Finite Group Databasebeta

← #29597161

Subgroups — #29597161

Order 15616.

522 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840197C211yesmaximal, characteristic
2C2×#16839572C211yesmaximal, characteristic, complemented
3#21447534C211yesmaximal, characteristic, complemented
4#21446695C211yesmaximal, characteristic, complemented
5#21443924C211yesmaximal, characteristic, complemented
6#21443903C211yesmaximal, characteristic, complemented
7C61×#2943C211yesmaximal, characteristic, complemented
8C22×D488C2211yescharacteristic
9#16840197—22no—
10#16840197C414yescomplemented
11C2×#14519720—21no—
12C2×#14519718—21no—
13C2×#14519717C2211yescharacteristic
14C2×#14519717C2211yescharacteristic
15C2×#14519709C2211yescharacteristic
16C2×#14519699—21no—
17#16839664—21no—
18#16839572—22no—
19#16839562—22no—
20C2×#135×C61C2211yescharacteristic
21C4×#41×C61—21no—
22C61×#442—21no—
23C61×#441—21no—
24C61×#440—22no—
25C61×#427C2211yescharacteristic
26C61×#416—21no—
27C2×#97×C61C2211yescharacteristic
28C22×D244—21no—
29C2×D488—21no—
30C2×D488—21no—
31C2×D488—21no—
32C2×D488—21no—
33C2×D488—21no—
34C2×D488C2×C412yescomplemented
35C2×C4⋊Dic61—21no—
36C2×#11758198—42no—
37#14519720—24no—
38#14519718—24no—
39#14519717—21no—
40#14519717—21no—
41#14519717—21no—
42#14519717C2×C412yescomplemented
43C2×#11758185—21no—
44C2×#11758185—21no—
45#14519709—21no—
46#14519709—21no—
47#14519699—42no—
48C2×#41×C61—21no—
49#135×C61—21no—
50#135×C61—21no—
51#135×C61C2×C412yes—
52#135×C61D412yes—
53C2×Q16×C61D411yescharacteristic
54C2×SD16×C61—21no—
55C2×D8×C61D411yescharacteristic
56C22×C8×C61D411yescharacteristic
57C22×C8×C61C2311yescharacteristic
58C4×Q8×C61—22no—
59C4×D4×C61—22no—
60C4×D4×C61—42no—
61#117×C61—21no—
62#117×C61—41no—
63C2×C42×C61—41no—
64C2×C42×C61D411yescharacteristic
65#107×C61D412yes—
66#106×C61—21no—
67#103×C61—22no—
68#102×C61—22no—
69#97×C61—21no—
70#97×C61—21no—
71C23×D61—41no—
72#41×C61—22no—
73#41×C61—22no—
74#41×C61—41no—
75#41×C61—41no—
76C2×Q8×C61—21no—
77C2×D4×C61—21no—
78C2×D4×C61—41no—
79C22×C4×C61—42no—
80C22×C4×C61—41no—
81C22×C4×C61D812yes—
82C22×C4×C61C2×D411yescharacteristic
83C22×Dic61—41no—
84C2×D244—22no—
85C2×D244—41no—
86C2×D244—41no—
87C2×D244—41no—
88C2×D244—41no—
89C2×D244—41no—
90Q16×C61—21no—
91Q16×C61C22⋊C412yescomplemented
92SD16×C61—22no—
93SD16×C61—22no—
94D8×C61—21no—
95D8×C61C22⋊C412yescomplemented
96C2×C8×C61—21no—
97C2×C8×C61—21no—
98C2×C8×C61—21no—
99C2×C8×C61C22×C411yescharacteristic
100C2×C8×C61C2×D411yescharacteristic
101C2×C8×C61C2×D411yescharacteristic
102C2×C8×C61C2×D411yescharacteristic
103C2×C8×C61#4111yescharacteristic
104C2×C8×C61#4111yescharacteristic
105C4⋊C4×C61—22no—
106C4⋊C4×C61—42no—
107C22⋊C4×C61—42no—
108C22⋊C4×C61—41no—
109C42×C61—21no—
110C42×C61—21no—
111C42×C61—42no—
112C42×C61—41no—
113#11758198—84no—
114C4⋊Dic61—41no—
115C4⋊Dic61—41no—
116D488—22no—
117D488—22no—
118D488—41no—
119D488—41no—
120#11758185—22no—
121#11758185—41no—
122C23×C61—41no—
