Finite Group Databasebeta

← C139×#10028 #48004624

Subgroups — C139×#10028 #48004624

Order 35584.

512 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 102 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#3245×C139C211yesmaximal, characteristic
2#3112×C139C212yesmaximal, complemented
3#1985×C139C211yesmaximal, characteristic, complemented
4#1530×C139C212yesmaximal, complemented
5#1290×C139C211yesmaximal, characteristic, complemented
6#532×C139C2212yes—
7C2×C4×Q8×C139C2211yescharacteristic
8#480×C139—22no—
9#477×C139—22no—
10#474×C139—22no—
11#466×C139—22no—
12#460×C139—22no—
13#459×C139—22no—
14#448×C139—22no—
15#440×C139—24no—
16#432×C139C2212yes—
17C2×C4⋊C8×C139C2211yescharacteristic
18C2×#97×C139C2211yescharacteristic
19#336×C139—22no—
20#329×C139—24no—
21C2×#41×C139—22no—
22C22×Q8×C139D411yescharacteristic
23C2×SD16×C139—24no—
24C2×D8×C139—22no—
25C22×C8×C139—21no—
26C22×C8×C139D412yes—
27C4⋊Q8×C139D412yes—
28#127×C139D412yes—
29#124×C139—22no—
30#121×C139—22no—
31#121×C139—22no—
32C4×Q8×C139—22no—
33C4×Q8×C139—22no—
34C4×D4×C139—22no—
35C4×D4×C139—22no—
36C2×C4⋊C4×C139—21no—
37C2×C4⋊C4×C139D411yescharacteristic
38C2×C42×C139—21no—
39C2×C42×C139C2311yescharacteristic
40#107×C139—24no—
41#107×C139—22no—
42C4⋊C8×C139—22no—
43C4⋊C8×C139—22no—
44#103×C139—24no—
45#102×C139—24no—
46#102×C139—24no—
47C22⋊C8×C139—22no—
48#97×C139—22no—
49#97×C139D414yes—
50#41×C139—84no—
51C2×Q8×C139—22no—
52C2×Q8×C139—22no—
53C2×Q8×C139—42no—
54C2×D4×C139—22no—
55C2×D4×C139—22no—
56C2×D4×C139—22no—
57C2×D4×C139—42no—
58C22×C4×C139—21no—
59C22×C4×C139—21no—
60C22×C4×C139—42no—
61C22×C4×C139C2×D411yescharacteristic
62C22×C4×C139C2×D411yescharacteristic
63C22×C4×C139#4111yescharacteristic
64SD16×C139—48no—
65D8×C139—82no—
66C2×C8×C139—22no—
67C2×C8×C139—24no—
68C2×C8×C139—22no—
69C2×C8×C139—41no—
70C2×C8×C139—41no—
71C2×C8×C139—42no—
72C4⋊C4×C139—22no—
73C4⋊C4×C139—22no—
74C4⋊C4×C139—22no—
75C4⋊C4×C139—42no—
76C22⋊C4×C139—42no—
77C22⋊C4×C139—42no—
78C42×C139—41no—
79C42×C139—41no—
80C42×C139C2×D412yes—
81C42×C139C2×D412yes—
82C23×C139—42no—
83C23×C139#12111yescharacteristic
84Q8×C139—24no—
85Q8×C139—42no—
86Q8×C139—82no—
87D4×C139—44no—
88D4×C139—42no—
89D4×C139—42no—
90D4×C139—82no—
91D4×C139—84no—
92C2×C4×C139—22no—
93C2×C4×C139—21no—
94C2×C4×C139—21no—
95C2×C4×C139—22no—
96C2×C4×C139—41no—
97C2×C4×C139—41no—
98C2×C4×C139—41no—
99C2×C4×C139—41no—
100C2×C4×C139—42no—
101C2×C4×C139—42no—
102C2×C4×C139—84no—
103C2×C4×C139#12012yes—
104C2×C4×C139#12011yescharacteristic
105C2×C4×C139#12112yes—
106C2×C4×C139#12711yescharacteristic
107C8×C139—42no—
108C8×C139—44no—
109C8×C139—42no—
110C22×C139—21no—
111C22×C139—21no—
112C22×C139—82no—
113C22×C139—82no—
114C22×C139—82no—
115C22×C139#39211yescharacteristic
116C22×C139#47212yes—
117C4×C139—21no—
118C4×C139—22no—
119C4×C139—22no—
120C4×C139—42no—
121C4×C139—81no—
122C4×C139—82no—
123C4×C139#45511yescharacteristic
124C4×C139#45611yescharacteristic
125C2×C139—22no—
126C2×C139—162no—
127C2×C139#200711yescharacteristic
128C2×C139#201011yescharacteristic
129C2×C139#201811yescharacteristic
