Finite Group Databasebeta

← C127×#8388 #44572061

Subgroups — C127×#8388 #44572061

Order 32512.

966 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Q8×C127C211yesmaximal, characteristic
2C127×#1801C211yesmaximal, characteristic, complemented
3C127×#1546C212yesmaximal, complemented
4C127×#1486C212yesmaximal
5C127×#1461C211yesmaximal, characteristic, complemented
6C23×Q8×C127—21no—
7D4×Q8×C127—24no—
8D4×Q8×C127—24no—
9C2×C4⋊Q8×C127C412yes—
10C2×C4⋊Q8×C127C2211yescharacteristic
11C2×C22⋊Q8×C127—21no—
12C2×C22⋊Q8×C127—22no—
13C2×C4×Q8×C127C2211yescharacteristic
14C2×C4×D4×C127C412yes—
15C2×C4×D4×C127C2211yescharacteristic
16#431×C127C2212yes—
17#423×C127C2212yes—
18C2×#101×C127—21no—
19#343×C127—21no—
20#332×C127—24no—
21D4⋊C8×C127—24no—
22#324×C127—22no—
23C22×Q8×C127—28no—
24C22×Q8×C127—22no—
25C22×Q8×C127—21no—
26C22×Q8×C127—44no—
27C22×Q8×C127—42no—
28C22×Q8×C127—42no—
29C22×Q8×C127D411yescharacteristic
30C22×D4×C127C2×C411yescharacteristic
31C23×C4×C127—22no—
32C23×C4×C127—21no—
33C2×M16×C127—22no—
34C4⋊Q8×C127—24no—
35C4⋊Q8×C127—24no—
36C4⋊Q8×C127—22no—
37C4⋊Q8×C127D414yes—
38C22⋊Q8×C127—28no—
39C22⋊Q8×C127—216no—
40C4×Q8×C127—22no—
41C4×Q8×C127—22no—
42C4×D4×C127—24no—
43C4×D4×C127—24no—
44C4×D4×C127—22no—
45C4×D4×C127D414yes—
46C2×C4⋊C4×C127—22no—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊C4×C127C2×C412yes—
49C2×C4⋊C4×C127C2×C411yescharacteristic
50C2×C4⋊C4×C127D412yes—
51C2×C4⋊C4×C127D411yescharacteristic
52C2×C22⋊C4×C127—22no—
53C2×C22⋊C4×C127—21no—
54C2×C42×C127C2×C412yes—
55C2×C42×C127C2311yescharacteristic
56C4⋊C8×C127—22no—
57C4⋊C8×C127—22no—
58C4⋊C8×C127—22no—
59#101×C127—42no—
60C22⋊C8×C127—22no—
61C4×C8×C127—22no—
62C24×C127—21no—
63C2×Q8×C127—28no—
64C2×Q8×C127—22no—
65C2×Q8×C127—24no—
66C2×Q8×C127—22no—
67C2×Q8×C127—44no—
68C2×Q8×C127—416no—
69C2×Q8×C127—416no—
70C2×Q8×C127—44no—
71C2×Q8×C127—41no—
72C2×Q8×C127—41no—
73C2×Q8×C127—42no—
74C2×Q8×C127D812yes—
75C2×Q8×C127SD1612yes—
76C2×D4×C127—24no—
77C2×D4×C127—21no—
78C2×D4×C127C22⋊C412yes—
79C22×C4×C127—28no—
80C22×C4×C127—22no—
81C22×C4×C127—21no—
82C22×C4×C127—24no—
83C22×C4×C127—44no—
84C22×C4×C127—44no—
85C22×C4×C127—41no—
86C22×C4×C127—41no—
87C22×C4×C127—42no—
88C22×C4×C127C22⋊C412yes—
89C22×C4×C127C22⋊C412yes—
90C22×C4×C127C22×C411yescharacteristic
91C22×C4×C127C2×D411yescharacteristic
92C22×C4×C127C2×D411yescharacteristic
93M16×C127—42no—
94M16×C127—42no—
95C2×C8×C127—42no—
96C2×C8×C127—42no—
97C4⋊C4×C127—28no—
98C4⋊C4×C127—21no—
99C4⋊C4×C127—22no—
100C4⋊C4×C127—24no—
101C4⋊C4×C127—24no—
102C4⋊C4×C127—22no—
103C4⋊C4×C127C22⋊C414yes—
104C4⋊C4×C127C22⋊C412yes—
105C22⋊C4×C127—28no—
106C22⋊C4×C127—24no—
107C42×C127—22no—
108C42×C127—22no—
109C42×C127C2×D412yes—
110C42×C127C2×D412yes—
