Finite Group Databasebeta

← C127×#10493 #44574166

Subgroups — C127×#10493 #44574166

Order 32512.

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

normal subgroups only

This group has 372 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×#3209C211yesmaximal, characteristic
2C127×#1966C211yesmaximal, characteristic
3C127×#1574C211yesmaximal, characteristic
4C127×#1561C211yesmaximal, characteristic
5C127×#1548C211yesmaximal, characteristic
6C127×#1485C211yesmaximal, characteristic
7C127×#1299C211yesmaximal, characteristic
8#533×C127C2211yescharacteristic
9C2×C4⋊Q8×C127C2211yescharacteristic
10#494×C127—21no—
11#487×C127—21no—
12#462×C127—21no—
13#462×C127—21no—
14#451×C127—22no—
15#431×C127C2211yescharacteristic
16#431×C127C2211yescharacteristic
17#423×C127C2211yescharacteristic
18#423×C127C2211yescharacteristic
19C2×#101×C127—22no—
20C4×M16×C127C2211yescharacteristic
21#335×C127—21no—
22#334×C127—21no—
23#333×C127—22no—
24#332×C127—21no—
25#332×C127—21no—
26Q8⋊C8×C127—22no—
27C22×Q8×C127D412yes—
28C2×Q16×C127—22no—
29C2×Q16×C127—22no—
30C2×M16×C127—21no—
31C2×M16×C127—21no—
32C2×M16×C127—21no—
33C4⋊Q8×C127—21no—
34C4⋊Q8×C127—21no—
35C4⋊Q8×C127—21no—
36C4⋊Q8×C127—21no—
37C4⋊Q8×C127D411yescharacteristic
38C4⋊Q8×C127D411yescharacteristic
39#125×C127—21no—
40C22⋊Q8×C127—21no—
41C22⋊Q8×C127—21no—
42C4×Q8×C127—21no—
43C4×Q8×C127—21no—
44#117×C127—21no—
45C2×C4⋊C4×C127—21no—
46C2×C4⋊C4×C127—21no—
47C2×C42×C127C2311yescharacteristic
48C4⋊C8×C127—21no—
49C4⋊C8×C127—21no—
50C4⋊C8×C127—21no—
51C4⋊C8×C127—21no—
52C4⋊C8×C127D412yes—
53C4⋊C8×C127D411yescharacteristic
54C4⋊C8×C127D411yescharacteristic
55#103×C127—22no—
56#103×C127—22no—
57#101×C127—44no—
58C22⋊C8×C127—21no—
59C22⋊C8×C127—21no—
60#97×C127—21no—
61C4×C8×C127—21no—
62C4×C8×C127—21no—
63C4×C8×C127—21no—
64C2×Q8×C127—22no—
65C2×Q8×C127—21no—
66C2×Q8×C127—21no—
67C2×Q8×C127—22no—
68C2×Q8×C127—42no—
69C2×Q8×C127—42no—
70C22×C4×C127—22no—
71C22×C4×C127C2×D411yescharacteristic
72C22×C4×C127#4111yescharacteristic
73C22×C4×C127#4111yescharacteristic
74Q16×C127—82no—
75Q16×C127—82no—
76M16×C127—22no—
77M16×C127—41no—
78M16×C127—42no—
79M16×C127—81no—
80C2×C8×C127—21no—
81C2×C8×C127—21no—
82C2×C8×C127—22no—
83C2×C8×C127—41no—
84C2×C8×C127—41no—
85C2×C8×C127—41no—
86C4⋊C4×C127—21no—
87C4⋊C4×C127—21no—
88C4⋊C4×C127—21no—
89C4⋊C4×C127—21no—
90C4⋊C4×C127—41no—
91C4⋊C4×C127—41no—
92C4⋊C4×C127—41no—
93C4⋊C4×C127—41no—
94C4⋊C4×C127—41no—
95C4⋊C4×C127—41no—
96C22⋊C4×C127—41no—
97C42×C127—41no—
98C42×C127C2×D411yescharacteristic
99C42×C127C2×D411yescharacteristic
100C42×C127C2×D411yescharacteristic
101C42×C127#4111yescharacteristic
102C23×C127#12311yescharacteristic
103Q8×C127—41no—
104Q8×C127—42no—
105Q8×C127—41no—
106Q8×C127—42no—
107Q8×C127—41no—
108Q8×C127—41no—
109Q8×C127—82no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—21no—
114C2×C4×C127—22no—
115C2×C4×C127—44no—
116C2×C4×C127—41no—
117C2×C4×C127—41no—
118C2×C4×C127—42no—
119C2×C4×C127#12011yescharacteristic
120C2×C4×C127#12111yescharacteristic
121C2×C4×C127#12111yescharacteristic
122C2×C4×C127#12111yescharacteristic
123C2×C4×C127#12311yescharacteristic
124C2×C4×C127#12411yescharacteristic
125C8×C127—42no—
126C8×C127—41no—
127C8×C127—41no—
128C8×C127—42no—
129C8×C127—81no—
130C8×C127—81no—
131C22×C127—21no—
132C22×C127—21no—
133C22×C127—21no—
134C22×C127#39411yescharacteristic
135C4×C127—21no—
136C4×C127—21no—
137C4×C127—21no—
138C4×C127—81no—
139C4×C127—82no—
140C4×C127—81no—
141C4×C127#45311yescharacteristic
142C4×C127#45511yescharacteristic
143C4×C127#47111yescharacteristic
