Finite Group Databasebeta

← C107×#8919 #41034883

Subgroups — C107×#8919 #41034883

Order 27392.

336 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C107×#2987C211yesmaximal, characteristic
2C107×#1995C211yesmaximal, characteristic
3C107×#1569C212yesmaximal
4C107×#1526C211yesmaximal, characteristic
5C107×#1300C212yesmaximal
6#533×C107C2211yescharacteristic
7#446×C107—22no—
8#446×C107—22no—
9#433×C107—22no—
10#432×C107C2212yes—
11#423×C107C2211yescharacteristic
12C4×M16×C107C2212yes—
13#376×C107C2211yescharacteristic
14#339×C107—22no—
15#335×C107—22no—
16#334×C107—22no—
17#330×C107C411yescharacteristic, complemented
18#330×C107C412yescomplemented
19#330×C107C411yescharacteristic, complemented
20C2×M16×C107—22no—
21C2×M16×C107—21no—
22C4⋊Q8×C107Q812yes—
23#125×C107C2×C411yescharacteristic
24#125×C107C2×C411yescharacteristic
25C22⋊Q8×C107—22no—
26C4×Q8×C107—22no—
27#117×C107D412yes—
28C2×C42×C107—21no—
29C2×C42×C107C2311yescharacteristic
30C4⋊C8×C107—22no—
31C4⋊C8×C107—22no—
32C4⋊C8×C107—22no—
33C4⋊C8×C107D412yes—
34C4⋊C8×C107D412yes—
35C22⋊C8×C107—22no—
36#97×C107—22no—
37#97×C107—22no—
38#97×C107C2×C412yes—
39#97×C107C2×C412yes—
40C4×C8×C107—22no—
41C4×C8×C107—22no—
42#95×C107—22no—
43C2×Q8×C107—22no—
44C22×C4×C107—41no—
45C22×C4×C107C2×D411yescharacteristic
46C22×C4×C107#4112yes—
47M16×C107—44no—
48M16×C107—42no—
49C2×C8×C107—22no—
50C2×C8×C107—22no—
51C2×C8×C107—22no—
52C2×C8×C107—22no—
53C2×C8×C107—41no—
54C4⋊C4×C107—22no—
55C4⋊C4×C107—22no—
56C4⋊C4×C107—22no—
57C4⋊C4×C107C4⋊C412yes—
58C4⋊C4×C107C4⋊C412yes—
59C22⋊C4×C107—22no—
60C42×C107—22no—
61C42×C107—22no—
62C42×C107—41no—
63C42×C107C22×C411yescharacteristic
64C42×C107C2×D412yes—
65C42×C107C2×Q811yescharacteristic
66C23×C107#12311yescharacteristic
67Q8×C107—82no—
68C2×C4×C107—21no—
69C2×C4×C107—21no—
70C2×C4×C107—22no—
71C2×C4×C107—22no—
72C2×C4×C107—42no—
73C2×C4×C107—42no—
74C2×C4×C107—82no—
75C2×C4×C107C2×C4⋊C411yescharacteristic
76C2×C4×C107C4×D412yes—
77C2×C4×C107#12011yescharacteristic
78C2×C4×C107C22⋊Q812yes—
79C8×C107—24no—
80C8×C107—42no—
81C8×C107—42no—
82C8×C107—42no—
83C8×C107—81no—
84C22×C107—21no—
85C22×C107—22no—
86C22×C107#38511yescharacteristic
87C4×C107—21no—
88C4×C107—22no—
89C4×C107—22no—
90C4×C107—42no—
91C4×C107—42no—
92C4×C107—82no—
93C4×C107#45411yescharacteristic
94C4×C107#45611yescharacteristic
95#8919C10711yesmaximal, characteristic, direct product factor, Sylow
96C2×C107—41no—
97C2×C107#185711yescharacteristic
98C2×C107#186112yes—
99#2987C2×C10711yescharacteristic
100#1995C2×C10711yescharacteristic
101#1569C2×C10712yes—
102#1526C2×C10711yescharacteristic
103#1300C2×C10712yes—
104C107#891911yescharacteristic, direct product factor, Sylow
105#533C22×C10711yescharacteristic
106#446—22no—
107#446—22no—
108#433—22no—
109#432C22×C10712yes—
110#423C22×C10711yescharacteristic
111C4×M16C22×C10712yes—
112#376C22×C10711yescharacteristic
113#339—22no—
114#335—22no—
115#334—22no—
116#330C4×C10711yescharacteristic, complemented
117#330C4×C10712yescomplemented
118#330C4×C10711yescharacteristic, complemented
119C2×M16—22no—
120C2×M16—21no—
121C4⋊Q8Q8×C10712yes—
122#125C2×C4×C10711yescharacteristic
123#125C2×C4×C10711yescharacteristic
124C22⋊Q8—22no—
125C4×Q8—22no—
126#117D4×C10712yes—
127C2×C42—21no—
128C2×C42C23×C10711yescharacteristic
129C4⋊C8—22no—
130C4⋊C8—22no—
131C4⋊C8—22no—
132C4⋊C8D4×C10712yes—
133C4⋊C8D4×C10712yes—
134C22⋊C8—22no—
135#97—22no—
136#97—22no—
137#97C2×C4×C10712yes—
138#97C2×C4×C10712yes—
139C4×C8—22no—
140C4×C8—22no—
141#95—22no—
142C2×Q8—22no—
143C22×C4—41no—
144C22×C4C2×D4×C10711yescharacteristic
145C22×C4#41×C10712yes—
146M16—44no—
147M16—42no—
148C2×C8—22no—
149C2×C8—22no—
150C2×C8—22no—
151C2×C8—22no—
152C2×C8—41no—
153C4⋊C4—22no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4C4⋊C4×C10712yes—
157C4⋊C4C4⋊C4×C10712yes—
158C22⋊C4—22no—
159C42—22no—
160C42—22no—
161C42—41no—
162C42C22×C4×C10711yescharacteristic
163C42C2×D4×C10712yes—
164C42C2×Q8×C10711yescharacteristic
165C23#123×C10711yescharacteristic
166Q8—82no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—82no—
174C2×C4C2×C4⋊C4×C10711yescharacteristic
175C2×C4C4×D4×C10712yes—
176C2×C4#120×C10711yescharacteristic
177C2×C4C22⋊Q8×C10712yes—
178C8—24no—
179C8—42no—
180C8—42no—
181C8—42no—
182C8—81no—
183C22—22no—
184C22—21no—
185C22#385×C10711yescharacteristic
186C4—22no—
187C4—22no—
188C4—21no—
189C4—42no—
190C4—42no—
191C4—82no—
192C4#454×C10711yescharacteristic
193C4#456×C10711yescharacteristic
194C2—41no—
195C2C107×#185711yescharacteristic
196C2C107×#186112yes—
subgroupG/H
centerC2×C4×C107#120
commutatorC42C22×C4×C107
Frattini, cosocleC2×C42C23×C107
socleC22×C107#385
prime radicalC23×C107#123
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C107 ◁ C2×C42×C107 ◁ G

Complements

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

NH ≅ G/Ntype
17. #330×C107C4semidirect
18. #330×C107C4semidirect
19. #330×C107C4semidirect
95. #8919C107direct (N × H)
104. C107#8919direct (N × H)
116. #330C4×C107semidirect
117. #330C4×C107semidirect
118. #330C4×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#29872
C107×#19952
C107×#15692
C107×#15262
C107×#13002
#8919107