Finite Group Databasebeta

← C139×#18147 #48012743

Subgroups — C139×#18147 #48012743

Order 35584.

1210 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C139C211yesmaximal, characteristic
2#3094×C139C212yesmaximal, complemented
3#2484×C139C211yesmaximal, characteristic, complemented
4#1616×C139C214yesmaximal, complemented
5#1610×C139C214yesmaximal, complemented
6#1510×C139C212yesmaximal, complemented
7#1463×C139C211yesmaximal, characteristic, complemented
8C22×#41×C139—21no—
9#537×C139—24no—
10#537×C139—22no—
11#537×C139C2214yes—
12C2×C22⋊Q8×C139—22no—
13C2×#121×C139—22no—
14C2×#121×C139—21no—
15C2×#121×C139C2212yes—
16C2×#117×C139C2211yescharacteristic
17C22×C4⋊C4×C139C2211yescharacteristic
18#482×C139—24no—
19#481×C139C2214yescomplemented
20#480×C139C2214yescomplemented
21#428×C139—22no—
22#418×C139—22no—
23#407×C139C2212yes—
24#400×C139C2212yescomplemented
25#398×C139C2212yescomplemented
26#387×C139—22no—
27#385×C139—21no—
28#381×C139—21no—
29#381×C139C2211yescharacteristic
30#327×C139C2218yescomplemented
31#324×C139C2214yescomplemented
32C2×#41×C139—24no—
33C2×#41×C139—24no—
34C2×#41×C139—48no—
35C22×Q8×C139—21no—
36C22×D4×C139—21no—
37C22×D4×C139—22no—
38C22×D4×C139—21no—
39C22×D4×C139D412yes—
40C23×C4×C139—22no—
41C23×C4×C139D411yescharacteristic
42C23×C4×C139D411yescharacteristic
43C23×C4×C139C2311yescharacteristic
44C2×M16×C139—22no—
45C22⋊Q8×C139—28no—
46C22⋊Q8×C139—28no—
47#121×C139—24no—
48#121×C139—28no—
49#121×C139—28no—
50#121×C139—24no—
51#121×C139—22no—
52#121×C139—22no—
53#121×C139D414yes—
54#121×C139C2314yes—
55#117×C139—22no—
56#117×C139—22no—
57C2×C4⋊C4×C139—21no—
58C2×C4⋊C4×C139—22no—
59C2×C4⋊C4×C139—22no—
60C2×C4⋊C4×C139—22no—
61C2×C4⋊C4×C139D412yes—
62C2×C4⋊C4×C139D412yes—
63C2×C4⋊C4×C139C2311yescharacteristic
64C2×C4⋊C4×C139C2311yescharacteristic
65C2×C4⋊C4×C139C2312yes—
66C2×C22⋊C4×C139—22no—
67C2×C22⋊C4×C139—22no—
68C2×C22⋊C4×C139—21no—
69C2×C22⋊C4×C139—21no—
70C2×C42×C139—21no—
71#107×C139—24no—
72#106×C139—24no—
73#102×C139—24no—
74#102×C139—24no—
75C22⋊C8×C139—22no—
76C22⋊C8×C139C2314yes—
77#95×C139—22no—
78#95×C139—22no—
79#95×C139—22no—
80#95×C139—21no—
81#95×C139C2312yes—
82C24×C139—22no—
83C24×C139C2×D411yescharacteristic
84#41×C139—416no—
85#41×C139—48no—
86#41×C139—48no—
87C2×Q8×C139—24no—
88C2×Q8×C139—44no—
89C2×D4×C139—24no—
90C2×D4×C139—24no—
91C2×D4×C139—24no—
92C2×D4×C139—24no—
93C2×D4×C139—22no—
94C2×D4×C139—44no—
95C2×D4×C139—44no—
96C2×D4×C139—48no—
97C2×D4×C139—82no—
98C2×D4×C139C2×D414yes—
99C22×C4×C139—21no—
100C22×C4×C139—21no—
101C22×C4×C139—24no—
102C22×C4×C139—28no—
103C22×C4×C139—21no—
104C22×C4×C139—22no—
105C22×C4×C139—21no—
106C22×C4×C139—22no—
107C22×C4×C139—21no—
108C22×C4×C139—21no—
109C22×C4×C139—42no—
110C22×C4×C139—48no—
111C22×C4×C139—42no—
112C22×C4×C139C2×D412yes—
113C22×C4×C139C2×D412yes—
114C22×C4×C139C2×D412yes—
115C22×C4×C139C2×D411yescharacteristic
116C22×C4×C139C2×D412yes—
117C22×C4×C139C2411yescharacteristic
118M16×C139—44no—
119C2×C8×C139—24no—
120C4⋊C4×C139—24no—
121C4⋊C4×C139—24no—
122C4⋊C4×C139—22no—
123C4⋊C4×C139—24no—
124C4⋊C4×C139—22no—
125C4⋊C4×C139—22no—
126C4⋊C4×C139—44no—
127C4⋊C4×C139C2×D414yes—
128C22⋊C4×C139—28no—
129C22⋊C4×C139—24no—
130C22⋊C4×C139—24no—
131C22⋊C4×C139—42no—
132C22⋊C4×C139—41no—
