Finite Group Databasebeta

← C127×#10830 #44574503

Subgroups — C127×#10830 #44574503

Order 32512.

678 conjugacy classes of subgroups.

The subgroup lattice has 334 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2274C211yesmaximal, characteristic
2C2×#344×C127C212yesmaximal
3C2×#344×C127C212yesmaximal
4C2×#343×C127C211yesmaximal, characteristic
5C2×#343×C127C211yesmaximal, characteristic
6C22×M16×C127C2212yes—
7C22×M16×C127C2212yes—
8C2×#117×C127C2211yescharacteristic
9C2×#117×C127C2211yescharacteristic
10C22×C4⋊C4×C127C2211yescharacteristic
11C4×C4⋊C4×C127—22no—
12C4×C4⋊C4×C127—22no—
13C4×C22⋊C4×C127C414yes—
14#344×C127—24no—
15#344×C127C418yescomplemented
16#343×C127—22no—
17#343×C127—22no—
18C23×C4×C127C2×C412yes—
19C23×C4×C127C2311yescharacteristic
20C2×M16×C127—22no—
21C2×M16×C127—22no—
22C2×M16×C127—22no—
23C2×M16×C127—22no—
24C2×M16×C127—22no—
25C2×M16×C127—22no—
26C2×M16×C127—22no—
27C2×M16×C127—22no—
28C2×M16×C127—22no—
29C2×M16×C127—22no—
30C2×M16×C127C2×C414yes—
31C2×M16×C127C2×C414yes—
32C22×C8×C127—22no—
33C22×C8×C127—22no—
34#117×C127—22no—
35#117×C127—21no—
36#117×C127—21no—
37#117×C127C2×C414yes—
38#117×C127D412yes—
39#117×C127Q812yes—
40C2×C4⋊C4×C127—21no—
41C2×C4⋊C4×C127—21no—
42C2×C4⋊C4×C127—22no—
43C2×C4⋊C4×C127—22no—
44C2×C4⋊C4×C127D412yes—
45C2×C4⋊C4×C127D412yes—
46C2×C22⋊C4×C127C2×C412yes—
47C2×C22⋊C4×C127C2×C412yes—
48C2×C42×C127—21no—
49C2×C42×C127—21no—
50C2×C42×C127—24no—
51#95×C127—24no—
52C24×C127C22×C411yescharacteristic
53C22×C4×C127—22no—
54C22×C4×C127—22no—
55C22×C4×C127—22no—
56C22×C4×C127—22no—
57C22×C4×C127—82no—
58C22×C4×C127C22⋊C414yes—
59C22×C4×C127C22×C412yes—
60C22×C4×C127C2×D411yescharacteristic
61C22×C4×C127C2×D411yescharacteristic
62C22×C4×C127C2×D411yescharacteristic
63C22×C4×C127C2×Q811yescharacteristic
64C22×C4×C127#4111yescharacteristic
65C22×C4×C127#4111yescharacteristic
66C22×C4×C127#4112yes—
67C22×C4×C127#4112yes—
68C22×C4×C127#4112yes—
69M16×C127—24no—
70M16×C127—24no—
71M16×C127—24no—
72M16×C127—24no—
73M16×C127—42no—
74M16×C127—42no—
75M16×C127—42no—
76M16×C127—42no—
77C2×C8×C127—24no—
78C2×C8×C127—24no—
79C2×C8×C127—42no—
80C2×C8×C127—42no—
81C2×C8×C127—42no—
82C2×C8×C127—42no—
83C4⋊C4×C127—24no—
84C4⋊C4×C127—22no—
85C4⋊C4×C127—22no—
86C4⋊C4×C127—24no—
87C4⋊C4×C127—24no—
88C22⋊C4×C127—22no—
89C22⋊C4×C127—22no—
90C22⋊C4×C127C4214yes—
91C22⋊C4×C127C4⋊C414yes—
92C42×C127—24no—
93C42×C127—22no—
94C42×C127—22no—
95C42×C127—84no—
96C23×C127—41no—
97C23×C127—41no—
98C23×C127C2×C4211yescharacteristic
99C23×C127C2×C22⋊C411yescharacteristic
100C23×C127C2×C4⋊C411yescharacteristic
101C23×C127#11711yescharacteristic
102C23×C127#11711yescharacteristic
103C23×C127#11711yescharacteristic
104C23×C127#11711yescharacteristic
105C2×C4×C127—24no—
106C2×C4×C127—24no—
