Finite Group Databasebeta

← C127×#11738 #44575411

Subgroups — C127×#11738 #44575411

Order 32512.

400 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2632C211yesmaximal, characteristic
2C4×#101×C127C211yesmaximal, characteristic, complemented
3C127×#1461C211yesmaximal, characteristic, complemented
4C127×#1354C212yesmaximal, complemented
5C127×#1345C212yesmaximal
6C2×#124×C127C411yescharacteristic
7C2×C4×Q8×C127C2211yescharacteristic
8#431×C127—21no—
9C2×#101×C127—21no—
10C4×M16×C127—21no—
11#399×C127—21no—
12#395×C127C411yescharacteristic
13#395×C127C2211yescharacteristic
14#394×C127C411yescharacteristic
15#394×C127C2211yescharacteristic
16#393×C127—21no—
17#388×C127—21no—
18#388×C127—21no—
19#383×C127C411yescharacteristic
20#343×C127C2212yes—
21#324×C127—21no—
22#324×C127C2212yes—
23C22×Q8×C127C2×C411yescharacteristic
24C22×Q8×C127D411yescharacteristic
25C22×D4×C127C2×C411yescharacteristic
26C2×M16×C127—22no—
27#124×C127—41no—
28#124×C127—41no—
29C4×Q8×C127—41no—
30C4×Q8×C127—41no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127C2×C411yescharacteristic
34C2×C4⋊C4×C127D411yescharacteristic
35C2×C4⋊C4×C127C2311yescharacteristic
36C2×C22⋊C4×C127—21no—
37C2×C22⋊C4×C127—21no—
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C42×C127C2×C411yescharacteristic
43C2×C42×C127D411yescharacteristic
44C2×C42×C127D411yescharacteristic
45C4⋊C8×C127—41no—
46#101×C127—24no—
47C22⋊C8×C127—22no—
48#97×C127—41no—
49C4×C8×C127—41no—
50C4×C8×C127—41no—
51#95×C127—21no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127C2×C411yescharacteristic
56#95×C127C2×C411yescharacteristic
57C24×C127—21no—
58C2×Q8×C127—22no—
59C2×Q8×C127—22no—
60C2×Q8×C127—41no—
61C2×Q8×C127—41no—
62C2×Q8×C127—81no—
63C2×D4×C127—41no—
64C2×D4×C127—81no—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127C22⋊C411yescharacteristic
69C22×C4×C127C22⋊C411yescharacteristic
70C22×C4×C127C22⋊C411yescharacteristic
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127C22×C411yescharacteristic
73C22×C4×C127C2×D411yescharacteristic
74C22×C4×C127C2×D411yescharacteristic
75M16×C127—24no—
76M16×C127—42no—
77C2×C8×C127—42no—
78C2×C8×C127—42no—
79C4⋊C4×C127—41no—
80C4⋊C4×C127—41no—
81C4⋊C4×C127—41no—
82C4⋊C4×C127—81no—
83C4⋊C4×C127—81no—
84C22⋊C4×C127—42no—
85C22⋊C4×C127—41no—
86C22⋊C4×C127—41no—
87C22⋊C4×C127—42no—
88C22⋊C4×C127—42no—
89C22⋊C4×C127—81no—
90C22⋊C4×C127—81no—
91C42×C127—21no—
92C42×C127—21no—
93C42×C127—21no—
94C42×C127—21no—
95C42×C127—21no—
96C42×C127—21no—
97C23×C127—41no—
98C23×C127—41no—
99C23×C127—41no—
100C23×C127—41no—
101C23×C127—41no—
102C23×C127—41no—
103C23×C127—41no—
104C23×C127C2×C22⋊C411yescharacteristic
105Q8×C127—44no—
106Q8×C127—82no—
107D4×C127—82no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
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×C127—41no—
131C2×C4×C127#9911yescharacteristic
132C2×C4×C127#9911yescharacteristic
133C2×C4×C127#10412yes—
134C2×C4×C127#13512yes—
135C8×C127—44no—
136C8×C127—82no—
137C22×C127—21no—
138C22×C127—21no—
139C22×C127—81no—
140C22×C127—81no—
141C22×C127—81no—
142C22×C127—81no—
143C22×C127—81no—
144C22×C127—81no—
145C22×C127—81no—
146C22×C127C2×#9911yescharacteristic
147C22×C127#41611yescharacteristic
148C22×C127C2×#10411yescharacteristic
149C4×C127—21no—
150C4×C127—21no—
151C4×C127—22no—
152C4×C127—22no—
153C4×C127—41no—
154C4×C127—41no—
155C4×C127—41no—
156C4×C127—41no—
157C4×C127—81no—
158C4×C127—81no—
159C4×C127—81no—
160#11738C12711yesmaximal, characteristic, direct product factor, Sylow
161C2×C127—21no—
162C2×C127—21no—
163C2×C127—161no—
164C2×C127#150111yescharacteristic
165C2×C127#212211yescharacteristic
