Finite Group Databasebeta

← C127×#18295 #44581968

Subgroups — C127×#18295 #44581968

Order 32512.

940 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#544×C127C211yesmaximal, characteristic
2C127×#3189C212yesmaximal
3C127×#2627C211yesmaximal, characteristic
4C127×#1617C214yesmaximal, complemented
5C127×#1605C214yesmaximal, complemented
6C127×#1520C212yesmaximal
7C2×#324×C127C211yesmaximal, characteristic
8#544×C127—24no—
9#544×C127—22no—
10#544×C127C2214yes—
11C2×C4⋊Q8×C127—22no—
12C2×#125×C127—22no—
13C2×C22⋊Q8×C127—21no—
14C2×C22⋊Q8×C127C2212yes—
15C2×C22⋊Q8×C127C2211yescharacteristic
16C2×#117×C127—21no—
17C22×C4⋊C4×C127C2211yescharacteristic
18#484×C127—22no—
19#484×C127C2214yes—
20#467×C127—24no—
21#451×C127—22no—
22#451×C127C2214yes—
23C2×C22⋊C8×C127C2212yes—
24#400×C127C2212yes—
25#398×C127—22no—
26#395×C127C2212yes—
27#385×C127—21no—
28#381×C127—21no—
29#380×C127C2211yescharacteristic
30#328×C127C2218yes—
31#324×C127C2214yes—
32C22×Q8×C127—21no—
33C22×Q8×C127D412yes—
34C22×Q8×C127C2311yescharacteristic
35C23×C4×C127D411yescharacteristic
36C23×C4×C127D411yescharacteristic
37C23×C4×C127C2311yescharacteristic
38C2×Q16×C127—24no—
39C22×C8×C127—22no—
40C4⋊Q8×C127—28no—
41C4⋊Q8×C127—28no—
42#125×C127—28no—
43#125×C127—28no—
44C22⋊Q8×C127—24no—
45C22⋊Q8×C127—24no—
46C22⋊Q8×C127—22no—
47C22⋊Q8×C127—22no—
48C22⋊Q8×C127—22no—
49C22⋊Q8×C127—22no—
50C22⋊Q8×C127D414yes—
51C22⋊Q8×C127C2314yes—
52#117×C127—24no—
53#117×C127—24no—
54C2×C4⋊C4×C127—21no—
55C2×C4⋊C4×C127—21no—
56C2×C4⋊C4×C127—21no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127—22no—
59C2×C4⋊C4×C127—22no—
60C2×C4⋊C4×C127—22no—
61C2×C4⋊C4×C127—21no—
62C2×C4⋊C4×C127—21no—
63C2×C4⋊C4×C127—22no—
64C2×C4⋊C4×C127D412yes—
65C2×C4⋊C4×C127D412yes—
66C2×C4⋊C4×C127C2311yescharacteristic
67C2×C4⋊C4×C127C2312yes—
68C2×C22⋊C4×C127—22no—
69C2×C22⋊C4×C127—21no—
70C2×C22⋊C4×C127—21no—
71C2×C42×C127—22no—
72#107×C127—24no—
73#103×C127—24no—
74#103×C127—24no—
75C22⋊C8×C127—22no—
76C22⋊C8×C127C2314yes—
77#95×C127—22no—
78#95×C127—22no—
79#95×C127—22no—
80#95×C127C2312yes—
81C24×C127C2×D411yescharacteristic
82C2×Q8×C127—24no—
83C2×Q8×C127—22no—
84C2×Q8×C127—22no—
85C2×Q8×C127—81no—
86C2×Q8×C127—82no—
87C2×Q8×C127—82no—
88C2×Q8×C127C2×D414yes—
89C22×C4×C127—21no—
90C22×C4×C127—21no—
91C22×C4×C127—22no—
92C22×C4×C127—22no—
93C22×C4×C127—22no—
94C22×C4×C127—21no—
95C22×C4×C127—21no—
96C22×C4×C127—21no—
97C22×C4×C127—22no—
98C22×C4×C127—21no—
99C22×C4×C127—81no—
100C22×C4×C127—81no—
101C22×C4×C127Q1614yescomplemented
102C22×C4×C127C2×D412yes—
103C22×C4×C127C2×D412yes—
104C22×C4×C127C2×D411yescharacteristic
105C22×C4×C127C2×D412yes—
106C22×C4×C127C2×D412yes—
107C22×C4×C127C2411yescharacteristic
108Q16×C127—84no—
109C2×C8×C127—24no—
110C2×C8×C127—82no—
111C4⋊C4×C127—24no—
112C4⋊C4×C127—24no—
113C4⋊C4×C127—24no—
114C4⋊C4×C127—28no—
115C4⋊C4×C127—24no—
116C4⋊C4×C127—24no—
117C4⋊C4×C127—22no—
118C4⋊C4×C127—24no—
119C4⋊C4×C127—24no—
120C4⋊C4×C127—22no—
121C4⋊C4×C127—42no—
122C4⋊C4×C127—81no—
