Finite Group Databasebeta

← C137×#8989 #46858375

Subgroups — C137×#8989 #46858375

Order 35072.

540 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3101×C137C211yesmaximal, characteristic
2D4×M16×C137C211yesmaximal, characteristic
3#1986×C137C211yesmaximal, characteristic, complemented
4C4×#102×C137C211yesmaximal, characteristic
5#1493×C137C211yesmaximal, characteristic, complemented
6#1303×C137C211yesmaximal, characteristic, complemented
7#1278×C137C211yesmaximal, characteristic, complemented
8C22×M16×C137—21no—
9#533×C137C2211yescharacteristic
10C2×C4×D4×C137C2211yescharacteristic
11#483×C137—21no—
12#476×C137C411yescharacteristic, complemented
13#476×C137C411yescharacteristic, complemented
14#461×C137C411yescharacteristic, complemented
15#461×C137C411yescharacteristic, complemented
16#450×C137—21no—
17C4×SD16×C137—21no—
18C4×SD16×C137—21no—
19#436×C137—21no—
20#435×C137—22no—
21C8×D4×C137—21no—
22#431×C137C2211yescharacteristic
23#423×C137C2211yescharacteristic
24C2×#102×C137—21no—
25#407×C137—21no—
26C4×M16×C137C2211yescharacteristic
27C2×C4×C8×C137C2211yescharacteristic
28C4×C4⋊C4×C137C2211yescharacteristic
29#340×C137—21no—
30#339×C137—21no—
31#339×C137—21no—
32Q8⋊C8×C137—22no—
33C22×D4×C137D411yescharacteristic
34C23×C4×C137—21no—
35C2×SD16×C137—21no—
36C2×SD16×C137—21no—
37C2×M16×C137—22no—
38C2×M16×C137—21no—
39C2×M16×C137—42no—
40C2×M16×C137—42no—
41C2×M16×C137D411yescharacteristic
42C2×M16×C137D411yescharacteristic
43C22×C8×C137—22no—
44C22×C8×C137—21no—
45C4⋊Q8×C137C2×C411yescharacteristic
46C4⋊Q8×C137C2×C411yescharacteristic
47#125×C137—21no—
48C22⋊Q8×C137—21no—
49C22⋊Q8×C137—21no—
50C4×Q8×C137—21no—
51C4×Q8×C137—21no—
52C4×D4×C137—21no—
53C4×D4×C137—21no—
54C4×D4×C137C2×C411yescharacteristic
55C4×D4×C137C2×C411yescharacteristic
56C4×D4×C137D411yescharacteristic
57C4×D4×C137D411yescharacteristic
58#117×C137—21no—
59C2×C4⋊C4×C137—21no—
60C2×C4⋊C4×C137D411yescharacteristic
61C2×C22⋊C4×C137—21no—
62C2×C42×C137—21no—
63C2×C42×C137C2311yescharacteristic
64#106×C137—21no—
65#106×C137—21no—
66C4⋊C8×C137—21no—
67C4⋊C8×C137C2×C411yescharacteristic
68C4⋊C8×C137C2×C411yescharacteristic
69C4⋊C8×C137D412yes—
70#103×C137—21no—
71#103×C137—21no—
72#102×C137—24no—
73#102×C137—21no—
74#102×C137—21no—
75C22⋊C8×C137—22no—
76C22⋊C8×C137—22no—
77C22⋊C8×C137—21no—
78#97×C137—21no—
79C4×C8×C137—21no—
80C4×C8×C137—21no—
81C4×C8×C137—21no—
82C4×C8×C137—21no—
83#95×C137—21no—
84C24×C137—21no—
85C2×Q8×C137—21no—
86C2×Q8×C137—21no—
87C2×D4×C137—22no—
88C2×D4×C137—21no—
89C2×D4×C137—41no—
90C2×D4×C137C22⋊C411yescharacteristic
91C2×D4×C137C22⋊C411yescharacteristic
92C22×C4×C137—21no—
93C22×C4×C137—21no—
94C22×C4×C137—21no—
95C22×C4×C137—21no—
96C22×C4×C137—21no—
97C22×C4×C137—41no—
98C22×C4×C137—41no—
99C22×C4×C137—41no—
100C22×C4×C137—41no—
101C22×C4×C137—41no—
102C22×C4×C137C2×D411yescharacteristic
