Finite Group Databasebeta

← C137×#8869 #46858255

Subgroups — C137×#8869 #46858255

Order 35072.

658 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2325×C137C211yesmaximal, characteristic
2#1874×C137C211yesmaximal, characteristic
3#1852×C137C211yesmaximal, characteristic, complemented
4C2×#327×C137C211yesmaximal, characteristic
5#1442×C137C211yesmaximal, characteristic, complemented
6#1294×C137C211yesmaximal, characteristic, complemented
7#1280×C137C211yesmaximal, characteristic, complemented
8C2×#121×C137C2211yescharacteristic
9C2×C4×D4×C137—21no—
10C22×C4⋊C4×C137C2211yescharacteristic
11C2×#107×C137—21no—
12C2×#102×C137—21no—
13C2×C22⋊C8×C137C2211yescharacteristic
14C2×C22⋊C8×C137C2211yescharacteristic
15#388×C137—21no—
16#387×C137—21no—
17#386×C137—21no—
18#386×C137—21no—
19#385×C137—21no—
20#380×C137C2211yescharacteristic
21C2×#95×C137—21no—
22C2×#95×C137—21no—
23C2×#95×C137C2211yescharacteristic
24C2×#95×C137C2211yescharacteristic
25#340×C137—21no—
26#340×C137—21no—
27#327×C137C414yescomplemented
28C22×D4×C137—21no—
29C22×D4×C137D411yescharacteristic
30C23×C4×C137—21no—
31C23×C4×C137—21no—
32C23×C4×C137—21no—
33C23×C4×C137D411yescharacteristic
34C23×C4×C137D411yescharacteristic
35C23×C4×C137C2311yescharacteristic
36C22×C8×C137—21no—
37C22×C8×C137—21no—
38#121×C137—21no—
39#121×C137—21no—
40#121×C137C2×C412yes—
41#121×C137Q812yes—
42C4×D4×C137—42no—
43C4×D4×C137—42no—
44C2×C4⋊C4×C137—21no—
45C2×C4⋊C4×C137—21no—
46C2×C4⋊C4×C137—21no—
47C2×C4⋊C4×C137—42no—
48C2×C4⋊C4×C137D411yescharacteristic
49C2×C4⋊C4×C137D411yescharacteristic
50C2×C4⋊C4×C137D411yescharacteristic
51C2×C22⋊C4×C137—21no—
52C2×C22⋊C4×C137—21no—
53C2×C22⋊C4×C137—21no—
54C2×C22⋊C4×C137—21no—
55C2×C22⋊C4×C137—21no—
56C2×C42×C137—21no—
57#107×C137—42no—
58#102×C137—42no—
59C22⋊C8×C137—21no—
60C22⋊C8×C137—21no—
61C22⋊C8×C137—21no—
62C22⋊C8×C137C2×C412yescomplemented
63#95×C137—21no—
64#95×C137—21no—
65#95×C137—21no—
66#95×C137—21no—
67#95×C137—21no—
68#95×C137—21no—
69#95×C137—42no—
70#95×C137—42no—
71#95×C137C2×C412yescomplemented
72C24×C137—21no—
73C24×C137C2×D411yescharacteristic
74C2×D4×C137—22no—
75C2×D4×C137—22no—
76C2×D4×C137—21no—
77C2×D4×C137—41no—
78C2×D4×C137—41no—
79C2×D4×C137—41no—
80C2×D4×C137—41no—
81C2×D4×C137—41no—
82C2×D4×C137—41no—
83C2×D4×C137C4⋊C412yes—
84C22×C4×C137—21no—
85C22×C4×C137—21no—
86C22×C4×C137—21no—
87C22×C4×C137—22no—
88C22×C4×C137—22no—
89C22×C4×C137—21no—
90C22×C4×C137—21no—
91C22×C4×C137—21no—
92C22×C4×C137—21no—
93C22×C4×C137—21no—
94C22×C4×C137—41no—
95C22×C4×C137—41no—
96C22×C4×C137—42no—
97C22×C4×C137—41no—
98C22×C4×C137—41no—
99C22×C4×C137—41no—
100C22×C4×C137—41no—
101C22×C4×C137—41no—
102C22×C4×C137—41no—
103C22×C4×C137—41no—
104C22×C4×C137—41no—
105C22×C4×C137—41no—
106C22×C4×C137—41no—
107C22×C4×C137—41no—
108C22×C4×C137—41no—
109C22×C4×C137—41no—
110C22×C4×C137—41no—
111C22×C4×C137—41no—
112C22×C4×C137—41no—
113C22×C4×C137—81no—
114C22×C4×C137—81no—
115C22×C4×C137D812yes—
116C22×C4×C137C22×C411yescharacteristic
117C22×C4×C137C2×D411yescharacteristic
