Finite Group Databasebeta

← C137×#8981 #46858367

Subgroups — C137×#8981 #46858367

Order 35072.

664 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#474×C137C211yesmaximal, characteristic
2D4×C4⋊C4×C137C211yesmaximal, characteristic
3#1990×C137C211yesmaximal, characteristic, complemented
4#1981×C137C211yesmaximal, characteristic, complemented
5C2×D4⋊C8×C137C211yesmaximal, characteristic
6#1296×C137C211yesmaximal, characteristic, complemented
7#1279×C137C211yesmaximal, characteristic, complemented
8C2×C4⋊Q8×C137C2211yescharacteristic
9C2×C4×D4×C137—21no—
10C2×C4×D4×C137C2211yescharacteristic
11C22×C4⋊C4×C137—21no—
12#474×C137—22no—
13#474×C137C414yescomplemented
14C2×#107×C137—21no—
15C2×C4⋊C8×C137C2211yescharacteristic
16C2×C4⋊C8×C137C2211yescharacteristic
17C2×#103×C137—21no—
18C2×#103×C137—21no—
19C2×#102×C137—21no—
20C2×C4×C8×C137C2211yescharacteristic
21#389×C137—21no—
22#385×C137—22no—
23#384×C137C2211yescharacteristic
24#380×C137—21no—
25C4×C4⋊C4×C137C2211yescharacteristic
26#340×C137—22no—
27D4⋊C8×C137—22no—
28C22×Q8×C137—21no—
29C22×D4×C137D411yescharacteristic
30C23×C4×C137—21no—
31C23×C4×C137—22no—
32C22×C8×C137—21no—
33C22×C8×C137—21no—
34C22×C8×C137—21no—
35C4⋊Q8×C137—21no—
36C4⋊Q8×C137—21no—
37C4⋊Q8×C137—21no—
38C4⋊Q8×C137C2×C412yescomplemented
39C4×D4×C137—21no—
40C4×D4×C137—21no—
41C4×D4×C137—42no—
42C4×D4×C137—42no—
43C4×D4×C137C2×C412yes—
44C4×D4×C137D412yes—
45C2×C4⋊C4×C137—21no—
46C2×C4⋊C4×C137—21no—
47C2×C4⋊C4×C137—22no—
48C2×C4⋊C4×C137—21no—
49C2×C4⋊C4×C137—21no—
50C2×C4⋊C4×C137—42no—
51C2×C4⋊C4×C137—42no—
52C2×C4⋊C4×C137D411yescharacteristic
53C2×C4⋊C4×C137D411yescharacteristic
54C2×C4⋊C4×C137D411yescharacteristic
55C2×C4⋊C4×C137D412yes—
56C2×C22⋊C4×C137—21no—
57C2×C22⋊C4×C137—22no—
58C2×C42×C137—21no—
59C2×C42×C137C2311yescharacteristic
60#107×C137—24no—
61C4⋊C8×C137—21no—
62C4⋊C8×C137—21no—
63C4⋊C8×C137—21no—
64C4⋊C8×C137C2×C412yescomplemented
65#103×C137—42no—
66#103×C137—42no—
67#102×C137—24no—
68C4×C8×C137—21no—
69C4×C8×C137—21no—
70#95×C137—22no—
71#95×C137—21no—
72C24×C137—21no—
73C2×Q8×C137—22no—
74C2×Q8×C137—41no—
75C2×Q8×C137—41no—
76C2×Q8×C137—41no—
77C2×Q8×C137—41no—
78C2×Q8×C137—41no—
79C2×D4×C137—21no—
80C2×D4×C137—21no—
81C2×D4×C137—21no—
82C2×D4×C137C22⋊C412yes—
83C2×D4×C137SD1612yes—
84C2×D4×C137Q1612yes—
85C22×C4×C137—21no—
86C22×C4×C137—21no—
87C22×C4×C137—22no—
88C22×C4×C137—22no—
89C22×C4×C137—21no—
90C22×C4×C137—22no—
91C22×C4×C137—44no—
92C22×C4×C137—41no—
93C22×C4×C137—41no—
94C22×C4×C137—41no—
95C22×C4×C137—41no—
96C22×C4×C137—44no—
97C22×C4×C137—41no—
98C22×C4×C137—82no—
99C22×C4×C137C2×D411yescharacteristic
100C22×C4×C137C2×D411yescharacteristic
101C22×C4×C137C2×D411yescharacteristic
102C2×C8×C137—22no—
103C2×C8×C137—22no—
104C2×C8×C137—41no—
105C2×C8×C137—41no—
106C2×C8×C137—41no—
107C2×C8×C137—41no—
108C2×C8×C137—41no—
109C2×C8×C137—41no—
110C2×C8×C137—41no—
111C4⋊C4×C137—21no—
112C4⋊C4×C137—21no—
