Finite Group Databasebeta

← C127×#9502 #44573175

Subgroups — C127×#9502 #44573175

Order 32512.

660 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 660 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2483C211yesmaximal, characteristic
2C127×#2312C211yesmaximal, characteristic
3C127×#1819C212yesmaximal
4C127×#1819C211yesmaximal, characteristic
5C127×#1304C212yesmaximal
6C22×C22⋊C4×C127C2211yescharacteristic
7C22×C22⋊C4×C127C2211yescharacteristic
8#397×C127—22no—
9#388×C127—24no—
10#385×C127—21no—
11#385×C127C412yescomplemented
12#381×C127—21no—
13#381×C127C412yescomplemented
14#380×C127—21no—
15#379×C127C2212yes—
16#379×C127C2211yescharacteristic
17#379×C127C2212yes—
18C4×C22⋊C4×C127—21no—
19#342×C127—24no—
20#342×C127—22no—
21C25×C127C2311yescharacteristic
22C23×C4×C127C2×C411yescharacteristic
23C23×C4×C127C2×C411yescharacteristic
24C23×C4×C127D411yescharacteristic
25C23×C4×C127D411yescharacteristic
26C2×C4⋊C4×C127—22no—
27C2×C4⋊C4×C127—22no—
28C2×C22⋊C4×C127—22no—
29C2×C22⋊C4×C127—22no—
30C2×C22⋊C4×C127—22no—
31C2×C22⋊C4×C127—21no—
32C2×C22⋊C4×C127—21no—
33C2×C22⋊C4×C127—22no—
34C2×C22⋊C4×C127—21no—
35C2×C22⋊C4×C127—22no—
36C2×C22⋊C4×C127—22no—
37C2×C22⋊C4×C127—22no—
38C2×C22⋊C4×C127—22no—
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—22no—
41C2×C22⋊C4×C127C2×C412yes—
42C2×C22⋊C4×C127C2×C412yes—
43C2×C22⋊C4×C127D412yes—
44C2×C22⋊C4×C127D414yes—
45C2×C42×C127—22no—
46#95×C127—22no—
47#95×C127—22no—
48#95×C127—22no—
49#95×C127—22no—
50#95×C127—22no—
51C24×C127—42no—
52C24×C127—42no—
53C24×C127—81no—
54C24×C127C22×C411yescharacteristic
55C24×C127C2×D411yescharacteristic
56C24×C127C2×D411yescharacteristic
57C24×C127C2×D412yes—
58C24×C127#4112yes—
59C22×C4×C127—21no—
60C22×C4×C127—21no—
61C22×C4×C127—21no—
62C22×C4×C127—21no—
63C22×C4×C127—21no—
64C22×C4×C127—22no—
65C22×C4×C127—21no—
66C22×C4×C127—24no—
67C22×C4×C127—22no—
68C22×C4×C127—22no—
69C22×C4×C127—42no—
70C22×C4×C127—42no—
71C22×C4×C127—42no—
72C22×C4×C127—81no—
73C22×C4×C127—81no—
74C22×C4×C127C22⋊C412yes—
75C22×C4×C127C22⋊C412yes—
76C4⋊C4×C127—82no—
77C4⋊C4×C127—82no—
78C22⋊C4×C127—24no—
79C22⋊C4×C127—24no—
80C22⋊C4×C127—44no—
81C22⋊C4×C127—42no—
82C22⋊C4×C127—41no—
83C22⋊C4×C127—42no—
84C22⋊C4×C127—41no—
85C22⋊C4×C127—42no—
86C22⋊C4×C127—44no—
87C22⋊C4×C127—44no—
88C22⋊C4×C127—44no—
89C22⋊C4×C127—82no—
90C22⋊C4×C127—81no—
91C22⋊C4×C127—82no—
92C42×C127—82no—
93C23×C127—22no—
94C23×C127—22no—
95C23×C127—22no—
96C23×C127—22no—
97C23×C127—24no—
98C23×C127—41no—
99C23×C127—41no—
100C23×C127—41no—
101C23×C127—41no—
102C23×C127—42no—
103C23×C127—42no—
104C23×C127—41no—
105C23×C127—42no—
106C23×C127—42no—
107C23×C127—42no—
108C23×C127—88no—
109C23×C127C2×C22⋊C411yescharacteristic
110C23×C127C4×D412yes—
111C23×C127#12011yescharacteristic
112C23×C127#12112yes—
113C23×C127#12311yescharacteristic
114C2×C4×C127—22no—
115C2×C4×C127—22no—
116C2×C4×C127—42no—
117C2×C4×C127—42no—
118C2×C4×C127—42no—
119C2×C4×C127—42no—
120C2×C4×C127—44no—
121C2×C4×C127—42no—
122C2×C4×C127—44no—
123C2×C4×C127—42no—
124C2×C4×C127—42no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—42no—
128C2×C4×C127—42no—
129C2×C4×C127—44no—
130C2×C4×C127—81no—
131C2×C4×C127—81no—
132C2×C4×C127—82no—
133C2×C4×C127—82no—
134C2×C4×C127—82no—
135C2×C4×C127—82no—
136C2×C4×C127—82no—
137C22×C127—21no—
138C22×C127—21no—
139C22×C127—21no—
140C22×C127—21no—
141C22×C127—22no—
142C22×C127—21no—
143C22×C127—22no—
144C22×C127—22no—
145C22×C127—22no—
146C22×C127—21no—
147C22×C127—22no—
148C22×C127—22no—
149C22×C127—21no—
150C22×C127—44no—
151C22×C127—44no—
152C22×C127—84no—
153C22×C127—82no—
154C22×C127—84no—
155C22×C127#38611yescharacteristic
156C22×C127#41012yes—
157C22×C127#45812yes—
158C4×C127—42no—
159C4×C127—42no—
160C4×C127—84no—
161C4×C127—82no—
162C4×C127—81no—
