Finite Group Databasebeta

← C137×#13583 #46862969

Subgroups — C137×#13583 #46862969

Order 35072.

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

normal subgroups only

This group has 416 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#3147×C137C211yesmaximal, characteristic
2#2126×C137C212yesmaximal, complemented
3#1409×C137C212yesmaximal, complemented
4#1408×C137C212yesmaximal, complemented
5C2×#135×C137—22no—
6#532×C137C411yescharacteristic, complemented
7#532×C137C2211yescharacteristic
8#495×C137—22no—
9#494×C137C411yescharacteristic, complemented
10#493×C137C2211yescharacteristic
11#492×C137C411yescharacteristic, complemented
12#492×C137C2211yescharacteristic
13#410×C137—22no—
14C2×C4×C8×C137C411yescharacteristic, complemented
15#354×C137—22no—
16#353×C137C2214yes—
17C2×#41×C137—21no—
18C2×#41×C137D412yes—
19#135×C137—44no—
20#135×C137—44no—
21C2×Q16×C137—22no—
22C2×SD16×C137—22no—
23C2×SD16×C137—22no—
24C2×D8×C137—22no—
25C22×C8×C137—21no—
26C4⋊Q8×C137C2×C411yescharacteristic
27C4⋊Q8×C137C2×C411yescharacteristic
28#127×C137C2×C411yescharacteristic
29#127×C137C2311yescharacteristic
30#124×C137—21no—
31#124×C137D412yes—
32#121×C137—41no—
33#121×C137—41no—
34C4×D4×C137—41no—
35C4×D4×C137—41no—
36#117×C137—42no—
37C2×C42×C137C2×C411yescharacteristic
38#99×C137—24no—
39#99×C137—42no—
40C4×C8×C137—21no—
41C4×C8×C137C2×C411yescharacteristic
42C4×C8×C137C2×C411yescharacteristic
43#41×C137—42no—
44#41×C137—42no—
45#41×C137—42no—
46#41×C137—42no—
47C2×Q8×C137—21no—
48C2×Q8×C137C22⋊C412yes—
49C2×D4×C137—22no—
50C2×D4×C137—21no—
51C2×D4×C137—41no—
52C2×D4×C137—41no—
53C2×D4×C137—41no—
54C2×D4×C137C2×D412yes—
55C22×C4×C137—21no—
56C22×C4×C137—22no—
57C22×C4×C137—41no—
58C22×C4×C137C22⋊C411yescharacteristic
59Q16×C137—44no—
60SD16×C137—44no—
61SD16×C137—44no—
62D8×C137—44no—
63C2×C8×C137—22no—
64C2×C8×C137—22no—
65C2×C8×C137—21no—
66C2×C8×C137—21no—
67C4⋊C4×C137—41no—
68C4⋊C4×C137—41no—
69C4⋊C4×C137—82no—
70C22⋊C4×C137—42no—
71C22⋊C4×C137—42no—
72C22⋊C4×C137—44no—
73C42×C137—21no—
74C42×C137—82no—
75C42×C137C22⋊C411yescharacteristic
76C42×C137C22×C411yescharacteristic
77C23×C137—22no—
78C23×C137—41no—
79C23×C137#9911yescharacteristic
80Q8×C137—42no—
81Q8×C137—42no—
82D4×C137—42no—
83D4×C137—42no—
84D4×C137—82no—
85D4×C137—82no—
86D4×C137—82no—
87D4×C137—82no—
88C2×C4×C137—21no—
89C2×C4×C137—21no—
90C2×C4×C137—21no—
91C2×C4×C137—21no—
92C2×C4×C137—22no—
93C2×C4×C137—42no—
94C2×C4×C137—42no—
95C2×C4×C137—42no—
96C2×C4×C137—41no—
97C2×C4×C137—81no—
98C2×C4×C137—81no—
99C2×C4×C137—84no—
100C2×C4×C137#9911yescharacteristic
101C2×C4×C137C2×C22⋊C411yescharacteristic
102C8×C137—22no—
103C8×C137—22no—
104C22×C137—21no—
105C22×C137—41no—
106C22×C137—42no—
107C22×C137—82no—
108C22×C137—82no—
109C22×C137—81no—
110C22×C137C2×#9911yescharacteristic
111C4×C137—22no—
112C4×C137—21no—
113C4×C137—41no—
114C4×C137—42no—
115C4×C137—81no—
116C4×C137—164no—
117C4×C137#35311yescharacteristic
118C4×C137#35311yescharacteristic
119C2×C137—21no—
120C2×C137—41no—
121C2×C137—82no—
122C2×C137—161no—
123C2×C137C2×#35311yescharacteristic
124#13583C13711yesmaximal, characteristic, direct product factor, Sylow
125C137#1358311yescharacteristic, direct product factor, Sylow
