Finite Group Databasebeta

← C139×#7404 #48002000

Subgroups — C139×#7404 #48002000

Order 35584.

304 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 46 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
1#2014×C139C211yesmaximal, characteristic
2#1394×C139C211yesmaximal, characteristic, complemented
3#1319×C139C211yesmaximal, characteristic, complemented
4C22×SD16×C139—21no—
5C2×#127×C139C411yescharacteristic
6C2×#102×C139—21no—
7C2×#101×C139—21no—
8#391×C139C2211yescharacteristic
9#336×C139C411yescharacteristic
10#324×C139—21no—
11C22×Q8×C139D411yescharacteristic
12C22×D4×C139—21no—
13C22×D4×C139—41no—
14C2×SD16×C139—42no—
15C2×SD16×C139—42no—
16C2×SD16×C139—41no—
17C2×SD16×C139—41no—
18C2×M16×C139—41no—
19C22×C8×C139—21no—
20#127×C139—42no—
21C2×C4⋊C4×C139D411yescharacteristic
22C2×C42×C139C2×C411yescharacteristic
23#102×C139—42no—
24#101×C139—22no—
25#101×C139—41no—
26C22⋊C8×C139—41no—
27#95×C139—41no—
28C24×C139—41no—
29C2×Q8×C139—21no—
30C2×Q8×C139—41no—
31C2×Q8×C139—41no—
32C2×Q8×C139D811yescharacteristic
33C2×Q8×C139SD1611yescharacteristic
34C2×D4×C139—22no—
35C2×D4×C139—41no—
36C2×D4×C139—41no—
37C2×D4×C139—41no—
38C2×D4×C139—42no—
39C2×D4×C139—42no—
40C2×D4×C139—41no—
41C2×D4×C139—41no—
42C2×D4×C139—82no—
43C2×D4×C139—82no—
44C22×C4×C139—21no—
45C22×C4×C139—21no—
46C22×C4×C139—21no—
47C22×C4×C139C22⋊C411yescharacteristic
48SD16×C139—44no—
49SD16×C139—44no—
50M16×C139—42no—
51M16×C139—81no—
52C2×C8×C139—22no—
53C2×C8×C139—41no—
54C2×C8×C139—41no—
55C2×C8×C139—81no—
56C2×C8×C139—81no—
57C4⋊C4×C139—41no—
58C42×C139—41no—
59C23×C139—42no—
60C23×C139—82no—
61C23×C139—82no—
62C23×C139—81no—
63C23×C139—81no—
64C23×C139#9911yescharacteristic
65Q8×C139—41no—
66Q8×C139—41no—
67Q8×C139—81no—
68D4×C139—42no—
69D4×C139—42no—
70D4×C139—81no—
71D4×C139—81no—
72D4×C139—84no—
73D4×C139—84no—
74C2×C4×C139—21no—
75C2×C4×C139—21no—
76C2×C4×C139—22no—
77C2×C4×C139—21no—
78C2×C4×C139—21no—
79C2×C4×C139—41no—
80C2×C4×C139—41no—
81C2×C4×C139—41no—
82C2×C4×C139—41no—
83C2×C4×C139—41no—
84C2×C4×C139—81no—
85C2×C4×C139#10211yescharacteristic
86C2×C4×C139#10411yescharacteristic
87C8×C139—42no—
88C8×C139—82no—
89C8×C139—161no—
90C22×C139—21no—
91C22×C139—21no—
92C22×C139—84no—
93C22×C139—82no—
94C22×C139—162no—
95C22×C139—161no—
96C22×C139—161no—
97C22×C139#32711yescharacteristic
98C22×C139AΣL(1,𝔽16)11yescharacteristic
99C22×C139#35311yescharacteristic
100C4×C139—21no—
101C4×C139—21no—
102C4×C139—42no—
103C4×C139—41no—
104C4×C139—41no—
105C4×C139—81no—
106C2×C139—21no—
107C2×C139—21no—
108C2×C139—162no—
109C2×C139#134311yescharacteristic
110C2×C139#140611yescharacteristic
111C2×C139#141011yescharacteristic
112#7404C13911yesmaximal, characteristic, direct product factor, Sylow
113C139#740411yescharacteristic, direct product factor, Sylow
114#2014C2×C13911yescharacteristic
115#1394C2×C13911yescharacteristic, complemented
116#1319C2×C13911yescharacteristic, complemented
117C22×SD16—21no—
118C2×#127C4×C13911yescharacteristic
119C2×#102—21no—
120C2×#101—21no—
121#391C22×C13911yescharacteristic
122#336C4×C13911yescharacteristic
123#324—21no—
124C22×Q8D4×C13911yescharacteristic
125C22×D4—21no—
126C22×D4—41no—
127C2×SD16—42no—
128C2×SD16—42no—
129C2×SD16—41no—
130C2×SD16—41no—
131C2×M16—41no—
132C22×C8—21no—
133#127—42no—
134C2×C4⋊C4D4×C13911yescharacteristic
135C2×C42C2×C4×C13911yescharacteristic
136#102—42no—
137#101—22no—
138#101—41no—
139C22⋊C8—41no—
140#95—41no—
141C24—41no—
142C2×Q8—21no—
143C2×Q8—41no—
144C2×Q8—41no—
145C2×Q8D8×C13911yescharacteristic
146C2×Q8SD16×C13911yescharacteristic
147C2×D4—22no—
148C2×D4—41no—
149C2×D4—41no—
150C2×D4—41no—
151C2×D4—42no—
152C2×D4—42no—
153C2×D4—41no—
154C2×D4—41no—
155C2×D4—82no—
156C2×D4—82no—
157C22×C4—21no—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4C22⋊C4×C13911yescharacteristic
161SD16—44no—
162SD16—44no—
163M16—42no—
164M16—81no—
165C2×C8—22no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8—81no—
169C2×C8—81no—
170C4⋊C4—41no—
171C42—41no—
172C23—42no—
173C23—82no—
174C23—82no—
175C23—81no—
176C23—81no—
177C23#99×C13911yescharacteristic
178Q8—41no—
179Q8—41no—
180Q8—81no—
181D4—42no—
182D4—42no—
183D4—81no—
184D4—81no—
185D4—84no—
186D4—84no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—81no—
198C2×C4#102×C13911yescharacteristic
199C2×C4#104×C13911yescharacteristic
200C8—42no—
201C8—82no—
202C8—161no—
203C22—21no—
204C22—21no—
205C22—84no—
206C22—82no—
207C22—162no—
208C22—161no—
209C22—161no—
210C22#327×C13911yescharacteristic
211C22AΣL(1,𝔽16)×C13911yescharacteristic
212C22#353×C13911yescharacteristic
213C4—21no—
214C4—21no—
215C4—42no—
216C4—41no—
217C4—41no—
218C4—81no—
219C2—21no—
220C2—21no—
221C2—162no—
222C2#1343×C13911yescharacteristic
223C2#1406×C13911yescharacteristic
224C2#1410×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#353
commutatorC2×C42C2×C4×C139
Frattini, cosocle#391C22×C139
prime radicalC2×#127×C139C4
LCSG ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C139 ◁ C22×C4×C139 ◁ #391×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1394×C139C2semidirect
3. #1319×C139C2semidirect
112. #7404C139direct (N × H)
113. C139#7404direct (N × H)
115. #1394C2×C139semidirect
116. #1319C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2014×C1392
#1394×C1392
#1319×C1392
#7404139