Finite Group Databasebeta

← C127×#10532 #44574205

Subgroups — C127×#10532 #44574205

Order 32512.

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

normal subgroups only

This group has 380 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×#3254C211yesmaximal, characteristic
2C127×#1848C211yesmaximal, characteristic, complemented
3C127×#1561C211yesmaximal, characteristic, complemented
4C127×#1560C211yesmaximal, characteristic
5C127×#1493C211yesmaximal, characteristic, complemented
6C127×#1492C211yesmaximal, characteristic
7C127×#1309C211yesmaximal, 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—
15C2×#108×C127—22no—
16#423×C127C2211yescharacteristic
17#423×C127C2211yescharacteristic
18#423×C127C2211yescharacteristic
19#423×C127C2211yescharacteristic
20C2×C4×C8×C127C2211yescharacteristic
21#333×C127—21no—
22#332×C127—21no—
23#332×C127—21no—
24#331×C127—21no—
25Q8⋊C8×C127—22no—
26D4⋊C8×C127—22no—
27C2×#41×C127—21no—
28C2×SD16×C127—22no—
29C2×M16×C127—21no—
30C2×M16×C127—21no—
31C2×M16×C127—21no—
32C2×M16×C127D412yes—
33C22×C8×C127—21no—
34C4⋊Q8×C127D411yescharacteristic
35C4⋊Q8×C127D411yescharacteristic
36C4⋊Q8×C127D411yescharacteristic
37#127×C127D411yescharacteristic
38#125×C127—21no—
39#124×C127—21no—
40C22⋊Q8×C127—21no—
41C22⋊Q8×C127—21no—
42#121×C127—21no—
43#121×C127—21no—
44C4×Q8×C127—21no—
45C4×Q8×C127—21no—
46C4×D4×C127—21no—
47C4×D4×C127—21no—
48#117×C127—21no—
49C2×C42×C127C2311yescharacteristic
50#108×C127—44no—
51#107×C127—22no—
52C4⋊C8×C127—21no—
53C4⋊C8×C127—21no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57C4⋊C8×C127—21no—
58C4⋊C8×C127—21no—
59C4⋊C8×C127—21no—
60#103×C127—22no—
61#102×C127—22no—
62C4×C8×C127—21no—
63C4×C8×C127D412yes—
64#41×C127—81no—
65#41×C127—81no—
66C2×Q8×C127—21no—
67C2×Q8×C127—21no—
68C2×Q8×C127—21no—
69C2×D4×C127—21no—
70C2×D4×C127—21no—
71C2×D4×C127—21no—
72C2×D4×C127—41no—
73C22×C4×C127—41no—
74C22×C4×C127C2×D411yescharacteristic
75C22×C4×C127#4111yescharacteristic
76C22×C4×C127#4111yescharacteristic
77SD16×C127—82no—
78M16×C127—42no—
79M16×C127—42no—
80M16×C127—81no—
81M16×C127—81no—
82C2×C8×C127—22no—
83C2×C8×C127—22no—
84C2×C8×C127—22no—
85C2×C8×C127—22no—
86C2×C8×C127—41no—
87C2×C8×C127—41no—
88C2×C8×C127—41no—
89C4⋊C4×C127—21no—
90C4⋊C4×C127—21no—
91C4⋊C4×C127—21no—
92C4⋊C4×C127—21no—
93C4⋊C4×C127—21no—
94C4⋊C4×C127—21no—
95C4⋊C4×C127—41no—
96C4⋊C4×C127—41no—
97C22⋊C4×C127—41no—
98C22⋊C4×C127—41no—
99C22⋊C4×C127—41no—
100C42×C127—41no—
101C42×C127C2×D411yescharacteristic
102C42×C127C2×D411yescharacteristic
103C42×C127C2×D411yescharacteristic
104C42×C127#4111yescharacteristic
105C23×C127—41no—
106C23×C127#12411yescharacteristic
107Q8×C127—41no—
108Q8×C127—41no—
109Q8×C127—41no—
110Q8×C127—41no—
111Q8×C127—81no—
112D4×C127—41no—
113D4×C127—41no—
114D4×C127—41no—
115D4×C127—41no—
116D4×C127—81no—
117D4×C127—82no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—21no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—81no—
128C2×C4×C127—81no—
129C2×C4×C127#12011yescharacteristic
130C2×C4×C127#12111yescharacteristic
131C2×C4×C127#12111yescharacteristic
132C2×C4×C127#12111yescharacteristic
133C2×C4×C127#12311yescharacteristic
134C2×C4×C127#12311yescharacteristic
135C8×C127—24no—
136C8×C127—42no—
137C8×C127—81no—
138C8×C127—81no—
139C8×C127—81no—
140C22×C127—21no—
141C22×C127—21no—
142C22×C127—21no—
143C22×C127—81no—
144C22×C127—81no—
145C22×C127—81no—
146C22×C127#39411yescharacteristic
147C4×C127—21no—
148C4×C127—21no—
149C4×C127—21no—
150C4×C127—81no—
151C4×C127—81no—
152C4×C127—81no—
153C4×C127#45311yescharacteristic
154C4×C127#45611yescharacteristic
155C4×C127#47111yescharacteristic
156C4×C127#47111yescharacteristic
157C4×C127#47211yescharacteristic
158C4×C127#47311yescharacteristic
