Finite Group Databasebeta

← C139×#18148 #48012744

Subgroups — C139×#18148 #48012744

Order 35584.

930 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#544×C139C211yesmaximal, characteristic
2#3095×C139C212yesmaximal
3#2484×C139C211yesmaximal, characteristic
4#1617×C139C214yesmaximal, complemented
5#1611×C139C214yesmaximal, complemented
6#1511×C139C212yesmaximal
7#1463×C139C211yesmaximal, characteristic
8#544×C139—24no—
9#544×C139—22no—
10#544×C139C2214yes—
11C2×C4⋊Q8×C139—22no—
12C2×#125×C139—22no—
13C2×C22⋊Q8×C139—21no—
14C2×C22⋊Q8×C139C2212yes—
15C2×#117×C139—21no—
16C2×#117×C139C2211yescharacteristic
17C22×C4⋊C4×C139C2211yescharacteristic
18#485×C139—24no—
19#484×C139C2214yes—
20#483×C139C2214yes—
21#428×C139—22no—
22#419×C139—22no—
23#407×C139C2212yes—
24#400×C139C2212yes—
25#398×C139C2212yes—
26#387×C139—22no—
27#385×C139—21no—
28#381×C139—21no—
29#381×C139C2211yescharacteristic
30#328×C139C2218yes—
31#324×C139C2214yes—
32C22×Q8×C139—21no—
33C22×Q8×C139D412yes—
34C23×C4×C139D411yescharacteristic
35C23×C4×C139D411yescharacteristic
36C23×C4×C139C2311yescharacteristic
37C2×M16×C139—22no—
38C4⋊Q8×C139—28no—
39C4⋊Q8×C139—28no—
40#125×C139—28no—
41#125×C139—28no—
42C22⋊Q8×C139—24no—
43C22⋊Q8×C139—24no—
44C22⋊Q8×C139—22no—
45C22⋊Q8×C139—22no—
46C22⋊Q8×C139D414yes—
47C22⋊Q8×C139C2314yes—
48#117×C139—24no—
49#117×C139—24no—
50#117×C139—22no—
51#117×C139—22no—
52C2×C4⋊C4×C139—21no—
53C2×C4⋊C4×C139—21no—
54C2×C4⋊C4×C139—21no—
55C2×C4⋊C4×C139—22no—
56C2×C4⋊C4×C139—22no—
57C2×C4⋊C4×C139—22no—
58C2×C4⋊C4×C139—22no—
59C2×C4⋊C4×C139—22no—
60C2×C4⋊C4×C139D412yes—
61C2×C4⋊C4×C139D412yes—
62C2×C4⋊C4×C139C2311yescharacteristic
63C2×C4⋊C4×C139C2311yescharacteristic
64C2×C4⋊C4×C139C2312yes—
65C2×C22⋊C4×C139—22no—
66C2×C22⋊C4×C139—21no—
67C2×C22⋊C4×C139—21no—
68C2×C42×C139—22no—
69C2×C42×C139—21no—
70#107×C139—24no—
71#106×C139—24no—
72#103×C139—24no—
73#103×C139—24no—
74C22⋊C8×C139—22no—
75C22⋊C8×C139C2314yes—
76#95×C139—22no—
77#95×C139—22no—
78#95×C139—22no—
79#95×C139—21no—
80#95×C139C2312yes—
81C24×C139C2×D411yescharacteristic
82C2×Q8×C139—24no—
83C2×Q8×C139—22no—
84C2×Q8×C139—44no—
85C2×Q8×C139—82no—
86C2×Q8×C139C2×D414yes—
87C22×C4×C139—21no—
88C22×C4×C139—21no—
89C22×C4×C139—24no—
90C22×C4×C139—22no—
91C22×C4×C139—22no—
92C22×C4×C139—21no—
93C22×C4×C139—21no—
94C22×C4×C139—22no—
95C22×C4×C139—21no—
96C22×C4×C139—21no—
97C22×C4×C139—42no—
98C22×C4×C139—42no—
99C22×C4×C139C2×D412yes—
100C22×C4×C139C2×D412yes—
101C22×C4×C139C2×D412yes—
102C22×C4×C139C2×D411yescharacteristic
103C22×C4×C139C2×D412yes—
104C22×C4×C139C2411yescharacteristic
105M16×C139—44no—
106C2×C8×C139—24no—
107C4⋊C4×C139—24no—
108C4⋊C4×C139—24no—
109C4⋊C4×C139—24no—
110C4⋊C4×C139—28no—
111C4⋊C4×C139—24no—
112C4⋊C4×C139—24no—
113C4⋊C4×C139—22no—
114C4⋊C4×C139—24no—
