Finite Group Databasebeta

← C127×#11829 #44575502

Subgroups — C127×#11829 #44575502

Order 32512.

416 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2398C211yesmaximal, characteristic
2C127×#1801C211yesmaximal, characteristic, complemented
3C127×#1467C211yesmaximal, characteristic, complemented
4C127×#1353C212yesmaximal, complemented
5C127×#1345C212yesmaximal
6C2×C4×Q8×C127C2211yescharacteristic
7C2×C4×D4×C127C411yescharacteristic
8#432×C127—21no—
9#423×C127—21no—
10C2×#101×C127—21no—
11#400×C127C411yescharacteristic
12#400×C127C2211yescharacteristic
13#397×C127—21no—
14#394×C127C411yescharacteristic
15#394×C127C2211yescharacteristic
16#393×C127—21no—
17C4×C22⋊C4×C127—21no—
18C4×C22⋊C4×C127—21no—
19#376×C127C411yescharacteristic
20#343×C127C2212yes—
21#324×C127—21no—
22#324×C127C2212yes—
23C22×Q8×C127D411yescharacteristic
24C22×D4×C127C2×C411yescharacteristic
25C23×C4×C127—21no—
26C2×M16×C127—22no—
27C4×Q8×C127—41no—
28C4×Q8×C127—41no—
29C4×D4×C127—41no—
30C4×D4×C127—41no—
31C2×C4⋊C4×C127C2×C411yescharacteristic
32C2×C4⋊C4×C127C2×C411yescharacteristic
33C2×C4⋊C4×C127D411yescharacteristic
34C2×C4⋊C4×C127C2311yescharacteristic
35C2×C22⋊C4×C127—21no—
36C2×C22⋊C4×C127—21no—
37C2×C22⋊C4×C127—21no—
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127—21no—
40C2×C42×C127—21no—
41C2×C42×C127C2×C411yescharacteristic
42C2×C42×C127D411yescharacteristic
43C2×C42×C127D411yescharacteristic
44C4⋊C8×C127—41no—
45C4⋊C8×C127—41no—
46C4⋊C8×C127—41no—
47#101×C127—42no—
48C22⋊C8×C127—22no—
49#97×C127—41no—
50#95×C127—21no—
51#95×C127—21no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127C2×C411yescharacteristic
56#95×C127C2×C411yescharacteristic
57C24×C127—21no—
58C2×Q8×C127—21no—
59C2×Q8×C127—21no—
60C2×Q8×C127—41no—
61C2×Q8×C127—41no—
62C2×D4×C127—41no—
63C2×D4×C127—42no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—42no—
68C22×C4×C127—42no—
69C22×C4×C127—41no—
70C22×C4×C127—41no—
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127C22⋊C411yescharacteristic
73C22×C4×C127C22⋊C411yescharacteristic
74C22×C4×C127C22⋊C411yescharacteristic
75C22×C4×C127C22×C411yescharacteristic
76C22×C4×C127C2×D411yescharacteristic
77C22×C4×C127C2×D411yescharacteristic
78M16×C127—42no—
79M16×C127—42no—
80C2×C8×C127—42no—
81C2×C8×C127—42no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C22⋊C4×C127—42no—
87C22⋊C4×C127—42no—
88C22⋊C4×C127—42no—
89C22⋊C4×C127—42no—
90C22⋊C4×C127—41no—
91C22⋊C4×C127—41no—
92C42×C127—21no—
93C42×C127—21no—
94C42×C127—21no—
95C42×C127—21no—
96C42×C127—21no—
97C42×C127—21no—
98C42×C127—42no—
99C23×C127—22no—
100C23×C127—41no—
101C23×C127—41no—
102C23×C127—41no—
103C23×C127—41no—
104C23×C127—41no—
105C23×C127—41no—
106C23×C127C2×C22⋊C411yescharacteristic
107Q8×C127—42no—
108Q8×C127—42no—
109D4×C127—42no—
110D4×C127—42no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—22no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—41no—
130C2×C4×C127—41no—
131C2×C4×C127—41no—
132C2×C4×C127—41no—
133C2×C4×C127—41no—
134C2×C4×C127—41no—
135C2×C4×C127—82no—
136C2×C4×C127—82no—
137C2×C4×C127#9911yescharacteristic
138C2×C4×C127#9911yescharacteristic
139C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C127#13711yescharacteristic
141C8×C127—82no—
142C8×C127—82no—
143C22×C127—21no—
144C22×C127—21no—
145C22×C127—42no—
146C22×C127—42no—
147C22×C127—42no—
148C22×C127—81no—
149C22×C127—81no—
150C22×C127—81no—
151C22×C127—81no—
152C22×C127C2×#9911yescharacteristic
153C22×C127#41711yescharacteristic
154C22×C127#42111yescharacteristic
155C4×C127—21no—
156C4×C127—21no—
157C4×C127—21no—
158C4×C127—41no—
159C4×C127—41no—
160C4×C127—41no—
161C4×C127—41no—
