Finite Group Databasebeta

← C137×#14654 #46864040

Subgroups — C137×#14654 #46864040

Order 35072.

1030 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#400×C137C211yesmaximal, characteristic
2#1445×C137C211yesmaximal, characteristic
3#1442×C137C212yesmaximal
4#1442×C137C212yesmaximal
5#1442×C137C212yesmaximal
6#1442×C137C212yesmaximal
7#1441×C137C212yesmaximal
8#1436×C137C211yesmaximal, characteristic
9#1436×C137C212yesmaximal
10C22×C4⋊C4×C137C2212yes—
11C22×C4⋊C4×C137C2212yes—
12C22×C4⋊C4×C137C2211yescharacteristic
13C22×C4⋊C4×C137C2211yescharacteristic
14C22×C42×C137C2211yescharacteristic
15#400×C137C418yescomplemented
16C2×#95×C137C2212yes—
17C2×#95×C137C2212yes—
18C2×#95×C137C2212yes—
19C2×#95×C137C2212yes—
20C2×#95×C137C2212yes—
21C2×#95×C137C2211yescharacteristic
22C2×#95×C137C2212yes—
23C2×#95×C137C2212yes—
24C2×#95×C137C2212yes—
25C2×#95×C137C2212yes—
26C2×#95×C137C2212yes—
27C2×#95×C137C2211yescharacteristic
28C2×#95×C137C2211yescharacteristic
29C2×#95×C137C2212yes—
30C2×#95×C137C2211yescharacteristic
31C2×#95×C137C2212yes—
32C23×C4×C137C2312yes—
33C23×C4×C137C2312yes—
34C23×C4×C137C2312yes—
35C23×C4×C137C2311yescharacteristic
36C23×C4×C137C2312yes—
37C23×C4×C137C2311yescharacteristic
38C23×C4×C137C2311yescharacteristic
39C23×C4×C137C2312yes—
40C23×C4×C137C2312yes—
41C2×C4⋊C4×C137—24no—
42C2×C4⋊C4×C137—41no—
43C2×C4⋊C4×C137—41no—
44C2×C4⋊C4×C137—41no—
45C2×C4⋊C4×C137—41no—
46C2×C4⋊C4×C137—42no—
47C2×C4⋊C4×C137—42no—
48C2×C4⋊C4×C137—42no—
49C2×C4⋊C4×C137—42no—
50C2×C4⋊C4×C137—42no—
51C2×C4⋊C4×C137C2×C414yes—
52C2×C4⋊C4×C137C2×C414yes—
53C2×C42×C137—42no—
54C2×C42×C137—41no—
55#95×C137—24no—
56#95×C137—24no—
57#95×C137—42no—
58#95×C137—42no—
59#95×C137—42no—
60#95×C137—42no—
61#95×C137—42no—
62#95×C137—42no—
63#95×C137—41no—
64#95×C137—41no—
65#95×C137—42no—
66#95×C137—42no—
67#95×C137—41no—
68#95×C137C2×C414yes—
69#95×C137C2×C418yes—
70#95×C137C2×C418yes—
71C24×C137C2411yescharacteristic
72C22×C4×C137—22no—
73C22×C4×C137—22no—
74C22×C4×C137—22no—
75C22×C4×C137—22no—
76C22×C4×C137—22no—
77C22×C4×C137—22no—
78C22×C4×C137—22no—
79C22×C4×C137—21no—
80C22×C4×C137—21no—
81C22×C4×C137—22no—
82C22×C4×C137—21no—
83C22×C4×C137—22no—
84C22×C4×C137—22no—
85C22×C4×C137—22no—
86C22×C4×C137—22no—
87C22×C4×C137—22no—
88C22×C4×C137—21no—
89C22×C4×C137—22no—
90C22×C4×C137—21no—
91C22×C4×C137—21no—
92C22×C4×C137—22no—
93C22×C4×C137—22no—
94C22×C4×C137—22no—
95C22×C4×C137—22no—
96C22×C4×C137—22no—
97C22×C4×C137—22no—
98C22×C4×C137—22no—
99C22×C4×C137—22no—
100C22×C4×C137—22no—
101C22×C4×C137—22no—
102C22×C4×C137—22no—
103C22×C4×C137—22no—
104C22×C4×C137—22no—
105C22×C4×C137—22no—
106C22×C4×C137—22no—
107C22×C4×C137—22no—
108C22×C4×C137—22no—
109C22×C4×C137—22no—
110C22×C4×C137—22no—
111C22×C4×C137—22no—
112C22×C4×C137—22no—
113C22×C4×C137—22no—
114C22×C4×C137—22no—
115C22×C4×C137—22no—
116C22×C4×C137—22no—
117C22×C4×C137—22no—
118C22×C4×C137—22no—
119C22×C4×C137—22no—
120C22×C4×C137—22no—
121C22×C4×C137—22no—
122C22×C4×C137—22no—
123C22×C4×C137C22×C414yes—
124C22×C4×C137C22×C412yes—
125C22×C4×C137C22×C412yes—
126C22×C4×C137C22×C414yes—
127C22×C4×C137C22×C412yes—
128C22×C4×C137#4114yes—
129C4⋊C4×C137—44no—
