Finite Group Databasebeta

← C139×#18066 #48012662

Subgroups — C139×#18066 #48012662

Order 35584.

722 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3169×C139C211yesmaximal, characteristic
2#2935×C139C212yesmaximal, complemented
3#1589×C139C212yesmaximal, complemented
4#1581×C139C214yesmaximal, complemented
5C8×D8×C139C212yesmaximal, complemented
6C2×#335×C139C211yesmaximal, characteristic, complemented
7#1480×C139C212yesmaximal, complemented
8C8×M16×C139C211yesmaximal, characteristic, complemented
9C2×#131×C139—22no—
10#532×C139C2212yes—
11#500×C139C411yescharacteristic
12#493×C139C411yescharacteristic
13#486×C139C412yes—
14#466×C139C412yes—
15#466×C139C412yes—
16C4×D8×C139C2212yes—
17C4×D8×C139C2212yes—
18#436×C139C2214yes—
19#435×C139—24no—
20C8×D4×C139C2214yes—
21#431×C139C2211yescharacteristic
22C2×C4⋊C8×C139C2212yes—
23#408×C139—22no—
24C4×M16×C139C2211yescharacteristic
25C2×C4×C8×C139C2211yescharacteristic
26#335×C139C2211yescharacteristic
27#335×C139C2212yes—
28#335×C139C2211yescharacteristic
29D4⋊C8×C139C2214yes—
30D4⋊C8×C139C2214yes—
31#322×C139C2212yes—
32C82×C139C2212yes—
33C2×#41×C139—22no—
34C2×D8×C139C2×C412yes—
35C2×D8×C139C2×C412yes—
36#131×C139—48no—
37C2×M16×C139—24no—
38C2×M16×C139D411yescharacteristic
39C2×M16×C139D411yescharacteristic
40C22×C8×C139—22no—
41C22×C8×C139—24no—
42C22×C8×C139C2×C411yescharacteristic
43C22×C8×C139C2×C411yescharacteristic
44C4⋊Q8×C139C2×C412yes—
45#127×C139C2×C412yes—
46#124×C139—22no—
47#121×C139—22no—
48#121×C139C2×C414yes—
49C4×D4×C139—22no—
50C4×D4×C139C2314yes—
51C2×C42×C139C2311yescharacteristic
52#107×C139C2×C412yes—
53#107×C139C2×C412yes—
54C4⋊C8×C139—22no—
55C4⋊C8×C139—21no—
56C4⋊C8×C139C2312yes—
57C4⋊C8×C139C2312yes—
58#102×C139C2×C414yes—
59#102×C139C2×C414yes—
60C22⋊C8×C139—21no—
61C22⋊C8×C139—24no—
62C22⋊C8×C139—24no—
63#97×C139D412yes—
64C4×C8×C139C2×C411yescharacteristic
65C4×C8×C139C2×C411yescharacteristic
66C4×C8×C139C2312yes—
67C4×C8×C139C2311yescharacteristic
68C4×C8×C139C2311yescharacteristic
69C4×C8×C139C2312yes—
70#41×C139—44no—
71#41×C139—44no—
72C2×Q8×C139—22no—
73C2×D4×C139—24no—
74C2×D4×C139—22no—
75C2×D4×C139—22no—
76C2×D4×C139C22×C414yes—
77C22×C4×C139—24no—
78C22×C4×C139C22×C411yescharacteristic
79C22×C4×C139C2×D411yescharacteristic
80C22×C4×C139#4111yescharacteristic
81D8×C139—24no—
82D8×C139—42no—
83M16×C139—22no—
84M16×C139—48no—
85M16×C139D814yescomplemented
86C2×C8×C139—22no—
87C2×C8×C139—22no—
88C2×C8×C139—22no—
89C2×C8×C139—22no—
90C2×C8×C139—41no—
91C2×C8×C139—44no—
92C2×C8×C139—48no—
93C2×C8×C139C22×C411yescharacteristic
94C2×C8×C139C22×C411yescharacteristic
95C2×C8×C139C22×C411yescharacteristic
96C2×C8×C139C22×C411yescharacteristic
97C2×C8×C139C2×D412yes—
98C2×C8×C139C2×D412yes—
99C4⋊C4×C139—22no—
100C4⋊C4×C139C22×C414yes—
101C22⋊C4×C139—24no—
102C22⋊C4×C139—24no—
103C42×C139C22×C411yescharacteristic
104C42×C139C2×D411yescharacteristic
105C42×C139#4111yescharacteristic
106C42×C139C2411yescharacteristic
107C23×C139—24no—
108C23×C139C4×D411yescharacteristic
109Q8×C139—44no—
110D4×C139—24no—
