Finite Group Databasebeta

← C137×#9546 #46858932

Subgroups — C137×#9546 #46858932

Order 35072.

444 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#1954×C137C211yesmaximal, characteristic
2#1770×C137C211yesmaximal, characteristic, complemented
3C4×#102×C137C211yesmaximal, characteristic
4C2×#334×C137C211yesmaximal, characteristic, complemented
5C2×D4⋊C8×C137C211yesmaximal, characteristic
6#1279×C137C211yesmaximal, characteristic, complemented
7#1273×C137C211yesmaximal, characteristic, complemented
8C2×C4×D4×C137C2211yescharacteristic
9C2×C4⋊C8×C137C2211yescharacteristic
10C2×C4⋊C8×C137C2211yescharacteristic
11C2×#102×C137C411yescharacteristic
12C2×#102×C137C411yescharacteristic
13C2×C22⋊C8×C137—21no—
14C2×C22⋊C8×C137—21no—
15C2×#97×C137—21no—
16C2×C4×C8×C137C2211yescharacteristic
17C2×C4×C8×C137C2211yescharacteristic
18C2×C4×C8×C137C2211yescharacteristic
19C4×C4⋊C4×C137C2211yescharacteristic
20#340×C137C411yescharacteristic
21#340×C137C411yescharacteristic
22#336×C137—21no—
23#334×C137—22no—
24D4⋊C8×C137—22no—
25C22×D4×C137C2×C411yescharacteristic
26C23×C4×C137—21no—
27C22×C8×C137—21no—
28C22×C8×C137—21no—
29C22×C8×C137—21no—
30C22×C8×C137C2×C411yescharacteristic
31C22×C8×C137C2×C411yescharacteristic
32C22×C8×C137D411yescharacteristic
33C22×C8×C137D411yescharacteristic
34C4×D4×C137—21no—
35C4×D4×C137—21no—
36C4×D4×C137—21no—
37C4×D4×C137—21no—
38C2×C4⋊C4×C137C2×C411yescharacteristic
39C2×C4⋊C4×C137C2×C411yescharacteristic
40C2×C4⋊C4×C137C2×C411yescharacteristic
41C2×C22⋊C4×C137—21no—
42C2×C42×C137—21no—
43C2×C42×C137C2311yescharacteristic
44C4⋊C8×C137—21no—
45C4⋊C8×C137—21no—
46C4⋊C8×C137—21no—
47C4⋊C8×C137D412yes—
48#102×C137—22no—
49#102×C137—22no—
50C22⋊C8×C137—42no—
51C22⋊C8×C137—42no—
52#97×C137—42no—
53C4×C8×C137—21no—
54C4×C8×C137—21no—
55C4×C8×C137—21no—
56C4×C8×C137—21no—
57C4×C8×C137—21no—
58C4×C8×C137—21no—
59#95×C137—21no—
60C24×C137—21no—
61C2×D4×C137—21no—
62C2×D4×C137—21no—
63C2×D4×C137—21no—
64C2×D4×C137—21no—
65C2×D4×C137—21no—
66C2×D4×C137M1612yes—
67C22×C4×C137—21no—
68C22×C4×C137—21no—
69C22×C4×C137—21no—
70C22×C4×C137—41no—
71C22×C4×C137—41no—
72C22×C4×C137—41no—
73C22×C4×C137—41no—
74C22×C4×C137—41no—
75C22×C4×C137—41no—
76C22×C4×C137C22×C411yescharacteristic
77C22×C4×C137C2×D411yescharacteristic
78C22×C4×C137#4111yescharacteristic
79C2×C8×C137—21no—
80C2×C8×C137—21no—
81C2×C8×C137—21no—
82C2×C8×C137—21no—
83C2×C8×C137—22no—
84C2×C8×C137—21no—
85C2×C8×C137—22no—
86C2×C8×C137—21no—
87C2×C8×C137—21no—
88C2×C8×C137—21no—
89C2×C8×C137—21no—
90C2×C8×C137—21no—
91C2×C8×C137—41no—
92C2×C8×C137—41no—
93C2×C8×C137—41no—
94C2×C8×C137—41no—
95C2×C8×C137—41no—
96C2×C8×C137—41no—
97C2×C8×C137—41no—
98C2×C8×C137M1612yes—
99C2×C8×C137SD1612yes—
100C4⋊C4×C137—21no—
101C4⋊C4×C137—21no—
102C4⋊C4×C137—21no—
103C4⋊C4×C137—21no—
104C4⋊C4×C137—21no—
105C4⋊C4×C137—21no—
106C22⋊C4×C137—41no—
107C22⋊C4×C137—41no—
108C42×C137—41no—
109C42×C137—41no—
110C42×C137C2×D411yescharacteristic
111C42×C137#4111yescharacteristic
112C42×C137#4111yescharacteristic
113C42×C137#4111yescharacteristic
114C23×C137—22no—
115C23×C137—41no—
116C23×C137—41no—
117C23×C137—41no—
118C23×C137—41no—
119C23×C137—41no—
120C23×C137—41no—
121C23×C137C4×D411yescharacteristic
122D4×C137—22no—
123D4×C137—22no—
124D4×C137—41no—
125D4×C137—41no—
126C2×C4×C137—21no—
127C2×C4×C137—21no—
128C2×C4×C137—41no—
129C2×C4×C137—41no—
130C2×C4×C137—41no—
