Finite Group Databasebeta

← C137×#9910 #46859296

Subgroups — C137×#9910 #46859296

Order 35072.

640 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2851×C137C211yesmaximal, characteristic
2#1797×C137C211yesmaximal, characteristic
3C4×#95×C137C211yesmaximal, characteristic
4#1294×C137C212yesmaximal
5#1294×C137C212yesmaximal
6C2×#125×C137C411yescharacteristic, complemented
7C22×C42×C137—21no—
8C22×C42×C137C2211yescharacteristic
9C2×C4⋊C8×C137—21no—
10C2×C22⋊C8×C137C2212yes—
11#389×C137C411yescharacteristic, complemented
12#389×C137C411yescharacteristic, complemented
13#387×C137—21no—
14#387×C137—21no—
15#385×C137—21no—
16#385×C137—21no—
17#382×C137C411yescharacteristic, complemented
18#380×C137C2211yescharacteristic
19#380×C137C2211yescharacteristic
20C2×#95×C137—21no—
21C2×#95×C137C2212yes—
22#336×C137—21no—
23C23×C4×C137—22no—
24C23×C4×C137D411yescharacteristic
25C23×C4×C137D411yescharacteristic
26C23×C4×C137C2311yescharacteristic
27C22×C8×C137—22no—
28#125×C137—42no—
29C2×C4⋊C4×C137—21no—
30C2×C4⋊C4×C137—21no—
31C2×C4⋊C4×C137—21no—
32C2×C4⋊C4×C137—21no—
33C2×C4⋊C4×C137C2×C411yescharacteristic
34C2×C4⋊C4×C137C2×C411yescharacteristic
35C2×C4⋊C4×C137C2×C411yescharacteristic
36C2×C4⋊C4×C137C2×C411yescharacteristic
37C2×C22⋊C4×C137—21no—
38C2×C22⋊C4×C137—21no—
39C2×C42×C137—24no—
40C2×C42×C137—42no—
41C2×C42×C137—42no—
42C2×C42×C137—42no—
43C2×C42×C137C2×C411yescharacteristic
44C2×C42×C137C2×C411yescharacteristic
45C2×C42×C137D411yescharacteristic
46C2×C42×C137D411yescharacteristic
47C4⋊C8×C137—42no—
48C22⋊C8×C137—24no—
49#95×C137—24no—
50#95×C137—21no—
51#95×C137—21no—
52#95×C137—21no—
53#95×C137—21no—
54#95×C137—21no—
55#95×C137—21no—
56#95×C137—22no—
57#95×C137Q814yes—
58C24×C137C2×D411yescharacteristic
59C22×C4×C137—21no—
60C22×C4×C137—21no—
61C22×C4×C137—22no—
62C22×C4×C137—22no—
63C22×C4×C137—24no—
64C22×C4×C137—24no—
65C22×C4×C137—24no—
66C22×C4×C137—22no—
67C22×C4×C137—22no—
68C22×C4×C137—21no—
69C22×C4×C137—21no—
70C22×C4×C137—21no—
71C22×C4×C137—21no—
72C22×C4×C137—41no—
73C22×C4×C137—41no—
74C22×C4×C137—41no—
75C22×C4×C137—42no—
76C22×C4×C137—42no—
77C22×C4×C137—42no—
78C22×C4×C137—42no—
79C22×C4×C137C22⋊C411yescharacteristic
80C22×C4×C137C22⋊C411yescharacteristic
81C22×C4×C137C22⋊C411yescharacteristic
82C22×C4×C137C22⋊C411yescharacteristic
83C22×C4×C137C22×C411yescharacteristic
84C22×C4×C137C2×D411yescharacteristic
85C22×C4×C137C2×Q812yes—
86C22×C4×C137#4112yes—
87C2×C8×C137—42no—
88C2×C8×C137—42no—
89C2×C8×C137—42no—
90C4⋊C4×C137—41no—
91C4⋊C4×C137—41no—
92C4⋊C4×C137—41no—
93C4⋊C4×C137—41no—
94C4⋊C4×C137—42no—
95C4⋊C4×C137—42no—
96C4⋊C4×C137—42no—
97C4⋊C4×C137—42no—
98C22⋊C4×C137—42no—
99C22⋊C4×C137—41no—
100C22⋊C4×C137—41no—
101C42×C137—22no—
102C42×C137—22no—
103C42×C137—41no—
104C42×C137—41no—
105C42×C137—48no—
106C23×C137—21no—
107C23×C137—21no—
108C23×C137—21no—
109C23×C137—21no—
110C23×C137C2×C22⋊C411yescharacteristic
111C23×C137C22⋊Q812yes—
112C23×C137#13512yes—
113C23×C137AGL(1,ℤ/8)11yescharacteristic
114C23×C137#13711yescharacteristic
115C2×C4×C137—24no—
116C2×C4×C137—24no—
117C2×C4×C137—21no—
118C2×C4×C137—21no—
