Finite Group Databasebeta

← C127×#21384 #44585057

Subgroups — C127×#21384 #44585057

Order 32512.

1094 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3455C211yesmaximal, characteristic
2C127×#2873C211yesmaximal, characteristic, complemented
3C127×#2298C211yesmaximal, characteristic, complemented
4C127×#1986C212yesmaximal, complemented
5C127×#1980C212yesmaximal, complemented
6C127×#1871C214yesmaximal, complemented
7C127×#1759C212yesmaximal, complemented
8C4×#104×C127C212yesmaximal, complemented
9C22×M16×C127C2212yes—
10#542×C127C414yescomplemented
11#541×C127C412yescomplemented
12#540×C127C412yescomplemented
13#539×C127—22no—
14#538×C127—22no—
15#533×C127C2211yescharacteristic
16#532×C127C2211yescharacteristic
17#529×C127—24no—
18#525×C127C2212yes—
19C4×#41×C127C2212yes—
20C2×#117×C127C2211yescharacteristic
21C2×#104×C127C2214yes—
22C2×#104×C127C2214yes—
23#405×C127—24no—
24C4×M16×C127C2212yes—
25C4×M16×C127C2212yes—
26#388×C127—22no—
27#387×C127—22no—
28C4×C4⋊C4×C127C2212yes—
29C4×C22⋊C4×C127C2212yes—
30#376×C127C2211yescharacteristic
31C43×C127C2211yescharacteristic
32#339×C127C2214yes—
33#339×C127C2214yes—
34C2×#41×C127C2312yes—
35C23×C4×C127C2311yescharacteristic
36C2×M16×C127—22no—
37C2×M16×C127—28no—
38C2×M16×C127C2314yes—
39C22×C8×C127—22no—
40C4⋊Q8×C127C2×C411yescharacteristic
41C4⋊Q8×C127C2×C412yes—
42#127×C127C2×C411yescharacteristic
43#126×C127—24no—
44#126×C127—24no—
45#125×C127—24no—
46#125×C127C2×C412yes—
47#124×C127—24no—
48#124×C127C2×C412yes—
49#123×C127—22no—
50#123×C127—24no—
51#123×C127—24no—
52C22⋊Q8×C127—22no—
53C22⋊Q8×C127—24no—
54C22⋊Q8×C127C2×C414yes—
55#121×C127—22no—
56#121×C127—24no—
57#121×C127C2×C414yes—
58#120×C127—22no—
59C4×Q8×C127—22no—
60C4×Q8×C127C2×C414yes—
61C4×D4×C127—24no—
62C4×D4×C127—24no—
63C4×D4×C127—22no—
64C4×D4×C127C2×C414yes—
65#117×C127—22no—
66#117×C127C2×C412yes—
67#117×C127C2×C412yes—
68#117×C127D414yes—
69#117×C127C2312yes—
70C2×C4⋊C4×C127—22no—
71C2×C4⋊C4×C127D412yes—
72C2×C22⋊C4×C127—22no—
73C2×C22⋊C4×C127D412yes—
74C2×C42×C127—22no—
75C2×C42×C127—22no—
76C2×C42×C127C2312yes—
77C2×C42×C127C2312yes—
78C2×C42×C127C2311yescharacteristic
79C2×C42×C127C2311yescharacteristic
80#104×C127—28no—
81#104×C127—28no—
82#97×C127—22no—
83#97×C127—22no—
84C4×C8×C127—22no—
85C4×C8×C127—22no—
86#95×C127—22no—
87#95×C127—22no—
88#95×C127—22no—
89C24×C127C2×D411yescharacteristic
90#41×C127—24no—
91#41×C127—24no—
92C2×Q8×C127—22no—
93C2×Q8×C127C22×C412yes—
94C2×D4×C127—22no—
95C2×D4×C127—24no—
96C2×D4×C127—22no—
