Finite Group Databasebeta

← C2×#1944×C139 #48015749

Subgroups — C2×#1944×C139 #48015749

Order 35584.

1142 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#107×C139C211yesmaximal, characteristic
2C22×#106×C139C211yesmaximal, characteristic
3C22×#97×C139C211yesmaximal, characteristic
4C2×#389×C139C212yesmaximal
5#1944×C139C218yesmaximal, direct product factor
6C2×#340×C139C212yesmaximal
7C23×C8×C139C2211yescharacteristic
8C23×C8×C139C2211yescharacteristic
9C22×C4⋊C4×C139—22no—
10C22×C4⋊C4×C139C2212yes—
11C22×C4⋊C4×C139C2212yes—
12C22×C42×C139C2211yescharacteristic
13C2×#107×C139—24no—
14C2×#107×C139C2214yes—
15C2×#106×C139C418yescomplemented
16C2×#106×C139C2214yes—
17C2×#97×C139—24no—
18C2×#97×C139C2214yes—
19#389×C139—24no—
20#389×C139C2218yes—
21C2×#95×C139—22no—
22#340×C139C2218yes—
23C23×C4×C139—22no—
24C23×C4×C139—22no—
25C23×C4×C139D411yescharacteristic
26C23×C4×C139D411yescharacteristic
27C23×C4×C139C2311yescharacteristic
28C22×C8×C139—22no—
29C22×C8×C139—22no—
30C22×C8×C139C2×C414yes—
31C22×C8×C139D414yes—
32C22×C8×C139Q814yes—
33C22×C8×C139Q814yes—
34C22×C8×C139C2312yes—
35C22×C8×C139C2312yes—
36C2×C4⋊C4×C139—22no—
37C2×C4⋊C4×C139—24no—
38C2×C4⋊C4×C139—24no—
39C2×C4⋊C4×C139—24no—
40C2×C4⋊C4×C139—28no—
41C2×C4⋊C4×C139—22no—
42C2×C4⋊C4×C139—48no—
43C2×C4⋊C4×C139C2×C418yes—
44C2×C4⋊C4×C139C2314yes—
45C2×C4⋊C4×C139C2314yes—
46C2×C42×C139—22no—
47C2×C42×C139—22no—
48C2×C42×C139D412yes—
49C2×C42×C139C2312yes—
50#107×C139—28no—
51#106×C139C2×C4116yescomplemented
52#97×C139—28no—
53#95×C139—28no—
54C24×C139C2×D411yescharacteristic
55C22×C4×C139—28no—
56C22×C4×C139—22no—
57C22×C4×C139—22no—
58C22×C4×C139—24no—
59C22×C4×C139—24no—
60C22×C4×C139—24no—
61C22×C4×C139—24no—
62C22×C4×C139—44no—
63C22×C4×C139—44no—
64C22×C4×C139—44no—
65C22×C4×C139—44no—
66C22×C4×C139—44no—
67C22×C4×C139C22×C412yes—
68C22×C4×C139C2×D412yes—
69C22×C4×C139C2×D412yes—
70C22×C4×C139C2×D412yes—
71C22×C4×C139C2×D411yescharacteristic
72C22×C4×C139C2×Q812yes—
73C22×C4×C139C2×Q812yes—
74C22×C4×C139#4112yes—
75C22×C4×C139#4112yes—
76C22×C4×C139C2411yescharacteristic
77C2×C8×C139—28no—
78C2×C8×C139—22no—
79C2×C8×C139—22no—
80C2×C8×C139C4⋊C4116yescomplemented
81C2×C8×C139C22×C414yes—
82C2×C8×C139C2×D414yes—
83C2×C8×C139C2×Q814yes—
84C2×C8×C139C2×Q814yes—
85C4⋊C4×C139—28no—
86C4⋊C4×C139—24no—
87C4⋊C4×C139—24no—
88C4⋊C4×C139—24no—
89C4⋊C4×C139—416no—
90C4⋊C4×C139—44no—
91C4⋊C4×C139C22×C418yes—
92C42×C139—24no—
93C42×C139—22no—
94C42×C139—22no—
95C23×C139C4×D412yes—
96C23×C139#12112yes—
97C23×C139C4⋊Q812yes—
98C23×C139AGL(1,ℤ/8)14yes—
99C23×C139#13714yes—
100C23×C139C22×D411yescharacteristic
101C2×C4×C139—28no—
102C2×C4×C139—22no—
103C2×C4×C139—22no—
104C2×C4×C139—24no—
105C2×C4×C139—24no—
106C2×C4×C139—44no—
107C2×C4×C139—44no—
108C2×C4×C139—416no—
109C2×C4×C139—44no—
110C2×C4×C139—44no—
111C2×C4×C139—44no—
112C2×C4×C139—44no—
113C2×C4×C139—44no—
114C2×C4×C139—88no—
115C2×C4×C139C2×C4⋊C414yes—
