Finite Group Databasebeta

← C139×#36474 #48031070

Subgroups — C139×#36474 #48031070

Order 35584.

2102 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
1C2×Q82×C139C211yesmaximal, characteristic
2C2×#557×C139C211yesmaximal, characteristic
3#2862×C139C213yesmaximal
4#2567×C139C213yesmaximal
5#2550×C139C2112yesmaximal
6#2546×C139C213yesmaximal
7#2351×C139C214yesmaximal
8C4×C4⋊Q8×C139C213yesmaximal
9C42×Q8×C139C211yesmaximal, characteristic
10Q82×C139—28no—
11#557×C139—28no—
12C2×C4⋊Q8×C139C2213yes—
13C2×C4⋊Q8×C139C2213yes—
14C2×C4⋊Q8×C139C2216yes—
15C2×C4⋊Q8×C139C2213yes—
16C2×#125×C139C2216yes—
17C2×C4×Q8×C139C2213yes—
18C2×C4×Q8×C139C2213yes—
19C2×C4×Q8×C139C2212yes—
20C2×C4×Q8×C139C2212yes—
21C2×C4×Q8×C139C2211yescharacteristic
22C2×C4×Q8×C139C2212yes—
23#398×C139C22112yes—
24#395×C139C22112yes—
25#391×C139C2216yes—
26#391×C139C22112yes—
27#391×C139C2211yescharacteristic
28#391×C139C2213yes—
29#389×C139C22112yes—
30#389×C139C22112yes—
31#389×C139C22112yes—
32#384×C139C2213yes—
33#382×C139C22112yes—
34C4×C4⋊C4×C139C2213yes—
35C4×C4⋊C4×C139C2216yes—
36C4×C4⋊C4×C139C22112yes—
37C43×C139C2213yes—
38C22×Q8×C139C2313yes—
39C22×Q8×C139C2311yescharacteristic
40C22×Q8×C139C2316yes—
41C22×Q8×C139C2311yescharacteristic
42C4⋊Q8×C139—212no—
43C4⋊Q8×C139—224no—
44C4⋊Q8×C139—212no—
45C4⋊Q8×C139—212no—
46#125×C139—224no—
47C4×Q8×C139—28no—
48C4×Q8×C139—28no—
49C4×Q8×C139—212no—
50C4×Q8×C139—212no—
51C4×Q8×C139D418yes—
52C4×Q8×C139Q8116yescomplemented
53C2×C4⋊C4×C139C2316yes—
54C2×C4⋊C4×C139C2316yes—
55C2×C4⋊C4×C139C2316yes—
56C2×C4⋊C4×C139C23112yes—
57C2×C4⋊C4×C139C2311yescharacteristic
58C2×C4⋊C4×C139C2316yes—
59C2×C4⋊C4×C139C2316yes—
60C2×C4⋊C4×C139C2313yes—
61C2×C4⋊C4×C139C23112yes—
62C2×C4⋊C4×C139C2313yes—
63C2×C4⋊C4×C139C2316yes—
64C2×C42×C139C2316yes—
65C2×C42×C139C2316yes—
66C2×C42×C139C2313yes—
67C2×C42×C139C2311yescharacteristic
68C2×C42×C139C2316yes—
69C2×C42×C139C2313yes—
70C2×C42×C139C2316yes—
71#95×C139C2316yes—
72#95×C139C23124yes—
73#95×C139C2314yes—
74#95×C139C23112yes—
75C2×Q8×C139—22no—
76C2×Q8×C139—26no—
77C2×Q8×C139—212no—
78C2×Q8×C139—26no—
79C2×Q8×C139—22no—
80C2×Q8×C139—26no—
81C2×Q8×C139—412no—
82C2×Q8×C139C2×D414yes—
83C2×Q8×C139C2×Q818yes—
84C2×Q8×C139#4114yes—
85C22×C4×C139C2416yes—
86C22×C4×C139C2416yes—
87C22×C4×C139C2412yes—
88C22×C4×C139C2413yes—
89C22×C4×C139C2412yes—
90C22×C4×C139C2416yes—
91C22×C4×C139C2412yes—
92C22×C4×C139C2413yes—
93C22×C4×C139C2411yescharacteristic
94C4⋊C4×C139—22no—
95C4⋊C4×C139—212no—
96C4⋊C4×C139—212no—
97C4⋊C4×C139—212no—
98C4⋊C4×C139—212no—
99C4⋊C4×C139—26no—
100C4⋊C4×C139—212no—
101C4⋊C4×C139—224no—
102C4⋊C4×C139—412no—
103C4⋊C4×C139C2×D4112yes—
104C4⋊C4×C139C2×Q8124yes—
105C42×C139—212no—
106C42×C139—212no—
