Finite Group Databasebeta

← C139×#10947 #48005543

Subgroups — C139×#10947 #48005543

Order 35584.

914 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#419×C139C212yesmaximal
2#2873×C139C211yesmaximal, characteristic
3#2310×C139C211yesmaximal, characteristic
4#1740×C139C211yesmaximal, characteristic
5C2×H(3,ℤ/4)×C139C212yesmaximal
6C23×Q8×C139C2211yescharacteristic
7C22×M16×C139C2212yes—
8C2×#117×C139C2212yes—
9C2×#117×C139C2211yescharacteristic
10C2×#117×C139C2211yescharacteristic
11#419×C139—24no—
12#419×C139C418yescomplemented
13C2×#103×C139—24no—
14#405×C139—24no—
15C4×M16×C139—22no—
16#391×C139—22no—
17#391×C139C414yescomplemented
18#381×C139—22no—
19#342×C139—22no—
20H(3,ℤ/4)×C139—24no—
21C22×Q8×C139—21no—
22C22×Q8×C139—22no—
23C22×Q8×C139—22no—
24C22×Q8×C139—22no—
25C22×Q8×C139—22no—
26C22×Q8×C139—22no—
27C22×Q8×C139C2×C414yes—
28C22×Q8×C139C2×C412yes—
29C23×C4×C139—21no—
30C23×C4×C139C2311yescharacteristic
31C2×M16×C139—22no—
32C2×M16×C139—22no—
33C2×M16×C139—22no—
34C2×M16×C139—22no—
35C2×M16×C139C2×C414yes—
36C2×M16×C139D414yes—
37C22×C8×C139D414yes—
38#117×C139—22no—
39#117×C139—22no—
40#117×C139—22no—
41#117×C139—22no—
42#117×C139—22no—
43#117×C139—22no—
44#117×C139—22no—
45#117×C139C2×C414yes—
46C2×C4⋊C4×C139—22no—
47C2×C4⋊C4×C139—21no—
48C2×C4⋊C4×C139C2×C412yes—
49C2×C22⋊C4×C139—22no—
50C2×C22⋊C4×C139—21no—
51C2×C22⋊C4×C139D412yes—
52C2×C42×C139—22no—
53C2×C42×C139C2×C412yes—
54C2×C42×C139D412yes—
55#103×C139—216no—
56#97×C139—24no—
57C4×C8×C139—24no—
58#95×C139—28no—
59C24×C139C2×D411yescharacteristic
60C2×Q8×C139—22no—
61C2×Q8×C139—24no—
62C2×Q8×C139—24no—
63C2×Q8×C139—24no—
64C2×Q8×C139—24no—
65C2×Q8×C139—24no—
66C2×Q8×C139—24no—
67C2×Q8×C139—24no—
68C2×Q8×C139—41no—
69C2×Q8×C139—42no—
70C2×Q8×C139—42no—
71C2×Q8×C139—41no—
72C2×Q8×C139—42no—
73C2×Q8×C139—42no—
74C2×Q8×C139—42no—
75C2×Q8×C139C4214yes—
76C22×C4×C139—22no—
77C22×C4×C139—24no—
78C22×C4×C139—22no—
79C22×C4×C139—42no—
80C22×C4×C139—41no—
81C22×C4×C139—41no—
82C22×C4×C139—42no—
83C22×C4×C139C22⋊C414yes—
84C22×C4×C139C22×C412yes—
85C22×C4×C139C22×C411yescharacteristic
86C22×C4×C139C2×D412yes—
87C22×C4×C139C2×D412yes—
88C22×C4×C139C2×D411yescharacteristic
89C22×C4×C139#4112yes—
90C22×C4×C139#4112yes—
91C22×C4×C139#4112yes—
92M16×C139—24no—
93M16×C139—24no—
94M16×C139—24no—
95M16×C139—24no—
96C2×C8×C139—24no—
97C2×C8×C139—24no—
98C2×C8×C139C22⋊C418yes—
99C4⋊C4×C139—24no—
100C4⋊C4×C139—24no—
101C4⋊C4×C139—42no—
102C4⋊C4×C139—42no—
103C22⋊C4×C139—24no—
104C22⋊C4×C139—24no—
105C22⋊C4×C139—41no—
106C22⋊C4×C139—41no—
107C22⋊C4×C139—42no—
108C42×C139—22no—
109C42×C139—22no—
110C42×C139—24no—
111C42×C139—24no—
112C42×C139—42no—
113C23×C139—42no—
114C23×C139C2×C22⋊C411yescharacteristic
115C23×C139C4×D412yes—
116C23×C139#12112yes—
