Finite Group Databasebeta

← C41×#1520 #19105300

Subgroups — C41×#1520 #19105300

Order 5248.

288 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 108 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×C22⋊Q8×C41C211yesmaximal, characteristic
2C2×C22⋊C8×C41C211yesmaximal, characteristic
3C41×#380C211yesmaximal, characteristic
4C41×#328C214yesmaximal, complemented
5C22×Q8×C41C411yescharacteristic, complemented
6C23×C4×C41C2211yescharacteristic
7C22×C8×C41—21no—
8C22⋊Q8×C41—21no—
9C22⋊Q8×C41—21no—
10C22⋊Q8×C41C412yescomplemented
11C22⋊Q8×C41C2212yes—
12C2×C4⋊C4×C41—21no—
13C2×C4⋊C4×C41—21no—
14C2×C4⋊C4×C41C411yescharacteristic, complemented
15C2×C22⋊C4×C41—21no—
16C2×C22⋊C4×C41—21no—
17C22⋊C8×C41—21no—
18C22⋊C8×C41C2212yes—
19#95×C41C2212yes—
20C24×C41D411yescharacteristic
21C2×Q8×C41—21no—
22C2×Q8×C41—42no—
23C2×Q8×C41C2×C412yes—
24C22×C4×C41—21no—
25C22×C4×C41—21no—
26C22×C4×C41—22no—
27C22×C4×C41—42no—
28C22×C4×C41C2×C411yescharacteristic
29C22×C4×C41C2×C411yescharacteristic
30C22×C4×C41D411yescharacteristic
31C22×C4×C41D411yescharacteristic
32C22×C4×C41D411yescharacteristic
33C22×C4×C41C2311yescharacteristic
34C2×C8×C41—22no—
35C2×C8×C41—42no—
36C4⋊C4×C41—22no—
37C4⋊C4×C41—21no—
38C4⋊C4×C41—22no—
39C4⋊C4×C41—42no—
40C4⋊C4×C41C2×C412yes—
41C22⋊C4×C41—22no—
42C22⋊C4×C41—22no—
43C22⋊C4×C41—42no—
44C23×C41—41no—
45C23×C41—41no—
46C23×C41C22⋊C411yescharacteristic
47C23×C41C22⋊C411yescharacteristic
48C23×C41SD1612yes—
49C23×C41Q1612yes—
50C23×C41C2×D411yescharacteristic
51Q8×C41—42no—
52Q8×C41—42no—
53C2×C4×C41—22no—
54C2×C4×C41—22no—
55C2×C4×C41—22no—
56C2×C4×C41—22no—
57C2×C4×C41—22no—
58C2×C4×C41—41no—
59C2×C4×C41—41no—
60C2×C4×C41—41no—
61C2×C4×C41—42no—
62C2×C4×C41—42no—
63C2×C4×C41—42no—
64C2×C4×C41—42no—
65C2×C4×C41—42no—
66C2×C4×C41C22⋊C411yescharacteristic
67C2×C4×C41C22⋊C411yescharacteristic
68C2×C4×C41C22×C411yescharacteristic
69C2×C4×C41C2×D411yescharacteristic
70C8×C41—42no—
71C22×C41—21no—
72C22×C41—21no—
73C22×C41—21no—
74C22×C41—21no—
75C22×C41—21no—
76C22×C41—21no—
77C22×C41—42no—
78C22×C41—42no—
79C22×C41#10312yes—
80C22×C41#10312yes—
81C22×C41C2×C22⋊C411yescharacteristic
82C22×C41C2×SD1611yescharacteristic
83C22×C41C2×Q1611yescharacteristic
84C4×C41—21no—
85C4×C41—21no—
86C4×C41—21no—
87C4×C41—42no—
88C4×C41—42no—
89C4×C41—82no—
90C4×C41#9912yes—
91#1520C4111yesmaximal, characteristic, direct product factor, Sylow
92C2×C41—21no—
93C2×C41—22no—
94C2×C41—22no—
95C2×C41—21no—
96C2×C41C2×#9911yescharacteristic
97C2×C41C2×#10311yescharacteristic
98C2×C41#42111yescharacteristic
99C2×C22⋊Q8C2×C4111yescharacteristic
100C2×C22⋊C8C2×C4111yescharacteristic
