Finite Group Databasebeta

← C127×#11739 #44575412

Subgroups — C127×#11739 #44575412

Order 32512.

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

normal subgroups only

This group has 420 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×#2638C211yesmaximal, characteristic
2C4×#100×C127C211yesmaximal, characteristic
3C127×#1459C211yesmaximal, characteristic
4C127×#1354C212yesmaximal, complemented
5C127×#1346C212yesmaximal, complemented
6C2×C22⋊Q8×C127C411yescharacteristic
7C2×C4×D4×C127C2211yescharacteristic
8C2×#100×C127—21no—
9C2×C22⋊C8×C127—21no—
10C4×M16×C127—21no—
11#398×C127C2211yescharacteristic
12#397×C127—21no—
13#397×C127C411yescharacteristic
14#395×C127C2211yescharacteristic
15#394×C127—21no—
16#393×C127C411yescharacteristic
17#387×C127—21no—
18#385×C127—21no—
19#381×C127C411yescharacteristic
20#343×C127C2212yes—
21#324×C127C2212yes—
22#323×C127—21no—
23C22×Q8×C127C2×C411yescharacteristic
24C22×D4×C127D411yescharacteristic
25C23×C4×C127C2×C411yescharacteristic
26C23×C4×C127D411yescharacteristic
27C2×M16×C127—22no—
28C22×C8×C127—41no—
29C22⋊Q8×C127—41no—
30C22⋊Q8×C127—41no—
31C4×D4×C127—41no—
32C4×D4×C127—41no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127C2×C411yescharacteristic
37C2×C4⋊C4×C127C2311yescharacteristic
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127C2×C411yescharacteristic
43C2×C22⋊C4×C127D411yescharacteristic
44C2×C42×C127D411yescharacteristic
45#100×C127—24no—
46C22⋊C8×C127—22no—
47C22⋊C8×C127—41no—
48#97×C127—41no—
49C4×C8×C127—41no—
50#95×C127—21no—
51#95×C127—21no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127C2×C411yescharacteristic
56#95×C127C2×C411yescharacteristic
57C24×C127C22⋊C411yescharacteristic
58C24×C127C22⋊C411yescharacteristic
59C2×Q8×C127—41no—
60C2×Q8×C127—81no—
61C2×D4×C127—22no—
62C2×D4×C127—22no—
63C2×D4×C127—41no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127—21no—
71C22×C4×C127—21no—
72C22×C4×C127—81no—
73C22×C4×C127—81no—
74C22×C4×C127C22⋊C411yescharacteristic
75C22×C4×C127C22⋊C411yescharacteristic
76C22×C4×C127C22×C411yescharacteristic
77C22×C4×C127C2×D411yescharacteristic
78C22×C4×C127C2×D411yescharacteristic
79M16×C127—24no—
80M16×C127—42no—
81C2×C8×C127—42no—
82C2×C8×C127—42no—
83C2×C8×C127—82no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C4⋊C4×C127—41no—
87C4⋊C4×C127—41no—
88C4⋊C4×C127—42no—
89C4⋊C4×C127—81no—
90C22⋊C4×C127—41no—
91C22⋊C4×C127—41no—
92C22⋊C4×C127—42no—
93C22⋊C4×C127—42no—
94C22⋊C4×C127—81no—
95C22⋊C4×C127—81no—
96C42×C127—21no—
97C42×C127—21no—
98C23×C127—21no—
99C23×C127—21no—
100C23×C127—21no—
101C23×C127—21no—
102C23×C127—21no—
103C23×C127—41no—
104C23×C127—41no—
105C23×C127—41no—
106C23×C127—41no—
107C23×C127#10412yes—
108C23×C127C2×C22⋊C411yescharacteristic
109Q8×C127—82no—
110D4×C127—44no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—41no—
117C2×C4×C127—42no—
118C2×C4×C127—41no—
119C2×C4×C127—41no—
120C2×C4×C127—41no—
121C2×C4×C127—41no—
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—81no—
134C2×C4×C127—81no—
135C2×C4×C127—81no—
136C2×C4×C127#9911yescharacteristic
137C2×C4×C127#9911yescharacteristic
138C2×C4×C127#13512yes—
139C8×C127—44no—
140C8×C127—82no—
141C22×C127—21no—
142C22×C127—21no—
143C22×C127—22no—
144C22×C127—42no—
145C22×C127—41no—
146C22×C127—41no—
147C22×C127—41no—
148C22×C127—41no—
149C22×C127—41no—
150C22×C127—81no—
151C22×C127—81no—
152C22×C127—81no—
153C22×C127C2×#9911yescharacteristic
154C22×C127#41611yescharacteristic
155C22×C127C2×#10411yescharacteristic
156C4×C127—21no—
157C4×C127—21no—
158C4×C127—22no—
159C4×C127—41no—
160C4×C127—41no—
161C4×C127—41no—
162C4×C127—81no—
163C4×C127—81no—
164C4×C127—81no—
165C4×C127—81no—
