Finite Group Databasebeta

← C127×#2033 #30634985

Subgroups — C127×#2033 #30634985

Order 16256.

368 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C2×#121×C127C211yesmaximal, characteristic
2C2×#107×C127C211yesmaximal, characteristic, complemented
3C2×#102×C127C211yesmaximal, characteristic, complemented
4C2×#102×C127C211yesmaximal, characteristic, complemented
5C2×C22⋊C8×C127C211yesmaximal, characteristic, complemented
6#380×C127C211yesmaximal, characteristic, complemented
7#340×C127C211yesmaximal, characteristic, complemented
8C22×D4×C127—21no—
9C22×D4×C127C2211yescharacteristic
10C23×C4×C127C2211yescharacteristic
11C22×C8×C127C2211yescharacteristic
12C22×C8×C127C2211yescharacteristic
13#121×C127—22no—
14#121×C127—22no—
15C2×C4⋊C4×C127C2211yescharacteristic
16C2×C4⋊C4×C127C2211yescharacteristic
17C2×C4⋊C4×C127C2211yescharacteristic
18C2×C22⋊C4×C127—21no—
19C2×C22⋊C4×C127—21no—
20#107×C127—22no—
21#102×C127—22no—
22#102×C127—22no—
23C22⋊C8×C127—22no—
24#95×C127—21no—
25C24×C127—21no—
26C24×C127D411yescharacteristic
27C2×D4×C127—24no—
28C2×D4×C127—21no—
29C2×D4×C127—21no—
30C2×D4×C127—21no—
31C2×D4×C127—21no—
32C2×D4×C127—21no—
33C2×D4×C127—42no—
34C2×D4×C127—42no—
35C2×D4×C127D412yes—
36C22×C4×C127—21no—
37C22×C4×C127—21no—
38C22×C4×C127—21no—
39C22×C4×C127—21no—
40C22×C4×C127—21no—
41C22×C4×C127—21no—
42C22×C4×C127—21no—
43C22×C4×C127—21no—
44C22×C4×C127—21no—
45C22×C4×C127D411yescharacteristic
46C22×C4×C127C2311yescharacteristic
47C2×C8×C127—21no—
48C2×C8×C127—21no—
49C2×C8×C127—21no—
50C2×C8×C127—21no—
51C2×C8×C127—21no—
52C2×C8×C127D412yescomplemented
53C4⋊C4×C127—21no—
54C4⋊C4×C127—21no—
55C4⋊C4×C127—21no—
56C4⋊C4×C127—21no—
57C4⋊C4×C127—21no—
58C4⋊C4×C127D412yes—
59C22⋊C4×C127—24no—
60C22⋊C4×C127—42no—
61C23×C127—21no—
62C23×C127—21no—
63C23×C127—21no—
64C23×C127—21no—
65C23×C127—21no—
66C23×C127—21no—
67C23×C127—22no—
68C23×C127—41no—
69C23×C127—41no—
70C23×C127—41no—
71C23×C127—41no—
72C23×C127—41no—
73C23×C127—41no—
74C23×C127D812yes—
75C23×C127C2×D411yescharacteristic
76D4×C127—22no—
77D4×C127—22no—
78D4×C127—48no—
79D4×C127—41no—
80D4×C127—41no—
81C2×C4×C127—21no—
82C2×C4×C127—22no—
83C2×C4×C127—21no—
84C2×C4×C127—21no—
85C2×C4×C127—41no—
86C2×C4×C127—41no—
87C2×C4×C127—41no—
88C2×C4×C127—41no—
89C2×C4×C127—41no—
90C2×C4×C127—41no—
91C2×C4×C127—41no—
92C2×C4×C127—41no—
93C2×C4×C127—41no—
94C2×C4×C127—41no—
95C2×C4×C127—41no—
96C2×C4×C127—41no—
97C2×C4×C127C2×D411yescharacteristic
98C2×C4×C127C2×D411yescharacteristic
99C2×C4×C127C2×D411yescharacteristic
100C2×C4×C127#4111yescharacteristic
101C2×C4×C127#4111yescharacteristic
102C2×C4×C127#4111yescharacteristic
103C8×C127—22no—
104C8×C127—41no—
105C22×C127—22no—
106C22×C127—22no—
107C22×C127—22no—
108C22×C127—41no—
109C22×C127—41no—
110C22×C127—41no—
111C22×C127—41no—
112C22×C127—42no—
113C22×C127—42no—
114C22×C127—42no—
115C22×C127—81no—
116C22×C127—81no—
117C22×C127—81no—
118C22×C127—81no—
119C22×C127#12011yescharacteristic
120C22×C127#12111yescharacteristic
121C22×C127#12311yescharacteristic
122C22×C127C2×D811yescharacteristic
123C22×C127#13511yescharacteristic
124C22×C127AGL(1,ℤ/8)11yescharacteristic
125C22×C127#13711yescharacteristic
126C4×C127—41no—
127C4×C127—42no—
128C4×C127—81no—
129C4×C127—81no—
130C4×C127#12111yescharacteristic
131C4×C127#12111yescharacteristic
132C4×C127#12311yescharacteristic
133C4×C127#12411yescharacteristic
134C2×C127—42no—
135C2×C127—82no—
136C2×C127#39411yescharacteristic
137C2×C127#44711yescharacteristic
138C2×C127#45211yescharacteristic
139C2×C127#46611yescharacteristic
140C2×C127#46811yescharacteristic
141C2×C127#48011yescharacteristic
142C2×C127#48211yescharacteristic
