Finite Group Databasebeta

← C137×#19489 #46868875

Subgroups — C137×#19489 #46868875

Order 35072.

646 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3227×C137C211yesmaximal, characteristic, complemented
2#3106×C137C211yesmaximal, characteristic
3#3039×C137C211yesmaximal, characteristic, complemented
4#2990×C137C211yesmaximal, characteristic, complemented
5#1702×C137C212yesmaximal, complemented
6#1692×C137C212yesmaximal, complemented
7#1681×C137C212yesmaximal, complemented
8#1671×C137C212yesmaximal, complemented
9#1574×C137C211yesmaximal, characteristic, complemented
10#1560×C137C211yesmaximal, characteristic, complemented
11#1549×C137C211yesmaximal, characteristic, complemented
12C2×#137×C137—21no—
13#532×C137C2211yescharacteristic
14C2×C4⋊Q8×C137C2211yescharacteristic
15C4×#41×C137C2211yescharacteristic
16#498×C137C2212yes—
17#486×C137C2212yes—
18#482×C137—21no—
19#481×C137—22no—
20#477×C137C2211yescharacteristic
21#476×C137—21no—
22#476×C137—21no—
23#476×C137C2211yescharacteristic
24#462×C137—21no—
25#462×C137C2212yes—
26#461×C137—21no—
27#461×C137C2212yes—
28#460×C137C2211yescharacteristic
29#459×C137C2211yescharacteristic
30#449×C137—21no—
31#446×C137C2212yes—
32C4×SD16×C137—21no—
33C4×D8×C137—21no—
34#435×C137—22no—
35C8×D4×C137C2212yes—
36#432×C137—21no—
37#431×C137C2211yescharacteristic
38#431×C137C2211yescharacteristic
39#423×C137C2211yescharacteristic
40#423×C137C2211yescharacteristic
41C2×C4⋊C8×C137—21no—
42#419×C137—21no—
43#335×C137C2212yes—
44#334×C137C2212yes—
45#333×C137C2212yes—
46#332×C137C2212yes—
47#332×C137C2212yes—
48#331×C137C2212yes—
49C2×#41×C137—21no—
50C2×#41×C137D411yescharacteristic
51C22×Q8×C137—21no—
52#137×C137—44no—
53C2×Q16×C137—22no—
54C2×SD16×C137—21no—
55C2×SD16×C137—22no—
56C2×D8×C137—21no—
57C2×M16×C137—21no—
58C2×M16×C137—21no—
59C22×C8×C137—22no—
60C4⋊Q8×C137—21no—
61C4⋊Q8×C137—21no—
62C4⋊Q8×C137—21no—
63C4⋊Q8×C137C2312yes—
64C4⋊Q8×C137C2311yescharacteristic
65#127×C137C2311yescharacteristic
66#124×C137—21no—
67#121×C137—21no—
68#121×C137—21no—
69C4×Q8×C137D411yescharacteristic
70C4×Q8×C137C2311yescharacteristic
71C4×D4×C137—21no—
72C4×D4×C137—21no—
73C4×D4×C137—21no—
74C4×D4×C137—21no—
75C4×D4×C137D411yescharacteristic
76C4×D4×C137C2311yescharacteristic
77#117×C137—21no—
78#117×C137D411yescharacteristic
79C2×C4⋊C4×C137—21no—
80C2×C4⋊C4×C137—21no—
81C2×C42×C137—21no—
82C2×C42×C137C2311yescharacteristic
83#107×C137—21no—
84#106×C137—22no—
85#106×C137—22no—
86#106×C137—21no—
87C4⋊C8×C137—22no—
88C4⋊C8×C137—21no—
89C4⋊C8×C137—21no—
90C4⋊C8×C137D411yescharacteristic
91C4⋊C8×C137D411yescharacteristic
92C4⋊C8×C137C2312yes—
93C4⋊C8×C137C2312yes—
94C4⋊C8×C137C2311yescharacteristic
95C4⋊C8×C137C2311yescharacteristic
96#103×C137—21no—
97#103×C137—22no—
98#103×C137—22no—
99#102×C137—21no—
100#102×C137—22no—
101#102×C137—22no—
102#102×C137—21no—
103#102×C137—21no—
104C22⋊C8×C137—21no—
105C22⋊C8×C137—22no—
106C22⋊C8×C137D412yes—
107#97×C137—22no—
108C4×C8×C137—21no—
109C4×C8×C137C2312yes—