107C2×C4×C127—24no—
108C2×C4×C127—42no—
109C2×C4×C127—42no—
110C2×C4×C127—42no—
111C2×C4×C127—42no—
112C2×C4×C127—44no—
113C2×C4×C127—82no—
114C2×C4×C127—82no—
115C2×C4×C127#11712yes—
116C2×C4×C127#11712yes—
117C2×C4×C127C4×D412yes—
118C2×C4×C127C4×D412yes—
119C2×C4×C127C4×D412yes—
120C2×C4×C127C4×Q812yes—
121C2×C4×C127#12111yescharacteristic
122C2×C4×C127#12111yescharacteristic
123C2×C4×C127C22⋊Q811yescharacteristic
124C2×C4×C127C22⋊Q811yescharacteristic
125C2×C4×C127#12312yes—
126C2×C4×C127#12312yes—
127C2×C4×C127#12412yes—
128C2×C4×C127#12512yes—
129C2×C4×C127#12612yes—
130C2×C4×C127#12612yes—
131C8×C127—44no—
132C8×C127—44no—
133C22×C127—21no—
134C22×C127—21no—
135C22×C127—21no—
136C22×C127—21no—
137C22×C127—21no—
138C22×C127—21no—
139C22×C127—41no—
140C22×C127—41no—
141C22×C127—41no—
142C22×C127—41no—
143C22×C127#37611yescharacteristic
144C22×C127C4×C22⋊C411yescharacteristic
145C22×C127C4×C4⋊C411yescharacteristic
146C22×C127#38011yescharacteristic
147C22×C127#38111yescharacteristic
148C22×C127#38211yescharacteristic
149C22×C127#38311yescharacteristic
150C4×C127—44no—
151C4×C127—44no—
152C4×C127—44no—
153C4×C127#38712yes—
154C4×C127#38712yes—
155C4×C127#38812yes—
156C4×C127#38812yes—
157#10830C12711yesmaximal, characteristic, direct product factor, Sylow
158C2×C127—21no—
159C2×C127—21no—
160C2×C127—21no—
161C2×C127—21no—
162C2×C127—21no—
163C2×C127—21no—
164C2×C127#143411yescharacteristic
165C2×C127#182911yescharacteristic
166C2×C127#183011yescharacteristic
167#2274C2×C12711yescharacteristic
168C2×#344C2×C12712yes—
169C2×#344C2×C12712yes—
170C2×#343C2×C12711yescharacteristic
171C2×#343C2×C12711yescharacteristic
172C127#1083011yescharacteristic, direct product factor, Sylow
173C22×M16C22×C12712yes—
174C22×M16C22×C12712yes—
175C2×#117C22×C12711yescharacteristic
176C2×#117C22×C12711yescharacteristic
177C22×C4⋊C4C22×C12711yescharacteristic
178C4×C4⋊C4—22no—
179C4×C4⋊C4—22no—
180C4×C22⋊C4C4×C12714yes—
181#344—24no—
182#344C4×C12718yescomplemented
183#343—22no—
184#343—22no—
185C23×C4C2×C4×C12712yes—
186C23×C4C23×C12711yescharacteristic
187C2×M16—22no—
188C2×M16—22no—
189C2×M16—22no—
190C2×M16—22no—
191C2×M16—22no—
192C2×M16—22no—
193C2×M16—22no—
194C2×M16—22no—
195C2×M16—22no—
196C2×M16—22no—
197C2×M16C2×C4×C12714yes—
198C2×M16C2×C4×C12714yes—
199C22×C8—22no—
200C22×C8—22no—
201#117—22no—
202#117—21no—
203#117—21no—
204#117C2×C4×C12714yes—
205#117D4×C12712yes—
206#117Q8×C12712yes—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—22no—
211C2×C4⋊C4D4×C12712yes—
212C2×C4⋊C4D4×C12712yes—
213C2×C22⋊C4C2×C4×C12712yes—
214C2×C22⋊C4C2×C4×C12712yes—
215C2×C42—21no—
216C2×C42—21no—
217C2×C42—24no—
218#95—24no—
219C24C22×C4×C12711yescharacteristic
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—22no—
