Finite Group Databasebeta

← C127×#10829 #44574502

Subgroups — C127×#10829 #44574502

Order 32512.

906 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×#2273C211yesmaximal, characteristic
2C2×#342×C127C211yesmaximal, characteristic
3C2×#342×C127C211yesmaximal, characteristic
4C2×#342×C127C212yesmaximal
5C2×#342×C127C212yesmaximal
6C22×C22⋊C4×C127C2212yes—
7C22×C22⋊C4×C127C2212yes—
8C22×C22⋊C4×C127C2211yescharacteristic
9C22×C22⋊C4×C127C2211yescharacteristic
10C22×C22⋊C4×C127C2211yescharacteristic
11C4×C22⋊C4×C127—22no—
12C4×C22⋊C4×C127—22no—
13C4×C22⋊C4×C127C414yescomplemented
14#342×C127—22no—
15#342×C127—22no—
16#342×C127—24no—
17#342×C127C418yescomplemented
18C25×C127C2311yescharacteristic
19C23×C4×C127—21no—
20C23×C4×C127—21no—
21C23×C4×C127—22no—
22C23×C4×C127—22no—
23C23×C4×C127C2×C412yes—
24C2×C22⋊C4×C127—21no—
25C2×C22⋊C4×C127—21no—
26C2×C22⋊C4×C127—22no—
27C2×C22⋊C4×C127—21no—
28C2×C22⋊C4×C127—21no—
29C2×C22⋊C4×C127—22no—
30C2×C22⋊C4×C127—22no—
31C2×C22⋊C4×C127—22no—
32C2×C22⋊C4×C127—22no—
33C2×C22⋊C4×C127—22no—
34C2×C22⋊C4×C127—22no—
35C2×C22⋊C4×C127—22no—
36C2×C22⋊C4×C127—22no—
37C2×C22⋊C4×C127—22no—
38C2×C22⋊C4×C127—22no—
39C2×C22⋊C4×C127—22no—
40C2×C22⋊C4×C127—22no—
41C2×C22⋊C4×C127C2×C414yes—
42C2×C22⋊C4×C127C2×C414yes—
43C2×C22⋊C4×C127C2×C414yes—
44C2×C22⋊C4×C127C2×C412yes—
45C2×C22⋊C4×C127C2×C412yes—
46C2×C22⋊C4×C127D412yes—
47C2×C22⋊C4×C127D412yes—
48C2×C22⋊C4×C127D412yes—
49C2×C22⋊C4×C127Q812yes—
50C2×C42×C127—24no—
51#95×C127—24no—
52C24×C127—82no—
53C24×C127C22×C411yescharacteristic
54C24×C127C22×C412yes—
55C24×C127C2×D411yescharacteristic
56C24×C127C2×D411yescharacteristic
57C24×C127C2×D411yescharacteristic
58C24×C127C2×Q811yescharacteristic
59C24×C127#4112yes—
60C24×C127#4112yes—
61C24×C127#4111yescharacteristic
62C24×C127#4111yescharacteristic
63C24×C127#4112yes—
64C22×C4×C127—22no—
65C22×C4×C127—22no—
66C22×C4×C127—22no—
67C22×C4×C127—22no—
68C22×C4×C127—24no—
69C22×C4×C127—22no—
70C22×C4×C127—22no—
71C22×C4×C127—24no—
72C22×C4×C127—24no—
73C22×C4×C127—42no—
74C22×C4×C127—42no—
75C22×C4×C127—42no—
76C22×C4×C127—42no—
77C22×C4×C127—82no—
78C22×C4×C127—82no—
79C22×C4×C127—82no—
80C22×C4×C127—84no—
81C22×C4×C127—84no—
82C22×C4×C127C22⋊C414yes—
83C22⋊C4×C127—22no—
84C22⋊C4×C127—22no—
85C22⋊C4×C127—24no—
86C22⋊C4×C127—22no—
87C22⋊C4×C127—22no—
88C22⋊C4×C127—24no—
89C22⋊C4×C127—24no—
90C22⋊C4×C127—24no—
91C22⋊C4×C127—24no—
92C22⋊C4×C127—24no—
93C22⋊C4×C127—24no—
94C22⋊C4×C127—42no—
95C22⋊C4×C127—42no—
96C22⋊C4×C127—42no—
97C22⋊C4×C127—42no—
98C22⋊C4×C127C4214yes—
99C22⋊C4×C127C4⋊C414yes—
100C42×C127—84no—
101C23×C127—42no—
102C23×C127—42no—
103C23×C127—42no—
104C23×C127—44no—
105C23×C127—44no—
106C23×C127—82no—
107C23×C127—81no—
108C23×C127—81no—
109C23×C127—81no—
110C23×C127—82no—
111C23×C127—81no—
112C23×C127C2×C4211yescharacteristic
113C23×C127C2×C22⋊C411yescharacteristic
114C23×C127C2×C4⋊C411yescharacteristic
115C23×C127#11711yescharacteristic
116C23×C127#11711yescharacteristic
117C23×C127#11711yescharacteristic
118C23×C127#11712yes—
119C23×C127#11712yes—
120C23×C127#11711yescharacteristic
121C23×C127C4×D412yes—
122C23×C127C4×D412yes—
123C23×C127C4×D412yes—
124C23×C127C4×Q812yes—
125C23×C127#12111yescharacteristic
126C23×C127#12111yescharacteristic