111C23×C127—24no—
112C23×C127—22no—
113C23×C127—42no—
114C23×C127—41no—
115C23×C127—41no—
116C23×C127C2×C22⋊C411yescharacteristic
117Q8×C127—24no—
118Q8×C127—24no—
119Q8×C127—416no—
120Q8×C127—44no—
121Q8×C127—44no—
122D4×C127—24no—
123D4×C127—22no—
124D4×C127#10114yescomplemented
125C2×C4×C127—22no—
126C2×C4×C127—22no—
127C2×C4×C127—22no—
128C2×C4×C127—22no—
129C2×C4×C127—24no—
130C2×C4×C127—22no—
131C2×C4×C127—41no—
132C2×C4×C127—416no—
133C2×C4×C127—42no—
134C2×C4×C127—41no—
135C2×C4×C127—42no—
136C2×C4×C127—41no—
137C2×C4×C127—44no—
138C2×C4×C127—44no—
139C2×C4×C127—42no—
140C2×C4×C127#10214yes—
141C2×C4×C127C2×C22⋊C411yescharacteristic
142C2×C4×C127C2×C22⋊C411yescharacteristic
143C2×C4×C127#12012yes—
144C2×C4×C127#12012yes—
145C2×C4×C127C2×D811yescharacteristic
146C2×C4×C127C2×SD1611yescharacteristic
147C2×C4×C127AGL(1,ℤ/8)12yes—
148C8×C127—82no—
149C8×C127—82no—
150C22×C127—21no—
151C22×C127—21no—
152C22×C127—24no—
153C22×C127—44no—
154C22×C127—44no—
155C22×C127—42no—
156C22×C127—42no—
157C22×C127#37911yescharacteristic
158C22×C127C2×#10211yescharacteristic
159C22×C127#41811yescharacteristic
160C4×C127—22no—
161C4×C127—21no—
162C4×C127—24no—
163C4×C127—42no—
164C4×C127—44no—
165C4×C127—42no—
166C4×C127C2×#10112yes—
167C4×C127#44712yes—
168C4×C127#45012yes—
169#8388C12711yesmaximal, characteristic, direct product factor, Sylow
170C2×C127—21no—
171C2×C127—21no—
172C2×C127—44no—
173C2×C127#178411yescharacteristic
174C2×C127#178611yescharacteristic
175C2×C127#179611yescharacteristic
176C2×D4×Q8C2×C12711yescharacteristic
177#1801C2×C12711yescharacteristic, complemented
178#1546C2×C12712yescomplemented
179#1486C2×C12712yes—
180#1461C2×C12711yescharacteristic, complemented
181C127#838811yescharacteristic, direct product factor, Sylow
182C23×Q8—21no—
183D4×Q8—24no—
184D4×Q8—24no—
185C2×C4⋊Q8C4×C12712yes—
186C2×C4⋊Q8C22×C12711yescharacteristic
187C2×C22⋊Q8—21no—
188C2×C22⋊Q8—22no—
189C2×C4×Q8C22×C12711yescharacteristic
190C2×C4×D4C4×C12712yes—
191C2×C4×D4C22×C12711yescharacteristic
192#431C22×C12712yes—
193#423C22×C12712yes—
194C2×#101—21no—
195#343—21no—
196#332—24no—
197D4⋊C8—24no—
198#324—22no—
199C22×Q8—28no—
200C22×Q8—22no—
201C22×Q8—21no—
202C22×Q8—44no—
203C22×Q8—42no—
204C22×Q8—42no—
205C22×Q8D4×C12711yescharacteristic
206C22×D4C2×C4×C12711yescharacteristic
207C23×C4—22no—
208C23×C4—21no—
209C2×M16—22no—
210C4⋊Q8—24no—
211C4⋊Q8—24no—
212C4⋊Q8—22no—
213C4⋊Q8D4×C12714yes—
214C22⋊Q8—28no—
215C22⋊Q8—216no—
216C4×Q8—22no—
217C4×Q8—22no—
218C4×D4—24no—
219C4×D4—24no—
220C4×D4—22no—
221C4×D4D4×C12714yes—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4C2×C4×C12712yes—
225C2×C4⋊C4C2×C4×C12711yescharacteristic
226C2×C4⋊C4D4×C12712yes—
227C2×C4⋊C4D4×C12711yescharacteristic
228C2×C22⋊C4—22no—
