Finite Group Databasebeta

← C139×#12771 #48007367

Subgroups — C139×#12771 #48007367

Order 35584.

728 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 138 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#3550×C139C211yesmaximal, characteristic
2#2132×C139C211yesmaximal, characteristic
3#2123×C139C212yesmaximal, complemented
4#1915×C139C212yesmaximal, complemented
5#1884×C139C211yesmaximal, characteristic
6#568×C139C2211yescharacteristic
7#563×C139—21no—
8#563×C139C412yescomplemented
9#559×C139C412yescomplemented
10Q82×C139—21no—
11#556×C139—22no—
12D4×Q8×C139—22no—
13#542×C139—24no—
14#536×C139—21no—
15#536×C139C2212yes—
16#533×C139—21no—
17#532×C139C2211yescharacteristic
18#421×C139—21no—
19#413×C139C2212yes—
20C2×#101×C139—22no—
21#410×C139C2211yescharacteristic
22#356×C139—21no—
23#355×C139—21no—
24#352×C139—24no—
25#344×C139—22no—
26#339×C139—21no—
27C2×#41×C139D411yescharacteristic
28C2×#41×C139C2311yescharacteristic
29C22×Q8×C139—21no—
30C22×Q8×C139D412yes—
31#131×C139—42no—
32C2×M16×C139—22no—
33C2×M16×C139—21no—
34C2×M16×C139—22no—
35C4⋊Q8×C139—21no—
36C4⋊Q8×C139—21no—
37C4⋊Q8×C139—24no—
38C4⋊Q8×C139—22no—
39C4⋊Q8×C139—22no—
40C4⋊Q8×C139D411yescharacteristic
41#127×C139C2×C411yescharacteristic
42#126×C139—24no—
43#126×C139—24no—
44#125×C139—22no—
45#124×C139—22no—
46#124×C139—22no—
47#124×C139—24no—
48#124×C139C2×C411yescharacteristic
49#124×C139D411yescharacteristic
50#123×C139—22no—
51#123×C139—22no—
52#123×C139C2×C414yes—
53#123×C139D414yes—
54C22⋊Q8×C139—22no—
55C22⋊Q8×C139—22no—
56C22⋊Q8×C139—24no—
57C22⋊Q8×C139—24no—
58C22⋊Q8×C139—22no—
59C22⋊Q8×C139—22no—
60#121×C139—22no—
61C4×Q8×C139—22no—
62C4×Q8×C139—24no—
63C4×Q8×C139—22no—
64C4×D4×C139—24no—
65C4×D4×C139—22no—
66#117×C139—22no—
67#117×C139—21no—
68#117×C139—21no—
69#117×C139D412yes—
70C2×C42×C139D411yescharacteristic
71#104×C139—42no—
72#101×C139—22no—
73#101×C139—44no—
74#100×C139—22no—
75#99×C139—22no—
76#41×C139—41no—
77#41×C139—41no—
78#41×C139—41no—
79#41×C139—41no—
80C2×Q8×C139—22no—
81C2×Q8×C139—22no—
82C2×Q8×C139—22no—
83C2×Q8×C139—22no—
84C2×Q8×C139—42no—
85C2×Q8×C139—42no—
86C2×Q8×C139—81no—
87C2×Q8×C139—81no—
88C2×Q8×C139C22⋊C411yescharacteristic
89C2×Q8×C139C2×D411yescharacteristic
90C2×D4×C139—22no—
91C2×D4×C139—21no—
92C2×D4×C139C22⋊C411yescharacteristic
93C2×D4×C139C22×C411yescharacteristic
94C2×D4×C139C2×D412yes—
95C22×C4×C139—21no—
96C22×C4×C139—22no—
97C22×C4×C139—21no—
98C22×C4×C139C22⋊C414yes—
99C22×C4×C139C2×D411yescharacteristic
100C22×C4×C139C2×D412yes—
101M16×C139—24no—
102M16×C139—22no—
103M16×C139—41no—
104M16×C139—42no—
105M16×C139—42no—
106C2×C8×C139—41no—
107C2×C8×C139—42no—
108C2×C8×C139—42no—
109C4⋊C4×C139—22no—
110C4⋊C4×C139—22no—
111C4⋊C4×C139—22no—
112C4⋊C4×C139—24no—
113C4⋊C4×C139—24no—
114C4⋊C4×C139—24no—
115C4⋊C4×C139—22no—
116C4⋊C4×C139—24no—
117C4⋊C4×C139—22no—
118C4⋊C4×C139—41no—
119C22⋊C4×C139—22no—
120C22⋊C4×C139—24no—
