Finite Group Databasebeta

← C137×#10160 #46859546

Subgroups — C137×#10160 #46859546

Order 35072.

578 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3205×C137C211yesmaximal, characteristic
2#3141×C137C211yesmaximal, characteristic, complemented
3C2×#486×C137C211yesmaximal, characteristic, complemented
4#1965×C137C211yesmaximal, characteristic, complemented
5#1548×C137C211yesmaximal, characteristic, complemented
6#1492×C137C211yesmaximal, characteristic, complemented
7#1278×C137C211yesmaximal, characteristic, complemented
8#532×C137C2211yescharacteristic
9C2×C4⋊Q8×C137C2211yescharacteristic
10C2×#127×C137C2211yescharacteristic
11#493×C137—21no—
12#489×C137—22no—
13#487×C137—21no—
14#486×C137—22no—
15#486×C137—21no—
16#486×C137—21no—
17#486×C137—22no—
18#459×C137—22no—
19#447×C137—22no—
20#431×C137C2211yescharacteristic
21#423×C137C2211yescharacteristic
22#417×C137—22no—
23C2×#102×C137—22no—
24C2×#100×C137—22no—
25C4×M16×C137C2211yescharacteristic
26C2×C4×C8×C137C2211yescharacteristic
27#333×C137—22no—
28D4⋊C8×C137—22no—
29C2×#41×C137—21no—
30C22×Q8×C137—21no—
31C22×D4×C137—21no—
32C22×D4×C137—21no—
33C22×D4×C137D412yes—
34C2×D8×C137—24no—
35C2×M16×C137—21no—
36C2×M16×C137D412yes—
37C22×C8×C137—21no—
38C4⋊Q8×C137—21no—
39C4⋊Q8×C137—21no—
40C4⋊Q8×C137—21no—
41C4⋊Q8×C137D411yescharacteristic
42C4⋊Q8×C137D412yes—
43#127×C137—21no—
44#127×C137—21no—
45#127×C137—21no—
46#127×C137—21no—
47#127×C137D411yescharacteristic
48#124×C137—21no—
49#121×C137—21no—
50#121×C137—21no—
51C4×D4×C137—21no—
52C4×D4×C137—21no—
53C2×C4⋊C4×C137—21no—
54C2×C4⋊C4×C137—21no—
55C2×C42×C137C2311yescharacteristic
56C4⋊C8×C137—21no—
57C4⋊C8×C137—21no—
58C4⋊C8×C137D412yes—
59#103×C137—24no—
60#102×C137—28no—
61#102×C137—24no—
62#102×C137—24no—
63#100×C137—44no—
64C22⋊C8×C137—21no—
65#97×C137—21no—
66C4×C8×C137—21no—
67C4×C8×C137—21no—
68C4×C8×C137—21no—
69C4×C8×C137D412yes—
70C24×C137—22no—
71#41×C137—42no—
72#41×C137—42no—
73C2×Q8×C137—21no—
74C2×Q8×C137—22no—
75C2×Q8×C137—41no—
76C2×Q8×C137—82no—
77C2×D4×C137—21no—
78C2×D4×C137—22no—
79C2×D4×C137—22no—
80C2×D4×C137—21no—
81C2×D4×C137—21no—
82C2×D4×C137—44no—
83C2×D4×C137—41no—
84C2×D4×C137—41no—
85C2×D4×C137—41no—
86C2×D4×C137—41no—
87C2×D4×C137—41no—
88C2×D4×C137—42no—
89C2×D4×C137—42no—
90C2×D4×C137—82no—
91C22×C4×C137—41no—
92C22×C4×C137—41no—
93C22×C4×C137C2×D411yescharacteristic
94C22×C4×C137C2×D411yescharacteristic
95C22×C4×C137#4111yescharacteristic
96D8×C137—84no—
97M16×C137—22no—
98M16×C137—22no—
99M16×C137—42no—
100C2×C8×C137—22no—
101C2×C8×C137—22no—
102C2×C8×C137—22no—
103C2×C8×C137—42no—
104C2×C8×C137—41no—
105C4⋊C4×C137—22no—
106C4⋊C4×C137—21no—
107C4⋊C4×C137—22no—
108C4⋊C4×C137—21no—
109C4⋊C4×C137—41no—
110C4⋊C4×C137—41no—
111C22⋊C4×C137—41no—
112C22⋊C4×C137—41no—
113C42×C137C2×D411yescharacteristic
114C42×C137C2×D411yescharacteristic
115C42×C137C2×D411yescharacteristic
116C42×C137C2×D411yescharacteristic