119C2×C4×C137—21no—
120C2×C4×C137—21no—
121C2×C4×C137—21no—
122C2×C4×C137—21no—
123C2×C4×C137—21no—
124C2×C4×C137—21no—
125C2×C4×C137—21no—
126C2×C4×C137—21no—
127C2×C4×C137—28no—
128C2×C4×C137—21no—
129C2×C4×C137—21no—
130C2×C4×C137—21no—
131C2×C4×C137—42no—
132C2×C4×C137—42no—
133C2×C4×C137—44no—
134C2×C4×C137—44no—
135C2×C4×C137—44no—
136C2×C4×C137—44no—
137C2×C4×C137—44no—
138C2×C4×C137—44no—
139C2×C4×C137—44no—
140C2×C4×C137—41no—
141C2×C4×C137—41no—
142C2×C4×C137—41no—
143C2×C4×C137—41no—
144C2×C4×C137—41no—
145C2×C4×C137—41no—
146C2×C4×C137—41no—
147C2×C4×C137—41no—
148C2×C4×C137—41no—
149C2×C4×C137—41no—
150C2×C4×C137—41no—
151C2×C4×C137—41no—
152C2×C4×C137#9912yes—
153C2×C4×C137#10412yes—
154C2×C4×C137#10412yes—
155C2×C4×C137C4×Q812yes—
156C2×C4×C137#12411yescharacteristic
157C2×C4×C137C4⋊Q811yescharacteristic
158C8×C137—82no—
159C22×C137—22no—
160C22×C137—22no—
161C22×C137—22no—
162C22×C137—22no—
163C22×C137—21no—
164C22×C137—21no—
165C22×C137—21no—
166C22×C137—21no—
167C22×C137#39111yescharacteristic
168C22×C137C2×#9911yescharacteristic
169C22×C137#41011yescharacteristic
170C22×C137#41611yescharacteristic
171C22×C137#41711yescharacteristic
172C22×C137C2×#10411yescharacteristic
173C22×C137C2×#10411yescharacteristic
174C22×C137#47812yes—
175C22×C137#47912yes—
176C4×C137—21no—
177C4×C137—22no—
178C4×C137—21no—
179C4×C137—22no—
180C4×C137—22no—
181C4×C137—22no—
182C4×C137—48no—
183C4×C137—41no—
184C4×C137—81no—
185C4×C137—81no—
186C4×C137—81no—
187C4×C137—81no—
188C2×C137—22no—
189C2×C137—22no—
190C2×C137#150011yescharacteristic
191C2×C137#150111yescharacteristic
192C2×C137#150411yescharacteristic
193C2×C137#150911yescharacteristic
194C2×C137#198911yescharacteristic
195C2×C137#199411yescharacteristic
196C2×C137#199611yescharacteristic
197#9910C13711yesmaximal, characteristic, direct product factor, Sylow
198C137#991011yescharacteristic, direct product factor, Sylow
199#2851C2×C13711yescharacteristic
200#1797C2×C13711yescharacteristic
201C4×#95C2×C13711yescharacteristic
202#1294C2×C13712yes—
203#1294C2×C13712yes—
204C2×#125C4×C13711yescharacteristic, complemented
205C22×C42—21no—
206C22×C42C22×C13711yescharacteristic
207C2×C4⋊C8—21no—
208C2×C22⋊C8C22×C13712yes—
209#389C4×C13711yescharacteristic, complemented
210#389C4×C13711yescharacteristic, complemented
211#387—21no—
212#387—21no—
213#385—21no—
214#385—21no—
215#382C4×C13711yescharacteristic, complemented
216#380C22×C13711yescharacteristic
217#380C22×C13711yescharacteristic
218C2×#95—21no—
219C2×#95C22×C13712yes—
220#336—21no—
221C23×C4—22no—
222C23×C4D4×C13711yescharacteristic
223C23×C4D4×C13711yescharacteristic
224C23×C4C23×C13711yescharacteristic
225C22×C8—22no—
226#125—42no—
227C2×C4⋊C4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4C2×C4×C13711yescharacteristic
232C2×C4⋊C4C2×C4×C13711yescharacteristic
233C2×C4⋊C4C2×C4×C13711yescharacteristic
234C2×C4⋊C4C2×C4×C13711yescharacteristic
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C42—24no—
238C2×C42—42no—
239C2×C42—42no—
240C2×C42—42no—
241C2×C42C2×C4×C13711yescharacteristic
242C2×C42C2×C4×C13711yescharacteristic
243C2×C42D4×C13711yescharacteristic
