Finite Group Databasebeta

← C127×#13032 #44576705

Subgroups — C127×#13032 #44576705

Order 32512.

476 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#509×C127C211yesmaximal, characteristic
2C127×#2957C211yesmaximal, characteristic, complemented
3C127×#2148C211yesmaximal, characteristic, complemented
4C2×#361×C127C211yesmaximal, characteristic, complemented
5C127×#1978C211yesmaximal, characteristic, complemented
6C127×#1388C211yesmaximal, characteristic, complemented
7C127×#1378C211yesmaximal, characteristic, complemented
8C2×#135×C127C2211yescharacteristic
9C22×D8×C127C2211yescharacteristic
10#568×C127—21no—
11#509×C127—22no—
12#509×C127C414yescomplemented
13C2×SD32×C127—21no—
14C2×D16×C127—21no—
15C2×M32×C127C2211yescharacteristic
16C2×M32×C127C2211yescharacteristic
17#444×C127—22no—
18#443×C127—22no—
19C2×#108×C127C2211yescharacteristic
20C2×#108×C127C2211yescharacteristic
21#421×C127—21no—
22#418×C127—21no—
23C2×#100×C127—21no—
24#405×C127C2211yescharacteristic
25#362×C127—21no—
26#361×C127—21no—
27#361×C127—22no—
28C2×#41×C127—21no—
29C22×D4×C127—21no—
30#135×C127—21no—
31#135×C127—21no—
32#135×C127C2×C412yes—
33#135×C127D412yes—
34C2×Q16×C127D411yescharacteristic
35C2×SD16×C127—21no—
36C2×D8×C127—21no—
37C2×D8×C127—21no—
38C2×D8×C127—21no—
39C2×D8×C127—21no—
40C2×D8×C127—21no—
41C2×D8×C127C2×C412yes—
42C2×D8×C127D411yescharacteristic
43#131×C127—24no—
44#131×C127—42no—
45C2×M16×C127—21no—
46C2×M16×C127—21no—
47C2×M16×C127—42no—
48C2×M16×C127D411yescharacteristic
49C22×C8×C127C2311yescharacteristic
50#117×C127D411yescharacteristic
51SD32×C127—24no—
52D16×C127—24no—
53M32×C127—21no—
54M32×C127—21no—
55M32×C127—21no—
56M32×C127C2×C412yes—
57C2×C16×C127—21no—
58C2×C16×C127—21no—
59#108×C127—21no—
60#108×C127—21no—
61#108×C127—21no—
62#108×C127D412yes—
63#104×C127—24no—
64#102×C127—42no—
65#100×C127—42no—
66#97×C127—21no—
67C4×C8×C127—21no—
68C24×C127—41no—
69#41×C127—22no—
70#41×C127—22no—
71#41×C127—41no—
72#41×C127—41no—
73C2×Q8×C127—21no—
74C2×D4×C127—22no—
75C2×D4×C127—21no—
76C2×D4×C127—41no—
77C2×D4×C127—41no—
78C2×D4×C127—41no—
79C2×D4×C127—41no—
80C2×D4×C127—41no—
81C2×D4×C127—41no—
82C22×C4×C127—41no—
83C22×C4×C127C2×D411yescharacteristic
84Q16×C127—21no—
85Q16×C127C22⋊C412yes—
86SD16×C127—22no—
87SD16×C127—22no—
88D8×C127—22no—
89D8×C127—22no—
90D8×C127—21no—
91D8×C127—41no—
92D8×C127—41no—
93D8×C127C22⋊C412yes—
94M16×C127—21no—
95M16×C127—22no—
96M16×C127—44no—
97M16×C127—41no—
98M16×C127—41no—
99M16×C127—41no—
100M16×C127D812yes—
101C2×C8×C127—21no—
102C2×C8×C127—44no—
103C2×C8×C127—41no—
104C2×C8×C127—41no—
105C2×C8×C127C22×C411yescharacteristic
106C2×C8×C127C2×D411yescharacteristic
107C2×C8×C127C2×D411yescharacteristic
108C2×C8×C127C2×D411yescharacteristic
109C2×C8×C127#4111yescharacteristic
110C2×C8×C127#4111yescharacteristic
111C4⋊C4×C127—21no—
112C22⋊C4×C127—21no—
113C42×C127—21no—
114C16×C127—22no—
115C16×C127—41no—
