Finite Group Databasebeta

← C127×#12325 #44575998

Subgroups — C127×#12325 #44575998

Order 32512.

384 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 82 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×#3277C211yesmaximal, characteristic, complemented
2C127×#2250C211yesmaximal, characteristic, complemented
3C127×#2207C211yesmaximal, characteristic, complemented
4C127×#1687C211yesmaximal, characteristic, complemented
5C127×#1360C211yesmaximal, characteristic, complemented
6C127×#1334C211yesmaximal, characteristic, complemented
7C127×#1330C211yesmaximal, characteristic, complemented
8C2×#137×C127—21no—
9#548×C127—21no—
10C2×SD32×C127—21no—
11C2×SD32×C127—21no—
12C2×D16×C127—21no—
13#495×C127C2211yescharacteristic
14#493×C127C2211yescharacteristic
15#468×C127—21no—
16#464×C127—21no—
17#459×C127—21no—
18#451×C127—21no—
19#449×C127—21no—
20C4×Q16×C127C2211yescharacteristic
21#436×C127C2211yescharacteristic
22C4⋊C16×C127C2211yescharacteristic
23#357×C127—21no—
24#346×C127C2211yescharacteristic
25#334×C127C2211yescharacteristic
26#331×C127—21no—
27C2×#41×C127—21no—
28C22×Q8×C127—21no—
29#137×C127—42no—
30#137×C127—42no—
31C2×Q16×C127—21no—
32C2×Q16×C127D411yescharacteristic
33C2×Q16×C127D411yescharacteristic
34C2×SD16×C127—21no—
35C2×SD16×C127—21no—
36C2×D8×C127—21no—
37C2×D8×C127—21no—
38C2×D8×C127—41no—
39C2×D8×C127D411yescharacteristic
40C2×M16×C127—21no—
41#127×C127—21no—
42#124×C127—21no—
43#124×C127—41no—
44C22⋊Q8×C127—21no—
45C22⋊Q8×C127—41no—
46#121×C127—21no—
47#121×C127—41no—
48C4×Q8×C127—21no—
49C4×D4×C127—41no—
50C4×D4×C127D411yescharacteristic
51SD32×C127—42no—
52SD32×C127—42no—
53D16×C127—42no—
54C2×C16×C127—21no—
55C2×C16×C127—21no—
56#107×C127D411yescharacteristic
57C4⋊C8×C127—21no—
58C4⋊C8×C127D411yescharacteristic
59#103×C127—21no—
60#103×C127—21no—
61#102×C127—21no—
62#102×C127—41no—
63C22⋊C8×C127—21no—
64C4×C8×C127C2311yescharacteristic
65#41×C127—42no—
66#41×C127—81no—
67C2×Q8×C127—21no—
68C2×Q8×C127—21no—
69C2×Q8×C127—41no—
70C2×Q8×C127—42no—
71C2×Q8×C127—81no—
72C2×D4×C127—21no—
73C2×D4×C127—41no—
74C2×D4×C127—41no—
75C2×D4×C127—41no—
76C2×D4×C127—41no—
77C2×D4×C127—41no—
78C2×D4×C127D811yescharacteristic
79C22×C4×C127—21no—
80C22×C4×C127—41no—
81C22×C4×C127—41no—
82Q16×C127—21no—
83Q16×C127—41no—
84Q16×C127—42no—
85Q16×C127D812yescomplemented
86SD16×C127—42no—
87SD16×C127—41no—
88SD16×C127—41no—
89D8×C127—41no—
90D8×C127—41no—
91D8×C127—41no—
92D8×C127—41no—
93D8×C127—41no—
94D8×C127—82no—
95M16×C127—41no—
96M16×C127—41no—
97C2×C8×C127—21no—
98C2×C8×C127—41no—
99C2×C8×C127C2×D411yescharacteristic
100C2×C8×C127C2×D411yescharacteristic
101C4⋊C4×C127—21no—
102C4⋊C4×C127—41no—
103C4⋊C4×C127—41no—
104C4⋊C4×C127D811yescharacteristic
105C22⋊C4×C127—21no—
106C22⋊C4×C127—41no—
107C22⋊C4×C127—41no—
108C22⋊C4×C127—41no—
109C22⋊C4×C127—41no—
110C42×C127—41no—
111C42×C127C2×D411yescharacteristic
112C16×C127—22no—
113C16×C127—41no—
114C23×C127—21no—
115C23×C127—41no—
116C23×C127—81no—
117Q8×C127—22no—
118Q8×C127—41no—
119Q8×C127—41no—
120Q8×C127—41no—
121Q8×C127—82no—
122D4×C127—41no—
123D4×C127—41no—
124D4×C127—41no—
125D4×C127—81no—
126D4×C127—81no—
127D4×C127—82no—
128D4×C127—82no—
129D4×C127—81no—
130D4×C127—81no—
131D4×C127—161no—
132C2×C4×C127—21no—
133C2×C4×C127—41no—
134C2×C4×C127—41no—
135C2×C4×C127—41no—
136C2×C4×C127—41no—
137C2×C4×C127—41no—
138C2×C4×C127—82no—
139C2×C4×C127—82no—
140C2×C4×C127#12011yescharacteristic
141C2×C4×C127C2×D811yescharacteristic
142C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
143C8×C127—21no—
144C8×C127—41no—
145C8×C127—81no—
146C8×C127C2×D811yescharacteristic
147C8×C127AGL(1,ℤ/8)11yescharacteristic
148C22×C127—41no—
149C22×C127—41no—
150C22×C127—41no—
151C22×C127—81no—
152C22×C127—81no—
153C22×C127—81no—
154C22×C127—161no—
155C22×C127—161no—
156C22×C127—161no—
157C22×C127#44711yescharacteristic
158C4×C127—21no—
159C4×C127—21no—
160C4×C127—41no—
161C4×C127—42no—
162C4×C127—81no—
163C4×C127—81no—
164C4×C127#44711yescharacteristic
165C4×C127#45311yescharacteristic
166#12325C12711yesmaximal, characteristic, direct product factor, Sylow
167C2×C127—81no—
168C2×C127—161no—
169C2×C127—321no—
170C2×C127#161911yescharacteristic
