Finite Group Databasebeta

← C23×#10429 #19158055

Subgroups — C23×#10429 #19158055

Order 5888.

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

normal subgroups only

This group has 402 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×#1847C211yesmaximal, characteristic
4C2×C23×#330C212yesmaximal
5C23×#1295C211yesmaximal, characteristic
6C2×C23×#125C2212yes—
7C2×C23×#107—21no—
8C2×C23×#106—21no—
9C2×C23×#97C2212yes—
10C2×C23×#97C2211yescharacteristic
11C23×#400—22no—
12C23×#398—21no—
13C23×#398—21no—
14C23×#398—22no—
15C23×#384C2211yescharacteristic
16C23×#382C2211yescharacteristic
17C23×#340—22no—
18C23×#340—22no—
19C23×#330—24no—
20C22×C8×C23—21no—
21C22×C8×C23—22no—
22C23×#125—22no—
23C23×#125—22no—
24C23×#125—22no—
25C23×#125—22no—
26C2×C4⋊C4×C23—22no—
27C2×C4⋊C4×C23—22no—
28C2×C4⋊C4×C23—22no—
29C2×C4⋊C4×C23—21no—
30C2×C4⋊C4×C23—21no—
31C2×C4⋊C4×C23—21no—
32C2×C4⋊C4×C23D412yes—
33C2×C4⋊C4×C23D412yes—
34C2×C4⋊C4×C23D411yescharacteristic
35C2×C4⋊C4×C23D411yescharacteristic
36C2×C42×C23C2311yescharacteristic
37C23×#107—42no—
38C23×#106—42no—
39C23×#97—22no—
40C23×#97—21no—
41C23×#97—22no—
42C23×#97D412yes—
43C23×#95—22no—
44C23×#95—22no—
45C23×#95—21no—
46C23×#95—21no—
47C23×#95—22no—
48C22×C4×C23—22no—
49C22×C4×C23—22no—
50C22×C4×C23—21no—
51C22×C4×C23—21no—
52C22×C4×C23—41no—
53C22×C4×C23C2×D412yes—
54C22×C4×C23C2×D411yescharacteristic
55C2×C8×C23—22no—
56C2×C8×C23—22no—
57C2×C8×C23—22no—
58C2×C8×C23—24no—
59C2×C8×C23—42no—
60C2×C8×C23—42no—
61C4⋊C4×C23—22no—
62C4⋊C4×C23—22no—
63C4⋊C4×C23—22no—
64C4⋊C4×C23—22no—
65C4⋊C4×C23—41no—
66C4⋊C4×C23—41no—
67C4⋊C4×C23—41no—
68C4⋊C4×C23—41no—
69C4⋊C4×C23—44no—
70C4⋊C4×C23—42no—
71C4⋊C4×C23—42no—
72C4⋊C4×C23—42no—
73C4⋊C4×C23—42no—
74C4⋊C4×C23—81no—
75C4⋊C4×C23—81no—
76C42×C23C2×D411yescharacteristic
77C42×C23#4111yescharacteristic
78C42×C23#4112yes—
79#10429C2311yesmaximal, characteristic, direct product factor, Sylow
80C23×C23#12011yescharacteristic
81C2×C4×C23—21no—
82C2×C4×C23—22no—
83C2×C4×C23—22no—
84C2×C4×C23—21no—
85C2×C4×C23—42no—
86C2×C4×C23—42no—
87C2×C4×C23—41no—
88C2×C4×C23—41no—
89C2×C4×C23—42no—
90C2×C4×C23—42no—
91C2×C4×C23—42no—
92C2×C4×C23—42no—
93C2×C4×C23—42no—
94C2×C4×C23—42no—
95C2×C4×C23—81no—
96C2×C4×C23—82no—
97C2×C4×C23#12112yes—
98C2×C4×C23#12111yescharacteristic
99C2×C4×C23#12312yes—
100C2×C4×C23#12411yescharacteristic
101C8×C23—24no—
102C8×C23—44no—
103#2822C2×C2311yescharacteristic
104#1992C2×C2312yes—
105#1847C2×C2311yescharacteristic
106C2×#330C2×C2312yes—
107#1295C2×C2311yescharacteristic
108C22×C23#39411yescharacteristic
109C22×C23#45311yescharacteristic
110C22×C23#45412yes—
111C22×C23#45612yes—
112C22×C23#45611yescharacteristic
113C4×C23—22no—
114C4×C23—22no—
115C4×C23—21no—
116C4×C23—21no—
117C4×C23—81no—
118C4×C23—81no—
119C4×C23—82no—
120C4×C23—82no—
121C4×C23—161no—
122C2×#125C22×C2312yes—
123C2×#107—21no—
124C2×#106—21no—
125C2×#97C22×C2312yes—
126C2×#97C22×C2311yescharacteristic
127#400—22no—
128#398—21no—
129#398—21no—
130#398—22no—
131#384C22×C2311yescharacteristic
132#382C22×C2311yescharacteristic
133#340—22no—
134#340—22no—
135#330—24no—
136C2×C23#165711yescharacteristic
137C2×C23#166011yescharacteristic
138C2×C23#166312yes—
139C2×C23#203812yes—
140C2×C23#203911yescharacteristic
141C22×C8—21no—
142C22×C8—22no—
143#125—22no—
144#125—22no—
145#125—22no—
146#125—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—21no—
153C2×C4⋊C4D4×C2312yes—
154C2×C4⋊C4D4×C2312yes—
155C2×C4⋊C4D4×C2311yescharacteristic
156C2×C4⋊C4D4×C2311yescharacteristic
157C2×C42C23×C2311yescharacteristic
158#107—42no—
159#106—42no—
160#97—22no—
161#97—21no—
162#97—22no—
163#97D4×C2312yes—
164#95—22no—
165#95—22no—
166#95—21no—
167#95—21no—
168#95—22no—
169C23#1042911yescharacteristic, direct product factor, Sylow
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—41no—
175C22×C4C2×D4×C2312yes—
176C22×C4C2×D4×C2311yescharacteristic
177C2×C8—22no—
178C2×C8—22no—
179C2×C8—22no—
180C2×C8—24no—
181C2×C8—42no—
182C2×C8—42no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—41no—
190C4⋊C4—41no—
191C4⋊C4—44no—
192C4⋊C4—42no—
193C4⋊C4—42no—
194C4⋊C4—42no—
195C4⋊C4—42no—
196C4⋊C4—81no—
197C4⋊C4—81no—
198C42C2×D4×C2311yescharacteristic
199C42#41×C2311yescharacteristic
200C42#41×C2312yes—
201C23C23×#12011yescharacteristic
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—81no—
217C2×C4—82no—
218C2×C4C23×#12112yes—
219C2×C4C23×#12111yescharacteristic
220C2×C4C23×#12312yes—
221C2×C4C23×#12411yescharacteristic
222C8—24no—
223C8—44no—
224C22C23×#39411yescharacteristic
225C22C23×#45311yescharacteristic
226C22C23×#45412yes—
227C22C23×#45612yes—
228C22C23×#45611yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—81no—
234C4—81no—
235C4—82no—
236C4—82no—
237C4—161no—
238C2C23×#165711yescharacteristic
239C2C23×#166011yescharacteristic
240C2C23×#166312yes—
241C2C23×#203812yes—
242C2C23×#203911yescharacteristic
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
79. #10429C23direct (N × H)
169. C23#10429direct (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×#18472
C2×C23×#3302
C23×#12952
#1042923