Finite Group Databasebeta

← C139×#13428 #48008024

Subgroups — C139×#13428 #48008024

Order 35584.

444 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 90 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#2734×C139C211yesmaximal, characteristic
2C2×#356×C139C212yesmaximal
3#1886×C139C212yesmaximal
4#1857×C139C211yesmaximal, characteristic
5#1394×C139C211yesmaximal, characteristic
6C2×C4⋊Q8×C139C2212yes—
7#519×C139C2211yescharacteristic
8#428×C139—21no—
9#419×C139—22no—
10C2×#101×C139C2212yes—
11C2×#101×C139C2211yescharacteristic
12#398×C139—21no—
13#395×C139—22no—
14#391×C139C2211yescharacteristic
15#389×C139—21no—
16#387×C139—22no—
17#356×C139—24no—
18#339×C139—21no—
19#339×C139—22no—
20C22×Q8×C139D412yes—
21C22×Q8×C139C2311yescharacteristic
22C2×M16×C139—21no—
23C2×M16×C139—22no—
24C4⋊Q8×C139—22no—
25C4⋊Q8×C139—22no—
26C4⋊Q8×C139—22no—
27C4⋊Q8×C139—22no—
28C4×Q8×C139—41no—
29C4×Q8×C139—41no—
30#117×C139—22no—
31#117×C139—21no—
32C2×C4⋊C4×C139—21no—
33C2×C4⋊C4×C139—22no—
34C2×C4⋊C4×C139—22no—
35C2×C4⋊C4×C139—21no—
36C2×C4⋊C4×C139—21no—
37C2×C4⋊C4×C139D411yescharacteristic
38C2×C42×C139D412yes—
39C2×C42×C139D411yescharacteristic
40#107×C139—41no—
41#106×C139—41no—
42#103×C139—42no—
43#103×C139—42no—
44#101×C139—21no—
45#101×C139—22no—
46#101×C139—22no—
47#101×C139D412yes—
48#95×C139—22no—
49#95×C139—22no—
50#95×C139—21no—
51#95×C139—22no—
52C2×Q8×C139—22no—
53C2×Q8×C139—22no—
54C2×Q8×C139—41no—
55C2×Q8×C139—41no—
56C2×Q8×C139—42no—
57C2×Q8×C139—42no—
58C2×Q8×C139C2×D411yescharacteristic
59C2×Q8×C139#4111yescharacteristic
60C2×Q8×C139#4112yes—
61C22×C4×C139—21no—
62C22×C4×C139—22no—
63C22×C4×C139—21no—
64C22×C4×C139—22no—
65C22×C4×C139C2×D412yes—
66C22×C4×C139C2×D411yescharacteristic
67M16×C139—22no—
68M16×C139—41no—
69M16×C139—42no—
70M16×C139—42no—
71C2×C8×C139—41no—
72C2×C8×C139—42no—
73C4⋊C4×C139—24no—
74C4⋊C4×C139—22no—
75C4⋊C4×C139—22no—
76C4⋊C4×C139—21no—
77C4⋊C4×C139—21no—
78C4⋊C4×C139—41no—
79C4⋊C4×C139—42no—
80C4⋊C4×C139—42no—
81C4⋊C4×C139—42no—
82C4⋊C4×C139—42no—
83C4⋊C4×C139—81no—
84C4⋊C4×C139—81no—
85C22⋊C4×C139—41no—
86C42×C139—22no—
87C42×C139—22no—
88C42×C139—41no—
89C42×C139—41no—
90C42×C139—42no—
91C23×C139#12011yescharacteristic
92Q8×C139—41no—
93Q8×C139—41no—
94Q8×C139—42no—
95Q8×C139—44no—
96Q8×C139—82no—
97C2×C4×C139—21no—
98C2×C4×C139—22no—
99C2×C4×C139—21no—
100C2×C4×C139—22no—
101C2×C4×C139—22no—
102C2×C4×C139—24no—
103C2×C4×C139—41no—
104C2×C4×C139—42no—
105C2×C4×C139—42no—
106C2×C4×C139—41no—
107C2×C4×C139—42no—
108C2×C4×C139—42no—
109C2×C4×C139—41no—
110C2×C4×C139—41no—
111C2×C4×C139—41no—
112C2×C4×C139—42no—
113C2×C4×C139—42no—
114C2×C4×C139#12112yes—
115C2×C4×C139#12111yescharacteristic
116C2×C4×C139#12312yes—
117C2×C4×C139#12411yescharacteristic
118C8×C139—42no—
119C8×C139—82no—
120C22×C139—21no—
121C22×C139—21no—
122C22×C139#39411yescharacteristic
123C22×C139B(4,𝔽2)11yescharacteristic
124C22×C139#45811yescharacteristic
125C4×C139—21no—
126C4×C139—22no—
127C4×C139—22no—
128C4×C139—21no—
129C4×C139—44no—
130C4×C139—42no—
131C4×C139—81no—
132C4×C139—81no—
133C4×C139—81no—
134C4×C139—82no—
135C2×C139—21no—
