Finite Group Databasebeta

← C127×#9514 #44573187

Subgroups — C127×#9514 #44573187

Order 32512.

478 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 118 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×#2921C211yesmaximal, characteristic
2C127×#2484C211yesmaximal, characteristic
3C127×#1822C211yesmaximal, characteristic
4C127×#1463C212yesmaximal
5C127×#1306C212yesmaximal
6C2×#117×C127C2211yescharacteristic
7C22×C4⋊C4×C127C2211yescharacteristic
8#433×C127—24no—
9#423×C127—21no—
10#407×C127C2212yes—
11#407×C127C2212yes—
12C4×M16×C127—21no—
13#400×C127—21no—
14#398×C127—21no—
15#387×C127—21no—
16#387×C127—21no—
17#385×C127C411yescharacteristic
18#385×C127C411yescharacteristic
19#381×C127C411yescharacteristic
20#381×C127C411yescharacteristic
21#381×C127C2211yescharacteristic
22#343×C127—21no—
23#343×C127—21no—
24#324×C127—24no—
25C23×C4×C127C2×C411yescharacteristic
26C23×C4×C127C2×C411yescharacteristic
27C23×C4×C127C2311yescharacteristic
28C2×M16×C127—22no—
29C2×M16×C127—22no—
30#117×C127—22no—
31#117×C127—22no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—22no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127—22no—
38C2×C4⋊C4×C127D411yescharacteristic
39C2×C4⋊C4×C127D411yescharacteristic
40C2×C22⋊C4×C127C2×C411yescharacteristic
41C2×C22⋊C4×C127C2×C411yescharacteristic
42C2×C22⋊C4×C127C2×C411yescharacteristic
43C2×C22⋊C4×C127C2×C411yescharacteristic
44C2×C42×C127D411yescharacteristic
45C2×C42×C127D411yescharacteristic
46C4⋊C8×C127—24no—
47C22⋊C8×C127—22no—
48C22⋊C8×C127—22no—
49C22⋊C8×C127—22no—
50C22⋊C8×C127D414yes—
51#97×C127—22no—
52C4×C8×C127—22no—
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—21no—
61C24×C127C22×C411yescharacteristic
62C22×C4×C127—21no—
63C22×C4×C127—22no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—22no—
68C22×C4×C127—42no—
69C22×C4×C127—41no—
70C22×C4×C127—41no—
71C22×C4×C127—41no—
72C22×C4×C127—41no—
73C22×C4×C127C22⋊C411yescharacteristic
74C22×C4×C127C22⋊C411yescharacteristic
75C22×C4×C127C22⋊C411yescharacteristic
76C22×C4×C127C22⋊C411yescharacteristic
77C22×C4×C127C2×D411yescharacteristic
78C22×C4×C127C2×D411yescharacteristic
79C22×C4×C127C2×D412yes—
80C22×C4×C127#4112yes—
81M16×C127—42no—
82M16×C127—42no—
83M16×C127—42no—
84M16×C127—42no—
85C2×C8×C127—24no—
86C2×C8×C127—42no—
87C4⋊C4×C127—22no—
88C4⋊C4×C127—22no—
89C4⋊C4×C127—42no—
90C4⋊C4×C127—42no—
91C4⋊C4×C127—41no—
92C4⋊C4×C127—42no—
93C4⋊C4×C127—41no—
94C22⋊C4×C127—22no—
95C22⋊C4×C127—22no—
96C22⋊C4×C127—41no—
97C22⋊C4×C127—41no—
98C42×C127—21no—
99C42×C127—21no—
100C42×C127—21no—
101C42×C127—21no—
102C23×C127—21no—
103C23×C127—21no—
104C23×C127—41no—
105C23×C127—41no—
106C23×C127C2×C22⋊C411yescharacteristic
107C23×C127C4×D412yes—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—22no—
113C2×C4×C127—24no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—42no—
119C2×C4×C127—42no—
120C2×C4×C127—41no—
121C2×C4×C127—42no—
122C2×C4×C127—41no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
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—82no—
137C2×C4×C127#12011yescharacteristic
138C2×C4×C127#12112yes—
139C2×C4×C127#12311yescharacteristic
140C8×C127—44no—
141C8×C127—82no—
142C22×C127—21no—
143C22×C127—21no—
144C22×C127—22no—
145C22×C127—22no—
146C22×C127—22no—
147C22×C127—42no—
148C22×C127—42no—
149C22×C127#38611yescharacteristic
150C22×C127#41011yescharacteristic
151C22×C127#41011yescharacteristic
152C4×C127—21no—
153C4×C127—22no—
154C4×C127—21no—
155C4×C127—42no—
156C4×C127—41no—
157C4×C127—41no—
158C4×C127—41no—
159C4×C127—41no—
160C4×C127—81no—
161C4×C127—81no—
