Finite Group Databasebeta

← C127×#10084 #44573757

Subgroups — C127×#10084 #44573757

Order 32512.

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

normal subgroups only

This group has 484 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
1C2×#501×C127C211yesmaximal, characteristic
2C2×#491×C127C211yesmaximal, characteristic
3C127×#2822C211yesmaximal, characteristic
4C127×#1993C211yesmaximal, characteristic
5C2×#330×C127C211yesmaximal, characteristic
6C2×#330×C127C211yesmaximal, characteristic
7C127×#1295C211yesmaximal, characteristic
8C2×C4⋊Q8×C127C2211yescharacteristic
9C2×#125×C127C2211yescharacteristic
10C2×#125×C127C2211yescharacteristic
11#501×C127—22no—
12#501×C127—22no—
13#491×C127—22no—
14#491×C127—22no—
15C2×#107×C127—21no—
16C2×#106×C127—21no—
17C2×#103×C127—21no—
18C2×#103×C127—21no—
19C2×#97×C127C2211yescharacteristic
20C2×#97×C127C2211yescharacteristic
21C2×#97×C127C2211yescharacteristic
22#400×C127—21no—
23#400×C127—21no—
24#398×C127—22no—
25#398×C127—21no—
26#398×C127—21no—
27#382×C127C2211yescharacteristic
28#340×C127—22no—
29#330×C127—22no—
30#330×C127—22no—
31C22×Q8×C127—21no—
32C22×C8×C127—21no—
33C22×C8×C127—21no—
34C22×C8×C127—21no—
35C4⋊Q8×C127—21no—
36C4⋊Q8×C127—21no—
37C4⋊Q8×C127—21no—
38C4⋊Q8×C127D412yes—
39#125×C127—21no—
40#125×C127—21no—
41#125×C127—21no—
42#125×C127—21no—
43#125×C127—21no—
44#125×C127—21no—
45#125×C127—21no—
46#125×C127—21no—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊C4×C127—21no—
49C2×C4⋊C4×C127—21no—
50C2×C4⋊C4×C127—21no—
51C2×C4⋊C4×C127—21no—
52C2×C4⋊C4×C127—21no—
53C2×C4⋊C4×C127—22no—
54C2×C4⋊C4×C127D411yescharacteristic
55C2×C4⋊C4×C127D411yescharacteristic
56C2×C4⋊C4×C127D411yescharacteristic
57C2×C4⋊C4×C127D411yescharacteristic
58C2×C4⋊C4×C127D412yes—
59C2×C42×C127C2311yescharacteristic
60#107×C127—24no—
61#106×C127—24no—
62#103×C127—24no—
63#103×C127—24no—
64#97×C127—21no—
65#97×C127—21no—
66#97×C127—21no—
67#97×C127—21no—
68#97×C127D412yes—
69#97×C127D412yes—
70#95×C127—22no—
71#95×C127—22no—
72#95×C127—22no—
73#95×C127—21no—
74#95×C127—21no—
75C2×Q8×C127—22no—
76C2×Q8×C127—44no—
77C2×Q8×C127—41no—
78C22×C4×C127—22no—
79C22×C4×C127—21no—
80C22×C4×C127—21no—
81C22×C4×C127—21no—
82C22×C4×C127—21no—
83C22×C4×C127—41no—
84C22×C4×C127C2×D411yescharacteristic
85C22×C4×C127C2×D411yescharacteristic
86C22×C4×C127C2×D411yescharacteristic
87C2×C8×C127—24no—
88C2×C8×C127—22no—
89C2×C8×C127—22no—
90C2×C8×C127—22no—
91C2×C8×C127—42no—
92C2×C8×C127—41no—
93C2×C8×C127—41no—
94C4⋊C4×C127—21no—
95C4⋊C4×C127—21no—
96C4⋊C4×C127—21no—
97C4⋊C4×C127—22no—
98C4⋊C4×C127—21no—
99C4⋊C4×C127—22no—
100C4⋊C4×C127—21no—
101C4⋊C4×C127—21no—
102C4⋊C4×C127—21no—
103C4⋊C4×C127—21no—
104C4⋊C4×C127—42no—
105C4⋊C4×C127—41no—
106C4⋊C4×C127—41no—
107C4⋊C4×C127—41no—
108C4⋊C4×C127—41no—
109C4⋊C4×C127—41no—
110C4⋊C4×C127—41no—
111C4⋊C4×C127—41no—
112C4⋊C4×C127—41no—
113C4⋊C4×C127—41no—
114C4⋊C4×C127—41no—
115C4⋊C4×C127—82no—
116C42×C127C2×D411yescharacteristic
117C42×C127C2×D411yescharacteristic
118C42×C127C2×D411yescharacteristic
119C42×C127#4111yescharacteristic
120C23×C127#12011yescharacteristic
121Q8×C127—44no—
122Q8×C127—82no—
123C2×C4×C127—22no—
124C2×C4×C127—21no—
125C2×C4×C127—22no—
126C2×C4×C127—21no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—41no—
130C2×C4×C127—41no—
131C2×C4×C127—42no—
132C2×C4×C127—42no—
133C2×C4×C127—42no—
134C2×C4×C127—42no—
135C2×C4×C127—41no—
136C2×C4×C127—41no—
137C2×C4×C127—42no—
138C2×C4×C127—42no—
139C2×C4×C127—41no—
140C2×C4×C127—41no—
141C2×C4×C127—82no—
142C2×C4×C127#12011yescharacteristic
143C2×C4×C127#12011yescharacteristic
144C2×C4×C127#12111yescharacteristic
145C2×C4×C127#12111yescharacteristic
146C2×C4×C127#12111yescharacteristic
147C2×C4×C127#12711yescharacteristic
148C8×C127—24no—
149C8×C127—42no—
150C8×C127—42no—
151C22×C127#39211yescharacteristic
152C22×C127#45412yes—
153C22×C127#45511yescharacteristic
154C22×C127#45611yescharacteristic
155C22×C127#45612yes—
156C4×C127—21no—
