Finite Group Databasebeta

← C139×#35957 #48030553

Subgroups — C139×#35957 #48030553

Order 35584.

2000 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C139C211yesmaximal, characteristic
2C2×#557×C139C211yesmaximal, characteristic
3#2660×C139C213yesmaximal
4#2584×C139C213yesmaximal
5#2567×C139C213yesmaximal
6#2552×C139C216yesmaximal
7#2550×C139C216yesmaximal
8#2399×C139C213yesmaximal
9#2351×C139C212yesmaximal
10Q8×C4⋊C4×C139C212yesmaximal
11#2276×C139C211yesmaximal, characteristic
12#557×C139—28no—
13#557×C139—28no—
14C2×C4⋊Q8×C139C2213yes—
15C2×C4⋊Q8×C139C2213yes—
16C2×#125×C139C2216yes—
17C2×#125×C139C2213yes—
18C2×#125×C139C2213yes—
19C2×C4×Q8×C139C2213yes—
20C2×C4×Q8×C139C2213yes—
21C2×C4×Q8×C139C2211yescharacteristic
22C2×C4×Q8×C139C2212yes—
23C2×C4×Q8×C139C2211yescharacteristic
24C2×C4×Q8×C139C2211yescharacteristic
25C2×C4×Q8×C139C2212yes—
26#398×C139C22112yes—
27#398×C139C2216yes—
28#398×C139C2213yes—
29#398×C139C2211yescharacteristic
30#395×C139C2216yes—
31#395×C139C2213yes—
32#395×C139C2216yes—
33#395×C139C2213yes—
34#391×C139C2216yes—
35#389×C139C22112yes—
36#389×C139C2216yes—
37#389×C139C2216yes—
38#389×C139C2216yes—
39#389×C139C2216yes—
40#384×C139C2216yes—
41#384×C139C2216yes—
42#382×C139C2216yes—
43C4×C4⋊C4×C139C2216yes—
44C4×C4⋊C4×C139C2213yes—
45C4×C4⋊C4×C139C2216yes—
46C4×C4⋊C4×C139C2216yes—
47#376×C139C2213yes—
48C22×Q8×C139C2313yes—
49C22×Q8×C139C2313yes—
50C22×Q8×C139C2311yescharacteristic
51C4⋊Q8×C139—212no—
52C4⋊Q8×C139—212no—
53#125×C139—212no—
54#125×C139—224no—
55#125×C139—212no—
56C4×Q8×C139—28no—
57C4×Q8×C139—24no—
58C4×Q8×C139—24no—
59C4×Q8×C139—212no—
60C4×Q8×C139—212no—
61C4×Q8×C139D418yes—
62C4×Q8×C139Q8116yescomplemented
63C2×C4⋊C4×C139C2311yescharacteristic
64C2×C4⋊C4×C139C2313yes—
65C2×C4⋊C4×C139C2312yes—
66C2×C4⋊C4×C139C2316yes—
67C2×C4⋊C4×C139C2311yescharacteristic
68C2×C4⋊C4×C139C2313yes—
69C2×C4⋊C4×C139C2316yes—
70C2×C4⋊C4×C139C2316yes—
71C2×C4⋊C4×C139C2313yes—
72C2×C4⋊C4×C139C2313yes—
73C2×C4⋊C4×C139C2316yes—
74C2×C4⋊C4×C139C2316yes—
75C2×C4⋊C4×C139C2316yes—
76C2×C4⋊C4×C139C2316yes—
77C2×C4⋊C4×C139C23112yes—
78C2×C4⋊C4×C139C2313yes—
79C2×C4⋊C4×C139C2316yes—
80C2×C42×C139C2313yes—
81C2×C42×C139C2316yes—
82C2×C42×C139C2313yes—
83C2×C42×C139C2316yes—
84C2×C42×C139C2313yes—
85C2×C42×C139C2316yes—
86#95×C139C2311yescharacteristic
87#95×C139C2313yes—
88#95×C139C2316yes—
