Finite Group Databasebeta

← C139×#32991 #48027587

Subgroups — C139×#32991 #48027587

Order 35584.

1238 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#519×C139C211yesmaximal, characteristic, complemented
2#3094×C139C212yesmaximal
3#2436×C139C211yesmaximal, characteristic
4#1888×C139C214yesmaximal, complemented
5#1857×C139C214yesmaximal, complemented
6#1826×C139C212yesmaximal, complemented
7#1784×C139C211yesmaximal, characteristic, complemented
8C23×Q8×C139C2211yescharacteristic
9C2×#124×C139C2212yes—
10C2×#121×C139C2211yescharacteristic
11#519×C139—22no—
12#519×C139—24no—
13#519×C139C2214yes—
14C2×C4×Q8×C139—22no—
15C2×C4×Q8×C139—22no—
16C2×#117×C139—22no—
17C2×#117×C139C2212yes—
18#482×C139—24no—
19#481×C139—22no—
20#480×C139—22no—
21#428×C139C2214yes—
22#418×C139C2214yes—
23C2×#101×C139C2214yes—
24#407×C139C2212yes—
25#393×C139—22no—
26#391×C139C2212yes—
27#386×C139—22no—
28C4×C22⋊C4×C139C2211yescharacteristic
29#339×C139C2218yes—
30C22×Q8×C139—28no—
31C22×Q8×C139—22no—
32C22×Q8×C139—22no—
33C22×Q8×C139D412yes—
34C22×Q8×C139C2312yes—
35C22×D4×C139—21no—
36C22×D4×C139C2311yescharacteristic
37C23×C4×C139D412yes—
38C23×C4×C139C2311yescharacteristic
39C2×M16×C139C2314yes—
40#124×C139—28no—
41#121×C139—22no—
42#121×C139—22no—
43C4×Q8×C139—28no—
44C4×Q8×C139—28no—
45C4×Q8×C139—28no—
46C4×Q8×C139—28no—
47#117×C139—28no—
48#117×C139—28no—
49#117×C139—22no—
50#117×C139—22no—
51#117×C139D414yes—
52#117×C139C2314yes—
53C2×C4⋊C4×C139—22no—
54C2×C4⋊C4×C139—22no—
55C2×C4⋊C4×C139D412yes—
56C2×C4⋊C4×C139D412yes—
57C2×C4⋊C4×C139C2311yescharacteristic
58C2×C22⋊C4×C139—22no—
59C2×C22⋊C4×C139—21no—
60C2×C22⋊C4×C139—21no—
61C2×C22⋊C4×C139—24no—
62C2×C42×C139—24no—
63C2×C42×C139—22no—
64C2×C42×C139C2312yes—
65#107×C139—24no—
66#106×C139—24no—
67#102×C139—24no—
68#102×C139—24no—
69#101×C139—28no—
70C22⋊C8×C139—22no—
71C22⋊C8×C139—22no—
72#95×C139—21no—
73#95×C139—24no—
74C24×C139—21no—
75C24×C139C2×D411yescharacteristic
76C2×Q8×C139—216no—
77C2×Q8×C139—216no—
78C2×Q8×C139—24no—
79C2×Q8×C139—28no—
80C2×Q8×C139—24no—
81C2×Q8×C139—24no—
82C2×Q8×C139#4118yes—
83C2×D4×C139—22no—
84C2×D4×C139—24no—
85C2×D4×C139—44no—
86C2×D4×C139—41no—
87C2×D4×C139—41no—
88C22×C4×C139—22no—
89C22×C4×C139—22no—
90C22×C4×C139—28no—
91C22×C4×C139—24no—
92C22×C4×C139—22no—
93C22×C4×C139—22no—
94C22×C4×C139—21no—
95C22×C4×C139—22no—
96C22×C4×C139C2×D411yescharacteristic
97C22×C4×C139C2×D412yes—
98C22×C4×C139C2×D412yes—
99C22×C4×C139C2×D414yes—
100C22×C4×C139C2411yescharacteristic
101M16×C139—28no—
102C2×C8×C139—24no—
103C4⋊C4×C139—28no—
104C4⋊C4×C139—28no—
105C4⋊C4×C139—22no—
106C4⋊C4×C139—22no—
107C4⋊C4×C139—22no—
108C4⋊C4×C139C2×D414yes—
109C4⋊C4×C139C2×D414yes—
110C22⋊C4×C139—24no—
111C22⋊C4×C139—24no—
112C22⋊C4×C139—42no—
113C22⋊C4×C139—42no—