130C4⋊C4×C137—44no—
131C4⋊C4×C137—48no—
132C4⋊C4×C137—48no—
133C42×C137—44no—
134C23×C137C23×C411yescharacteristic
135C23×C137C2×#4112yes—
136C23×C137H(5,𝔽2)11yescharacteristic
137C23×C137H(5,𝔽2)11yescharacteristic
138C23×C137H(5,𝔽2)12yes—
139C23×C137H(5,𝔽2)12yes—
140C23×C1372−1+412yes—
141C23×C1372−1+412yes—
142C23×C1372−1+412yes—
143C2×C4×C137—22no—
144C2×C4×C137—24no—
145C2×C4×C137—22no—
146C2×C4×C137—22no—
147C2×C4×C137—22no—
148C2×C4×C137—24no—
149C2×C4×C137—22no—
150C2×C4×C137—24no—
151C2×C4×C137—24no—
152C2×C4×C137—24no—
153C2×C4×C137—24no—
154C2×C4×C137—24no—
155C2×C4×C137—24no—
156C2×C4×C137—24no—
157C2×C4×C137—24no—
158C2×C4×C137—24no—
159C2×C4×C137—42no—
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—42no—
171C2×C4×C137—42no—
172C2×C4×C137—42no—
173C2×C4×C137—42no—
174C2×C4×C137—42no—
175C2×C4×C137—42no—
176C2×C4×C137—41no—
177C2×C4×C137—41no—
178C2×C4×C137—42no—
179C2×C4×C137—42no—
180C2×C4×C137—42no—
181C2×C4×C137—42no—
182C2×C4×C137—42no—
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—42no—
191C2×C4×C137—42no—
192C2×C4×C137—42no—
193C2×C4×C137—42no—
194C2×C4×C137—42no—
195C2×C4×C137—42no—
196C2×C4×C137—42no—
197C2×C4×C137—42no—
198C2×C4×C137—42no—
199C2×C4×C137—42no—
200C22×C137C4×#4111yescharacteristic
201C22×C137#51811yescharacteristic
202C22×C137#51911yescharacteristic
203C22×C137#52012yes—
204C22×C137#52012yes—
205C22×C137#53812yes—
206C22×C137#53912yes—
207C22×C137#53912yes—
208C22×C137#54112yes—
209C22×C137#54212yes—
210C22×C137#54212yes—
211C22×C137#56011yescharacteristic
212C22×C137H(3,𝔽4)11yescharacteristic
213C22×C137#56212yes—
214C22×C137#56212yes—
215C22×C137#56212yes—
216C22×C137#56312yes—
217C22×C137#56312yes—
218C22×C137#56311yescharacteristic
219C22×C137#56311yescharacteristic
220C22×C137#56412yes—
221C4×C137—44no—
222C4×C137—42no—
223C4×C137—44no—
224C4×C137—42no—
225C4×C137—42no—
226C4×C137—44no—
227C4×C137—82no—
228C4×C137—82no—
229C4×C137—82no—
230C2×C137#233211yescharacteristic
231C2×C137#233412yes—
232C2×C137#237611yescharacteristic
233C2×C137#237911yescharacteristic
234C2×C137#238212yes—
235C2×C137#282712yes—
236C2×C137#283212yes—
237C2×C137#283912yes—
238C2×C137#283912yes—
239#14654C13711yesmaximal, characteristic, direct product factor, Sylow
240C137#1465411yescharacteristic, direct product factor, Sylow
241C2×#400C2×C13711yescharacteristic
242#1445C2×C13711yescharacteristic
243#1442C2×C13712yes—
244#1442C2×C13712yes—
245#1442C2×C13712yes—
246#1442C2×C13712yes—
247#1441C2×C13712yes—
248#1436C2×C13712yes—
249#1436C2×C13711yescharacteristic
250C22×C4⋊C4C22×C13712yes—
251C22×C4⋊C4C22×C13712yes—
252C22×C4⋊C4C22×C13711yescharacteristic
253C22×C4⋊C4C22×C13711yescharacteristic
254C22×C42C22×C13711yescharacteristic
255#400C4×C13718yescomplemented
256C2×#95C22×C13712yes—
257C2×#95C22×C13712yes—
258C2×#95C22×C13712yes—
259C2×#95C22×C13712yes—
260C2×#95C22×C13712yes—
261C2×#95C22×C13711yescharacteristic
262C2×#95C22×C13712yes—
263C2×#95C22×C13712yes—
264C2×#95C22×C13712yes—
265C2×#95C22×C13712yes—
266C2×#95C22×C13712yes—
267C2×#95C22×C13711yescharacteristic
268C2×#95C22×C13711yescharacteristic
269C2×#95C22×C13712yes—
270C2×#95C22×C13711yescharacteristic
