Finite Group Databasebeta

← C127×#11877 #44575550

Subgroups — C127×#11877 #44575550

Order 32512.

644 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 644 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2541C211yesmaximal, characteristic
2C127×#1799C211yesmaximal, characteristic, complemented
3C127×#1459C211yesmaximal, characteristic, complemented
4C127×#1343C214yesmaximal, complemented
5C2×#127×C127—21no—
6C2×#127×C127C411yescharacteristic, complemented
7C2×#121×C127—21no—
8C2×#121×C127—21no—
9C2×C4×D4×C127C2211yescharacteristic
10C2×#99×C127—21no—
11C2×C22⋊C8×C127—21no—
12#392×C127C412yescomplemented
13#392×C127C2212yes—
14#390×C127—21no—
15#380×C127—21no—
16C4×C4⋊C4×C127C411yescharacteristic, complemented
17#342×C127C2212yes—
18#324×C127—21no—
19#323×C127C2212yes—
20C22×D4×C127—22no—
21C22×D4×C127—22no—
22C22×D4×C127—21no—
23C22×D4×C127—21no—
24C22×D4×C127C2×C412yes—
25C22×D4×C127D411yescharacteristic
26C23×C4×C127D411yescharacteristic
27C23×C4×C127D411yescharacteristic
28C22×C8×C127—41no—
29#127×C127—41no—
30#127×C127—41no—
31#127×C127—42no—
32#127×C127—42no—
33#121×C127—44no—
34#121×C127—44no—
35C4×D4×C127—41no—
36C4×D4×C127—41no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127—41no—
39C2×C4⋊C4×C127D411yescharacteristic
40C2×C22⋊C4×C127—22no—
41C2×C22⋊C4×C127—22no—
42C2×C22⋊C4×C127—22no—
43C2×C22⋊C4×C127C2×C411yescharacteristic
44C2×C22⋊C4×C127C2311yescharacteristic
45C2×C42×C127—21no—
46C2×C42×C127C2×C411yescharacteristic
47#99×C127—42no—
48C22⋊C8×C127—22no—
49C22⋊C8×C127—41no—
50#95×C127—41no—
51#95×C127C2×C412yes—
52C24×C127—22no—
53C24×C127C22⋊C411yescharacteristic
54C24×C127C2×D411yescharacteristic
55C2×D4×C127—41no—
56C2×D4×C127—41no—
57C2×D4×C127—42no—
58C2×D4×C127—42no—
59C2×D4×C127—42no—
60C2×D4×C127—44no—
61C2×D4×C127—44no—
62C2×D4×C127—42no—
63C2×D4×C127—42no—
64C2×D4×C127—44no—
65C2×D4×C127—42no—
66C2×D4×C127—42no—
67C2×D4×C127—41no—
68C2×D4×C127—41no—
69C2×D4×C127—42no—
70C2×D4×C127—82no—
71C2×D4×C127—82no—
72C2×D4×C127—82no—
73C2×D4×C127D812yes—
74C2×D4×C127SD1612yes—
75C22×C4×C127—22no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—21no—
80C22×C4×C127—42no—
81C22×C4×C127—42no—
82C22×C4×C127—42no—
83C22×C4×C127C22⋊C411yescharacteristic
84C22×C4×C127C22⋊C411yescharacteristic
85C22×C4×C127C22⋊C411yescharacteristic
86C22×C4×C127C22×C411yescharacteristic
87C22×C4×C127C2×D411yescharacteristic
88C2×C8×C127—42no—
89C2×C8×C127—82no—
90C4⋊C4×C127—24no—
91C4⋊C4×C127—41no—
92C4⋊C4×C127—82no—
93C22⋊C4×C127—41no—
94C22⋊C4×C127—41no—
95C22⋊C4×C127—44no—
96C22⋊C4×C127—44no—
97C22⋊C4×C127—42no—
98C22⋊C4×C127—42no—
99C42×C127—21no—
100C42×C127—21no—
101C42×C127—42no—
102C23×C127—21no—
103C23×C127—21no—
104C23×C127—21no—
105C23×C127—21no—
106C23×C127—41no—
107C23×C127—41no—
108C23×C127—41no—
109C23×C127—41no—
110C23×C127—42no—
111C23×C127—42no—
112C23×C127—42no—
113C23×C127—42no—
114C23×C127—42no—
115C23×C127—42no—
116C23×C127—42no—
117C23×C127#10212yes—