159#10532C12711yesmaximal, characteristic, direct product factor, Sylow
160C2×C127—41no—
161C2×C127—161no—
162C2×C127#203911yescharacteristic
163C2×C127#205111yescharacteristic
164C2×C127#205211yescharacteristic
165#3254C2×C12711yescharacteristic
166#1848C2×C12711yescharacteristic, complemented
167#1561C2×C12711yescharacteristic, complemented
168#1560C2×C12711yescharacteristic
169#1493C2×C12711yescharacteristic, complemented
170#1492C2×C12711yescharacteristic
171#1309C2×C12711yescharacteristic, complemented
172C127#1053211yescharacteristic, direct product factor, Sylow
173#533C22×C12711yescharacteristic
174#532C22×C12711yescharacteristic
175#477—21no—
176#474—21no—
177#468—22no—
178#461—21no—
179#460—21no—
180C2×#108—22no—
181#423C22×C12711yescharacteristic
182#423C22×C12711yescharacteristic
183#423C22×C12711yescharacteristic
184#423C22×C12711yescharacteristic
185C2×C4×C8C22×C12711yescharacteristic
186#333—21no—
187#332—21no—
188#332—21no—
189#331—21no—
190Q8⋊C8—22no—
191D4⋊C8—22no—
192C2×#41—21no—
193C2×SD16—22no—
194C2×M16—21no—
195C2×M16—21no—
196C2×M16—21no—
197C2×M16D4×C12712yes—
198C22×C8—21no—
199C4⋊Q8D4×C12711yescharacteristic
200C4⋊Q8D4×C12711yescharacteristic
201C4⋊Q8D4×C12711yescharacteristic
202#127D4×C12711yescharacteristic
203#125—21no—
204#124—21no—
205C22⋊Q8—21no—
206C22⋊Q8—21no—
207#121—21no—
208#121—21no—
209C4×Q8—21no—
210C4×Q8—21no—
211C4×D4—21no—
212C4×D4—21no—
213#117—21no—
214C2×C42C23×C12711yescharacteristic
215#108—44no—
216#107—22no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—21no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225#103—22no—
226#102—22no—
227C4×C8—21no—
228C4×C8D4×C12712yes—
229#41—81no—
230#41—81no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×D4—21no—
235C2×D4—21no—
236C2×D4—21no—
237C2×D4—41no—
238C22×C4—41no—
239C22×C4C2×D4×C12711yescharacteristic
240C22×C4#41×C12711yescharacteristic
241C22×C4#41×C12711yescharacteristic
242SD16—82no—
243M16—42no—
244M16—42no—
245M16—81no—
246M16—81no—
247C2×C8—22no—
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—22no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C42—41no—
266C42C2×D4×C12711yescharacteristic
267C42C2×D4×C12711yescharacteristic
268C42C2×D4×C12711yescharacteristic
269C42#41×C12711yescharacteristic
270C23—41no—
271C23#124×C12711yescharacteristic
272Q8—41no—
273Q8—41no—
274Q8—41no—
275Q8—41no—
276Q8—81no—
277D4—41no—
278D4—41no—
279D4—41no—
280D4—41no—
281D4—81no—
282D4—82no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—81no—
293C2×C4—81no—
294C2×C4#120×C12711yescharacteristic
295C2×C4#121×C12711yescharacteristic
296C2×C4#121×C12711yescharacteristic
297C2×C4#121×C12711yescharacteristic
298C2×C4#123×C12711yescharacteristic
299C2×C4#123×C12711yescharacteristic
300C8—24no—
301C8—42no—
302C8—81no—
303C8—81no—
304C8—81no—
305C22—21no—
306C22—21no—
307C22—21no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22#394×C12711yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—81no—
316C4—81no—
317C4—81no—
318C4#453×C12711yescharacteristic
319C4#456×C12711yescharacteristic
320C4#471×C12711yescharacteristic
321C4#471×C12711yescharacteristic
322C4#472×C12711yescharacteristic
323C4#473×C12711yescharacteristic
324C2—41no—
325C2—161no—
326C2C127×#203911yescharacteristic
327C2C127×#205111yescharacteristic
328C2C127×#205211yescharacteristic
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×#1848C2semidirect
3. C127×#1561C2semidirect
5. C127×#1493C2semidirect
7. C127×#1309C2semidirect
159. #10532C127direct (N × H)
166. #1848C2×C127semidirect
167. #1561C2×C127semidirect
169. #1493C2×C127semidirect
171. #1309C2×C127semidirect
172. C127#10532direct (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×#18482
C127×#15612
C127×#15602
C127×#14932
C127×#14922
C127×#13092
#10532127