Finite Group Databasebeta

← C127×#19436 #44583109

Subgroups — C127×#19436 #44583109

Order 32512.

590 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3210C211yesmaximal, characteristic
2C127×#3113C211yesmaximal, characteristic, complemented
3C127×#3103C211yesmaximal, characteristic
4C127×#2983C211yesmaximal, characteristic, complemented
5C127×#1702C212yesmaximal, complemented
6C127×#1700C212yesmaximal, complemented
7C127×#1690C212yesmaximal, complemented
8C127×#1686C212yesmaximal, complemented
9C127×#1572C211yesmaximal, characteristic, complemented
10C127×#1553C211yesmaximal, characteristic
11C127×#1544C211yesmaximal, characteristic, complemented
12#533×C127C2211yescharacteristic
13#532×C127C2211yescharacteristic
14C2×C4×Q8×C127C2211yescharacteristic
15#494×C127C2211yescharacteristic
16#492×C127C2211yescharacteristic
17#487×C127C2211yescharacteristic
18#486×C127C2211yescharacteristic
19#483×C127—21no—
20#481×C127—21no—
21#475×C127C2212yes—
22#475×C127C2212yes—
23#464×C127—22no—
24#462×C127C2212yes—
25#460×C127C2212yes—
26#452×C127—22no—
27#451×C127—21no—
28#448×C127—21no—
29#446×C127—22no—
30#446×C127C2212yes—
31#446×C127C2212yes—
32#441×C127—22no—
33C4×SD16×C127—22no—
34#432×C127—22no—
35#432×C127C2211yescharacteristic
36#431×C127C2211yescharacteristic
37#431×C127C2211yescharacteristic
38#431×C127C2211yescharacteristic
39#335×C127C2212yes—
40#334×C127C2212yes—
41#332×C127C2212yes—
42#332×C127C2212yes—
43#332×C127C2212yes—
44#331×C127C2212yes—
45C2×#41×C127—21no—
46C22×Q8×C127D411yescharacteristic
47C2×Q16×C127—22no—
48C2×Q16×C127—22no—
49C2×SD16×C127—22no—
50C2×SD16×C127—22no—
51C4⋊Q8×C127C2311yescharacteristic
52C4⋊Q8×C127C2311yescharacteristic
53C4⋊Q8×C127C2311yescharacteristic
54#127×C127C2311yescharacteristic
55#125×C127—21no—
56#124×C127—21no—
57C22⋊Q8×C127—21no—
58C22⋊Q8×C127—21no—
59#121×C127—21no—
60#121×C127—21no—
61C4×Q8×C127—21no—
62C4×Q8×C127—21no—
63C4×Q8×C127—21no—
64C4×Q8×C127—21no—
65C4×Q8×C127D412yes—
66C4×Q8×C127C2312yes—
67C4×D4×C127—21no—
68C4×D4×C127—21no—
69#117×C127—21no—
70C2×C4⋊C4×C127—21no—
71C2×C4⋊C4×C127D411yescharacteristic
72C2×C42×C127—21no—
73C2×C42×C127C2311yescharacteristic
74#106×C127—22no—
75#106×C127—22no—
76C4⋊C8×C127—22no—
77C4⋊C8×C127—22no—
78C4⋊C8×C127D412yes—
79C4⋊C8×C127C2312yes—
80C4⋊C8×C127C2312yes—
81C4⋊C8×C127C2312yes—
82#103×C127—22no—
83#103×C127—22no—
84#103×C127—22no—
85#103×C127—22no—
86#102×C127—22no—
87#102×C127—22no—
88C22⋊C8×C127—21no—
89C22⋊C8×C127—21no—
90C22⋊C8×C127—21no—
91C22⋊C8×C127D412yes—
92#97×C127—22no—
93#97×C127—22no—
94#97×C127—21no—
95C4×C8×C127—21no—
96C4×C8×C127—21no—
97C4×C8×C127C2311yescharacteristic
98C4×C8×C127C2311yescharacteristic
99#41×C127—82no—
100C2×Q8×C127—21no—
101C2×Q8×C127—21no—
102C2×Q8×C127—21no—
103C2×Q8×C127—21no—
104C2×Q8×C127—42no—
105C2×Q8×C127C2×D412yes—
106C2×D4×C127—21no—
107C2×D4×C127—21no—
108C2×D4×C127—21no—
109C2×D4×C127—41no—
110C22×C4×C127—21no—
111C22×C4×C127—21no—
112C22×C4×C127—41no—
113C22×C4×C127C2×D411yescharacteristic
114C22×C4×C127C2×D411yescharacteristic
115C22×C4×C127#4111yescharacteristic
116Q16×C127—44no—
117Q16×C127—82no—
118SD16×C127—44no—
119SD16×C127—82no—
120C2×C8×C127—22no—
121C2×C8×C127—22no—
122C2×C8×C127—22no—
123C2×C8×C127C2×D412yes—
124C2×C8×C127C2×D412yes—
125C4⋊C4×C127—22no—
126C4⋊C4×C127—21no—
127C4⋊C4×C127—22no—
128C4⋊C4×C127—21no—
129C4⋊C4×C127—21no—
130C4⋊C4×C127—21no—
