Finite Group Databasebeta

← C2×#20289853 #28312448

Subgroups — C2×#20289853 #28312448

Order 13568.

398 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 64 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
1C2×#16811534C212yesmaximal
2#20289853C214yesmaximal, direct product factor
3C2×#16811003C211yesmaximal, characteristic
4C2×#13133278—22no—
5#16811534—22no—
6#16811534C2214yes—
7C22×Dic212—22no—
8C2×#13133217C411yescharacteristic
9C2×#13133217C2211yescharacteristic
10#16811003—22no—
11#16811003C412yes—
12#16811003C2212yes—
13C2×C4×C8×C53C411yescharacteristic
14C2×#11719940—42no—
15#13133278—24no—
16#13133278—42no—
17C22×Dic106—21no—
18C22×Dic106D412yes—
19C2×Dic212—24no—
20C2×Dic212—24no—
21C2×Dic212—44no—
22C2×Dic212—44no—
23#13133217—21no—
24#13133217—41no—
25#13133217—41no—
26#13133217C2×C412yes—
27#13133217C2×C411yescharacteristic
28#13133217D412yes—
29#13133217C2311yescharacteristic
30C2×C4⋊Dic53—41no—
31C2×C4⋊Dic53—41no—
32C22×C8×C53—21no—
33C2×C42×C53C2×C411yescharacteristic
34C4×C8×C53—21no—
35C4×C8×C53C2×C412yes—
36C22×C4×C53—21no—
37C22×C4×C53C22⋊C411yescharacteristic
38C22×Dic53—22no—
39C22×Dic53—41no—
40C2×Dic106—22no—
41C2×Dic106—22no—
42C2×Dic106—42no—
43C2×Dic106—42no—
44C2×Dic106—42no—
45C2×Dic106—42no—
46C2×Dic106—41no—
47C2×Dic106C22⋊C412yes—
48C2×Dic106C2×D412yes—
49#11719940—44no—
50#11719940—82no—
51C2×#88324—82no—
52C2×C8×C53—22no—
53C2×C8×C53—22no—
54C2×C8×C53—22no—
55C42×C53—21no—
56C42×C53C22⋊C411yescharacteristic
57C42×C53C22×C411yescharacteristic
58C4⋊Dic53—41no—
59C4⋊Dic53—42no—
60C4⋊Dic53—41no—
61C4⋊Dic53—42no—
62C4⋊Dic53—42no—
63Dic212—48no—
64Dic212—48no—
65C23×C53#9911yescharacteristic
66C2×C4×C53—24no—
67C2×C4×C53—21no—
68C2×C4×C53—21no—
69C2×C4×C53—21no—
70C2×C4×C53—21no—
71C2×C4×C53#9911yescharacteristic
72C2×C4×C53C2×C22⋊C411yescharacteristic
73C2×Dic53—22no—
74C2×Dic53—22no—
75C2×Dic53—42no—
76C2×Dic53—42no—
77C2×Dic53—42no—
78C2×Dic53—81no—
79C2×Dic53—81no—
80Dic106—42no—
81Dic106—42no—
82Dic106—44no—
83Dic106—82no—
84Dic106—82no—
85#88324—84no—
86C8×C53—24no—
87C2×#1411—531nomaximal, Sylow
88C22×C53—22no—
89C22×C53#35311yescharacteristic
90C22×C53#35311yescharacteristic
91C22×C53C2×#9911yescharacteristic
92C4×C53—22no—
93C4×C53—22no—
94C4×C53—21no—
95C4×C53—21no—
96Dic53—42no—
97Dic53—42no—
98Dic53—82no—
99C2×#494—531no—
100C2×#356—532no—
101#1411—534no—
102C2×C53—21no—
103C2×C53—21no—
104C2×C53#141112yescomplemented
105C2×C53C2×#35311yescharacteristic
106C22×Q16—1062no—
107C2×C4⋊Q8—531no—
108C2×C4⋊Q8—531no—
109#494—532no—
110#494—532no—
111#494—1062no—
112C2×#101—1062no—
113C2×C4×C8#615711yescharacteristic
114#356—534no—
115#356—1062no—
116C53C2×#141111yescharacteristic, complemented, Sylow
117C22×Q8—532no—
118C22×Q8—1061no—
119C2×Q16—1064no—
120C2×Q16—1064no—
121C2×Q16—2124no—
122C2×Q16—2124no—
123C2×M16—2122no—
124C22×C8—21no—
125C4⋊Q8—532no—
126C4⋊Q8—531no—
127C4⋊Q8—531no—
128C4⋊Q8—532no—
129C4⋊Q8—1061no—
130C4⋊Q8—2121no—
131C4⋊Q8—2121no—
132C2×C4⋊C4—2121no—
133C2×C4⋊C4—2121no—
134C2×C42C2×#615711yescharacteristic
135#101—1064no—
136#101—2122no—
137C4×C8—21no—
138C4×C8C2×#615712yes—
139C2×Q8—532no—
140C2×Q8—532no—
141C2×Q8—1062no—
142C2×Q8—1062no—
143C2×Q8—2122no—
144C2×Q8—2122no—
145C2×Q8—2122no—
146C2×Q8—2122no—
147C2×Q8—2121no—
148C22×C4—21no—
149C22×C4—1062no—
150C22×C4—2121no—
151C22×C4C22⋊#615711yescharacteristic
152Q16—2128no—
153Q16—2128no—
154M16—4242no—
155M16—2124no—
156C2×C8—22no—
157C2×C8—22no—
158C2×C8—22no—
159C2×C8—4242no—
160C4⋊C4—2122no—
161C4⋊C4—2121no—
162C4⋊C4—2121no—
163C4⋊C4—2122no—
164C4⋊C4—2122no—
165C42—21no—
166C42C22⋊#615711yescharacteristic
167C42C22×#615711yescharacteristic
168C23#1313327611yescharacteristic
169Q8—4242no—
170Q8—4242no—
171Q8—2124no—
172Q8—2122no—
173Q8—2122no—
174C2×C4—24no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—1062no—
180C2×C4—1062no—
181C2×C4—4241no—
182C2×C4—4241no—
183C2×C4—2122no—
184C2×C4—2122no—
185C2×C4—2122no—
186C2×C4#1313327611yescharacteristic
187C2×C4C2×C22⋊#615711yescharacteristic
188C8—24no—
189C8—4244no—
190C22—22no—
191C22#1681152811yescharacteristic
192C22#1681152811yescharacteristic
193C22C2×#1313327611yescharacteristic
194C4—22no—
195C4—22no—
196C4—21no—
197C4—21no—
198C4—4242no—
199C4—2122no—
200C4—2122no—
201C2—21no—
202C2—21no—
203C2#2028985312yesdirect product factor
204C2C2×#1681152811yescharacteristic
subgroupG/H
centerC22#16811528
commutatorC42×C53C22×C4
FrattiniC42C22×#6157
FittingC2×C4×C8×C53C4
socleC22×C53#353
prime radicalC23×C53#99
cosocle#13133217C23
hypercenterC2×C4×C8#6157
hypocenterC53C2×#1411
LCSG ▷ C42×C53 ▷ C2×C4×C53 ▷ C22×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
2. #20289853C2direct (N × H)
104. C2×C53#1411semidirect
116. C53C2×#1411semidirect
203. C2#20289853direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168115342
#202898532
C2×#168110032
C2×#141153