Finite Group Databasebeta

← C137×#18948 #46868334

Subgroups — C137×#18948 #46868334

Order 35072.

880 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3550×C137C211yesmaximal, characteristic, complemented
2#3245×C137C211yesmaximal, characteristic
3#3228×C137C211yesmaximal, characteristic, complemented
4#3216×C137C211yesmaximal, characteristic, complemented
5#1652×C137C212yesmaximal, complemented
6#1649×C137C212yesmaximal, complemented
7#1628×C137C212yesmaximal, complemented
8#1627×C137C212yesmaximal, complemented
9#1552×C137C211yesmaximal, characteristic, complemented
10#1496×C137C211yesmaximal, characteristic, complemented
11#1481×C137C211yesmaximal, characteristic, complemented
12#563×C137—22no—
13#559×C137—21no—
14Q82×C137—21no—
15#556×C137—21no—
16#556×C137C2212yes—
17D4×Q8×C137—21no—
18D4×Q8×C137C2212yes—
19#542×C137—22no—
20#542×C137—22no—
21#536×C137—22no—
22#533×C137C2211yescharacteristic
23#533×C137C2211yescharacteristic
24#532×C137C2211yescharacteristic
25#532×C137C2211yescharacteristic
26#500×C137C2211yescharacteristic
27#498×C137C2211yescharacteristic
28#497×C137—21no—
29#489×C137—21no—
30#486×C137C2211yescharacteristic
31#486×C137C2211yescharacteristic
32#482×C137—22no—
33#478×C137—22no—
34#474×C137—21no—
35#474×C137C2212yes—
36#466×C137—22no—
37#462×C137C2212yes—
38#460×C137C2212yes—
39#459×C137—21no—
40#459×C137C2212yes—
41#452×C137—22no—
42#432×C137C2211yescharacteristic
43#431×C137C2211yescharacteristic
44C2×C4⋊C8×C137C2211yescharacteristic
45#332×C137C2212yes—
46#332×C137C2212yes—
47Q8⋊C8×C137C2212yes—
48Q8⋊C8×C137C2212yes—
49D4⋊C8×C137C2212yes—
50D4⋊C8×C137C2212yes—
51C2×#41×C137—21no—
52C2×#41×C137—21no—
53C22×Q8×C137—22no—
54C2×Q16×C137—22no—
55C2×SD16×C137—22no—
56C2×D8×C137—22no—
57C22×C8×C137—21no—
58C4⋊Q8×C137—24no—
59C4⋊Q8×C137—22no—
60C4⋊Q8×C137—22no—
61C4⋊Q8×C137D411yescharacteristic
62C4⋊Q8×C137D411yescharacteristic
63C4⋊Q8×C137D411yescharacteristic
64C4⋊Q8×C137C2311yescharacteristic
65C4⋊Q8×C137C2311yescharacteristic
66C4⋊Q8×C137C2311yescharacteristic
67#127×C137D411yescharacteristic
68#127×C137C2311yescharacteristic
69#126×C137—24no—
70#126×C137—24no—
71#125×C137—21no—
72#125×C137D412yes—
73#124×C137—24no—
74#124×C137—22no—
75#124×C137—22no—
76#124×C137—21no—
77#124×C137—21no—
78#123×C137—24no—
79#123×C137—24no—
80C22⋊Q8×C137—24no—
81C22⋊Q8×C137—22no—
82C22⋊Q8×C137—21no—
83C22⋊Q8×C137—21no—
84C22⋊Q8×C137—21no—
85C22⋊Q8×C137—22no—
86C22⋊Q8×C137—24no—
87C22⋊Q8×C137D412yes—
88#121×C137—21no—
89#121×C137—21no—
90#121×C137—21no—
91#121×C137D412yes—
92C4×Q8×C137—22no—
93C4×Q8×C137—22no—
94C4×Q8×C137—21no—
95C4×Q8×C137—21no—
96C4×Q8×C137—21no—
97C4×Q8×C137C2312yes—
98C4×D4×C137—22no—
99C4×D4×C137—22no—
100C4×D4×C137—21no—
101C4×D4×C137—21no—
102C4×D4×C137—21no—
103C4×D4×C137C2312yes—
104#117×C137—21no—
105#117×C137—22no—
106#117×C137D412yes—
107C2×C42×C137C2311yescharacteristic
108#107×C137—22no—
109#107×C137—22no—
110#106×C137—22no—
111C4⋊C8×C137—21no—
112C4⋊C8×C137—21no—
113C4⋊C8×C137C2312yes—
114C4⋊C8×C137C2312yes—
115#103×C137—22no—
116#102×C137—22no—
117#102×C137—22no—
118#102×C137—22no—
