Finite Group Databasebeta

← C127×#11811 #44575484

Subgroups — C127×#11811 #44575484

Order 32512.

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

normal subgroups only

This group has 496 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×#2626C211yesmaximal, characteristic
2C127×#1819C211yesmaximal, characteristic
3C127×#1462C211yesmaximal, characteristic
4C127×#1352C212yesmaximal, complemented
5C127×#1351C212yesmaximal, complemented
6C2×C22⋊Q8×C127C411yescharacteristic, complemented
7C22×C22⋊C4×C127C2211yescharacteristic
8#407×C127—21no—
9#399×C127C411yescharacteristic, complemented
10#399×C127C2211yescharacteristic
11#396×C127—21no—
12#396×C127—21no—
13#393×C127C411yescharacteristic, complemented
14#393×C127C2211yescharacteristic
15#385×C127—21no—
16#380×C127C411yescharacteristic, complemented
17#379×C127—21no—
18#379×C127—21no—
19#342×C127—21no—
20#342×C127C2212yes—
21#323×C127—21no—
22#323×C127C2212yes—
23C25×C127D411yescharacteristic
24C22×Q8×C127C2×C411yescharacteristic
25C23×C4×C127C2×C411yescharacteristic
26C23×C4×C127D411yescharacteristic
27C2×M16×C127—41no—
28C22⋊Q8×C127—41no—
29C22⋊Q8×C127—41no—
30C2×C4⋊C4×C127—21no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127C2×C411yescharacteristic
35C2×C22⋊C4×C127—21no—
36C2×C22⋊C4×C127—21no—
37C2×C22⋊C4×C127—22no—
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—41no—
43C2×C22⋊C4×C127—41no—
44C2×C22⋊C4×C127—41no—
45C2×C22⋊C4×C127—41no—
46C2×C22⋊C4×C127C2×C411yescharacteristic
47C2×C22⋊C4×C127D411yescharacteristic
48C2×C22⋊C4×C127D411yescharacteristic
49C2×C22⋊C4×C127C2311yescharacteristic
50C22⋊C8×C127—22no—
51C22⋊C8×C127—41no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127C2×C411yescharacteristic
55#95×C127C2×C411yescharacteristic
56C24×C127—21no—
57C24×C127—21no—
58C24×C127—22no—
59C24×C127—41no—
60C24×C127—81no—
61C24×C127—81no—
62C24×C127C22⋊C411yescharacteristic
63C24×C127C22⋊C411yescharacteristic
64C24×C127C2×D411yescharacteristic
65C2×Q8×C127—41no—
66C2×Q8×C127—81no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127—21no—
71C22×C4×C127—21no—
72C22×C4×C127—21no—
73C22×C4×C127—21no—
74C22×C4×C127—21no—
75C22×C4×C127—42no—
76C22×C4×C127—81no—
77C22×C4×C127—81no—
78C22×C4×C127C22⋊C411yescharacteristic
79C22×C4×C127C22⋊C411yescharacteristic
80C22×C4×C127C22×C411yescharacteristic
81C22×C4×C127C2×D411yescharacteristic
82M16×C127—82no—
83C2×C8×C127—42no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—42no—
86C4⋊C4×C127—81no—
87C4⋊C4×C127—81no—
88C4⋊C4×C127—81no—
89C22⋊C4×C127—41no—
90C22⋊C4×C127—41no—
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—42no—
98C22⋊C4×C127—81no—
99C22⋊C4×C127—81no—
100C22⋊C4×C127—81no—
101C22⋊C4×C127—81no—
102C22⋊C4×C127—82no—
103C22⋊C4×C127—82no—
104C23×C127—21no—
105C23×C127—21no—
106C23×C127—21no—
107C23×C127—21no—
108C23×C127—21no—
109C23×C127—21no—
110C23×C127—21no—
111C23×C127—41no—
112C23×C127—41no—
