Finite Group Databasebeta

← C139×#34179 #48028775

Subgroups — C139×#34179 #48028775

Order 35584.

2390 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
1C22×#117×C139C211yesmaximal, characteristic
2#2347×C139C218yesmaximal, complemented
3#2346×C139C218yesmaximal, complemented
4#2316×C139C212yesmaximal, complemented
5#2312×C139C214yesmaximal
6#2283×C139C214yesmaximal, complemented
7#2280×C139C212yesmaximal
8#2274×C139C212yesmaximal, complemented
9C24×C4×C139C2211yescharacteristic
10C2×#117×C139C4116yescomplemented
11C2×#117×C139C2214yes—
12C2×#117×C139C2214yes—
13C2×#117×C139C2214yes—
14C22×C4⋊C4×C139C2211yescharacteristic
15C22×C4⋊C4×C139C2211yescharacteristic
16C22×C22⋊C4×C139C2212yes—
17C22×C42×C139C2212yes—
18#389×C139C22116yescomplemented
19#388×C139C22132yes—
20#383×C139C2218yescomplemented
21#382×C139C2218yescomplemented
22#381×C139C2214yes—
23#380×C139C2214yes—
24#380×C139C2214yes—
25#380×C139C2218yes—
26#379×C139C2214yes—
27C4×C4⋊C4×C139C22116yescomplemented
28C4×C4⋊C4×C139C2218yescomplemented
29C4×C22⋊C4×C139C2218yes—
30C4×C22⋊C4×C139C2214yes—
31C4×C22⋊C4×C139C2214yes—
32#376×C139C2218yescomplemented
33C25×C139C2311yescharacteristic
34C23×C4×C139—28no—
35C23×C4×C139C2×C418yes—
36C23×C4×C139C2311yescharacteristic
37C23×C4×C139C2312yes—
38C23×C4×C139C2312yes—
39C23×C4×C139C2312yes—
40C23×C4×C139C2312yes—
41C23×C4×C139C2311yescharacteristic
42#117×C139—216no—
43#117×C139C2×C4132yes—
44#117×C139C2×C4132yes—
45C2×C4⋊C4×C139C2×C418yes—
46C2×C4⋊C4×C139C2×C418yes—
47C2×C4⋊C4×C139C2318yes—
48C2×C4⋊C4×C139C23116yes—
49C2×C4⋊C4×C139C2314yes—
50C2×C4⋊C4×C139C2314yes—
51C2×C22⋊C4×C139C2×C4116yes—
52C2×C22⋊C4×C139C2318yes—
53C2×C22⋊C4×C139C2318yes—
54C2×C22⋊C4×C139C2318yes—
55C2×C22⋊C4×C139C2318yes—
56C2×C42×C139C2×C4116yes—
57C2×C42×C139C2318yes—
58C2×C42×C139C23116yes—
59C2×C42×C139C2314yes—
60C2×C42×C139C2314yes—
61#95×C139C2318yes—
62#95×C139C23116yes—
63#95×C139C2318yes—
64#95×C139C23116yes—
65C24×C139—24no—
66C24×C139—42no—
67C24×C139—42no—
68C24×C139C22×C414yes—
69C24×C139C2412yes—
70C24×C139C2411yescharacteristic
71C22×C4×C139—24no—
72C22×C4×C139—232no—
73C22×C4×C139—28no—
74C22×C4×C139—28no—
75C22×C4×C139—44no—
76C22×C4×C139—44no—
77C22×C4×C139C22×C414yes—
78C22×C4×C139C22×C418yes—
79C22×C4×C139C22×C418yes—
80C22×C4×C139C22×C418yes—
81C22×C4×C139C22×C418yes—
82C22×C4×C139C22×C414yes—
83C22×C4×C139#4118yes—
84C22×C4×C139C24116yes—
85C22×C4×C139C2411yescharacteristic
86C22×C4×C139C2411yescharacteristic
87C22×C4×C139C2414yes—
88C22×C4×C139C2414yes—
89C22×C4×C139C2412yes—
90C4⋊C4×C139—216no—
91C4⋊C4×C139—416no—
92C4⋊C4×C139C22×C4116yes—
93C4⋊C4×C139C22×C4116yes—
94C22⋊C4×C139—216no—
95C22⋊C4×C139—48no—
96C22⋊C4×C139—48no—
97C22⋊C4×C139C22×C4132yes—
98C42×C139—216no—
99C42×C139—416no—
100C42×C139C22×C4116yes—
101C42×C139C22×C4116yes—
102C23×C139—22no—
103C23×C139—22no—
104C23×C139—28no—
105C23×C139—24no—
106C23×C139—24no—
107C23×C139—24no—
108C23×C139—44no—
109C23×C139—44no—
110C23×C139—416no—
111C23×C139C23×C414yes—
