Finite Group Databasebeta

← C2×C127×#1405 #44577244

Subgroups — C2×C127×#1405 #44577244

Order 32512.

484 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 94 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×#456×C127C211yesmaximal, characteristic
2C2×#356×C127C211yesmaximal, characteristic, complemented
3C2×#333×C127C211yesmaximal, characteristic, complemented
4C127×#1405C214yesmaximal, direct product factor
5C2×2−1+4×C127C411yescharacteristic
6C2×#137×C127—21no—
7C2×C4⋊Q8×C127C2211yescharacteristic
8#456×C127—21no—
9#456×C127—21no—
10#456×C127C412yes—
11#456×C127C2212yes—
12C2×C4⋊C8×C127—21no—
13C2×#104×C127—21no—
14C2×#101×C127—21no—
15C2×#101×C127C411yescharacteristic
16#356×C127—21no—
17#356×C127C2212yescomplemented
18#333×C127—21no—
19#333×C127C2212yescomplemented
202−1+4×C127—21no—
212−1+4×C127—41no—
222−1+4×C127—42no—
232−1+4×C127C2×C412yes—
24C2×#41×C127—21no—
25C2×#41×C127—41no—
26C2×#41×C127—41no—
27C22×Q8×C127—41no—
28C22×Q8×C127C2×C411yescharacteristic
29C22×Q8×C127D411yescharacteristic
30#137×C127—22no—
31#137×C127—22no—
32#137×C127—42no—
33C2×Q16×C127—41no—
34C2×SD16×C127—41no—
35C2×M16×C127—21no—
36C2×M16×C127—41no—
37C22×C8×C127—41no—
38C4⋊Q8×C127—41no—
39C4⋊Q8×C127C2×C411yescharacteristic
40C4⋊Q8×C127D411yescharacteristic
41C4⋊Q8×C127D411yescharacteristic
42C4⋊Q8×C127C2311yescharacteristic
43C2×C4⋊C4×C127—41no—
44C2×C42×C127D411yescharacteristic
45C4⋊C8×C127—22no—
46C4⋊C8×C127—41no—
47#104×C127—22no—
48#104×C127—22no—
49#101×C127—21no—
50#101×C127—22no—
51#101×C127—41no—
52#101×C127C2×C412yes—
53#41×C127—22no—
54#41×C127—22no—
55#41×C127—41no—
56#41×C127—42no—
57#41×C127—42no—
58#41×C127—42no—
59#41×C127—42no—
60#41×C127—44no—
61#41×C127—42no—
62#41×C127—42no—
63#41×C127—41no—
64C2×Q8×C127—21no—
65C2×Q8×C127—21no—
66C2×Q8×C127—21no—
67C2×Q8×C127—41no—
68C2×Q8×C127—41no—
69C2×Q8×C127—41no—
70C2×Q8×C127—41no—
71C2×Q8×C127—42no—
72C2×Q8×C127—42no—
73C2×Q8×C127—44no—
74C2×Q8×C127—41no—
75C2×Q8×C127C22⋊C411yescharacteristic
76C2×Q8×C127C22⋊C411yescharacteristic
77C2×Q8×C127C22×C411yescharacteristic
78C2×Q8×C127C2×D411yescharacteristic
79C2×D4×C127—21no—
80C2×D4×C127—41no—
81C2×D4×C127—41no—
82C22×C4×C127—21no—
83C22×C4×C127—21no—
84C22×C4×C127—21no—
85C22×C4×C127—41no—
86C22×C4×C127—42no—
87C22×C4×C127C22⋊C411yescharacteristic
88Q16×C127—42no—
89Q16×C127—42no—
90SD16×C127—42no—
91SD16×C127—42no—
92M16×C127—22no—
93M16×C127—41no—
94M16×C127—42no—
95M16×C127—81no—
96C2×C8×C127—41no—
97C2×C8×C127—42no—
98C2×C8×C127—82no—
99C2×C8×C127—81no—
100C4⋊C4×C127—41no—
101C4⋊C4×C127—41no—
102C4⋊C4×C127—41no—
103C4⋊C4×C127—41no—
104C42×C127—21no—
105C42×C127C22⋊C411yescharacteristic