116C23×C127—41no—
117C23×C127—42no—
118C23×C127—81no—
119C23×C127—81no—
120C23×C127—162no—
121C23×C127#13511yescharacteristic
122Q8×C127—22no—
123Q8×C127—41no—
124D4×C127—22no—
125D4×C127—42no—
126D4×C127—42no—
127D4×C127—42no—
128D4×C127—42no—
129D4×C127—41no—
130D4×C127—81no—
131D4×C127—81no—
132C2×C4×C127—41no—
133C2×C4×C127—42no—
134C2×C4×C127—42no—
135C2×C4×C127—41no—
136C2×C4×C127C4×D411yescharacteristic
137C2×C4×C127#12011yescharacteristic
138C2×C4×C127#12111yescharacteristic
139C2×C4×C127C2×D811yescharacteristic
140C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
142C8×C127—22no—
143C8×C127—42no—
144C8×C127—81no—
145C8×C127C2×C22⋊C411yescharacteristic
146C8×C127C4×D411yescharacteristic
147C8×C127#12111yescharacteristic
148C8×C127#12311yescharacteristic
149C22×C127—41no—
150C22×C127—42no—
151C22×C127—82no—
152C22×C127—161no—
153C22×C127—162no—
154C22×C127—162no—
155C22×C127—162no—
156C22×C127C4×D811yescharacteristic
157C22×C127#44911yescharacteristic
158C22×C127#46311yescharacteristic
159C4×C127—42no—
160C4×C127—81no—
161C4×C127#38611yescharacteristic
162C4×C127#44211yescharacteristic
163C4×C127#44711yescharacteristic
164C4×C127#45911yescharacteristic
165#13032C12711yesmaximal, characteristic, direct product factor, Sylow
166C2×C127—21no—
167C2×C127—21no—
168C2×C127—21no—
169C2×C127—82no—
170C2×C127—162no—
171C2×C127#187911yescharacteristic
172C2×#509C2×C12711yescharacteristic
173#2957C2×C12711yescharacteristic, complemented
174#2148C2×C12711yescharacteristic, complemented
175C2×#361C2×C12711yescharacteristic, complemented
176#1978C2×C12711yescharacteristic, complemented
177#1388C2×C12711yescharacteristic, complemented
178#1378C2×C12711yescharacteristic, complemented
179C127#1303211yescharacteristic, direct product factor, Sylow
180C2×#135C22×C12711yescharacteristic
181C22×D8C22×C12711yescharacteristic
182#568—21no—
183#509—22no—
184#509C4×C12714yescomplemented
185C2×SD32—21no—
186C2×D16—21no—
187C2×M32C22×C12711yescharacteristic
188C2×M32C22×C12711yescharacteristic
189#444—22no—
190#443—22no—
191C2×#108C22×C12711yescharacteristic
192C2×#108C22×C12711yescharacteristic
193#421—21no—
194#418—21no—
195C2×#100—21no—
196#405C22×C12711yescharacteristic
197#362—21no—
198#361—21no—
199#361—22no—
200C2×#41—21no—
201C22×D4—21no—
202#135—21no—
203#135—21no—
204#135C2×C4×C12712yes—
205#135D4×C12712yes—
206C2×Q16D4×C12711yescharacteristic
207C2×SD16—21no—
208C2×D8—21no—
209C2×D8—21no—
210C2×D8—21no—
211C2×D8—21no—
212C2×D8—21no—
213C2×D8C2×C4×C12712yes—
214C2×D8D4×C12711yescharacteristic
215#131—24no—
216#131—42no—
217C2×M16—21no—
218C2×M16—21no—
219C2×M16—42no—
220C2×M16D4×C12711yescharacteristic
221C22×C8C23×C12711yescharacteristic
222#117D4×C12711yescharacteristic
223SD32—24no—
224D16—24no—
225M32—21no—
226M32—21no—
227M32—21no—
228M32C2×C4×C12712yes—
229C2×C16—21no—
230C2×C16—21no—
231#108—21no—
232#108—21no—
233#108—21no—
