Finite Group Databasebeta

← C107×#9008 #41034972

Subgroups — C107×#9008 #41034972

Order 27392.

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

normal subgroups only

This group has 398 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×#3135C211yesmaximal, characteristic
2C107×#2987C211yesmaximal, characteristic, complemented
3C107×#1544C211yesmaximal, characteristic, complemented
4C107×#1496C212yesmaximal
5C107×#1302C212yesmaximal, complemented
6#533×C107C2211yescharacteristic
7#532×C107C2211yescharacteristic
8#491×C107C412yes—
9#490×C107C412yes—
10#489×C107—22no—
11#446×C107—24no—
12#433×C107—22no—
13#432×C107C2212yes—
14#431×C107C2212yes—
15#416×C107—22no—
16C2×#97×C107C2211yescharacteristic
17#332×C107—22no—
18D4⋊C8×C107—24no—
19C2×#41×C107—21no—
20C22×C8×C107—21no—
21C4⋊Q8×C107C2×C411yescharacteristic
22C4⋊Q8×C107D412yes—
23#127×C107C2×C411yescharacteristic
24#125×C107C2×C412yes—
25#124×C107—21no—
26C22⋊Q8×C107—22no—
27#121×C107—22no—
28C4×Q8×C107—22no—
29C4×D4×C107—22no—
30#117×C107D412yes—
31C2×C42×C107C2311yescharacteristic
32C4⋊C8×C107—24no—
33C4⋊C8×C107—22no—
34C4⋊C8×C107D414yes—
35#103×C107—24no—
36#102×C107—24no—
37C22⋊C8×C107—22no—
38C22⋊C8×C107—22no—
39#97×C107—22no—
40#97×C107—21no—
41#97×C107—22no—
42#97×C107C2×C412yes—
43C4×C8×C107—22no—
44C4×C8×C107—22no—
45#41×C107—44no—
46C2×Q8×C107—22no—
47C2×Q8×C107—21no—
48C2×D4×C107—21no—
49C2×D4×C107—22no—
50C2×D4×C107—41no—
51C22×C4×C107—41no—
52C22×C4×C107C2×D411yescharacteristic
53C22×C4×C107#4112yes—
54C2×C8×C107—22no—
55C2×C8×C107—24no—
56C2×C8×C107—42no—
57C2×C8×C107—42no—
58C4⋊C4×C107—24no—
59C4⋊C4×C107—22no—
60C4⋊C4×C107—22no—
61C4⋊C4×C107C22⋊C414yes—
62C22⋊C4×C107—22no—
63C22⋊C4×C107—42no—
64C42×C107—22no—
65C42×C107C22×C411yescharacteristic
66C42×C107C2×D411yescharacteristic
67C42×C107C2×D412yes—
68C23×C107—41no—
69C23×C107#12311yescharacteristic
70Q8×C107—42no—
71Q8×C107—82no—
72D4×C107—44no—
73D4×C107—42no—
74D4×C107—82no—
75C2×C4×C107—22no—
76C2×C4×C107—24no—
77C2×C4×C107—42no—
78C2×C4×C107—41no—
79C2×C4×C107—82no—
80C2×C4×C107C2×C22⋊C411yescharacteristic
81C2×C4×C107C4×D412yes—
82C2×C4×C107#12011yescharacteristic
83C2×C4×C107#12112yes—
84C8×C107—42no—
85C8×C107—44no—
86C8×C107—82no—
87C22×C107—22no—
88C22×C107—21no—
89C22×C107—82no—
90C22×C107—81no—
91C22×C107#38611yescharacteristic
92C4×C107—22no—
93C4×C107—22no—
94C4×C107—21no—
95C4×C107—44no—
96C4×C107—81no—
97C4×C107#45412yes—
98#9008C10711yesmaximal, characteristic, direct product factor, Sylow
99C2×C107—41no—
100C2×C107—161no—
101C2×C107#188112yes—
102C2×C107#188811yescharacteristic
103#3135C2×C10711yescharacteristic
104#2987C2×C10711yescharacteristic, complemented
105#1544C2×C10711yescharacteristic, complemented
106#1496C2×C10712yes—
107#1302C2×C10712yescomplemented
108C107#900811yescharacteristic, direct product factor, Sylow
109#533C22×C10711yescharacteristic
110#532C22×C10711yescharacteristic
111#491C4×C10712yes—
112#490C4×C10712yes—
113#489—22no—
114#446—24no—
115#433—22no—
116#432C22×C10712yes—
117#431C22×C10712yes—
118#416—22no—
119C2×#97C22×C10711yescharacteristic
120#332—22no—
121D4⋊C8—24no—
122C2×#41—21no—
123C22×C8—21no—
124C4⋊Q8C2×C4×C10711yescharacteristic
125C4⋊Q8D4×C10712yes—
126#127C2×C4×C10711yescharacteristic
127#125C2×C4×C10712yes—
128#124—21no—
129C22⋊Q8—22no—
130#121—22no—
131C4×Q8—22no—
132C4×D4—22no—
133#117D4×C10712yes—
134C2×C42C23×C10711yescharacteristic
135C4⋊C8—24no—
136C4⋊C8—22no—
137C4⋊C8D4×C10714yes—
138#103—24no—
139#102—24no—
140C22⋊C8—22no—
141C22⋊C8—22no—
142#97—22no—
143#97—21no—
144#97—22no—
145#97C2×C4×C10712yes—
146C4×C8—22no—
147C4×C8—22no—
148#41—44no—
149C2×Q8—22no—
150C2×Q8—21no—
151C2×D4—21no—
152C2×D4—22no—
153C2×D4—41no—
154C22×C4—41no—
155C22×C4C2×D4×C10711yescharacteristic
156C22×C4#41×C10712yes—
157C2×C8—22no—
158C2×C8—24no—
159C2×C8—42no—
160C2×C8—42no—
161C4⋊C4—24no—
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4C22⋊C4×C10714yes—
165C22⋊C4—22no—
166C22⋊C4—42no—
167C42—22no—
168C42C22×C4×C10711yescharacteristic
169C42C2×D4×C10711yescharacteristic
170C42C2×D4×C10712yes—
171C23—41no—
172C23#123×C10711yescharacteristic
173Q8—42no—
174Q8—82no—
175D4—42no—
176D4—44no—
177D4—82no—
178C2×C4—22no—
179C2×C4—24no—
180C2×C4—42no—
181C2×C4—41no—
182C2×C4—82no—
183C2×C4C2×C22⋊C4×C10711yescharacteristic
184C2×C4C4×D4×C10712yes—
185C2×C4#120×C10711yescharacteristic
186C2×C4#121×C10712yes—
187C8—42no—
188C8—44no—
189C8—82no—
190C22—22no—
191C22—21no—
192C22—82no—
193C22—81no—
194C22#386×C10711yescharacteristic
195C4—22no—
196C4—22no—
197C4—21no—
198C4—44no—
199C4—81no—
200C4#454×C10712yes—
201C2—41no—
202C2—161no—
203C2C107×#188112yes—
204C2C107×#188811yescharacteristic
subgroupG/H
centerC2×C4×C107#120
commutatorC42C22×C4×C107
Frattini, cosocleC2×C42C23×C107
socleC22×C107#386
prime radical#532×C107C22
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
2. C107×#2987C2semidirect
3. C107×#1544C2semidirect
5. C107×#1302C2semidirect
98. #9008C107direct (N × H)
104. #2987C2×C107semidirect
105. #1544C2×C107semidirect
107. #1302C2×C107semidirect
108. C107#9008direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#31352
C107×#29872
C107×#15442
C107×#14962
C107×#13022
#9008107