114C22⋊C4×C139—48no—
115C42×C139—216no—
116C42×C139—24no—
117C42×C139—24no—
118C42×C139—24no—
119C23×C139—22no—
120C23×C139—22no—
121C23×C139—41no—
122C23×C139—42no—
123C23×C139—42no—
124C23×C139—41no—
125C23×C139—42no—
126C23×C139#12011yescharacteristic
127C23×C139#12011yescharacteristic
128C23×C139C22×D411yescharacteristic
129Q8×C139—216no—
130Q8×C139—216no—
131D4×C139—44no—
132D4×C139—82no—
133D4×C139—82no—
134C2×C4×C139—28no—
135C2×C4×C139—28no—
136C2×C4×C139—24no—
137C2×C4×C139—22no—
138C2×C4×C139—24no—
139C2×C4×C139—24no—
140C2×C4×C139—24no—
141C2×C4×C139—24no—
142C2×C4×C139—24no—
143C2×C4×C139—44no—
144C2×C4×C139—44no—
145C2×C4×C139—42no—
146C2×C4×C139—42no—
147C2×C4×C139—42no—
148C2×C4×C139—41no—
149C2×C4×C139—42no—
150C2×C4×C139#12012yes—
151C2×C4×C139#12318yes—
152C2×C4×C139C22×D412yes—
153C2×C4×C139C2×#4114yes—
154C8×C139—44no—
155C22×C139—21no—
156C22×C139—21no—
157C22×C139—21no—
158C22×C139—21no—
159C22×C139—21no—
160C22×C139—21no—
161C22×C139—21no—
162C22×C139—44no—
163C22×C139—84no—
164C22×C139—81no—
165C22×C139—81no—
166C22×C139—81no—
167C22×C139#45412yes—
168C22×C139C2×#12011yescharacteristic
169C22×C139C2×#12312yes—
170C4×C139—22no—
171C4×C139—28no—
172C4×C139—44no—
173C4×C139—44no—
174C4×C139—82no—
175C4×C139—81no—
176C4×C139#52514yes—
177C2×C139—22no—
178C2×C139—22no—
179C2×C139—41no—
180C2×C139—161no—
181C2×C139#284911yescharacteristic
182C2×C139C2×#45411yescharacteristic
183C2×C139#302011yescharacteristic
184#32991C13911yesmaximal, characteristic, direct product factor, Sylow
185C139#3299111yescharacteristic, direct product factor, Sylow
186C2×#519C2×C13911yescharacteristic, complemented
187#3094C2×C13912yes—
188#2436C2×C13911yescharacteristic
189#1888C2×C13914yescomplemented
190#1857C2×C13914yescomplemented
191#1826C2×C13912yescomplemented
192#1784C2×C13911yescharacteristic, complemented
193C23×Q8C22×C13911yescharacteristic
194C2×#124C22×C13912yes—
195C2×#121C22×C13911yescharacteristic
196#519—22no—
197#519—24no—
198#519C22×C13914yes—
199C2×C4×Q8—22no—
200C2×C4×Q8—22no—
201C2×#117—22no—
202C2×#117C22×C13912yes—
203#482—24no—
204#481—22no—
205#480—22no—
206#428C22×C13914yes—
207#418C22×C13914yes—
208C2×#101C22×C13914yes—
209#407C22×C13912yes—
210#393—22no—
211#391C22×C13912yes—
212#386—22no—
213C4×C22⋊C4C22×C13911yescharacteristic
214#339C22×C13918yes—
215C22×Q8—28no—
216C22×Q8—22no—
217C22×Q8—22no—
218C22×Q8D4×C13912yes—
219C22×Q8C23×C13912yes—
220C22×D4—21no—
221C22×D4C23×C13911yescharacteristic
222C23×C4D4×C13912yes—
223C23×C4C23×C13911yescharacteristic
224C2×M16C23×C13914yes—
225#124—28no—
226#121—22no—
227#121—22no—
228C4×Q8—28no—
229C4×Q8—28no—
230C4×Q8—28no—
231C4×Q8—28no—
232#117—28no—
233#117—28no—
234#117—22no—
235#117—22no—
236#117D4×C13914yes—
237#117C23×C13914yes—
238C2×C4⋊C4—22no—
