Finite Group Databasebeta

← C137×#13381 #46862767

Subgroups — C137×#13381 #46862767

Order 35072.

498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C137C211yesmaximal, characteristic
2C2×#367×C137C211yesmaximal, characteristic, complemented
3C2×#357×C137C211yesmaximal, characteristic, complemented
4C2×#357×C137C211yesmaximal, characteristic, complemented
5C2×C22⋊C16×C137C211yesmaximal, characteristic, complemented
6#1808×C137C211yesmaximal, characteristic, complemented
7#1380×C137C211yesmaximal, characteristic, complemented
8C22×D8×C137C2211yescharacteristic
9C23×C8×C137C2211yescharacteristic
10C2×#121×C137—21no—
11C22×C16×C137C2211yescharacteristic
12C22×C16×C137C2211yescharacteristic
13#466×C137—22no—
14#466×C137—22no—
15C2×#107×C137C2211yescharacteristic
16C2×#107×C137C2211yescharacteristic
17C2×#107×C137C2211yescharacteristic
18C2×#102×C137—21no—
19#380×C137—21no—
20#367×C137—22no—
21#357×C137—22no—
22#357×C137—22no—
23C22⋊C16×C137—22no—
24#340×C137—21no—
25C22×D4×C137—21no—
26C22×D4×C137—41no—
27C23×C4×C137D411yescharacteristic
28C2×D8×C137—21no—
29C2×D8×C137—21no—
30C2×D8×C137—21no—
31C2×D8×C137—21no—
32C2×D8×C137—21no—
33C2×D8×C137D412yes—
34C22×C8×C137—21no—
35C22×C8×C137—21no—
36C22×C8×C137—21no—
37C22×C8×C137—21no—
38C22×C8×C137—21no—
39C22×C8×C137—21no—
40C22×C8×C137D411yescharacteristic
41C22×C8×C137C2311yescharacteristic
42#121×C137—24no—
43#121×C137—42no—
44C2×C4⋊C4×C137—21no—
45C2×C4⋊C4×C137—21no—
46C2×C4⋊C4×C137—21no—
47C2×C22⋊C4×C137—41no—
48C2×C22⋊C4×C137—41no—
49C2×C16×C137—21no—
50C2×C16×C137—21no—
51C2×C16×C137—21no—
52C2×C16×C137—21no—
53C2×C16×C137—21no—
54C2×C16×C137D412yescomplemented
55#107×C137—21no—
56#107×C137—21no—
57#107×C137—21no—
58#107×C137—21no—
59#107×C137—21no—
60#107×C137D412yes—
61#102×C137—24no—
62#95×C137—41no—
63C24×C137—41no—
64C24×C137D811yescharacteristic
65C2×D4×C137—22no—
66C2×D4×C137—44no—
67C2×D4×C137—41no—
68C2×D4×C137—41no—
69C2×D4×C137—41no—
70C2×D4×C137—41no—
71C2×D4×C137—41no—
72C2×D4×C137—82no—
73C2×D4×C137—82no—
74C22×C4×C137—21no—
75C22×C4×C137—21no—
76C22×C4×C137—21no—
77C22×C4×C137—21no—
78C22×C4×C137—21no—
79C22×C4×C137—21no—
80C22×C4×C137—41no—
81C22×C4×C137—41no—
82C22×C4×C137—41no—
83C22×C4×C137D811yescharacteristic
84C22×C4×C137C2×D411yescharacteristic
85D8×C137—22no—
86D8×C137—22no—
87D8×C137—41no—
88D8×C137—41no—
89C2×C8×C137—21no—
90C2×C8×C137—21no—
91C2×C8×C137—21no—
92C2×C8×C137—41no—
93C2×C8×C137—41no—
94C2×C8×C137—41no—
95C2×C8×C137—41no—
96C2×C8×C137C2×D411yescharacteristic
97C2×C8×C137C2×D411yescharacteristic
98C2×C8×C137C2×D411yescharacteristic
99C2×C8×C137#4111yescharacteristic
100C2×C8×C137#4111yescharacteristic
101C2×C8×C137#4111yescharacteristic
102C4⋊C4×C137—22no—
103C4⋊C4×C137—41no—
104C4⋊C4×C137—41no—
105C4⋊C4×C137—41no—
106C4⋊C4×C137—41no—
107C4⋊C4×C137—41no—
108C22⋊C4×C137—44no—
109C22⋊C4×C137—82no—
110C16×C137—22no—
111C16×C137—41no—
112C23×C137—21no—
113C23×C137—21no—
114C23×C137—21no—
115C23×C137—21no—
116C23×C137—21no—
117C23×C137—21no—
118C23×C137—42no—
119C23×C137—81no—
120C23×C137—81no—
121C23×C137—81no—
122C23×C137—81no—
123C23×C137—81no—
124C23×C137—81no—
125C23×C137SD3212yes—
126C23×C137C2×D811yescharacteristic
127D4×C137—42no—
