Finite Group Databasebeta

← C139×#12203 #48006799

Subgroups — C139×#12203 #48006799

Order 35584.

532 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 74 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#2483×C139C211yesmaximal, characteristic
2#2029×C139C211yesmaximal, characteristic
3#1608×C139C212yesmaximal, complemented
4#1344×C139C212yesmaximal, complemented
5#1316×C139C211yesmaximal, characteristic
6#543×C139C2211yescharacteristic
7C22×C22⋊C4×C139—21no—
8#483×C139—22no—
9#397×C139—21no—
10#397×C139C2212yes—
11#385×C139—22no—
12#381×C139—22no—
13#379×C139—21no—
14#379×C139C2211yescharacteristic
15#342×C139—21no—
16#342×C139C2211yescharacteristic
17#328×C139—22no—
18#323×C139C2212yes—
19C25×C139D411yescharacteristic
20C23×C4×C139—21no—
21C23×C4×C139—21no—
22C22⋊Q8×C139—22no—
23C22⋊Q8×C139—42no—
24C2×C4⋊C4×C139—21no—
25C2×C4⋊C4×C139D412yes—
26C2×C22⋊C4×C139—22no—
27C2×C22⋊C4×C139—22no—
28C2×C22⋊C4×C139—21no—
29C2×C22⋊C4×C139—22no—
30C2×C22⋊C4×C139—21no—
31C2×C22⋊C4×C139—42no—
32C2×C22⋊C4×C139—42no—
33C2×C22⋊C4×C139—42no—
34C2×C22⋊C4×C139D411yescharacteristic
35C2×C22⋊C4×C139C2311yescharacteristic
36#106×C139—42no—
37#103×C139—42no—
38C22⋊C8×C139—22no—
39#95×C139—21no—
40#95×C139—22no—
41#95×C139—22no—
42#95×C139D412yes—
43C24×C139—21no—
44C24×C139—21no—
45C24×C139—41no—
46C24×C139—44no—
47C24×C139—41no—
48C24×C139SD1612yes—
49C24×C139C2×D411yescharacteristic
50C2×Q8×C139—22no—
51C22×C4×C139—22no—
52C22×C4×C139—21no—
53C22×C4×C139—22no—
54C22×C4×C139—22no—
55C22×C4×C139—42no—
56C22×C4×C139—42no—
57C22×C4×C139—44no—
58C22×C4×C139—41no—
59C22×C4×C139—81no—
60C22×C4×C139—81no—
61C22×C4×C139C2×D412yes—
62C2×C8×C139—42no—
63C4⋊C4×C139—22no—
64C4⋊C4×C139—42no—
65C4⋊C4×C139—42no—
66C4⋊C4×C139—81no—
67C22⋊C4×C139—41no—
68C22⋊C4×C139—44no—
69C22⋊C4×C139—44no—
70C22⋊C4×C139—41no—
71C22⋊C4×C139—41no—
72C22⋊C4×C139—42no—
73C22⋊C4×C139—42no—
74C22⋊C4×C139—41no—
75C22⋊C4×C139—41no—
76C22⋊C4×C139—41no—
77C22⋊C4×C139—84no—
78C23×C139—24no—
79C23×C139—22no—
80C23×C139—21no—
81C23×C139—21no—
82C23×C139—42no—
83C23×C139—44no—
84C23×C139—42no—
85C23×C139—42no—
86C23×C139—44no—
87C23×C139—41no—
88C23×C139—41no—
89C23×C139—44no—
90C23×C139—81no—
91C23×C139—84no—
92C23×C139—82no—
93C23×C139#12011yescharacteristic
94C23×C139C2×SD1611yescharacteristic
95C23×C139AGL(1,ℤ/8)11yescharacteristic
96Q8×C139—82no—
97C2×C4×C139—22no—
98C2×C4×C139—42no—
99C2×C4×C139—42no—
100C2×C4×C139—44no—
101C2×C4×C139—42no—
102C2×C4×C139—42no—
103C2×C4×C139—41no—
104C2×C4×C139—42no—
105C2×C4×C139—42no—
106C2×C4×C139—42no—
107C2×C4×C139—84no—
108C2×C4×C139—84no—
109C2×C4×C139—82no—
110C2×C4×C139—81no—
111C2×C4×C139—82no—
112C8×C139—82no—
113C22×C139—22no—
114C22×C139—24no—
115C22×C139—21no—
116C22×C139—21no—
117C22×C139—41no—
118C22×C139—41no—
119C22×C139—42no—
120C22×C139—44no—
121C22×C139—44no—
122C22×C139—42no—
123C22×C139—42no—
124C22×C139—44no—
125C22×C139—81no—
126C22×C139—84no—
127C22×C139—82no—
128C22×C139#45011yescharacteristic
129C22×C139#45511yescharacteristic
130C22×C139B(4,𝔽2)11yescharacteristic
131C4×C139—42no—
132C4×C139—81no—
133C4×C139—82no—
134C4×C139—82no—
135C4×C139—82no—
136C4×C139—161no—
137C2×C139—21no—
138C2×C139—21no—
139C2×C139—41no—
140C2×C139—44no—
141C2×C139—41no—
142C2×C139#160111yescharacteristic
