Finite Group Databasebeta

← C139×#13352 #48007948

Subgroups — C139×#13352 #48007948

Order 35584.

682 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 94 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#3202×C139C211yesmaximal, characteristic, complemented
2#3028×C139C212yesmaximal
3#2129×C139C212yesmaximal, complemented
4#1794×C139C211yesmaximal, characteristic
5#1391×C139C211yesmaximal, characteristic, complemented
6#585×C139C2211yescharacteristic
7#536×C139—22no—
8#536×C139C2212yes—
9#485×C139—22no—
10#470×C139—21no—
11#467×C139—21no—
12#458×C139—24no—
13#458×C139—24no—
14#451×C139—22no—
15#421×C139—21no—
16#416×C139—21no—
17#410×C139—22no—
18#410×C139C2211yescharacteristic
19#410×C139C2212yes—
20#408×C139C2211yescharacteristic
21#354×C139—24no—
222−1+4×C139—21no—
232−1+4×C139—41no—
24H(5,𝔽2)×C139—22no—
25H(5,𝔽2)×C139—41no—
26H(5,𝔽2)×C139D412yes—
27C2×#41×C139—22no—
28C2×#41×C139—21no—
29C2×#41×C139—42no—
30C2×#41×C139C2311yescharacteristic
31C22×Q8×C139D412yes—
32C2×Q16×C139—21no—
33C2×Q16×C139—21no—
34C2×M16×C139D411yescharacteristic
35C22×C8×C139D411yescharacteristic
36C4⋊Q8×C139—22no—
37C4⋊Q8×C139—42no—
38#124×C139—22no—
39#124×C139—42no—
40#123×C139—28no—
41#123×C139—22no—
42#123×C139—22no—
43C22⋊Q8×C139—22no—
44C22⋊Q8×C139—22no—
45C22⋊Q8×C139—44no—
46#117×C139—22no—
47#117×C139—21no—
48#117×C139D412yes—
49#107×C139—21no—
50#106×C139—21no—
51#104×C139—42no—
52#103×C139—22no—
53#103×C139—22no—
54#103×C139—41no—
55#102×C139—41no—
56#99×C139—28no—
57#99×C139—22no—
58#99×C139—22no—
59#99×C139D414yes—
60C22⋊C8×C139—22no—
61#41×C139—22no—
62#41×C139—22no—
63#41×C139—41no—
64#41×C139—41no—
65#41×C139—42no—
66#41×C139—42no—
67#41×C139—42no—
68#41×C139—41no—
69#41×C139—44no—
70#41×C139—42no—
71#41×C139—41no—
72#41×C139—42no—
73C2×Q8×C139—22no—
74C2×Q8×C139—21no—
75C2×Q8×C139—22no—
76C2×Q8×C139—22no—
77C2×Q8×C139—42no—
78C2×Q8×C139—42no—
79C2×Q8×C139—42no—
80C2×Q8×C139#4111yescharacteristic
81C2×D4×C139—21no—
82C2×D4×C139—22no—
83C2×D4×C139—24no—
84C2×D4×C139—42no—
85C2×D4×C139—44no—
86C2×D4×C139—41no—
87C2×D4×C139C2×D411yescharacteristic
88C2×D4×C139C2×D412yes—
89C22×C4×C139—24no—
90C22×C4×C139—22no—
91C22×C4×C139—41no—
92C22×C4×C139C2×D412yes—
93C22×C4×C139C2×D411yescharacteristic
94Q16×C139—81no—
95Q16×C139—81no—
96M16×C139—41no—
97C2×C8×C139—21no—
98C2×C8×C139—21no—
99C2×C8×C139—41no—
100C4⋊C4×C139—22no—
101C4⋊C4×C139—42no—
102C4⋊C4×C139—48no—
103C4⋊C4×C139—41no—
104C4⋊C4×C139—42no—
105C4⋊C4×C139—42no—
106C22⋊C4×C139—22no—
107C22⋊C4×C139—24no—
108C22⋊C4×C139—48no—
109C22⋊C4×C139—42no—
110C22⋊C4×C139—42no—
111C22⋊C4×C139—41no—
112C42×C139—22no—
113C42×C139—42no—
114C42×C139—41no—
115C23×C139—24no—
116C23×C139—41no—
117C23×C139#12012yes—
118C23×C139#12711yescharacteristic
119Q8×C139—22no—
120Q8×C139—41no—
121Q8×C139—42no—
122Q8×C139—41no—
123Q8×C139—42no—
124Q8×C139—42no—
125Q8×C139—82no—
126D4×C139—22no—
127D4×C139—41no—
128D4×C139—42no—
129D4×C139—42no—
130D4×C139—44no—
131D4×C139—42no—
132D4×C139—42no—
133D4×C139—41no—
134C2×C4×C139—21no—
135C2×C4×C139—22no—
136C2×C4×C139—21no—
137C2×C4×C139—22no—
138C2×C4×C139—24no—
139C2×C4×C139—44no—
140C2×C4×C139—42no—
141C2×C4×C139—41no—
142C2×C4×C139—42no—
143C2×C4×C139—44no—
144C2×C4×C139—44no—
145C2×C4×C139—42no—
146C2×C4×C139—42no—
147C2×C4×C139—81no—
148C2×C4×C139#12011yescharacteristic
149C2×C4×C139#12112yes—
150C2×C4×C139#12111yescharacteristic
151C8×C139—41no—
152C8×C139—41no—
153C22×C139—22no—
154C22×C139—21no—
155C22×C139—42no—
156C22×C139—41no—
157C22×C139—42no—
158C22×C139—84no—
159C22×C139—161no—
160C22×C139#39211yescharacteristic
161C4×C139—21no—
162C4×C139—22no—
163C4×C139—42no—
164C4×C139—82no—
165C4×C139—84no—
166C4×C139—82no—
167C4×C139—161no—
168C4×C139B(4,𝔽2)11yescharacteristic
169C4×C139B(4,𝔽2)11yescharacteristic