123C4⋊C4×C127—82no—
124C4⋊C4×C127C2×D414yes—
125C22⋊C4×C127—24no—
126C22⋊C4×C127—24no—
127C22⋊C4×C127—41no—
128C22⋊C4×C127—41no—
129C22⋊C4×C127—42no—
130C42×C127—28no—
131C23×C127—41no—
132C23×C127—41no—
133C23×C127#12011yescharacteristic
134C23×C127#12011yescharacteristic
135C23×C127C2×Q1612yes—
136C23×C127#13712yes—
137C23×C127C22×D411yescharacteristic
138Q8×C127—44no—
139Q8×C127—44no—
140Q8×C127—82no—
141Q8×C127—84no—
142C2×C4×C127—22no—
143C2×C4×C127—22no—
144C2×C4×C127—24no—
145C2×C4×C127—24no—
146C2×C4×C127—24no—
147C2×C4×C127—24no—
148C2×C4×C127—22no—
149C2×C4×C127—41no—
150C2×C4×C127—42no—
151C2×C4×C127—42no—
152C2×C4×C127—41no—
153C2×C4×C127—44no—
154C2×C4×C127—42no—
155C2×C4×C127—44no—
156C2×C4×C127—42no—
157C2×C4×C127—42no—
158C2×C4×C127—42no—
159C2×C4×C127—42no—
160C2×C4×C127—42no—
161C2×C4×C127—41no—
162C2×C4×C127—41no—
163C2×C4×C127—42no—
164C2×C4×C127—81no—
165C2×C4×C127#12012yes—
166C2×C4×C127C2×Q1614yes—
167C2×C4×C127C22×D412yes—
168C8×C127—44no—
169C22×C127—21no—
170C22×C127—21no—
171C22×C127—21no—
172C22×C127—21no—
173C22×C127—21no—
174C22×C127—21no—
175C22×C127—42no—
176C22×C127—42no—
177C22×C127#45112yes—
178C22×C127#45112yes—
179C22×C127C2×#12011yescharacteristic
180C22×C127C22×Q1611yescharacteristic
181C22×C127C2×#13711yescharacteristic
182C4×C127—24no—
183C4×C127—22no—
184C4×C127—22no—
185C4×C127—44no—
186C4×C127—42no—
187C4×C127—44no—
188C4×C127—82no—
189C4×C127—81no—
190C4×C127—81no—
191#18295C12711yesmaximal, characteristic, direct product factor, Sylow
192C2×C127—21no—
193C2×C127—21no—
194C2×C127—22no—
195C2×C127—22no—
196C2×C127C2×#45111yescharacteristic
197C2×C127#302011yescharacteristic
198C2×C127#302611yescharacteristic
199C2×#544C2×C12711yescharacteristic
200#3189C2×C12712yes—
201#2627C2×C12711yescharacteristic
202#1617C2×C12714yescomplemented
203#1605C2×C12714yescomplemented
204#1520C2×C12712yes—
205C2×#324C2×C12711yescharacteristic
206C127#1829511yescharacteristic, direct product factor, Sylow
207#544—24no—
208#544—22no—
209#544C22×C12714yes—
210C2×C4⋊Q8—22no—
211C2×#125—22no—
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8C22×C12712yes—
214C2×C22⋊Q8C22×C12711yescharacteristic
215C2×#117—21no—
216C22×C4⋊C4C22×C12711yescharacteristic
217#484—22no—
218#484C22×C12714yes—
219#467—24no—
220#451—22no—
221#451C22×C12714yes—
222C2×C22⋊C8C22×C12712yes—
223#400C22×C12712yes—
224#398—22no—
225#395C22×C12712yes—
226#385—21no—
227#381—21no—
228#380C22×C12711yescharacteristic
229#328C22×C12718yes—
230#324C22×C12714yes—
231C22×Q8—21no—
232C22×Q8D4×C12712yes—
233C22×Q8C23×C12711yescharacteristic
234C23×C4D4×C12711yescharacteristic
235C23×C4D4×C12711yescharacteristic
236C23×C4C23×C12711yescharacteristic
237C2×Q16—24no—
238C22×C8—22no—
239C4⋊Q8—28no—
240C4⋊Q8—28no—
241#125—28no—
242#125—28no—
243C22⋊Q8—24no—
244C22⋊Q8—24no—
245C22⋊Q8—22no—
246C22⋊Q8—22no—
247C22⋊Q8—22no—
248C22⋊Q8—22no—
249C22⋊Q8D4×C12714yes—
250C22⋊Q8C23×C12714yes—
251#117—24no—
252#117—24no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—22no—