107C42×C139—26no—
108C42×C139—22no—
109C42×C139—46no—
110C42×C139C2×D4112yes—
111C42×C139C2×Q8124yes—
112C23×C139C2511yescharacteristic
113Q8×C139—28no—
114Q8×C139—412no—
115Q8×C139—812no—
116Q8×C139C4⋊Q8116yescomplemented
117C2×C4×C139—22no—
118C2×C4×C139—26no—
119C2×C4×C139—22no—
120C2×C4×C139—22no—
121C2×C4×C139—22no—
122C2×C4×C139—26no—
123C2×C4×C139—26no—
124C2×C4×C139—22no—
125C2×C4×C139—26no—
126C2×C4×C139—26no—
127C2×C4×C139—26no—
128C2×C4×C139—26no—
129C2×C4×C139—24no—
130C2×C4×C139—212no—
131C2×C4×C139C22×D416yes—
132C2×C4×C139C22×D416yes—
133C2×C4×C139C22×D412yes—
134C2×C4×C139C22×Q814yes—
135C2×C4×C139C22×Q8112yes—
136C2×C4×C139C22×Q8112yes—
137C2×C4×C139C2×#4114yes—
138C2×C4×C139C2×#4112yes—
139C2×C4×C1392−1+412yes—
140C22×C139C23×D411yescharacteristic
141C22×C139C23×Q812yes—
142C22×C139C22×#4111yescharacteristic
143C22×C139C2×2−1+411yescharacteristic
144C22×C139#58512yes—
145C4×C139—24no—
146C4×C139—212no—
147C4×C139—26no—
148C4×C139—24no—
149C4×C139—46no—
150C4×C139—42no—
151C4×C139—46no—
152C4×C139C2×C4⋊Q8112yes—
153C4×C139#54814yes—
154C2×C139C22×C4⋊Q811yescharacteristic
155C2×C139C2×#54811yescharacteristic
156C2×C139Q8×#4112yes—
157C2×C139#350011yescharacteristic
158C2×C139#350212yes—
159#36474C13911yesmaximal, characteristic, direct product factor, Sylow
160C139#3647411yescharacteristic, direct product factor, Sylow
161C2×Q82C2×C13911yescharacteristic
162C2×#557C2×C13911yescharacteristic
163#2862C2×C13913yes—
164#2567C2×C13913yes—
165#2550C2×C139112yes—
166#2546C2×C13913yes—
167#2351C2×C13914yes—
168C4×C4⋊Q8C2×C13913yes—
169C42×Q8C2×C13911yescharacteristic
170Q82—28no—
171#557—28no—
172C2×C4⋊Q8C22×C13913yes—
173C2×C4⋊Q8C22×C13913yes—
174C2×C4⋊Q8C22×C13913yes—
175C2×C4⋊Q8C22×C13916yes—
176C2×#125C22×C13916yes—
177C2×C4×Q8C22×C13913yes—
178C2×C4×Q8C22×C13913yes—
179C2×C4×Q8C22×C13912yes—
180C2×C4×Q8C22×C13912yes—
181C2×C4×Q8C22×C13911yescharacteristic
182C2×C4×Q8C22×C13912yes—
183#398C22×C139112yes—
184#395C22×C139112yes—
185#391C22×C13911yescharacteristic
186#391C22×C13913yes—
187#391C22×C13916yes—
188#391C22×C139112yes—
189#389C22×C139112yes—
190#389C22×C139112yes—
191#389C22×C139112yes—
192#384C22×C13913yes—
193#382C22×C139112yes—
194C4×C4⋊C4C22×C139112yes—
195C4×C4⋊C4C22×C13913yes—
196C4×C4⋊C4C22×C13916yes—
197C43C22×C13913yes—
198C22×Q8C23×C13913yes—
199C22×Q8C23×C13911yescharacteristic
200C22×Q8C23×C13916yes—
201C22×Q8C23×C13911yescharacteristic
202C4⋊Q8—212no—
203C4⋊Q8—224no—
204C4⋊Q8—212no—
205C4⋊Q8—212no—
206#125—224no—
207C4×Q8—28no—
208C4×Q8—28no—
209C4×Q8—212no—
210C4×Q8—212no—
211C4×Q8D4×C13918yes—
212C4×Q8Q8×C139116yescomplemented
213C2×C4⋊C4C23×C13911yescharacteristic
214C2×C4⋊C4C23×C13916yes—
215C2×C4⋊C4C23×C13916yes—
