Finite Group Databasebeta

← C127×#9335 #44573008

Subgroups — C127×#9335 #44573008

Order 32512.

400 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 114 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×#3234C211yesmaximal, characteristic
2C127×#2980C211yesmaximal, characteristic
3C127×#1553C211yesmaximal, characteristic
4C127×#1534C211yesmaximal, characteristic, complemented
5C127×#1470C211yesmaximal, characteristic, complemented
6C127×#1308C211yesmaximal, characteristic, complemented
7C127×#1287C211yesmaximal, characteristic, complemented
8#532×C127C2211yescharacteristic
9C2×#125×C127C2211yescharacteristic
10#501×C127—21no—
11#490×C127—21no—
12#481×C127C412yes—
13#480×C127C412yes—
14#478×C127—22no—
15#435×C127—22no—
16#435×C127—22no—
17#432×C127C2211yescharacteristic
18#432×C127C2211yescharacteristic
19#432×C127C2211yescharacteristic
20#432×C127C2211yescharacteristic
21#431×C127C2211yescharacteristic
22#408×C127—22no—
23#332×C127—21no—
24#331×C127—21no—
25#330×C127—22no—
26#324×C127—22no—
27C2×#41×C127—21no—
28C2×M16×C127—22no—
29C22×C8×C127—22no—
30C4⋊Q8×C127D411yescharacteristic
31#127×C127D411yescharacteristic
32#125×C127—21no—
33#125×C127—21no—
34#125×C127—21no—
35#125×C127—21no—
36#124×C127—21no—
37#121×C127—21no—
38#121×C127C2×C412yes—
39C4×D4×C127—21no—
40C4×D4×C127D412yes—
41C2×C4⋊C4×C127—21no—
42C2×C4⋊C4×C127—21no—
43C2×C4⋊C4×C127C2×C411yescharacteristic
44C2×C4⋊C4×C127C2×C411yescharacteristic
45C2×C42×C127C2311yescharacteristic
46#107×C127—22no—
47#106×C127—22no—
48C4⋊C8×C127—21no—
49C4⋊C8×C127—21no—
50C4⋊C8×C127—21no—
51C4⋊C8×C127—21no—
52C4⋊C8×C127—21no—
53#102×C127—22no—
54#102×C127—22no—
55C22⋊C8×C127—24no—
56C22⋊C8×C127—21no—
57C22⋊C8×C127—21no—
58C22⋊C8×C127—21no—
59C22⋊C8×C127C2×C412yes—
60C22⋊C8×C127D412yes—
61#97×C127—21no—
62#97×C127—21no—
63#97×C127—21no—
64#97×C127D412yes—
65C4×C8×C127—21no—
66#41×C127—81no—
67#41×C127—81no—
68C2×Q8×C127—21no—
69C2×D4×C127—22no—
70C2×D4×C127—21no—
71C2×D4×C127—21no—
72C2×D4×C127C22⋊C412yes—
73C22×C4×C127—22no—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127C22×C411yescharacteristic
77C22×C4×C127C2×D411yescharacteristic
78C22×C4×C127#4111yescharacteristic
79M16×C127—82no—
80C2×C8×C127—22no—
81C2×C8×C127—22no—
82C2×C8×C127—22no—
83C2×C8×C127—41no—
84C2×C8×C127—41no—
85C2×C8×C127—82no—
86C4⋊C4×C127—21no—
87C4⋊C4×C127—21no—
88C4⋊C4×C127—21no—
89C4⋊C4×C127—21no—
90C4⋊C4×C127—21no—
91C4⋊C4×C127—41no—
92C4⋊C4×C127—41no—
93C4⋊C4×C127—41no—
94C4⋊C4×C127—41no—
95C4⋊C4×C127C22⋊C412yes—
96C22⋊C4×C127—22no—
97C22⋊C4×C127—22no—
98C42×C127C2×D411yescharacteristic
99C42×C127C2×D411yescharacteristic
100C42×C127C2×D411yescharacteristic
101C42×C127#4111yescharacteristic
102C23×C127—22no—
103C23×C127C4×D411yescharacteristic
104Q8×C127—81no—
105D4×C127—42no—
106D4×C127—81no—
107D4×C127—81no—
108D4×C127—82no—
109C2×C4×C127—22no—
110C2×C4×C127—41no—
111C2×C4×C127—41no—
112C2×C4×C127—41no—
113C2×C4×C127—42no—
114C2×C4×C127—42no—
115C2×C4×C127—42no—
116C2×C4×C127—41no—
117C2×C4×C127—41no—
118C2×C4×C127—81no—
119C2×C4×C127C2×C22⋊C411yescharacteristic
120C2×C4×C127C4×D411yescharacteristic
121C2×C4×C127#12011yescharacteristic
122C2×C4×C127#12111yescharacteristic
123C2×C4×C127#12111yescharacteristic
124C2×C4×C127#12311yescharacteristic
125C8×C127—42no—
126C8×C127—42no—
127C8×C127—42no—
128C8×C127—81no—
129C8×C127—81no—
130C22×C127—21no—
131C22×C127—21no—
132C22×C127—21no—
133C22×C127—42no—
134C22×C127—42no—
135C22×C127—42no—
136C22×C127#38611yescharacteristic
137C4×C127—21no—
138C4×C127—21no—
139C4×C127—21no—
140C4×C127—21no—
141C4×C127—21no—
142C4×C127—21no—
143C4×C127—42no—
144C4×C127—81no—
145C4×C127—81no—
146#9335C12711yesmaximal, characteristic, direct product factor, Sylow
147C2×C127—41no—
148C2×C127—82no—
149C2×C127#188111yescharacteristic
