Finite Group Databasebeta

← C127×#11810 #44575483

Subgroups — C127×#11810 #44575483

Order 32512.

402 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2396C211yesmaximal, characteristic
2C127×#1820C211yesmaximal, characteristic
3C127×#1464C211yesmaximal, characteristic
4C127×#1352C212yesmaximal
5C127×#1351C212yesmaximal
6C2×C4×Q8×C127C411yescharacteristic, complemented
7C2×#117×C127C2211yescharacteristic
8#432×C127—21no—
9#400×C127C411yescharacteristic, complemented
10#399×C127C2211yescharacteristic
11#398×C127—21no—
12#396×C127—21no—
13#395×C127C411yescharacteristic, complemented
14#393×C127C2211yescharacteristic
15#381×C127—21no—
16C4×C4⋊C4×C127—21no—
17C4×C4⋊C4×C127C411yescharacteristic, complemented
18C4×C22⋊C4×C127—21no—
19#342×C127—21no—
20#342×C127C2212yes—
21#324×C127—21no—
22#323×C127C2212yes—
23C22×Q8×C127C2×C411yescharacteristic
24C23×C4×C127D411yescharacteristic
25C4×Q8×C127—41no—
26C4×Q8×C127—41no—
27#117×C127—41no—
28#117×C127—41no—
29C2×C4⋊C4×C127—21no—
30C2×C4⋊C4×C127—21no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127C2×C411yescharacteristic
34C2×C4⋊C4×C127C2×C411yescharacteristic
35C2×C4⋊C4×C127D411yescharacteristic
36C2×C22⋊C4×C127—21no—
37C2×C22⋊C4×C127—21no—
38C2×C22⋊C4×C127—22no—
39C2×C22⋊C4×C127D411yescharacteristic
40C2×C22⋊C4×C127C2311yescharacteristic
41C2×C42×C127—21no—
42C2×C42×C127—21no—
43C2×C42×C127C2×C411yescharacteristic
44C2×C42×C127D411yescharacteristic
45C4⋊C8×C127—41no—
46C22⋊C8×C127—22no—
47#97×C127—41no—
48#95×C127—21no—
49#95×C127—21no—
50#95×C127—21no—
51#95×C127—21no—
52#95×C127—41no—
53#95×C127—41no—
54#95×C127C2×C411yescharacteristic
55#95×C127C2×C411yescharacteristic
56C24×C127C2×D411yescharacteristic
57C2×Q8×C127—42no—
58C2×Q8×C127—41no—
59C22×C4×C127—21no—
60C22×C4×C127—21no—
61C22×C4×C127—22no—
62C22×C4×C127—21no—
63C22×C4×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—41no—
67C22×C4×C127—42no—
68C22×C4×C127C22⋊C411yescharacteristic
69C22×C4×C127C22⋊C411yescharacteristic
70C22×C4×C127C22⋊C411yescharacteristic
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127C22×C411yescharacteristic
73C22×C4×C127C2×D411yescharacteristic
74C2×C8×C127—42no—
75C4⋊C4×C127—41no—
76C4⋊C4×C127—41no—
77C4⋊C4×C127—41no—
78C4⋊C4×C127—42no—
79C4⋊C4×C127—42no—
80C4⋊C4×C127—42no—
81C4⋊C4×C127—42no—
82C22⋊C4×C127—41no—
83C22⋊C4×C127—41no—
84C22⋊C4×C127—42no—
85C22⋊C4×C127—42no—
86C22⋊C4×C127—42no—
87C22⋊C4×C127—42no—
88C42×C127—21no—
89C42×C127—21no—
90C42×C127—21no—
91C42×C127—21no—
92C42×C127—42no—
93C42×C127—41no—
94C42×C127—41no—
95C23×C127—21no—
96C23×C127—21no—
97C23×C127—41no—
98C23×C127—41no—
99C23×C127C2×C22⋊C411yescharacteristic
100C23×C127#13712yes—
101Q8×C127—42no—
102Q8×C127—42no—
103C2×C4×C127—21no—
104C2×C4×C127—21no—
105C2×C4×C127—22no—
106C2×C4×C127—22no—
107C2×C4×C127—21no—
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—42no—
115C2×C4×C127—42no—
116C2×C4×C127—41no—
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×C127—82no—
131C2×C4×C127—82no—
132C2×C4×C127—82no—
133C2×C4×C127#9911yescharacteristic
134C2×C4×C127#9911yescharacteristic
135C8×C127—82no—
136C22×C127—21no—
137C22×C127—21no—
138C22×C127—22no—
139C22×C127—42no—
140C22×C127—41no—
141C22×C127—41no—
142C22×C127—81no—
143C22×C127C2×#9911yescharacteristic
144C22×C127#41911yescharacteristic
145C22×C127#42111yescharacteristic
146C4×C127—21no—
147C4×C127—21no—
148C4×C127—42no—
149C4×C127—41no—
150C4×C127—42no—
151C4×C127—41no—
152C4×C127—41no—
153C4×C127—41no—
154C4×C127—41no—
155C4×C127—81no—
156C4×C127—81no—
157C4×C127—162no—
158#11810C12711yesmaximal, characteristic, direct product factor, Sylow
159C2×C127—21no—
160C2×C127—21no—
161C2×C127—42no—
