Finite Group Databasebeta

← C127×#11884 #44575557

Subgroups — C127×#11884 #44575557

Order 32512.

510 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2543C211yesmaximal, characteristic
2C127×#1800C211yesmaximal, characteristic, complemented
3C127×#1459C211yesmaximal, characteristic, complemented
4C127×#1346C212yesmaximal, complemented
5C127×#1345C212yesmaximal, complemented
6C2×#121×C127—21no—
7C2×#121×C127C411yescharacteristic
8C2×C4×D4×C127C2211yescharacteristic
9#423×C127—21no—
10C2×#100×C127—21no—
11C2×C22⋊C8×C127—21no—
12#398×C127C2211yescharacteristic
13#397×C127C411yescharacteristic
14#394×C127C2211yescharacteristic
15#392×C127C411yescharacteristic
16#388×C127—21no—
17#386×C127—21no—
18#386×C127—21no—
19C2×#95×C127C411yescharacteristic
20#343×C127C2212yes—
21#324×C127C2212yes—
22#323×C127—21no—
23C22×D4×C127—21no—
24C22×D4×C127—21no—
25C22×D4×C127C2×C411yescharacteristic
26C22×D4×C127D411yescharacteristic
27C23×C4×C127—21no—
28C23×C4×C127C2×C411yescharacteristic
29C23×C4×C127D411yescharacteristic
30C2×M16×C127—22no—
31C22×C8×C127—41no—
32#121×C127—42no—
33#121×C127—42no—
34#121×C127—41no—
35#121×C127—41no—
36C4×D4×C127—41no—
37C4×D4×C127—41no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127C2×C411yescharacteristic
40C2×C4⋊C4×C127C2311yescharacteristic
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—21no—
45C2×C22⋊C4×C127—21no—
46C2×C22⋊C4×C127C2×C411yescharacteristic
47C2×C22⋊C4×C127D411yescharacteristic
48C2×C42×C127D411yescharacteristic
49C4⋊C8×C127—41no—
50C4⋊C8×C127—41no—
51#100×C127—42no—
52C22⋊C8×C127—22no—
53C22⋊C8×C127—41no—
54#95×C127—21no—
55#95×C127—21no—
56#95×C127—21no—
57#95×C127C2×C411yescharacteristic
58#95×C127C2×C411yescharacteristic
59C24×C127—21no—
60C24×C127C22⋊C411yescharacteristic
61C24×C127C22⋊C411yescharacteristic
62C2×D4×C127—41no—
63C2×D4×C127—41no—
64C2×D4×C127—41no—
65C2×D4×C127—42no—
66C2×D4×C127—42no—
67C2×D4×C127—42no—
68C2×D4×C127—42no—
69C2×D4×C127—42no—
70C2×D4×C127—81no—
71C2×D4×C127—81no—
72C2×D4×C127D812yes—
73C2×D4×C127SD1612yes—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—21no—
80C22×C4×C127—21no—
81C22×C4×C127—42no—
82C22×C4×C127—42no—
83C22×C4×C127—81no—
84C22×C4×C127—81no—
85C22×C4×C127—81no—
86C22×C4×C127C22⋊C411yescharacteristic
87C22×C4×C127C22⋊C411yescharacteristic
88C22×C4×C127C22×C411yescharacteristic
89C22×C4×C127C2×D411yescharacteristic
90C22×C4×C127C2×D411yescharacteristic
91M16×C127—42no—
92M16×C127—42no—
93C2×C8×C127—42no—
94C2×C8×C127—42no—
95C2×C8×C127—82no—
96C4⋊C4×C127—41no—
97C4⋊C4×C127—41no—
98C4⋊C4×C127—41no—
99C4⋊C4×C127—41no—
100C22⋊C4×C127—41no—
101C22⋊C4×C127—41no—
102C22⋊C4×C127—42no—
103C22⋊C4×C127—42no—
104C22⋊C4×C127—41no—
105C22⋊C4×C127—41no—
106C22⋊C4×C127—41no—
107C22⋊C4×C127—41no—
108C22⋊C4×C127—81no—
109C42×C127—21no—
110C42×C127—21no—
111C23×C127—21no—
112C23×C127—21no—
113C23×C127—21no—
114C23×C127—21no—
115C23×C127—41no—
116C23×C127—41no—
117C23×C127—41no—
118C23×C127—41no—
119C23×C127—41no—
120C23×C127—41no—
121C23×C127—41no—
122C23×C127—41no—
123C23×C127—41no—
124C23×C127—41no—
125C23×C127—41no—
126C23×C127#10212yes—
127C23×C127#10212yes—
128C23×C127C2×C22⋊C411yescharacteristic
129D4×C127—42no—
130D4×C127—42no—
131D4×C127—84no—
132D4×C127—82no—
133D4×C127—84no—
134C2×C4×C127—21no—
135C2×C4×C127—21no—
136C2×C4×C127—22no—
137C2×C4×C127—21no—
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—41no—
141C2×C4×C127—42no—
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—41no—
152C2×C4×C127—41no—
153C2×C4×C127—81no—
154C2×C4×C127—81no—
155C2×C4×C127—81no—
156C2×C4×C127—84no—
157C2×C4×C127#9911yescharacteristic
158C2×C4×C127#9911yescharacteristic
159C2×C4×C127C2×D811yescharacteristic
160C2×C4×C127C2×SD1611yescharacteristic
161C8×C127—82no—
162C8×C127—82no—
163C22×C127—21no—
164C22×C127—21no—
165C22×C127—22no—
166C22×C127—22no—
167C22×C127—42no—
168C22×C127—42no—
169C22×C127—42no—
170C22×C127—41no—
171C22×C127—41no—
172C22×C127—41no—
173C22×C127—41no—
174C22×C127—81no—
175C22×C127—81no—
176C22×C127—81no—
177C22×C127—81no—
178C22×C127—81no—
179C22×C127—81no—
180C22×C127—81no—
181C22×C127—81no—
182C22×C127C2×#9911yescharacteristic
183C22×C127C2×#10211yescharacteristic
184C22×C127#42111yescharacteristic
185C4×C127—21no—
186C4×C127—21no—
187C4×C127—21no—
188C4×C127—21no—
189C4×C127—42no—
190C4×C127—41no—
191C4×C127—41no—
