Finite Group Databasebeta

← C139×#9261 #48003857

Subgroups — C139×#9261 #48003857

Order 35584.

566 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C139C211yesmaximal, characteristic
2#2345×C139C211yesmaximal, characteristic, complemented
3#1964×C139C211yesmaximal, characteristic
4#1824×C139C211yesmaximal, characteristic, complemented
5#1519×C139C211yesmaximal, characteristic
6#1289×C139C211yesmaximal, characteristic, complemented
7#1282×C139C211yesmaximal, characteristic, complemented
8C2×#121×C139C2211yescharacteristic
9C22×C4⋊C4×C139C2211yescharacteristic
10#481×C139—22no—
11#481×C139—21no—
12#481×C139—21no—
13C2×#106×C139C412yescomplemented
14C2×#102×C139C412yescomplemented
15C2×#99×C139—21no—
16C2×#99×C139—21no—
17C2×C22⋊C8×C139C2211yescharacteristic
18C2×C22⋊C8×C139C2211yescharacteristic
19#389×C139—21no—
20#387×C139—22no—
21#380×C139—21no—
22#380×C139C2211yescharacteristic
23#380×C139C2211yescharacteristic
24C4×C4⋊C4×C139—21no—
25C4×C22⋊C4×C139—21no—
26C4×C22⋊C4×C139C2211yescharacteristic
27#340×C139—22no—
28#327×C139—22no—
29C22×D4×C139—21no—
30C22×D4×C139C2×C411yescharacteristic
31C23×C4×C139—21no—
32C23×C4×C139C2311yescharacteristic
33C22×C8×C139—21no—
34C22×C8×C139C2×C412yes—
35#121×C139—21no—
36#121×C139—21no—
37#121×C139—21no—
38#121×C139—21no—
39C2×C4⋊C4×C139—21no—
40C2×C4⋊C4×C139—21no—
41C2×C4⋊C4×C139—21no—
42C2×C4⋊C4×C139—21no—
43C2×C4⋊C4×C139—21no—
44C2×C4⋊C4×C139—22no—
45C2×C4⋊C4×C139C2×C411yescharacteristic
46C2×C4⋊C4×C139C2×C412yes—
47C2×C4⋊C4×C139D412yes—
48C2×C4⋊C4×C139D411yescharacteristic
49C2×C4⋊C4×C139D411yescharacteristic
50C2×C22⋊C4×C139—21no—
51C2×C22⋊C4×C139—21no—
52C2×C22⋊C4×C139—21no—
53C2×C22⋊C4×C139D411yescharacteristic
54C2×C22⋊C4×C139D411yescharacteristic
55C2×C42×C139—21no—
56C2×C42×C139—22no—
57#106×C139—22no—
58#106×C139—22no—
59#102×C139—22no—
60#102×C139—22no—
61#99×C139—42no—
62#99×C139—42no—
63C22⋊C8×C139—21no—
64C22⋊C8×C139—21no—
65C22⋊C8×C139—21no—
66C22⋊C8×C139—21no—
67#95×C139—22no—
68#95×C139—22no—
69#95×C139—21no—
70#95×C139—21no—
71#95×C139D412yes—
72C24×C139—21no—
73C24×C139C2×D411yescharacteristic
74C2×D4×C139—21no—
75C2×D4×C139—21no—
76C2×D4×C139—42no—
77C2×D4×C139—41no—
78C2×D4×C139—41no—
79C2×D4×C139—41no—
80C2×D4×C139—41no—
81C2×D4×C139—41no—
82C2×D4×C139—41no—
83C22×C4×C139—21no—
84C22×C4×C139—21no—
85C22×C4×C139—21no—
86C22×C4×C139—22no—
87C22×C4×C139—22no—
88C22×C4×C139—21no—
89C22×C4×C139—21no—
90C22×C4×C139—22no—
91C22×C4×C139—42no—
92C22×C4×C139—41no—
93C22×C4×C139—82no—
94C22×C4×C139C22×C411yescharacteristic
95C22×C4×C139C2×D411yescharacteristic
96C22×C4×C139C2×D411yescharacteristic
97C22×C4×C139C2×D411yescharacteristic
98C22×C4×C139#4111yescharacteristic
99C22×C4×C139#4111yescharacteristic
100C2×C8×C139—22no—
101C2×C8×C139—42no—
102C2×C8×C139—42no—
103C2×C8×C139—41no—
104C4⋊C4×C139—22no—
105C4⋊C4×C139—22no—
106C4⋊C4×C139—21no—
107C4⋊C4×C139—21no—
108C4⋊C4×C139—21no—
109C4⋊C4×C139—21no—
110C4⋊C4×C139—42no—
111C4⋊C4×C139—42no—
112C4⋊C4×C139—82no—
113C4⋊C4×C139C22⋊C412yes—
114C4⋊C4×C139C22⋊C412yes—
115C22⋊C4×C139—21no—
116C22⋊C4×C139—21no—
117C22⋊C4×C139—21no—
118C22⋊C4×C139—41no—
119C22⋊C4×C139—41no—
120C22⋊C4×C139—41no—
121C22⋊C4×C139—41no—
122C22⋊C4×C139—41no—
123C22⋊C4×C139—41no—
124C22⋊C4×C139SD1612yes—
125C42×C139—42no—
126C42×C139—82no—
127C23×C139—41no—
128C23×C139—41no—
129C23×C139—41no—
130C23×C139—41no—
131C23×C139—41no—
132C23×C139—81no—
133C23×C139—81no—
134C23×C139C4×D411yescharacteristic
135C23×C139#12011yescharacteristic
136C23×C139#12111yescharacteristic