144C4×C127#47311yescharacteristic
145C4×C127#47312yes—
146#10493C12711yesmaximal, characteristic, direct product factor, Sylow
147C2×C127—41no—
148C2×C127#203711yescharacteristic
149C2×C127#204711yescharacteristic
150C2×C127#205211yescharacteristic
151#3209C2×C12711yescharacteristic
152#1966C2×C12711yescharacteristic
153#1574C2×C12711yescharacteristic
154#1561C2×C12711yescharacteristic
155#1548C2×C12711yescharacteristic
156#1485C2×C12711yescharacteristic
157#1299C2×C12711yescharacteristic
158C127#1049311yescharacteristic, direct product factor, Sylow
159#533C22×C12711yescharacteristic
160C2×C4⋊Q8C22×C12711yescharacteristic
161#494—21no—
162#487—21no—
163#462—21no—
164#462—21no—
165#451—22no—
166#431C22×C12711yescharacteristic
167#431C22×C12711yescharacteristic
168#423C22×C12711yescharacteristic
169#423C22×C12711yescharacteristic
170C2×#101—22no—
171C4×M16C22×C12711yescharacteristic
172#335—21no—
173#334—21no—
174#333—22no—
175#332—21no—
176#332—21no—
177Q8⋊C8—22no—
178C22×Q8D4×C12712yes—
179C2×Q16—22no—
180C2×Q16—22no—
181C2×M16—21no—
182C2×M16—21no—
183C2×M16—21no—
184C4⋊Q8—21no—
185C4⋊Q8—21no—
186C4⋊Q8—21no—
187C4⋊Q8—21no—
188C4⋊Q8D4×C12711yescharacteristic
189C4⋊Q8D4×C12711yescharacteristic
190#125—21no—
191C22⋊Q8—21no—
192C22⋊Q8—21no—
193C4×Q8—21no—
194C4×Q8—21no—
195#117—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C42C23×C12711yescharacteristic
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8D4×C12712yes—
204C4⋊C8D4×C12711yescharacteristic
205C4⋊C8D4×C12711yescharacteristic
206#103—22no—
207#103—22no—
208#101—44no—
209C22⋊C8—21no—
210C22⋊C8—21no—
211#97—21no—
212C4×C8—21no—
213C4×C8—21no—
214C4×C8—21no—
215C2×Q8—22no—
216C2×Q8—21no—
217C2×Q8—21no—
218C2×Q8—22no—
219C2×Q8—42no—
220C2×Q8—42no—
221C22×C4—22no—
222C22×C4C2×D4×C12711yescharacteristic
223C22×C4#41×C12711yescharacteristic
224C22×C4#41×C12711yescharacteristic
225Q16—82no—
226Q16—82no—
227M16—22no—
228M16—41no—
229M16—42no—
230M16—81no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—22no—
234C2×C8—41no—
235C2×C8—41no—
236C2×C8—41no—
237C4⋊C4—21no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C22⋊C4—41no—
248C42—41no—
249C42C2×D4×C12711yescharacteristic
250C42C2×D4×C12711yescharacteristic
251C42C2×D4×C12711yescharacteristic
252C42#41×C12711yescharacteristic
253C23#123×C12711yescharacteristic
254Q8—41no—
255Q8—42no—
256Q8—41no—
257Q8—42no—
258Q8—41no—
259Q8—41no—
260Q8—82no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—22no—
265C2×C4—21no—
266C2×C4—44no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—42no—
270C2×C4#120×C12711yescharacteristic
271C2×C4#121×C12711yescharacteristic
272C2×C4#121×C12711yescharacteristic
273C2×C4#121×C12711yescharacteristic
274C2×C4#123×C12711yescharacteristic
275C2×C4#124×C12711yescharacteristic
276C8—42no—
277C8—41no—
278C8—41no—
279C8—42no—
280C8—81no—
281C8—81no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22#394×C12711yescharacteristic
286C4—21no—
287C4—21no—
288C4—21no—
289C4—82no—
290C4—81no—
291C4—81no—
292C4#453×C12711yescharacteristic
293C4#455×C12711yescharacteristic
294C4#471×C12711yescharacteristic
295C4#473×C12712yes—
296C4#473×C12711yescharacteristic
297C2—41no—
298C2C127×#203711yescharacteristic
299C2C127×#204711yescharacteristic
300C2C127×#205211yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127#123
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
146. #10493C127direct (N × H)
158. C127#10493direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32092
C127×#19662
C127×#15742
C127×#15612
C127×#15482
C127×#14852
C127×#12992
#10493127