Finite Group Databasebeta

← C127×#9485 #44573158

Subgroups — C127×#9485 #44573158

Order 32512.

626 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 150 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×#2972C211yesmaximal, characteristic, complemented
2C127×#2535C211yesmaximal, characteristic
3C127×#1800C211yesmaximal, characteristic, complemented
4C127×#1486C212yesmaximal, complemented
5C127×#1286C212yesmaximal, complemented
6C2×#121×C127—21no—
7C2×C4×D4×C127C2211yescharacteristic
8C2×C4×D4×C127C2211yescharacteristic
9C8×D4×C127—24no—
10#431×C127C2212yes—
11#423×C127C2212yes—
12C2×#100×C127—21no—
13C2×C22⋊C8×C127—22no—
14#397×C127C412yes—
15#392×C127C412yes—
16#386×C127—22no—
17#382×C127C2211yescharacteristic
18#380×C127—21no—
19#343×C127—21no—
20D4⋊C8×C127—24no—
21C22×D4×C127—22no—
22C22×D4×C127C2×C411yescharacteristic
23C22×D4×C127D411yescharacteristic
24C23×C4×C127—21no—
25C23×C4×C127D412yes—
26C2×M16×C127—22no—
27C22×C8×C127—24no—
28#121×C127—42no—
29#121×C127—42no—
30C4×D4×C127—22no—
31C4×D4×C127—22no—
32C4×D4×C127—22no—
33C4×D4×C127—22no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127C2×C411yescharacteristic
36C2×C4⋊C4×C127D411yescharacteristic
37C2×C22⋊C4×C127—22no—
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127—22no—
40C2×C22⋊C4×C127C2×C412yes—
41C2×C42×C127C2311yescharacteristic
42C4⋊C8×C127—22no—
43C4⋊C8×C127—22no—
44C4⋊C8×C127—22no—
45#100×C127—42no—
46C22⋊C8×C127—24no—
47C22⋊C8×C127—22no—
48C4×C8×C127D414yescomplemented
49#95×C127—22no—
50#95×C127—21no—
51#95×C127C2×C412yes—
52C24×C127—21no—
53C24×C127C22⋊C412yes—
54C2×D4×C127—22no—
55C2×D4×C127—22no—
56C2×D4×C127—22no—
57C2×D4×C127—42no—
58C2×D4×C127—44no—
59C2×D4×C127—44no—
60C2×D4×C127—82no—
61C2×D4×C127D812yes—
62C2×D4×C127SD1612yes—
63C22×C4×C127—22no—
64C22×C4×C127—22no—
65C22×C4×C127—22no—
66C22×C4×C127—21no—
67C22×C4×C127—42no—
68C22×C4×C127—41no—
69C22×C4×C127—41no—
70C22×C4×C127—42no—
71C22×C4×C127—82no—
72C22×C4×C127C22⋊C412yes—
73C22×C4×C127C22×C411yescharacteristic
74C22×C4×C127C2×D411yescharacteristic
75C22×C4×C127C2×D411yescharacteristic
76M16×C127—42no—
77M16×C127—42no—
78C2×C8×C127—24no—
79C2×C8×C127—42no—
80C2×C8×C127—84no—
81C4⋊C4×C127—22no—
82C4⋊C4×C127—22no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C22⋊C4×C127—24no—
86C22⋊C4×C127—44no—
87C22⋊C4×C127—41no—
88C22⋊C4×C127—41no—
89C22⋊C4×C127—82no—
90C42×C127C2×D412yes—
91C42×C127#4112yes—
92C23×C127—22no—
93C23×C127—22no—
94C23×C127—22no—
95C23×C127—42no—
96C23×C127—42no—
97C23×C127—41no—
98C23×C127—41no—
99C23×C127—41no—
100C23×C127—41no—
101C23×C127—41no—
102C23×C127—41no—
103C23×C127#10214yes—
104C23×C127C2×C22⋊C411yescharacteristic
105D4×C127—24no—
106D4×C127—24no—
107D4×C127—24no—
108D4×C127—42no—
109D4×C127—88no—
110C2×C4×C127—22no—
111C2×C4×C127—41no—
112C2×C4×C127—41no—
113C2×C4×C127—44no—
114C2×C4×C127—42no—
115C2×C4×C127—42no—
116C2×C4×C127—42no—
117C2×C4×C127—41no—
118C2×C4×C127—41no—
119C2×C4×C127—42no—
120C2×C4×C127—41no—
121C2×C4×C127—82no—
122C2×C4×C127—82no—
123C2×C4×C127—82no—
124C2×C4×C127C4×D412yes—
125C2×C4×C127#12011yescharacteristic
126C2×C4×C127#12112yes—
127C2×C4×C127#12311yescharacteristic
128C2×C4×C127C2×D811yescharacteristic
129C2×C4×C127C2×SD1611yescharacteristic
130C2×C4×C127#13512yes—
131C8×C127—44no—
132C8×C127—82no—
133C22×C127—21no—
134C22×C127—21no—
135C22×C127—24no—
136C22×C127—44no—
137C22×C127—42no—
138C22×C127—42no—
139C22×C127—42no—
140C22×C127—42no—
141C22×C127—42no—
142C22×C127—82no—
143C22×C127—81no—
144C22×C127—81no—
145C22×C127—81no—
146C22×C127—81no—
147C22×C127#38611yescharacteristic
148C22×C127C2×#10211yescharacteristic
149C22×C127#41611yescharacteristic
150C4×C127—22no—
151C4×C127—21no—
152C4×C127—21no—
153C4×C127—42no—
154C4×C127—82no—
155C4×C127—81no—
156C4×C127#46512yes—
157C4×C127#46612yes—
158#9485C12711yesmaximal, characteristic, direct product factor, Sylow
159C2×C127—21no—
160C2×C127—21no—
161C2×C127—44no—