118C22×C4×C137C2×D411yescharacteristic
119C22×C4×C137C2×Q811yescharacteristic
120C22×C4×C137#4111yescharacteristic
121C22×C4×C137#4111yescharacteristic
122C2×C8×C137—22no—
123C2×C8×C137—41no—
124C2×C8×C137—41no—
125C2×C8×C137—41no—
126C2×C8×C137—41no—
127C2×C8×C137—41no—
128C4⋊C4×C137—21no—
129C4⋊C4×C137—22no—
130C4⋊C4×C137—22no—
131C4⋊C4×C137—41no—
132C4⋊C4×C137—41no—
133C4⋊C4×C137—41no—
134C4⋊C4×C137—41no—
135C4⋊C4×C137—42no—
136C4⋊C4×C137C4⋊C412yes—
137C22⋊C4×C137—22no—
138C22⋊C4×C137—22no—
139C22⋊C4×C137—42no—
140C22⋊C4×C137—41no—
141C22⋊C4×C137—41no—
142C22⋊C4×C137—81no—
143C22⋊C4×C137—81no—
144C42×C137—42no—
145C23×C137—21no—
146C23×C137—21no—
147C23×C137—21no—
148C23×C137—21no—
149C23×C137—22no—
150C23×C137—41no—
151C23×C137—41no—
152C23×C137—41no—
153C23×C137—41no—
154C23×C137—41no—
155C23×C137—41no—
156C23×C137C4×D411yescharacteristic
157C23×C137#12011yescharacteristic
158C23×C137C22⋊Q811yescharacteristic
159C23×C137C2×D811yescharacteristic
160C23×C137#13511yescharacteristic
161C23×C137AGL(1,ℤ/8)11yescharacteristic
162C23×C137#13711yescharacteristic
163D4×C137—42no—
164D4×C137—42no—
165D4×C137—42no—
166D4×C137—42no—
167D4×C137—42no—
168D4×C137—81no—
169C2×C4×C137—21no—
170C2×C4×C137—21no—
171C2×C4×C137—21no—
172C2×C4×C137—21no—
173C2×C4×C137—22no—
174C2×C4×C137—22no—
175C2×C4×C137—41no—
176C2×C4×C137—41no—
177C2×C4×C137—41no—
178C2×C4×C137—41no—
179C2×C4×C137—41no—
180C2×C4×C137—41no—
181C2×C4×C137—41no—
182C2×C4×C137—41no—
183C2×C4×C137—42no—
184C2×C4×C137—42no—
185C2×C4×C137—42no—
186C2×C4×C137—42no—
187C2×C4×C137—42no—
188C2×C4×C137—42no—
189C2×C4×C137—42no—
190C2×C4×C137—41no—
191C2×C4×C137—41no—
192C2×C4×C137—41no—
193C2×C4×C137—41no—
194C2×C4×C137—41no—
195C2×C4×C137—41no—
196C2×C4×C137—41no—
197C2×C4×C137—41no—
198C2×C4×C137—42no—
199C2×C4×C137—41no—
200C2×C4×C137—81no—
201C2×C4×C137—84no—
202C2×C4×C137—81no—
203C2×C4×C137—81no—
204C2×C4×C137—81no—
205C2×C4×C137—81no—
206C2×C4×C137—81no—
207C2×C4×C137—81no—
208C2×C4×C137—81no—
209C2×C4×C137—81no—
210C2×C4×C137—81no—
211C2×C4×C137C2×C4⋊C411yescharacteristic
212C2×C4×C137C4×D411yescharacteristic
213C2×C4×C137C22⋊Q811yescharacteristic
214C2×C4×C137#12311yescharacteristic
215C8×C137—42no—
216C8×C137—81no—
217C22×C137—21no—
218C22×C137—21no—
219C22×C137—21no—
220C22×C137—21no—
221C22×C137—21no—
222C22×C137—21no—
223C22×C137—21no—
224C22×C137—21no—
225C22×C137—21no—
226C22×C137—21no—
227C22×C137—21no—
228C22×C137—21no—
229C22×C137—42no—
230C22×C137—42no—
231C22×C137—42no—
232C22×C137—81no—
233C22×C137—81no—
234C22×C137—81no—
235C22×C137—81no—
236C22×C137#38511yescharacteristic
237C22×C137C4×D811yescharacteristic
238C22×C137#44011yescharacteristic
239C22×C137#44711yescharacteristic
240C22×C137#45211yescharacteristic
241C22×C137#45411yescharacteristic
242C22×C137#45511yescharacteristic
243C22×C137B(4,𝔽2)11yescharacteristic
244C22×C137#45811yescharacteristic
245C22×C137#47411yescharacteristic
246C22×C137#47811yescharacteristic
247C4×C137—21no—
248C4×C137—21no—
249C4×C137—21no—
250C4×C137—21no—
251C4×C137—42no—
252C4×C137—42no—
