Finite Group Databasebeta

← C137×#11836 #46861222

Subgroups — C137×#11836 #46861222

Order 35072.

286 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3183×C137C211yesmaximal, characteristic
2#2165×C137C211yesmaximal, characteristic, complemented
3#1841×C137C211yesmaximal, characteristic, complemented
4#1342×C137C211yesmaximal, characteristic, complemented
5#1341×C137C211yesmaximal, characteristic
6#1340×C137C211yesmaximal, characteristic, complemented
7#1339×C137C211yesmaximal, characteristic
8#529×C137—21no—
9#499×C137C411yescharacteristic, complemented
10#495×C137C411yescharacteristic, complemented
11#488×C137—21no—
12#470×C137C2211yescharacteristic
13#469×C137C2211yescharacteristic
14#468×C137—21no—
15#442×C137C411yescharacteristic, complemented
16#441×C137C411yescharacteristic, complemented
17#440×C137—21no—
18C4×M16×C137C2211yescharacteristic
19#364×C137—21no—
20#349×C137C2211yescharacteristic
21#349×C137C2211yescharacteristic
22#347×C137—21no—
23#344×C137—21no—
24#339×C137—21no—
25#338×C137C2211yescharacteristic
26H(3,ℤ/4)×C137C2211yescharacteristic
27C2×Q16×C137C2×C411yescharacteristic
28C2×SD16×C137—21no—
29C2×D8×C137C2×C411yescharacteristic
30C2×M16×C137—21no—
31C2×M16×C137D411yescharacteristic
32C2×M16×C137C2311yescharacteristic
33#126×C137—41no—
34#125×C137—21no—
35#124×C137—21no—
36#123×C137—41no—
37C22⋊Q8×C137—21no—
38#121×C137—21no—
39C4×Q8×C137—21no—
40C4×D4×C137—21no—
41C4×D4×C137—41no—
42#117×C137—21no—
43#117×C137—41no—
44C2×C42×C137D411yescharacteristic
45M32×C137—21no—
46M32×C137—21no—
47#107×C137—21no—
48#106×C137C2×C411yescharacteristic
49#106×C137C2×C411yescharacteristic
50#103×C137—21no—
51#103×C137—21no—
52#102×C137—21no—
53#102×C137—21no—
54#97×C137C2×C411yescharacteristic
55#97×C137D411yescharacteristic
56C4×C8×C137C2×C411yescharacteristic
57C4×C8×C137D411yescharacteristic
58C2×Q8×C137—21no—
59C2×D4×C137—21no—
60C2×D4×C137—41no—
61C22×C4×C137—21no—
62C22×C4×C137—41no—
63C22×C4×C137C2×D411yescharacteristic
64Q16×C137—41no—
65SD16×C137—42no—
66D8×C137—41no—
67M16×C137—41no—
68M16×C137—41no—
69M16×C137—41no—
70M16×C137—41no—
71C2×C8×C137—41no—
72C2×C8×C137C22⋊C411yescharacteristic
73C2×C8×C137C22⋊C411yescharacteristic
74C2×C8×C137C22×C411yescharacteristic
75C2×C8×C137C2×D411yescharacteristic
76C4⋊C4×C137—21no—
77C4⋊C4×C137—21no—
78C4⋊C4×C137—41no—
79C4⋊C4×C137—41no—
80C4⋊C4×C137—41no—
81C4⋊C4×C137—41no—
82C4⋊C4×C137—41no—
83C22⋊C4×C137—41no—
84C22⋊C4×C137—41no—
85C22⋊C4×C137—41no—
86C22⋊C4×C137—41no—
87C22⋊C4×C137—41no—
88C22⋊C4×C137—41no—
89C42×C137—21no—
90C42×C137—41no—
91C42×C137—41no—
92C42×C137C22⋊C411yescharacteristic
93C42×C137C22⋊C411yescharacteristic
94C16×C137—41no—
95C16×C137—41no—
96C23×C137—41no—
97C23×C137AGL(1,ℤ/8)11yescharacteristic
98Q8×C137—41no—
99Q8×C137—41no—
100D4×C137—41no—
101D4×C137—41no—
102D4×C137—82no—
103C2×C4×C137—21no—
104C2×C4×C137—21no—
105C2×C4×C137—21no—
106C2×C4×C137—21no—
107C2×C4×C137—41no—
108C2×C4×C137—41no—
109C2×C4×C137—41no—
110C2×C4×C137—81no—
111C2×C4×C137—82no—
112C2×C4×C137—81no—
113C2×C4×C137C2×C22⋊C411yescharacteristic
114C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
115C8×C137—21no—
116C8×C137—21no—
117C8×C137—21no—
118C8×C137—21no—
119C8×C137—81no—
120C22×C137—21no—
121C22×C137—41no—
122C22×C137—81no—
123C22×C137—81no—
124C22×C137—81no—
125C22×C137#41811yescharacteristic
126C4×C137—21no—
127C4×C137—41no—
128C4×C137—41no—
129C4×C137—81no—
130C4×C137—81no—
131C4×C137—81no—
132C4×C137—161no—
133C4×C137#41011yescharacteristic
134C4×C137#42111yescharacteristic
135C2×C137—21no—
136C2×C137—41no—
137C2×C137—161no—
138C2×C137#151411yescharacteristic
139#11836C13711yesmaximal, characteristic, direct product factor, Sylow
140C137#1183611yescharacteristic, direct product factor, Sylow
141#3183C2×C13711yescharacteristic
142#2165C2×C13711yescharacteristic, complemented