170C2×C139—21no—
171C2×C139—42no—
172C2×C139—41no—
173C2×C139—82no—
174C2×C139#202111yescharacteristic
175#13352C13911yesmaximal, characteristic, direct product factor, Sylow
176C139#1335211yescharacteristic, direct product factor, Sylow
177#3202C2×C13911yescharacteristic, complemented
178#3028C2×C13912yes—
179#2129C2×C13912yescomplemented
180#1794C2×C13911yescharacteristic
181#1391C2×C13911yescharacteristic, complemented
182#585C22×C13911yescharacteristic
183#536—22no—
184#536C22×C13912yes—
185#485—22no—
186#470—21no—
187#467—21no—
188#458—24no—
189#458—24no—
190#451—22no—
191#421—21no—
192#416—21no—
193#410—22no—
194#410C22×C13911yescharacteristic
195#410C22×C13912yes—
196#408C22×C13911yescharacteristic
197#354—24no—
1982−1+4—21no—
1992−1+4—41no—
200H(5,𝔽2)—22no—
201H(5,𝔽2)—41no—
202H(5,𝔽2)D4×C13912yes—
203C2×#41—22no—
204C2×#41—21no—
205C2×#41—42no—
206C2×#41C23×C13911yescharacteristic
207C22×Q8D4×C13912yes—
208C2×Q16—21no—
209C2×Q16—21no—
210C2×M16D4×C13911yescharacteristic
211C22×C8D4×C13911yescharacteristic
212C4⋊Q8—22no—
213C4⋊Q8—42no—
214#124—22no—
215#124—42no—
216#123—28no—
217#123—22no—
218#123—22no—
219C22⋊Q8—22no—
220C22⋊Q8—22no—
221C22⋊Q8—44no—
222#117—22no—
223#117—21no—
224#117D4×C13912yes—
225#107—21no—
226#106—21no—
227#104—42no—
228#103—22no—
229#103—22no—
230#103—41no—
231#102—41no—
232#99—28no—
233#99—22no—
234#99—22no—
235#99D4×C13914yes—
236C22⋊C8—22no—
237#41—22no—
238#41—22no—
239#41—41no—
240#41—41no—
241#41—42no—
242#41—42no—
243#41—42no—
244#41—41no—
245#41—44no—
246#41—42no—
247#41—41no—
248#41—42no—
249C2×Q8—22no—
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—22no—
253C2×Q8—42no—
254C2×Q8—42no—
255C2×Q8—42no—
256C2×Q8#41×C13911yescharacteristic
257C2×D4—21no—
258C2×D4—22no—
259C2×D4—24no—
260C2×D4—42no—
261C2×D4—44no—
262C2×D4—41no—
263C2×D4C2×D4×C13911yescharacteristic
264C2×D4C2×D4×C13912yes—
265C22×C4—24no—
266C22×C4—22no—
267C22×C4—41no—
268C22×C4C2×D4×C13912yes—
269C22×C4C2×D4×C13911yescharacteristic
270Q16—81no—
271Q16—81no—
272M16—41no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—41no—
276C4⋊C4—22no—
277C4⋊C4—42no—
278C4⋊C4—48no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C22⋊C4—22no—
283C22⋊C4—24no—
284C22⋊C4—48no—
285C22⋊C4—42no—
286C22⋊C4—42no—
287C22⋊C4—41no—
288C42—22no—
289C42—42no—
290C42—41no—
291C23—24no—
292C23—41no—
293C23#120×C13912yes—
294C23#127×C13911yescharacteristic
295Q8—22no—
296Q8—41no—
297Q8—42no—
298Q8—41no—
299Q8—42no—
300Q8—42no—
301Q8—82no—
302D4—22no—
303D4—41no—
304D4—42no—
305D4—42no—
306D4—44no—
307D4—42no—
308D4—42no—
309D4—41no—
310C2×C4—21no—
311C2×C4—22no—
312C2×C4—21no—
313C2×C4—22no—
314C2×C4—24no—
315C2×C4—44no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—81no—
324C2×C4#120×C13911yescharacteristic
325C2×C4#121×C13912yes—
326C2×C4#121×C13911yescharacteristic
327C8—41no—
328C8—41no—
329C22—22no—
330C22—21no—
331C22—42no—
332C22—41no—
333C22—42no—
334C22—84no—
335C22—161no—
336C22#392×C13911yescharacteristic
337C4—21no—
338C4—22no—
339C4—42no—
340C4—82no—
341C4—84no—
342C4—82no—
343C4—161no—
344C4B(4,𝔽2)×C13911yescharacteristic
345C4B(4,𝔽2)×C13911yescharacteristic
346C2—21no—
347C2—42no—
348C2—41no—
349C2—82no—
350C2#2021×C13911yescharacteristic
subgroupG/H
center, socleC2×C139#2021
commutator, Frattini, cosocleC2×#41C23×C139
prime radical#585×C139C22
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C139 ◁ C2×C4×C139 ◁ C2×#41×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3202×C139C2semidirect
3. #2129×C139C2semidirect
5. #1391×C139C2semidirect
175. #13352C139direct (N × H)
176. C139#13352direct (N × H)
177. #3202C2×C139semidirect
179. #2129C2×C139semidirect
181. #1391C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3202×C1392
#3028×C1392
#2129×C1392
#1794×C1392
#1391×C1392
#13352139