229C2×C22⋊C4—21no—
230C2×C42C2×C4×C12712yes—
231C2×C42C23×C12711yescharacteristic
232C4⋊C8—22no—
233C4⋊C8—22no—
234C4⋊C8—22no—
235#101—42no—
236C22⋊C8—22no—
237C4×C8—22no—
238C24—21no—
239C2×Q8—28no—
240C2×Q8—22no—
241C2×Q8—24no—
242C2×Q8—22no—
243C2×Q8—44no—
244C2×Q8—416no—
245C2×Q8—416no—
246C2×Q8—44no—
247C2×Q8—41no—
248C2×Q8—41no—
249C2×Q8—42no—
250C2×Q8D8×C12712yes—
251C2×Q8SD16×C12712yes—
252C2×D4—24no—
253C2×D4—21no—
254C2×D4C22⋊C4×C12712yes—
255C22×C4—28no—
256C22×C4—22no—
257C22×C4—21no—
258C22×C4—24no—
259C22×C4—44no—
260C22×C4—44no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—42no—
264C22×C4C22⋊C4×C12712yes—
265C22×C4C22⋊C4×C12712yes—
266C22×C4C22×C4×C12711yescharacteristic
267C22×C4C2×D4×C12711yescharacteristic
268C22×C4C2×D4×C12711yescharacteristic
269M16—42no—
270M16—42no—
271C2×C8—42no—
272C2×C8—42no—
273C4⋊C4—28no—
274C4⋊C4—21no—
275C4⋊C4—22no—
276C4⋊C4—24no—
277C4⋊C4—24no—
278C4⋊C4—22no—
279C4⋊C4C22⋊C4×C12714yes—
280C4⋊C4C22⋊C4×C12712yes—
281C22⋊C4—28no—
282C22⋊C4—24no—
283C42—22no—
284C42—22no—
285C42C2×D4×C12712yes—
286C42C2×D4×C12712yes—
287C23—24no—
288C23—22no—
289C23—42no—
290C23—41no—
291C23—41no—
292C23C2×C22⋊C4×C12711yescharacteristic
293Q8—24no—
294Q8—24no—
295Q8—416no—
296Q8—44no—
297Q8—44no—
298D4—24no—
299D4—22no—
300D4#101×C12714yescomplemented
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—41no—
308C2×C4—416no—
309C2×C4—42no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—44no—
314C2×C4—44no—
315C2×C4—42no—
316C2×C4#102×C12714yes—
317C2×C4C2×C22⋊C4×C12711yescharacteristic
318C2×C4C2×C22⋊C4×C12711yescharacteristic
319C2×C4#120×C12712yes—
320C2×C4#120×C12712yes—
321C2×C4C2×D8×C12711yescharacteristic
322C2×C4C2×SD16×C12711yescharacteristic
323C2×C4AGL(1,ℤ/8)×C12712yes—
324C8—82no—
325C8—82no—
326C22—21no—
327C22—21no—
328C22—24no—
329C22—44no—
330C22—44no—
331C22—42no—
332C22—42no—
333C22#379×C12711yescharacteristic
334C22C2×#102×C12711yescharacteristic
335C22#418×C12711yescharacteristic
336C4—21no—
337C4—24no—
338C4—22no—
339C4—44no—
340C4—42no—
341C4—42no—
342C4C2×#101×C12712yes—
343C4#447×C12712yes—
344C4#450×C12712yes—
345C2—21no—
346C2—21no—
347C2—44no—
348C2C127×#178411yescharacteristic
349C2C127×#178611yescharacteristic
350C2C127×#179611yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC22×D4×C127C2×C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1801C2semidirect
3. C127×#1546C2semidirect
5. C127×#1461C2semidirect
124. D4×C127#101semidirect
169. #8388C127direct (N × H)
177. #1801C2×C127semidirect
178. #1546C2×C127semidirect
180. #1461C2×C127semidirect
181. C127#8388direct (N × H)
300. D4#101×C127semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Q8×C1272
C127×#18012
C127×#15462
C127×#14862
C127×#14612
#8388127