Finite Group Databasebeta

← C103×#7483 #39912758

Subgroups — C103×#7483 #39912758

Order 26368.

262 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 66 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×#356×C103C211yesmaximal, characteristic
2C103×#1886C211yesmaximal, characteristic
3C103×#1558C211yesmaximal, characteristic
4C2×C4⋊Q8×C103C2211yescharacteristic
5#519×C103C411yescharacteristic
6#432×C103—21no—
7#419×C103—21no—
8C2×#101×C103—21no—
9C2×#101×C103C411yescharacteristic
10#356×C103—21no—
11#356×C103C412yescomplemented
12#339×C103—21no—
13#333×C103—21no—
14#333×C103C412yescomplemented
15C22×Q8×C103C2×C411yescharacteristic
16C22×Q8×C103D411yescharacteristic
17C2×M16×C103—21no—
18C2×M16×C103—41no—
19C4⋊Q8×C103—41no—
20C4⋊Q8×C103C2×C411yescharacteristic
21C4⋊Q8×C103C2×C411yescharacteristic
22C4⋊Q8×C103D411yescharacteristic
23C4⋊Q8×C103Q811yescharacteristic
24C4×Q8×C103—42no—
25#117×C103—21no—
26#117×C103—41no—
27C2×C4⋊C4×C103—41no—
28C2×C42×C103D411yescharacteristic
29C4⋊C8×C103—22no—
30#103×C103—42no—
31#101×C103—22no—
32#101×C103—41no—
33#101×C103—41no—
34C22⋊C8×C103—41no—
35#97×C103—41no—
36C2×Q8×C103—21no—
37C2×Q8×C103—21no—
38C2×Q8×C103—41no—
39C2×Q8×C103—41no—
40C2×Q8×C103—41no—
41C2×Q8×C103—41no—
42C2×Q8×C103C4211yescharacteristic
43C2×Q8×C103C22⋊C411yescharacteristic
44C2×Q8×C103C4⋊C411yescharacteristic
45C2×Q8×C103C4⋊C411yescharacteristic
46C22×C4×C103—21no—
47C22×C4×C103—21no—
48C22×C4×C103—21no—
49C22×C4×C103C22⋊C411yescharacteristic
50M16×C103—42no—
51M16×C103—41no—
52M16×C103—41no—
53M16×C103—81no—
54C2×C8×C103—42no—
55C2×C8×C103—41no—
56C2×C8×C103—81no—
57C4⋊C4×C103—22no—
58C4⋊C4×C103—41no—
59C4⋊C4×C103—41no—
60C4⋊C4×C103—41no—
61C4⋊C4×C103—41no—
62C4⋊C4×C103—42no—
63C22⋊C4×C103—41no—
64C42×C103—21no—
65C42×C103—41no—
66C42×C103—42no—
67C42×C103C22⋊C411yescharacteristic
68C42×C103C4⋊C411yescharacteristic
69C23×C103#9911yescharacteristic
70Q8×C103—41no—
71Q8×C103—41no—
72Q8×C103—41no—
73Q8×C103—41no—
74Q8×C103—42no—
75Q8×C103—81no—
76C2×C4×C103—21no—
77C2×C4×C103—21no—
78C2×C4×C103—21no—
79C2×C4×C103—21no—
80C2×C4×C103—21no—
81C2×C4×C103—21no—
82C2×C4×C103—21no—
83C2×C4×C103—21no—
84C2×C4×C103—42no—
85C2×C4×C103—41no—
86C2×C4×C103—41no—
87C2×C4×C103—41no—
88C2×C4×C103—41no—
89C2×C4×C103—42no—
90C2×C4×C103#9511yescharacteristic
91C2×C4×C103#9911yescharacteristic
92C8×C103—82no—
93C8×C103—81no—
94C8×C103—82no—
95C22×C103—41no—
96C22×C103#34211yescharacteristic
97C22×C103AΣL(1,𝔽16)11yescharacteristic
98C22×C103#35211yescharacteristic
99C4×C103—22no—
100C4×C103—21no—
101C4×C103—21no—
102C4×C103—41no—
103C4×C103—41no—
104C4×C103—41no—
105C4×C103—41no—
106C4×C103—41no—
107C4×C103—82no—
108#7483C10311yesmaximal, characteristic, direct product factor, Sylow
109C2×C103—21no—
110C2×C103—21no—
