Finite Group Databasebeta

← #29665475

Subgroups — #29665475

Order 15616.

662 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455628C211yesmaximal, characteristic, complemented
2#21455268C211yesmaximal, characteristic
3#21454927C211yesmaximal, characteristic, complemented
4#21445232C212yesmaximal, complemented
5#21445225C212yesmaximal, complemented
6#21445198C212yesmaximal, complemented
7#21445191C212yesmaximal, complemented
8#21444590C211yesmaximal, characteristic, complemented
9#21444496C211yesmaximal, characteristic, complemented
10C2×#16839511C211yesmaximal, characteristic, complemented
11C61×#3227C211yesmaximal, characteristic, complemented
12C2×#14519797—21no—
13C4×#11758222C2211yescharacteristic
14#16840054C2212yes—
15#16840049C2212yes—
16#16840044—21no—
17#16840039—21no—
18#16839981—21no—
19#16839974—21no—
20#16839969C2211yescharacteristic
21#16839964C2211yescharacteristic
22#16839959C2211yescharacteristic
23#16839954C2211yescharacteristic
24C8×Dic122C2212yes—
25C8×D244C2212yes—
26#16839825—22no—
27#16839814—21no—
28#16839802—21no—
29#16839786C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C4⋊C8×D61—21no—
33#16839761—21no—
34#16839758—21no—
35#16839513C2212yes—
36#16839513C2212yes—
37#16839511C2212yes—
38#16839511C2212yes—
39#16839508C2212yes—
40#16839506C2212yes—
41C61×#532C2211yescharacteristic
42C2×C4⋊Q8×C61C2211yescharacteristic
43C61×#498C2212yes—
44C61×#486C2212yes—
45C61×#481—22no—
46C61×#476—21no—
47C61×#476—21no—
48C61×#431C2211yescharacteristic
49C2×#11758222D411yescharacteristic
50#14519797—44no—
51C2×#11758202—21no—
52C2×#11758200—21no—
53C2×#11758201—21no—
54C2×#11758199—21no—
55C2×#11758194—21no—
56C22×#92418—21no—
57C22×#92418—21no—
58C2×C8×D61—22no—
59C4×Dic122D411yescharacteristic
60C4×Dic122C2311yescharacteristic
61C4×D244D411yescharacteristic
62C4×D244C2311yescharacteristic
63C4×C22⋊D61—21no—
64C4×C22⋊D61—21no—
65#14519736D411yescharacteristic
66#14519734—21no—
67C42×D61—21no—
68#14519710—22no—
69#14519708—22no—
70C4⋊#92418—21no—
71C4⋊#92418—21no—
72C4⋊#92418—21no—
73C4⋊#92418C2311yescharacteristic
74C4⋊#92418C2311yescharacteristic
75C4⋊#92418C2312yes—
76C4⋊#92418C2312yes—
77#14519706—22no—
78#14519701—21no—
79#14519701—21no—
80#14519700—22no—
81#14519698—21no—
82#14519698—21no—
83#14519697—22no—
84#14519689—22no—
85C8×Dic61—22no—
86C2×#41×C61—21no—
87C22×Q8×C61—21no—
88C4⋊Q8×C61—21no—
89C4⋊Q8×C61—21no—
90C4⋊Q8×C61—21no—
91C4⋊Q8×C61C2312yes—
92C4⋊Q8×C61C2311yescharacteristic
93#127×C61C2311yescharacteristic
94#124×C61—21no—
95#121×C61—21no—
96#121×C61—21no—
97C4×D4×C61—21no—
98C4×D4×C61—21no—
99C2×C4⋊C4×C61—21no—
100C2×C4⋊C4×C61—21no—
101C2×C42×C61C2311yescharacteristic
102#106×C61—22no—
103#106×C61—22no—
104C4⋊C8×C61D411yescharacteristic
105C4⋊C8×C61D411yescharacteristic