192C4×C127—41no—
193C4×C127—81no—
194C4×C127—81no—
195#11884C12711yesmaximal, characteristic, direct product factor, Sylow
196C2×C127—21no—
197C2×C127—21no—
198C2×C127—42no—
199C2×C127—42no—
200C2×C127—161no—
201C2×C127#151911yescharacteristic
202C2×C127#212111yescharacteristic
203C2×C127#213211yescharacteristic
204#2543C2×C12711yescharacteristic
205#1800C2×C12711yescharacteristic, complemented
206#1459C2×C12711yescharacteristic, complemented
207#1346C2×C12712yescomplemented
208#1345C2×C12712yescomplemented
209C127#1188411yescharacteristic, direct product factor, Sylow
210C2×#121—21no—
211C2×#121C4×C12711yescharacteristic
212C2×C4×D4C22×C12711yescharacteristic
213#423—21no—
214C2×#100—21no—
215C2×C22⋊C8—21no—
216#398C22×C12711yescharacteristic
217#397C4×C12711yescharacteristic
218#394C22×C12711yescharacteristic
219#392C4×C12711yescharacteristic
220#388—21no—
221#386—21no—
222#386—21no—
223C2×#95C4×C12711yescharacteristic
224#343C22×C12712yes—
225#324C22×C12712yes—
226#323—21no—
227C22×D4—21no—
228C22×D4—21no—
229C22×D4C2×C4×C12711yescharacteristic
230C22×D4D4×C12711yescharacteristic
231C23×C4—21no—
232C23×C4C2×C4×C12711yescharacteristic
233C23×C4D4×C12711yescharacteristic
234C2×M16—22no—
235C22×C8—41no—
236#121—42no—
237#121—42no—
238#121—41no—
239#121—41no—
240C4×D4—41no—
241C4×D4—41no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4C2×C4×C12711yescharacteristic
244C2×C4⋊C4C23×C12711yescharacteristic
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C22⋊C4—21no—
248C2×C22⋊C4—21no—
249C2×C22⋊C4—21no—
250C2×C22⋊C4C2×C4×C12711yescharacteristic
251C2×C22⋊C4D4×C12711yescharacteristic
252C2×C42D4×C12711yescharacteristic
253C4⋊C8—41no—
254C4⋊C8—41no—
255#100—42no—
256C22⋊C8—22no—
257C22⋊C8—41no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95C2×C4×C12711yescharacteristic
262#95C2×C4×C12711yescharacteristic
263C24—21no—
264C24C22⋊C4×C12711yescharacteristic
265C24C22⋊C4×C12711yescharacteristic
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—41no—
269C2×D4—42no—
270C2×D4—42no—
271C2×D4—42no—
272C2×D4—42no—
273C2×D4—42no—
274C2×D4—81no—
275C2×D4—81no—
276C2×D4D8×C12712yes—
277C2×D4SD16×C12712yes—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—42no—
286C22×C4—42no—
287C22×C4—81no—
288C22×C4—81no—
289C22×C4—81no—
290C22×C4C22⋊C4×C12711yescharacteristic
291C22×C4C22⋊C4×C12711yescharacteristic
292C22×C4C22×C4×C12711yescharacteristic
293C22×C4C2×D4×C12711yescharacteristic
294C22×C4C2×D4×C12711yescharacteristic
295M16—42no—
296M16—42no—
297C2×C8—42no—
298C2×C8—42no—
299C2×C8—82no—
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—42no—
307C22⋊C4—42no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—81no—
313C42—21no—
314C42—21no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23#102×C12712yes—
331C23#102×C12712yes—
332C23C2×C22⋊C4×C12711yescharacteristic
333D4—42no—
334D4—42no—
335D4—84no—
336D4—82no—
337D4—84no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—22no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—84no—
361C2×C4#99×C12711yescharacteristic
362C2×C4#99×C12711yescharacteristic
363C2×C4C2×D8×C12711yescharacteristic
364C2×C4C2×SD16×C12711yescharacteristic
365C8—82no—
366C8—82no—
367C22—21no—
368C22—21no—
369C22—22no—
370C22—22no—
371C22—42no—
372C22—42no—
373C22—42no—
374C22—41no—
375C22—41no—
376C22—41no—
377C22—41no—
378C22—81no—
379C22—81no—
380C22—81no—
381C22—81no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—81no—
386C22C2×#99×C12711yescharacteristic
387C22C2×#102×C12711yescharacteristic
388C22#421×C12711yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—42no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4—81no—
398C4—81no—
399C2—21no—
400C2—21no—
401C2—42no—
402C2—42no—
403C2—161no—
404C2C127×#151911yescharacteristic
405C2C127×#212111yescharacteristic
406C2C127×#213211yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC127×#2543C2
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. C127×#1800C2semidirect
3. C127×#1459C2semidirect
4. C127×#1346C2semidirect
5. C127×#1345C2semidirect
195. #11884C127direct (N × H)
205. #1800C2×C127semidirect
206. #1459C2×C127semidirect
207. #1346C2×C127semidirect
208. #1345C2×C127semidirect
209. C127#11884direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#25432
C127×#18002
C127×#14592
C127×#13462
C127×#13452
#11884127