Finite Group Databasebeta

← C139×#8525 #48003121

Subgroups — C139×#8525 #48003121

Order 35584.

694 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#544×C139C211yesmaximal, characteristic
2#1556×C139C212yesmaximal, complemented
3#1534×C139C212yesmaximal, complemented
4#1464×C139C211yesmaximal, characteristic
5#1464×C139C211yesmaximal, characteristic
6#544×C139—24no—
7#544×C139—24no—
8C2×C4⋊Q8×C139—21no—
9C2×C4⋊Q8×C139C411yescharacteristic
10C2×C4⋊Q8×C139C2211yescharacteristic
11C2×#125×C139—21no—
12C2×#125×C139C411yescharacteristic
13C2×#125×C139C2211yescharacteristic
14C2×C22⋊Q8×C139—21no—
15C2×C22⋊Q8×C139—21no—
16C2×#117×C139C411yescharacteristic
17C2×#117×C139C2211yescharacteristic
18C22×C4⋊C4×C139C411yescharacteristic
19#432×C139C2212yes—
20#432×C139C2212yes—
21#332×C139—24no—
22#330×C139—24no—
23#324×C139—21no—
24#324×C139—21no—
25#323×C139—21no—
26#323×C139—21no—
27C22×Q8×C139—21no—
28C22×Q8×C139—21no—
29C23×C4×C139—21no—
30C23×C4×C139C2×C411yescharacteristic
31C4⋊Q8×C139—28no—
32C4⋊Q8×C139—22no—
33C4⋊Q8×C139—22no—
34C4⋊Q8×C139—22no—
35C4⋊Q8×C139D414yes—
36#125×C139—28no—
37#125×C139—22no—
38#125×C139—22no—
39#125×C139—22no—
40#125×C139D414yes—
41C22⋊Q8×C139—28no—
42C22⋊Q8×C139—28no—
43#117×C139—22no—
44#117×C139—22no—
45#117×C139—22no—
46#117×C139—22no—
47C2×C4⋊C4×C139—21no—
48C2×C4⋊C4×C139—21no—
49C2×C4⋊C4×C139—21no—
50C2×C4⋊C4×C139—21no—
51C2×C4⋊C4×C139—21no—
52C2×C4⋊C4×C139—21no—
53C2×C4⋊C4×C139—21no—
54C2×C4⋊C4×C139—22no—
55C2×C4⋊C4×C139—22no—
56C2×C4⋊C4×C139C2×C411yescharacteristic
57C2×C4⋊C4×C139C2×C411yescharacteristic
58C2×C4⋊C4×C139C2×C411yescharacteristic
59C2×C4⋊C4×C139C2×C411yescharacteristic
60C2×C4⋊C4×C139D411yescharacteristic
61C2×C4⋊C4×C139D411yescharacteristic
62C2×C22⋊C4×C139—21no—
63C2×C22⋊C4×C139D411yescharacteristic
64C2×C22⋊C4×C139D411yescharacteristic
65C2×C42×C139—21no—
66C2×C42×C139C2×C411yescharacteristic
67C2×C42×C139C2311yescharacteristic
68C4⋊C8×C139—22no—
69C4⋊C8×C139—22no—
70C22⋊C8×C139—22no—
71C22⋊C8×C139—22no—
72#97×C139—22no—
73#97×C139—22no—
74C24×C139C22⋊C411yescharacteristic
75C2×Q8×C139—24no—
76C2×Q8×C139—24no—
77C2×Q8×C139—82no—
78C2×Q8×C139—82no—
79C22×C4×C139—22no—
80C22×C4×C139—22no—
81C22×C4×C139—21no—
82C22×C4×C139—21no—
83C22×C4×C139—21no—
84C22×C4×C139—21no—
85C22×C4×C139—21no—
86C22×C4×C139—21no—
87C22×C4×C139—24no—
88C22×C4×C139—82no—
89C22×C4×C139C22⋊C411yescharacteristic
90C22×C4×C139C22⋊C411yescharacteristic
91C22×C4×C139C22⋊C411yescharacteristic
92C22×C4×C139C22×C411yescharacteristic
93C22×C4×C139C2×D411yescharacteristic
94C22×C4×C139C2×D411yescharacteristic
95C2×C8×C139—42no—
96C2×C8×C139—42no—
97C4⋊C4×C139—24no—
98C4⋊C4×C139—24no—
99C4⋊C4×C139—24no—
100C4⋊C4×C139—24no—
101C4⋊C4×C139—21no—
102C4⋊C4×C139—21no—
103C4⋊C4×C139—21no—
104C4⋊C4×C139—21no—
105C4⋊C4×C139—24no—
106C4⋊C4×C139—24no—
