Finite Group Databasebeta

← C139×#8455 #48003051

Subgroups — C139×#8455 #48003051

Order 35584.

1038 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1038 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3486×C139C211yesmaximal, characteristic
2#1784×C139C211yesmaximal, characteristic, complemented
3#1504×C139C214yesmaximal, complemented
4#1446×C139C211yesmaximal, characteristic, complemented
5C2×2−1+4×C139C411yescharacteristic, complemented
6C23×Q8×C139C2211yescharacteristic
7D4×Q8×C139—24no—
8#548×C139—24no—
9#536×C139—22no—
10#536×C139C412yescomplemented
11#525×C139—22no—
12#525×C139C2212yes—
13#519×C139C411yescharacteristic, complemented
14C2×#101×C139—22no—
15#407×C139C2212yes—
16C2×#95×C139—22no—
17C2×#95×C139C2212yes—
18#328×C139—24no—
19#327×C139—24no—
202−1+4×C139—44no—
21C2×#41×C139—22no—
22C2×#41×C139—22no—
23C2×#41×C139C2×C412yes—
24C22×Q8×C139—22no—
25C22×Q8×C139—24no—
26C22×Q8×C139—44no—
27C22×Q8×C139C2×C411yescharacteristic
28C22×Q8×C139C2×C411yescharacteristic
29C22×Q8×C139D412yes—
30C23×C4×C139—22no—
31C23×C4×C139D412yes—
32C23×C4×C139C2311yescharacteristic
33C2×M16×C139—22no—
34C4⋊Q8×C139—24no—
35C4⋊Q8×C139—22no—
36#124×C139—24no—
37#124×C139—22no—
38#123×C139—24no—
39#123×C139—22no—
40C22⋊Q8×C139—24no—
41C22⋊Q8×C139—28no—
42C22⋊Q8×C139—24no—
43C22⋊Q8×C139D414yes—
44#121×C139—24no—
45#121×C139D414yes—
46#120×C139—22no—
47C4×Q8×C139—24no—
48C4×D4×C139—28no—
49C4×D4×C139—24no—
50#117×C139—22no—
51#117×C139C2×C412yes—
52#101×C139—44no—
53C22⋊C8×C139—24no—
54#95×C139—24no—
55#95×C139—44no—
56C24×C139C2×D411yescharacteristic
57#41×C139—44no—
58#41×C139—44no—
59#41×C139—48no—
60#41×C139—44no—
61C2×Q8×C139—22no—
62C2×Q8×C139—24no—
63C2×Q8×C139—24no—
64C2×Q8×C139—22no—
65C2×Q8×C139—22no—
66C2×Q8×C139—24no—
67C2×Q8×C139—42no—
68C2×Q8×C139—42no—
69C2×Q8×C139—416no—
70C2×Q8×C139—48no—
71C2×Q8×C139C22⋊C412yes—
72C2×D4×C139—22no—
73C2×D4×C139—22no—
74C2×D4×C139—24no—
75C2×D4×C139C22⋊C412yes—
76C22×C4×C139—24no—
77C22×C4×C139—24no—
78C22×C4×C139—24no—
79C22×C4×C139—22no—
80C22×C4×C139—24no—
81C22×C4×C139—42no—
82C22×C4×C139—42no—
83C22×C4×C139—44no—
84C22×C4×C139—42no—
85C22×C4×C139—44no—
86C22×C4×C139—42no—
87C22×C4×C139C22⋊C412yes—
88C22×C4×C139C22⋊C412yes—
89C22×C4×C139C22×C411yescharacteristic
90C22×C4×C139C2×D411yescharacteristic
91C22×C4×C139C2×D414yes—
92M16×C139—44no—
93C2×C8×C139—42no—
94C4⋊C4×C139—24no—
95C4⋊C4×C139—28no—
96C4⋊C4×C139—24no—
97C4⋊C4×C139C22⋊C414yes—
98C22⋊C4×C139—28no—
99C22⋊C4×C139—22no—
100C22⋊C4×C139—24no—
101C22⋊C4×C139—24no—
102C42×C139—24no—
103C42×C139—22no—
104C23×C139—22no—
