Finite Group Databasebeta

← C139×#36466 #48031062

Subgroups — C139×#36466 #48031062

Order 35584.

2086 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#557×C139C212yesmaximal
2#2859×C139C213yesmaximal
3#2584×C139C216yesmaximal
4#2552×C139C213yesmaximal
5#2551×C139C213yesmaximal
6#2550×C139C216yesmaximal
7#2351×C139C212yesmaximal
8Q8×C4⋊C4×C139C211yesmaximal, characteristic
9Q8×C4⋊C4×C139C211yesmaximal, characteristic
10C4×C4⋊Q8×C139C213yesmaximal
11C42×Q8×C139C211yesmaximal, characteristic
12#557×C139—216no—
13C2×C4⋊Q8×C139C2216yes—
14C2×C4⋊Q8×C139C2213yes—
15C2×#125×C139C2216yes—
16C2×#125×C139C2216yes—
17C2×C4×Q8×C139C2216yes—
18C2×C4×Q8×C139C2212yes—
19C2×C4×Q8×C139C2212yes—
20C2×C4×Q8×C139C2211yescharacteristic
21C2×C4×Q8×C139C2211yescharacteristic
22C2×C4×Q8×C139C2211yescharacteristic
23#398×C139C22112yes—
24#395×C139C22112yes—
25#391×C139C2216yes—
26#389×C139C2216yes—
27#389×C139C2216yes—
28#389×C139C2216yes—
29#389×C139C2216yes—
30#389×C139C2216yes—
31#389×C139C2216yes—
32#389×C139C2211yescharacteristic
33#389×C139C2216yes—
34#389×C139C2213yes—
35#389×C139C2216yes—
36#384×C139C2213yes—
37#384×C139C2213yes—
38#384×C139C2213yes—
39#382×C139C2216yes—
40C4×C4⋊C4×C139C2213yes—
41C4×C4⋊C4×C139C2213yes—
42C4×C4⋊C4×C139C2213yes—
43C4×C4⋊C4×C139C2216yes—
44C4×C4⋊C4×C139C2213yes—
45C4×C4⋊C4×C139C2213yes—
46C43×C139C2213yes—
47C22×Q8×C139C2316yes—
48C22×Q8×C139C2311yescharacteristic
49C4⋊Q8×C139—224no—
50C4⋊Q8×C139—212no—
51#125×C139—224no—
52#125×C139—224no—
53C4×Q8×C139—28no—
54C4×Q8×C139—28no—
55C4×Q8×C139—224no—
56C4×Q8×C139D418yes—
57C4×Q8×C139Q818yescomplemented
58C4×Q8×C139Q818yescomplemented
59C2×C4⋊C4×C139C2316yes—
60C2×C4⋊C4×C139C23112yes—
61C2×C4⋊C4×C139C2316yes—
62C2×C4⋊C4×C139C2312yes—
63C2×C4⋊C4×C139C2316yes—
64C2×C4⋊C4×C139C2316yes—
65C2×C4⋊C4×C139C2316yes—
66C2×C4⋊C4×C139C2313yes—
67C2×C4⋊C4×C139C2311yescharacteristic
68C2×C4⋊C4×C139C2313yes—
69C2×C4⋊C4×C139C2316yes—
70C2×C4⋊C4×C139C2316yes—
71C2×C4⋊C4×C139C2316yes—
72C2×C4⋊C4×C139C2313yes—
73C2×C4⋊C4×C139C2313yes—
74C2×C4⋊C4×C139C2313yes—
75C2×C4⋊C4×C139C2311yescharacteristic
76C2×C42×C139C2316yes—
77C2×C42×C139C2316yes—
78C2×C42×C139C2313yes—
79C2×C42×C139C2311yescharacteristic
80C2×C42×C139C2313yes—
81C2×C42×C139C2313yes—
82C2×C42×C139C2313yes—
83C2×C42×C139C2313yes—
84C2×C42×C139C2313yes—
85#95×C139C2316yes—
86#95×C139C2316yes—
87#95×C139C23112yes—
88#95×C139C2316yes—
89#95×C139C2312yes—
90#95×C139C2316yes—
91C2×Q8×C139—212no—
92C2×Q8×C139—212no—
93C2×Q8×C139—46no—
94C2×Q8×C139C2×D414yes—
95C2×Q8×C139C2×Q814yes—
