Finite Group Databasebeta

← #29662623

Subgroups — #29662623

Order 15616.

694 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456245C211yesmaximal, characteristic
2#21455850C211yesmaximal, characteristic, complemented
3C2×#16839893C211yesmaximal, characteristic, complemented
4#21445311C212yesmaximal, complemented
5#21445301C212yesmaximal, complemented
6#21445293C212yesmaximal, complemented
7#21445289C212yesmaximal, complemented
8#21444565C211yesmaximal, characteristic, complemented
9#21444468C211yesmaximal, characteristic, complemented
10#21444466C211yesmaximal, characteristic, complemented
11C61×#3103C211yesmaximal, characteristic, complemented
12C2×#14519797—21no—
13C2×#14519797—21no—
14#16840312C2211yescharacteristic
15#16840144—21no—
16#16840144—21no—
17#16840141C2211yescharacteristic
18#16840138C2211yescharacteristic
19#16840136C2211yescharacteristic
20#16840134C2211yescharacteristic
21#16840080—21no—
22#16840047C2212yes—
23#16839962C2212yes—
24#16839901—21no—
25#16839893—21no—
26#16839893—21no—
27#16839893C2212yes—
28#16839893C2212yes—
29C4×#11758201—22no—
30#16839815C2211yescharacteristic
31C2×C4⋊#92418—21no—
32C2×C4⋊#92418C2211yescharacteristic
33C2×#14519688—21no—
34C2×C4×#92418C2211yescharacteristic
35#16839514C2212yes—
36#16839512C2212yes—
37#16839508C2212yes—
38#16839507C2212yes—
39#16839506C2212yes—
40#16839505C2212yes—
41C61×#532C2211yescharacteristic
42C2×C4×Q8×C61C2211yescharacteristic
43C61×#481—21no—
44C61×#475C2212yes—
45C61×#460C2212yes—
46C61×#448—21no—
47C4×SD16×C61—22no—
48C61×#431C2211yescharacteristic
49C2×#11758222—21no—
50#14519797—44no—
51#14519797—44no—
52C2×#11758202—21no—
53C2×#11758202—21no—
54C2×#11758200—21no—
55C2×#11758200—21no—
56C2×#11758201—22no—
57C2×#11758201—21no—
58C2×#11758201—21no—
59C2×#11758199—21no—
60C2×#11758199—21no—
61C22×#92418—21no—
62C22×#92418D411yescharacteristic
63C22×#92418D411yescharacteristic
64#14519777C2311yescharacteristic
65#14519774C2311yescharacteristic
66#14519765—21no—
67#14519751—21no—
68#14519751—21no—
69C4×D244—21no—
70C4×D244—21no—
71#14519708—22no—
72C4⋊#92418—21no—
73C4⋊#92418—22no—
74C4⋊#92418—22no—
75C4⋊#92418C2312yes—
76C4⋊#92418C2312yes—
77#14519701—22no—
78#14519697—22no—
79C22⋊#92418—21no—
80#14519688—22no—
81#14519688—22no—
82C4×#92418—21no—
83C4×#92418D411yescharacteristic
84C4×#92418D411yescharacteristic
85C4×#92418C2311yescharacteristic
86C4×#92418C2311yescharacteristic
87C2×#41×C61—21no—
88C22×Q8×C61D411yescharacteristic
89C2×SD16×C61—22no—
90C4⋊Q8×C61C2311yescharacteristic
91#127×C61C2311yescharacteristic
92#124×C61—21no—
93#121×C61—21no—
94#121×C61—21no—
95C4×Q8×C61—21no—
96C4×Q8×C61—21no—
97C4×Q8×C61D412yes—
98C4×Q8×C61C2312yes—
99C4×D4×C61—21no—
100C4×D4×C61—21no—
101C2×C4⋊C4×C61—21no—
102C2×C4⋊C4×C61D411yescharacteristic
103C2×C42×C61—21no—