105C23×C139—22no—
106C23×C139—22no—
107C23×C139—22no—
108C23×C139C2×C22⋊C411yescharacteristic
109C23×C139#12012yes—
110Q8×C139—28no—
111Q8×C139—48no—
112Q8×C139—42no—
113Q8×C139—44no—
114Q8×C139—44no—
115D4×C139—42no—
116D4×C139—44no—
117D4×C139—44no—
118D4×C139—44no—
119D4×C139—44no—
120C2×C4×C139—22no—
121C2×C4×C139—22no—
122C2×C4×C139—22no—
123C2×C4×C139—22no—
124C2×C4×C139—24no—
125C2×C4×C139—22no—
126C2×C4×C139—22no—
127C2×C4×C139—22no—
128C2×C4×C139—22no—
129C2×C4×C139—44no—
130C2×C4×C139—48no—
131C2×C4×C139—48no—
132C2×C4×C139—44no—
133C2×C4×C139—48no—
134C2×C4×C139—44no—
135C2×C4×C139—84no—
136C2×C4×C139—82no—
137C2×C4×C139—82no—
138C2×C4×C139#9914yes—
139C2×C4×C139C2×C22⋊C412yes—
140C2×C4×C139#12012yes—
141C8×C139—82no—
142C22×C139—24no—
143C22×C139—22no—
144C22×C139—22no—
145C22×C139—22no—
146C22×C139—22no—
147C22×C139—22no—
148C22×C139—44no—
149C22×C139—42no—
150C22×C139#37911yescharacteristic
151C22×C139C2×#9912yes—
152C22×C139#45412yes—
153C22×C139#45612yes—
154C4×C139—22no—
155C4×C139—24no—
156C4×C139—22no—
157C4×C139—44no—
158C4×C139—42no—
159C4×C139—42no—
160C4×C139—84no—
161C2×C139—22no—
162C2×C139—22no—
163C2×C139—22no—
164C2×C139—82no—
165C2×C139#178111yescharacteristic
166C2×C139#179312yes—
167#8455C13911yesmaximal, characteristic, direct product factor, Sylow
168C139#845511yescharacteristic, direct product factor, Sylow
169#3486C2×C13911yescharacteristic
170#1784C2×C13911yescharacteristic, complemented
171#1504C2×C13914yescomplemented
172#1446C2×C13911yescharacteristic, complemented
173C2×2−1+4C4×C13911yescharacteristic, complemented
174C23×Q8C22×C13911yescharacteristic
175D4×Q8—24no—
176#548—24no—
177#536—22no—
178#536C4×C13912yescomplemented
179#525—22no—
180#525C22×C13912yes—
181#519C4×C13911yescharacteristic, complemented
182C2×#101—22no—
183#407C22×C13912yes—
184C2×#95—22no—
185C2×#95C22×C13912yes—
186#328—24no—
187#327—24no—
1882−1+4—44no—
189C2×#41—22no—
190C2×#41—22no—
191C2×#41C2×C4×C13912yes—
192C22×Q8—22no—
193C22×Q8—24no—
194C22×Q8—44no—
195C22×Q8C2×C4×C13911yescharacteristic
196C22×Q8C2×C4×C13911yescharacteristic
197C22×Q8D4×C13912yes—
198C23×C4—22no—
199C23×C4D4×C13912yes—
200C23×C4C23×C13911yescharacteristic
201C2×M16—22no—
202C4⋊Q8—24no—
203C4⋊Q8—22no—
204#124—24no—
205#124—22no—
206#123—24no—
207#123—22no—
208C22⋊Q8—24no—
209C22⋊Q8—28no—
210C22⋊Q8—24no—
211C22⋊Q8D4×C13914yes—
212#121—24no—
213#121D4×C13914yes—
214#120—22no—
215C4×Q8—24no—
216C4×D4—28no—
217C4×D4—24no—
218#117—22no—
219#117C2×C4×C13912yes—
220#101—44no—
221C22⋊C8—24no—
222#95—24no—
223#95—44no—