136C2×C139—21no—
137C2×C139#204411yescharacteristic
138C2×C139#220311yescharacteristic
139C2×C139#220511yescharacteristic
140#13428C13911yesmaximal, characteristic, direct product factor, Sylow
141C139#1342811yescharacteristic, direct product factor, Sylow
142#2734C2×C13911yescharacteristic
143C2×#356C2×C13912yes—
144#1886C2×C13912yes—
145#1857C2×C13911yescharacteristic
146#1394C2×C13911yescharacteristic
147C2×C4⋊Q8C22×C13912yes—
148#519C22×C13911yescharacteristic
149#428—21no—
150#419—22no—
151C2×#101C22×C13912yes—
152C2×#101C22×C13911yescharacteristic
153#398—21no—
154#395—22no—
155#391C22×C13911yescharacteristic
156#389—21no—
157#387—22no—
158#356—24no—
159#339—21no—
160#339—22no—
161C22×Q8D4×C13912yes—
162C22×Q8C23×C13911yescharacteristic
163C2×M16—21no—
164C2×M16—22no—
165C4⋊Q8—22no—
166C4⋊Q8—22no—
167C4⋊Q8—22no—
168C4⋊Q8—22no—
169C4×Q8—41no—
170C4×Q8—41no—
171#117—22no—
172#117—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4D4×C13911yescharacteristic
179C2×C42D4×C13912yes—
180C2×C42D4×C13911yescharacteristic
181#107—41no—
182#106—41no—
183#103—42no—
184#103—42no—
185#101—21no—
186#101—22no—
187#101—22no—
188#101D4×C13912yes—
189#95—21no—
190#95—22no—
191#95—22no—
192#95—22no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—41no—
196C2×Q8—41no—
197C2×Q8—42no—
198C2×Q8—42no—
199C2×Q8C2×D4×C13911yescharacteristic
200C2×Q8#41×C13911yescharacteristic
201C2×Q8#41×C13912yes—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4C2×D4×C13912yes—
207C22×C4C2×D4×C13911yescharacteristic
208M16—22no—
209M16—41no—
210M16—42no—
211M16—42no—
212C2×C8—41no—
213C2×C8—42no—
214C4⋊C4—24no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—21no—
218C4⋊C4—21no—
219C4⋊C4—41no—
220C4⋊C4—42no—
221C4⋊C4—42no—
222C4⋊C4—42no—
223C4⋊C4—42no—
224C4⋊C4—81no—
225C4⋊C4—81no—
226C22⋊C4—41no—
227C42—22no—
228C42—22no—
229C42—41no—
230C42—41no—
231C42—42no—
232C23#120×C13911yescharacteristic
233Q8—41no—
234Q8—41no—
235Q8—42no—
236Q8—44no—
237Q8—82no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—24no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4#121×C13912yes—
256C2×C4#121×C13911yescharacteristic
257C2×C4#123×C13912yes—
258C2×C4#124×C13911yescharacteristic
259C8—42no—
260C8—82no—
261C22—21no—
262C22—21no—
263C22#394×C13911yescharacteristic
264C22B(4,𝔽2)×C13911yescharacteristic
265C22#458×C13911yescharacteristic
266C4—21no—
267C4—22no—
268C4—22no—
269C4—21no—
270C4—44no—
271C4—42no—
272C4—82no—
273C4—81no—
274C4—81no—
275C4—81no—
276C2—21no—
277C2—21no—
278C2#2044×C13911yescharacteristic
279C2#2203×C13911yescharacteristic
280C2#2205×C13911yescharacteristic
subgroupG/H
center, socleC22×C139B(4,𝔽2)
commutator, Frattini, cosocleC22×Q8C23×C139
prime radicalC23×C139#120
LCSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C139 ◁ C22×Q8×C139 ◁ G

Complements

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

NH ≅ G/Ntype
140. #13428C139direct (N × H)
141. C139#13428direct (N × H)

Maximal subgroups

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

subgroupindex
#2734×C1392
C2×#356×C1392
#1886×C1392
#1857×C1392
#1394×C1392
#13428139