Finite Group Databasebeta

← C127×#9494 #44573167

Subgroups — C127×#9494 #44573167

Order 32512.

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

normal subgroups only

This group has 514 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, complemented
2C127×#2598C211yesmaximal, characteristic
3C127×#1490C212yesmaximal, complemented
4C127×#1464C211yesmaximal, characteristic, complemented
5C127×#1288C212yesmaximal, complemented
6C2×C4×D4×C127C2211yescharacteristic
7C2×#117×C127C2211yescharacteristic
8#433×C127—24no—
9#432×C127C2212yes—
10#423×C127—21no—
11#407×C127—21no—
12C4×M16×C127C2212yes—
13#400×C127C411yescharacteristic
14#399×C127C411yescharacteristic
15#394×C127C411yescharacteristic
16#392×C127C411yescharacteristic
17#388×C127—21no—
18#386×C127—21no—
19#386×C127—21no—
20#385×C127—21no—
21#383×C127C2211yescharacteristic
22D4⋊C8×C127—24no—
23#324×C127—21no—
24#323×C127—21no—
25C22×D4×C127—21no—
26C22×D4×C127C2×C411yescharacteristic
27C23×C4×C127—21no—
28C23×C4×C127D411yescharacteristic
29C2×M16×C127—22no—
30C4×D4×C127—22no—
31C4×D4×C127—22no—
32#117×C127—22no—
33#117×C127—22no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127C2×C411yescharacteristic
36C2×C4⋊C4×C127C2×C411yescharacteristic
37C2×C4⋊C4×C127D411yescharacteristic
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127C2×C411yescharacteristic
44C2×C22⋊C4×C127D411yescharacteristic
45C2×C42×C127D411yescharacteristic
46C2×C42×C127C2311yescharacteristic
47C4⋊C8×C127—24no—
48C4⋊C8×C127—22no—
49C22⋊C8×C127—24no—
50C22⋊C8×C127—22no—
51#97×C127—22no—
52#97×C127—22no—
53C4×C8×C127D414yescomplemented
54#95×C127—21no—
55#95×C127—21no—
56#95×C127—21no—
57#95×C127—21no—
58#95×C127C2×C411yescharacteristic
59#95×C127C2×C411yescharacteristic
60C24×C127—21no—
61C24×C127C22⋊C411yescharacteristic
62C2×D4×C127—22no—
63C2×D4×C127—42no—
64C2×D4×C127—42no—
65C2×D4×C127—42no—
66C2×D4×C127—81no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127—21no—
71C22×C4×C127—21no—
72C22×C4×C127—41no—
73C22×C4×C127—41no—
74C22×C4×C127—42no—
75C22×C4×C127—81no—
76C22×C4×C127—81no—
77C22×C4×C127C22⋊C411yescharacteristic
78C22×C4×C127C22⋊C411yescharacteristic
79C22×C4×C127C22⋊C411yescharacteristic
80C22×C4×C127C22×C411yescharacteristic
81C22×C4×C127C2×D411yescharacteristic
82C22×C4×C127C2×D411yescharacteristic
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—22no—
90C4⋊C4×C127—81no—
91C22⋊C4×C127—22no—
92C22⋊C4×C127—22no—
93C22⋊C4×C127—42no—
94C22⋊C4×C127—42no—
95C22⋊C4×C127—41no—
96C22⋊C4×C127—41no—
97C22⋊C4×C127—81no—
98C22⋊C4×C127—81no—
99C42×C127—21no—
100C42×C127—21no—
101C42×C127C2×D412yes—
102C42×C127#4112yes—
103C23×C127—22no—
104C23×C127—21no—
105C23×C127—21no—
106C23×C127—21no—
107C23×C127—41no—
108C23×C127—41no—
109C23×C127—41no—
110C23×C127—41no—
111C23×C127—41no—
112C23×C127—41no—
113C23×C127—41no—
114C23×C127—41no—
115C23×C127C2×C22⋊C411yescharacteristic
116D4×C127—24no—
117D4×C127—42no—
118D4×C127—84no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—21no—
124C2×C4×C127—21no—
125C2×C4×C127—21no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—42no—
129C2×C4×C127—42no—
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—84no—
142C2×C4×C127C4×D412yes—
143C2×C4×C127#12011yescharacteristic
144C2×C4×C127#12112yes—
145C2×C4×C127#12311yescharacteristic
146C8×C127—44no—
147C8×C127—82no—
148C22×C127—21no—
149C22×C127—21no—
150C22×C127—42no—
151C22×C127—42no—
152C22×C127—42no—
153C22×C127—42no—
154C22×C127—41no—
155C22×C127—41no—
156C22×C127—41no—
157C22×C127—81no—
158C22×C127—81no—
159C22×C127—81no—
160C22×C127—81no—
161C22×C127—81no—
162C22×C127#38611yescharacteristic
163C22×C127#42111yescharacteristic
164C22×C127#42111yescharacteristic
165C4×C127—22no—
166C4×C127—21no—
167C4×C127—21no—
168C4×C127—22no—
169C4×C127—41no—
170C4×C127—41no—
171C4×C127—41no—
172C4×C127—81no—
173C4×C127—81no—
174C4×C127—81no—
175#9494C12711yesmaximal, characteristic, direct product factor, Sylow
