Finite Group Databasebeta

← C139×#8581 #48003177

Subgroups — C139×#8581 #48003177

Order 35584.

540 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#124×C139C211yesmaximal, characteristic
2#1767×C139C211yesmaximal, characteristic, complemented
3#1767×C139C211yesmaximal, characteristic, complemented
4C2×#329×C139C212yesmaximal
5#1295×C139C212yesmaximal, complemented
6C2×#124×C139C2211yescharacteristic
7C2×C4×Q8×C139C411yescharacteristic
8C2×C4×D4×C139C411yescharacteristic
9C2×C4⋊C8×C139—21no—
10C2×C4⋊C8×C139—21no—
11C2×#97×C139C2212yes—
12C2×#97×C139C2212yes—
13#391×C139C411yescharacteristic
14#390×C139C411yescharacteristic
15#388×C139—21no—
16#388×C139—21no—
17#382×C139C2211yescharacteristic
18C4×C22⋊C4×C139—21no—
19C4×C22⋊C4×C139—21no—
20C43×C139C2211yescharacteristic
21#336×C139—21no—
22#336×C139—21no—
23#329×C139—24no—
24C22×Q8×C139C2×C411yescharacteristic
25C22×D4×C139C2×C411yescharacteristic
26C23×C4×C139—21no—
27C22×C8×C139—22no—
28C22×C8×C139—22no—
29#124×C139—21no—
30#124×C139—21no—
31#124×C139D412yes—
32#124×C139Q812yes—
33C4×Q8×C139—42no—
34C4×D4×C139—42no—
35C2×C4⋊C4×C139—21no—
36C2×C4⋊C4×C139C2×C411yescharacteristic
37C2×C4⋊C4×C139C2×C411yescharacteristic
38C2×C22⋊C4×C139—21no—
39C2×C22⋊C4×C139—21no—
40C2×C22⋊C4×C139—21no—
41C2×C22⋊C4×C139—21no—
42C2×C22⋊C4×C139—21no—
43C2×C42×C139—21no—
44C2×C42×C139C2×C411yescharacteristic
45C2×C42×C139C2×C411yescharacteristic
46C2×C42×C139D411yescharacteristic
47C2×C42×C139D411yescharacteristic
48C2×C42×C139D411yescharacteristic
49C2×C42×C139D411yescharacteristic
50C2×C42×C139C2311yescharacteristic
51C4⋊C8×C139—24no—
52C4⋊C8×C139—24no—
53#97×C139—22no—
54#97×C139—22no—
55#97×C139—22no—
56#97×C139—22no—
57#95×C139—21no—
58#95×C139—21no—
59#95×C139—21no—
60#95×C139—21no—
61C24×C139—21no—
62C2×Q8×C139—21no—
63C2×Q8×C139—41no—
64C2×Q8×C139—41no—
65C2×Q8×C139C4⋊C412yes—
66C2×D4×C139—21no—
67C2×D4×C139—41no—
68C2×D4×C139—41no—
69C2×D4×C139C4⋊C412yes—
70C22×C4×C139—21no—
71C22×C4×C139—21no—
72C22×C4×C139—21no—
73C22×C4×C139—42no—
74C22×C4×C139—42no—
75C22×C4×C139—42no—
76C22×C4×C139C22⋊C411yescharacteristic
77C22×C4×C139C22⋊C411yescharacteristic
78C22×C4×C139C22⋊C411yescharacteristic
79C22×C4×C139C22⋊C411yescharacteristic
80C22×C4×C139C22×C411yescharacteristic
81C22×C4×C139C2×D411yescharacteristic
82C22×C4×C139C2×D411yescharacteristic
83C2×C8×C139—24no—
84C2×C8×C139—24no—
85C2×C8×C139—42no—
86C2×C8×C139—42no—
87C2×C8×C139—42no—
88C2×C8×C139—42no—
89C4⋊C4×C139—41no—
90C4⋊C4×C139—41no—
91C4⋊C4×C139—42no—
92C22⋊C4×C139—22no—
93C22⋊C4×C139—22no—
94C22⋊C4×C139—22no—
95C22⋊C4×C139—22no—
96C22⋊C4×C139—42no—
97C22⋊C4×C139—42no—
98C22⋊C4×C139—42no—
99C42×C139—22no—
100C42×C139—22no—
101C42×C139—22no—
102C42×C139—41no—
103C42×C139—41no—
104C42×C139—41no—
105C42×C139—42no—
106C42×C139C2×D411yescharacteristic
107C42×C139C2×Q811yescharacteristic
108C42×C139#4111yescharacteristic
109C42×C139#4111yescharacteristic
110C23×C139—22no—
111C23×C139—41no—
112C23×C139—41no—
113C23×C139—41no—
114C23×C139—41no—
115C23×C139—41no—
116C23×C139—41no—
117C23×C139C2×C22⋊C411yescharacteristic
118Q8×C139—42no—
119Q8×C139—42no—
120D4×C139—42no—
