Finite Group Databasebeta

← C139×#7772 #48002368

Subgroups — C139×#7772 #48002368

Order 35584.

416 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 102 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#2726×C139C211yesmaximal, characteristic
2#2058×C139C211yesmaximal, characteristic
3#2057×C139C211yesmaximal, characteristic
4#2043×C139C211yesmaximal, characteristic
5#1271×C139C211yesmaximal, characteristic
6#1271×C139C211yesmaximal, characteristic
7#1271×C139C211yesmaximal, characteristic
8C2×C4⋊Q8×C139C2211yescharacteristic
9C2×#125×C139—21no—
10C2×#107×C139—21no—
11C2×#106×C139—21no—
12C2×#103×C139—21no—
13C2×#103×C139—21no—
14#398×C139—21no—
15#398×C139—21no—
16#398×C139—21no—
17#389×C139—21no—
18#389×C139C2211yescharacteristic
19#389×C139C2211yescharacteristic
20#389×C139C2211yescharacteristic
21#387×C139—21no—
22#340×C139—21no—
23#340×C139—21no—
24#336×C139C2211yescharacteristic
25#336×C139C2211yescharacteristic
26#336×C139C2211yescharacteristic
27C22×Q8×C139—21no—
28C22×C8×C139—21no—
29C22×C8×C139—21no—
30C22×C8×C139—21no—
31C4⋊Q8×C139—42no—
32#125×C139—42no—
33#125×C139—42no—
34C2×C4⋊C4×C139—21no—
35C2×C4⋊C4×C139—21no—
36C2×C4⋊C4×C139—21no—
37C2×C4⋊C4×C139—21no—
38C2×C4⋊C4×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×C139D411yescharacteristic
44C2×C4⋊C4×C139D411yescharacteristic
45C2×C4⋊C4×C139D411yescharacteristic
46C2×C4⋊C4×C139D411yescharacteristic
47C2×C4⋊C4×C139D411yescharacteristic
48C2×C4⋊C4×C139D411yescharacteristic
49C2×C42×C139—21no—
50C2×C42×C139C2311yescharacteristic
51#107×C139—42no—
52#106×C139—42no—
53#103×C139—42no—
54#103×C139—42no—
55#95×C139—21no—
56#95×C139—21no—
57#95×C139—21no—
58#95×C139—21no—
59#95×C139—21no—
60#95×C139—21no—
61C2×Q8×C139—22no—
62C2×Q8×C139—41no—
63C2×Q8×C139—41no—
64C2×Q8×C139—41no—
65C2×Q8×C139—41no—
66C2×Q8×C139—41no—
67C22×C4×C139—21no—
68C22×C4×C139—21no—
69C22×C4×C139—21no—
70C22×C4×C139—21no—
71C22×C4×C139—21no—
72C22×C4×C139—21no—
73C22×C4×C139—41no—
74C22×C4×C139C2×D411yescharacteristic
75C22×C4×C139C2×D411yescharacteristic
76C22×C4×C139C2×D411yescharacteristic
77C2×C8×C139—22no—
78C2×C8×C139—22no—
79C2×C8×C139—41no—
80C2×C8×C139—41no—
81C2×C8×C139—41no—
82C2×C8×C139—41no—
83C2×C8×C139—41no—
84C2×C8×C139—41no—
85C2×C8×C139—41no—
86C4⋊C4×C139—21no—
87C4⋊C4×C139—21no—
88C4⋊C4×C139—22no—
89C4⋊C4×C139—22no—
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—42no—
97C4⋊C4×C139—42no—
98C4⋊C4×C139—41no—
99C4⋊C4×C139—41no—
100C4⋊C4×C139—41no—
101C4⋊C4×C139—41no—
102C4⋊C4×C139—41no—
103C4⋊C4×C139—41no—
104C4⋊C4×C139—41no—
105C4⋊C4×C139—41no—
106C4⋊C4×C139—81no—
107C4⋊C4×C139SD1612yes—
108C4⋊C4×C139Q1612yes—
109C42×C139—41no—
110C42×C139—42no—
111C23×C139#12011yescharacteristic
112Q8×C139—42no—
113Q8×C139—42no—
114Q8×C139—81no—
115Q8×C139—81no—
116C2×C4×C139—21no—
117C2×C4×C139—21no—
118C2×C4×C139—21no—
119C2×C4×C139—21no—
120C2×C4×C139—21no—
121C2×C4×C139—21no—
122C2×C4×C139—22no—
123C2×C4×C139—22no—
124C2×C4×C139—41no—
125C2×C4×C139—41no—
126C2×C4×C139—41no—
127C2×C4×C139—41no—
128C2×C4×C139—41no—
129C2×C4×C139—41no—
130C2×C4×C139—41no—
131C2×C4×C139—41no—
132C2×C4×C139—41no—
133C2×C4×C139—41no—
134C2×C4×C139—41no—
135C2×C4×C139—41no—
136C2×C4×C139—41no—
137C2×C4×C139—42no—
138C2×C4×C139—41no—
139C2×C4×C139—41no—
140C2×C4×C139—41no—
141C2×C4×C139—81no—
142C2×C4×C139—81no—
143C2×C4×C139C2×SD1611yescharacteristic
144C2×C4×C139C2×Q1611yescharacteristic
145C2×C4×C139#13511yescharacteristic
146C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C139AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C139#13711yescharacteristic
149C8×C139—42no—
150C8×C139—42no—
151C8×C139—81no—
152C22×C139#44911yescharacteristic
153C22×C139#45011yescharacteristic
154C22×C139#45111yescharacteristic
155C22×C139#45411yescharacteristic
156C22×C139#45611yescharacteristic
157C22×C139#45611yescharacteristic
158C22×C139B(4,𝔽2)11yescharacteristic
