Finite Group Databasebeta

← C127×#10494 #44574167

Subgroups — C127×#10494 #44574167

Order 32512.

344 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 98 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×#3229C211yesmaximal, characteristic
2C127×#1997C211yesmaximal, characteristic
3C127×#1574C211yesmaximal, characteristic
4C127×#1561C211yesmaximal, characteristic
5C127×#1549C211yesmaximal, characteristic
6C127×#1485C211yesmaximal, characteristic
7C127×#1299C211yesmaximal, characteristic
8#533×C127C2211yescharacteristic
9C2×C4⋊Q8×C127C2211yescharacteristic
10#498×C127—21no—
11#487×C127—21no—
12#483×C127—22no—
13#475×C127—21no—
14#475×C127—21no—
15#431×C127C2211yescharacteristic
16#431×C127C2211yescharacteristic
17#423×C127C2211yescharacteristic
18#423×C127C2211yescharacteristic
19C4×M16×C127C2211yescharacteristic
20#343×C127—22no—
21#335×C127—21no—
22#334×C127—21no—
23#332×C127—21no—
24#332×C127—21no—
25#332×C127—22no—
26Q8⋊C8×C127—22no—
27C22×Q8×C127—21no—
28C2×M16×C127—21no—
29C2×M16×C127—21no—
30C2×M16×C127—21no—
31C4⋊Q8×C127—21no—
32C4⋊Q8×C127—21no—
33C4⋊Q8×C127—21no—
34C4⋊Q8×C127—21no—
35C4⋊Q8×C127D411yescharacteristic
36C4⋊Q8×C127D411yescharacteristic
37#125×C127—21no—
38C22⋊Q8×C127—21no—
39C22⋊Q8×C127—21no—
40C4×Q8×C127—21no—
41C4×Q8×C127—21no—
42#117×C127—21no—
43C2×C4⋊C4×C127—21no—
44C2×C4⋊C4×C127D412yes—
45C2×C42×C127C2311yescharacteristic
46#106×C127—22no—
47#106×C127—22no—
48C4⋊C8×C127—21no—
49C4⋊C8×C127—21no—
50C4⋊C8×C127—21no—
51C4⋊C8×C127—21no—
52C4⋊C8×C127D412yes—
53C4⋊C8×C127D411yescharacteristic
54C4⋊C8×C127D411yescharacteristic
55#103×C127—22no—
56#103×C127—22no—
57C22⋊C8×C127—21no—
58C22⋊C8×C127—21no—
59#97×C127—21no—
60C4×C8×C127—21no—
61C4×C8×C127—21no—
62C4×C8×C127—21no—
63C2×Q8×C127—21no—
64C2×Q8×C127—21no—
65C2×Q8×C127—41no—
66C2×Q8×C127—41no—
67C2×Q8×C127—82no—
68C22×C4×C127—22no—
69C22×C4×C127C2×D411yescharacteristic
70C22×C4×C127#4111yescharacteristic
71C22×C4×C127#4111yescharacteristic
72M16×C127—22no—
73M16×C127—41no—
74M16×C127—42no—
75M16×C127—81no—
76C2×C8×C127—21no—
77C2×C8×C127—21no—
78C2×C8×C127—22no—
79C2×C8×C127—41no—
80C2×C8×C127—41no—
81C2×C8×C127—41no—
82C4⋊C4×C127—22no—
83C4⋊C4×C127—21no—
84C4⋊C4×C127—22no—
85C4⋊C4×C127—21no—
86C4⋊C4×C127—21no—
87C4⋊C4×C127—21no—
88C4⋊C4×C127—41no—
89C4⋊C4×C127—41no—
90C4⋊C4×C127—41no—
91C4⋊C4×C127—41no—
92C22⋊C4×C127—41no—
93C42×C127—41no—
94C42×C127C2×D411yescharacteristic
95C42×C127C2×D411yescharacteristic
96C42×C127C2×D411yescharacteristic
97C42×C127#4111yescharacteristic
98C23×C127#12311yescharacteristic
99Q8×C127—41no—
100Q8×C127—41no—
101Q8×C127—41no—
102Q8×C127—41no—
103Q8×C127—82no—
104Q8×C127—82no—
105C2×C4×C127—21no—
106C2×C4×C127—21no—
107C2×C4×C127—21no—
108C2×C4×C127—22no—
109C2×C4×C127—21no—
110C2×C4×C127—41no—
111C2×C4×C127—41no—
112C2×C4×C127—42no—
113C2×C4×C127—82no—
114C2×C4×C127#12011yescharacteristic
115C2×C4×C127#12111yescharacteristic
116C2×C4×C127#12111yescharacteristic
117C2×C4×C127#12111yescharacteristic
118C2×C4×C127#12311yescharacteristic
119C2×C4×C127#12411yescharacteristic
120C8×C127—42no—
121C8×C127—41no—
122C8×C127—41no—
123C8×C127—42no—
124C8×C127—81no—
125C8×C127—81no—
126C22×C127—21no—
127C22×C127—21no—
128C22×C127—21no—
129C22×C127#39411yescharacteristic
130C4×C127—21no—
131C4×C127—21no—
132C4×C127—21no—
133C4×C127—81no—
134C4×C127—81no—
135C4×C127—82no—
136C4×C127#45411yescharacteristic
137C4×C127#45611yescharacteristic
138C4×C127#47111yescharacteristic
139C4×C127#47112yes—
140C4×C127#47311yescharacteristic
