Finite Group Databasebeta

← C127×#10526 #44574199

Subgroups — C127×#10526 #44574199

Order 32512.

364 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 90 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×#3254C211yesmaximal, characteristic
2C127×#1849C211yesmaximal, characteristic, complemented
3C127×#1559C211yesmaximal, characteristic, complemented
4C127×#1557C211yesmaximal, characteristic
5C127×#1531C211yesmaximal, characteristic, complemented
6C127×#1530C211yesmaximal, characteristic
7C127×#1307C211yesmaximal, characteristic, complemented
8#533×C127C2211yescharacteristic
9#532×C127C2211yescharacteristic
10#477×C127—21no—
11#474×C127—21no—
12#468×C127—22no—
13#461×C127—21no—
14#460×C127—21no—
15#432×C127C2211yescharacteristic
16#432×C127C2211yescharacteristic
17C2×#108×C127—22no—
18#423×C127C2211yescharacteristic
19#423×C127C2211yescharacteristic
20C2×#97×C127C2211yescharacteristic
21#333×C127—21no—
22#332×C127—21no—
23#332×C127—21no—
24#331×C127—21no—
25#330×C127—22no—
26#329×C127—22no—
27C2×#41×C127—21no—
28C2×SD16×C127—22no—
29C2×M16×C127—21no—
30C2×M16×C127D412yes—
31C22×C8×C127—21no—
32C4⋊Q8×C127D411yescharacteristic
33C4⋊Q8×C127D411yescharacteristic
34C4⋊Q8×C127D411yescharacteristic
35#127×C127D411yescharacteristic
36#125×C127—21no—
37#124×C127—21no—
38C22⋊Q8×C127—21no—
39C22⋊Q8×C127—21no—
40#121×C127—21no—
41#121×C127—21no—
42C4×Q8×C127—21no—
43C4×Q8×C127—21no—
44C4×D4×C127—21no—
45C4×D4×C127—21no—
46#117×C127—21no—
47C2×C42×C127C2311yescharacteristic
48#108×C127—44no—
49#107×C127—22no—
50C4⋊C8×C127—21no—
51C4⋊C8×C127—21no—
52C4⋊C8×C127—21no—
53C4⋊C8×C127—21no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56#103×C127—22no—
57#102×C127—22no—
58C22⋊C8×C127—21no—
59C22⋊C8×C127—21no—
60#97×C127—21no—
61#97×C127—21no—
62#97×C127—21no—
63#97×C127D412yes—
64#41×C127—82no—
65C2×Q8×C127—21no—
66C2×Q8×C127—21no—
67C2×Q8×C127—21no—
68C2×D4×C127—21no—
69C2×D4×C127—21no—
70C2×D4×C127—21no—
71C2×D4×C127—41no—
72C22×C4×C127—41no—
73C22×C4×C127C2×D411yescharacteristic
74C22×C4×C127#4111yescharacteristic
75C22×C4×C127#4111yescharacteristic
76SD16×C127—82no—
77M16×C127—42no—
78M16×C127—42no—
79C2×C8×C127—22no—
80C2×C8×C127—22no—
81C2×C8×C127—22no—
82C2×C8×C127—22no—
83C2×C8×C127—41no—
84C2×C8×C127—41no—
85C2×C8×C127—41no—
86C4⋊C4×C127—21no—
87C4⋊C4×C127—21no—
88C4⋊C4×C127—21no—
89C4⋊C4×C127—21no—
90C4⋊C4×C127—21no—
91C4⋊C4×C127—21no—
92C4⋊C4×C127—41no—
93C4⋊C4×C127—41no—
94C22⋊C4×C127—41no—
95C22⋊C4×C127—41no—
96C22⋊C4×C127—41no—
97C42×C127—41no—
98C42×C127C2×D411yescharacteristic
99C42×C127C2×D411yescharacteristic
100C42×C127C2×D411yescharacteristic
101C42×C127#4111yescharacteristic
102C23×C127—41no—
103C23×C127#12411yescharacteristic
104Q8×C127—41no—
105Q8×C127—41no—
106Q8×C127—81no—
107Q8×C127—81no—
108D4×C127—41no—
109D4×C127—41no—
110D4×C127—81no—
111D4×C127—81no—
112D4×C127—82no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—41no—
116C2×C4×C127—41no—
117C2×C4×C127—41no—
118C2×C4×C127—41no—
119C2×C4×C127—41no—
120C2×C4×C127—82no—
121C2×C4×C127#12011yescharacteristic
122C2×C4×C127#12111yescharacteristic
123C2×C4×C127#12111yescharacteristic
124C2×C4×C127#12111yescharacteristic
125C2×C4×C127#12311yescharacteristic
126C2×C4×C127#12311yescharacteristic
127C8×C127—24no—
128C8×C127—42no—
129C8×C127—81no—
130C8×C127—81no—
131C8×C127—81no—
132C22×C127—21no—
133C22×C127—21no—
134C22×C127—21no—
135C22×C127—81no—
136C22×C127—81no—
137C22×C127—81no—
138C22×C127#39411yescharacteristic
139C4×C127—21no—
140C4×C127—21no—
141C4×C127—21no—
142C4×C127—21no—
143C4×C127—21no—
144C4×C127—81no—
145C4×C127—81no—
146C4×C127—81no—
147C4×C127#45311yescharacteristic
