Finite Group Databasebeta

← C127×#2037 #30634989

Subgroups — C127×#2037 #30634989

Order 16256.

326 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 84 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#535×C127C211yesmaximal, characteristic
2#428×C127C211yesmaximal, characteristic, complemented
3C2×#104×C127C211yesmaximal, characteristic, complemented
4#417×C127C211yesmaximal, characteristic, complemented
5C2×#100×C127C211yesmaximal, characteristic, complemented
6#390×C127C211yesmaximal, characteristic, complemented
7#339×C127C211yesmaximal, characteristic, complemented
8C2×#41×C127C2211yescharacteristic
9C22×D4×C127C2211yescharacteristic
10C2×M16×C127C2211yescharacteristic
11C2×M16×C127C2211yescharacteristic
12#127×C127—21no—
13#124×C127—21no—
14#121×C127—21no—
15#121×C127—21no—
16#120×C127—22no—
17#117×C127C2211yescharacteristic
18C2×C4⋊C4×C127C2211yescharacteristic
19C2×C22⋊C4×C127—22no—
20C2×C42×C127C2211yescharacteristic
21#107×C127—21no—
22#106×C127—21no—
23#104×C127—22no—
24#103×C127—21no—
25#102×C127—21no—
26#100×C127—22no—
27C24×C127D412yes—
28#41×C127—21no—
29#41×C127—21no—
30#41×C127—21no—
31#41×C127—21no—
32C2×Q8×C127D411yescharacteristic
33C2×D4×C127—21no—
34C2×D4×C127—22no—
35C2×D4×C127—22no—
36C2×D4×C127—21no—
37C2×D4×C127—21no—
38C2×D4×C127—21no—
39C2×D4×C127—21no—
40C2×D4×C127—21no—
41C2×D4×C127—21no—
42C2×D4×C127D411yescharacteristic
43C22×C4×C127—21no—
44C22×C4×C127—21no—
45C22×C4×C127—21no—
46C22×C4×C127C2311yescharacteristic
47M16×C127—21no—
48M16×C127—21no—
49M16×C127—21no—
50M16×C127D412yescomplemented
51C2×C8×C127—21no—
52C2×C8×C127—21no—
53C4⋊C4×C127—21no—
54C4⋊C4×C127—21no—
55C4⋊C4×C127D411yescharacteristic
56C4⋊C4×C127D411yescharacteristic
57C22⋊C4×C127—22no—
58C22⋊C4×C127—22no—
59C22⋊C4×C127—21no—
60C22⋊C4×C127—44no—
61C42×C127—21no—
62C42×C127—21no—
63C42×C127—21no—
64C23×C127—22no—
65C23×C127—21no—
66C23×C127—22no—
67C23×C127—22no—
68C23×C127—42no—
69C23×C127—42no—
70C23×C127C2×D411yescharacteristic
71Q8×C127—21no—
72Q8×C127—21no—
73D4×C127—21no—
74D4×C127—21no—
75D4×C127—41no—
76D4×C127—41no—
77D4×C127—41no—
78D4×C127—41no—
79D4×C127—41no—
80D4×C127—41no—
81D4×C127—82no—
82D4×C127—82no—
83C2×C4×C127—22no—
84C2×C4×C127—21no—
85C2×C4×C127—21no—
86C2×C4×C127—21no—
87C2×C4×C127—41no—
88C2×C4×C127—41no—
89C2×C4×C127—41no—
90C2×C4×C127—41no—
91C2×C4×C127—42no—
92C2×C4×C127—41no—
93C2×C4×C127C2×D411yescharacteristic
94C2×C4×C127C2×D411yescharacteristic
95C2×C4×C127C2×D411yescharacteristic
96C2×C4×C127#4111yescharacteristic
97C2×C4×C127#4111yescharacteristic
98C2×C4×C127#4111yescharacteristic
99C8×C127—22no—
100C8×C127—41no—
101C22×C127—21no—
102C22×C127—21no—
103C22×C127—44no—
104C22×C127—41no—
105C22×C127—42no—
106C22×C127—41no—
107C22×C127—42no—
108C22×C127—41no—
109C22×C127—42no—
110C22×C127—82no—
111C22×C127#12011yescharacteristic
112C22×C127#12111yescharacteristic
113C22×C127#12311yescharacteristic
114C4×C127—42no—
115C4×C127—41no—
116C4×C127—41no—
117C4×C127—41no—
118C4×C127—81no—
119C4×C127#12111yescharacteristic
120C4×C127#12111yescharacteristic
121C4×C127#12311yescharacteristic
122C4×C127#12411yescharacteristic
123C2×C127—21no—
124C2×C127—21no—
125C2×C127—81no—
126C2×C127—82no—
127C2×C127#39411yescharacteristic
128C2×C127#45311yescharacteristic
129C2×C127#45511yescharacteristic
130#2037C12711yesmaximal, characteristic, direct product factor, Sylow