118C23×C127C2×C22⋊C411yescharacteristic
119C23×C127C2×D811yescharacteristic
120C23×C127C2×SD1611yescharacteristic
121D4×C127—42no—
122D4×C127—42no—
123D4×C127—82no—
124D4×C127—84no—
125D4×C127—88no—
126D4×C127—84no—
127D4×C127—84no—
128D4×C127—84no—
129D4×C127—82no—
130C2×C4×C127—21no—
131C2×C4×C127—21no—
132C2×C4×C127—22no—
133C2×C4×C127—24no—
134C2×C4×C127—21no—
135C2×C4×C127—21no—
136C2×C4×C127—21no—
137C2×C4×C127—42no—
138C2×C4×C127—42no—
139C2×C4×C127—42no—
140C2×C4×C127—42no—
141C2×C4×C127—41no—
142C2×C4×C127—41no—
143C2×C4×C127—41no—
144C2×C4×C127—81no—
145C2×C4×C127—81no—
146C2×C4×C127—82no—
147C2×C4×C127—82no—
148C2×C4×C127—82no—
149C2×C4×C127#9911yescharacteristic
150C2×C4×C127#9911yescharacteristic
151C2×C4×C127#10212yes—
152C8×C127—82no—
153C22×C127—21no—
154C22×C127—21no—
155C22×C127—21no—
156C22×C127—22no—
157C22×C127—21no—
158C22×C127—42no—
159C22×C127—41no—
160C22×C127—41no—
161C22×C127—41no—
162C22×C127—41no—
163C22×C127—41no—
164C22×C127—41no—
165C22×C127—81no—
166C22×C127—81no—
167C22×C127—82no—
168C22×C127—82no—
169C22×C127—82no—
170C22×C127—82no—
171C22×C127—82no—
172C22×C127—82no—
173C22×C127—82no—
174C22×C127C2×#9911yescharacteristic
175C22×C127C2×#10211yescharacteristic
176C22×C127#42111yescharacteristic
177C4×C127—21no—
178C4×C127—22no—
179C4×C127—44no—
180C4×C127—41no—
181C4×C127—41no—
182C4×C127—41no—
183C4×C127—162no—
184C4×C127#35312yes—
185#11877C12711yesmaximal, characteristic, direct product factor, Sylow
186C2×C127—21no—
187C2×C127—21no—
188C2×C127—41no—
189C2×C127—42no—
190C2×C127—41no—
191C2×C127—162no—
192C2×C127#151911yescharacteristic
193C2×C127#212211yescharacteristic
194C2×C127C2×#35311yescharacteristic
195#2541C2×C12711yescharacteristic
196#1799C2×C12711yescharacteristic, complemented
197#1459C2×C12711yescharacteristic, complemented
198#1343C2×C12714yescomplemented
199C127#1187711yescharacteristic, direct product factor, Sylow
200C2×#127—21no—
201C2×#127C4×C12711yescharacteristic, complemented
202C2×#121—21no—
203C2×#121—21no—
204C2×C4×D4C22×C12711yescharacteristic
205C2×#99—21no—
206C2×C22⋊C8—21no—
207#392C4×C12712yescomplemented
208#392C22×C12712yes—
209#390—21no—
210#380—21no—
211C4×C4⋊C4C4×C12711yescharacteristic, complemented
212#342C22×C12712yes—
213#324—21no—
214#323C22×C12712yes—
215C22×D4—22no—
216C22×D4—22no—
217C22×D4—21no—
218C22×D4—21no—
219C22×D4C2×C4×C12712yes—
220C22×D4D4×C12711yescharacteristic
221C23×C4D4×C12711yescharacteristic
222C23×C4D4×C12711yescharacteristic
223C22×C8—41no—
224#127—41no—
225#127—41no—
226#127—42no—
227#127—42no—
228#121—44no—
229#121—44no—
230C4×D4—41no—
231C4×D4—41no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—41no—
234C2×C4⋊C4D4×C12711yescharacteristic
235C2×C22⋊C4—22no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4C2×C4×C12711yescharacteristic
239C2×C22⋊C4C23×C12711yescharacteristic
240C2×C42—21no—
241C2×C42C2×C4×C12711yescharacteristic
242#99—42no—
243C22⋊C8—22no—
244C22⋊C8—41no—
245#95—41no—
