C2×C61—21no—
266C2×C61#160111yescharacteristic
267C2×C61#160211yescharacteristic
268C2×C61#160411yescharacteristic
269C2×C61#160511yescharacteristic
270C2×C61#202411yescharacteristic
271C2×C61#202811yescharacteristic
272C2×C61#202911yescharacteristic
273C23×Q8—611no—
274C2×C22⋊Q8—1221no—
275C2×#103—1221no—
276C2×#103—1221no—
277C2×#103—1221no—
278C2×#103—1221no—
279C2×C22⋊C8—611no—
280C2×C22⋊C8C2×D6111yescharacteristic
281#398—1221no—
282#398—1221no—
283#395—1221no—
284#395—1221no—
285#380—611no—
286#380—1221no—
287#380C2×D6111yescharacteristic
288C2×#95—611no—
289C2×#95—1221no—
290C2×#95—1221no—
291C2×#95C2×D6111yescharacteristic
292C61#1034111yescharacteristic, complemented, Sylow
293C22×Q8—612no—
294C22×Q8—1221no—
295C22×Q8—1221no—
296C22×Q8—1221no—
297C22×Q8—1221no—
298C22×Q8—1221no—
299C22×Q8—1221no—
300C22×Q8—2442no—
301C22×Q8—2442no—
302C23×C4—21no—
303C23×C4—611no—
304C23×C4—611no—
305C23×C4—1221no—
306C23×C4C22×D6111yescharacteristic
307C22×C8—21no—
308C22×C8—1221no—
309C22⋊Q8—2442no—
310C22⋊Q8—2442no—
311C2×C4⋊C4—611no—
312C2×C4⋊C4—611no—
313C2×C4⋊C4—1221no—
314C2×C4⋊C4—1221no—
315C2×C4⋊C4—1221no—
316C2×C4⋊C4—1221no—
317C2×C4⋊C4—1221no—
318C2×C4⋊C4D24411yescharacteristic
319C2×C4⋊C4D24411yescharacteristic
320C2×C22⋊C4—21no—
321C2×C22⋊C4—1221no—
322#103—2442no—
323#103—2442no—
324#103—2442no—
325#103—2442no—
326C22⋊C8—21no—
327C22⋊C8—21no—
328C22⋊C8—1221no—
329C22⋊C8—1221no—
330#95—21no—
331#95—21no—
332#95—21no—
333#95—1221no—
334#95—1221no—
335#95—1221no—
336#95—1221no—
337#95—1221no—
338#95—2442no—
339#95—2442no—
340C24D4×D6111yescharacteristic
341C2×Q8—1222no—
342C2×Q8—1222no—
343C2×Q8—1222no—
344C2×Q8—1222no—
345C2×Q8—1222no—
346C2×Q8—1222no—
347C2×Q8—4881no—
348C2×Q8—4881no—
349C2×Q8—2441no—
350C2×Q8—2441no—
351C2×Q8—2441no—
352C2×Q8—2441no—
353C2×Q8—2444no—
354C2×Q8—2442no—
355C2×Q8—2444no—
356C2×Q8—2444no—
357C2×Q8—2444no—
358C2×Q8—2441no—
359C2×Q8—2441no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—41no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—612no—
372C22×C4—612no—
373C22×C4—1221no—
374C22×C4—1221no—
375C22×C4—1222no—
376C22×C4—1222no—
377C22×C4—1221no—
378C22×C4—1221no—
379C22×C4—1222no—
380C22×C4—1221no—
381C22×C4—1221no—
382C22×C4—2441no—
383C22×C4—2441no—
384C22×C4—2441no—
385C22×C4—2441no—
386C22×C4—2441no—
387C22×C4—2441no—
388C22×C4—2441no—
389C22×C4—2441no—
390C22×C4C2×D24411yescharacteristic
391C22×C4#1175822211yescharacteristic
392C22×C4#1175822211yescharacteristic
393C22×C4D4×D6111yescharacteristic
394C22×C4#1175822411yescharacteristic
395C22×C4Q8×D6111yescharacteristic
396C2×C8—41no—
397C2×C8—41no—
398C2×C8—41no—
399C2×C8—2441no—
400C2×C8—2441no—
401C2×C8—2441no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—4881no—
405C4⋊C4—4881no—
406C4⋊C4—2441no—
407C4⋊C4—2441no—
408C4⋊C4—2442no—
409C4⋊C4—2442no—
410C4⋊C4—2442no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—2441no—
414C22⋊C4—2441no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23#1451974711yescharacteristic
420C23#1451975511yescharacteristic
421C23#1451976311yescharacteristic
422C23SD16×D6111yescharacteristic
423C23Q16×D6111yescharacteristic
424C23#1451980111yescharacteristic
425C23#1451980611yescharacteristic
426Q8—1224no—
427Q8—1224no—
428Q8—4884no—
429Q8—2442no—
430Q8—2442no—
431Q8—2442no—
432Q8—2442no—
433Q8—2442no—
434Q8—2442no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—42no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—81no—
453C2×C4—81no—
454C2×C4—81no—
455C2×C4—81no—
456C2×C4—1224no—
457C2×C4—1222no—
458C2×C4—1222no—
459C2×C4—4881no—
460C2×C4—4881no—
461C2×C4—2441no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4—2441no—
465C2×C4—2441no—
466C2×C4—2441no—
467C2×C4—2442no—
468C2×C4—2442no—
469C2×C4—2442no—
470C2×C4—2441no—
471C2×C4—2441no—
472C2×C4—2441no—
473C2×C4—2442no—
474C2×C4—2442no—
475C2×C4—2441no—
476C2×C4—2442no—
477C2×C4—2442no—
478C2×C4—2442no—
479C2×C4#1451975511yescharacteristic
480C2×C4#1451975711yescharacteristic
481C2×C4#1451976311yescharacteristic
482C2×C4#1451976511yescharacteristic
483C8—81no—
484C8—4881no—
485C22—21no—
486C22—21no—
487C22—21no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22#1683967511yescharacteristic
498C22#1683991411yescharacteristic
499C22#1683991911yescharacteristic
500C22#1683994111yescharacteristic
501C22#1683994611yescharacteristic
502C22#1683995011yescharacteristic
503C22#1683995011yescharacteristic
504C22#1684004611yescharacteristic
505C22#1684005611yescharacteristic
506C22#1684011111yescharacteristic
507C22#1684012011yescharacteristic
508C4—21no—
509C4—21no—
510C4—21no—
511C4—21no—
512C4—82no—
513C4—81no—
514C4—81no—
515C4—4881no—
516C4—4881no—
517C4—2444no—
518C4—2442no—
519C4—2442no—
520C2—21no—
521C2—21no—
522C2—21no—
523C2—21no—
524C2#2144477211yescharacteristic
525C2#2144477711yescharacteristic
526C2#2144478911yescharacteristic
527C2#2144479411yescharacteristic
528C2#2144695911yescharacteristic
529C2#2144697911yescharacteristic
530C2#2144698411yescharacteristic
subgroupG/H
centerC23#14519747
commutator, cosocleC23×C4×C61C23
FrattiniC23×C4C22×D61
FittingC61×#1294C2
socleC23×C61#120
prime radicalC24×C61C2×D4
hypercenter#1294D61
hypocenterC61#10341
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
35. C22×Dic122Q8semidirect
292. C61#10341semidirect

Maximal subgroups

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

subgroupindex
#214519362
#214457552
#214457532
#214440892
#214436982
#214436612
C61×#12942
#1034161