Finite Group Databasebeta

← C139×#33818 #48028414

Subgroups — C139×#33818 #48028414

Order 35584.

490 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3170×C139C211yesmaximal, characteristic, complemented
2#3168×C139C211yesmaximal, characteristic
3#2229×C139C212yesmaximal, complemented
4#2227×C139C211yesmaximal, characteristic, complemented
5#2226×C139C211yesmaximal, characteristic, complemented
6#2220×C139C212yesmaximal
7#2219×C139C212yesmaximal, complemented
8#2211×C139C212yesmaximal, complemented
9#2209×C139C211yesmaximal, characteristic, complemented
10#2208×C139C211yesmaximal, characteristic, complemented
11#2150×C139C211yesmaximal, characteristic, complemented
12#533×C139—21no—
13#529×C139—21no—
14C2×Q32×C139C2212yes—
15C2×SD32×C139C2212yes—
16C2×M32×C139C2212yes—
17#500×C139C2211yescharacteristic
18#499×C139C2211yescharacteristic
19#495×C139C2211yescharacteristic
20#494×C139C2211yescharacteristic
21#488×C139—21no—
22#487×C139—21no—
23#467×C139—21no—
24#467×C139C2211yescharacteristic
25#467×C139C2212yes—
26#466×C139C2211yescharacteristic
27#465×C139—21no—
28C4×Q16×C139—21no—
29C4×Q16×C139C2211yescharacteristic
30C4×Q16×C139C2212yes—
31C4×SD16×C139—21no—
32C4×D8×C139C2211yescharacteristic
33C2×C4×C8×C139C2211yescharacteristic
34#367×C139C2212yes—
35#366×C139C2212yes—
36C4⋊C16×C139C2211yescharacteristic
37C4⋊C16×C139C2211yescharacteristic
38C4⋊C16×C139C2212yes—
39#358×C139C2212yes—
40#358×C139C2212yes—
41#358×C139C2212yes—
42#357×C139C2212yes—
43C2×Q16×C139—21no—
44C2×Q16×C139C2312yes—
45C2×Q16×C139C2311yescharacteristic
46C2×SD16×C139—21no—
47C2×D8×C139C2311yescharacteristic
48C22×C8×C139D411yescharacteristic
49C22×C8×C139C2311yescharacteristic
50C4⋊Q8×C139—21no—
51C4⋊Q8×C139—21no—
52#126×C139—41no—
53#125×C139—21no—
54#125×C139—41no—
55#124×C139—21no—
56#123×C139—41no—
57C22⋊Q8×C139—21no—
58C22⋊Q8×C139—22no—
59C22⋊Q8×C139—41no—
60#121×C139—21no—
61C4×Q8×C139—21no—
62C4×Q8×C139—22no—
63C4×Q8×C139—41no—
64C4×D4×C139—21no—
65C4×D4×C139—41no—
66#117×C139—41no—
67#117×C139—41no—
68C2×C42×C139D411yescharacteristic
69Q32×C139—42no—
70SD32×C139—42no—
71M32×C139—42no—
72C2×C16×C139C2312yes—
73C2×C16×C139C2312yes—
74#107×C139—21no—
75#107×C139C2311yescharacteristic
76#107×C139C2311yescharacteristic
77#107×C139C2312yes—
78#106×C139—21no—
79#103×C139—21no—
80#103×C139—22no—
81#103×C139—21no—
82#103×C139—22no—
83#102×C139—21no—
84#102×C139—21no—
85C4×C8×C139D411yescharacteristic
86C4×C8×C139D411yescharacteristic
87C4×C8×C139C2311yescharacteristic
88C4×C8×C139C2311yescharacteristic
89C2×Q8×C139—21no—
90C2×Q8×C139—22no—
91C2×Q8×C139—41no—
92C2×D4×C139—21no—
93C2×D4×C139—41no—
94C22×C4×C139—41no—
95C22×C4×C139D811yescharacteristic
96C22×C4×C139D811yescharacteristic
97C22×C4×C139C2×D411yescharacteristic
98Q16×C139—22no—
99Q16×C139—21no—
100Q16×C139—22no—
101Q16×C139—21no—
102Q16×C139—42no—
103SD16×C139—42no—
104D8×C139—21no—
105D8×C139—21no—
106C2×C8×C139—21no—
107C2×C8×C139—21no—
108C2×C8×C139—41no—
109C2×C8×C139C2×D411yescharacteristic
110C2×C8×C139C2×D411yescharacteristic
111C2×C8×C139C2×D411yescharacteristic
112C2×C8×C139C2411yescharacteristic
113C4⋊C4×C139—21no—
114C4⋊C4×C139—21no—
115C4⋊C4×C139—22no—
116C4⋊C4×C139—41no—
117C4⋊C4×C139—41no—
118C4⋊C4×C139—41no—
119C4⋊C4×C139—41no—
120C4⋊C4×C139—41no—
121C4⋊C4×C139—42no—
122C4⋊C4×C139—41no—
123C4⋊C4×C139—42no—
124C4⋊C4×C139—41no—
125C22⋊C4×C139—42no—
126C22⋊C4×C139—41no—
127C22⋊C4×C139—41no—
128C22⋊C4×C139—41no—