216C2×C4⋊C4C23×C13916yes—
217C2×C4⋊C4C23×C13913yes—
218C2×C4⋊C4C23×C13916yes—
219C2×C4⋊C4C23×C13916yes—
220C2×C4⋊C4C23×C139112yes—
221C2×C4⋊C4C23×C139112yes—
222C2×C4⋊C4C23×C13913yes—
223C2×C4⋊C4C23×C13916yes—
224C2×C42C23×C13916yes—
225C2×C42C23×C13916yes—
226C2×C42C23×C13913yes—
227C2×C42C23×C13911yescharacteristic
228C2×C42C23×C13916yes—
229C2×C42C23×C13913yes—
230C2×C42C23×C13916yes—
231#95C23×C13914yes—
232#95C23×C13916yes—
233#95C23×C139112yes—
234#95C23×C139124yes—
235C2×Q8—22no—
236C2×Q8—26no—
237C2×Q8—212no—
238C2×Q8—26no—
239C2×Q8—22no—
240C2×Q8—26no—
241C2×Q8—412no—
242C2×Q8C2×D4×C13914yes—
243C2×Q8C2×Q8×C13918yes—
244C2×Q8#41×C13914yes—
245C22×C4C24×C13916yes—
246C22×C4C24×C13916yes—
247C22×C4C24×C13912yes—
248C22×C4C24×C13913yes—
249C22×C4C24×C13912yes—
250C22×C4C24×C13916yes—
251C22×C4C24×C13912yes—
252C22×C4C24×C13913yes—
253C22×C4C24×C13911yescharacteristic
254C4⋊C4—22no—
255C4⋊C4—212no—
256C4⋊C4—212no—
257C4⋊C4—212no—
258C4⋊C4—212no—
259C4⋊C4—26no—
260C4⋊C4—212no—
261C4⋊C4—224no—
262C4⋊C4—412no—
263C4⋊C4C2×D4×C139112yes—
264C4⋊C4C2×Q8×C139124yes—
265C42—212no—
266C42—212no—
267C42—26no—
268C42—22no—
269C42—46no—
270C42C2×D4×C139112yes—
271C42C2×Q8×C139124yes—
272C23C25×C13911yescharacteristic
273Q8—28no—
274Q8—412no—
275Q8—812no—
276Q8C4⋊Q8×C139116yescomplemented
277C2×C4—22no—
278C2×C4—26no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—26no—
283C2×C4—26no—
284C2×C4—22no—
285C2×C4—26no—
286C2×C4—26no—
287C2×C4—26no—
288C2×C4—26no—
289C2×C4—24no—
290C2×C4—212no—
291C2×C4C22×D4×C13916yes—
292C2×C4C22×D4×C13916yes—
293C2×C4C22×D4×C13912yes—
294C2×C4C22×Q8×C13914yes—
295C2×C4C22×Q8×C139112yes—
296C2×C4C22×Q8×C139112yes—
297C2×C4C2×#41×C13914yes—
298C2×C4C2×#41×C13912yes—
299C2×C42−1+4×C13912yes—
300C22C23×D4×C13911yescharacteristic
301C22C23×Q8×C13912yes—
302C22C22×#41×C13911yescharacteristic
303C22C2×2−1+4×C13911yescharacteristic
304C22#585×C13912yes—
305C4—24no—
306C4—212no—
307C4—26no—
308C4—24no—
309C4—46no—
310C4—46no—
311C4—42no—
312C4C2×C4⋊Q8×C139112yes—
313C4#548×C13914yes—
314C2C22×C4⋊Q8×C13911yescharacteristic
315C2C2×#548×C13911yescharacteristic
316C2Q8×#41×C13912yes—
317C2#3500×C13911yescharacteristic
318C2#3502×C13912yes—
subgroupG/H
center, socle, prime radicalC23×C139C25
commutator, Frattini, cosocleC23C25×C139
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
52. C4×Q8×C139Q8semidirect
116. Q8×C139C4⋊Q8semidirect
159. #36474C139direct (N × H)
160. C139#36474direct (N × H)
212. C4×Q8Q8×C139semidirect
276. Q8C4⋊Q8×C139semidirect

Maximal subgroups

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

subgroupindex
C2×Q82×C1392
C2×#557×C1392
#2862×C1392
#2567×C1392
#2550×C1392
#2546×C1392
#2351×C1392
C4×C4⋊Q8×C1392
C42×Q8×C1392
#36474139