Finite Group Databasebeta

← C127×#11735 #44575408

Subgroups — C127×#11735 #44575408

Order 32512.

440 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2395C211yesmaximal, characteristic
2C4×#100×C127C211yesmaximal, characteristic
3C127×#1459C211yesmaximal, characteristic
4C127×#1353C212yesmaximal, complemented
5C127×#1346C212yesmaximal, complemented
6C2×C4×D4×C127C2211yescharacteristic
7C2×#117×C127C411yescharacteristic
8C2×#100×C127—21no—
9C2×C22⋊C8×C127—21no—
10C4×M16×C127—21no—
11#400×C127C2211yescharacteristic
12#399×C127C411yescharacteristic
13#398×C127C2211yescharacteristic
14#397×C127—21no—
15#397×C127C411yescharacteristic
16#394×C127—21no—
17C4×C4⋊C4×C127—21no—
18C4×C22⋊C4×C127—21no—
19C4×C22⋊C4×C127C411yescharacteristic
20#343×C127C2212yes—
21#324×C127C2212yes—
22#323×C127—21no—
23C22×D4×C127D411yescharacteristic
24C23×C4×C127C2×C411yescharacteristic
25C23×C4×C127D411yescharacteristic
26C2×M16×C127—22no—
27C22×C8×C127—41no—
28C4×D4×C127—41no—
29C4×D4×C127—41no—
30#117×C127—41no—
31#117×C127—41no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127C2×C411yescharacteristic
35C2×C4⋊C4×C127C2×C411yescharacteristic
36C2×C4⋊C4×C127C2311yescharacteristic
37C2×C22⋊C4×C127—21no—
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127C2×C411yescharacteristic
42C2×C22⋊C4×C127D411yescharacteristic
43C2×C42×C127—21no—
44C2×C42×C127—21no—
45C2×C42×C127D411yescharacteristic
46#100×C127—24no—
47C22⋊C8×C127—22no—
48C22⋊C8×C127—41no—
49#97×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×C127C22⋊C411yescharacteristic
58C24×C127C22⋊C411yescharacteristic
59C2×D4×C127—22no—
60C2×D4×C127—22no—
61C2×D4×C127—41no—
62C22×C4×C127—21no—
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—21no—
70C22×C4×C127—42no—
71C22×C4×C127—42no—
72C22×C4×C127C22⋊C411yescharacteristic
73C22×C4×C127C22⋊C411yescharacteristic
74C22×C4×C127C22×C411yescharacteristic
75C22×C4×C127C2×D411yescharacteristic
76C22×C4×C127C2×D411yescharacteristic
77M16×C127—24no—
78M16×C127—42no—
79C2×C8×C127—42no—
80C2×C8×C127—42no—
81C2×C8×C127—82no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—42no—
86C4⋊C4×C127—42no—
87C22⋊C4×C127—41no—
88C22⋊C4×C127—41no—
89C22⋊C4×C127—42no—
90C22⋊C4×C127—42no—
91C22⋊C4×C127—42no—
92C22⋊C4×C127—42no—
93C42×C127—21no—
94C42×C127—21no—
95C42×C127—42no—
96C42×C127—41no—
97C42×C127—41no—
98C23×C127—21no—
99C23×C127—21no—
100C23×C127—21no—
101C23×C127—21no—
102C23×C127—21no—
103C23×C127—41no—
104C23×C127—41no—
105C23×C127—41no—
106C23×C127—41no—
107C23×C127#10412yes—
108C23×C127C2×C22⋊C411yescharacteristic
109D4×C127—44no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—22no—
113C2×C4×C127—22no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—42no—
118C2×C4×C127—41no—
119C2×C4×C127—41no—
120C2×C4×C127—42no—
121C2×C4×C127—42no—
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—41no—
132C2×C4×C127—41no—
133C2×C4×C127—41no—
134C2×C4×C127—81no—
135C2×C4×C127#9911yescharacteristic
136C2×C4×C127#9911yescharacteristic
137C2×C4×C127#13512yes—
138C8×C127—44no—
139C8×C127—82no—
140C22×C127—21no—
141C22×C127—21no—
142C22×C127—22no—
143C22×C127—42no—
144C22×C127—41no—
145C22×C127—41no—
146C22×C127—41no—
147C22×C127—41no—
148C22×C127—41no—
149C22×C127—81no—
150C22×C127—81no—
151C22×C127—81no—
152C22×C127C2×#9911yescharacteristic
153C22×C127#41611yescharacteristic
154C22×C127C2×#10411yescharacteristic
155C4×C127—21no—
156C4×C127—22no—
157C4×C127—42no—
158C4×C127—41no—
159C4×C127—41no—
160C4×C127—41no—
161C4×C127—81no—
162C4×C127—81no—
163C4×C127—81no—
164C4×C127#35212yes—
165#11735C12711yesmaximal, characteristic, direct product factor, Sylow
166C2×C127—21no—