119#102×C137—22no—
120#102×C137—22no—
121C22⋊C8×C137—21no—
122C22⋊C8×C137—21no—
123#97×C137—21no—
124C4×C8×C137C2311yescharacteristic
125C4×C8×C137C2311yescharacteristic
126#41×C137—82no—
127#41×C137—82no—
128C2×Q8×C137—24no—
129C2×Q8×C137—21no—
130C2×Q8×C137—21no—
131C2×Q8×C137—21no—
132C2×Q8×C137—21no—
133C2×Q8×C137—21no—
134C2×Q8×C137—82no—
135C2×Q8×C137—82no—
136C2×Q8×C137C2×D412yes—
137C2×D4×C137—22no—
138C2×D4×C137—21no—
139C2×D4×C137—21no—
140C2×D4×C137—21no—
141C2×D4×C137—21no—
142C2×D4×C137—21no—
143C2×D4×C137—41no—
144C2×D4×C137C2×D412yes—
145C22×C4×C137—24no—
146C22×C4×C137—22no—
147C22×C4×C137—41no—
148C22×C4×C137C2×D411yescharacteristic
149C22×C4×C137C2×D411yescharacteristic
150C22×C4×C137C2×D411yescharacteristic
151Q16×C137—82no—
152SD16×C137—82no—
153D8×C137—82no—
154C2×C8×C137—21no—
155C2×C8×C137—21no—
156C2×C8×C137—22no—
157C2×C8×C137—22no—
158C2×C8×C137—81no—
159C4⋊C4×C137—24no—
160C4⋊C4×C137—24no—
161C4⋊C4×C137—21no—
162C4⋊C4×C137—21no—
163C4⋊C4×C137—21no—
164C4⋊C4×C137—21no—
165C4⋊C4×C137—22no—
166C4⋊C4×C137—22no—
167C4⋊C4×C137—22no—
168C4⋊C4×C137—21no—
169C4⋊C4×C137—21no—
170C4⋊C4×C137—22no—
171C4⋊C4×C137—21no—
172C4⋊C4×C137—21no—
173C4⋊C4×C137C2×D412yes—
174C4⋊C4×C137C2×D412yes—
175C4⋊C4×C137C2×D412yes—
176C4⋊C4×C137C2×D412yes—
177C22⋊C4×C137—24no—
178C22⋊C4×C137—24no—
179C22⋊C4×C137—24no—
180C22⋊C4×C137—22no—
181C22⋊C4×C137—22no—
182C22⋊C4×C137—22no—
183C22⋊C4×C137—22no—
184C22⋊C4×C137—41no—
185C22⋊C4×C137—41no—
186C42×C137—24no—
187C42×C137—22no—
188C42×C137—22no—
189C42×C137C2×D411yescharacteristic
190C42×C137C2×D411yescharacteristic
191C42×C137C2×D411yescharacteristic
192C42×C137C2411yescharacteristic
193C23×C137—22no—
194C23×C137—41no—
195C23×C137#12011yescharacteristic
196Q8×C137—22no—
197Q8×C137—22no—
198Q8×C137—42no—
199Q8×C137—42no—
200Q8×C137—41no—
201Q8×C137—41no—
202Q8×C137—42no—
203Q8×C137—81no—
204Q8×C137—84no—
205D4×C137—22no—
206D4×C137—22no—
207D4×C137—42no—
208D4×C137—42no—
209D4×C137—42no—
210D4×C137—41no—
211D4×C137—41no—
212D4×C137—81no—
213D4×C137—82no—
214D4×C137—82no—
215C2×C4×C137—22no—
216C2×C4×C137—21no—
217C2×C4×C137—21no—
218C2×C4×C137—22no—
219C2×C4×C137—22no—
220C2×C4×C137—22no—
221C2×C4×C137—22no—
222C2×C4×C137—22no—
223C2×C4×C137—41no—
224C2×C4×C137—42no—
225C2×C4×C137—42no—
226C2×C4×C137—41no—
227C2×C4×C137—82no—
228C2×C4×C137—84no—
229C2×C4×C137#12011yescharacteristic
230C2×C4×C137#12011yescharacteristic
231C2×C4×C137#12011yescharacteristic
232C2×C4×C137C22×D411yescharacteristic
233C2×C4×C137C22×D411yescharacteristic
234C2×C4×C137C22×D411yescharacteristic
235C8×C137—41no—
236C8×C137—41no—
237C8×C137—42no—
238C8×C137—42no—
239C22×C137—21no—
240C22×C137—21no—
241C22×C137—21no—
242C22×C137—42no—
243C22×C137—42no—
244C22×C137—42no—
245C22×C137—81no—
246C22×C137—81no—
247C22×C137—81no—
248C22×C137C2×#12011yescharacteristic
249C4×C137—21no—
250C4×C137—21no—
251C4×C137—21no—
252C4×C137—21no—
253C4×C137—42no—
254C4×C137—42no—
255C4×C137—42no—
256C4×C137—42no—
257C4×C137—42no—
258C4×C137—81no—
259C4×C137#57612yes—
260C4×C137#57711yescharacteristic
261C4×C137#57811yescharacteristic