97C2×D4×C127C22×C412yes—
98C22×C4×C127—24no—
99C22×C4×C127—22no—
100C22×C4×C127—22no—
101C22×C4×C127—24no—
102C22×C4×C127—22no—
103C22×C4×C127C22×C412yes—
104C22×C4×C127C2×D411yescharacteristic
105C22×C4×C127C2×D412yes—
106C22×C4×C127C2×D412yes—
107C22×C4×C127C2×D412yes—
108C22×C4×C127C2411yescharacteristic
109M16×C127—28no—
110M16×C127—24no—
111M16×C127#4118yes—
112C2×C8×C127—28no—
113C2×C8×C127—24no—
114C4⋊C4×C127—24no—
115C4⋊C4×C127—22no—
116C4⋊C4×C127—24no—
117C4⋊C4×C127—24no—
118C4⋊C4×C127—22no—
119C4⋊C4×C127—44no—
120C4⋊C4×C127C22⋊C414yes—
121C4⋊C4×C127C22⋊C414yes—
122C4⋊C4×C127C22×C414yes—
123C22⋊C4×C127—24no—
124C22⋊C4×C127—22no—
125C22⋊C4×C127—24no—
126C22⋊C4×C127—24no—
127C22⋊C4×C127—24no—
128C22⋊C4×C127—44no—
129C22⋊C4×C127C22⋊C414yes—
130C22⋊C4×C127C22⋊C414yes—
131C42×C127—24no—
132C42×C127—22no—
133C42×C127—24no—
134C42×C127—24no—
135C42×C127—44no—
136C42×C127C22×C412yes—
137C42×C127C22×C411yescharacteristic
138C42×C127C22×C411yescharacteristic
139C42×C127C2×D412yes—
140C42×C127C2×D412yes—
141C23×C127—22no—
142C23×C127—22no—
143C23×C127—42no—
144C23×C127C2×C22⋊C412yes—
145C23×C127C22×D411yescharacteristic
146Q8×C127—22no—
147Q8×C127—22no—
148Q8×C127—82no—
149D4×C127—22no—
150D4×C127—22no—
151D4×C127—44no—
152D4×C127—82no—
153D4×C127—84no—
154C2×C4×C127—22no—
155C2×C4×C127—24no—
156C2×C4×C127—22no—
157C2×C4×C127—22no—
158C2×C4×C127—24no—
159C2×C4×C127—22no—
160C2×C4×C127—24no—
161C2×C4×C127—42no—
162C2×C4×C127—42no—
163C2×C4×C127—42no—
164C2×C4×C127—42no—
165C2×C4×C127—44no—
166C2×C4×C127—42no—
167C2×C4×C127—42no—
168C2×C4×C127—42no—
169C2×C4×C127—84no—
170C2×C4×C127C2×C22⋊C414yes—
171C2×C4×C127C2×C22⋊C412yes—
172C2×C4×C127C2×C22⋊C412yes—
173C2×C4×C127C2×C22⋊C412yes—
174C2×C4×C127C23×C411yescharacteristic
175C2×C4×C127C22×D411yescharacteristic
176C2×C4×C127C2×#4114yes—
177C8×C127—28no—
178C22×C127—22no—
179C22×C127—24no—
180C22×C127—22no—
181C22×C127—44no—
182C22×C127—42no—
183C22×C127—82no—
184C22×C127C22×C22⋊C411yescharacteristic
185C22×C127#53212yes—
186C4×C127—24no—
187C4×C127—22no—
188C4×C127—22no—
189C4×C127—22no—
190C4×C127—44no—
191C4×C127—44no—
192C4×C127—42no—
193C4×C127—82no—
194C4×C127C4×#4112yes—
195C4×C127#52512yes—
196#21384C12711yesmaximal, characteristic, direct product factor, Sylow
197C2×C127—22no—
198C2×C127—42no—
199C2×C127—82no—
200C2×C127#229711yescharacteristic
201C2×C127#290112yes—
202#3455C2×C12711yescharacteristic
203#2873C2×C12711yescharacteristic, complemented
204#2298C2×C12711yescharacteristic, complemented
