Finite Group Databasebeta

← C127×#11851 #44575524

Subgroups — C127×#11851 #44575524

Order 32512.

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

normal subgroups only

This group has 418 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×#2610C211yesmaximal, characteristic
2C127×#1822C211yesmaximal, characteristic, complemented
3C127×#1458C211yesmaximal, characteristic, complemented
4C127×#1354C212yesmaximal, complemented
5C127×#1345C212yesmaximal, complemented
6C2×#124×C127C411yescharacteristic
7C2×#117×C127C2211yescharacteristic
8#431×C127—21no—
9#407×C127—21no—
10#395×C127C2211yescharacteristic
11#394×C127C2211yescharacteristic
12#393×C127C411yescharacteristic
13#392×C127C411yescharacteristic
14#390×C127—21no—
15#388×C127—21no—
16#388×C127—21no—
17#386×C127—21no—
18#376×C127C411yescharacteristic
19#343×C127—21no—
20#343×C127C2212yes—
21#324×C127C2212yes—
22#323×C127—21no—
23C22×Q8×C127C2×C411yescharacteristic
24C22×D4×C127—21no—
25C22×D4×C127C2×C411yescharacteristic
26C23×C4×C127D411yescharacteristic
27C2×M16×C127—22no—
28#124×C127—41no—
29#124×C127—41no—
30#117×C127—41no—
31#117×C127—41no—
32C2×C4⋊C4×C127—21no—
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×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127C2×C411yescharacteristic
42C2×C22⋊C4×C127D411yescharacteristic
43C2×C42×C127—21no—
44C2×C42×C127C2×C411yescharacteristic
45C2×C42×C127D411yescharacteristic
46C4⋊C8×C127—41no—
47C22⋊C8×C127—22no—
48C22⋊C8×C127—41no—
49C22⋊C8×C127—41no—
50C4×C8×C127—41no—
51#95×C127—21no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127C2×C411yescharacteristic
55#95×C127C2×C411yescharacteristic
56C24×C127—21no—
57C24×C127C22⋊C411yescharacteristic
58C2×Q8×C127—41no—
59C2×Q8×C127—81no—
60C2×D4×C127—41no—
61C2×D4×C127—42no—
62C2×D4×C127—42no—
63C2×D4×C127—81no—
64C2×D4×C127—81no—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—22no—
69C22×C4×C127—21no—
70C22×C4×C127—21no—
71C22×C4×C127—41no—
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—81no—
85C22⋊C4×C127—41no—
86C22⋊C4×C127—41no—
87C22⋊C4×C127—42no—
88C22⋊C4×C127—42no—
89C22⋊C4×C127—41no—
90C22⋊C4×C127—41no—
91C22⋊C4×C127—42no—
92C22⋊C4×C127—81no—
93C22⋊C4×C127—81no—
94C42×C127—21no—
95C42×C127—21no—
96C42×C127—21no—
97C42×C127—21no—
98C42×C127—42no—
99C23×C127—21no—
100C23×C127—21no—
101C23×C127—21no—
102C23×C127—41no—
103C23×C127—41no—
104C23×C127—41no—
105C23×C127—41no—
106C23×C127—41no—
107C23×C127—41no—
108C23×C127—41no—
109C23×C127—41no—
110C23×C127—41no—
111C23×C127C2×C22⋊C411yescharacteristic
112Q8×C127—82no—
113D4×C127—84no—
114D4×C127—82no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—22no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—21no—
124C2×C4×C127—42no—
125C2×C4×C127—42no—
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—41no—
136C2×C4×C127—41no—
137C2×C4×C127—41no—
138C2×C4×C127#9911yescharacteristic
139C2×C4×C127#9911yescharacteristic
140C2×C4×C127#13512yes—
141C8×C127—82no—
142C8×C127—82no—
143C22×C127—21no—
144C22×C127—21no—
145C22×C127—42no—
146C22×C127—41no—
147C22×C127—41no—
148C22×C127—41no—
149C22×C127—81no—
150C22×C127—81no—
151C22×C127—81no—
152C22×C127—81no—
153C22×C127—81no—
154C22×C127—81no—
155C22×C127—81no—
156C22×C127—81no—
157C22×C127C2×#9911yescharacteristic
158C22×C127#41611yescharacteristic
159C22×C127#42111yescharacteristic
160C4×C127—22no—
161C4×C127—21no—
162C4×C127—21no—
163C4×C127—42no—
164C4×C127—41no—
165C4×C127—41no—
166C4×C127—41no—
167C4×C127—41no—
168C4×C127—81no—
169C4×C127—81no—
170#11851C12711yesmaximal, characteristic, direct product factor, Sylow
171C2×C127—21no—
172C2×C127—21no—
173C2×C127—81no—
174C2×C127—161no—
175C2×C127#151611yescharacteristic