110#41×C137—22no—
111#41×C137—41no—
112#41×C137—82no—
113C2×Q8×C137—22no—
114C2×Q8×C137—21no—
115C2×Q8×C137—42no—
116C2×Q8×C137—42no—
117C2×Q8×C137—41no—
118C2×Q8×C137C2×D411yescharacteristic
119C2×D4×C137—21no—
120C2×D4×C137—21no—
121C2×D4×C137—21no—
122C2×D4×C137—21no—
123C2×D4×C137—41no—
124C2×D4×C137C2×D411yescharacteristic
125C22×C4×C137—21no—
126C22×C4×C137—21no—
127C22×C4×C137—21no—
128C22×C4×C137—41no—
129C22×C4×C137—41no—
130C22×C4×C137C2×D411yescharacteristic
131C22×C4×C137C2×D411yescharacteristic
132C22×C4×C137#4111yescharacteristic
133Q16×C137—44no—
134SD16×C137—42no—
135SD16×C137—44no—
136D8×C137—42no—
137M16×C137—42no—
138M16×C137—81no—
139C2×C8×C137—21no—
140C2×C8×C137—21no—
141C2×C8×C137—22no—
142C2×C8×C137—22no—
143C2×C8×C137—82no—
144C2×C8×C137C2×D412yes—
145C2×C8×C137C2×D412yes—
146C4⋊C4×C137—21no—
147C4⋊C4×C137—21no—
148C4⋊C4×C137—22no—
149C4⋊C4×C137—21no—
150C4⋊C4×C137—21no—
151C4⋊C4×C137—22no—
152C4⋊C4×C137—41no—
153C4⋊C4×C137—41no—
154C4⋊C4×C137C2×D411yescharacteristic
155C4⋊C4×C137C2×D411yescharacteristic
156C22⋊C4×C137—21no—
157C22⋊C4×C137—21no—
158C22⋊C4×C137—21no—
159C22⋊C4×C137—41no—
160C22⋊C4×C137—41no—
161C42×C137—21no—
162C42×C137—21no—
163C42×C137—21no—
164C42×C137C2×D411yescharacteristic
165C42×C137C2×D411yescharacteristic
166C42×C137#4111yescharacteristic
167C42×C137C2411yescharacteristic
168C23×C137—21no—
169C23×C137—41no—
170C23×C137#12111yescharacteristic
171Q8×C137—21no—
172Q8×C137—21no—
173Q8×C137—42no—
174Q8×C137—42no—
175Q8×C137—81no—
176Q8×C137—82no—
177D4×C137—21no—
178D4×C137—42no—
179D4×C137—41no—
180D4×C137—41no—
181D4×C137—41no—
182D4×C137—41no—
183D4×C137—81no—
184D4×C137—82no—
185D4×C137AGL(1,ℤ/8)12yes—
186C2×C4×C137—21no—
187C2×C4×C137—21no—
188C2×C4×C137—21no—
189C2×C4×C137—21no—
190C2×C4×C137—22no—
191C2×C4×C137—21no—
192C2×C4×C137—21no—
193C2×C4×C137—21no—
194C2×C4×C137—42no—
195C2×C4×C137—41no—
196C2×C4×C137—41no—
197C2×C4×C137—42no—
198C2×C4×C137—41no—
199C2×C4×C137—42no—
200C2×C4×C137—82no—
201C2×C4×C137—82no—
202C2×C4×C137#12111yescharacteristic
203C2×C4×C137#12111yescharacteristic
204C2×C4×C137#12111yescharacteristic
205C2×C4×C137C22×D411yescharacteristic
206C2×C4×C137C22×D411yescharacteristic
207C2×C4×C137C2×#4111yescharacteristic
208C8×C137—22no—
209C8×C137—22no—
210C8×C137—42no—
211C8×C137—41no—
212C8×C137—41no—
213C8×C137—42no—
214C22×C137—21no—
215C22×C137—21no—
216C22×C137—22no—
217C22×C137—21no—
218C22×C137—41no—
219C22×C137—41no—
220C22×C137—81no—
221C22×C137—81no—
222C22×C137—81no—
223C22×C137C2×#12111yescharacteristic
224C4×C137—21no—
225C4×C137—21no—
226C4×C137—21no—
227C4×C137—41no—
228C4×C137—41no—
229C4×C137—41no—
230C4×C137—82no—
231C4×C137—81no—
232C4×C137#47112yes—
233C4×C137C2×AGL(1,ℤ/8)11yescharacteristic
234C4×C137#57511yescharacteristic
235C4×C137#57711yescharacteristic
236C4×C137#57811yescharacteristic
237C2×C137—41no—
238C2×C137—42no—
239C2×C137—161no—
240C2×C137#304611yescharacteristic
241C2×C137#305511yescharacteristic
