Finite Group Databasebeta

← C127×#13333 #44577006

Subgroups — C127×#13333 #44577006

Order 32512.

546 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 122 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×#510×C127C212yesmaximal
2C2×#494×C127C211yesmaximal, characteristic, complemented
3C2×#362×C127C212yesmaximal, complemented
4C127×#1974C211yesmaximal, characteristic
5C127×#1376C211yesmaximal, characteristic, complemented
6C2×#135×C127C2211yescharacteristic
7C22×Q16×C127—21no—
8C22×Q16×C127C2212yes—
9C2×C4⋊Q8×C127—21no—
10#510×C127—24no—
11#510×C127—24no—
12C2×Q32×C127—22no—
13C2×SD32×C127—22no—
14C2×M32×C127C2212yes—
15#494×C127—24no—
16C2×#108×C127C2211yescharacteristic
17C2×#104×C127—21no—
18#408×C127—21no—
19C2×C4×C8×C127C2211yescharacteristic
20#362×C127—24no—
21C2×#41×C127—21no—
22C22×Q8×C127—22no—
23#135×C127—22no—
24#135×C127—22no—
25C2×Q16×C127—24no—
26C2×Q16×C127—22no—
27C2×Q16×C127—22no—
28C2×Q16×C127—22no—
29C2×Q16×C127—22no—
30C2×Q16×C127—22no—
31C2×Q16×C127—42no—
32C2×Q16×C127—42no—
33C2×Q16×C127D411yescharacteristic
34C2×Q16×C127D414yes—
35C2×SD16×C127—21no—
36C2×D8×C127D411yescharacteristic
37C2×M16×C127—21no—
38C22×C8×C127D411yescharacteristic
39C22×C8×C127C2311yescharacteristic
40C4⋊Q8×C127—24no—
41C4⋊Q8×C127—42no—
42C2×C4⋊C4×C127—42no—
43C2×C42×C127D411yescharacteristic
44Q32×C127—28no—
45SD32×C127—28no—
46M32×C127—22no—
47M32×C127D414yes—
48C2×C16×C127—22no—
49#108×C127—22no—
50#104×C127—42no—
51C22⋊C8×C127—42no—
52C4×C8×C127—22no—
53#41×C127—41no—
54#41×C127—41no—
55#41×C127—41no—
56#41×C127—41no—
57C2×Q8×C127—24no—
58C2×Q8×C127—21no—
59C2×Q8×C127—42no—
60C2×Q8×C127—42no—
61C2×Q8×C127—42no—
62C2×Q8×C127—42no—
63C2×Q8×C127—42no—
64C2×D4×C127—21no—
65C2×D4×C127—41no—
66C22×C4×C127—21no—
67C22×C4×C127—42no—
68C22×C4×C127—41no—
69C22×C4×C127C2×D411yescharacteristic
70Q16×C127—24no—
71Q16×C127—22no—
72Q16×C127—24no—
73Q16×C127—48no—
74Q16×C127—42no—
75Q16×C127—42no—
76SD16×C127—42no—
77D8×C127—22no—
78M16×C127—41no—
79M16×C127—41no—
80C2×C8×C127—21no—
81C2×C8×C127—21no—
82C2×C8×C127—41no—
83C2×C8×C127D812yes—
84C2×C8×C127C2×D411yescharacteristic
85C2×C8×C127C2×D412yes—
86C2×C8×C127C2×D412yes—
87C2×C8×C127#4111yescharacteristic
88C4⋊C4×C127—48no—
89C42×C127—21no—
90C42×C127D812yes—
91C16×C127—24no—
92C23×C127—41no—
93C23×C127AGL(1,ℤ/8)11yescharacteristic
94Q8×C127—41no—
95Q8×C127—44no—
96Q8×C127—44no—
97Q8×C127—41no—
98Q8×C127—82no—
99Q8×C127—82no—
100D4×C127—41no—
101D4×C127—41no—
102D4×C127—81no—
103D4×C127—81no—
104C2×C4×C127—24no—
105C2×C4×C127—22no—
106C2×C4×C127—44no—
107C2×C4×C127—41no—
108C2×C4×C127—82no—
109C2×C4×C127—82no—
110C2×C4×C127—81no—
111C2×C4×C127—81no—
112C2×C4×C127#12011yescharacteristic
113C2×C4×C127#12111yescharacteristic
114C2×C4×C127#12711yescharacteristic
115C2×C4×C127C2×D811yescharacteristic
116C2×C4×C127C2×D811yescharacteristic
117C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
118C8×C127—22no—
119C8×C127—81no—
120C8×C127#12012yes—
121C8×C127#12112yes—
122C22×C127—22no—
123C22×C127—82no—
124C22×C127—81no—
125C22×C127#44711yescharacteristic
126C22×C127#45911yescharacteristic
127C22×C127#49611yescharacteristic
128C4×C127—24no—
129C4×C127—81no—
130C4×C127—84no—
131C4×C127#39211yescharacteristic
132C4×C127#44711yescharacteristic
133C4×C127#45911yescharacteristic
134C4×C127#49311yescharacteristic
135#13333C12711yesmaximal, characteristic, direct product factor, Sylow
136C2×C127—21no—
137C2×C127—21no—
138C2×C127—161no—
