Finite Group Databasebeta

← C127×#11871 #44575544

Subgroups — C127×#11871 #44575544

Order 32512.

360 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C127×#3059C211yesmaximal, characteristic
2C127×#2115C211yesmaximal, characteristic
3C127×#1813C211yesmaximal, characteristic
4C127×#1342C214yesmaximal, complemented
5C22×Q16×C127C411yescharacteristic
6C2×#131×C127C2211yescharacteristic
7#536×C127—21no—
8C2×M32×C127—21no—
9#470×C127C412yes—
10#470×C127C2212yes—
11#467×C127—21no—
12#467×C127—21no—
13C2×#108×C127—21no—
14#427×C127C411yescharacteristic
15#419×C127—21no—
16#413×C127—21no—
17#349×C127—21no—
18#349×C127C2212yes—
19#338×C127C2212yes—
20C2×#41×C127D411yescharacteristic
21C22×Q8×C127—21no—
22C2×Q16×C127—21no—
23C2×Q16×C127—41no—
24C2×Q16×C127—41no—
25C2×Q16×C127C2×C412yes—
26#131×C127—41no—
27#131×C127—41no—
28C2×M16×C127—22no—
29C2×M16×C127C2×C411yescharacteristic
30C2×M16×C127D411yescharacteristic
31C2×M16×C127C2311yescharacteristic
32C22×C8×C127C2×C411yescharacteristic
33C22×C8×C127D411yescharacteristic
34C22×C8×C127D411yescharacteristic
35C4⋊Q8×C127—41no—
36#124×C127—41no—
37#123×C127—41no—
38#123×C127—41no—
39C22⋊Q8×C127—22no—
40C22⋊Q8×C127—22no—
41#117×C127—21no—
42M32×C127—22no—
43M32×C127—41no—
44C2×C16×C127—41no—
45#108×C127—41no—
46#108×C127—41no—
47#107×C127—21no—
48#106×C127C2×C412yes—
49#103×C127—22no—
50#103×C127—22no—
51#101×C127—41no—
52#100×C127—41no—
53#41×C127—41no—
54#41×C127—41no—
55C2×Q8×C127—22no—
56C2×Q8×C127—42no—
57C2×Q8×C127—42no—
58C2×Q8×C127—41no—
59C2×Q8×C127D811yescharacteristic
60C2×D4×C127D811yescharacteristic
61C2×D4×C127SD1611yescharacteristic
62C2×D4×C127SD1611yescharacteristic
63C22×C4×C127—41no—
64C22×C4×C127C22⋊C411yescharacteristic
65C22×C4×C127C22⋊C411yescharacteristic
66C22×C4×C127C2×D411yescharacteristic
67Q16×C127—42no—
68Q16×C127—41no—
69Q16×C127—41no—
70M16×C127—41no—
71M16×C127—41no—
72M16×C127—41no—
73M16×C127—42no—
74M16×C127—42no—
75C2×C8×C127—21no—
76C2×C8×C127—21no—
77C2×C8×C127—21no—
78C2×C8×C127—21no—
79C2×C8×C127—21no—
80C2×C8×C127—21no—
81C2×C8×C127—42no—
82C2×C8×C127C22⋊C411yescharacteristic
83C2×C8×C127C22⋊C411yescharacteristic
84C2×C8×C127C22×C411yescharacteristic
85C2×C8×C127C2×D411yescharacteristic
86C4⋊C4×C127—22no—
87C4⋊C4×C127—42no—
88C4⋊C4×C127—42no—
89C22⋊C4×C127—41no—
90C22⋊C4×C127—42no—
91C22⋊C4×C127—42no—
92C42×C127—41no—
93C16×C127—42no—
94C23×C127#10211yescharacteristic
95C23×C127#10211yescharacteristic
96C23×C127C2×SD1611yescharacteristic
97Q8×C127—41no—
98Q8×C127—42no—
99Q8×C127—42no—
100Q8×C127—82no—
101D4×C127—41no—
102D4×C127—41no—
103D4×C127—41no—
104C2×C4×C127—21no—
105C2×C4×C127—21no—
106C2×C4×C127—21no—
107C2×C4×C127—21no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—42no—
111C2×C4×C127—42no—
112C2×C4×C127—82no—
113C2×C4×C127#10211yescharacteristic
114C2×C4×C127#10211yescharacteristic
115C2×C4×C127C2×C22⋊C411yescharacteristic
116C2×C4×C127C2×D811yescharacteristic
117C8×C127—21no—
118C8×C127—21no—
119C8×C127—21no—
120C8×C127—82no—
121C8×C127#9911yescharacteristic
122C8×C127#9911yescharacteristic
123C22×C127—21no—
124C22×C127—21no—
125C22×C127—21no—
126C22×C127—41no—
127C22×C127—41no—
128C22×C127—41no—
129C22×C127C2×#10211yescharacteristic
130C4×C127—21no—
131C4×C127—21no—
132C4×C127—21no—
133C4×C127—82no—
134C4×C127—82no—
135C4×C127C2×#9911yescharacteristic
136C4×C127#42111yescharacteristic
137#11871C12711yesmaximal, characteristic, direct product factor, Sylow
