Finite Group Databasebeta

← C137×#9371 #46858757

Subgroups — C137×#9371 #46858757

Order 35072.

442 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3214×C137C211yesmaximal, characteristic
2#2981×C137C211yesmaximal, characteristic, complemented
3#1551×C137C211yesmaximal, characteristic, complemented
4#1536×C137C211yesmaximal, characteristic, complemented
5#1480×C137C211yesmaximal, characteristic, complemented
6#1290×C137C211yesmaximal, characteristic, complemented
7#1287×C137C211yesmaximal, characteristic, complemented
8#532×C137C2211yescharacteristic
9#532×C137C2211yescharacteristic
10#496×C137C412yes—
11#489×C137C412yes—
12#461×C137—21no—
13#459×C137—21no—
14#449×C137—22no—
15#436×C137—21no—
16#435×C137—22no—
17C8×D4×C137—21no—
18#432×C137C2211yescharacteristic
19#432×C137C2211yescharacteristic
20#432×C137C2211yescharacteristic
21#431×C137C2211yescharacteristic
22C2×C4⋊C8×C137C2211yescharacteristic
23#408×C137—22no—
24#333×C137—21no—
25#331×C137—21no—
26#329×C137—22no—
27D4⋊C8×C137—21no—
28D4⋊C8×C137—21no—
29C2×#41×C137—21no—
30C2×#41×C137D412yes—
31C2×SD16×C137—22no—
32C2×D8×C137—22no—
33C2×M16×C137—22no—
34C22×C8×C137—22no—
35C22×C8×C137—21no—
36C4⋊Q8×C137C2×C411yescharacteristic
37C4⋊Q8×C137D411yescharacteristic
38#127×C137C2×C411yescharacteristic
39#127×C137D411yescharacteristic
40#124×C137—21no—
41#124×C137C2×C412yes—
42#121×C137—21no—
43#121×C137—21no—
44#121×C137—21no—
45#121×C137—21no—
46C4×D4×C137—21no—
47C4×D4×C137—21no—
48C4×D4×C137—21no—
49C4×D4×C137—21no—
50C2×C42×C137C2311yescharacteristic
51C4⋊C8×C137—21no—
52C4⋊C8×C137—21no—
53C4⋊C8×C137—21no—
54C4⋊C8×C137—21no—
55C4⋊C8×C137—21no—
56C4⋊C8×C137—21no—
57#103×C137—22no—
58#102×C137—22no—
59C22⋊C8×C137—22no—
60C22⋊C8×C137—22no—
61C22⋊C8×C137—21no—
62C22⋊C8×C137—21no—
63C22⋊C8×C137—21no—
64C22⋊C8×C137—21no—
65#97×C137—21no—
66#97×C137C2×C412yes—
67#97×C137D412yes—
68C4×C8×C137D411yescharacteristic
69C4×C8×C137D411yescharacteristic
70#41×C137—81no—
71#41×C137—81no—
72#41×C137—82no—
73C2×Q8×C137—21no—
74C2×Q8×C137C22⋊C412yes—
75C2×D4×C137—22no—
76C2×D4×C137—21no—
77C2×D4×C137—21no—
78C2×D4×C137—21no—
79C2×D4×C137—21no—
80C2×D4×C137—21no—
81C2×D4×C137—41no—
82C2×D4×C137C22⋊C412yes—
83C22×C4×C137—22no—
84C22×C4×C137—41no—
85C22×C4×C137C2×D411yescharacteristic
86C22×C4×C137#4111yescharacteristic
87C22×C4×C137#4111yescharacteristic
88SD16×C137—82no—
89D8×C137—82no—
90M16×C137—82no—
91C2×C8×C137—22no—
92C2×C8×C137—21no—
93C2×C8×C137—21no—
94C2×C8×C137—22no—
95C2×C8×C137—41no—
96C2×C8×C137—41no—
97C2×C8×C137—82no—
98C2×C8×C137—81no—
99C4⋊C4×C137—21no—
100C4⋊C4×C137—21no—
101C4⋊C4×C137—21no—
102C4⋊C4×C137—21no—
103C22⋊C4×C137—22no—
104C22⋊C4×C137—22no—
105C22⋊C4×C137—41no—
106C22⋊C4×C137—41no—
107C42×C137C22×C411yescharacteristic
108C42×C137C2×D411yescharacteristic