106#102×C61—22no—
107#102×C61—22no—
108C22⋊C8×C61D412yes—
109C4×C8×C61C2312yes—
110#41×C61—42no—
111#41×C61—42no—
112C2×Q8×C61—21no—
113C2×Q8×C61—22no—
114C2×Q8×C61—41no—
115C2×Q8×C61—82no—
116C2×D4×C61—21no—
117C2×D4×C61—21no—
118C2×D4×C61—21no—
119C2×D4×C61—41no—
120C22×C4×C61—41no—
121C22×C4×C61—41no—
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61#4111yescharacteristic
125C2×C22⋊D61—21no—
126#11758222—22no—
127#11758222SD1614yes—
128C2×D244C2×D411yescharacteristic
129C2×C4×D61—21no—
130C2×C4×D61—21no—
131C2×C4×D61—21no—
132C2×Dic122C2×D411yescharacteristic
133C2×C8×C61C2×D412yes—
134C2×C8×C61C2×D412yes—
135C4⋊C4×C61—22no—
136C4⋊C4×C61—21no—
137C4⋊C4×C61—22no—
138C4⋊C4×C61—21no—
139C4⋊C4×C61—41no—
140C4⋊C4×C61—41no—
141C22⋊C4×C61—41no—
142C22⋊C4×C61—41no—
143C42×C61C2×D411yescharacteristic
144C42×C61C2×D411yescharacteristic
145C42×C61#4111yescharacteristic
146C42×C61C2411yescharacteristic
147C22⋊Dic61—21no—
148#11758202—42no—
149#11758201—42no—
150#11758200—42no—
151#11758199—42no—
152#11758198—21no—
153#11758198—21no—
154C4⋊Dic61C2×D411yescharacteristic
155C4⋊Dic61C2×D411yescharacteristic
156#11758196—21no—
157#11758196—21no—
158C4×Dic61—21no—
159C4×Dic61—21no—
160C4×Dic61—21no—
161#11758194—42no—
162C2×#92418—22no—
163C2×#92418—22no—
164C2×#92418—21no—
165C2×#92418—21no—
166C2×#92418—42no—
167C2×#92418—81no—
168C8×D61—82no—
169C23×C61—41no—
170C23×C61#12111yescharacteristic
171C22×D61—21no—
172Q8×C61—41no—
173Q8×C61—41no—
174Q8×C61—82no—
175Q8×C61—82no—
176D4×C61—41no—
177D4×C61—41no—
178D4×C61—41no—
179D4×C61—41no—
180D4×C61—81no—
181D4×C61—82no—
182C2×C4×C61—21no—
183C2×C4×C61—21no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—42no—
187C2×C4×C61—82no—
188C2×C4×C61—82no—
189C2×C4×C61#12111yescharacteristic
190C2×C4×C61#12111yescharacteristic
191C2×C4×C61#12111yescharacteristic
192C2×C4×C61C2×SD1612yes—
193C2×C4×C61#13512yes—
194C2×C4×C61C22×D411yescharacteristic
195C2×C4×C61C22×D411yescharacteristic
196C2×C4×C61C2×#4111yescharacteristic
197C22⋊D61—24no—
198C2×Dic61—21no—
199C2×Dic61—21no—
200C2×Dic61—21no—
201D244—21no—
202D244C2×SD1612yes—
203C4×D61—24no—
204C4×D61—41no—
205C4×D61—41no—
206C4×D61—81no—
207Dic122—21no—
208Dic122C2×SD1612yes—
209C8×C61—22no—
210C8×C61—22no—
211#92418—41no—
212#92418—41no—
213#92418—42no—
214#92418—42no—
215#19414—611nomaximal, Sylow
216C22×C61—21no—
217C22×C61—21no—
218C22×C61—81no—
219C22×C61—81no—
220C22×C61—81no—
221C22×C61#46512yes—
222C22×C61C2×#12111yescharacteristic
223C2×D61—22no—
224C2×D61—41no—
225C2×D61—41no—
226C4×C61—21no—
227C4×C61—21no—
228C4×C61—21no—
229C4×C61—81no—
230C4×C61—82no—
231C4×C61#46512yes—
232C4×C61C22×SD1611yescharacteristic
233C4×C61C2×#13511yescharacteristic
234C4×C61#57711yescharacteristic