111D4×C139—24no—
112D4×C139—48no—
113D4×C139—44no—
114D4×C139—82no—
115C2×C4×C139—21no—
116C2×C4×C139—21no—
117C2×C4×C139—24no—
118C2×C4×C139—41no—
119C2×C4×C139—44no—
120C2×C4×C139—44no—
121C2×C4×C139C4×D411yescharacteristic
122C2×C4×C139C4×D411yescharacteristic
123C2×C4×C139C4×D411yescharacteristic
124C2×C4×C139C2×D812yes—
125C2×C4×C139#13512yes—
126C2×C4×C139C23×C411yescharacteristic
127C2×C4×C139C22×D411yescharacteristic
128C2×C4×C139C2×#4111yescharacteristic
129C8×C139—21no—
130C8×C139—21no—
131C8×C139—21no—
132C8×C139—22no—
133C8×C139—42no—
134C8×C139—42no—
135C8×C139—42no—
136C8×C139#13112yescomplemented
137C8×C139C2×D814yes—
138C22×C139—21no—
139C22×C139—21no—
140C22×C139—44no—
141C22×C139—44no—
142C22×C139—44no—
143C22×C139C4×D812yes—
144C22×C139C2×C4×D411yescharacteristic
145C4×C139—21no—
146C4×C139—21no—
147C4×C139—21no—
148C4×C139—44no—
149C4×C139C4×D812yes—
150C4×C139C2×#13111yescharacteristic
151C4×C139#56811yescharacteristic
152C4×C139C22×D811yescharacteristic
153C4×C139C2×#13511yescharacteristic
154C2×C139—22no—
155C2×C139—84no—
156C2×C139#293511yescharacteristic
157C2×C139C2×C4×D811yescharacteristic
158C2×C139#295711yescharacteristic
159#18066C13911yesmaximal, characteristic, direct product factor, Sylow
160C139#1806611yescharacteristic, direct product factor, Sylow
161#3169C2×C13911yescharacteristic
162#2935C2×C13912yescomplemented
163#1589C2×C13912yescomplemented
164#1581C2×C13914yescomplemented
165C8×D8C2×C13912yescomplemented
166C2×#335C2×C13911yescharacteristic, complemented
167#1480C2×C13912yescomplemented
168C8×M16C2×C13911yescharacteristic, complemented
169C2×#131—22no—
170#532C22×C13912yes—
171#500C4×C13911yescharacteristic
172#493C4×C13911yescharacteristic
173#486C4×C13912yes—
174#466C4×C13912yes—
175#466C4×C13912yes—
176C4×D8C22×C13912yes—
177C4×D8C22×C13912yes—
178#436C22×C13914yes—
179#435—24no—
180C8×D4C22×C13914yes—
181#431C22×C13911yescharacteristic
182C2×C4⋊C8C22×C13912yes—
183#408—22no—
184C4×M16C22×C13911yescharacteristic
185C2×C4×C8C22×C13911yescharacteristic
186#335C22×C13911yescharacteristic
187#335C22×C13912yes—
188#335C22×C13911yescharacteristic
189D4⋊C8C22×C13914yes—
190D4⋊C8C22×C13914yes—
191#322C22×C13912yes—
192C82C22×C13912yes—
193C2×#41—22no—
194C2×D8C2×C4×C13912yes—
195C2×D8C2×C4×C13912yes—
196#131—48no—
197C2×M16—24no—
198C2×M16D4×C13911yescharacteristic
199C2×M16D4×C13911yescharacteristic
200C22×C8—22no—
201C22×C8—24no—
202C22×C8C2×C4×C13911yescharacteristic
203C22×C8C2×C4×C13911yescharacteristic
204C4⋊Q8C2×C4×C13912yes—
205#127C2×C4×C13912yes—
206#124—22no—
207#121—22no—
208#121C2×C4×C13914yes—
209C4×D4—22no—
210C4×D4C23×C13914yes—
211C2×C42C23×C13911yescharacteristic
212#107C2×C4×C13912yes—
213#107C2×C4×C13912yes—
214C4⋊C8—22no—
215C4⋊C8—21no—
216C4⋊C8C23×C13912yes—
217C4⋊C8C23×C13912yes—
218#102C2×C4×C13914yes—
219#102C2×C4×C13914yes—
220C22⋊C8—21no—
221C22⋊C8—24no—
222C22⋊C8—24no—
223#97D4×C13912yes—
224C4×C8C2×C4×C13911yescharacteristic
225C4×C8C2×C4×C13911yescharacteristic
226C4×C8C23×C13912yes—