242C2×C137C2×#47111yescharacteristic
243#19489C13711yesmaximal, characteristic, direct product factor, Sylow
244C137#1948911yescharacteristic, direct product factor, Sylow
245#3227C2×C13711yescharacteristic, complemented
246#3106C2×C13711yescharacteristic
247#3039C2×C13711yescharacteristic, complemented
248#2990C2×C13711yescharacteristic, complemented
249#1702C2×C13712yescomplemented
250#1692C2×C13712yescomplemented
251#1681C2×C13712yescomplemented
252#1671C2×C13712yescomplemented
253#1574C2×C13711yescharacteristic, complemented
254#1560C2×C13711yescharacteristic, complemented
255#1549C2×C13711yescharacteristic, complemented
256C2×#137—21no—
257#532C22×C13711yescharacteristic
258C2×C4⋊Q8C22×C13711yescharacteristic
259C4×#41C22×C13711yescharacteristic
260#498C22×C13712yes—
261#486C22×C13712yes—
262#482—21no—
263#481—22no—
264#477C22×C13711yescharacteristic
265#476—21no—
266#476—21no—
267#476C22×C13711yescharacteristic
268#462—21no—
269#462C22×C13712yes—
270#461—21no—
271#461C22×C13712yes—
272#460C22×C13711yescharacteristic
273#459C22×C13711yescharacteristic
274#449—21no—
275#446C22×C13712yes—
276C4×SD16—21no—
277C4×D8—21no—
278#435—22no—
279C8×D4C22×C13712yes—
280#432—21no—
281#431C22×C13711yescharacteristic
282#431C22×C13711yescharacteristic
283#423C22×C13711yescharacteristic
284#423C22×C13711yescharacteristic
285C2×C4⋊C8—21no—
286#419—21no—
287#335C22×C13712yes—
288#334C22×C13712yes—
289#333C22×C13712yes—
290#332C22×C13712yes—
291#332C22×C13712yes—
292#331C22×C13712yes—
293C2×#41—21no—
294C2×#41D4×C13711yescharacteristic
295C22×Q8—21no—
296#137—44no—
297C2×Q16—22no—
298C2×SD16—21no—
299C2×SD16—22no—
300C2×D8—21no—
301C2×M16—21no—
302C2×M16—21no—
303C22×C8—22no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8—21no—
307C4⋊Q8C23×C13712yes—
308C4⋊Q8C23×C13711yescharacteristic
309#127C23×C13711yescharacteristic
310#124—21no—
311#121—21no—
312#121—21no—
313C4×Q8D4×C13711yescharacteristic
314C4×Q8C23×C13711yescharacteristic
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—21no—
319C4×D4D4×C13711yescharacteristic
320C4×D4C23×C13711yescharacteristic
321#117—21no—
322#117D4×C13711yescharacteristic
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C42—21no—
326C2×C42C23×C13711yescharacteristic
327#107—21no—
328#106—22no—
329#106—22no—
330#106—21no—
331C4⋊C8—22no—
332C4⋊C8—21no—
333C4⋊C8—21no—
334C4⋊C8D4×C13711yescharacteristic
335C4⋊C8D4×C13711yescharacteristic
336C4⋊C8C23×C13712yes—
337C4⋊C8C23×C13712yes—
338C4⋊C8C23×C13711yescharacteristic
339C4⋊C8C23×C13711yescharacteristic
340#103—21no—
341#103—22no—
342#103—22no—
343#102—21no—
344#102—22no—
345#102—22no—
346#102—21no—
347#102—21no—
348C22⋊C8—21no—
349C22⋊C8—22no—
350C22⋊C8D4×C13712yes—
351#97—22no—
352C4×C8—21no—
353C4×C8C23×C13712yes—
354#41—22no—
355#41—41no—
356#41—82no—
357C2×Q8—22no—
358C2×Q8—21no—
359C2×Q8—42no—
360C2×Q8—42no—
361C2×Q8—41no—
362C2×Q8C2×D4×C13711yescharacteristic
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—21no—
366C2×D4—21no—
367C2×D4—41no—
