Finite Group Databasebeta

← C127×#12485 #44576158

Subgroups — C127×#12485 #44576158

Order 32512.

248 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 78 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×#2226C211yesmaximal, characteristic, complemented
2C127×#2206C211yesmaximal, characteristic
3C127×#1706C211yesmaximal, characteristic, complemented
4C127×#1589C211yesmaximal, characteristic, complemented
5C127×#1370C211yesmaximal, characteristic, complemented
6C127×#1365C211yesmaximal, characteristic, complemented
7C127×#1361C211yesmaximal, characteristic, complemented
8C2×D16×C127—21no—
9#500×C127C2211yescharacteristic
10#493×C127C2211yescharacteristic
11#492×C127—21no—
12#486×C127—21no—
13C4×D8×C127C2211yescharacteristic
14#436×C127—21no—
15#367×C127—21no—
16C4⋊C16×C127C2211yescharacteristic
17C4⋊C16×C127C2211yescharacteristic
18#357×C127—21no—
19#357×C127—21no—
20#335×C127C2211yescharacteristic
21D4⋊C8×C127—21no—
22C82×C127C2211yescharacteristic
23C2×SD16×C127—42no—
24C2×D8×C127—21no—
25C2×D8×C127—21no—
26C2×D8×C127D411yescharacteristic
27C2×M16×C127—41no—
28C4⋊Q8×C127—21no—
29#127×C127—21no—
30C4×D4×C127—21no—
31D16×C127—42no—
32C2×C16×C127—21no—
33C2×C16×C127—21no—
34#107×C127—21no—
35#107×C127—21no—
36#107×C127D411yescharacteristic
37C4⋊C8×C127—21no—
38#102×C127—21no—
39#102×C127—41no—
40#102×C127—41no—
41C22⋊C8×C127—41no—
42C4×C8×C127D411yescharacteristic
43C4×C8×C127D411yescharacteristic
44C4×C8×C127C2311yescharacteristic
45C2×Q8×C127—41no—
46C2×D4×C127—21no—
47C2×D4×C127—41no—
48C2×D4×C127—41no—
49C2×D4×C127—41no—
50C22×C4×C127—41no—
51SD16×C127—84no—
52D8×C127—21no—
53D8×C127—21no—
54D8×C127—41no—
55D8×C127—41no—
56D8×C127—81no—
57M16×C127—82no—
58C2×C8×C127—21no—
59C2×C8×C127—41no—
60C2×C8×C127D811yescharacteristic
61C2×C8×C127D811yescharacteristic
62C2×C8×C127C2×D411yescharacteristic
63C2×C8×C127#4111yescharacteristic
64C4⋊C4×C127—21no—
65C4⋊C4×C127—41no—
66C4⋊C4×C127—41no—
67C22⋊C4×C127—41no—
68C42×C127C2×D411yescharacteristic
69C16×C127—41no—
70C16×C127—41no—
71C23×C127—41no—
72C23×C127—81no—
73Q8×C127—82no—
74D4×C127—41no—
75D4×C127—41no—
76D4×C127—82no—
77D4×C127—81no—
78D4×C127—81no—
79D4×C127—81no—
80D4×C127—81no—
81C2×C4×C127—41no—
82C2×C4×C127—81no—
83C2×C4×C127—81no—
84C2×C4×C127—81no—
85C2×C4×C127#12111yescharacteristic
86C2×C4×C127C2×D811yescharacteristic
87C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
88C8×C127—22no—
89C8×C127—21no—
90C8×C127—21no—
91C8×C127—21no—
92C8×C127—81no—
93C8×C127AGL(1,ℤ/8)11yescharacteristic
94C8×C127#13711yescharacteristic
95C22×C127—81no—
96C22×C127—81no—
97C22×C127—81no—
98C22×C127—161no—
99C22×C127—161no—
100C22×C127—161no—
101C22×C127#45911yescharacteristic
102C4×C127—21no—
103C4×C127—81no—
104C4×C127—161no—
105C4×C127#46811yescharacteristic
106C4×C127#47111yescharacteristic
107C4×C127#50811yescharacteristic
108C4×C127#50911yescharacteristic
109#12485C12711yesmaximal, characteristic, direct product factor, Sylow
110C2×C127—161no—
111C2×C127—321no—
112C2×C127#168511yescharacteristic
113C2×C127#221011yescharacteristic
114C2×C127#221311yescharacteristic
115#2226C2×C12711yescharacteristic, complemented
116#2206C2×C12711yescharacteristic