167C2×C127—21no—
168C2×C127—42no—
169C2×C127—81no—
170C2×C127#150111yescharacteristic
171C2×C127C2×#35211yescharacteristic
172C2×C127#213211yescharacteristic
173#2395C2×C12711yescharacteristic
174C4×#100C2×C12711yescharacteristic
175#1459C2×C12711yescharacteristic
176#1353C2×C12712yescomplemented
177#1346C2×C12712yescomplemented
178C127#1173511yescharacteristic, direct product factor, Sylow
179C2×C4×D4C22×C12711yescharacteristic
180C2×#117C4×C12711yescharacteristic
181C2×#100—21no—
182C2×C22⋊C8—21no—
183C4×M16—21no—
184#400C22×C12711yescharacteristic
185#399C4×C12711yescharacteristic
186#398C22×C12711yescharacteristic
187#397—21no—
188#397C4×C12711yescharacteristic
189#394—21no—
190C4×C4⋊C4—21no—
191C4×C22⋊C4—21no—
192C4×C22⋊C4C4×C12711yescharacteristic
193#343C22×C12712yes—
194#324C22×C12712yes—
195#323—21no—
196C22×D4D4×C12711yescharacteristic
197C23×C4C2×C4×C12711yescharacteristic
198C23×C4D4×C12711yescharacteristic
199C2×M16—22no—
200C22×C8—41no—
201C4×D4—41no—
202C4×D4—41no—
203#117—41no—
204#117—41no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4C2×C4×C12711yescharacteristic
208C2×C4⋊C4C2×C4×C12711yescharacteristic
209C2×C4⋊C4C23×C12711yescharacteristic
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4C2×C4×C12711yescharacteristic
215C2×C22⋊C4D4×C12711yescharacteristic
216C2×C42—21no—
217C2×C42—21no—
218C2×C42D4×C12711yescharacteristic
219#100—24no—
220C22⋊C8—22no—
221C22⋊C8—41no—
222#97—41no—
223C4×C8—41no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95C2×C4×C12711yescharacteristic
229#95C2×C4×C12711yescharacteristic
230C24C22⋊C4×C12711yescharacteristic
231C24C22⋊C4×C12711yescharacteristic
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—41no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—42no—
244C22×C4—42no—
245C22×C4C22⋊C4×C12711yescharacteristic
246C22×C4C22⋊C4×C12711yescharacteristic
247C22×C4C22×C4×C12711yescharacteristic
248C22×C4C2×D4×C12711yescharacteristic
249C22×C4C2×D4×C12711yescharacteristic
250M16—24no—
251M16—42no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—82no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C4⋊C4—42no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C42—21no—
267C42—21no—
268C42—42no—
269C42—41no—
270C42—41no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23#104×C12712yes—
281C23C2×C22⋊C4×C12711yescharacteristic
282D4—44no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—42no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—81no—
308C2×C4#99×C12711yescharacteristic
309C2×C4#99×C12711yescharacteristic
310C2×C4#135×C12712yes—
311C8—44no—
312C8—82no—
313C22—21no—
314C22—21no—
315C22—22no—
316C22—42no—
317C22—41no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22C2×#99×C12711yescharacteristic
326C22#416×C12711yescharacteristic
327C22C2×#104×C12711yescharacteristic
328C4—21no—
329C4—22no—
330C4—42no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C4—81no—
337C4#352×C12712yes—
338C2—21no—
339C2—21no—
340C2—42no—
341C2—81no—
342C2C127×#150111yescharacteristic
343C2C2×#352×C12711yescharacteristic
344C2C127×#213211yescharacteristic
subgroupG/H
centerC2×C4×C127#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
socleC22×C127C2×#99
prime radicalC22×D4×C127D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C22×C4×C127 ◁ C2×C4×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1353C2semidirect
5. C127×#1346C2semidirect
165. #11735C127direct (N × H)
176. #1353C2×C127semidirect
177. #1346C2×C127semidirect
178. C127#11735direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#23952
C4×#100×C1272
C127×#14592
C127×#13532
C127×#13462
#11735127