113C23×C127—42no—
114C23×C127—42no—
115C23×C127—41no—
116C23×C127—41no—
117C23×C127—41no—
118C23×C127—41no—
119C23×C127—42no—
120C23×C127—42no—
121C23×C127—81no—
122C23×C127—81no—
123C23×C127—84no—
124C23×C127—84no—
125C23×C127#9911yescharacteristic
126C23×C127#9911yescharacteristic
127C23×C127C2×C22⋊C411yescharacteristic
128C23×C127#13712yes—
129Q8×C127—82no—
130C2×C4×C127—21no—
131C2×C4×C127—21no—
132C2×C4×C127—21no—
133C2×C4×C127—21no—
134C2×C4×C127—42no—
135C2×C4×C127—41no—
136C2×C4×C127—41no—
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—41no—
147C2×C4×C127—41no—
148C2×C4×C127—41no—
149C2×C4×C127—41no—
150C2×C4×C127—41no—
151C2×C4×C127—81no—
152C2×C4×C127—81no—
153C2×C4×C127—81no—
154C2×C4×C127—82no—
155C2×C4×C127—82no—
156C2×C4×C127—82no—
157C8×C127—82no—
158C22×C127—21no—
159C22×C127—21no—
160C22×C127—21no—
161C22×C127—21no—
162C22×C127—21no—
163C22×C127—21no—
164C22×C127—22no—
165C22×C127—21no—
166C22×C127—21no—
167C22×C127—42no—
168C22×C127—42no—
169C22×C127—42no—
170C22×C127—42no—
171C22×C127—41no—
172C22×C127—41no—
173C22×C127—41no—
174C22×C127—41no—
175C22×C127—41no—
176C22×C127—81no—
177C22×C127—81no—
178C22×C127—84no—
179C22×C127—84no—
180C22×C127C2×#9911yescharacteristic
181C22×C127#41911yescharacteristic
182C22×C127#42111yescharacteristic
183C4×C127—41no—
184C4×C127—41no—
185C4×C127—41no—
186C4×C127—41no—
187C4×C127—81no—
188C4×C127—81no—
189C4×C127—81no—
190C4×C127—81no—
191C4×C127—162no—
192#11811C12711yesmaximal, characteristic, direct product factor, Sylow
193C2×C127—21no—
194C2×C127—21no—
195C2×C127—42no—
196C2×C127—41no—
197C2×C127—41no—
198C2×C127—81no—
199C2×C127#151111yescharacteristic
200C2×C127#212111yescharacteristic
201C2×C127#212711yescharacteristic
202#2626C2×C12711yescharacteristic
203#1819C2×C12711yescharacteristic
204#1462C2×C12711yescharacteristic
205#1352C2×C12712yescomplemented
206#1351C2×C12712yescomplemented
207C127#1181111yescharacteristic, direct product factor, Sylow
208C2×C22⋊Q8C4×C12711yescharacteristic, complemented
209C22×C22⋊C4C22×C12711yescharacteristic
210#407—21no—
211#399C4×C12711yescharacteristic, complemented
212#399C22×C12711yescharacteristic
213#396—21no—
214#396—21no—
215#393C4×C12711yescharacteristic, complemented
216#393C22×C12711yescharacteristic
217#385—21no—
218#380C4×C12711yescharacteristic, complemented
219#379—21no—
220#379—21no—
221#342—21no—
222#342C22×C12712yes—
223#323—21no—
224#323C22×C12712yes—
225C25D4×C12711yescharacteristic
226C22×Q8C2×C4×C12711yescharacteristic
227C23×C4C2×C4×C12711yescharacteristic
228C23×C4D4×C12711yescharacteristic
229C2×M16—41no—
230C22⋊Q8—41no—
231C22⋊Q8—41no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C2×C4×C12711yescharacteristic
237C2×C22⋊C4—21no—
238C2×C22⋊C4—21no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—41no—
245C2×C22⋊C4—41no—
246C2×C22⋊C4—41no—
247C2×C22⋊C4—41no—
248C2×C22⋊C4C2×C4×C12711yescharacteristic