224C24C2×D4×C13911yescharacteristic
225#41—44no—
226#41—44no—
227#41—48no—
228#41—44no—
229C2×Q8—22no—
230C2×Q8—24no—
231C2×Q8—24no—
232C2×Q8—22no—
233C2×Q8—22no—
234C2×Q8—24no—
235C2×Q8—42no—
236C2×Q8—42no—
237C2×Q8—416no—
238C2×Q8—48no—
239C2×Q8C22⋊C4×C13912yes—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—24no—
243C2×D4C22⋊C4×C13912yes—
244C22×C4—24no—
245C22×C4—24no—
246C22×C4—24no—
247C22×C4—22no—
248C22×C4—24no—
249C22×C4—42no—
250C22×C4—42no—
251C22×C4—44no—
252C22×C4—42no—
253C22×C4—44no—
254C22×C4—42no—
255C22×C4C22⋊C4×C13912yes—
256C22×C4C22⋊C4×C13912yes—
257C22×C4C22×C4×C13911yescharacteristic
258C22×C4C2×D4×C13911yescharacteristic
259C22×C4C2×D4×C13914yes—
260M16—44no—
261C2×C8—42no—
262C4⋊C4—24no—
263C4⋊C4—28no—
264C4⋊C4—24no—
265C4⋊C4C22⋊C4×C13914yes—
266C22⋊C4—28no—
267C22⋊C4—22no—
268C22⋊C4—24no—
269C22⋊C4—24no—
270C42—24no—
271C42—22no—
272C23—22no—
273C23—22no—
274C23—22no—
275C23—22no—
276C23C2×C22⋊C4×C13911yescharacteristic
277C23#120×C13912yes—
278Q8—28no—
279Q8—48no—
280Q8—42no—
281Q8—44no—
282Q8—44no—
283D4—42no—
284D4—44no—
285D4—44no—
286D4—44no—
287D4—44no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—24no—
295C2×C4—22no—
296C2×C4—22no—
297C2×C4—44no—
298C2×C4—48no—
299C2×C4—48no—
300C2×C4—44no—
301C2×C4—48no—
302C2×C4—44no—
303C2×C4—84no—
304C2×C4—82no—
305C2×C4—82no—
306C2×C4#99×C13914yes—
307C2×C4C2×C22⋊C4×C13912yes—
308C2×C4#120×C13912yes—
309C8—82no—
310C22—24no—
311C22—22no—
312C22—22no—
313C22—22no—
314C22—22no—
315C22—22no—
316C22—42no—
317C22—44no—
318C22#379×C13911yescharacteristic
319C22C2×#99×C13912yes—
320C22#454×C13912yes—
321C22#456×C13912yes—
322C4—22no—
323C4—24no—
324C4—22no—
325C4—42no—
326C4—42no—
327C4—44no—
328C4—84no—
329C2—22no—
330C2—22no—
331C2—22no—
332C2—82no—
333C2#1781×C13911yescharacteristic
334C2#1793×C13912yes—
subgroupG/H
center, socleC22×C139#379
commutatorC22×C4C22×C4×C139
Frattini, cosocleC23×C4C23×C139
prime radical#3486×C139C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C23×C4×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1784×C139C2semidirect
3. #1504×C139C2semidirect
4. #1446×C139C2semidirect
5. C2×2−1+4×C139C4semidirect
10. #536×C139C4semidirect
13. #519×C139C4semidirect
167. #8455C139direct (N × H)
168. C139#8455direct (N × H)
170. #1784C2×C139semidirect
171. #1504C2×C139semidirect
172. #1446C2×C139semidirect
173. C2×2−1+4C4×C139semidirect
178. #536C4×C139semidirect
181. #519C4×C139semidirect

Maximal subgroups

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

subgroupindex
#3486×C1392
#1784×C1392
#1504×C1392
#1446×C1392
#8455139