Finite Group Databasebeta

← #30601949

Subgroups — #30601949

Order 15616.

506 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461744C211yesmaximal, characteristic, complemented
2#21461329C212yesmaximal, complemented
3#21461327C212yesmaximal
4#21461033C211yesmaximal, characteristic, complemented
5#492×D61C211yesmaximal, characteristic
6#16840780C2212yes—
7#16840767C2212yes—
8#16840638—22no—
9#16840621—24no—
10#16840620—24no—
11#92420⋊C8—22no—
12C2×SD16×D61—22no—
13C4⋊Q8×D61C2211yescharacteristic
14#127×D61C2211yescharacteristic
15#16840136C411yescharacteristic
16#16840135C411yescharacteristic
17#16840134C411yescharacteristic
18#16840133—22no—
19C4×C8×D61C2211yescharacteristic
20C61×#492C411yescharacteristic
21C2×#11758213—22no—
22#14519844—22no—
23#14519844—22no—
24#14519844D414yes—
25#14519834—22no—
26C4×#92420—22no—
27C2×Q8×D61—21no—
28C2×D4×D61—21no—
29C2×D4×D61—22no—
30C2×#11758190—22no—
31C2×#11758200—22no—
32C2×#11758201—22no—
33SD16×D61—48no—
34C2×C8×D61D412yes—
35#14519777C2×C411yescharacteristic
36#14519776—22no—
37#14519775—21no—
38#14519774C2×C411yescharacteristic
39#14519773—22no—
40#14519773—21no—
41C4⋊C4×D61—22no—
42C42×D61C2311yescharacteristic
43C4×#92418C2×C411yescharacteristic
44C8×Dic61D412yes—
45C2×SD16×C61—22no—
46C4⋊Q8×C61C2×C411yescharacteristic
47#127×C61C2×C411yescharacteristic
48C4×C8×C61C2×C411yescharacteristic
49C23×D61—41no—
50C2×Q8×C61—21no—
51C2×D4×C61—21no—
52C2×D4×C61—22no—
53C2×C22⋊D61—42no—
54C2×C22⋊D61—41no—
55Q8×D61—44no—
56D4×D61—44no—
57D4×D61—84no—
58C2×D244—21no—
59C2×D244—22no—
60C2×C4×D61—41no—
61C2×C4×D61C2×D411yescharacteristic
62C2×C4×D61#4112yes—
63C2×Dic122—21no—
64C2×Dic122—41no—
65C2×#92420—24no—
66C2×#92420—42no—
67#11758213—44no—
68SD16×C61—44no—
69C2×C8×C61C22⋊C412yes—
70C4⋊C4×C61—22no—
71C42×C61C22×C411yescharacteristic
72#11758201—44no—
73#11758200—44no—
74C4⋊Dic61—22no—
75#11758196—42no—
76C4×Dic61C2×D411yescharacteristic
77C4×Dic61C2×D412yes—
78C2×#92418C22⋊C412yes—
79#11758190—44no—
80C8×D61—24no—
81C23×C61—41no—
82C22×D61—41no—
83C22×D61—84no—
84C22×D61—82no—
85C22×D61#12411yescharacteristic
86Q8×C61—42no—
87D4×C61—42no—
88D4×C61—82no—
89C2×C4×C61—41no—
90C2×C4×C61C2×C22⋊C411yescharacteristic
91C2×C4×C61C4×D412yes—
92C22⋊D61—84no—
93C22⋊D61—82no—
94C2×Dic61—41no—
95C2×Dic61#12112yes—
96C2×Dic61#12711yescharacteristic
97D244—42no—
98D244—82no—
99C4×D61—24no—
100C4×D61—82no—
101C4×D61AGL(1,ℤ/8)14yes—
102Dic122—42no—
103Dic122—82no—
104#92420—44no—
105#92420—82no—
106C8×C61—22no—
107#92418—22no—
108#9777—611nomaximal, Sylow
109C22×C61—81no—
110C22×C61—82no—
111C22×C61#39011yescharacteristic
112C2×D61—22no—
113C2×D61—81no—
114C2×D61—82no—
115C2×D61—164no—
116C2×D61#49012yes—
117C4×C61—22no—
118C4×C61—81no—
119C4×C61#41812yes—
120Dic61—81no—
121Dic61#47114yes—
122Dic61#49612yes—