121C22⋊C4×C139—22no—
122C22⋊C4×C139—24no—
123C22⋊C4×C139—24no—
124C22⋊C4×C139—22no—
125C22⋊C4×C139—41no—
126C22⋊C4×C139C22⋊C414yes—
127C42×C139—24no—
128C42×C139—22no—
129C42×C139—22no—
130C42×C139—21no—
131C42×C139—41no—
132C42×C139C22⋊C411yescharacteristic
133C42×C139C22⋊C411yescharacteristic
134C23×C139—21no—
135C23×C139C2×C22⋊C412yes—
136C23×C139#12011yescharacteristic
137Q8×C139—41no—
138Q8×C139—41no—
139Q8×C139—44no—
140Q8×C139—42no—
141Q8×C139—42no—
142Q8×C139—82no—
143Q8×C139—82no—
144D4×C139—41no—
145D4×C139—42no—
146D4×C139—41no—
147D4×C139—44no—
148D4×C139—81no—
149C2×C4×C139—21no—
150C2×C4×C139—21no—
151C2×C4×C139—22no—
152C2×C4×C139—21no—
153C2×C4×C139—22no—
154C2×C4×C139—24no—
155C2×C4×C139—21no—
156C2×C4×C139—21no—
157C2×C4×C139—24no—
158C2×C4×C139—42no—
159C2×C4×C139—41no—
160C2×C4×C139—41no—
161C2×C4×C139—44no—
162C2×C4×C139—82no—
163C2×C4×C139—81no—
164C2×C4×C139C2×C22⋊C411yescharacteristic
165C2×C4×C139#12012yes—
166C2×C4×C139#12011yescharacteristic
167C8×C139—42no—
168C8×C139—82no—
169C22×C139—22no—
170C22×C139—21no—
171C22×C139—41no—
172C22×C139—42no—
173C22×C139—42no—
174C22×C139—41no—
175C22×C139#37911yescharacteristic
176C4×C139—22no—
177C4×C139—22no—
178C4×C139—21no—
179C4×C139—41no—
180C4×C139—44no—
181C4×C139—41no—
182C4×C139—44no—
183C4×C139—161no—
184C4×C139B(4,𝔽2)11yescharacteristic
185C4×C139#45811yescharacteristic
186C2×C139—21no—
187C2×C139—41no—
188C2×C139—42no—
189C2×C139—81no—
190C2×C139#179011yescharacteristic
191#12771C13911yesmaximal, characteristic, direct product factor, Sylow
192C139#1277111yescharacteristic, direct product factor, Sylow
193#3550C2×C13911yescharacteristic
194#2132C2×C13911yescharacteristic
195#2123C2×C13912yescomplemented
196#1915C2×C13912yescomplemented
197#1884C2×C13911yescharacteristic
198#568C22×C13911yescharacteristic
199#563—21no—
200#563C4×C13912yescomplemented
201#559C4×C13912yescomplemented
202Q82—21no—
203#556—22no—
204D4×Q8—22no—
205#542—24no—
206#536—21no—
207#536C22×C13912yes—
208#533—21no—
209#532C22×C13911yescharacteristic
210#421—21no—
211#413C22×C13912yes—
212C2×#101—22no—
213#410C22×C13911yescharacteristic
214#356—21no—
215#355—21no—
216#352—24no—
217#344—22no—
218#339—21no—
219C2×#41D4×C13911yescharacteristic
220C2×#41C23×C13911yescharacteristic
221C22×Q8—21no—
222C22×Q8D4×C13912yes—
223#131—42no—
224C2×M16—21no—
225C2×M16—22no—
226C2×M16—22no—
227C4⋊Q8—21no—
228C4⋊Q8—21no—
229C4⋊Q8—24no—
230C4⋊Q8—22no—
231C4⋊Q8—22no—
232C4⋊Q8D4×C13911yescharacteristic
233#127C2×C4×C13911yescharacteristic
234#126—24no—
235#126—24no—
236#125—22no—
237#124—22no—
238#124—22no—
239#124—24no—
240#124C2×C4×C13911yescharacteristic
241#124D4×C13911yescharacteristic
242#123—22no—
243#123—22no—
244#123C2×C4×C13914yes—
245#123D4×C13914yes—
246C22⋊Q8—22no—
247C22⋊Q8—22no—
248C22⋊Q8—24no—
249C22⋊Q8—24no—
250C22⋊Q8—22no—
251C22⋊Q8—22no—
252#121—22no—
253C4×Q8—22no—
254C4×Q8—24no—
255C4×Q8—22no—
