Finite Group Databasebeta

← C139×#7313 #48001909

Subgroups — C139×#7313 #48001909

Order 35584.

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

normal subgroups only

This group has 470 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#1785×C139C211yesmaximal, characteristic
2#1782×C139C211yesmaximal, characteristic
3#1782×C139C211yesmaximal, characteristic
4C22×#41×C139C2211yescharacteristic
5C2×#101×C139C412yescomplemented
6C2×#100×C139—21no—
7C2×#99×C139—21no—
8C2×#99×C139—21no—
9C2×#99×C139—21no—
10C2×#99×C139C412yescomplemented
11#407×C139—21no—
12#381×C139—21no—
13#381×C139C412yescomplemented
14C2×#41×C139—42no—
15C2×#41×C139—42no—
16C2×#41×C139—42no—
17C22×Q8×C139C2×C411yescharacteristic
18C22×D4×C139C2×C411yescharacteristic
19C22×D4×C139D411yescharacteristic
20C22×D4×C139D411yescharacteristic
21C23×C4×C139C2×C411yescharacteristic
22C23×C4×C139D411yescharacteristic
23C23×C4×C139Q811yescharacteristic
24C2×M16×C139—22no—
25C2×C22⋊C4×C139—22no—
26C2×C22⋊C4×C139—22no—
27#101×C139—42no—
28#100×C139—42no—
29#99×C139—42no—
30#99×C139—42no—
31#99×C139—42no—
32#99×C139—42no—
33C22⋊C8×C139—42no—
34#95×C139—42no—
35#95×C139—42no—
36C24×C139C22⋊C411yescharacteristic
37C24×C139C22⋊C411yescharacteristic
38C24×C139C4⋊C411yescharacteristic
39#41×C139—416no—
40C2×Q8×C139—22no—
41C2×Q8×C139—41no—
42C2×Q8×C139—41no—
43C2×D4×C139—22no—
44C2×D4×C139—22no—
45C2×D4×C139—22no—
46C2×D4×C139—22no—
47C2×D4×C139—22no—
48C2×D4×C139—41no—
49C2×D4×C139—41no—
50C2×D4×C139—41no—
51C2×D4×C139—41no—
52C22×C4×C139—22no—
53C22×C4×C139—22no—
54C22×C4×C139—22no—
55C22×C4×C139—41no—
56C22×C4×C139—41no—
57C22×C4×C139—41no—
58C22×C4×C139—41no—
59C22×C4×C139—41no—
60C22×C4×C139—41no—
61C22×C4×C139—42no—
62C22×C4×C139—42no—
63C22×C4×C139C4211yescharacteristic
64C22×C4×C139C22⋊C411yescharacteristic
65C22×C4×C139C4⋊C411yescharacteristic
66C22×C4×C139C4⋊C411yescharacteristic
67M16×C139—42no—
68M16×C139—42no—
69C2×C8×C139—42no—
70C22⋊C4×C139—42no—
71C22⋊C4×C139—42no—
72C22⋊C4×C139—42no—
73C22⋊C4×C139—42no—
74C23×C139—21no—
75C23×C139—21no—
76C23×C139—21no—
77C23×C139—21no—
78C23×C139—21no—
79C23×C139—21no—
80C23×C139—21no—
81C23×C139—81no—
82C23×C139—81no—
83C23×C139—81no—
84C23×C139#9511yescharacteristic
85C23×C139#9912yes—
86C23×C139#9912yes—
87Q8×C139—44no—
88D4×C139—44no—
89D4×C139—44no—
90D4×C139—44no—
91C2×C4×C139—21no—
92C2×C4×C139—21no—
93C2×C4×C139—21no—
94C2×C4×C139—21no—
95C2×C4×C139—21no—
96C2×C4×C139—21no—
97C2×C4×C139—21no—
98C2×C4×C139—21no—
99C2×C4×C139—21no—
100C2×C4×C139—21no—
101C2×C4×C139—21no—
102C2×C4×C139—44no—
103C2×C4×C139—44no—
104C2×C4×C139—44no—
105C2×C4×C139—82no—
106C2×C4×C139—82no—
107C2×C4×C139—84no—
108C2×C4×C139—84no—
109C2×C4×C139#9912yes—
110C8×C139—82no—
111C22×C139—22no—
112C22×C139—22no—
113C22×C139—41no—
114C22×C139—42no—
115C22×C139—42no—
116C22×C139—42no—
117C22×C139—41no—
118C22×C139—81no—
119C22×C139—81no—
120C22×C139—81no—
121C22×C139—81no—
122C22×C139—81no—
123C22×C139—81no—
124C22×C139#34211yescharacteristic
125C22×C139#34211yescharacteristic
126C22×C139#34211yescharacteristic
127C4×C139—22no—
128C4×C139—41no—
129C4×C139—41no—
130C4×C139—41no—
131C4×C139—162no—
132C4×C139—162no—
133C2×C139—21no—
134C2×C139—21no—
135C2×C139—21no—
136C2×C139—42no—
137C2×C139—42no—
138C2×C139—81no—
139C2×C139#130411yescharacteristic
