Finite Group Databasebeta

← C127×#11578 #44575251

Subgroups — C127×#11578 #44575251

Order 32512.

426 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2579C211yesmaximal, characteristic
2C127×#1466C211yesmaximal, characteristic
3C127×#1459C211yesmaximal, characteristic
4C127×#1326C212yesmaximal, complemented
5C127×#1326C212yesmaximal, complemented
6C2×C4×D4×C127C2211yescharacteristic
7C22×C4⋊C4×C127C411yescharacteristic
8#432×C127—21no—
9C2×C22⋊C8×C127—21no—
10#398×C127—21no—
11#396×C127—21no—
12#387×C127—21no—
13#386×C127C411yescharacteristic
14#386×C127C411yescharacteristic
15#385×C127—21no—
16#385×C127C2211yescharacteristic
17#385×C127C2211yescharacteristic
18#380×C127C411yescharacteristic
19#324×C127—21no—
20#323×C127—21no—
21#323×C127C2212yes—
22#323×C127C2212yes—
23C22×D4×C127C2×C411yescharacteristic
24C23×C4×C127C2×C411yescharacteristic
25C23×C4×C127C2×C411yescharacteristic
26C23×C4×C127C2×C411yescharacteristic
27C23×C4×C127D411yescharacteristic
28C22×C8×C127—41no—
29C4×D4×C127—41no—
30C4×D4×C127—41no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—41no—
37C2×C4⋊C4×C127—41no—
38C2×C4⋊C4×C127D411yescharacteristic
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127C2×C411yescharacteristic
42C2×C22⋊C4×C127C2×C411yescharacteristic
43C2×C22⋊C4×C127D411yescharacteristic
44C2×C22⋊C4×C127C2311yescharacteristic
45C2×C42×C127D411yescharacteristic
46C4⋊C8×C127—41no—
47C22⋊C8×C127—22no—
48C22⋊C8×C127—22no—
49C22⋊C8×C127—41no—
50#97×C127—41no—
51#95×C127—21no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127—21no—
56C24×C127C22⋊C411yescharacteristic
57C24×C127C22×C411yescharacteristic
58C2×D4×C127—22no—
59C2×D4×C127—22no—
60C2×D4×C127—41no—
61C22×C4×C127—21no—
62C22×C4×C127—21no—
63C22×C4×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—42no—
70C22×C4×C127—41no—
71C22×C4×C127—41no—
72C22×C4×C127—81no—
73C22×C4×C127—81no—
74C22×C4×C127—81no—
75C22×C4×C127C22⋊C411yescharacteristic
76C22×C4×C127C22⋊C411yescharacteristic
77C22×C4×C127C22⋊C411yescharacteristic
78C22×C4×C127C2×D411yescharacteristic
79C22×C4×C127C2×D411yescharacteristic
80C2×C8×C127—42no—
81C2×C8×C127—42no—
82C2×C8×C127—82no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—42no—
85C4⋊C4×C127—42no—
86C4⋊C4×C127—41no—
87C4⋊C4×C127—41no—
88C4⋊C4×C127—81no—
89C4⋊C4×C127—81no—
90C22⋊C4×C127—22no—
91C22⋊C4×C127—22no—
92C22⋊C4×C127—41no—
93C22⋊C4×C127—41no—
94C22⋊C4×C127—42no—
95C22⋊C4×C127—81no—
96C42×C127—21no—
97C42×C127—21no—
98C23×C127—21no—
99C23×C127—21no—
100C23×C127—21no—
101C23×C127—21no—
102C23×C127—41no—
103C23×C127—41no—
104C23×C127—41no—
105C23×C127—41no—
106C23×C127#10112yes—
107C23×C127C2×C22⋊C411yescharacteristic
108C23×C127#13112yes—
109D4×C127—44no—
110C2×C4×C127—22no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—41no—
118C2×C4×C127—42no—
119C2×C4×C127—41no—
120C2×C4×C127—42no—
121C2×C4×C127—41no—
122C2×C4×C127—41no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
125C2×C4×C127—42no—
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—81no—
136C2×C4×C127—81no—
137C2×C4×C127—81no—
138C2×C4×C127—82no—
139C2×C4×C127#9911yescharacteristic
140C2×C4×C127#9911yescharacteristic
141C8×C127—82no—
142C8×C127—82no—
143C22×C127—21no—
144C22×C127—21no—
145C22×C127—22no—
146C22×C127—22no—
147C22×C127—42no—
148C22×C127—42no—
149C22×C127—42no—
150C22×C127—41no—
151C22×C127—41no—
152C22×C127—41no—
153C22×C127—41no—
154C22×C127—81no—
155C22×C127#40811yescharacteristic
156C22×C127C2×#9911yescharacteristic
157C22×C127C2×#10111yescharacteristic
158C4×C127—21no—
159C4×C127—21no—
160C4×C127—41no—
161C4×C127—42no—
162C4×C127—41no—
163C4×C127—41no—
164C4×C127—41no—
165C4×C127—81no—
166C4×C127—81no—