137C23×C139C2×SD1611yescharacteristic
138C23×C139#13511yescharacteristic
139C23×C139AGL(1,ℤ/8)11yescharacteristic
140C23×C139#13711yescharacteristic
141D4×C139—42no—
142D4×C139—81no—
143D4×C139—81no—
144D4×C139—81no—
145D4×C139—81no—
146D4×C139—81no—
147C2×C4×C139—22no—
148C2×C4×C139—22no—
149C2×C4×C139—22no—
150C2×C4×C139—22no—
151C2×C4×C139—22no—
152C2×C4×C139—22no—
153C2×C4×C139—41no—
154C2×C4×C139—41no—
155C2×C4×C139—41no—
156C2×C4×C139—41no—
157C2×C4×C139—41no—
158C2×C4×C139—42no—
159C2×C4×C139—42no—
160C2×C4×C139—41no—
161C2×C4×C139—42no—
162C2×C4×C139—42no—
163C2×C4×C139—41no—
164C2×C4×C139—41no—
165C2×C4×C139—41no—
166C2×C4×C139—41no—
167C2×C4×C139—41no—
168C2×C4×C139—42no—
169C2×C4×C139—82no—
170C2×C4×C139—82no—
171C2×C4×C139—81no—
172C2×C4×C139—81no—
173C2×C4×C139—81no—
174C2×C4×C139C2×C22⋊C411yescharacteristic
175C2×C4×C139C4×D411yescharacteristic
176C2×C4×C139#12111yescharacteristic
177C2×C4×C139#12311yescharacteristic
178C8×C139—42no—
179C8×C139—81no—
180C22×C139—21no—
181C22×C139—21no—
182C22×C139—21no—
183C22×C139—21no—
184C22×C139—21no—
185C22×C139—21no—
186C22×C139—41no—
187C22×C139—41no—
188C22×C139—41no—
189C22×C139—41no—
190C22×C139—81no—
191C22×C139—81no—
192C22×C139—81no—
193C22×C139—161no—
194C22×C139—161no—
195C22×C139#38611yescharacteristic
196C22×C139C4×SD1611yescharacteristic
197C22×C139#44011yescharacteristic
198C22×C139#44811yescharacteristic
199C22×C139#44911yescharacteristic
200C22×C139#46011yescharacteristic
201C22×C139#46411yescharacteristic
202C4×C139—21no—
203C4×C139—21no—
204C4×C139—21no—
205C4×C139—42no—
206C4×C139—42no—
207C4×C139—42no—
208C4×C139—81no—
209C4×C139—82no—
210C4×C139—81no—
211C4×C139—161no—
212C4×C139#41012yes—
213C2×C139—21no—
214C2×C139—21no—
215C2×C139—21no—
216C2×C139—21no—
217C2×C139—21no—
218C2×C139—21no—
219C2×C139—161no—
220C2×C139#188011yescharacteristic
221C2×C139#189911yescharacteristic
222C2×C139#190411yescharacteristic
223#9261C13911yesmaximal, characteristic, direct product factor, Sylow
224C139#926111yescharacteristic, direct product factor, Sylow
225C2×#481C2×C13911yescharacteristic
226#2345C2×C13911yescharacteristic, complemented
227#1964C2×C13911yescharacteristic
228#1824C2×C13911yescharacteristic, complemented
229#1519C2×C13911yescharacteristic
230#1289C2×C13911yescharacteristic, complemented
231#1282C2×C13911yescharacteristic, complemented
232C2×#121C22×C13911yescharacteristic
233C22×C4⋊C4C22×C13911yescharacteristic
234#481—22no—
235#481—21no—
236#481—21no—
237C2×#106C4×C13912yescomplemented
238C2×#102C4×C13912yescomplemented
239C2×#99—21no—
240C2×#99—21no—
241C2×C22⋊C8C22×C13911yescharacteristic
242C2×C22⋊C8C22×C13911yescharacteristic
243#389—21no—
244#387—22no—
245#380—21no—
246#380C22×C13911yescharacteristic
247#380C22×C13911yescharacteristic
248C4×C4⋊C4—21no—
249C4×C22⋊C4—21no—
250C4×C22⋊C4C22×C13911yescharacteristic
251#340—22no—
252#327—22no—
253C22×D4—21no—
254C22×D4C2×C4×C13911yescharacteristic
255C23×C4—21no—
256C23×C4C23×C13911yescharacteristic
257C22×C8—21no—
258C22×C8C2×C4×C13912yes—
259#121—21no—
260#121—21no—
261#121—21no—
262#121—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4C2×C4×C13911yescharacteristic
270C2×C4⋊C4C2×C4×C13912yes—
271C2×C4⋊C4D4×C13912yes—
272C2×C4⋊C4D4×C13911yescharacteristic
273C2×C4⋊C4D4×C13911yescharacteristic
274C2×C22⋊C4—21no—
275C2×C22⋊C4—21no—
276C2×C22⋊C4—21no—
277C2×C22⋊C4D4×C13911yescharacteristic
278C2×C22⋊C4D4×C13911yescharacteristic
279C2×C42—21no—
280C2×C42—22no—
281#106—22no—
282#106—22no—
