Finite Group Databasebeta

← C107×#13198 #41039162

Subgroups — C107×#13198 #41039162

Order 27392.

410 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 138 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×#2955C211yesmaximal, characteristic
2C107×#2151C211yesmaximal, characteristic, complemented
3C107×#2117C212yesmaximal, complemented
4C107×#2113C212yesmaximal, complemented
5C107×#2110C211yesmaximal, characteristic, complemented
6#575×C107C411yescharacteristic
7C2×#131×C107C2212yes—
8C2×M32×C107C2211yescharacteristic
9C2×M32×C107C2212yes—
10C22×C16×C107C2211yescharacteristic
11#444×C107—22no—
12#443×C107—22no—
13#430×C107C411yescharacteristic
14#421×C107C412yes—
15#405×C107C2211yescharacteristic
16C4⋊C16×C107—22no—
17#350×C107—24no—
18C22⋊C16×C107—24no—
19#347×C107—22no—
20C2×#41×C107C2×C412yes—
21#137×C107—22no—
22AGL(1,ℤ/8)×C107—22no—
23#135×C107—22no—
24#131×C107—22no—
25#131×C107—22no—
26#131×C107—22no—
27#131×C107—22no—
28C2×M16×C107—22no—
29C2×M16×C107C2×C412yes—
30C2×M16×C107C2×C411yescharacteristic
31C22×C8×C107—22no—
32C22×C8×C107C2311yescharacteristic
33#117×C107C2×C411yescharacteristic
34M32×C107—22no—
35M32×C107—22no—
36M32×C107—22no—
37C2×C16×C107—22no—
38C2×C16×C107—21no—
39C2×C16×C107—21no—
40C2×C16×C107D414yes—
41#108×C107—22no—
42#104×C107—24no—
43#97×C107D412yes—
44C4×C8×C107D412yes—
45#41×C107—22no—
46#41×C107—22no—
47#41×C107—22no—
48#41×C107—22no—
49C2×Q8×C107M1612yes—
50C2×D4×C107—22no—
51C2×D4×C107M1612yes—
52C22×C4×C107—22no—
53C22×C4×C107C22×C411yescharacteristic
54Q16×C107—22no—
55SD16×C107—24no—
56D8×C107—22no—
57M16×C107—22no—
58M16×C107—22no—
59M16×C107—22no—
60M16×C107—42no—
61M16×C107—42no—
62C2×C8×C107—22no—
63C2×C8×C107—42no—
64C2×C8×C107—42no—
65C2×C8×C107C22⋊C412yes—
66C2×C8×C107C2×D411yescharacteristic
67C2×C8×C107C2×D412yes—
68C2×C8×C107C2×D411yescharacteristic
69C2×C8×C107#4112yes—
70C4⋊C4×C107—21no—
71C22⋊C4×C107—21no—
72C42×C107C22⋊C412yes—
73C16×C107—24no—
74C16×C107—41no—
75C16×C107—41no—
76C23×C107—22no—
77C23×C107#13111yescharacteristic
78Q8×C107—22no—
79Q8×C107—22no—
80D4×C107—22no—
81D4×C107—22no—
82D4×C107—42no—
83D4×C107—42no—
84C2×C4×C107—22no—
85C2×C4×C107—22no—
86C2×C4×C107—42no—
87C2×C4×C107—42no—
88C2×C4×C107C2×C22⋊C411yescharacteristic
89C2×C4×C107C4×D412yes—
90C2×C4×C107C2×M1612yes—
91C2×C4×C107#13111yescharacteristic
92C8×C107—22no—
93C8×C107—42no—
94C8×C107#12112yes—
95C8×C107#12411yescharacteristic
96C8×C107#12711yescharacteristic
97C22×C107—41no—
98C22×C107—44no—
99C22×C107—42no—
100C22×C107#40811yescharacteristic
101C22×C107#43512yes—
102C4×C107—42no—
103C4×C107—42no—
104C4×C107#39011yescharacteristic
105C4×C107#40711yescharacteristic
106C4×C107#43512yes—
107#13198C10711yesmaximal, characteristic, direct product factor, Sylow
108C2×C107—21no—
109C2×C107—22no—
110C2×C107—82no—
111C2×C107#195511yescharacteristic
112#2955C2×C10711yescharacteristic
113#2151C2×C10711yescharacteristic, complemented
