Finite Group Databasebeta

← C103×#13668 #39918943

Subgroups — C103×#13668 #39918943

Order 26368.

284 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 74 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×#3414C211yesmaximal, characteristic
2C103×#2264C212yesmaximal, complemented
3C103×#2219C211yesmaximal, characteristic, complemented
4C103×#1418C212yesmaximal, complemented
5C103×#1400C211yesmaximal, characteristic, complemented
6C2×#135×C103—21no—
7#510×C103—22no—
8#509×C103—22no—
9#508×C103—21no—
10#508×C103C2212yes—
11C2×Q32×C103C2211yescharacteristic, complemented
12C2×M32×C103C2211yescharacteristic
13#467×C103—21no—
14Q64×C103—22no—
15SD64×C103—22no—
16M64×C103C2212yescomplemented
17#367×C103C2211yescharacteristic, complemented
18#358×C103—21no—
19C2×#41×C103—41no—
20#135×C103—22no—
21#135×C103—22no—
22#135×C103—41no—
23#135×C103—41no—
24C2×Q16×C103—21no—
25C2×Q16×C103—21no—
26C2×SD16×C103—41no—
27C2×D8×C103—21no—
28C22×C8×C103D411yescharacteristic
29C22⋊Q8×C103—41no—
30Q32×C103—21no—
31Q32×C103—22no—
32Q32×C103D412yes—
33SD32×C103—22no—
34SD32×C103—22no—
35D16×C103—21no—
36D16×C103D412yes—
37M32×C103—22no—
38C2×C16×C103D411yescharacteristic
39C2×C16×C103C2311yescharacteristic
40#107×C103—21no—
41#103×C103—41no—
42C32×C103—22no—
43#41×C103—42no—
44#41×C103—42no—
45#41×C103—81no—
46#41×C103—81no—
47C2×Q8×C103—41no—
48C2×Q8×C103—41no—
49C2×D4×C103—41no—
50C2×D4×C103—81no—
51C22×C4×C103—81no—
52C22×C4×C103D811yescharacteristic
53Q16×C103—22no—
54Q16×C103—41no—
55Q16×C103—41no—
56Q16×C103—41no—
57SD16×C103—42no—
58SD16×C103—42no—
59D8×C103—22no—
60D8×C103—41no—
61C2×C8×C103—21no—
62C2×C8×C103—21no—
63C2×C8×C103D811yescharacteristic
64C2×C8×C103C2×D411yescharacteristic
65C4⋊C4×C103—41no—
66C4⋊C4×C103—81no—
67C22⋊C4×C103—81no—
68C16×C103—21no—
69C16×C103C2×D412yes—
70C23×C103—81no—
71C23×C103D1611yescharacteristic
72Q8×C103—42no—
73Q8×C103—81no—
74Q8×C103—81no—
75Q8×C103—81no—
76D4×C103—42no—
77D4×C103—81no—
78D4×C103—82no—
79D4×C103—82no—
80C2×C4×C103—21no—
81C2×C4×C103—21no—
82C2×C4×C103—82no—
83C2×C4×C103—81no—
84C2×C4×C103—82no—
85C2×C4×C103—81no—
86C2×C4×C103—81no—
87C2×C4×C103D1611yescharacteristic
88C2×C4×C103C2×D811yescharacteristic
89C8×C103—21no—
90C8×C103#12011yescharacteristic
91C8×C103AGL(1,ℤ/8)11yescharacteristic
92C22×C103—21no—
93C22×C103—41no—
94C22×C103—82no—
95C22×C103—162no—
96C22×C103C2×D1611yescharacteristic
97C4×C103—21no—
98C4×C103—82no—
99C4×C103—161no—
100C4×C103—161no—
101C4×C103#44711yescharacteristic
102C4×C103#50911yescharacteristic
103#13668C10311yesmaximal, characteristic, direct product factor, Sylow
104C2×C103—21no—
105C2×C103—41no—
106C2×C103—162no—
107C2×C103#218411yescharacteristic
108#3414C2×C10311yescharacteristic
109#2264C2×C10312yescomplemented
110#2219C2×C10311yescharacteristic, complemented
111#1418C2×C10312yescomplemented