128D4×C137—42no—
129D4×C137—88no—
130D4×C137—81no—
131D4×C137—81no—
132C2×C4×C137—21no—
133C2×C4×C137—21no—
134C2×C4×C137—21no—
135C2×C4×C137—41no—
136C2×C4×C137—41no—
137C2×C4×C137—41no—
138C2×C4×C137—41no—
139C2×C4×C137—42no—
140C2×C4×C137—81no—
141C2×C4×C137—81no—
142C2×C4×C137—81no—
143C2×C4×C137—81no—
144C2×C4×C137—81no—
145C2×C4×C137—81no—
146C2×C4×C137—81no—
147C2×C4×C137—81no—
148C2×C4×C137#12011yescharacteristic
149C2×C4×C137#12111yescharacteristic
150C2×C4×C137#12311yescharacteristic
151C2×C4×C137#13511yescharacteristic
152C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
153C2×C4×C137#13711yescharacteristic
154C8×C137—41no—
155C8×C137#12111yescharacteristic
156C8×C137#12111yescharacteristic
157C8×C137#12311yescharacteristic
158C8×C137#12411yescharacteristic
159C22×C137—22no—
160C22×C137—22no—
161C22×C137—22no—
162C22×C137—41no—
163C22×C137—41no—
164C22×C137—41no—
165C22×C137—41no—
166C22×C137—82no—
167C22×C137—82no—
168C22×C137—82no—
169C22×C137—161no—
170C22×C137—161no—
171C22×C137—161no—
172C22×C137—161no—
173C22×C137#44711yescharacteristic
174C22×C137#46611yescharacteristic
175C22×C137#48011yescharacteristic
176C22×C137C2×SD3211yescharacteristic
177C22×C137#50811yescharacteristic
178C22×C137#50911yescharacteristic
179C22×C137#50911yescharacteristic
180C4×C137—41no—
181C4×C137—82no—
182C4×C137—161no—
183C4×C137—161no—
184C4×C137#39411yescharacteristic
185C4×C137#45211yescharacteristic
186C4×C137#46811yescharacteristic
187C4×C137#48211yescharacteristic
188C2×C137—42no—
189C2×C137—162no—
190C2×C137#203311yescharacteristic
191C2×C137#218611yescharacteristic
192C2×C137#218711yescharacteristic
193C2×C137#221711yescharacteristic
194C2×C137#221811yescharacteristic
195C2×C137#223311yescharacteristic
196C2×C137#223411yescharacteristic
197#13381C13711yesmaximal, characteristic, direct product factor, Sylow
198C137#1338111yescharacteristic, direct product factor, Sylow
199C2×#466C2×C13711yescharacteristic
200C2×#367C2×C13711yescharacteristic, complemented
201C2×#357C2×C13711yescharacteristic, complemented
202C2×#357C2×C13711yescharacteristic, complemented
203C2×C22⋊C16C2×C13711yescharacteristic, complemented
204#1808C2×C13711yescharacteristic, complemented
205#1380C2×C13711yescharacteristic, complemented
206C22×D8C22×C13711yescharacteristic
207C23×C8C22×C13711yescharacteristic
208C2×#121—21no—
209C22×C16C22×C13711yescharacteristic
210C22×C16C22×C13711yescharacteristic
211#466—22no—
212#466—22no—
213C2×#107C22×C13711yescharacteristic
214C2×#107C22×C13711yescharacteristic
215C2×#107C22×C13711yescharacteristic
216C2×#102—21no—
217#380—21no—
218#367—22no—
219#357—22no—
220#357—22no—
221C22⋊C16—22no—
222#340—21no—
223C22×D4—21no—
224C22×D4—41no—
225C23×C4D4×C13711yescharacteristic
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—21no—
229C2×D8—21no—
230C2×D8—21no—
231C2×D8D4×C13712yes—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8D4×C13711yescharacteristic
239C22×C8C23×C13711yescharacteristic
240#121—24no—
241#121—42no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C22⋊C4—41no—
246C2×C22⋊C4—41no—
247C2×C16—21no—
248C2×C16—21no—
249C2×C16—21no—
250C2×C16—21no—
251C2×C16—21no—
252C2×C16D4×C13712yescomplemented