127C23×C127C22⋊Q811yescharacteristic
128C23×C127C22⋊Q811yescharacteristic
129C23×C127#12312yes—
130C23×C127#12312yes—
131C23×C127#12412yes—
132C23×C127#12512yes—
133C23×C127#12612yes—
134C23×C127#12612yes—
135C2×C4×C127—24no—
136C2×C4×C127—24no—
137C2×C4×C127—24no—
138C2×C4×C127—44no—
139C2×C4×C127—44no—
140C2×C4×C127—44no—
141C2×C4×C127—44no—
142C2×C4×C127—44no—
143C2×C4×C127—82no—
144C2×C4×C127—82no—
145C2×C4×C127—84no—
146C2×C4×C127—82no—
147C2×C4×C127—82no—
148C2×C4×C127—84no—
149C2×C4×C127—84no—
150C2×C4×C127—84no—
151C2×C4×C127—84no—
152C2×C4×C127—84no—
153C2×C4×C127—84no—
154C22×C127—22no—
155C22×C127—22no—
156C22×C127—22no—
157C22×C127—24no—
158C22×C127—24no—
159C22×C127—42no—
160C22×C127—42no—
161C22×C127—42no—
162C22×C127—41no—
163C22×C127—41no—
164C22×C127—42no—
165C22×C127—42no—
166C22×C127—41no—
167C22×C127—41no—
168C22×C127—41no—
169C22×C127—41no—
170C22×C127—42no—
171C22×C127—42no—
172C22×C127—42no—
173C22×C127—41no—
174C22×C127—41no—
175C22×C127—42no—
176C22×C127—42no—
177C22×C127#37611yescharacteristic
178C22×C127C4×C22⋊C411yescharacteristic
179C22×C127C4×C4⋊C411yescharacteristic
180C22×C127#38011yescharacteristic
181C22×C127#38111yescharacteristic
182C22×C127#38211yescharacteristic
183C22×C127#38311yescharacteristic
184C22×C127#38712yes—
185C22×C127#38712yes—
186C22×C127#38812yes—
187C22×C127#38812yes—
188C4×C127—44no—
189C4×C127—44no—
190C4×C127—44no—
191C4×C127—84no—
192C4×C127—84no—
193#10829C12711yesmaximal, characteristic, direct product factor, Sylow
194C2×C127—21no—
195C2×C127—21no—
196C2×C127—22no—
197C2×C127—22no—
198C2×C127—21no—
199C2×C127—21no—
200C2×C127—21no—
201C2×C127—21no—
202C2×C127—22no—
203C2×C127—22no—
204C2×C127#143411yescharacteristic
205C2×C127#182812yes—
206#2273C2×C12711yescharacteristic
207C2×#342C2×C12711yescharacteristic
208C2×#342C2×C12711yescharacteristic
209C2×#342C2×C12712yes—
210C2×#342C2×C12712yes—
211C127#1082911yescharacteristic, direct product factor, Sylow
212C22×C22⋊C4C22×C12712yes—
213C22×C22⋊C4C22×C12712yes—
214C22×C22⋊C4C22×C12711yescharacteristic
215C22×C22⋊C4C22×C12711yescharacteristic
216C22×C22⋊C4C22×C12711yescharacteristic
217C4×C22⋊C4—22no—
218C4×C22⋊C4—22no—
219C4×C22⋊C4C4×C12714yescomplemented
220#342—22no—
221#342—22no—
222#342—24no—
223#342C4×C12718yescomplemented
224C25C23×C12711yescharacteristic
225C23×C4—21no—
226C23×C4—21no—
227C23×C4—22no—
228C23×C4—22no—
229C23×C4C2×C4×C12712yes—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—22no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—22no—
236C2×C22⋊C4—22no—
237C2×C22⋊C4—22no—
238C2×C22⋊C4—22no—
239C2×C22⋊C4—22no—
240C2×C22⋊C4—22no—
241C2×C22⋊C4—22no—
242C2×C22⋊C4—22no—
243C2×C22⋊C4—22no—
244C2×C22⋊C4—22no—
245C2×C22⋊C4—22no—
246C2×C22⋊C4—22no—
247C2×C22⋊C4C2×C4×C12714yes—
248C2×C22⋊C4C2×C4×C12714yes—
249C2×C22⋊C4C2×C4×C12714yes—
250C2×C22⋊C4C2×C4×C12712yes—
251C2×C22⋊C4C2×C4×C12712yes—
252C2×C22⋊C4D4×C12712yes—
253C2×C22⋊C4D4×C12712yes—
254C2×C22⋊C4D4×C12712yes—
255C2×C22⋊C4Q8×C12712yes—
256C2×C42—24no—
257#95—24no—
258C24—82no—
259C24C22×C4×C12711yescharacteristic
260C24C22×C4×C12712yes—
261C24C2×D4×C12711yescharacteristic
262C24C2×D4×C12711yescharacteristic
263C24C2×D4×C12711yescharacteristic
264C24C2×Q8×C12711yescharacteristic