162C2×C127#151111yescharacteristic
163C2×C127#212011yescharacteristic
164C2×C127#212611yescharacteristic
165#2396C2×C12711yescharacteristic
166#1820C2×C12711yescharacteristic
167#1464C2×C12711yescharacteristic
168#1352C2×C12712yes—
169#1351C2×C12712yes—
170C127#1181011yescharacteristic, direct product factor, Sylow
171C2×C4×Q8C4×C12711yescharacteristic, complemented
172C2×#117C22×C12711yescharacteristic
173#432—21no—
174#400C4×C12711yescharacteristic, complemented
175#399C22×C12711yescharacteristic
176#398—21no—
177#396—21no—
178#395C4×C12711yescharacteristic, complemented
179#393C22×C12711yescharacteristic
180#381—21no—
181C4×C4⋊C4—21no—
182C4×C4⋊C4C4×C12711yescharacteristic, complemented
183C4×C22⋊C4—21no—
184#342—21no—
185#342C22×C12712yes—
186#324—21no—
187#323C22×C12712yes—
188C22×Q8C2×C4×C12711yescharacteristic
189C23×C4D4×C12711yescharacteristic
190C4×Q8—41no—
191C4×Q8—41no—
192#117—41no—
193#117—41no—
194C2×C4⋊C4—21no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4C2×C4×C12711yescharacteristic
199C2×C4⋊C4C2×C4×C12711yescharacteristic
200C2×C4⋊C4D4×C12711yescharacteristic
201C2×C22⋊C4—21no—
202C2×C22⋊C4—21no—
203C2×C22⋊C4—22no—
204C2×C22⋊C4D4×C12711yescharacteristic
205C2×C22⋊C4C23×C12711yescharacteristic
206C2×C42—21no—
207C2×C42—21no—
208C2×C42C2×C4×C12711yescharacteristic
209C2×C42D4×C12711yescharacteristic
210C4⋊C8—41no—
211C22⋊C8—22no—
212#97—41no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—41no—
218#95—41no—
219#95C2×C4×C12711yescharacteristic
220#95C2×C4×C12711yescharacteristic
221C24C2×D4×C12711yescharacteristic
222C2×Q8—42no—
223C2×Q8—41no—
224C22×C4—21no—
225C22×C4—21no—
226C22×C4—22no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—41no—
232C22×C4—42no—
233C22×C4C22⋊C4×C12711yescharacteristic
234C22×C4C22⋊C4×C12711yescharacteristic
235C22×C4C22⋊C4×C12711yescharacteristic
236C22×C4C22⋊C4×C12711yescharacteristic
237C22×C4C22×C4×C12711yescharacteristic
238C22×C4C2×D4×C12711yescharacteristic
239C2×C8—42no—
240C4⋊C4—41no—
241C4⋊C4—41no—
242C4⋊C4—41no—
243C4⋊C4—42no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4—42no—
247C22⋊C4—41no—
248C22⋊C4—41no—
249C22⋊C4—42no—
250C22⋊C4—42no—
251C22⋊C4—42no—
252C22⋊C4—42no—
253C42—21no—
254C42—21no—
255C42—21no—
256C42—21no—
257C42—42no—
258C42—41no—
259C42—41no—
260C23—21no—
261C23—21no—
262C23—41no—
263C23—41no—
264C23C2×C22⋊C4×C12711yescharacteristic
265C23#137×C12712yes—
266Q8—42no—
267Q8—42no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
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×C4—41no—
295C2×C4—82no—
296C2×C4—82no—
297C2×C4—82no—
298C2×C4#99×C12711yescharacteristic
299C2×C4#99×C12711yescharacteristic
300C8—82no—
301C22—21no—
302C22—21no—
303C22—22no—
304C22—42no—
305C22—41no—
306C22—41no—
307C22—81no—
308C22C2×#99×C12711yescharacteristic
309C22#419×C12711yescharacteristic
310C22#421×C12711yescharacteristic
311C4—21no—
312C4—21no—
313C4—42no—
314C4—42no—
315C4—41no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—81no—
321C4—81no—
322C4—162no—
323C2—21no—
324C2—21no—
325C2—42no—
326C2C127×#151111yescharacteristic
327C2C127×#212011yescharacteristic
328C2C127×#212611yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C22⋊C4C23×C127
prime radicalC24×C127C2×D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×C4×Q8×C127C4semidirect
9. #400×C127C4semidirect
13. #395×C127C4semidirect
17. C4×C4⋊C4×C127C4semidirect
158. #11810C127direct (N × H)
170. C127#11810direct (N × H)
171. C2×C4×Q8C4×C127semidirect
174. #400C4×C127semidirect
178. #395C4×C127semidirect
182. C4×C4⋊C4C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#23962
C127×#18202
C127×#14642
C127×#13522
C127×#13512
#11810127