368C2×D4C2×D4×C13711yescharacteristic
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4C2×D4×C13711yescharacteristic
375C22×C4C2×D4×C13711yescharacteristic
376C22×C4#41×C13711yescharacteristic
377Q16—44no—
378SD16—42no—
379SD16—44no—
380D8—42no—
381M16—42no—
382M16—81no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—22no—
386C2×C8—22no—
387C2×C8—82no—
388C2×C8C2×D4×C13712yes—
389C2×C8C2×D4×C13712yes—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—22no—
396C4⋊C4—41no—
397C4⋊C4—41no—
398C4⋊C4C2×D4×C13711yescharacteristic
399C4⋊C4C2×D4×C13711yescharacteristic
400C22⋊C4—21no—
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C42—21no—
406C42—21no—
407C42—21no—
408C42C2×D4×C13711yescharacteristic
409C42C2×D4×C13711yescharacteristic
410C42#41×C13711yescharacteristic
411C42C24×C13711yescharacteristic
412C23—21no—
413C23—41no—
414C23#121×C13711yescharacteristic
415Q8—21no—
416Q8—21no—
417Q8—42no—
418Q8—42no—
419Q8—81no—
420Q8—82no—
421D4—21no—
422D4—42no—
423D4—41no—
424D4—41no—
425D4—41no—
426D4—41no—
427D4—81no—
428D4—82no—
429D4AGL(1,ℤ/8)×C13712yes—
430C2×C4—22no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—42no—
444C2×C4—82no—
445C2×C4—82no—
446C2×C4#121×C13711yescharacteristic
447C2×C4#121×C13711yescharacteristic
448C2×C4#121×C13711yescharacteristic
449C2×C4C22×D4×C13711yescharacteristic
450C2×C4C22×D4×C13711yescharacteristic
451C2×C4C2×#41×C13711yescharacteristic
452C8—22no—
453C8—22no—
454C8—42no—
455C8—41no—
456C8—41no—
457C8—42no—
458C22—21no—
459C22—21no—
460C22—22no—
461C22—21no—
462C22—41no—
463C22—41no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22C2×#121×C13711yescharacteristic
468C4—21no—
469C4—21no—
470C4—21no—
471C4—41no—
472C4—41no—
473C4—41no—
474C4—82no—
475C4—81no—
476C4#471×C13712yes—
477C4C2×AGL(1,ℤ/8)×C13711yescharacteristic
478C4#575×C13711yescharacteristic
479C4#577×C13711yescharacteristic
480C4#578×C13711yescharacteristic
481C2—41no—
482C2—42no—
483C2—161no—
484C2#3046×C13711yescharacteristic
485C2#3055×C13711yescharacteristic
486C2C2×#471×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#121
commutator, Frattini, cosocleC42C24×C137
prime radical#3106×C137C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3227×C137C2semidirect
3. #3039×C137C2semidirect
4. #2990×C137C2semidirect
5. #1702×C137C2semidirect
6. #1692×C137C2semidirect
7. #1681×C137C2semidirect
8. #1671×C137C2semidirect
9. #1574×C137C2semidirect
10. #1560×C137C2semidirect
11. #1549×C137C2semidirect
243. #19489C137direct (N × H)
244. C137#19489direct (N × H)
245. #3227C2×C137semidirect
247. #3039C2×C137semidirect
248. #2990C2×C137semidirect
249. #1702C2×C137semidirect
250. #1692C2×C137semidirect
251. #1681C2×C137semidirect
252. #1671C2×C137semidirect
253. #1574C2×C137semidirect
254. #1560C2×C137semidirect
255. #1549C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3227×C1372
#3106×C1372
#3039×C1372
#2990×C1372
#1702×C1372
#1692×C1372
#1681×C1372
#1671×C1372
#1574×C1372
#1560×C1372
#1549×C1372
#19489137