Finite Group Databasebeta

← C137×#10301 #46859687

Subgroups — C137×#10301 #46859687

Order 35072.

554 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 106 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#3254×C137C212yesmaximal, complemented
2#3253×C137C211yesmaximal, characteristic
3#1994×C137C211yesmaximal, characteristic, complemented
4#1962×C137C212yesmaximal, complemented
5#1309×C137C211yesmaximal, characteristic, complemented
6#533×C137C2211yescharacteristic
7#532×C137C2212yes—
8#477×C137—22no—
9#476×C137—22no—
10#474×C137—22no—
11#469×C137—22no—
12#468×C137—24no—
13#461×C137—22no—
14#460×C137—22no—
15#459×C137—22no—
16#423×C137C2212yes—
17#423×C137C2211yescharacteristic
18C2×#104×C137—24no—
19C43×C137C2211yescharacteristic
20#339×C137—22no—
21C2×#41×C137—22no—
22C2×SD16×C137—24no—
23C2×D8×C137—22no—
24C2×M16×C137D414yes—
25C2×M16×C137D412yes—
26C4⋊Q8×C137D412yes—
27C4⋊Q8×C137D412yes—
28#127×C137D412yes—
29#125×C137—21no—
30#124×C137—22no—
31C22⋊Q8×C137—22no—
32#121×C137—22no—
33#121×C137—22no—
34C4×Q8×C137—22no—
35C4×D4×C137—22no—
36C4×D4×C137—22no—
37#117×C137—21no—
38C2×C42×C137—22no—
39C2×C42×C137—21no—
40C2×C42×C137C2311yescharacteristic
41#107×C137—24no—
42#106×C137—22no—
43C4⋊C8×C137—22no—
44C4⋊C8×C137—22no—
45C4⋊C8×C137—22no—
46#104×C137—48no—
47#103×C137—24no—
48#102×C137—24no—
49#102×C137—24no—
50#41×C137—44no—
51#41×C137—44no—
52C2×Q8×C137—22no—
53C2×Q8×C137—22no—
54C2×D4×C137—22no—
55C2×D4×C137—22no—
56C2×D4×C137—22no—
57C2×D4×C137—42no—
58C22×C4×C137—41no—
59C22×C4×C137—42no—
60C22×C4×C137C2×D411yescharacteristic
61C22×C4×C137C2×D412yes—
62SD16×C137—84no—
63D8×C137—82no—
64M16×C137—44no—
65M16×C137—42no—
66C2×C8×C137—22no—
67C2×C8×C137—24no—
68C4⋊C4×C137—22no—
69C4⋊C4×C137—22no—
70C4⋊C4×C137—22no—
71C4⋊C4×C137—22no—
72C4⋊C4×C137—42no—
73C22⋊C4×C137—41no—
74C22⋊C4×C137—42no—
75C22⋊C4×C137—42no—
76C42×C137—24no—
77C42×C137—22no—
78C42×C137—42no—
79C42×C137—41no—
80C42×C137—41no—
81C42×C137C2×D411yescharacteristic
82C42×C137C2×D412yes—
83C42×C137#4111yescharacteristic
84C23×C137—42no—
85C23×C137#12711yescharacteristic
86Q8×C137—44no—
87Q8×C137—42no—
88Q8×C137—42no—
89D4×C137—44no—
90D4×C137—42no—
91D4×C137—42no—
92D4×C137—42no—
93D4×C137—42no—
94D4×C137—84no—
95C2×C4×C137—22no—
96C2×C4×C137—22no—
97C2×C4×C137—21no—
98C2×C4×C137—21no—
99C2×C4×C137—44no—
100C2×C4×C137—42no—
101C2×C4×C137—42no—
102C2×C4×C137—42no—
103C2×C4×C137—82no—
104C2×C4×C137—82no—
105C2×C4×C137#12012yes—
106C2×C4×C137#12011yescharacteristic
107C2×C4×C137#12111yescharacteristic
108C2×C4×C137#12112yes—
109C8×C137—44no—
110C8×C137—42no—
111C22×C137—22no—
112C22×C137—21no—
113C22×C137—82no—
114C22×C137—82no—
115C22×C137—82no—
116C22×C137#39211yescharacteristic
117C4×C137—22no—
118C4×C137—21no—
119C4×C137—44no—
120C4×C137—82no—
121C4×C137—82no—
122C4×C137#45312yes—
123C4×C137#45412yes—
124C4×C137#45511yescharacteristic
125C4×C137#45611yescharacteristic
126C2×C137—41no—
127C2×C137—162no—
128C2×C137#200612yes—
129C2×C137#200711yescharacteristic
130#10301C13711yesmaximal, characteristic, direct product factor, Sylow
