Finite Group Databasebeta

← C127×#10033 #44573706

Subgroups — C127×#10033 #44573706

Order 32512.

550 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3135C211yesmaximal, characteristic, complemented
2C127×#3101C211yesmaximal, characteristic, complemented
3C127×#3100C211yesmaximal, characteristic
4C127×#1955C211yesmaximal, characteristic, complemented
5C127×#1481C211yesmaximal, characteristic, complemented
6C127×#1480C211yesmaximal, characteristic, complemented
7C127×#1275C211yesmaximal, characteristic, complemented
8#533×C127C2211yescharacteristic
9#532×C127C2211yescharacteristic
10C2×C4×D4×C127C2211yescharacteristic
11#491×C127—21no—
12#490×C127—21no—
13#489×C127—21no—
14#489×C127—21no—
15#483×C127—21no—
16#480×C127—21no—
17#476×C127—21no—
18#474×C127—21no—
19#461×C127—21no—
20#459×C127—21no—
21#450×C127—21no—
22#447×C127—21no—
23C4×SD16×C127—22no—
24C4×D8×C127—22no—
25#431×C127C2211yescharacteristic
26#431×C127C2211yescharacteristic
27C2×C4⋊C8×C127C2211yescharacteristic
28#416×C127—22no—
29C2×C22⋊C8×C127—22no—
30C2×#97×C127C2211yescharacteristic
31Q8⋊C8×C127—22no—
32D4⋊C8×C127—22no—
33C2×#41×C127—21no—
34C22×D4×C127D411yescharacteristic
35C23×C4×C127—21no—
36C2×SD16×C127—22no—
37C2×D8×C127—22no—
38C22×C8×C127—21no—
39C22×C8×C127D412yes—
40C4⋊Q8×C127D411yescharacteristic
41C4⋊Q8×C127D411yescharacteristic
42C4⋊Q8×C127D411yescharacteristic
43#127×C127D411yescharacteristic
44#125×C127—21no—
45#124×C127—21no—
46C22⋊Q8×C127—21no—
47C22⋊Q8×C127—21no—
48#121×C127—21no—
49#121×C127—21no—
50C4×Q8×C127—21no—
51C4×Q8×C127—21no—
52C4×D4×C127—21no—
53C4×D4×C127—21no—
54C4×D4×C127—21no—
55C4×D4×C127—21no—
56C4×D4×C127—21no—
57C4×D4×C127—21no—
58#117×C127—21no—
59C2×C4⋊C4×C127D411yescharacteristic
60C2×C22⋊C4×C127—21no—
61C2×C42×C127C2311yescharacteristic
62#107×C127—22no—
63#106×C127—22no—
64C4⋊C8×C127—21no—
65C4⋊C8×C127—21no—
66C4⋊C8×C127—21no—
67C4⋊C8×C127—21no—
68#103×C127—22no—
69#103×C127—22no—
70#103×C127—22no—
71#102×C127—22no—
72#102×C127—22no—
73#102×C127—22no—
74#102×C127—22no—
75#102×C127—22no—
76C22⋊C8×C127—21no—
77C22⋊C8×C127—21no—
78C22⋊C8×C127—44no—
79#97×C127—21no—
80#97×C127—21no—
81C4×C8×C127D412yes—
82C4×C8×C127D412yes—
83C24×C127—21no—
84#41×C127—42no—
85#41×C127—42no—
86C2×Q8×C127—21no—
87C2×Q8×C127—21no—
88C2×Q8×C127—21no—
89C2×D4×C127—21no—
90C2×D4×C127—21no—
91C2×D4×C127—21no—
92C2×D4×C127—21no—
93C2×D4×C127—21no—
94C2×D4×C127—42no—
95C2×D4×C127—41no—
96C22×C4×C127—21no—
97C22×C4×C127—41no—
98C22×C4×C127—41no—
99C22×C4×C127—41no—
100C22×C4×C127—42no—
101C22×C4×C127—42no—
102C22×C4×C127C2×D411yescharacteristic
103C22×C4×C127C2×D411yescharacteristic
104C22×C4×C127#4111yescharacteristic
105SD16×C127—44no—
106D8×C127—44no—
107C2×C8×C127—22no—
108C2×C8×C127—22no—
109C2×C8×C127—22no—
110C2×C8×C127—22no—
111C2×C8×C127—22no—
112C2×C8×C127—41no—
113C2×C8×C127—42no—
114C4⋊C4×C127—21no—
115C4⋊C4×C127—21no—
116C4⋊C4×C127—21no—
117C4⋊C4×C127—21no—
118C4⋊C4×C127—21no—
119C4⋊C4×C127—21no—
120C4⋊C4×C127—21no—
121C4⋊C4×C127—21no—
122C4⋊C4×C127—41no—
123C4⋊C4×C127—41no—
124C22⋊C4×C127—41no—
125C22⋊C4×C127—41no—
126C22⋊C4×C127—41no—
127C22⋊C4×C127—41no—
128C22⋊C4×C127—41no—
129C42×C127—41no—
130C42×C127C2×D411yescharacteristic
