Finite Group Databasebeta

← C23×#7831 #19155457

Subgroups — C23×#7831 #19155457

Order 5888.

350 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2809C211yesmaximal, characteristic
2C23×#2100C212yesmaximal
3C23×#2095C211yesmaximal, characteristic
4C23×#1272C211yesmaximal, characteristic
5C23×#1271C212yesmaximal
6C2×C23×#107—21no—
7C2×C23×#103—21no—
8C23×#400—21no—
9C23×#398—22no—
10C23×#391—21no—
11C23×#391C2211yescharacteristic
12C23×#389C2212yes—
13C23×#387—22no—
14C23×#384C2211yescharacteristic
15C23×#340—22no—
16C23×#340—22no—
17C23×#336C2211yescharacteristic
18C23×#336C2212yes—
19C22×Q8×C23D411yescharacteristic
20C22×C8×C23—21no—
21C22×C8×C23—22no—
22C2×C4⋊C4×C23—22no—
23C2×C4⋊C4×C23—22no—
24C2×C4⋊C4×C23—21no—
25C2×C4⋊C4×C23—21no—
26C2×C4⋊C4×C23—21no—
27C2×C4⋊C4×C23D412yes—
28C2×C4⋊C4×C23D412yes—
29C2×C4⋊C4×C23D411yescharacteristic
30C2×C42×C23—21no—
31C2×C42×C23C2311yescharacteristic
32C23×#107—42no—
33C23×#103—42no—
34C23×#95—21no—
35C23×#95—22no—
36C23×#95—22no—
37C23×#95—22no—
38C23×#95—22no—
39C2×Q8×C23—21no—
40C2×Q8×C23—41no—
41C2×Q8×C23—41no—
42C2×Q8×C23Q1612yes—
43C22×C4×C23—21no—
44C22×C4×C23—22no—
45C22×C4×C23—22no—
46C22×C4×C23—21no—
47C22×C4×C23—41no—
48C22×C4×C23C2×D411yescharacteristic
49C22×C4×C23C2×D412yes—
50C2×C8×C23—22no—
51C2×C8×C23—41no—
52C2×C8×C23—41no—
53C2×C8×C23—42no—
54C2×C8×C23—42no—
55C2×C8×C23—42no—
56C4⋊C4×C23—22no—
57C4⋊C4×C23—22no—
58C4⋊C4×C23—41no—
59C4⋊C4×C23—42no—
60C4⋊C4×C23—41no—
61C4⋊C4×C23—41no—
62C4⋊C4×C23—44no—
63C4⋊C4×C23—42no—
64C4⋊C4×C23—42no—
65C4⋊C4×C23—81no—
66C4⋊C4×C23—81no—
67C42×C23—41no—
68C42×C23—81no—
69#7831C2311yesmaximal, characteristic, direct product factor, Sylow
70C23×C23#12011yescharacteristic
71Q8×C23—42no—
72Q8×C23—81no—
73C2×C4×C23—21no—
74C2×C4×C23—22no—
75C2×C4×C23—22no—
76C2×C4×C23—21no—
77C2×C4×C23—22no—
78C2×C4×C23—41no—
79C2×C4×C23—41no—
80C2×C4×C23—42no—
81C2×C4×C23—42no—
82C2×C4×C23—42no—
83C2×C4×C23—41no—
84C2×C4×C23—42no—
85C2×C4×C23—42no—
86C2×C4×C23—42no—
87C2×C4×C23—42no—
88C2×C4×C23—81no—
89C2×C4×C23—82no—
90C2×C4×C23C2×Q1611yescharacteristic
91C2×C4×C23#13512yes—
92C2×C4×C23#13711yescharacteristic
93C2×C4×C23#13712yes—
94C8×C23—42no—
95C8×C23—82no—
96#2809C2×C2311yescharacteristic
97#2100C2×C2312yes—
98#2095C2×C2311yescharacteristic
99#1272C2×C2311yescharacteristic
100#1271C2×C2312yes—
101C22×C23#45111yescharacteristic
102C22×C23#45212yes—
103C22×C23#45311yescharacteristic
104C22×C23#45412yes—
105C22×C23#45811yescharacteristic
106C4×C23—21no—
107C4×C23—21no—
108C4×C23—22no—
109C4×C23—22no—
110C4×C23—42no—
111C4×C23—82no—
112C4×C23—82no—
113C4×C23—81no—
114C4×C23—161no—
115C2×#107—21no—
116C2×#103—21no—
117#400—21no—
118#398—22no—
119#391—21no—
120#391C22×C2311yescharacteristic
121#389C22×C2312yes—
122#387—22no—
123#384C22×C2311yescharacteristic
124#340—22no—
125#340—22no—
126#336C22×C2311yescharacteristic
127#336C22×C2312yes—
128C2×C23#161411yescharacteristic
129C2×C23#161512yes—
130C2×C23#163411yescharacteristic
131C2×C23#163612yes—
132C2×C23#165711yescharacteristic
133C22×Q8D4×C2311yescharacteristic
134C22×C8—21no—
135C22×C8—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—21no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—21no—
141C2×C4⋊C4D4×C2312yes—
142C2×C4⋊C4D4×C2312yes—
143C2×C4⋊C4D4×C2311yescharacteristic
144C2×C42—21no—
145C2×C42C23×C2311yescharacteristic
146#107—42no—
147#103—42no—
148#95—21no—
149#95—22no—
150#95—22no—
151#95—22no—
152#95—22no—
153C23#783111yescharacteristic, direct product factor, Sylow
154C2×Q8—21no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8Q16×C2312yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—41no—
163C22×C4C2×D4×C2311yescharacteristic
164C22×C4C2×D4×C2312yes—
165C2×C8—22no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—42no—
169C2×C8—42no—
170C2×C8—42no—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—44no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—81no—
181C4⋊C4—81no—
182C42—41no—
183C42—81no—
184C23C23×#12011yescharacteristic
185Q8—42no—
186Q8—81no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—41no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—42no—
202C2×C4—81no—
203C2×C4—82no—
204C2×C4C2×Q16×C2311yescharacteristic
205C2×C4C23×#13512yes—
206C2×C4C23×#13711yescharacteristic
207C2×C4C23×#13712yes—
208C8—42no—
209C8—82no—
210C22C23×#45111yescharacteristic
211C22C23×#45212yes—
212C22C23×#45311yescharacteristic
213C22C23×#45412yes—
214C22C23×#45811yescharacteristic
215C4—21no—
216C4—21no—
217C4—22no—
218C4—22no—
219C4—42no—
220C4—82no—
221C4—81no—
222C4—82no—
223C4—161no—
224C2C23×#161411yescharacteristic
225C2C23×#161512yes—
226C2C23×#163411yescharacteristic
227C2C23×#163612yes—
228C2C23×#165711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C23#120
commutator, Frattini, cosocleC2×C42C23×C23
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C23 ◁ C2×C42×C23 ◁ G

Complements

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

NH ≅ G/Ntype
69. #7831C23direct (N × H)
153. C23#7831direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#28092
C23×#21002
C23×#20952
C23×#12722
C23×#12712
#783123