Finite Group Databasebeta

← C137×#19260 #46868646

Subgroups — C137×#19260 #46868646

Order 35072.

656 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3167×C137C211yesmaximal, characteristic
2#3078×C137C211yesmaximal, characteristic, complemented
3#3037×C137C211yesmaximal, characteristic
4C2×C8×Q8×C137C211yesmaximal, characteristic, complemented
5#1680×C137C212yesmaximal, complemented
6#1678×C137C212yesmaximal, complemented
7#1672×C137C212yesmaximal, complemented
8#1666×C137C212yesmaximal, complemented
9#1566×C137C211yesmaximal, characteristic, complemented
10#1550×C137C211yesmaximal, characteristic, complemented
11#1547×C137C211yesmaximal, characteristic
12C2×#137×C137—21no—
13#533×C137C2211yescharacteristic
14#532×C137C2211yescharacteristic
15C2×C4×Q8×C137C2211yescharacteristic
16#498×C137C2211yescharacteristic
17#492×C137C2211yescharacteristic
18#487×C137C2211yescharacteristic
19#486×C137C2211yescharacteristic
20#479×C137—22no—
21#477×C137C2212yes—
22#475×C137C2212yes—
23#465×C137—21no—
24#465×C137—21no—
25#464×C137—22no—
26#462×C137C2212yes—
27#460×C137C2212yes—
28C8×Q8×C137—21no—
29C8×Q8×C137—21no—
30C8×Q8×C137C2212yes—
31C8×Q8×C137C2212yes—
32C4×SD16×C137—21no—
33C4×SD16×C137—21no—
34#428×C137—21no—
35#423×C137C2211yescharacteristic
36#423×C137C2211yescharacteristic
37C2×C4⋊C8×C137—21no—
38C2×C4⋊C8×C137C2211yescharacteristic
39#419×C137—21no—
40#417×C137—21no—
41C2×C4×C8×C137—21no—
42C2×C4×C8×C137C2211yescharacteristic
43#334×C137C2212yes—
44#334×C137C2212yes—
45#333×C137C2212yes—
46#332×C137C2212yes—
47#332×C137C2212yes—
48#331×C137C2212yes—
49C2×#41×C137—21no—
50C22×Q8×C137D411yescharacteristic
51#137×C137—44no—
52C2×Q16×C137—22no—
53C2×SD16×C137—22no—
54C2×SD16×C137—21no—
55C2×SD16×C137—21no—
56C2×M16×C137—21no—
57C2×M16×C137—21no—
58C22×C8×C137—21no—
59C22×C8×C137D411yescharacteristic
60C22×C8×C137D411yescharacteristic
61C4⋊Q8×C137C2311yescharacteristic
62C4⋊Q8×C137C2311yescharacteristic
63C4⋊Q8×C137C2311yescharacteristic
64#127×C137C2311yescharacteristic
65#125×C137—21no—
66#124×C137—21no—
67C22⋊Q8×C137—21no—
68C22⋊Q8×C137—21no—
69#121×C137—21no—
70#121×C137—21no—
71C4×Q8×C137—21no—
72C4×Q8×C137—21no—
73C4×Q8×C137—21no—
74C4×Q8×C137—21no—
75C4×Q8×C137D412yes—
76C4×Q8×C137C2312yes—
77C4×D4×C137—21no—
78C4×D4×C137—21no—
79#117×C137—21no—
80C2×C4⋊C4×C137—21no—
81C2×C4⋊C4×C137D411yescharacteristic
82C2×C42×C137—21no—
83C2×C42×C137C2311yescharacteristic
84#107×C137—22no—
85#106×C137—21no—
86#106×C137—21no—
87#106×C137—22no—
88C4⋊C8×C137—22no—
89C4⋊C8×C137—22no—
90C4⋊C8×C137—21no—
91C4⋊C8×C137—21no—
92C4⋊C8×C137—21no—
93C4⋊C8×C137C2312yes—
94C4⋊C8×C137C2312yes—
95C4⋊C8×C137C2312yes—
96#103×C137—22no—
97#103×C137—22no—
98#103×C137—21no—
99#103×C137—21no—
100#103×C137—22no—
101#102×C137—21no—
102#102×C137—21no—
103#102×C137—22no—
104C4×C8×C137—22no—
105C4×C8×C137—22no—
106C4×C8×C137D411yescharacteristic
107C4×C8×C137D411yescharacteristic
108C4×C8×C137C2311yescharacteristic
109C4×C8×C137C2311yescharacteristic
