Finite Group Databasebeta

← C127×#13484 #44577157

Subgroups — C127×#13484 #44577157

Order 32512.

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

normal subgroups only

This group has 330 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
1C127×#2139C212yesmaximal
2C127×#1974C211yesmaximal, characteristic
3C127×#1845C211yesmaximal, characteristic, complemented
4C127×#1387C212yesmaximal, complemented
5C127×#1376C211yesmaximal, characteristic, complemented
6C2×#135×C127C2211yescharacteristic
7C2×M32×C127C2212yes—
8C2×#108×C127C2211yescharacteristic
9C2×#107×C127—21no—
10C2×#107×C127C2212yes—
11C2×#104×C127—21no—
12#408×C127—21no—
13C2×C4×C8×C127C2211yescharacteristic
14#384×C127—21no—
15#358×C127—22no—
16#357×C127—22no—
17C2×#41×C127—21no—
18#135×C127—22no—
19#135×C127—22no—
20C2×Q16×C127D411yescharacteristic
21C2×SD16×C127—21no—
22C2×D8×C127D411yescharacteristic
23C2×M16×C127—21no—
24C22×C8×C127D411yescharacteristic
25C22×C8×C127C2311yescharacteristic
26C2×C4⋊C4×C127—22no—
27C2×C4⋊C4×C127—42no—
28C2×C42×C127D411yescharacteristic
29M32×C127—22no—
30M32×C127—22no—
31C2×C16×C127—22no—
32#108×C127—22no—
33#107×C127—22no—
34#107×C127—22no—
35#107×C127—42no—
36#104×C127—42no—
37C22⋊C8×C127—42no—
38C4×C8×C127—22no—
39#41×C127—41no—
40#41×C127—41no—
41#41×C127—41no—
42#41×C127—41no—
43C2×Q8×C127—21no—
44C2×D4×C127—21no—
45C2×D4×C127—41no—
46C22×C4×C127—21no—
47C22×C4×C127—41no—
48C22×C4×C127—42no—
49C22×C4×C127C2×D411yescharacteristic
50Q16×C127—22no—
51SD16×C127—42no—
52D8×C127—22no—
53M16×C127—41no—
54M16×C127—41no—
55C2×C8×C127—21no—
56C2×C8×C127—21no—
57C2×C8×C127—41no—
58C2×C8×C127D812yes—
59C2×C8×C127C2×D411yescharacteristic
60C2×C8×C127#4112yes—
61C2×C8×C127#4112yes—
62C2×C8×C127#4111yescharacteristic
63C4⋊C4×C127—42no—
64C4⋊C4×C127—42no—
65C4⋊C4×C127—84no—
66C42×C127—21no—
67C42×C127SD1612yes—
68C16×C127—42no—
69C23×C127—41no—
70C23×C127AGL(1,ℤ/8)11yescharacteristic
71Q8×C127—41no—
72Q8×C127—41no—
73D4×C127—41no—
74D4×C127—41no—
75D4×C127—81no—
76D4×C127—81no—
77C2×C4×C127—22no—
78C2×C4×C127—22no—
79C2×C4×C127—22no—
80C2×C4×C127—41no—
81C2×C4×C127—81no—
82C2×C4×C127—81no—
83C2×C4×C127—84no—
84C2×C4×C127—82no—
85C2×C4×C127#12111yescharacteristic
86C2×C4×C127#12311yescharacteristic
87C2×C4×C127#12411yescharacteristic
88C2×C4×C127C2×D811yescharacteristic
89C2×C4×C127C2×SD1611yescharacteristic
90C2×C4×C127#13711yescharacteristic
91C8×C127—22no—
92C8×C127—81no—
93C8×C127#12312yes—
94C8×C127#12612yes—
95C22×C127—21no—
96C22×C127—21no—
97C22×C127—81no—
98C22×C127—81no—
99C22×C127—81no—
100C22×C127#45911yescharacteristic
101C22×C127#48111yescharacteristic
102C22×C127#48911yescharacteristic
103C4×C127—24no—
104C4×C127—81no—
105C4×C127—162no—
106C4×C127#39711yescharacteristic
107C4×C127#46111yescharacteristic
108C4×C127#48011yescharacteristic
109C4×C127#48611yescharacteristic
110#13484C12711yesmaximal, characteristic, direct product factor, Sylow
111C2×C127—21no—
112C2×C127—21no—
113C2×C127—161no—
114C2×C127#207111yescharacteristic
115C2×C127#221311yescharacteristic
