Finite Group Databasebeta

← C109×#10372 #42128366

Subgroups — C109×#10372 #42128366

Order 27904.

402 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C109×#2402C211yesmaximal, characteristic, complemented
2C109×#1963C211yesmaximal, characteristic
3C109×#1502C212yesmaximal
4C109×#1303C212yesmaximal, complemented
5C109×#1274C211yesmaximal, characteristic, complemented
6#532×C109C2211yescharacteristic
7#431×C109C2212yes—
8#423×C109C2211yescharacteristic
9C2×#104×C109—22no—
10#400×C109—22no—
11#398×C109—22no—
12C4×C4⋊C4×C109—22no—
13C4×C4⋊C4×C109C2212yes—
14#376×C109C2211yescharacteristic
15#327×C109—22no—
16#327×C109—22no—
17C2×#41×C109—21no—
18C2×M16×C109—21no—
19C4⋊Q8×C109Q811yescharacteristic
20#127×C109Q811yescharacteristic
21#124×C109—21no—
22#121×C109—22no—
23C4×D4×C109—22no—
24C2×C4⋊C4×C109—22no—
25C2×C4⋊C4×C109—22no—
26C2×C4⋊C4×C109—22no—
27C2×C42×C109—22no—
28C2×C42×C109D412yes—
29C2×C42×C109C2311yescharacteristic
30C4⋊C8×C109—22no—
31C4⋊C8×C109—22no—
32#104×C109—44no—
33C22⋊C8×C109—22no—
34C4×C8×C109—22no—
35#95×C109—22no—
36#95×C109—22no—
37#95×C109—22no—
38#95×C109D412yes—
39#95×C109D412yes—
40#41×C109—42no—
41#41×C109—42no—
42C2×Q8×C109—21no—
43C2×D4×C109—21no—
44C2×D4×C109—22no—
45C2×D4×C109—41no—
46C22×C4×C109—22no—
47C22×C4×C109—22no—
48C22×C4×C109—22no—
49C22×C4×C109—41no—
50C22×C4×C109C2×D412yes—
51C22×C4×C109C2×D411yescharacteristic
52M16×C109—42no—
53C2×C8×C109—42no—
54C2×C8×C109—41no—
55C4⋊C4×C109—22no—
56C4⋊C4×C109—44no—
57C4⋊C4×C109—44no—
58C4⋊C4×C109—44no—
59C22⋊C4×C109—42no—
60C42×C109—22no—
61C42×C109—22no—
62C42×C109—42no—
63C42×C109—42no—
64C42×C109C2×Q811yescharacteristic
65C42×C109#4111yescharacteristic
66C42×C109#4112yes—
67C23×C109—41no—
68C23×C109#12011yescharacteristic
69Q8×C109—42no—
70D4×C109—42no—
71D4×C109—82no—
72D4×C109—82no—
73C2×C4×C109—24no—
74C2×C4×C109—42no—
75C2×C4×C109—42no—
76C2×C4×C109—42no—
77C2×C4×C109—42no—
78C2×C4×C109—42no—
79C2×C4×C109—42no—
80C2×C4×C109—42no—
81C2×C4×C109—41no—
82C2×C4×C109—42no—
83C2×C4×C109—42no—
84C2×C4×C109—81no—
85C2×C4×C109—81no—
86C2×C4×C109C22⋊Q812yes—
87C2×C4×C109C22⋊Q811yescharacteristic
88C2×C4×C109#12412yes—
89C2×C4×C109#12411yescharacteristic
90C2×C4×C109#13512yes—
91C2×C4×C109AGL(1,ℤ/8)12yes—
92C8×C109—82no—
93C8×C109—81no—
94C22×C109—22no—
95C22×C109—81no—
96C22×C109—82no—
97C22×C109#39311yescharacteristic
98C22×C109#44912yes—
99C4×C109—22no—
100C4×C109—22no—
101C4×C109—44no—
102C4×C109—82no—
103C4×C109—82no—
104C4×C109—81no—
105C4×C109#47812yes—
106C4×C109#48811yescharacteristic
107C4×C109#49011yescharacteristic
108#10372C10911yesmaximal, characteristic, direct product factor, Sylow
109C2×C109—22no—
110C2×C109—161no—
111C2×C109#202511yescharacteristic
112C2×C109#203112yes—