223C22×C4—22no—
224C22×C4—82no—
225C22×C4C22⋊C4×C12714yes—
226C22×C4C22×C4×C12712yes—
227C22×C4C2×D4×C12711yescharacteristic
228C22×C4C2×D4×C12711yescharacteristic
229C22×C4C2×D4×C12711yescharacteristic
230C22×C4C2×Q8×C12711yescharacteristic
231C22×C4#41×C12711yescharacteristic
232C22×C4#41×C12711yescharacteristic
233C22×C4#41×C12712yes—
234C22×C4#41×C12712yes—
235C22×C4#41×C12712yes—
236M16—24no—
237M16—24no—
238M16—24no—
239M16—24no—
240M16—42no—
241M16—42no—
242M16—42no—
243M16—42no—
244C2×C8—24no—
245C2×C8—24no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—42no—
249C2×C8—42no—
250C4⋊C4—24no—
251C4⋊C4—22no—
252C4⋊C4—22no—
253C4⋊C4—24no—
254C4⋊C4—24no—
255C22⋊C4—22no—
256C22⋊C4—22no—
257C22⋊C4C42×C12714yes—
258C22⋊C4C4⋊C4×C12714yes—
259C42—24no—
260C42—22no—
261C42—22no—
262C42—84no—
263C23—41no—
264C23—41no—
265C23C2×C42×C12711yescharacteristic
266C23C2×C22⋊C4×C12711yescharacteristic
267C23C2×C4⋊C4×C12711yescharacteristic
268C23#117×C12711yescharacteristic
269C23#117×C12711yescharacteristic
270C23#117×C12711yescharacteristic
271C23#117×C12711yescharacteristic
272C2×C4—24no—
273C2×C4—24no—
274C2×C4—24no—
275C2×C4—42no—
276C2×C4—42no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—44no—
280C2×C4—82no—
281C2×C4—82no—
282C2×C4#117×C12712yes—
283C2×C4#117×C12712yes—
284C2×C4C4×D4×C12712yes—
285C2×C4C4×D4×C12712yes—
286C2×C4C4×D4×C12712yes—
287C2×C4C4×Q8×C12712yes—
288C2×C4#121×C12711yescharacteristic
289C2×C4#121×C12711yescharacteristic
290C2×C4C22⋊Q8×C12711yescharacteristic
291C2×C4C22⋊Q8×C12711yescharacteristic
292C2×C4#123×C12712yes—
293C2×C4#123×C12712yes—
294C2×C4#124×C12712yes—
295C2×C4#125×C12712yes—
296C2×C4#126×C12712yes—
297C2×C4#126×C12712yes—
298C8—44no—
299C8—44no—
300C22—21no—
301C22—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—21no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22#376×C12711yescharacteristic
311C22C4×C22⋊C4×C12711yescharacteristic
312C22C4×C4⋊C4×C12711yescharacteristic
313C22#380×C12711yescharacteristic
314C22#381×C12711yescharacteristic
315C22#382×C12711yescharacteristic
316C22#383×C12711yescharacteristic
317C4—44no—
318C4—44no—
319C4—44no—
320C4#387×C12712yes—
321C4#387×C12712yes—
322C4#388×C12712yes—
323C4#388×C12712yes—
324C2—21no—
325C2—21no—
326C2—21no—
327C2—21no—
328C2—21no—
329C2—21no—
330C2C127×#143411yescharacteristic
331C2C127×#182911yescharacteristic
332C2C127×#183011yescharacteristic
subgroupG/H
center, socleC22×C127#381
commutatorC23C2×C42×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127C22×C4
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
15. #344×C127C4semidirect
157. #10830C127direct (N × H)
172. C127#10830direct (N × H)
182. #344C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22742
C2×#344×C1272
C2×#343×C1272
#10830127