Finite Group Databasebeta

← C139×#9951 #48004547

Subgroups — C139×#9951 #48004547

Order 35584.

610 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3187×C139C211yesmaximal, characteristic
2C2×#481×C139C211yesmaximal, characteristic
3#2502×C139C211yesmaximal, characteristic, complemented
4#1964×C139C211yesmaximal, characteristic
5#1824×C139C211yesmaximal, characteristic, complemented
6#1520×C139C211yesmaximal, characteristic, complemented
7#1282×C139C211yesmaximal, characteristic, complemented
8C2×C22⋊Q8×C139C2211yescharacteristic
9C2×#121×C139C2211yescharacteristic
10C22×C4⋊C4×C139C2211yescharacteristic
11#483×C139—21no—
12#481×C139—22no—
13#481×C139—21no—
14#481×C139—22no—
15#465×C139—22no—
16#450×C139—21no—
17#448×C139—21no—
18C2×#106×C139—21no—
19C2×#102×C139—21no—
20C2×#99×C139—22no—
21C2×C22⋊C8×C139C2211yescharacteristic
22C2×C22⋊C8×C139C2211yescharacteristic
23#398×C139—22no—
24#391×C139—21no—
25#385×C139—22no—
26#384×C139—21no—
27#380×C139C2211yescharacteristic
28C4×C22⋊C4×C139C2211yescharacteristic
29#340×C139—22no—
30#328×C139—22no—
31C22×Q8×C139D411yescharacteristic
32C22×D4×C139—21no—
33C22×D4×C139D411yescharacteristic
34C23×C4×C139—21no—
35C23×C4×C139C2311yescharacteristic
36C2×SD16×C139—22no—
37C22×C8×C139—21no—
38C22×C8×C139D412yes—
39C22⋊Q8×C139—21no—
40C22⋊Q8×C139—21no—
41C22⋊Q8×C139—21no—
42C22⋊Q8×C139—21no—
43#121×C139—21no—
44#121×C139—21no—
45#121×C139—21no—
46#121×C139—21no—
47C2×C4⋊C4×C139—21no—
48C2×C4⋊C4×C139—21no—
49C2×C4⋊C4×C139—21no—
50C2×C4⋊C4×C139—21no—
51C2×C4⋊C4×C139—21no—
52C2×C4⋊C4×C139—21no—
53C2×C4⋊C4×C139—21no—
54C2×C4⋊C4×C139—24no—
55C2×C4⋊C4×C139D412yes—
56C2×C4⋊C4×C139D411yescharacteristic
57C2×C4⋊C4×C139D411yescharacteristic
58C2×C22⋊C4×C139—21no—
59C2×C22⋊C4×C139—21no—
60C2×C22⋊C4×C139—21no—
61C2×C22⋊C4×C139D412yes—
62C2×C42×C139—21no—
63#106×C139—24no—
64#106×C139—22no—
65#103×C139—22no—
66#102×C139—24no—
67#102×C139—22no—
68#99×C139—44no—
69C22⋊C8×C139—21no—
70C22⋊C8×C139—21no—
71C22⋊C8×C139—21no—
72C22⋊C8×C139D412yes—
73#95×C139—24no—
74#95×C139—21no—
75#95×C139—21no—
76C24×C139—21no—
77C24×C139C2×D411yescharacteristic
78C2×Q8×C139—21no—
79C2×Q8×C139—21no—
80C2×Q8×C139—42no—
81C2×D4×C139—21no—
82C2×D4×C139—21no—
83C2×D4×C139—42no—
84C2×D4×C139—41no—
85C2×D4×C139—41no—
86C2×D4×C139—42no—
87C2×D4×C139—42no—
88C22×C4×C139—22no—
89C22×C4×C139—21no—
90C22×C4×C139—22no—
91C22×C4×C139—21no—
92C22×C4×C139—21no—
93C22×C4×C139—42no—
94C22×C4×C139—41no—
95C22×C4×C139—41no—
96C22×C4×C139—41no—
97C22×C4×C139—82no—
98C22×C4×C139C2×D411yescharacteristic
99C22×C4×C139C2×D411yescharacteristic
100C22×C4×C139C2×D411yescharacteristic
101C22×C4×C139C2×D411yescharacteristic
102C22×C4×C139C2×D411yescharacteristic
103C22×C4×C139#4111yescharacteristic
104SD16×C139—82no—
105C2×C8×C139—22no—
106C2×C8×C139—22no—
107C2×C8×C139—42no—
108C2×C8×C139—42no—
109C4⋊C4×C139—22no—
110C4⋊C4×C139—21no—
111C4⋊C4×C139—21no—
112C4⋊C4×C139—21no—
113C4⋊C4×C139—22no—
114C4⋊C4×C139—21no—
115C4⋊C4×C139—42no—
116C4⋊C4×C139—41no—
117C4⋊C4×C139—41no—
118C4⋊C4×C139—41no—
119C4⋊C4×C139—41no—
120C4⋊C4×C139—84no—
121C22⋊C4×C139—22no—
122C22⋊C4×C139—41no—
123C22⋊C4×C139—41no—
124C22⋊C4×C139—41no—
125C22⋊C4×C139—41no—
126C22⋊C4×C139—42no—
127C22⋊C4×C139SD1614yescomplemented
