Finite Group Databasebeta

← C127×#21829 #44585502

Subgroups — C127×#21829 #44585502

Order 32512.

1194 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊Q8×C127C211yesmaximal, characteristic
2C127×#2920C212yesmaximal
3C127×#1997C218yesmaximal, complemented
4C127×#1821C214yesmaximal
5C23×Q8×C127C412yes—
6C2×C4⋊Q8×C127—22no—
7C2×C4⋊Q8×C127—22no—
8C2×C4⋊Q8×C127—22no—
9C2×C4⋊Q8×C127—22no—
10C2×C4⋊Q8×C127C414yes—
11C2×C4⋊Q8×C127C2214yes—
12C22×C4⋊C4×C127C412yes—
13C22×C4⋊C4×C127C2212yes—
14C22×C42×C127C2211yescharacteristic
15#432×C127—22no—
16#432×C127—22no—
17#431×C127—22no—
18#431×C127—22no—
19#423×C127C2214yes—
20#407×C127C2214yes—
21C4×M16×C127C2214yes—
22#343×C127C22116yes—
23C22×Q8×C127—24no—
24C22×Q8×C127—22no—
25C22×Q8×C127—22no—
26C22×Q8×C127—48no—
27C22×Q8×C127C2×C418yes—
28C23×C4×C127C2×C411yescharacteristic
29C23×C4×C127C2×C411yescharacteristic
30C23×C4×C127C2×C414yes—
31C23×C4×C127C2311yescharacteristic
32C2×M16×C127C2318yes—
33C4⋊Q8×C127—24no—
34C4⋊Q8×C127—24no—
35C4⋊Q8×C127—24no—
36C4⋊Q8×C127—24no—
37C4⋊Q8×C127—24no—
38C4⋊Q8×C127—24no—
39C4⋊Q8×C127—24no—
40C4⋊Q8×C127—24no—
41C2×C4⋊C4×C127—22no—
42C2×C4⋊C4×C127—24no—
43C2×C4⋊C4×C127—22no—
44C2×C4⋊C4×C127—24no—
45C2×C4⋊C4×C127—24no—
46C2×C4⋊C4×C127C2×C418yes—
47C2×C4⋊C4×C127C2×C414yes—
48C2×C4⋊C4×C127C2314yes—
49C2×C42×C127C2×C412yes—
50C2×C42×C127D412yes—
51C2×C42×C127D412yes—
52C2×C42×C127D412yes—
53C2×C42×C127D412yes—
54C2×C42×C127C2312yes—
55C4⋊C8×C127—24no—
56C4⋊C8×C127—24no—
57C22⋊C8×C127—24no—
58C22⋊C8×C127—24no—
59#97×C127—24no—
60C4×C8×C127—24no—
61C24×C127C22×C411yescharacteristic
62C2×Q8×C127—28no—
63C2×Q8×C127—28no—
64C2×Q8×C127—416no—
65C2×Q8×C127—48no—
66C2×Q8×C127—416no—
67C2×Q8×C127—48no—
68C22×C4×C127—24no—
69C22×C4×C127—24no—
70C22×C4×C127—24no—
71C22×C4×C127—24no—
72C22×C4×C127—24no—
73C22×C4×C127—48no—
74C22×C4×C127C22⋊C411yescharacteristic
75C22×C4×C127C22⋊C412yes—
76C22×C4×C127C22⋊C411yescharacteristic
77C22×C4×C127C22⋊C412yes—
78C22×C4×C127C22⋊C411yescharacteristic
79C22×C4×C127C22⋊C411yescharacteristic
80C22×C4×C127C22×C411yescharacteristic
81C22×C4×C127C22×C412yes—
82C22×C4×C127C22×C412yes—
83C22×C4×C127C22×C418yes—
84C22×C4×C127C2×D412yes—
85C22×C4×C127C2×D412yes—
86C22×C4×C127C2411yescharacteristic
87M16×C127—216no—
88C2×C8×C127—28no—
89C4⋊C4×C127—28no—
90C4⋊C4×C127—28no—
91C4⋊C4×C127—28no—
92C4⋊C4×C127—28no—
93C42×C127C22⋊C412yes—
94C42×C127C22⋊C412yes—
95C42×C127C22⋊C412yes—
96C42×C127C22⋊C412yes—
97C42×C127C2×D412yes—
98C42×C127C2×D412yes—
99C42×C127C2×D412yes—
100C42×C127C2×D412yes—
101C23×C127—22no—