249C2×C22⋊C4D4×C12711yescharacteristic
250C2×C22⋊C4D4×C12711yescharacteristic
251C2×C22⋊C4C23×C12711yescharacteristic
252C22⋊C8—22no—
253C22⋊C8—41no—
254#95—21no—
255#95—21no—
256#95C2×C4×C12711yescharacteristic
257#95C2×C4×C12711yescharacteristic
258C24—21no—
259C24—21no—
260C24—22no—
261C24—41no—
262C24—81no—
263C24—81no—
264C24C22⋊C4×C12711yescharacteristic
265C24C22⋊C4×C12711yescharacteristic
266C24C2×D4×C12711yescharacteristic
267C2×Q8—41no—
268C2×Q8—81no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—42no—
278C22×C4—81no—
279C22×C4—81no—
280C22×C4C22⋊C4×C12711yescharacteristic
281C22×C4C22⋊C4×C12711yescharacteristic
282C22×C4C22×C4×C12711yescharacteristic
283C22×C4C2×D4×C12711yescharacteristic
284M16—82no—
285C2×C8—42no—
286C4⋊C4—41no—
287C4⋊C4—42no—
288C4⋊C4—81no—
289C4⋊C4—81no—
290C4⋊C4—81no—
291C22⋊C4—41no—
292C22⋊C4—41no—
293C22⋊C4—41no—
294C22⋊C4—41no—
295C22⋊C4—42no—
296C22⋊C4—41no—
297C22⋊C4—41no—
298C22⋊C4—42no—
299C22⋊C4—42no—
300C22⋊C4—81no—
301C22⋊C4—81no—
302C22⋊C4—81no—
303C22⋊C4—81no—
304C22⋊C4—82no—
305C22⋊C4—82no—
306C23—21no—
307C23—21no—
308C23—21no—
309C23—21no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—41no—
314C23—41no—
315C23—42no—
316C23—42no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—42no—
322C23—42no—
323C23—81no—
324C23—81no—
325C23—84no—
326C23—84no—
327C23#99×C12711yescharacteristic
328C23#99×C12711yescharacteristic
329C23C2×C22⋊C4×C12711yescharacteristic
330C23#137×C12712yes—
331Q8—82no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—42no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—82no—
357C2×C4—82no—
358C2×C4—82no—
359C8—82no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—22no—
367C22—21no—
368C22—21no—
369C22—42no—
370C22—42no—
371C22—42no—
372C22—42no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—81no—
379C22—81no—
380C22—84no—
381C22—84no—
382C22C2×#99×C12711yescharacteristic
383C22#419×C12711yescharacteristic
384C22#421×C12711yescharacteristic
385C4—41no—
386C4—41no—
387C4—41no—
388C4—41no—
389C4—81no—
390C4—81no—
391C4—81no—
392C4—81no—
393C4—162no—
394C2—21no—
395C2—21no—
396C2—42no—
397C2—41no—
398C2—41no—
399C2—81no—
400C2C127×#151111yescharacteristic
401C2C127×#212111yescharacteristic
402C2C127×#212711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C22⋊C4C23×C127
prime radicalC25×C127D4
LCSG ▷ C22×C4 ▷ C23 ▷ 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
4. C127×#1352C2semidirect
5. C127×#1351C2semidirect
6. C2×C22⋊Q8×C127C4semidirect
9. #399×C127C4semidirect
13. #393×C127C4semidirect
16. #380×C127C4semidirect
192. #11811C127direct (N × H)
205. #1352C2×C127semidirect
206. #1351C2×C127semidirect
207. C127#11811direct (N × H)
208. C2×C22⋊Q8C4×C127semidirect
211. #399C4×C127semidirect
215. #393C4×C127semidirect
218. #380C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#26262
C127×#18192
C127×#14622
C127×#13522
C127×#13512
#11811127