159C4×C139—21no—
160C4×C139—21no—
161C4×C139—21no—
162C4×C139—21no—
163C4×C139—21no—
164C4×C139—21no—
165C4×C139—42no—
166C4×C139—42no—
167C4×C139—81no—
168C4×C139—82no—
169C4×C139—81no—
170C4×C139—81no—
171C4×C139—81no—
172C2×C139#159711yescharacteristic
173C2×C139#160411yescharacteristic
174C2×C139#160511yescharacteristic
175C2×C139#163711yescharacteristic
176C2×C139#164811yescharacteristic
177C2×C139#165411yescharacteristic
178C2×C139#166311yescharacteristic
179#7772C13911yesmaximal, characteristic, direct product factor, Sylow
180C139#777211yescharacteristic, direct product factor, Sylow
181#2726C2×C13911yescharacteristic
182#2058C2×C13911yescharacteristic
183#2057C2×C13911yescharacteristic
184#2043C2×C13911yescharacteristic
185#1271C2×C13911yescharacteristic
186#1271C2×C13911yescharacteristic
187#1271C2×C13911yescharacteristic
188C2×C4⋊Q8C22×C13911yescharacteristic
189C2×#125—21no—
190C2×#107—21no—
191C2×#106—21no—
192C2×#103—21no—
193C2×#103—21no—
194#398—21no—
195#398—21no—
196#398—21no—
197#389—21no—
198#389C22×C13911yescharacteristic
199#389C22×C13911yescharacteristic
200#389C22×C13911yescharacteristic
201#387—21no—
202#340—21no—
203#340—21no—
204#336C22×C13911yescharacteristic
205#336C22×C13911yescharacteristic
206#336C22×C13911yescharacteristic
207C22×Q8—21no—
208C22×C8—21no—
209C22×C8—21no—
210C22×C8—21no—
211C4⋊Q8—42no—
212#125—42no—
213#125—42no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4D4×C13911yescharacteristic
224C2×C4⋊C4D4×C13911yescharacteristic
225C2×C4⋊C4D4×C13911yescharacteristic
226C2×C4⋊C4D4×C13911yescharacteristic
227C2×C4⋊C4D4×C13911yescharacteristic
228C2×C4⋊C4D4×C13911yescharacteristic
229C2×C42—21no—
230C2×C42C23×C13911yescharacteristic
231#107—42no—
232#106—42no—
233#103—42no—
234#103—42no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×Q8—41no—
245C2×Q8—41no—
246C2×Q8—41no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—41no—
254C22×C4C2×D4×C13911yescharacteristic
255C22×C4C2×D4×C13911yescharacteristic
256C22×C4C2×D4×C13911yescharacteristic
257C2×C8—22no—
258C2×C8—22no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—41no—
264C2×C8—41no—
265C2×C8—41no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—22no—
269C4⋊C4—22no—
270C4⋊C4—21no—
271C4⋊C4—21no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—42no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—81no—
287C4⋊C4SD16×C13912yes—
288C4⋊C4Q16×C13912yes—
289C42—41no—
290C42—42no—
291C23#120×C13911yescharacteristic
292Q8—42no—
293Q8—42no—
294Q8—81no—
295Q8—81no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4C2×SD16×C13911yescharacteristic
324C2×C4C2×Q16×C13911yescharacteristic
325C2×C4#135×C13911yescharacteristic
326C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
327C2×C4AGL(1,ℤ/8)×C13911yescharacteristic
328C2×C4#137×C13911yescharacteristic
329C8—42no—
330C8—42no—
331C8—81no—
332C22#449×C13911yescharacteristic
333C22#450×C13911yescharacteristic
334C22#451×C13911yescharacteristic
335C22#454×C13911yescharacteristic
336C22#456×C13911yescharacteristic
337C22#456×C13911yescharacteristic
338C22B(4,𝔽2)×C13911yescharacteristic
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—21no—
344C4—21no—
345C4—42no—
346C4—42no—
347C4—81no—
348C4—82no—
349C4—81no—
350C4—81no—
351C4—81no—
352C2#1597×C13911yescharacteristic
353C2#1604×C13911yescharacteristic
354C2#1605×C13911yescharacteristic
355C2#1637×C13911yescharacteristic
356C2#1648×C13911yescharacteristic
357C2#1654×C13911yescharacteristic
358C2#1663×C13911yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C139#120
commutator, Frattini, cosocleC2×C42C23×C139
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
179. #7772C139direct (N × H)
180. C139#7772direct (N × H)

Maximal subgroups

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

subgroupindex
#2726×C1392
#2058×C1392
#2057×C1392
#2043×C1392
#1271×C1392
#7772139