107C4⋊C4×C139—24no—
108C4⋊C4×C139—22no—
109C4⋊C4×C139—22no—
110C4⋊C4×C139C22⋊C412yes—
111C4⋊C4×C139C22⋊C412yes—
112C4⋊C4×C139C22⋊C412yes—
113C4⋊C4×C139C22⋊C412yes—
114C22⋊C4×C139—24no—
115C22⋊C4×C139—22no—
116C22⋊C4×C139—22no—
117C42×C139—24no—
118C42×C139—21no—
119C42×C139—21no—
120C42×C139C2×D412yes—
121C42×C139C2×D412yes—
122C23×C139—21no—
123C23×C139—21no—
124C23×C139—41no—
125C23×C139—41no—
126C23×C139#10112yes—
127C23×C139C2×C22⋊C411yescharacteristic
128Q8×C139—84no—
129Q8×C139—84no—
130C2×C4×C139—24no—
131C2×C4×C139—24no—
132C2×C4×C139—21no—
133C2×C4×C139—21no—
134C2×C4×C139—21no—
135C2×C4×C139—21no—
136C2×C4×C139—21no—
137C2×C4×C139—22no—
138C2×C4×C139—21no—
139C2×C4×C139—22no—
140C2×C4×C139—22no—
141C2×C4×C139—22no—
142C2×C4×C139—41no—
143C2×C4×C139—41no—
144C2×C4×C139—42no—
145C2×C4×C139—42no—
146C2×C4×C139—42no—
147C2×C4×C139—42no—
148C2×C4×C139—41no—
149C2×C4×C139—41no—
150C2×C4×C139—84no—
151C2×C4×C139#10112yes—
152C2×C4×C139C2×C22⋊C411yescharacteristic
153C2×C4×C139C2×C22⋊C411yescharacteristic
154C2×C4×C139#12012yes—
155C2×C4×C139#12012yes—
156C8×C139—82no—
157C8×C139—82no—
158C22×C139—21no—
159C22×C139—21no—
160C22×C139—22no—
161C22×C139—42no—
162C22×C139—42no—
163C22×C139—41no—
164C22×C139—41no—
165C22×C139#37911yescharacteristic
166C22×C139C2×#10111yescharacteristic
167C22×C139C2×#10111yescharacteristic
168C4×C139—22no—
169C4×C139—22no—
170C4×C139—22no—
171C4×C139—21no—
172C4×C139—21no—
173C4×C139—42no—
174C4×C139—42no—
175C4×C139—42no—
176C4×C139—41no—
177C4×C139—41no—
178C4×C139—42no—
179C2×C139—21no—
180C2×C139—21no—
181C2×C139—42no—
182C2×C139#178411yescharacteristic
183C2×C139#179511yescharacteristic
184C2×C139#179611yescharacteristic
185#8525C13911yesmaximal, characteristic, direct product factor, Sylow
186C139#852511yescharacteristic, direct product factor, Sylow
187C2×#544C2×C13911yescharacteristic
188#1556C2×C13912yescomplemented
189#1534C2×C13912yescomplemented
190#1464C2×C13911yescharacteristic
191#1464C2×C13911yescharacteristic
192#544—24no—
193#544—24no—
194C2×C4⋊Q8—21no—
195C2×C4⋊Q8C4×C13911yescharacteristic
196C2×C4⋊Q8C22×C13911yescharacteristic
197C2×#125—21no—
198C2×#125C4×C13911yescharacteristic
199C2×#125C22×C13911yescharacteristic
200C2×C22⋊Q8—21no—
201C2×C22⋊Q8—21no—
202C2×#117C4×C13911yescharacteristic
203C2×#117C22×C13911yescharacteristic
204C22×C4⋊C4C4×C13911yescharacteristic
205#432C22×C13912yes—
206#432C22×C13912yes—
207#332—24no—
208#330—24no—
209#324—21no—
210#324—21no—
211#323—21no—
212#323—21no—
213C22×Q8—21no—
214C22×Q8—21no—
215C23×C4—21no—
216C23×C4C2×C4×C13911yescharacteristic
217C4⋊Q8—28no—
218C4⋊Q8—22no—
219C4⋊Q8—22no—
220C4⋊Q8—22no—
221C4⋊Q8D4×C13914yes—
222#125—28no—
223#125—22no—
224#125—22no—
225#125—22no—
226#125D4×C13914yes—
227C22⋊Q8—28no—
228C22⋊Q8—28no—
229#117—22no—
230#117—22no—
231#117—22no—