262C2×C137—41no—
263C2×C137—82no—
264C2×C137—161no—
265C2×C137#300811yescharacteristic
266C2×C137#301311yescharacteristic
267C2×C137#302011yescharacteristic
268#18948C13711yesmaximal, characteristic, direct product factor, Sylow
269C137#1894811yescharacteristic, direct product factor, Sylow
270#3550C2×C13711yescharacteristic, complemented
271#3245C2×C13711yescharacteristic
272#3228C2×C13711yescharacteristic, complemented
273#3216C2×C13711yescharacteristic, complemented
274#1652C2×C13712yescomplemented
275#1649C2×C13712yescomplemented
276#1628C2×C13712yescomplemented
277#1627C2×C13712yescomplemented
278#1552C2×C13711yescharacteristic, complemented
279#1496C2×C13711yescharacteristic, complemented
280#1481C2×C13711yescharacteristic, complemented
281#563—22no—
282#559—21no—
283Q82—21no—
284#556—21no—
285#556C22×C13712yes—
286D4×Q8—21no—
287D4×Q8C22×C13712yes—
288#542—22no—
289#542—22no—
290#536—22no—
291#533C22×C13711yescharacteristic
292#533C22×C13711yescharacteristic
293#532C22×C13711yescharacteristic
294#532C22×C13711yescharacteristic
295#500C22×C13711yescharacteristic
296#498C22×C13711yescharacteristic
297#497—21no—
298#489—21no—
299#486C22×C13711yescharacteristic
300#486C22×C13711yescharacteristic
301#482—22no—
302#478—22no—
303#474—21no—
304#474C22×C13712yes—
305#466—22no—
306#462C22×C13712yes—
307#460C22×C13712yes—
308#459—21no—
309#459C22×C13712yes—
310#452—22no—
311#432C22×C13711yescharacteristic
312#431C22×C13711yescharacteristic
313C2×C4⋊C8C22×C13711yescharacteristic
314#332C22×C13712yes—
315#332C22×C13712yes—
316Q8⋊C8C22×C13712yes—
317Q8⋊C8C22×C13712yes—
318D4⋊C8C22×C13712yes—
319D4⋊C8C22×C13712yes—
320C2×#41—21no—
321C2×#41—21no—
322C22×Q8—22no—
323C2×Q16—22no—
324C2×SD16—22no—
325C2×D8—22no—
326C22×C8—21no—
327C4⋊Q8—24no—
328C4⋊Q8—22no—
329C4⋊Q8—22no—
330C4⋊Q8D4×C13711yescharacteristic
331C4⋊Q8D4×C13711yescharacteristic
332C4⋊Q8D4×C13711yescharacteristic
333C4⋊Q8C23×C13711yescharacteristic
334C4⋊Q8C23×C13711yescharacteristic
335C4⋊Q8C23×C13711yescharacteristic
336#127D4×C13711yescharacteristic
337#127C23×C13711yescharacteristic
338#126—24no—
339#126—24no—
340#125—21no—
341#125D4×C13712yes—
342#124—24no—
343#124—22no—
344#124—22no—
345#124—21no—
346#124—21no—
347#123—24no—
348#123—24no—
349C22⋊Q8—24no—
350C22⋊Q8—22no—
351C22⋊Q8—21no—
352C22⋊Q8—21no—
353C22⋊Q8—21no—
354C22⋊Q8—22no—
355C22⋊Q8—24no—
356C22⋊Q8D4×C13712yes—
357#121—21no—
358#121—21no—
359#121—21no—
360#121D4×C13712yes—
361C4×Q8—22no—
362C4×Q8—22no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8C23×C13712yes—
367C4×D4—22no—
368C4×D4—22no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4C23×C13712yes—
373#117—21no—
374#117—22no—
375#117D4×C13712yes—
376C2×C42C23×C13711yescharacteristic
377#107—22no—
378#107—22no—
379#106—22no—
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8C23×C13712yes—
383C4⋊C8C23×C13712yes—
384#103—22no—
385#102—22no—
386#102—22no—
387#102—22no—
388#102—22no—
389#102—22no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392#97—21no—
393C4×C8C23×C13711yescharacteristic
394C4×C8C23×C13711yescharacteristic
