Finite Group Databasebeta

← C23×#7405 #19155031

Subgroups — C23×#7405 #19155031

Order 5888.

252 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C23×#2016C211yesmaximal, characteristic
2C23×#1394C211yesmaximal, characteristic
3C23×#1319C211yesmaximal, characteristic
4C22×Q16×C23—21no—
5C2×C23×C4⋊Q8C411yescharacteristic
6C2×C23×#103—21no—
7C2×C23×#101—21no—
8C23×#391C2211yescharacteristic
9C23×#336C411yescharacteristic
10C23×#324—21no—
11C22×Q8×C23—21no—
12C22×Q8×C23D411yescharacteristic
13C2×Q16×C23—42no—
14C2×Q16×C23—42no—
15C2×Q16×C23—41no—
16C2×Q16×C23—41no—
17C2×M16×C23—41no—
18C22×C8×C23—21no—
19C23×C4⋊Q8—42no—
20C2×C4⋊C4×C23—41no—
21C2×C4⋊C4×C23D411yescharacteristic
22C2×C42×C23C2×C411yescharacteristic
23C23×#103—42no—
24C23×#101—22no—
25C23×#101—41no—
26C23×C22⋊C8—41no—
27C23×#95—41no—
28C2×Q8×C23—21no—
29C2×Q8×C23—22no—
30C2×Q8×C23—41no—
31C2×Q8×C23—41no—
32C2×Q8×C23—41no—
33C2×Q8×C23—41no—
34C2×Q8×C23—41no—
35C2×Q8×C23—41no—
36C2×Q8×C23—41no—
37C2×Q8×C23D811yescharacteristic
38C2×Q8×C23SD1611yescharacteristic
39C22×C4×C23—21no—
40C22×C4×C23—21no—
41C22×C4×C23—21no—
42C22×C4×C23—41no—
43C22×C4×C23C22⋊C411yescharacteristic
44Q16×C23—44no—
45Q16×C23—44no—
46M16×C23—42no—
47M16×C23—81no—
48C2×C8×C23—22no—
49C2×C8×C23—41no—
50C2×C8×C23—41no—
51C2×C8×C23—81no—
52C2×C8×C23—81no—
53C4⋊C4×C23—41no—
54C4⋊C4×C23—42no—
55C4⋊C4×C23—42no—
56C42×C23—41no—
57#7405C2311yesmaximal, characteristic, direct product factor, Sylow
58C23×C23#9911yescharacteristic
59Q8×C23—41no—
60Q8×C23—41no—
61Q8×C23—42no—
62Q8×C23—42no—
63Q8×C23—81no—
64Q8×C23—81no—
65Q8×C23—81no—
66C2×C4×C23—21no—
67C2×C4×C23—21no—
68C2×C4×C23—22no—
69C2×C4×C23—21no—
70C2×C4×C23—21no—
71C2×C4×C23—41no—
72C2×C4×C23—41no—
73C2×C4×C23—41no—
74C2×C4×C23—41no—
75C2×C4×C23—42no—
76C2×C4×C23—41no—
77C2×C4×C23—81no—
78C2×C4×C23—81no—
79C2×C4×C23—81no—
80C2×C4×C23#10211yescharacteristic
81C2×C4×C23#10411yescharacteristic
82C8×C23—42no—
83C8×C23—82no—
84C8×C23—161no—
85#2016C2×C2311yescharacteristic
86#1394C2×C2311yescharacteristic
87#1319C2×C2311yescharacteristic
88C22×C23—21no—
89C22×C23—21no—
90C22×C23#32711yescharacteristic
91C22×C23AΣL(1,𝔽16)11yescharacteristic
92C22×C23#35311yescharacteristic
93C4×C23—21no—
94C4×C23—21no—
95C4×C23—42no—
96C4×C23—41no—
97C4×C23—41no—
98C4×C23—82no—
99C4×C23—81no—
100C22×Q16—21no—
101C2×C4⋊Q8C4×C2311yescharacteristic
102C2×#103—21no—
103C2×#101—21no—
104#391C22×C2311yescharacteristic
105#336C4×C2311yescharacteristic
106#324—21no—
107C2×C23—21no—
108C2×C23—21no—
109C2×C23#134311yescharacteristic
110C2×C23#140711yescharacteristic
111C2×C23#141111yescharacteristic
112C22×Q8—21no—
113C22×Q8D4×C2311yescharacteristic
114C2×Q16—42no—
115C2×Q16—42no—
116C2×Q16—41no—
117C2×Q16—41no—
118C2×M16—41no—
119C22×C8—21no—
120C4⋊Q8—42no—
121C2×C4⋊C4—41no—
122C2×C4⋊C4D4×C2311yescharacteristic
123C2×C42C2×C4×C2311yescharacteristic
124#103—42no—
125#101—22no—
126#101—41no—
127C22⋊C8—41no—
128#95—41no—
129C23#740511yescharacteristic, direct product factor, Sylow
130C2×Q8—21no—
131C2×Q8—22no—
132C2×Q8—41no—
133C2×Q8—41no—
134C2×Q8—41no—
135C2×Q8—41no—
136C2×Q8—41no—
137C2×Q8—41no—
138C2×Q8—41no—
139C2×Q8D8×C2311yescharacteristic
140C2×Q8SD16×C2311yescharacteristic
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4—41no—
145C22×C4C22⋊C4×C2311yescharacteristic
146Q16—44no—
147Q16—44no—
148M16—42no—
149M16—81no—
150C2×C8—22no—
151C2×C8—41no—
152C2×C8—41no—
153C2×C8—81no—
154C2×C8—81no—
155C4⋊C4—41no—
156C4⋊C4—42no—
157C4⋊C4—42no—
158C42—41no—
159C23C23×#9911yescharacteristic
160Q8—41no—
161Q8—41no—
162Q8—42no—
163Q8—42no—
164Q8—81no—
165Q8—81no—
166Q8—81no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—41no—
178C2×C4—81no—
179C2×C4—81no—
180C2×C4—81no—
181C2×C4C23×#10211yescharacteristic
182C2×C4C23×#10411yescharacteristic
183C8—42no—
184C8—82no—
185C8—161no—
186C22—21no—
187C22—21no—
188C22C23×#32711yescharacteristic
189C22C23×AΣL(1,𝔽16)11yescharacteristic
190C22C23×#35311yescharacteristic
191C4—21no—
192C4—21no—
193C4—42no—
194C4—41no—
195C4—41no—
196C4—81no—
197C4—82no—
198C2—21no—
199C2—21no—
200C2C23×#134311yescharacteristic
201C2C23×#140711yescharacteristic
202C2C23×#141111yescharacteristic
subgroupG/H
center, socleC22×C23#353
commutatorC2×C42C2×C4×C23
Frattini, cosocle#391C22×C23
prime radicalC23×C23#99
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C23×C23 ◁ C22×C4×C23 ◁ C23×#391 ◁ G

Complements

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

NH ≅ G/Ntype
57. #7405C23direct (N × H)
129. C23#7405direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#20162
C23×#13942
C23×#13192
#740523