130#10028C13911yesmaximal, characteristic, direct product factor, Sylow
131C139#1002811yescharacteristic, direct product factor, Sylow
132#3245C2×C13911yescharacteristic
133#3112C2×C13912yescomplemented
134#1985C2×C13911yescharacteristic, complemented
135#1530C2×C13912yescomplemented
136#1290C2×C13911yescharacteristic, complemented
137#532C22×C13912yes—
138C2×C4×Q8C22×C13911yescharacteristic
139#480—22no—
140#477—22no—
141#474—22no—
142#466—22no—
143#460—22no—
144#459—22no—
145#448—22no—
146#440—24no—
147#432C22×C13912yes—
148C2×C4⋊C8C22×C13911yescharacteristic
149C2×#97C22×C13911yescharacteristic
150#336—22no—
151#329—24no—
152C2×#41—22no—
153C22×Q8D4×C13911yescharacteristic
154C2×SD16—24no—
155C2×D8—22no—
156C22×C8—21no—
157C22×C8D4×C13912yes—
158C4⋊Q8D4×C13912yes—
159#127D4×C13912yes—
160#124—22no—
161#121—22no—
162#121—22no—
163C4×Q8—22no—
164C4×Q8—22no—
165C4×D4—22no—
166C4×D4—22no—
167C2×C4⋊C4—21no—
168C2×C4⋊C4D4×C13911yescharacteristic
169C2×C42—21no—
170C2×C42C23×C13911yescharacteristic
171#107—24no—
172#107—22no—
173C4⋊C8—22no—
174C4⋊C8—22no—
175#103—24no—
176#102—24no—
177#102—24no—
178C22⋊C8—22no—
179#97—22no—
180#97D4×C13914yes—
181#41—84no—
182C2×Q8—22no—
183C2×Q8—22no—
184C2×Q8—42no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—22no—
188C2×D4—42no—
189C22×C4—21no—
190C22×C4—21no—
191C22×C4—42no—
192C22×C4C2×D4×C13911yescharacteristic
193C22×C4C2×D4×C13911yescharacteristic
194C22×C4#41×C13911yescharacteristic
195SD16—48no—
196D8—82no—
197C2×C8—22no—
198C2×C8—24no—
199C2×C8—22no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—42no—
203C4⋊C4—22no—
204C4⋊C4—22no—
205C4⋊C4—22no—
206C4⋊C4—42no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C42—41no—
210C42—41no—
211C42C2×D4×C13912yes—
212C42C2×D4×C13912yes—
213C23—42no—
214C23#121×C13911yescharacteristic
215Q8—24no—
216Q8—42no—
217Q8—82no—
218D4—44no—
219D4—42no—
220D4—42no—
221D4—82no—
222D4—84no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—42no—
233C2×C4—84no—
234C2×C4#120×C13912yes—
235C2×C4#120×C13911yescharacteristic
236C2×C4#121×C13912yes—
237C2×C4#127×C13911yescharacteristic
238C8—42no—
239C8—44no—
240C8—42no—
241C22—21no—
242C22—21no—
243C22—82no—
244C22—82no—
245C22—82no—
246C22#392×C13911yescharacteristic
247C22#472×C13912yes—
248C4—21no—
249C4—22no—
250C4—22no—
251C4—42no—
252C4—81no—
253C4—82no—
254C4#455×C13911yescharacteristic
255C4#456×C13911yescharacteristic
256C2—22no—
257C2—162no—
258C2#2007×C13911yescharacteristic
259C2#2010×C13911yescharacteristic
260C2#2018×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#392
commutator, Frattini, cosocleC2×C42C23×C139
prime radical#3245×C139C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3112×C139C2semidirect
3. #1985×C139C2semidirect
4. #1530×C139C2semidirect
5. #1290×C139C2semidirect
130. #10028C139direct (N × H)
131. C139#10028direct (N × H)
133. #3112C2×C139semidirect
134. #1985C2×C139semidirect
135. #1530C2×C139semidirect
136. #1290C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3245×C1392
#3112×C1392
#1985×C1392
#1530×C1392
#1290×C1392
#10028139