129C22⋊C4×C139—41no—
130C22⋊C4×C139—41no—
131C42×C139—41no—
132C42×C139—42no—
133C42×C139D811yescharacteristic
134C42×C139D811yescharacteristic
135C42×C139C2×D411yescharacteristic
136C42×C139C2×D411yescharacteristic
137C16×C139—22no—
138C16×C139—22no—
139C23×C139—41no—
140C23×C139C2×D811yescharacteristic
141Q8×C139—42no—
142Q8×C139—41no—
143Q8×C139—41no—
144Q8×C139—42no—
145Q8×C139—82no—
146D4×C139—41no—
147D4×C139—41no—
148D4×C139—82no—
149C2×C4×C139—21no—
150C2×C4×C139—21no—
151C2×C4×C139—22no—
152C2×C4×C139—41no—
153C2×C4×C139—41no—
154C2×C4×C139—41no—
155C2×C4×C139—42no—
156C2×C4×C139—42no—
157C2×C4×C139—41no—
158C2×C4×C139—82no—
159C2×C4×C139C2×D811yescharacteristic
160C2×C4×C139C2×D811yescharacteristic
161C2×C4×C139C2×D811yescharacteristic
162C2×C4×C139C2×D811yescharacteristic
163C2×C4×C139C2×D811yescharacteristic
164C2×C4×C139C22×D411yescharacteristic
165C8×C139—21no—
166C8×C139—21no—
167C8×C139—21no—
168C8×C139H(5,𝔽2)11yescharacteristic
169C8×C1392−1+411yescharacteristic
170C22×C139—21no—
171C22×C139—21no—
172C22×C139—21no—
173C22×C139—81no—
174C22×C139—81no—
175C22×C139—81no—
176C22×C139C22×D811yescharacteristic
177C4×C139—21no—
178C4×C139—21no—
179C4×C139—21no—
180C4×C139—21no—
181C4×C139—81no—
182C4×C139—81no—
183C4×C139—82no—
184C4×C139—81no—
185C4×C139—82no—
186C4×C139#51012yes—
187C4×C139#53711yescharacteristic
188C4×C139#57511yescharacteristic
189C2×C139—41no—
190C2×C139—161no—
191C2×C139#324511yescharacteristic
192C2×C139C2×#51011yescharacteristic
193C2×C139#341411yescharacteristic
194#33818C13911yesmaximal, characteristic, direct product factor, Sylow
195C139#3381811yescharacteristic, direct product factor, Sylow
196#3170C2×C13911yescharacteristic, complemented
197#3168C2×C13911yescharacteristic
198#2229C2×C13912yescomplemented
199#2227C2×C13911yescharacteristic, complemented
200#2226C2×C13911yescharacteristic, complemented
201#2220C2×C13912yes—
202#2219C2×C13912yescomplemented
203#2211C2×C13912yescomplemented
204#2209C2×C13911yescharacteristic, complemented
205#2208C2×C13911yescharacteristic, complemented
206#2150C2×C13911yescharacteristic, complemented
207#533—21no—
208#529—21no—
209C2×Q32C22×C13912yes—
210C2×SD32C22×C13912yes—
211C2×M32C22×C13912yes—
212#500C22×C13911yescharacteristic
213#499C22×C13911yescharacteristic
214#495C22×C13911yescharacteristic
215#494C22×C13911yescharacteristic
216#488—21no—
217#487—21no—
218#467—21no—
219#467C22×C13911yescharacteristic
220#467C22×C13912yes—
221#466C22×C13911yescharacteristic
222#465—21no—
223C4×Q16—21no—
224C4×Q16C22×C13911yescharacteristic
225C4×Q16C22×C13912yes—
226C4×SD16—21no—
227C4×D8C22×C13911yescharacteristic
228C2×C4×C8C22×C13911yescharacteristic
229#367C22×C13912yes—
230#366C22×C13912yes—
231C4⋊C16C22×C13911yescharacteristic
232C4⋊C16C22×C13911yescharacteristic
233C4⋊C16C22×C13912yes—
234#358C22×C13912yes—
235#358C22×C13912yes—
236#358C22×C13912yes—
237#357C22×C13912yes—
238C2×Q16—21no—
239C2×Q16C23×C13912yes—
240C2×Q16C23×C13911yescharacteristic
241C2×SD16—21no—
242C2×D8C23×C13911yescharacteristic
243C22×C8D4×C13911yescharacteristic
244C22×C8C23×C13911yescharacteristic
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247#126—41no—
248#125—21no—
249#125—41no—
250#124—21no—
251#123—41no—
252C22⋊Q8—21no—
253C22⋊Q8—22no—
254C22⋊Q8—41no—
255#121—21no—
256C4×Q8—21no—
257C4×Q8—22no—
258C4×Q8—41no—
259C4×D4—21no—
260C4×D4—41no—
261#117—41no—
262#117—41no—
263C2×C42D4×C13911yescharacteristic
264Q32—42no—
