Finite Group Databasebeta

← C137×#13436 #46862822

Subgroups — C137×#13436 #46862822

Order 35072.

438 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 86 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#3199×C137C211yesmaximal, characteristic
2#2122×C137C212yesmaximal, complemented
3#1910×C137C212yesmaximal, complemented
4#1858×C137C211yesmaximal, characteristic, complemented
5#1391×C137C211yesmaximal, characteristic, complemented
6#568×C137C2211yescharacteristic
7#535×C137C2212yes—
8#482×C137—22no—
9#469×C137—21no—
10#466×C137—21no—
11#447×C137—22no—
12#430×C137—21no—
13#418×C137—22no—
14#413×C137C2211yescharacteristic
15#410×C137C2212yes—
16#408×C137C2211yescharacteristic
17AΣL(1,𝔽16)×C137—24no—
18#341×C137—21no—
19H(3,ℤ/4)×C137—22no—
20C2×#41×C137C2311yescharacteristic
21C22×D4×C137D412yes—
22C2×D8×C137—21no—
23C2×D8×C137—21no—
24#131×C137—42no—
25C2×M16×C137—22no—
26C2×M16×C137—21no—
27C2×M16×C137—21no—
28C2×M16×C137D411yescharacteristic
29C22×C8×C137D411yescharacteristic
30#127×C137—22no—
31#124×C137—22no—
32#121×C137—22no—
33#121×C137—22no—
34#120×C137—22no—
35#120×C137—22no—
36#117×C137—22no—
37#117×C137D412yes—
38#108×C137—42no—
39#107×C137—21no—
40#106×C137—21no—
41#102×C137—22no—
42#102×C137—22no—
43#102×C137—44no—
44#101×C137—21no—
45#100×C137D412yes—
46#99×C137—22no—
47#99×C137—22no—
48C22⋊C8×C137—22no—
49C24×C137—22no—
50#41×C137—41no—
51#41×C137—41no—
52C2×Q8×C137#4111yescharacteristic
53C2×D4×C137—22no—
54C2×D4×C137—22no—
55C2×D4×C137—42no—
56C2×D4×C137—42no—
57C2×D4×C137—42no—
58C2×D4×C137—42no—
59C2×D4×C137C2×D411yescharacteristic
60C2×D4×C137#4112yes—
61C22×C4×C137C2×D411yescharacteristic
62C22×C4×C137C2×D412yes—
63D8×C137—81no—
64D8×C137—81no—
65M16×C137—22no—
66M16×C137—22no—
67M16×C137—41no—
68M16×C137—42no—
69M16×C137—41no—
70M16×C137—41no—
71C2×C8×C137—24no—
72C2×C8×C137—21no—
73C2×C8×C137—21no—
74C2×C8×C137—41no—
75C2×C8×C137—41no—
76C2×C8×C137—41no—
77C4⋊C4×C137—22no—
78C4⋊C4×C137—42no—
79C22⋊C4×C137—22no—
80C22⋊C4×C137—42no—
81C22⋊C4×C137—42no—
82C22⋊C4×C137—42no—
83C42×C137—22no—
84C42×C137—42no—
85C23×C137—42no—
86C23×C137—82no—
87C23×C137—162no—
88C23×C137#12112yes—
89C23×C137#12411yescharacteristic
90Q8×C137—41no—
91D4×C137—41no—
92D4×C137—42no—
93D4×C137—44no—
94D4×C137—42no—
95D4×C137—42no—
96D4×C137—162no—
97D4×C137—162no—
98C2×C4×C137—22no—
99C2×C4×C137—21no—
100C2×C4×C137—22no—
101C2×C4×C137—21no—
102C2×C4×C137—42no—
103C2×C4×C137—82no—
104C2×C4×C137#12011yescharacteristic
105C2×C4×C137#12111yescharacteristic
106C2×C4×C137#12312yes—
107C8×C137—42no—
108C8×C137—42no—
109C8×C137—41no—
110C8×C137—41no—
111C22×C137—22no—
112C22×C137—21no—
113C22×C137—41no—
114C22×C137—42no—
115C22×C137—82no—
116C22×C137—82no—
117C22×C137—82no—
118C22×C137—164no—
119C22×C137#39411yescharacteristic
120C4×C137—21no—
121C4×C137—22no—
122C4×C137—82no—
123C4×C137—162no—
124C4×C137B(4,𝔽2)11yescharacteristic
125C4×C137#45811yescharacteristic
126C2×C137—21no—
127C2×C137—42no—
128C2×C137—41no—
129C2×C137—162no—
130C2×C137#204411yescharacteristic
131#13436C13711yesmaximal, characteristic, direct product factor, Sylow
