Finite Group Databasebeta

← C127×#11502 #44575175

Subgroups — C127×#11502 #44575175

Order 32512.

714 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 714 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2308C211yesmaximal, characteristic
2C127×#1462C212yesmaximal, complemented
3C127×#1317C212yesmaximal, complemented
4C127×#1316C212yesmaximal, complemented
5C23×D4×C127C411yescharacteristic
6C22×C22⋊C4×C127C411yescharacteristic
7C22×C22⋊C4×C127C2211yescharacteristic
8#407×C127—22no—
9#386×C127—22no—
10#386×C127—22no—
11#381×C127C411yescharacteristic
12#381×C127C2211yescharacteristic
13#379×C127C411yescharacteristic
14#379×C127C2211yescharacteristic
15#323×C127—22no—
16#323×C127C2214yes—
17C25×C127C2×C411yescharacteristic
18C25×C127C2×C411yescharacteristic
19C22×D4×C127—21no—
20C22×D4×C127—21no—
21C22×D4×C127—22no—
22C22×D4×C127—22no—
23C22×D4×C127—41no—
24C22×D4×C127—41no—
25C22×D4×C127—42no—
26C23×C4×C127—21no—
27C23×C4×C127C2×C411yescharacteristic
28C23×C4×C127D412yes—
29C2×M16×C127—42no—
30C2×C22⋊C4×C127—21no—
31C2×C22⋊C4×C127—22no—
32C2×C22⋊C4×C127—22no—
33C2×C22⋊C4×C127—41no—
34C2×C22⋊C4×C127—41no—
35C2×C22⋊C4×C127—42no—
36C2×C22⋊C4×C127C2×C411yescharacteristic
37C2×C22⋊C4×C127C2×C411yescharacteristic
38C2×C22⋊C4×C127C2×C411yescharacteristic
39C2×C22⋊C4×C127D412yes—
40C2×C22⋊C4×C127C2311yescharacteristic
41C22⋊C8×C127—24no—
42C22⋊C8×C127—42no—
43#95×C127—22no—
44#95×C127—22no—
45C24×C127—21no—
46C24×C127—21no—
47C24×C127—22no—
48C24×C127—21no—
49C24×C127—21no—
50C24×C127—21no—
51C24×C127—21no—
52C24×C127—41no—
53C24×C127—41no—
54C24×C127—82no—
55C24×C127—82no—
56C24×C127C22⋊C411yescharacteristic
57C24×C127C22⋊C411yescharacteristic
58C24×C127M1612yescomplemented
59C24×C127C22×C411yescharacteristic
60C2×D4×C127—24no—
61C2×D4×C127—24no—
62C2×D4×C127—44no—
63C2×D4×C127—44no—
64C2×D4×C127—42no—
65C2×D4×C127—42no—
66C2×D4×C127—44no—
67C2×D4×C127—44no—
68C2×D4×C127—41no—
69C2×D4×C127—41no—
70C2×D4×C127—42no—
71C22×C4×C127—22no—
72C22×C4×C127—21no—
73C22×C4×C127—21no—
74C22×C4×C127—22no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—41no—
78C22×C4×C127—41no—
79C22×C4×C127—42no—
80C22×C4×C127—82no—
81C22×C4×C127—82no—
82C22×C4×C127C22⋊C412yes—
83C22×C4×C127M1612yescomplemented
84C22×C4×C127C2×D412yes—
85M16×C127—84no—
86C2×C8×C127—44no—
87C22⋊C4×C127—41no—
88C22⋊C4×C127—42no—
89C22⋊C4×C127—41no—
90C22⋊C4×C127—42no—
91C22⋊C4×C127—41no—
92C22⋊C4×C127—41no—
93C22⋊C4×C127—82no—
94C22⋊C4×C127—82no—
95C23×C127—22no—
96C23×C127—22no—
97C23×C127—22no—
98C23×C127—22no—
99C23×C127—21no—
100C23×C127—21no—
101C23×C127—21no—
102C23×C127—21no—
103C23×C127—21no—
104C23×C127—21no—
105C23×C127—22no—
106C23×C127—42no—
107C23×C127—42no—
108C23×C127—42no—
109C23×C127—42no—
110C23×C127—42no—
111C23×C127—42no—
112C23×C127—42no—
113C23×C127—41no—
114C23×C127—41no—
115C23×C127—82no—
116C23×C127—82no—
117C23×C127—82no—