143#1841C2×C13711yescharacteristic, complemented
144#1342C2×C13711yescharacteristic, complemented
145#1341C2×C13711yescharacteristic
146#1340C2×C13711yescharacteristic, complemented
147#1339C2×C13711yescharacteristic
148#529—21no—
149#499C4×C13711yescharacteristic, complemented
150#495C4×C13711yescharacteristic, complemented
151#488—21no—
152#470C22×C13711yescharacteristic
153#469C22×C13711yescharacteristic
154#468—21no—
155#442C4×C13711yescharacteristic, complemented
156#441C4×C13711yescharacteristic, complemented
157#440—21no—
158C4×M16C22×C13711yescharacteristic
159#364—21no—
160#349C22×C13711yescharacteristic
161#349C22×C13711yescharacteristic
162#347—21no—
163#344—21no—
164#339—21no—
165#338C22×C13711yescharacteristic
166H(3,ℤ/4)C22×C13711yescharacteristic
167C2×Q16C2×C4×C13711yescharacteristic
168C2×SD16—21no—
169C2×D8C2×C4×C13711yescharacteristic
170C2×M16—21no—
171C2×M16D4×C13711yescharacteristic
172C2×M16C23×C13711yescharacteristic
173#126—41no—
174#125—21no—
175#124—21no—
176#123—41no—
177C22⋊Q8—21no—
178#121—21no—
179C4×Q8—21no—
180C4×D4—21no—
181C4×D4—41no—
182#117—21no—
183#117—41no—
184C2×C42D4×C13711yescharacteristic
185M32—21no—
186M32—21no—
187#107—21no—
188#106C2×C4×C13711yescharacteristic
189#106C2×C4×C13711yescharacteristic
190#103—21no—
191#103—21no—
192#102—21no—
193#102—21no—
194#97C2×C4×C13711yescharacteristic
195#97D4×C13711yescharacteristic
196C4×C8C2×C4×C13711yescharacteristic
197C4×C8D4×C13711yescharacteristic
198C2×Q8—21no—
199C2×D4—21no—
200C2×D4—41no—
201C22×C4—21no—
202C22×C4—41no—
203C22×C4C2×D4×C13711yescharacteristic
204Q16—41no—
205SD16—42no—
206D8—41no—
207M16—41no—
208M16—41no—
209M16—41no—
210M16—41no—
211C2×C8—41no—
212C2×C8C22⋊C4×C13711yescharacteristic
213C2×C8C22⋊C4×C13711yescharacteristic
214C2×C8C22×C4×C13711yescharacteristic
215C2×C8C2×D4×C13711yescharacteristic
216C4⋊C4—21no—
217C4⋊C4—21no—
218C4⋊C4—41no—
219C4⋊C4—41no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C22⋊C4—41no—
224C22⋊C4—41no—
225C22⋊C4—41no—
226C22⋊C4—41no—
227C22⋊C4—41no—
228C22⋊C4—41no—
229C42—21no—
230C42—41no—
231C42—41no—
232C42C22⋊C4×C13711yescharacteristic
233C42C22⋊C4×C13711yescharacteristic
234C16—41no—
235C16—41no—
236C23—41no—
237C23AGL(1,ℤ/8)×C13711yescharacteristic
238Q8—41no—
239Q8—41no—
240D4—41no—
241D4—41no—
242D4—82no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—41no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—81no—
251C2×C4—82no—
252C2×C4—81no—
253C2×C4C2×C22⋊C4×C13711yescharacteristic
254C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
255C8—21no—
256C8—21no—
257C8—21no—
258C8—21no—
259C8—81no—
260C22—21no—
261C22—41no—
262C22—81no—
263C22—81no—
264C22—81no—
265C22#418×C13711yescharacteristic
266C4—21no—
267C4—41no—
268C4—41no—
269C4—81no—
270C4—81no—
271C4—81no—
272C4—161no—
273C4#410×C13711yescharacteristic
274C4#421×C13711yescharacteristic
275C2—21no—
276C2—41no—
277C2—161no—
278C2#1514×C13711yescharacteristic
subgroupG/H
center, socleC2×C137#1514
commutatorC2×C8C22×C4×C137
Frattini, cosocleC2×M16C23×C137
prime radical#469×C137C22
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C137 ◁ C2×C4×C137 ◁ C4×M16×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2165×C137C2semidirect
3. #1841×C137C2semidirect
4. #1342×C137C2semidirect
6. #1340×C137C2semidirect
9. #499×C137C4semidirect
10. #495×C137C4semidirect
15. #442×C137C4semidirect
16. #441×C137C4semidirect
139. #11836C137direct (N × H)
140. C137#11836direct (N × H)
142. #2165C2×C137semidirect
143. #1841C2×C137semidirect
144. #1342C2×C137semidirect
146. #1340C2×C137semidirect
149. #499C4×C137semidirect
150. #495C4×C137semidirect
155. #442C4×C137semidirect
156. #441C4×C137semidirect

Maximal subgroups

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

subgroupindex
#3183×C1372
#2165×C1372
#1841×C1372
#1342×C1372
#1341×C1372
#1340×C1372
#1339×C1372
#11836137