117C23×C139#12411yescharacteristic
118C23×C139#12711yescharacteristic
119Q8×C139—28no—
120Q8×C139—44no—
121Q8×C139—44no—
122Q8×C139—44no—
123C2×C4×C139—24no—
124C2×C4×C139—24no—
125C2×C4×C139—42no—
126C2×C4×C139—44no—
127C2×C4×C139—44no—
128C2×C4×C139—42no—
129C2×C4×C139—44no—
130C2×C4×C139—44no—
131C2×C4×C139—42no—
132C2×C4×C139—44no—
133C2×C4×C139—84no—
134C2×C4×C139C2×C4211yescharacteristic
135C2×C4×C139C2×C22⋊C412yes—
136C2×C4×C139#11712yes—
137C2×C4×C139#11711yescharacteristic
138C2×C4×C139C4×D412yes—
139C2×C4×C139C4×D412yes—
140C2×C4×C139C4×D412yes—
141C2×C4×C139C4×D412yes—
142C2×C4×C139C4×D412yes—
143C2×C4×C139#12011yescharacteristic
144C2×C4×C139#12112yes—
145C2×C4×C139#12112yes—
146C2×C4×C139#12312yes—
147C2×C4×C139#12311yescharacteristic
148C2×C4×C139#12412yes—
149C2×C4×C139#12612yes—
150C8×C139—28no—
151C22×C139—22no—
152C22×C139—24no—
153C22×C139—42no—
154C22×C139—41no—
155C22×C139—41no—
156C22×C139C4×C22⋊C411yescharacteristic
157C22×C139#38611yescharacteristic
158C22×C139#38812yes—
159C22×C139#39012yes—
160C22×C139#39011yescharacteristic
161C4×C139—44no—
162C4×C139—44no—
163C4×C139—82no—
164C4×C139—84no—
165C4×C139C4×C22⋊C412yes—
166C4×C139#38612yes—
167C4×C139#38812yes—
168C4×C139#38812yes—
169C2×C139—21no—
170C2×C139—22no—
171C2×C139—21no—
172C2×C139—22no—
173C2×C139#143711yescharacteristic
174C2×C139#190912yes—
175#10947C13911yesmaximal, characteristic, direct product factor, Sylow
176C139#1094711yescharacteristic, direct product factor, Sylow
177C2×#419C2×C13912yes—
178#2873C2×C13911yescharacteristic
179#2310C2×C13911yescharacteristic
180#1740C2×C13911yescharacteristic
181C2×H(3,ℤ/4)C2×C13912yes—
182C23×Q8C22×C13911yescharacteristic
183C22×M16C22×C13912yes—
184C2×#117C22×C13912yes—
185C2×#117C22×C13911yescharacteristic
186C2×#117C22×C13911yescharacteristic
187#419—24no—
188#419C4×C13918yescomplemented
189C2×#103—24no—
190#405—24no—
191C4×M16—22no—
192#391—22no—
193#391C4×C13914yescomplemented
194#381—22no—
195#342—22no—
196H(3,ℤ/4)—24no—
197C22×Q8—21no—
198C22×Q8—22no—
199C22×Q8—22no—
200C22×Q8—22no—
201C22×Q8—22no—
202C22×Q8—22no—
203C22×Q8C2×C4×C13912yes—
204C22×Q8C2×C4×C13914yes—
205C23×C4—21no—
206C23×C4C23×C13911yescharacteristic
207C2×M16—22no—
208C2×M16—22no—
209C2×M16—22no—
210C2×M16—22no—
211C2×M16C2×C4×C13914yes—
212C2×M16D4×C13914yes—
213C22×C8D4×C13914yes—
214#117—22no—
215#117—22no—
216#117—22no—
217#117—22no—
218#117—22no—
219#117—22no—
220#117—22no—
221#117C2×C4×C13914yes—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4C2×C4×C13912yes—
225C2×C22⋊C4—22no—
226C2×C22⋊C4—21no—
227C2×C22⋊C4D4×C13912yes—
228C2×C42—22no—
229C2×C42C2×C4×C13912yes—
230C2×C42D4×C13912yes—
231#103—216no—
232#97—24no—
233C4×C8—24no—
234#95—28no—
235C24C2×D4×C13911yescharacteristic
