Finite Group Databasebeta

← C2×#2056×C139 #48018134

Subgroups — C2×#2056×C139 #48018134

Order 35584.

1486 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q16×C139C211yesmaximal, characteristic
2C22×C4⋊C8×C139C211yesmaximal, characteristic
3C22×#103×C139C212yesmaximal
4C2×#391×C139C212yesmaximal
5#2056×C139C218yesmaximal, direct product factor
6C2×#340×C139C211yesmaximal, characteristic
7C23×Q8×C139C2212yes—
8C22×Q16×C139—28no—
9C22×Q16×C139—24no—
10C22×Q16×C139C2214yes—
11C23×C8×C139C2211yescharacteristic
12C23×C8×C139C2211yescharacteristic
13C22×C4⋊C4×C139C2212yes—
14C22×C42×C139C2211yescharacteristic
15C2×C4⋊C8×C139—24no—
16C2×C4⋊C8×C139C2214yes—
17C2×#103×C139—28no—
18C2×#103×C139C2218yes—
19#391×C139—24no—
20#391×C139C2218yes—
21C2×#95×C139—22no—
22C2×#95×C139—22no—
23#340×C139C2214yes—
24C22×Q8×C139—22no—
25C22×Q8×C139—24no—
26C22×Q8×C139—24no—
27C22×Q8×C139—24no—
28C22×Q8×C139—24no—
29C22×Q8×C139—24no—
30C22×Q8×C139D418yes—
31C22×Q8×C139C2314yes—
32C23×C4×C139—22no—
33C23×C4×C139—22no—
34C23×C4×C139D411yescharacteristic
35C23×C4×C139D411yescharacteristic
36C23×C4×C139C2311yescharacteristic
37C2×Q16×C139—232no—
38C2×Q16×C139—216no—
39C2×Q16×C139—28no—
40C22×C8×C139—24no—
41C22×C8×C139—24no—
42C22×C8×C139—22no—
43C22×C8×C139D414yes—
44C22×C8×C139C2312yes—
45C22×C8×C139C2312yes—
46C2×C4⋊C4×C139—24no—
47C2×C4⋊C4×C139—24no—
48C2×C4⋊C4×C139—22no—
49C2×C4⋊C4×C139C2314yes—
50C2×C42×C139—22no—
51C2×C42×C139—22no—
52C2×C42×C139D412yes—
53C2×C42×C139C2312yes—
54C4⋊C8×C139—28no—
55#103×C139—216no—
56#95×C139—28no—
57#95×C139—28no—
58C24×C139C2×D411yescharacteristic
59C2×Q8×C139—28no—
60C2×Q8×C139—24no—
61C2×Q8×C139—216no—
62C2×Q8×C139—216no—
63C2×Q8×C139—24no—
64C2×Q8×C139—24no—
65C2×Q8×C139—24no—
66C2×Q8×C139—24no—
67C2×Q8×C139—44no—
68C2×Q8×C139—44no—
69C2×Q8×C139—48no—
70C2×Q8×C139—48no—
71C2×Q8×C139C2×D418yes—
72C22×C4×C139—22no—
73C22×C4×C139—22no—
74C22×C4×C139—22no—
75C22×C4×C139—28no—
76C22×C4×C139—24no—
77C22×C4×C139—24no—
78C22×C4×C139—24no—
79C22×C4×C139—44no—
80C22×C4×C139—44no—
81C22×C4×C139—44no—
82C22×C4×C139—44no—
83C22×C4×C139—44no—
84C22×C4×C139Q1614yescomplemented
85C22×C4×C139C2×D412yes—
86C22×C4×C139C2×D412yes—
87C22×C4×C139C2×D414yes—
88C22×C4×C139C2×D412yes—
89C22×C4×C139C2×D411yescharacteristic
90C22×C4×C139#4112yes—
91C22×C4×C139#4114yes—
92C22×C4×C139C2411yescharacteristic
93Q16×C139—232no—
94C2×C8×C139—28no—
95C2×C8×C139—24no—
96C2×C8×C139—24no—
97C2×C8×C139—22no—
98C2×C8×C139—44no—
99C2×C8×C139C2×D414yes—
100C4⋊C4×C139—24no—
101C4⋊C4×C139—24no—
102C4⋊C4×C139—44no—
103C42×C139—24no—
104C42×C139—22no—
105C42×C139—22no—
106C23×C139#12114yes—
107C23×C139#12112yes—
108C23×C139C2×Q1612yes—
109C23×C139#13512yes—
110C23×C139#13714yes—
111C23×C139C22×D411yescharacteristic
112Q8×C139—28no—
113Q8×C139—28no—
114Q8×C139—44no—
115Q8×C139—44no—
