Finite Group Databasebeta

← C139×#7813 #48002409

Subgroups — C139×#7813 #48002409

Order 35584.

350 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 98 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#2809×C139C211yesmaximal, characteristic
2#2099×C139C211yesmaximal, characteristic
3#2084×C139C211yesmaximal, characteristic
4#2072×C139C211yesmaximal, characteristic
5#1272×C139C211yesmaximal, characteristic
6#1271×C139C211yesmaximal, characteristic
7#1271×C139C211yesmaximal, characteristic
8C2×#106×C139—21no—
9C2×#103×C139—21no—
10#400×C139—21no—
11#398×C139—21no—
12#398×C139—21no—
13#391×C139—21no—
14#391×C139C2211yescharacteristic
15#389×C139C2211yescharacteristic
16#389×C139C2211yescharacteristic
17#387×C139—21no—
18#387×C139—21no—
19#384×C139C2211yescharacteristic
20#340×C139—21no—
21#340×C139—21no—
22#340×C139—21no—
23#340×C139—21no—
24#336×C139C2211yescharacteristic
25#336×C139C2211yescharacteristic
26#336×C139C2211yescharacteristic
27C22×Q8×C139D411yescharacteristic
28C22×C8×C139—21no—
29C22×C8×C139—21no—
30C22×C8×C139—21no—
31C2×C4⋊C4×C139—21no—
32C2×C4⋊C4×C139—21no—
33C2×C4⋊C4×C139—21no—
34C2×C4⋊C4×C139—21no—
35C2×C4⋊C4×C139—21no—
36C2×C4⋊C4×C139—21no—
37C2×C4⋊C4×C139—21no—
38C2×C4⋊C4×C139D411yescharacteristic
39C2×C4⋊C4×C139D411yescharacteristic
40C2×C4⋊C4×C139D411yescharacteristic
41C2×C4⋊C4×C139D411yescharacteristic
42C2×C4⋊C4×C139D411yescharacteristic
43C2×C42×C139—21no—
44C2×C42×C139C2311yescharacteristic
45#106×C139—42no—
46#103×C139—42no—
47#95×C139—21no—
48#95×C139—21no—
49#95×C139—21no—
50#95×C139—21no—
51#95×C139—21no—
52#95×C139—21no—
53#95×C139—21no—
54#95×C139—21no—
55#95×C139—21no—
56C2×Q8×C139—21no—
57C2×Q8×C139—41no—
58C2×Q8×C139—41no—
59C2×Q8×C139SD1612yes—
60C22×C4×C139—21no—
61C22×C4×C139—21no—
62C22×C4×C139—21no—
63C22×C4×C139—21no—
64C22×C4×C139—21no—
65C22×C4×C139—21no—
66C22×C4×C139—41no—
67C22×C4×C139C2×D411yescharacteristic
68C22×C4×C139C2×D411yescharacteristic
69C22×C4×C139C2×D411yescharacteristic
70C2×C8×C139—22no—
71C2×C8×C139—41no—
72C2×C8×C139—41no—
73C2×C8×C139—41no—
74C2×C8×C139—41no—
75C2×C8×C139—41no—
76C2×C8×C139—41no—
77C2×C8×C139—41no—
78C2×C8×C139—41no—
79C4⋊C4×C139—21no—
80C4⋊C4×C139—21no—
81C4⋊C4×C139—21no—
82C4⋊C4×C139—21no—
83C4⋊C4×C139—41no—
84C4⋊C4×C139—41no—
85C4⋊C4×C139—41no—
86C4⋊C4×C139—42no—
87C4⋊C4×C139—41no—
88C4⋊C4×C139—41no—
89C4⋊C4×C139—41no—
90C4⋊C4×C139—41no—
91C4⋊C4×C139—41no—
92C4⋊C4×C139—41no—
93C4⋊C4×C139—41no—
94C4⋊C4×C139—41no—
95C4⋊C4×C139—81no—
96C4⋊C4×C139—81no—
97C42×C139—41no—
98C42×C139—81no—
99C23×C139#12011yescharacteristic
100Q8×C139—42no—
101Q8×C139—81no—
102C2×C4×C139—21no—
103C2×C4×C139—21no—
104C2×C4×C139—21no—
105C2×C4×C139—21no—
106C2×C4×C139—21no—
107C2×C4×C139—21no—
108C2×C4×C139—22no—
109C2×C4×C139—41no—
110C2×C4×C139—41no—
111C2×C4×C139—41no—
112C2×C4×C139—41no—
113C2×C4×C139—41no—
114C2×C4×C139—41no—
115C2×C4×C139—41no—
116C2×C4×C139—41no—
117C2×C4×C139—41no—
118C2×C4×C139—41no—
119C2×C4×C139—41no—
120C2×C4×C139—41no—
121C2×C4×C139—41no—
122C2×C4×C139—41no—
123C2×C4×C139—41no—
124C2×C4×C139—41no—
125C2×C4×C139—41no—
126C2×C4×C139—81no—
127C2×C4×C139—81no—
128C2×C4×C139—81no—
129C2×C4×C139C2×SD1611yescharacteristic
130C2×C4×C139#13511yescharacteristic
131C2×C4×C139#13511yescharacteristic
132C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
133C2×C4×C139#13711yescharacteristic
134C2×C4×C139#13711yescharacteristic
135C8×C139—42no—
136C8×C139—81no—
137C8×C139—81no—
138C22×C139#44811yescharacteristic
139C22×C139#44911yescharacteristic
140C22×C139#45211yescharacteristic
