Finite Group Databasebeta

← C139×#18181 #48012777

Subgroups — C139×#18181 #48012777

Order 35584.

970 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3501×C139C211yesmaximal, characteristic
2#3113×C139C212yesmaximal, complemented
3#2398×C139C211yesmaximal, characteristic
4#1608×C139C214yesmaximal, complemented
5#1602×C139C214yesmaximal, complemented
6#1506×C139C212yesmaximal, complemented
7#1466×C139C211yesmaximal, characteristic
8#554×C139—22no—
9#554×C139—24no—
10D4×Q8×C139—22no—
11#544×C139—21no—
12#543×C139C2214yes—
13#533×C139C2212yes—
14C2×C22⋊Q8×C139—22no—
15#518×C139—21no—
16C2×C4×Q8×C139C2211yescharacteristic
17C2×C4×D4×C139C2211yescharacteristic
18#483×C139C2214yes—
19#475×C139—22no—
20#462×C139—22no—
21#451×C139C2214yes—
22#441×C139—24no—
23#432×C139C2212yes—
24#400×C139—21no—
25#397×C139C2212yes—
26#394×C139—21no—
27#393×C139C2212yes—
28C4×C22⋊C4×C139—22no—
29#376×C139C2211yescharacteristic
30#328×C139C2218yes—
31#323×C139C2214yes—
32C22×Q8×C139—22no—
33C22×Q8×C139C2311yescharacteristic
34C22×D4×C139D411yescharacteristic
35C23×C4×C139D412yes—
36C2×Q16×C139—24no—
37C4⋊Q8×C139—24no—
38C4⋊Q8×C139D412yes—
39C4⋊Q8×C139D412yes—
40#125×C139—24no—
41#125×C139—22no—
42C22⋊Q8×C139—24no—
43C22⋊Q8×C139—24no—
44C22⋊Q8×C139—28no—
45C22⋊Q8×C139—22no—
46C22⋊Q8×C139—24no—
47C22⋊Q8×C139—28no—
48C22⋊Q8×C139C2314yes—
49C4×Q8×C139—22no—
50C4×Q8×C139—22no—
51C4×Q8×C139—22no—
52C4×Q8×C139D414yes—
53C4×D4×C139—24no—
54C4×D4×C139—24no—
55C4×D4×C139—22no—
56C4×D4×C139—22no—
57#117×C139—22no—
58C2×C4⋊C4×C139—22no—
59C2×C4⋊C4×C139—24no—
60C2×C4⋊C4×C139—21no—
61C2×C4⋊C4×C139D411yescharacteristic
62C2×C4⋊C4×C139C2311yescharacteristic
63C2×C22⋊C4×C139—24no—
64C2×C22⋊C4×C139—22no—
65C2×C22⋊C4×C139—22no—
66C2×C22⋊C4×C139C2312yes—
67C2×C42×C139—21no—
68C2×C42×C139—21no—
69C2×C42×C139C2311yescharacteristic
70#106×C139—24no—
71C4⋊C8×C139—22no—
72#103×C139—24no—
73#103×C139—24no—
74C22⋊C8×C139C2314yes—
75#97×C139—22no—
76#95×C139—22no—
77#95×C139—21no—
78#95×C139—22no—
79#95×C139C2312yes—
80C24×C139C2×D412yes—
81C2×Q8×C139—24no—
82C2×Q8×C139—22no—
83C2×Q8×C139—22no—
84C2×Q8×C139—42no—
85C2×Q8×C139—84no—
86C2×Q8×C139C2×D414yes—
87C2×D4×C139—24no—
88C2×D4×C139—22no—
89C22×C4×C139—21no—
90C22×C4×C139—24no—
91C22×C4×C139—24no—
92C22×C4×C139—22no—
93C22×C4×C139—22no—
94C22×C4×C139—22no—
95C22×C4×C139—21no—
96C22×C4×C139—44no—
97C22×C4×C139C2×D411yescharacteristic
98C22×C4×C139C2×D411yescharacteristic
99C22×C4×C139C2×D412yes—
100C22×C4×C139C2411yescharacteristic
101Q16×C139—48no—
102C2×C8×C139—24no—
103C4⋊C4×C139—24no—
104C4⋊C4×C139—28no—
105C4⋊C4×C139—22no—
106C4⋊C4×C139—24no—
107C4⋊C4×C139—22no—
108C4⋊C4×C139—22no—
109C4⋊C4×C139—22no—
110C4⋊C4×C139—24no—
111C4⋊C4×C139—22no—
112C4⋊C4×C139—42no—
113C4⋊C4×C139C2×D414yes—