128C42×C139—42no—
129C23×C139—41no—
130C23×C139—41no—
131C23×C139—41no—
132C23×C139—42no—
133C23×C139—81no—
134C23×C139—81no—
135C23×C139#12011yescharacteristic
136C23×C139#12111yescharacteristic
137C23×C139#12711yescharacteristic
138C23×C139C2×SD1612yes—
139C23×C139#13712yes—
140Q8×C139—42no—
141Q8×C139—81no—
142D4×C139—42no—
143D4×C139—42no—
144D4×C139—82no—
145D4×C139—81no—
146D4×C139—81no—
147C2×C4×C139—22no—
148C2×C4×C139—22no—
149C2×C4×C139—22no—
150C2×C4×C139—24no—
151C2×C4×C139—41no—
152C2×C4×C139—41no—
153C2×C4×C139—41no—
154C2×C4×C139—42no—
155C2×C4×C139—42no—
156C2×C4×C139—42no—
157C2×C4×C139—44no—
158C2×C4×C139—42no—
159C2×C4×C139—41no—
160C2×C4×C139—41no—
161C2×C4×C139—41no—
162C2×C4×C139—42no—
163C2×C4×C139—42no—
164C2×C4×C139—82no—
165C2×C4×C139—82no—
166C2×C4×C139—81no—
167C2×C4×C139—81no—
168C2×C4×C139—81no—
169C2×C4×C139#12011yescharacteristic
170C2×C4×C139#12011yescharacteristic
171C2×C4×C139#12111yescharacteristic
172C2×C4×C139#12111yescharacteristic
173C8×C139—42no—
174C8×C139—42no—
175C22×C139—21no—
176C22×C139—21no—
177C22×C139—21no—
178C22×C139—21no—
179C22×C139—21no—
180C22×C139—21no—
181C22×C139—42no—
182C22×C139—42no—
183C22×C139—81no—
184C22×C139—81no—
185C22×C139—81no—
186C22×C139—162no—
187C22×C139#39211yescharacteristic
188C22×C139#44812yes—
189C22×C139#46112yes—
190C22×C139#49211yescharacteristic
191C22×C139#49711yescharacteristic
192C4×C139—21no—
193C4×C139—21no—
194C4×C139—21no—
195C4×C139—44no—
196C4×C139—81no—
197C4×C139—82no—
198C4×C139—81no—
199C4×C139—81no—
200C4×C139—161no—
201C4×C139#45812yes—
202C2×C139—22no—
203C2×C139—21no—
204C2×C139—22no—
205C2×C139—21no—
206C2×C139—161no—
207C2×C139#200811yescharacteristic
208C2×C139#201311yescharacteristic
209C2×C139#202211yescharacteristic
210#9951C13911yesmaximal, characteristic, direct product factor, Sylow
211C139#995111yescharacteristic, direct product factor, Sylow
212#3187C2×C13911yescharacteristic
213C2×#481C2×C13911yescharacteristic
214#2502C2×C13911yescharacteristic, complemented
215#1964C2×C13911yescharacteristic
216#1824C2×C13911yescharacteristic, complemented
217#1520C2×C13911yescharacteristic, complemented
218#1282C2×C13911yescharacteristic, complemented
219C2×C22⋊Q8C22×C13911yescharacteristic
220C2×#121C22×C13911yescharacteristic
221C22×C4⋊C4C22×C13911yescharacteristic
222#483—21no—
223#481—22no—
224#481—21no—
225#481—22no—
226#465—22no—
227#450—21no—
228#448—21no—
229C2×#106—21no—
230C2×#102—21no—
231C2×#99—22no—
232C2×C22⋊C8C22×C13911yescharacteristic
233C2×C22⋊C8C22×C13911yescharacteristic
234#398—22no—
235#391—21no—
236#385—22no—
237#384—21no—
238#380C22×C13911yescharacteristic
239C4×C22⋊C4C22×C13911yescharacteristic
240#340—22no—
241#328—22no—
242C22×Q8D4×C13911yescharacteristic
243C22×D4—21no—
244C22×D4D4×C13911yescharacteristic
245C23×C4—21no—
246C23×C4C23×C13911yescharacteristic
247C2×SD16—22no—
248C22×C8—21no—
249C22×C8D4×C13912yes—
250C22⋊Q8—21no—
251C22⋊Q8—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254#121—21no—
255#121—21no—
256#121—21no—
257#121—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—24no—
266C2×C4⋊C4D4×C13912yes—
267C2×C4⋊C4D4×C13911yescharacteristic
268C2×C4⋊C4D4×C13911yescharacteristic
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4D4×C13912yes—