150C2×C127#190411yescharacteristic
151C2×C127#191511yescharacteristic
152#3234C2×C12711yescharacteristic
153#2980C2×C12711yescharacteristic
154#1553C2×C12711yescharacteristic
155#1534C2×C12711yescharacteristic, complemented
156#1470C2×C12711yescharacteristic, complemented
157#1308C2×C12711yescharacteristic, complemented
158#1287C2×C12711yescharacteristic, complemented
159C127#933511yescharacteristic, direct product factor, Sylow
160#532C22×C12711yescharacteristic
161C2×#125C22×C12711yescharacteristic
162#501—21no—
163#490—21no—
164#481C4×C12712yes—
165#480C4×C12712yes—
166#478—22no—
167#435—22no—
168#435—22no—
169#432C22×C12711yescharacteristic
170#432C22×C12711yescharacteristic
171#432C22×C12711yescharacteristic
172#432C22×C12711yescharacteristic
173#431C22×C12711yescharacteristic
174#408—22no—
175#332—21no—
176#331—21no—
177#330—22no—
178#324—22no—
179C2×#41—21no—
180C2×M16—22no—
181C22×C8—22no—
182C4⋊Q8D4×C12711yescharacteristic
183#127D4×C12711yescharacteristic
184#125—21no—
185#125—21no—
186#125—21no—
187#125—21no—
188#124—21no—
189#121—21no—
190#121C2×C4×C12712yes—
191C4×D4—21no—
192C4×D4D4×C12712yes—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4C2×C4×C12711yescharacteristic
196C2×C4⋊C4C2×C4×C12711yescharacteristic
197C2×C42C23×C12711yescharacteristic
198#107—22no—
199#106—22no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205#102—22no—
206#102—22no—
207C22⋊C8—24no—
208C22⋊C8—21no—
209C22⋊C8—21no—
210C22⋊C8—21no—
211C22⋊C8C2×C4×C12712yes—
212C22⋊C8D4×C12712yes—
213#97—21no—
214#97—21no—
215#97—21no—
216#97D4×C12712yes—
217C4×C8—21no—
218#41—81no—
219#41—81no—
220C2×Q8—21no—
221C2×D4—22no—
222C2×D4—21no—
223C2×D4—21no—
224C2×D4C22⋊C4×C12712yes—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4C22×C4×C12711yescharacteristic
229C22×C4C2×D4×C12711yescharacteristic
230C22×C4#41×C12711yescharacteristic
231M16—82no—
232C2×C8—22no—
233C2×C8—22no—
234C2×C8—22no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—82no—
238C4⋊C4—21no—
239C4⋊C4—21no—
240C4⋊C4—21no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—41no—
244C4⋊C4—41no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4C22⋊C4×C12712yes—
248C22⋊C4—22no—
249C22⋊C4—22no—
250C42C2×D4×C12711yescharacteristic
251C42C2×D4×C12711yescharacteristic
252C42C2×D4×C12711yescharacteristic
253C42#41×C12711yescharacteristic
254C23—22no—
255C23C4×D4×C12711yescharacteristic
256Q8—81no—
257D4—42no—
258D4—81no—
259D4—81no—
260D4—82no—
261C2×C4—22no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—42no—
266C2×C4—42no—
267C2×C4—42no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—81no—
271C2×C4C2×C22⋊C4×C12711yescharacteristic
272C2×C4C4×D4×C12711yescharacteristic
273C2×C4#120×C12711yescharacteristic
274C2×C4#121×C12711yescharacteristic
275C2×C4#121×C12711yescharacteristic
276C2×C4#123×C12711yescharacteristic
277C8—42no—
278C8—42no—
279C8—42no—
280C8—81no—
281C8—81no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—42no—
286C22—42no—
287C22—42no—
288C22#386×C12711yescharacteristic
289C4—21no—
290C4—21no—
291C4—21no—
292C4—21no—
293C4—21no—
294C4—21no—
295C4—42no—
296C4—81no—
297C4—81no—
298C2—41no—
299C2—82no—
300C2C127×#188111yescharacteristic
301C2C127×#190411yescharacteristic
302C2C127×#191511yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radical#532×C127C22
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1534C2semidirect
5. C127×#1470C2semidirect
6. C127×#1308C2semidirect
7. C127×#1287C2semidirect
146. #9335C127direct (N × H)
155. #1534C2×C127semidirect
156. #1470C2×C127semidirect
157. #1308C2×C127semidirect
158. #1287C2×C127semidirect
159. C127#9335direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32342
C127×#29802
C127×#15532
C127×#15342
C127×#14702
C127×#13082
C127×#12872
#9335127