116C2×C4×C139C4×D412yes—
117C2×C4×C139C4×Q814yes—
118C2×C4×C139#12112yes—
119C2×C4×C139C22⋊Q814yes—
120C2×C4×C139#12514yes—
121C2×C4×C139C4⋊Q812yes—
122C2×C4×C139C23×C411yescharacteristic
123C2×C4×C139C22×D411yescharacteristic
124C2×C4×C139C22×Q811yescharacteristic
125C2×C4×C139C22×Q811yescharacteristic
126C2×C4×C139C2×#4111yescharacteristic
127C2×C4×C139C2×#4111yescharacteristic
128C8×C139—24no—
129C8×C139C2×C4⋊C418yescomplemented
130C22×C139#38914yes—
131C22×C139#44018yes—
132C22×C139#46914yes—
133C22×C139#47014yes—
134C22×C139#50118yes—
135C22×C139C2×C4×D411yescharacteristic
136C22×C139C2×#12111yescharacteristic
137C22×C139C2×C4⋊Q811yescharacteristic
138C22×C139C2×AGL(1,ℤ/8)12yes—
139C22×C139C2×#13712yes—
140C4×C139—48no—
141C4×C139—42no—
142C4×C139—42no—
143C4×C139—84no—
144C4×C139#38914yes—
145C4×C139C22×C4⋊C411yescharacteristic
146C4×C139C2×C4×Q811yescharacteristic
147C4×C139C2×C22⋊Q811yescharacteristic
148C4×C139C2×#12511yescharacteristic
149C2×C139#194418yesdirect product factor
150C2×C139C2×#38911yescharacteristic
151C2×C139C2×#44012yes—
152C2×C139C2×#46911yescharacteristic
153C2×C139C2×#47011yescharacteristic
154C2×C139C2×#50112yes—
155C2×#1944C13911yesmaximal, characteristic, direct product factor, Sylow
156C139C2×#194411yescharacteristic, direct product factor, Sylow
157C22×#107C2×C13911yescharacteristic
158C22×#106C2×C13911yescharacteristic
159C22×#97C2×C13911yescharacteristic
160C2×#389C2×C13912yes—
161#1944C2×C13918yesdirect product factor
162C2×#340C2×C13912yes—
163C23×C8C22×C13911yescharacteristic
164C23×C8C22×C13911yescharacteristic
165C22×C4⋊C4—22no—
166C22×C4⋊C4C22×C13912yes—
167C22×C4⋊C4C22×C13912yes—
168C22×C42C22×C13911yescharacteristic
169C2×#107—24no—
170C2×#107C22×C13914yes—
171C2×#106C4×C13918yescomplemented
172C2×#106C22×C13914yes—
173C2×#97—24no—
174C2×#97C22×C13914yes—
175#389—24no—
176#389C22×C13918yes—
177C2×#95—22no—
178#340C22×C13918yes—
179C23×C4—22no—
180C23×C4—22no—
181C23×C4D4×C13911yescharacteristic
182C23×C4D4×C13911yescharacteristic
183C23×C4C23×C13911yescharacteristic
184C22×C8—22no—
185C22×C8—22no—
186C22×C8C2×C4×C13914yes—
187C22×C8D4×C13914yes—
188C22×C8Q8×C13914yes—
189C22×C8Q8×C13914yes—
190C22×C8C23×C13912yes—
191C22×C8C23×C13912yes—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—24no—
194C2×C4⋊C4—24no—
195C2×C4⋊C4—24no—
196C2×C4⋊C4—28no—
197C2×C4⋊C4—22no—
198C2×C4⋊C4—48no—
199C2×C4⋊C4C2×C4×C13918yes—
200C2×C4⋊C4C23×C13914yes—
201C2×C4⋊C4C23×C13914yes—
202C2×C42—22no—
203C2×C42—22no—
204C2×C42D4×C13912yes—
205C2×C42C23×C13912yes—
206#107—28no—
207#106C2×C4×C139116yescomplemented
208#97—28no—
209#95—28no—
210C24C2×D4×C13911yescharacteristic
211C22×C4—28no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—24no—
215C22×C4—24no—
216C22×C4—24no—
217C22×C4—24no—
218C22×C4—44no—
219C22×C4—44no—
220C22×C4—44no—
221C22×C4—44no—
222C22×C4—44no—
223C22×C4C22×C4×C13912yes—
224C22×C4C2×D4×C13912yes—
