Finite Group Databasebeta

← C127×#12579 #44576252

Subgroups — C127×#12579 #44576252

Order 32512.

736 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#413×C127C212yesmaximal
2C127×#2879C211yesmaximal, characteristic
3C127×#1392C214yesmaximal, complemented
4C22×#41×C127C2211yescharacteristic
5C22×M16×C127—22no—
6C22×M16×C127C411yescharacteristic
7C22×M16×C127C411yescharacteristic
8#413×C127—22no—
9#413×C127—22no—
10#413×C127C414yes—
11#413×C127C2214yes—
12C2×#101×C127—22no—
13C2×#100×C127C414yes—
14#408×C127—22no—
15#408×C127C412yes—
16#408×C127C2212yes—
17#407×C127—22no—
18C2×#41×C127—42no—
19C2×#41×C127—42no—
20C2×#41×C127C2×C412yes—
21C2×#41×C127C2×C411yescharacteristic
22C2×#41×C127D411yescharacteristic
23C2×#41×C127D412yes—
24C2×#41×C127Q811yescharacteristic
25C2×#41×C127C2311yescharacteristic
26C22×Q8×C127D411yescharacteristic
27C22×D4×C127C2×C412yes—
28C22×D4×C127Q811yescharacteristic
29C23×C4×C127C2×C411yescharacteristic
30C23×C4×C127D412yes—
31C2×M16×C127—21no—
32C2×M16×C127—21no—
33C2×M16×C127—21no—
34C2×M16×C127—24no—
35C2×M16×C127—24no—
36C2×M16×C127—24no—
37C2×M16×C127—42no—
38C2×M16×C127—42no—
39C2×M16×C127—42no—
40C2×M16×C127—42no—
41C2×M16×C127—42no—
42C2×M16×C127C2×C412yes—
43C22×C8×C127—21no—
44C22×C8×C127—42no—
45C22×C8×C127C2×C412yes—
46#101×C127—24no—
47#101×C127—24no—
48#100×C127—24no—
49#100×C127C2×C418yes—
50C22⋊C8×C127—24no—
51C22⋊C8×C127—24no—
52C24×C127C4211yescharacteristic
53C24×C127C4⋊C412yes—
54#41×C127—42no—
55#41×C127—42no—
56#41×C127—41no—
57#41×C127—41no—
58#41×C127—42no—
59#41×C127—42no—
60#41×C127—42no—
61#41×C127—42no—
62#41×C127—41no—
63#41×C127—41no—
64C2×Q8×C127—42no—
65C2×Q8×C127C22⋊C412yes—
66C2×Q8×C127C4⋊C411yescharacteristic
67C2×Q8×C127C2×D411yescharacteristic
68C2×D4×C127—42no—
69C2×D4×C127—42no—
70C2×D4×C127—42no—
71C2×D4×C127C4212yes—
72C2×D4×C127C22⋊C412yes—
73C2×D4×C127C4⋊C412yes—
74C2×D4×C127C4⋊C412yes—
75C2×D4×C127C4⋊C411yescharacteristic
76C2×D4×C127C22×C412yes—
77C2×D4×C127C2×Q811yescharacteristic
78C22×C4×C127—22no—
79C22×C4×C127—22no—
80C22×C4×C127—22no—
81C22×C4×C127—22no—
82C22×C4×C127—22no—
83C22×C4×C127—22no—
84C22×C4×C127C4211yescharacteristic
85C22×C4×C127C22⋊C412yes—
86C22×C4×C127C22⋊C411yescharacteristic
87C22×C4×C127C22⋊C412yes—
88C22×C4×C127C22⋊C412yes—
89C22×C4×C127C22⋊C411yescharacteristic
90C22×C4×C127C4⋊C412yes—
91C22×C4×C127C4⋊C411yescharacteristic
92C22×C4×C127C4⋊C411yescharacteristic
93C22×C4×C127C22×C411yescharacteristic
94C22×C4×C127C2×D412yes—
95M16×C127—28no—
96M16×C127—44no—
97M16×C127—44no—
98M16×C127—44no—
99M16×C127—42no—
100M16×C127—42no—
101M16×C127—42no—
102M16×C127—42no—
103C2×C8×C127—22no—
104C2×C8×C127—22no—
105C2×C8×C127—42no—
106C2×C8×C127—44no—
107C2×C8×C127—44no—
108C2×C8×C127—44no—
109C2×C8×C127—42no—
110C23×C127—22no—
111C23×C127—22no—
112C23×C127—22no—
113C23×C127—82no—
114C23×C127—81no—
115C23×C127#9512yes—