232#117—22no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—22no—
241C2×C4⋊C4—22no—
242C2×C4⋊C4C2×C4×C13911yescharacteristic
243C2×C4⋊C4C2×C4×C13911yescharacteristic
244C2×C4⋊C4C2×C4×C13911yescharacteristic
245C2×C4⋊C4C2×C4×C13911yescharacteristic
246C2×C4⋊C4D4×C13911yescharacteristic
247C2×C4⋊C4D4×C13911yescharacteristic
248C2×C22⋊C4—21no—
249C2×C22⋊C4D4×C13911yescharacteristic
250C2×C22⋊C4D4×C13911yescharacteristic
251C2×C42—21no—
252C2×C42C2×C4×C13911yescharacteristic
253C2×C42C23×C13911yescharacteristic
254C4⋊C8—22no—
255C4⋊C8—22no—
256C22⋊C8—22no—
257C22⋊C8—22no—
258#97—22no—
259#97—22no—
260C24C22⋊C4×C13911yescharacteristic
261C2×Q8—24no—
262C2×Q8—24no—
263C2×Q8—82no—
264C2×Q8—82no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—24no—
274C22×C4—82no—
275C22×C4C22⋊C4×C13911yescharacteristic
276C22×C4C22⋊C4×C13911yescharacteristic
277C22×C4C22⋊C4×C13911yescharacteristic
278C22×C4C22×C4×C13911yescharacteristic
279C22×C4C2×D4×C13911yescharacteristic
280C22×C4C2×D4×C13911yescharacteristic
281C2×C8—42no—
282C2×C8—42no—
283C4⋊C4—24no—
284C4⋊C4—24no—
285C4⋊C4—24no—
286C4⋊C4—24no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—24no—
292C4⋊C4—24no—
293C4⋊C4—24no—
294C4⋊C4—22no—
295C4⋊C4—22no—
296C4⋊C4C22⋊C4×C13912yes—
297C4⋊C4C22⋊C4×C13912yes—
298C4⋊C4C22⋊C4×C13912yes—
299C4⋊C4C22⋊C4×C13912yes—
300C22⋊C4—24no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C42—24no—
304C42—21no—
305C42—21no—
306C42C2×D4×C13912yes—
307C42C2×D4×C13912yes—
308C23—21no—
309C23—21no—
310C23—41no—
311C23—41no—
312C23#101×C13912yes—
313C23C2×C22⋊C4×C13911yescharacteristic
314Q8—84no—
315Q8—84no—
316C2×C4—24no—
317C2×C4—24no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—84no—
337C2×C4#101×C13912yes—
338C2×C4C2×C22⋊C4×C13911yescharacteristic
339C2×C4C2×C22⋊C4×C13911yescharacteristic
340C2×C4#120×C13912yes—
341C2×C4#120×C13912yes—
342C8—82no—
343C8—82no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22—42no—
348C22—42no—
349C22—41no—
350C22—41no—
351C22#379×C13911yescharacteristic
352C22C2×#101×C13911yescharacteristic
353C22C2×#101×C13911yescharacteristic
354C4—22no—
355C4—21no—
356C4—21no—
357C4—22no—
358C4—22no—
359C4—42no—
360C4—42no—
361C4—42no—
362C4—41no—
363C4—42no—
364C4—41no—
365C2—21no—
366C2—21no—
367C2—42no—
368C2#1784×C13911yescharacteristic
369C2#1795×C13911yescharacteristic
370C2#1796×C13911yescharacteristic
subgroupG/H
center, socleC22×C139#379
commutatorC22×C4C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radicalC24×C139C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1556×C139C2semidirect
3. #1534×C139C2semidirect
185. #8525C139direct (N × H)
186. C139#8525direct (N × H)
188. #1556C2×C139semidirect
189. #1534C2×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#544×C1392
#1556×C1392
#1534×C1392
#1464×C1392
#8525139