103C22×C4×C137C2×D411yescharacteristic
104C22×C4×C137#4111yescharacteristic
105SD16×C137—42no—
106SD16×C137—42no—
107M16×C137—21no—
108M16×C137—21no—
109M16×C137—21no—
110M16×C137—44no—
111M16×C137—41no—
112M16×C137—41no—
113M16×C137SD1612yescomplemented
114C2×C8×C137—21no—
115C2×C8×C137—22no—
116C2×C8×C137—21no—
117C2×C8×C137—21no—
118C2×C8×C137—21no—
119C2×C8×C137—22no—
120C2×C8×C137—44no—
121C2×C8×C137—41no—
122C2×C8×C137—41no—
123C4⋊C4×C137—21no—
124C4⋊C4×C137—22no—
125C4⋊C4×C137—21no—
126C4⋊C4×C137—21no—
127C4⋊C4×C137—21no—
128C4⋊C4×C137—21no—
129C4⋊C4×C137—41no—
130C4⋊C4×C137—41no—
131C4⋊C4×C137—41no—
132C4⋊C4×C137C22⋊C411yescharacteristic
133C4⋊C4×C137C22⋊C411yescharacteristic
134C22⋊C4×C137—21no—
135C22⋊C4×C137—21no—
136C22⋊C4×C137—21no—
137C22⋊C4×C137—21no—
138C22⋊C4×C137—41no—
139C42×C137—41no—
140C42×C137—41no—
141C42×C137—41no—
142C42×C137C22×C411yescharacteristic
143C42×C137C2×D411yescharacteristic
144C42×C137C2×D411yescharacteristic
145C42×C137#4111yescharacteristic
146C23×C137—21no—
147C23×C137—21no—
148C23×C137—42no—
149C23×C137—41no—
150C23×C137—41no—
151C23×C137—81no—
152C23×C137#12111yescharacteristic
153Q8×C137—42no—
154Q8×C137—41no—
155Q8×C137—41no—
156D4×C137—21no—
157D4×C137—21no—
158D4×C137—21no—
159D4×C137—42no—
160D4×C137#10412yes—
161C2×C4×C137—21no—
162C2×C4×C137—21no—
163C2×C4×C137—21no—
164C2×C4×C137—21no—
165C2×C4×C137—41no—
166C2×C4×C137—41no—
167C2×C4×C137—41no—
168C2×C4×C137—41no—
169C2×C4×C137—41no—
170C2×C4×C137—41no—
171C2×C4×C137—41no—
172C2×C4×C137—41no—
173C2×C4×C137—41no—
174C2×C4×C137—41no—
175C2×C4×C137—41no—
176C2×C4×C137—42no—
177C2×C4×C137—41no—
178C2×C4×C137—41no—
179C2×C4×C137—81no—
180C2×C4×C137—81no—
181C2×C4×C137C2×C22⋊C411yescharacteristic
182C2×C4×C137C4×D411yescharacteristic
183C2×C4×C137C4×D411yescharacteristic
184C2×C4×C137#12011yescharacteristic
185C2×C4×C137#12111yescharacteristic
186C2×C4×C137#12311yescharacteristic
187C2×C4×C137C2×SD1611yescharacteristic
188C2×C4×C137#13511yescharacteristic
189C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
190C2×C4×C137#13711yescharacteristic
191C8×C137—22no—
192C8×C137—42no—
193C8×C137—41no—
194C8×C137—41no—
195C8×C137—42no—
196C8×C137—41no—
197C22×C137—21no—
198C22×C137—21no—
199C22×C137—22no—
200C22×C137—41no—
201C22×C137—41no—
202C22×C137—41no—
203C22×C137—41no—
204C22×C137—41no—
205C22×C137—82no—
206C22×C137—82no—
207C22×C137#38611yescharacteristic
208C22×C137#46111yescharacteristic
209C22×C137#46311yescharacteristic
210C4×C137—21no—
211C4×C137—21no—
212C4×C137—21no—
213C4×C137—41no—
214C4×C137—41no—
215C4×C137—82no—
216C4×C137—81no—
217C4×C137—81no—
218C4×C137C2×#10411yescharacteristic
219C4×C137#42111yescharacteristic
220C4×C137C4×SD1611yescharacteristic
221C4×C137#44011yescharacteristic
222C4×C137#45011yescharacteristic
223C4×C137#45211yescharacteristic
224C2×C137—21no—
225C2×C137—21no—
226C2×C137—42no—