131C42×C127C2×D411yescharacteristic
132C42×C127C2×D411yescharacteristic
133C42×C127C2×D411yescharacteristic
134C23×C127—22no—
135C23×C127—41no—
136C23×C127—42no—
137C23×C127—41no—
138C23×C127—42no—
139C23×C127—41no—
140C23×C127#12111yescharacteristic
141Q8×C127—42no—
142Q8×C127—42no—
143Q8×C127—42no—
144D4×C127—22no—
145D4×C127—22no—
146D4×C127—41no—
147D4×C127—41no—
148D4×C127—42no—
149D4×C127—42no—
150D4×C127—42no—
151D4×C127—82no—
152C2×C4×C127—41no—
153C2×C4×C127—41no—
154C2×C4×C127—41no—
155C2×C4×C127—41no—
156C2×C4×C127—41no—
157C2×C4×C127—41no—
158C2×C4×C127—42no—
159C2×C4×C127—82no—
160C2×C4×C127—81no—
161C2×C4×C127—81no—
162C2×C4×C127—81no—
163C2×C4×C127—81no—
164C2×C4×C127#12011yescharacteristic
165C2×C4×C127#12011yescharacteristic
166C2×C4×C127#12011yescharacteristic
167C2×C4×C127#12111yescharacteristic
168C2×C4×C127#12111yescharacteristic
169C2×C4×C127#12711yescharacteristic
170C2×C4×C127#13512yes—
171C2×C4×C127AGL(1,ℤ/8)12yes—
172C8×C127—42no—
173C8×C127—42no—
174C8×C127—42no—
175C8×C127—81no—
176C22×C127—21no—
177C22×C127—21no—
178C22×C127—44no—
179C22×C127—42no—
180C22×C127—82no—
181C22×C127—81no—
182C22×C127—81no—
183C22×C127—81no—
184C22×C127—81no—
185C22×C127—81no—
186C22×C127#39211yescharacteristic
187C22×C127#46312yes—
188C4×C127—21no—
189C4×C127—21no—
190C4×C127—21no—
191C4×C127—21no—
192C4×C127—81no—
193C4×C127—81no—
194C4×C127—81no—
195C4×C127—81no—
196C4×C127#44912yes—
197C4×C127#49511yescharacteristic
198C4×C127#49611yescharacteristic
199#10033C12711yesmaximal, characteristic, direct product factor, Sylow
200C2×C127—22no—
201C2×C127—82no—
202C2×C127—161no—
203C2×C127#201011yescharacteristic
204C2×C127#201211yescharacteristic
205C2×C127#201711yescharacteristic
206#3135C2×C12711yescharacteristic, complemented
207#3101C2×C12711yescharacteristic, complemented
208#3100C2×C12711yescharacteristic
209#1955C2×C12711yescharacteristic, complemented
210#1481C2×C12711yescharacteristic, complemented
211#1480C2×C12711yescharacteristic, complemented
212#1275C2×C12711yescharacteristic, complemented
213C127#1003311yescharacteristic, direct product factor, Sylow
214#533C22×C12711yescharacteristic
215#532C22×C12711yescharacteristic
216C2×C4×D4C22×C12711yescharacteristic
217#491—21no—
218#490—21no—
219#489—21no—
220#489—21no—
221#483—21no—
222#480—21no—
223#476—21no—
224#474—21no—
225#461—21no—
226#459—21no—
227#450—21no—
228#447—21no—
229C4×SD16—22no—
230C4×D8—22no—
231#431C22×C12711yescharacteristic
232#431C22×C12711yescharacteristic
233C2×C4⋊C8C22×C12711yescharacteristic
234#416—22no—
235C2×C22⋊C8—22no—
236C2×#97C22×C12711yescharacteristic
237Q8⋊C8—22no—
238D4⋊C8—22no—
239C2×#41—21no—
240C22×D4D4×C12711yescharacteristic
241C23×C4—21no—
242C2×SD16—22no—
243C2×D8—22no—
244C22×C8—21no—
245C22×C8D4×C12712yes—
246C4⋊Q8D4×C12711yescharacteristic
247C4⋊Q8D4×C12711yescharacteristic
248C4⋊Q8D4×C12711yescharacteristic
249#127D4×C12711yescharacteristic
250#125—21no—
251#124—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254#121—21no—
255#121—21no—
256C4×Q8—21no—
257C4×Q8—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—21no—
261C4×D4—21no—
262C4×D4—21no—
263C4×D4—21no—
264#117—21no—
265C2×C4⋊C4D4×C12711yescharacteristic
