Finite Group Databasebeta

← C127×#11729 #44575402

Subgroups — C127×#11729 #44575402

Order 32512.

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

normal subgroups only

This group has 486 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×#2635C211yesmaximal, characteristic
2C4×#99×C127C211yesmaximal, characteristic, complemented
3C127×#1460C211yesmaximal, characteristic, complemented
4C127×#1352C212yesmaximal, complemented
5C127×#1343C212yesmaximal, complemented
6C2×#121×C127C411yescharacteristic, complemented
7C2×C4×D4×C127C2211yescharacteristic
8#431×C127—21no—
9C2×#99×C127—21no—
10#400×C127C411yescharacteristic, complemented
11#399×C127C2211yescharacteristic
12#394×C127—21no—
13#394×C127C411yescharacteristic, complemented
14#392×C127—21no—
15#392×C127C2211yescharacteristic
16#388×C127—21no—
17#386×C127—21no—
18#381×C127C411yescharacteristic, complemented
19C4×C22⋊C4×C127—21no—
20#342×C127C2212yes—
21#323×C127—21no—
22#323×C127C2212yes—
23C22×D4×C127—21no—
24C22×D4×C127—21no—
25C22×D4×C127C2×C411yescharacteristic
26C22×D4×C127D411yescharacteristic
27C23×C4×C127C2×C411yescharacteristic
28C23×C4×C127D411yescharacteristic
29#121×C127—41no—
30#121×C127—41no—
31C4×D4×C127—41no—
32C4×D4×C127—41no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127C2×C411yescharacteristic
35C2×C4⋊C4×C127C2×C411yescharacteristic
36C2×C22⋊C4×C127—22no—
37C2×C22⋊C4×C127—21no—
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127D411yescharacteristic
44C2×C22⋊C4×C127C2311yescharacteristic
45C2×C42×C127—41no—
46C2×C42×C127D411yescharacteristic
47C4⋊C8×C127—41no—
48#99×C127—24no—
49C22⋊C8×C127—22no—
50C4×C8×C127—41no—
51#95×C127—21no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127—41no—
55#95×C127C2×C411yescharacteristic
56#95×C127C2×C411yescharacteristic
57C24×C127—21no—
58C24×C127C22⋊C411yescharacteristic
59C24×C127C2×D411yescharacteristic
60C2×D4×C127—22no—
61C2×D4×C127—22no—
62C2×D4×C127—41no—
63C2×D4×C127—41no—
64C2×D4×C127—42no—
65C2×D4×C127—42no—
66C2×D4×C127—81no—
67C2×D4×C127—81no—
68C2×D4×C127—81no—
69C2×D4×C127—81no—
70C2×D4×C127—81no—
71C22×C4×C127—21no—
72C22×C4×C127—21no—
73C22×C4×C127—21no—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—42no—
79C22×C4×C127—81no—
80C22×C4×C127—81no—
81C22×C4×C127C22⋊C411yescharacteristic
82C22×C4×C127C22⋊C411yescharacteristic
83C22×C4×C127C22⋊C411yescharacteristic
84C22×C4×C127C22×C411yescharacteristic
85C22×C4×C127C2×D411yescharacteristic
86C2×C8×C127—42no—
87C4⋊C4×C127—41no—
88C4⋊C4×C127—41no—
89C4⋊C4×C127—81no—
90C22⋊C4×C127—24no—
91C22⋊C4×C127—41no—
92C22⋊C4×C127—41no—
93C22⋊C4×C127—42no—
94C22⋊C4×C127—41no—
95C22⋊C4×C127—41no—
96C22⋊C4×C127—42no—
97C22⋊C4×C127—81no—
98C22⋊C4×C127—81no—
99C22⋊C4×C127—81no—
100C22⋊C4×C127—81no—
101C42×C127—21no—
102C42×C127—21no—
103C42×C127—82no—
104C23×C127—21no—
105C23×C127—21no—
106C23×C127—21no—
107C23×C127—21no—
108C23×C127—21no—
109C23×C127—41no—
110C23×C127—41no—
111C23×C127—41no—