101#380C2×C4111yescharacteristic
102#328C2×C4114yescomplemented
103C41#152011yescharacteristic, direct product factor, Sylow
104C22×Q8C4×C4111yescharacteristic, complemented
105C23×C4C22×C4111yescharacteristic
106C22×C8—21no—
107C22⋊Q8—21no—
108C22⋊Q8—21no—
109C22⋊Q8C4×C4112yescomplemented
110C22⋊Q8C22×C4112yes—
111C2×C4⋊C4—21no—
112C2×C4⋊C4—21no—
113C2×C4⋊C4C4×C4111yescharacteristic, complemented
114C2×C22⋊C4—21no—
115C2×C22⋊C4—21no—
116C22⋊C8—21no—
117C22⋊C8C22×C4112yes—
118#95C22×C4112yes—
119C24D4×C4111yescharacteristic
120C2×Q8—21no—
121C2×Q8—42no—
122C2×Q8C2×C4×C4112yes—
123C22×C4—21no—
124C22×C4—21no—
125C22×C4—22no—
126C22×C4—42no—
127C22×C4C2×C4×C4111yescharacteristic
128C22×C4C2×C4×C4111yescharacteristic
129C22×C4D4×C4111yescharacteristic
130C22×C4D4×C4111yescharacteristic
131C22×C4D4×C4111yescharacteristic
132C22×C4C23×C4111yescharacteristic
133C2×C8—22no—
134C2×C8—42no—
135C4⋊C4—22no—
136C4⋊C4—21no—
137C4⋊C4—22no—
138C4⋊C4—42no—
139C4⋊C4C2×C4×C4112yes—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4—42no—
143C23—41no—
144C23—41no—
145C23C22⋊C4×C4111yescharacteristic
146C23C22⋊C4×C4111yescharacteristic
147C23SD16×C4112yes—
148C23Q16×C4112yes—
149C23C2×D4×C4111yescharacteristic
150Q8—42no—
151Q8—42no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4C22⋊C4×C4111yescharacteristic
166C2×C4C22⋊C4×C4111yescharacteristic
167C2×C4C22×C4×C4111yescharacteristic
168C2×C4C2×D4×C4111yescharacteristic
169C8—42no—
170C22—21no—
171C22—21no—
172C22—21no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—42no—
177C22—42no—
178C22#103×C4112yes—
179C22#103×C4112yes—
180C22C2×C22⋊C4×C4111yescharacteristic
181C22C2×SD16×C4111yescharacteristic
182C22C2×Q16×C4111yescharacteristic
183C4—21no—
184C4—21no—
185C4—21no—
186C4—42no—
187C4—42no—
188C4—82no—
189C4#99×C4112yes—
190C2—21no—
191C2—22no—
192C2—22no—
193C2—21no—
194C2C2×#99×C4111yescharacteristic
195C2C2×#103×C4111yescharacteristic
196C2C41×#42111yescharacteristic
subgroupG/H
center, socleC22×C41C2×C22⋊C4
commutatorC2×C4C22×C4×C41
Frattini, cosocleC22×C4C23×C41
prime radicalC24×C41D4
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C41 ◁ C23×C4×C41 ◁ G

Complements

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

NH ≅ G/Ntype
4. C41×#328C2semidirect
5. C22×Q8×C41C4semidirect
10. C22⋊Q8×C41C4semidirect
14. C2×C4⋊C4×C41C4semidirect
91. #1520C41direct (N × H)
102. #328C2×C41semidirect
103. C41#1520direct (N × H)
104. C22×Q8C4×C41semidirect
109. C22⋊Q8C4×C41semidirect
113. C2×C4⋊C4C4×C41semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊Q8×C412
C2×C22⋊C8×C412
C41×#3802
C41×#3282
#152041