166#11739C12711yesmaximal, characteristic, direct product factor, Sylow
167C2×C127—21no—
168C2×C127—21no—
169C2×C127—42no—
170C2×C127—81no—
171C2×C127#150111yescharacteristic
172C2×C127#212111yescharacteristic
173C2×C127#213511yescharacteristic
174#2638C2×C12711yescharacteristic
175C4×#100C2×C12711yescharacteristic
176#1459C2×C12711yescharacteristic
177#1354C2×C12712yescomplemented
178#1346C2×C12712yescomplemented
179C127#1173911yescharacteristic, direct product factor, Sylow
180C2×C22⋊Q8C4×C12711yescharacteristic
181C2×C4×D4C22×C12711yescharacteristic
182C2×#100—21no—
183C2×C22⋊C8—21no—
184C4×M16—21no—
185#398C22×C12711yescharacteristic
186#397—21no—
187#397C4×C12711yescharacteristic
188#395C22×C12711yescharacteristic
189#394—21no—
190#393C4×C12711yescharacteristic
191#387—21no—
192#385—21no—
193#381C4×C12711yescharacteristic
194#343C22×C12712yes—
195#324C22×C12712yes—
196#323—21no—
197C22×Q8C2×C4×C12711yescharacteristic
198C22×D4D4×C12711yescharacteristic
199C23×C4C2×C4×C12711yescharacteristic
200C23×C4D4×C12711yescharacteristic
201C2×M16—22no—
202C22×C8—41no—
203C22⋊Q8—41no—
204C22⋊Q8—41no—
205C4×D4—41no—
206C4×D4—41no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4C2×C4×C12711yescharacteristic
211C2×C4⋊C4C23×C12711yescharacteristic
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4C2×C4×C12711yescharacteristic
217C2×C22⋊C4D4×C12711yescharacteristic
218C2×C42D4×C12711yescharacteristic
219#100—24no—
220C22⋊C8—22no—
221C22⋊C8—41no—
222#97—41no—
223C4×C8—41no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95C2×C4×C12711yescharacteristic
230#95C2×C4×C12711yescharacteristic
231C24C22⋊C4×C12711yescharacteristic
232C24C22⋊C4×C12711yescharacteristic
233C2×Q8—41no—
234C2×Q8—81no—
235C2×D4—22no—
236C2×D4—22no—
237C2×D4—41no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—81no—
247C22×C4—81no—
248C22×C4C22⋊C4×C12711yescharacteristic
249C22×C4C22⋊C4×C12711yescharacteristic
250C22×C4C22×C4×C12711yescharacteristic
251C22×C4C2×D4×C12711yescharacteristic
252C22×C4C2×D4×C12711yescharacteristic
253M16—24no—
254M16—42no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—82no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—42no—
263C4⋊C4—81no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—42no—
267C22⋊C4—42no—
268C22⋊C4—81no—
269C22⋊C4—81no—
270C42—21no—
271C42—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23#104×C12712yes—
282C23C2×C22⋊C4×C12711yescharacteristic
283Q8—82no—
284D4—44no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
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—41no—
307C2×C4—81no—
308C2×C4—81no—
309C2×C4—81no—
310C2×C4#99×C12711yescharacteristic
311C2×C4#99×C12711yescharacteristic
312C2×C4#135×C12712yes—
313C8—44no—
314C8—82no—
315C22—21no—
316C22—21no—
317C22—22no—
318C22—42no—
319C22—41no—
320C22—41no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—81no—
325C22—81no—
326C22—81no—
327C22C2×#99×C12711yescharacteristic
328C22#416×C12711yescharacteristic
329C22C2×#104×C12711yescharacteristic
330C4—21no—
331C4—21no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—41no—
336C4—81no—
337C4—81no—
338C4—81no—
339C4—81no—
340C2—21no—
341C2—21no—
342C2—42no—
343C2—81no—
344C2C127×#150111yescharacteristic
345C2C127×#212111yescharacteristic
346C2C127×#213511yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC22×D4×C127D4
LCSG ▷ C22×C4 ▷ C23 ▷ 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×#1354C2semidirect
5. C127×#1346C2semidirect
166. #11739C127direct (N × H)
177. #1354C2×C127semidirect
178. #1346C2×C127semidirect
179. C127#11739direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#26382
C4×#100×C1272
C127×#14592
C127×#13542
C127×#13462
#11739127