283#102—22no—
284#102—22no—
285#99—42no—
286#99—42no—
287C22⋊C8—21no—
288C22⋊C8—21no—
289C22⋊C8—21no—
290C22⋊C8—21no—
291#95—22no—
292#95—22no—
293#95—21no—
294#95—21no—
295#95D4×C13912yes—
296C24—21no—
297C24C2×D4×C13911yescharacteristic
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—42no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4—41no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—22no—
312C22×C4—21no—
313C22×C4—21no—
314C22×C4—22no—
315C22×C4—42no—
316C22×C4—41no—
317C22×C4—82no—
318C22×C4C22×C4×C13911yescharacteristic
319C22×C4C2×D4×C13911yescharacteristic
320C22×C4C2×D4×C13911yescharacteristic
321C22×C4C2×D4×C13911yescharacteristic
322C22×C4#41×C13911yescharacteristic
323C22×C4#41×C13911yescharacteristic
324C2×C8—22no—
325C2×C8—42no—
326C2×C8—42no—
327C2×C8—41no—
328C4⋊C4—22no—
329C4⋊C4—22no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—21no—
333C4⋊C4—21no—
334C4⋊C4—42no—
335C4⋊C4—42no—
336C4⋊C4—82no—
337C4⋊C4C22⋊C4×C13912yes—
338C4⋊C4C22⋊C4×C13912yes—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—21no—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C22⋊C4—41no—
346C22⋊C4—41no—
347C22⋊C4—41no—
348C22⋊C4SD16×C13912yes—
349C42—42no—
350C42—82no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—41no—
356C23—81no—
357C23—81no—
358C23C4×D4×C13911yescharacteristic
359C23#120×C13911yescharacteristic
360C23#121×C13911yescharacteristic
361C23C2×SD16×C13911yescharacteristic
362C23#135×C13911yescharacteristic
363C23AGL(1,ℤ/8)×C13911yescharacteristic
364C23#137×C13911yescharacteristic
365D4—42no—
366D4—81no—
367D4—81no—
368D4—81no—
369D4—81no—
370D4—81no—
371C2×C4—22no—
372C2×C4—22no—
373C2×C4—22no—
374C2×C4—22no—
375C2×C4—22no—
376C2×C4—22no—
377C2×C4—41no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—42no—
383C2×C4—42no—
384C2×C4—41no—
385C2×C4—42no—
386C2×C4—42no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—42no—
392C2×C4—41no—
393C2×C4—82no—
394C2×C4—82no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4C2×C22⋊C4×C13911yescharacteristic
399C2×C4C4×D4×C13911yescharacteristic
400C2×C4#121×C13911yescharacteristic
401C2×C4#123×C13911yescharacteristic
402C8—42no—
403C8—81no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—161no—
418C22—161no—
419C22#386×C13911yescharacteristic
420C22C4×SD16×C13911yescharacteristic
421C22#440×C13911yescharacteristic
422C22#448×C13911yescharacteristic
423C22#449×C13911yescharacteristic
424C22#460×C13911yescharacteristic
425C22#464×C13911yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—42no—
430C4—42no—
431C4—42no—
432C4—81no—
433C4—82no—
434C4—81no—
435C4—161no—
436C4#410×C13912yes—
437C2—21no—
438C2—21no—
439C2—21no—
440C2—21no—
441C2—21no—
442C2—21no—
443C2—161no—
444C2#1880×C13911yescharacteristic
445C2#1899×C13911yescharacteristic
446C2#1904×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#386
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radicalC2×#121×C139C22
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. #2345×C139C2semidirect
4. #1824×C139C2semidirect
6. #1289×C139C2semidirect
7. #1282×C139C2semidirect
13. C2×#106×C139C4semidirect
14. C2×#102×C139C4semidirect
223. #9261C139direct (N × H)
224. C139#9261direct (N × H)
226. #2345C2×C139semidirect
228. #1824C2×C139semidirect
230. #1289C2×C139semidirect
231. #1282C2×C139semidirect
237. C2×#106C4×C139semidirect
238. C2×#102C4×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#481×C1392
#2345×C1392
#1964×C1392
#1824×C1392
#1519×C1392
#1289×C1392
#1282×C1392
#9261139