205#1986C2×C12712yescomplemented
206#1980C2×C12712yescomplemented
207#1871C2×C12714yescomplemented
208#1759C2×C12712yescomplemented
209C4×#104C2×C12712yescomplemented
210C127#2138411yescharacteristic, direct product factor, Sylow
211C22×M16C22×C12712yes—
212#542C4×C12714yescomplemented
213#541C4×C12712yescomplemented
214#540C4×C12712yescomplemented
215#539—22no—
216#538—22no—
217#533C22×C12711yescharacteristic
218#532C22×C12711yescharacteristic
219#529—24no—
220#525C22×C12712yes—
221C4×#41C22×C12712yes—
222C2×#117C22×C12711yescharacteristic
223C2×#104C22×C12714yes—
224C2×#104C22×C12714yes—
225#405—24no—
226C4×M16C22×C12712yes—
227C4×M16C22×C12712yes—
228#388—22no—
229#387—22no—
230C4×C4⋊C4C22×C12712yes—
231C4×C22⋊C4C22×C12712yes—
232#376C22×C12711yescharacteristic
233C43C22×C12711yescharacteristic
234#339C22×C12714yes—
235#339C22×C12714yes—
236C2×#41C23×C12712yes—
237C23×C4C23×C12711yescharacteristic
238C2×M16—22no—
239C2×M16—28no—
240C2×M16C23×C12714yes—
241C22×C8—22no—
242C4⋊Q8C2×C4×C12711yescharacteristic
243C4⋊Q8C2×C4×C12712yes—
244#127C2×C4×C12711yescharacteristic
245#126—24no—
246#126—24no—
247#125—24no—
248#125C2×C4×C12712yes—
249#124—24no—
250#124C2×C4×C12712yes—
251#123—22no—
252#123—24no—
253#123—24no—
254C22⋊Q8—22no—
255C22⋊Q8—24no—
256C22⋊Q8C2×C4×C12714yes—
257#121—22no—
258#121—24no—
259#121C2×C4×C12714yes—
260#120—22no—
261C4×Q8—22no—
262C4×Q8C2×C4×C12714yes—
263C4×D4—24no—
264C4×D4—24no—
265C4×D4—22no—
266C4×D4C2×C4×C12714yes—
267#117—22no—
268#117C2×C4×C12712yes—
269#117C2×C4×C12712yes—
270#117D4×C12714yes—
271#117C23×C12712yes—
272C2×C4⋊C4—22no—
273C2×C4⋊C4D4×C12712yes—
274C2×C22⋊C4—22no—
275C2×C22⋊C4D4×C12712yes—
276C2×C42—22no—
277C2×C42—22no—
278C2×C42C23×C12712yes—
279C2×C42C23×C12712yes—
280C2×C42C23×C12711yescharacteristic
281C2×C42C23×C12711yescharacteristic
282#104—28no—
283#104—28no—
284#97—22no—
285#97—22no—
286C4×C8—22no—
287C4×C8—22no—
288#95—22no—
289#95—22no—
290#95—22no—
291C24C2×D4×C12711yescharacteristic
292#41—24no—
293#41—24no—
294C2×Q8—22no—
295C2×Q8C22×C4×C12712yes—
296C2×D4—22no—
297C2×D4—24no—
298C2×D4—22no—
299C2×D4C22×C4×C12712yes—
300C22×C4—24no—
301C22×C4—22no—
302C22×C4—22no—
303C22×C4—24no—
304C22×C4—22no—
305C22×C4C22×C4×C12712yes—
306C22×C4C2×D4×C12711yescharacteristic
307C22×C4C2×D4×C12712yes—
308C22×C4C2×D4×C12712yes—
309C22×C4C2×D4×C12712yes—
310C22×C4C24×C12711yescharacteristic
311M16—28no—
312M16—24no—
313M16#41×C12718yes—
314C2×C8—28no—
315C2×C8—24no—
316C4⋊C4—24no—
317C4⋊C4—22no—
