Finite Group Databasebeta

← #29576589

Subgroups — #29576589

Order 15616.

648 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456567C211yesmaximal, characteristic
2#21448869C211yesmaximal, characteristic, complemented
3#21444386C211yesmaximal, characteristic, complemented
4C2×#16839496C211yesmaximal, characteristic, complemented
5#21443697C211yesmaximal, characteristic, complemented
6#21443667C211yesmaximal, characteristic, complemented
7C61×#1964C211yesmaximal, characteristic, complemented
8C2×#14519751C2211yescharacteristic
9C2×#14519737—21no—
10#16840075C412yescomplemented
11#16840073—21no—
12#16839996—22no—
13#16839896C412yescomplemented
14#16839895—21no—
15C2×C22⋊#92418C2211yescharacteristic
16C2×C22⋊#92418C2211yescharacteristic
17#16839653—21no—
18#16839647—21no—
19#16839640—21no—
20#16839639—21no—
21C4×#11758198—21no—
22C2×#14519684C2211yescharacteristic
23#16839496—21no—
24#16839496—21no—
25#16839495—22no—
26C2×#121×C61C2211yescharacteristic
27C2×#99×C61—21no—
28C2×#99×C61—21no—
29C61×#380C2211yescharacteristic
30C4×C22⋊C4×C61C2211yescharacteristic
31C22×D244D411yescharacteristic
32C22×C22⋊D61—21no—
33C23×Dic61—21no—
34C22×C4×D61—21no—
35C2×#11758199—22no—
36C22×#92418—21no—
37C22×#92418—21no—
38#14519751—21no—
39#14519751—21no—
40#14519751C2×C412yes—
41#14519751D412yes—
42#14519737—42no—
43#14519737—42no—
44C2×C4⋊Dic61D411yescharacteristic
45C2×#11758196—21no—
46C2×#11758198—21no—
47C2×#11758198—21no—
48C2×#11758198—21no—
49C2×#11758198—21no—
50C2×C4×Dic61—21no—
51#14519710—22no—
52#14519698—22no—
53#14519697—22no—
54C22⋊#92418—21no—
55C22⋊#92418—21no—
56C22⋊#92418—21no—
57C22⋊#92418C2×C412yescomplemented
58#14519684—21no—
59#14519684—21no—
60#14519684—21no—
61#14519684D411yescharacteristic
62#14519684D411yescharacteristic
63C22×D4×C61—21no—
64C22×D4×C61C2×C411yescharacteristic, complemented
65C23×C4×C61C2311yescharacteristic
66#121×C61—21no—
67#121×C61—21no—
68#121×C61—21no—
69#121×C61—21no—
70C2×C4⋊C4×C61—21no—
71C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
72C2×C22⋊C4×C61—21no—
73C2×C22⋊C4×C61—21no—
74C2×C22⋊C4×C61D411yescharacteristic
75C2×C22⋊C4×C61D411yescharacteristic
76C2×C42×C61—21no—
77#99×C61—42no—
78#99×C61—42no—
79#95×C61—21no—
80#95×C61—21no—
81C24×C61—21no—
82C24×C61C2×D411yescharacteristic
83C23×D61—21no—
84C2×D4×C61—21no—
85C2×D4×C61—21no—
86C2×D4×C61—41no—
87C2×D4×C61—41no—
88C2×D4×C61—41no—
89C2×D4×C61—41no—
90C2×D4×C61—41no—
91C2×D4×C61—41no—
92C2×D4×C61—81no—
93C22×C4×C61—21no—
94C22×C4×C61—21no—
95C22×C4×C61—21no—
96C22×C4×C61—41no—
97C22×C4×C61—81no—
98C22×C4×C61C22×C411yescharacteristic
99C22×C4×C61C2×D411yescharacteristic
100C22×C4×C61C2×D411yescharacteristic
101C22×C4×C61C2×D411yescharacteristic
102C22×C4×C61#4111yescharacteristic
103C22×C4×C61#4111yescharacteristic
104C2×C22⋊D61—22no—
105C2×C22⋊D61—22no—
106C2×C22⋊D61—41no—
107C2×C22⋊D61—41no—
108C2×C22⋊D61—41no—
109C2×C22⋊D61—41no—