117#1706C2×C12711yescharacteristic, complemented
118#1589C2×C12711yescharacteristic, complemented
119#1370C2×C12711yescharacteristic, complemented
120#1365C2×C12711yescharacteristic, complemented
121#1361C2×C12711yescharacteristic, complemented
122C127#1248511yescharacteristic, direct product factor, Sylow
123C2×D16—21no—
124#500C22×C12711yescharacteristic
125#493C22×C12711yescharacteristic
126#492—21no—
127#486—21no—
128C4×D8C22×C12711yescharacteristic
129#436—21no—
130#367—21no—
131C4⋊C16C22×C12711yescharacteristic
132C4⋊C16C22×C12711yescharacteristic
133#357—21no—
134#357—21no—
135#335C22×C12711yescharacteristic
136D4⋊C8—21no—
137C82C22×C12711yescharacteristic
138C2×SD16—42no—
139C2×D8—21no—
140C2×D8—21no—
141C2×D8D4×C12711yescharacteristic
142C2×M16—41no—
143C4⋊Q8—21no—
144#127—21no—
145C4×D4—21no—
146D16—42no—
147C2×C16—21no—
148C2×C16—21no—
149#107—21no—
150#107—21no—
151#107D4×C12711yescharacteristic
152C4⋊C8—21no—
153#102—21no—
154#102—41no—
155#102—41no—
156C22⋊C8—41no—
157C4×C8D4×C12711yescharacteristic
158C4×C8D4×C12711yescharacteristic
159C4×C8C23×C12711yescharacteristic
160C2×Q8—41no—
161C2×D4—21no—
162C2×D4—41no—
163C2×D4—41no—
164C2×D4—41no—
165C22×C4—41no—
166SD16—84no—
167D8—21no—
168D8—21no—
169D8—41no—
170D8—41no—
171D8—81no—
172M16—82no—
173C2×C8—21no—
174C2×C8—41no—
175C2×C8D8×C12711yescharacteristic
176C2×C8D8×C12711yescharacteristic
177C2×C8C2×D4×C12711yescharacteristic
178C2×C8#41×C12711yescharacteristic
179C4⋊C4—21no—
180C4⋊C4—41no—
181C4⋊C4—41no—
182C22⋊C4—41no—
183C42C2×D4×C12711yescharacteristic
184C16—41no—
185C16—41no—
186C23—41no—
187C23—81no—
188Q8—82no—
189D4—41no—
190D4—41no—
191D4—82no—
192D4—81no—
193D4—81no—
194D4—81no—
195D4—81no—
196C2×C4—41no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—81no—
200C2×C4#121×C12711yescharacteristic
201C2×C4C2×D8×C12711yescharacteristic
202C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
203C8—22no—
204C8—21no—
205C8—21no—
206C8—21no—
207C8—81no—
208C8AGL(1,ℤ/8)×C12711yescharacteristic
209C8#137×C12711yescharacteristic
210C22—81no—
211C22—81no—
212C22—81no—
213C22—161no—
214C22—161no—
215C22—161no—
216C22#459×C12711yescharacteristic
217C4—21no—
218C4—81no—
219C4—161no—
220C4#468×C12711yescharacteristic
221C4#471×C12711yescharacteristic
222C4#508×C12711yescharacteristic
223C4#509×C12711yescharacteristic
224C2—161no—
225C2—321no—
226C2C127×#168511yescharacteristic
227C2C127×#221011yescharacteristic
228C2C127×#221311yescharacteristic
subgroupG/H
center, socleC22×C127#459
commutator, Frattini, cosocleC4×C8C23×C127
prime radicalC127×#2206C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ C82×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2226C2semidirect
3. C127×#1706C2semidirect
4. C127×#1589C2semidirect
5. C127×#1370C2semidirect
6. C127×#1365C2semidirect
7. C127×#1361C2semidirect
109. #12485C127direct (N × H)
115. #2226C2×C127semidirect
117. #1706C2×C127semidirect
118. #1589C2×C127semidirect
119. #1370C2×C127semidirect
120. #1365C2×C127semidirect
121. #1361C2×C127semidirect
122. C127#12485direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#22262
C127×#22062
C127×#17062
C127×#15892
C127×#13702
C127×#13652
C127×#13612
#12485127