114#2117C2×C10712yescomplemented
115#2113C2×C10712yescomplemented
116#2110C2×C10711yescharacteristic, complemented
117C107#1319811yescharacteristic, direct product factor, Sylow
118#575C4×C10711yescharacteristic
119C2×#131C22×C10712yes—
120C2×M32C22×C10711yescharacteristic
121C2×M32C22×C10712yes—
122C22×C16C22×C10711yescharacteristic
123#444—22no—
124#443—22no—
125#430C4×C10711yescharacteristic
126#421C4×C10712yes—
127#405C22×C10711yescharacteristic
128C4⋊C16—22no—
129#350—24no—
130C22⋊C16—24no—
131#347—22no—
132C2×#41C2×C4×C10712yes—
133#137—22no—
134AGL(1,ℤ/8)—22no—
135#135—22no—
136#131—22no—
137#131—22no—
138#131—22no—
139#131—22no—
140C2×M16—22no—
141C2×M16C2×C4×C10712yes—
142C2×M16C2×C4×C10711yescharacteristic
143C22×C8—22no—
144C22×C8C23×C10711yescharacteristic
145#117C2×C4×C10711yescharacteristic
146M32—22no—
147M32—22no—
148M32—22no—
149C2×C16—22no—
150C2×C16—21no—
151C2×C16—21no—
152C2×C16D4×C10714yes—
153#108—22no—
154#104—24no—
155#97D4×C10712yes—
156C4×C8D4×C10712yes—
157#41—22no—
158#41—22no—
159#41—22no—
160#41—22no—
161C2×Q8M16×C10712yes—
162C2×D4—22no—
163C2×D4M16×C10712yes—
164C22×C4—22no—
165C22×C4C22×C4×C10711yescharacteristic
166Q16—22no—
167SD16—24no—
168D8—22no—
169M16—22no—
170M16—22no—
171M16—22no—
172M16—42no—
173M16—42no—
174C2×C8—22no—
175C2×C8—42no—
176C2×C8—42no—
177C2×C8C22⋊C4×C10712yes—
178C2×C8C2×D4×C10711yescharacteristic
179C2×C8C2×D4×C10712yes—
180C2×C8C2×D4×C10711yescharacteristic
181C2×C8#41×C10712yes—
182C4⋊C4—21no—
183C22⋊C4—21no—
184C42C22⋊C4×C10712yes—
185C16—24no—
186C16—41no—
187C16—41no—
188C23—22no—
189C23#131×C10711yescharacteristic
190Q8—22no—
191Q8—22no—
192D4—22no—
193D4—22no—
194D4—42no—
195D4—42no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4C2×C22⋊C4×C10711yescharacteristic
201C2×C4C4×D4×C10712yes—
202C2×C4C2×M16×C10712yes—
203C2×C4#131×C10711yescharacteristic
204C8—22no—
205C8—42no—
206C8#121×C10712yes—
207C8#124×C10711yescharacteristic
208C8#127×C10711yescharacteristic
209C22—41no—
210C22—44no—
211C22—42no—
212C22#408×C10711yescharacteristic
213C22#435×C10712yes—
214C4—42no—
215C4—42no—
216C4#390×C10711yescharacteristic
217C4#407×C10711yescharacteristic
218C4#435×C10712yes—
219C2—21no—
220C2—22no—
221C2—82no—
222C2C107×#195511yescharacteristic
subgroupG/H
centerC8×C107#127
commutatorC22×C4C22×C4×C107
Frattini, cosocleC22×C8C23×C107
socleC2×C107#1955
prime radical#575×C107C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C8×C107 ◁ C22×C8×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2151C2semidirect
3. C107×#2117C2semidirect
4. C107×#2113C2semidirect
5. C107×#2110C2semidirect
107. #13198C107direct (N × H)
113. #2151C2×C107semidirect
114. #2117C2×C107semidirect
115. #2113C2×C107semidirect
116. #2110C2×C107semidirect
117. C107#13198direct (N × H)

Maximal subgroups

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

subgroupindex
C107×#29552
C107×#21512
C107×#21172
C107×#21132
C107×#21102
#13198107