96C2×Q8×C139C2×Q814yes—
97C22×C4×C139C2412yes—
98C22×C4×C139C2416yes—
99C22×C4×C139C2416yes—
100C22×C4×C139C2413yes—
101C22×C4×C139C2411yescharacteristic
102C22×C4×C139C2411yescharacteristic
103C22×C4×C139C2413yes—
104C22×C4×C139C2413yes—
105C22×C4×C139C2412yes—
106C22×C4×C139C2413yes—
107C22×C4×C139C2411yescharacteristic
108C4⋊C4×C139—24no—
109C4⋊C4×C139—212no—
110C4⋊C4×C139—212no—
111C4⋊C4×C139—212no—
112C4⋊C4×C139—212no—
113C4⋊C4×C139—224no—
114C4⋊C4×C139—212no—
115C4⋊C4×C139—26no—
116C4⋊C4×C139—22no—
117C4⋊C4×C139—26no—
118C4⋊C4×C139—46no—
119C4⋊C4×C139—46no—
120C4⋊C4×C139—46no—
121C4⋊C4×C139C2×D4112yes—
122C4⋊C4×C139C2×Q8112yes—
123C4⋊C4×C139C2×Q8112yes—
124C4⋊C4×C139#4114yes—
125C42×C139—212no—
126C42×C139—212no—
127C42×C139—26no—
128C42×C139—22no—
129C42×C139—43no—
130C42×C139—43no—
131C42×C139C2×D4112yes—
132C42×C139C2×Q8112yes—
133C42×C139C2×Q8112yes—
134C23×C139C2511yescharacteristic
135Q8×C139—424no—
136Q8×C139C4⋊Q8116yescomplemented
137C2×C4×C139—22no—
138C2×C4×C139—23no—
139C2×C4×C139—23no—
140C2×C4×C139—21no—
141C2×C4×C139—21no—
142C2×C4×C139—21no—
143C2×C4×C139—21no—
144C2×C4×C139—23no—
145C2×C4×C139—23no—
146C2×C4×C139—23no—
147C2×C4×C139—23no—
148C2×C4×C139—22no—
149C2×C4×C139—22no—
150C2×C4×C139—26no—
151C2×C4×C139—26no—
152C2×C4×C139—26no—
153C2×C4×C139—22no—
154C2×C4×C139—26no—
155C2×C4×C139—22no—
156C2×C4×C139—26no—
157C2×C4×C139—26no—
158C2×C4×C139C22×D412yes—
159C2×C4×C139C22×D416yes—
160C2×C4×C139C22×D416yes—
161C2×C4×C139C22×Q812yes—
162C2×C4×C139C22×Q816yes—
163C2×C4×C139C22×Q816yes—
164C2×C4×C139C22×Q816yes—
165C2×C4×C139C22×Q816yes—
166C2×C4×C139C22×Q812yes—
167C2×C4×C139C2×#4114yes—
168C2×C4×C139C2×#4112yes—
169C2×C4×C1392−1+412yes—
170C22×C139C23×D411yescharacteristic
171C22×C139C23×Q811yescharacteristic
172C22×C139C23×Q811yescharacteristic
173C22×C139C22×#4111yescharacteristic
174C22×C139C2×2−1+411yescharacteristic
175C22×C139#58511yescharacteristic
176C22×C139#58511yescharacteristic
177C4×C139—26no—
178C4×C139—24no—
179C4×C139—26no—
180C4×C139—22no—
181C4×C139—22no—
182C4×C139—26no—
183C4×C139—46no—
184C4×C139—42no—
185C4×C139—46no—
186C4×C139C2×C4⋊Q8112yes—
187C4×C139#55714yescomplemented
188C2×C139C22×C4⋊Q811yescharacteristic
189C2×C139D4×#4111yescharacteristic
190C2×C139C2×#55711yescharacteristic
191C2×C139Q8×#4111yescharacteristic
192C2×C139#349711yescharacteristic
193C2×C139#350211yescharacteristic
194C2×C139#350411yescharacteristic
195#36466C13911yesmaximal, characteristic, direct product factor, Sylow
196C139#3646611yescharacteristic, direct product factor, Sylow