118C23×C127—84no—
119C23×C127—82no—
120C23×C127—82no—
121C23×C127—82no—
122C23×C127—84no—
123C23×C127—84no—
124C23×C127#9911yescharacteristic
125C23×C127#9911yescharacteristic
126C23×C127#10012yes—
127C23×C127C2×C22⋊C411yescharacteristic
128C23×C127C2×M1611yescharacteristic
129C23×C127C2×M1611yescharacteristic
130D4×C127—44no—
131D4×C127—44no—
132D4×C127—48no—
133C2×C4×C127—22no—
134C2×C4×C127—22no—
135C2×C4×C127—22no—
136C2×C4×C127—44no—
137C2×C4×C127—42no—
138C2×C4×C127—41no—
139C2×C4×C127—41no—
140C2×C4×C127—42no—
141C2×C4×C127—42no—
142C2×C4×C127—42no—
143C2×C4×C127—42no—
144C2×C4×C127—42no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—82no—
148C2×C4×C127—84no—
149C8×C127—84no—
150C22×C127—22no—
151C22×C127—22no—
152C22×C127—22no—
153C22×C127—21no—
154C22×C127—21no—
155C22×C127—21no—
156C22×C127—21no—
157C22×C127—22no—
158C22×C127—42no—
159C22×C127—41no—
160C22×C127—41no—
161C22×C127—42no—
162C22×C127—42no—
163C22×C127—42no—
164C22×C127—42no—
165C22×C127—42no—
166C22×C127—42no—
167C22×C127—42no—
168C22×C127—42no—
169C22×C127—42no—
170C22×C127—82no—
171C22×C127—82no—
172C22×C127—82no—
173C22×C127—82no—
174C22×C127—82no—
175C22×C127—84no—
176C22×C127—84no—
177C22×C127—82no—
178C22×C127#40711yescharacteristic
179C22×C127C2×#9911yescharacteristic
180C22×C127C2×#10011yescharacteristic
181C4×C127—42no—
182C4×C127—42no—
183C4×C127—42no—
184C4×C127—81no—
185C4×C127—81no—
186#11502C12711yesmaximal, characteristic, direct product factor, Sylow
187C2×C127—21no—
188C2×C127—21no—
189C2×C127—41no—
190C2×C127—41no—
191C2×C127—42no—
192C2×C127—41no—
193C2×C127—41no—
194C2×C127—82no—
195C2×C127#146211yescharacteristic
196C2×C127#212112yes—
197#2308C2×C12711yescharacteristic
198#1462C2×C12712yescomplemented
199#1317C2×C12712yescomplemented
200#1316C2×C12712yescomplemented
201C127#1150211yescharacteristic, direct product factor, Sylow
202C23×D4C4×C12711yescharacteristic
203C22×C22⋊C4C4×C12711yescharacteristic
204C22×C22⋊C4C22×C12711yescharacteristic
205#407—22no—
206#386—22no—
207#386—22no—
208#381C4×C12711yescharacteristic
209#381C22×C12711yescharacteristic
210#379C4×C12711yescharacteristic
211#379C22×C12711yescharacteristic
212#323—22no—
213#323C22×C12714yes—
214C25C2×C4×C12711yescharacteristic
215C25C2×C4×C12711yescharacteristic
216C22×D4—21no—
217C22×D4—21no—
218C22×D4—22no—
219C22×D4—22no—
220C22×D4—41no—
221C22×D4—41no—
222C22×D4—42no—
223C23×C4—21no—
224C23×C4C2×C4×C12711yescharacteristic
225C23×C4D4×C12712yes—
226C2×M16—42no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—22no—
229C2×C22⋊C4—22no—
230C2×C22⋊C4—41no—
231C2×C22⋊C4—41no—
232C2×C22⋊C4—42no—
233C2×C22⋊C4C2×C4×C12711yescharacteristic
234C2×C22⋊C4C2×C4×C12711yescharacteristic
235C2×C22⋊C4C2×C4×C12711yescharacteristic
236C2×C22⋊C4D4×C12712yes—
237C2×C22⋊C4C23×C12711yescharacteristic
238C22⋊C8—24no—
239C22⋊C8—42no—
240#95—22no—
241#95—22no—