265SD32—42no—
266M32—42no—
267C2×C16C23×C13912yes—
268C2×C16C23×C13912yes—
269#107—21no—
270#107C23×C13912yes—
271#107C23×C13911yescharacteristic
272#107C23×C13911yescharacteristic
273#106—21no—
274#103—21no—
275#103—22no—
276#103—21no—
277#103—22no—
278#102—21no—
279#102—21no—
280C4×C8D4×C13911yescharacteristic
281C4×C8D4×C13911yescharacteristic
282C4×C8C23×C13911yescharacteristic
283C4×C8C23×C13911yescharacteristic
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×D4—21no—
288C2×D4—41no—
289C22×C4—41no—
290C22×C4D8×C13911yescharacteristic
291C22×C4D8×C13911yescharacteristic
292C22×C4C2×D4×C13911yescharacteristic
293Q16—22no—
294Q16—21no—
295Q16—22no—
296Q16—21no—
297Q16—42no—
298SD16—42no—
299D8—21no—
300D8—21no—
301C2×C8—21no—
302C2×C8—21no—
303C2×C8—41no—
304C2×C8C2×D4×C13911yescharacteristic
305C2×C8C2×D4×C13911yescharacteristic
306C2×C8C2×D4×C13911yescharacteristic
307C2×C8C24×C13911yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—22no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—41no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—42no—
317C4⋊C4—41no—
318C4⋊C4—42no—
319C4⋊C4—41no—
320C22⋊C4—42no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—41no—
324C22⋊C4—41no—
325C22⋊C4—41no—
326C42—41no—
327C42—42no—
328C42D8×C13911yescharacteristic
329C42D8×C13911yescharacteristic
330C42C2×D4×C13911yescharacteristic
331C42C2×D4×C13911yescharacteristic
332C16—22no—
333C16—22no—
334C23—41no—
335C23C2×D8×C13911yescharacteristic
336Q8—42no—
337Q8—41no—
338Q8—41no—
339Q8—42no—
340Q8—82no—
341D4—41no—
342D4—41no—
343D4—82no—
344C2×C4—22no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—82no—
354C2×C4C2×D8×C13911yescharacteristic
355C2×C4C2×D8×C13911yescharacteristic
356C2×C4C2×D8×C13911yescharacteristic
357C2×C4C2×D8×C13911yescharacteristic
358C2×C4C2×D8×C13911yescharacteristic
359C2×C4C22×D4×C13911yescharacteristic
360C8—21no—
361C8—21no—
362C8—21no—
363C8H(5,𝔽2)×C13911yescharacteristic
364C82−1+4×C13911yescharacteristic
365C22—21no—
366C22—21no—
367C22—21no—
368C22—81no—
369C22—81no—
370C22—81no—
371C22C22×D8×C13911yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—81no—
377C4—81no—
378C4—82no—
379C4—81no—
380C4—82no—
381C4#510×C13912yes—
382C4#537×C13911yescharacteristic
383C4#575×C13911yescharacteristic
384C2—41no—
385C2—161no—
386C2#3245×C13911yescharacteristic
387C2C2×#510×C13911yescharacteristic
388C2#3414×C13911yescharacteristic
subgroupG/H
center, socleC22×C139C22×D8
commutator, Frattini, cosocleC2×C8C24×C139
prime radical#466×C139C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C139 ◁ C2×C42×C139 ◁ C2×C4×C8×C139 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3170×C139C2semidirect
3. #2229×C139C2semidirect
4. #2227×C139C2semidirect
5. #2226×C139C2semidirect
7. #2219×C139C2semidirect
8. #2211×C139C2semidirect
9. #2209×C139C2semidirect
10. #2208×C139C2semidirect
11. #2150×C139C2semidirect
194. #33818C139direct (N × H)
195. C139#33818direct (N × H)
196. #3170C2×C139semidirect
198. #2229C2×C139semidirect
199. #2227C2×C139semidirect
200. #2226C2×C139semidirect
202. #2219C2×C139semidirect
203. #2211C2×C139semidirect
204. #2209C2×C139semidirect
205. #2208C2×C139semidirect
206. #2150C2×C139semidirect

Maximal subgroups

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

subgroupindex
#3170×C1392
#3168×C1392
#2229×C1392
#2227×C1392
#2226×C1392
#2220×C1392
#2219×C1392
#2211×C1392
#2209×C1392
#2208×C1392
#2150×C1392
#33818139