Finite Group Databasebeta

← C109×#3093 #28360347

Subgroups — C109×#3093 #28360347

Order 13952.

414 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 184 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
1#525×C109C211yesmaximal, characteristic
2C2×#117×C109C211yesmaximal, characteristic, complemented
3#485×C109C214yesmaximal, complemented
4#482×C109C214yesmaximal, complemented
5#428×C109C212yesmaximal, complemented
6#417×C109C212yesmaximal, complemented
7#407×C109C211yesmaximal, characteristic, complemented
8C2×#41×C109C2211yescharacteristic
9C23×C4×C109C2211yescharacteristic
10C2×M16×C109C2212yes—
11#123×C109—21no—
12C22⋊Q8×C109C2212yes—
13#121×C109C2212yes—
14#120×C109—21no—
15C4×D4×C109—22no—
16#117×C109—22no—
17#117×C109C2214yes—
18#117×C109C2211yescharacteristic
19C2×C4⋊C4×C109C2212yes—
20C2×C22⋊C4×C109—21no—
21C2×C42×C109—21no—
22#107×C109C2214yescomplemented
23#106×C109C2214yescomplemented
24#103×C109C2214yescomplemented
25#102×C109C2214yescomplemented
26C22⋊C8×C109C2214yes—
27C24×C109D411yescharacteristic
28#41×C109—24no—
29C2×Q8×C109C2311yescharacteristic
30C2×D4×C109—22no—
31C2×D4×C109—21no—
32C2×D4×C109C2311yescharacteristic
33C22×C4×C109—24no—
34C22×C4×C109—22no—
35C22×C4×C109—21no—
36C22×C4×C109D411yescharacteristic
37C22×C4×C109D412yes—
38C22×C4×C109C2312yes—
39C22×C4×C109C2311yescharacteristic
40M16×C109—24no—
41C2×C8×C109C2314yes—
42C4⋊C4×C109—22no—
43C4⋊C4×C109—22no—
44C4⋊C4×C109C2314yes—
45C4⋊C4×C109C2312yes—
46C22⋊C4×C109—24no—
47C22⋊C4×C109—21no—
48C22⋊C4×C109—22no—
49C22⋊C4×C109—22no—
50C42×C109—24no—
51C42×C109—21no—
52C23×C109—22no—
53C23×C109—21no—
54C23×C109—42no—
55C23×C109C2×D412yes—
56C23×C109C2×D411yescharacteristic
57Q8×C109—22no—
58D4×C109—22no—
59D4×C109—44no—
60D4×C109—42no—
61C2×C4×C109—22no—
62C2×C4×C109—24no—
63C2×C4×C109—24no—
64C2×C4×C109—24no—
65C2×C4×C109—22no—
66C2×C4×C109—21no—
67C2×C4×C109—44no—
68C2×C4×C109—42no—
69C2×C4×C109C2×D412yes—
70C2×C4×C109C2×D411yescharacteristic
71C2×C4×C109#4114yes—
72C2×C4×C109C2411yescharacteristic
73C8×C109—24no—
74C22×C109—22no—
75C22×C109—22no—
76C22×C109—22no—
77C22×C109—22no—
78C22×C109—44no—
79C22×C109—41no—
80C22×C109—42no—
81C22×C109#12312yes—
82C22×C109C22×D411yescharacteristic
83C4×C109—22no—
84C4×C109—41no—
85C4×C109—44no—
86C4×C109—42no—
87C4×C109#12312yes—
88C4×C109C2×#4112yes—
89C2×C109—22no—
90C2×C109—42no—
91C2×C109—81no—
92C2×C109C2×#12311yescharacteristic
93C2×C109#57512yes—
94#3093C10911yesmaximal, characteristic, direct product factor, Sylow
95C109#309311yescharacteristic, direct product factor, Sylow
96#525C2×C10911yescharacteristic
97C2×#117C2×C10911yescharacteristic, complemented
98#485C2×C10914yescomplemented
99#482C2×C10914yescomplemented
100#428C2×C10912yescomplemented
101#417C2×C10912yescomplemented
