Finite Group Databasebeta

← C127×#19295 #44582968

Subgroups — C127×#19295 #44582968

Order 32512.

648 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#498×C127C211yesmaximal, characteristic, complemented
2C127×#3079C211yesmaximal, characteristic
3C127×#3039C211yesmaximal, characteristic
4C127×#2965C211yesmaximal, characteristic
5C127×#1692C214yesmaximal, complemented
6C127×#1691C214yesmaximal, complemented
7C127×#1567C211yesmaximal, characteristic, complemented
8C127×#1548C211yesmaximal, characteristic, complemented
9C127×#1546C211yesmaximal, characteristic, complemented
10C2×#137×C127—21no—
11C2×C4⋊Q8×C127C2211yescharacteristic
12C2×C4⋊Q8×C127C2211yescharacteristic
13C4×#41×C127C2211yescharacteristic
14#498×C127—21no—
15#498×C127—21no—
16#498×C127C2214yes—
17#477×C127C2212yes—
18#476×C127C2212yes—
19#475×C127—21no—
20#474×C127—21no—
21#462×C127—21no—
22#462×C127C2212yes—
23#461×C127—21no—
24#461×C127C2212yes—
25#446×C127C2212yes—
26#436×C127C2212yes—
27#435×C127—22no—
28#431×C127—21no—
29#431×C127C2211yescharacteristic
30#428×C127—21no—
31C2×#106×C127—22no—
32#423×C127C2211yescharacteristic
33#423×C127C2211yescharacteristic
34#419×C127—21no—
35#417×C127—21no—
36C4×M16×C127—21no—
37C2×C4×C8×C127C2211yescharacteristic
38#335×C127C2214yes—
39#333×C127C2214yes—
40#332×C127C2214yes—
41C2×#41×C127D411yescharacteristic
42C22×Q8×C127—21no—
43C22×Q8×C127—21no—
44#137×C127—44no—
45C2×Q16×C127—22no—
46C2×SD16×C127—22no—
47C2×M16×C127—21no—
48C2×M16×C127—21no—
49C2×M16×C127—22no—
50C22×C8×C127D412yes—
51C4⋊Q8×C127—21no—
52C4⋊Q8×C127—21no—
53C4⋊Q8×C127—21no—
54C4⋊Q8×C127—21no—
55C4⋊Q8×C127—21no—
56C4⋊Q8×C127—21no—
57C4⋊Q8×C127C2312yes—
58C4⋊Q8×C127C2312yes—
59C4×Q8×C127D411yescharacteristic
60C4×Q8×C127C2311yescharacteristic
61C4×D4×C127—21no—
62C4×D4×C127—21no—
63C4×D4×C127D411yescharacteristic
64C4×D4×C127C2311yescharacteristic
65#117×C127—21no—
66#117×C127D411yescharacteristic
67C2×C4⋊C4×C127—21no—
68C2×C4⋊C4×C127—21no—
69C2×C4⋊C4×C127—21no—
70C2×C4⋊C4×C127—21no—
71C2×C42×C127—21no—
72C2×C42×C127C2311yescharacteristic
73#107×C127—22no—
74#106×C127—24no—
75#106×C127—24no—
76#106×C127—22no—
77C4⋊C8×C127—22no—
78C4⋊C8×C127—21no—
79C4⋊C8×C127—21no—
80C4⋊C8×C127C2312yes—
81C4⋊C8×C127C2312yes—
82C4⋊C8×C127C2312yes—
83#103×C127—22no—
84#103×C127—22no—
85#103×C127—22no—
86#102×C127—22no—
87C22⋊C8×C127—21no—
88C22⋊C8×C127—22no—
89#97×C127—22no—
90C4×C8×C127—21no—
91C4×C8×C127D411yescharacteristic
92C4×C8×C127D411yescharacteristic
93C4×C8×C127C2312yes—
94#41×C127—22no—
95#41×C127—22no—
96C2×Q8×C127—22no—
97C2×Q8×C127—22no—