123C23×C61C2×D811yescharacteristic
124C22×D61—42no—
125C22×D61—82no—
126C22×D61—82no—
127C22×D61—81no—
128C22×D61—81no—
129Q8×C61—22no—
130Q8×C61—41no—
131D4×C61—22no—
132D4×C61—42no—
133D4×C61—42no—
134D4×C61—41no—
135C2×C4×C61—22no—
136C2×C4×C61—41no—
137C2×C4×C61—42no—
138C2×C4×C61—42no—
139C2×C4×C61—42no—
140C2×C4×C61—42no—
141C2×C4×C61—84no—
142C2×C4×C61C4×D411yescharacteristic
143C2×C4×C61#12011yescharacteristic
144C2×C4×C61#12111yescharacteristic
145C2×C4×C61#13511yescharacteristic
146C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
148C2×Dic61—82no—
149C2×Dic61—81no—
150D244—42no—
151D244—42no—
152D244—81no—
153D244—81no—
154C8×C61—41no—
155C8×C61C2×C22⋊C411yescharacteristic
156C8×C61C4×D411yescharacteristic
157C8×C61#12111yescharacteristic
158C8×C61#12311yescharacteristic
159#13025—611nomaximal, Sylow
160C22×C61—22no—
161C22×C61—42no—
162C22×C61—82no—
163C22×C61C4×D811yescharacteristic
164C22×C61#44711yescharacteristic
165C22×C61#45911yescharacteristic
166C2×D61—84no—
167C2×D61—82no—
168C2×D61—161no—
169C2×D61—161no—
170C2×D61—162no—
171C4×C61—42no—
172C4×C61—42no—
173C4×C61—82no—
174C4×C61#38611yescharacteristic
175C4×C61#44211yescharacteristic
176C4×C61#44911yescharacteristic
177C4×C61#46311yescharacteristic
178Dic61—161no—
179C2×#509—611no—
180#2943D6111yescharacteristic, complemented
181C2×#360—611no—
182#2140—611no—
183#1972—611no—
184#1386—611no—
185#1377—611no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—82no—
189C2×C61#187911yescharacteristic
190C2×C61#219012yes—
191D61—162no—
192C2×#135C2×D6111yescharacteristic
193C22×D8—611no—
194C4×#41—21no—
195#509—614no—
196#509—1222no—
197C2×SD32—1221no—
198C2×D16—1221no—
199C2×M32—611no—
200C2×M32—611no—
201#442—21no—
202#441—21no—
203#440—22no—
204#427C2×D6111yescharacteristic
205C2×#106—611no—
206#416—21no—
207C2×#102—1221no—
208C2×#97C2×D6111yescharacteristic
209#390—1221no—
210#360—1222no—
211#357—1222no—
212C61#1302511yescharacteristic, complemented, Sylow
213C2×#41—21no—
214C22×D4—1221no—
215#135—21no—
216#135—21no—
217#135C4×D6112yes—
218#135D24412yes—
219C2×Q16C22⋊D6111yescharacteristic
220C2×SD16—21no—
221C2×D8—612no—
222C2×D8—1221no—
223C2×D8—1221no—
224C2×D8—1221no—
225C2×D8—1221no—
226C2×D8—1221no—
227C2×D8C22⋊D6111yescharacteristic
228C22×C8C22⋊D6111yescharacteristic
229C22×C8C22×D6111yescharacteristic
230C4×Q8—22no—
231C4×D4—22no—
232C4×D4—42no—
233#117—21no—
234#117—41no—
235C2×C4⋊C4—1221no—
236C2×C22⋊C4—2442no—
237C2×C42—41no—
238C2×C42C22⋊D6111yescharacteristic
239SD32—1224no—
240D16—1224no—
241M32—612no—
242M32—1221no—
243M32—1221no—
244M32—1221no—
245C2×C16—1221no—
246C2×C16—1221no—
247#107C22⋊D6112yes—
248#106—21no—
249#106—1221no—
250#106—1221no—
251#103—22no—
252#102—22no—
253#102—2442no—
254#97—21no—
255#97—21no—
256C24—2441no—
257#41—22no—
258#41—22no—
259#41—41no—
260#41—41no—
261C2×Q8—21no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—1222no—
265C2×D4—2441no—
266C2×D4—2441no—
267C2×D4—2441no—
268C2×D4—2441no—
