Finite Group Databasebeta

← #29573012

Subgroups — #29573012

Order 15616.

388 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 93 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#21454530C211yesmaximal, characteristic
2#21444580C212yesmaximal, complemented
3#21444453C212yesmaximal
4#21443730C211yesmaximal, characteristic, complemented
5C61×#1307C211yesmaximal, characteristic, complemented
6C2×#14519785C412yes—
7#16840312C2211yescharacteristic
8#16839839—22no—
9#16839827—22no—
10#16839819C2212yes—
11#16839730C412yes—
12C2×C4×#92418C2211yescharacteristic
13#16839514—22no—
14#16839512—22no—
15#16839501—24no—
16C61×#432C2212yes—
17C61×#423C2211yescharacteristic
18C2×#11758222C2×C412yes—
19#14519785—44no—
20C2×#11758189—22no—
21C22×#92418C2×C411yescharacteristic
22C22×#92418C2×C411yescharacteristic
23C2×C8×D61—22no—
24#14519777Q811yescharacteristic
25#14519774Q811yescharacteristic
26#14519765D412yes—
27#14519751—22no—
28C4×D244—22no—
29C4⋊#92418—22no—
30C22⋊#92418—22no—
31#14519689—24no—
32#14519688—22no—
33C4×#92418D412yes—
34C4×#92418D412yes—
35C2×M16×C61C2×C412yes—
36C2×C42×C61C2311yescharacteristic
37C4⋊C8×C61—22no—
38C4⋊C8×C61—22no—
39C22⋊C8×C61—22no—
40#97×C61—22no—
41C22×C4×C61C22×C411yescharacteristic
42C22×C4×C61#4112yes—
43C2×C22⋊D61—22no—
44#11758222—42no—
45#11758222—42no—
46C2×D244—22no—
47C2×D244C4⋊C412yes—
48C2×C4×D61—22no—
49C2×Dic122C4⋊C412yes—
50M16×C61—42no—
51C2×C8×C61—22no—
52C2×C8×C61—42no—
53C42×C61C2×D412yes—
54C42×C61C2×D411yescharacteristic
55C42×C61C2×Q811yescharacteristic
56#11758198—24no—
57C4⋊Dic61—22no—
58C2×#92418—22no—
59C2×#92418—41no—
60C2×#92418—42no—
61C2×#92418C22⋊C412yes—
62C2×#92418C22⋊C411yescharacteristic
63C2×#92418C22⋊C411yescharacteristic
64#11758189—44no—
65C8×D61—44no—
66C23×C61#11711yescharacteristic
67C22×D61—22no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—42no—
71C2×C4×C61C2×C22⋊C411yescharacteristic
72C2×C4×C61C2×C4⋊C411yescharacteristic
73C2×C4×C61#12112yes—
74C2×C4×C61C22⋊Q812yes—
75C22⋊D61—44no—
76C2×Dic61—22no—
77D244—42no—
78D244—44no—
79C4×D61—42no—
80C4×D61—42no—
81Dic122—42no—
82C8×C61—42no—
83C8×C61—82no—
84#92418—21no—
85#92418—22no—
86#92418—82no—
87#92418#10012yes—
88#8632—611nomaximal, Sylow
89C22×C61—21no—
90C22×C61—22no—
91C22×C61#38011yescharacteristic
92C2×D61—42no—
93C2×D61—44no—
94C4×C61—21no—
95C4×C61—22no—
96C4×C61—22no—
97C4×C61C2×#10011yescharacteristic
98C4×C61#41311yescharacteristic
99Dic61—42no—
100#2931—611no—
101#1568—612no—
102#1536—612no—
103#1307—611no—
104#1307D6111yescharacteristic, complemented
105C2×C61—41no—
106C2×C61#180011yescharacteristic
107C2×C61#181412yes—
108D61—82no—
109C2×#131—612no—
110#532—611no—
111#436—1222no—
112C8×D4—1222no—
113#432—612no—
114#432C2×D6112yes—
115#423C2×D6111yescharacteristic
116#408—612no—
117C2×C4×C8—611no—
118#335—1222no—
119#334—1222no—
120#329—1224no—
121C61#863211yescharacteristic, complemented, Sylow
122C2×#41—612no—
123#131—2444no—
124C2×M16—1222no—
125C2×M16C4×D6112yes—
126C22×C8—611no—
127C22×C8—611no—
128C22×C8—1222no—
129C4⋊Q8—611no—
130#127—611no—
131#124—612no—
132#121—1222no—
133C4×D4—1222no—
134C2×C42C22×D6111yescharacteristic
135C4⋊C8—22no—
136C4⋊C8—22no—
137C4⋊C8—1222no—
138C22⋊C8—22no—
139C22⋊C8—1224no—
140C22⋊C8—1222no—
141#97—22no—
142#97—1222no—
143C4×C8—612no—
144C4×C8—612no—
145#41—2442no—
146#41—2442no—
147C2×Q8—612no—
148C2×D4—612no—
149C2×D4—1222no—
150C2×D4—1222no—
151C22×C4—1222no—
152C22×C4C2×C4×D6111yescharacteristic
153C22×C4#1175822212yes—
154M16—42no—
155M16—2444no—
156C2×C8—22no—
157C2×C8—42no—
158C2×C8—611no—
159C2×C8—612no—
160C2×C8—611no—
161C2×C8—1222no—
162C2×C8—2444no—
163C2×C8—2441no—
164C2×C8—2442no—
165C4⋊C4—1222no—
166C22⋊C4—1224no—
167C42D4×D6112yes—
168C42D4×D6111yescharacteristic
169C42Q8×D6111yescharacteristic
170C23—1222no—
171C23#1451973411yescharacteristic
172Q8—2442no—
173D4—2442no—
174D4—2444no—
175D4—2444no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—42no—
179C2×C4—1222no—
180C2×C4—2442no—
181C2×C4—2442no—
182C2×C4C22⋊C4×D6111yescharacteristic
183C2×C4C4⋊C4×D6111yescharacteristic
184C2×C4#1451975012yes—
185C2×C4#1451975512yes—
186C8—42no—
187C8—82no—
188C8—612no—
189C8—1221no—
190C8—1222no—
191C8—4882no—
192C22—21no—
193C22—22no—
194C22—2442no—
195C22—2444no—
196C22#1683962111yescharacteristic
197C4—21no—
198C4—22no—
199C4—22no—
200C4—2442no—
201C4#100×D6111yescharacteristic
202C4#1683974511yescharacteristic
203C2—41no—
204C2—4882no—
205C2#2144581011yescharacteristic
206C2#2144587212yes—
subgroupG/H
centerC22#16839621
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1307C2
socleC22×C61#380
prime radical#16840312C22
cosocleC2×C42×C61C23
hypercenter#1307D61
hypocenterC61#8632
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1307

Complements

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

NH ≅ G/Ntype
2. #21444580C2semidirect
4. #21443730C2semidirect
5. C61×#1307C2semidirect
104. #1307D61semidirect
121. C61#8632semidirect

Maximal subgroups

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

subgroupindex
#214545302
#214445802
#214444532
#214437302
C61×#13072
#863261