197C2×#557C2×C13912yes—
198#2859C2×C13913yes—
199#2584C2×C13916yes—
200#2552C2×C13913yes—
201#2551C2×C13913yes—
202#2550C2×C13916yes—
203#2351C2×C13912yes—
204Q8×C4⋊C4C2×C13911yescharacteristic
205Q8×C4⋊C4C2×C13911yescharacteristic
206C4×C4⋊Q8C2×C13913yes—
207C42×Q8C2×C13911yescharacteristic
208#557—216no—
209C2×C4⋊Q8C22×C13913yes—
210C2×C4⋊Q8C22×C13916yes—
211C2×#125C22×C13916yes—
212C2×#125C22×C13916yes—
213C2×C4×Q8C22×C13916yes—
214C2×C4×Q8C22×C13912yes—
215C2×C4×Q8C22×C13912yes—
216C2×C4×Q8C22×C13911yescharacteristic
217C2×C4×Q8C22×C13911yescharacteristic
218C2×C4×Q8C22×C13911yescharacteristic
219#398C22×C139112yes—
220#395C22×C139112yes—
221#391C22×C13916yes—
222#389C22×C13911yescharacteristic
223#389C22×C13916yes—
224#389C22×C13913yes—
225#389C22×C13916yes—
226#389C22×C13916yes—
227#389C22×C13916yes—
228#389C22×C13916yes—
229#389C22×C13916yes—
230#389C22×C13916yes—
231#389C22×C13916yes—
232#384C22×C13913yes—
233#384C22×C13913yes—
234#384C22×C13913yes—
235#382C22×C13916yes—
236C4×C4⋊C4C22×C13913yes—
237C4×C4⋊C4C22×C13913yes—
238C4×C4⋊C4C22×C13916yes—
239C4×C4⋊C4C22×C13913yes—
240C4×C4⋊C4C22×C13913yes—
241C4×C4⋊C4C22×C13913yes—
242C43C22×C13913yes—
243C22×Q8C23×C13916yes—
244C22×Q8C23×C13911yescharacteristic
245C4⋊Q8—224no—
246C4⋊Q8—212no—
247#125—224no—
248#125—224no—
249C4×Q8—28no—
250C4×Q8—28no—
251C4×Q8—224no—
252C4×Q8D4×C13918yes—
253C4×Q8Q8×C13918yescomplemented
254C4×Q8Q8×C13918yescomplemented
255C2×C4⋊C4C23×C13912yes—
256C2×C4⋊C4C23×C13916yes—
257C2×C4⋊C4C23×C13916yes—
258C2×C4⋊C4C23×C13916yes—
259C2×C4⋊C4C23×C13916yes—
260C2×C4⋊C4C23×C139112yes—
261C2×C4⋊C4C23×C13913yes—
262C2×C4⋊C4C23×C13916yes—
263C2×C4⋊C4C23×C13911yescharacteristic
264C2×C4⋊C4C23×C13913yes—
265C2×C4⋊C4C23×C13916yes—
266C2×C4⋊C4C23×C13916yes—
267C2×C4⋊C4C23×C13916yes—
268C2×C4⋊C4C23×C13913yes—
269C2×C4⋊C4C23×C13913yes—
270C2×C4⋊C4C23×C13913yes—
271C2×C4⋊C4C23×C13911yescharacteristic
272C2×C42C23×C13916yes—
273C2×C42C23×C13916yes—
274C2×C42C23×C13913yes—
275C2×C42C23×C13911yescharacteristic
276C2×C42C23×C13913yes—
277C2×C42C23×C13913yes—
278C2×C42C23×C13913yes—
279C2×C42C23×C13913yes—
280C2×C42C23×C13913yes—
281#95C23×C13912yes—
282#95C23×C13916yes—
283#95C23×C13916yes—
284#95C23×C13916yes—
285#95C23×C13916yes—
286#95C23×C139112yes—
287C2×Q8—212no—
288C2×Q8—212no—
289C2×Q8—46no—
290C2×Q8C2×D4×C13914yes—
291C2×Q8C2×Q8×C13914yes—
292C2×Q8C2×Q8×C13914yes—
293C22×C4C24×C13912yes—
294C22×C4C24×C13916yes—
295C22×C4C24×C13916yes—
296C22×C4C24×C13913yes—
297C22×C4C24×C13911yescharacteristic
298C22×C4C24×C13911yescharacteristic
