Finite Group Databasebeta

← C127×#10636 #44574309

Subgroups — C127×#10636 #44574309

Order 32512.

278 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 98 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×#1993C211yesmaximal, characteristic
2C127×#1838C211yesmaximal, characteristic
3C127×#1549C211yesmaximal, characteristic
4C127×#1548C211yesmaximal, characteristic
5C127×#1286C211yesmaximal, characteristic
6C127×#1286C211yesmaximal, characteristic
7C127×#1281C211yesmaximal, characteristic
8C2×C4⋊Q8×C127C2211yescharacteristic
9#431×C127C2211yescharacteristic
10#431×C127C2211yescharacteristic
11#423×C127C2211yescharacteristic
12#423×C127C2211yescharacteristic
13C2×#97×C127C2211yescharacteristic
14#382×C127C2211yescharacteristic
15#341×C127—21no—
16#341×C127—21no—
17#340×C127—21no—
18#340×C127—21no—
19#333×C127—22no—
20#332×C127—22no—
21C22×Q8×C127—21no—
22C2×M16×C127—21no—
23C2×M16×C127—21no—
24C22×C8×C127D411yescharacteristic
25C22×C8×C127D411yescharacteristic
26C4⋊Q8×C127—21no—
27C4⋊Q8×C127—21no—
28C4⋊Q8×C127—21no—
29C4⋊Q8×C127D412yes—
30C2×C4⋊C4×C127—21no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C42×C127C2311yescharacteristic
34C4⋊C8×C127—21no—
35C4⋊C8×C127—21no—
36C4⋊C8×C127—21no—
37C4⋊C8×C127—21no—
38C4⋊C8×C127—21no—
39C4⋊C8×C127—21no—
40C22⋊C8×C127—21no—
41C22⋊C8×C127—21no—
42#97×C127—21no—
43#97×C127—21no—
44C4×C8×C127—21no—
45C4×C8×C127—21no—
46#95×C127—21no—
47#95×C127—21no—
48C2×Q8×C127—22no—
49C2×Q8×C127—41no—
50C2×Q8×C127—82no—
51C22×C4×C127—41no—
52C22×C4×C127—41no—
53C22×C4×C127C2×D411yescharacteristic
54C22×C4×C127#4111yescharacteristic
55C22×C4×C127#4111yescharacteristic
56M16×C127—41no—
57M16×C127—41no—
58M16×C127—41no—
59M16×C127—41no—
60C2×C8×C127—21no—
61C2×C8×C127—21no—
62C2×C8×C127—21no—
63C2×C8×C127—21no—
64C2×C8×C127—21no—
65C2×C8×C127—21no—
66C2×C8×C127—41no—
67C2×C8×C127—41no—
68C2×C8×C127—41no—
69C2×C8×C127—41no—
70C4⋊C4×C127—22no—
71C4⋊C4×C127—22no—
72C4⋊C4×C127—41no—
73C4⋊C4×C127—41no—
74C4⋊C4×C127—41no—
75C4⋊C4×C127—41no—
76C42×C127C2×D411yescharacteristic
77C42×C127#4111yescharacteristic
78C42×C127#4111yescharacteristic
79C42×C127#4111yescharacteristic
80C23×C127#12411yescharacteristic
81Q8×C127—82no—
82Q8×C127—82no—
83C2×C4×C127—41no—
84C2×C4×C127—41no—
85C2×C4×C127—42no—
86C2×C4×C127—82no—
87C2×C4×C127—81no—
88C2×C4×C127—81no—
89C2×C4×C127—81no—
90C2×C4×C127#12111yescharacteristic
91C2×C4×C127#12311yescharacteristic
92C2×C4×C127#12311yescharacteristic
93C2×C4×C127#12311yescharacteristic
94C2×C4×C127#12611yescharacteristic
95C2×C4×C127#12611yescharacteristic
96C2×C4×C127#13511yescharacteristic
97C2×C4×C127#13511yescharacteristic
98C2×C4×C127#13711yescharacteristic
99C2×C4×C127#13711yescharacteristic
100C8×C127—41no—
101C8×C127—41no—
102C8×C127—81no—
103C8×C127—81no—
104C8×C127—81no—
105C8×C127—81no—
106C22×C127—21no—
107C22×C127—21no—
108C22×C127#39711yescharacteristic
109C22×C127#48811yescharacteristic
110C22×C127#49111yescharacteristic
111C4×C127—21no—
112C4×C127—21no—
113C4×C127—21no—
114C4×C127—21no—
115C4×C127—82no—
116C4×C127—161no—
117C4×C127#46411yescharacteristic
118C4×C127#46411yescharacteristic
119C4×C127#48511yescharacteristic
120C4×C127#48511yescharacteristic
121#10636C12711yesmaximal, characteristic, direct product factor, Sylow
122C2×C127—21no—
123C2×C127—21no—