102#407C2×C10911yescharacteristic, complemented
103C2×#41C22×C10911yescharacteristic
104C23×C4C22×C10911yescharacteristic
105C2×M16C22×C10912yes—
106#123—21no—
107C22⋊Q8C22×C10912yes—
108#121C22×C10912yes—
109#120—21no—
110C4×D4—22no—
111#117—22no—
112#117C22×C10914yes—
113#117C22×C10911yescharacteristic
114C2×C4⋊C4C22×C10912yes—
115C2×C22⋊C4—21no—
116C2×C42—21no—
117#107C22×C10914yescomplemented
118#106C22×C10914yescomplemented
119#103C22×C10914yescomplemented
120#102C22×C10914yescomplemented
121C22⋊C8C22×C10914yes—
122C24D4×C10911yescharacteristic
123#41—24no—
124C2×Q8C23×C10911yescharacteristic
125C2×D4—22no—
126C2×D4—21no—
127C2×D4C23×C10911yescharacteristic
128C22×C4—24no—
129C22×C4—22no—
130C22×C4—21no—
131C22×C4D4×C10911yescharacteristic
132C22×C4D4×C10912yes—
133C22×C4C23×C10912yes—
134C22×C4C23×C10911yescharacteristic
135M16—24no—
136C2×C8C23×C10914yes—
137C4⋊C4—22no—
138C4⋊C4—22no—
139C4⋊C4C23×C10914yes—
140C4⋊C4C23×C10912yes—
141C22⋊C4—24no—
142C22⋊C4—21no—
143C22⋊C4—22no—
144C22⋊C4—22no—
145C42—24no—
146C42—21no—
147C23—22no—
148C23—21no—
149C23—42no—
150C23C2×D4×C10912yes—
151C23C2×D4×C10911yescharacteristic
152Q8—22no—
153D4—22no—
154D4—44no—
155D4—42no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—22no—
161C2×C4—21no—
162C2×C4—44no—
163C2×C4—42no—
164C2×C4C2×D4×C10912yes—
165C2×C4C2×D4×C10911yescharacteristic
166C2×C4#41×C10914yes—
167C2×C4C24×C10911yescharacteristic
168C8—24no—
169C22—22no—
170C22—22no—
171C22—22no—
172C22—22no—
173C22—44no—
174C22—41no—
175C22—42no—
176C22#123×C10912yes—
177C22C22×D4×C10911yescharacteristic
178C4—22no—
179C4—41no—
180C4—44no—
181C4—42no—
182C4#123×C10912yes—
183C4C2×#41×C10912yes—
184C2—22no—
185C2—42no—
186C2—81no—
187C2C2×#123×C10911yescharacteristic
188C2#575×C10912yes—
subgroupG/H
center, socleC22×C109C22×D4
commutator, Frattini, cosocleC2×C4C24×C109
prime radical#525×C109C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ C23×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#117×C109C2semidirect
3. #485×C109C2semidirect
4. #482×C109C2semidirect
5. #428×C109C2semidirect
6. #417×C109C2semidirect
7. #407×C109C2semidirect
22. #107×C109C22semidirect
23. #106×C109C22semidirect
24. #103×C109C22semidirect
25. #102×C109C22semidirect
94. #3093C109direct (N × H)
95. C109#3093direct (N × H)
97. C2×#117C2×C109semidirect
98. #485C2×C109semidirect
99. #482C2×C109semidirect
100. #428C2×C109semidirect
101. #417C2×C109semidirect
102. #407C2×C109semidirect
117. #107C22×C109semidirect
118. #106C22×C109semidirect
119. #103C22×C109semidirect
120. #102C22×C109semidirect

Maximal subgroups

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

subgroupindex
#525×C1092
C2×#117×C1092
#485×C1092
#482×C1092
#428×C1092
#417×C1092
#407×C1092
#3093109