112C23×C127—41no—
113C23×C127—41no—
114C23×C127—41no—
115C23×C127—41no—
116C23×C127—41no—
117C23×C127—41no—
118C23×C127—41no—
119C23×C127—41no—
120C23×C127C2×C22⋊C411yescharacteristic
121C23×C127#13512yes—
122D4×C127—44no—
123D4×C127—82no—
124D4×C127—84no—
125D4×C127—84no—
126C2×C4×C127—21no—
127C2×C4×C127—21no—
128C2×C4×C127—21no—
129C2×C4×C127—21no—
130C2×C4×C127—21no—
131C2×C4×C127—41no—
132C2×C4×C127—42no—
133C2×C4×C127—41no—
134C2×C4×C127—41no—
135C2×C4×C127—41no—
136C2×C4×C127—44no—
137C2×C4×C127—41no—
138C2×C4×C127—41no—
139C2×C4×C127—41no—
140C2×C4×C127—41no—
141C2×C4×C127—41no—
142C2×C4×C127—41no—
143C2×C4×C127—41no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127—81no—
147C2×C4×C127—81no—
148C2×C4×C127—81no—
149C2×C4×C127—82no—
150C2×C4×C127—82no—
151C2×C4×C127#9911yescharacteristic
152C2×C4×C127#9911yescharacteristic
153C2×C4×C127#10412yes—
154C8×C127—82no—
155C22×C127—21no—
156C22×C127—21no—
157C22×C127—22no—
158C22×C127—42no—
159C22×C127—41no—
160C22×C127—41no—
161C22×C127—41no—
162C22×C127—41no—
163C22×C127—41no—
164C22×C127—81no—
165C22×C127—81no—
166C22×C127—81no—
167C22×C127—81no—
168C22×C127—81no—
169C22×C127—81no—
170C22×C127—81no—
171C22×C127—81no—
172C22×C127—81no—
173C22×C127—81no—
174C22×C127C2×#9911yescharacteristic
175C22×C127#41611yescharacteristic
176C22×C127C2×#10411yescharacteristic
177C4×C127—21no—
178C4×C127—21no—
179C4×C127—22no—
180C4×C127—41no—
181C4×C127—41no—
182C4×C127—41no—
183C4×C127—81no—
184C4×C127—81no—
185C4×C127—84no—
186C4×C127—81no—
187#11729C12711yesmaximal, characteristic, direct product factor, Sylow
188C2×C127—21no—
189C2×C127—21no—
190C2×C127—42no—
191C2×C127—81no—
192C2×C127—161no—
193C2×C127#150111yescharacteristic
194C2×C127#212111yescharacteristic
195C2×C127#212811yescharacteristic
196#2635C2×C12711yescharacteristic
197C4×#99C2×C12711yescharacteristic, complemented
198#1460C2×C12711yescharacteristic, complemented
199#1352C2×C12712yescomplemented
200#1343C2×C12712yescomplemented
201C127#1172911yescharacteristic, direct product factor, Sylow
202C2×#121C4×C12711yescharacteristic, complemented
203C2×C4×D4C22×C12711yescharacteristic
204#431—21no—
205C2×#99—21no—
206#400C4×C12711yescharacteristic, complemented
207#399C22×C12711yescharacteristic
208#394—21no—
209#394C4×C12711yescharacteristic, complemented
210#392—21no—
211#392C22×C12711yescharacteristic
212#388—21no—
213#386—21no—
214#381C4×C12711yescharacteristic, complemented
215C4×C22⋊C4—21no—
216#342C22×C12712yes—
217#323—21no—
218#323C22×C12712yes—
219C22×D4—21no—
220C22×D4—21no—
221C22×D4C2×C4×C12711yescharacteristic
222C22×D4D4×C12711yescharacteristic
223C23×C4C2×C4×C12711yescharacteristic
224C23×C4D4×C12711yescharacteristic
225#121—41no—
226#121—41no—
227C4×D4—41no—
228C4×D4—41no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4C2×C4×C12711yescharacteristic
231C2×C4⋊C4C2×C4×C12711yescharacteristic
232C2×C22⋊C4—22no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4D4×C12711yescharacteristic