117C23×C137—41no—
118C23×C137—42no—
119C23×C137—44no—
120C23×C137—82no—
121C23×C137—82no—
122C23×C137#12111yescharacteristic
123Q8×C137—42no—
124Q8×C137—82no—
125Q8×C137—82no—
126D4×C137—44no—
127D4×C137—42no—
128D4×C137—42no—
129D4×C137—44no—
130D4×C137—42no—
131D4×C137—82no—
132D4×C137—82no—
133D4×C137—82no—
134D4×C137—82no—
135D4×C137—81no—
136D4×C137—81no—
137C2×C4×C137—22no—
138C2×C4×C137—22no—
139C2×C4×C137—41no—
140C2×C4×C137—42no—
141C2×C4×C137—82no—
142C2×C4×C137—81no—
143C2×C4×C137—81no—
144C2×C4×C137#12011yescharacteristic
145C2×C4×C137#12011yescharacteristic
146C2×C4×C137#12011yescharacteristic
147C2×C4×C137#12111yescharacteristic
148C2×C4×C137#12111yescharacteristic
149C2×C4×C137#12711yescharacteristic
150C2×C4×C137#13512yes—
151C2×C4×C137AGL(1,ℤ/8)12yes—
152C8×C137—42no—
153C8×C137—42no—
154C8×C137—42no—
155C8×C137—81no—
156C22×C137—21no—
157C22×C137—21no—
158C22×C137—82no—
159C22×C137—81no—
160C22×C137—81no—
161C22×C137—82no—
162C22×C137—81no—
163C22×C137—82no—
164C22×C137—164no—
165C22×C137#39211yescharacteristic
166C22×C137#46312yes—
167C4×C137—21no—
168C4×C137—21no—
169C4×C137—81no—
170C4×C137—82no—
171C4×C137#44912yes—
172C4×C137#45512yes—
173C4×C137#47212yes—
174C4×C137#49511yescharacteristic
175C4×C137#49611yescharacteristic
176C2×C137—22no—
177C2×C137—161no—
178C2×C137—162no—
179C2×C137#200411yescharacteristic
180C2×C137#201211yescharacteristic
181C2×C137#201811yescharacteristic
182#10160C13711yesmaximal, characteristic, direct product factor, Sylow
183C137#1016011yescharacteristic, direct product factor, Sylow
184#3205C2×C13711yescharacteristic
185#3141C2×C13711yescharacteristic, complemented
186C2×#486C2×C13711yescharacteristic, complemented
187#1965C2×C13711yescharacteristic, complemented
188#1548C2×C13711yescharacteristic, complemented
189#1492C2×C13711yescharacteristic, complemented
190#1278C2×C13711yescharacteristic, complemented
191#532C22×C13711yescharacteristic
192C2×C4⋊Q8C22×C13711yescharacteristic
193C2×#127C22×C13711yescharacteristic
194#493—21no—
195#489—22no—
196#487—21no—
197#486—22no—
198#486—21no—
199#486—21no—
200#486—22no—
201#459—22no—
202#447—22no—
203#431C22×C13711yescharacteristic
204#423C22×C13711yescharacteristic
205#417—22no—
206C2×#102—22no—
207C2×#100—22no—
208C4×M16C22×C13711yescharacteristic
209C2×C4×C8C22×C13711yescharacteristic
210#333—22no—
211D4⋊C8—22no—
212C2×#41—21no—
213C22×Q8—21no—
214C22×D4—21no—
215C22×D4—21no—
216C22×D4D4×C13712yes—
217C2×D8—24no—
218C2×M16—21no—
219C2×M16D4×C13712yes—
220C22×C8—21no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—21no—
224C4⋊Q8D4×C13712yes—
225C4⋊Q8D4×C13711yescharacteristic
226#127—21no—
227#127—21no—
228#127—21no—
229#127—21no—
230#127D4×C13711yescharacteristic
231#124—21no—
232#121—21no—
233#121—21no—
234C4×D4—21no—
235C4×D4—21no—
236C2×C4⋊C4—21no—
237C2×C4⋊C4—21no—
238C2×C42C23×C13711yescharacteristic
239C4⋊C8—21no—
240C4⋊C8—21no—
241C4⋊C8D4×C13712yes—
