Finite Group Databasebeta

← C139×#9394 #48003990

Subgroups — C139×#9394 #48003990

Order 35584.

506 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 154 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#2982×C139C211yesmaximal, characteristic
2#2546×C139C211yesmaximal, characteristic
3#1801×C139C211yesmaximal, characteristic
4#1546×C139C212yesmaximal
5#1303×C139C212yesmaximal
6C2×C4⋊Q8×C139—21no—
7C2×C4⋊Q8×C139C2211yescharacteristic
8C2×C4×Q8×C139C2211yescharacteristic
9C8×Q8×C139—24no—
10#431×C139—22no—
11#431×C139C2212yes—
12#423×C139C2212yes—
13C2×#101×C139—21no—
14#398×C139C414yes—
15#391×C139—21no—
16#389×C139—22no—
17C4×C4⋊C4×C139C2211yescharacteristic
18#343×C139—21no—
19#332×C139—24no—
20C22×Q8×C139—21no—
21C22×Q8×C139D411yescharacteristic
22C2×M16×C139—22no—
23C4⋊Q8×C139—22no—
24C4⋊Q8×C139—22no—
25C4⋊Q8×C139—42no—
26C4⋊Q8×C139—42no—
27C4×Q8×C139—22no—
28C4×Q8×C139—22no—
29C2×C4⋊C4×C139—21no—
30C2×C4⋊C4×C139—24no—
31C2×C4⋊C4×C139—21no—
32C2×C4⋊C4×C139C2×C412yes—
33C2×C4⋊C4×C139C2×C412yes—
34C2×C4⋊C4×C139D411yescharacteristic
35C2×C42×C139—21no—
36C2×C42×C139D412yes—
37C2×C42×C139C2311yescharacteristic
38C4⋊C8×C139—24no—
39C4⋊C8×C139—22no—
40C4⋊C8×C139—22no—
41C4⋊C8×C139D414yes—
42#101×C139—42no—
43C22⋊C8×C139—22no—
44C4×C8×C139—24no—
45C4×C8×C139—22no—
46#95×C139—24no—
47#95×C139C2×C412yes—
48C2×Q8×C139—22no—
49C2×Q8×C139—22no—
50C2×Q8×C139—42no—
51C2×Q8×C139—41no—
52C2×Q8×C139—41no—
53C2×Q8×C139—42no—
54C2×Q8×C139D812yes—
55C2×Q8×C139SD1612yes—
56C22×C4×C139—22no—
57C22×C4×C139—22no—
58C22×C4×C139C22⋊C412yes—
59C22×C4×C139C22⋊C412yes—
60C22×C4×C139C22×C411yescharacteristic
61C22×C4×C139C2×D411yescharacteristic
62C22×C4×C139C2×D411yescharacteristic
63M16×C139—42no—
64M16×C139—42no—
65C2×C8×C139—24no—
66C2×C8×C139—42no—
67C4⋊C4×C139—24no—
68C4⋊C4×C139—24no—
69C4⋊C4×C139—22no—
70C4⋊C4×C139—24no—
71C4⋊C4×C139—48no—
72C4⋊C4×C139—41no—
73C4⋊C4×C139—41no—
74C42×C139—22no—
75C42×C139—22no—
76C42×C139—41no—
77C42×C139—41no—
78C42×C139C2×D412yes—
79C42×C139#4112yes—
80C23×C139C2×C22⋊C411yescharacteristic
81Q8×C139—24no—
82Q8×C139—24no—
83Q8×C139—82no—
84Q8×C139—82no—
85C2×C4×C139—22no—
86C2×C4×C139—22no—
87C2×C4×C139—22no—
88C2×C4×C139—24no—
89C2×C4×C139—22no—
90C2×C4×C139—41no—
91C2×C4×C139—42no—
92C2×C4×C139—42no—
93C2×C4×C139—42no—
94C2×C4×C139—42no—
95C2×C4×C139—42no—
96C2×C4×C139—42no—
97C2×C4×C139#10214yes—
98C2×C4×C139C4×D412yes—
99C2×C4×C139#12011yescharacteristic
100C2×C4×C139#12112yes—
101C2×C4×C139#12311yescharacteristic
102C2×C4×C139C2×D811yescharacteristic
103C2×C4×C139C2×SD1611yescharacteristic
104C2×C4×C139#13512yes—
105C8×C139—44no—
106C8×C139—82no—
107C22×C139—21no—
108C22×C139—21no—
109C22×C139#38611yescharacteristic
110C22×C139C2×#10211yescharacteristic
111C22×C139#41611yescharacteristic
112C4×C139—21no—
113C4×C139—24no—
114C4×C139—22no—
115C4×C139—44no—
116C4×C139—42no—
117C4×C139—82no—
118C4×C139#45612yes—
119C4×C139#46512yes—
120C4×C139#46612yes—
121C2×C139—21no—
122C2×C139—21no—
123C2×C139#188611yescharacteristic
124C2×C139#189311yescharacteristic
125C2×C139#191511yescharacteristic