131C2×C4×C137—41no—
132C2×C4×C137—41no—
133C2×C4×C137—41no—
134C2×C4×C137—41no—
135C2×C4×C137—41no—
136C2×C4×C137—41no—
137C2×C4×C137—81no—
138C2×C4×C137—81no—
139C2×C4×C137—81no—
140C2×C4×C137—81no—
141C2×C4×C137#11711yescharacteristic
142C2×C4×C137C4×D411yescharacteristic
143C2×C4×C137#12111yescharacteristic
144C2×C4×C137#12311yescharacteristic
145C2×C4×C137#12411yescharacteristic
146C2×C4×C137#12611yescharacteristic
147C2×C4×C137C2×M1611yescharacteristic
148C2×C4×C137C2×M1611yescharacteristic
149C2×C4×C137#13111yescharacteristic
150C2×C4×C137#13111yescharacteristic
151C2×C4×C137C2×SD1611yescharacteristic
152C2×C4×C137#13511yescharacteristic
153C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
155C8×C137—22no—
156C8×C137—22no—
157C8×C137—42no—
158C8×C137—41no—
159C8×C137—42no—
160C8×C137—41no—
161C8×C137—81no—
162C22×C137—42no—
163C22×C137—42no—
164C22×C137—42no—
165C22×C137—81no—
166C22×C137—81no—
167C22×C137—81no—
168C22×C137—81no—
169C22×C137#38811yescharacteristic
170C22×C137#43511yescharacteristic
171C22×C137#43611yescharacteristic
172C22×C137C4×SD1611yescharacteristic
173C22×C137#44211yescharacteristic
174C22×C137#44311yescharacteristic
175C22×C137#44411yescharacteristic
176C4×C137—21no—
177C4×C137—21no—
178C4×C137—81no—
179C4×C137—81no—
180C4×C137—81no—
181C4×C137#43211yescharacteristic
182C4×C137#43311yescharacteristic
183C4×C137#43511yescharacteristic
184C4×C137#43511yescharacteristic
185C4×C137#46011yescharacteristic
186C4×C137#46311yescharacteristic
187C4×C137#48111yescharacteristic
188C4×C137#48211yescharacteristic
189C2×C137—82no—
190C2×C137#158211yescharacteristic
191C2×C137#158611yescharacteristic
192C2×C137#159011yescharacteristic
193C2×C137#159411yescharacteristic
194C2×C137#192411yescharacteristic
195C2×C137#192611yescharacteristic
196C2×C137#192911yescharacteristic
197#9546C13711yesmaximal, characteristic, direct product factor, Sylow
198C137#954611yescharacteristic, direct product factor, Sylow
199#1954C2×C13711yescharacteristic
200#1770C2×C13711yescharacteristic, complemented
201C4×#102C2×C13711yescharacteristic
202C2×#334C2×C13711yescharacteristic, complemented
203C2×D4⋊C8C2×C13711yescharacteristic
204#1279C2×C13711yescharacteristic, complemented
205#1273C2×C13711yescharacteristic, complemented
206C2×C4×D4C22×C13711yescharacteristic
207C2×C4⋊C8C22×C13711yescharacteristic
208C2×C4⋊C8C22×C13711yescharacteristic
209C2×#102C4×C13711yescharacteristic
210C2×#102C4×C13711yescharacteristic
211C2×C22⋊C8—21no—
212C2×C22⋊C8—21no—
213C2×#97—21no—
214C2×C4×C8C22×C13711yescharacteristic
215C2×C4×C8C22×C13711yescharacteristic
216C2×C4×C8C22×C13711yescharacteristic
217C4×C4⋊C4C22×C13711yescharacteristic
218#340C4×C13711yescharacteristic
219#340C4×C13711yescharacteristic
220#336—21no—
221#334—22no—
222D4⋊C8—22no—
223C22×D4C2×C4×C13711yescharacteristic
224C23×C4—21no—
225C22×C8—21no—
226C22×C8—21no—
227C22×C8—21no—
228C22×C8C2×C4×C13711yescharacteristic
229C22×C8C2×C4×C13711yescharacteristic
230C22×C8D4×C13711yescharacteristic
231C22×C8D4×C13711yescharacteristic
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236C2×C4⋊C4C2×C4×C13711yescharacteristic
237C2×C4⋊C4C2×C4×C13711yescharacteristic
238C2×C4⋊C4C2×C4×C13711yescharacteristic
239C2×C22⋊C4—21no—
240C2×C42—21no—
241C2×C42C23×C13711yescharacteristic
242C4⋊C8—21no—
243C4⋊C8—21no—
244C4⋊C8—21no—
245C4⋊C8D4×C13712yes—
246#102—22no—
247#102—22no—
