Finite Group Databasebeta

← C127×#11904 #44575577

Subgroups — C127×#11904 #44575577

Order 32512.

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

normal subgroups only

This group has 568 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×#2409C211yesmaximal, characteristic
2C127×#1800C211yesmaximal, characteristic
3C127×#1459C211yesmaximal, characteristic
4C127×#1354C214yesmaximal, complemented
5C23×Q8×C127C411yescharacteristic
6C2×C22⋊Q8×C127—21no—
7C2×C4×D4×C127C2211yescharacteristic
8#423×C127—21no—
9C2×#100×C127—21no—
10C2×C22⋊C8×C127—21no—
11#395×C127C2212yes—
12#393×C127C412yes—
13#391×C127—21no—
14#386×C127—21no—
15#385×C127—21no—
16#380×C127C411yescharacteristic
17#343×C127C2212yes—
18#324×C127C2212yes—
19#323×C127—21no—
20C22×Q8×C127—21no—
21C22×Q8×C127—41no—
22C22×Q8×C127—41no—
23C22×Q8×C127—44no—
24C22×Q8×C127C2×C412yes—
25C22×D4×C127D411yescharacteristic
26C23×C4×C127—21no—
27C23×C4×C127C2×C411yescharacteristic
28C23×C4×C127D411yescharacteristic
29C2×M16×C127—22no—
30C22×C8×C127—41no—
31C22⋊Q8×C127—44no—
32C4×D4×C127—41no—
33C4×D4×C127—41no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127—22no—
36C2×C4⋊C4×C127C2311yescharacteristic
37C2×C22⋊C4×C127—22no—
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127C2×C411yescharacteristic
40C2×C22⋊C4×C127D411yescharacteristic
41C2×C42×C127D411yescharacteristic
42C4⋊C8×C127—41no—
43C4⋊C8×C127—41no—
44#100×C127—42no—
45C22⋊C8×C127—22no—
46C22⋊C8×C127—41no—
47#95×C127—22no—
48#95×C127—22no—
49#95×C127C2×C412yes—
50C24×C127C22⋊C411yescharacteristic
51C24×C127C22⋊C411yescharacteristic
52C2×Q8×C127—24no—
53C2×Q8×C127—44no—
54C2×Q8×C127—42no—
55C2×Q8×C127—42no—
56C2×Q8×C127—44no—
57C2×Q8×C127—48no—
58C2×Q8×C127—44no—
59C2×Q8×C127—41no—
60C2×Q8×C127—41no—
61C2×D4×C127—41no—
62C2×D4×C127—41no—
63C2×D4×C127SD1612yes—
64C2×D4×C127Q1612yes—
65C22×C4×C127—22no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127—22no—
71C22×C4×C127—44no—
72C22×C4×C127—42no—
73C22×C4×C127—42no—
74C22×C4×C127—42no—
75C22×C4×C127C22⋊C411yescharacteristic
76C22×C4×C127C22⋊C411yescharacteristic
77C22×C4×C127C22×C411yescharacteristic
78C22×C4×C127C2×D411yescharacteristic
79C22×C4×C127C2×D411yescharacteristic
80M16×C127—42no—
81M16×C127—42no—
82C2×C8×C127—42no—
83C2×C8×C127—42no—
84C2×C8×C127—82no—
85C4⋊C4×C127—41no—
86C4⋊C4×C127—42no—
87C4⋊C4×C127—44no—
88C22⋊C4×C127—41no—
89C22⋊C4×C127—41no—
90C22⋊C4×C127—44no—
91C22⋊C4×C127—42no—
92C42×C127—21no—
93C42×C127—21no—
94C23×C127—21no—
95C23×C127—21no—
96C23×C127—21no—
97C23×C127—21no—
98C23×C127—41no—
99C23×C127—41no—
100C23×C127—41no—
101C23×C127—41no—
102C23×C127#10312yes—
103C23×C127#10312yes—
104C23×C127C2×C22⋊C411yescharacteristic
105Q8×C127—44no—
106Q8×C127—44no—
107Q8×C127—44no—
108Q8×C127—44no—
109D4×C127—42no—
110D4×C127—42no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—22no—
114C2×C4×C127—24no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—42no—
119C2×C4×C127—42no—
120C2×C4×C127—48no—
121C2×C4×C127—42no—
122C2×C4×C127—42no—
123C2×C4×C127—42no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—42no—
128C2×C4×C127—42no—
129C2×C4×C127—42no—
130C2×C4×C127—81no—
131C2×C4×C127#9911yescharacteristic
132C2×C4×C127#9911yescharacteristic
133C2×C4×C127C2×SD1611yescharacteristic
134C2×C4×C127C2×Q1611yescharacteristic
135C8×C127—82no—
136C8×C127—82no—
137C22×C127—21no—
138C22×C127—21no—
139C22×C127—22no—
140C22×C127—22no—
141C22×C127—42no—
142C22×C127—42no—
143C22×C127—42no—
144C22×C127—41no—
145C22×C127—41no—
146C22×C127—41no—
147C22×C127—41no—
148C22×C127—81no—
149C22×C127C2×#9911yescharacteristic
150C22×C127C2×#10311yescharacteristic
151C22×C127#42111yescharacteristic
152C4×C127—21no—
153C4×C127—21no—
154C4×C127—21no—
155C4×C127—41no—
156C4×C127—44no—
157C4×C127—41no—
158C4×C127—41no—