176C2×C127—21no—
177C2×C127—21no—
178C2×C127—81no—
179C2×C127—82no—
180C2×C127#189111yescharacteristic
181C2×C127#189711yescharacteristic
182C2×C127#191011yescharacteristic
183#2921C2×C12711yescharacteristic, complemented
184#2598C2×C12711yescharacteristic
185#1490C2×C12712yescomplemented
186#1464C2×C12711yescharacteristic, complemented
187#1288C2×C12712yescomplemented
188C127#949411yescharacteristic, direct product factor, Sylow
189C2×C4×D4C22×C12711yescharacteristic
190C2×#117C22×C12711yescharacteristic
191#433—24no—
192#432C22×C12712yes—
193#423—21no—
194#407—21no—
195C4×M16C22×C12712yes—
196#400C4×C12711yescharacteristic
197#399C4×C12711yescharacteristic
198#394C4×C12711yescharacteristic
199#392C4×C12711yescharacteristic
200#388—21no—
201#386—21no—
202#386—21no—
203#385—21no—
204#383C22×C12711yescharacteristic
205D4⋊C8—24no—
206#324—21no—
207#323—21no—
208C22×D4—21no—
209C22×D4C2×C4×C12711yescharacteristic
210C23×C4—21no—
211C23×C4D4×C12711yescharacteristic
212C2×M16—22no—
213C4×D4—22no—
214C4×D4—22no—
215#117—22no—
216#117—22no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C2×C4×C12711yescharacteristic
219C2×C4⋊C4C2×C4×C12711yescharacteristic
220C2×C4⋊C4D4×C12711yescharacteristic
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4—21no—
224C2×C22⋊C4—21no—
225C2×C22⋊C4—21no—
226C2×C22⋊C4C2×C4×C12711yescharacteristic
227C2×C22⋊C4D4×C12711yescharacteristic
228C2×C42D4×C12711yescharacteristic
229C2×C42C23×C12711yescharacteristic
230C4⋊C8—24no—
231C4⋊C8—22no—
232C22⋊C8—24no—
233C22⋊C8—22no—
234#97—22no—
235#97—22no—
236C4×C8D4×C12714yescomplemented
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241#95C2×C4×C12711yescharacteristic
242#95C2×C4×C12711yescharacteristic
243C24—21no—
244C24C22⋊C4×C12711yescharacteristic
245C2×D4—22no—
246C2×D4—42no—
247C2×D4—42no—
248C2×D4—42no—
249C2×D4—81no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—42no—
258C22×C4—81no—
259C22×C4—81no—
260C22×C4C22⋊C4×C12711yescharacteristic
261C22×C4C22⋊C4×C12711yescharacteristic
262C22×C4C22⋊C4×C12711yescharacteristic
263C22×C4C22×C4×C12711yescharacteristic
264C22×C4C2×D4×C12711yescharacteristic
265C22×C4C2×D4×C12711yescharacteristic
266M16—42no—
267M16—42no—
268C2×C8—24no—
269C2×C8—42no—
270C4⋊C4—22no—
271C4⋊C4—22no—
272C4⋊C4—22no—
273C4⋊C4—81no—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C22⋊C4—42no—
277C22⋊C4—42no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C22⋊C4—81no—
281C22⋊C4—81no—
282C42—21no—
283C42—21no—
284C42C2×D4×C12712yes—
285C42#41×C12712yes—
286C23—22no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23C2×C22⋊C4×C12711yescharacteristic
299D4—24no—
300D4—42no—
301D4—84no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
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—41no—
324C2×C4—84no—
325C2×C4C4×D4×C12712yes—
326C2×C4#120×C12711yescharacteristic
327C2×C4#121×C12712yes—
328C2×C4#123×C12711yescharacteristic
329C8—44no—
330C8—82no—
331C22—21no—
332C22—21no—
333C22—42no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22#386×C12711yescharacteristic
346C22#421×C12711yescharacteristic
347C22#421×C12711yescharacteristic
348C4—22no—
349C4—21no—
350C4—21no—
351C4—22no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—81no—
357C4—81no—
358C2—21no—
359C2—21no—
360C2—81no—
361C2—82no—
362C2C127×#189111yescharacteristic
363C2C127×#189711yescharacteristic
364C2C127×#191011yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radical#392×C127C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2921C2semidirect
3. C127×#1490C2semidirect
4. C127×#1464C2semidirect
5. C127×#1288C2semidirect
53. C4×C8×C127D4semidirect
175. #9494C127direct (N × H)
183. #2921C2×C127semidirect
185. #1490C2×C127semidirect
186. #1464C2×C127semidirect
187. #1288C2×C127semidirect
188. C127#9494direct (N × H)
236. C4×C8D4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#29212
C127×#25982
C127×#14902
C127×#14642
C127×#12882
#9494127