141C22×C139#45411yescharacteristic
142C22×C139#45511yescharacteristic
143C22×C139#45611yescharacteristic
144C22×C139#45811yescharacteristic
145C4×C139—21no—
146C4×C139—21no—
147C4×C139—21no—
148C4×C139—21no—
149C4×C139—21no—
150C4×C139—21no—
151C4×C139—42no—
152C4×C139—81no—
153C4×C139—81no—
154C4×C139—81no—
155C4×C139—81no—
156C4×C139—81no—
157C4×C139—161no—
158C2×C139#160811yescharacteristic
159C2×C139#160911yescharacteristic
160C2×C139#161511yescharacteristic
161C2×C139#162611yescharacteristic
162C2×C139#164611yescharacteristic
163C2×C139#165311yescharacteristic
164C2×C139#166411yescharacteristic
165#7813C13911yesmaximal, characteristic, direct product factor, Sylow
166C139#781311yescharacteristic, direct product factor, Sylow
167#2809C2×C13911yescharacteristic
168#2099C2×C13911yescharacteristic
169#2084C2×C13911yescharacteristic
170#2072C2×C13911yescharacteristic
171#1272C2×C13911yescharacteristic
172#1271C2×C13911yescharacteristic
173#1271C2×C13911yescharacteristic
174C2×#106—21no—
175C2×#103—21no—
176#400—21no—
177#398—21no—
178#398—21no—
179#391—21no—
180#391C22×C13911yescharacteristic
181#389C22×C13911yescharacteristic
182#389C22×C13911yescharacteristic
183#387—21no—
184#387—21no—
185#384C22×C13911yescharacteristic
186#340—21no—
187#340—21no—
188#340—21no—
189#340—21no—
190#336C22×C13911yescharacteristic
191#336C22×C13911yescharacteristic
192#336C22×C13911yescharacteristic
193C22×Q8D4×C13911yescharacteristic
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4D4×C13911yescharacteristic
205C2×C4⋊C4D4×C13911yescharacteristic
206C2×C4⋊C4D4×C13911yescharacteristic
207C2×C4⋊C4D4×C13911yescharacteristic
208C2×C4⋊C4D4×C13911yescharacteristic
209C2×C42—21no—
210C2×C42C23×C13911yescharacteristic
211#106—42no—
212#103—42no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222C2×Q8—21no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×Q8SD16×C13912yes—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—41no—
233C22×C4C2×D4×C13911yescharacteristic
234C22×C4C2×D4×C13911yescharacteristic
235C22×C4C2×D4×C13911yescharacteristic
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—81no—
262C4⋊C4—81no—
263C42—41no—
264C42—81no—
265C23#120×C13911yescharacteristic
266Q8—42no—
267Q8—81no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4—81no—
295C2×C4C2×SD16×C13911yescharacteristic
296C2×C4#135×C13911yescharacteristic
297C2×C4#135×C13911yescharacteristic
298C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
299C2×C4#137×C13911yescharacteristic
300C2×C4#137×C13911yescharacteristic
301C8—42no—
302C8—81no—
303C8—81no—
304C22#448×C13911yescharacteristic
305C22#449×C13911yescharacteristic
306C22#452×C13911yescharacteristic
307C22#454×C13911yescharacteristic
308C22#455×C13911yescharacteristic
309C22#456×C13911yescharacteristic
310C22#458×C13911yescharacteristic
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—42no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—81no—
322C4—81no—
323C4—161no—
324C2#1608×C13911yescharacteristic
325C2#1609×C13911yescharacteristic
326C2#1615×C13911yescharacteristic
327C2#1626×C13911yescharacteristic
328C2#1646×C13911yescharacteristic
329C2#1653×C13911yescharacteristic
330C2#1664×C13911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C139#120
commutator, Frattini, cosocleC2×C42C23×C139
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
165. #7813C139direct (N × H)
166. C139#7813direct (N × H)

Maximal subgroups

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

subgroupindex
#2809×C1392
#2099×C1392
#2084×C1392
#2072×C1392
#1272×C1392
#1271×C1392
#7813139