131C127#203711yescharacteristic, direct product factor, Sylow
132#535C2×C12711yescharacteristic
133#428C2×C12711yescharacteristic, complemented
134C2×#104C2×C12711yescharacteristic, complemented
135#417C2×C12711yescharacteristic, complemented
136C2×#100C2×C12711yescharacteristic, complemented
137#390C2×C12711yescharacteristic, complemented
138#339C2×C12711yescharacteristic, complemented
139C2×#41C22×C12711yescharacteristic
140C22×D4C22×C12711yescharacteristic
141C2×M16C22×C12711yescharacteristic
142C2×M16C22×C12711yescharacteristic
143#127—21no—
144#124—21no—
145#121—21no—
146#121—21no—
147#120—22no—
148#117C22×C12711yescharacteristic
149C2×C4⋊C4C22×C12711yescharacteristic
150C2×C22⋊C4—22no—
151C2×C42C22×C12711yescharacteristic
152#107—21no—
153#106—21no—
154#104—22no—
155#103—21no—
156#102—21no—
157#100—22no—
158C24D4×C12712yes—
159#41—21no—
160#41—21no—
161#41—21no—
162#41—21no—
163C2×Q8D4×C12711yescharacteristic
164C2×D4—21no—
165C2×D4—22no—
166C2×D4—22no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4D4×C12711yescharacteristic
174C22×C4—21no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4C23×C12711yescharacteristic
178M16—21no—
179M16—21no—
180M16—21no—
181M16D4×C12712yescomplemented
182C2×C8—21no—
183C2×C8—21no—
184C4⋊C4—21no—
185C4⋊C4—21no—
186C4⋊C4D4×C12711yescharacteristic
187C4⋊C4D4×C12711yescharacteristic
188C22⋊C4—22no—
189C22⋊C4—22no—
190C22⋊C4—21no—
191C22⋊C4—44no—
192C42—21no—
193C42—21no—
194C42—21no—
195C23—22no—
196C23—21no—
197C23—22no—
198C23—22no—
199C23—42no—
200C23—42no—
201C23C2×D4×C12711yescharacteristic
202Q8—21no—
203Q8—21no—
204D4—21no—
205D4—21no—
206D4—41no—
207D4—41no—
208D4—41no—
209D4—41no—
210D4—41no—
211D4—41no—
212D4—82no—
213D4—82no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—42no—
223C2×C4—41no—
224C2×C4C2×D4×C12711yescharacteristic
225C2×C4C2×D4×C12711yescharacteristic
226C2×C4C2×D4×C12711yescharacteristic
227C2×C4#41×C12711yescharacteristic
228C2×C4#41×C12711yescharacteristic
229C2×C4#41×C12711yescharacteristic
230C8—22no—
231C8—41no—
232C22—21no—
233C22—21no—
234C22—44no—
235C22—41no—
236C22—42no—
237C22—41no—
238C22—42no—
239C22—41no—
240C22—42no—
241C22—82no—
242C22#120×C12711yescharacteristic
243C22#121×C12711yescharacteristic
244C22#123×C12711yescharacteristic
245C4—42no—
246C4—41no—
247C4—41no—
248C4—41no—
249C4—81no—
250C4#121×C12711yescharacteristic
251C4#121×C12711yescharacteristic
252C4#123×C12711yescharacteristic
253C4#124×C12711yescharacteristic
254C2—21no—
255C2—21no—
256C2—82no—
257C2—81no—
258C2#394×C12711yescharacteristic
259C2#453×C12711yescharacteristic
260C2#455×C12711yescharacteristic
subgroupG/H
center, socleC22×C127#120
commutator, Frattini, cosocleC22×C4C23×C127
prime radical#535×C127C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. #428×C127C2semidirect
3. C2×#104×C127C2semidirect
4. #417×C127C2semidirect
5. C2×#100×C127C2semidirect
6. #390×C127C2semidirect
7. #339×C127C2semidirect
50. M16×C127D4semidirect
130. #2037C127direct (N × H)
131. C127#2037direct (N × H)
133. #428C2×C127semidirect
134. C2×#104C2×C127semidirect
135. #417C2×C127semidirect
136. C2×#100C2×C127semidirect
137. #390C2×C127semidirect
138. #339C2×C127semidirect
181. M16D4×C127semidirect

Maximal subgroups

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

subgroupindex
#535×C1272
#428×C1272
C2×#104×C1272
#417×C1272
C2×#100×C1272
#390×C1272
#339×C1272
#2037127