113C4⋊C4×C137—22no—
114C4⋊C4×C137—22no—
115C4⋊C4×C137—21no—
116C4⋊C4×C137—21no—
117C4⋊C4×C137—42no—
118C4⋊C4×C137—44no—
119C4⋊C4×C137—41no—
120C4⋊C4×C137—41no—
121C4⋊C4×C137—41no—
122C4⋊C4×C137—41no—
123C4⋊C4×C137—41no—
124C4⋊C4×C137—41no—
125C4⋊C4×C137C22⋊C412yes—
126C4⋊C4×C137D812yes—
127C22⋊C4×C137—22no—
128C22⋊C4×C137—22no—
129C22⋊C4×C137—44no—
130C42×C137—41no—
131C42×C137—41no—
132C42×C137C22×C411yescharacteristic
133C42×C137C2×D411yescharacteristic
134C42×C137#4111yescharacteristic
135C42×C137#4111yescharacteristic
136C23×C137—22no—
137C23×C137—22no—
138C23×C137—22no—
139C23×C137—41no—
140C23×C137—41no—
141C23×C137—41no—
142C23×C137—41no—
143C23×C137#12011yescharacteristic
144Q8×C137—42no—
145Q8×C137—42no—
146Q8×C137—81no—
147Q8×C137—81no—
148D4×C137—22no—
149D4×C137—22no—
150D4×C137—22no—
151D4×C137#10314yescomplemented
152C2×C4×C137—21no—
153C2×C4×C137—21no—
154C2×C4×C137—22no—
155C2×C4×C137—22no—
156C2×C4×C137—41no—
157C2×C4×C137—41no—
158C2×C4×C137—41no—
159C2×C4×C137—41no—
160C2×C4×C137—42no—
161C2×C4×C137—42no—
162C2×C4×C137—42no—
163C2×C4×C137—42no—
164C2×C4×C137—42no—
165C2×C4×C137—42no—
166C2×C4×C137—41no—
167C2×C4×C137—41no—
168C2×C4×C137—42no—
169C2×C4×C137—42no—
170C2×C4×C137—41no—
171C2×C4×C137—88no—
172C2×C4×C137—81no—
173C2×C4×C137—81no—
174C2×C4×C137C2×C22⋊C411yescharacteristic
175C2×C4×C137C4×D411yescharacteristic
176C2×C4×C137C4×D411yescharacteristic
177C2×C4×C137#12111yescharacteristic
178C2×C4×C137#12111yescharacteristic
179C2×C4×C137#12311yescharacteristic
180C2×C4×C137C2×D811yescharacteristic
181C2×C4×C137C2×SD1611yescharacteristic
182C2×C4×C137C2×Q1611yescharacteristic
183C2×C4×C137#13511yescharacteristic
184C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
185C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
186C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
187C2×C4×C137#13711yescharacteristic
188C8×C137—42no—
189C8×C137—42no—
190C8×C137—81no—
191C22×C137—24no—
192C22×C137—42no—
193C22×C137—42no—
194C22×C137—42no—
195C22×C137—42no—
196C22×C137—42no—
197C22×C137—42no—
198C22×C137#38611yescharacteristic
199C22×C137#44711yescharacteristic
200C22×C137#44911yescharacteristic
201C22×C137#45011yescharacteristic
202C22×C137#45111yescharacteristic
203C22×C137#45511yescharacteristic
204C22×C137#45611yescharacteristic
205C4×C137—21no—
206C4×C137—21no—
207C4×C137—42no—
208C4×C137—42no—
209C4×C137—82no—
210C4×C137—82no—
211C4×C137—81no—
212C4×C137C2×#10311yescharacteristic
213C4×C137#41711yescharacteristic
214C4×C137C4×D811yescharacteristic
215C4×C137#44211yescharacteristic
216C4×C137#45911yescharacteristic
217C4×C137#46311yescharacteristic
218C4×C137#48311yescharacteristic
219C4×C137#48411yescharacteristic
220C2×C137—44no—
221C2×C137#163911yescharacteristic
222C2×C137#164411yescharacteristic
223C2×C137#164911yescharacteristic
224C2×C137#165411yescharacteristic
225C2×C137#187211yescharacteristic
226C2×C137#187911yescharacteristic