111C2×C103—21no—
112C2×C103#139011yescharacteristic
113C2×#356C2×C10311yescharacteristic
114#1886C2×C10311yescharacteristic
115#1558C2×C10311yescharacteristic
116C103#748311yescharacteristic, direct product factor, Sylow
117C2×C4⋊Q8C22×C10311yescharacteristic
118#519C4×C10311yescharacteristic
119#432—21no—
120#419—21no—
121C2×#101—21no—
122C2×#101C4×C10311yescharacteristic
123#356—21no—
124#356C4×C10312yescomplemented
125#339—21no—
126#333—21no—
127#333C4×C10312yescomplemented
128C22×Q8C2×C4×C10311yescharacteristic
129C22×Q8D4×C10311yescharacteristic
130C2×M16—21no—
131C2×M16—41no—
132C4⋊Q8—41no—
133C4⋊Q8C2×C4×C10311yescharacteristic
134C4⋊Q8C2×C4×C10311yescharacteristic
135C4⋊Q8D4×C10311yescharacteristic
136C4⋊Q8Q8×C10311yescharacteristic
137C4×Q8—42no—
138#117—21no—
139#117—41no—
140C2×C4⋊C4—41no—
141C2×C42D4×C10311yescharacteristic
142C4⋊C8—22no—
143#103—42no—
144#101—22no—
145#101—41no—
146#101—41no—
147C22⋊C8—41no—
148#97—41no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—41no—
152C2×Q8—41no—
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8C42×C10311yescharacteristic
156C2×Q8C22⋊C4×C10311yescharacteristic
157C2×Q8C4⋊C4×C10311yescharacteristic
158C2×Q8C4⋊C4×C10311yescharacteristic
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—21no—
162C22×C4C22⋊C4×C10311yescharacteristic
163M16—42no—
164M16—41no—
165M16—41no—
166M16—81no—
167C2×C8—42no—
168C2×C8—41no—
169C2×C8—81no—
170C4⋊C4—22no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—42no—
176C22⋊C4—41no—
177C42—21no—
178C42—41no—
179C42—42no—
180C42C22⋊C4×C10311yescharacteristic
181C42C4⋊C4×C10311yescharacteristic
182C23#99×C10311yescharacteristic
183Q8—41no—
184Q8—41no—
185Q8—41no—
186Q8—41no—
187Q8—42no—
188Q8—81no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—21no—
197C2×C4—42no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—42no—
203C2×C4#95×C10311yescharacteristic
204C2×C4#99×C10311yescharacteristic
205C8—81no—
206C8—82no—
207C8—82no—
208C22—41no—
209C22#342×C10311yescharacteristic
210C22AΣL(1,𝔽16)×C10311yescharacteristic
211C22#352×C10311yescharacteristic
212C4—22no—
213C4—21no—
214C4—21no—
215C4—41no—
216C4—41no—
217C4—41no—
218C4—41no—
219C4—41no—
220C4—82no—
221C2—21no—
222C2—21no—
223C2—21no—
224C2C103×#139011yescharacteristic
subgroupG/H
center, socleC2×C103#1390
commutatorC2×Q8C42×C103
Frattini, cosocleC2×C4⋊Q8C22×C103
prime radicalC23×C103#99
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C103 ◁ C23×C103 ◁ C22×C4×C103 ◁ C2×C4⋊Q8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
11. #356×C103C4semidirect
14. #333×C103C4semidirect
108. #7483C103direct (N × H)
116. C103#7483direct (N × H)
124. #356C4×C103semidirect
127. #333C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#356×C1032
C103×#18862
C103×#15582
#7483103