Finite Group Databasebeta

← C139×#12144 #48006740

Subgroups — C139×#12144 #48006740

Order 35584.

398 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2795×C139C211yesmaximal, characteristic, complemented
2#2039×C139C211yesmaximal, characteristic, complemented
3#1616×C139C211yesmaximal, characteristic, complemented
4#1598×C139C211yesmaximal, characteristic
5#1353×C139C211yesmaximal, characteristic, complemented
6#1345×C139C211yesmaximal, characteristic, complemented
7#1325×C139C211yesmaximal, characteristic, complemented
8#537×C139C2211yescharacteristic
9#481×C139—21no—
10#447×C139—21no—
11C2×#104×C139—21no—
12#417×C139—21no—
13#400×C139C2211yescharacteristic
14#396×C139—21no—
15#394×C139—21no—
16#394×C139C2211yescharacteristic
17#388×C139—21no—
18#388×C139—21no—
19#388×C139—21no—
20#387×C139—21no—
21#384×C139C2211yescharacteristic
22#343×C139C2211yescharacteristic
23#327×C139—21no—
24#327×C139—21no—
25#324×C139C2211yescharacteristic
26#324×C139C2211yescharacteristic
27C2×#41×C139—21no—
28C22×D4×C139D411yescharacteristic
29C2×D8×C139—41no—
30C2×M16×C139—21no—
31C22⋊Q8×C139—41no—
32#121×C139—21no—
33#121×C139—21no—
34#121×C139—41no—
35C2×C4⋊C4×C139—21no—
36C2×C4⋊C4×C139—21no—
37C2×C4⋊C4×C139—21no—
38C2×C4⋊C4×C139D411yescharacteristic
39C2×C4⋊C4×C139D411yescharacteristic
40C2×C4⋊C4×C139C2311yescharacteristic
41C2×C22⋊C4×C139—21no—
42C2×C22⋊C4×C139—21no—
43C2×C22⋊C4×C139—21no—
44C2×C22⋊C4×C139—21no—
45C2×C22⋊C4×C139—21no—
46C2×C22⋊C4×C139—21no—
47C2×C42×C139—21no—
48C2×C42×C139D411yescharacteristic
49#106×C139—41no—
50#104×C139—42no—
51#103×C139—41no—
52#102×C139—41no—
53#102×C139—41no—
54#102×C139—41no—
55C22⋊C8×C139—21no—
56C22⋊C8×C139—21no—
57#95×C139—21no—
58#95×C139—21no—
59#95×C139—21no—
60#95×C139—21no—
61#95×C139D411yescharacteristic
62#95×C139D411yescharacteristic
63C24×C139—21no—
64#41×C139—41no—
65#41×C139—41no—
66#41×C139—41no—
67#41×C139—41no—
68C2×Q8×C139—21no—
69C2×D4×C139—21no—
70C2×D4×C139—21no—
71C2×D4×C139—21no—
72C2×D4×C139—41no—
73C2×D4×C139—41no—
74C2×D4×C139—81no—
75C22×C4×C139—21no—
76C22×C4×C139—21no—
77C22×C4×C139—21no—
78C22×C4×C139—21no—
79C22×C4×C139—21no—
80C22×C4×C139—41no—
81C22×C4×C139C2×D411yescharacteristic
82C22×C4×C139C2×D411yescharacteristic
83C22×C4×C139C2×D411yescharacteristic
84D8×C139—82no—
85M16×C139—41no—
86M16×C139—41no—
87C2×C8×C139—41no—
88C2×C8×C139—41no—
89C2×C8×C139—41no—
90C4⋊C4×C139—21no—
91C4⋊C4×C139—21no—
92C4⋊C4×C139—41no—
93C4⋊C4×C139—41no—
94C4⋊C4×C139—41no—
95C4⋊C4×C139—42no—
96C4⋊C4×C139—81no—
97C4⋊C4×C139—81no—
98C22⋊C4×C139—42no—
99C22⋊C4×C139—42no—
100C22⋊C4×C139—41no—
101C22⋊C4×C139—41no—
102C22⋊C4×C139—41no—
103C22⋊C4×C139—41no—
104C22⋊C4×C139—81no—
105C22⋊C4×C139—81no—
106C22⋊C4×C139—81no—
107C42×C139—21no—
108C42×C139—21no—
109C42×C139—81no—
110C23×C139—41no—
111C23×C139—41no—
112C23×C139—41no—
113C23×C139—41no—
114C23×C139—41no—
115C23×C139—41no—
116C23×C139—41no—
117C23×C139—41no—
118C23×C139#12011yescharacteristic
119Q8×C139—41no—
120Q8×C139—41no—
121D4×C139—41no—
122D4×C139—41no—
123D4×C139—42no—
124D4×C139—81no—
125D4×C139—81no—
126D4×C139—81no—
127D4×C139—81no—
128D4×C139—81no—
129C2×C4×C139—21no—
130C2×C4×C139—21no—
131C2×C4×C139—22no—
132C2×C4×C139—21no—
133C2×C4×C139—21no—
134C2×C4×C139—41no—
135C2×C4×C139—41no—
136C2×C4×C139—41no—
137C2×C4×C139—41no—
138C2×C4×C139—41no—
139C2×C4×C139—41no—
140C2×C4×C139—41no—
141C2×C4×C139—41no—
142C2×C4×C139—41no—
143C2×C4×C139—41no—
144C2×C4×C139—41no—
145C2×C4×C139—41no—
146C2×C4×C139—41no—
147C2×C4×C139—41no—
148C2×C4×C139—41no—
149C2×C4×C139—41no—
150C2×C4×C139—41no—
151C2×C4×C139—81no—
152C2×C4×C139—81no—
153C2×C4×C139#13511yescharacteristic
154C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
155C8×C139—81no—
156C8×C139—81no—
157C8×C139—81no—
158C22×C139—21no—
159C22×C139—21no—
160C22×C139—81no—
161C22×C139—81no—
162C22×C139—81no—
163C22×C139—81no—
164C22×C139—81no—
165C22×C139—81no—
166C22×C139—81no—
167C22×C139—81no—
168C22×C139—81no—
169C22×C139—81no—
170C22×C139#44911yescharacteristic
171C22×C139#45411yescharacteristic
172C22×C139B(4,𝔽2)11yescharacteristic
173C4×C139—21no—
174C4×C139—21no—