265C24#41×C12712yes—
266C24#41×C12712yes—
267C24#41×C12711yescharacteristic
268C24#41×C12711yescharacteristic
269C24#41×C12712yes—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—24no—
275C22×C4—22no—
276C22×C4—22no—
277C22×C4—24no—
278C22×C4—24no—
279C22×C4—42no—
280C22×C4—42no—
281C22×C4—42no—
282C22×C4—42no—
283C22×C4—82no—
284C22×C4—82no—
285C22×C4—82no—
286C22×C4—84no—
287C22×C4—84no—
288C22×C4C22⋊C4×C12714yes—
289C22⋊C4—22no—
290C22⋊C4—22no—
291C22⋊C4—24no—
292C22⋊C4—22no—
293C22⋊C4—22no—
294C22⋊C4—24no—
295C22⋊C4—24no—
296C22⋊C4—24no—
297C22⋊C4—24no—
298C22⋊C4—24no—
299C22⋊C4—24no—
300C22⋊C4—42no—
301C22⋊C4—42no—
302C22⋊C4—42no—
303C22⋊C4—42no—
304C22⋊C4C42×C12714yes—
305C22⋊C4C4⋊C4×C12714yes—
306C42—84no—
307C23—42no—
308C23—42no—
309C23—42no—
310C23—44no—
311C23—44no—
312C23—82no—
313C23—81no—
314C23—81no—
315C23—81no—
316C23—82no—
317C23—81no—
318C23C2×C42×C12711yescharacteristic
319C23C2×C22⋊C4×C12711yescharacteristic
320C23C2×C4⋊C4×C12711yescharacteristic
321C23#117×C12711yescharacteristic
322C23#117×C12711yescharacteristic
323C23#117×C12711yescharacteristic
324C23#117×C12712yes—
325C23#117×C12712yes—
326C23#117×C12711yescharacteristic
327C23C4×D4×C12712yes—
328C23C4×D4×C12712yes—
329C23C4×D4×C12712yes—
330C23C4×Q8×C12712yes—
331C23#121×C12711yescharacteristic
332C23#121×C12711yescharacteristic
333C23C22⋊Q8×C12711yescharacteristic
334C23C22⋊Q8×C12711yescharacteristic
335C23#123×C12712yes—
336C23#123×C12712yes—
337C23#124×C12712yes—
338C23#125×C12712yes—
339C23#126×C12712yes—
340C23#126×C12712yes—
341C2×C4—24no—
342C2×C4—24no—
343C2×C4—24no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—44no—
348C2×C4—44no—
349C2×C4—82no—
350C2×C4—82no—
351C2×C4—84no—
352C2×C4—82no—
353C2×C4—82no—
354C2×C4—84no—
355C2×C4—84no—
356C2×C4—84no—
357C2×C4—84no—
358C2×C4—84no—
359C2×C4—84no—
360C22—22no—
361C22—22no—
362C22—22no—
363C22—24no—
364C22—24no—
365C22—42no—
366C22—42no—
367C22—42no—
368C22—41no—
369C22—41no—
370C22—42no—
371C22—42no—
372C22—41no—
373C22—41no—
374C22—41no—
375C22—41no—
376C22—42no—
377C22—42no—
378C22—42no—
379C22—41no—
380C22—41no—
381C22—42no—
382C22—42no—
383C22#376×C12711yescharacteristic
384C22C4×C22⋊C4×C12711yescharacteristic
385C22C4×C4⋊C4×C12711yescharacteristic
386C22#380×C12711yescharacteristic
387C22#381×C12711yescharacteristic
388C22#382×C12711yescharacteristic
389C22#383×C12711yescharacteristic
390C22#387×C12712yes—
391C22#387×C12712yes—
392C22#388×C12712yes—
393C22#388×C12712yes—
394C4—44no—
395C4—44no—
396C4—44no—
397C4—84no—
398C4—84no—
399C2—21no—
400C2—21no—
401C2—22no—
402C2—22no—
403C2—21no—
404C2—21no—
405C2—21no—
406C2—21no—
407C2—22no—
408C2—22no—
409C2C127×#143411yescharacteristic
410C2C127×#182812yes—
subgroupG/H
center, socleC22×C127#381
commutatorC23C2×C42×C127
Frattini, cosocleC25C23×C127
prime radicalC25×C127C23
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C25×C127 ◁ G

Complements

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

NH ≅ G/Ntype
13. C4×C22⋊C4×C127C4semidirect
17. #342×C127C4semidirect
193. #10829C127direct (N × H)
211. C127#10829direct (N × H)
219. C4×C22⋊C4C4×C127semidirect
223. #342C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#22732
C2×#342×C1272
#10829127