Finite Group Databasebeta

← C139×#10573 #48005169

Subgroups — C139×#10573 #48005169

Order 35584.

494 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 162 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#2551×C139C211yesmaximal, characteristic
2#1947×C139C212yesmaximal
3#1845×C139C211yesmaximal, characteristic
4#1296×C139C211yesmaximal, characteristic
5#1279×C139C212yesmaximal
6C2×C4⋊Q8×C139—22no—
7C2×#107×C139—22no—
8C2×#107×C139—22no—
9C2×C4⋊C8×C139C2212yes—
10C2×C4×C8×C139C2211yescharacteristic
11#395×C139—22no—
12#389×C139—22no—
13#384×C139C2211yescharacteristic
14#384×C139C2211yescharacteristic
15C4×C4⋊C4×C139C2212yes—
16#340×C139—22no—
17C22×Q8×C139—22no—
18C22×C8×C139—21no—
19C22×C8×C139—22no—
20C4⋊Q8×C139—44no—
21C4⋊Q8×C139—44no—
22C2×C4⋊C4×C139—24no—
23C2×C4⋊C4×C139—22no—
24C2×C4⋊C4×C139—21no—
25C2×C4⋊C4×C139—22no—
26C2×C4⋊C4×C139D412yes—
27C2×C4⋊C4×C139D412yes—
28C2×C4⋊C4×C139D412yes—
29C2×C42×C139—22no—
30C2×C42×C139C2311yescharacteristic
31#107×C139—44no—
32#107×C139—44no—
33C4⋊C8×C139—22no—
34C4⋊C8×C139Q814yescomplemented
35C4×C8×C139—21no—
36C4×C8×C139Q812yescomplemented
37#95×C139—22no—
38#95×C139—22no—
39C2×Q8×C139—48no—
40C2×Q8×C139—82no—
41C22×C4×C139—22no—
42C22×C4×C139—22no—
43C22×C4×C139—22no—
44C22×C4×C139—41no—
45C22×C4×C139C2×D411yescharacteristic
46C22×C4×C139C2×D412yes—
47C2×C8×C139—22no—
48C2×C8×C139—22no—
49C2×C8×C139—22no—
50C2×C8×C139—24no—
51C2×C8×C139—42no—
52C2×C8×C139—42no—
53C4⋊C4×C139—22no—
54C4⋊C4×C139—22no—
55C4⋊C4×C139—42no—
56C4⋊C4×C139—48no—
57C4⋊C4×C139—42no—
58C4⋊C4×C139—42no—
59C4⋊C4×C139—42no—
60C4⋊C4×C139—42no—
61C4⋊C4×C139—42no—
62C4⋊C4×C139D814yes—
63C4⋊C4×C139Q1614yes—
64C42×C139—42no—
65C42×C139—42no—
66C42×C139C2×Q811yescharacteristic
67C42×C139C2×Q812yes—
68C42×C139#4111yescharacteristic
69C23×C139#12011yescharacteristic
70Q8×C139—88no—
71C2×C4×C139—21no—
72C2×C4×C139—21no—
73C2×C4×C139—24no—
74C2×C4×C139—24no—
75C2×C4×C139—42no—
76C2×C4×C139—42no—
77C2×C4×C139—42no—
78C2×C4×C139—42no—
79C2×C4×C139—44no—
80C2×C4×C139—42no—
81C2×C4×C139—82no—
82C2×C4×C139—81no—
83C2×C4×C139C22⋊Q811yescharacteristic
84C2×C4×C139C22⋊Q812yes—
85C2×C4×C139C4⋊Q811yescharacteristic
86C2×C4×C139C4⋊Q812yes—
87C2×C4×C139C2×D812yes—
88C2×C4×C139C2×Q1612yes—
89C2×C4×C139AGL(1,ℤ/8)12yes—
90C2×C4×C139#13712yes—
91C8×C139—24no—
92C8×C139—44no—
93C22×C139#39511yescharacteristic
94C22×C139#44712yes—
95C22×C139#45112yes—
96C22×C139#45311yescharacteristic
97C22×C139#45611yescharacteristic
98C4×C139—21no—
99C4×C139—21no—
100C4×C139—44no—
101C4×C139—44no—
102C4×C139—82no—
103C4×C139—161no—
104C4×C139#47412yes—
105C4×C139#47712yes—
106C4×C139#50012yes—
107C4×C139#50112yes—
108C2×C139#161911yescharacteristic
109C2×C139#163311yescharacteristic
110C2×C139#164912yes—
111C2×C139#205712yes—
112C2×C139#206011yescharacteristic
113#10573C13911yesmaximal, characteristic, direct product factor, Sylow