234#108D4×C12712yes—
235#104—24no—
236#102—42no—
237#100—42no—
238#97—21no—
239C4×C8—21no—
240C24—41no—
241#41—22no—
242#41—22no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×D4—22no—
247C2×D4—21no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C22×C4—41no—
255C22×C4C2×D4×C12711yescharacteristic
256Q16—21no—
257Q16C22⋊C4×C12712yes—
258SD16—22no—
259SD16—22no—
260D8—22no—
261D8—22no—
262D8—21no—
263D8—41no—
264D8—41no—
265D8C22⋊C4×C12712yes—
266M16—21no—
267M16—22no—
268M16—44no—
269M16—41no—
270M16—41no—
271M16—41no—
272M16D8×C12712yes—
273C2×C8—21no—
274C2×C8—44no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8C22×C4×C12711yescharacteristic
278C2×C8C2×D4×C12711yescharacteristic
279C2×C8C2×D4×C12711yescharacteristic
280C2×C8C2×D4×C12711yescharacteristic
281C2×C8#41×C12711yescharacteristic
282C2×C8#41×C12711yescharacteristic
283C4⋊C4—21no—
284C22⋊C4—21no—
285C42—21no—
286C16—22no—
287C16—41no—
288C23—41no—
289C23—42no—
290C23—81no—
291C23—81no—
292C23—162no—
293C23#135×C12711yescharacteristic
294Q8—22no—
295Q8—41no—
296D4—22no—
297D4—42no—
298D4—42no—
299D4—42no—
300D4—42no—
301D4—41no—
302D4—81no—
303D4—81no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4C4×D4×C12711yescharacteristic
309C2×C4#120×C12711yescharacteristic
310C2×C4#121×C12711yescharacteristic
311C2×C4C2×D8×C12711yescharacteristic
312C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
313C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
314C8—22no—
315C8—42no—
316C8—81no—
317C8C2×C22⋊C4×C12711yescharacteristic
318C8C4×D4×C12711yescharacteristic
319C8#121×C12711yescharacteristic
320C8#123×C12711yescharacteristic
321C22—41no—
322C22—42no—
323C22—82no—
324C22—161no—
325C22—162no—
326C22—162no—
327C22—162no—
328C22C4×D8×C12711yescharacteristic
329C22#449×C12711yescharacteristic
330C22#463×C12711yescharacteristic
331C4—42no—
332C4—81no—
333C4#386×C12711yescharacteristic
334C4#442×C12711yescharacteristic
335C4#447×C12711yescharacteristic
336C4#459×C12711yescharacteristic
337C2—21no—
338C2—21no—
339C2—21no—
340C2—82no—
341C2—162no—
342C2C127×#187911yescharacteristic
subgroupG/H
center, socleC2×C127#1879
commutatorC2×C8C22×C4×C127
Frattini, cosocleC22×C8C23×C127
prime radicalC2×#509×C127C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C4×C127 ◁ #405×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2957C2semidirect
3. C127×#2148C2semidirect
4. C2×#361×C127C2semidirect
5. C127×#1978C2semidirect
6. C127×#1388C2semidirect
7. C127×#1378C2semidirect
12. #509×C127C4semidirect
165. #13032C127direct (N × H)
173. #2957C2×C127semidirect
174. #2148C2×C127semidirect
175. C2×#361C2×C127semidirect
176. #1978C2×C127semidirect
177. #1388C2×C127semidirect
178. #1378C2×C127semidirect
179. C127#13032direct (N × H)
184. #509C4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#509×C1272
C127×#29572
C127×#21482
C2×#361×C1272
C127×#19782
C127×#13882
C127×#13782
#13032127