131C4⋊C4×C127—21no—
132C4⋊C4×C127—21no—
133C4⋊C4×C127—21no—
134C4⋊C4×C127—41no—
135C4⋊C4×C127—41no—
136C4⋊C4×C127C2×D412yes—
137C22⋊C4×C127—41no—
138C22⋊C4×C127—41no—
139C22⋊C4×C127—41no—
140C42×C127—22no—
141C42×C127—22no—
142C42×C127—41no—
143C42×C127C2×D411yescharacteristic
144C42×C127C2×D411yescharacteristic
145C42×C127#4111yescharacteristic
146C42×C127C2411yescharacteristic
147C23×C127—41no—
148C23×C127#12111yescharacteristic
149Q8×C127—22no—
150Q8×C127—22no—
151Q8×C127—42no—
152Q8×C127—42no—
153Q8×C127—42no—
154Q8×C127—42no—
155D4×C127—42no—
156D4×C127—42no—
157D4×C127—81no—
158D4×C127—82no—
159C2×C4×C127—22no—
160C2×C4×C127—22no—
161C2×C4×C127—22no—
162C2×C4×C127—22no—
163C2×C4×C127—41no—
164C2×C4×C127—42no—
165C2×C4×C127—41no—
166C2×C4×C127—41no—
167C2×C4×C127—41no—
168C2×C4×C127—82no—
169C2×C4×C127—81no—
170C2×C4×C127#12111yescharacteristic
171C2×C4×C127#12111yescharacteristic
172C2×C4×C127#12111yescharacteristic
173C2×C4×C127C22×D411yescharacteristic
174C2×C4×C127C22×D411yescharacteristic
175C2×C4×C127C2×#4111yescharacteristic
176C8×C127—22no—
177C8×C127—22no—
178C8×C127—42no—
179C8×C127—42no—
180C8×C127—42no—
181C22×C127—21no—
182C22×C127—21no—
183C22×C127—21no—
184C22×C127—81no—
185C22×C127—81no—
186C22×C127—81no—
187C22×C127C2×#12111yescharacteristic
188C4×C127—21no—
189C4×C127—21no—
190C4×C127—21no—
191C4×C127—21no—
192C4×C127—42no—
193C4×C127—42no—
194C4×C127—81no—
195C4×C127—81no—
196C4×C127—81no—
197C4×C127#57512yes—
198C4×C127#57712yes—
199#19436C12711yesmaximal, characteristic, direct product factor, Sylow
200C2×C127—41no—
201C2×C127—161no—
202C2×C127#304311yescharacteristic
203C2×C127#305411yescharacteristic
204C2×C127#306911yescharacteristic
205#3210C2×C12711yescharacteristic
206#3113C2×C12711yescharacteristic, complemented
207#3103C2×C12711yescharacteristic
208#2983C2×C12711yescharacteristic, complemented
209#1702C2×C12712yescomplemented
210#1700C2×C12712yescomplemented
211#1690C2×C12712yescomplemented
212#1686C2×C12712yescomplemented
213#1572C2×C12711yescharacteristic, complemented
214#1553C2×C12711yescharacteristic
215#1544C2×C12711yescharacteristic, complemented
216C127#1943611yescharacteristic, direct product factor, Sylow
217#533C22×C12711yescharacteristic
218#532C22×C12711yescharacteristic
219C2×C4×Q8C22×C12711yescharacteristic
220#494C22×C12711yescharacteristic
221#492C22×C12711yescharacteristic
222#487C22×C12711yescharacteristic
223#486C22×C12711yescharacteristic
224#483—21no—
225#481—21no—
226#475C22×C12712yes—
227#475C22×C12712yes—
228#464—22no—
229#462C22×C12712yes—
230#460C22×C12712yes—
231#452—22no—
232#451—21no—
233#448—21no—
234#446—22no—
235#446C22×C12712yes—
236#446C22×C12712yes—
237#441—22no—
238C4×SD16—22no—
239#432—22no—
240#432C22×C12711yescharacteristic
241#431C22×C12711yescharacteristic
242#431C22×C12711yescharacteristic
243#431C22×C12711yescharacteristic
244#335C22×C12712yes—
245#334C22×C12712yes—
246#332C22×C12712yes—
247#332C22×C12712yes—
248#332C22×C12712yes—
249#331C22×C12712yes—
250C2×#41—21no—
251C22×Q8D4×C12711yescharacteristic
252C2×Q16—22no—
253C2×Q16—22no—
254C2×SD16—22no—
255C2×SD16—22no—
256C4⋊Q8C23×C12711yescharacteristic
257C4⋊Q8C23×C12711yescharacteristic
258C4⋊Q8C23×C12711yescharacteristic
259#127C23×C12711yescharacteristic
260#125—21no—
261#124—21no—
262C22⋊Q8—21no—
263C22⋊Q8—21no—
264#121—21no—
265#121—21no—
266C4×Q8—21no—
267C4×Q8—21no—