159C4×C127—82no—
160C4×C127AΣL(1,𝔽16)12yes—
161#11904C12711yesmaximal, characteristic, direct product factor, Sylow
162C2×C127—21no—
163C2×C127—21no—
164C2×C127—42no—
165C2×C127—42no—
166C2×C127#152011yescharacteristic
167C2×C127C2×AΣL(1,𝔽16)11yescharacteristic
168C2×C127#213511yescharacteristic
169#2409C2×C12711yescharacteristic
170#1800C2×C12711yescharacteristic
171#1459C2×C12711yescharacteristic
172#1354C2×C12714yescomplemented
173C127#1190411yescharacteristic, direct product factor, Sylow
174C23×Q8C4×C12711yescharacteristic
175C2×C22⋊Q8—21no—
176C2×C4×D4C22×C12711yescharacteristic
177#423—21no—
178C2×#100—21no—
179C2×C22⋊C8—21no—
180#395C22×C12712yes—
181#393C4×C12712yes—
182#391—21no—
183#386—21no—
184#385—21no—
185#380C4×C12711yescharacteristic
186#343C22×C12712yes—
187#324C22×C12712yes—
188#323—21no—
189C22×Q8—21no—
190C22×Q8—41no—
191C22×Q8—41no—
192C22×Q8—44no—
193C22×Q8C2×C4×C12712yes—
194C22×D4D4×C12711yescharacteristic
195C23×C4—21no—
196C23×C4C2×C4×C12711yescharacteristic
197C23×C4D4×C12711yescharacteristic
198C2×M16—22no—
199C22×C8—41no—
200C22⋊Q8—44no—
201C4×D4—41no—
202C4×D4—41no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4C23×C12711yescharacteristic
206C2×C22⋊C4—22no—
207C2×C22⋊C4—21no—
208C2×C22⋊C4C2×C4×C12711yescharacteristic
209C2×C22⋊C4D4×C12711yescharacteristic
210C2×C42D4×C12711yescharacteristic
211C4⋊C8—41no—
212C4⋊C8—41no—
213#100—42no—
214C22⋊C8—22no—
215C22⋊C8—41no—
216#95—22no—
217#95—22no—
218#95C2×C4×C12712yes—
219C24C22⋊C4×C12711yescharacteristic
220C24C22⋊C4×C12711yescharacteristic
221C2×Q8—24no—
222C2×Q8—44no—
223C2×Q8—42no—
224C2×Q8—42no—
225C2×Q8—44no—
226C2×Q8—48no—
227C2×Q8—44no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×D4—41no—
231C2×D4—41no—
232C2×D4SD16×C12712yes—
233C2×D4Q16×C12712yes—
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—44no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—42no—
244C22×C4C22⋊C4×C12711yescharacteristic
245C22×C4C22⋊C4×C12711yescharacteristic
246C22×C4C22×C4×C12711yescharacteristic
247C22×C4C2×D4×C12711yescharacteristic
248C22×C4C2×D4×C12711yescharacteristic
249M16—42no—
250M16—42no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—82no—
254C4⋊C4—41no—
255C4⋊C4—42no—
256C4⋊C4—44no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—44no—
260C22⋊C4—42no—
261C42—21no—
262C42—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23—41no—
271C23#103×C12712yes—
272C23#103×C12712yes—
273C23C2×C22⋊C4×C12711yescharacteristic
274Q8—44no—
275Q8—44no—
276Q8—44no—
277Q8—44no—
278D4—42no—
279D4—42no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—48no—
290C2×C4—42no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—42no—
298C2×C4—42no—
299C2×C4—81no—
300C2×C4#99×C12711yescharacteristic
301C2×C4#99×C12711yescharacteristic
302C2×C4C2×SD16×C12711yescharacteristic
303C2×C4C2×Q16×C12711yescharacteristic
304C8—82no—
305C8—82no—
306C22—21no—
307C22—21no—
308C22—22no—
309C22—22no—
310C22—42no—
311C22—42no—
312C22—42no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22—81no—
318C22C2×#99×C12711yescharacteristic
319C22C2×#103×C12711yescharacteristic
320C22#421×C12711yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—41no—
325C4—44no—
326C4—41no—
327C4—41no—
328C4—82no—
329C4AΣL(1,𝔽16)×C12712yes—
330C2—21no—
331C2—21no—
332C2—42no—
333C2—42no—
334C2C127×#152011yescharacteristic
335C2C2×AΣL(1,𝔽16)×C12711yescharacteristic
336C2C127×#213511yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC22×D4×C127D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×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×#1354C2semidirect
161. #11904C127direct (N × H)
172. #1354C2×C127semidirect
173. C127#11904direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#24092
C127×#18002
C127×#14592
C127×#13542
#11904127