106C42×C127C2×D411yescharacteristic
107C23×C127—41no—
108C23×C127#9911yescharacteristic
109Q8×C127—22no—
110Q8×C127—41no—
111Q8×C127—41no—
112Q8×C127—41no—
113Q8×C127—41no—
114Q8×C127—42no—
115Q8×C127—41no—
116Q8×C127—42no—
117Q8×C127—42no—
118Q8×C127—81no—
119D4×C127—22no—
120D4×C127—41no—
121D4×C127—42no—
122D4×C127—42no—
123D4×C127—42no—
124D4×C127—42no—
125C2×C4×C127—22no—
126C2×C4×C127—22no—
127C2×C4×C127—21no—
128C2×C4×C127—21no—
129C2×C4×C127—21no—
130C2×C4×C127—21no—
131C2×C4×C127—21no—
132C2×C4×C127—21no—
133C2×C4×C127—21no—
134C2×C4×C127—21no—
135C2×C4×C127—42no—
136C2×C4×C127—42no—
137C2×C4×C127—44no—
138C2×C4×C127—44no—
139C2×C4×C127—41no—
140C2×C4×C127—41no—
141C2×C4×C127—41no—
142C2×C4×C127—41no—
143C2×C4×C127—41no—
144C2×C4×C127#9911yescharacteristic
145C2×C4×C127C2×C22⋊C411yescharacteristic
146C8×C127—42no—
147C8×C127—82no—
148C8×C127—82no—
149C22×C127—22no—
150C22×C127—42no—
151C22×C127—82no—
152C22×C127AΣL(1,𝔽16)11yescharacteristic
153C22×C127AΣL(1,𝔽16)11yescharacteristic
154C22×C127C2×#9911yescharacteristic
155C4×C127—21no—
156C4×C127—22no—
157C4×C127—21no—
158C4×C127—21no—
159C4×C127—21no—
160C4×C127—41no—
161C4×C127—41no—
162C4×C127—41no—
163C4×C127—41no—
164C4×C127—42no—
165C2×#1405C12711yesmaximal, characteristic, direct product factor, Sylow
166C2×C127—21no—
167C2×C127—21no—
168C2×C127—82no—
169C2×C127#140512yesdirect product factor
170C2×C127C2×AΣL(1,𝔽16)11yescharacteristic
171C2×#456C2×C12711yescharacteristic
172C2×#356C2×C12711yescharacteristic, complemented
173C2×#333C2×C12711yescharacteristic, complemented
174#1405C2×C12714yesdirect product factor
175C127C2×#140511yescharacteristic, direct product factor, Sylow
176C2×2−1+4C4×C12711yescharacteristic
177C2×#137—21no—
178C2×C4⋊Q8C22×C12711yescharacteristic
179#456—21no—
180#456—21no—
181#456C4×C12712yes—
182#456C22×C12712yes—
183C2×C4⋊C8—21no—
184C2×#104—21no—
185C2×#101—21no—
186C2×#101C4×C12711yescharacteristic
187#356—21no—
188#356C22×C12712yescomplemented
189#333—21no—
190#333C22×C12712yescomplemented
1912−1+4—21no—
1922−1+4—41no—
1932−1+4—42no—
1942−1+4C2×C4×C12712yes—
195C2×#41—21no—
196C2×#41—41no—
197C2×#41—41no—
198C22×Q8—41no—
199C22×Q8C2×C4×C12711yescharacteristic
200C22×Q8D4×C12711yescharacteristic
201#137—22no—
202#137—22no—
203#137—42no—
204C2×Q16—41no—
205C2×SD16—41no—
206C2×M16—21no—
207C2×M16—41no—
208C22×C8—41no—
209C4⋊Q8—41no—
210C4⋊Q8C2×C4×C12711yescharacteristic
211C4⋊Q8D4×C12711yescharacteristic
212C4⋊Q8D4×C12711yescharacteristic
213C4⋊Q8C23×C12711yescharacteristic
214C2×C4⋊C4—41no—
215C2×C42D4×C12711yescharacteristic
216C4⋊C8—22no—
217C4⋊C8—41no—
218#104—22no—
219#104—22no—