263C2×C4⋊C4D4×C12712yes—
264C2×C4⋊C4D4×C12712yes—
265C2×C4⋊C4C23×C12711yescharacteristic
266C2×C4⋊C4C23×C12712yes—
267C2×C22⋊C4—22no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C42—22no—
271#107—24no—
272#103—24no—
273#103—24no—
274C22⋊C8—22no—
275C22⋊C8C23×C12714yes—
276#95—22no—
277#95—22no—
278#95—22no—
279#95C23×C12712yes—
280C24C2×D4×C12711yescharacteristic
281C2×Q8—24no—
282C2×Q8—22no—
283C2×Q8—22no—
284C2×Q8—81no—
285C2×Q8—82no—
286C2×Q8—82no—
287C2×Q8C2×D4×C12714yes—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—22no—
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—22no—
297C22×C4—21no—
298C22×C4—81no—
299C22×C4—81no—
300C22×C4Q16×C12714yescomplemented
301C22×C4C2×D4×C12712yes—
302C22×C4C2×D4×C12712yes—
303C22×C4C2×D4×C12711yescharacteristic
304C22×C4C2×D4×C12712yes—
305C22×C4C2×D4×C12712yes—
306C22×C4C24×C12711yescharacteristic
307Q16—84no—
308C2×C8—24no—
309C2×C8—82no—
310C4⋊C4—24no—
311C4⋊C4—24no—
312C4⋊C4—24no—
313C4⋊C4—28no—
314C4⋊C4—24no—
315C4⋊C4—24no—
316C4⋊C4—22no—
317C4⋊C4—24no—
318C4⋊C4—24no—
319C4⋊C4—22no—
320C4⋊C4—42no—
321C4⋊C4—81no—
322C4⋊C4—82no—
323C4⋊C4C2×D4×C12714yes—
324C22⋊C4—24no—
325C22⋊C4—24no—
326C22⋊C4—41no—
327C22⋊C4—41no—
328C22⋊C4—42no—
329C42—28no—
330C23—41no—
331C23—41no—
332C23#120×C12711yescharacteristic
333C23#120×C12711yescharacteristic
334C23C2×Q16×C12712yes—
335C23#137×C12712yes—
336C23C22×D4×C12711yescharacteristic
337Q8—44no—
338Q8—44no—
339Q8—82no—
340Q8—84no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—24no—
344C2×C4—24no—
345C2×C4—24no—
346C2×C4—24no—
347C2×C4—22no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—41no—
352C2×C4—42no—
353C2×C4—44no—
354C2×C4—44no—
355C2×C4—42no—
356C2×C4—42no—
357C2×C4—42no—
358C2×C4—42no—
359C2×C4—42no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—81no—
364C2×C4#120×C12712yes—
365C2×C4C2×Q16×C12714yes—
366C2×C4C22×D4×C12712yes—
367C8—44no—
368C22—21no—
369C22—21no—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—21no—
374C22—42no—
375C22—42no—
376C22#451×C12712yes—
377C22#451×C12712yes—
378C22C2×#120×C12711yescharacteristic
379C22C22×Q16×C12711yescharacteristic
380C22C2×#137×C12711yescharacteristic
381C4—24no—
382C4—22no—
383C4—22no—
384C4—44no—
385C4—42no—
386C4—44no—
387C4—82no—
388C4—81no—
389C4—81no—
390C2—21no—
391C2—21no—
392C2—22no—
393C2—22no—
394C2C2×#451×C12711yescharacteristic
395C2C127×#302011yescharacteristic
396C2C127×#302611yescharacteristic
subgroupG/H
center, socleC22×C127C2×#120
commutator, Frattini, cosocleC22×C4C24×C127
prime radicalC24×C127C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1617C2semidirect
5. C127×#1605C2semidirect
101. C22×C4×C127Q16semidirect
191. #18295C127direct (N × H)
202. #1617C2×C127semidirect
203. #1605C2×C127semidirect
206. C127#18295direct (N × H)
300. C22×C4Q16×C127semidirect

Maximal subgroups

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

subgroupindex
C2×#544×C1272
C127×#31892
C127×#26272
C127×#16172
C127×#16052
C127×#15202
C2×#324×C1272
#18295127