121D4×C139—42no—
122C2×C4×C139—21no—
123C2×C4×C139—21no—
124C2×C4×C139—21no—
125C2×C4×C139—21no—
126C2×C4×C139—21no—
127C2×C4×C139—21no—
128C2×C4×C139—21no—
129C2×C4×C139—21no—
130C2×C4×C139—21no—
131C2×C4×C139—21no—
132C2×C4×C139—21no—
133C2×C4×C139—21no—
134C2×C4×C139—22no—
135C2×C4×C139—21no—
136C2×C4×C139—21no—
137C2×C4×C139—21no—
138C2×C4×C139—41no—
139C2×C4×C139—41no—
140C2×C4×C139—41no—
141C2×C4×C139—41no—
142C2×C4×C139—41no—
143C2×C4×C139—41no—
144C2×C4×C139—41no—
145C2×C4×C139—41no—
146C2×C4×C139—84no—
147C2×C4×C139#10012yes—
148C2×C4×C139#10412yes—
149C2×C4×C139#10412yes—
150C2×C4×C139C2×C4⋊C411yescharacteristic
151C2×C4×C139#11711yescharacteristic
152C2×C4×C139#12111yescharacteristic
153C2×C4×C139#12111yescharacteristic
154C2×C4×C139C22⋊Q811yescharacteristic
155C2×C4×C139C22⋊Q811yescharacteristic
156C8×C139—44no—
157C8×C139—44no—
158C22×C139—42no—
159C22×C139—42no—
160C22×C139—42no—
161C22×C139—81no—
162C22×C139—81no—
163C22×C139—81no—
164C22×C139—81no—
165C22×C139#38011yescharacteristic
166C22×C139C2×#10011yescharacteristic
167C22×C139#41311yescharacteristic
168C22×C139C2×#10411yescharacteristic
169C22×C139C2×#10411yescharacteristic
170C22×C139#42111yescharacteristic
171C22×C139#42111yescharacteristic
172C4×C139—21no—
173C4×C139—21no—
174C4×C139—21no—
175C4×C139—21no—
176C4×C139—21no—
177C4×C139—21no—
178C4×C139—22no—
179C4×C139—22no—
180C4×C139—22no—
181C4×C139—42no—
182C4×C139—41no—
183C4×C139—81no—
184C4×C139—81no—
185C2×C139—82no—
186C2×C139#152411yescharacteristic
187C2×C139#152711yescharacteristic
188C2×C139#153011yescharacteristic
189C2×C139#153511yescharacteristic
190C2×C139#180011yescharacteristic
191C2×C139#180611yescharacteristic
192C2×C139#180611yescharacteristic
193#8581C13911yesmaximal, characteristic, direct product factor, Sylow
194C139#858111yescharacteristic, direct product factor, Sylow
195C4×#124C2×C13911yescharacteristic
196#1767C2×C13911yescharacteristic, complemented
197#1767C2×C13911yescharacteristic, complemented
198C2×#329C2×C13912yes—
199#1295C2×C13912yescomplemented
200C2×#124C22×C13911yescharacteristic
201C2×C4×Q8C4×C13911yescharacteristic
202C2×C4×D4C4×C13911yescharacteristic
203C2×C4⋊C8—21no—
204C2×C4⋊C8—21no—
205C2×#97C22×C13912yes—
206C2×#97C22×C13912yes—
207#391C4×C13911yescharacteristic
208#390C4×C13911yescharacteristic
209#388—21no—
210#388—21no—
211#382C22×C13911yescharacteristic
212C4×C22⋊C4—21no—
213C4×C22⋊C4—21no—
214C43C22×C13911yescharacteristic
215#336—21no—
216#336—21no—
217#329—24no—
218C22×Q8C2×C4×C13911yescharacteristic
219C22×D4C2×C4×C13911yescharacteristic
220C23×C4—21no—
221C22×C8—22no—
222C22×C8—22no—
223#124—21no—
224#124—21no—
225#124D4×C13912yes—
226#124Q8×C13912yes—
227C4×Q8—42no—
228C4×D4—42no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4C2×C4×C13911yescharacteristic
231C2×C4⋊C4C2×C4×C13911yescharacteristic
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C42—21no—
238C2×C42C2×C4×C13911yescharacteristic
239C2×C42C2×C4×C13911yescharacteristic
240C2×C42D4×C13911yescharacteristic
241C2×C42D4×C13911yescharacteristic
242C2×C42D4×C13911yescharacteristic
243C2×C42D4×C13911yescharacteristic