116Q8×C139—416no—
117C2×C4×C139—22no—
118C2×C4×C139—22no—
119C2×C4×C139—28no—
120C2×C4×C139—22no—
121C2×C4×C139—28no—
122C2×C4×C139—24no—
123C2×C4×C139—44no—
124C2×C4×C139—44no—
125C2×C4×C139—416no—
126C2×C4×C139—44no—
127C2×C4×C139—44no—
128C2×C4×C139—44no—
129C2×C4×C139—44no—
130C2×C4×C139—88no—
131C2×C4×C139#12014yes—
132C2×C4×C139#12112yes—
133C2×C4×C139#12114yes—
134C2×C4×C139#12318yes—
135C2×C4×C139#12414yes—
136C2×C4×C139C2×Q1614yescomplemented
137C2×C4×C139C22×D412yes—
138C2×C4×C139C22×D411yescharacteristic
139C2×C4×C139C2×#4111yescharacteristic
140C2×C4×C139C2×#4112yes—
141C8×C139—24no—
142C8×C139—42no—
143C22×C139#39414yes—
144C22×C139#46218yes—
145C22×C139#46418yes—
146C22×C139#46714yes—
147C22×C139#47014yes—
148C22×C139C2×#12112yes—
149C22×C139C2×#12111yescharacteristic
150C22×C139C22×Q1611yescharacteristic
151C22×C139C2×#13511yescharacteristic
152C22×C139C2×#13712yes—
153C4×C139—24no—
154C4×C139—48no—
155C4×C139—42no—
156C4×C139—84no—
157C4×C139#39414yes—
158C4×C139C2×#12011yescharacteristic
159C4×C139C2×#12312yes—
160C4×C139C2×#12411yescharacteristic
161C2×C139#205618yesdirect product factor
162C2×C139C2×#39411yescharacteristic
163C2×C139C2×#46212yes—
164C2×C139C2×#46412yes—
165C2×C139C2×#46711yescharacteristic
166C2×C139C2×#47011yescharacteristic
167C2×#2056C13911yesmaximal, characteristic, direct product factor, Sylow
168C139C2×#205611yescharacteristic, direct product factor, Sylow
169C23×Q16C2×C13911yescharacteristic
170C22×C4⋊C8C2×C13911yescharacteristic
171C22×#103C2×C13912yes—
172C2×#391C2×C13912yes—
173#2056C2×C13918yesdirect product factor
174C2×#340C2×C13911yescharacteristic
175C23×Q8C22×C13912yes—
176C22×Q16—28no—
177C22×Q16—24no—
178C22×Q16C22×C13914yes—
179C23×C8C22×C13911yescharacteristic
180C23×C8C22×C13911yescharacteristic
181C22×C4⋊C4C22×C13912yes—
182C22×C42C22×C13911yescharacteristic
183C2×C4⋊C8—24no—
184C2×C4⋊C8C22×C13914yes—
185C2×#103—28no—
186C2×#103C22×C13918yes—
187#391—24no—
188#391C22×C13918yes—
189C2×#95—22no—
190C2×#95—22no—
191#340C22×C13914yes—
192C22×Q8—22no—
193C22×Q8—24no—
194C22×Q8—24no—
195C22×Q8—24no—
196C22×Q8—24no—
197C22×Q8—24no—
198C22×Q8D4×C13918yes—
199C22×Q8C23×C13914yes—
200C23×C4—22no—
201C23×C4—22no—
202C23×C4D4×C13911yescharacteristic
203C23×C4D4×C13911yescharacteristic
204C23×C4C23×C13911yescharacteristic
205C2×Q16—232no—
206C2×Q16—216no—
207C2×Q16—28no—
208C22×C8—24no—
209C22×C8—24no—
210C22×C8—22no—
211C22×C8D4×C13914yes—
212C22×C8C23×C13912yes—
213C22×C8C23×C13912yes—
214C2×C4⋊C4—24no—
215C2×C4⋊C4—24no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4C23×C13914yes—
218C2×C42—22no—
219C2×C42—22no—
220C2×C42D4×C13912yes—
221C2×C42C23×C13912yes—
222C4⋊C8—28no—
223#103—216no—
224#95—28no—
225#95—28no—
226C24C2×D4×C13911yescharacteristic
227C2×Q8—28no—
228C2×Q8—24no—
229C2×Q8—216no—