167C4×C127—81no—
168#11578C12711yesmaximal, characteristic, direct product factor, Sylow
169C2×C127—21no—
170C2×C127—21no—
171C2×C127—42no—
172C2×C127—42no—
173C2×C127#147211yescharacteristic
174C2×C127#212011yescharacteristic
175C2×C127#212111yescharacteristic
176#2579C2×C12711yescharacteristic
177#1466C2×C12711yescharacteristic
178#1459C2×C12711yescharacteristic
179#1326C2×C12712yescomplemented
180#1326C2×C12712yescomplemented
181C127#1157811yescharacteristic, direct product factor, Sylow
182C2×C4×D4C22×C12711yescharacteristic
183C22×C4⋊C4C4×C12711yescharacteristic
184#432—21no—
185C2×C22⋊C8—21no—
186#398—21no—
187#396—21no—
188#387—21no—
189#386C4×C12711yescharacteristic
190#386C4×C12711yescharacteristic
191#385—21no—
192#385C22×C12711yescharacteristic
193#385C22×C12711yescharacteristic
194#380C4×C12711yescharacteristic
195#324—21no—
196#323—21no—
197#323C22×C12712yes—
198#323C22×C12712yes—
199C22×D4C2×C4×C12711yescharacteristic
200C23×C4C2×C4×C12711yescharacteristic
201C23×C4C2×C4×C12711yescharacteristic
202C23×C4C2×C4×C12711yescharacteristic
203C23×C4D4×C12711yescharacteristic
204C22×C8—41no—
205C4×D4—41no—
206C4×D4—41no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—41no—
213C2×C4⋊C4—41no—
214C2×C4⋊C4D4×C12711yescharacteristic
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4C2×C4×C12711yescharacteristic
218C2×C22⋊C4C2×C4×C12711yescharacteristic
219C2×C22⋊C4D4×C12711yescharacteristic
220C2×C22⋊C4C23×C12711yescharacteristic
221C2×C42D4×C12711yescharacteristic
222C4⋊C8—41no—
223C22⋊C8—22no—
224C22⋊C8—22no—
225C22⋊C8—41no—
226#97—41no—
227#95—21no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232C24C22⋊C4×C12711yescharacteristic
233C24C22×C4×C12711yescharacteristic
234C2×D4—22no—
235C2×D4—22no—
236C2×D4—41no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—42no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4—81no—
251C22×C4C22⋊C4×C12711yescharacteristic
252C22×C4C22⋊C4×C12711yescharacteristic
253C22×C4C22⋊C4×C12711yescharacteristic
254C22×C4C2×D4×C12711yescharacteristic
255C22×C4C2×D4×C12711yescharacteristic
256C2×C8—42no—
257C2×C8—42no—
258C2×C8—82no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—81no—
265C4⋊C4—81no—
266C22⋊C4—22no—
267C22⋊C4—22no—
268C22⋊C4—41no—
269C22⋊C4—41no—
270C22⋊C4—42no—
271C22⋊C4—81no—
272C42—21no—
273C42—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23#101×C12712yes—
283C23C2×C22⋊C4×C12711yescharacteristic
284C23#131×C12712yes—
285D4—44no—
286C2×C4—22no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—41no—
294C2×C4—42no—
295C2×C4—41no—
296C2×C4—42no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—82no—
315C2×C4#99×C12711yescharacteristic
316C2×C4#99×C12711yescharacteristic
317C8—82no—
318C8—82no—
319C22—21no—
320C22—21no—
321C22—22no—
322C22—22no—
323C22—42no—
324C22—42no—
325C22—42no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22#408×C12711yescharacteristic
332C22C2×#99×C12711yescharacteristic
333C22C2×#101×C12711yescharacteristic
334C4—21no—
335C4—21no—
336C4—41no—
337C4—42no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—81no—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—42no—
348C2C127×#147211yescharacteristic
349C2C127×#212011yescharacteristic
350C2C127×#212111yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC24C22×C4×C127
Frattini, cosocleC2×C22⋊C4C23×C127
prime radicalC22×D4×C127C2×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1326C2semidirect
5. C127×#1326C2semidirect
168. #11578C127direct (N × H)
179. #1326C2×C127semidirect
180. #1326C2×C127semidirect
181. C127#11578direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#25792
C127×#14662
C127×#14592
C127×#13262
#11578127