98C2×Q8×C127—41no—
99C2×Q8×C127—41no—
100C2×Q8×C127—42no—
101C2×Q8×C127—42no—
102C2×Q8×C127—82no—
103C2×Q8×C127C2×D411yescharacteristic
104C2×D4×C127—21no—
105C2×D4×C127C2×D411yescharacteristic
106C22×C4×C127—21no—
107C22×C4×C127—21no—
108C22×C4×C127—21no—
109C22×C4×C127—41no—
110C22×C4×C127—41no—
111C22×C4×C127C2×D411yescharacteristic
112C22×C4×C127C2×D411yescharacteristic
113C22×C4×C127#4111yescharacteristic
114Q16×C127—44no—
115SD16×C127—44no—
116M16×C127—42no—
117M16×C127—42no—
118M16×C127—44no—
119C2×C8×C127—24no—
120C2×C8×C127—22no—
121C2×C8×C127—22no—
122C2×C8×C127—22no—
123C2×C8×C127C2×D412yes—
124C2×C8×C127C2×D412yes—
125C4⋊C4×C127—21no—
126C4⋊C4×C127—21no—
127C4⋊C4×C127—22no—
128C4⋊C4×C127—22no—
129C4⋊C4×C127—22no—
130C4⋊C4×C127—22no—
131C4⋊C4×C127—41no—
132C4⋊C4×C127—41no—
133C4⋊C4×C127—41no—
134C4⋊C4×C127—41no—
135C4⋊C4×C127C2×D411yescharacteristic
136C4⋊C4×C127C2×D411yescharacteristic
137C22⋊C4×C127—21no—
138C22⋊C4×C127—21no—
139C22⋊C4×C127—21no—
140C42×C127—21no—
141C42×C127—21no—
142C42×C127—21no—
143C42×C127C2×D411yescharacteristic
144C42×C127C2×D411yescharacteristic
145C42×C127#4111yescharacteristic
146C42×C127C2411yescharacteristic
147C23×C127—21no—
148C23×C127#12111yescharacteristic
149Q8×C127—21no—
150Q8×C127—21no—
151Q8×C127—42no—
152Q8×C127—42no—
153Q8×C127—82no—
154Q8×C127—82no—
155Q8×C127—82no—
156D4×C127—21no—
157D4×C127—21no—
158D4×C127—42no—
159C2×C4×C127—22no—
160C2×C4×C127—22no—
161C2×C4×C127—21no—
162C2×C4×C127—21no—
163C2×C4×C127—21no—
164C2×C4×C127—42no—
165C2×C4×C127—42no—
166C2×C4×C127—42no—
167C2×C4×C127—42no—
168C2×C4×C127—42no—
169C2×C4×C127—82no—
170C2×C4×C127—82no—
171C2×C4×C127#12111yescharacteristic
172C2×C4×C127#12111yescharacteristic
173C2×C4×C127#12111yescharacteristic
174C2×C4×C127AGL(1,ℤ/8)12yes—
175C2×C4×C127#13712yes—
176C2×C4×C127C22×D411yescharacteristic
177C2×C4×C127C22×D411yescharacteristic
178C2×C4×C127C2×#4111yescharacteristic
179C8×C127—22no—
180C8×C127—42no—
181C8×C127—42no—
182C8×C127—42no—
183C8×C127#13714yescomplemented
184C22×C127—21no—
185C22×C127—21no—
186C22×C127—41no—
187C22×C127—41no—
188C22×C127—41no—
189C22×C127#46812yes—
190C22×C127C2×#12111yescharacteristic
191C4×C127—21no—
192C4×C127—21no—
193C4×C127—41no—
194C4×C127—41no—
195C4×C127—41no—
196C4×C127—82no—
197C4×C127—82no—
198C4×C127#46812yes—
199C4×C127#47112yes—
200C4×C127C2×AGL(1,ℤ/8)11yescharacteristic
201C4×C127C2×#13712yes—
202C4×C127C2×#13711yescharacteristic
203#19295C12711yesmaximal, characteristic, direct product factor, Sylow
204C2×C127—22no—
205C2×C127—81no—
206C2×C127#303911yescharacteristic