175C4×C139—42no—
176C4×C139—41no—
177C4×C139—41no—
178C4×C139—81no—
179C4×C139—81no—
180C4×C139—81no—
181C4×C139—81no—
182C4×C139—81no—
183C2×C139—21no—
184C2×C139—21no—
185C2×C139—161no—
186C2×C139—161no—
187C2×C139#159711yescharacteristic
188C2×C139#220011yescharacteristic
189C2×C139#220411yescharacteristic
190#12144C13911yesmaximal, characteristic, direct product factor, Sylow
191C139#1214411yescharacteristic, direct product factor, Sylow
192#2795C2×C13911yescharacteristic, complemented
193#2039C2×C13911yescharacteristic, complemented
194#1616C2×C13911yescharacteristic, complemented
195#1598C2×C13911yescharacteristic
196#1353C2×C13911yescharacteristic, complemented
197#1345C2×C13911yescharacteristic, complemented
198#1325C2×C13911yescharacteristic, complemented
199#537C22×C13911yescharacteristic
200#481—21no—
201#447—21no—
202C2×#104—21no—
203#417—21no—
204#400C22×C13911yescharacteristic
205#396—21no—
206#394—21no—
207#394C22×C13911yescharacteristic
208#388—21no—
209#388—21no—
210#388—21no—
211#387—21no—
212#384C22×C13911yescharacteristic
213#343C22×C13911yescharacteristic
214#327—21no—
215#327—21no—
216#324C22×C13911yescharacteristic
217#324C22×C13911yescharacteristic
218C2×#41—21no—
219C22×D4D4×C13911yescharacteristic
220C2×D8—41no—
221C2×M16—21no—
222C22⋊Q8—41no—
223#121—21no—
224#121—21no—
225#121—41no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4D4×C13911yescharacteristic
230C2×C4⋊C4D4×C13911yescharacteristic
231C2×C4⋊C4C23×C13911yescharacteristic
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C42—21no—
239C2×C42D4×C13911yescharacteristic
240#106—41no—
241#104—42no—
242#103—41no—
243#102—41no—
244#102—41no—
245#102—41no—
246C22⋊C8—21no—
247C22⋊C8—21no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95D4×C13911yescharacteristic
253#95D4×C13911yescharacteristic
254C24—21no—
255#41—41no—
256#41—41no—
257#41—41no—
258#41—41no—
259C2×Q8—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—81no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—41no—
272C22×C4C2×D4×C13911yescharacteristic
273C22×C4C2×D4×C13911yescharacteristic
274C22×C4C2×D4×C13911yescharacteristic
275D8—82no—
276M16—41no—
277M16—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—41no—
281C4⋊C4—21no—
282C4⋊C4—21no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—42no—
287C4⋊C4—81no—
288C4⋊C4—81no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—81no—
296C22⋊C4—81no—
297C22⋊C4—81no—
298C42—21no—
299C42—21no—
300C42—81no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23#120×C13911yescharacteristic
310Q8—41no—
311Q8—41no—
312D4—41no—
313D4—41no—
314D4—42no—
315D4—81no—
316D4—81no—
317D4—81no—
318D4—81no—
319D4—81no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4#135×C13911yescharacteristic
345C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
346C8—81no—
347C8—81no—
348C8—81no—
349C22—21no—
350C22—21no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22#449×C13911yescharacteristic
362C22#454×C13911yescharacteristic
363C22B(4,𝔽2)×C13911yescharacteristic
364C4—21no—
365C4—21no—
366C4—42no—
367C4—41no—
368C4—41no—
369C4—81no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4—81no—
374C2—21no—
375C2—21no—
376C2—161no—
377C2—161no—
378C2#1597×C13911yescharacteristic
379C2#2200×C13911yescharacteristic
380C2#2204×C13911yescharacteristic
subgroupG/H
center, socleC22×C139B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C139
prime radical#1598×C139C2
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C139 ◁ C2×C4⋊C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2795×C139C2semidirect
2. #2039×C139C2semidirect
3. #1616×C139C2semidirect
5. #1353×C139C2semidirect
6. #1345×C139C2semidirect
7. #1325×C139C2semidirect
190. #12144C139direct (N × H)
191. C139#12144direct (N × H)
192. #2795C2×C139semidirect
193. #2039C2×C139semidirect
194. #1616C2×C139semidirect
196. #1353C2×C139semidirect
197. #1345C2×C139semidirect
198. #1325C2×C139semidirect

Maximal subgroups

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

subgroupindex
#2795×C1392
#2039×C1392
#1616×C1392
#1598×C1392
#1353×C1392
#1345×C1392
#1325×C1392
#12144139