89#95×C139C2316yes—
90#95×C139C2316yes—
91#95×C139C23112yes—
92#95×C139C2312yes—
93#95×C139C2316yes—
94C2×Q8×C139—26no—
95C2×Q8×C139—26no—
96C2×Q8×C139—26no—
97C2×Q8×C139—43no—
98C2×Q8×C139—46no—
99C2×Q8×C139C2×D414yes—
100C2×Q8×C139C2×Q818yes—
101C22×C4×C139C2413yes—
102C22×C4×C139C2412yes—
103C22×C4×C139C2416yes—
104C22×C4×C139C2411yescharacteristic
105C22×C4×C139C2413yes—
106C22×C4×C139C2411yescharacteristic
107C22×C4×C139C2413yes—
108C22×C4×C139C2412yes—
109C22×C4×C139C2416yes—
110C22×C4×C139C2411yescharacteristic
111C22×C4×C139C2413yes—
112C4⋊C4×C139—22no—
113C4⋊C4×C139—22no—
114C4⋊C4×C139—26no—
115C4⋊C4×C139—212no—
116C4⋊C4×C139—26no—
117C4⋊C4×C139—26no—
118C4⋊C4×C139—26no—
119C4⋊C4×C139—212no—
120C4⋊C4×C139—212no—
121C4⋊C4×C139—212no—
122C4⋊C4×C139—24no—
123C4⋊C4×C139—46no—
124C4⋊C4×C139—46no—
125C4⋊C4×C139—46no—
126C4⋊C4×C139—412no—
127C4⋊C4×C139C2×D4112yes—
128C4⋊C4×C139C2×Q8124yes—
129C42×C139—26no—
130C42×C139—212no—
131C42×C139—26no—
132C42×C139—46no—
133C42×C139C2×D4112yes—
134C42×C139C2×Q8124yes—
135C23×C139C2511yescharacteristic
136Q8×C139—412no—
137Q8×C139—412no—
138Q8×C139C4⋊Q8116yes—
139C2×C4×C139—21no—
140C2×C4×C139—22no—
141C2×C4×C139—23no—
142C2×C4×C139—26no—
143C2×C4×C139—23no—
144C2×C4×C139—22no—
145C2×C4×C139—26no—
146C2×C4×C139—22no—
147C2×C4×C139—21no—
148C2×C4×C139—21no—
149C2×C4×C139—22no—
150C2×C4×C139—23no—
151C2×C4×C139—26no—
152C2×C4×C139—23no—
153C2×C4×C139—22no—
154C2×C4×C139—23no—
155C2×C4×C139—22no—
156C2×C4×C139—26no—
157C2×C4×C139—22no—
158C2×C4×C139—26no—
159C2×C4×C139—26no—
160C2×C4×C139—23no—
161C2×C4×C139C22×D412yes—
162C2×C4×C139C22×D416yes—
163C2×C4×C139C22×D416yes—
164C2×C4×C139C22×Q814yes—
165C2×C4×C139C22×Q8112yes—
166C2×C4×C139C22×Q8112yes—
167C2×C4×C1392−1+412yes—
168C22×C139C23×D411yescharacteristic
169C22×C139C23×Q812yes—
170C22×C139C2×2−1+411yescharacteristic
171C22×C139#58512yes—
172C22×C139#58511yescharacteristic
173C4×C139—22no—
174C4×C139—26no—
175C4×C139—22no—
176C4×C139—24no—
177C4×C139—212no—
178C4×C139—41no—
179C4×C139—43no—
180C4×C139—46no—
181C4×C139—42no—
182C4×C139—43no—
183C4×C139C2×C4⋊Q8112yes—
184C2×C139C22×C4⋊Q811yescharacteristic
185C2×C139#348711yescharacteristic
186C2×C139#348911yescharacteristic
187C2×C139#350212yes—
188C2×C139#350412yes—
189#35957C13911yesmaximal, characteristic, direct product factor, Sylow
