Finite Group Databasebeta

← C103×#9068 #39914343

Subgroups — C103×#9068 #39914343

Order 26368.

404 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 126 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
1C103×#3160C211yesmaximal, characteristic
2C103×#2986C211yesmaximal, characteristic
3C103×#1526C211yesmaximal, characteristic
4C103×#1485C212yesmaximal
5C103×#1278C212yesmaximal
6#533×C103C2211yescharacteristic
7#533×C103C2211yescharacteristic
8#500×C103C412yes—
9#499×C103—22no—
10#498×C103C412yes—
11#446×C103—22no—
12C8×Q8×C103—22no—
13#433×C103—22no—
14#431×C103C2212yes—
15#427×C103—22no—
16C4×M16×C103C2212yes—
17C2×C4×C8×C103C2211yescharacteristic
18#330×C103—22no—
19Q8⋊C8×C103—22no—
20Q8⋊C8×C103—22no—
21C2×M16×C103—22no—
22C22×C8×C103—21no—
23C4⋊Q8×C103C2×C412yes—
24C4⋊Q8×C103C2×C412yes—
25#125×C103—21no—
26#125×C103D412yes—
27C22⋊Q8×C103—22no—
28C22⋊Q8×C103—22no—
29C4×Q8×C103—22no—
30C4×Q8×C103—22no—
31#117×C103—21no—
32#117×C103D412yes—
33C2×C42×C103C2311yescharacteristic
34#107×C103—24no—
35#106×C103—24no—
36C4⋊C8×C103—24no—
37C4⋊C8×C103D412yes—
38C4⋊C8×C103D412yes—
39C22⋊C8×C103—22no—
40#97×C103—22no—
41#97×C103—22no—
42C4×C8×C103—22no—
43C4×C8×C103—21no—
44C4×C8×C103—22no—
45C4×C8×C103—22no—
46C4×C8×C103C2×C411yescharacteristic
47C4×C8×C103C2×C411yescharacteristic
48C2×Q8×C103—22no—
49C2×Q8×C103—22no—
50C22×C4×C103C2×D411yescharacteristic
51C22×C4×C103#4112yes—
52M16×C103—24no—
53M16×C103—42no—
54C2×C8×C103—24no—
55C2×C8×C103—21no—
56C2×C8×C103—21no—
57C2×C8×C103—22no—
58C2×C8×C103—22no—
59C2×C8×C103—42no—
60C4⋊C4×C103—22no—
61C4⋊C4×C103—24no—
62C4⋊C4×C103—22no—
63C4⋊C4×C103—22no—
64C4⋊C4×C103—42no—
65C4⋊C4×C103C22⋊C414yes—
66C22⋊C4×C103—22no—
67C22⋊C4×C103—41no—
68C42×C103—22no—
69C42×C103—41no—
70C42×C103C22×C411yescharacteristic
71C42×C103C2×D411yescharacteristic
72C42×C103C2×D412yes—
73C23×C103#12311yescharacteristic
74Q8×C103—42no—
75Q8×C103—42no—
76Q8×C103—42no—
77Q8×C103—42no—
78C2×C4×C103—22no—
79C2×C4×C103—22no—
80C2×C4×C103—22no—
81C2×C4×C103—24no—
82C2×C4×C103—42no—
83C2×C4×C103C2×C22⋊C411yescharacteristic
84C2×C4×C103C4×D412yes—
85C2×C4×C103#12011yescharacteristic
86C2×C4×C103#12112yes—
87C8×C103—22no—
88C8×C103—22no—
89C8×C103—44no—
90C8×C103—42no—
91C8×C103—42no—
92C22×C103—22no—
93C22×C103—21no—
94C22×C103#38611yescharacteristic
95C4×C103—22no—
96C4×C103—21no—
97C4×C103—44no—
98C4×C103—82no—
99C4×C103#44312yes—
100C4×C103#44412yes—
101C4×C103#45612yes—
102#9068C10311yesmaximal, characteristic, direct product factor, Sylow