110C22×Dic61—21no—
111C22×Dic61—21no—
112C22×Dic61—21no—
113C22×Dic61—42no—
114C22×Dic61—41no—
115C22×Dic61—41no—
116C22×Dic61—81no—
117C2×D244—21no—
118C2×D244—81no—
119C2×D244C22⋊C412yes—
120C2×C4×D61—42no—
121C2×C4×D61—42no—
122C2×C4×D61—81no—
123C4⋊C4×C61—21no—
124C4⋊C4×C61—21no—
125C4⋊C4×C61—81no—
126C22⋊C4×C61—21no—
127C22⋊C4×C61—21no—
128C22⋊C4×C61—21no—
129C22⋊C4×C61—41no—
130C22⋊C4×C61—41no—
131C22⋊C4×C61—41no—
132C22⋊C4×C61—41no—
133C22⋊C4×C61D812yescomplemented
134C42×C61—81no—
135#11758199—82no—
136#11758198—22no—
137#11758198—22no—
138#11758198—42no—
139#11758198—42no—
140#11758198—81no—
141C4⋊Dic61—21no—
142C4⋊Dic61C22⋊C412yes—
143#11758196—42no—
144C4×Dic61—42no—
145C2×#92418—22no—
146C2×#92418—41no—
147C2×#92418—81no—
148C2×#92418—81no—
149C23×C61—41no—
150C23×C61—41no—
151C23×C61—41no—
152C23×C61—41no—
153C23×C61—41no—
154C23×C61—81no—
155C23×C61—81no—
156C23×C61C4×D411yescharacteristic
157C23×C61#12011yescharacteristic
158C23×C61#12111yescharacteristic
159C23×C61C2×D811yescharacteristic
160C23×C61#13511yescharacteristic
161C23×C61AGL(1,ℤ/8)11yescharacteristic
162C23×C61AGL(1,ℤ/8)11yescharacteristic
163C22×D61—22no—
164C22×D61—41no—
165C22×D61—41no—
166C22×D61—41no—
167C22×D61—41no—
168C22×D61—41no—
169C22×D61—41no—
170D4×C61—42no—
171D4×C61—81no—
172D4×C61—81no—
173D4×C61—81no—
174D4×C61—81no—
175D4×C61—81no—
176C2×C4×C61—22no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61—41no—
181C2×C4×C61—41no—
182C2×C4×C61—41no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—41no—
188C2×C4×C61—41no—
189C2×C4×C61—41no—
190C2×C4×C61—41no—
191C2×C4×C61—81no—
192C2×C4×C61—81no—
193C2×C4×C61—81no—
194C2×C4×C61C2×C22⋊C411yescharacteristic
195C2×C4×C61C4×D411yescharacteristic
196C2×C4×C61#12111yescharacteristic
197C2×C4×C61#12311yescharacteristic
198C22⋊D61—42no—
199C22⋊D61—42no—
200C22⋊D61—42no—
201C22⋊D61—42no—
202C2×Dic61—22no—
203C2×Dic61—22no—
204C2×Dic61—41no—
205C2×Dic61—41no—
206C2×Dic61—41no—
207C2×Dic61—41no—
208C2×Dic61—41no—
209C2×Dic61—41no—
210C2×Dic61—41no—
211C2×Dic61—82no—
212C2×Dic61—82no—
213D244—42no—
214D244—81no—
215C4×D61—84no—
216#92418—42no—
217#92418—81no—
218#9277—611nomaximal, Sylow
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—21no—
222C22×C61—21no—
223C22×C61—21no—
224C22×C61—21no—
225C22×C61—41no—
226C22×C61—41no—
227C22×C61—41no—
228C22×C61—41no—
229C22×C61—81no—
230C22×C61—81no—
231C22×C61—81no—
232C22×C61—161no—
233C22×C61—161no—
234C22×C61#38611yescharacteristic
235C22×C61C4×D811yescharacteristic
236C22×C61#44211yescharacteristic
237C22×C61#44711yescharacteristic
238C22×C61#44911yescharacteristic
239C22×C61#45911yescharacteristic
240C22×C61#46311yescharacteristic
241C2×D61—42no—
242C2×D61—42no—
243C2×D61—42no—
244C2×D61—81no—
245C2×D61—81no—
246C2×D61—81no—
247C2×D61—81no—
248C4×C61—21no—
249C4×C61—21no—
250C4×C61—21no—
251C4×C61—21no—
252C4×C61—42no—
253C4×C61—81no—
254C4×C61—81no—
255C4×C61—161no—