190C139#3595711yescharacteristic, direct product factor, Sylow
191C2×#557C2×C13911yescharacteristic
192C2×#557C2×C13911yescharacteristic
193#2660C2×C13913yes—
194#2584C2×C13913yes—
195#2567C2×C13913yes—
196#2552C2×C13916yes—
197#2550C2×C13916yes—
198#2399C2×C13913yes—
199#2351C2×C13912yes—
200Q8×C4⋊C4C2×C13912yes—
201#2276C2×C13911yescharacteristic
202#557—28no—
203#557—28no—
204C2×C4⋊Q8C22×C13913yes—
205C2×C4⋊Q8C22×C13913yes—
206C2×#125C22×C13913yes—
207C2×#125C22×C13916yes—
208C2×#125C22×C13913yes—
209C2×C4×Q8C22×C13913yes—
210C2×C4×Q8C22×C13913yes—
211C2×C4×Q8C22×C13911yescharacteristic
212C2×C4×Q8C22×C13912yes—
213C2×C4×Q8C22×C13911yescharacteristic
214C2×C4×Q8C22×C13911yescharacteristic
215C2×C4×Q8C22×C13912yes—
216#398C22×C13913yes—
217#398C22×C13911yescharacteristic
218#398C22×C13916yes—
219#398C22×C139112yes—
220#395C22×C13913yes—
221#395C22×C13916yes—
222#395C22×C13913yes—
223#395C22×C13916yes—
224#391C22×C13916yes—
225#389C22×C13916yes—
226#389C22×C13916yes—
227#389C22×C13916yes—
228#389C22×C13916yes—
229#389C22×C139112yes—
230#384C22×C13916yes—
231#384C22×C13916yes—
232#382C22×C13916yes—
233C4×C4⋊C4C22×C13913yes—
234C4×C4⋊C4C22×C13916yes—
235C4×C4⋊C4C22×C13916yes—
236C4×C4⋊C4C22×C13916yes—
237#376C22×C13913yes—
238C22×Q8C23×C13913yes—
239C22×Q8C23×C13913yes—
240C22×Q8C23×C13911yescharacteristic
241C4⋊Q8—212no—
242C4⋊Q8—212no—
243#125—212no—
244#125—224no—
245#125—212no—
246C4×Q8—28no—
247C4×Q8—24no—
248C4×Q8—24no—
249C4×Q8—212no—
250C4×Q8—212no—
251C4×Q8D4×C13918yes—
252C4×Q8Q8×C139116yescomplemented
253C2×C4⋊C4C23×C13911yescharacteristic
254C2×C4⋊C4C23×C13911yescharacteristic
255C2×C4⋊C4C23×C13913yes—
256C2×C4⋊C4C23×C13913yes—
257C2×C4⋊C4C23×C13916yes—
258C2×C4⋊C4C23×C13913yes—
259C2×C4⋊C4C23×C13913yes—
260C2×C4⋊C4C23×C13916yes—
261C2×C4⋊C4C23×C13916yes—
262C2×C4⋊C4C23×C13916yes—
263C2×C4⋊C4C23×C13912yes—
264C2×C4⋊C4C23×C13916yes—
265C2×C4⋊C4C23×C13916yes—
266C2×C4⋊C4C23×C13916yes—
267C2×C4⋊C4C23×C139112yes—
268C2×C4⋊C4C23×C13913yes—
269C2×C4⋊C4C23×C13916yes—
270C2×C42C23×C13913yes—
271C2×C42C23×C13916yes—
272C2×C42C23×C13913yes—
273C2×C42C23×C13916yes—
274C2×C42C23×C13913yes—
275C2×C42C23×C13916yes—
276#95C23×C13911yescharacteristic
277#95C23×C13913yes—
278#95C23×C13916yes—
279#95C23×C13912yes—
280#95C23×C13916yes—
281#95C23×C13916yes—
282#95C23×C13916yes—
283#95C23×C139112yes—
284C2×Q8—26no—
285C2×Q8—26no—
286C2×Q8—26no—
