Finite Group Databasebeta

← C127×#12177 #44575850

Subgroups — C127×#12177 #44575850

Order 32512.

432 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 74 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×#2763C211yesmaximal, characteristic, complemented
2C127×#2044C211yesmaximal, characteristic
3C127×#1601C211yesmaximal, characteristic
4C127×#1601C211yesmaximal, characteristic
5C127×#1351C211yesmaximal, characteristic, complemented
6C127×#1351C211yesmaximal, characteristic, complemented
7C127×#1326C211yesmaximal, characteristic, complemented
8#534×C127C2211yescharacteristic
9#448×C127—21no—
10#448×C127—21no—
11C2×#99×C127—21no—
12#400×C127—21no—
13#395×C127—21no—
14#393×C127C2211yescharacteristic
15#393×C127C2211yescharacteristic
16#391×C127—21no—
17#388×C127—21no—
18#386×C127—21no—
19#385×C127—21no—
20#385×C127C2211yescharacteristic
21#382×C127—21no—
22#342×C127C2211yescharacteristic
23#327×C127—21no—
24#327×C127—21no—
25#323×C127C2211yescharacteristic
26#323×C127C2211yescharacteristic
27C22×Q8×C127D411yescharacteristic
28C22×Q8×C127D411yescharacteristic
29C22×D4×C127—21no—
30C23×C4×C127D411yescharacteristic
31C2×SD16×C127—41no—
32C2×SD16×C127—41no—
33#123×C127—41no—
34#121×C127—21no—
35#121×C127—21no—
36#120×C127—41no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127—21no—
40C2×C4⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—41no—
45C2×C22⋊C4×C127D411yescharacteristic
46C2×C22⋊C4×C127C2311yescharacteristic
47C2×C42×C127—21no—
48#103×C127—41no—
49#103×C127—41no—
50#99×C127—42no—
51C22⋊C8×C127—21no—
52C22⋊C8×C127—21no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127—21no—
56#95×C127—21no—
57#95×C127—21no—
58#95×C127—21no—
59#95×C127—21no—
60#95×C127—41no—
61#95×C127D411yescharacteristic
62#95×C127D411yescharacteristic
63C24×C127—21no—
64C24×C127C2×D411yescharacteristic
65C2×Q8×C127—42no—
66C2×Q8×C127—41no—
67C2×Q8×C127—41no—
68C2×Q8×C127—81no—
69C2×D4×C127—21no—
70C2×D4×C127—21no—
71C2×D4×C127—41no—
72C2×D4×C127—41no—
73C2×D4×C127—41no—
74C2×D4×C127—41no—
75C2×D4×C127—41no—
76C2×D4×C127—41no—
77C22×C4×C127—21no—
78C22×C4×C127—21no—
79C22×C4×C127—21no—
80C22×C4×C127—21no—
81C22×C4×C127—21no—
82C22×C4×C127—21no—
83C22×C4×C127—21no—
84C22×C4×C127—41no—
85C22×C4×C127—41no—
86C22×C4×C127—81no—
87C22×C4×C127C2×D411yescharacteristic
88C22×C4×C127C2×D411yescharacteristic
89SD16×C127—82no—
90SD16×C127—82no—
91C2×C8×C127—41no—
92C2×C8×C127—41no—
93C4⋊C4×C127—21no—
94C4⋊C4×C127—21no—
95C4⋊C4×C127—81no—
96C4⋊C4×C127—81no—
97C4⋊C4×C127—81no—
98C4⋊C4×C127—81no—
99C22⋊C4×C127—21no—
100C22⋊C4×C127—41no—
101C22⋊C4×C127—42no—
102C22⋊C4×C127—41no—
103C22⋊C4×C127—41no—
104C22⋊C4×C127—41no—
105C22⋊C4×C127—41no—
106C22⋊C4×C127—81no—
107C22⋊C4×C127—82no—
108C22⋊C4×C127SD1612yescomplemented
109C42×C127—42no—
110C23×C127—21no—
111C23×C127—21no—
112C23×C127—41no—
113C23×C127—41no—
114C23×C127—41no—
115C23×C127—41no—
116C23×C127—41no—
117C23×C127—81no—
118C23×C127—81no—
119C23×C127#12011yescharacteristic
120C23×C127C2×SD1611yescharacteristic
121C23×C127#13711yescharacteristic
122Q8×C127—42no—
123Q8×C127—42no—
124Q8×C127—81no—
125Q8×C127—81no—
126D4×C127—81no—
127D4×C127—81no—
128D4×C127—81no—
129D4×C127—81no—
130D4×C127—81no—
131D4×C127—81no—
132C2×C4×C127—22no—
133C2×C4×C127—22no—
134C2×C4×C127—21no—
135C2×C4×C127—21no—
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—41no—
152C2×C4×C127—42no—
153C2×C4×C127—41no—
154C2×C4×C127—41no—
155C2×C4×C127—41no—
156C2×C4×C127—41no—
157C2×C4×C127—41no—
158C2×C4×C127—81no—
159C2×C4×C127—81no—
160C2×C4×C127—81no—
161C2×C4×C127—81no—
162C8×C127—81no—
163C8×C127—81no—
164C22×C127—21no—
165C22×C127—21no—
166C22×C127—21no—
167C22×C127—21no—
168C22×C127—41no—
169C22×C127—41no—
170C22×C127—41no—
171C22×C127—41no—
172C22×C127—81no—
173C22×C127—82no—
174C22×C127—81no—
175C22×C127—81no—
176C22×C127—81no—
177C22×C127—161no—
178C22×C127#44811yescharacteristic
179C22×C127#45411yescharacteristic
180C22×C127B(4,𝔽2)11yescharacteristic
181C4×C127—42no—
182C4×C127—41no—
183C4×C127—42no—
184C4×C127—41no—
185C4×C127—81no—
186C4×C127—81no—
187C4×C127—81no—
188C4×C127—81no—
189C4×C127—81no—
190C4×C127—161no—