244C2×C42D4×C13711yescharacteristic
245C4⋊C8—42no—
246C22⋊C8—24no—
247#95—24no—
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95—21no—
253#95—21no—
254#95—22no—
255#95Q8×C13714yes—
256C24C2×D4×C13711yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—24no—
262C22×C4—24no—
263C22×C4—24no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—42no—
274C22×C4—42no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4C22⋊C4×C13711yescharacteristic
278C22×C4C22⋊C4×C13711yescharacteristic
279C22×C4C22⋊C4×C13711yescharacteristic
280C22×C4C22⋊C4×C13711yescharacteristic
281C22×C4C22×C4×C13711yescharacteristic
282C22×C4C2×D4×C13711yescharacteristic
283C22×C4C2×Q8×C13712yes—
284C22×C4#41×C13712yes—
285C2×C8—42no—
286C2×C8—42no—
287C2×C8—42no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—42no—
293C4⋊C4—42no—
294C4⋊C4—42no—
295C4⋊C4—42no—
296C22⋊C4—42no—
297C22⋊C4—41no—
298C22⋊C4—41no—
299C42—22no—
300C42—22no—
301C42—41no—
302C42—41no—
303C42—48no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23C2×C22⋊C4×C13711yescharacteristic
309C23C22⋊Q8×C13712yes—
310C23#135×C13712yes—
311C23AGL(1,ℤ/8)×C13711yescharacteristic
312C23#137×C13711yescharacteristic
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—21no—
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—28no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—44no—
334C2×C4—44no—
335C2×C4—44no—
336C2×C4—44no—
337C2×C4—44no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4#99×C13712yes—
351C2×C4#104×C13712yes—
352C2×C4#104×C13712yes—
353C2×C4C4×Q8×C13712yes—
354C2×C4#124×C13711yescharacteristic
355C2×C4C4⋊Q8×C13711yescharacteristic
356C8—82no—
357C22—22no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—22no—
364C22—22no—
365C22#391×C13711yescharacteristic
366C22C2×#99×C13711yescharacteristic
367C22#410×C13711yescharacteristic
368C22#416×C13711yescharacteristic
369C22#417×C13711yescharacteristic
370C22C2×#104×C13711yescharacteristic
371C22C2×#104×C13711yescharacteristic
372C22#478×C13712yes—
373C22#479×C13712yes—
374C4—22no—
375C4—22no—
376C4—22no—
377C4—21no—
378C4—22no—
379C4—21no—
380C4—48no—
381C4—41no—
382C4—81no—
383C4—81no—
384C4—81no—
385C4—81no—
386C2—22no—
387C2—22no—
388C2#1500×C13711yescharacteristic
389C2#1501×C13711yescharacteristic
390C2#1504×C13711yescharacteristic
391C2#1509×C13711yescharacteristic
392C2#1989×C13711yescharacteristic
393C2#1994×C13711yescharacteristic
394C2#1996×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C2×C22⋊C4
commutatorC22×C4C22×C4×C137
Frattini, cosocleC23×C4C23×C137
prime radicalC24×C137C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C137 ◁ C22×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×#125×C137C4semidirect
11. #389×C137C4semidirect
12. #389×C137C4semidirect
17. #382×C137C4semidirect
197. #9910C137direct (N × H)
198. C137#9910direct (N × H)
204. C2×#125C4×C137semidirect
209. #389C4×C137semidirect
210. #389C4×C137semidirect
215. #382C4×C137semidirect

Maximal subgroups

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

subgroupindex
#2851×C1372
#1797×C1372
C4×#95×C1372
#1294×C1372
#9910137