162C4×C127—81no—
163#9514C12711yesmaximal, characteristic, direct product factor, Sylow
164C2×C127—21no—
165C2×C127—21no—
166C2×C127—42no—
167C2×C127#189111yescharacteristic
168C2×C127#189911yescharacteristic
169C2×C127#191511yescharacteristic
170#2921C2×C12711yescharacteristic
171#2484C2×C12711yescharacteristic
172#1822C2×C12711yescharacteristic
173#1463C2×C12712yes—
174#1306C2×C12712yes—
175C127#951411yescharacteristic, direct product factor, Sylow
176C2×#117C22×C12711yescharacteristic
177C22×C4⋊C4C22×C12711yescharacteristic
178#433—24no—
179#423—21no—
180#407C22×C12712yes—
181#407C22×C12712yes—
182C4×M16—21no—
183#400—21no—
184#398—21no—
185#387—21no—
186#387—21no—
187#385C4×C12711yescharacteristic
188#385C4×C12711yescharacteristic
189#381C4×C12711yescharacteristic
190#381C4×C12711yescharacteristic
191#381C22×C12711yescharacteristic
192#343—21no—
193#343—21no—
194#324—24no—
195C23×C4C2×C4×C12711yescharacteristic
196C23×C4C2×C4×C12711yescharacteristic
197C23×C4C23×C12711yescharacteristic
198C2×M16—22no—
199C2×M16—22no—
200#117—22no—
201#117—22no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—22no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—22no—
208C2×C4⋊C4D4×C12711yescharacteristic
209C2×C4⋊C4D4×C12711yescharacteristic
210C2×C22⋊C4C2×C4×C12711yescharacteristic
211C2×C22⋊C4C2×C4×C12711yescharacteristic
212C2×C22⋊C4C2×C4×C12711yescharacteristic
213C2×C22⋊C4C2×C4×C12711yescharacteristic
214C2×C42D4×C12711yescharacteristic
215C2×C42D4×C12711yescharacteristic
216C4⋊C8—24no—
217C22⋊C8—22no—
218C22⋊C8—22no—
219C22⋊C8—22no—
220C22⋊C8D4×C12714yes—
221#97—22no—
222C4×C8—22no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231C24C22×C4×C12711yescharacteristic
232C22×C4—21no—
233C22×C4—22no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—42no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4C22⋊C4×C12711yescharacteristic
244C22×C4C22⋊C4×C12711yescharacteristic
245C22×C4C22⋊C4×C12711yescharacteristic
246C22×C4C22⋊C4×C12711yescharacteristic
247C22×C4C2×D4×C12711yescharacteristic
248C22×C4C2×D4×C12711yescharacteristic
249C22×C4C2×D4×C12712yes—
250C22×C4#41×C12712yes—
251M16—42no—
252M16—42no—
253M16—42no—
254M16—42no—
255C2×C8—24no—
256C2×C8—42no—
257C4⋊C4—22no—
258C4⋊C4—22no—
259C4⋊C4—42no—
260C4⋊C4—42no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C4⋊C4—41no—
264C22⋊C4—22no—
265C22⋊C4—22no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C42—21no—
269C42—21no—
270C42—21no—
271C42—21no—
272C23—21no—
273C23—21no—
274C23—41no—
275C23—41no—
276C23C2×C22⋊C4×C12711yescharacteristic
277C23C4×D4×C12712yes—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—82no—
307C2×C4#120×C12711yescharacteristic
308C2×C4#121×C12712yes—
309C2×C4#123×C12711yescharacteristic
310C8—44no—
311C8—82no—
312C22—21no—
313C22—21no—
314C22—22no—
315C22—22no—
316C22—22no—
317C22—42no—
318C22—42no—
319C22#386×C12711yescharacteristic
320C22#410×C12711yescharacteristic
321C22#410×C12711yescharacteristic
322C4—21no—
323C4—22no—
324C4—21no—
325C4—42no—
326C4—41no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—81no—
331C4—81no—
332C4—81no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2C127×#189111yescharacteristic
337C2C127×#189911yescharacteristic
338C2C127×#191511yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC24C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127C22×C4
LCSG ▷ C24 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
163. #9514C127direct (N × H)
175. C127#9514direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#29212
C127×#24842
C127×#18222
C127×#14632
C127×#13062
#9514127