Finite Group Databasebeta

← C137×#9038 #46858424

Subgroups — C137×#9038 #46858424

Order 35072.

468 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3091×C137C211yesmaximal, characteristic
2#2976×C137C211yesmaximal, characteristic
3#1826×C137C211yesmaximal, characteristic, complemented
4#1818×C137C211yesmaximal, characteristic, complemented
5#1501×C137C211yesmaximal, characteristic
6#1298×C137C211yesmaximal, characteristic, complemented
7#1282×C137C211yesmaximal, characteristic, complemented
8#525×C137C2211yescharacteristic
9C2×#117×C137C2211yescharacteristic
10#485×C137—21no—
11#484×C137C411yescharacteristic, complemented
12#483×C137C411yescharacteristic, complemented
13#482×C137—21no—
14#481×C137C411yescharacteristic, complemented
15#480×C137C411yescharacteristic, complemented
16#436×C137—21no—
17#435×C137—21no—
18#435×C137—21no—
19C8×D4×C137—21no—
20#433×C137—21no—
21#427×C137—21no—
22#416×C137—21no—
23#408×C137—21no—
24#407×C137C2211yescharacteristic
25C2×C22⋊C8×C137C2211yescharacteristic
26C2×C22⋊C8×C137C2211yescharacteristic
27C2×C22⋊C8×C137C2211yescharacteristic
28C4×C22⋊C4×C137C2211yescharacteristic
29#339×C137—21no—
30#339×C137—21no—
31#336×C137—21no—
32#336×C137—21no—
33#328×C137—21no—
34#327×C137—21no—
35C2×#41×C137D411yescharacteristic
36C23×C4×C137C2311yescharacteristic
37C2×M16×C137—21no—
38C2×M16×C137D411yescharacteristic
39C2×M16×C137D411yescharacteristic
40C22×C8×C137—21no—
41C22×C8×C137—21no—
42C22×C8×C137—21no—
43C22×C8×C137D411yescharacteristic
44C22×C8×C137D411yescharacteristic
45#123×C137—21no—
46C22⋊Q8×C137C2×C411yescharacteristic
47C22⋊Q8×C137D411yescharacteristic
48#121×C137C2×C411yescharacteristic
49#121×C137D411yescharacteristic
50#120×C137—21no—
51C4×D4×C137—21no—
52C4×D4×C137—21no—
53#117×C137—21no—
54#117×C137—21no—
55#117×C137—21no—
56#117×C137—21no—
57#117×C137D411yescharacteristic
58C2×C4⋊C4×C137C2×C411yescharacteristic
59C2×C4⋊C4×C137C2×C411yescharacteristic
60C2×C22⋊C4×C137—21no—
61C2×C22⋊C4×C137—21no—
62C2×C42×C137—21no—
63C2×C42×C137—21no—
64#107×C137—21no—
65#107×C137—21no—
66#106×C137—21no—
67#106×C137—21no—
68C4⋊C8×C137—21no—
69C4⋊C8×C137—21no—
70#103×C137—21no—
71#103×C137—21no—
72#102×C137—21no—
73#102×C137—21no—
74C22⋊C8×C137—21no—
75C22⋊C8×C137—21no—
76C22⋊C8×C137—21no—
77C22⋊C8×C137—21no—
78C22⋊C8×C137—21no—
79C22⋊C8×C137—21no—
80C22⋊C8×C137—21no—
81C22⋊C8×C137—21no—
82C22⋊C8×C137—21no—
83C22⋊C8×C137C2×C411yescharacteristic
84C22⋊C8×C137C2×C411yescharacteristic
85#97×C137—21no—
86C4×C8×C137—21no—
87#95×C137—21no—
88C24×C137#4111yescharacteristic
89#41×C137—41no—
90#41×C137—41no—
91C2×Q8×C137C22⋊C411yescharacteristic
92C2×D4×C137—21no—
93C2×D4×C137—21no—
94C2×D4×C137—21no—
95C2×D4×C137C22⋊C411yescharacteristic
96C22×C4×C137—21no—
97C22×C4×C137—21no—
98C22×C4×C137—21no—
