Finite Group Databasebeta

← C139×#18287 #48012883

Subgroups — C139×#18287 #48012883

Order 35584.

1064 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#543×C139C211yesmaximal, characteristic
2#3189×C139C212yesmaximal, complemented
3#2626×C139C211yesmaximal, characteristic
4#1614×C139C214yesmaximal, complemented
5#1602×C139C214yesmaximal, complemented
6#1520×C139C212yesmaximal, complemented
7C2×#323×C139C211yesmaximal, characteristic
8#543×C139—24no—
9#543×C139—22no—
10#543×C139C2214yes—
11C2×C22⋊Q8×C139—22no—
12C2×C22⋊Q8×C139—21no—
13C2×C22⋊Q8×C139—22no—
14C2×C22⋊Q8×C139C2212yes—
15C2×C22⋊Q8×C139C2211yescharacteristic
16C22×C22⋊C4×C139—21no—
17C22×C22⋊C4×C139C2211yescharacteristic
18#484×C139—22no—
19#484×C139C2214yescomplemented
20#467×C139—24no—
21#451×C139—22no—
22#451×C139C2214yescomplemented
23C2×C22⋊C8×C139C2212yes—
24#399×C139C2212yes—
25#396×C139—22no—
26#393×C139C2212yes—
27#385×C139—21no—
28#380×C139C2211yescharacteristic
29#379×C139—21no—
30#328×C139C2218yescomplemented
31#323×C139C2214yes—
32C25×C139D411yescharacteristic
33C22×Q8×C139—21no—
34C22×Q8×C139D412yes—
35C22×Q8×C139C2311yescharacteristic
36C23×C4×C139—21no—
37C23×C4×C139—21no—
38C23×C4×C139D411yescharacteristic
39C23×C4×C139C2311yescharacteristic
40C2×Q16×C139—24no—
41C22×C8×C139—22no—
42C22⋊Q8×C139—28no—
43C22⋊Q8×C139—28no—
44C22⋊Q8×C139—24no—
45C22⋊Q8×C139—28no—
46C22⋊Q8×C139—24no—
47C22⋊Q8×C139—22no—
48C22⋊Q8×C139—22no—
49C22⋊Q8×C139—28no—
50C22⋊Q8×C139—22no—
51C22⋊Q8×C139—22no—
52C22⋊Q8×C139D414yes—
53C22⋊Q8×C139C2314yes—
54C2×C4⋊C4×C139—21no—
55C2×C4⋊C4×C139—22no—
56C2×C4⋊C4×C139—22no—
57C2×C4⋊C4×C139—21no—
58C2×C4⋊C4×C139—21no—
59C2×C4⋊C4×C139—22no—
60C2×C4⋊C4×C139D412yes—
61C2×C4⋊C4×C139C2311yescharacteristic
62C2×C22⋊C4×C139—22no—
63C2×C22⋊C4×C139—24no—
64C2×C22⋊C4×C139—22no—
65C2×C22⋊C4×C139—24no—
66C2×C22⋊C4×C139—22no—
67C2×C22⋊C4×C139—22no—
68C2×C22⋊C4×C139—21no—
69C2×C22⋊C4×C139—21no—
70C2×C22⋊C4×C139—22no—
71C2×C22⋊C4×C139—22no—
72C2×C22⋊C4×C139D412yes—
73C2×C22⋊C4×C139C2312yes—
74#107×C139—24no—
75#103×C139—24no—
76#103×C139—24no—
77C22⋊C8×C139—22no—
78C22⋊C8×C139C2314yes—
79#95×C139—22no—
80#95×C139C2312yes—
81C24×C139—21no—
82C24×C139—21no—
83C24×C139—22no—
84C24×C139—81no—
85C24×C139—81no—
86C24×C139Q1614yescomplemented
87C24×C139C2×D412yes—
88C24×C139C2×D411yescharacteristic
89C2×Q8×C139—24no—
90C2×Q8×C139—22no—
91C2×Q8×C139—22no—
92C2×Q8×C139—81no—
93C2×Q8×C139—82no—
94C2×Q8×C139—82no—
95C2×Q8×C139C2×D414yes—
96C22×C4×C139—22no—
97C22×C4×C139—21no—
98C22×C4×C139—22no—
99C22×C4×C139—24no—