253#107—21no—
254#107—21no—
255#107—21no—
256#107—21no—
257#107—21no—
258#107D4×C13712yes—
259#102—24no—
260#95—41no—
261C24—41no—
262C24D8×C13711yescharacteristic
263C2×D4—22no—
264C2×D4—44no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—41no—
270C2×D4—82no—
271C2×D4—82no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4D8×C13711yescharacteristic
282C22×C4C2×D4×C13711yescharacteristic
283D8—22no—
284D8—22no—
285D8—41no—
286D8—41no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8C2×D4×C13711yescharacteristic
295C2×C8C2×D4×C13711yescharacteristic
296C2×C8C2×D4×C13711yescharacteristic
297C2×C8#41×C13711yescharacteristic
298C2×C8#41×C13711yescharacteristic
299C2×C8#41×C13711yescharacteristic
300C4⋊C4—22no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C22⋊C4—44no—
307C22⋊C4—82no—
308C16—22no—
309C16—41no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—42no—
317C23—81no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23—81no—
322C23—81no—
323C23SD32×C13712yes—
324C23C2×D8×C13711yescharacteristic
325D4—42no—
326D4—42no—
327D4—88no—
328D4—81no—
329D4—81no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4#120×C13711yescharacteristic
347C2×C4#121×C13711yescharacteristic
348C2×C4#123×C13711yescharacteristic
349C2×C4#135×C13711yescharacteristic
350C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
351C2×C4#137×C13711yescharacteristic
352C8—41no—
353C8#121×C13711yescharacteristic
354C8#121×C13711yescharacteristic
355C8#123×C13711yescharacteristic
356C8#124×C13711yescharacteristic
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22—161no—
368C22—161no—
369C22—161no—
370C22—161no—
371C22#447×C13711yescharacteristic
372C22#466×C13711yescharacteristic
373C22#480×C13711yescharacteristic
374C22C2×SD32×C13711yescharacteristic
375C22#508×C13711yescharacteristic
376C22#509×C13711yescharacteristic
377C22#509×C13711yescharacteristic
378C4—41no—
379C4—82no—
380C4—161no—
381C4—161no—
382C4#394×C13711yescharacteristic
383C4#452×C13711yescharacteristic
384C4#468×C13711yescharacteristic
385C4#482×C13711yescharacteristic
386C2—42no—
387C2—162no—
388C2#2033×C13711yescharacteristic
389C2#2186×C13711yescharacteristic
390C2#2187×C13711yescharacteristic
391C2#2217×C13711yescharacteristic
392C2#2218×C13711yescharacteristic
393C2#2233×C13711yescharacteristic
394C2#2234×C13711yescharacteristic
subgroupG/H
center, socleC23×C137C2×D8
commutator, Frattini, cosocleC22×C8C23×C137
prime radicalC2×#466×C137C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C137 ◁ C23×C4×C137 ◁ C23×C8×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#367×C137C2semidirect
3. C2×#357×C137C2semidirect
4. C2×#357×C137C2semidirect
5. C2×C22⋊C16×C137C2semidirect
6. #1808×C137C2semidirect
7. #1380×C137C2semidirect
54. C2×C16×C137D4semidirect
197. #13381C137direct (N × H)
198. C137#13381direct (N × H)
200. C2×#367C2×C137semidirect
201. C2×#357C2×C137semidirect
202. C2×#357C2×C137semidirect
203. C2×C22⋊C16C2×C137semidirect
204. #1808C2×C137semidirect
205. #1380C2×C137semidirect
252. C2×C16D4×C137semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1372
C2×#367×C1372
C2×#357×C1372
C2×C22⋊C16×C1372
#1808×C1372
#1380×C1372
#13381137