266C2×C22⋊C4—21no—
267C2×C42C23×C12711yescharacteristic
268#107—22no—
269#106—22no—
270C4⋊C8—21no—
271C4⋊C8—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274#103—22no—
275#103—22no—
276#103—22no—
277#102—22no—
278#102—22no—
279#102—22no—
280#102—22no—
281#102—22no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—44no—
285#97—21no—
286#97—21no—
287C4×C8D4×C12712yes—
288C4×C8D4×C12712yes—
289C24—21no—
290#41—42no—
291#41—42no—
292C2×Q8—21no—
293C2×Q8—21no—
294C2×Q8—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—21no—
299C2×D4—21no—
300C2×D4—42no—
301C2×D4—41no—
302C22×C4—21no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4—41no—
306C22×C4—42no—
307C22×C4—42no—
308C22×C4C2×D4×C12711yescharacteristic
309C22×C4C2×D4×C12711yescharacteristic
310C22×C4#41×C12711yescharacteristic
311SD16—44no—
312D8—44no—
313C2×C8—22no—
314C2×C8—22no—
315C2×C8—22no—
316C2×C8—22no—
317C2×C8—22no—
318C2×C8—41no—
319C2×C8—42no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C22⋊C4—41no—
331C22⋊C4—41no—
332C22⋊C4—41no—
333C22⋊C4—41no—
334C22⋊C4—41no—
335C42—41no—
336C42C2×D4×C12711yescharacteristic
337C42C2×D4×C12711yescharacteristic
338C42C2×D4×C12711yescharacteristic
339C42C2×D4×C12711yescharacteristic
340C23—22no—
341C23—41no—
342C23—42no—
343C23—41no—
344C23—42no—
345C23—41no—
346C23#121×C12711yescharacteristic
347Q8—42no—
348Q8—42no—
349Q8—42no—
350D4—22no—
351D4—22no—
352D4—41no—
353D4—41no—
354D4—42no—
355D4—42no—
356D4—42no—
357D4—82no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—42no—
365C2×C4—81no—
366C2×C4—81no—
367C2×C4—82no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4#120×C12711yescharacteristic
371C2×C4#120×C12711yescharacteristic
372C2×C4#120×C12711yescharacteristic
373C2×C4#121×C12711yescharacteristic
374C2×C4#121×C12711yescharacteristic
375C2×C4#127×C12711yescharacteristic
376C2×C4#135×C12712yes—
377C2×C4AGL(1,ℤ/8)×C12712yes—
378C8—42no—
379C8—42no—
380C8—42no—
381C8—81no—
382C22—21no—
383C22—21no—
384C22—44no—
385C22—42no—
386C22—82no—
387C22—81no—
388C22—81no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22#392×C12711yescharacteristic
393C22#463×C12712yes—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—21no—
398C4—81no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4#449×C12712yes—
403C4#495×C12711yescharacteristic
404C4#496×C12711yescharacteristic
405C2—22no—
406C2—82no—
407C2—161no—
408C2C127×#201011yescharacteristic
409C2C127×#201211yescharacteristic
410C2C127×#201711yescharacteristic
subgroupG/H
centerC2×C4×C127#127
commutator, Frattini, cosocleC2×C42C23×C127
socleC22×C127#392
prime radicalC127×#3100C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3135C2semidirect
2. C127×#3101C2semidirect
4. C127×#1955C2semidirect
5. C127×#1481C2semidirect
6. C127×#1480C2semidirect
7. C127×#1275C2semidirect
199. #10033C127direct (N × H)
206. #3135C2×C127semidirect
207. #3101C2×C127semidirect
209. #1955C2×C127semidirect
210. #1481C2×C127semidirect
211. #1480C2×C127semidirect
212. #1275C2×C127semidirect
213. C127#10033direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31352
C127×#31012
C127×#31002
C127×#19552
C127×#14812
C127×#14802
C127×#12752
#10033127