100C22×C4×C139—24no—
101C22×C4×C139—21no—
102C22×C4×C139—21no—
103C22×C4×C139—22no—
104C22×C4×C139—21no—
105C22×C4×C139—81no—
106C22×C4×C139—81no—
107C22×C4×C139—82no—
108C22×C4×C139—82no—
109C22×C4×C139C2×D412yes—
110C22×C4×C139C2×D411yescharacteristic
111C22×C4×C139C2×D412yes—
112C22×C4×C139C2×D412yes—
113C22×C4×C139C2411yescharacteristic
114Q16×C139—84no—
115C2×C8×C139—24no—
116C2×C8×C139—82no—
117C4⋊C4×C139—24no—
118C4⋊C4×C139—28no—
119C4⋊C4×C139—24no—
120C4⋊C4×C139—22no—
121C4⋊C4×C139—24no—
122C4⋊C4×C139—22no—
123C4⋊C4×C139—42no—
124C4⋊C4×C139—81no—
125C4⋊C4×C139—82no—
126C4⋊C4×C139C2×D414yes—
127C22⋊C4×C139—28no—
128C22⋊C4×C139—24no—
129C22⋊C4×C139—24no—
130C22⋊C4×C139—24no—
131C22⋊C4×C139—24no—
132C22⋊C4×C139—41no—
133C22⋊C4×C139—41no—
134C22⋊C4×C139—42no—
135C22⋊C4×C139—82no—
136C22⋊C4×C139—82no—
137C23×C139—22no—
138C23×C139—24no—
139C23×C139—22no—
140C23×C139—24no—
141C23×C139—41no—
142C23×C139—41no—
143C23×C139—42no—
144C23×C139—42no—
145C23×C139—42no—
146C23×C139—42no—
147C23×C139—81no—
148C23×C139—81no—
149C23×C139—84no—
150C23×C139—84no—
151C23×C139#12011yescharacteristic
152C23×C139#12011yescharacteristic
153C23×C139C2×Q1614yes—
154C23×C139C2×Q1612yes—
155C23×C139#13712yes—
156C23×C139C22×D411yescharacteristic
157Q8×C139—44no—
158Q8×C139—44no—
159Q8×C139—82no—
160Q8×C139—84no—
161C2×C4×C139—24no—
162C2×C4×C139—22no—
163C2×C4×C139—24no—
164C2×C4×C139—41no—
165C2×C4×C139—42no—
166C2×C4×C139—42no—
167C2×C4×C139—41no—
168C2×C4×C139—42no—
169C2×C4×C139—44no—
170C2×C4×C139—44no—
171C2×C4×C139—42no—
172C2×C4×C139—42no—
173C2×C4×C139—42no—
174C2×C4×C139—42no—
175C2×C4×C139—42no—
176C2×C4×C139—41no—
177C2×C4×C139—41no—
178C2×C4×C139—42no—
179C2×C4×C139—81no—
180C2×C4×C139—84no—
181C2×C4×C139—84no—
182C2×C4×C139#12012yes—
183C2×C4×C139C22×D412yes—
184C8×C139—44no—
185C22×C139—21no—
186C22×C139—21no—
187C22×C139—21no—
188C22×C139—21no—
189C22×C139—21no—
190C22×C139—21no—
191C22×C139—24no—
192C22×C139—42no—
193C22×C139—42no—
194C22×C139—44no—
195C22×C139—48no—
196C22×C139—42no—
197C22×C139—42no—
198C22×C139—82no—
199C22×C139—84no—
200C22×C139#45112yes—
201C22×C139#45112yes—
202C22×C139C2×#12011yescharacteristic
203C22×C139C22×Q1611yescharacteristic
204C22×C139C2×#13711yescharacteristic
205C4×C139—22no—
206C4×C139—22no—
207C4×C139—42no—
208C4×C139—44no—
209C4×C139—44no—
210C4×C139—82no—
211C4×C139—81no—
212C4×C139—81no—
213C2×C139—21no—
214C2×C139—21no—
215C2×C139—22no—
216C2×C139—22no—
217C2×C139—44no—
218C2×C139C2×#45111yescharacteristic
219C2×C139#301911yescharacteristic
