Finite Group Databasebeta

← C127×#9492 #44573165

Subgroups — C127×#9492 #44573165

Order 32512.

600 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2873C211yesmaximal, characteristic, complemented
2C127×#2598C211yesmaximal, characteristic
3C127×#1490C212yesmaximal, complemented
4C127×#1464C211yesmaximal, characteristic, complemented
5C127×#1288C212yesmaximal, complemented
6C22×M16×C127—21no—
7C2×C4×D4×C127C2211yescharacteristic
8C2×#117×C127C2211yescharacteristic
9#432×C127C2212yes—
10#405×C127—24no—
11C4×M16×C127—21no—
12C4×M16×C127C2212yes—
13#400×C127C411yescharacteristic
14#399×C127C411yescharacteristic
15#394×C127C411yescharacteristic
16#392×C127C411yescharacteristic
17#388×C127—21no—
18#386×C127—21no—
19#386×C127—21no—
20#385×C127—21no—
21#383×C127C2211yescharacteristic
22D4⋊C8×C127—24no—
23#324×C127—21no—
24#323×C127—21no—
25C22×D4×C127—21no—
26C22×D4×C127C2×C411yescharacteristic
27C23×C4×C127—21no—
28C23×C4×C127D411yescharacteristic
29C2×M16×C127—24no—
30C2×M16×C127—24no—
31C2×M16×C127—22no—
32C2×M16×C127—22no—
33C22×C8×C127—22no—
34C4×D4×C127—22no—
35C4×D4×C127—22no—
36#117×C127—22no—
37#117×C127—22no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127C2×C411yescharacteristic
40C2×C4⋊C4×C127C2×C411yescharacteristic
41C2×C4⋊C4×C127D411yescharacteristic
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—21no—
45C2×C22⋊C4×C127—21no—
46C2×C22⋊C4×C127—21no—
47C2×C22⋊C4×C127C2×C411yescharacteristic
48C2×C22⋊C4×C127D411yescharacteristic
49C2×C42×C127D411yescharacteristic
50C2×C42×C127C2311yescharacteristic
51C4⋊C8×C127—22no—
52C22⋊C8×C127—22no—
53#97×C127—22no—
54#97×C127—22no—
55#97×C127—22no—
56C4×C8×C127—22no—
57C4×C8×C127D414yescomplemented
58#95×C127—21no—
59#95×C127—21no—
60#95×C127—21no—
61#95×C127—21no—
62#95×C127C2×C411yescharacteristic
63#95×C127C2×C411yescharacteristic
64C24×C127—21no—
65C24×C127C22⋊C411yescharacteristic
66C2×D4×C127—22no—
67C2×D4×C127—42no—
68C2×D4×C127—42no—
69C2×D4×C127—42no—
70C2×D4×C127—81no—
71C22×C4×C127—22no—
72C22×C4×C127—22no—
73C22×C4×C127—21no—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—42no—
79C22×C4×C127—81no—
80C22×C4×C127—81no—
81C22×C4×C127C22⋊C411yescharacteristic
82C22×C4×C127C22⋊C411yescharacteristic
83C22×C4×C127C22⋊C411yescharacteristic
84C22×C4×C127C22×C411yescharacteristic
85C22×C4×C127C2×D411yescharacteristic
86C22×C4×C127C2×D411yescharacteristic
87M16×C127—28no—
88M16×C127—24no—
89M16×C127—24no—
90C2×C8×C127—28no—
91C2×C8×C127—24no—
92C2×C8×C127—42no—
93C4⋊C4×C127—22no—
94C4⋊C4×C127—22no—
95C4⋊C4×C127—22no—
96C4⋊C4×C127—81no—
97C22⋊C4×C127—22no—
98C22⋊C4×C127—22no—
99C22⋊C4×C127—42no—
100C22⋊C4×C127—42no—
101C22⋊C4×C127—41no—
102C22⋊C4×C127—41no—
103C22⋊C4×C127—81no—
104C22⋊C4×C127—81no—
105C42×C127—21no—
106C42×C127—21no—
107C42×C127C2×D412yes—
108C42×C127#4112yes—
109C23×C127—21no—
110C23×C127—21no—
