Finite Group Databasebeta

← C127×#11876 #44575549

Subgroups — C127×#11876 #44575549

Order 32512.

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

normal subgroups only

This group has 522 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×#1799C211yesmaximal, characteristic, complemented
3C127×#1460C211yesmaximal, characteristic, complemented
4C127×#1344C212yesmaximal, complemented
5C127×#1343C212yesmaximal, complemented
6C2×#121×C127—21no—
7C2×#121×C127C411yescharacteristic, complemented
8C2×C4×D4×C127C2211yescharacteristic
9#431×C127—21no—
10C2×#99×C127—21no—
11#398×C127C411yescharacteristic, complemented
12#397×C127C2211yescharacteristic
13#394×C127C411yescharacteristic, complemented
14#392×C127C2211yescharacteristic
15#388×C127—21no—
16#386×C127—21no—
17#386×C127—21no—
18#380×C127—21no—
19C2×#95×C127C411yescharacteristic, complemented
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×C127—21no—
28C23×C4×C127C2×C411yescharacteristic
29C23×C4×C127D411yescharacteristic
30#121×C127—42no—
31#121×C127—42no—
32#121×C127—41no—
33#121×C127—41no—
34C4×D4×C127—41no—
35C4×D4×C127—41no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127—41no—
38C2×C4⋊C4×C127C2×C411yescharacteristic
39C2×C4⋊C4×C127C2×C411yescharacteristic
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—22no—
45C2×C22⋊C4×C127—21no—
46C2×C22⋊C4×C127D411yescharacteristic
47C2×C22⋊C4×C127C2311yescharacteristic
48C2×C42×C127D411yescharacteristic
49C4⋊C8×C127—41no—
50#99×C127—42no—
51C22⋊C8×C127—22no—
52C4×C8×C127—41no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127—21no—
56#95×C127—41no—
57#95×C127C2×C411yescharacteristic
58#95×C127C2×C411yescharacteristic
59C24×C127—21no—
60C24×C127C22⋊C411yescharacteristic
61C24×C127C2×D411yescharacteristic
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—41no—
70C2×D4×C127—41no—
71C2×D4×C127—81no—
72C2×D4×C127—81no—
73C2×D4×C127D812yes—
74C2×D4×C127SD1612yes—
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—21no—
82C22×C4×C127—42no—
83C22×C4×C127—42no—
84C22×C4×C127—42no—
85C22×C4×C127—81no—
86C22×C4×C127—81no—
87C22×C4×C127—81no—
88C22×C4×C127C22⋊C411yescharacteristic
89C22×C4×C127C22⋊C411yescharacteristic
90C22×C4×C127C22⋊C411yescharacteristic
91C22×C4×C127C22×C411yescharacteristic
92C22×C4×C127C2×D411yescharacteristic
93C2×C8×C127—42no—
94C4⋊C4×C127—41no—
95C4⋊C4×C127—41no—
96C4⋊C4×C127—42no—
97C4⋊C4×C127—82no—
98C22⋊C4×C127—41no—
99C22⋊C4×C127—41no—
100C22⋊C4×C127—42no—
101C22⋊C4×C127—41no—
102C22⋊C4×C127—41no—
103C22⋊C4×C127—41no—
104C22⋊C4×C127—41no—
105C22⋊C4×C127—42no—
106C22⋊C4×C127—42no—
107C22⋊C4×C127—42no—
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×C127C2×C22⋊C411yescharacteristic
128C23×C127C2×D811yescharacteristic
129C23×C127C2×SD1611yescharacteristic
130D4×C127—42no—
131D4×C127—42no—
132D4×C127—82no—
133D4×C127—82no—
134D4×C127—82no—
135D4×C127—84no—
136C2×C4×C127—21no—
137C2×C4×C127—21no—
138C2×C4×C127—22no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—41no—
143C2×C4×C127—42no—
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—41no—
154C2×C4×C127—41no—
155C2×C4×C127—81no—
156C2×C4×C127—81no—
157C2×C4×C127—81no—
158C2×C4×C127—84no—
159C2×C4×C127—82no—
160C2×C4×C127—82no—
161C2×C4×C127—82no—
162C2×C4×C127#9911yescharacteristic
163C2×C4×C127#9911yescharacteristic
164C2×C4×C127#10212yes—
165C8×C127—82no—
166C22×C127—21no—
167C22×C127—21no—
168C22×C127—21no—
169C22×C127—22no—
170C22×C127—21no—
171C22×C127—42no—
172C22×C127—41no—
173C22×C127—41no—
174C22×C127—42no—
175C22×C127—41no—
176C22×C127—41no—
177C22×C127—41no—
178C22×C127—41no—
179C22×C127—81no—
180C22×C127—81no—
181C22×C127—81no—
182C22×C127—81no—
183C22×C127—81no—
184C22×C127—81no—
185C22×C127—81no—
186C22×C127—81no—
187C22×C127C2×#9911yescharacteristic
188C22×C127C2×#10211yescharacteristic
189C22×C127#42111yescharacteristic
190C4×C127—21no—
191C4×C127—21no—
192C4×C127—22no—
193C4×C127—42no—
194C4×C127—41no—
195C4×C127—41no—
196C4×C127—41no—
197C4×C127—81no—
198C4×C127—81no—
199C4×C127—162no—
200#11876C12711yesmaximal, characteristic, direct product factor, Sylow
201C2×C127—21no—
202C2×C127—21no—
203C2×C127—41no—
204C2×C127—42no—
205C2×C127—41no—
206C2×C127—161no—
207C2×C127#151911yescharacteristic
208C2×C127#212111yescharacteristic
209C2×C127#212611yescharacteristic
210#2543C2×C12711yescharacteristic
211#1799C2×C12711yescharacteristic, complemented