110#41×C137—42no—
111#41×C137—42no—
112C2×Q8×C137—21no—
113C2×Q8×C137—22no—
114C2×Q8×C137—21no—
115C2×Q8×C137—21no—
116C2×Q8×C137—21no—
117C2×Q8×C137SD1614yescomplemented
118C2×Q8×C137C2×D412yes—
119C2×D4×C137—21no—
120C2×D4×C137—21no—
121C2×D4×C137—21no—
122C2×D4×C137—41no—
123C22×C4×C137—21no—
124C22×C4×C137—21no—
125C22×C4×C137—41no—
126C22×C4×C137C2×D411yescharacteristic
127C22×C4×C137C2×D411yescharacteristic
128C22×C4×C137#4111yescharacteristic
129Q16×C137—44no—
130SD16×C137—42no—
131SD16×C137—44no—
132SD16×C137—42no—
133M16×C137—42no—
134M16×C137—42no—
135C2×C8×C137—22no—
136C2×C8×C137—22no—
137C2×C8×C137—22no—
138C2×C8×C137—22no—
139C2×C8×C137—41no—
140C2×C8×C137—42no—
141C2×C8×C137C2×D411yescharacteristic
142C2×C8×C137C2×D411yescharacteristic
143C2×C8×C137C2×D411yescharacteristic
144C2×C8×C137C2×D411yescharacteristic
145C4⋊C4×C137—22no—
146C4⋊C4×C137—21no—
147C4⋊C4×C137—22no—
148C4⋊C4×C137—21no—
149C4⋊C4×C137—21no—
150C4⋊C4×C137—21no—
151C4⋊C4×C137—21no—
152C4⋊C4×C137—21no—
153C4⋊C4×C137—21no—
154C4⋊C4×C137—41no—
155C4⋊C4×C137—41no—
156C4⋊C4×C137C2×D412yes—
157C22⋊C4×C137—41no—
158C22⋊C4×C137—41no—
159C22⋊C4×C137—41no—
160C42×C137—22no—
161C42×C137—22no—
162C42×C137—41no—
163C42×C137C2×D411yescharacteristic
164C42×C137C2×D411yescharacteristic
165C42×C137#4111yescharacteristic
166C42×C137C2411yescharacteristic
167C23×C137—41no—
168C23×C137#12111yescharacteristic
169Q8×C137—22no—
170Q8×C137—24no—
171Q8×C137—41no—
172Q8×C137—41no—
173Q8×C137—41no—
174Q8×C137—41no—
175Q8×C137—81no—
176Q8×C137C2×SD1614yes—
177D4×C137—41no—
178D4×C137—41no—
179D4×C137—41no—
180D4×C137—41no—
181D4×C137—81no—
182D4×C137—82no—
183C2×C4×C137—22no—
184C2×C4×C137—24no—
185C2×C4×C137—21no—
186C2×C4×C137—21no—
187C2×C4×C137—22no—
188C2×C4×C137—41no—
189C2×C4×C137—42no—
190C2×C4×C137—41no—
191C2×C4×C137—41no—
192C2×C4×C137—41no—
193C2×C4×C137—82no—
194C2×C4×C137#12111yescharacteristic
195C2×C4×C137#12111yescharacteristic
196C2×C4×C137#12111yescharacteristic
197C2×C4×C137C2×SD1612yes—
198C2×C4×C137#13512yes—
199C2×C4×C137C22×D411yescharacteristic
200C2×C4×C137C22×D411yescharacteristic
201C2×C4×C137C2×#4111yescharacteristic
202C8×C137—21no—
203C8×C137—21no—
204C8×C137—21no—
205C8×C137—42no—
206C8×C137—42no—
207C8×C137—42no—
208C8×C137#13712yescomplemented
209C22×C137—21no—
210C22×C137—21no—
211C22×C137—81no—
212C22×C137—81no—
213C22×C137—81no—
214C22×C137#46512yes—
215C22×C137C2×#12111yescharacteristic
216C4×C137—21no—
217C4×C137—24no—
218C4×C137—21no—
219C4×C137—21no—
220C4×C137—42no—
221C4×C137—81no—
222C4×C137—81no—
223C4×C137—81no—
224C4×C137#46512yes—
225C4×C137C22×SD1611yescharacteristic
226C4×C137C2×#13511yescharacteristic
227C4×C137C2×#13711yescharacteristic
228C4×C137#57511yescharacteristic
229C2×C137—22no—
230C2×C137—161no—
231C2×C137#303711yescharacteristic
232C2×C137C2×#46511yescharacteristic
233C2×C137#306711yescharacteristic
234#19260C13711yesmaximal, characteristic, direct product factor, Sylow