140#7313C13911yesmaximal, characteristic, direct product factor, Sylow
141C139#731311yescharacteristic, direct product factor, Sylow
142#1785C2×C13911yescharacteristic
143#1782C2×C13911yescharacteristic
144#1782C2×C13911yescharacteristic
145C22×#41C22×C13911yescharacteristic
146C2×#101C4×C13912yescomplemented
147C2×#100—21no—
148C2×#99—21no—
149C2×#99—21no—
150C2×#99—21no—
151C2×#99C4×C13912yescomplemented
152#407—21no—
153#381—21no—
154#381C4×C13912yescomplemented
155C2×#41—42no—
156C2×#41—42no—
157C2×#41—42no—
158C22×Q8C2×C4×C13911yescharacteristic
159C22×D4C2×C4×C13911yescharacteristic
160C22×D4D4×C13911yescharacteristic
161C22×D4D4×C13911yescharacteristic
162C23×C4C2×C4×C13911yescharacteristic
163C23×C4D4×C13911yescharacteristic
164C23×C4Q8×C13911yescharacteristic
165C2×M16—22no—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—22no—
168#101—42no—
169#100—42no—
170#99—42no—
171#99—42no—
172#99—42no—
173#99—42no—
174C22⋊C8—42no—
175#95—42no—
176#95—42no—
177C24C22⋊C4×C13911yescharacteristic
178C24C22⋊C4×C13911yescharacteristic
179C24C4⋊C4×C13911yescharacteristic
180#41—416no—
181C2×Q8—22no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×D4—22no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—22no—
188C2×D4—22no—
189C2×D4—41no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4—41no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—22no—
196C22×C4—41no—
197C22×C4—41no—
198C22×C4—41no—
199C22×C4—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—42no—
203C22×C4—42no—
204C22×C4C42×C13911yescharacteristic
205C22×C4C22⋊C4×C13911yescharacteristic
206C22×C4C4⋊C4×C13911yescharacteristic
207C22×C4C4⋊C4×C13911yescharacteristic
208M16—42no—
209M16—42no—
210C2×C8—42no—
211C22⋊C4—42no—
212C22⋊C4—42no—
213C22⋊C4—42no—
214C22⋊C4—42no—
215C23—21no—
216C23—21no—
217C23—21no—
218C23—21no—
219C23—21no—
220C23—21no—
221C23—21no—
222C23—81no—
223C23—81no—
224C23—81no—
225C23#95×C13911yescharacteristic
226C23#99×C13912yes—
227C23#99×C13912yes—
228Q8—44no—
229D4—44no—
230D4—44no—
231D4—44no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—44no—
244C2×C4—44no—
245C2×C4—44no—
246C2×C4—82no—
247C2×C4—82no—
248C2×C4—84no—
249C2×C4—84no—
250C2×C4#99×C13912yes—
251C8—82no—
252C22—22no—
253C22—22no—
254C22—41no—
255C22—42no—
256C22—42no—
257C22—42no—
258C22—41no—
259C22—81no—
260C22—81no—
261C22—81no—
262C22—81no—
263C22—81no—
264C22—81no—
265C22#342×C13911yescharacteristic
266C22#342×C13911yescharacteristic
267C22#342×C13911yescharacteristic
268C4—22no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—162no—
273C4—162no—
274C2—21no—
275C2—21no—
276C2—21no—
277C2—42no—
278C2—42no—
279C2—81no—
280C2#1304×C13911yescharacteristic
subgroupG/H
center, socleC2×C139#1304
commutatorC22×C4C42×C139
Frattini, cosocleC22×#41C22×C139
prime radicalC22×#41×C139C22
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C139 ◁ C23×C139 ◁ C22×#41×C139 ◁ G

Complements

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

NH ≅ G/Ntype
5. C2×#101×C139C4semidirect
10. C2×#99×C139C4semidirect
13. #381×C139C4semidirect
140. #7313C139direct (N × H)
141. C139#7313direct (N × H)
146. C2×#101C4×C139semidirect
151. C2×#99C4×C139semidirect
154. #381C4×C139semidirect

Maximal subgroups

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

subgroupindex
#1785×C1392
#1782×C1392
#7313139