171C2×C127#219011yescharacteristic
172C2×C127#219311yescharacteristic
173#3277C2×C12711yescharacteristic, complemented
174#2250C2×C12711yescharacteristic, complemented
175#2207C2×C12711yescharacteristic, complemented
176#1687C2×C12711yescharacteristic, complemented
177#1360C2×C12711yescharacteristic, complemented
178#1334C2×C12711yescharacteristic, complemented
179#1330C2×C12711yescharacteristic, complemented
180C127#1232511yescharacteristic, direct product factor, Sylow
181C2×#137—21no—
182#548—21no—
183C2×SD32—21no—
184C2×SD32—21no—
185C2×D16—21no—
186#495C22×C12711yescharacteristic
187#493C22×C12711yescharacteristic
188#468—21no—
189#464—21no—
190#459—21no—
191#451—21no—
192#449—21no—
193C4×Q16C22×C12711yescharacteristic
194#436C22×C12711yescharacteristic
195C4⋊C16C22×C12711yescharacteristic
196#357—21no—
197#346C22×C12711yescharacteristic
198#334C22×C12711yescharacteristic
199#331—21no—
200C2×#41—21no—
201C22×Q8—21no—
202#137—42no—
203#137—42no—
204C2×Q16—21no—
205C2×Q16D4×C12711yescharacteristic
206C2×Q16D4×C12711yescharacteristic
207C2×SD16—21no—
208C2×SD16—21no—
209C2×D8—21no—
210C2×D8—21no—
211C2×D8—41no—
212C2×D8D4×C12711yescharacteristic
213C2×M16—21no—
214#127—21no—
215#124—21no—
216#124—41no—
217C22⋊Q8—21no—
218C22⋊Q8—41no—
219#121—21no—
220#121—41no—
221C4×Q8—21no—
222C4×D4—41no—
223C4×D4D4×C12711yescharacteristic
224SD32—42no—
225SD32—42no—
226D16—42no—
227C2×C16—21no—
228C2×C16—21no—
229#107D4×C12711yescharacteristic
230C4⋊C8—21no—
231C4⋊C8D4×C12711yescharacteristic
232#103—21no—
233#103—21no—
234#102—21no—
235#102—41no—
236C22⋊C8—21no—
237C4×C8C23×C12711yescharacteristic
238#41—42no—
239#41—81no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—41no—
243C2×Q8—42no—
244C2×Q8—81no—
245C2×D4—21no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4D8×C12711yescharacteristic
252C22×C4—21no—
253C22×C4—41no—
254C22×C4—41no—
255Q16—21no—
256Q16—41no—
257Q16—42no—
258Q16D8×C12712yescomplemented
259SD16—42no—
260SD16—41no—
261SD16—41no—
262D8—41no—
263D8—41no—
264D8—41no—
265D8—41no—
266D8—41no—
267D8—82no—
268M16—41no—
269M16—41no—
270C2×C8—21no—
271C2×C8—41no—
272C2×C8C2×D4×C12711yescharacteristic
273C2×C8C2×D4×C12711yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4D8×C12711yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—41no—
280C22⋊C4—41no—
281C22⋊C4—41no—
282C22⋊C4—41no—
283C42—41no—
284C42C2×D4×C12711yescharacteristic
285C16—22no—
286C16—41no—
287C23—21no—
288C23—41no—
289C23—81no—
290Q8—22no—
291Q8—41no—
292Q8—41no—
293Q8—41no—
294Q8—82no—
295D4—41no—
296D4—41no—
297D4—41no—
298D4—81no—
299D4—81no—
300D4—82no—
301D4—82no—
302D4—81no—
303D4—81no—
304D4—161no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—82no—
312C2×C4—82no—
313C2×C4#120×C12711yescharacteristic
314C2×C4C2×D8×C12711yescharacteristic
315C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
316C8—21no—
317C8—41no—
318C8—81no—
319C8C2×D8×C12711yescharacteristic
320C8AGL(1,ℤ/8)×C12711yescharacteristic
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22—161no—
328C22—161no—
329C22—161no—
330C22#447×C12711yescharacteristic
331C4—21no—
332C4—21no—
333C4—41no—
334C4—42no—
335C4—81no—
336C4—81no—
337C4#447×C12711yescharacteristic
338C4#453×C12711yescharacteristic
339C2—81no—
340C2—161no—
341C2—321no—
342C2C127×#161911yescharacteristic
343C2C127×#219011yescharacteristic
344C2C127×#219311yescharacteristic
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC4×C8C23×C127
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C42×C127 ◁ #436×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3277C2semidirect
2. C127×#2250C2semidirect
3. C127×#2207C2semidirect
4. C127×#1687C2semidirect
5. C127×#1360C2semidirect
6. C127×#1334C2semidirect
7. C127×#1330C2semidirect
85. Q16×C127D8semidirect
166. #12325C127direct (N × H)
173. #3277C2×C127semidirect
174. #2250C2×C127semidirect
175. #2207C2×C127semidirect
176. #1687C2×C127semidirect
177. #1360C2×C127semidirect
178. #1334C2×C127semidirect
179. #1330C2×C127semidirect
180. C127#12325direct (N × H)
258. Q16D8×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32772
C127×#22502
C127×#22072
C127×#16872
C127×#13602
C127×#13342
C127×#13302
#12325127