220#101—21no—
221#101—22no—
222#101—41no—
223#101C2×C4×C12712yes—
224#41—22no—
225#41—22no—
226#41—41no—
227#41—42no—
228#41—42no—
229#41—42no—
230#41—42no—
231#41—44no—
232#41—42no—
233#41—42no—
234#41—41no—
235C2×Q8—21no—
236C2×Q8—21no—
237C2×Q8—21no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—42no—
243C2×Q8—42no—
244C2×Q8—44no—
245C2×Q8—41no—
246C2×Q8C22⋊C4×C12711yescharacteristic
247C2×Q8C22⋊C4×C12711yescharacteristic
248C2×Q8C22×C4×C12711yescharacteristic
249C2×Q8C2×D4×C12711yescharacteristic
250C2×D4—21no—
251C2×D4—41no—
252C2×D4—41no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—41no—
257C22×C4—42no—
258C22×C4C22⋊C4×C12711yescharacteristic
259Q16—42no—
260Q16—42no—
261SD16—42no—
262SD16—42no—
263M16—22no—
264M16—41no—
265M16—42no—
266M16—81no—
267C2×C8—41no—
268C2×C8—42no—
269C2×C8—82no—
270C2×C8—81no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—41no—
275C42—21no—
276C42C22⋊C4×C12711yescharacteristic
277C42C2×D4×C12711yescharacteristic
278C23—41no—
279C23#99×C12711yescharacteristic
280Q8—22no—
281Q8—41no—
282Q8—41no—
283Q8—41no—
284Q8—41no—
285Q8—42no—
286Q8—41no—
287Q8—42no—
288Q8—42no—
289Q8—81no—
290D4—22no—
291D4—41no—
292D4—42no—
293D4—42no—
294D4—42no—
295D4—42no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—44no—
309C2×C4—44no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4#99×C12711yescharacteristic
316C2×C4C2×C22⋊C4×C12711yescharacteristic
317C8—42no—
318C8—82no—
319C8—82no—
320C22—22no—
321C22—42no—
322C22—82no—
323C22AΣL(1,𝔽16)×C12711yescharacteristic
324C22AΣL(1,𝔽16)×C12711yescharacteristic
325C22C2×#99×C12711yescharacteristic
326C4—21no—
327C4—22no—
328C4—21no—
329C4—21no—
330C4—21no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—42no—
336C2—21no—
337C2—21no—
338C2—82no—
339C2C127×#140512yesdirect product factor
340C2C2×AΣL(1,𝔽16)×C12711yescharacteristic
subgroupG/H
center, socleC22×C127AΣL(1,𝔽16)
commutatorC2×Q8C22×C4×C127
Frattini, cosocleC4⋊Q8C23×C127
prime radicalC2×2−1+4×C127C4
LCSG ▷ C2×Q8 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C22×C4×C127 ◁ C2×C4⋊Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#356×C127C2semidirect
3. C2×#333×C127C2semidirect
4. C127×#1405C2direct (N × H)
17. #356×C127C22semidirect
19. #333×C127C22semidirect
165. C2×#1405C127direct (N × H)
169. C2×C127#1405direct (N × H)
172. C2×#356C2×C127semidirect
173. C2×#333C2×C127semidirect
174. #1405C2×C127direct (N × H)
175. C127C2×#1405direct (N × H)
188. #356C22×C127semidirect
190. #333C22×C127semidirect
339. C2C127×#1405direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#456×C1272
C2×#356×C1272
C2×#333×C1272
C127×#14052
C2×#1405127