230C2×Q8—216no—
231C2×Q8—24no—
232C2×Q8—24no—
233C2×Q8—24no—
234C2×Q8—24no—
235C2×Q8—44no—
236C2×Q8—44no—
237C2×Q8—48no—
238C2×Q8—48no—
239C2×Q8C2×D4×C13918yes—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—28no—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4—24no—
247C22×C4—44no—
248C22×C4—44no—
249C22×C4—44no—
250C22×C4—44no—
251C22×C4—44no—
252C22×C4Q16×C13914yescomplemented
253C22×C4C2×D4×C13912yes—
254C22×C4C2×D4×C13912yes—
255C22×C4C2×D4×C13914yes—
256C22×C4C2×D4×C13912yes—
257C22×C4C2×D4×C13911yescharacteristic
258C22×C4#41×C13912yes—
259C22×C4#41×C13914yes—
260C22×C4C24×C13911yescharacteristic
261Q16—232no—
262C2×C8—28no—
263C2×C8—24no—
264C2×C8—24no—
265C2×C8—22no—
266C2×C8—44no—
267C2×C8C2×D4×C13914yes—
268C4⋊C4—24no—
269C4⋊C4—24no—
270C4⋊C4—44no—
271C42—24no—
272C42—22no—
273C42—22no—
274C23#121×C13914yes—
275C23#121×C13912yes—
276C23C2×Q16×C13912yes—
277C23#135×C13912yes—
278C23#137×C13914yes—
279C23C22×D4×C13911yescharacteristic
280Q8—28no—
281Q8—28no—
282Q8—44no—
283Q8—44no—
284Q8—416no—
285C2×C4—28no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—28no—
290C2×C4—24no—
291C2×C4—44no—
292C2×C4—44no—
293C2×C4—44no—
294C2×C4—416no—
295C2×C4—44no—
296C2×C4—44no—
297C2×C4—44no—
298C2×C4—88no—
299C2×C4#120×C13914yes—
300C2×C4#121×C13912yes—
301C2×C4#121×C13914yes—
302C2×C4#123×C13918yes—
303C2×C4#124×C13914yes—
304C2×C4C2×Q16×C13914yescomplemented
305C2×C4C22×D4×C13912yes—
306C2×C4C22×D4×C13911yescharacteristic
307C2×C4C2×#41×C13911yescharacteristic
308C2×C4C2×#41×C13912yes—
309C8—24no—
310C8—42no—
311C22#394×C13914yes—
312C22#462×C13918yes—
313C22#464×C13918yes—
314C22#467×C13914yes—
315C22#470×C13914yes—
316C22C2×#121×C13912yes—
317C22C2×#121×C13911yescharacteristic
318C22C22×Q16×C13911yescharacteristic
319C22C2×#135×C13911yescharacteristic
320C22C2×#137×C13912yes—
321C4—24no—
322C4—42no—
323C4—48no—
324C4—84no—
325C4#394×C13914yes—
326C4C2×#120×C13911yescharacteristic
327C4C2×#123×C13912yes—
328C4C2×#124×C13911yescharacteristic
329C2#2056×C13918yesdirect product factor
330C2C2×#394×C13911yescharacteristic
331C2C2×#462×C13912yes—
332C2C2×#464×C13912yes—
333C2C2×#467×C13911yescharacteristic
334C2C2×#470×C13911yescharacteristic
subgroupG/H
center, socle, prime radicalC24×C139C2×D4
commutator, Frattini, cosocleC22×C4C24×C139
LCSG ▷ C22×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. #2056×C139C2direct (N × H)
84. C22×C4×C139Q16semidirect
136. C2×C4×C139C2×Q16semidirect
161. C2×C139#2056direct (N × H)
167. C2×#2056C139direct (N × H)
168. C139C2×#2056direct (N × H)
173. #2056C2×C139direct (N × H)
252. C22×C4Q16×C139semidirect
304. C2×C4C2×Q16×C139semidirect
329. C2#2056×C139direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Q16×C1392
C22×C4⋊C8×C1392
C22×#103×C1392
C2×#391×C1392
#2056×C1392
C2×#340×C1392
C2×#2056139