253C4×C137—82no—
254C4×C137—81no—
255C4×C137—82no—
256C4×C137—81no—
257C4×C137—81no—
258C2×C137—21no—
259C2×C137—21no—
260C2×C137—21no—
261C2×C137—21no—
262C2×C137—82no—
263C2×C137#159811yescharacteristic
264C2×C137#160611yescharacteristic
265C2×C137#160711yescharacteristic
266C2×C137#161511yescharacteristic
267C2×C137#186011yescharacteristic
268C2×C137#186211yescharacteristic
269C2×C137#186711yescharacteristic
270#8869C13711yesmaximal, characteristic, direct product factor, Sylow
271C137#886911yescharacteristic, direct product factor, Sylow
272#2325C2×C13711yescharacteristic
273#1874C2×C13711yescharacteristic
274#1852C2×C13711yescharacteristic, complemented
275C2×#327C2×C13711yescharacteristic
276#1442C2×C13711yescharacteristic, complemented
277#1294C2×C13711yescharacteristic, complemented
278#1280C2×C13711yescharacteristic, complemented
279C2×#121C22×C13711yescharacteristic
280C2×C4×D4—21no—
281C22×C4⋊C4C22×C13711yescharacteristic
282C2×#107—21no—
283C2×#102—21no—
284C2×C22⋊C8C22×C13711yescharacteristic
285C2×C22⋊C8C22×C13711yescharacteristic
286#388—21no—
287#387—21no—
288#386—21no—
289#386—21no—
290#385—21no—
291#380C22×C13711yescharacteristic
292C2×#95—21no—
293C2×#95—21no—
294C2×#95C22×C13711yescharacteristic
295C2×#95C22×C13711yescharacteristic
296#340—21no—
297#340—21no—
298#327C4×C13714yescomplemented
299C22×D4—21no—
300C22×D4D4×C13711yescharacteristic
301C23×C4—21no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4D4×C13711yescharacteristic
305C23×C4D4×C13711yescharacteristic
306C23×C4C23×C13711yescharacteristic
307C22×C8—21no—
308C22×C8—21no—
309#121—21no—
310#121—21no—
311#121C2×C4×C13712yes—
312#121Q8×C13712yes—
313C4×D4—42no—
314C4×D4—42no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—42no—
319C2×C4⋊C4D4×C13711yescharacteristic
320C2×C4⋊C4D4×C13711yescharacteristic
321C2×C4⋊C4D4×C13711yescharacteristic
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C42—21no—
328#107—42no—
329#102—42no—
330C22⋊C8—21no—
331C22⋊C8—21no—
332C22⋊C8—21no—
333C22⋊C8C2×C4×C13712yescomplemented
334#95—21no—
335#95—21no—
336#95—21no—
337#95—21no—
338#95—21no—
339#95—21no—
340#95—42no—
341#95—42no—
342#95C2×C4×C13712yescomplemented
343C24—21no—
344C24C2×D4×C13711yescharacteristic
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—21no—
348C2×D4—41no—
349C2×D4—41no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4C4⋊C4×C13712yes—
355C22×C4—21no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—21no—
364C22×C4—21no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—42no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—41no—
380C22×C4—41no—
381C22×C4—41no—
382C22×C4—41no—
383C22×C4—41no—
384C22×C4—81no—
385C22×C4—81no—
386C22×C4D8×C13712yes—
387C22×C4C22×C4×C13711yescharacteristic
388C22×C4C2×D4×C13711yescharacteristic
389C22×C4C2×D4×C13711yescharacteristic
390C22×C4C2×Q8×C13711yescharacteristic
391C22×C4#41×C13711yescharacteristic
392C22×C4#41×C13711yescharacteristic
393C2×C8—22no—
394C2×C8—41no—
395C2×C8—41no—
396C2×C8—41no—
397C2×C8—41no—
398C2×C8—41no—