318C4⋊C4—24no—
319C4⋊C4—24no—
320C4⋊C4—22no—
321C4⋊C4—44no—
322C4⋊C4C22⋊C4×C12714yes—
323C4⋊C4C22⋊C4×C12714yes—
324C4⋊C4C22×C4×C12714yes—
325C22⋊C4—24no—
326C22⋊C4—22no—
327C22⋊C4—24no—
328C22⋊C4—24no—
329C22⋊C4—24no—
330C22⋊C4—44no—
331C22⋊C4C22⋊C4×C12714yes—
332C22⋊C4C22⋊C4×C12714yes—
333C42—24no—
334C42—22no—
335C42—24no—
336C42—24no—
337C42—44no—
338C42C22×C4×C12712yes—
339C42C22×C4×C12711yescharacteristic
340C42C22×C4×C12711yescharacteristic
341C42C2×D4×C12712yes—
342C42C2×D4×C12712yes—
343C23—22no—
344C23—22no—
345C23—42no—
346C23C2×C22⋊C4×C12712yes—
347C23C22×D4×C12711yescharacteristic
348Q8—22no—
349Q8—22no—
350Q8—82no—
351D4—22no—
352D4—22no—
353D4—44no—
354D4—82no—
355D4—84no—
356C2×C4—22no—
357C2×C4—24no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—24no—
361C2×C4—22no—
362C2×C4—24no—
363C2×C4—42no—
364C2×C4—42no—
365C2×C4—42no—
366C2×C4—42no—
367C2×C4—44no—
368C2×C4—42no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—84no—
372C2×C4C2×C22⋊C4×C12714yes—
373C2×C4C2×C22⋊C4×C12712yes—
374C2×C4C2×C22⋊C4×C12712yes—
375C2×C4C2×C22⋊C4×C12712yes—
376C2×C4C23×C4×C12711yescharacteristic
377C2×C4C22×D4×C12711yescharacteristic
378C2×C4C2×#41×C12714yes—
379C8—28no—
380C22—22no—
381C22—24no—
382C22—22no—
383C22—44no—
384C22—42no—
385C22—82no—
386C22C22×C22⋊C4×C12711yescharacteristic
387C22#532×C12712yes—
388C4—24no—
389C4—22no—
390C4—22no—
391C4—22no—
392C4—44no—
393C4—44no—
394C4—42no—
395C4—82no—
396C4C4×#41×C12712yes—
397C4#525×C12712yes—
398C2—22no—
399C2—42no—
400C2—82no—
401C2C127×#229711yescharacteristic
402C2C127×#290112yes—
subgroupG/H
centerC2×C4×C127C22×D4
commutatorC2×C4C23×C4×C127
Frattini, cosocleC22×C4C24×C127
socleC22×C127C22×C22⋊C4
prime radicalC127×#3455C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2873C2semidirect
3. C127×#2298C2semidirect
4. C127×#1986C2semidirect
5. C127×#1980C2semidirect
6. C127×#1871C2semidirect
7. C127×#1759C2semidirect
8. C4×#104×C127C2semidirect
10. #542×C127C4semidirect
11. #541×C127C4semidirect
12. #540×C127C4semidirect
196. #21384C127direct (N × H)
203. #2873C2×C127semidirect
204. #2298C2×C127semidirect
205. #1986C2×C127semidirect
206. #1980C2×C127semidirect
207. #1871C2×C127semidirect
208. #1759C2×C127semidirect
209. C4×#104C2×C127semidirect
210. C127#21384direct (N × H)
212. #542C4×C127semidirect
213. #541C4×C127semidirect
214. #540C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#34552
C127×#28732
C127×#22982
C127×#19862
C127×#19802
C127×#18712
C127×#17592
C4×#104×C1272
#21384127