225C22×C4C2×D4×C13912yes—
226C22×C4C2×D4×C13912yes—
227C22×C4C2×D4×C13911yescharacteristic
228C22×C4C2×Q8×C13912yes—
229C22×C4C2×Q8×C13912yes—
230C22×C4#41×C13912yes—
231C22×C4#41×C13912yes—
232C22×C4C24×C13911yescharacteristic
233C2×C8—28no—
234C2×C8—22no—
235C2×C8—22no—
236C2×C8C4⋊C4×C139116yescomplemented
237C2×C8C22×C4×C13914yes—
238C2×C8C2×D4×C13914yes—
239C2×C8C2×Q8×C13914yes—
240C2×C8C2×Q8×C13914yes—
241C4⋊C4—28no—
242C4⋊C4—24no—
243C4⋊C4—24no—
244C4⋊C4—24no—
245C4⋊C4—416no—
246C4⋊C4—44no—
247C4⋊C4C22×C4×C13918yes—
248C42—24no—
249C42—22no—
250C42—22no—
251C23C4×D4×C13912yes—
252C23#121×C13912yes—
253C23C4⋊Q8×C13912yes—
254C23AGL(1,ℤ/8)×C13914yes—
255C23#137×C13914yes—
256C23C22×D4×C13911yescharacteristic
257C2×C4—28no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—24no—
261C2×C4—24no—
262C2×C4—416no—
263C2×C4—44no—
264C2×C4—44no—
265C2×C4—44no—
266C2×C4—44no—
267C2×C4—44no—
268C2×C4—44no—
269C2×C4—44no—
270C2×C4—88no—
271C2×C4C2×C4⋊C4×C13914yes—
272C2×C4C4×D4×C13912yes—
273C2×C4C4×Q8×C13914yes—
274C2×C4#121×C13912yes—
275C2×C4C22⋊Q8×C13914yes—
276C2×C4#125×C13914yes—
277C2×C4C4⋊Q8×C13912yes—
278C2×C4C23×C4×C13911yescharacteristic
279C2×C4C22×D4×C13911yescharacteristic
280C2×C4C22×Q8×C13911yescharacteristic
281C2×C4C22×Q8×C13911yescharacteristic
282C2×C4C2×#41×C13911yescharacteristic
283C2×C4C2×#41×C13911yescharacteristic
284C8—24no—
285C8C2×C4⋊C4×C13918yescomplemented
286C22#389×C13914yes—
287C22#440×C13918yes—
288C22#469×C13914yes—
289C22#470×C13914yes—
290C22#501×C13918yes—
291C22C2×C4×D4×C13911yescharacteristic
292C22C2×#121×C13911yescharacteristic
293C22C2×C4⋊Q8×C13911yescharacteristic
294C22C2×AGL(1,ℤ/8)×C13912yes—
295C22C2×#137×C13912yes—
296C4—42no—
297C4—42no—
298C4—48no—
299C4—84no—
300C4#389×C13914yes—
301C4C22×C4⋊C4×C13911yescharacteristic
302C4C2×C4×Q8×C13911yescharacteristic
303C4C2×C22⋊Q8×C13911yescharacteristic
304C4C2×#125×C13911yescharacteristic
305C2#1944×C13918yesdirect product factor
306C2C2×#389×C13911yescharacteristic
307C2C2×#440×C13912yes—
308C2C2×#469×C13911yescharacteristic
309C2C2×#470×C13911yescharacteristic
310C2C2×#501×C13912yes—
subgroupG/H
center, socle, prime radicalC24×C139C2×D4
commutatorC2×C4C23×C4×C139
Frattini, cosocleC22×C4C24×C139
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C139 ◁ C22×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
5. #1944×C139C2direct (N × H)
15. C2×#106×C139C4semidirect
51. #106×C139C2×C4semidirect
80. C2×C8×C139C4⋊C4semidirect
129. C8×C139C2×C4⋊C4semidirect
149. C2×C139#1944direct (N × H)
155. C2×#1944C139direct (N × H)
156. C139C2×#1944direct (N × H)
161. #1944C2×C139direct (N × H)
171. C2×#106C4×C139semidirect
207. #106C2×C4×C139semidirect
236. C2×C8C4⋊C4×C139semidirect
285. C8C2×C4⋊C4×C139semidirect
305. C2#1944×C139direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#107×C1392
C22×#106×C1392
C22×#97×C1392
C2×#389×C1392
#1944×C1392
C2×#340×C1392
C2×#1944139