Finite Group Databasebeta

← C23×#10428 #19158054

Subgroups — C23×#10428 #19158054

Order 5888.

386 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2822C211yesmaximal, characteristic
2C23×#1992C212yesmaximal
3C23×#1836C211yesmaximal, characteristic
4C2×C23×#330C212yesmaximal
5C23×#1295C211yesmaximal, characteristic
6C2×C23×#125C2212yes—
7C2×C23×#97C2212yes—
8C2×C23×#97C2211yescharacteristic
9C23×#400—22no—
10C23×#398—22no—
11C23×#398—22no—
12C23×#384C2211yescharacteristic
13C23×#382C2211yescharacteristic
14C23×#340—22no—
15C23×#340—22no—
16C23×#340—22no—
17C23×#330—24no—
18C22×C8×C23—22no—
19C22×C8×C23—21no—
20C23×#125—22no—
21C23×#125—22no—
22C23×#125—22no—
23C23×#125—22no—
24C2×C4⋊C4×C23—22no—
25C2×C4⋊C4×C23—22no—
26C2×C4⋊C4×C23—22no—
27C2×C4⋊C4×C23—21no—
28C2×C4⋊C4×C23—22no—
29C2×C4⋊C4×C23D412yes—
30C2×C4⋊C4×C23D412yes—
31C2×C4⋊C4×C23D412yes—
32C2×C42×C23C2311yescharacteristic
33C23×#97—22no—
34C23×#97—21no—
35C23×#97—22no—
36C23×#97D412yes—
37C23×#95—24no—
38C23×#95—22no—
39C23×#95—22no—
40C22×C4×C23—22no—
41C22×C4×C23—22no—
42C22×C4×C23—22no—
43C22×C4×C23—41no—
44C22×C4×C23C2×D412yes—
45C22×C4×C23C2×D411yescharacteristic
46C2×C8×C23—24no—
47C2×C8×C23—22no—
48C2×C8×C23—42no—
49C2×C8×C23—41no—
50C2×C8×C23—41no—
51C2×C8×C23—42no—
52C4⋊C4×C23—22no—
53C4⋊C4×C23—22no—
54C4⋊C4×C23—22no—
55C4⋊C4×C23—22no—
56C4⋊C4×C23—42no—
57C4⋊C4×C23—44no—
58C4⋊C4×C23—42no—
59C4⋊C4×C23—42no—
60C4⋊C4×C23—42no—
61C4⋊C4×C23—42no—
62C4⋊C4×C23—42no—
63C4⋊C4×C23—82no—
64C42×C23C2×D411yescharacteristic
65C42×C23#4111yescharacteristic
66C42×C23#4112yes—
67#10428C2311yesmaximal, characteristic, direct product factor, Sylow
68C23×C23#12011yescharacteristic
69C2×C4×C23—22no—
70C2×C4×C23—21no—
71C2×C4×C23—21no—
72C2×C4×C23—22no—
73C2×C4×C23—42no—
74C2×C4×C23—42no—
75C2×C4×C23—42no—
76C2×C4×C23—42no—
77C2×C4×C23—42no—
78C2×C4×C23—42no—
79C2×C4×C23—42no—
80C2×C4×C23—42no—
81C2×C4×C23—42no—
82C2×C4×C23—81no—
83C2×C4×C23—82no—
84C2×C4×C23#12112yes—
85C2×C4×C23#12111yescharacteristic
86C2×C4×C23#12312yes—
87C2×C4×C23#12411yescharacteristic
88C8×C23—44no—
89C8×C23—42no—
90#2822C2×C2311yescharacteristic
91#1992C2×C2312yes—
92#1836C2×C2311yescharacteristic
93C2×#330C2×C2312yes—
94#1295C2×C2311yescharacteristic
95C22×C23#39411yescharacteristic
96C22×C23#45411yescharacteristic
97C22×C23#45412yes—
98C22×C23#45511yescharacteristic
99C22×C23#45612yes—
100C4×C23—22no—
101C4×C23—22no—
102C4×C23—21no—
103C4×C23—21no—
104C4×C23—82no—
105C4×C23—82no—
106C4×C23—82no—
107C4×C23—161no—
108C2×#125C22×C2312yes—
109C2×#97C22×C2312yes—
110C2×#97C22×C2311yescharacteristic
111#400—22no—
112#398—22no—
113#398—22no—
114#384C22×C2311yescharacteristic
115#382C22×C2311yescharacteristic
116#340—22no—
117#340—22no—
118#340—22no—
119#330—24no—
120C2×C23#165811yescharacteristic
121C2×C23#166311yescharacteristic
122C2×C23#166412yes—
123C2×C23#203812yes—
124C2×C23#204011yescharacteristic
125C22×C8—22no—
126C22×C8—21no—
127#125—22no—
128#125—22no—
129#125—22no—
130#125—22no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4D4×C2312yes—
137C2×C4⋊C4D4×C2312yes—
138C2×C4⋊C4D4×C2312yes—
139C2×C42C23×C2311yescharacteristic
140#97—22no—
141#97—21no—
142#97—22no—
143#97D4×C2312yes—
144#95—24no—
145#95—22no—
146#95—22no—
147C23#1042811yescharacteristic, direct product factor, Sylow
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—41no—
152C22×C4C2×D4×C2312yes—
153C22×C4C2×D4×C2311yescharacteristic
154C2×C8—24no—
155C2×C8—22no—
156C2×C8—42no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8—42no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—42no—
165C4⋊C4—44no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—42no—
170C4⋊C4—42no—
171C4⋊C4—82no—
172C42C2×D4×C2311yescharacteristic
173C42#41×C2311yescharacteristic
174C42#41×C2312yes—
175C23C23×#12011yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—81no—
190C2×C4—82no—
191C2×C4C23×#12112yes—
192C2×C4C23×#12111yescharacteristic
193C2×C4C23×#12312yes—
194C2×C4C23×#12411yescharacteristic
195C8—44no—
196C8—42no—
197C22C23×#39411yescharacteristic
198C22C23×#45411yescharacteristic
199C22C23×#45412yes—
200C22C23×#45511yescharacteristic
201C22C23×#45612yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—82no—
208C4—82no—
209C4—161no—
210C2C23×#165811yescharacteristic
211C2C23×#166311yescharacteristic
212C2C23×#166412yes—
213C2C23×#203812yes—
214C2C23×#204011yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C23#120
commutator, Frattini, cosocleC2×C42C23×C23
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C23 ◁ C2×C42×C23 ◁ G

Complements

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

NH ≅ G/Ntype
67. #10428C23direct (N × H)
147. C23#10428direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#28222
C23×#19922
C23×#18362
C2×C23×#3302
C23×#12952
#1042823