273C2×C42—21no—
274#106—24no—
275#106—22no—
276#103—22no—
277#102—24no—
278#102—22no—
279#99—44no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8D4×C13912yes—
284#95—24no—
285#95—21no—
286#95—21no—
287C24—21no—
288C24C2×D4×C13911yescharacteristic
289C2×Q8—21no—
290C2×Q8—21no—
291C2×Q8—42no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—42no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—42no—
298C2×D4—42no—
299C22×C4—22no—
300C22×C4—21no—
301C22×C4—22no—
302C22×C4—21no—
303C22×C4—21no—
304C22×C4—42no—
305C22×C4—41no—
306C22×C4—41no—
307C22×C4—41no—
308C22×C4—82no—
309C22×C4C2×D4×C13911yescharacteristic
310C22×C4C2×D4×C13911yescharacteristic
311C22×C4C2×D4×C13911yescharacteristic
312C22×C4C2×D4×C13911yescharacteristic
313C22×C4C2×D4×C13911yescharacteristic
314C22×C4#41×C13911yescharacteristic
315SD16—82no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—42no—
319C2×C8—42no—
320C4⋊C4—22no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—22no—
325C4⋊C4—21no—
326C4⋊C4—42no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—84no—
332C22⋊C4—22no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—41no—
337C22⋊C4—42no—
338C22⋊C4SD16×C13914yescomplemented
339C42—42no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—42no—
344C23—81no—
345C23—81no—
346C23#120×C13911yescharacteristic
347C23#121×C13911yescharacteristic
348C23#127×C13911yescharacteristic
349C23C2×SD16×C13912yes—
350C23#137×C13912yes—
351Q8—42no—
352Q8—81no—
353D4—42no—
354D4—42no—
355D4—82no—
356D4—81no—
357D4—81no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—22no—
361C2×C4—24no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—42no—
368C2×C4—44no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—42no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4#120×C13911yescharacteristic
381C2×C4#120×C13911yescharacteristic
382C2×C4#121×C13911yescharacteristic
383C2×C4#121×C13911yescharacteristic
384C8—42no—
385C8—42no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—42no—
393C22—42no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22—162no—
398C22#392×C13911yescharacteristic
399C22#448×C13912yes—
400C22#461×C13912yes—
401C22#492×C13911yescharacteristic
402C22#497×C13911yescharacteristic
403C4—21no—
404C4—21no—
405C4—21no—
406C4—44no—
407C4—82no—
408C4—81no—
409C4—81no—
410C4—81no—
411C4—161no—
412C4#458×C13912yes—
413C2—22no—
414C2—21no—
415C2—22no—
416C2—21no—
417C2—161no—
418C2#2008×C13911yescharacteristic
419C2#2013×C13911yescharacteristic
420C2#2022×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#392
commutator, Frattini, cosocleC23×C4C23×C139
prime radicalC2×#121×C139C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2502×C139C2semidirect
5. #1824×C139C2semidirect
6. #1520×C139C2semidirect
7. #1282×C139C2semidirect
127. C22⋊C4×C139SD16semidirect
210. #9951C139direct (N × H)
211. C139#9951direct (N × H)
214. #2502C2×C139semidirect
216. #1824C2×C139semidirect
217. #1520C2×C139semidirect
218. #1282C2×C139semidirect
338. C22⋊C4SD16×C139semidirect

Maximal subgroups

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

subgroupindex
#3187×C1392
C2×#481×C1392
#2502×C1392
#1964×C1392
#1824×C1392
#1520×C1392
#1282×C1392
#9951139