Finite Group Databasebeta

← C127×#10614 #44574287

Subgroups — C127×#10614 #44574287

Order 32512.

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

normal subgroups only

This group has 276 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×#1574C211yesmaximal, characteristic
2C127×#1574C211yesmaximal, characteristic
3C127×#1574C211yesmaximal, characteristic
4C127×#1549C211yesmaximal, characteristic
5C127×#1548C211yesmaximal, characteristic
6C127×#1546C211yesmaximal, characteristic
7C127×#1309C211yesmaximal, characteristic
8C2×C4⋊Q8×C127C2211yescharacteristic
9#431×C127C2211yescharacteristic
10#431×C127C2211yescharacteristic
11#431×C127C2211yescharacteristic
12#423×C127C2211yescharacteristic
13#423×C127C2211yescharacteristic
14#423×C127C2211yescharacteristic
15#335×C127—21no—
16#335×C127—21no—
17#335×C127—21no—
18#334×C127—21no—
19#334×C127—21no—
20#334×C127—21no—
21#333×C127—21no—
22#333×C127—21no—
23#332×C127—21no—
24#332×C127—21no—
25#332×C127—21no—
26#332×C127—21no—
27C22×Q8×C127—21no—
28C2×M16×C127—21no—
29C2×M16×C127—21no—
30C2×M16×C127—21no—
31C4⋊Q8×C127—21no—
32C4⋊Q8×C127—21no—
33C4⋊Q8×C127—21no—
34C4⋊Q8×C127Q812yes—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—21no—
37C2×C42×C127C2311yescharacteristic
38C4⋊C8×C127—21no—
39C4⋊C8×C127—21no—
40C4⋊C8×C127—21no—
41C4⋊C8×C127—21no—
42C4⋊C8×C127—21no—
43C4⋊C8×C127—21no—
44C4⋊C8×C127D411yescharacteristic
45C4⋊C8×C127D411yescharacteristic
46C4⋊C8×C127D411yescharacteristic
47C4⋊C8×C127D411yescharacteristic
48C4⋊C8×C127D411yescharacteristic
49C4⋊C8×C127D411yescharacteristic
50C22⋊C8×C127—21no—
51C22⋊C8×C127—21no—
52C22⋊C8×C127—21no—
53C4×C8×C127—21no—
54C4×C8×C127—21no—
55C4×C8×C127—21no—
56C2×Q8×C127—22no—
57C2×Q8×C127—41no—
58C2×Q8×C127—81no—
59C2×Q8×C127—81no—
60C22×C4×C127—41no—
61C22×C4×C127#4111yescharacteristic
62C22×C4×C127#4111yescharacteristic
63C22×C4×C127#4111yescharacteristic
64M16×C127—81no—
65M16×C127—81no—
66M16×C127—81no—
67C2×C8×C127—21no—
68C2×C8×C127—21no—
69C2×C8×C127—21no—
70C2×C8×C127—21no—
71C2×C8×C127—21no—
72C2×C8×C127—21no—
73C2×C8×C127—41no—
74C2×C8×C127—41no—
75C2×C8×C127—41no—
76C4⋊C4×C127—22no—
77C4⋊C4×C127—22no—
78C4⋊C4×C127—41no—
79C4⋊C4×C127—41no—
80C42×C127C2×D411yescharacteristic
81C42×C127C2×D411yescharacteristic
82C42×C127C2×D411yescharacteristic
83C42×C127C2×Q811yescharacteristic
84C23×C127#12611yescharacteristic
85Q8×C127—82no—
86Q8×C127—81no—
87Q8×C127—81no—
88C2×C4×C127—21no—
89C2×C4×C127—21no—
90C2×C4×C127—21no—
91C2×C4×C127—21no—
92C2×C4×C127—21no—
93C2×C4×C127—21no—
94C2×C4×C127—42no—
95C2×C4×C127—82no—
96C2×C4×C127#12111yescharacteristic
97C2×C4×C127#12111yescharacteristic
98C2×C4×C127#12111yescharacteristic
99C2×C4×C127C22⋊Q811yescharacteristic
100C2×C4×C127C22⋊Q811yescharacteristic
101C2×C4×C127C22⋊Q811yescharacteristic
102C8×C127—41no—
103C8×C127—41no—
104C8×C127—41no—
105C8×C127—41no—
106C8×C127—41no—
107C8×C127—41no—
108C8×C127—81no—
109C8×C127—81no—
110C8×C127—81no—
111C22×C127—21no—
112C22×C127—21no—
113C22×C127—21no—
114C22×C127#39611yescharacteristic
115C4×C127—21no—
116C4×C127—21no—
117C4×C127—21no—
118C4×C127—82no—
119C4×C127#47111yescharacteristic
120C4×C127#47111yescharacteristic
121C4×C127#47111yescharacteristic
122C4×C127#47211yescharacteristic
123C4×C127#47311yescharacteristic
124C4×C127#47311yescharacteristic