227C2×C137—81no—
228C2×C137#187111yescharacteristic
229C2×C137#187711yescharacteristic
230C2×C137#188111yescharacteristic
231#8989C13711yesmaximal, characteristic, direct product factor, Sylow
232C137#898911yescharacteristic, direct product factor, Sylow
233#3101C2×C13711yescharacteristic
234D4×M16C2×C13711yescharacteristic
235#1986C2×C13711yescharacteristic, complemented
236C4×#102C2×C13711yescharacteristic
237#1493C2×C13711yescharacteristic, complemented
238#1303C2×C13711yescharacteristic, complemented
239#1278C2×C13711yescharacteristic, complemented
240C22×M16—21no—
241#533C22×C13711yescharacteristic
242C2×C4×D4C22×C13711yescharacteristic
243#483—21no—
244#476C4×C13711yescharacteristic, complemented
245#476C4×C13711yescharacteristic, complemented
246#461C4×C13711yescharacteristic, complemented
247#461C4×C13711yescharacteristic, complemented
248#450—21no—
249C4×SD16—21no—
250C4×SD16—21no—
251#436—21no—
252#435—22no—
253C8×D4—21no—
254#431C22×C13711yescharacteristic
255#423C22×C13711yescharacteristic
256C2×#102—21no—
257#407—21no—
258C4×M16C22×C13711yescharacteristic
259C2×C4×C8C22×C13711yescharacteristic
260C4×C4⋊C4C22×C13711yescharacteristic
261#340—21no—
262#339—21no—
263#339—21no—
264Q8⋊C8—22no—
265C22×D4D4×C13711yescharacteristic
266C23×C4—21no—
267C2×SD16—21no—
268C2×SD16—21no—
269C2×M16—22no—
270C2×M16—21no—
271C2×M16—42no—
272C2×M16—42no—
273C2×M16D4×C13711yescharacteristic
274C2×M16D4×C13711yescharacteristic
275C22×C8—22no—
276C22×C8—21no—
277C4⋊Q8C2×C4×C13711yescharacteristic
278C4⋊Q8C2×C4×C13711yescharacteristic
279#125—21no—
280C22⋊Q8—21no—
281C22⋊Q8—21no—
282C4×Q8—21no—
283C4×Q8—21no—
284C4×D4—21no—
285C4×D4—21no—
286C4×D4C2×C4×C13711yescharacteristic
287C4×D4C2×C4×C13711yescharacteristic
288C4×D4D4×C13711yescharacteristic
289C4×D4D4×C13711yescharacteristic
290#117—21no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4D4×C13711yescharacteristic
293C2×C22⋊C4—21no—
294C2×C42—21no—
295C2×C42C23×C13711yescharacteristic
296#106—21no—
297#106—21no—
298C4⋊C8—21no—
299C4⋊C8C2×C4×C13711yescharacteristic
300C4⋊C8C2×C4×C13711yescharacteristic
301C4⋊C8D4×C13712yes—
302#103—21no—
303#103—21no—
304#102—24no—
305#102—21no—
306#102—21no—
307C22⋊C8—22no—
308C22⋊C8—22no—
309C22⋊C8—21no—
310#97—21no—
311C4×C8—21no—
312C4×C8—21no—
313C4×C8—21no—
314C4×C8—21no—
315#95—21no—
316C24—21no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×D4—22no—
320C2×D4—21no—
321C2×D4—41no—
322C2×D4C22⋊C4×C13711yescharacteristic
323C2×D4C22⋊C4×C13711yescharacteristic
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4C2×D4×C13711yescharacteristic
335C22×C4C2×D4×C13711yescharacteristic
336C22×C4#41×C13711yescharacteristic
337SD16—42no—
338SD16—42no—
339M16—21no—
340M16—21no—
341M16—21no—
342M16—44no—
343M16—41no—
344M16—41no—
345M16SD16×C13712yescomplemented
346C2×C8—21no—
347C2×C8—22no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—22no—
