Finite Group Databasebeta

← C103×#7376 #39912651

Subgroups — C103×#7376 #39912651

Order 26368.

202 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 50 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×#1857C211yesmaximal, characteristic
2C103×#1319C211yesmaximal, characteristic
3C103×#1272C211yesmaximal, characteristic
4#519×C103C411yescharacteristic
5#428×C103—21no—
6C2×#101×C103C411yescharacteristic
7#391×C103C2211yescharacteristic
8#339×C103—21no—
9#336×C103—21no—
10#324×C103—21no—
11C22×Q8×C103C2×C411yescharacteristic
12C2×M16×C103—21no—
13C22×C8×C103—41no—
14C4×Q8×C103—41no—
15C4×Q8×C103—41no—
16#117×C103—21no—
17#117×C103—41no—
18C2×C4⋊C4×C103D411yescharacteristic
19C2×C42×C103D411yescharacteristic
20#107×C103—41no—
21#106×C103—41no—
22#101×C103—21no—
23#101×C103C812yescomplemented
24C22⋊C8×C103—41no—
25#95×C103—41no—
26C2×Q8×C103—21no—
27C2×Q8×C103—41no—
28C2×Q8×C103—41no—
29C2×Q8×C103C2×C811yescharacteristic
30C2×Q8×C103M1611yescharacteristic
31C22×C4×C103—21no—
32C22×C4×C103—21no—
33C22×C4×C103—21no—
34C22×C4×C103C22⋊C411yescharacteristic
35M16×C103—22no—
36M16×C103—41no—
37C2×C8×C103—41no—
38C2×C8×C103—42no—
39C2×C8×C103—81no—
40C2×C8×C103—81no—
41C2×C8×C103—81no—
42C4⋊C4×C103—21no—
43C4⋊C4×C103—21no—
44C4⋊C4×C103—41no—
45C4⋊C4×C103—41no—
46C4⋊C4×C103—41no—
47C22⋊C4×C103—41no—
48C42×C103—41no—
49C42×C103—41no—
50C42×C103—42no—
51C23×C103#9911yescharacteristic
52Q8×C103—41no—
53Q8×C103—41no—
54Q8×C103—42no—
55C2×C4×C103—21no—
56C2×C4×C103—21no—
57C2×C4×C103—21no—
58C2×C4×C103—21no—
59C2×C4×C103—21no—
60C2×C4×C103—21no—
61C2×C4×C103—41no—
62C2×C4×C103—41no—
63C2×C4×C103—41no—
64C2×C4×C103—41no—
65C2×C4×C103—41no—
66C2×C4×C103—41no—
67C2×C4×C103—41no—
68C2×C4×C103—81no—
69C2×C4×C103C22⋊C811yescharacteristic
70C2×C4×C103#10111yescharacteristic
71C8×C103—42no—
72C8×C103—82no—
73C8×C103—161no—
74C22×C103—21no—
75C22×C103—21no—
76C22×C103#32411yescharacteristic
77C22×C103AΣL(1,𝔽16)11yescharacteristic
78C22×C103#35211yescharacteristic
79C4×C103—21no—
80C4×C103—21no—
81C4×C103—41no—
82C4×C103—41no—
83C4×C103—41no—
84C4×C103—41no—
85C4×C103—81no—
86C4×C103—81no—
87C4×C103—81no—
88#7376C10311yesmaximal, characteristic, direct product factor, Sylow
89C2×C103—21no—
90C2×C103—21no—
91C2×C103#132611yescharacteristic
92C2×C103#140411yescharacteristic
93C2×C103#140511yescharacteristic
94#1857C2×C10311yescharacteristic
95#1319C2×C10311yescharacteristic
96#1272C2×C10311yescharacteristic
97C103#737611yescharacteristic, direct product factor, Sylow
98#519C4×C10311yescharacteristic
99#428—21no—
100C2×#101C4×C10311yescharacteristic
101#391C22×C10311yescharacteristic
102#339—21no—
103#336—21no—
104#324—21no—
105C22×Q8C2×C4×C10311yescharacteristic
106C2×M16—21no—
107C22×C8—41no—
108C4×Q8—41no—
109C4×Q8—41no—
110#117—21no—
111#117—41no—
112C2×C4⋊C4D4×C10311yescharacteristic
113C2×C42D4×C10311yescharacteristic
114#107—41no—
115#106—41no—
116#101—21no—
117#101C8×C10312yescomplemented
118C22⋊C8—41no—
119#95—41no—
120C2×Q8—21no—
121C2×Q8—41no—
122C2×Q8—41no—
123C2×Q8C2×C8×C10311yescharacteristic
124C2×Q8M16×C10311yescharacteristic
125C22×C4—21no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4C22⋊C4×C10311yescharacteristic
129M16—22no—
130M16—41no—
131C2×C8—41no—
132C2×C8—42no—
133C2×C8—81no—
134C2×C8—81no—
135C2×C8—81no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—41no—
139C4⋊C4—41no—
140C4⋊C4—41no—
141C22⋊C4—41no—
142C42—41no—
143C42—41no—
144C42—42no—
145C23#99×C10311yescharacteristic
146Q8—41no—
147Q8—41no—
148Q8—42no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—81no—
163C2×C4C22⋊C8×C10311yescharacteristic
164C2×C4#101×C10311yescharacteristic
165C8—42no—
166C8—82no—
167C8—161no—
168C22—21no—
169C22—21no—
170C22#324×C10311yescharacteristic
171C22AΣL(1,𝔽16)×C10311yescharacteristic
172C22#352×C10311yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—41no—
178C4—41no—
179C4—81no—
180C4—81no—
181C4—81no—
182C2—21no—
183C2—21no—
184C2C103×#132611yescharacteristic
185C2C103×#140411yescharacteristic
186C2C103×#140511yescharacteristic
subgroupG/H
center, socleC22×C103AΣL(1,𝔽16)
commutatorC2×Q8C2×C8×C103
Frattini, cosocle#391C22×C103
prime radicalC23×C103#99
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C103 ◁ C22×C4×C103 ◁ #391×C103 ◁ G

Complements

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

NH ≅ G/Ntype
23. #101×C103C8semidirect
88. #7376C103direct (N × H)
97. C103#7376direct (N × H)
117. #101C8×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#18572
C103×#13192
C103×#12722
#7376103