399C4⋊C4—21no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—42no—
407C4⋊C4C4⋊C4×C13712yes—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—42no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4—81no—
414C22⋊C4—81no—
415C42—42no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—22no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23C4×D4×C13711yescharacteristic
428C23#120×C13711yescharacteristic
429C23C22⋊Q8×C13711yescharacteristic
430C23C2×D8×C13711yescharacteristic
431C23#135×C13711yescharacteristic
432C23AGL(1,ℤ/8)×C13711yescharacteristic
433C23#137×C13711yescharacteristic
434D4—42no—
435D4—42no—
436D4—42no—
437D4—42no—
438D4—42no—
439D4—81no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—41no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—41no—
454C2×C4—42no—
455C2×C4—42no—
456C2×C4—42no—
457C2×C4—42no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—42no—
470C2×C4—41no—
471C2×C4—81no—
472C2×C4—84no—
473C2×C4—81no—
474C2×C4—81no—
475C2×C4—81no—
476C2×C4—81no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—81no—
480C2×C4—81no—
481C2×C4—81no—
482C2×C4C2×C4⋊C4×C13711yescharacteristic
483C2×C4C4×D4×C13711yescharacteristic
484C2×C4C22⋊Q8×C13711yescharacteristic
485C2×C4#123×C13711yescharacteristic
486C8—42no—
487C8—81no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—21no—
499C22—21no—
500C22—42no—
501C22—42no—
502C22—42no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22#385×C13711yescharacteristic
508C22C4×D8×C13711yescharacteristic
509C22#440×C13711yescharacteristic
510C22#447×C13711yescharacteristic
511C22#452×C13711yescharacteristic
512C22#454×C13711yescharacteristic
513C22#455×C13711yescharacteristic
514C22B(4,𝔽2)×C13711yescharacteristic
515C22#458×C13711yescharacteristic
516C22#474×C13711yescharacteristic
517C22#478×C13711yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—42no—
524C4—82no—
525C4—82no—
526C4—81no—
527C4—81no—
528C4—81no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—21no—
533C2—82no—
534C2#1598×C13711yescharacteristic
535C2#1606×C13711yescharacteristic
536C2#1607×C13711yescharacteristic
537C2#1615×C13711yescharacteristic
538C2#1860×C13711yescharacteristic
539C2#1862×C13711yescharacteristic
540C2#1867×C13711yescharacteristic
subgroupG/H
center, socleC23×C137#120
commutatorC22×C4C22×C4×C137
Frattini, cosocleC23×C4C23×C137
prime radicalC2×#121×C137C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1852×C137C2semidirect
5. #1442×C137C2semidirect
6. #1294×C137C2semidirect
7. #1280×C137C2semidirect
27. #327×C137C4semidirect
62. C22⋊C8×C137C2×C4semidirect
71. #95×C137C2×C4semidirect
270. #8869C137direct (N × H)
271. C137#8869direct (N × H)
274. #1852C2×C137semidirect
276. #1442C2×C137semidirect
277. #1294C2×C137semidirect
278. #1280C2×C137semidirect
298. #327C4×C137semidirect
333. C22⋊C8C2×C4×C137semidirect
342. #95C2×C4×C137semidirect

Maximal subgroups

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

subgroupindex
#2325×C1372
#1874×C1372
#1852×C1372
C2×#327×C1372
#1442×C1372
#1294×C1372
#1280×C1372
#8869137