131C137#1030111yescharacteristic, direct product factor, Sylow
132#3254C2×C13712yescomplemented
133#3253C2×C13711yescharacteristic
134#1994C2×C13711yescharacteristic, complemented
135#1962C2×C13712yescomplemented
136#1309C2×C13711yescharacteristic, complemented
137#533C22×C13711yescharacteristic
138#532C22×C13712yes—
139#477—22no—
140#476—22no—
141#474—22no—
142#469—22no—
143#468—24no—
144#461—22no—
145#460—22no—
146#459—22no—
147#423C22×C13712yes—
148#423C22×C13711yescharacteristic
149C2×#104—24no—
150C43C22×C13711yescharacteristic
151#339—22no—
152C2×#41—22no—
153C2×SD16—24no—
154C2×D8—22no—
155C2×M16D4×C13712yes—
156C2×M16D4×C13714yes—
157C4⋊Q8D4×C13712yes—
158C4⋊Q8D4×C13712yes—
159#127D4×C13712yes—
160#125—21no—
161#124—22no—
162C22⋊Q8—22no—
163#121—22no—
164#121—22no—
165C4×Q8—22no—
166C4×D4—22no—
167C4×D4—22no—
168#117—21no—
169C2×C42—21no—
170C2×C42—22no—
171C2×C42C23×C13711yescharacteristic
172#107—24no—
173#106—22no—
174C4⋊C8—22no—
175C4⋊C8—22no—
176C4⋊C8—22no—
177#104—48no—
178#103—24no—
179#102—24no—
180#102—24no—
181#41—44no—
182#41—44no—
183C2×Q8—22no—
184C2×Q8—22no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—22no—
188C2×D4—42no—
189C22×C4—41no—
190C22×C4—42no—
191C22×C4C2×D4×C13711yescharacteristic
192C22×C4C2×D4×C13712yes—
193SD16—84no—
194D8—82no—
195M16—44no—
196M16—42no—
197C2×C8—22no—
198C2×C8—24no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—22no—
202C4⋊C4—22no—
203C4⋊C4—42no—
204C22⋊C4—41no—
205C22⋊C4—42no—
206C22⋊C4—42no—
207C42—24no—
208C42—22no—
209C42—42no—
210C42—41no—
211C42—41no—
212C42C2×D4×C13711yescharacteristic
213C42C2×D4×C13712yes—
214C42#41×C13711yescharacteristic
215C23—42no—
216C23#127×C13711yescharacteristic
217Q8—44no—
218Q8—42no—
219Q8—42no—
220D4—44no—
221D4—42no—
222D4—42no—
223D4—42no—
224D4—42no—
225D4—84no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—44no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—82no—
235C2×C4—82no—
236C2×C4#120×C13712yes—
237C2×C4#120×C13711yescharacteristic
238C2×C4#121×C13711yescharacteristic
239C2×C4#121×C13712yes—
240C8—44no—
241C8—42no—
242C22—22no—
243C22—21no—
244C22—82no—
245C22—82no—
246C22—82no—
247C22#392×C13711yescharacteristic
248C4—22no—
249C4—21no—
250C4—44no—
251C4—82no—
252C4—82no—
253C4#453×C13712yes—
254C4#454×C13712yes—
255C4#455×C13711yescharacteristic
256C4#456×C13711yescharacteristic
257C2—41no—
258C2—162no—
259C2#2006×C13712yes—
260C2#2007×C13711yescharacteristic
subgroupG/H
center, socleC22×C137#392
commutator, Frattini, cosocleC2×C42C23×C137
prime radical#3253×C137C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C137 ◁ C2×C42×C137 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3254×C137C2semidirect
3. #1994×C137C2semidirect
4. #1962×C137C2semidirect
5. #1309×C137C2semidirect
130. #10301C137direct (N × H)
131. C137#10301direct (N × H)
132. #3254C2×C137semidirect
134. #1994C2×C137semidirect
135. #1962C2×C137semidirect
136. #1309C2×C137semidirect

Maximal subgroups

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

subgroupindex
#3254×C1372
#3253×C1372
#1994×C1372
#1962×C1372
#1309×C1372
#10301137