99C22×C4×C137—41no—
100C22×C4×C137—41no—
101C22×C4×C137—41no—
102C22×C4×C137C22×C411yescharacteristic
103C22×C4×C137C2×D411yescharacteristic
104C22×C4×C137C2×D411yescharacteristic
105C22×C4×C137C2×D411yescharacteristic
106C22×C4×C137C2×D411yescharacteristic
107C22×C4×C137#4111yescharacteristic
108M16×C137—41no—
109M16×C137—41no—
110M16×C137—81no—
111C2×C8×C137—21no—
112C2×C8×C137—21no—
113C2×C8×C137—21no—
114C2×C8×C137—21no—
115C2×C8×C137—21no—
116C2×C8×C137—21no—
117C2×C8×C137—41no—
118C2×C8×C137—41no—
119C2×C8×C137—41no—
120C2×C8×C137—41no—
121C2×C8×C137—41no—
122C2×C8×C137—41no—
123C2×C8×C137—41no—
124C2×C8×C137—81no—
125C4⋊C4×C137—21no—
126C4⋊C4×C137—21no—
127C4⋊C4×C137—21no—
128C4⋊C4×C137—21no—
129C4⋊C4×C137—21no—
130C4⋊C4×C137—21no—
131C4⋊C4×C137C22⋊C411yescharacteristic
132C4⋊C4×C137C22⋊C411yescharacteristic
133C22⋊C4×C137—21no—
134C22⋊C4×C137—21no—
135C22⋊C4×C137—21no—
136C22⋊C4×C137—21no—
137C22⋊C4×C137—21no—
138C22⋊C4×C137—22no—
139C22⋊C4×C137—41no—
140C22⋊C4×C137—41no—
141C22⋊C4×C137—41no—
142C42×C137—21no—
143C42×C137—41no—
144C42×C137—41no—
145C42×C137—41no—
146C42×C137—41no—
147C23×C137—21no—
148C23×C137—21no—
149C23×C137—21no—
150C23×C137—41no—
151C23×C137—41no—
152C23×C137C4×D411yescharacteristic
153C23×C137#12111yescharacteristic
154C23×C137#12311yescharacteristic
155Q8×C137—41no—
156D4×C137—41no—
157D4×C137—41no—
158D4×C137—41no—
159D4×C137—81no—
160D4×C137—81no—
161C2×C4×C137—21no—
162C2×C4×C137—21no—
163C2×C4×C137—21no—
164C2×C4×C137—21no—
165C2×C4×C137—21no—
166C2×C4×C137—21no—
167C2×C4×C137—21no—
168C2×C4×C137—21no—
169C2×C4×C137—21no—
170C2×C4×C137—41no—
171C2×C4×C137—41no—
172C2×C4×C137—41no—
173C2×C4×C137—41no—
174C2×C4×C137—41no—
175C2×C4×C137—42no—
176C2×C4×C137—42no—
177C2×C4×C137—41no—
178C2×C4×C137—41no—
179C2×C4×C137—41no—
180C2×C4×C137—41no—
181C2×C4×C137—81no—
182C2×C4×C137—81no—
183C2×C4×C137C2×C22⋊C411yescharacteristic
184C2×C4×C137C4×D411yescharacteristic
185C2×C4×C137#12011yescharacteristic
186C2×C4×C137#12111yescharacteristic
187C8×C137—41no—
188C8×C137—41no—
189C8×C137—41no—
190C8×C137—41no—
191C8×C137—41no—
192C8×C137—41no—
193C8×C137—81no—
194C22×C137—21no—
195C22×C137—21no—
196C22×C137—21no—
197C22×C137—21no—
198C22×C137—21no—
199C22×C137—21no—
200C22×C137—21no—
201C22×C137—21no—
202C22×C137—41no—
203C22×C137—41no—
204C22×C137—41no—
205C22×C137—81no—
206C22×C137—81no—
207C22×C137#38611yescharacteristic
208C22×C137#44311yescharacteristic
209C22×C137#44411yescharacteristic
210C4×C137—21no—
211C4×C137—21no—
212C4×C137—21no—
213C4×C137—41no—
214C4×C137—41no—
215C4×C137—41no—
216C4×C137—82no—
217C4×C137—81no—
218C4×C137—81no—
219C4×C137#45811yescharacteristic
220C4×C137#45811yescharacteristic
221C2×C137—21no—
222C2×C137—21no—
223C2×C137—41no—
224C2×C137—41no—