109C42×C137C2×D411yescharacteristic
110C42×C137C2×D411yescharacteristic
111C23×C137—22no—
112C23×C137—41no—
113C23×C137#12311yescharacteristic
114Q8×C137—42no—
115Q8×C137—81no—
116D4×C137—42no—
117D4×C137—41no—
118D4×C137—41no—
119D4×C137—42no—
120D4×C137—41no—
121D4×C137—41no—
122D4×C137—81no—
123D4×C137—81no—
124D4×C137—82no—
125D4×C137—82no—
126C2×C4×C137—21no—
127C2×C4×C137—21no—
128C2×C4×C137—22no—
129C2×C4×C137—41no—
130C2×C4×C137—41no—
131C2×C4×C137—42no—
132C2×C4×C137—42no—
133C2×C4×C137—41no—
134C2×C4×C137—81no—
135C2×C4×C137—81no—
136C2×C4×C137C2×C22⋊C411yescharacteristic
137C2×C4×C137C4×D411yescharacteristic
138C2×C4×C137C4×D411yescharacteristic
139C2×C4×C137#12011yescharacteristic
140C2×C4×C137#12111yescharacteristic
141C2×C4×C137#12111yescharacteristic
142C8×C137—41no—
143C8×C137—42no—
144C8×C137—41no—
145C8×C137—42no—
146C8×C137—81no—
147C8×C137—81no—
148C22×C137—21no—
149C22×C137—21no—
150C22×C137—21no—
151C22×C137—42no—
152C22×C137—42no—
153C22×C137—42no—
154C22×C137—81no—
155C22×C137—81no—
156C22×C137—81no—
157C22×C137#38611yescharacteristic
158C4×C137—21no—
159C4×C137—21no—
160C4×C137—21no—
161C4×C137—21no—
162C4×C137—21no—
163C4×C137—42no—
164C4×C137—81no—
165C4×C137#47111yescharacteristic
166C4×C137#47211yescharacteristic
167C2×C137—41no—
168C2×C137—82no—
169C2×C137—161no—
170C2×C137#188111yescharacteristic
171C2×C137#190711yescharacteristic
172C2×C137#191111yescharacteristic
173#9371C13711yesmaximal, characteristic, direct product factor, Sylow
174C137#937111yescharacteristic, direct product factor, Sylow
175#3214C2×C13711yescharacteristic
176#2981C2×C13711yescharacteristic, complemented
177#1551C2×C13711yescharacteristic, complemented
178#1536C2×C13711yescharacteristic, complemented
179#1480C2×C13711yescharacteristic, complemented
180#1290C2×C13711yescharacteristic, complemented
181#1287C2×C13711yescharacteristic, complemented
182#532C22×C13711yescharacteristic
183#532C22×C13711yescharacteristic
184#496C4×C13712yes—
185#489C4×C13712yes—
186#461—21no—
187#459—21no—
188#449—22no—
189#436—21no—
190#435—22no—
191C8×D4—21no—
192#432C22×C13711yescharacteristic
193#432C22×C13711yescharacteristic
194#432C22×C13711yescharacteristic
195#431C22×C13711yescharacteristic
196C2×C4⋊C8C22×C13711yescharacteristic
197#408—22no—
198#333—21no—
199#331—21no—
200#329—22no—
201D4⋊C8—21no—
202D4⋊C8—21no—
203C2×#41—21no—
204C2×#41D4×C13712yes—
205C2×SD16—22no—
206C2×D8—22no—
207C2×M16—22no—
208C22×C8—22no—
209C22×C8—21no—
210C4⋊Q8C2×C4×C13711yescharacteristic
211C4⋊Q8D4×C13711yescharacteristic
212#127C2×C4×C13711yescharacteristic
213#127D4×C13711yescharacteristic
214#124—21no—
215#124C2×C4×C13712yes—
216#121—21no—
217#121—21no—
218#121—21no—
219#121—21no—
220C4×D4—21no—
221C4×D4—21no—
222C4×D4—21no—
223C4×D4—21no—