114C22⋊C4×C139—28no—
115C22⋊C4×C139—24no—
116C22⋊C4×C139—24no—
117C22⋊C4×C139—44no—
118C22⋊C4×C139—44no—
119C42×C139—24no—
120C42×C139—42no—
121C42×C139—41no—
122C42×C139—41no—
123C42×C139C2×D412yes—
124C42×C139C2×D412yes—
125C23×C139—22no—
126C23×C139—22no—
127C23×C139—42no—
128C23×C139—42no—
129C23×C139#13714yes—
130C23×C139C22×D411yescharacteristic
131Q8×C139—24no—
132Q8×C139—44no—
133Q8×C139—42no—
134Q8×C139—44no—
135Q8×C139—84no—
136D4×C139—28no—
137C2×C4×C139—22no—
138C2×C4×C139—22no—
139C2×C4×C139—22no—
140C2×C4×C139—24no—
141C2×C4×C139—24no—
142C2×C4×C139—22no—
143C2×C4×C139—41no—
144C2×C4×C139—41no—
145C2×C4×C139—41no—
146C2×C4×C139—44no—
147C2×C4×C139—42no—
148C2×C4×C139—42no—
149C2×C4×C139—42no—
150C2×C4×C139—41no—
151C2×C4×C139—42no—
152C2×C4×C139—42no—
153C2×C4×C139—82no—
154C2×C4×C139—84no—
155C2×C4×C139—84no—
156C2×C4×C139#12012yes—
157C2×C4×C139#12011yescharacteristic
158C2×C4×C139#12011yescharacteristic
159C2×C4×C139C22×D412yes—
160C8×C139—44no—
161C22×C139—21no—
162C22×C139—21no—
163C22×C139—24no—
164C22×C139—44no—
165C22×C139—42no—
166C22×C139—42no—
167C22×C139—82no—
168C22×C139C2×#12011yescharacteristic
169C22×C139C2×#13712yes—
170C4×C139—22no—
171C4×C139—21no—
172C4×C139—22no—
173C4×C139—42no—
174C4×C139—44no—
175C4×C139—42no—
176C4×C139—44no—
177C4×C139—82no—
178C4×C139—81no—
179C4×C139#45512yes—
180C2×C139—22no—
181C2×C139—44no—
182C2×C139#300411yescharacteristic
183C2×C139C2×#45511yescharacteristic
184C2×C139#302511yescharacteristic
185#18181C13911yesmaximal, characteristic, direct product factor, Sylow
186C139#1818111yescharacteristic, direct product factor, Sylow
187#3501C2×C13911yescharacteristic
188#3113C2×C13912yescomplemented
189#2398C2×C13911yescharacteristic
190#1608C2×C13914yescomplemented
191#1602C2×C13914yescomplemented
192#1506C2×C13912yescomplemented
193#1466C2×C13911yescharacteristic
194#554—22no—
195#554—24no—
196D4×Q8—22no—
197#544—21no—
198#543C22×C13914yes—
199#533C22×C13912yes—
200C2×C22⋊Q8—22no—
201#518—21no—
202C2×C4×Q8C22×C13911yescharacteristic
203C2×C4×D4C22×C13911yescharacteristic
204#483C22×C13914yes—
205#475—22no—
206#462—22no—
207#451C22×C13914yes—
208#441—24no—
209#432C22×C13912yes—
210#400—21no—
211#397C22×C13912yes—
212#394—21no—
213#393C22×C13912yes—
214C4×C22⋊C4—22no—
215#376C22×C13911yescharacteristic
216#328C22×C13918yes—
217#323C22×C13914yes—
218C22×Q8—22no—
219C22×Q8C23×C13911yescharacteristic
220C22×D4D4×C13911yescharacteristic
221C23×C4D4×C13912yes—
222C2×Q16—24no—
223C4⋊Q8—24no—
224C4⋊Q8D4×C13912yes—
225C4⋊Q8D4×C13912yes—
226#125—24no—
227#125—22no—
228C22⋊Q8—24no—
229C22⋊Q8—24no—
230C22⋊Q8—28no—
231C22⋊Q8—22no—
232C22⋊Q8—24no—
233C22⋊Q8—28no—
234C22⋊Q8C23×C13914yes—
235C4×Q8—22no—
236C4×Q8—22no—
237C4×Q8—22no—
238C4×Q8D4×C13914yes—
239C4×D4—24no—
