Finite Group Databasebeta

← C127×#12158 #44575831

Subgroups — C127×#12158 #44575831

Order 32512.

434 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 82 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×#3245C211yesmaximal, characteristic, complemented
2C127×#2184C212yesmaximal, complemented
3C127×#2054C211yesmaximal, characteristic, complemented
4C127×#1347C212yesmaximal, complemented
5C127×#1322C211yesmaximal, characteristic, complemented
6C22×D8×C127C2211yescharacteristic
7#532×C127—21no—
8C2×D16×C127—22no—
9#474×C127—22no—
10#466×C127—21no—
11#466×C127C2212yes—
12#459×C127—22no—
13C2×C4⋊C8×C127C2211yescharacteristic
14C2×#102×C127—21no—
15#390×C127—21no—
16#357×C127—22no—
17C22⋊C16×C127C2212yes—
18#340×C127C2211yescharacteristic
19C2×#41×C127—41no—
20C22×D4×C127—21no—
21C2×D8×C127—21no—
22C2×D8×C127—22no—
23C2×D8×C127—42no—
24C2×D8×C127D412yes—
25C22×C8×C127D411yescharacteristic
26C22×C8×C127C2311yescharacteristic
27C4⋊Q8×C127—21no—
28#127×C127—21no—
29#124×C127—41no—
30#121×C127—22no—
31#121×C127—41no—
32C4×D4×C127—22no—
33C4×D4×C127—41no—
34C2×C4⋊C4×C127—21no—
35C2×C22⋊C4×C127—41no—
36C2×C22⋊C4×C127—41no—
37C2×C42×C127D411yescharacteristic
38D16×C127—44no—
39C2×C16×C127—22no—
40#107×C127—21no—
41#107×C127D412yes—
42C4⋊C8×C127—22no—
43#102×C127—22no—
44#102×C127—22no—
45#102×C127—42no—
46C24×C127—41no—
47#41×C127—82no—
48#41×C127—82no—
49C2×Q8×C127—41no—
50C2×D4×C127—22no—
51C2×D4×C127—22no—
52C2×D4×C127—41no—
53C2×D4×C127—41no—
54C2×D4×C127—41no—
55C2×D4×C127—41no—
56C2×D4×C127—41no—
57C2×D4×C127—42no—
58C2×D4×C127—41no—
59C2×D4×C127—41no—
60C22×C4×C127—42no—
61C22×C4×C127—41no—
62C22×C4×C127D811yescharacteristic
63C22×C4×C127D811yescharacteristic
64C22×C4×C127C2×D411yescharacteristic
65D8×C127—24no—
66D8×C127—42no—
67D8×C127—42no—
68D8×C127—81no—
69C2×C8×C127—21no—
70C2×C8×C127—41no—
71C2×C8×C127—41no—
72C2×C8×C127C2×D412yes—
73C4⋊C4×C127—22no—
74C4⋊C4×C127—41no—
75C4⋊C4×C127—41no—
76C4⋊C4×C127—41no—
77C22⋊C4×C127—42no—
78C22⋊C4×C127—42no—
79C22⋊C4×C127—82no—
80C22⋊C4×C127—82no—
81C42×C127—21no—
82C42×C127—21no—
83C16×C127—42no—
84C23×C127—42no—
85C23×C127—42no—
86C23×C127—81no—
87C23×C127—81no—
88C23×C127—81no—
89C23×C127—81no—
90C23×C127—81no—
91C23×C127—81no—
92C23×C127C2×D811yescharacteristic
93Q8×C127—82no—
94D4×C127—42no—
95D4×C127—42no—
96D4×C127—42no—
97D4×C127—42no—
98D4×C127—81no—
99D4×C127—82no—
100D4×C127—82no—
101D4×C127—82no—
102D4×C127—82no—
103D4×C127—81no—
104C2×C4×C127—21no—
105C2×C4×C127—21no—
106C2×C4×C127—21no—
107C2×C4×C127—21no—
108C2×C4×C127—21no—
109C2×C4×C127—41no—
110C2×C4×C127—42no—
111C2×C4×C127—84no—
112C2×C4×C127—81no—
113C2×C4×C127—81no—
114C2×C4×C127—81no—
115C2×C4×C127D1612yescomplemented
116C2×C4×C127#12011yescharacteristic
117C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
118C8×C127—22no—
119C8×C127—41no—
120C22×C127—21no—
121C22×C127—21no—
122C22×C127—82no—
123C22×C127—82no—
124C22×C127—82no—
125C22×C127—82no—
126C22×C127—82no—
127C22×C127—82no—
128C22×C127—161no—
129C22×C127—161no—
130C22×C127—161no—
131C22×C127—161no—
132C22×C127#44711yescharacteristic
133C22×C127C2×D1611yescharacteristic
134C22×C127#50911yescharacteristic
135C4×C127—21no—
136C4×C127—22no—
137C4×C127—41no—
138C4×C127—82no—
139C4×C127—161no—
140C4×C127#45411yescharacteristic
141C4×C127B(4,𝔽2)11yescharacteristic
142#12158C12711yesmaximal, characteristic, direct product factor, Sylow
143C2×C127—21no—
144C2×C127—21no—
145C2×C127—162no—
146C2×C127—162no—
147C2×C127#159811yescharacteristic