227C2×C137#188211yescharacteristic
228#8981C13711yesmaximal, characteristic, direct product factor, Sylow
229C137#898111yescharacteristic, direct product factor, Sylow
230C2×#474C2×C13711yescharacteristic
231D4×C4⋊C4C2×C13711yescharacteristic
232#1990C2×C13711yescharacteristic, complemented
233#1981C2×C13711yescharacteristic, complemented
234C2×D4⋊C8C2×C13711yescharacteristic
235#1296C2×C13711yescharacteristic, complemented
236#1279C2×C13711yescharacteristic, complemented
237C2×C4⋊Q8C22×C13711yescharacteristic
238C2×C4×D4—21no—
239C2×C4×D4C22×C13711yescharacteristic
240C22×C4⋊C4—21no—
241#474—22no—
242#474C4×C13714yescomplemented
243C2×#107—21no—
244C2×C4⋊C8C22×C13711yescharacteristic
245C2×C4⋊C8C22×C13711yescharacteristic
246C2×#103—21no—
247C2×#103—21no—
248C2×#102—21no—
249C2×C4×C8C22×C13711yescharacteristic
250#389—21no—
251#385—22no—
252#384C22×C13711yescharacteristic
253#380—21no—
254C4×C4⋊C4C22×C13711yescharacteristic
255#340—22no—
256D4⋊C8—22no—
257C22×Q8—21no—
258C22×D4D4×C13711yescharacteristic
259C23×C4—21no—
260C23×C4—22no—
261C22×C8—21no—
262C22×C8—21no—
263C22×C8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8—21no—
267C4⋊Q8C2×C4×C13712yescomplemented
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—42no—
271C4×D4—42no—
272C4×D4C2×C4×C13712yes—
273C4×D4D4×C13712yes—
274C2×C4⋊C4—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4—22no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—42no—
280C2×C4⋊C4—42no—
281C2×C4⋊C4D4×C13711yescharacteristic
282C2×C4⋊C4D4×C13711yescharacteristic
283C2×C4⋊C4D4×C13711yescharacteristic
284C2×C4⋊C4D4×C13712yes—
285C2×C22⋊C4—21no—
286C2×C22⋊C4—22no—
287C2×C42—21no—
288C2×C42C23×C13711yescharacteristic
289#107—24no—
290C4⋊C8—21no—
291C4⋊C8—21no—
292C4⋊C8—21no—
293C4⋊C8C2×C4×C13712yescomplemented
294#103—42no—
295#103—42no—
296#102—24no—
297C4×C8—21no—
298C4×C8—21no—
299#95—22no—
300#95—21no—
301C24—21no—
302C2×Q8—22no—
303C2×Q8—41no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×Q8—41no—
308C2×D4—21no—
309C2×D4—21no—
310C2×D4—21no—
311C2×D4C22⋊C4×C13712yes—
312C2×D4SD16×C13712yes—
313C2×D4Q16×C13712yes—
314C22×C4—21no—
315C22×C4—21no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—44no—
321C22×C4—41no—
322C22×C4—41no—
323C22×C4—41no—
324C22×C4—41no—
325C22×C4—44no—
326C22×C4—41no—
327C22×C4—82no—
328C22×C4C2×D4×C13711yescharacteristic
329C22×C4C2×D4×C13711yescharacteristic
330C22×C4C2×D4×C13711yescharacteristic
331C2×C8—22no—
332C2×C8—22no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—41no—
340C4⋊C4—21no—
341C4⋊C4—21no—
342C4⋊C4—22no—
343C4⋊C4—22no—
344C4⋊C4—21no—
345C4⋊C4—21no—
346C4⋊C4—42no—
347C4⋊C4—44no—
348C4⋊C4—41no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C4⋊C4—41no—
352C4⋊C4—41no—
353C4⋊C4—41no—
354C4⋊C4C22⋊C4×C13712yes—
355C4⋊C4D8×C13712yes—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—44no—
359C42—41no—
360C42—41no—
361C42C22×C4×C13711yescharacteristic