102C23×C127—22no—
103C23×C127—22no—
104C23×C127C2×C22⋊C411yescharacteristic
105C23×C127C2×C22⋊C411yescharacteristic
106C23×C127C23×C411yescharacteristic
107Q8×C127—416no—
108Q8×C127—416no—
109C2×C4×C127—22no—
110C2×C4×C127—22no—
111C2×C4×C127—22no—
112C2×C4×C127—24no—
113C2×C4×C127—24no—
114C2×C4×C127—24no—
115C2×C4×C127—24no—
116C2×C4×C127—24no—
117C2×C4×C127—24no—
118C2×C4×C127—28no—
119C2×C4×C127—48no—
120C2×C4×C127—48no—
121C2×C4×C127—48no—
122C2×C4×C127#10014yes—
123C2×C4×C127#10114yes—
124C2×C4×C127C2×C22⋊C412yes—
125C2×C4×C127C2×C22⋊C412yes—
126C2×C4×C127C2×C22⋊C412yes—
127C2×C4×C127C2×C22⋊C412yes—
128C2×C4×C127C2×C22⋊C412yes—
129C2×C4×C127C22×D412yes—
130C2×C4×C1272−1+414yes—
131C8×C127—48no—
132C22×C127—28no—
133C22×C127—21no—
134C22×C127—21no—
135C22×C127—21no—
136C22×C127—21no—
137C22×C127—21no—
138C22×C127—21no—
139C22×C127C2×#10012yes—
140C22×C127C2×#10112yes—
141C22×C127C22×C22⋊C411yescharacteristic
142C22×C127#51912yes—
143C4×C127—22no—
144C4×C127—22no—
145C4×C127—22no—
146C4×C127—48no—
147C4×C127C2×#10014yes—
148C4×C127C2×#10114yes—
149C4×C127#53614yes—
150#21829C12711yesmaximal, characteristic, direct product factor, Sylow
151C2×C127—22no—
152C2×C127—22no—
153C2×C127—22no—
154C2×C127#231011yescharacteristic
155C2×C127C22×#10011yescharacteristic
156C2×C127C22×#10111yescharacteristic
157C22×C4⋊Q8C2×C12711yescharacteristic
158#2920C2×C12712yes—
159#1997C2×C12718yescomplemented
160#1821C2×C12714yes—
161C127#2182911yescharacteristic, direct product factor, Sylow
162C23×Q8C4×C12712yes—
163C2×C4⋊Q8—22no—
164C2×C4⋊Q8—22no—
165C2×C4⋊Q8—22no—
166C2×C4⋊Q8—22no—
167C2×C4⋊Q8C4×C12714yes—
168C2×C4⋊Q8C22×C12714yes—
169C22×C4⋊C4C4×C12712yes—
170C22×C4⋊C4C22×C12712yes—
171C22×C42C22×C12711yescharacteristic
172#432—22no—
173#432—22no—
174#431—22no—
175#431—22no—
176#423C22×C12714yes—
177#407C22×C12714yes—
178C4×M16C22×C12714yes—
179#343C22×C127116yes—
180C22×Q8—24no—
181C22×Q8—22no—
182C22×Q8—22no—
183C22×Q8—48no—
184C22×Q8C2×C4×C12718yes—
185C23×C4C2×C4×C12711yescharacteristic
186C23×C4C2×C4×C12711yescharacteristic
187C23×C4C2×C4×C12714yes—
188C23×C4C23×C12711yescharacteristic
189C2×M16C23×C12718yes—
190C4⋊Q8—24no—
191C4⋊Q8—24no—
192C4⋊Q8—24no—
193C4⋊Q8—24no—
194C4⋊Q8—24no—
195C4⋊Q8—24no—
196C4⋊Q8—24no—
197C4⋊Q8—24no—
198C2×C4⋊C4—22no—
199C2×C4⋊C4—24no—
200C2×C4⋊C4—22no—
201C2×C4⋊C4—24no—
202C2×C4⋊C4—24no—
203C2×C4⋊C4C2×C4×C12718yes—
204C2×C4⋊C4C2×C4×C12714yes—
205C2×C4⋊C4C23×C12714yes—
206C2×C42C2×C4×C12712yes—
207C2×C42D4×C12712yes—
208C2×C42D4×C12712yes—
209C2×C42D4×C12712yes—
210C2×C42D4×C12712yes—