103C2×C103—41no—
104C2×C103#187612yes—
105C2×C103#188611yescharacteristic
106#3160C2×C10311yescharacteristic
107#2986C2×C10311yescharacteristic
108#1526C2×C10311yescharacteristic
109#1485C2×C10312yes—
110#1278C2×C10312yes—
111C103#906811yescharacteristic, direct product factor, Sylow
112#533C22×C10311yescharacteristic
113#533C22×C10311yescharacteristic
114#500C4×C10312yes—
115#499—22no—
116#498C4×C10312yes—
117#446—22no—
118C8×Q8—22no—
119#433—22no—
120#431C22×C10312yes—
121#427—22no—
122C4×M16C22×C10312yes—
123C2×C4×C8C22×C10311yescharacteristic
124#330—22no—
125Q8⋊C8—22no—
126Q8⋊C8—22no—
127C2×M16—22no—
128C22×C8—21no—
129C4⋊Q8C2×C4×C10312yes—
130C4⋊Q8C2×C4×C10312yes—
131#125—21no—
132#125D4×C10312yes—
133C22⋊Q8—22no—
134C22⋊Q8—22no—
135C4×Q8—22no—
136C4×Q8—22no—
137#117—21no—
138#117D4×C10312yes—
139C2×C42C23×C10311yescharacteristic
140#107—24no—
141#106—24no—
142C4⋊C8—24no—
143C4⋊C8D4×C10312yes—
144C4⋊C8D4×C10312yes—
145C22⋊C8—22no—
146#97—22no—
147#97—22no—
148C4×C8—22no—
149C4×C8—21no—
150C4×C8—22no—
151C4×C8—22no—
152C4×C8C2×C4×C10311yescharacteristic
153C4×C8C2×C4×C10311yescharacteristic
154C2×Q8—22no—
155C2×Q8—22no—
156C22×C4C2×D4×C10311yescharacteristic
157C22×C4#41×C10312yes—
158M16—24no—
159M16—42no—
160C2×C8—24no—
161C2×C8—21no—
162C2×C8—21no—
163C2×C8—22no—
164C2×C8—22no—
165C2×C8—42no—
166C4⋊C4—22no—
167C4⋊C4—24no—
168C4⋊C4—22no—
169C4⋊C4—22no—
170C4⋊C4—42no—
171C4⋊C4C22⋊C4×C10314yes—
172C22⋊C4—22no—
173C22⋊C4—41no—
174C42—22no—
175C42—41no—
176C42C22×C4×C10311yescharacteristic
177C42C2×D4×C10311yescharacteristic
178C42C2×D4×C10312yes—
179C23#123×C10311yescharacteristic
180Q8—42no—
181Q8—42no—
182Q8—42no—
183Q8—42no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—24no—
188C2×C4—42no—
189C2×C4C2×C22⋊C4×C10311yescharacteristic
190C2×C4C4×D4×C10312yes—
191C2×C4#120×C10311yescharacteristic
192C2×C4#121×C10312yes—
193C8—22no—
194C8—22no—
195C8—44no—
196C8—42no—
197C8—42no—
198C22—22no—
199C22—21no—
200C22#386×C10311yescharacteristic
201C4—22no—
202C4—21no—
203C4—44no—
204C4—82no—
205C4#443×C10312yes—
206C4#444×C10312yes—
207C4#456×C10312yes—
208C2—41no—
209C2C103×#187612yes—
210C2C103×#188611yescharacteristic
subgroupG/H
centerC2×C4×C103#120
commutatorC42C22×C4×C103
Frattini, cosocleC2×C42C23×C103
socleC22×C103#386
prime radicalC23×C103#123
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
102. #9068C103direct (N × H)
111. C103#9068direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#31602
C103×#29862
C103×#15262
C103×#14852
C103×#12782
#9068103