395#41—82no—
396#41—82no—
397C2×Q8—24no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—82no—
404C2×Q8—82no—
405C2×Q8C2×D4×C13712yes—
406C2×D4—22no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4—41no—
413C2×D4C2×D4×C13712yes—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—41no—
417C22×C4C2×D4×C13711yescharacteristic
418C22×C4C2×D4×C13711yescharacteristic
419C22×C4C2×D4×C13711yescharacteristic
420Q16—82no—
421SD16—82no—
422D8—82no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—81no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4C2×D4×C13712yes—
443C4⋊C4C2×D4×C13712yes—
444C4⋊C4C2×D4×C13712yes—
445C4⋊C4C2×D4×C13712yes—
446C22⋊C4—24no—
447C22⋊C4—24no—
448C22⋊C4—24no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—41no—
454C22⋊C4—41no—
455C42—24no—
456C42—22no—
457C42—22no—
458C42C2×D4×C13711yescharacteristic
459C42C2×D4×C13711yescharacteristic
460C42C2×D4×C13711yescharacteristic
461C42C24×C13711yescharacteristic
462C23—22no—
463C23—41no—
464C23#120×C13711yescharacteristic
465Q8—22no—
466Q8—22no—
467Q8—42no—
468Q8—42no—
469Q8—41no—
470Q8—41no—
471Q8—42no—
472Q8—81no—
473Q8—84no—
474D4—22no—
475D4—22no—
476D4—42no—
477D4—42no—
478D4—42no—
479D4—41no—
480D4—41no—
481D4—81no—
482D4—82no—
483D4—82no—
484C2×C4—22no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—22no—
492C2×C4—41no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—41no—
496C2×C4—82no—
497C2×C4—84no—
498C2×C4#120×C13711yescharacteristic
499C2×C4#120×C13711yescharacteristic
500C2×C4#120×C13711yescharacteristic
501C2×C4C22×D4×C13711yescharacteristic
502C2×C4C22×D4×C13711yescharacteristic
503C2×C4C22×D4×C13711yescharacteristic
504C8—41no—
505C8—41no—
506C8—42no—
507C8—42no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—81no—
515C22—81no—
516C22—81no—
517C22C2×#120×C13711yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—42no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—81no—
528C4#576×C13712yes—
529C4#577×C13711yescharacteristic
530C4#578×C13711yescharacteristic
531C2—41no—
532C2—82no—
533C2—161no—
534C2#3008×C13711yescharacteristic
535C2#3013×C13711yescharacteristic
536C2#3020×C13711yescharacteristic
subgroupG/H
center, socleC22×C137C2×#120
commutator, Frattini, cosocleC42C24×C137
prime radical#3245×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. #3550×C137C2semidirect
3. #3228×C137C2semidirect
4. #3216×C137C2semidirect
5. #1652×C137C2semidirect
6. #1649×C137C2semidirect
7. #1628×C137C2semidirect
8. #1627×C137C2semidirect
9. #1552×C137C2semidirect
10. #1496×C137C2semidirect
11. #1481×C137C2semidirect
268. #18948C137direct (N × H)
269. C137#18948direct (N × H)
270. #3550C2×C137semidirect
272. #3228C2×C137semidirect
273. #3216C2×C137semidirect
274. #1652C2×C137semidirect
275. #1649C2×C137semidirect
276. #1628C2×C137semidirect
277. #1627C2×C137semidirect
278. #1552C2×C137semidirect
279. #1496C2×C137semidirect
280. #1481C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3550×C1372
#3245×C1372
#3228×C1372
#3216×C1372
#1652×C1372
#1649×C1372
#1628×C1372
#1627×C1372
#1552×C1372
#1496×C1372
#1481×C1372
#18948137