148C4×C127#45611yescharacteristic
149#10526C12711yesmaximal, characteristic, direct product factor, Sylow
150C2×C127—41no—
151C2×C127—161no—
152C2×C127#203911yescharacteristic
153C2×C127#204811yescharacteristic
154C2×C127#204911yescharacteristic
155#3254C2×C12711yescharacteristic
156#1849C2×C12711yescharacteristic, complemented
157#1559C2×C12711yescharacteristic, complemented
158#1557C2×C12711yescharacteristic
159#1531C2×C12711yescharacteristic, complemented
160#1530C2×C12711yescharacteristic
161#1307C2×C12711yescharacteristic, complemented
162C127#1052611yescharacteristic, direct product factor, Sylow
163#533C22×C12711yescharacteristic
164#532C22×C12711yescharacteristic
165#477—21no—
166#474—21no—
167#468—22no—
168#461—21no—
169#460—21no—
170#432C22×C12711yescharacteristic
171#432C22×C12711yescharacteristic
172C2×#108—22no—
173#423C22×C12711yescharacteristic
174#423C22×C12711yescharacteristic
175C2×#97C22×C12711yescharacteristic
176#333—21no—
177#332—21no—
178#332—21no—
179#331—21no—
180#330—22no—
181#329—22no—
182C2×#41—21no—
183C2×SD16—22no—
184C2×M16—21no—
185C2×M16D4×C12712yes—
186C22×C8—21no—
187C4⋊Q8D4×C12711yescharacteristic
188C4⋊Q8D4×C12711yescharacteristic
189C4⋊Q8D4×C12711yescharacteristic
190#127D4×C12711yescharacteristic
191#125—21no—
192#124—21no—
193C22⋊Q8—21no—
194C22⋊Q8—21no—
195#121—21no—
196#121—21no—
197C4×Q8—21no—
198C4×Q8—21no—
199C4×D4—21no—
200C4×D4—21no—
201#117—21no—
202C2×C42C23×C12711yescharacteristic
203#108—44no—
204#107—22no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211#103—22no—
212#102—22no—
213C22⋊C8—21no—
214C22⋊C8—21no—
215#97—21no—
216#97—21no—
217#97—21no—
218#97D4×C12712yes—
219#41—82no—
220C2×Q8—21no—
221C2×Q8—21no—
222C2×Q8—21no—
223C2×D4—21no—
224C2×D4—21no—
225C2×D4—21no—
226C2×D4—41no—
227C22×C4—41no—
228C22×C4C2×D4×C12711yescharacteristic
229C22×C4#41×C12711yescharacteristic
230C22×C4#41×C12711yescharacteristic
231SD16—82no—
232M16—42no—
233M16—42no—
234C2×C8—22no—
235C2×C8—22no—
236C2×C8—22no—
237C2×C8—22no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C22⋊C4—41no—
250C22⋊C4—41no—
251C22⋊C4—41no—
252C42—41no—
253C42C2×D4×C12711yescharacteristic
254C42C2×D4×C12711yescharacteristic
255C42C2×D4×C12711yescharacteristic
256C42#41×C12711yescharacteristic
257C23—41no—
258C23#124×C12711yescharacteristic
259Q8—41no—
260Q8—41no—
261Q8—81no—
262Q8—81no—
263D4—41no—
264D4—41no—
265D4—81no—
266D4—81no—
267D4—82no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—82no—
276C2×C4#120×C12711yescharacteristic
277C2×C4#121×C12711yescharacteristic
278C2×C4#121×C12711yescharacteristic
279C2×C4#121×C12711yescharacteristic
280C2×C4#123×C12711yescharacteristic
281C2×C4#123×C12711yescharacteristic
282C8—24no—
283C8—42no—
284C8—81no—
285C8—81no—
286C8—81no—
287C22—21no—
288C22—21no—
289C22—21no—
290C22—81no—
291C22—81no—
292C22—81no—
293C22#394×C12711yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—21no—
299C4—81no—
300C4—81no—
301C4—81no—
302C4#453×C12711yescharacteristic
303C4#456×C12711yescharacteristic
304C2—41no—
305C2—161no—
306C2C127×#203911yescharacteristic
307C2C127×#204811yescharacteristic
308C2C127×#204911yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radical#532×C127C22
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
2. C127×#1849C2semidirect
3. C127×#1559C2semidirect
5. C127×#1531C2semidirect
7. C127×#1307C2semidirect
149. #10526C127direct (N × H)
156. #1849C2×C127semidirect
157. #1559C2×C127semidirect
159. #1531C2×C127semidirect
161. #1307C2×C127semidirect
162. C127#10526direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32542
C127×#18492
C127×#15592
C127×#15572
C127×#15312
C127×#15302
C127×#13072
#10526127