Finite Group Databasebeta

← C127×#13069 #44576742

Subgroups — C127×#13069 #44576742

Order 32512.

450 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3407C211yesmaximal, characteristic
2C2×#473×C127C211yesmaximal, characteristic
3C2×#362×C127C211yesmaximal, characteristic, complemented
4C127×#2141C211yesmaximal, characteristic, complemented
5C127×#1814C211yesmaximal, characteristic
6C127×#1389C211yesmaximal, characteristic, complemented
7C127×#1385C211yesmaximal, characteristic, complemented
8C2×#137×C127—21no—
9C22×Q16×C127C2211yescharacteristic
10C2×#131×C127C2211yescharacteristic
11#504×C127—22no—
12#504×C127—22no—
13C2×M32×C127—22no—
14C2×M32×C127C2211yescharacteristic
15C2×M32×C127C2211yescharacteristic
16#473×C127—22no—
17#473×C127C414yescomplemented
18C2×#108×C127C2211yescharacteristic
19C2×#108×C127C2211yescharacteristic
20#427×C127C2211yescharacteristic
21#421×C127—21no—
22C2×#101×C127—21no—
23#362×C127—22no—
24#358×C127—22no—
25#344×C127—21no—
26C2×#41×C127D411yescharacteristic
27C22×Q8×C127—21no—
28#137×C127—24no—
29#137×C127—42no—
30C2×Q16×C127—21no—
31C2×Q16×C127—21no—
32C2×Q16×C127—21no—
33C2×Q16×C127—21no—
34C2×Q16×C127—21no—
35C2×Q16×C127—41no—
36C2×Q16×C127C2×C412yes—
37C2×SD16×C127—41no—
38#131×C127—21no—
39#131×C127—21no—
40#131×C127C2×C412yes—
41#131×C127D412yes—
42C2×M16×C127—21no—
43C2×M16×C127—21no—
44C2×M16×C127—21no—
45C2×M16×C127D411yescharacteristic
46C22×C8×C127—21no—
47C22×C8×C127C2311yescharacteristic
48#117×C127—21no—
49M32×C127—24no—
50M32×C127—21no—
51M32×C127—21no—
52M32×C127—21no—
53M32×C127D412yes—
54C2×C16×C127—24no—
55C2×C16×C127—21no—
56C2×C16×C127D412yes—
57#108×C127—21no—
58#108×C127—21no—
59#108×C127—21no—
60#108×C127C2×C412yes—
61#107×C127—21no—
62#106×C127—21no—
63#104×C127—42no—
64#101×C127—24no—
65#41×C127—21no—
66#41×C127—21no—
67#41×C127C22⋊C412yes—
68#41×C127D812yes—
69C2×Q8×C127—22no—
70C2×Q8×C127—41no—
71C2×Q8×C127—41no—
72C2×Q8×C127—41no—
73C2×Q8×C127—41no—
74C2×Q8×C127—41no—
75C2×Q8×C127SD1611yescharacteristic
76C2×D4×C127—21no—
77C2×D4×C127SD1611yescharacteristic
78C22×C4×C127—21no—
79C22×C4×C127—41no—
80C22×C4×C127C2×D411yescharacteristic
81Q16×C127—22no—
82Q16×C127—22no—
83Q16×C127—44no—
84Q16×C127—41no—
85Q16×C127—41no—
86SD16×C127—44no—
87M16×C127—21no—
88M16×C127—22no—
89M16×C127—22no—
90M16×C127—22no—
91M16×C127—41no—
92M16×C127—41no—
93M16×C127—41no—
94M16×C127C22⋊C412yes—
95C2×C8×C127—21no—
96C2×C8×C127—22no—
97C2×C8×C127—22no—
98C2×C8×C127—41no—
99C2×C8×C127—41no—
100C2×C8×C127C22×C411yescharacteristic
101C2×C8×C127C2×D411yescharacteristic
102C2×C8×C127C2×D411yescharacteristic
103C2×C8×C127C2×D411yescharacteristic
104C2×C8×C127#4111yescharacteristic
105C2×C8×C127#4111yescharacteristic
106C4⋊C4×C127—41no—
107C22⋊C4×C127—41no—
108C42×C127—41no—