132C137#1343611yescharacteristic, direct product factor, Sylow
133#3199C2×C13711yescharacteristic
134#2122C2×C13712yescomplemented
135#1910C2×C13712yescomplemented
136#1858C2×C13711yescharacteristic, complemented
137#1391C2×C13711yescharacteristic, complemented
138#568C22×C13711yescharacteristic
139#535C22×C13712yes—
140#482—22no—
141#469—21no—
142#466—21no—
143#447—22no—
144#430—21no—
145#418—22no—
146#413C22×C13711yescharacteristic
147#410C22×C13712yes—
148#408C22×C13711yescharacteristic
149AΣL(1,𝔽16)—24no—
150#341—21no—
151H(3,ℤ/4)—22no—
152C2×#41C23×C13711yescharacteristic
153C22×D4D4×C13712yes—
154C2×D8—21no—
155C2×D8—21no—
156#131—42no—
157C2×M16—22no—
158C2×M16—21no—
159C2×M16—21no—
160C2×M16D4×C13711yescharacteristic
161C22×C8D4×C13711yescharacteristic
162#127—22no—
163#124—22no—
164#121—22no—
165#121—22no—
166#120—22no—
167#120—22no—
168#117—22no—
169#117D4×C13712yes—
170#108—42no—
171#107—21no—
172#106—21no—
173#102—22no—
174#102—22no—
175#102—44no—
176#101—21no—
177#100D4×C13712yes—
178#99—22no—
179#99—22no—
180C22⋊C8—22no—
181C24—22no—
182#41—41no—
183#41—41no—
184C2×Q8#41×C13711yescharacteristic
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—42no—
188C2×D4—42no—
189C2×D4—42no—
190C2×D4—42no—
191C2×D4C2×D4×C13711yescharacteristic
192C2×D4#41×C13712yes—
193C22×C4C2×D4×C13711yescharacteristic
194C22×C4C2×D4×C13712yes—
195D8—81no—
196D8—81no—
197M16—22no—
198M16—22no—
199M16—41no—
200M16—42no—
201M16—41no—
202M16—41no—
203C2×C8—24no—
204C2×C8—21no—
205C2×C8—21no—
206C2×C8—41no—
207C2×C8—41no—
208C2×C8—41no—
209C4⋊C4—22no—
210C4⋊C4—42no—
211C22⋊C4—22no—
212C22⋊C4—42no—
213C22⋊C4—42no—
214C22⋊C4—42no—
215C42—22no—
216C42—42no—
217C23—42no—
218C23—82no—
219C23—162no—
220C23#121×C13712yes—
221C23#124×C13711yescharacteristic
222Q8—41no—
223D4—41no—
224D4—42no—
225D4—44no—
226D4—42no—
227D4—42no—
228D4—162no—
229D4—162no—
230C2×C4—22no—
231C2×C4—21no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—42no—
235C2×C4—82no—
236C2×C4#120×C13711yescharacteristic
237C2×C4#121×C13711yescharacteristic
238C2×C4#123×C13712yes—
239C8—42no—
240C8—42no—
241C8—41no—
242C8—41no—
243C22—22no—
244C22—21no—
245C22—41no—
246C22—42no—
247C22—82no—
248C22—82no—
249C22—82no—
250C22—164no—
251C22#394×C13711yescharacteristic
252C4—21no—
253C4—22no—
254C4—82no—
255C4—162no—
256C4B(4,𝔽2)×C13711yescharacteristic
257C4#458×C13711yescharacteristic
258C2—21no—
259C2—42no—
260C2—41no—
261C2—162no—
262C2#2044×C13711yescharacteristic
subgroupG/H
center, socleC2×C137#2044
commutator, Frattini, cosocleC2×#41C23×C137
prime radical#3199×C137C2
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C137 ◁ C2×C4×C137 ◁ C2×#41×C137 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2122×C137C2semidirect
3. #1910×C137C2semidirect
4. #1858×C137C2semidirect
5. #1391×C137C2semidirect
131. #13436C137direct (N × H)
132. C137#13436direct (N × H)
134. #2122C2×C137semidirect
135. #1910C2×C137semidirect
136. #1858C2×C137semidirect
137. #1391C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3199×C1372
#2122×C1372
#1910×C1372
#1858×C1372
#1391×C1372
#13436137