114C139#1057311yescharacteristic, direct product factor, Sylow
115#2551C2×C13911yescharacteristic
116#1947C2×C13912yes—
117#1845C2×C13911yescharacteristic
118#1296C2×C13911yescharacteristic
119#1279C2×C13912yes—
120C2×C4⋊Q8—22no—
121C2×#107—22no—
122C2×#107—22no—
123C2×C4⋊C8C22×C13912yes—
124C2×C4×C8C22×C13911yescharacteristic
125#395—22no—
126#389—22no—
127#384C22×C13911yescharacteristic
128#384C22×C13911yescharacteristic
129C4×C4⋊C4C22×C13912yes—
130#340—22no—
131C22×Q8—22no—
132C22×C8—21no—
133C22×C8—22no—
134C4⋊Q8—44no—
135C4⋊Q8—44no—
136C2×C4⋊C4—24no—
137C2×C4⋊C4—22no—
138C2×C4⋊C4—22no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4D4×C13912yes—
141C2×C4⋊C4D4×C13912yes—
142C2×C4⋊C4D4×C13912yes—
143C2×C42—22no—
144C2×C42C23×C13911yescharacteristic
145#107—44no—
146#107—44no—
147C4⋊C8—22no—
148C4⋊C8Q8×C13914yescomplemented
149C4×C8—21no—
150C4×C8Q8×C13912yescomplemented
151#95—22no—
152#95—22no—
153C2×Q8—48no—
154C2×Q8—82no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4—22no—
158C22×C4—41no—
159C22×C4C2×D4×C13911yescharacteristic
160C22×C4C2×D4×C13912yes—
161C2×C8—22no—
162C2×C8—22no—
163C2×C8—22no—
164C2×C8—24no—
165C2×C8—42no—
166C2×C8—42no—
167C4⋊C4—22no—
168C4⋊C4—22no—
169C4⋊C4—42no—
170C4⋊C4—48no—
171C4⋊C4—42no—
172C4⋊C4—42no—
173C4⋊C4—42no—
174C4⋊C4—42no—
175C4⋊C4—42no—
176C4⋊C4D8×C13914yes—
177C4⋊C4Q16×C13914yes—
178C42—42no—
179C42—42no—
180C42C2×Q8×C13911yescharacteristic
181C42C2×Q8×C13912yes—
182C42#41×C13911yescharacteristic
183C23#120×C13911yescharacteristic
184Q8—88no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—24no—
188C2×C4—24no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—42no—
195C2×C4—82no—
196C2×C4—81no—
197C2×C4C22⋊Q8×C13911yescharacteristic
198C2×C4C22⋊Q8×C13912yes—
199C2×C4C4⋊Q8×C13911yescharacteristic
200C2×C4C4⋊Q8×C13912yes—
201C2×C4C2×D8×C13912yes—
202C2×C4C2×Q16×C13912yes—
203C2×C4AGL(1,ℤ/8)×C13912yes—
204C2×C4#137×C13912yes—
205C8—24no—
206C8—44no—
207C22#395×C13911yescharacteristic
208C22#447×C13912yes—
209C22#451×C13912yes—
210C22#453×C13911yescharacteristic
211C22#456×C13911yescharacteristic
212C4—21no—
213C4—21no—
214C4—44no—
215C4—44no—
216C4—82no—
217C4—161no—
218C4#474×C13912yes—
219C4#477×C13912yes—
220C4#500×C13912yes—
221C4#501×C13912yes—
222C2#1619×C13911yescharacteristic
223C2#1633×C13911yescharacteristic
224C2#1649×C13912yes—
225C2#2057×C13912yes—
226C2#2060×C13911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C139#120
commutator, Frattini, cosocleC2×C42C23×C139
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
34. C4⋊C8×C139Q8semidirect
36. C4×C8×C139Q8semidirect
113. #10573C139direct (N × H)
114. C139#10573direct (N × H)
148. C4⋊C8Q8×C139semidirect
150. C4×C8Q8×C139semidirect

Maximal subgroups

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

subgroupindex
#2551×C1392
#1947×C1392
#1845×C1392
#1296×C1392
#1279×C1392
#10573139