207C2×C127C2×#46811yescharacteristic
208C2×C127C2×#47111yescharacteristic
209C2×#498C2×C12711yescharacteristic, complemented
210#3079C2×C12711yescharacteristic
211#3039C2×C12711yescharacteristic
212#2965C2×C12711yescharacteristic
213#1692C2×C12714yescomplemented
214#1691C2×C12714yescomplemented
215#1567C2×C12711yescharacteristic, complemented
216#1548C2×C12711yescharacteristic, complemented
217#1546C2×C12711yescharacteristic, complemented
218C127#1929511yescharacteristic, direct product factor, Sylow
219C2×#137—21no—
220C2×C4⋊Q8C22×C12711yescharacteristic
221C2×C4⋊Q8C22×C12711yescharacteristic
222C4×#41C22×C12711yescharacteristic
223#498—21no—
224#498—21no—
225#498C22×C12714yes—
226#477C22×C12712yes—
227#476C22×C12712yes—
228#475—21no—
229#474—21no—
230#462—21no—
231#462C22×C12712yes—
232#461—21no—
233#461C22×C12712yes—
234#446C22×C12712yes—
235#436C22×C12712yes—
236#435—22no—
237#431—21no—
238#431C22×C12711yescharacteristic
239#428—21no—
240C2×#106—22no—
241#423C22×C12711yescharacteristic
242#423C22×C12711yescharacteristic
243#419—21no—
244#417—21no—
245C4×M16—21no—
246C2×C4×C8C22×C12711yescharacteristic
247#335C22×C12714yes—
248#333C22×C12714yes—
249#332C22×C12714yes—
250C2×#41D4×C12711yescharacteristic
251C22×Q8—21no—
252C22×Q8—21no—
253#137—44no—
254C2×Q16—22no—
255C2×SD16—22no—
256C2×M16—21no—
257C2×M16—21no—
258C2×M16—22no—
259C22×C8D4×C12712yes—
260C4⋊Q8—21no—
261C4⋊Q8—21no—
262C4⋊Q8—21no—
263C4⋊Q8—21no—
264C4⋊Q8—21no—
265C4⋊Q8—21no—
266C4⋊Q8C23×C12712yes—
267C4⋊Q8C23×C12712yes—
268C4×Q8D4×C12711yescharacteristic
269C4×Q8C23×C12711yescharacteristic
270C4×D4—21no—
271C4×D4—21no—
272C4×D4D4×C12711yescharacteristic
273C4×D4C23×C12711yescharacteristic
274#117—21no—
275#117D4×C12711yescharacteristic
276C2×C4⋊C4—21no—
277C2×C4⋊C4—21no—
278C2×C4⋊C4—21no—
279C2×C4⋊C4—21no—
280C2×C42—21no—
281C2×C42C23×C12711yescharacteristic
282#107—22no—
283#106—24no—
284#106—24no—
285#106—22no—
286C4⋊C8—22no—
287C4⋊C8—21no—
288C4⋊C8—21no—
289C4⋊C8C23×C12712yes—
290C4⋊C8C23×C12712yes—
291C4⋊C8C23×C12712yes—
292#103—22no—
293#103—22no—
294#103—22no—
295#102—22no—
296C22⋊C8—21no—
297C22⋊C8—22no—
298#97—22no—
299C4×C8—21no—
300C4×C8D4×C12711yescharacteristic
301C4×C8D4×C12711yescharacteristic
302C4×C8C23×C12712yes—
303#41—22no—
304#41—22no—
305C2×Q8—22no—
306C2×Q8—22no—
307C2×Q8—41no—
308C2×Q8—41no—
309C2×Q8—42no—
310C2×Q8—42no—
311C2×Q8—82no—
312C2×Q8C2×D4×C12711yescharacteristic
313C2×D4—21no—
314C2×D4C2×D4×C12711yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—41no—
319C22×C4—41no—
320C22×C4C2×D4×C12711yescharacteristic