235C137#1926011yescharacteristic, direct product factor, Sylow
236#3167C2×C13711yescharacteristic
237#3078C2×C13711yescharacteristic, complemented
238#3037C2×C13711yescharacteristic
239C2×C8×Q8C2×C13711yescharacteristic, complemented
240#1680C2×C13712yescomplemented
241#1678C2×C13712yescomplemented
242#1672C2×C13712yescomplemented
243#1666C2×C13712yescomplemented
244#1566C2×C13711yescharacteristic, complemented
245#1550C2×C13711yescharacteristic, complemented
246#1547C2×C13711yescharacteristic
247C2×#137—21no—
248#533C22×C13711yescharacteristic
249#532C22×C13711yescharacteristic
250C2×C4×Q8C22×C13711yescharacteristic
251#498C22×C13711yescharacteristic
252#492C22×C13711yescharacteristic
253#487C22×C13711yescharacteristic
254#486C22×C13711yescharacteristic
255#479—22no—
256#477C22×C13712yes—
257#475C22×C13712yes—
258#465—21no—
259#465—21no—
260#464—22no—
261#462C22×C13712yes—
262#460C22×C13712yes—
263C8×Q8—21no—
264C8×Q8—21no—
265C8×Q8C22×C13712yes—
266C8×Q8C22×C13712yes—
267C4×SD16—21no—
268C4×SD16—21no—
269#428—21no—
270#423C22×C13711yescharacteristic
271#423C22×C13711yescharacteristic
272C2×C4⋊C8—21no—
273C2×C4⋊C8C22×C13711yescharacteristic
274#419—21no—
275#417—21no—
276C2×C4×C8—21no—
277C2×C4×C8C22×C13711yescharacteristic
278#334C22×C13712yes—
279#334C22×C13712yes—
280#333C22×C13712yes—
281#332C22×C13712yes—
282#332C22×C13712yes—
283#331C22×C13712yes—
284C2×#41—21no—
285C22×Q8D4×C13711yescharacteristic
286#137—44no—
287C2×Q16—22no—
288C2×SD16—22no—
289C2×SD16—21no—
290C2×SD16—21no—
291C2×M16—21no—
292C2×M16—21no—
293C22×C8—21no—
294C22×C8D4×C13711yescharacteristic
295C22×C8D4×C13711yescharacteristic
296C4⋊Q8C23×C13711yescharacteristic
297C4⋊Q8C23×C13711yescharacteristic
298C4⋊Q8C23×C13711yescharacteristic
299#127C23×C13711yescharacteristic
300#125—21no—
301#124—21no—
302C22⋊Q8—21no—
303C22⋊Q8—21no—
304#121—21no—
305#121—21no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×Q8—21no—
310C4×Q8D4×C13712yes—
311C4×Q8C23×C13712yes—
312C4×D4—21no—
313C4×D4—21no—
314#117—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4D4×C13711yescharacteristic
317C2×C42—21no—
318C2×C42C23×C13711yescharacteristic
319#107—22no—
320#106—21no—
321#106—21no—
322#106—22no—
323C4⋊C8—22no—
324C4⋊C8—22no—
325C4⋊C8—21no—
326C4⋊C8—21no—
327C4⋊C8—21no—
328C4⋊C8C23×C13712yes—
329C4⋊C8C23×C13712yes—
330C4⋊C8C23×C13712yes—
331#103—22no—
332#103—22no—
333#103—21no—
334#103—21no—
335#103—22no—
336#102—21no—
337#102—21no—
338#102—22no—
339C4×C8—22no—
340C4×C8—22no—
341C4×C8D4×C13711yescharacteristic
342C4×C8D4×C13711yescharacteristic
343C4×C8C23×C13711yescharacteristic
344C4×C8C23×C13711yescharacteristic
345#41—42no—
346#41—42no—
347C2×Q8—21no—
348C2×Q8—22no—
349C2×Q8—21no—
350C2×Q8—21no—
351C2×Q8—21no—
352C2×Q8SD16×C13714yescomplemented
353C2×Q8C2×D4×C13712yes—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—41no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—41no—
361C22×C4C2×D4×C13711yescharacteristic
362C22×C4C2×D4×C13711yescharacteristic
