Finite Group Databasebeta

← #29567531

Subgroups — #29567531

Order 15616.

244 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 37 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#21446923C211yesmaximal, characteristic
2#21443745C211yesmaximal, characteristic, complemented
3C61×#1391C211yesmaximal, characteristic, complemented
4#16840562C411yescharacteristic, complemented
5#16840560—21no—
6#16839728—21no—
7C22⋊#11758185—21no—
8#16839520C411yescharacteristic, complemented
9C61×#410—21no—
10C61×#408C2211yescharacteristic
11C2×#11758222—21no—
12#14519810—41no—
13#14519808—41no—
14#14519807—41no—
15#14519805—41no—
16#14519803—41no—
17#14519802—41no—
18#14519799—41no—
19#14519797—42no—
20C2×#11758194—21no—
21C2×#11758185—41no—
22#14519689—42no—
23C2×#41×C61D411yescharacteristic
24C2×M16×C61C2×C411yescharacteristic
25C22×C8×C61D411yescharacteristic
26#117×C61—41no—
27#99×C61—22no—
28#99×C61—41no—
29C22⋊C8×C61—41no—
30#41×C61—41no—
31#41×C61—41no—
32C2×Q8×C61SD1611yescharacteristic
33C2×D4×C61—21no—
34C2×D4×C61D811yescharacteristic
35C22×C4×C61—21no—
36C22×C4×C61C22⋊C411yescharacteristic
37C2×C22⋊D61—41no—
38#11758222—41no—
39#11758222—41no—
40#11758222—41no—
41#11758222—41no—
42C2×D244—21no—
43C2×C4×D61—41no—
44C2×Dic122—21no—
45M16×C61—41no—
46C2×C8×C61—21no—
47C2×C8×C61—21no—
48C2×C8×C61—41no—
49C4⋊C4×C61—81no—
50C22⋊C4×C61—42no—
51C42×C61—81no—
52#11758202—42no—
53#11758201—42no—
54#11758200—42no—
55#11758199—42no—
56#11758194—41no—
57#11758194—41no—
58C2×#92418—22no—
59Dic244—41no—
60D488—41no—
61#11758190—42no—
62#11758185—81no—
63C23×C61—21no—
64C23×C61#10411yescharacteristic
65C22×D61—41no—
66Q8×C61—41no—
67D4×C61—41no—
68D4×C61—81no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—41no—
73C2×C4×C61—41no—
74C2×C4×C61—82no—
75C2×C4×C61#9911yescharacteristic
76C2×C4×C61#10211yescharacteristic
77C22⋊D61—81no—
78C22⋊D61—81no—
79C2×Dic61—41no—
80D244—41no—
81D244—41no—
82C4×D61—81no—
83C4×D61—81no—
84Dic122—41no—
85Dic122—41no—
86C8×C61—41no—
87C8×C61—41no—
88#92418—42no—
89#7406—611nomaximal, Sylow
90C22×C61—21no—
91C22×C61—41no—
92C22×C61—41no—
93C22×C61—81no—
94C22×C61#32711yescharacteristic
95C2×D61—82no—
96C2×D61—81no—
97C4×C61—21no—
98C4×C61—41no—
99C4×C61—162no—
100C4×C61AΣL(1,𝔽16)11yescharacteristic
101C4×C61#35311yescharacteristic
102Dic61—81no—
103#2017—611no—
104#1391D6111yescharacteristic, complemented
105#1315—611no—
106C2×C61—21no—
107C2×C61—41no—
108C2×C61—81no—
109C2×C61#134311yescharacteristic
110D61—161no—
111#575—611no—
112#575—1221no—
113#410—21no—
114#408—1221no—
115#408C2×D6111yescharacteristic
116C22⋊C16—1221no—
117#338—611no—
118C61#740611yescharacteristic, complemented, Sylow
119C2×#41—1221no—
120C2×#41C22⋊D6111yescharacteristic
121#137—2441no—
122#137—2441no—
123#137—2441no—
124AGL(1,ℤ/8)—2441no—
125AGL(1,ℤ/8)—2441no—
126AGL(1,ℤ/8)—2441no—
127#135—2441no—
128#135—2442no—
129C2×M16—1221no—
130C2×M16C4×D6111yescharacteristic
131C22×C8D24411yescharacteristic
132#117—41no—
133C2×C16—2441no—
134#99—22no—
135#99—41no—
136C22⋊C8—41no—
137C22⋊C8—2442no—
138#41—41no—
139#41—41no—
140#41—2441no—
141#41—2441no—
142#41—2441no—
143#41—2441no—
144C2×Q8—1221no—
145C2×Q8#1175820111yescharacteristic
146C2×D4—21no—
147C2×D4—1221no—
148C2×D4—2441no—
149C2×D4#1175819911yescharacteristic
150C22×C4—21no—
151C22×C4—2441no—
152C22×C4#1175819811yescharacteristic
153Q16—2441no—
154Q16—2442no—
155SD16—2442no—
156SD16—2442no—
157SD16—2442no—
158D8—2441no—
159D8—2442no—
160M16—41no—
161M16—2441no—
162M16—2441no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—41no—
166C2×C8—1222no—
167C4⋊C4—81no—
168C22⋊C4—42no—
169C42—81no—
170C16—4881no—
171C23—21no—
172C23—2441no—
173C23#1451970511yescharacteristic
174Q8—41no—
175Q8—2441no—
176Q8—2441no—
177D4—41no—
178D4—81no—
179D4—4881no—
180D4—4881no—
181D4—2441no—
182D4—2441no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—82no—
189C2×C4—4881no—
190C2×C4—4881no—
191C2×C4—2441no—
192C2×C4#1451969111yescharacteristic
193C2×C4#1451969711yescharacteristic
194C8—41no—
195C8—41no—
196C8—2442no—
197C22—21no—
198C22—41no—
199C22—41no—
200C22—81no—
201C22—4882no—
202C22—4881no—
203C22#1683949511yescharacteristic
204C4—21no—
205C4—41no—
206C4—162no—
207C4—4881no—
208C4#1683954811yescharacteristic
209C4#1683955411yescharacteristic
210C2—21no—
211C2—41no—
212C2—81no—
213C2—9761no—
214C2#2144381511yescharacteristic
subgroupG/H
centerC4#16839554
commutatorC2×M16×C61C2×C4
Frattini#408C2×D61
FittingC61×#1391C2
socleC2×C61#1343
prime radical#21446923C2
cosocleC61×#408C22
hypercenter#1391D61
hypocenterC61#7406
LCSG ▷ C2×M16×C61 ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ #408 ◁ #1391

Complements

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

NH ≅ G/Ntype
2. #21443745C2semidirect
3. C61×#1391C2semidirect
4. #16840562C4semidirect
8. #16839520C4semidirect
104. #1391D61semidirect
118. C61#7406semidirect

Maximal subgroups

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

subgroupindex
#214469232
#214437452
C61×#13912
#740661