Finite Group Databasebeta

← C137×#7819 #46857205

Subgroups — C137×#7819 #46857205

Order 35072.

434 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 98 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#2724×C137C211yesmaximal, characteristic
2#2093×C137C211yesmaximal, characteristic
3#2084×C137C212yesmaximal, complemented
4#1271×C137C212yesmaximal, complemented
5#1270×C137C211yesmaximal, characteristic
6C2×#123×C137—21no—
7C2×#107×C137—21no—
8C2×#106×C137—22no—
9C2×#102×C137—21no—
10#398×C137—21no—
11#397×C137—22no—
12#390×C137C2211yescharacteristic
13#389×C137C2212yes—
14#385×C137—22no—
15#384×C137C2211yescharacteristic
16#340×C137—22no—
17#336×C137C2212yes—
18#336×C137C2211yescharacteristic
19C22×D4×C137D411yescharacteristic
20C23×C4×C137—21no—
21C22×C8×C137—21no—
22C22×C8×C137—22no—
23#123×C137—42no—
24#123×C137—42no—
25C2×C4⋊C4×C137—22no—
26C2×C4⋊C4×C137—21no—
27C2×C4⋊C4×C137—22no—
28C2×C4⋊C4×C137—21no—
29C2×C4⋊C4×C137D412yes—
30C2×C4⋊C4×C137D412yes—
31C2×C4⋊C4×C137D411yescharacteristic
32C2×C22⋊C4×C137—22no—
33C2×C22⋊C4×C137—21no—
34C2×C22⋊C4×C137—22no—
35C2×C42×C137C2311yescharacteristic
36#107×C137—42no—
37#106×C137—44no—
38#102×C137—42no—
39#95×C137—22no—
40#95×C137—21no—
41#95×C137—22no—
42C24×C137—21no—
43C2×D4×C137—21no—
44C2×D4×C137—41no—
45C2×D4×C137—41no—
46C2×D4×C137SD1612yes—
47C22×C4×C137—21no—
48C22×C4×C137—22no—
49C22×C4×C137—22no—
50C22×C4×C137—42no—
51C22×C4×C137—41no—
52C22×C4×C137—81no—
53C22×C4×C137—81no—
54C22×C4×C137C2×D411yescharacteristic
55C22×C4×C137C2×D412yes—
56C2×C8×C137—22no—
57C2×C8×C137—24no—
58C2×C8×C137—42no—
59C2×C8×C137—41no—
60C2×C8×C137—42no—
61C2×C8×C137—41no—
62C4⋊C4×C137—22no—
63C4⋊C4×C137—22no—
64C4⋊C4×C137—41no—
65C4⋊C4×C137—42no—
66C4⋊C4×C137—41no—
67C4⋊C4×C137—41no—
68C4⋊C4×C137—42no—
69C4⋊C4×C137—42no—
70C4⋊C4×C137—42no—
71C4⋊C4×C137—42no—
72C4⋊C4×C137—81no—
73C22⋊C4×C137—42no—
74C22⋊C4×C137—44no—
75C22⋊C4×C137—42no—
76C22⋊C4×C137—42no—
77C42×C137—41no—
78C23×C137—22no—
79C23×C137—42no—
80C23×C137—41no—
81C23×C137—42no—
82C23×C137—41no—
83C23×C137#12011yescharacteristic
84D4×C137—42no—
85D4×C137—81no—
86C2×C4×C137—21no—
87C2×C4×C137—22no—
88C2×C4×C137—22no—
89C2×C4×C137—21no—
90C2×C4×C137—42no—
91C2×C4×C137—42no—
92C2×C4×C137—42no—
93C2×C4×C137—42no—
94C2×C4×C137—41no—
95C2×C4×C137—42no—
96C2×C4×C137—42no—
97C2×C4×C137—42no—
98C2×C4×C137—84no—
99C2×C4×C137—82no—
100C2×C4×C137—81no—
101C2×C4×C137C2×SD1611yescharacteristic
102C2×C4×C137#13512yes—
103C2×C4×C137AGL(1,ℤ/8)12yes—
104C2×C4×C137AGL(1,ℤ/8)11yescharacteristic
105C8×C137—44no—
106C8×C137—42no—
107C22×C137—42no—
108C22×C137—44no—
109C22×C137—82no—
110C22×C137—81no—
111C22×C137—81no—
112C22×C137#44912yes—
113C22×C137#45011yescharacteristic
114C22×C137#45311yescharacteristic
115C22×C137#45612yes—
116C22×C137#45811yescharacteristic
117C4×C137—22no—
118C4×C137—22no—
119C4×C137—21no—
120C4×C137—21no—
121C4×C137—82no—
122C4×C137—81no—
123C4×C137—82no—
124C4×C137—161no—
125C2×C137—82no—
126C2×C137#160912yes—
127C2×C137#161311yescharacteristic
128C2×C137#162011yescharacteristic
129C2×C137#165412yes—