235C4×C61#57811yescharacteristic
236Dic61—22no—
237Dic61—41no—
238Dic61—41no—
239#3227D6111yescharacteristic, complemented
240#3079—611no—
241#3035—611no—
242#2988—611no—
243#1678—612no—
244#1677—612no—
245#1672—612no—
246#1671—612no—
247#1570—611no—
248#1547—611no—
249C2×#333—611no—
250C2×C61—22no—
251C2×C61—161no—
252C2×C61#304611yescharacteristic
253C2×C61C2×#46511yescharacteristic
254C2×C61#306811yescharacteristic
255D61—42no—
256C2×#135—1221no—
257#532C2×D6111yescharacteristic
258C2×C4⋊Q8C2×D6111yescharacteristic
259C4×#41—611no—
260#498C2×D6112yes—
261#486C2×D6112yes—
262#481—22no—
263#477—612no—
264#476—21no—
265#476—21no—
266#476—612no—
267#475—1221no—
268#474—1221no—
269#464—1221no—
270#463—1221no—
271#462—611no—
272#461—611no—
273#460—611no—
274#459—611no—
275C8×Q8—612no—
276C8×D4—612no—
277C8×D4—1222no—
278#431—1221no—
279#431C2×D6111yescharacteristic
280#428—1221no—
281#423—611no—
282C2×C4⋊C8—611no—
283C2×C4⋊C8—611no—
284C2×C4⋊C8—1221no—
285#417—1221no—
286#416—1221no—
287#334—612no—
288#334—612no—
289#333—612no—
290#333—612no—
291#332—612no—
292#331—612no—
293C61#1941411yescharacteristic, complemented, Sylow
294C2×#41—21no—
295C2×#41—611no—
296C22×Q8—21no—
297#135—2444no—
298C2×Q16—1221no—
299C2×SD16—1221no—
300C2×SD16—1221no—
301C2×D8—1221no—
302C2×M16—1221no—
303C22×C8—1221no—
304C22×C8—1221no—
305C22×C8—1222no—
306C4⋊Q8—21no—
307C4⋊Q8—21no—
308C4⋊Q8—21no—
309C4⋊Q8C22×D6112yes—
310C4⋊Q8C22×D6111yescharacteristic
311#127C22×D6111yescharacteristic
312#124—21no—
313#121—21no—
314#121—21no—
315C4×Q8—611no—
316C4×Q8—611no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4—611no—
320C4×D4—611no—
321C4×D4—1221no—
322C4×D4—1221no—
323#117—611no—
324#117—1221no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—21no—
327C2×C42—1221no—
328C2×C42C22×D6111yescharacteristic
329#107—1222no—
330#106—22no—
331#106—22no—
332#106—1222no—
333C4⋊C8—612no—
334C4⋊C8—612no—
335C4⋊C8—611no—
336C4⋊C8—611no—
337C4⋊C8—1222no—
338C4⋊C8—1221no—
339C4⋊C8—1221no—
340C4⋊C8—1221no—
341C4⋊C8C22⋊D6111yescharacteristic
342C4⋊C8C22⋊D6111yescharacteristic
343#103—1222no—
344#103—1221no—
345#103—1221no—
346#102—22no—
347#102—22no—
348#102—1222no—
349#102—1221no—
350#102—1221no—
351C22⋊C8—1222no—
352C22⋊C8C22⋊D6112yes—
353C4×C8—1222no—
354C4×C8C22×D6112yes—
355#41—42no—
356#41—42no—
357#41—614no—
358#41—1222no—
359C2×Q8—21no—
360C2×Q8—22no—
361C2×Q8—41no—
362C2×Q8—82no—
363C2×Q8—611no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4—611no—
369C2×D4—1221no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—1221no—
373C22×C4—1221no—
374C22×C4—1221no—
375C22×C4D4×D6111yescharacteristic
376C22×C4#1175822411yescharacteristic
377C22×C4C2×C22⋊D6111yescharacteristic
378Q16—2442no—
379SD16—2442no—
380SD16—2442no—
381D8—2442no—