227C4×C8C23×C13911yescharacteristic
228C4×C8C23×C13911yescharacteristic
229C4×C8C23×C13912yes—
230#41—44no—
231#41—44no—
232C2×Q8—22no—
233C2×D4—24no—
234C2×D4—22no—
235C2×D4—22no—
236C2×D4C22×C4×C13914yes—
237C22×C4—24no—
238C22×C4C22×C4×C13911yescharacteristic
239C22×C4C2×D4×C13911yescharacteristic
240C22×C4#41×C13911yescharacteristic
241D8—24no—
242D8—42no—
243M16—22no—
244M16—48no—
245M16D8×C13914yescomplemented
246C2×C8—22no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—44no—
252C2×C8—48no—
253C2×C8C22×C4×C13911yescharacteristic
254C2×C8C22×C4×C13911yescharacteristic
255C2×C8C22×C4×C13911yescharacteristic
256C2×C8C22×C4×C13911yescharacteristic
257C2×C8C2×D4×C13912yes—
258C2×C8C2×D4×C13912yes—
259C4⋊C4—22no—
260C4⋊C4C22×C4×C13914yes—
261C22⋊C4—24no—
262C22⋊C4—24no—
263C42C22×C4×C13911yescharacteristic
264C42C2×D4×C13911yescharacteristic
265C42#41×C13911yescharacteristic
266C42C24×C13911yescharacteristic
267C23—24no—
268C23C4×D4×C13911yescharacteristic
269Q8—44no—
270D4—24no—
271D4—24no—
272D4—48no—
273D4—44no—
274D4—82no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—24no—
278C2×C4—41no—
279C2×C4—44no—
280C2×C4—44no—
281C2×C4C4×D4×C13911yescharacteristic
282C2×C4C4×D4×C13911yescharacteristic
283C2×C4C4×D4×C13911yescharacteristic
284C2×C4C2×D8×C13912yes—
285C2×C4#135×C13912yes—
286C2×C4C23×C4×C13911yescharacteristic
287C2×C4C22×D4×C13911yescharacteristic
288C2×C4C2×#41×C13911yescharacteristic
289C8—21no—
290C8—21no—
291C8—21no—
292C8—22no—
293C8—42no—
294C8—42no—
295C8—42no—
296C8#131×C13912yescomplemented
297C8C2×D8×C13914yes—
298C22—21no—
299C22—21no—
300C22—44no—
301C22—44no—
302C22—44no—
303C22C4×D8×C13912yes—
304C22C2×C4×D4×C13911yescharacteristic
305C4—21no—
306C4—21no—
307C4—21no—
308C4—44no—
309C4C4×D8×C13912yes—
310C4C2×#131×C13911yescharacteristic
311C4#568×C13911yescharacteristic
312C4C22×D8×C13911yescharacteristic
313C4C2×#135×C13911yescharacteristic
314C2—22no—
315C2—84no—
316C2#2935×C13911yescharacteristic
317C2C2×C4×D8×C13911yescharacteristic
318C2#2957×C13911yescharacteristic
subgroupG/H
centerC2×C4×C139C22×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC42C24×C139
socleC22×C139C2×C4×D4
prime radical#3169×C139C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C139 ◁ C4×M16×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2935×C139C2semidirect
3. #1589×C139C2semidirect
4. #1581×C139C2semidirect
5. C8×D8×C139C2semidirect
6. C2×#335×C139C2semidirect
7. #1480×C139C2semidirect
8. C8×M16×C139C2semidirect
85. M16×C139D8semidirect
136. C8×C139#131semidirect
159. #18066C139direct (N × H)
160. C139#18066direct (N × H)
162. #2935C2×C139semidirect
163. #1589C2×C139semidirect
164. #1581C2×C139semidirect
165. C8×D8C2×C139semidirect
166. C2×#335C2×C139semidirect
167. #1480C2×C139semidirect
168. C8×M16C2×C139semidirect
245. M16D8×C139semidirect
296. C8#131×C139semidirect

Maximal subgroups

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

subgroupindex
#3169×C1392
#2935×C1392
#1589×C1392
#1581×C1392
C8×D8×C1392
C2×#335×C1392
#1480×C1392
C8×M16×C1392
#18066139