166C2×C127#213311yescharacteristic
167#2632C2×C12711yescharacteristic
168C4×#101C2×C12711yescharacteristic, complemented
169#1461C2×C12711yescharacteristic, complemented
170#1354C2×C12712yescomplemented
171#1345C2×C12712yes—
172C127#1173811yescharacteristic, direct product factor, Sylow
173C2×#124C4×C12711yescharacteristic
174C2×C4×Q8C22×C12711yescharacteristic
175#431—21no—
176C2×#101—21no—
177C4×M16—21no—
178#399—21no—
179#395C4×C12711yescharacteristic
180#395C22×C12711yescharacteristic
181#394C4×C12711yescharacteristic
182#394C22×C12711yescharacteristic
183#393—21no—
184#388—21no—
185#388—21no—
186#383C4×C12711yescharacteristic
187#343C22×C12712yes—
188#324—21no—
189#324C22×C12712yes—
190C22×Q8C2×C4×C12711yescharacteristic
191C22×Q8D4×C12711yescharacteristic
192C22×D4C2×C4×C12711yescharacteristic
193C2×M16—22no—
194#124—41no—
195#124—41no—
196C4×Q8—41no—
197C4×Q8—41no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4C2×C4×C12711yescharacteristic
201C2×C4⋊C4D4×C12711yescharacteristic
202C2×C4⋊C4C23×C12711yescharacteristic
203C2×C22⋊C4—21no—
204C2×C22⋊C4—21no—
205C2×C22⋊C4—21no—
206C2×C22⋊C4—21no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4—21no—
209C2×C42C2×C4×C12711yescharacteristic
210C2×C42D4×C12711yescharacteristic
211C2×C42D4×C12711yescharacteristic
212C4⋊C8—41no—
213#101—24no—
214C22⋊C8—22no—
215#97—41no—
216C4×C8—41no—
217C4×C8—41no—
218#95—21no—
219#95—21no—
220#95—21no—
221#95—21no—
222#95C2×C4×C12711yescharacteristic
223#95C2×C4×C12711yescharacteristic
224C24—21no—
225C2×Q8—22no—
226C2×Q8—22no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—81no—
230C2×D4—41no—
231C2×D4—81no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4C22⋊C4×C12711yescharacteristic
236C22×C4C22⋊C4×C12711yescharacteristic
237C22×C4C22⋊C4×C12711yescharacteristic
238C22×C4C22⋊C4×C12711yescharacteristic
239C22×C4C22×C4×C12711yescharacteristic
240C22×C4C2×D4×C12711yescharacteristic
241C22×C4C2×D4×C12711yescharacteristic
242M16—24no—
243M16—42no—
244C2×C8—42no—
245C2×C8—42no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—81no—
250C4⋊C4—81no—
251C22⋊C4—42no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C22⋊C4—42no—
255C22⋊C4—42no—
256C22⋊C4—81no—
257C22⋊C4—81no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42—21no—
262C42—21no—
263C42—21no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23C2×C22⋊C4×C12711yescharacteristic
272Q8—44no—
273Q8—82no—
274D4—82no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
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×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4#99×C12711yescharacteristic
299C2×C4#99×C12711yescharacteristic
300C2×C4#104×C12712yes—
301C2×C4#135×C12712yes—
302C8—44no—
303C8—82no—
304C22—21no—
305C22—21no—
306C22—81no—
307C22—81no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22C2×#99×C12711yescharacteristic
314C22#416×C12711yescharacteristic
315C22C2×#104×C12711yescharacteristic
316C4—21no—
317C4—21no—
318C4—22no—
319C4—22no—
320C4—41no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—81no—
325C4—81no—
326C4—81no—
327C2—21no—
328C2—21no—
329C2—161no—
330C2C127×#150111yescharacteristic
331C2C127×#212211yescharacteristic
332C2C127×#213311yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC22×D4×C127C2×C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#101×C127C2semidirect
3. C127×#1461C2semidirect
4. C127×#1354C2semidirect
160. #11738C127direct (N × H)
168. C4×#101C2×C127semidirect
169. #1461C2×C127semidirect
170. #1354C2×C127semidirect
172. C127#11738direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#26322
C4×#101×C1272
C127×#14612
C127×#13542
C127×#13452
#11738127