240C4×D4—24no—
241C4×D4—22no—
242C4×D4—22no—
243#117—22no—
244C2×C4⋊C4—22no—
245C2×C4⋊C4—24no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4D4×C13911yescharacteristic
248C2×C4⋊C4C23×C13911yescharacteristic
249C2×C22⋊C4—24no—
250C2×C22⋊C4—22no—
251C2×C22⋊C4—22no—
252C2×C22⋊C4C23×C13912yes—
253C2×C42—21no—
254C2×C42—21no—
255C2×C42C23×C13911yescharacteristic
256#106—24no—
257C4⋊C8—22no—
258#103—24no—
259#103—24no—
260C22⋊C8C23×C13914yes—
261#97—22no—
262#95—21no—
263#95—22no—
264#95—22no—
265#95C23×C13912yes—
266C24C2×D4×C13912yes—
267C2×Q8—24no—
268C2×Q8—22no—
269C2×Q8—22no—
270C2×Q8—42no—
271C2×Q8—84no—
272C2×Q8C2×D4×C13914yes—
273C2×D4—24no—
274C2×D4—22no—
275C22×C4—21no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—22no—
281C22×C4—21no—
282C22×C4—44no—
283C22×C4C2×D4×C13911yescharacteristic
284C22×C4C2×D4×C13911yescharacteristic
285C22×C4C2×D4×C13912yes—
286C22×C4C24×C13911yescharacteristic
287Q16—48no—
288C2×C8—24no—
289C4⋊C4—24no—
290C4⋊C4—28no—
291C4⋊C4—22no—
292C4⋊C4—24no—
293C4⋊C4—22no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4—24no—
297C4⋊C4—22no—
298C4⋊C4—42no—
299C4⋊C4C2×D4×C13914yes—
300C22⋊C4—28no—
301C22⋊C4—24no—
302C22⋊C4—24no—
303C22⋊C4—44no—
304C22⋊C4—44no—
305C42—24no—
306C42—42no—
307C42—41no—
308C42—41no—
309C42C2×D4×C13912yes—
310C42C2×D4×C13912yes—
311C23—22no—
312C23—22no—
313C23—42no—
314C23—42no—
315C23#137×C13914yes—
316C23C22×D4×C13911yescharacteristic
317Q8—24no—
318Q8—44no—
319Q8—42no—
320Q8—44no—
321Q8—84no—
322D4—28no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—22no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—44no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—82no—
340C2×C4—84no—
341C2×C4—84no—
342C2×C4#120×C13912yes—
343C2×C4#120×C13911yescharacteristic
344C2×C4#120×C13911yescharacteristic
345C2×C4C22×D4×C13912yes—
346C8—44no—
347C22—21no—
348C22—21no—
349C22—24no—
350C22—44no—
351C22—42no—
352C22—42no—
353C22—82no—
354C22C2×#120×C13911yescharacteristic
355C22C2×#137×C13912yes—
356C4—22no—
357C4—22no—
358C4—21no—
359C4—42no—
360C4—44no—
361C4—42no—
362C4—44no—
363C4—82no—
364C4—81no—
365C4#455×C13912yes—
366C2—22no—
367C2—44no—
368C2#3004×C13911yescharacteristic
369C2C2×#455×C13911yescharacteristic
370C2#3025×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC22×D4×C139D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3113×C139C2semidirect
4. #1608×C139C2semidirect
5. #1602×C139C2semidirect
6. #1506×C139C2semidirect
185. #18181C139direct (N × H)
186. C139#18181direct (N × H)
188. #3113C2×C139semidirect
190. #1608C2×C139semidirect
191. #1602C2×C139semidirect
192. #1506C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3501×C1392
#3113×C1392
#2398×C1392
#1608×C1392
#1602×C1392
#1506×C1392
#1466×C1392
#18181139