104C2×C42×C61C2311yescharacteristic
105#106×C61—22no—
106C4⋊C8×C61C2312yes—
107#103×C61—22no—
108#102×C61—22no—
109C22⋊C8×C61—21no—
110C4×C8×C61—21no—
111#41×C61—42no—
112#41×C61—42no—
113C2×Q8×C61—21no—
114C2×Q8×C61—21no—
115C2×Q8×C61—42no—
116C2×Q8×C61C2×D412yes—
117C2×D4×C61—21no—
118C2×D4×C61—21no—
119C2×D4×C61—21no—
120C2×D4×C61—41no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—41no—
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61#4111yescharacteristic
127C2×C22⋊D61—41no—
128#11758222—42no—
129#11758222—42no—
130C2×D244—21no—
131C2×D244—21no—
132C2×D244—21no—
133C2×C4×D61—41no—
134C2×Dic122—21no—
135SD16×C61—44no—
136C2×C8×C61—22no—
137C4⋊C4×C61—22no—
138C4⋊C4×C61—21no—
139C4⋊C4×C61—22no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61—21no—
142C4⋊C4×C61C2×D412yes—
143C22⋊C4×C61—41no—
144C22⋊C4×C61—41no—
145C42×C61—22no—
146C42×C61—22no—
147C42×C61C2×D411yescharacteristic
148C42×C61C2×D411yescharacteristic
149C42×C61#4111yescharacteristic
150C42×C61C2411yescharacteristic
151#11758202—42no—
152#11758202—42no—
153#11758201—42no—
154#11758201—44no—
155#11758201—42no—
156#11758200—42no—
157#11758200—42no—
158#11758199—42no—
159#11758199—42no—
160#11758198—41no—
161#11758198—41no—
162C4⋊Dic61—21no—
163C4⋊Dic61—21no—
164C2×#92418—22no—
165C2×#92418—22no—
166C2×#92418—22no—
167C2×#92418—42no—
168C2×#92418SD1614yescomplemented
169C2×#92418C2×D411yescharacteristic
170C2×#92418C2×D411yescharacteristic
171C2×#92418C2×D411yescharacteristic
172C2×#92418C2×D411yescharacteristic
173C23×C61—41no—
174C23×C61#12111yescharacteristic
175C22×D61—41no—
176Q8×C61—22no—
177Q8×C61—22no—
178Q8×C61—42no—
179Q8×C61—41no—
180Q8×C61—41no—
181D4×C61—41no—
182D4×C61—41no—
183D4×C61—42no—
184D4×C61—81no—
185D4×C61—82no—
186C2×C4×C61—22no—
187C2×C4×C61—22no—
188C2×C4×C61—22no—
189C2×C4×C61—41no—
190C2×C4×C61—42no—
191C2×C4×C61—42no—
192C2×C4×C61—41no—
193C2×C4×C61—82no—
194C2×C4×C61#12111yescharacteristic
195C2×C4×C61#12111yescharacteristic
196C2×C4×C61#12111yescharacteristic
197C2×C4×C61C2×SD1612yes—
198C2×C4×C61AGL(1,ℤ/8)12yes—
199C2×C4×C61C22×D411yescharacteristic
200C2×C4×C61C22×D411yescharacteristic
201C2×C4×C61C2×#4111yescharacteristic
202C22⋊D61—82no—
203C2×Dic61—41no—
204D244—41no—
205D244—41no—
206D244—42no—
207D244—81no—
208C4×D61—82no—
209Dic122—41no—
210Dic122—41no—
211C8×C61—42no—
212#92418—21no—
213#92418—21no—
214#92418—42no—
215#92418—42no—
216#92418C2×SD1612yes—
217#92418C2×SD1612yes—
218#19146—611nomaximal, Sylow
219C22×C61—21no—
220C22×C61—21no—
221C22×C61—81no—
222C22×C61—81no—
223C22×C61—81no—
224C22×C61#46012yes—
225C22×C61C2×#12111yescharacteristic
226C2×D61—81no—
227C2×D61—81no—
228C2×D61—81no—
229C4×C61—21no—
230C4×C61—21no—
231C4×C61—21no—
232C4×C61—42no—
233C4×C61—42no—
234C4×C61—81no—
235C4×C61#46012yes—
236C4×C61C22×SD1611yescharacteristic