133C22⋊C4×C139—41no—
134C42×C139—42no—
135C23×C139—22no—
136C23×C139—22no—
137C23×C139—24no—
138C23×C139—41no—
139C23×C139—44no—
140C23×C139—44no—
141C23×C139—44no—
142C23×C139#12011yescharacteristic
143C23×C139#12011yescharacteristic
144C23×C139C22×D411yescharacteristic
145Q8×C139—48no—
146D4×C139—44no—
147D4×C139—48no—
148D4×C139—48no—
149D4×C139—48no—
150D4×C139—82no—
151D4×C139—84no—
152C2×C4×C139—24no—
153C2×C4×C139—24no—
154C2×C4×C139—22no—
155C2×C4×C139—22no—
156C2×C4×C139—24no—
157C2×C4×C139—22no—
158C2×C4×C139—24no—
159C2×C4×C139—42no—
160C2×C4×C139—41no—
161C2×C4×C139—41no—
162C2×C4×C139—416no—
163C2×C4×C139—44no—
164C2×C4×C139—42no—
165C2×C4×C139—42no—
166C2×C4×C139—42no—
167C2×C4×C139—42no—
168C2×C4×C139—42no—
169C2×C4×C139—41no—
170C2×C4×C139—41no—
171C2×C4×C139—42no—
172C2×C4×C139—42no—
173C2×C4×C139—81no—
174C2×C4×C139#12012yes—
175C2×C4×C139AGL(1,ℤ/8)14yes—
176C2×C4×C139C22×D412yes—
177C8×C139—44no—
178C22×C139—21no—
179C22×C139—21no—
180C22×C139—21no—
181C22×C139—21no—
182C22×C139—21no—
183C22×C139—21no—
184C22×C139—21no—
185C22×C139—44no—
186C22×C139—44no—
187C22×C139—44no—
188C22×C139—44no—
189C22×C139—88no—
190C22×C139#45812yes—
191C22×C139C2×#12011yescharacteristic
192C22×C139C2×AGL(1,ℤ/8)12yes—
193C4×C139—24no—
194C4×C139—22no—
195C4×C139—22no—
196C4×C139—44no—
197C4×C139—42no—
198C4×C139—82no—
199C4×C139—81no—
200C4×C139—81no—
201C2×C139—22no—
202C2×C139—22no—
203C2×C139—41no—
204C2×C139—84no—
205C2×C139#300311yescharacteristic
206C2×C139#302011yescharacteristic
207C2×C139C2×#45811yescharacteristic
208#18147C13911yesmaximal, characteristic, direct product factor, Sylow
209C139#1814711yescharacteristic, direct product factor, Sylow
210C2×#537C2×C13911yescharacteristic
211#3094C2×C13912yescomplemented
212#2484C2×C13911yescharacteristic, complemented
213#1616C2×C13914yescomplemented
214#1610C2×C13914yescomplemented
215#1510C2×C13912yescomplemented
216#1463C2×C13911yescharacteristic, complemented
217C22×#41—21no—
218#537—24no—
219#537—22no—
220#537C22×C13914yes—
221C2×C22⋊Q8—22no—
222C2×#121—22no—
223C2×#121—21no—
224C2×#121C22×C13912yes—
225C2×#117C22×C13911yescharacteristic
226C22×C4⋊C4C22×C13911yescharacteristic
227#482—24no—
228#481C22×C13914yescomplemented
229#480C22×C13914yescomplemented
230#428—22no—
231#418—22no—
232#407C22×C13912yes—
233#400C22×C13912yescomplemented
234#398C22×C13912yescomplemented
235#387—22no—
236#385—21no—
237#381—21no—
238#381C22×C13911yescharacteristic
239#327C22×C13918yescomplemented
240#324C22×C13914yescomplemented
241C2×#41—24no—
242C2×#41—24no—
243C2×#41—48no—
244C22×Q8—21no—
245C22×D4—21no—
246C22×D4—22no—
247C22×D4—21no—
248C22×D4D4×C13912yes—
249C23×C4—22no—
250C23×C4D4×C13911yescharacteristic
251C23×C4D4×C13911yescharacteristic
252C23×C4C23×C13911yescharacteristic
253C2×M16—22no—
254C22⋊Q8—28no—
255C22⋊Q8—28no—
256#121—24no—
257#121—28no—
258#121—28no—
259#121—24no—
260#121—22no—
261#121—22no—
262#121D4×C13914yes—
263#121C23×C13914yes—
264#117—22no—
265#117—22no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—22no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4—22no—
270C2×C4⋊C4D4×C13912yes—
271C2×C4⋊C4D4×C13912yes—
272C2×C4⋊C4C23×C13911yescharacteristic
273C2×C4⋊C4C23×C13911yescharacteristic
274C2×C4⋊C4C23×C13912yes—