220C2×C139#302611yescharacteristic
221#18287C13911yesmaximal, characteristic, direct product factor, Sylow
222C139#1828711yescharacteristic, direct product factor, Sylow
223C2×#543C2×C13911yescharacteristic
224#3189C2×C13912yescomplemented
225#2626C2×C13911yescharacteristic
226#1614C2×C13914yescomplemented
227#1602C2×C13914yescomplemented
228#1520C2×C13912yescomplemented
229C2×#323C2×C13911yescharacteristic
230#543—24no—
231#543—22no—
232#543C22×C13914yes—
233C2×C22⋊Q8—22no—
234C2×C22⋊Q8—21no—
235C2×C22⋊Q8—22no—
236C2×C22⋊Q8C22×C13912yes—
237C2×C22⋊Q8C22×C13911yescharacteristic
238C22×C22⋊C4—21no—
239C22×C22⋊C4C22×C13911yescharacteristic
240#484—22no—
241#484C22×C13914yescomplemented
242#467—24no—
243#451—22no—
244#451C22×C13914yescomplemented
245C2×C22⋊C8C22×C13912yes—
246#399C22×C13912yes—
247#396—22no—
248#393C22×C13912yes—
249#385—21no—
250#380C22×C13911yescharacteristic
251#379—21no—
252#328C22×C13918yescomplemented
253#323C22×C13914yes—
254C25D4×C13911yescharacteristic
255C22×Q8—21no—
256C22×Q8D4×C13912yes—
257C22×Q8C23×C13911yescharacteristic
258C23×C4—21no—
259C23×C4—21no—
260C23×C4D4×C13911yescharacteristic
261C23×C4C23×C13911yescharacteristic
262C2×Q16—24no—
263C22×C8—22no—
264C22⋊Q8—28no—
265C22⋊Q8—28no—
266C22⋊Q8—24no—
267C22⋊Q8—28no—
268C22⋊Q8—24no—
269C22⋊Q8—22no—
270C22⋊Q8—22no—
271C22⋊Q8—28no—
272C22⋊Q8—22no—
273C22⋊Q8—22no—
274C22⋊Q8D4×C13914yes—
275C22⋊Q8C23×C13914yes—
276C2×C4⋊C4—21no—
277C2×C4⋊C4—22no—
278C2×C4⋊C4—22no—
279C2×C4⋊C4—21no—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—22no—
282C2×C4⋊C4D4×C13912yes—
283C2×C4⋊C4C23×C13911yescharacteristic
284C2×C22⋊C4—22no—
285C2×C22⋊C4—24no—
286C2×C22⋊C4—22no—
287C2×C22⋊C4—24no—
288C2×C22⋊C4—22no—
289C2×C22⋊C4—22no—
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C22⋊C4—22no—
293C2×C22⋊C4—22no—
294C2×C22⋊C4D4×C13912yes—
295C2×C22⋊C4C23×C13912yes—
296#107—24no—
297#103—24no—
298#103—24no—
299C22⋊C8—22no—
300C22⋊C8C23×C13914yes—
301#95—22no—
302#95C23×C13912yes—
303C24—21no—
304C24—21no—
305C24—22no—
306C24—81no—
307C24—81no—
308C24Q16×C13914yescomplemented
309C24C2×D4×C13912yes—
310C24C2×D4×C13911yescharacteristic
311C2×Q8—24no—
312C2×Q8—22no—
313C2×Q8—22no—
314C2×Q8—81no—
315C2×Q8—82no—
316C2×Q8—82no—
317C2×Q8C2×D4×C13914yes—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—22no—
321C22×C4—24no—
322C22×C4—24no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—21no—
327C22×C4—81no—
328C22×C4—81no—
329C22×C4—82no—
330C22×C4—82no—
331C22×C4C2×D4×C13912yes—
332C22×C4C2×D4×C13911yescharacteristic