212#1460C2×C12711yescharacteristic, complemented
213#1344C2×C12712yescomplemented
214#1343C2×C12712yescomplemented
215C127#1187611yescharacteristic, direct product factor, Sylow
216C2×#121—21no—
217C2×#121C4×C12711yescharacteristic, complemented
218C2×C4×D4C22×C12711yescharacteristic
219#431—21no—
220C2×#99—21no—
221#398C4×C12711yescharacteristic, complemented
222#397C22×C12711yescharacteristic
223#394C4×C12711yescharacteristic, complemented
224#392C22×C12711yescharacteristic
225#388—21no—
226#386—21no—
227#386—21no—
228#380—21no—
229C2×#95C4×C12711yescharacteristic, complemented
230#342C22×C12712yes—
231#323—21no—
232#323C22×C12712yes—
233C22×D4—21no—
234C22×D4—21no—
235C22×D4C2×C4×C12711yescharacteristic
236C22×D4D4×C12711yescharacteristic
237C23×C4—21no—
238C23×C4C2×C4×C12711yescharacteristic
239C23×C4D4×C12711yescharacteristic
240#121—42no—
241#121—42no—
242#121—41no—
243#121—41no—
244C4×D4—41no—
245C4×D4—41no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—41no—
248C2×C4⋊C4C2×C4×C12711yescharacteristic
249C2×C4⋊C4C2×C4×C12711yescharacteristic
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—22no—
255C2×C22⋊C4—21no—
256C2×C22⋊C4D4×C12711yescharacteristic
257C2×C22⋊C4C23×C12711yescharacteristic
258C2×C42D4×C12711yescharacteristic
259C4⋊C8—41no—
260#99—42no—
261C22⋊C8—22no—
262C4×C8—41no—
263#95—21no—
264#95—21no—
265#95—21no—
266#95—41no—
267#95C2×C4×C12711yescharacteristic
268#95C2×C4×C12711yescharacteristic
269C24—21no—
270C24C22⋊C4×C12711yescharacteristic
271C24C2×D4×C12711yescharacteristic
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—42no—
276C2×D4—42no—
277C2×D4—42no—
278C2×D4—42no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—81no—
282C2×D4—81no—
283C2×D4D8×C12712yes—
284C2×D4SD16×C12712yes—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—21no—
292C22×C4—42no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—81no—
296C22×C4—81no—
297C22×C4—81no—
298C22×C4C22⋊C4×C12711yescharacteristic
299C22×C4C22⋊C4×C12711yescharacteristic
300C22×C4C22⋊C4×C12711yescharacteristic
301C22×C4C22×C4×C12711yescharacteristic
302C22×C4C2×D4×C12711yescharacteristic
303C2×C8—42no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—42no—
307C4⋊C4—82no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—42no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—42no—
316C22⋊C4—42no—
317C22⋊C4—42no—
318C22⋊C4—81no—
319C42—21no—
320C42—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—41no—
326C23—41no—
327C23—41no—
328C23—41no—
329C23—41no—
330C23—41no—
331C23—41no—
332C23—41no—
333C23—41no—
334C23—41no—
335C23—41no—
336C23#102×C12712yes—
337C23C2×C22⋊C4×C12711yescharacteristic
338C23C2×D8×C12711yescharacteristic
339C23C2×SD16×C12711yescharacteristic
340D4—42no—
341D4—42no—
342D4—82no—
343D4—82no—
344D4—82no—
345D4—84no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—84no—
369C2×C4—82no—
370C2×C4—82no—
371C2×C4—82no—
372C2×C4#99×C12711yescharacteristic
373C2×C4#99×C12711yescharacteristic
374C2×C4#102×C12712yes—
375C8—82no—
376C22—21no—
377C22—21no—
378C22—21no—
379C22—22no—
380C22—21no—
381C22—42no—
382C22—41no—
383C22—41no—
384C22—42no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22—81no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22—81no—
397C22C2×#99×C12711yescharacteristic
398C22C2×#102×C12711yescharacteristic
399C22#421×C12711yescharacteristic
400C4—21no—
401C4—21no—
402C4—22no—
403C4—42no—
404C4—41no—
405C4—41no—
406C4—41no—
407C4—81no—
408C4—81no—
409C4—162no—
410C2—21no—
411C2—21no—
412C2—41no—
413C2—42no—
414C2—41no—
415C2—161no—
416C2C127×#151911yescharacteristic
417C2C127×#212111yescharacteristic
418C2C127×#212611yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C22⋊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×#1799C2semidirect
3. C127×#1460C2semidirect
4. C127×#1344C2semidirect
5. C127×#1343C2semidirect
7. C2×#121×C127C4semidirect
11. #398×C127C4semidirect
13. #394×C127C4semidirect
19. C2×#95×C127C4semidirect
200. #11876C127direct (N × H)
211. #1799C2×C127semidirect
212. #1460C2×C127semidirect
213. #1344C2×C127semidirect
214. #1343C2×C127semidirect
215. C127#11876direct (N × H)
217. C2×#121C4×C127semidirect
221. #398C4×C127semidirect
223. #394C4×C127semidirect
229. C2×#95C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#25432
C127×#17992
C127×#14602
C127×#13442
C127×#13432
#11876127