126#3147C2×C13711yescharacteristic
127#2126C2×C13712yescomplemented
128#1409C2×C13712yescomplemented
129#1408C2×C13712yescomplemented
130C2×#135—22no—
131#532C4×C13711yescharacteristic, complemented
132#532C22×C13711yescharacteristic
133#495—22no—
134#494C4×C13711yescharacteristic, complemented
135#493C22×C13711yescharacteristic
136#492C4×C13711yescharacteristic, complemented
137#492C22×C13711yescharacteristic
138#410—22no—
139C2×C4×C8C4×C13711yescharacteristic, complemented
140#354—22no—
141#353C22×C13714yes—
142C2×#41—21no—
143C2×#41D4×C13712yes—
144#135—44no—
145#135—44no—
146C2×Q16—22no—
147C2×SD16—22no—
148C2×SD16—22no—
149C2×D8—22no—
150C22×C8—21no—
151C4⋊Q8C2×C4×C13711yescharacteristic
152C4⋊Q8C2×C4×C13711yescharacteristic
153#127C2×C4×C13711yescharacteristic
154#127C23×C13711yescharacteristic
155#124—21no—
156#124D4×C13712yes—
157#121—41no—
158#121—41no—
159C4×D4—41no—
160C4×D4—41no—
161#117—42no—
162C2×C42C2×C4×C13711yescharacteristic
163#99—24no—
164#99—42no—
165C4×C8—21no—
166C4×C8C2×C4×C13711yescharacteristic
167C4×C8C2×C4×C13711yescharacteristic
168#41—42no—
169#41—42no—
170#41—42no—
171#41—42no—
172C2×Q8—21no—
173C2×Q8C22⋊C4×C13712yes—
174C2×D4—22no—
175C2×D4—21no—
176C2×D4—41no—
177C2×D4—41no—
178C2×D4—41no—
179C2×D4C2×D4×C13712yes—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—41no—
183C22×C4C22⋊C4×C13711yescharacteristic
184Q16—44no—
185SD16—44no—
186SD16—44no—
187D8—44no—
188C2×C8—22no—
189C2×C8—22no—
190C2×C8—21no—
191C2×C8—21no—
192C4⋊C4—41no—
193C4⋊C4—41no—
194C4⋊C4—82no—
195C22⋊C4—42no—
196C22⋊C4—42no—
197C22⋊C4—44no—
198C42—21no—
199C42—82no—
200C42C22⋊C4×C13711yescharacteristic
201C42C22×C4×C13711yescharacteristic
202C23—22no—
203C23—41no—
204C23#99×C13711yescharacteristic
205Q8—42no—
206Q8—42no—
207D4—42no—
208D4—42no—
209D4—82no—
210D4—82no—
211D4—82no—
212D4—82no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—41no—
222C2×C4—81no—
223C2×C4—81no—
224C2×C4—84no—
225C2×C4#99×C13711yescharacteristic
226C2×C4C2×C22⋊C4×C13711yescharacteristic
227C8—22no—
228C8—22no—
229C22—21no—
230C22—41no—
231C22—42no—
232C22—82no—
233C22—82no—
234C22—81no—
235C22C2×#99×C13711yescharacteristic
236C4—22no—
237C4—21no—
238C4—41no—
239C4—42no—
240C4—81no—
241C4—164no—
242C4#353×C13711yescharacteristic
243C4#353×C13711yescharacteristic
244C2—21no—
245C2—41no—
246C2—82no—
247C2—161no—
248C2C2×#353×C13711yescharacteristic
subgroupG/H
centerC4×C137#353
commutatorC42C22×C4×C137
Frattini, cosocle#127C23×C137
socleC2×C137C2×#353
prime radical#3147×C137C2
LCSG ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C137 ◁ C2×C4×C137 ◁ C22×C4×C137 ◁ #532×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2126×C137C2semidirect
3. #1409×C137C2semidirect
4. #1408×C137C2semidirect
6. #532×C137C4semidirect
9. #494×C137C4semidirect
11. #492×C137C4semidirect
14. C2×C4×C8×C137C4semidirect
124. #13583C137direct (N × H)
125. C137#13583direct (N × H)
127. #2126C2×C137semidirect
128. #1409C2×C137semidirect
129. #1408C2×C137semidirect
131. #532C4×C137semidirect
134. #494C4×C137semidirect
136. #492C4×C137semidirect
139. C2×C4×C8C4×C137semidirect

Maximal subgroups

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

subgroupindex
#3147×C1372
#2126×C1372
#1409×C1372
#1408×C1372
#13583137