Finite Group Databasebeta

← C109×#8913 #42126907

Subgroups — C109×#8913 #42126907

Order 27904.

428 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 134 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×#2382C211yesmaximal, characteristic
2C109×#1992C211yesmaximal, characteristic
3C109×#1847C212yesmaximal
4C2×#330×C109C211yesmaximal, characteristic
5C109×#1295C212yesmaximal
6C2×#125×C109C2211yescharacteristic
7C2×#107×C109—22no—
8C2×#106×C109—22no—
9C2×#97×C109C2211yescharacteristic
10C2×#97×C109C2212yes—
11#389×C109—22no—
12#387×C109—22no—
13#387×C109—22no—
14#384×C109C2211yescharacteristic
15#382×C109C2212yes—
16#340×C109—22no—
17#330×C109C414yescomplemented
18C22×C8×C109—22no—
19C22×C8×C109—21no—
20#125×C109—22no—
21#125×C109C2×C412yes—
22#125×C109Q812yes—
23C2×C4⋊C4×C109—22no—
24C2×C4⋊C4×C109—21no—
25C2×C4⋊C4×C109—22no—
26C2×C4⋊C4×C109—22no—
27C2×C4⋊C4×C109D412yes—
28C2×C4⋊C4×C109D412yes—
29C2×C4⋊C4×C109D412yes—
30C2×C42×C109—22no—
31C2×C42×C109C2311yescharacteristic
32#107×C109—44no—
33#106×C109—44no—
34#97×C109—22no—
35#97×C109—22no—
36#97×C109C2×C414yes—
37#95×C109—22no—
38#95×C109—22no—
39#95×C109—22no—
40#95×C109—22no—
41C22×C4×C109—22no—
42C22×C4×C109—22no—
43C22×C4×C109—22no—
44C22×C4×C109—41no—
45C22×C4×C109C2×D411yescharacteristic
46C22×C4×C109C2×D412yes—
47C2×C8×C109—24no—
48C2×C8×C109—24no—
49C2×C8×C109—24no—
50C2×C8×C109—22no—
51C2×C8×C109—41no—
52C2×C8×C109—41no—
53C4⋊C4×C109—24no—
54C4⋊C4×C109—24no—
55C4⋊C4×C109—22no—
56C4⋊C4×C109—42no—
57C4⋊C4×C109—42no—
58C4⋊C4×C109—42no—
59C4⋊C4×C109—42no—
60C4⋊C4×C109—42no—
61C4⋊C4×C109—82no—
62C4⋊C4×C109C4⋊C414yes—
63C42×C109—82no—
64C42×C109C22×C411yescharacteristic
65C42×C109C2×Q811yescharacteristic
66C42×C109#4112yes—
67C23×C109#12011yescharacteristic
68C2×C4×C109—22no—
69C2×C4×C109—21no—
70C2×C4×C109—21no—
71C2×C4×C109—22no—
72C2×C4×C109—24no—
73C2×C4×C109—42no—
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—82no—
82C2×C4×C109—81no—
83C2×C4×C109C2×C4⋊C411yescharacteristic
84C2×C4×C109C4×D412yes—
85C2×C4×C109C22⋊Q812yes—
86C2×C4×C109#12311yescharacteristic
87C8×C109—28no—
88C8×C109—42no—
89C22×C109#38511yescharacteristic
90C22×C109#45312yes—
91C22×C109#45411yescharacteristic
92C22×C109#45611yescharacteristic
93C22×C109#45612yes—
94C4×C109—21no—
95C4×C109—21no—
96C4×C109—22no—
97C4×C109—22no—
98C4×C109—44no—
99C4×C109—82no—
100C4×C109—82no—
101C4×C109—161no—
102#8913C10911yesmaximal, characteristic, direct product factor, Sylow
103C2×C109#165611yescharacteristic
104C2×C109#166012yes—
105C2×C109#166311yescharacteristic
106C2×C109#185711yescharacteristic
107C2×C109#185912yes—
108#2382C2×C10911yescharacteristic
109#1992C2×C10911yescharacteristic
110#1847C2×C10912yes—
111C2×#330C2×C10911yescharacteristic
112#1295C2×C10912yes—
113C109#891311yescharacteristic, direct product factor, Sylow
114C2×#125C22×C10911yescharacteristic
115C2×#107—22no—
116C2×#106—22no—
117C2×#97C22×C10911yescharacteristic
118C2×#97C22×C10912yes—
119#389—22no—
120#387—22no—
121#387—22no—
122#384C22×C10911yescharacteristic
123#382C22×C10912yes—
124#340—22no—
125#330C4×C10914yescomplemented
126C22×C8—22no—
127C22×C8—21no—
128#125—22no—
129#125C2×C4×C10912yes—
130#125Q8×C10912yes—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—21no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4D4×C10912yes—
136C2×C4⋊C4D4×C10912yes—
137C2×C4⋊C4D4×C10912yes—
138C2×C42—22no—
139C2×C42C23×C10911yescharacteristic
140#107—44no—
141#106—44no—
142#97—22no—
143#97—22no—
144#97C2×C4×C10914yes—
145#95—22no—
146#95—22no—
147#95—22no—
148#95—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—22no—
152C22×C4—41no—
153C22×C4C2×D4×C10911yescharacteristic
154C22×C4C2×D4×C10912yes—
155C2×C8—24no—
156C2×C8—24no—
157C2×C8—24no—
158C2×C8—22no—
159C2×C8—41no—
160C2×C8—41no—
161C4⋊C4—24no—
162C4⋊C4—24no—
163C4⋊C4—22no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—82no—
170C4⋊C4C4⋊C4×C10914yes—
171C42—82no—
172C42C22×C4×C10911yescharacteristic
173C42C2×Q8×C10911yescharacteristic
174C42#41×C10912yes—
175C23#120×C10911yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4C2×C4⋊C4×C10911yescharacteristic
192C2×C4C4×D4×C10912yes—
193C2×C4C22⋊Q8×C10912yes—
194C2×C4#123×C10911yescharacteristic
195C8—28no—
196C8—42no—
197C22#385×C10911yescharacteristic
198C22#453×C10912yes—
199C22#454×C10911yescharacteristic
200C22#456×C10911yescharacteristic
201C22#456×C10912yes—
202C4—21no—
203C4—21no—
204C4—22no—
205C4—22no—
206C4—44no—
207C4—82no—
208C4—82no—
209C4—161no—
210C2C109×#165611yescharacteristic
211C2C109×#166012yes—
212C2C109×#166311yescharacteristic
213C2C109×#185711yescharacteristic
214C2C109×#185912yes—
subgroupG/H
center, socle, prime radicalC23×C109#120
commutatorC42C22×C4×C109
Frattini, cosocleC2×C42C23×C109
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C109 ◁ C2×C42×C109 ◁ G

Complements

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

NH ≅ G/Ntype
17. #330×C109C4semidirect
102. #8913C109direct (N × H)
113. C109#8913direct (N × H)
125. #330C4×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#23822
C109×#19922
C109×#18472
C2×#330×C1092
C109×#12952
#8913109