256C4×D4—24no—
257C4×D4—22no—
258#117—22no—
259#117—21no—
260#117—21no—
261#117D4×C13912yes—
262C2×C42D4×C13911yescharacteristic
263#104—42no—
264#101—22no—
265#101—44no—
266#100—22no—
267#99—22no—
268#41—41no—
269#41—41no—
270#41—41no—
271#41—41no—
272C2×Q8—22no—
273C2×Q8—22no—
274C2×Q8—22no—
275C2×Q8—22no—
276C2×Q8—42no—
277C2×Q8—42no—
278C2×Q8—81no—
279C2×Q8—81no—
280C2×Q8C22⋊C4×C13911yescharacteristic
281C2×Q8C2×D4×C13911yescharacteristic
282C2×D4—22no—
283C2×D4—21no—
284C2×D4C22⋊C4×C13911yescharacteristic
285C2×D4C22×C4×C13911yescharacteristic
286C2×D4C2×D4×C13912yes—
287C22×C4—21no—
288C22×C4—22no—
289C22×C4—21no—
290C22×C4C22⋊C4×C13914yes—
291C22×C4C2×D4×C13911yescharacteristic
292C22×C4C2×D4×C13912yes—
293M16—24no—
294M16—22no—
295M16—41no—
296M16—42no—
297M16—42no—
298C2×C8—41no—
299C2×C8—42no—
300C2×C8—42no—
301C4⋊C4—22no—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—24no—
305C4⋊C4—24no—
306C4⋊C4—24no—
307C4⋊C4—22no—
308C4⋊C4—22no—
309C4⋊C4—24no—
310C4⋊C4—41no—
311C22⋊C4—22no—
312C22⋊C4—24no—
313C22⋊C4—22no—
314C22⋊C4—24no—
315C22⋊C4—24no—
316C22⋊C4—22no—
317C22⋊C4—41no—
318C22⋊C4C22⋊C4×C13914yes—
319C42—24no—
320C42—22no—
321C42—21no—
322C42—22no—
323C42—41no—
324C42C22⋊C4×C13911yescharacteristic
325C42C22⋊C4×C13911yescharacteristic
326C23—21no—
327C23C2×C22⋊C4×C13912yes—
328C23#120×C13911yescharacteristic
329Q8—41no—
330Q8—41no—
331Q8—44no—
332Q8—42no—
333Q8—42no—
334Q8—82no—
335Q8—82no—
336D4—41no—
337D4—42no—
338D4—41no—
339D4—44no—
340D4—81no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—22no—
346C2×C4—24no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—24no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—44no—
354C2×C4—82no—
355C2×C4—81no—
356C2×C4C2×C22⋊C4×C13911yescharacteristic
357C2×C4#120×C13912yes—
358C2×C4#120×C13911yescharacteristic
359C8—42no—
360C8—82no—
361C22—22no—
362C22—21no—
363C22—41no—
364C22—42no—
365C22—42no—
366C22—41no—
367C22#379×C13911yescharacteristic
368C4—22no—
369C4—22no—
370C4—21no—
371C4—41no—
372C4—44no—
373C4—41no—
374C4—44no—
375C4—161no—
376C4B(4,𝔽2)×C13911yescharacteristic
377C4#458×C13911yescharacteristic
378C2—21no—
379C2—41no—
380C2—42no—
381C2—81no—
382C2#1790×C13911yescharacteristic
subgroupG/H
center, socleC2×C139#1790
commutatorC2×D4C22×C4×C139
Frattini, cosocleC2×#41C23×C139
prime radical#532×C139C22
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C139 ◁ C2×C4×C139 ◁ C2×#41×C139 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2123×C139C2semidirect
4. #1915×C139C2semidirect
8. #563×C139C4semidirect
9. #559×C139C4semidirect
191. #12771C139direct (N × H)
192. C139#12771direct (N × H)
195. #2123C2×C139semidirect
196. #1915C2×C139semidirect
200. #563C4×C139semidirect
201. #559C4×C139semidirect

Maximal subgroups

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

subgroupindex
#3550×C1392
#2132×C1392
#2123×C1392
#1915×C1392
#1884×C1392
#12771139