239C2×C4⋊C4—22no—
240C2×C4⋊C4D4×C13912yes—
241C2×C4⋊C4D4×C13912yes—
242C2×C4⋊C4C23×C13911yescharacteristic
243C2×C22⋊C4—22no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—24no—
247C2×C42—24no—
248C2×C42—22no—
249C2×C42C23×C13912yes—
250#107—24no—
251#106—24no—
252#102—24no—
253#102—24no—
254#101—28no—
255C22⋊C8—22no—
256C22⋊C8—22no—
257#95—21no—
258#95—24no—
259C24—21no—
260C24C2×D4×C13911yescharacteristic
261C2×Q8—216no—
262C2×Q8—216no—
263C2×Q8—24no—
264C2×Q8—28no—
265C2×Q8—24no—
266C2×Q8—24no—
267C2×Q8#41×C13918yes—
268C2×D4—22no—
269C2×D4—24no—
270C2×D4—44no—
271C2×D4—41no—
272C2×D4—41no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—28no—
276C22×C4—24no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4C2×D4×C13911yescharacteristic
282C22×C4C2×D4×C13912yes—
283C22×C4C2×D4×C13912yes—
284C22×C4C2×D4×C13914yes—
285C22×C4C24×C13911yescharacteristic
286M16—28no—
287C2×C8—24no—
288C4⋊C4—28no—
289C4⋊C4—28no—
290C4⋊C4—22no—
291C4⋊C4—22no—
292C4⋊C4—22no—
293C4⋊C4C2×D4×C13914yes—
294C4⋊C4C2×D4×C13914yes—
295C22⋊C4—24no—
296C22⋊C4—24no—
297C22⋊C4—42no—
298C22⋊C4—42no—
299C22⋊C4—48no—
300C42—216no—
301C42—24no—
302C42—24no—
303C42—24no—
304C23—22no—
305C23—22no—
306C23—41no—
307C23—42no—
308C23—42no—
309C23—41no—
310C23—42no—
311C23#120×C13911yescharacteristic
312C23#120×C13911yescharacteristic
313C23C22×D4×C13911yescharacteristic
314Q8—216no—
315Q8—216no—
316D4—44no—
317D4—82no—
318D4—82no—
319C2×C4—28no—
320C2×C4—28no—
321C2×C4—24no—
322C2×C4—22no—
323C2×C4—24no—
324C2×C4—24no—
325C2×C4—24no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—44no—
329C2×C4—44no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4#120×C13912yes—
336C2×C4#123×C13918yes—
337C2×C4C22×D4×C13912yes—
338C2×C4C2×#41×C13914yes—
339C8—44no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—44no—
348C22—84no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22#454×C13912yes—
353C22C2×#120×C13911yescharacteristic
354C22C2×#123×C13912yes—
355C4—22no—
356C4—28no—
357C4—44no—
358C4—44no—
359C4—82no—
360C4—81no—
361C4#525×C13914yes—
362C2—22no—
363C2—22no—
364C2—41no—
365C2—161no—
366C2#2849×C13911yescharacteristic
367C2C2×#454×C13911yescharacteristic
368C2#3020×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#121×C139C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#519×C139C2semidirect
4. #1888×C139C2semidirect
5. #1857×C139C2semidirect
6. #1826×C139C2semidirect
7. #1784×C139C2semidirect
184. #32991C139direct (N × H)
185. C139#32991direct (N × H)
186. C2×#519C2×C139semidirect
189. #1888C2×C139semidirect
190. #1857C2×C139semidirect
191. #1826C2×C139semidirect
192. #1784C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#519×C1392
#3094×C1392
#2436×C1392
#1888×C1392
#1857×C1392
#1826×C1392
#1784×C1392
#32991139