112C23×C139C23×C412yes—
113C23×C139C2×#4114yes—
114C23×C139C2511yescharacteristic
115C2×C4×C139—28no—
116C2×C4×C139—22no—
117C2×C4×C139—22no—
118C2×C4×C139—28no—
119C2×C4×C139—28no—
120C2×C4×C139—216no—
121C2×C4×C139—216no—
122C2×C4×C139—216no—
123C2×C4×C139—216no—
124C2×C4×C139—216no—
125C2×C4×C139—48no—
126C2×C4×C139—48no—
127C2×C4×C139#117116yes—
128C2×C4×C139C23×C412yes—
129C2×C4×C139C23×C412yes—
130C2×C4×C139C23×C418yes—
131C2×C4×C139C23×C418yes—
132C2×C4×C139C23×C414yes—
133C2×C4×C139C2×#4118yes—
134C22×C139—22no—
135C22×C139—22no—
136C22×C139—28no—
137C22×C139—24no—
138C22×C139—24no—
139C22×C139—24no—
140C22×C139—416no—
141C22×C139—48no—
142C22×C139C2×#11714yes—
143C22×C139C24×C411yescharacteristic
144C22×C139C22×#4112yes—
145C22×C139#58512yes—
146C22×C139#58512yes—
147C4×C139—22no—
148C4×C139—22no—
149C4×C139—28no—
150C4×C139—28no—
151C4×C139—416no—
152C4×C139C2×#11718yes—
153C2×C139—24no—
154C2×C139—44no—
155C2×C139C22×#11711yescharacteristic
156C2×C139#342811yescharacteristic
157C2×C139#342811yescharacteristic
158C2×C139#349314yes—
159#34179C13911yesmaximal, characteristic, direct product factor, Sylow
160C139#3417911yescharacteristic, direct product factor, Sylow
161C22×#117C2×C13911yescharacteristic
162#2347C2×C13918yescomplemented
163#2346C2×C13918yescomplemented
164#2316C2×C13912yescomplemented
165#2312C2×C13914yes—
166#2283C2×C13914yescomplemented
167#2280C2×C13912yes—
168#2274C2×C13912yescomplemented
169C24×C4C22×C13911yescharacteristic
170C2×#117C4×C139116yescomplemented
171C2×#117C22×C13914yes—
172C2×#117C22×C13914yes—
173C2×#117C22×C13914yes—
174C22×C4⋊C4C22×C13911yescharacteristic
175C22×C4⋊C4C22×C13911yescharacteristic
176C22×C22⋊C4C22×C13912yes—
177C22×C42C22×C13912yes—
178#389C22×C139116yescomplemented
179#388C22×C139132yes—
180#383C22×C13918yescomplemented
181#382C22×C13918yescomplemented
182#381C22×C13914yes—
183#380C22×C13918yes—
184#380C22×C13914yes—
185#380C22×C13914yes—
186#379C22×C13914yes—
187C4×C4⋊C4C22×C139116yescomplemented
188C4×C4⋊C4C22×C13918yescomplemented
189C4×C22⋊C4C22×C13918yes—
190C4×C22⋊C4C22×C13914yes—
191C4×C22⋊C4C22×C13914yes—
192#376C22×C13918yescomplemented
193C25C23×C13911yescharacteristic
194C23×C4—28no—
195C23×C4C2×C4×C13918yes—
196C23×C4C23×C13912yes—
197C23×C4C23×C13912yes—
198C23×C4C23×C13911yescharacteristic
199C23×C4C23×C13912yes—
200C23×C4C23×C13912yes—
201C23×C4C23×C13911yescharacteristic
202#117—216no—
203#117C2×C4×C139132yes—
204#117C2×C4×C139132yes—
205C2×C4⋊C4C2×C4×C13918yes—
206C2×C4⋊C4C2×C4×C13918yes—
207C2×C4⋊C4C23×C13918yes—
208C2×C4⋊C4C23×C139116yes—
209C2×C4⋊C4C23×C13914yes—
210C2×C4⋊C4C23×C13914yes—
211C2×C22⋊C4C2×C4×C139116yes—
212C2×C22⋊C4C23×C13918yes—
213C2×C22⋊C4C23×C13918yes—
214C2×C22⋊C4C23×C13918yes—
215C2×C22⋊C4C23×C13918yes—
216C2×C42C2×C4×C139116yes—
217C2×C42C23×C13918yes—
218C2×C42C23×C139116yes—
219C2×C42C23×C13914yes—
220C2×C42C23×C13914yes—
221#95C23×C13918yes—
222#95C23×C139116yes—
223#95C23×C13918yes—
224#95C23×C139116yes—