139C2×C127#201111yescharacteristic
140C2×C127#221412yes—
141C2×#510C2×C12712yes—
142C2×#494C2×C12711yescharacteristic, complemented
143C2×#362C2×C12712yescomplemented
144#1974C2×C12711yescharacteristic
145#1376C2×C12711yescharacteristic, complemented
146C127#1333311yescharacteristic, direct product factor, Sylow
147C2×#135C22×C12711yescharacteristic
148C22×Q16—21no—
149C22×Q16C22×C12712yes—
150C2×C4⋊Q8—21no—
151#510—24no—
152#510—24no—
153C2×Q32—22no—
154C2×SD32—22no—
155C2×M32C22×C12712yes—
156#494—24no—
157C2×#108C22×C12711yescharacteristic
158C2×#104—21no—
159#408—21no—
160C2×C4×C8C22×C12711yescharacteristic
161#362—24no—
162C2×#41—21no—
163C22×Q8—22no—
164#135—22no—
165#135—22no—
166C2×Q16—24no—
167C2×Q16—22no—
168C2×Q16—22no—
169C2×Q16—22no—
170C2×Q16—22no—
171C2×Q16—22no—
172C2×Q16—42no—
173C2×Q16—42no—
174C2×Q16D4×C12714yes—
175C2×Q16D4×C12711yescharacteristic
176C2×SD16—21no—
177C2×D8D4×C12711yescharacteristic
178C2×M16—21no—
179C22×C8D4×C12711yescharacteristic
180C22×C8C23×C12711yescharacteristic
181C4⋊Q8—24no—
182C4⋊Q8—42no—
183C2×C4⋊C4—42no—
184C2×C42D4×C12711yescharacteristic
185Q32—28no—
186SD32—28no—
187M32—22no—
188M32D4×C12714yes—
189C2×C16—22no—
190#108—22no—
191#104—42no—
192C22⋊C8—42no—
193C4×C8—22no—
194#41—41no—
195#41—41no—
196#41—41no—
197#41—41no—
198C2×Q8—24no—
199C2×Q8—21no—
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8—42no—
203C2×Q8—42no—
204C2×Q8—42no—
205C2×D4—21no—
206C2×D4—41no—
207C22×C4—21no—
208C22×C4—42no—
209C22×C4—41no—
210C22×C4C2×D4×C12711yescharacteristic
211Q16—24no—
212Q16—22no—
213Q16—24no—
214Q16—48no—
215Q16—42no—
216Q16—42no—
217SD16—42no—
218D8—22no—
219M16—41no—
220M16—41no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—41no—
224C2×C8D8×C12712yes—
225C2×C8C2×D4×C12711yescharacteristic
226C2×C8C2×D4×C12712yes—
227C2×C8C2×D4×C12712yes—
228C2×C8#41×C12711yescharacteristic
229C4⋊C4—48no—
230C42—21no—
231C42D8×C12712yes—
232C16—24no—
233C23—41no—
234C23AGL(1,ℤ/8)×C12711yescharacteristic
235Q8—41no—
236Q8—44no—
237Q8—44no—
238Q8—41no—
239Q8—82no—
240Q8—82no—
241D4—41no—
242D4—41no—
243D4—81no—
244D4—81no—
245C2×C4—24no—
246C2×C4—22no—
247C2×C4—44no—
248C2×C4—41no—
249C2×C4—82no—
250C2×C4—82no—
251C2×C4—81no—
252C2×C4—81no—
253C2×C4#120×C12711yescharacteristic
254C2×C4#121×C12711yescharacteristic
255C2×C4#127×C12711yescharacteristic
256C2×C4C2×D8×C12711yescharacteristic
257C2×C4C2×D8×C12711yescharacteristic
258C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
259C8—22no—
260C8—81no—
261C8#120×C12712yes—
262C8#121×C12712yes—
263C22—22no—
264C22—82no—
265C22—81no—
266C22#447×C12711yescharacteristic
267C22#459×C12711yescharacteristic
268C22#496×C12711yescharacteristic
269C4—24no—
270C4—81no—
271C4—84no—
272C4#392×C12711yescharacteristic
273C4#447×C12711yescharacteristic
274C4#459×C12711yescharacteristic
275C4#493×C12711yescharacteristic
276C2—21no—
277C2—21no—
278C2—161no—
279C2C127×#201111yescharacteristic
280C2C127×#221412yes—
subgroupG/H
center, socleC22×C127#459
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC2×#135×C127C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#494×C127C2semidirect
3. C2×#362×C127C2semidirect
5. C127×#1376C2semidirect
135. #13333C127direct (N × H)
142. C2×#494C2×C127semidirect
143. C2×#362C2×C127semidirect
145. #1376C2×C127semidirect
146. C127#13333direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#510×C1272
C2×#494×C1272
C2×#362×C1272
C127×#19742
C127×#13762
#13333127