224C2×C42C23×C13711yescharacteristic
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8—21no—
231#103—22no—
232#102—22no—
233C22⋊C8—22no—
234C22⋊C8—22no—
235C22⋊C8—21no—
236C22⋊C8—21no—
237C22⋊C8—21no—
238C22⋊C8—21no—
239#97—21no—
240#97C2×C4×C13712yes—
241#97D4×C13712yes—
242C4×C8D4×C13711yescharacteristic
243C4×C8D4×C13711yescharacteristic
244#41—81no—
245#41—81no—
246#41—82no—
247C2×Q8—21no—
248C2×Q8C22⋊C4×C13712yes—
249C2×D4—22no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4—41no—
256C2×D4C22⋊C4×C13712yes—
257C22×C4—22no—
258C22×C4—41no—
259C22×C4C2×D4×C13711yescharacteristic
260C22×C4#41×C13711yescharacteristic
261C22×C4#41×C13711yescharacteristic
262SD16—82no—
263D8—82no—
264M16—82no—
265C2×C8—22no—
266C2×C8—21no—
267C2×C8—21no—
268C2×C8—22no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—82no—
272C2×C8—81no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C22⋊C4—22no—
278C22⋊C4—22no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C42C22×C4×C13711yescharacteristic
282C42C2×D4×C13711yescharacteristic
283C42C2×D4×C13711yescharacteristic
284C42C2×D4×C13711yescharacteristic
285C23—22no—
286C23—41no—
287C23#123×C13711yescharacteristic
288Q8—42no—
289Q8—81no—
290D4—42no—
291D4—41no—
292D4—41no—
293D4—42no—
294D4—41no—
295D4—41no—
296D4—81no—
297D4—81no—
298D4—82no—
299D4—82no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—22no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4C2×C22⋊C4×C13711yescharacteristic
311C2×C4C4×D4×C13711yescharacteristic
312C2×C4C4×D4×C13711yescharacteristic
313C2×C4#120×C13711yescharacteristic
314C2×C4#121×C13711yescharacteristic
315C2×C4#121×C13711yescharacteristic
316C8—41no—
317C8—42no—
318C8—41no—
319C8—42no—
320C8—81no—
321C8—81no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22#386×C13711yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—21no—
337C4—42no—
338C4—81no—
339C4#471×C13711yescharacteristic
340C4#472×C13711yescharacteristic
341C2—41no—
342C2—82no—
343C2—161no—
344C2#1881×C13711yescharacteristic
345C2#1907×C13711yescharacteristic
346C2#1911×C13711yescharacteristic
subgroupG/H
center, socleC22×C137#386
commutatorC42C22×C4×C137
Frattini, cosocleC2×C42C23×C137
prime radical#3214×C137C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2981×C137C2semidirect
3. #1551×C137C2semidirect
4. #1536×C137C2semidirect
5. #1480×C137C2semidirect
6. #1290×C137C2semidirect
7. #1287×C137C2semidirect
173. #9371C137direct (N × H)
174. C137#9371direct (N × H)
176. #2981C2×C137semidirect
177. #1551C2×C137semidirect
178. #1536C2×C137semidirect
179. #1480C2×C137semidirect
180. #1290C2×C137semidirect
181. #1287C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3214×C1372
#2981×C1372
#1551×C1372
#1536×C1372
#1480×C1372
#1290×C1372
#1287×C1372
#9371137