126#9394C13911yesmaximal, characteristic, direct product factor, Sylow
127C139#939411yescharacteristic, direct product factor, Sylow
128#2982C2×C13911yescharacteristic
129#2546C2×C13911yescharacteristic
130#1801C2×C13911yescharacteristic
131#1546C2×C13912yes—
132#1303C2×C13912yes—
133C2×C4⋊Q8—21no—
134C2×C4⋊Q8C22×C13911yescharacteristic
135C2×C4×Q8C22×C13911yescharacteristic
136C8×Q8—24no—
137#431—22no—
138#431C22×C13912yes—
139#423C22×C13912yes—
140C2×#101—21no—
141#398C4×C13914yes—
142#391—21no—
143#389—22no—
144C4×C4⋊C4C22×C13911yescharacteristic
145#343—21no—
146#332—24no—
147C22×Q8—21no—
148C22×Q8D4×C13911yescharacteristic
149C2×M16—22no—
150C4⋊Q8—22no—
151C4⋊Q8—22no—
152C4⋊Q8—42no—
153C4⋊Q8—42no—
154C4×Q8—22no—
155C4×Q8—22no—
156C2×C4⋊C4—21no—
157C2×C4⋊C4—24no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4C2×C4×C13912yes—
160C2×C4⋊C4C2×C4×C13912yes—
161C2×C4⋊C4D4×C13911yescharacteristic
162C2×C42—21no—
163C2×C42D4×C13912yes—
164C2×C42C23×C13911yescharacteristic
165C4⋊C8—24no—
166C4⋊C8—22no—
167C4⋊C8—22no—
168C4⋊C8D4×C13914yes—
169#101—42no—
170C22⋊C8—22no—
171C4×C8—24no—
172C4×C8—22no—
173#95—24no—
174#95C2×C4×C13912yes—
175C2×Q8—22no—
176C2×Q8—22no—
177C2×Q8—42no—
178C2×Q8—41no—
179C2×Q8—41no—
180C2×Q8—42no—
181C2×Q8D8×C13912yes—
182C2×Q8SD16×C13912yes—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4C22⋊C4×C13912yes—
186C22×C4C22⋊C4×C13912yes—
187C22×C4C22×C4×C13911yescharacteristic
188C22×C4C2×D4×C13911yescharacteristic
189C22×C4C2×D4×C13911yescharacteristic
190M16—42no—
191M16—42no—
192C2×C8—24no—
193C2×C8—42no—
194C4⋊C4—24no—
195C4⋊C4—24no—
196C4⋊C4—22no—
197C4⋊C4—24no—
198C4⋊C4—48no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C42—22no—
202C42—22no—
203C42—41no—
204C42—41no—
205C42C2×D4×C13912yes—
206C42#41×C13912yes—
207C23C2×C22⋊C4×C13911yescharacteristic
208Q8—24no—
209Q8—24no—
210Q8—82no—
211Q8—82no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—22no—
215C2×C4—24no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4#102×C13914yes—
225C2×C4C4×D4×C13912yes—
226C2×C4#120×C13911yescharacteristic
227C2×C4#121×C13912yes—
228C2×C4#123×C13911yescharacteristic
229C2×C4C2×D8×C13911yescharacteristic
230C2×C4C2×SD16×C13911yescharacteristic
231C2×C4#135×C13912yes—
232C8—44no—
233C8—82no—
234C22—21no—
235C22—21no—
236C22#386×C13911yescharacteristic
237C22C2×#102×C13911yescharacteristic
238C22#416×C13911yescharacteristic
239C4—21no—
240C4—24no—
241C4—22no—
242C4—44no—
243C4—42no—
244C4—82no—
245C4#456×C13912yes—
246C4#465×C13912yes—
247C4#466×C13912yes—
248C2—21no—
249C2—21no—
250C2#1886×C13911yescharacteristic
251C2#1893×C13911yescharacteristic
252C2#1915×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#386
commutatorC22×C4C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radicalC23×C139C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
126. #9394C139direct (N × H)
127. C139#9394direct (N × H)

Maximal subgroups

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

subgroupindex
#2982×C1392
#2546×C1392
#1801×C1392
#1546×C1392
#1303×C1392
#9394139