248C22⋊C8—42no—
249C22⋊C8—42no—
250#97—42no—
251C4×C8—21no—
252C4×C8—21no—
253C4×C8—21no—
254C4×C8—21no—
255C4×C8—21no—
256C4×C8—21no—
257#95—21no—
258C24—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4M16×C13712yes—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4C22×C4×C13711yescharacteristic
275C22×C4C2×D4×C13711yescharacteristic
276C22×C4#41×C13711yescharacteristic
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—21no—
283C2×C8—22no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—41no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8—41no—
296C2×C8M16×C13712yes—
297C2×C8SD16×C13712yes—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—21no—
303C4⋊C4—21no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C42—41no—
307C42—41no—
308C42C2×D4×C13711yescharacteristic
309C42#41×C13711yescharacteristic
310C42#41×C13711yescharacteristic
311C42#41×C13711yescharacteristic
312C23—22no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23C4×D4×C13711yescharacteristic
320D4—22no—
321D4—22no—
322D4—41no—
323D4—41no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4#117×C13711yescharacteristic
340C2×C4C4×D4×C13711yescharacteristic
341C2×C4#121×C13711yescharacteristic
342C2×C4#123×C13711yescharacteristic
343C2×C4#124×C13711yescharacteristic
344C2×C4#126×C13711yescharacteristic
345C2×C4C2×M16×C13711yescharacteristic
346C2×C4C2×M16×C13711yescharacteristic
347C2×C4#131×C13711yescharacteristic
348C2×C4#131×C13711yescharacteristic
349C2×C4C2×SD16×C13711yescharacteristic
350C2×C4#135×C13711yescharacteristic
351C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
352C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
353C8—22no—
354C8—22no—
355C8—42no—
356C8—41no—
357C8—42no—
358C8—41no—
359C8—81no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22#388×C13711yescharacteristic
368C22#435×C13711yescharacteristic
369C22#436×C13711yescharacteristic
370C22C4×SD16×C13711yescharacteristic
371C22#442×C13711yescharacteristic
372C22#443×C13711yescharacteristic
373C22#444×C13711yescharacteristic
374C4—21no—
375C4—21no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4#432×C13711yescharacteristic
380C4#433×C13711yescharacteristic
381C4#435×C13711yescharacteristic
382C4#435×C13711yescharacteristic
383C4#460×C13711yescharacteristic
384C4#463×C13711yescharacteristic
385C4#481×C13711yescharacteristic
386C4#482×C13711yescharacteristic
387C2—82no—
388C2#1582×C13711yescharacteristic
389C2#1586×C13711yescharacteristic
390C2#1590×C13711yescharacteristic
391C2#1594×C13711yescharacteristic
392C2#1924×C13711yescharacteristic
393C2#1926×C13711yescharacteristic
394C2#1929×C13711yescharacteristic
subgroupG/H
centerC22×C4×C137C2×D4
commutatorC22×C4C22×C4×C137
Frattini, cosocleC2×C42C23×C137
socleC23×C137C4×D4
prime radicalC22×D4×C137C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C137 ◁ C2×C4×C8×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1770×C137C2semidirect
4. C2×#334×C137C2semidirect
6. #1279×C137C2semidirect
7. #1273×C137C2semidirect
197. #9546C137direct (N × H)
198. C137#9546direct (N × H)
200. #1770C2×C137semidirect
202. C2×#334C2×C137semidirect
204. #1279C2×C137semidirect
205. #1273C2×C137semidirect

Maximal subgroups

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

subgroupindex
#1954×C1372
#1770×C1372
C4×#102×C1372
C2×#334×C1372
C2×D4⋊C8×C1372
#1279×C1372
#1273×C1372
#9546137