Finite Group Databasebeta

← C127×#9455 #44573128

Subgroups — C127×#9455 #44573128

Order 32512.

554 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2973C211yesmaximal, characteristic
2C127×#2542C211yesmaximal, characteristic
3C127×#1556C212yesmaximal, complemented
4C127×#1466C211yesmaximal, characteristic
5C127×#1285C212yesmaximal, complemented
6C2×C4⋊Q8×C127C2211yescharacteristic
7C2×C22⋊Q8×C127—21no—
8C2×C22⋊Q8×C127—21no—
9C2×C4×D4×C127C2211yescharacteristic
10#435×C127—24no—
11#432×C127C2212yes—
12#432×C127C2212yes—
13#407×C127—21no—
14C2×C22⋊C8×C127—21no—
15#399×C127—21no—
16#399×C127—21no—
17#390×C127C412yes—
18#384×C127C412yes—
19C4×C4⋊C4×C127C2211yescharacteristic
20#332×C127—24no—
21#323×C127—21no—
22#323×C127—21no—
23C22×Q8×C127—21no—
24C22×D4×C127C2×C411yescharacteristic
25C23×C4×C127D411yescharacteristic
26C23×C4×C127D411yescharacteristic
27C2×M16×C127—22no—
28C22×C8×C127—22no—
29C4⋊Q8×C127—22no—
30C4⋊Q8×C127—22no—
31C22⋊Q8×C127—44no—
32C22⋊Q8×C127—44no—
33C4×D4×C127—22no—
34C4×D4×C127—22no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—22no—
37C2×C4⋊C4×C127—22no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127C2×C412yes—
40C2×C4⋊C4×C127C2×C411yescharacteristic
41C2×C22⋊C4×C127—22no—
42C2×C22⋊C4×C127—22no—
43C2×C22⋊C4×C127D411yescharacteristic
44C2×C22⋊C4×C127D411yescharacteristic
45C2×C42×C127C2×C412yes—
46C2×C42×C127C2311yescharacteristic
47C4⋊C8×C127—22no—
48C4⋊C8×C127D414yes—
49C22⋊C8×C127—22no—
50C22⋊C8×C127—22no—
51C22⋊C8×C127—22no—
52C22⋊C8×C127—22no—
53#97×C127—22no—
54#97×C127—22no—
55#95×C127—21no—
56C24×C127C22⋊C411yescharacteristic
57C24×C127C22⋊C411yescharacteristic
58C2×Q8×C127—42no—
59C2×Q8×C127—42no—
60C2×Q8×C127—41no—
61C2×Q8×C127—41no—
62C2×D4×C127—22no—
63C2×D4×C127—22no—
64C2×D4×C127—41no—
65C22×C4×C127—22no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127—22no—
71C22×C4×C127—42no—
72C22×C4×C127—42no—
73C22×C4×C127C22⋊C411yescharacteristic
74C22×C4×C127C22⋊C411yescharacteristic
75C22×C4×C127C22×C411yescharacteristic
76C22×C4×C127C2×D411yescharacteristic
77C22×C4×C127C2×D411yescharacteristic
78M16×C127—82no—
79C2×C8×C127—24no—
80C2×C8×C127—42no—
81C2×C8×C127—82no—
82C4⋊C4×C127—24no—
83C4⋊C4×C127—22no—
84C4⋊C4×C127—24no—
85C4⋊C4×C127—44no—
86C4⋊C4×C127—44no—
87C4⋊C4×C127—42no—
88C22⋊C4×C127—22no—
89C22⋊C4×C127—22no—
90C22⋊C4×C127—44no—
91C22⋊C4×C127—44no—
92C42×C127—42no—
93C42×C127C2×D412yes—
94C42×C127#4112yes—
95C23×C127—21no—
96C23×C127—21no—
97C23×C127—21no—
98C23×C127—21no—
99C23×C127—21no—
100C23×C127—41no—
101C23×C127—41no—
102C23×C127—41no—
103C23×C127—41no—
104C23×C127#10112yes—
105C23×C127C2×C22⋊C411yescharacteristic
106Q8×C127—82no—
107Q8×C127—82no—
108D4×C127—44no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—22no—
112C2×C4×C127—24no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—41no—
116C2×C4×C127—42no—
117C2×C4×C127—42no—
118C2×C4×C127—42no—
119C2×C4×C127—42no—
120C2×C4×C127—41no—
121C2×C4×C127—41no—
122C2×C4×C127—42no—
123C2×C4×C127—42no—
124C2×C4×C127—42no—
125C2×C4×C127—81no—
126C2×C4×C127—81no—
127C2×C4×C127C4×D412yes—
128C2×C4×C127#12011yescharacteristic
129C2×C4×C127#12112yes—
130C2×C4×C127#12311yescharacteristic
131C8×C127—44no—
132C8×C127—82no—
133C22×C127—21no—
134C22×C127—21no—
135C22×C127—22no—
136C22×C127—42no—
137C22×C127—42no—
138C22×C127—41no—
139C22×C127—41no—
140C22×C127—41no—
141C22×C127—41no—
142C22×C127—41no—
143C22×C127—81no—
144C22×C127—81no—
145C22×C127#38611yescharacteristic
146C22×C127C2×#10111yescharacteristic
147C22×C127#41311yescharacteristic
148C4×C127—21no—
149C4×C127—22no—
150C4×C127—22no—
151C4×C127—44no—
152C4×C127—41no—
153C4×C127—41no—
154C4×C127—82no—
155C4×C127#45312yes—
