Finite Group Databasebeta

← C127×#2019 #30634971

Subgroups — C127×#2019 #30634971

Order 16256.

362 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C2×#137×C127C211yesmaximal, characteristic, complemented
2C2×AGL(1,ℤ/8)×C127C211yesmaximal, characteristic
3C22×SD16×C127C211yesmaximal, characteristic, complemented
4C2×#101×C127C211yesmaximal, characteristic, complemented
5C2×#100×C127C211yesmaximal, characteristic, complemented
6#408×C127C211yesmaximal, characteristic, complemented
7#341×C127C211yesmaximal, characteristic, complemented
8C2×#41×C127C2211yescharacteristic
9C22×Q8×C127C2211yescharacteristic
10C22×D4×C127C2211yescharacteristic
11#137×C127—22no—
12#137×C127—22no—
13AGL(1,ℤ/8)×C127—22no—
14AGL(1,ℤ/8)×C127—22no—
15C2×Q16×C127—21no—
16C2×SD16×C127—22no—
17C2×SD16×C127—21no—
18C2×SD16×C127—22no—
19C2×SD16×C127—21no—
20C2×SD16×C127—22no—
21C2×D8×C127—21no—
22C2×M16×C127C2211yescharacteristic
23C2×M16×C127C2211yescharacteristic
24C2×M16×C127C2211yescharacteristic
25C22×C8×C127C2211yescharacteristic
26#101×C127—22no—
27#100×C127—22no—
28C22⋊C8×C127—22no—
29C24×C127—21no—
30#41×C127—21no—
31#41×C127—21no—
32#41×C127—21no—
33#41×C127—21no—
34C2×Q8×C127—21no—
35C2×Q8×C127—21no—
36C2×Q8×C127—21no—
37C2×Q8×C127—21no—
38C2×Q8×C127—21no—
39C2×Q8×C127D411yescharacteristic
40C2×Q8×C127D412yes—
41C2×D4×C127—21no—
42C2×D4×C127—21no—
43C2×D4×C127—21no—
44C2×D4×C127—21no—
45C2×D4×C127—21no—
46C2×D4×C127—21no—
47C2×D4×C127D411yescharacteristic
48C2×D4×C127D412yes—
49C22×C4×C127—21no—
50C22×C4×C127—21no—
51C22×C4×C127C2311yescharacteristic
52Q16×C127—24no—
53SD16×C127—28no—
54SD16×C127—24no—
55SD16×C127—24no—
56D8×C127—24no—
57M16×C127—21no—
58M16×C127—21no—
59M16×C127—21no—
60M16×C127—21no—
61M16×C127D412yes—
62M16×C127D412yes—
63C2×C8×C127—21no—
64C2×C8×C127—21no—
65C2×C8×C127—21no—
66C2×C8×C127—21no—
67C2×C8×C127—21no—
68C2×C8×C127D412yes—
69C23×C127—21no—
70C23×C127—22no—
71C23×C127—41no—
72C23×C127—41no—
73C23×C127—82no—
74C23×C127#4111yescharacteristic
75Q8×C127—22no—
76Q8×C127—21no—
77Q8×C127—22no—
78Q8×C127—21no—
79Q8×C127—41no—
80Q8×C127—41no—
81D4×C127—21no—
82D4×C127—22no—
83D4×C127—22no—
84D4×C127—21no—
85D4×C127—41no—
86D4×C127—41no—
87D4×C127—41no—
88D4×C127—41no—
89C2×C4×C127—22no—
90C2×C4×C127—21no—
91C2×C4×C127—41no—
92C2×C4×C127—41no—
93C2×C4×C127—41no—
94C2×C4×C127—41no—
95C2×C4×C127C2×D411yescharacteristic
96C2×C4×C127C2×D411yescharacteristic
97C2×C4×C127C2×D411yescharacteristic
98C2×C4×C127C2×D411yescharacteristic
99C2×C4×C127C2×D411yescharacteristic
100C2×C4×C127C2×D411yescharacteristic
101C8×C127—22no—
102C8×C127—22no—
103C8×C127—22no—
104C8×C127—41no—
105C22×C127—22no—
106C22×C127—41no—
107C22×C127—42no—
108C22×C127—42no—
109C22×C127—82no—
110C22×C127—82no—
111C22×C127—82no—
112C22×C127#12111yescharacteristic
113C22×C127#12111yescharacteristic
114C22×C127#12111yescharacteristic
115C4×C127—41no—
116C4×C127—42no—
117C4×C127#12011yescharacteristic
118C4×C127#12011yescharacteristic
119C4×C127#12011yescharacteristic
120C4×C127#12711yescharacteristic
121C2×C127—21no—
122C2×C127—21no—
123C2×C127—81no—
124C2×C127—82no—
125C2×C127#39211yescharacteristic
126C2×C127#47112yes—
127#2019C12711yesmaximal, characteristic, direct product factor, Sylow