109C16×C127—22no—
110C16×C127—22no—
111C23×C127—21no—
112C23×C127#13511yescharacteristic
113Q8×C127—21no—
114Q8×C127—42no—
115Q8×C127—42no—
116Q8×C127—81no—
117Q8×C127—81no—
118Q8×C127#10212yes—
119D4×C127—22no—
120D4×C127—22no—
121D4×C127—21no—
122D4×C127#10212yes—
123C2×C4×C127—21no—
124C2×C4×C127—22no—
125C2×C4×C127—22no—
126C2×C4×C127—42no—
127C2×C4×C127—81no—
128C2×C4×C127—81no—
129C2×C4×C127—81no—
130C2×C4×C127C2×C22⋊C411yescharacteristic
131C2×C4×C127#12111yescharacteristic
132C2×C4×C127#12111yescharacteristic
133C2×C4×C127C2×D811yescharacteristic
134C2×C4×C127C2×SD1611yescharacteristic
135C2×C4×C127#13511yescharacteristic
136C8×C127—22no—
137C8×C127—42no—
138C8×C127—81no—
139C8×C127C4×D411yescharacteristic
140C8×C127C4×D411yescharacteristic
141C8×C127#12011yescharacteristic
142C8×C127#12311yescharacteristic
143C22×C127—22no—
144C22×C127—41no—
145C22×C127—81no—
146C22×C127#41611yescharacteristic
147C22×C127#46511yescharacteristic
148C22×C127#46611yescharacteristic
149C4×C127—22no—
150C4×C127—82no—
151C4×C127—161no—
152C4×C127#38611yescharacteristic
153C4×C127C2×#10211yescharacteristic
154C4×C127#46511yescharacteristic
155C4×C127#46611yescharacteristic
156#13069C12711yesmaximal, characteristic, direct product factor, Sylow
157C2×C127—21no—
158C2×C127—21no—
159C2×C127—21no—
160C2×C127—42no—
161C2×C127#189311yescharacteristic
162#3407C2×C12711yescharacteristic
163C2×#473C2×C12711yescharacteristic
164C2×#362C2×C12711yescharacteristic, complemented
165#2141C2×C12711yescharacteristic, complemented
166#1814C2×C12711yescharacteristic
167#1389C2×C12711yescharacteristic, complemented
168#1385C2×C12711yescharacteristic, complemented
169C127#1306911yescharacteristic, direct product factor, Sylow
170C2×#137—21no—
171C22×Q16C22×C12711yescharacteristic
172C2×#131C22×C12711yescharacteristic
173#504—22no—
174#504—22no—
175C2×M32—22no—
176C2×M32C22×C12711yescharacteristic
177C2×M32C22×C12711yescharacteristic
178#473—22no—
179#473C4×C12714yescomplemented
180C2×#108C22×C12711yescharacteristic
181C2×#108C22×C12711yescharacteristic
182#427C22×C12711yescharacteristic
183#421—21no—
184C2×#101—21no—
185#362—22no—
186#358—22no—
187#344—21no—
188C2×#41D4×C12711yescharacteristic
189C22×Q8—21no—
190#137—24no—
191#137—42no—
192C2×Q16—21no—
193C2×Q16—21no—
194C2×Q16—21no—
195C2×Q16—21no—
196C2×Q16—21no—
197C2×Q16—41no—
198C2×Q16C2×C4×C12712yes—
199C2×SD16—41no—
200#131—21no—
201#131—21no—
202#131C2×C4×C12712yes—
203#131D4×C12712yes—
204C2×M16—21no—
205C2×M16—21no—
206C2×M16—21no—
207C2×M16D4×C12711yescharacteristic
208C22×C8—21no—
209C22×C8C23×C12711yescharacteristic
210#117—21no—
211M32—24no—
212M32—21no—
213M32—21no—
214M32—21no—
215M32D4×C12712yes—
216C2×C16—24no—
217C2×C16—21no—
218C2×C16D4×C12712yes—
219#108—21no—