268C4×Q8—21no—
269C4×Q8—21no—
270C4×Q8D4×C12712yes—
271C4×Q8C23×C12712yes—
272C4×D4—21no—
273C4×D4—21no—
274#117—21no—
275C2×C4⋊C4—21no—
276C2×C4⋊C4D4×C12711yescharacteristic
277C2×C42—21no—
278C2×C42C23×C12711yescharacteristic
279#106—22no—
280#106—22no—
281C4⋊C8—22no—
282C4⋊C8—22no—
283C4⋊C8D4×C12712yes—
284C4⋊C8C23×C12712yes—
285C4⋊C8C23×C12712yes—
286C4⋊C8C23×C12712yes—
287#103—22no—
288#103—22no—
289#103—22no—
290#103—22no—
291#102—22no—
292#102—22no—
293C22⋊C8—21no—
294C22⋊C8—21no—
295C22⋊C8—21no—
296C22⋊C8D4×C12712yes—
297#97—22no—
298#97—22no—
299#97—21no—
300C4×C8—21no—
301C4×C8—21no—
302C4×C8C23×C12711yescharacteristic
303C4×C8C23×C12711yescharacteristic
304#41—82no—
305C2×Q8—21no—
306C2×Q8—21no—
307C2×Q8—21no—
308C2×Q8—21no—
309C2×Q8—42no—
310C2×Q8C2×D4×C12712yes—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—21no—
314C2×D4—41no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—41no—
318C22×C4C2×D4×C12711yescharacteristic
319C22×C4C2×D4×C12711yescharacteristic
320C22×C4#41×C12711yescharacteristic
321Q16—44no—
322Q16—82no—
323SD16—44no—
324SD16—82no—
325C2×C8—22no—
326C2×C8—22no—
327C2×C8—22no—
328C2×C8C2×D4×C12712yes—
329C2×C8C2×D4×C12712yes—
330C4⋊C4—22no—
331C4⋊C4—21no—
332C4⋊C4—22no—
333C4⋊C4—21no—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—21no—
339C4⋊C4—41no—
340C4⋊C4—41no—
341C4⋊C4C2×D4×C12712yes—
342C22⋊C4—41no—
343C22⋊C4—41no—
344C22⋊C4—41no—
345C42—22no—
346C42—22no—
347C42—41no—
348C42C2×D4×C12711yescharacteristic
349C42C2×D4×C12711yescharacteristic
350C42#41×C12711yescharacteristic
351C42C24×C12711yescharacteristic
352C23—41no—
353C23#121×C12711yescharacteristic
354Q8—22no—
355Q8—22no—
356Q8—42no—
357Q8—42no—
358Q8—42no—
359Q8—42no—
360D4—42no—
361D4—42no—
362D4—81no—
363D4—82no—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—22no—
367C2×C4—22no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—82no—
374C2×C4—81no—
375C2×C4#121×C12711yescharacteristic
376C2×C4#121×C12711yescharacteristic
377C2×C4#121×C12711yescharacteristic
378C2×C4C22×D4×C12711yescharacteristic
379C2×C4C22×D4×C12711yescharacteristic
380C2×C4C2×#41×C12711yescharacteristic
381C8—22no—
382C8—22no—
383C8—42no—
384C8—42no—
385C8—42no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—81no—
390C22—81no—
391C22—81no—
392C22C2×#121×C12711yescharacteristic
393C4—21no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—42no—
398C4—42no—
399C4—81no—
400C4—81no—
401C4—81no—
402C4#575×C12712yes—
403C4#577×C12712yes—
404C2—41no—
405C2—161no—
406C2C127×#304311yescharacteristic
407C2C127×#305411yescharacteristic
408C2C127×#306911yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radical#532×C127C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#3113C2semidirect
4. C127×#2983C2semidirect
5. C127×#1702C2semidirect
6. C127×#1700C2semidirect
7. C127×#1690C2semidirect
8. C127×#1686C2semidirect
9. C127×#1572C2semidirect
11. C127×#1544C2semidirect
199. #19436C127direct (N × H)
206. #3113C2×C127semidirect
208. #2983C2×C127semidirect
209. #1702C2×C127semidirect
210. #1700C2×C127semidirect
211. #1690C2×C127semidirect
212. #1686C2×C127semidirect
213. #1572C2×C127semidirect
215. #1544C2×C127semidirect
216. C127#19436direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32102
C127×#31132
C127×#31032
C127×#29832
C127×#17022
C127×#17002
C127×#16902
C127×#16862
C127×#15722
C127×#15532
C127×#15442
#19436127