148C2×C127#218411yescharacteristic
149C2×C127#219011yescharacteristic
150#3245C2×C12711yescharacteristic, complemented
151#2184C2×C12712yescomplemented
152#2054C2×C12711yescharacteristic, complemented
153#1347C2×C12712yescomplemented
154#1322C2×C12711yescharacteristic, complemented
155C127#1215811yescharacteristic, direct product factor, Sylow
156C22×D8C22×C12711yescharacteristic
157#532—21no—
158C2×D16—22no—
159#474—22no—
160#466—21no—
161#466C22×C12712yes—
162#459—22no—
163C2×C4⋊C8C22×C12711yescharacteristic
164C2×#102—21no—
165#390—21no—
166#357—22no—
167C22⋊C16C22×C12712yes—
168#340C22×C12711yescharacteristic
169C2×#41—41no—
170C22×D4—21no—
171C2×D8—21no—
172C2×D8—22no—
173C2×D8—42no—
174C2×D8D4×C12712yes—
175C22×C8D4×C12711yescharacteristic
176C22×C8C23×C12711yescharacteristic
177C4⋊Q8—21no—
178#127—21no—
179#124—41no—
180#121—22no—
181#121—41no—
182C4×D4—22no—
183C4×D4—41no—
184C2×C4⋊C4—21no—
185C2×C22⋊C4—41no—
186C2×C22⋊C4—41no—
187C2×C42D4×C12711yescharacteristic
188D16—44no—
189C2×C16—22no—
190#107—21no—
191#107D4×C12712yes—
192C4⋊C8—22no—
193#102—22no—
194#102—22no—
195#102—42no—
196C24—41no—
197#41—82no—
198#41—82no—
199C2×Q8—41no—
200C2×D4—22no—
201C2×D4—22no—
202C2×D4—41no—
203C2×D4—41no—
204C2×D4—41no—
205C2×D4—41no—
206C2×D4—41no—
207C2×D4—42no—
208C2×D4—41no—
209C2×D4—41no—
210C22×C4—42no—
211C22×C4—41no—
212C22×C4D8×C12711yescharacteristic
213C22×C4D8×C12711yescharacteristic
214C22×C4C2×D4×C12711yescharacteristic
215D8—24no—
216D8—42no—
217D8—42no—
218D8—81no—
219C2×C8—21no—
220C2×C8—41no—
221C2×C8—41no—
222C2×C8C2×D4×C12712yes—
223C4⋊C4—22no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C22⋊C4—42no—
228C22⋊C4—42no—
229C22⋊C4—82no—
230C22⋊C4—82no—
231C42—21no—
232C42—21no—
233C16—42no—
234C23—42no—
235C23—42no—
236C23—81no—
237C23—81no—
238C23—81no—
239C23—81no—
240C23—81no—
241C23—81no—
242C23C2×D8×C12711yescharacteristic
243Q8—82no—
244D4—42no—
245D4—42no—
246D4—42no—
247D4—42no—
248D4—81no—
249D4—82no—
250D4—82no—
251D4—82no—
252D4—82no—
253D4—81no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—42no—
261C2×C4—84no—
262C2×C4—81no—
263C2×C4—81no—
264C2×C4—81no—
265C2×C4D16×C12712yescomplemented
266C2×C4#120×C12711yescharacteristic
267C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
268C8—22no—
269C8—41no—
270C22—21no—
271C22—21no—
272C22—82no—
273C22—82no—
274C22—82no—
275C22—82no—
276C22—82no—
277C22—82no—
278C22—161no—
279C22—161no—
280C22—161no—
281C22—161no—
282C22#447×C12711yescharacteristic
283C22C2×D16×C12711yescharacteristic
284C22#509×C12711yescharacteristic
285C4—21no—
286C4—22no—
287C4—41no—
288C4—82no—
289C4—161no—
290C4#454×C12711yescharacteristic
291C4B(4,𝔽2)×C12711yescharacteristic
292C2—21no—
293C2—21no—
294C2—162no—
295C2—162no—
296C2C127×#159811yescharacteristic
297C2C127×#218411yescharacteristic
298C2C127×#219011yescharacteristic
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC22×C8C23×C127
LCSG ▷ C22×C8 ▷ C2×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
1. C127×#3245C2semidirect
2. C127×#2184C2semidirect
3. C127×#2054C2semidirect
4. C127×#1347C2semidirect
5. C127×#1322C2semidirect
115. C2×C4×C127D16semidirect
142. #12158C127direct (N × H)
150. #3245C2×C127semidirect
151. #2184C2×C127semidirect
152. #2054C2×C127semidirect
153. #1347C2×C127semidirect
154. #1322C2×C127semidirect
155. C127#12158direct (N × H)
265. C2×C4D16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32452
C127×#21842
C127×#20542
C127×#13472
C127×#13222
#12158127