124C2×C127#207411yescharacteristic
125C2×C127#208111yescharacteristic
126C2×C127#208211yescharacteristic
127#1993C2×C12711yescharacteristic
128#1838C2×C12711yescharacteristic
129#1549C2×C12711yescharacteristic
130#1548C2×C12711yescharacteristic
131#1286C2×C12711yescharacteristic
132#1286C2×C12711yescharacteristic
133#1281C2×C12711yescharacteristic
134C127#1063611yescharacteristic, direct product factor, Sylow
135C2×C4⋊Q8C22×C12711yescharacteristic
136#431C22×C12711yescharacteristic
137#431C22×C12711yescharacteristic
138#423C22×C12711yescharacteristic
139#423C22×C12711yescharacteristic
140C2×#97C22×C12711yescharacteristic
141#382C22×C12711yescharacteristic
142#341—21no—
143#341—21no—
144#340—21no—
145#340—21no—
146#333—22no—
147#332—22no—
148C22×Q8—21no—
149C2×M16—21no—
150C2×M16—21no—
151C22×C8D4×C12711yescharacteristic
152C22×C8D4×C12711yescharacteristic
153C4⋊Q8—21no—
154C4⋊Q8—21no—
155C4⋊Q8—21no—
156C4⋊Q8D4×C12712yes—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—21no—
160C2×C42C23×C12711yescharacteristic
161C4⋊C8—21no—
162C4⋊C8—21no—
163C4⋊C8—21no—
164C4⋊C8—21no—
165C4⋊C8—21no—
166C4⋊C8—21no—
167C22⋊C8—21no—
168C22⋊C8—21no—
169#97—21no—
170#97—21no—
171C4×C8—21no—
172C4×C8—21no—
173#95—21no—
174#95—21no—
175C2×Q8—22no—
176C2×Q8—41no—
177C2×Q8—82no—
178C22×C4—41no—
179C22×C4—41no—
180C22×C4C2×D4×C12711yescharacteristic
181C22×C4#41×C12711yescharacteristic
182C22×C4#41×C12711yescharacteristic
183M16—41no—
184M16—41no—
185M16—41no—
186M16—41no—
187C2×C8—21no—
188C2×C8—21no—
189C2×C8—21no—
190C2×C8—21no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—41no—
194C2×C8—41no—
195C2×C8—41no—
196C2×C8—41no—
197C4⋊C4—22no—
198C4⋊C4—22no—
199C4⋊C4—41no—
200C4⋊C4—41no—
201C4⋊C4—41no—
202C4⋊C4—41no—
203C42C2×D4×C12711yescharacteristic
204C42#41×C12711yescharacteristic
205C42#41×C12711yescharacteristic
206C42#41×C12711yescharacteristic
207C23#124×C12711yescharacteristic
208Q8—82no—
209Q8—82no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—42no—
213C2×C4—82no—
214C2×C4—81no—
215C2×C4—81no—
216C2×C4—81no—
217C2×C4#121×C12711yescharacteristic
218C2×C4#123×C12711yescharacteristic
219C2×C4#123×C12711yescharacteristic
220C2×C4#123×C12711yescharacteristic
221C2×C4#126×C12711yescharacteristic
222C2×C4#126×C12711yescharacteristic
223C2×C4#135×C12711yescharacteristic
224C2×C4#135×C12711yescharacteristic
225C2×C4#137×C12711yescharacteristic
226C2×C4#137×C12711yescharacteristic
227C8—41no—
228C8—41no—
229C8—81no—
230C8—81no—
231C8—81no—
232C8—81no—
233C22—21no—
234C22—21no—
235C22#397×C12711yescharacteristic
236C22#488×C12711yescharacteristic
237C22#491×C12711yescharacteristic
238C4—21no—
239C4—21no—
240C4—21no—
241C4—21no—
242C4—82no—
243C4—161no—
244C4#464×C12711yescharacteristic
245C4#464×C12711yescharacteristic
246C4#485×C12711yescharacteristic
247C4#485×C12711yescharacteristic
248C2—21no—
249C2—21no—
250C2C127×#207411yescharacteristic
251C2C127×#208111yescharacteristic
252C2C127×#208211yescharacteristic
subgroupG/H
center, socleC22×C127#397
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127#124
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
121. #10636C127direct (N × H)
134. C127#10636direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#19932
C127×#18382
C127×#15492
C127×#15482
C127×#12862
C127×#12812
#10636127