123C2×#492—611no—
124#1837—611no—
125#1546—612no—
126#1545—612no—
127#1452—611no—
128C2×C61—161no—
129C2×C61#196111yescharacteristic
130C2×C61#197712yes—
131D61—22no—
132D61—161no—
133C22×SD16—1222no—
134C2×C4⋊Q8—611no—
135C2×#127—611no—
136#492—611no—
137#492—611no—
138#492—611no—
139#492—1222no—
140#492#692311yescharacteristic
141#431—612no—
142#423—612no—
143C2×C4×C8—611no—
144#341—1222no—
145#332—1224no—
146#331—1224no—
147#322—1222no—
148C61#977711yescharacteristic, complemented, Sylow
149C22×Q8—1221no—
150C22×D4—1222no—
151C22×D4—1221no—
152C2×SD16—22no—
153C2×SD16—1222no—
154C2×SD16—1222no—
155C2×SD16—1222no—
156C2×SD16—2448no—
157C2×M16—1222no—
158C22×C8—612no—
159C4⋊Q8—611no—
160C4⋊Q8—1222no—
161C4⋊Q8—1221no—
162C4⋊Q8C2×#692311yescharacteristic
163#127—611no—
164#127—1222no—
165#127—1221no—
166#127C2×#692311yescharacteristic
167C2×C4⋊C4—1222no—
168C2×C42—611no—
169C4⋊C8—614no—
170C4⋊C8—1222no—
171C4⋊C8—1222no—
172C22⋊C8—1222no—
173C4×C8—612no—
174C4×C8—611no—
175C4×C8—1222no—
176C4×C8C2×#692311yescharacteristic
177C24—2441no—
178C2×Q8—21no—
179C2×Q8—1221no—
180C2×Q8—2441no—
181C2×Q8—2444no—
182C2×D4—21no—
183C2×D4—22no—
184C2×D4—1221no—
185C2×D4—1222no—
186C2×D4—4884no—
187C2×D4—2444no—
188C2×D4—2442no—
189C2×D4—2441no—
190C22×C4—611no—
191C22×C4—612no—
192C22×C4—2441no—
193SD16—44no—
194SD16—2444no—
195SD16—2444no—
196SD16—2444no—
197M16—2444no—
198C2×C8—612no—
199C2×C8—1224no—
200C2×C8—1224no—
201C2×C8—2442no—
202C2×C8C22⋊#692312yes—
203C4⋊C4—22no—
204C4⋊C4—1222no—
205C4⋊C4—2442no—
206C42—611no—
207C42—612no—
208C42C22×#692311yescharacteristic
209C23—41no—
210C23—611no—
211C23—4882no—
212C23—4884no—
213C23—2441no—
214Q8—42no—
215Q8—4882no—
216Q8—2442no—
217D4—42no—
218D4—82no—
219D4—4882no—
220D4—4884no—
221D4—4882no—
222D4—2442no—
223C2×C4—41no—
224C2×C4—612no—
225C2×C4—611no—
226C2×C4—614no—
227C2×C4—1224no—
228C2×C4—4882no—
229C2×C4—2441no—
230C2×C4C2×C22⋊#692311yescharacteristic
231C2×C4D4×#692312yes—
232C8—22no—
233C8—1222no—
234C8—4882no—
235C8—2444no—
236C22—81no—
237C22—82no—
238C22—612no—
239C22—1222no—
240C22—9764no—
241C22—4881no—
242C22—4882no—
243C22#1684071411yescharacteristic
244C4—22no—
245C4—81no—
246C4—612no—
247C4—614no—
248C4—4881no—
249C4#1684075412yes—
250C2—161no—
251C2—1222no—
252C2—9761no—
253C2#2146195111yescharacteristic
254C2#2146197912yes—
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#492C4
socleC22×C61#390
prime radical#127×D61C22
cosocleC42×D61C23
hypercenter#492#6923
hypocenterC61#9777
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #21461744C2semidirect
2. #21461329C2semidirect
4. #21461033C2semidirect
148. C61#9777semidirect

Maximal subgroups

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

subgroupindex
#214617442
#214613292
#214613272
#214610332
#492×D612
#977761