256Dic61—42no—
257Dic61—42no—
258Dic61—81no—
259#3186—611no—
260#2364—611no—
261#1964D6111yescharacteristic, complemented
262#1519—611no—
263C2×#327—611no—
264#1294—611no—
265#1282—611no—
266C2×C61—21no—
267C2×C61—21no—
268C2×C61—21no—
269C2×C61—21no—
270C2×C61—21no—
271C2×C61—21no—
272C2×C61—161no—
273C2×C61#187911yescharacteristic
274C2×C61#190611yescharacteristic
275C2×C61#191311yescharacteristic
276D61—82no—
277C2×#121—611no—
278C2×#121C2×D6111yescharacteristic
279C2×C4×D4—1221no—
280#480—612no—
281#480—1221no—
282#466—1222no—
283#447—612no—
284#447—1221no—
285C2×#99—21no—
286C2×#99—21no—
287C2×C22⋊C8—611no—
288C2×C22⋊C8—611no—
289#388—1221no—
290#387—1221no—
291#386—1221no—
292#386—1221no—
293#380C2×D6111yescharacteristic
294C4×C22⋊C4—1221no—
295C4×C22⋊C4C2×D6111yescharacteristic
296C2×#95—611no—
297#327—1222no—
298#327—1221no—
299#327—1221no—
300C61#927711yescharacteristic, complemented, Sylow
301C22×D4—21no—
302C22×D4—611no—
303C22×D4—1221no—
304C22×D4C4×D6111yescharacteristic, complemented
305C23×C4—1221no—
306C23×C4—1221no—
307C23×C4C22×D6111yescharacteristic
308C2×D8—1222no—
309C22×C8—1221no—
310C22×C8—1221no—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#121—612no—
316#121—612no—
317#121—1221no—
318#121—1221no—
319C4×D4—2442no—
320C4×D4—2442no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—611no—
323C2×C4⋊C4—1221no—
324C2×C4⋊C4C4×D6111yescharacteristic, complemented
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—1221no—
328C2×C22⋊C4—1221no—
329C2×C22⋊C4—1221no—
330C2×C22⋊C4—1221no—
331C2×C22⋊C4C22⋊D6111yescharacteristic
332C2×C22⋊C4C22⋊D6111yescharacteristic
333C2×C42—21no—
334C2×C42—1221no—
335#107—1222no—
336#102—1222no—
337#102—1222no—
338#99—42no—
339#99—42no—
340C22⋊C8—612no—
341C22⋊C8—1221no—
342C22⋊C8—1221no—
343C22⋊C8—1221no—
344#95—21no—
345#95—21no—
346#95—611no—
347#95—611no—
348#95—1221no—
349#95—1221no—
350#95—1221no—
351C24—21no—
352C24—1221no—
353C24C2×C22⋊D6111yescharacteristic
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—81no—
363C2×D4—612no—
364C2×D4—1222no—
365C2×D4—1222no—
366C2×D4—1221no—
367C2×D4—4881no—
368C2×D4—2441no—
369C2×D4—2441no—
370C2×D4—2441no—
371C2×D4—2441no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—41no—
376C22×C4—81no—
377C22×C4—1221no—
378C22×C4—1221no—
379C22×C4—1221no—
380C22×C4—4881no—
381C22×C4—4881no—
382C22×C4—2442no—
383C22×C4—2442no—
384C22×C4—2442no—
385C22×C4—2441no—
386C22×C4—2441no—
387C22×C4C2×C4×D6111yescharacteristic
388C22×C4#1175822211yescharacteristic
389C22×C4D4×D6111yescharacteristic
390C22×C4D4×D6111yescharacteristic
391C22×C4D4×D6111yescharacteristic
392C22×C4#1175822411yescharacteristic
393D8—4882no—
394C2×C8—1222no—
395C2×C8—4881no—
396C2×C8—4881no—
397C2×C8—2441no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—81no—
401C4⋊C4—612no—
402C4⋊C4—1221no—
403C4⋊C4—2442no—
404C22⋊C4—21no—
405C22⋊C4—21no—