125#10614C12711yesmaximal, characteristic, direct product factor, Sylow
126C2×C127—41no—
127C2×C127#206311yescharacteristic
128C2×C127#206411yescharacteristic
129C2×C127#206411yescharacteristic
130#1574C2×C12711yescharacteristic
131#1574C2×C12711yescharacteristic
132#1574C2×C12711yescharacteristic
133#1549C2×C12711yescharacteristic
134#1548C2×C12711yescharacteristic
135#1546C2×C12711yescharacteristic
136#1309C2×C12711yescharacteristic
137C127#1061411yescharacteristic, direct product factor, Sylow
138C2×C4⋊Q8C22×C12711yescharacteristic
139#431C22×C12711yescharacteristic
140#431C22×C12711yescharacteristic
141#431C22×C12711yescharacteristic
142#423C22×C12711yescharacteristic
143#423C22×C12711yescharacteristic
144#423C22×C12711yescharacteristic
145#335—21no—
146#335—21no—
147#335—21no—
148#334—21no—
149#334—21no—
150#334—21no—
151#333—21no—
152#333—21no—
153#332—21no—
154#332—21no—
155#332—21no—
156#332—21no—
157C22×Q8—21no—
158C2×M16—21no—
159C2×M16—21no—
160C2×M16—21no—
161C4⋊Q8—21no—
162C4⋊Q8—21no—
163C4⋊Q8—21no—
164C4⋊Q8Q8×C12712yes—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C42C23×C12711yescharacteristic
168C4⋊C8—21no—
169C4⋊C8—21no—
170C4⋊C8—21no—
171C4⋊C8—21no—
172C4⋊C8—21no—
173C4⋊C8—21no—
174C4⋊C8D4×C12711yescharacteristic
175C4⋊C8D4×C12711yescharacteristic
176C4⋊C8D4×C12711yescharacteristic
177C4⋊C8D4×C12711yescharacteristic
178C4⋊C8D4×C12711yescharacteristic
179C4⋊C8D4×C12711yescharacteristic
180C22⋊C8—21no—
181C22⋊C8—21no—
182C22⋊C8—21no—
183C4×C8—21no—
184C4×C8—21no—
185C4×C8—21no—
186C2×Q8—22no—
187C2×Q8—41no—
188C2×Q8—81no—
189C2×Q8—81no—
190C22×C4—41no—
191C22×C4#41×C12711yescharacteristic
192C22×C4#41×C12711yescharacteristic
193C22×C4#41×C12711yescharacteristic
194M16—81no—
195M16—81no—
196M16—81no—
197C2×C8—21no—
198C2×C8—21no—
199C2×C8—21no—
200C2×C8—21no—
201C2×C8—21no—
202C2×C8—21no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8—41no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C42C2×D4×C12711yescharacteristic
211C42C2×D4×C12711yescharacteristic
212C42C2×D4×C12711yescharacteristic
213C42C2×Q8×C12711yescharacteristic
214C23#126×C12711yescharacteristic
215Q8—82no—
216Q8—81no—
217Q8—81no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—42no—
225C2×C4—82no—
226C2×C4#121×C12711yescharacteristic
227C2×C4#121×C12711yescharacteristic
228C2×C4#121×C12711yescharacteristic
229C2×C4C22⋊Q8×C12711yescharacteristic
230C2×C4C22⋊Q8×C12711yescharacteristic
231C2×C4C22⋊Q8×C12711yescharacteristic
232C8—41no—
233C8—41no—
234C8—41no—
235C8—41no—
236C8—41no—
237C8—41no—
238C8—81no—
239C8—81no—
240C8—81no—
241C22—21no—
242C22—21no—
243C22—21no—
244C22#396×C12711yescharacteristic
245C4—21no—
246C4—21no—
247C4—21no—
248C4—82no—
249C4#471×C12711yescharacteristic
250C4#471×C12711yescharacteristic
251C4#471×C12711yescharacteristic
252C4#472×C12711yescharacteristic
253C4#473×C12711yescharacteristic
254C4#473×C12711yescharacteristic
255C2—41no—
256C2C127×#206311yescharacteristic
257C2C127×#206411yescharacteristic
258C2C127×#206411yescharacteristic
subgroupG/H
center, socleC22×C127#396
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127#126
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
125. #10614C127direct (N × H)
137. C127#10614direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#15742
C127×#15492
C127×#15482
C127×#15462
C127×#13092
#10614127