225C24—24no—
226C24—42no—
227C24—42no—
228C24C22×C4×C13914yes—
229C24C24×C13912yes—
230C24C24×C13911yescharacteristic
231C22×C4—24no—
232C22×C4—232no—
233C22×C4—28no—
234C22×C4—28no—
235C22×C4—44no—
236C22×C4—44no—
237C22×C4C22×C4×C13914yes—
238C22×C4C22×C4×C13918yes—
239C22×C4C22×C4×C13918yes—
240C22×C4C22×C4×C13918yes—
241C22×C4C22×C4×C13918yes—
242C22×C4C22×C4×C13914yes—
243C22×C4#41×C13918yes—
244C22×C4C24×C139116yes—
245C22×C4C24×C13911yescharacteristic
246C22×C4C24×C13911yescharacteristic
247C22×C4C24×C13914yes—
248C22×C4C24×C13914yes—
249C22×C4C24×C13912yes—
250C4⋊C4—216no—
251C4⋊C4—416no—
252C4⋊C4C22×C4×C139116yes—
253C4⋊C4C22×C4×C139116yes—
254C22⋊C4—216no—
255C22⋊C4—48no—
256C22⋊C4—48no—
257C22⋊C4C22×C4×C139132yes—
258C42—216no—
259C42—416no—
260C42C22×C4×C139116yes—
261C42C22×C4×C139116yes—
262C23—22no—
263C23—22no—
264C23—28no—
265C23—24no—
266C23—24no—
267C23—24no—
268C23—44no—
269C23—44no—
270C23—416no—
271C23C23×C4×C13914yes—
272C23C23×C4×C13912yes—
273C23C2×#41×C13914yes—
274C23C25×C13911yescharacteristic
275C2×C4—28no—
276C2×C4—22no—
277C2×C4—22no—
278C2×C4—28no—
279C2×C4—28no—
280C2×C4—216no—
281C2×C4—216no—
282C2×C4—216no—
283C2×C4—216no—
284C2×C4—216no—
285C2×C4—48no—
286C2×C4—48no—
287C2×C4#117×C139116yes—
288C2×C4C23×C4×C13912yes—
289C2×C4C23×C4×C13912yes—
290C2×C4C23×C4×C13918yes—
291C2×C4C23×C4×C13918yes—
292C2×C4C23×C4×C13914yes—
293C2×C4C2×#41×C13918yes—
294C22—22no—
295C22—22no—
296C22—28no—
297C22—24no—
298C22—24no—
299C22—24no—
300C22—416no—
301C22—48no—
302C22C2×#117×C13914yes—
303C22C24×C4×C13911yescharacteristic
304C22C22×#41×C13912yes—
305C22#585×C13912yes—
306C22#585×C13912yes—
307C4—22no—
308C4—22no—
309C4—28no—
310C4—28no—
311C4—416no—
312C4C2×#117×C13918yes—
313C2—24no—
314C2—44no—
315C2C22×#117×C13911yescharacteristic
316C2#3428×C13911yescharacteristic
317C2#3428×C13911yescharacteristic
318C2#3493×C13914yes—
subgroupG/H
center, socleC23×C139C25
commutatorC22C24×C4×C139
Frattini, cosocleC23C25×C139
prime radicalC25×C139C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2347×C139C2semidirect
3. #2346×C139C2semidirect
4. #2316×C139C2semidirect
6. #2283×C139C2semidirect
8. #2274×C139C2semidirect
10. C2×#117×C139C4semidirect
18. #389×C139C22semidirect
20. #383×C139C22semidirect
21. #382×C139C22semidirect
27. C4×C4⋊C4×C139C22semidirect
28. C4×C4⋊C4×C139C22semidirect
32. #376×C139C22semidirect
159. #34179C139direct (N × H)
160. C139#34179direct (N × H)
162. #2347C2×C139semidirect
163. #2346C2×C139semidirect
164. #2316C2×C139semidirect
166. #2283C2×C139semidirect
168. #2274C2×C139semidirect
170. C2×#117C4×C139semidirect
178. #389C22×C139semidirect
180. #383C22×C139semidirect
181. #382C22×C139semidirect
187. C4×C4⋊C4C22×C139semidirect
188. C4×C4⋊C4C22×C139semidirect
192. #376C22×C139semidirect

Maximal subgroups

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

subgroupindex
C22×#117×C1392
#2347×C1392
#2346×C1392
#2316×C1392
#2312×C1392
#2283×C1392
#2280×C1392
#2274×C1392
#34179139