Finite Group Databasebeta

← C127×#9493 #44573166

Subgroups — C127×#9493 #44573166

Order 32512.

458 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2921C211yesmaximal, characteristic
2C127×#2599C211yesmaximal, characteristic
3C127×#1491C212yesmaximal, complemented
4C127×#1464C211yesmaximal, characteristic
5C127×#1288C212yesmaximal, complemented
6C2×C4×Q8×C127C2211yescharacteristic
7C2×#117×C127C2211yescharacteristic
8#433×C127—24no—
9#432×C127C2212yes—
10#423×C127—21no—
11#407×C127—21no—
12C4×M16×C127C2212yes—
13#398×C127C411yescharacteristic
14#397×C127C411yescharacteristic
15#395×C127C411yescharacteristic
16#393×C127C411yescharacteristic
17#388×C127—21no—
18#387×C127—21no—
19#387×C127—21no—
20#385×C127—21no—
21#383×C127C2211yescharacteristic
22Q8⋊C8×C127—24no—
23#324×C127—21no—
24#323×C127—21no—
25C22×Q8×C127C2×C411yescharacteristic
26C23×C4×C127D411yescharacteristic
27C2×M16×C127—22no—
28C4×Q8×C127—22no—
29C4×Q8×C127—22no—
30#117×C127—22no—
31#117×C127—22no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127C2×C411yescharacteristic
36C2×C4⋊C4×C127C2×C411yescharacteristic
37C2×C4⋊C4×C127D411yescharacteristic
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127C2×C411yescharacteristic
41C2×C22⋊C4×C127D411yescharacteristic
42C2×C42×C127—21no—
43C2×C42×C127D411yescharacteristic
44C2×C42×C127C2311yescharacteristic
45C4⋊C8×C127—24no—
46C4⋊C8×C127—22no—
47C22⋊C8×C127—24no—
48C22⋊C8×C127—22no—
49#97×C127—22no—
50#97×C127—22no—
51C4×C8×C127D414yes—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127—21no—
56#95×C127—21no—
57#95×C127—21no—
58#95×C127C2×C411yescharacteristic
59#95×C127C2×C411yescharacteristic
60C24×C127C22⋊C411yescharacteristic
61C2×Q8×C127—22no—
62C2×Q8×C127—42no—
63C22×C4×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—41no—
70C22×C4×C127—41no—
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127C22⋊C411yescharacteristic
73C22×C4×C127C22⋊C411yescharacteristic
74C22×C4×C127C22×C411yescharacteristic
75C22×C4×C127C2×D411yescharacteristic
76C22×C4×C127C2×D411yescharacteristic
77M16×C127—42no—
78M16×C127—42no—
79C2×C8×C127—24no—
80C2×C8×C127—42no—
81C4⋊C4×C127—22no—
82C4⋊C4×C127—22no—
83C4⋊C4×C127—22no—
84C4⋊C4×C127—42no—
85C4⋊C4×C127—42no—
86C4⋊C4×C127—41no—
87C4⋊C4×C127—41no—
88C22⋊C4×C127—22no—
89C22⋊C4×C127—22no—
90C22⋊C4×C127—42no—
91C22⋊C4×C127—42no—
92C42×C127—21no—
93C42×C127—21no—
94C42×C127—42no—
95C42×C127C2×D412yes—
96C42×C127#4112yes—
97C23×C127—21no—
98C23×C127—21no—
99C23×C127—21no—
100C23×C127—41no—
101C23×C127—41no—
102C23×C127C2×C22⋊C411yescharacteristic
103Q8×C127—24no—
104Q8×C127—42no—
105C2×C4×C127—21no—
106C2×C4×C127—21no—
107C2×C4×C127—22no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—41no—
114C2×C4×C127—41no—
115C2×C4×C127—42no—
116C2×C4×C127—42no—
117C2×C4×C127—41no—
118C2×C4×C127—41no—
119C2×C4×C127—41no—
120C2×C4×C127—41no—
121C2×C4×C127—41no—
122C2×C4×C127—41no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—41no—
130C2×C4×C127C4×D412yes—
131C2×C4×C127#12011yescharacteristic
132C2×C4×C127#12112yes—
133C2×C4×C127#12311yescharacteristic
134C8×C127—44no—
135C8×C127—82no—
136C22×C127—21no—
137C22×C127—21no—
138C22×C127—42no—
139C22×C127—41no—
140C22×C127—41no—
141C22×C127—41no—
142C22×C127—81no—
143C22×C127#38611yescharacteristic
144C22×C127#42111yescharacteristic
145C22×C127#42111yescharacteristic
146C4×C127—22no—
147C4×C127—21no—
148C4×C127—21no—
149C4×C127—22no—
150C4×C127—41no—
151C4×C127—42no—
152C4×C127—41no—
153C4×C127—41no—
154C4×C127—81no—
155C4×C127—81no—
156C4×C127—81no—