143C2×C139#219712yes—
144#12203C13911yesmaximal, characteristic, direct product factor, Sylow
145C139#1220311yescharacteristic, direct product factor, Sylow
146#2483C2×C13911yescharacteristic
147#2029C2×C13911yescharacteristic
148#1608C2×C13912yescomplemented
149#1344C2×C13912yescomplemented
150#1316C2×C13911yescharacteristic
151#543C22×C13911yescharacteristic
152C22×C22⋊C4—21no—
153#483—22no—
154#397—21no—
155#397C22×C13912yes—
156#385—22no—
157#381—22no—
158#379—21no—
159#379C22×C13911yescharacteristic
160#342—21no—
161#342C22×C13911yescharacteristic
162#328—22no—
163#323C22×C13912yes—
164C25D4×C13911yescharacteristic
165C23×C4—21no—
166C23×C4—21no—
167C22⋊Q8—22no—
168C22⋊Q8—42no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4D4×C13912yes—
171C2×C22⋊C4—22no—
172C2×C22⋊C4—22no—
173C2×C22⋊C4—21no—
174C2×C22⋊C4—22no—
175C2×C22⋊C4—21no—
176C2×C22⋊C4—42no—
177C2×C22⋊C4—42no—
178C2×C22⋊C4—42no—
179C2×C22⋊C4D4×C13911yescharacteristic
180C2×C22⋊C4C23×C13911yescharacteristic
181#106—42no—
182#103—42no—
183C22⋊C8—22no—
184#95—21no—
185#95—22no—
186#95—22no—
187#95D4×C13912yes—
188C24—21no—
189C24—21no—
190C24—41no—
191C24—44no—
192C24—41no—
193C24SD16×C13912yes—
194C24C2×D4×C13911yescharacteristic
195C2×Q8—22no—
196C22×C4—22no—
197C22×C4—21no—
198C22×C4—22no—
199C22×C4—22no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—44no—
203C22×C4—41no—
204C22×C4—81no—
205C22×C4—81no—
206C22×C4C2×D4×C13912yes—
207C2×C8—42no—
208C4⋊C4—22no—
209C4⋊C4—42no—
210C4⋊C4—42no—
211C4⋊C4—81no—
212C22⋊C4—41no—
213C22⋊C4—44no—
214C22⋊C4—44no—
215C22⋊C4—41no—
216C22⋊C4—41no—
217C22⋊C4—42no—
218C22⋊C4—42no—
219C22⋊C4—41no—
220C22⋊C4—41no—
221C22⋊C4—41no—
222C22⋊C4—84no—
223C23—24no—
224C23—22no—
225C23—21no—
226C23—21no—
227C23—42no—
228C23—44no—
229C23—42no—
230C23—42no—
231C23—44no—
232C23—41no—
233C23—41no—
234C23—44no—
235C23—81no—
236C23—84no—
237C23—82no—
238C23#120×C13911yescharacteristic
239C23C2×SD16×C13911yescharacteristic
240C23AGL(1,ℤ/8)×C13911yescharacteristic
241Q8—82no—
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—44no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—41no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—84no—
253C2×C4—84no—
254C2×C4—82no—
255C2×C4—81no—
256C2×C4—82no—
257C8—82no—
258C22—22no—
259C22—24no—
260C22—21no—
261C22—21no—
262C22—41no—
263C22—41no—
264C22—42no—
265C22—44no—
266C22—44no—
267C22—42no—
268C22—42no—
269C22—44no—
270C22—81no—
271C22—84no—
272C22—82no—
273C22#450×C13911yescharacteristic
274C22#455×C13911yescharacteristic
275C22B(4,𝔽2)×C13911yescharacteristic
276C4—42no—
277C4—82no—
278C4—81no—
279C4—82no—
280C4—82no—
281C4—161no—
282C2—21no—
283C2—21no—
284C2—41no—
285C2—44no—
286C2—41no—
287C2#1601×C13911yescharacteristic
288C2#2197×C13912yes—
subgroupG/H
center, socleC22×C139B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C139
prime radicalC25×C139D4
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C139 ◁ C2×C22⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1608×C139C2semidirect
4. #1344×C139C2semidirect
144. #12203C139direct (N × H)
145. C139#12203direct (N × H)
148. #1608C2×C139semidirect
149. #1344C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2483×C1392
#2029×C1392
#1608×C1392
#1344×C1392
#1316×C1392
#12203139