271C2×#95C22×C13712yes—
272C23×C4C23×C13712yes—
273C23×C4C23×C13712yes—
274C23×C4C23×C13712yes—
275C23×C4C23×C13711yescharacteristic
276C23×C4C23×C13712yes—
277C23×C4C23×C13711yescharacteristic
278C23×C4C23×C13712yes—
279C23×C4C23×C13711yescharacteristic
280C23×C4C23×C13712yes—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—41no—
283C2×C4⋊C4—41no—
284C2×C4⋊C4—41no—
285C2×C4⋊C4—41no—
286C2×C4⋊C4—42no—
287C2×C4⋊C4—42no—
288C2×C4⋊C4—42no—
289C2×C4⋊C4—42no—
290C2×C4⋊C4—42no—
291C2×C4⋊C4C2×C4×C13714yes—
292C2×C4⋊C4C2×C4×C13714yes—
293C2×C42—42no—
294C2×C42—41no—
295#95—24no—
296#95—24no—
297#95—42no—
298#95—42no—
299#95—42no—
300#95—42no—
301#95—42no—
302#95—42no—
303#95—41no—
304#95—41no—
305#95—42no—
306#95—42no—
307#95—41no—
308#95C2×C4×C13714yes—
309#95C2×C4×C13718yes—
310#95C2×C4×C13718yes—
311C24C24×C13711yescharacteristic
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—22no—
322C22×C4—21no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—22no—
359C22×C4—22no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4C22×C4×C13714yes—
364C22×C4C22×C4×C13712yes—
365C22×C4C22×C4×C13714yes—
366C22×C4C22×C4×C13712yes—
367C22×C4C22×C4×C13712yes—
368C22×C4#41×C13714yes—
369C4⋊C4—44no—
370C4⋊C4—44no—
371C4⋊C4—48no—
372C4⋊C4—48no—
373C42—44no—
374C23C23×C4×C13711yescharacteristic
375C23C2×#41×C13712yes—
376C23H(5,𝔽2)×C13711yescharacteristic
377C23H(5,𝔽2)×C13711yescharacteristic
378C23H(5,𝔽2)×C13712yes—
379C23H(5,𝔽2)×C13712yes—
380C232−1+4×C13712yes—
381C232−1+4×C13712yes—
382C232−1+4×C13712yes—
383C2×C4—22no—
384C2×C4—24no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—24no—
389C2×C4—22no—
390C2×C4—24no—
391C2×C4—24no—
392C2×C4—24no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—24no—
398C2×C4—24no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C22C4×#41×C13711yescharacteristic
441C22#518×C13711yescharacteristic
442C22#519×C13711yescharacteristic
443C22#520×C13712yes—
444C22#520×C13712yes—
445C22#538×C13712yes—
446C22#539×C13712yes—
447C22#539×C13712yes—
448C22#541×C13712yes—
449C22#542×C13712yes—
450C22#542×C13712yes—
451C22#560×C13711yescharacteristic
452C22H(3,𝔽4)×C13711yescharacteristic
453C22#562×C13712yes—
454C22#562×C13712yes—
455C22#562×C13712yes—
456C22#563×C13712yes—
457C22#563×C13712yes—
458C22#563×C13711yescharacteristic
459C22#563×C13711yescharacteristic
460C22#564×C13712yes—
461C4—44no—
462C4—42no—
463C4—44no—
464C4—42no—
465C4—42no—
466C4—44no—
467C4—82no—
468C4—82no—
469C4—82no—
470C2#2332×C13711yescharacteristic
471C2#2334×C13712yes—
472C2#2376×C13711yescharacteristic
473C2#2379×C13711yescharacteristic
474C2#2382×C13712yes—
475C2#2827×C13712yes—
476C2#2832×C13712yes—
477C2#2839×C13712yes—
478C2#2839×C13712yes—
subgroupG/H
center, socle, prime radicalC24×C137C24
commutatorC23C23×C4×C137
Frattini, cosocleC24C24×C137
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C137 ◁ G

Complements

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

NH ≅ G/Ntype
15. #400×C137C4semidirect
239. #14654C137direct (N × H)
240. C137#14654direct (N × H)
255. #400C4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#400×C1372
#1445×C1372
#1442×C1372
#1441×C1372
#1436×C1372
#14654137