116C2×C127#221411yescharacteristic
117#2139C2×C12712yes—
118#1974C2×C12711yescharacteristic
119#1845C2×C12711yescharacteristic, complemented
120#1387C2×C12712yescomplemented
121#1376C2×C12711yescharacteristic, complemented
122C127#1348411yescharacteristic, direct product factor, Sylow
123C2×#135C22×C12711yescharacteristic
124C2×M32C22×C12712yes—
125C2×#108C22×C12711yescharacteristic
126C2×#107—21no—
127C2×#107C22×C12712yes—
128C2×#104—21no—
129#408—21no—
130C2×C4×C8C22×C12711yescharacteristic
131#384—21no—
132#358—22no—
133#357—22no—
134C2×#41—21no—
135#135—22no—
136#135—22no—
137C2×Q16D4×C12711yescharacteristic
138C2×SD16—21no—
139C2×D8D4×C12711yescharacteristic
140C2×M16—21no—
141C22×C8D4×C12711yescharacteristic
142C22×C8C23×C12711yescharacteristic
143C2×C4⋊C4—22no—
144C2×C4⋊C4—42no—
145C2×C42D4×C12711yescharacteristic
146M32—22no—
147M32—22no—
148C2×C16—22no—
149#108—22no—
150#107—22no—
151#107—22no—
152#107—42no—
153#104—42no—
154C22⋊C8—42no—
155C4×C8—22no—
156#41—41no—
157#41—41no—
158#41—41no—
159#41—41no—
160C2×Q8—21no—
161C2×D4—21no—
162C2×D4—41no—
163C22×C4—21no—
164C22×C4—41no—
165C22×C4—42no—
166C22×C4C2×D4×C12711yescharacteristic
167Q16—22no—
168SD16—42no—
169D8—22no—
170M16—41no—
171M16—41no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—41no—
175C2×C8D8×C12712yes—
176C2×C8C2×D4×C12711yescharacteristic
177C2×C8#41×C12712yes—
178C2×C8#41×C12712yes—
179C2×C8#41×C12711yescharacteristic
180C4⋊C4—42no—
181C4⋊C4—42no—
182C4⋊C4—84no—
183C42—21no—
184C42SD16×C12712yes—
185C16—42no—
186C23—41no—
187C23AGL(1,ℤ/8)×C12711yescharacteristic
188Q8—41no—
189Q8—41no—
190D4—41no—
191D4—41no—
192D4—81no—
193D4—81no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—41no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4—84no—
201C2×C4—82no—
202C2×C4#121×C12711yescharacteristic
203C2×C4#123×C12711yescharacteristic
204C2×C4#124×C12711yescharacteristic
205C2×C4C2×D8×C12711yescharacteristic
206C2×C4C2×SD16×C12711yescharacteristic
207C2×C4#137×C12711yescharacteristic
208C8—22no—
209C8—81no—
210C8#123×C12712yes—
211C8#126×C12712yes—
212C22—21no—
213C22—21no—
214C22—81no—
215C22—81no—
216C22—81no—
217C22#459×C12711yescharacteristic
218C22#481×C12711yescharacteristic
219C22#489×C12711yescharacteristic
220C4—24no—
221C4—81no—
222C4—162no—
223C4#397×C12711yescharacteristic
224C4#461×C12711yescharacteristic
225C4#480×C12711yescharacteristic
226C4#486×C12711yescharacteristic
227C2—21no—
228C2—21no—
229C2—161no—
230C2C127×#207111yescharacteristic
231C2C127×#221311yescharacteristic
232C2C127×#221411yescharacteristic
subgroupG/H
center, socleC22×C127#459
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC2×#135×C127C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1845C2semidirect
4. C127×#1387C2semidirect
5. C127×#1376C2semidirect
110. #13484C127direct (N × H)
119. #1845C2×C127semidirect
120. #1387C2×C127semidirect
121. #1376C2×C127semidirect
122. C127#13484direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#21392
C127×#19742
C127×#18452
C127×#13872
C127×#13762
#13484127