143#2033C12711yesmaximal, characteristic, direct product factor, Sylow
144C127#203311yescharacteristic, direct product factor, Sylow
145C2×#121C2×C12711yescharacteristic
146C2×#107C2×C12711yescharacteristic, complemented
147C2×#102C2×C12711yescharacteristic, complemented
148C2×#102C2×C12711yescharacteristic, complemented
149C2×C22⋊C8C2×C12711yescharacteristic, complemented
150#380C2×C12711yescharacteristic, complemented
151#340C2×C12711yescharacteristic, complemented
152C22×D4—21no—
153C22×D4C22×C12711yescharacteristic
154C23×C4C22×C12711yescharacteristic
155C22×C8C22×C12711yescharacteristic
156C22×C8C22×C12711yescharacteristic
157#121—22no—
158#121—22no—
159C2×C4⋊C4C22×C12711yescharacteristic
160C2×C4⋊C4C22×C12711yescharacteristic
161C2×C4⋊C4C22×C12711yescharacteristic
162C2×C22⋊C4—21no—
163C2×C22⋊C4—21no—
164#107—22no—
165#102—22no—
166#102—22no—
167C22⋊C8—22no—
168#95—21no—
169C24—21no—
170C24D4×C12711yescharacteristic
171C2×D4—24no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4—42no—
178C2×D4—42no—
179C2×D4D4×C12712yes—
180C22×C4—21no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—21no—
186C22×C4—21no—
187C22×C4—21no—
188C22×C4—21no—
189C22×C4D4×C12711yescharacteristic
190C22×C4C23×C12711yescharacteristic
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8D4×C12712yescomplemented
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—21no—
201C4⋊C4—21no—
202C4⋊C4D4×C12712yes—
203C22⋊C4—24no—
204C22⋊C4—42no—
205C23—21no—
206C23—21no—
207C23—21no—
208C23—21no—
209C23—21no—
210C23—21no—
211C23—22no—
212C23—41no—
213C23—41no—
214C23—41no—
215C23—41no—
216C23—41no—
217C23—41no—
218C23D8×C12712yes—
219C23C2×D4×C12711yescharacteristic
220D4—22no—
221D4—22no—
222D4—48no—
223D4—41no—
224D4—41no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—41no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4C2×D4×C12711yescharacteristic
242C2×C4C2×D4×C12711yescharacteristic
243C2×C4C2×D4×C12711yescharacteristic
244C2×C4#41×C12711yescharacteristic
245C2×C4#41×C12711yescharacteristic
246C2×C4#41×C12711yescharacteristic
247C8—22no—
248C8—41no—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—41no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—42no—
257C22—42no—
258C22—42no—
259C22—81no—
260C22—81no—
261C22—81no—
262C22—81no—
263C22#120×C12711yescharacteristic
264C22#121×C12711yescharacteristic
265C22#123×C12711yescharacteristic
266C22C2×D8×C12711yescharacteristic
267C22#135×C12711yescharacteristic
268C22AGL(1,ℤ/8)×C12711yescharacteristic
269C22#137×C12711yescharacteristic
270C4—41no—
271C4—42no—
272C4—81no—
273C4—81no—
274C4#121×C12711yescharacteristic
275C4#121×C12711yescharacteristic
276C4#123×C12711yescharacteristic
277C4#124×C12711yescharacteristic
278C2—42no—
279C2—82no—
280C2#394×C12711yescharacteristic
281C2#447×C12711yescharacteristic
282C2#452×C12711yescharacteristic
283C2#466×C12711yescharacteristic
284C2#468×C12711yescharacteristic
285C2#480×C12711yescharacteristic
286C2#482×C12711yescharacteristic
subgroupG/H
center, socleC23×C127C2×D4
commutator, Frattini, cosocleC22×C4C23×C127
prime radicalC2×#121×C127C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#107×C127C2semidirect
3. C2×#102×C127C2semidirect
4. C2×#102×C127C2semidirect
5. C2×C22⋊C8×C127C2semidirect
6. #380×C127C2semidirect
7. #340×C127C2semidirect
52. C2×C8×C127D4semidirect
143. #2033C127direct (N × H)
144. C127#2033direct (N × H)
146. C2×#107C2×C127semidirect
147. C2×#102C2×C127semidirect
148. C2×#102C2×C127semidirect
149. C2×C22⋊C8C2×C127semidirect
150. #380C2×C127semidirect
151. #340C2×C127semidirect
196. C2×C8D4×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#121×C1272
C2×#107×C1272
C2×#102×C1272
C2×C22⋊C8×C1272
#380×C1272
#340×C1272
#2033127