382M16—2442no—
383C2×C8—1222no—
384C2×C8—1221no—
385C2×C8—1221no—
386C2×C8—1222no—
387C2×C8—4882no—
388C2×C8—4881no—
389C2×C8—2442no—
390C2×C8C2×C22⋊D6112yes—
391C2×C8C2×C22⋊D6112yes—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4—611no—
399C4⋊C4—611no—
400C4⋊C4—1221no—
401C4⋊C4—1221no—
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—1221no—
405C22⋊C4—1221no—
406C22⋊C4—1221no—
407C42—1221no—
408C42—1221no—
409C42—1221no—
410C42D4×D6111yescharacteristic
411C42#1175822411yescharacteristic
412C42C2×C22⋊D6111yescharacteristic
413C42C23×D6111yescharacteristic
414C23—41no—
415C23—1221no—
416C23#1451974811yescharacteristic
417Q8—41no—
418Q8—41no—
419Q8—82no—
420Q8—82no—
421Q8—612no—
422Q8—1221no—
423D4—41no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—81no—
428D4—82no—
429D4—612no—
430D4—1224no—
431D4—1221no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—82no—
438C2×C4—82no—
439C2×C4—1221no—
440C2×C4—1224no—
441C2×C4—1221no—
442C2×C4—1221no—
443C2×C4—4881no—
444C2×C4—2441no—
445C2×C4—2441no—
446C2×C4#1451974811yescharacteristic
447C2×C4#1451974811yescharacteristic
448C2×C4#1451974811yescharacteristic
449C2×C4SD16×D6112yes—
450C2×C4#1451979812yes—
451C2×C4C2×D4×D6111yescharacteristic
452C2×C4C22×C22⋊D6111yescharacteristic
453C2×C4C2×#1175822411yescharacteristic
454C8—22no—
455C8—22no—
456C8—2441no—
457C8—2441no—
458C8—2442no—
459C8—2442no—
460C22—21no—
461C22—21no—
462C22—81no—
463C22—81no—
464C22—81no—
465C22—1222no—
466C22—2441no—
467C22—2441no—
468C22#1683998812yes—
469C22C2×#1451974811yescharacteristic
470C4—21no—
471C4—21no—
472C4—21no—
473C4—81no—
474C4—82no—
475C4—1222no—
476C4—2441no—
477C4—2441no—
478C4#1683998812yes—
479C4C2×SD16×D6111yescharacteristic
480C4C2×#1451979811yescharacteristic
481C4#1684057011yescharacteristic
482C4#1684057711yescharacteristic
483C2—22no—
484C2—161no—
485C2—2442no—
486C2#2145536511yescharacteristic
487C2C2×#1683998811yescharacteristic
488C2#2145554311yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3227C2
socleC22×C61C2×#121
prime radical#21455268C2
hypercenter#3227D61
hypocenterC61#19414
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3227

Complements

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

NH ≅ G/Ntype
1. #21455628C2semidirect
3. #21454927C2semidirect
4. #21445232C2semidirect
5. #21445225C2semidirect
6. #21445198C2semidirect
7. #21445191C2semidirect
8. #21444590C2semidirect
9. #21444496C2semidirect
10. C2×#16839511C2semidirect
11. C61×#3227C2semidirect
239. #3227D61semidirect
293. C61#19414semidirect

Maximal subgroups

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

subgroupindex
#214556282
#214552682
#214549272
#214452322
#214452252
#214451982
#214451912
#214445902
#214444962
C2×#168395112
C61×#32272
#1941461