128C127#201911yescharacteristic, direct product factor, Sylow
129C2×#137C2×C12711yescharacteristic, complemented
130C2×AGL(1,ℤ/8)C2×C12711yescharacteristic
131C22×SD16C2×C12711yescharacteristic, complemented
132C2×#101C2×C12711yescharacteristic, complemented
133C2×#100C2×C12711yescharacteristic, complemented
134#408C2×C12711yescharacteristic, complemented
135#341C2×C12711yescharacteristic, complemented
136C2×#41C22×C12711yescharacteristic
137C22×Q8C22×C12711yescharacteristic
138C22×D4C22×C12711yescharacteristic
139#137—22no—
140#137—22no—
141AGL(1,ℤ/8)—22no—
142AGL(1,ℤ/8)—22no—
143C2×Q16—21no—
144C2×SD16—22no—
145C2×SD16—21no—
146C2×SD16—22no—
147C2×SD16—21no—
148C2×SD16—22no—
149C2×D8—21no—
150C2×M16C22×C12711yescharacteristic
151C2×M16C22×C12711yescharacteristic
152C2×M16C22×C12711yescharacteristic
153C22×C8C22×C12711yescharacteristic
154#101—22no—
155#100—22no—
156C22⋊C8—22no—
157C24—21no—
158#41—21no—
159#41—21no—
160#41—21no—
161#41—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8D4×C12711yescharacteristic
168C2×Q8D4×C12712yes—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4D4×C12711yescharacteristic
176C2×D4D4×C12712yes—
177C22×C4—21no—
178C22×C4—21no—
179C22×C4C23×C12711yescharacteristic
180Q16—24no—
181SD16—28no—
182SD16—24no—
183SD16—24no—
184D8—24no—
185M16—21no—
186M16—21no—
187M16—21no—
188M16—21no—
189M16D4×C12712yes—
190M16D4×C12712yes—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8D4×C12712yes—
197C23—21no—
198C23—22no—
199C23—41no—
200C23—41no—
201C23—82no—
202C23#41×C12711yescharacteristic
203Q8—22no—
204Q8—21no—
205Q8—22no—
206Q8—21no—
207Q8—41no—
208Q8—41no—
209D4—21no—
210D4—22no—
211D4—22no—
212D4—21no—
213D4—41no—
214D4—41no—
215D4—41no—
216D4—41no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—41no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4C2×D4×C12711yescharacteristic
224C2×C4C2×D4×C12711yescharacteristic
225C2×C4C2×D4×C12711yescharacteristic
226C2×C4C2×D4×C12711yescharacteristic
227C2×C4C2×D4×C12711yescharacteristic
228C2×C4C2×D4×C12711yescharacteristic
229C8—22no—
230C8—22no—
231C8—22no—
232C8—41no—
233C22—22no—
234C22—41no—
235C22—42no—
236C22—42no—
237C22—82no—
238C22—82no—
239C22—82no—
240C22#121×C12711yescharacteristic
241C22#121×C12711yescharacteristic
242C22#121×C12711yescharacteristic
243C4—41no—
244C4—42no—
245C4#120×C12711yescharacteristic
246C4#120×C12711yescharacteristic
247C4#120×C12711yescharacteristic
248C4#127×C12711yescharacteristic
249C2—21no—
250C2—21no—
251C2—81no—
252C2—82no—
253C2#392×C12711yescharacteristic
254C2#471×C12712yes—
subgroupG/H
center, socleC22×C127#121
commutator, Frattini, cosocleC22×C4C23×C127
prime radicalC2×AGL(1,ℤ/8)×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
1. C2×#137×C127C2semidirect
3. C22×SD16×C127C2semidirect
4. C2×#101×C127C2semidirect
5. C2×#100×C127C2semidirect
6. #408×C127C2semidirect
7. #341×C127C2semidirect
127. #2019C127direct (N × H)
128. C127#2019direct (N × H)
129. C2×#137C2×C127semidirect
131. C22×SD16C2×C127semidirect
132. C2×#101C2×C127semidirect
133. C2×#100C2×C127semidirect
134. #408C2×C127semidirect
135. #341C2×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#137×C1272
C2×AGL(1,ℤ/8)×C1272
C22×SD16×C1272
C2×#101×C1272
C2×#100×C1272
#408×C1272
#341×C1272
#2019127