242#103—24no—
243#102—28no—
244#102—24no—
245#102—24no—
246#100—44no—
247C22⋊C8—21no—
248#97—21no—
249C4×C8—21no—
250C4×C8—21no—
251C4×C8—21no—
252C4×C8D4×C13712yes—
253C24—22no—
254#41—42no—
255#41—42no—
256C2×Q8—21no—
257C2×Q8—22no—
258C2×Q8—41no—
259C2×Q8—82no—
260C2×D4—21no—
261C2×D4—22no—
262C2×D4—22no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—44no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—82no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4C2×D4×C13711yescharacteristic
277C22×C4C2×D4×C13711yescharacteristic
278C22×C4#41×C13711yescharacteristic
279D8—84no—
280M16—22no—
281M16—22no—
282M16—42no—
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—22no—
286C2×C8—42no—
287C2×C8—41no—
288C4⋊C4—22no—
289C4⋊C4—21no—
290C4⋊C4—22no—
291C4⋊C4—21no—
292C4⋊C4—41no—
293C4⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—41no—
296C42C2×D4×C13711yescharacteristic
297C42C2×D4×C13711yescharacteristic
298C42C2×D4×C13711yescharacteristic
299C42C2×D4×C13711yescharacteristic
300C23—41no—
301C23—42no—
302C23—44no—
303C23—82no—
304C23—82no—
305C23#121×C13711yescharacteristic
306Q8—42no—
307Q8—82no—
308Q8—82no—
309D4—44no—
310D4—42no—
311D4—42no—
312D4—44no—
313D4—42no—
314D4—82no—
315D4—82no—
316D4—82no—
317D4—82no—
318D4—81no—
319D4—81no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—41no—
323C2×C4—42no—
324C2×C4—82no—
325C2×C4—81no—
326C2×C4—81no—
327C2×C4#120×C13711yescharacteristic
328C2×C4#120×C13711yescharacteristic
329C2×C4#120×C13711yescharacteristic
330C2×C4#121×C13711yescharacteristic
331C2×C4#121×C13711yescharacteristic
332C2×C4#127×C13711yescharacteristic
333C2×C4#135×C13712yes—
334C2×C4AGL(1,ℤ/8)×C13712yes—
335C8—42no—
336C8—42no—
337C8—42no—
338C8—81no—
339C22—21no—
340C22—21no—
341C22—81no—
342C22—82no—
343C22—82no—
344C22—81no—
345C22—81no—
346C22—82no—
347C22—164no—
348C22#392×C13711yescharacteristic
349C22#463×C13712yes—
350C4—21no—
351C4—21no—
352C4—82no—
353C4—81no—
354C4#449×C13712yes—
355C4#455×C13712yes—
356C4#472×C13712yes—
357C4#495×C13711yescharacteristic
358C4#496×C13711yescharacteristic
359C2—22no—
360C2—162no—
361C2—161no—
362C2#2004×C13711yescharacteristic
363C2#2012×C13711yescharacteristic
364C2#2018×C13711yescharacteristic
subgroupG/H
center, socleC22×C137#392
commutator, Frattini, cosocleC2×C42C23×C137
prime radical#3205×C137C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #3141×C137C2semidirect
3. C2×#486×C137C2semidirect
4. #1965×C137C2semidirect
5. #1548×C137C2semidirect
6. #1492×C137C2semidirect
7. #1278×C137C2semidirect
182. #10160C137direct (N × H)
183. C137#10160direct (N × H)
185. #3141C2×C137semidirect
186. C2×#486C2×C137semidirect
187. #1965C2×C137semidirect
188. #1548C2×C137semidirect
189. #1492C2×C137semidirect
190. #1278C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3205×C1372
#3141×C1372
C2×#486×C1372
#1965×C1372
#1548×C1372
#1492×C1372
#1278×C1372
#10160137