163C4×C127—81no—
164C4×C127—162no—
165#9502C12711yesmaximal, characteristic, direct product factor, Sylow
166C2×C127—22no—
167C2×C127—22no—
168C2×C127—42no—
169C2×C127—41no—
170C2×C127—42no—
171C2×C127#189011yescharacteristic
172C2×C127#189911yescharacteristic
173C2×C127#191311yescharacteristic
174#2483C2×C12711yescharacteristic
175#2312C2×C12711yescharacteristic
176#1819C2×C12712yes—
177#1819C2×C12711yescharacteristic
178#1304C2×C12712yes—
179C127#950211yescharacteristic, direct product factor, Sylow
180C22×C22⋊C4C22×C12711yescharacteristic
181C22×C22⋊C4C22×C12711yescharacteristic
182#397—22no—
183#388—24no—
184#385—21no—
185#385C4×C12712yescomplemented
186#381—21no—
187#381C4×C12712yescomplemented
188#380—21no—
189#379C22×C12712yes—
190#379C22×C12711yescharacteristic
191#379C22×C12712yes—
192C4×C22⋊C4—21no—
193#342—24no—
194#342—22no—
195C25C23×C12711yescharacteristic
196C23×C4C2×C4×C12711yescharacteristic
197C23×C4C2×C4×C12711yescharacteristic
198C23×C4D4×C12711yescharacteristic
199C23×C4D4×C12711yescharacteristic
200C2×C4⋊C4—22no—
201C2×C4⋊C4—22no—
202C2×C22⋊C4—22no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4—22no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—22no—
208C2×C22⋊C4—21no—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—22no—
215C2×C22⋊C4C2×C4×C12712yes—
216C2×C22⋊C4C2×C4×C12712yes—
217C2×C22⋊C4D4×C12712yes—
218C2×C22⋊C4D4×C12714yes—
219C2×C42—22no—
220#95—22no—
221#95—22no—
222#95—22no—
223#95—22no—
224#95—22no—
225C24—42no—
226C24—42no—
227C24—81no—
228C24C22×C4×C12711yescharacteristic
229C24C2×D4×C12711yescharacteristic
230C24C2×D4×C12711yescharacteristic
231C24C2×D4×C12712yes—
232C24#41×C12712yes—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—24no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—81no—
247C22×C4—81no—
248C22×C4C22⋊C4×C12712yes—
249C22×C4C22⋊C4×C12712yes—
250C4⋊C4—82no—
251C4⋊C4—82no—
252C22⋊C4—24no—
253C22⋊C4—24no—
254C22⋊C4—44no—
255C22⋊C4—42no—
256C22⋊C4—41no—
257C22⋊C4—42no—
258C22⋊C4—41no—
259C22⋊C4—42no—
260C22⋊C4—44no—
261C22⋊C4—44no—
262C22⋊C4—44no—
263C22⋊C4—82no—
264C22⋊C4—81no—
265C22⋊C4—82no—
266C42—82no—
267C23—22no—
268C23—22no—
269C23—22no—
270C23—22no—
271C23—24no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—42no—
277C23—42no—
278C23—41no—
279C23—42no—
280C23—42no—
281C23—42no—
282C23—88no—
283C23C2×C22⋊C4×C12711yescharacteristic
284C23C4×D4×C12712yes—
285C23#120×C12711yescharacteristic
286C23#121×C12712yes—
287C23#123×C12711yescharacteristic
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—44no—
295C2×C4—42no—
296C2×C4—44no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—44no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—82no—
309C2×C4—82no—
310C2×C4—82no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—21no—
317C22—22no—
318C22—22no—
319C22—22no—
320C22—21no—
321C22—22no—
322C22—22no—
323C22—21no—
324C22—44no—
325C22—44no—
326C22—84no—
327C22—82no—
328C22—84no—
329C22#386×C12711yescharacteristic
330C22#410×C12712yes—
331C22#458×C12712yes—
332C4—42no—
333C4—42no—
334C4—84no—
335C4—82no—
336C4—81no—
337C4—81no—
338C4—162no—
339C2—22no—
340C2—22no—
341C2—42no—
342C2—41no—
343C2—42no—
344C2C127×#189011yescharacteristic
345C2C127×#189911yescharacteristic
346C2C127×#191311yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC24C22×C4×C127
Frattini, cosocleC25C23×C127
prime radicalC25×C127C23
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C25×C127 ◁ G

Complements

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

NH ≅ G/Ntype
11. #385×C127C4semidirect
13. #381×C127C4semidirect
165. #9502C127direct (N × H)
179. C127#9502direct (N × H)
185. #385C4×C127semidirect
187. #381C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#24832
C127×#23122
C127×#18192
C127×#13042
#9502127