162C2×C127—82no—
163C2×C127#189111yescharacteristic
164C2×C127#189311yescharacteristic
165C2×C127#191111yescharacteristic
166#2972C2×C12711yescharacteristic, complemented
167#2535C2×C12711yescharacteristic
168#1800C2×C12711yescharacteristic, complemented
169#1486C2×C12712yescomplemented
170#1286C2×C12712yescomplemented
171C127#948511yescharacteristic, direct product factor, Sylow
172C2×#121—21no—
173C2×C4×D4C22×C12711yescharacteristic
174C2×C4×D4C22×C12711yescharacteristic
175C8×D4—24no—
176#431C22×C12712yes—
177#423C22×C12712yes—
178C2×#100—21no—
179C2×C22⋊C8—22no—
180#397C4×C12712yes—
181#392C4×C12712yes—
182#386—22no—
183#382C22×C12711yescharacteristic
184#380—21no—
185#343—21no—
186D4⋊C8—24no—
187C22×D4—22no—
188C22×D4C2×C4×C12711yescharacteristic
189C22×D4D4×C12711yescharacteristic
190C23×C4—21no—
191C23×C4D4×C12712yes—
192C2×M16—22no—
193C22×C8—24no—
194#121—42no—
195#121—42no—
196C4×D4—22no—
197C4×D4—22no—
198C4×D4—22no—
199C4×D4—22no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4C2×C4×C12711yescharacteristic
202C2×C4⋊C4D4×C12711yescharacteristic
203C2×C22⋊C4—22no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—22no—
206C2×C22⋊C4C2×C4×C12712yes—
207C2×C42C23×C12711yescharacteristic
208C4⋊C8—22no—
209C4⋊C8—22no—
210C4⋊C8—22no—
211#100—42no—
212C22⋊C8—24no—
213C22⋊C8—22no—
214C4×C8D4×C12714yescomplemented
215#95—22no—
216#95—21no—
217#95C2×C4×C12712yes—
218C24—21no—
219C24C22⋊C4×C12712yes—
220C2×D4—22no—
221C2×D4—22no—
222C2×D4—22no—
223C2×D4—42no—
224C2×D4—44no—
225C2×D4—44no—
226C2×D4—82no—
227C2×D4D8×C12712yes—
228C2×D4SD16×C12712yes—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—21no—
233C22×C4—42no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—42no—
237C22×C4—82no—
238C22×C4C22⋊C4×C12712yes—
239C22×C4C22×C4×C12711yescharacteristic
240C22×C4C2×D4×C12711yescharacteristic
241C22×C4C2×D4×C12711yescharacteristic
242M16—42no—
243M16—42no—
244C2×C8—24no—
245C2×C8—42no—
246C2×C8—84no—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C22⋊C4—24no—
252C22⋊C4—44no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—82no—
256C42C2×D4×C12712yes—
257C42#41×C12712yes—
258C23—22no—
259C23—22no—
260C23—22no—
261C23—42no—
262C23—42no—
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23#102×C12714yes—
270C23C2×C22⋊C4×C12711yescharacteristic
271D4—24no—
272D4—24no—
273D4—24no—
274D4—42no—
275D4—88no—
276C2×C4—22no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—44no—
280C2×C4—42no—
281C2×C4—42no—
282C2×C4—42no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—42no—
286C2×C4—41no—
287C2×C4—82no—
288C2×C4—82no—
289C2×C4—82no—
290C2×C4C4×D4×C12712yes—
291C2×C4#120×C12711yescharacteristic
292C2×C4#121×C12712yes—
293C2×C4#123×C12711yescharacteristic
294C2×C4C2×D8×C12711yescharacteristic
295C2×C4C2×SD16×C12711yescharacteristic
296C2×C4#135×C12712yes—
297C8—44no—
298C8—82no—
299C22—21no—
300C22—21no—
301C22—24no—
302C22—44no—
303C22—42no—
304C22—42no—
305C22—42no—
306C22—42no—
307C22—42no—
308C22—82no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22#386×C12711yescharacteristic
314C22C2×#102×C12711yescharacteristic
315C22#416×C12711yescharacteristic
316C4—22no—
317C4—21no—
318C4—21no—
319C4—42no—
320C4—82no—
321C4—81no—
322C4#465×C12712yes—
323C4#466×C12712yes—
324C2—21no—
325C2—21no—
326C2—44no—
327C2—82no—
328C2C127×#189111yescharacteristic
329C2C127×#189311yescharacteristic
330C2C127×#191111yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#2535C2
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×#2972C2semidirect
3. C127×#1800C2semidirect
4. C127×#1486C2semidirect
5. C127×#1286C2semidirect
48. C4×C8×C127D4semidirect
158. #9485C127direct (N × H)
166. #2972C2×C127semidirect
168. #1800C2×C127semidirect
169. #1486C2×C127semidirect
170. #1286C2×C127semidirect
171. C127#9485direct (N × H)
214. C4×C8D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29722
C127×#25352
C127×#18002
C127×#14862
C127×#12862
#9485127