Finite Group Databasebeta

← C127×#12146 #44575819

Subgroups — C127×#12146 #44575819

Order 32512.

380 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2792C211yesmaximal, characteristic, complemented
2C127×#2039C211yesmaximal, characteristic
3C127×#1610C211yesmaximal, characteristic
4C127×#1604C211yesmaximal, characteristic
5C127×#1354C211yesmaximal, characteristic, complemented
6C127×#1346C211yesmaximal, characteristic, complemented
7C127×#1325C211yesmaximal, characteristic, complemented
8#537×C127C2211yescharacteristic
9#480×C127—21no—
10#448×C127—21no—
11C2×#104×C127—21no—
12#417×C127—21no—
13#398×C127—21no—
14#398×C127C2211yescharacteristic
15#395×C127—21no—
16#395×C127C2211yescharacteristic
17#389×C127—21no—
18#389×C127—21no—
19#387×C127—21no—
20#387×C127—21no—
21#384×C127C2211yescharacteristic
22#343×C127C2211yescharacteristic
23#327×C127—21no—
24#327×C127—21no—
25#324×C127C2211yescharacteristic
26#324×C127C2211yescharacteristic
27C2×#41×C127—21no—
28C22×Q8×C127D411yescharacteristic
29C2×SD16×C127—41no—
30C2×M16×C127—21no—
31C22⋊Q8×C127—41no—
32#121×C127—21no—
33#121×C127—21no—
34#121×C127—41no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127—21no—
40C2×C4⋊C4×C127—21no—
41C2×C4⋊C4×C127—21no—
42C2×C4⋊C4×C127D411yescharacteristic
43C2×C4⋊C4×C127D411yescharacteristic
44C2×C4⋊C4×C127C2311yescharacteristic
45C2×C42×C127—21no—
46C2×C42×C127D411yescharacteristic
47#107×C127—41no—
48#104×C127—42no—
49#103×C127—41no—
50#103×C127—41no—
51#102×C127—41no—
52#102×C127—41no—
53C22⋊C8×C127—21no—
54C22⋊C8×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—21no—
61#95×C127D411yescharacteristic
62#95×C127D411yescharacteristic
63#41×C127—41no—
64#41×C127—41no—
65#41×C127—41no—
66#41×C127—41no—
67C2×Q8×C127—21no—
68C2×Q8×C127—41no—
69C2×Q8×C127—81no—
70C2×D4×C127—21no—
71C2×D4×C127—21no—
72C2×D4×C127—21no—
73C2×D4×C127—41no—
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—41no—
81C22×C4×C127C2×D411yescharacteristic
82C22×C4×C127C2×D411yescharacteristic
83C22×C4×C127C2×D411yescharacteristic
84SD16×C127—82no—
85M16×C127—41no—
86M16×C127—41no—
87C2×C8×C127—41no—
88C2×C8×C127—41no—
89C2×C8×C127—41no—
90C4⋊C4×C127—24no—
91C4⋊C4×C127—21no—
92C4⋊C4×C127—21no—
93C4⋊C4×C127—41no—
94C4⋊C4×C127—41no—
95C4⋊C4×C127—41no—
96C4⋊C4×C127—41no—
97C4⋊C4×C127—41no—
98C4⋊C4×C127—81no—
99C4⋊C4×C127—81no—
100C4⋊C4×C127—81no—
101C4⋊C4×C127—81no—
102C4⋊C4×C127—81no—
103C22⋊C4×C127—41no—
104C22⋊C4×C127—41no—
105C42×C127—21no—
106C42×C127—21no—
107C42×C127—81no—
108C23×C127—41no—
109C23×C127#12011yescharacteristic
110Q8×C127—41no—
111Q8×C127—41no—
112Q8×C127—42no—
113Q8×C127—81no—
114D4×C127—41no—
115D4×C127—41no—
116D4×C127—81no—
117D4×C127—81no—
118D4×C127—81no—
119D4×C127—81no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—22no—
123C2×C4×C127—22no—
124C2×C4×C127—22no—
125C2×C4×C127—21no—
126C2×C4×C127—21no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—41no—
130C2×C4×C127—41no—
131C2×C4×C127—41no—
132C2×C4×C127—41no—
133C2×C4×C127—41no—
134C2×C4×C127—41no—
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—81no—
146C2×C4×C127—81no—
147C2×C4×C127#13511yescharacteristic
148C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
149C8×C127—81no—
150C8×C127—81no—
151C8×C127—81no—
152C22×C127—21no—
153C22×C127—21no—
154C22×C127—81no—
155C22×C127—81no—
156C22×C127—81no—
157C22×C127#44911yescharacteristic
158C22×C127#45411yescharacteristic
159C22×C127B(4,𝔽2)11yescharacteristic
160C4×C127—21no—
161C4×C127—21no—
162C4×C127—42no—
163C4×C127—42no—
164C4×C127—42no—
165C4×C127—41no—
166C4×C127—41no—
167C4×C127—81no—
168C4×C127—81no—
169C4×C127—81no—
170C4×C127—81no—
171#12146C12711yesmaximal, characteristic, direct product factor, Sylow