211C2×C42C23×C12712yes—
212C4⋊C8—24no—
213C4⋊C8—24no—
214C22⋊C8—24no—
215C22⋊C8—24no—
216#97—24no—
217C4×C8—24no—
218C24C22×C4×C12711yescharacteristic
219C2×Q8—28no—
220C2×Q8—28no—
221C2×Q8—416no—
222C2×Q8—48no—
223C2×Q8—416no—
224C2×Q8—48no—
225C22×C4—24no—
226C22×C4—24no—
227C22×C4—24no—
228C22×C4—24no—
229C22×C4—24no—
230C22×C4—48no—
231C22×C4C22⋊C4×C12711yescharacteristic
232C22×C4C22⋊C4×C12712yes—
233C22×C4C22⋊C4×C12711yescharacteristic
234C22×C4C22⋊C4×C12712yes—
235C22×C4C22⋊C4×C12711yescharacteristic
236C22×C4C22⋊C4×C12711yescharacteristic
237C22×C4C22×C4×C12711yescharacteristic
238C22×C4C22×C4×C12712yes—
239C22×C4C22×C4×C12712yes—
240C22×C4C22×C4×C12718yes—
241C22×C4C2×D4×C12712yes—
242C22×C4C2×D4×C12712yes—
243C22×C4C24×C12711yescharacteristic
244M16—216no—
245C2×C8—28no—
246C4⋊C4—28no—
247C4⋊C4—28no—
248C4⋊C4—28no—
249C4⋊C4—28no—
250C42C22⋊C4×C12712yes—
251C42C22⋊C4×C12712yes—
252C42C22⋊C4×C12712yes—
253C42C22⋊C4×C12712yes—
254C42C2×D4×C12712yes—
255C42C2×D4×C12712yes—
256C42C2×D4×C12712yes—
257C42C2×D4×C12712yes—
258C23—22no—
259C23—22no—
260C23—22no—
261C23C2×C22⋊C4×C12711yescharacteristic
262C23C2×C22⋊C4×C12711yescharacteristic
263C23C23×C4×C12711yescharacteristic
264Q8—416no—
265Q8—416no—
266C2×C4—22no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—24no—
270C2×C4—24no—
271C2×C4—24no—
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—24no—
275C2×C4—28no—
276C2×C4—48no—
277C2×C4—48no—
278C2×C4—48no—
279C2×C4#100×C12714yes—
280C2×C4#101×C12714yes—
281C2×C4C2×C22⋊C4×C12712yes—
282C2×C4C2×C22⋊C4×C12712yes—
283C2×C4C2×C22⋊C4×C12712yes—
284C2×C4C2×C22⋊C4×C12712yes—
285C2×C4C2×C22⋊C4×C12712yes—
286C2×C4C22×D4×C12712yes—
287C2×C42−1+4×C12714yes—
288C8—48no—
289C22—28no—
290C22—21no—
291C22—21no—
292C22—21no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22C2×#100×C12712yes—
297C22C2×#101×C12712yes—
298C22C22×C22⋊C4×C12711yescharacteristic
299C22#519×C12712yes—
300C4—22no—
301C4—22no—
302C4—22no—
303C4—48no—
304C4C2×#100×C12714yes—
305C4C2×#101×C12714yes—
306C4#536×C12714yes—
307C2—22no—
308C2—22no—
309C2—22no—
310C2C127×#231011yescharacteristic
311C2C22×#100×C12711yescharacteristic
312C2C22×#101×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C22×C22⋊C4
commutatorC23C23×C4×C127
Frattini, cosocleC22×C4C24×C127
prime radicalC24×C127C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1997C2semidirect
150. #21829C127direct (N × H)
159. #1997C2×C127semidirect
161. C127#21829direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4⋊Q8×C1272
C127×#29202
C127×#19972
C127×#18212
#21829127