269C2×D4—2441no—
270C22×C4—42no—
271C22×C4—41no—
272C22×C4—2441no—
273C22×C4#1175819912yes—
274C22×C4C2×C22⋊D6111yescharacteristic
275Q16—21no—
276Q16#1175819812yescomplemented
277SD16—22no—
278SD16—22no—
279D8—21no—
280D8—1222no—
281D8—1222no—
282D8—2441no—
283D8—2441no—
284D8#1175819812yescomplemented
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8C2×C4×D6111yescharacteristic
289C2×C8C2×D24411yescharacteristic
290C2×C8#1175822211yescharacteristic
291C2×C8#1175822211yescharacteristic
292C2×C8C2×C22⋊D6111yescharacteristic
293C2×C8C2×C22⋊D6111yescharacteristic
294C4⋊C4—22no—
295C4⋊C4—42no—
296C4⋊C4—2441no—
297C4⋊C4—2441no—
298C22⋊C4—42no—
299C22⋊C4—41no—
300C22⋊C4—4884no—
301C42—21no—
302C42—21no—
303C42—42no—
304C42—41no—
305C16—1222no—
306C16—2441no—
307C23—41no—
308C23—4882no—
309C23—4882no—
310C23—4881no—
311C23—4881no—
312C23—2442no—
313C23C2×#1175819911yescharacteristic
314Q8—22no—
315Q8—41no—
316D4—22no—
317D4—42no—
318D4—42no—
319D4—41no—
320D4—4881no—
321D4—4881no—
322D4—2442no—
323D4—2442no—
324C2×C4—22no—
325C2×C4—41no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—84no—
331C2×C4—4882no—
332C2×C4—4881no—
333C2×C4C4×C22⋊D6111yescharacteristic
334C2×C4#1451974611yescharacteristic
335C2×C4#1451975111yescharacteristic
336C2×C4#1451979711yescharacteristic
337C2×C4#1451980211yescharacteristic
338C2×C4#1451980311yescharacteristic
339C8—41no—
340C8C2×#1175819811yescharacteristic
341C8C4×C22⋊D6111yescharacteristic
342C8#1451975111yescharacteristic
343C8#1451976011yescharacteristic
344C22—22no—
345C22—42no—
346C22—82no—
347C22—9761no—
348C22—9761no—
349C22—9762no—
350C22—4884no—
351C22—4882no—
352C22C4×#1175819911yescharacteristic
353C22#1683989611yescharacteristic
354C22#1683995711yescharacteristic
355C4—42no—
356C4—42no—
357C4—82no—
358C4—9761no—
359C4#1683964111yescharacteristic
360C4#1683987211yescharacteristic
361C4#1683990711yescharacteristic
362C4#1683997711yescharacteristic
363C2—21no—
364C2—21no—
365C2—82no—
366C2—9762no—
367C2#2144616711yescharacteristic
368C2#2144776512yes—
subgroupG/H
centerC22#16839896
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
FittingC61×#2943C2
socleC22×C61#447
prime radicalC2×#16840197C2
cosocleC22×C8×C61C23
hypercenter#2943D61
hypocenterC61#13025
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#97 ◁ #2943

Complements

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

NH ≅ G/Ntype
2. C2×#16839572C2semidirect
3. #21447534C2semidirect
4. #21446695C2semidirect
5. #21443924C2semidirect
6. #21443903C2semidirect
7. C61×#2943C2semidirect
10. #16840197C4semidirect
34. C2×D488C2×C4semidirect
42. #14519717C2×C4semidirect
91. Q16×C61C22⋊C4semidirect
95. D8×C61C22⋊C4semidirect
180. #2943D61semidirect
212. C61#13025semidirect
276. Q16#11758198semidirect
284. D8#11758198semidirect

Maximal subgroups

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

subgroupindex
C2×#168401972
C2×#168395722
#214475342
#214466952
#214439242
#214439032
C61×#29432
#1302561