Finite Group Databasebeta

← #29584996

Subgroups — #29584996

Order 15616.

372 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 99 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#21445994C211yesmaximal, characteristic, complemented
2#21444589C212yesmaximal, complemented
3#21444244C212yesmaximal
4#21443650C211yesmaximal, characteristic, complemented
5C61×#1955C211yesmaximal, characteristic
6#16839815C2212yes—
7C2×#14519713—22no—
8#16839786C2212yes—
9#16839512—24no—
10D4⋊#92418—24no—
11C2×C4×D4×C61C2211yescharacteristic
12C2×C4⋊C8×C61C2211yescharacteristic
13C2×C22⋊C8×C61—22no—
14C2×#97×C61C2211yescharacteristic
15C2×#11758194—22no—
16#14519713—44no—
17C4⋊#92418—22no—
18C4⋊#92418—22no—
19C4⋊#92418—22no—
20C22⋊#92418—22no—
21C4×#92418D414yes—
22C22×D4×C61Q811yescharacteristic
23C23×C4×C61—21no—
24C22×C8×C61—21no—
25C22×C8×C61D412yes—
26C4×D4×C61—22no—
27C4×D4×C61—22no—
28C2×C4⋊C4×C61Q811yescharacteristic
29C2×C22⋊C4×C61—21no—
30C2×C42×C61C2311yescharacteristic
31C4⋊C8×C61—22no—
32C22⋊C8×C61—44no—
33#97×C61—22no—
34C24×C61—21no—
35C2×D4×C61—22no—
36C2×D4×C61—42no—
37C22×C4×C61—21no—
38C22×C4×C61—41no—
39C22×C4×C61—41no—
40C22×C4×C61—42no—
41C22×C4×C61—42no—
42C22×C4×C61C2×D411yescharacteristic
43C22×C4×C61C2×Q811yescharacteristic
44C22×C4×C61#4111yescharacteristic
45C2×C8×C61—22no—
46C2×C8×C61—22no—
47C2×C8×C61—41no—
48C2×C8×C61—42no—
49C2×C8×C61SD1614yes—
50C4⋊C4×C61—22no—
51C22⋊C4×C61—42no—
52C42×C61C2×D412yes—
53C42×C61#4112yes—
54#11758194—44no—
55C2×#92418—24no—
56C2×#92418—42no—
57C23×C61—22no—
58C23×C61—41no—
59C23×C61—42no—
60C23×C61—41no—
61C23×C61—42no—
62C23×C61C22⋊Q811yescharacteristic
63D4×C61—24no—
64D4×C61—42no—
65C2×C4×C61—41no—
66C2×C4×C61—41no—
67C2×C4×C61—41no—
68C2×C4×C61—42no—
69C2×C4×C61—82no—
70C2×C4×C61—81no—
71C2×C4×C61—81no—
72C2×C4×C61C22⋊Q812yes—
73C2×C4×C61#12312yes—
74C2×C4×C61#12311yescharacteristic
75C2×C4×C61#12711yescharacteristic
76C2×C4×C61C2×SD1612yes—
77C2×C4×C61AGL(1,ℤ/8)12yes—
78C8×C61—24no—
79C8×C61—81no—
80#92418—44no—
81#92418—82no—
82#10661—611nomaximal, Sylow
83C22×C61—21no—
84C22×C61—21no—
85C22×C61—44no—
86C22×C61—42no—
87C22×C61—82no—
88C22×C61—81no—
89C22×C61—81no—
90C22×C61#39911yescharacteristic
91C22×C61#47612yes—
92C4×C61—22no—
93C4×C61—22no—
94C4×C61—81no—
95C4×C61#48112yes—
96C4×C61#49211yescharacteristic
97C4×C61#49611yescharacteristic
98#1955D6111yescharacteristic
99#1849—611no—
100#1570—612no—
101#1486—612no—
102#1275—611no—
103C2×C61—22no—
104C2×C61—82no—
105C2×C61#209111yescharacteristic
106C2×C61#209411yescharacteristic
107C2×C61#209811yescharacteristic
108C2×C4×D4C2×D6111yescharacteristic
109#431—612no—
110C2×#108—1222no—
111#423—612no—
112C2×C4⋊C8C2×D6111yescharacteristic
113C2×C22⋊C8—22no—
114C2×#97C2×D6111yescharacteristic
115#334—1224no—
116D4⋊C8—1224no—
117C61#1066111yescharacteristic, complemented, Sylow
118C22×D4Dic12211yescharacteristic
119C23×C4—21no—
120C2×M16—1222no—
121C22×C8—21no—
122C22×C8C22⋊D6112yes—
123C4×D4—22no—
124C4×D4—22no—
125C2×C4⋊C4Dic12211yescharacteristic
126C2×C22⋊C4—21no—
127C2×C42C22×D6111yescharacteristic
128#108—2444no—
129C4⋊C8—22no—
130C4⋊C8—1222no—
131C4⋊C8—1222no—
132C4⋊C8—1222no—
133C22⋊C8—44no—
134C22⋊C8—1222no—
135#97—22no—
136C4×C8—614no—
137C24—21no—
138C2×D4—22no—
139C2×D4—42no—
140C22×C4—21no—
141C22×C4—41no—
142C22×C4—41no—
143C22×C4—42no—
144C22×C4—42no—
145C22×C4C2×Dic12211yescharacteristic
146C22×C4#1175822211yescharacteristic
147C22×C4C2×C22⋊D6111yescharacteristic
148M16—2444no—
149C2×C8—22no—
150C2×C8—22no—
151C2×C8—41no—
152C2×C8—42no—
153C2×C8—1224no—
154C2×C8—2442no—
155C2×C8#1175820014yes—
156C4⋊C4—22no—
157C22⋊C4—42no—
158C42D4×D6112yes—
159C42#1175822412yes—
160C23—22no—
161C23—41no—
162C23—42no—
163C23—41no—
164C23—42no—
165C23#1451975611yescharacteristic
166D4—24no—
167D4—42no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—82no—
173C2×C4—81no—
174C2×C4—81no—
175C2×C4#1451975412yes—
176C2×C4#1451975811yescharacteristic
177C2×C4#1451975912yes—
178C2×C4#1451977311yescharacteristic
179C2×C4C2×#1175820012yes—
180C2×C4#1451980212yes—
181C8—24no—
182C8—81no—
183C8—4882no—
184C8—2444no—
185C22—21no—
186C22—21no—
187C22—44no—
188C22—42no—
189C22—82no—
190C22—81no—
191C22—81no—
192C22#1683969811yescharacteristic
193C22#1684005212yes—
194C4—22no—
195C4—22no—
196C4—81no—
197C4#1684007812yes—
198C4#1684013411yescharacteristic
199C4#1684015211yescharacteristic
200C2—22no—
201C2—82no—
202C2#2144733511yescharacteristic
203C2#2144735211yescharacteristic
204C2#2144737211yescharacteristic
subgroupG/H
centerC2×C4#14519773
commutator, cosocleC2×C42×C61C23
FrattiniC2×C42C22×D61
FittingC61×#1955C2
socleC22×C61#399
prime radicalC22×D4×C61Q8
hypercenter#1955D61
hypocenterC61#10661
LCSG ▷ C2×C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #21445994C2semidirect
2. #21444589C2semidirect
4. #21443650C2semidirect
117. C61#10661semidirect

Maximal subgroups

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

subgroupindex
#214459942
#214445892
#214442442
#214436502
C61×#19552
#1066161