162C4×C127—41no—
163C4×C127—81no—
164C4×C127—81no—
165C4×C127—81no—
166C4×C127#35512yes—
167#11829C12711yesmaximal, characteristic, direct product factor, Sylow
168C2×C127—21no—
169C2×C127—21no—
170C2×C127—82no—
171C2×C127#151311yescharacteristic
172C2×C127#212011yescharacteristic
173C2×C127C2×#35511yescharacteristic
174#2398C2×C12711yescharacteristic
175#1801C2×C12711yescharacteristic, complemented
176#1467C2×C12711yescharacteristic, complemented
177#1353C2×C12712yescomplemented
178#1345C2×C12712yes—
179C127#1182911yescharacteristic, direct product factor, Sylow
180C2×C4×Q8C22×C12711yescharacteristic
181C2×C4×D4C4×C12711yescharacteristic
182#432—21no—
183#423—21no—
184C2×#101—21no—
185#400C4×C12711yescharacteristic
186#400C22×C12711yescharacteristic
187#397—21no—
188#394C4×C12711yescharacteristic
189#394C22×C12711yescharacteristic
190#393—21no—
191C4×C22⋊C4—21no—
192C4×C22⋊C4—21no—
193#376C4×C12711yescharacteristic
194#343C22×C12712yes—
195#324—21no—
196#324C22×C12712yes—
197C22×Q8D4×C12711yescharacteristic
198C22×D4C2×C4×C12711yescharacteristic
199C23×C4—21no—
200C2×M16—22no—
201C4×Q8—41no—
202C4×Q8—41no—
203C4×D4—41no—
204C4×D4—41no—
205C2×C4⋊C4C2×C4×C12711yescharacteristic
206C2×C4⋊C4C2×C4×C12711yescharacteristic
207C2×C4⋊C4D4×C12711yescharacteristic
208C2×C4⋊C4C23×C12711yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C42—21no—
215C2×C42C2×C4×C12711yescharacteristic
216C2×C42D4×C12711yescharacteristic
217C2×C42D4×C12711yescharacteristic
218C4⋊C8—41no—
219C4⋊C8—41no—
220C4⋊C8—41no—
221#101—42no—
222C22⋊C8—22no—
223#97—41no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95C2×C4×C12711yescharacteristic
230#95C2×C4×C12711yescharacteristic
231C24—21no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×D4—41no—
237C2×D4—42no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4C22⋊C4×C12711yescharacteristic
246C22×C4C22⋊C4×C12711yescharacteristic
247C22×C4C22⋊C4×C12711yescharacteristic
248C22×C4C22⋊C4×C12711yescharacteristic
249C22×C4C22×C4×C12711yescharacteristic
250C22×C4C2×D4×C12711yescharacteristic
251C22×C4C2×D4×C12711yescharacteristic
252M16—42no—
253M16—42no—
254C2×C8—42no—
255C2×C8—42no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C22⋊C4—42no—
261C22⋊C4—42no—
262C22⋊C4—42no—
263C22⋊C4—42no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C42—42no—
273C23—22no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23C2×C22⋊C4×C12711yescharacteristic
281Q8—42no—
282Q8—42no—
283D4—42no—
284D4—42no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—82no—
310C2×C4—82no—
311C2×C4#99×C12711yescharacteristic
312C2×C4#99×C12711yescharacteristic
313C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
314C2×C4#137×C12711yescharacteristic
315C8—82no—
316C8—82no—
317C22—21no—
318C22—21no—
319C22—42no—
320C22—42no—
321C22—42no—
322C22—81no—
323C22—81no—
324C22—81no—
325C22—81no—
326C22C2×#99×C12711yescharacteristic
327C22#417×C12711yescharacteristic
328C22#421×C12711yescharacteristic
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—41no—
337C4—81no—
338C4—81no—
339C4—81no—
340C4#355×C12712yes—
341C2—21no—
342C2—21no—
343C2—82no—
344C2C127×#151311yescharacteristic
345C2C127×#212011yescharacteristic
346C2C2×#355×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC22×D4×C127C2×C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1801C2semidirect
3. C127×#1467C2semidirect
4. C127×#1353C2semidirect
167. #11829C127direct (N × H)
175. #1801C2×C127semidirect
176. #1467C2×C127semidirect
177. #1353C2×C127semidirect
179. C127#11829direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#23982
C127×#18012
C127×#14672
C127×#13532
C127×#13452
#11829127