111C23×C127—22no—
112C23×C127—41no—
113C23×C127—41no—
114C23×C127—41no—
115C23×C127—41no—
116C23×C127—41no—
117C23×C127—41no—
118C23×C127—41no—
119C23×C127—41no—
120C23×C127#10412yes—
121C23×C127C2×C22⋊C411yescharacteristic
122D4×C127—24no—
123D4×C127—42no—
124D4×C127—84no—
125C2×C4×C127—22no—
126C2×C4×C127—22no—
127C2×C4×C127—24no—
128C2×C4×C127—21no—
129C2×C4×C127—21no—
130C2×C4×C127—21no—
131C2×C4×C127—21no—
132C2×C4×C127—21no—
133C2×C4×C127—21no—
134C2×C4×C127—41no—
135C2×C4×C127—41no—
136C2×C4×C127—41no—
137C2×C4×C127—41no—
138C2×C4×C127—41no—
139C2×C4×C127—41no—
140C2×C4×C127—41no—
141C2×C4×C127—41no—
142C2×C4×C127—41no—
143C2×C4×C127—41no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—84no—
148C2×C4×C127#10412yes—
149C2×C4×C127C4×D412yes—
150C2×C4×C127#12011yescharacteristic
151C2×C4×C127#12112yes—
152C2×C4×C127#12311yescharacteristic
153C8×C127—28no—
154C8×C127—82no—
155C22×C127—21no—
156C22×C127—21no—
157C22×C127—22no—
158C22×C127—42no—
159C22×C127—42no—
160C22×C127—42no—
161C22×C127—41no—
162C22×C127—41no—
163C22×C127—42no—
164C22×C127—81no—
165C22×C127—81no—
166C22×C127—81no—
167C22×C127—81no—
168C22×C127—81no—
169C22×C127#38611yescharacteristic
170C22×C127C2×#10411yescharacteristic
171C22×C127C2×#10411yescharacteristic
172C4×C127—22no—
173C4×C127—21no—
174C4×C127—22no—
175C4×C127—21no—
176C4×C127—22no—
177C4×C127—41no—
178C4×C127—41no—
179C4×C127—81no—
180C4×C127—81no—
181C4×C127—81no—
182#9492C12711yesmaximal, characteristic, direct product factor, Sylow
183C2×C127—21no—
184C2×C127—21no—
185C2×C127—42no—
186C2×C127—82no—
187C2×C127#189111yescharacteristic
188C2×C127#189611yescharacteristic
189C2×C127#191011yescharacteristic
190#2873C2×C12711yescharacteristic, complemented
191#2598C2×C12711yescharacteristic
192#1490C2×C12712yescomplemented
193#1464C2×C12711yescharacteristic, complemented
194#1288C2×C12712yescomplemented
195C127#949211yescharacteristic, direct product factor, Sylow
196C22×M16—21no—
197C2×C4×D4C22×C12711yescharacteristic
198C2×#117C22×C12711yescharacteristic
199#432C22×C12712yes—
200#405—24no—
201C4×M16—21no—
202C4×M16C22×C12712yes—
203#400C4×C12711yescharacteristic
204#399C4×C12711yescharacteristic
205#394C4×C12711yescharacteristic
206#392C4×C12711yescharacteristic
207#388—21no—
208#386—21no—
209#386—21no—
210#385—21no—
211#383C22×C12711yescharacteristic
212D4⋊C8—24no—
213#324—21no—
214#323—21no—
215C22×D4—21no—
216C22×D4C2×C4×C12711yescharacteristic
217C23×C4—21no—
218C23×C4D4×C12711yescharacteristic
219C2×M16—22no—
220C2×M16—24no—
221C2×M16—24no—
222C2×M16—22no—
223C22×C8—22no—
224C4×D4—22no—
225C4×D4—22no—
226#117—22no—
227#117—22no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4C2×C4×C12711yescharacteristic
230C2×C4⋊C4C2×C4×C12711yescharacteristic
231C2×C4⋊C4D4×C12711yescharacteristic
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4C2×C4×C12711yescharacteristic