115C4⋊C4×C139—24no—
116C4⋊C4×C139—22no—
117C4⋊C4×C139—22no—
118C4⋊C4×C139—44no—
119C4⋊C4×C139C2×D414yes—
120C22⋊C4×C139—24no—
121C22⋊C4×C139—24no—
122C22⋊C4×C139—42no—
123C22⋊C4×C139—41no—
124C22⋊C4×C139—41no—
125C42×C139—28no—
126C42×C139—42no—
127C23×C139—22no—
128C23×C139—22no—
129C23×C139—41no—
130C23×C139#12011yescharacteristic
131C23×C139#12011yescharacteristic
132C23×C139C22×D411yescharacteristic
133Q8×C139—44no—
134Q8×C139—82no—
135Q8×C139—84no—
136C2×C4×C139—24no—
137C2×C4×C139—24no—
138C2×C4×C139—22no—
139C2×C4×C139—22no—
140C2×C4×C139—24no—
141C2×C4×C139—24no—
142C2×C4×C139—24no—
143C2×C4×C139—22no—
144C2×C4×C139—42no—
145C2×C4×C139—41no—
146C2×C4×C139—41no—
147C2×C4×C139—44no—
148C2×C4×C139—42no—
149C2×C4×C139—44no—
150C2×C4×C139—42no—
151C2×C4×C139—42no—
152C2×C4×C139—42no—
153C2×C4×C139—42no—
154C2×C4×C139—41no—
155C2×C4×C139—41no—
156C2×C4×C139—42no—
157C2×C4×C139—42no—
158C2×C4×C139—81no—
159C2×C4×C139#12012yes—
160C2×C4×C139#13714yes—
161C2×C4×C139C22×D412yes—
162C8×C139—44no—
163C22×C139—21no—
164C22×C139—21no—
165C22×C139—21no—
166C22×C139—21no—
167C22×C139—21no—
168C22×C139—21no—
169C22×C139—21no—
170C22×C139—44no—
171C22×C139#45812yes—
172C22×C139C2×#12011yescharacteristic
173C22×C139C2×#13712yes—
174C4×C139—24no—
175C4×C139—22no—
176C4×C139—22no—
177C4×C139—44no—
178C4×C139—42no—
179C4×C139—44no—
180C4×C139—82no—
181C4×C139—81no—
182C4×C139—81no—
183C2×C139—22no—
184C2×C139—22no—
185C2×C139—41no—
186C2×C139#300411yescharacteristic
187C2×C139#302011yescharacteristic
188C2×C139C2×#45811yescharacteristic
189#18148C13911yesmaximal, characteristic, direct product factor, Sylow
190C139#1814811yescharacteristic, direct product factor, Sylow
191C2×#544C2×C13911yescharacteristic
192#3095C2×C13912yes—
193#2484C2×C13911yescharacteristic
194#1617C2×C13914yescomplemented
195#1611C2×C13914yescomplemented
196#1511C2×C13912yes—
197#1463C2×C13911yescharacteristic
198#544—24no—
199#544—22no—
200#544C22×C13914yes—
201C2×C4⋊Q8—22no—
202C2×#125—22no—
203C2×C22⋊Q8—21no—
204C2×C22⋊Q8C22×C13912yes—
205C2×#117—21no—
206C2×#117C22×C13911yescharacteristic
207C22×C4⋊C4C22×C13911yescharacteristic
208#485—24no—
209#484C22×C13914yes—
210#483C22×C13914yes—
211#428—22no—
212#419—22no—
213#407C22×C13912yes—
214#400C22×C13912yes—
215#398C22×C13912yes—
216#387—22no—
217#385—21no—
218#381—21no—
219#381C22×C13911yescharacteristic
220#328C22×C13918yes—
221#324C22×C13914yes—
222C22×Q8—21no—
223C22×Q8D4×C13912yes—
224C23×C4D4×C13911yescharacteristic
225C23×C4D4×C13911yescharacteristic
226C23×C4C23×C13911yescharacteristic
227C2×M16—22no—
228C4⋊Q8—28no—
229C4⋊Q8—28no—
230#125—28no—
231#125—28no—
232C22⋊Q8—24no—
233C22⋊Q8—24no—
234C22⋊Q8—22no—
235C22⋊Q8—22no—
236C22⋊Q8D4×C13914yes—
237C22⋊Q8C23×C13914yes—
238#117—24no—
239#117—24no—