236C2×Q8—22no—
237C2×Q8—24no—
238C2×Q8—24no—
239C2×Q8—24no—
240C2×Q8—24no—
241C2×Q8—24no—
242C2×Q8—24no—
243C2×Q8—24no—
244C2×Q8—41no—
245C2×Q8—42no—
246C2×Q8—42no—
247C2×Q8—41no—
248C2×Q8—42no—
249C2×Q8—42no—
250C2×Q8—42no—
251C2×Q8C42×C13914yes—
252C22×C4—22no—
253C22×C4—24no—
254C22×C4—22no—
255C22×C4—42no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—42no—
259C22×C4C22⋊C4×C13914yes—
260C22×C4C22×C4×C13912yes—
261C22×C4C22×C4×C13911yescharacteristic
262C22×C4C2×D4×C13912yes—
263C22×C4C2×D4×C13912yes—
264C22×C4C2×D4×C13911yescharacteristic
265C22×C4#41×C13912yes—
266C22×C4#41×C13912yes—
267C22×C4#41×C13912yes—
268M16—24no—
269M16—24no—
270M16—24no—
271M16—24no—
272C2×C8—24no—
273C2×C8—24no—
274C2×C8C22⋊C4×C13918yes—
275C4⋊C4—24no—
276C4⋊C4—24no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C22⋊C4—24no—
280C22⋊C4—24no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C22⋊C4—42no—
284C42—22no—
285C42—22no—
286C42—24no—
287C42—24no—
288C42—42no—
289C23—42no—
290C23C2×C22⋊C4×C13911yescharacteristic
291C23C4×D4×C13912yes—
292C23#121×C13912yes—
293C23#124×C13911yescharacteristic
294C23#127×C13911yescharacteristic
295Q8—28no—
296Q8—44no—
297Q8—44no—
298Q8—44no—
299C2×C4—24no—
300C2×C4—24no—
301C2×C4—42no—
302C2×C4—44no—
303C2×C4—44no—
304C2×C4—42no—
305C2×C4—44no—
306C2×C4—44no—
307C2×C4—42no—
308C2×C4—44no—
309C2×C4—84no—
310C2×C4C2×C42×C13911yescharacteristic
311C2×C4C2×C22⋊C4×C13912yes—
312C2×C4#117×C13912yes—
313C2×C4#117×C13911yescharacteristic
314C2×C4C4×D4×C13912yes—
315C2×C4C4×D4×C13912yes—
316C2×C4C4×D4×C13912yes—
317C2×C4C4×D4×C13912yes—
318C2×C4C4×D4×C13912yes—
319C2×C4#120×C13911yescharacteristic
320C2×C4#121×C13912yes—
321C2×C4#121×C13912yes—
322C2×C4#123×C13912yes—
323C2×C4#123×C13911yescharacteristic
324C2×C4#124×C13912yes—
325C2×C4#126×C13912yes—
326C8—28no—
327C22—22no—
328C22—24no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22C4×C22⋊C4×C13911yescharacteristic
333C22#386×C13911yescharacteristic
334C22#388×C13912yes—
335C22#390×C13912yes—
336C22#390×C13911yescharacteristic
337C4—44no—
338C4—44no—
339C4—82no—
340C4—84no—
341C4C4×C22⋊C4×C13912yes—
342C4#386×C13912yes—
343C4#388×C13912yes—
344C4#388×C13912yes—
345C2—21no—
346C2—22no—
347C2—21no—
348C2—22no—
349C2#1437×C13911yescharacteristic
350C2#1909×C13912yes—
subgroupG/H
center, socleC22×C139#386
commutatorC2×C4C2×C42×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC24×C139C2×D4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
12. #419×C139C4semidirect
17. #391×C139C4semidirect
175. #10947C139direct (N × H)
176. C139#10947direct (N × H)
188. #419C4×C139semidirect
193. #391C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#419×C1392
#2873×C1392
#2310×C1392
#1740×C1392
C2×H(3,ℤ/4)×C1392
#10947139