299C22×C4C24×C13913yes—
300C22×C4C24×C13913yes—
301C22×C4C24×C13912yes—
302C22×C4C24×C13913yes—
303C22×C4C24×C13911yescharacteristic
304C4⋊C4—24no—
305C4⋊C4—212no—
306C4⋊C4—212no—
307C4⋊C4—212no—
308C4⋊C4—212no—
309C4⋊C4—224no—
310C4⋊C4—212no—
311C4⋊C4—26no—
312C4⋊C4—22no—
313C4⋊C4—26no—
314C4⋊C4—46no—
315C4⋊C4—46no—
316C4⋊C4—46no—
317C4⋊C4C2×D4×C139112yes—
318C4⋊C4C2×Q8×C139112yes—
319C4⋊C4C2×Q8×C139112yes—
320C4⋊C4#41×C13914yes—
321C42—212no—
322C42—212no—
323C42—26no—
324C42—22no—
325C42—43no—
326C42—43no—
327C42C2×D4×C139112yes—
328C42C2×Q8×C139112yes—
329C42C2×Q8×C139112yes—
330C23C25×C13911yescharacteristic
331Q8—424no—
332Q8C4⋊Q8×C139116yescomplemented
333C2×C4—22no—
334C2×C4—23no—
335C2×C4—23no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—23no—
341C2×C4—23no—
342C2×C4—23no—
343C2×C4—23no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—26no—
347C2×C4—26no—
348C2×C4—26no—
349C2×C4—22no—
350C2×C4—26no—
351C2×C4—22no—
352C2×C4—26no—
353C2×C4—26no—
354C2×C4C22×D4×C13912yes—
355C2×C4C22×D4×C13916yes—
356C2×C4C22×D4×C13916yes—
357C2×C4C22×Q8×C13912yes—
358C2×C4C22×Q8×C13916yes—
359C2×C4C22×Q8×C13916yes—
360C2×C4C22×Q8×C13916yes—
361C2×C4C22×Q8×C13916yes—
362C2×C4C22×Q8×C13912yes—
363C2×C4C2×#41×C13914yes—
364C2×C4C2×#41×C13912yes—
365C2×C42−1+4×C13912yes—
366C22C23×D4×C13911yescharacteristic
367C22C23×Q8×C13911yescharacteristic
368C22C23×Q8×C13911yescharacteristic
369C22C22×#41×C13911yescharacteristic
370C22C2×2−1+4×C13911yescharacteristic
371C22#585×C13911yescharacteristic
372C22#585×C13911yescharacteristic
373C4—26no—
374C4—24no—
375C4—26no—
376C4—22no—
377C4—22no—
378C4—26no—
379C4—46no—
380C4—42no—
381C4—46no—
382C4C2×C4⋊Q8×C139112yes—
383C4#557×C13914yescomplemented
384C2C22×C4⋊Q8×C13911yescharacteristic
385C2D4×#41×C13911yescharacteristic
386C2C2×#557×C13911yescharacteristic
387C2Q8×#41×C13911yescharacteristic
388C2#3497×C13911yescharacteristic
389C2#3502×C13911yescharacteristic
390C2#3504×C13911yescharacteristic
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
57. C4×Q8×C139Q8semidirect
58. C4×Q8×C139Q8semidirect
136. Q8×C139C4⋊Q8semidirect
187. C4×C139#557semidirect
195. #36466C139direct (N × H)
196. C139#36466direct (N × H)
253. C4×Q8Q8×C139semidirect
254. C4×Q8Q8×C139semidirect
332. Q8C4⋊Q8×C139semidirect
383. C4#557×C139semidirect

Maximal subgroups

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

subgroupindex
C2×#557×C1392
#2859×C1392
#2584×C1392
#2552×C1392
#2551×C1392
#2550×C1392
#2351×C1392
Q8×C4⋊C4×C1392
C4×C4⋊Q8×C1392
C42×Q8×C1392
#36466139