220#108—21no—
221#108—21no—
222#108C2×C4×C12712yes—
223#107—21no—
224#106—21no—
225#104—42no—
226#101—24no—
227#41—21no—
228#41—21no—
229#41C22⋊C4×C12712yes—
230#41D8×C12712yes—
231C2×Q8—22no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8SD16×C12711yescharacteristic
238C2×D4—21no—
239C2×D4SD16×C12711yescharacteristic
240C22×C4—21no—
241C22×C4—41no—
242C22×C4C2×D4×C12711yescharacteristic
243Q16—22no—
244Q16—22no—
245Q16—44no—
246Q16—41no—
247Q16—41no—
248SD16—44no—
249M16—21no—
250M16—22no—
251M16—22no—
252M16—22no—
253M16—41no—
254M16—41no—
255M16—41no—
256M16C22⋊C4×C12712yes—
257C2×C8—21no—
258C2×C8—22no—
259C2×C8—22no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8C22×C4×C12711yescharacteristic
263C2×C8C2×D4×C12711yescharacteristic
264C2×C8C2×D4×C12711yescharacteristic
265C2×C8C2×D4×C12711yescharacteristic
266C2×C8#41×C12711yescharacteristic
267C2×C8#41×C12711yescharacteristic
268C4⋊C4—41no—
269C22⋊C4—41no—
270C42—41no—
271C16—22no—
272C16—22no—
273C23—21no—
274C23#135×C12711yescharacteristic
275Q8—21no—
276Q8—42no—
277Q8—42no—
278Q8—81no—
279Q8—81no—
280Q8#102×C12712yes—
281D4—22no—
282D4—22no—
283D4—21no—
284D4#102×C12712yes—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—42no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4C2×C22⋊C4×C12711yescharacteristic
293C2×C4#121×C12711yescharacteristic
294C2×C4#121×C12711yescharacteristic
295C2×C4C2×D8×C12711yescharacteristic
296C2×C4C2×SD16×C12711yescharacteristic
297C2×C4#135×C12711yescharacteristic
298C8—22no—
299C8—42no—
300C8—81no—
301C8C4×D4×C12711yescharacteristic
302C8C4×D4×C12711yescharacteristic
303C8#120×C12711yescharacteristic
304C8#123×C12711yescharacteristic
305C22—22no—
306C22—41no—
307C22—81no—
308C22#416×C12711yescharacteristic
309C22#465×C12711yescharacteristic
310C22#466×C12711yescharacteristic
311C4—22no—
312C4—82no—
313C4—161no—
314C4#386×C12711yescharacteristic
315C4C2×#102×C12711yescharacteristic
316C4#465×C12711yescharacteristic
317C4#466×C12711yescharacteristic
318C2—21no—
319C2—21no—
320C2—21no—
321C2—42no—
322C2C127×#189311yescharacteristic
subgroupG/H
center, socleC2×C127#1893
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC2×#41×C127D4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C4×C127 ◁ C2×#131×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#362×C127C2semidirect
4. C127×#2141C2semidirect
6. C127×#1389C2semidirect
7. C127×#1385C2semidirect
17. #473×C127C4semidirect
156. #13069C127direct (N × H)
164. C2×#362C2×C127semidirect
165. #2141C2×C127semidirect
167. #1389C2×C127semidirect
168. #1385C2×C127semidirect
169. C127#13069direct (N × H)
179. #473C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34072
C2×#473×C1272
C2×#362×C1272
C127×#21412
C127×#18142
C127×#13892
C127×#13852
#13069127