244C2×C42C23×C13911yescharacteristic
245C4⋊C8—24no—
246C4⋊C8—24no—
247#97—22no—
248#97—22no—
249#97—22no—
250#97—22no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—21no—
255C24—21no—
256C2×Q8—21no—
257C2×Q8—41no—
258C2×Q8—41no—
259C2×Q8C4⋊C4×C13912yes—
260C2×D4—21no—
261C2×D4—41no—
262C2×D4—41no—
263C2×D4C4⋊C4×C13912yes—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—42no—
268C22×C4—42no—
269C22×C4—42no—
270C22×C4C22⋊C4×C13911yescharacteristic
271C22×C4C22⋊C4×C13911yescharacteristic
272C22×C4C22⋊C4×C13911yescharacteristic
273C22×C4C22⋊C4×C13911yescharacteristic
274C22×C4C22×C4×C13911yescharacteristic
275C22×C4C2×D4×C13911yescharacteristic
276C22×C4C2×D4×C13911yescharacteristic
277C2×C8—24no—
278C2×C8—24no—
279C2×C8—42no—
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—42no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—42no—
286C22⋊C4—22no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—22no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C22⋊C4—42no—
293C42—22no—
294C42—22no—
295C42—22no—
296C42—41no—
297C42—41no—
298C42—41no—
299C42—42no—
300C42C2×D4×C13911yescharacteristic
301C42C2×Q8×C13911yescharacteristic
302C42#41×C13911yescharacteristic
303C42#41×C13911yescharacteristic
304C23—22no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23C2×C22⋊C4×C13911yescharacteristic
312Q8—42no—
313Q8—42no—
314D4—42no—
315D4—42no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—84no—
341C2×C4#100×C13912yes—
342C2×C4#104×C13912yes—
343C2×C4#104×C13912yes—
344C2×C4C2×C4⋊C4×C13911yescharacteristic
345C2×C4#117×C13911yescharacteristic
346C2×C4#121×C13911yescharacteristic
347C2×C4#121×C13911yescharacteristic
348C2×C4C22⋊Q8×C13911yescharacteristic
349C2×C4C22⋊Q8×C13911yescharacteristic
350C8—44no—
351C8—44no—
352C22—42no—
353C22—42no—
354C22—42no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22#380×C13911yescharacteristic
360C22C2×#100×C13911yescharacteristic
361C22#413×C13911yescharacteristic
362C22C2×#104×C13911yescharacteristic
363C22C2×#104×C13911yescharacteristic
364C22#421×C13911yescharacteristic
365C22#421×C13911yescharacteristic
366C4—22no—
367C4—22no—
368C4—22no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—41no—
376C4—42no—
377C4—81no—
378C4—81no—
379C2—82no—
380C2#1524×C13911yescharacteristic
381C2#1527×C13911yescharacteristic
382C2#1530×C13911yescharacteristic
383C2#1535×C13911yescharacteristic
384C2#1800×C13911yescharacteristic
385C2#1806×C13911yescharacteristic
386C2#1806×C13911yescharacteristic
subgroupG/H
center, socleC23×C139C2×C22⋊C4
commutatorC22×C4C22×C4×C139
Frattini, cosocleC2×C42C23×C139
prime radicalC22×D4×C139C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C139 ◁ C43×C139 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1767×C139C2semidirect
3. #1767×C139C2semidirect
5. #1295×C139C2semidirect
193. #8581C139direct (N × H)
194. C139#8581direct (N × H)
196. #1767C2×C139semidirect
197. #1767C2×C139semidirect
199. #1295C2×C139semidirect

Maximal subgroups

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

subgroupindex
C4×#124×C1392
#1767×C1392
C2×#329×C1392
#1295×C1392
#8581139