362C42C2×D4×C13711yescharacteristic
363C42#41×C13711yescharacteristic
364C42#41×C13711yescharacteristic
365C23—22no—
366C23—22no—
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23#120×C13711yescharacteristic
373Q8—42no—
374Q8—42no—
375Q8—81no—
376Q8—81no—
377D4—22no—
378D4—22no—
379D4—22no—
380D4#103×C13714yescomplemented
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—22no—
384C2×C4—22no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—41no—
400C2×C4—88no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4C2×C22⋊C4×C13711yescharacteristic
404C2×C4C4×D4×C13711yescharacteristic
405C2×C4C4×D4×C13711yescharacteristic
406C2×C4#121×C13711yescharacteristic
407C2×C4#121×C13711yescharacteristic
408C2×C4#123×C13711yescharacteristic
409C2×C4C2×D8×C13711yescharacteristic
410C2×C4C2×SD16×C13711yescharacteristic
411C2×C4C2×Q16×C13711yescharacteristic
412C2×C4#135×C13711yescharacteristic
413C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
414C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
415C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
416C2×C4#137×C13711yescharacteristic
417C8—42no—
418C8—42no—
419C8—81no—
420C22—24no—
421C22—42no—
422C22—42no—
423C22—42no—
424C22—42no—
425C22—42no—
426C22—42no—
427C22#386×C13711yescharacteristic
428C22#447×C13711yescharacteristic
429C22#449×C13711yescharacteristic
430C22#450×C13711yescharacteristic
431C22#451×C13711yescharacteristic
432C22#455×C13711yescharacteristic
433C22#456×C13711yescharacteristic
434C4—21no—
435C4—21no—
436C4—42no—
437C4—42no—
438C4—82no—
439C4—82no—
440C4—81no—
441C4C2×#103×C13711yescharacteristic
442C4#417×C13711yescharacteristic
443C4C4×D8×C13711yescharacteristic
444C4#442×C13711yescharacteristic
445C4#459×C13711yescharacteristic
446C4#463×C13711yescharacteristic
447C4#483×C13711yescharacteristic
448C4#484×C13711yescharacteristic
449C2—44no—
450C2#1639×C13711yescharacteristic
451C2#1644×C13711yescharacteristic
452C2#1649×C13711yescharacteristic
453C2#1654×C13711yescharacteristic
454C2#1872×C13711yescharacteristic
455C2#1879×C13711yescharacteristic
456C2#1882×C13711yescharacteristic
subgroupG/H
center, socleC23×C137#120
commutatorC42C22×C4×C137
Frattini, cosocleC2×C42C23×C137
prime radicalC22×D4×C137D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1990×C137C2semidirect
4. #1981×C137C2semidirect
6. #1296×C137C2semidirect
7. #1279×C137C2semidirect
13. #474×C137C4semidirect
38. C4⋊Q8×C137C2×C4semidirect
64. C4⋊C8×C137C2×C4semidirect
151. D4×C137#103semidirect
228. #8981C137direct (N × H)
229. C137#8981direct (N × H)
232. #1990C2×C137semidirect
233. #1981C2×C137semidirect
235. #1296C2×C137semidirect
236. #1279C2×C137semidirect
242. #474C4×C137semidirect
267. C4⋊Q8C2×C4×C137semidirect
293. C4⋊C8C2×C4×C137semidirect
380. D4#103×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#474×C1372
D4×C4⋊C4×C1372
#1990×C1372
#1981×C1372
C2×D4⋊C8×C1372
#1296×C1372
#1279×C1372
#8981137