287C2×Q8—43no—
288C2×Q8—46no—
289C2×Q8C2×D4×C13914yes—
290C2×Q8C2×Q8×C13918yes—
291C22×C4C24×C13913yes—
292C22×C4C24×C13912yes—
293C22×C4C24×C13916yes—
294C22×C4C24×C13911yescharacteristic
295C22×C4C24×C13913yes—
296C22×C4C24×C13911yescharacteristic
297C22×C4C24×C13913yes—
298C22×C4C24×C13912yes—
299C22×C4C24×C13916yes—
300C22×C4C24×C13911yescharacteristic
301C22×C4C24×C13913yes—
302C4⋊C4—22no—
303C4⋊C4—22no—
304C4⋊C4—26no—
305C4⋊C4—212no—
306C4⋊C4—26no—
307C4⋊C4—26no—
308C4⋊C4—26no—
309C4⋊C4—212no—
310C4⋊C4—212no—
311C4⋊C4—212no—
312C4⋊C4—24no—
313C4⋊C4—46no—
314C4⋊C4—46no—
315C4⋊C4—46no—
316C4⋊C4—412no—
317C4⋊C4C2×D4×C139112yes—
318C4⋊C4C2×Q8×C139124yes—
319C42—26no—
320C42—212no—
321C42—26no—
322C42—46no—
323C42C2×D4×C139112yes—
324C42C2×Q8×C139124yes—
325C23C25×C13911yescharacteristic
326Q8—412no—
327Q8—412no—
328Q8C4⋊Q8×C139116yes—
329C2×C4—21no—
330C2×C4—22no—
331C2×C4—23no—
332C2×C4—26no—
333C2×C4—23no—
334C2×C4—22no—
335C2×C4—26no—
336C2×C4—22no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—22no—
340C2×C4—23no—
341C2×C4—26no—
342C2×C4—23no—
343C2×C4—22no—
344C2×C4—23no—
345C2×C4—22no—
346C2×C4—26no—
347C2×C4—22no—
348C2×C4—26no—
349C2×C4—26no—
350C2×C4—23no—
351C2×C4C22×D4×C13912yes—
352C2×C4C22×D4×C13916yes—
353C2×C4C22×D4×C13916yes—
354C2×C4C22×Q8×C13914yes—
355C2×C4C22×Q8×C139112yes—
356C2×C4C22×Q8×C139112yes—
357C2×C42−1+4×C13912yes—
358C22C23×D4×C13911yescharacteristic
359C22C23×Q8×C13912yes—
360C22C2×2−1+4×C13911yescharacteristic
361C22#585×C13912yes—
362C22#585×C13911yescharacteristic
363C4—22no—
364C4—26no—
365C4—22no—
366C4—24no—
367C4—212no—
368C4—46no—
369C4—41no—
370C4—43no—
371C4—43no—
372C4—42no—
373C4C2×C4⋊Q8×C139112yes—
374C2C22×C4⋊Q8×C13911yescharacteristic
375C2#3487×C13911yescharacteristic
376C2#3489×C13911yescharacteristic
377C2#3502×C13912yes—
378C2#3504×C13912yes—
subgroupG/H
center, socle, prime radicalC23×C139C25
commutator, Frattini, cosocleC23C25×C139
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C139 ◁ G

Complements

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

NH ≅ G/Ntype
62. C4×Q8×C139Q8semidirect
189. #35957C139direct (N × H)
190. C139#35957direct (N × H)
252. C4×Q8Q8×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#557×C1392
#2660×C1392
#2584×C1392
#2567×C1392
#2552×C1392
#2550×C1392
#2399×C1392
#2351×C1392
Q8×C4⋊C4×C1392
#2276×C1392
#35957139