141#10494C12711yesmaximal, characteristic, direct product factor, Sylow
142C2×C127—41no—
143C2×C127#203811yescharacteristic
144C2×C127#204611yescharacteristic
145C2×C127#205211yescharacteristic
146#3229C2×C12711yescharacteristic
147#1997C2×C12711yescharacteristic
148#1574C2×C12711yescharacteristic
149#1561C2×C12711yescharacteristic
150#1549C2×C12711yescharacteristic
151#1485C2×C12711yescharacteristic
152#1299C2×C12711yescharacteristic
153C127#1049411yescharacteristic, direct product factor, Sylow
154#533C22×C12711yescharacteristic
155C2×C4⋊Q8C22×C12711yescharacteristic
156#498—21no—
157#487—21no—
158#483—22no—
159#475—21no—
160#475—21no—
161#431C22×C12711yescharacteristic
162#431C22×C12711yescharacteristic
163#423C22×C12711yescharacteristic
164#423C22×C12711yescharacteristic
165C4×M16C22×C12711yescharacteristic
166#343—22no—
167#335—21no—
168#334—21no—
169#332—21no—
170#332—21no—
171#332—22no—
172Q8⋊C8—22no—
173C22×Q8—21no—
174C2×M16—21no—
175C2×M16—21no—
176C2×M16—21no—
177C4⋊Q8—21no—
178C4⋊Q8—21no—
179C4⋊Q8—21no—
180C4⋊Q8—21no—
181C4⋊Q8D4×C12711yescharacteristic
182C4⋊Q8D4×C12711yescharacteristic
183#125—21no—
184C22⋊Q8—21no—
185C22⋊Q8—21no—
186C4×Q8—21no—
187C4×Q8—21no—
188#117—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4D4×C12712yes—
191C2×C42C23×C12711yescharacteristic
192#106—22no—
193#106—22no—
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8D4×C12712yes—
199C4⋊C8D4×C12711yescharacteristic
200C4⋊C8D4×C12711yescharacteristic
201#103—22no—
202#103—22no—
203C22⋊C8—21no—
204C22⋊C8—21no—
205#97—21no—
206C4×C8—21no—
207C4×C8—21no—
208C4×C8—21no—
209C2×Q8—21no—
210C2×Q8—21no—
211C2×Q8—41no—
212C2×Q8—41no—
213C2×Q8—82no—
214C22×C4—22no—
215C22×C4C2×D4×C12711yescharacteristic
216C22×C4#41×C12711yescharacteristic
217C22×C4#41×C12711yescharacteristic
218M16—22no—
219M16—41no—
220M16—42no—
221M16—81no—
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—22no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—41no—
228C4⋊C4—22no—
229C4⋊C4—21no—
230C4⋊C4—22no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—21no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C22⋊C4—41no—
239C42—41no—
240C42C2×D4×C12711yescharacteristic
241C42C2×D4×C12711yescharacteristic
242C42C2×D4×C12711yescharacteristic
243C42#41×C12711yescharacteristic
244C23#123×C12711yescharacteristic
245Q8—41no—
246Q8—41no—
247Q8—41no—
248Q8—41no—
249Q8—82no—
250Q8—82no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—22no—
255C2×C4—21no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—82no—
260C2×C4#120×C12711yescharacteristic
261C2×C4#121×C12711yescharacteristic
262C2×C4#121×C12711yescharacteristic
263C2×C4#121×C12711yescharacteristic
264C2×C4#123×C12711yescharacteristic
265C2×C4#124×C12711yescharacteristic
266C8—42no—
267C8—41no—
268C8—41no—
269C8—42no—
270C8—81no—
271C8—81no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22#394×C12711yescharacteristic
276C4—21no—
277C4—21no—
278C4—21no—
279C4—81no—
280C4—82no—
281C4—81no—
282C4#454×C12711yescharacteristic
283C4#456×C12711yescharacteristic
284C4#471×C12712yes—
285C4#471×C12711yescharacteristic
286C4#473×C12711yescharacteristic
287C2—41no—
288C2C127×#203811yescharacteristic
289C2C127×#204611yescharacteristic
290C2C127×#205211yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127#123
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
141. #10494C127direct (N × H)
153. C127#10494direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32292
C127×#19972
C127×#15742
C127×#15612
C127×#15492
C127×#14852
C127×#12992
#10494127