240#117—22no—
241#117—22no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—22no—
246C2×C4⋊C4—22no—
247C2×C4⋊C4—22no—
248C2×C4⋊C4—22no—
249C2×C4⋊C4—22no—
250C2×C4⋊C4D4×C13912yes—
251C2×C4⋊C4D4×C13912yes—
252C2×C4⋊C4C23×C13911yescharacteristic
253C2×C4⋊C4C23×C13911yescharacteristic
254C2×C4⋊C4C23×C13912yes—
255C2×C22⋊C4—22no—
256C2×C22⋊C4—21no—
257C2×C22⋊C4—21no—
258C2×C42—22no—
259C2×C42—21no—
260#107—24no—
261#106—24no—
262#103—24no—
263#103—24no—
264C22⋊C8—22no—
265C22⋊C8C23×C13914yes—
266#95—22no—
267#95—22no—
268#95—21no—
269#95—22no—
270#95C23×C13912yes—
271C24C2×D4×C13911yescharacteristic
272C2×Q8—24no—
273C2×Q8—22no—
274C2×Q8—44no—
275C2×Q8—82no—
276C2×Q8C2×D4×C13914yes—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—24no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—42no—
288C22×C4—42no—
289C22×C4C2×D4×C13912yes—
290C22×C4C2×D4×C13912yes—
291C22×C4C2×D4×C13912yes—
292C22×C4C2×D4×C13911yescharacteristic
293C22×C4C2×D4×C13912yes—
294C22×C4C24×C13911yescharacteristic
295M16—44no—
296C2×C8—24no—
297C4⋊C4—24no—
298C4⋊C4—24no—
299C4⋊C4—24no—
300C4⋊C4—28no—
301C4⋊C4—24no—
302C4⋊C4—24no—
303C4⋊C4—22no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—22no—
307C4⋊C4—22no—
308C4⋊C4—44no—
309C4⋊C4C2×D4×C13914yes—
310C22⋊C4—24no—
311C22⋊C4—24no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C42—28no—
316C42—42no—
317C23—22no—
318C23—22no—
319C23—41no—
320C23#120×C13911yescharacteristic
321C23#120×C13911yescharacteristic
322C23C22×D4×C13911yescharacteristic
323Q8—44no—
324Q8—82no—
325Q8—84no—
326C2×C4—24no—
327C2×C4—24no—
328C2×C4—24no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—24no—
332C2×C4—24no—
333C2×C4—22no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—44no—
338C2×C4—42no—
339C2×C4—44no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—42no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—42no—
347C2×C4—42no—
348C2×C4—81no—
349C2×C4#120×C13912yes—
350C2×C4#137×C13914yes—
351C2×C4C22×D4×C13912yes—
352C8—44no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—44no—
361C22#458×C13912yes—
362C22C2×#120×C13911yescharacteristic
363C22C2×#137×C13912yes—
364C4—22no—
365C4—22no—
366C4—24no—
367C4—42no—
368C4—44no—
369C4—44no—
370C4—82no—
371C4—81no—
372C4—81no—
373C2—22no—
374C2—22no—
375C2—41no—
376C2#3004×C13911yescharacteristic
377C2#3020×C13911yescharacteristic
378C2C2×#458×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC24×C139C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1617×C139C2semidirect
5. #1611×C139C2semidirect
189. #18148C139direct (N × H)
190. C139#18148direct (N × H)
194. #1617C2×C139semidirect
195. #1611C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#544×C1392
#3095×C1392
#2484×C1392
#1617×C1392
#1611×C1392
#1511×C1392
#1463×C1392
#18148139