321C22×C4C2×D4×C12711yescharacteristic
322C22×C4#41×C12711yescharacteristic
323Q16—44no—
324SD16—44no—
325M16—42no—
326M16—42no—
327M16—44no—
328C2×C8—24no—
329C2×C8—22no—
330C2×C8—22no—
331C2×C8—22no—
332C2×C8C2×D4×C12712yes—
333C2×C8C2×D4×C12712yes—
334C4⋊C4—21no—
335C4⋊C4—21no—
336C4⋊C4—22no—
337C4⋊C4—22no—
338C4⋊C4—22no—
339C4⋊C4—22no—
340C4⋊C4—41no—
341C4⋊C4—41no—
342C4⋊C4—41no—
343C4⋊C4—41no—
344C4⋊C4C2×D4×C12711yescharacteristic
345C4⋊C4C2×D4×C12711yescharacteristic
346C22⋊C4—21no—
347C22⋊C4—21no—
348C22⋊C4—21no—
349C42—21no—
350C42—21no—
351C42—21no—
352C42C2×D4×C12711yescharacteristic
353C42C2×D4×C12711yescharacteristic
354C42#41×C12711yescharacteristic
355C42C24×C12711yescharacteristic
356C23—21no—
357C23#121×C12711yescharacteristic
358Q8—21no—
359Q8—21no—
360Q8—42no—
361Q8—42no—
362Q8—82no—
363Q8—82no—
364Q8—82no—
365D4—21no—
366D4—21no—
367D4—42no—
368C2×C4—22no—
369C2×C4—22no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—42no—
376C2×C4—42no—
377C2×C4—42no—
378C2×C4—82no—
379C2×C4—82no—
380C2×C4#121×C12711yescharacteristic
381C2×C4#121×C12711yescharacteristic
382C2×C4#121×C12711yescharacteristic
383C2×C4AGL(1,ℤ/8)×C12712yes—
384C2×C4#137×C12712yes—
385C2×C4C22×D4×C12711yescharacteristic
386C2×C4C22×D4×C12711yescharacteristic
387C2×C4C2×#41×C12711yescharacteristic
388C8—22no—
389C8—42no—
390C8—42no—
391C8—42no—
392C8#137×C12714yescomplemented
393C22—21no—
394C22—21no—
395C22—41no—
396C22—41no—
397C22—41no—
398C22#468×C12712yes—
399C22C2×#121×C12711yescharacteristic
400C4—21no—
401C4—21no—
402C4—41no—
403C4—41no—
404C4—41no—
405C4—82no—
406C4—82no—
407C4#468×C12712yes—
408C4#471×C12712yes—
409C4C2×AGL(1,ℤ/8)×C12711yescharacteristic
410C4C2×#137×C12712yes—
411C4C2×#137×C12711yescharacteristic
412C2—22no—
413C2—81no—
414C2C127×#303911yescharacteristic
415C2C2×#468×C12711yescharacteristic
416C2C2×#471×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×#41×C127D4
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
1. C2×#498×C127C2semidirect
5. C127×#1692C2semidirect
6. C127×#1691C2semidirect
7. C127×#1567C2semidirect
8. C127×#1548C2semidirect
9. C127×#1546C2semidirect
183. C8×C127#137semidirect
203. #19295C127direct (N × H)
209. C2×#498C2×C127semidirect
213. #1692C2×C127semidirect
214. #1691C2×C127semidirect
215. #1567C2×C127semidirect
216. #1548C2×C127semidirect
217. #1546C2×C127semidirect
218. C127#19295direct (N × H)
392. C8#137×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#498×C1272
C127×#30792
C127×#30392
C127×#29652
C127×#16922
C127×#16912
C127×#15672
C127×#15482
C127×#15462
#19295127