157C4×C127—21no—
158C4×C127—21no—
159C4×C127—21no—
160C4×C127—21no—
161C4×C127—21no—
162C4×C127—82no—
163C4×C127—81no—
164C4×C127—82no—
165C4×C127—81no—
166C4×C127—81no—
167C4×C127—81no—
168#10084C12711yesmaximal, characteristic, direct product factor, Sylow
169C2×C127#166312yes—
170C2×C127#166412yes—
171C2×C127#200311yescharacteristic
172C2×C127#200511yescharacteristic
173C2×C127#200711yescharacteristic
174C2×#501C2×C12711yescharacteristic
175C2×#491C2×C12711yescharacteristic
176#2822C2×C12711yescharacteristic
177#1993C2×C12711yescharacteristic
178C2×#330C2×C12711yescharacteristic
179C2×#330C2×C12711yescharacteristic
180#1295C2×C12711yescharacteristic
181C127#1008411yescharacteristic, direct product factor, Sylow
182C2×C4⋊Q8C22×C12711yescharacteristic
183C2×#125C22×C12711yescharacteristic
184C2×#125C22×C12711yescharacteristic
185#501—22no—
186#501—22no—
187#491—22no—
188#491—22no—
189C2×#107—21no—
190C2×#106—21no—
191C2×#103—21no—
192C2×#103—21no—
193C2×#97C22×C12711yescharacteristic
194C2×#97C22×C12711yescharacteristic
195C2×#97C22×C12711yescharacteristic
196#400—21no—
197#400—21no—
198#398—22no—
199#398—21no—
200#398—21no—
201#382C22×C12711yescharacteristic
202#340—22no—
203#330—22no—
204#330—22no—
205C22×Q8—21no—
206C22×C8—21no—
207C22×C8—21no—
208C22×C8—21no—
209C4⋊Q8—21no—
210C4⋊Q8—21no—
211C4⋊Q8—21no—
212C4⋊Q8D4×C12712yes—
213#125—21no—
214#125—21no—
215#125—21no—
216#125—21no—
217#125—21no—
218#125—21no—
219#125—21no—
220#125—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4—21no—
225C2×C4⋊C4—21no—
226C2×C4⋊C4—21no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4D4×C12711yescharacteristic
229C2×C4⋊C4D4×C12711yescharacteristic
230C2×C4⋊C4D4×C12711yescharacteristic
231C2×C4⋊C4D4×C12711yescharacteristic
232C2×C4⋊C4D4×C12712yes—
233C2×C42C23×C12711yescharacteristic
234#107—24no—
235#106—24no—
236#103—24no—
237#103—24no—
238#97—21no—
239#97—21no—
240#97—21no—
241#97—21no—
242#97D4×C12712yes—
243#97D4×C12712yes—
244#95—22no—
245#95—22no—
246#95—22no—
247#95—21no—
248#95—21no—
249C2×Q8—22no—
250C2×Q8—44no—
251C2×Q8—41no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—41no—
258C22×C4C2×D4×C12711yescharacteristic
259C22×C4C2×D4×C12711yescharacteristic
260C22×C4C2×D4×C12711yescharacteristic
261C2×C8—24no—
262C2×C8—22no—
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—42no—
266C2×C8—41no—
267C2×C8—41no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—21no—
273C4⋊C4—22no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C4⋊C4—42no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—41no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C4⋊C4—82no—
290C42C2×D4×C12711yescharacteristic
291C42C2×D4×C12711yescharacteristic
292C42C2×D4×C12711yescharacteristic
293C42#41×C12711yescharacteristic
294C23#120×C12711yescharacteristic
295Q8—44no—
296Q8—82no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—22no—
300C2×C4—21no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—82no—
316C2×C4#120×C12711yescharacteristic
317C2×C4#120×C12711yescharacteristic
318C2×C4#121×C12711yescharacteristic
319C2×C4#121×C12711yescharacteristic
320C2×C4#121×C12711yescharacteristic
321C2×C4#127×C12711yescharacteristic
322C8—24no—
323C8—42no—
324C8—42no—
325C22#392×C12711yescharacteristic
326C22#454×C12712yes—
327C22#455×C12711yescharacteristic
328C22#456×C12711yescharacteristic
329C22#456×C12712yes—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—82no—
337C4—81no—
338C4—82no—
339C4—81no—
340C4—81no—
341C4—81no—
342C2C127×#166312yes—
343C2C127×#166412yes—
344C2C127×#200311yescharacteristic
345C2C127×#200511yescharacteristic
346C2C127×#200711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C127#120
commutator, Frattini, cosocleC2×C42C23×C127
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
168. #10084C127direct (N × H)
181. C127#10084direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#501×C1272
C2×#491×C1272
C127×#28222
C127×#19932
C2×#330×C1272
C127×#12952
#10084127