191#12177C12711yesmaximal, characteristic, direct product factor, Sylow
192C2×C127—21no—
193C2×C127—21no—
194C2×C127—41no—
195C2×C127—41no—
196C2×C127—161no—
197C2×C127#159911yescharacteristic
198C2×C127#219711yescharacteristic
199C2×C127#219911yescharacteristic
200#2763C2×C12711yescharacteristic, complemented
201#2044C2×C12711yescharacteristic
202#1601C2×C12711yescharacteristic
203#1601C2×C12711yescharacteristic
204#1351C2×C12711yescharacteristic, complemented
205#1351C2×C12711yescharacteristic, complemented
206#1326C2×C12711yescharacteristic, complemented
207C127#1217711yescharacteristic, direct product factor, Sylow
208#534C22×C12711yescharacteristic
209#448—21no—
210#448—21no—
211C2×#99—21no—
212#400—21no—
213#395—21no—
214#393C22×C12711yescharacteristic
215#393C22×C12711yescharacteristic
216#391—21no—
217#388—21no—
218#386—21no—
219#385—21no—
220#385C22×C12711yescharacteristic
221#382—21no—
222#342C22×C12711yescharacteristic
223#327—21no—
224#327—21no—
225#323C22×C12711yescharacteristic
226#323C22×C12711yescharacteristic
227C22×Q8D4×C12711yescharacteristic
228C22×Q8D4×C12711yescharacteristic
229C22×D4—21no—
230C23×C4D4×C12711yescharacteristic
231C2×SD16—41no—
232C2×SD16—41no—
233#123—41no—
234#121—21no—
235#121—21no—
236#120—41no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—41no—
245C2×C22⋊C4D4×C12711yescharacteristic
246C2×C22⋊C4C23×C12711yescharacteristic
247C2×C42—21no—
248#103—41no—
249#103—41no—
250#99—42no—
251C22⋊C8—21no—
252C22⋊C8—21no—
253#95—21no—
254#95—21no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—41no—
261#95D4×C12711yescharacteristic
262#95D4×C12711yescharacteristic
263C24—21no—
264C24C2×D4×C12711yescharacteristic
265C2×Q8—42no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—81no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—41no—
272C2×D4—41no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C22×C4—21no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4—81no—
287C22×C4C2×D4×C12711yescharacteristic
288C22×C4C2×D4×C12711yescharacteristic
289SD16—82no—
290SD16—82no—
291C2×C8—41no—
292C2×C8—41no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4—81no—
296C4⋊C4—81no—
297C4⋊C4—81no—
298C4⋊C4—81no—
299C22⋊C4—21no—
300C22⋊C4—41no—
301C22⋊C4—42no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—81no—
307C22⋊C4—82no—
308C22⋊C4SD16×C12712yescomplemented
309C42—42no—
310C23—21no—
311C23—21no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—81no—
318C23—81no—
319C23#120×C12711yescharacteristic
320C23C2×SD16×C12711yescharacteristic
321C23#137×C12711yescharacteristic
322Q8—42no—
323Q8—42no—
324Q8—81no—
325Q8—81no—
326D4—81no—
327D4—81no—
328D4—81no—
329D4—81no—
330D4—81no—
331D4—81no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—41no—
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—42no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4—81no—
362C8—81no—
363C8—81no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22—21no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—81no—
373C22—82no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22—161no—
378C22#448×C12711yescharacteristic
379C22#454×C12711yescharacteristic
380C22B(4,𝔽2)×C12711yescharacteristic
381C4—42no—
382C4—41no—
383C4—42no—
384C4—41no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—81no—
390C4—161no—
391C2—21no—
392C2—21no—
393C2—41no—
394C2—41no—
395C2—161no—
396C2C127×#159911yescharacteristic
397C2C127×#219711yescharacteristic
398C2C127×#219911yescharacteristic
subgroupG/H
center, socleC22×C127B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C127
prime radical#534×C127C22
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C2×C22⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2763C2semidirect
5. C127×#1351C2semidirect
6. C127×#1351C2semidirect
7. C127×#1326C2semidirect
108. C22⋊C4×C127SD16semidirect
191. #12177C127direct (N × H)
200. #2763C2×C127semidirect
204. #1351C2×C127semidirect
205. #1351C2×C127semidirect
206. #1326C2×C127semidirect
207. C127#12177direct (N × H)
308. C22⋊C4SD16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#27632
C127×#20442
C127×#16012
C127×#13512
C127×#13262
#12177127