116C23×C127#9511yescharacteristic
117C23×C127#9511yescharacteristic
118C23×C127C2×C4211yescharacteristic
119C23×C127C2×C4⋊C412yes—
120Q8×C127—42no—
121Q8×C127—41no—
122Q8×C127—41no—
123D4×C127—42no—
124D4×C127—42no—
125D4×C127—42no—
126D4×C127—42no—
127D4×C127—41no—
128D4×C127—42no—
129D4×C127—41no—
130C2×C4×C127—22no—
131C2×C4×C127—22no—
132C2×C4×C127—22no—
133C2×C4×C127—22no—
134C2×C4×C127—22no—
135C2×C4×C127—22no—
136C2×C4×C127—22no—
137C2×C4×C127—22no—
138C2×C4×C127—22no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—22no—
142C2×C4×C127—22no—
143C2×C4×C127—21no—
144C2×C4×C127—22no—
145C2×C4×C127—21no—
146C2×C4×C127—22no—
147C2×C4×C127#9511yescharacteristic
148C2×C4×C127#9512yes—
149C2×C4×C127#9511yescharacteristic
150C2×C4×C127#9912yes—
151C2×C4×C127#9912yes—
152C2×C4×C127C2×C22⋊C412yes—
153C2×C4×C127C2×C22⋊C411yescharacteristic
154C2×C4×C127C2×C4⋊C411yescharacteristic
155C8×C127—48no—
156C8×C127—42no—
157C8×C127—42no—
158C22×C127—22no—
159C22×C127—21no—
160C22×C127—21no—
161C22×C127—22no—
162C22×C127—41no—
163C22×C127—42no—
164C22×C127—41no—
165C22×C127—41no—
166C22×C127—42no—
167C22×C127—44no—
168C22×C127—82no—
169C22×C127—82no—
170C22×C127#34212yes—
171C22×C127C2×#9511yescharacteristic
172C4×C127—22no—
173C4×C127—22no—
174C4×C127—21no—
175C4×C127—21no—
176C4×C127#34212yes—
177C4×C127C2×#9911yescharacteristic
178C4×C127C2×#9911yescharacteristic
179#12579C12711yesmaximal, characteristic, direct product factor, Sylow
180C2×C127—21no—
181C2×C127—22no—
182C2×C127—42no—
183C2×C127—42no—
184C2×C127—41no—
185C2×C127—41no—
186C2×C127C2×#34211yescharacteristic
187C2×#413C2×C12712yes—
188#2879C2×C12711yescharacteristic
189#1392C2×C12714yescomplemented
190C127#1257911yescharacteristic, direct product factor, Sylow
191C22×#41C22×C12711yescharacteristic
192C22×M16—22no—
193C22×M16C4×C12711yescharacteristic
194C22×M16C4×C12711yescharacteristic
195#413—22no—
196#413—22no—
197#413C4×C12714yes—
198#413C22×C12714yes—
199C2×#101—22no—
200C2×#100C4×C12714yes—
201#408—22no—
202#408C4×C12712yes—
203#408C22×C12712yes—
204#407—22no—
205C2×#41—42no—
206C2×#41—42no—
207C2×#41C2×C4×C12712yes—
208C2×#41C2×C4×C12711yescharacteristic
209C2×#41D4×C12711yescharacteristic
210C2×#41D4×C12712yes—
211C2×#41Q8×C12711yescharacteristic
212C2×#41C23×C12711yescharacteristic
213C22×Q8D4×C12711yescharacteristic
214C22×D4C2×C4×C12712yes—
215C22×D4Q8×C12711yescharacteristic
216C23×C4C2×C4×C12711yescharacteristic
217C23×C4D4×C12712yes—
218C2×M16—21no—
219C2×M16—21no—
220C2×M16—21no—
221C2×M16—24no—
222C2×M16—24no—
223C2×M16—24no—
224C2×M16—42no—
225C2×M16—42no—
226C2×M16—42no—
227C2×M16—42no—
228C2×M16—42no—
229C2×M16C2×C4×C12712yes—
230C22×C8—21no—
231C22×C8—42no—
232C22×C8C2×C4×C12712yes—
233#101—24no—
234#101—24no—
235#100—24no—
236#100C2×C4×C12718yes—
237C22⋊C8—24no—
238C22⋊C8—24no—
239C24C42×C12711yescharacteristic
240C24C4⋊C4×C12712yes—
241#41—42no—