352C2×C8—44no—
353C2×C8—41no—
354C2×C8—41no—
355C4⋊C4—21no—
356C4⋊C4—22no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—41no—
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4C22⋊C4×C13711yescharacteristic
365C4⋊C4C22⋊C4×C13711yescharacteristic
366C22⋊C4—21no—
367C22⋊C4—21no—
368C22⋊C4—21no—
369C22⋊C4—21no—
370C22⋊C4—41no—
371C42—41no—
372C42—41no—
373C42—41no—
374C42C22×C4×C13711yescharacteristic
375C42C2×D4×C13711yescharacteristic
376C42C2×D4×C13711yescharacteristic
377C42#41×C13711yescharacteristic
378C23—21no—
379C23—21no—
380C23—42no—
381C23—41no—
382C23—41no—
383C23—81no—
384C23#121×C13711yescharacteristic
385Q8—42no—
386Q8—41no—
387Q8—41no—
388D4—21no—
389D4—21no—
390D4—21no—
391D4—42no—
392D4#104×C13712yes—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4C2×C22⋊C4×C13711yescharacteristic
414C2×C4C4×D4×C13711yescharacteristic
415C2×C4C4×D4×C13711yescharacteristic
416C2×C4#120×C13711yescharacteristic
417C2×C4#121×C13711yescharacteristic
418C2×C4#123×C13711yescharacteristic
419C2×C4C2×SD16×C13711yescharacteristic
420C2×C4#135×C13711yescharacteristic
421C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
422C2×C4#137×C13711yescharacteristic
423C8—22no—
424C8—42no—
425C8—41no—
426C8—41no—
427C8—42no—
428C8—41no—
429C22—21no—
430C22—21no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—41no—
437C22—82no—
438C22—82no—
439C22#386×C13711yescharacteristic
440C22#461×C13711yescharacteristic
441C22#463×C13711yescharacteristic
442C4—21no—
443C4—21no—
444C4—21no—
445C4—41no—
446C4—41no—
447C4—82no—
448C4—81no—
449C4—81no—
450C4C2×#104×C13711yescharacteristic
451C4#421×C13711yescharacteristic
452C4C4×SD16×C13711yescharacteristic
453C4#440×C13711yescharacteristic
454C4#450×C13711yescharacteristic
455C4#452×C13711yescharacteristic
456C2—21no—
457C2—21no—
458C2—42no—
459C2—81no—
460C2#1871×C13711yescharacteristic
461C2#1877×C13711yescharacteristic
462C2#1881×C13711yescharacteristic
subgroupG/H
centerC2×C4×C137#120
commutatorC42C22×C4×C137
Frattini, cosocleC2×C42C23×C137
socleC22×C137#386
prime radicalC22×D4×C137D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1986×C137C2semidirect
5. #1493×C137C2semidirect
6. #1303×C137C2semidirect
7. #1278×C137C2semidirect
12. #476×C137C4semidirect
13. #476×C137C4semidirect
14. #461×C137C4semidirect
15. #461×C137C4semidirect
113. M16×C137SD16semidirect
231. #8989C137direct (N × H)
232. C137#8989direct (N × H)
235. #1986C2×C137semidirect
237. #1493C2×C137semidirect
238. #1303C2×C137semidirect
239. #1278C2×C137semidirect
244. #476C4×C137semidirect
245. #476C4×C137semidirect
246. #461C4×C137semidirect
247. #461C4×C137semidirect
345. M16SD16×C137semidirect

Maximal subgroups

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

subgroupindex
#3101×C1372
D4×M16×C1372
#1986×C1372
C4×#102×C1372
#1493×C1372
#1303×C1372
#1278×C1372
#8989137