176C2×C127#212211yescharacteristic
177C2×C127#213211yescharacteristic
178#2610C2×C12711yescharacteristic
179#1822C2×C12711yescharacteristic, complemented
180#1458C2×C12711yescharacteristic, complemented
181#1354C2×C12712yescomplemented
182#1345C2×C12712yescomplemented
183C127#1185111yescharacteristic, direct product factor, Sylow
184C2×#124C4×C12711yescharacteristic
185C2×#117C22×C12711yescharacteristic
186#431—21no—
187#407—21no—
188#395C22×C12711yescharacteristic
189#394C22×C12711yescharacteristic
190#393C4×C12711yescharacteristic
191#392C4×C12711yescharacteristic
192#390—21no—
193#388—21no—
194#388—21no—
195#386—21no—
196#376C4×C12711yescharacteristic
197#343—21no—
198#343C22×C12712yes—
199#324C22×C12712yes—
200#323—21no—
201C22×Q8C2×C4×C12711yescharacteristic
202C22×D4—21no—
203C22×D4C2×C4×C12711yescharacteristic
204C23×C4D4×C12711yescharacteristic
205C2×M16—22no—
206#124—41no—
207#124—41no—
208#117—41no—
209#117—41no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4D4×C12711yescharacteristic
212C2×C4⋊C4C23×C12711yescharacteristic
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4C2×C4×C12711yescharacteristic
220C2×C22⋊C4D4×C12711yescharacteristic
221C2×C42—21no—
222C2×C42C2×C4×C12711yescharacteristic
223C2×C42D4×C12711yescharacteristic
224C4⋊C8—41no—
225C22⋊C8—22no—
226C22⋊C8—41no—
227C22⋊C8—41no—
228C4×C8—41no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95C2×C4×C12711yescharacteristic
233#95C2×C4×C12711yescharacteristic
234C24—21no—
235C24C22⋊C4×C12711yescharacteristic
236C2×Q8—41no—
237C2×Q8—81no—
238C2×D4—41no—
239C2×D4—42no—
240C2×D4—42no—
241C2×D4—81no—
242C2×D4—81no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—22no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4C22⋊C4×C12711yescharacteristic
251C22×C4C22⋊C4×C12711yescharacteristic
252C22×C4C22⋊C4×C12711yescharacteristic
253C22×C4C22×C4×C12711yescharacteristic
254C22×C4C2×D4×C12711yescharacteristic
255C22×C4C2×D4×C12711yescharacteristic
256M16—42no—
257M16—42no—
258C2×C8—42no—
259C2×C8—42no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—81no—
263C22⋊C4—41no—
264C22⋊C4—41no—
265C22⋊C4—42no—
266C22⋊C4—42no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—42no—
270C22⋊C4—81no—
271C22⋊C4—81no—
272C42—21no—
273C42—21no—
274C42—21no—
275C42—21no—
276C42—42no—
277C23—21no—
278C23—21no—
279C23—21no—
280C23—41no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23C2×C22⋊C4×C12711yescharacteristic
290Q8—82no—
291D4—84no—
292D4—82no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4#99×C12711yescharacteristic
317C2×C4#99×C12711yescharacteristic
318C2×C4#135×C12712yes—
319C8—82no—
320C8—82no—
321C22—21no—
322C22—21no—
323C22—42no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22—81no—
331C22—81no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22C2×#99×C12711yescharacteristic
336C22#416×C12711yescharacteristic
337C22#421×C12711yescharacteristic
338C4—22no—
339C4—21no—
340C4—21no—
341C4—42no—
342C4—41no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—81no—
347C4—81no—
348C2—21no—
349C2—21no—
350C2—81no—
351C2—161no—
352C2C127×#151611yescharacteristic
353C2C127×#212211yescharacteristic
354C2C127×#213211yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radical#392×C127C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1822C2semidirect
3. C127×#1458C2semidirect
4. C127×#1354C2semidirect
5. C127×#1345C2semidirect
170. #11851C127direct (N × H)
179. #1822C2×C127semidirect
180. #1458C2×C127semidirect
181. #1354C2×C127semidirect
182. #1345C2×C127semidirect
183. C127#11851direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#26102
C127×#18222
C127×#14582
C127×#13542
C127×#13452
#11851127