242#41—42no—
243#41—41no—
244#41—41no—
245#41—42no—
246#41—42no—
247#41—42no—
248#41—42no—
249#41—41no—
250#41—41no—
251C2×Q8—42no—
252C2×Q8C22⋊C4×C12712yes—
253C2×Q8C4⋊C4×C12711yescharacteristic
254C2×Q8C2×D4×C12711yescharacteristic
255C2×D4—42no—
256C2×D4—42no—
257C2×D4—42no—
258C2×D4C42×C12712yes—
259C2×D4C22⋊C4×C12712yes—
260C2×D4C4⋊C4×C12712yes—
261C2×D4C4⋊C4×C12712yes—
262C2×D4C4⋊C4×C12711yescharacteristic
263C2×D4C22×C4×C12712yes—
264C2×D4C2×Q8×C12711yescharacteristic
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4C42×C12711yescharacteristic
272C22×C4C22⋊C4×C12712yes—
273C22×C4C22⋊C4×C12711yescharacteristic
274C22×C4C22⋊C4×C12712yes—
275C22×C4C22⋊C4×C12712yes—
276C22×C4C22⋊C4×C12711yescharacteristic
277C22×C4C4⋊C4×C12712yes—
278C22×C4C4⋊C4×C12711yescharacteristic
279C22×C4C4⋊C4×C12711yescharacteristic
280C22×C4C22×C4×C12711yescharacteristic
281C22×C4C2×D4×C12712yes—
282M16—28no—
283M16—44no—
284M16—44no—
285M16—44no—
286M16—42no—
287M16—42no—
288M16—42no—
289M16—42no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—42no—
293C2×C8—44no—
294C2×C8—44no—
295C2×C8—44no—
296C2×C8—42no—
297C23—22no—
298C23—22no—
299C23—22no—
300C23—82no—
301C23—81no—
302C23#95×C12712yes—
303C23#95×C12711yescharacteristic
304C23#95×C12711yescharacteristic
305C23C2×C42×C12711yescharacteristic
306C23C2×C4⋊C4×C12712yes—
307Q8—42no—
308Q8—41no—
309Q8—41no—
310D4—42no—
311D4—42no—
312D4—42no—
313D4—42no—
314D4—41no—
315D4—42no—
316D4—41no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—22no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—22no—
332C2×C4—22no—
333C2×C4—22no—
334C2×C4#95×C12711yescharacteristic
335C2×C4#95×C12712yes—
336C2×C4#95×C12711yescharacteristic
337C2×C4#99×C12712yes—
338C2×C4#99×C12712yes—
339C2×C4C2×C22⋊C4×C12712yes—
340C2×C4C2×C22⋊C4×C12711yescharacteristic
341C2×C4C2×C4⋊C4×C12711yescharacteristic
342C8—48no—
343C8—42no—
344C8—42no—
345C22—22no—
346C22—21no—
347C22—21no—
348C22—22no—
349C22—41no—
350C22—42no—
351C22—41no—
352C22—41no—
353C22—42no—
354C22—44no—
355C22—82no—
356C22—82no—
357C22#342×C12712yes—
358C22C2×#95×C12711yescharacteristic
359C4—22no—
360C4—22no—
361C4—21no—
362C4—21no—
363C4#342×C12712yes—
364C4C2×#99×C12711yescharacteristic
365C4C2×#99×C12711yescharacteristic
366C2—21no—
367C2—22no—
368C2—42no—
369C2—42no—
370C2—41no—
371C2—41no—
372C2C2×#342×C12711yescharacteristic
subgroupG/H
centerC4×C127C2×#99
commutatorC23C2×C42×C127
Frattini, cosocleC2×#41C23×C127
socleC2×C127C2×#342
prime radicalC22×#41×C127C22
LCSG ▷ C23 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C127 ◁ C22×C4×C127 ◁ C22×#41×C127 ◁ G

Complements

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

NH ≅ G/Ntype
3. C127×#1392C2semidirect
179. #12579C127direct (N × H)
189. #1392C2×C127semidirect
190. C127#12579direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#413×C1272
C127×#28792
C127×#13922
#12579127