112#1400C2×C10311yescharacteristic, complemented
113C103#1366811yescharacteristic, direct product factor, Sylow
114C2×#135—21no—
115#510—22no—
116#509—22no—
117#508—21no—
118#508C22×C10312yes—
119C2×Q32C22×C10311yescharacteristic, complemented
120C2×M32C22×C10311yescharacteristic
121#467—21no—
122Q64—22no—
123SD64—22no—
124M64C22×C10312yescomplemented
125#367C22×C10311yescharacteristic, complemented
126#358—21no—
127C2×#41—41no—
128#135—22no—
129#135—22no—
130#135—41no—
131#135—41no—
132C2×Q16—21no—
133C2×Q16—21no—
134C2×SD16—41no—
135C2×D8—21no—
136C22×C8D4×C10311yescharacteristic
137C22⋊Q8—41no—
138Q32—21no—
139Q32—22no—
140Q32D4×C10312yes—
141SD32—22no—
142SD32—22no—
143D16—21no—
144D16D4×C10312yes—
145M32—22no—
146C2×C16D4×C10311yescharacteristic
147C2×C16C23×C10311yescharacteristic
148#107—21no—
149#103—41no—
150C32—22no—
151#41—42no—
152#41—42no—
153#41—81no—
154#41—81no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×D4—41no—
158C2×D4—81no—
159C22×C4—81no—
160C22×C4D8×C10311yescharacteristic
161Q16—22no—
162Q16—41no—
163Q16—41no—
164Q16—41no—
165SD16—42no—
166SD16—42no—
167D8—22no—
168D8—41no—
169C2×C8—21no—
170C2×C8—21no—
171C2×C8D8×C10311yescharacteristic
172C2×C8C2×D4×C10311yescharacteristic
173C4⋊C4—41no—
174C4⋊C4—81no—
175C22⋊C4—81no—
176C16—21no—
177C16C2×D4×C10312yes—
178C23—81no—
179C23D16×C10311yescharacteristic
180Q8—42no—
181Q8—81no—
182Q8—81no—
183Q8—81no—
184D4—42no—
185D4—81no—
186D4—82no—
187D4—82no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—82no—
191C2×C4—81no—
192C2×C4—82no—
193C2×C4—81no—
194C2×C4—81no—
195C2×C4D16×C10311yescharacteristic
196C2×C4C2×D8×C10311yescharacteristic
197C8—21no—
198C8#120×C10311yescharacteristic
199C8AGL(1,ℤ/8)×C10311yescharacteristic
200C22—21no—
201C22—41no—
202C22—82no—
203C22—162no—
204C22C2×D16×C10311yescharacteristic
205C4—21no—
206C4—82no—
207C4—161no—
208C4—161no—
209C4#447×C10311yescharacteristic
210C4#509×C10311yescharacteristic
211C2—21no—
212C2—41no—
213C2—162no—
214C2C103×#218411yescharacteristic
subgroupG/H
center, socleC2×C103#2184
commutator, Frattini, cosocleC2×C16C23×C103
prime radicalC103×#3414C2
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C103 ◁ C2×C4×C103 ◁ C22×C8×C103 ◁ C2×M32×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C103×#2264C2semidirect
3. C103×#2219C2semidirect
4. C103×#1418C2semidirect
5. C103×#1400C2semidirect
11. C2×Q32×C103C22semidirect
16. M64×C103C22semidirect
17. #367×C103C22semidirect
103. #13668C103direct (N × H)
109. #2264C2×C103semidirect
110. #2219C2×C103semidirect
111. #1418C2×C103semidirect
112. #1400C2×C103semidirect
113. C103#13668direct (N × H)
119. C2×Q32C22×C103semidirect
124. M64C22×C103semidirect
125. #367C22×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#34142
C103×#22642
C103×#22192
C103×#14182
C103×#14002
#13668103