246#95C2×C4×C12712yes—
247C24—22no—
248C24C22⋊C4×C12711yescharacteristic
249C24C2×D4×C12711yescharacteristic
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—42no—
253C2×D4—42no—
254C2×D4—42no—
255C2×D4—44no—
256C2×D4—44no—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4—44no—
260C2×D4—42no—
261C2×D4—42no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—42no—
265C2×D4—82no—
266C2×D4—82no—
267C2×D4—82no—
268C2×D4D8×C12712yes—
269C2×D4SD16×C12712yes—
270C22×C4—22no—
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—42no—
276C22×C4—42no—
277C22×C4—42no—
278C22×C4C22⋊C4×C12711yescharacteristic
279C22×C4C22⋊C4×C12711yescharacteristic
280C22×C4C22⋊C4×C12711yescharacteristic
281C22×C4C22×C4×C12711yescharacteristic
282C22×C4C2×D4×C12711yescharacteristic
283C2×C8—42no—
284C2×C8—82no—
285C4⋊C4—24no—
286C4⋊C4—41no—
287C4⋊C4—82no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—44no—
291C22⋊C4—44no—
292C22⋊C4—42no—
293C22⋊C4—42no—
294C42—21no—
295C42—21no—
296C42—42no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—41no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—42no—
306C23—42no—
307C23—42no—
308C23—42no—
309C23—42no—
310C23—42no—
311C23—42no—
312C23#102×C12712yes—
313C23C2×C22⋊C4×C12711yescharacteristic
314C23C2×D8×C12711yescharacteristic
315C23C2×SD16×C12711yescharacteristic
316D4—42no—
317D4—42no—
318D4—82no—
319D4—84no—
320D4—88no—
321D4—84no—
322D4—84no—
323D4—84no—
324D4—82no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—22no—
328C2×C4—24no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—82no—
342C2×C4—82no—
343C2×C4—82no—
344C2×C4#99×C12711yescharacteristic
345C2×C4#99×C12711yescharacteristic
346C2×C4#102×C12712yes—
347C8—82no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—22no—
352C22—21no—
353C22—42no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—81no—
361C22—81no—
362C22—82no—
363C22—82no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22—82no—
368C22—82no—
369C22C2×#99×C12711yescharacteristic
370C22C2×#102×C12711yescharacteristic
371C22#421×C12711yescharacteristic
372C4—21no—
373C4—22no—
374C4—44no—
375C4—41no—
376C4—41no—
377C4—41no—
378C4—162no—
379C4#353×C12712yes—
380C2—21no—
381C2—21no—
382C2—41no—
383C2—42no—
384C2—41no—
385C2—162no—
386C2C127×#151911yescharacteristic
387C2C127×#212211yescharacteristic
388C2C2×#353×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C22⋊C4C23×C127
prime radicalC127×#2541C2
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×#1799C2semidirect
3. C127×#1459C2semidirect
4. C127×#1343C2semidirect
6. C2×#127×C127C4semidirect
12. #392×C127C4semidirect
16. C4×C4⋊C4×C127C4semidirect
185. #11877C127direct (N × H)
196. #1799C2×C127semidirect
197. #1459C2×C127semidirect
198. #1343C2×C127semidirect
199. C127#11877direct (N × H)
201. C2×#127C4×C127semidirect
207. #392C4×C127semidirect
211. C4×C4⋊C4C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#25412
C127×#17992
C127×#14592
C127×#13432
#11877127