240C2×C22⋊C4C23×C12711yescharacteristic
241C2×C42—41no—
242C2×C42D4×C12711yescharacteristic
243C4⋊C8—41no—
244#99—24no—
245C22⋊C8—22no—
246C4×C8—41no—
247#95—21no—
248#95—21no—
249#95—21no—
250#95—41no—
251#95C2×C4×C12711yescharacteristic
252#95C2×C4×C12711yescharacteristic
253C24—21no—
254C24C22⋊C4×C12711yescharacteristic
255C24C2×D4×C12711yescharacteristic
256C2×D4—22no—
257C2×D4—22no—
258C2×D4—41no—
259C2×D4—41no—
260C2×D4—42no—
261C2×D4—42no—
262C2×D4—81no—
263C2×D4—81no—
264C2×D4—81no—
265C2×D4—81no—
266C2×D4—81no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—42no—
275C22×C4—81no—
276C22×C4—81no—
277C22×C4C22⋊C4×C12711yescharacteristic
278C22×C4C22⋊C4×C12711yescharacteristic
279C22×C4C22⋊C4×C12711yescharacteristic
280C22×C4C22×C4×C12711yescharacteristic
281C22×C4C2×D4×C12711yescharacteristic
282C2×C8—42no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—81no—
286C22⋊C4—24no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—42no—
290C22⋊C4—41no—
291C22⋊C4—41no—
292C22⋊C4—42no—
293C22⋊C4—81no—
294C22⋊C4—81no—
295C22⋊C4—81no—
296C22⋊C4—81no—
297C42—21no—
298C42—21no—
299C42—82no—
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23—21no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23C2×C22⋊C4×C12711yescharacteristic
317C23#135×C12712yes—
318D4—44no—
319D4—82no—
320D4—84no—
321D4—84no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—41no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—44no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—82no—
346C2×C4—82no—
347C2×C4#99×C12711yescharacteristic
348C2×C4#99×C12711yescharacteristic
349C2×C4#104×C12712yes—
350C8—82no—
351C22—21no—
352C22—21no—
353C22—22no—
354C22—42no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22—81no—
368C22—81no—
369C22—81no—
370C22C2×#99×C12711yescharacteristic
371C22#416×C12711yescharacteristic
372C22C2×#104×C12711yescharacteristic
373C4—21no—
374C4—21no—
375C4—22no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—81no—
380C4—81no—
381C4—84no—
382C4—81no—
383C2—21no—
384C2—21no—
385C2—42no—
386C2—81no—
387C2—161no—
388C2C127×#150111yescharacteristic
389C2C127×#212111yescharacteristic
390C2C127×#212811yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C22⋊C4C23×C127
prime radicalC127×#2635C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#99×C127C2semidirect
3. C127×#1460C2semidirect
4. C127×#1352C2semidirect
5. C127×#1343C2semidirect
6. C2×#121×C127C4semidirect
10. #400×C127C4semidirect
13. #394×C127C4semidirect
18. #381×C127C4semidirect
187. #11729C127direct (N × H)
197. C4×#99C2×C127semidirect
198. #1460C2×C127semidirect
199. #1352C2×C127semidirect
200. #1343C2×C127semidirect
201. C127#11729direct (N × H)
202. C2×#121C4×C127semidirect
206. #400C4×C127semidirect
209. #394C4×C127semidirect
214. #381C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#26352
C4×#99×C1272
C127×#14602
C127×#13522
C127×#13432
#11729127