363C22×C4#41×C13711yescharacteristic
364Q16—44no—
365SD16—42no—
366SD16—44no—
367SD16—42no—
368M16—42no—
369M16—42no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—22no—
373C2×C8—22no—
374C2×C8—41no—
375C2×C8—42no—
376C2×C8C2×D4×C13711yescharacteristic
377C2×C8C2×D4×C13711yescharacteristic
378C2×C8C2×D4×C13711yescharacteristic
379C2×C8C2×D4×C13711yescharacteristic
380C4⋊C4—22no—
381C4⋊C4—21no—
382C4⋊C4—22no—
383C4⋊C4—21no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4C2×D4×C13712yes—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C42—22no—
396C42—22no—
397C42—41no—
398C42C2×D4×C13711yescharacteristic
399C42C2×D4×C13711yescharacteristic
400C42#41×C13711yescharacteristic
401C42C24×C13711yescharacteristic
402C23—41no—
403C23#121×C13711yescharacteristic
404Q8—24no—
405Q8—22no—
406Q8—41no—
407Q8—41no—
408Q8—41no—
409Q8—41no—
410Q8—81no—
411Q8C2×SD16×C13714yes—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—41no—
416D4—81no—
417D4—82no—
418C2×C4—24no—
419C2×C4—22no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—82no—
429C2×C4#121×C13711yescharacteristic
430C2×C4#121×C13711yescharacteristic
431C2×C4#121×C13711yescharacteristic
432C2×C4C2×SD16×C13712yes—
433C2×C4#135×C13712yes—
434C2×C4C22×D4×C13711yescharacteristic
435C2×C4C22×D4×C13711yescharacteristic
436C2×C4C2×#41×C13711yescharacteristic
437C8—21no—
438C8—21no—
439C8—21no—
440C8—42no—
441C8—42no—
442C8—42no—
443C8#137×C13712yescomplemented
444C22—21no—
445C22—21no—
446C22—81no—
447C22—81no—
448C22—81no—
449C22#465×C13712yes—
450C22C2×#121×C13711yescharacteristic
451C4—21no—
452C4—24no—
453C4—21no—
454C4—21no—
455C4—42no—
456C4—81no—
457C4—81no—
458C4—81no—
459C4#465×C13712yes—
460C4C22×SD16×C13711yescharacteristic
461C4C2×#135×C13711yescharacteristic
462C4C2×#137×C13711yescharacteristic
463C4#575×C13711yescharacteristic
464C2—22no—
465C2—161no—
466C2#3037×C13711yescharacteristic
467C2C2×#465×C13711yescharacteristic
468C2#3067×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#121
commutator, Frattini, cosocleC42C24×C137
prime radical#532×C137C22
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
2. #3078×C137C2semidirect
4. C2×C8×Q8×C137C2semidirect
5. #1680×C137C2semidirect
6. #1678×C137C2semidirect
7. #1672×C137C2semidirect
8. #1666×C137C2semidirect
9. #1566×C137C2semidirect
10. #1550×C137C2semidirect
117. C2×Q8×C137SD16semidirect
208. C8×C137#137semidirect
234. #19260C137direct (N × H)
235. C137#19260direct (N × H)
237. #3078C2×C137semidirect
239. C2×C8×Q8C2×C137semidirect
240. #1680C2×C137semidirect
241. #1678C2×C137semidirect
242. #1672C2×C137semidirect
243. #1666C2×C137semidirect
244. #1566C2×C137semidirect
245. #1550C2×C137semidirect
352. C2×Q8SD16×C137semidirect
443. C8#137×C137semidirect

Maximal subgroups

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

subgroupindex
#3167×C1372
#3078×C1372
#3037×C1372
C2×C8×Q8×C1372
#1680×C1372
#1678×C1372
#1672×C1372
#1666×C1372
#1566×C1372
#1550×C1372
#1547×C1372
#19260137