406C22⋊C4—21no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—1222no—
412C22⋊C4—1222no—
413C22⋊C4—4881no—
414C22⋊C4—2442no—
415C22⋊C4—2442no—
416C22⋊C4#1175819912yescomplemented
417C42—81no—
418C42—2442no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—81no—
425C23—81no—
426C23—1222no—
427C23—2441no—
428C23—2441no—
429C23—2441no—
430C23—2441no—
431C23—2441no—
432C23—2441no—
433C23C4×C22⋊D6111yescharacteristic
434C23#1451974511yescharacteristic
435C23#1451974811yescharacteristic
436C23C2×#1175819911yescharacteristic
437C23#1451979711yescharacteristic
438C23#1451980211yescharacteristic
439C23#1451980311yescharacteristic
440D4—42no—
441D4—81no—
442D4—81no—
443D4—81no—
444D4—81no—
445D4—81no—
446D4—4881no—
447D4—2442no—
448D4—2442no—
449D4—2442no—
450D4—2442no—
451D4—2442no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—81no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4—1222no—
471C2×C4—1222no—
472C2×C4—4884no—
473C2×C4—4882no—
474C2×C4—4882no—
475C2×C4—2441no—
476C2×C4—2441no—
477C2×C4—2441no—
478C2×C4—2441no—
479C2×C4—2441no—
480C2×C4—2441no—
481C2×C4—2441no—
482C2×C4C22⋊C4×D6111yescharacteristic
483C2×C4#1451973711yescharacteristic
484C2×C4#1451975011yescharacteristic
485C2×C4#1451975911yescharacteristic
486C8—4881no—
487C8—2442no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—161no—
502C22—161no—
503C22—4881no—
504C22—4881no—
505C22—4881no—
506C22—4881no—
507C22—2442no—
508C22—2442no—
509C22—2442no—
510C22#1683963811yescharacteristic
511C22C4×#1175819911yescharacteristic
512C22#1683987211yescharacteristic
513C22#1683989511yescharacteristic
514C22#1683990511yescharacteristic
515C22#1683995411yescharacteristic
516C22#1683997411yescharacteristic
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—42no—
522C4—81no—
523C4—81no—
524C4—161no—
525C4—4881no—
526C4—2442no—
527C4—2442no—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—21no—
533C2—21no—
534C2—161no—
535C2—4882no—
536C2#2144617011yescharacteristic
537C2#2144631711yescharacteristic
538C2#2144635811yescharacteristic
subgroupG/H
centerC22#16839638
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1964C2
socleC22×C61#386
prime radical#21456567C2
cosocleC23×C4×C61C23
hypercenter#1964D61
hypocenterC61#9277
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #21448869C2semidirect
3. #21444386C2semidirect
4. C2×#16839496C2semidirect
5. #21443697C2semidirect
6. #21443667C2semidirect
7. C61×#1964C2semidirect
10. #16840075C4semidirect
13. #16839896C4semidirect
57. C22⋊#92418C2×C4semidirect
64. C22×D4×C61C2×C4semidirect
71. C2×C4⋊C4×C61C2×C4semidirect
133. C22⋊C4×C61D8semidirect
261. #1964D61semidirect
300. C61#9277semidirect
304. C22×D4C4×D61semidirect
324. C2×C4⋊C4C4×D61semidirect
416. C22⋊C4#11758199semidirect

Maximal subgroups

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

subgroupindex
#214565672
#214488692
#214443862
C2×#168394962
#214436972
#214436672
C61×#19642
#927761