113#2402C2×C10911yescharacteristic, complemented
114#1963C2×C10911yescharacteristic
115#1502C2×C10912yes—
116#1303C2×C10912yescomplemented
117#1274C2×C10911yescharacteristic, complemented
118C109#1037211yescharacteristic, direct product factor, Sylow
119#532C22×C10911yescharacteristic
120#431C22×C10912yes—
121#423C22×C10911yescharacteristic
122C2×#104—22no—
123#400—22no—
124#398—22no—
125C4×C4⋊C4—22no—
126C4×C4⋊C4C22×C10912yes—
127#376C22×C10911yescharacteristic
128#327—22no—
129#327—22no—
130C2×#41—21no—
131C2×M16—21no—
132C4⋊Q8Q8×C10911yescharacteristic
133#127Q8×C10911yescharacteristic
134#124—21no—
135#121—22no—
136C4×D4—22no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—22no—
140C2×C42—22no—
141C2×C42D4×C10912yes—
142C2×C42C23×C10911yescharacteristic
143C4⋊C8—22no—
144C4⋊C8—22no—
145#104—44no—
146C22⋊C8—22no—
147C4×C8—22no—
148#95—22no—
149#95—22no—
150#95—22no—
151#95D4×C10912yes—
152#95D4×C10912yes—
153#41—42no—
154#41—42no—
155C2×Q8—21no—
156C2×D4—21no—
157C2×D4—22no—
158C2×D4—41no—
159C22×C4—22no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—41no—
163C22×C4C2×D4×C10912yes—
164C22×C4C2×D4×C10911yescharacteristic
165M16—42no—
166C2×C8—42no—
167C2×C8—41no—
168C4⋊C4—22no—
169C4⋊C4—44no—
170C4⋊C4—44no—
171C4⋊C4—44no—
172C22⋊C4—42no—
173C42—22no—
174C42—22no—
175C42—42no—
176C42—42no—
177C42C2×Q8×C10911yescharacteristic
178C42#41×C10912yes—
179C42#41×C10911yescharacteristic
180C23—41no—
181C23#120×C10911yescharacteristic
182Q8—42no—
183D4—42no—
184D4—82no—
185D4—82no—
186C2×C4—24no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—41no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4C22⋊Q8×C10912yes—
200C2×C4C22⋊Q8×C10911yescharacteristic
201C2×C4#124×C10912yes—
202C2×C4#124×C10911yescharacteristic
203C2×C4#135×C10912yes—
204C2×C4AGL(1,ℤ/8)×C10912yes—
205C8—82no—
206C8—81no—
207C22—22no—
208C22—81no—
209C22—82no—
210C22#393×C10911yescharacteristic
211C22#449×C10912yes—
212C4—22no—
213C4—22no—
214C4—44no—
215C4—82no—
216C4—82no—
217C4—81no—
218C4#478×C10912yes—
219C4#488×C10911yescharacteristic
220C4#490×C10911yescharacteristic
221C2—22no—
222C2—161no—
223C2C109×#202511yescharacteristic
224C2C109×#203112yes—
subgroupG/H
centerC2×C4×C109#124
commutator, Frattini, cosocleC2×C42C23×C109
socleC22×C109#393
prime radical#532×C109C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C109 ◁ C2×C42×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#2402C2semidirect
4. C109×#1303C2semidirect
5. C109×#1274C2semidirect
108. #10372C109direct (N × H)
113. #2402C2×C109semidirect
116. #1303C2×C109semidirect
117. #1274C2×C109semidirect
118. C109#10372direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#24022
C109×#19632
C109×#15022
C109×#13032
C109×#12742
#10372109