156#9455C12711yesmaximal, characteristic, direct product factor, Sylow
157C2×C127—21no—
158C2×C127—21no—
159C2×C127—42no—
160C2×C127—81no—
161C2×C127#188711yescharacteristic
162C2×C127#190111yescharacteristic
163C2×C127#190911yescharacteristic
164#2973C2×C12711yescharacteristic
165#2542C2×C12711yescharacteristic
166#1556C2×C12712yescomplemented
167#1466C2×C12711yescharacteristic
168#1285C2×C12712yescomplemented
169C127#945511yescharacteristic, direct product factor, Sylow
170C2×C4⋊Q8C22×C12711yescharacteristic
171C2×C22⋊Q8—21no—
172C2×C22⋊Q8—21no—
173C2×C4×D4C22×C12711yescharacteristic
174#435—24no—
175#432C22×C12712yes—
176#432C22×C12712yes—
177#407—21no—
178C2×C22⋊C8—21no—
179#399—21no—
180#399—21no—
181#390C4×C12712yes—
182#384C4×C12712yes—
183C4×C4⋊C4C22×C12711yescharacteristic
184#332—24no—
185#323—21no—
186#323—21no—
187C22×Q8—21no—
188C22×D4C2×C4×C12711yescharacteristic
189C23×C4D4×C12711yescharacteristic
190C23×C4D4×C12711yescharacteristic
191C2×M16—22no—
192C22×C8—22no—
193C4⋊Q8—22no—
194C4⋊Q8—22no—
195C22⋊Q8—44no—
196C22⋊Q8—44no—
197C4×D4—22no—
198C4×D4—22no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4C2×C4×C12712yes—
204C2×C4⋊C4C2×C4×C12711yescharacteristic
205C2×C22⋊C4—22no—
206C2×C22⋊C4—22no—
207C2×C22⋊C4D4×C12711yescharacteristic
208C2×C22⋊C4D4×C12711yescharacteristic
209C2×C42C2×C4×C12712yes—
210C2×C42C23×C12711yescharacteristic
211C4⋊C8—22no—
212C4⋊C8D4×C12714yes—
213C22⋊C8—22no—
214C22⋊C8—22no—
215C22⋊C8—22no—
216C22⋊C8—22no—
217#97—22no—
218#97—22no—
219#95—21no—
220C24C22⋊C4×C12711yescharacteristic
221C24C22⋊C4×C12711yescharacteristic
222C2×Q8—42no—
223C2×Q8—42no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—41no—
229C22×C4—22no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—22no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4C22⋊C4×C12711yescharacteristic
238C22×C4C22⋊C4×C12711yescharacteristic
239C22×C4C22×C4×C12711yescharacteristic
240C22×C4C2×D4×C12711yescharacteristic
241C22×C4C2×D4×C12711yescharacteristic
242M16—82no—
243C2×C8—24no—
244C2×C8—42no—
245C2×C8—82no—
246C4⋊C4—24no—
247C4⋊C4—22no—
248C4⋊C4—24no—
249C4⋊C4—44no—
250C4⋊C4—44no—
251C4⋊C4—42no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—44no—
255C22⋊C4—44no—
256C42—42no—
257C42C2×D4×C12712yes—
258C42#41×C12712yes—
259C23—21no—
260C23—21no—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23#101×C12712yes—
269C23C2×C22⋊C4×C12711yescharacteristic
270Q8—82no—
271Q8—82no—
272D4—44no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—22no—
276C2×C4—24no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—41no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—42no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4C4×D4×C12712yes—
292C2×C4#120×C12711yescharacteristic
293C2×C4#121×C12712yes—
294C2×C4#123×C12711yescharacteristic
295C8—44no—
296C8—82no—
297C22—21no—
298C22—21no—
299C22—22no—
300C22—42no—
301C22—42no—
302C22—41no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22—81no—
309C22#386×C12711yescharacteristic
310C22C2×#101×C12711yescharacteristic
311C22#413×C12711yescharacteristic
312C4—21no—
313C4—22no—
314C4—22no—
315C4—44no—
316C4—41no—
317C4—41no—
318C4—82no—
319C4#453×C12712yes—
320C2—21no—
321C2—21no—
322C2—42no—
323C2—81no—
324C2C127×#188711yescharacteristic
325C2C127×#190111yescharacteristic
326C2C127×#190911yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC22×D4×C127C2×C4
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
3. C127×#1556C2semidirect
5. C127×#1285C2semidirect
156. #9455C127direct (N × H)
166. #1556C2×C127semidirect
168. #1285C2×C127semidirect
169. C127#9455direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29732
C127×#25422
C127×#15562
C127×#14662
C127×#12852
#9455127