275C2×C22⋊C4—22no—
276C2×C22⋊C4—22no—
277C2×C22⋊C4—21no—
278C2×C22⋊C4—21no—
279C2×C42—21no—
280#107—24no—
281#106—24no—
282#102—24no—
283#102—24no—
284C22⋊C8—22no—
285C22⋊C8C23×C13914yes—
286#95—22no—
287#95—22no—
288#95—21no—
289#95—22no—
290#95C23×C13912yes—
291C24—22no—
292C24C2×D4×C13911yescharacteristic
293#41—416no—
294#41—48no—
295#41—48no—
296C2×Q8—24no—
297C2×Q8—44no—
298C2×D4—24no—
299C2×D4—24no—
300C2×D4—24no—
301C2×D4—24no—
302C2×D4—22no—
303C2×D4—44no—
304C2×D4—44no—
305C2×D4—48no—
306C2×D4—82no—
307C2×D4C2×D4×C13914yes—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—24no—
311C22×C4—28no—
312C22×C4—21no—
313C22×C4—22no—
314C22×C4—21no—
315C22×C4—22no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—42no—
319C22×C4—48no—
320C22×C4—42no—
321C22×C4C2×D4×C13912yes—
322C22×C4C2×D4×C13912yes—
323C22×C4C2×D4×C13912yes—
324C22×C4C2×D4×C13911yescharacteristic
325C22×C4C2×D4×C13912yes—
326C22×C4C24×C13911yescharacteristic
327M16—44no—
328C2×C8—24no—
329C4⋊C4—24no—
330C4⋊C4—24no—
331C4⋊C4—22no—
332C4⋊C4—24no—
333C4⋊C4—22no—
334C4⋊C4—22no—
335C4⋊C4—44no—
336C4⋊C4C2×D4×C13914yes—
337C22⋊C4—28no—
338C22⋊C4—24no—
339C22⋊C4—24no—
340C22⋊C4—42no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C42—42no—
344C23—22no—
345C23—22no—
346C23—24no—
347C23—41no—
348C23—44no—
349C23—44no—
350C23—44no—
351C23#120×C13911yescharacteristic
352C23#120×C13911yescharacteristic
353C23C22×D4×C13911yescharacteristic
354Q8—48no—
355D4—44no—
356D4—48no—
357D4—48no—
358D4—48no—
359D4—82no—
360D4—84no—
361C2×C4—24no—
362C2×C4—24no—
363C2×C4—24no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—24no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—416no—
372C2×C4—44no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—42no—
382C2×C4—81no—
383C2×C4#120×C13912yes—
384C2×C4AGL(1,ℤ/8)×C13914yes—
385C2×C4C22×D4×C13912yes—
386C8—44no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—44no—
395C22—44no—
396C22—44no—
397C22—44no—
398C22—88no—
399C22#458×C13912yes—
400C22C2×#120×C13911yescharacteristic
401C22C2×AGL(1,ℤ/8)×C13912yes—
402C4—22no—
403C4—22no—
404C4—24no—
405C4—42no—
406C4—44no—
407C4—82no—
408C4—81no—
409C4—81no—
410C2—22no—
411C2—22no—
412C2—41no—
413C2—84no—
414C2#3003×C13911yescharacteristic
415C2#3020×C13911yescharacteristic
416C2C2×#458×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC2×#537×C139C2
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
2. #3094×C139C2semidirect
3. #2484×C139C2semidirect
4. #1616×C139C2semidirect
5. #1610×C139C2semidirect
6. #1510×C139C2semidirect
7. #1463×C139C2semidirect
19. #481×C139C22semidirect
20. #480×C139C22semidirect
24. #400×C139C22semidirect
25. #398×C139C22semidirect
30. #327×C139C22semidirect
31. #324×C139C22semidirect
208. #18147C139direct (N × H)
209. C139#18147direct (N × H)
211. #3094C2×C139semidirect
212. #2484C2×C139semidirect
213. #1616C2×C139semidirect
214. #1610C2×C139semidirect
215. #1510C2×C139semidirect
216. #1463C2×C139semidirect
228. #481C22×C139semidirect
229. #480C22×C139semidirect
233. #400C22×C139semidirect
234. #398C22×C139semidirect
239. #327C22×C139semidirect
240. #324C22×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C1392
#3094×C1392
#2484×C1392
#1616×C1392
#1610×C1392
#1510×C1392
#1463×C1392
#18147139