157#9493C12711yesmaximal, characteristic, direct product factor, Sylow
158C2×C127—21no—
159C2×C127—21no—
160C2×C127—81no—
161C2×C127#189111yescharacteristic
162C2×C127#189711yescharacteristic
163C2×C127#190911yescharacteristic
164#2921C2×C12711yescharacteristic
165#2599C2×C12711yescharacteristic
166#1491C2×C12712yescomplemented
167#1464C2×C12711yescharacteristic
168#1288C2×C12712yescomplemented
169C127#949311yescharacteristic, direct product factor, Sylow
170C2×C4×Q8C22×C12711yescharacteristic
171C2×#117C22×C12711yescharacteristic
172#433—24no—
173#432C22×C12712yes—
174#423—21no—
175#407—21no—
176C4×M16C22×C12712yes—
177#398C4×C12711yescharacteristic
178#397C4×C12711yescharacteristic
179#395C4×C12711yescharacteristic
180#393C4×C12711yescharacteristic
181#388—21no—
182#387—21no—
183#387—21no—
184#385—21no—
185#383C22×C12711yescharacteristic
186Q8⋊C8—24no—
187#324—21no—
188#323—21no—
189C22×Q8C2×C4×C12711yescharacteristic
190C23×C4D4×C12711yescharacteristic
191C2×M16—22no—
192C4×Q8—22no—
193C4×Q8—22no—
194#117—22no—
195#117—22no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4C2×C4×C12711yescharacteristic
200C2×C4⋊C4C2×C4×C12711yescharacteristic
201C2×C4⋊C4D4×C12711yescharacteristic
202C2×C22⋊C4—21no—
203C2×C22⋊C4—21no—
204C2×C22⋊C4C2×C4×C12711yescharacteristic
205C2×C22⋊C4D4×C12711yescharacteristic
206C2×C42—21no—
207C2×C42D4×C12711yescharacteristic
208C2×C42C23×C12711yescharacteristic
209C4⋊C8—24no—
210C4⋊C8—22no—
211C22⋊C8—24no—
212C22⋊C8—22no—
213#97—22no—
214#97—22no—
215C4×C8D4×C12714yes—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95C2×C4×C12711yescharacteristic
223#95C2×C4×C12711yescharacteristic
224C24C22⋊C4×C12711yescharacteristic
225C2×Q8—22no—
226C2×Q8—42no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4C22⋊C4×C12711yescharacteristic
236C22×C4C22⋊C4×C12711yescharacteristic
237C22×C4C22⋊C4×C12711yescharacteristic
238C22×C4C22×C4×C12711yescharacteristic
239C22×C4C2×D4×C12711yescharacteristic
240C22×C4C2×D4×C12711yescharacteristic
241M16—42no—
242M16—42no—
243C2×C8—24no—
244C2×C8—42no—
245C4⋊C4—22no—
246C4⋊C4—22no—
247C4⋊C4—22no—
248C4⋊C4—42no—
249C4⋊C4—42no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C22⋊C4—22no—
253C22⋊C4—22no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C42—21no—
257C42—21no—
258C42—42no—
259C42C2×D4×C12712yes—
260C42#41×C12712yes—
261C23—21no—
262C23—21no—
263C23—21no—
264C23—41no—
265C23—41no—
266C23C2×C22⋊C4×C12711yescharacteristic
267Q8—24no—
268Q8—42no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—42no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4C4×D4×C12712yes—
295C2×C4#120×C12711yescharacteristic
296C2×C4#121×C12712yes—
297C2×C4#123×C12711yescharacteristic
298C8—44no—
299C8—82no—
300C22—21no—
301C22—21no—
302C22—42no—
303C22—41no—
304C22—41no—
305C22—41no—
306C22—81no—
307C22#386×C12711yescharacteristic
308C22#421×C12711yescharacteristic
309C22#421×C12711yescharacteristic
310C4—22no—
311C4—21no—
312C4—21no—
313C4—22no—
314C4—42no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—81no—
319C4—81no—
320C4—81no—
321C2—21no—
322C2—21no—
323C2—81no—
324C2C127×#189111yescharacteristic
325C2C127×#189711yescharacteristic
326C2C127×#190911yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC24×C127C22⋊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×#1491C2semidirect
5. C127×#1288C2semidirect
157. #9493C127direct (N × H)
166. #1491C2×C127semidirect
168. #1288C2×C127semidirect
169. C127#9493direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29212
C127×#25992
C127×#14912
C127×#14642
C127×#12882
#9493127