333C22×C4C2×D4×C13912yes—
334C22×C4C2×D4×C13912yes—
335C22×C4C24×C13911yescharacteristic
336Q16—84no—
337C2×C8—24no—
338C2×C8—82no—
339C4⋊C4—24no—
340C4⋊C4—28no—
341C4⋊C4—24no—
342C4⋊C4—22no—
343C4⋊C4—24no—
344C4⋊C4—22no—
345C4⋊C4—42no—
346C4⋊C4—81no—
347C4⋊C4—82no—
348C4⋊C4C2×D4×C13914yes—
349C22⋊C4—28no—
350C22⋊C4—24no—
351C22⋊C4—24no—
352C22⋊C4—24no—
353C22⋊C4—24no—
354C22⋊C4—41no—
355C22⋊C4—41no—
356C22⋊C4—42no—
357C22⋊C4—82no—
358C22⋊C4—82no—
359C23—24no—
360C23—22no—
361C23—24no—
362C23—22no—
363C23—41no—
364C23—41no—
365C23—42no—
366C23—42no—
367C23—42no—
368C23—42no—
369C23—81no—
370C23—81no—
371C23—84no—
372C23—84no—
373C23#120×C13911yescharacteristic
374C23#120×C13911yescharacteristic
375C23C2×Q16×C13914yes—
376C23C2×Q16×C13912yes—
377C23#137×C13912yes—
378C23C22×D4×C13911yescharacteristic
379Q8—44no—
380Q8—44no—
381Q8—82no—
382Q8—84no—
383C2×C4—24no—
384C2×C4—22no—
385C2×C4—24no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—44no—
391C2×C4—42no—
392C2×C4—44no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—42no—
401C2×C4—81no—
402C2×C4—84no—
403C2×C4—84no—
404C2×C4#120×C13912yes—
405C2×C4C22×D4×C13912yes—
406C8—44no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—24no—
414C22—42no—
415C22—42no—
416C22—44no—
417C22—48no—
418C22—42no—
419C22—42no—
420C22—82no—
421C22—84no—
422C22#451×C13912yes—
423C22#451×C13912yes—
424C22C2×#120×C13911yescharacteristic
425C22C22×Q16×C13911yescharacteristic
426C22C2×#137×C13911yescharacteristic
427C4—22no—
428C4—22no—
429C4—44no—
430C4—42no—
431C4—44no—
432C4—82no—
433C4—81no—
434C4—81no—
435C2—21no—
436C2—22no—
437C2—21no—
438C2—22no—
439C2—44no—
440C2C2×#451×C13911yescharacteristic
441C2#3019×C13911yescharacteristic
442C2#3026×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C2×#120
commutator, Frattini, cosocleC22×C4C24×C139
prime radicalC25×C139D4
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. #3189×C139C2semidirect
4. #1614×C139C2semidirect
5. #1602×C139C2semidirect
6. #1520×C139C2semidirect
19. #484×C139C22semidirect
22. #451×C139C22semidirect
30. #328×C139C22semidirect
86. C24×C139Q16semidirect
221. #18287C139direct (N × H)
222. C139#18287direct (N × H)
224. #3189C2×C139semidirect
226. #1614C2×C139semidirect
227. #1602C2×C139semidirect
228. #1520C2×C139semidirect
241. #484C22×C139semidirect
244. #451C22×C139semidirect
252. #328C22×C139semidirect
308. C24Q16×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#543×C1392
#3189×C1392
#2626×C1392
#1614×C1392
#1602×C1392
#1520×C1392
C2×#323×C1392
#18287139