138C2×C127—21no—
139C2×C127—41no—
140C2×C127—41no—
141C2×C127—41no—
142C2×C127#151911yescharacteristic
143#3059C2×C12711yescharacteristic
144#2115C2×C12711yescharacteristic
145#1813C2×C12711yescharacteristic
146#1342C2×C12714yescomplemented
147C127#1187111yescharacteristic, direct product factor, Sylow
148C22×Q16C4×C12711yescharacteristic
149C2×#131C22×C12711yescharacteristic
150#536—21no—
151C2×M32—21no—
152#470C4×C12712yes—
153#470C22×C12712yes—
154#467—21no—
155#467—21no—
156C2×#108—21no—
157#427C4×C12711yescharacteristic
158#419—21no—
159#413—21no—
160#349—21no—
161#349C22×C12712yes—
162#338C22×C12712yes—
163C2×#41D4×C12711yescharacteristic
164C22×Q8—21no—
165C2×Q16—21no—
166C2×Q16—41no—
167C2×Q16—41no—
168C2×Q16C2×C4×C12712yes—
169#131—41no—
170#131—41no—
171C2×M16—22no—
172C2×M16C2×C4×C12711yescharacteristic
173C2×M16D4×C12711yescharacteristic
174C2×M16C23×C12711yescharacteristic
175C22×C8C2×C4×C12711yescharacteristic
176C22×C8D4×C12711yescharacteristic
177C22×C8D4×C12711yescharacteristic
178C4⋊Q8—41no—
179#124—41no—
180#123—41no—
181#123—41no—
182C22⋊Q8—22no—
183C22⋊Q8—22no—
184#117—21no—
185M32—22no—
186M32—41no—
187C2×C16—41no—
188#108—41no—
189#108—41no—
190#107—21no—
191#106C2×C4×C12712yes—
192#103—22no—
193#103—22no—
194#101—41no—
195#100—41no—
196#41—41no—
197#41—41no—
198C2×Q8—22no—
199C2×Q8—42no—
200C2×Q8—42no—
201C2×Q8—41no—
202C2×Q8D8×C12711yescharacteristic
203C2×D4D8×C12711yescharacteristic
204C2×D4SD16×C12711yescharacteristic
205C2×D4SD16×C12711yescharacteristic
206C22×C4—41no—
207C22×C4C22⋊C4×C12711yescharacteristic
208C22×C4C22⋊C4×C12711yescharacteristic
209C22×C4C2×D4×C12711yescharacteristic
210Q16—42no—
211Q16—41no—
212Q16—41no—
213M16—41no—
214M16—41no—
215M16—41no—
216M16—42no—
217M16—42no—
218C2×C8—21no—
219C2×C8—21no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—42no—
225C2×C8C22⋊C4×C12711yescharacteristic
226C2×C8C22⋊C4×C12711yescharacteristic
227C2×C8C22×C4×C12711yescharacteristic
228C2×C8C2×D4×C12711yescharacteristic
229C4⋊C4—22no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C22⋊C4—41no—
233C22⋊C4—42no—
234C22⋊C4—42no—
235C42—41no—
236C16—42no—
237C23#102×C12711yescharacteristic
238C23#102×C12711yescharacteristic
239C23C2×SD16×C12711yescharacteristic
240Q8—41no—
241Q8—42no—
242Q8—42no—
243Q8—82no—
244D4—41no—
245D4—41no—
246D4—41no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—82no—
256C2×C4#102×C12711yescharacteristic
257C2×C4#102×C12711yescharacteristic
258C2×C4C2×C22⋊C4×C12711yescharacteristic
259C2×C4C2×D8×C12711yescharacteristic
260C8—21no—
261C8—21no—
262C8—21no—
263C8—82no—
264C8#99×C12711yescharacteristic
265C8#99×C12711yescharacteristic
266C22—21no—
267C22—21no—
268C22—21no—
269C22—41no—
270C22—41no—
271C22—41no—
272C22C2×#102×C12711yescharacteristic
273C4—21no—
274C4—21no—
275C4—21no—
276C4—82no—
277C4—82no—
278C4C2×#99×C12711yescharacteristic
279C4#421×C12711yescharacteristic
280C2—21no—
281C2—41no—
282C2—41no—
283C2—41no—
284C2C127×#151911yescharacteristic
subgroupG/H
center, socleC2×C127#1519
commutatorC2×C8C22×C4×C127
Frattini, cosocleC2×M16C23×C127
prime radicalC2×#41×C127D4
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C2×#131×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1342C2semidirect
137. #11871C127direct (N × H)
146. #1342C2×C127semidirect
147. C127#11871direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#30592
C127×#21152
C127×#18132
C127×#13422
#11871127