237C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
238C4×C61#57512yes—
239Dic61—81no—
240#3147—611no—
241#3103—611no—
242#3103D6111yescharacteristic, complemented
243C2×#446—611no—
244#1690—612no—
245#1688—612no—
246#1686—612no—
247#1686—612no—
248#1564—611no—
249#1540—611no—
250#1540—611no—
251C2×C61—22no—
252C2×C61—161no—
253C2×C61C2×#46011yescharacteristic
254C2×C61#305411yescharacteristic
255C2×C61#306711yescharacteristic
256D61—161no—
257C2×#135—1221no—
258C2×#135—1221no—
259#532—611no—
260#532C2×D6111yescharacteristic
261C2×C4×Q8C2×D6111yescharacteristic
262#495—1221no—
263#495—1221no—
264#494—611no—
265#493—611no—
266#492—611no—
267#492—611no—
268#481—21no—
269#481—1221no—
270#475—612no—
271#475C2×D6112yes—
272#460—612no—
273#460C2×D6112yes—
274#448—21no—
275#448—1221no—
276#446—612no—
277#446—612no—
278#446—1221no—
279#446—1221no—
280C4×SD16—22no—
281C4×SD16—1222no—
282#431—611no—
283#431C2×D6111yescharacteristic
284C2×C4⋊C8—611no—
285C2×C4⋊C8—1221no—
286C2×#97—1221no—
287C2×C4×C8—611no—
288#335—612no—
289#334—612no—
290#332—612no—
291#332—612no—
292#331—612no—
293#331—612no—
294C61#1914611yescharacteristic, complemented, Sylow
295C2×#41—21no—
296C2×#41—1221no—
297C22×Q8C22⋊D6111yescharacteristic
298#135—2444no—
299#135—2444no—
300C2×Q16—1221no—
301C2×Q16—1221no—
302C2×SD16—22no—
303C2×SD16—1221no—
304C2×SD16—1221no—
305C2×SD16—1221no—
306C2×SD16—1221no—
307C2×SD16—1222no—
308C2×D8—1221no—
309C2×D8—1221no—
310C22×C8—611no—
311C22×C8—611no—
312C22×C8—1221no—
313C4⋊Q8—611no—
314C4⋊Q8C22×D6111yescharacteristic
315#127—611no—
316#127C22×D6111yescharacteristic
317#124—21no—
318#124—1221no—
319#121—21no—
320#121—21no—
321#121—1221no—
322#121—1221no—
323C4×Q8—21no—
324C4×Q8—21no—
325C4×Q8C22⋊D6112yes—
326C4×Q8C22×D6112yes—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—1221no—
330C4×D4—1221no—
331C2×C4⋊C4—21no—
332C2×C4⋊C4C22⋊D6111yescharacteristic
333C2×C42—21no—
334C2×C42C22×D6111yescharacteristic
335#106—22no—
336#106—1222no—
337C4⋊C8—612no—
338C4⋊C8—612no—
339C4⋊C8—1222no—
340C4⋊C8—1222no—
341C4⋊C8—1221no—
342C4⋊C8C22×D6112yes—
343#103—22no—
344#103—1222no—
345#102—22no—
346#102—1222no—
347C22⋊C8—21no—
348C22⋊C8—1221no—
349#97—1222no—
350#97—1222no—
351C4×C8—21no—
352C4×C8—611no—
353C4×C8—611no—
354C4×C8—611no—
355C4×C8—611no—
356C4×C8—1221no—
357#41—42no—
358#41—42no—
359#41—2442no—
360#41—2442no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—42no—
364C2×Q8—1221no—
365C2×Q8C2×C22⋊D6112yes—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—41no—
370C2×D4—1221no—
371C2×D4—1221no—
372C2×D4—1221no—
373C2×D4—2441no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—41no—
377C22×C4—2441no—
378C22×C4D4×D6111yescharacteristic
379C22×C4#1175822411yescharacteristic
380C22×C4C2×C22⋊D6111yescharacteristic
381Q16—2442no—
382Q16—2442no—
383SD16—44no—