225C2×C137—81no—
226C2×C137#187611yescharacteristic
227C2×C137#188111yescharacteristic
228C2×C137#189011yescharacteristic
229#9038C13711yesmaximal, characteristic, direct product factor, Sylow
230C137#903811yescharacteristic, direct product factor, Sylow
231#3091C2×C13711yescharacteristic
232#2976C2×C13711yescharacteristic
233#1826C2×C13711yescharacteristic, complemented
234#1818C2×C13711yescharacteristic, complemented
235#1501C2×C13711yescharacteristic
236#1298C2×C13711yescharacteristic, complemented
237#1282C2×C13711yescharacteristic, complemented
238#525C22×C13711yescharacteristic
239C2×#117C22×C13711yescharacteristic
240#485—21no—
241#484C4×C13711yescharacteristic, complemented
242#483C4×C13711yescharacteristic, complemented
243#482—21no—
244#481C4×C13711yescharacteristic, complemented
245#480C4×C13711yescharacteristic, complemented
246#436—21no—
247#435—21no—
248#435—21no—
249C8×D4—21no—
250#433—21no—
251#427—21no—
252#416—21no—
253#408—21no—
254#407C22×C13711yescharacteristic
255C2×C22⋊C8C22×C13711yescharacteristic
256C2×C22⋊C8C22×C13711yescharacteristic
257C2×C22⋊C8C22×C13711yescharacteristic
258C4×C22⋊C4C22×C13711yescharacteristic
259#339—21no—
260#339—21no—
261#336—21no—
262#336—21no—
263#328—21no—
264#327—21no—
265C2×#41D4×C13711yescharacteristic
266C23×C4C23×C13711yescharacteristic
267C2×M16—21no—
268C2×M16D4×C13711yescharacteristic
269C2×M16D4×C13711yescharacteristic
270C22×C8—21no—
271C22×C8—21no—
272C22×C8—21no—
273C22×C8D4×C13711yescharacteristic
274C22×C8D4×C13711yescharacteristic
275#123—21no—
276C22⋊Q8C2×C4×C13711yescharacteristic
277C22⋊Q8D4×C13711yescharacteristic
278#121C2×C4×C13711yescharacteristic
279#121D4×C13711yescharacteristic
280#120—21no—
281C4×D4—21no—
282C4×D4—21no—
283#117—21no—
284#117—21no—
285#117—21no—
286#117—21no—
287#117D4×C13711yescharacteristic
288C2×C4⋊C4C2×C4×C13711yescharacteristic
289C2×C4⋊C4C2×C4×C13711yescharacteristic
290C2×C22⋊C4—21no—
291C2×C22⋊C4—21no—
292C2×C42—21no—
293C2×C42—21no—
294#107—21no—
295#107—21no—
296#106—21no—
297#106—21no—
298C4⋊C8—21no—
299C4⋊C8—21no—
300#103—21no—
301#103—21no—
302#102—21no—
303#102—21no—
304C22⋊C8—21no—
305C22⋊C8—21no—
306C22⋊C8—21no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309C22⋊C8—21no—
310C22⋊C8—21no—
311C22⋊C8—21no—
312C22⋊C8—21no—
313C22⋊C8C2×C4×C13711yescharacteristic
314C22⋊C8C2×C4×C13711yescharacteristic
315#97—21no—
316C4×C8—21no—
317#95—21no—
318C24#41×C13711yescharacteristic
319#41—41no—
320#41—41no—
321C2×Q8C22⋊C4×C13711yescharacteristic
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4C22⋊C4×C13711yescharacteristic
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4C22×C4×C13711yescharacteristic
333C22×C4C2×D4×C13711yescharacteristic
334C22×C4C2×D4×C13711yescharacteristic
335C22×C4C2×D4×C13711yescharacteristic