238C2×C22⋊C4D4×C12711yescharacteristic
239C2×C42D4×C12711yescharacteristic
240C2×C42C23×C12711yescharacteristic
241C4⋊C8—22no—
242C22⋊C8—22no—
243#97—22no—
244#97—22no—
245#97—22no—
246C4×C8—22no—
247C4×C8D4×C12714yescomplemented
248#95—21no—
249#95—21no—
250#95—21no—
251#95—21no—
252#95C2×C4×C12711yescharacteristic
253#95C2×C4×C12711yescharacteristic
254C24—21no—
255C24C22⋊C4×C12711yescharacteristic
256C2×D4—22no—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4—42no—
260C2×D4—81no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—21no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—42no—
269C22×C4—81no—
270C22×C4—81no—
271C22×C4C22⋊C4×C12711yescharacteristic
272C22×C4C22⋊C4×C12711yescharacteristic
273C22×C4C22⋊C4×C12711yescharacteristic
274C22×C4C22×C4×C12711yescharacteristic
275C22×C4C2×D4×C12711yescharacteristic
276C22×C4C2×D4×C12711yescharacteristic
277M16—28no—
278M16—24no—
279M16—24no—
280C2×C8—28no—
281C2×C8—24no—
282C2×C8—42no—
283C4⋊C4—22no—
284C4⋊C4—22no—
285C4⋊C4—22no—
286C4⋊C4—81no—
287C22⋊C4—22no—
288C22⋊C4—22no—
289C22⋊C4—42no—
290C22⋊C4—42no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—81no—
294C22⋊C4—81no—
295C42—21no—
296C42—21no—
297C42C2×D4×C12712yes—
298C42#41×C12712yes—
299C23—21no—
300C23—21no—
301C23—22no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23#104×C12712yes—
311C23C2×C22⋊C4×C12711yescharacteristic
312D4—24no—
313D4—42no—
314D4—84no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—24no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—84no—
338C2×C4#104×C12712yes—
339C2×C4C4×D4×C12712yes—
340C2×C4#120×C12711yescharacteristic
341C2×C4#121×C12712yes—
342C2×C4#123×C12711yescharacteristic
343C8—28no—
344C8—82no—
345C22—21no—
346C22—21no—
347C22—22no—
348C22—42no—
349C22—42no—
350C22—42no—
351C22—41no—
352C22—41no—
353C22—42no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22#386×C12711yescharacteristic
360C22C2×#104×C12711yescharacteristic
361C22C2×#104×C12711yescharacteristic
362C4—22no—
363C4—21no—
364C4—22no—
365C4—21no—
366C4—22no—
367C4—41no—
368C4—41no—
369C4—81no—
370C4—81no—
371C4—81no—
372C2—21no—
373C2—21no—
374C2—42no—
375C2—82no—
376C2C127×#189111yescharacteristic
377C2C127×#189611yescharacteristic
378C2C127×#191011yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radical#392×C127C4
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
1. C127×#2873C2semidirect
3. C127×#1490C2semidirect
4. C127×#1464C2semidirect
5. C127×#1288C2semidirect
57. C4×C8×C127D4semidirect
182. #9492C127direct (N × H)
190. #2873C2×C127semidirect
192. #1490C2×C127semidirect
193. #1464C2×C127semidirect
194. #1288C2×C127semidirect
195. C127#9492direct (N × H)
247. C4×C8D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#28732
C127×#25982
C127×#14902
C127×#14642
C127×#12882
#9492127