172C2×C127—21no—
173C2×C127—21no—
174C2×C127—161no—
175C2×C127#159711yescharacteristic
176C2×C127#220011yescharacteristic
177C2×C127#220511yescharacteristic
178#2792C2×C12711yescharacteristic, complemented
179#2039C2×C12711yescharacteristic
180#1610C2×C12711yescharacteristic
181#1604C2×C12711yescharacteristic
182#1354C2×C12711yescharacteristic, complemented
183#1346C2×C12711yescharacteristic, complemented
184#1325C2×C12711yescharacteristic, complemented
185C127#1214611yescharacteristic, direct product factor, Sylow
186#537C22×C12711yescharacteristic
187#480—21no—
188#448—21no—
189C2×#104—21no—
190#417—21no—
191#398—21no—
192#398C22×C12711yescharacteristic
193#395—21no—
194#395C22×C12711yescharacteristic
195#389—21no—
196#389—21no—
197#387—21no—
198#387—21no—
199#384C22×C12711yescharacteristic
200#343C22×C12711yescharacteristic
201#327—21no—
202#327—21no—
203#324C22×C12711yescharacteristic
204#324C22×C12711yescharacteristic
205C2×#41—21no—
206C22×Q8D4×C12711yescharacteristic
207C2×SD16—41no—
208C2×M16—21no—
209C22⋊Q8—41no—
210#121—21no—
211#121—21no—
212#121—41no—
213C2×C4⋊C4—21no—
214C2×C4⋊C4—21no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4D4×C12711yescharacteristic
221C2×C4⋊C4D4×C12711yescharacteristic
222C2×C4⋊C4C23×C12711yescharacteristic
223C2×C42—21no—
224C2×C42D4×C12711yescharacteristic
225#107—41no—
226#104—42no—
227#103—41no—
228#103—41no—
229#102—41no—
230#102—41no—
231C22⋊C8—21no—
232C22⋊C8—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95D4×C12711yescharacteristic
240#95D4×C12711yescharacteristic
241#41—41no—
242#41—41no—
243#41—41no—
244#41—41no—
245C2×Q8—21no—
246C2×Q8—41no—
247C2×Q8—81no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—21no—
251C2×D4—41no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4C2×D4×C12711yescharacteristic
260C22×C4C2×D4×C12711yescharacteristic
261C22×C4C2×D4×C12711yescharacteristic
262SD16—82no—
263M16—41no—
264M16—41no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C4⋊C4—24no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—81no—
277C4⋊C4—81no—
278C4⋊C4—81no—
279C4⋊C4—81no—
280C4⋊C4—81no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C42—21no—
284C42—21no—
285C42—81no—
286C23—41no—
287C23#120×C12711yescharacteristic
288Q8—41no—
289Q8—41no—
290Q8—42no—
291Q8—81no—
292D4—41no—
293D4—41no—
294D4—81no—
295D4—81no—
296D4—81no—
297D4—81no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—22no—
301C2×C4—22no—
302C2×C4—22no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4#135×C12711yescharacteristic
326C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
327C8—81no—
328C8—81no—
329C8—81no—
330C22—21no—
331C22—21no—
332C22—81no—
333C22—81no—
334C22—81no—
335C22#449×C12711yescharacteristic
336C22#454×C12711yescharacteristic
337C22B(4,𝔽2)×C12711yescharacteristic
338C4—21no—
339C4—21no—
340C4—42no—
341C4—42no—
342C4—42no—
343C4—41no—
344C4—41no—
345C4—81no—
346C4—81no—
347C4—81no—
348C4—81no—
349C2—21no—
350C2—21no—
351C2—161no—
352C2C127×#159711yescharacteristic
353C2C127×#220011yescharacteristic
354C2C127×#220511yescharacteristic
subgroupG/H
center, socleC22×C127B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C127
prime radical#537×C127C22
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C2×C4⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2792C2semidirect
5. C127×#1354C2semidirect
6. C127×#1346C2semidirect
7. C127×#1325C2semidirect
171. #12146C127direct (N × H)
178. #2792C2×C127semidirect
182. #1354C2×C127semidirect
183. #1346C2×C127semidirect
184. #1325C2×C127semidirect
185. C127#12146direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#27922
C127×#20392
C127×#16102
C127×#16042
C127×#13542
C127×#13462
C127×#13252
#12146127