336C22×C4C2×D4×C13711yescharacteristic
337C22×C4#41×C13711yescharacteristic
338M16—41no—
339M16—41no—
340M16—81no—
341C2×C8—21no—
342C2×C8—21no—
343C2×C8—21no—
344C2×C8—21no—
345C2×C8—21no—
346C2×C8—21no—
347C2×C8—41no—
348C2×C8—41no—
349C2×C8—41no—
350C2×C8—41no—
351C2×C8—41no—
352C2×C8—41no—
353C2×C8—41no—
354C2×C8—81no—
355C4⋊C4—21no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4C22⋊C4×C13711yescharacteristic
362C4⋊C4C22⋊C4×C13711yescharacteristic
363C22⋊C4—21no—
364C22⋊C4—21no—
365C22⋊C4—21no—
366C22⋊C4—21no—
367C22⋊C4—21no—
368C22⋊C4—22no—
369C22⋊C4—41no—
370C22⋊C4—41no—
371C22⋊C4—41no—
372C42—21no—
373C42—41no—
374C42—41no—
375C42—41no—
376C42—41no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—41no—
381C23—41no—
382C23C4×D4×C13711yescharacteristic
383C23#121×C13711yescharacteristic
384C23#123×C13711yescharacteristic
385Q8—41no—
386D4—41no—
387D4—41no—
388D4—41no—
389D4—81no—
390D4—81no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—81no—
412C2×C4—81no—
413C2×C4C2×C22⋊C4×C13711yescharacteristic
414C2×C4C4×D4×C13711yescharacteristic
415C2×C4#120×C13711yescharacteristic
416C2×C4#121×C13711yescharacteristic
417C8—41no—
418C8—41no—
419C8—41no—
420C8—41no—
421C8—41no—
422C8—41no—
423C8—81no—
424C22—21no—
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22—21no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—81no—
436C22—81no—
437C22#386×C13711yescharacteristic
438C22#443×C13711yescharacteristic
439C22#444×C13711yescharacteristic
440C4—21no—
441C4—21no—
442C4—21no—
443C4—41no—
444C4—41no—
445C4—41no—
446C4—82no—
447C4—81no—
448C4—81no—
449C4#458×C13711yescharacteristic
450C4#458×C13711yescharacteristic
451C2—21no—
452C2—21no—
453C2—41no—
454C2—41no—
455C2—81no—
456C2#1876×C13711yescharacteristic
457C2#1881×C13711yescharacteristic
458C2#1890×C13711yescharacteristic
subgroupG/H
centerC2×C4×C137#120
commutatorC22×C4C22×C4×C137
Frattini, cosocleC23×C4C23×C137
socleC22×C137#386
prime radical#525×C137C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C137 ◁ C23×C4×C137 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1826×C137C2semidirect
4. #1818×C137C2semidirect
6. #1298×C137C2semidirect
7. #1282×C137C2semidirect
11. #484×C137C4semidirect
12. #483×C137C4semidirect
14. #481×C137C4semidirect
15. #480×C137C4semidirect
229. #9038C137direct (N × H)
230. C137#9038direct (N × H)
233. #1826C2×C137semidirect
234. #1818C2×C137semidirect
236. #1298C2×C137semidirect
237. #1282C2×C137semidirect
241. #484C4×C137semidirect
242. #483C4×C137semidirect
244. #481C4×C137semidirect
245. #480C4×C137semidirect

Maximal subgroups

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

subgroupindex
#3091×C1372
#2976×C1372
#1826×C1372
#1818×C1372
#1501×C1372
#1298×C1372
#1282×C1372
#9038137