242C24—21no—
243C24—21no—
244C24—22no—
245C24—21no—
246C24—21no—
247C24—21no—
248C24—21no—
249C24—41no—
250C24—41no—
251C24—82no—
252C24—82no—
253C24C22⋊C4×C12711yescharacteristic
254C24C22⋊C4×C12711yescharacteristic
255C24M16×C12712yescomplemented
256C24C22×C4×C12711yescharacteristic
257C2×D4—24no—
258C2×D4—24no—
259C2×D4—44no—
260C2×D4—44no—
261C2×D4—42no—
262C2×D4—42no—
263C2×D4—44no—
264C2×D4—44no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—42no—
268C22×C4—22no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4—42no—
277C22×C4—82no—
278C22×C4—82no—
279C22×C4C22⋊C4×C12712yes—
280C22×C4M16×C12712yescomplemented
281C22×C4C2×D4×C12712yes—
282M16—84no—
283C2×C8—44no—
284C22⋊C4—41no—
285C22⋊C4—42no—
286C22⋊C4—41no—
287C22⋊C4—42no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—82no—
291C22⋊C4—82no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—22no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—22no—
303C23—42no—
304C23—42no—
305C23—42no—
306C23—42no—
307C23—42no—
308C23—42no—
309C23—42no—
310C23—41no—
311C23—41no—
312C23—82no—
313C23—82no—
314C23—82no—
315C23—84no—
316C23—82no—
317C23—82no—
318C23—82no—
319C23—84no—
320C23—84no—
321C23#99×C12711yescharacteristic
322C23#99×C12711yescharacteristic
323C23#100×C12712yes—
324C23C2×C22⋊C4×C12711yescharacteristic
325C23C2×M16×C12711yescharacteristic
326C23C2×M16×C12711yescharacteristic
327D4—44no—
328D4—44no—
329D4—48no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—44no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—82no—
345C2×C4—84no—
346C8—84no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—22no—
355C22—42no—
356C22—41no—
357C22—41no—
358C22—42no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—42no—
364C22—42no—
365C22—42no—
366C22—42no—
367C22—82no—
368C22—82no—
369C22—82no—
370C22—82no—
371C22—82no—
372C22—84no—
373C22—84no—
374C22—82no—
375C22#407×C12711yescharacteristic
376C22C2×#99×C12711yescharacteristic
377C22C2×#100×C12711yescharacteristic
378C4—42no—
379C4—42no—
380C4—42no—
381C4—81no—
382C4—81no—
383C2—21no—
384C2—21no—
385C2—41no—
386C2—41no—
387C2—41no—
388C2—41no—
389C2—42no—
390C2—82no—
391C2C127×#146211yescharacteristic
392C2C127×#212112yes—
subgroupG/H
center, socleC22×C127C2×#99
commutatorC24C22×C4×C127
Frattini, cosocleC2×C22⋊C4C23×C127
prime radicalC23×D4×C127C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C127 ◁ C22×C22⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1462C2semidirect
3. C127×#1317C2semidirect
4. C127×#1316C2semidirect
58. C24×C127M16semidirect
83. C22×C4×C127M16semidirect
186. #11502C127direct (N × H)
198. #1462C2×C127semidirect
199. #1317C2×C127semidirect
200. #1316C2×C127semidirect
201. C127#11502direct (N × H)
255. C24M16×C127semidirect
280. C22×C4M16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#23082
C127×#14622
C127×#13172
C127×#13162
#11502127