130C2×C137#166011yescharacteristic
131#7819C13711yesmaximal, characteristic, direct product factor, Sylow
132C137#781911yescharacteristic, direct product factor, Sylow
133#2724C2×C13711yescharacteristic
134#2093C2×C13711yescharacteristic
135#2084C2×C13712yescomplemented
136#1271C2×C13712yescomplemented
137#1270C2×C13711yescharacteristic
138C2×#123—21no—
139C2×#107—21no—
140C2×#106—22no—
141C2×#102—21no—
142#398—21no—
143#397—22no—
144#390C22×C13711yescharacteristic
145#389C22×C13712yes—
146#385—22no—
147#384C22×C13711yescharacteristic
148#340—22no—
149#336C22×C13712yes—
150#336C22×C13711yescharacteristic
151C22×D4D4×C13711yescharacteristic
152C23×C4—21no—
153C22×C8—22no—
154C22×C8—21no—
155#123—42no—
156#123—42no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—22no—
159C2×C4⋊C4—21no—
160C2×C4⋊C4—21no—
161C2×C4⋊C4D4×C13712yes—
162C2×C4⋊C4D4×C13712yes—
163C2×C4⋊C4D4×C13711yescharacteristic
164C2×C22⋊C4—22no—
165C2×C22⋊C4—21no—
166C2×C22⋊C4—22no—
167C2×C42C23×C13711yescharacteristic
168#107—42no—
169#106—44no—
170#102—42no—
171#95—22no—
172#95—21no—
173#95—22no—
174C24—21no—
175C2×D4—21no—
176C2×D4—41no—
177C2×D4—41no—
178C2×D4SD16×C13712yes—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—22no—
182C22×C4—42no—
183C22×C4—41no—
184C22×C4—81no—
185C22×C4—81no—
186C22×C4C2×D4×C13711yescharacteristic
187C22×C4C2×D4×C13712yes—
188C2×C8—22no—
189C2×C8—24no—
190C2×C8—42no—
191C2×C8—41no—
192C2×C8—42no—
193C2×C8—41no—
194C4⋊C4—22no—
195C4⋊C4—22no—
196C4⋊C4—41no—
197C4⋊C4—42no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—42no—
204C4⋊C4—81no—
205C22⋊C4—42no—
206C22⋊C4—44no—
207C22⋊C4—42no—
208C22⋊C4—42no—
209C42—41no—
210C23—22no—
211C23—42no—
212C23—41no—
213C23—42no—
214C23—41no—
215C23#120×C13711yescharacteristic
216D4—42no—
217D4—81no—
218C2×C4—21no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—42no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—84no—
231C2×C4—82no—
232C2×C4—81no—
233C2×C4C2×SD16×C13711yescharacteristic
234C2×C4#135×C13712yes—
235C2×C4AGL(1,ℤ/8)×C13712yes—
236C2×C4AGL(1,ℤ/8)×C13711yescharacteristic
237C8—44no—
238C8—42no—
239C22—42no—
240C22—44no—
241C22—82no—
242C22—81no—
243C22—81no—
244C22#449×C13712yes—
245C22#450×C13711yescharacteristic
246C22#453×C13711yescharacteristic
247C22#456×C13712yes—
248C22#458×C13711yescharacteristic
249C4—22no—
250C4—22no—
251C4—21no—
252C4—21no—
253C4—82no—
254C4—81no—
255C4—82no—
256C4—161no—
257C2—82no—
258C2#1609×C13712yes—
259C2#1613×C13711yescharacteristic
260C2#1620×C13711yescharacteristic
261C2#1654×C13712yes—
262C2#1660×C13711yescharacteristic
subgroupG/H
center, socleC23×C137#120
commutator, Frattini, cosocleC2×C42C23×C137
prime radicalC22×D4×C137D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
3. #2084×C137C2semidirect
4. #1271×C137C2semidirect
131. #7819C137direct (N × H)
132. C137#7819direct (N × H)
135. #2084C2×C137semidirect
136. #1271C2×C137semidirect

Maximal subgroups

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

subgroupindex
#2724×C1372
#2093×C1372
#2084×C1372
#1271×C1372
#1270×C1372
#7819137