384SD16—2442no—
385SD16—2442no—
386SD16—2442no—
387SD16—2442no—
388SD16—2444no—
389D8—2442no—
390D8—2442no—
391C2×C8—22no—
392C2×C8—611no—
393C2×C8—611no—
394C2×C8—614no—
395C2×C8—611no—
396C2×C8—611no—
397C2×C8—1222no—
398C2×C8—1222no—
399C2×C8—1222no—
400C2×C8—2442no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—21no—
404C4⋊C4—21no—
405C4⋊C4—21no—
406C4⋊C4—1221no—
407C4⋊C4—1221no—
408C4⋊C4C2×C22⋊D6112yes—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—2441no—
412C22⋊C4—2441no—
413C42—22no—
414C42—22no—
415C42D4×D6111yescharacteristic
416C42#1175822411yescharacteristic
417C42C2×C22⋊D6111yescharacteristic
418C42C23×D6111yescharacteristic
419C23—41no—
420C23—2441no—
421C23#1451974911yescharacteristic
422Q8—22no—
423Q8—22no—
424Q8—42no—
425Q8—41no—
426Q8—41no—
427Q8—2441no—
428Q8—2441no—
429D4—41no—
430D4—41no—
431D4—42no—
432D4—81no—
433D4—82no—
434D4—4881no—
435D4—4882no—
436D4—2441no—
437D4—2441no—
438D4—2442no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—41no—
446C2×C4—82no—
447C2×C4—4882no—
448C2×C4—2441no—
449C2×C4#1451974911yescharacteristic
450C2×C4#1451974911yescharacteristic
451C2×C4#1451974911yescharacteristic
452C2×C4SD16×D6112yes—
453C2×C4#1451980412yes—
454C2×C4C2×D4×D6111yescharacteristic
455C2×C4C22×C22⋊D6111yescharacteristic
456C2×C4C2×#1175822411yescharacteristic
457C8—42no—
458C8—612no—
459C8—612no—
460C8—1221no—
461C8—1221no—
462C8—2442no—
463C8—2442no—
464C22—21no—
465C22—21no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—4881no—
470C22—4881no—
471C22—4881no—
472C22#1683996012yes—
473C22C2×#1451974911yescharacteristic
474C4—21no—
475C4—21no—
476C4—21no—
477C4—42no—
478C4—42no—
479C4—81no—
480C4—4881no—
481C4#1683996012yes—
482C4C2×SD16×D6111yescharacteristic
483C4C2×#1451980411yescharacteristic
484C4#1684056012yes—
485C2—22no—
486C2—161no—
487C2—9761no—
488C2C2×#1683996011yescharacteristic
489C2#2145542511yescharacteristic
490C2#2145553611yescharacteristic
subgroupG/H
centerC2×C4#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3103C2
socleC22×C61C2×#121
prime radical#21456245C2
hypercenter#3103D61
hypocenterC61#19146
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3103

Complements

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

NH ≅ G/Ntype
2. #21455850C2semidirect
3. C2×#16839893C2semidirect
4. #21445311C2semidirect
5. #21445301C2semidirect
6. #21445293C2semidirect
7. #21445289C2semidirect
8. #21444565C2semidirect
9. #21444468C2semidirect
10. #21444466C2semidirect
11. C61×#3103C2semidirect
168. C2×#92418SD16semidirect
242. #3103D61semidirect
294. C61#19146semidirect

Maximal subgroups

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

subgroupindex
#214562452
#214558502
C2×#168398932
#214453112
#214453012
#214452932
#214452892
#214445652
#214444682
#214444662
C61×#31032
#1914661