Finite Group Databasebeta

← C127×#11737 #44575410

Subgroups — C127×#11737 #44575410

Order 32512.

470 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 470 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2635C211yesmaximal, characteristic
2C4×#100×C127C211yesmaximal, characteristic, complemented
3C127×#1459C211yesmaximal, characteristic, complemented
4C127×#1353C212yesmaximal, complemented
5C127×#1345C212yesmaximal, complemented
6C2×#121×C127C411yescharacteristic
7C2×C4×D4×C127C2211yescharacteristic
8C2×#100×C127—21no—
9C2×C22⋊C8×C127—21no—
10C4×M16×C127—21no—
11#400×C127C2211yescharacteristic
12#399×C127C411yescharacteristic
13#394×C127—21no—
14#394×C127C2211yescharacteristic
15#392×C127—21no—
16#392×C127C411yescharacteristic
17#388×C127—21no—
18#386×C127—21no—
19#381×C127C411yescharacteristic
20#343×C127C2212yes—
21#324×C127C2212yes—
22#323×C127—21no—
23C22×D4×C127—21no—
24C22×D4×C127—21no—
25C22×D4×C127C2×C411yescharacteristic
26C22×D4×C127D411yescharacteristic
27C23×C4×C127C2×C411yescharacteristic
28C23×C4×C127D411yescharacteristic
29C2×M16×C127—22no—
30C22×C8×C127—41no—
31#121×C127—41no—
32#121×C127—41no—
33C4×D4×C127—41no—
34C4×D4×C127—41no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127C2×C411yescharacteristic
37C2×C4⋊C4×C127C2311yescharacteristic
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127C2×C411yescharacteristic
45C2×C22⋊C4×C127D411yescharacteristic
46C2×C42×C127D411yescharacteristic
47#100×C127—24no—
48C22⋊C8×C127—22no—
49C22⋊C8×C127—41no—
50#97×C127—41no—
51C4×C8×C127—41no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127C2×C411yescharacteristic
56#95×C127C2×C411yescharacteristic
57C24×C127—21no—
58C24×C127C22⋊C411yescharacteristic
59C24×C127C22⋊C411yescharacteristic
60C2×D4×C127—22no—
61C2×D4×C127—22no—
62C2×D4×C127—41no—
63C2×D4×C127—41no—
64C2×D4×C127—42no—
65C2×D4×C127—42no—
66C2×D4×C127—81no—
67C2×D4×C127—81no—
68C2×D4×C127—81no—
69C2×D4×C127—81no—
70C2×D4×C127—81no—
71C22×C4×C127—21no—
72C22×C4×C127—21no—
73C22×C4×C127—21no—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—81no—
79C22×C4×C127—81no—
80C22×C4×C127C22⋊C411yescharacteristic
81C22×C4×C127C22⋊C411yescharacteristic
82C22×C4×C127C22×C411yescharacteristic
83C22×C4×C127C2×D411yescharacteristic
84C22×C4×C127C2×D411yescharacteristic
85M16×C127—24no—
86M16×C127—42no—
87C2×C8×C127—42no—
88C2×C8×C127—42no—
89C2×C8×C127—82no—
90C4⋊C4×C127—41no—
91C4⋊C4×C127—41no—
92C4⋊C4×C127—81no—
93C22⋊C4×C127—41no—
94C22⋊C4×C127—41no—
95C22⋊C4×C127—41no—
96C22⋊C4×C127—41no—
97C22⋊C4×C127—42no—
98C22⋊C4×C127—81no—
99C22⋊C4×C127—81no—
100C22⋊C4×C127—81no—
101C22⋊C4×C127—81no—
102C42×C127—21no—
103C42×C127—21no—
104C23×C127—21no—
105C23×C127—21no—
106C23×C127—21no—
107C23×C127—21no—
108C23×C127—21no—
109C23×C127—41no—
110C23×C127—41no—
111C23×C127—41no—
112C23×C127—41no—
113C23×C127—41no—
114C23×C127—41no—
115C23×C127—41no—
116C23×C127—41no—
117C23×C127—41no—
118C23×C127—41no—
119C23×C127—41no—
120C23×C127#10412yes—
121C23×C127C2×C22⋊C411yescharacteristic
122D4×C127—44no—
123D4×C127—82no—
124D4×C127—84no—
125D4×C127—84no—
126C2×C4×C127—21no—
127C2×C4×C127—21no—
128C2×C4×C127—21no—
129C2×C4×C127—21no—
130C2×C4×C127—21no—
131C2×C4×C127—41no—
132C2×C4×C127—42no—
133C2×C4×C127—41no—
134C2×C4×C127—41no—
135C2×C4×C127—41no—
136C2×C4×C127—41no—
137C2×C4×C127—41no—
138C2×C4×C127—41no—
139C2×C4×C127—41no—
140C2×C4×C127—41no—
141C2×C4×C127—41no—
142C2×C4×C127—41no—
143C2×C4×C127—41no—
144C2×C4×C127—41no—
145C2×C4×C127—81no—
146C2×C4×C127—81no—
147C2×C4×C127—81no—
148C2×C4×C127#9911yescharacteristic
149C2×C4×C127#9911yescharacteristic
150C2×C4×C127#13512yes—
151C8×C127—44no—
152C8×C127—82no—
153C22×C127—21no—
154C22×C127—21no—
155C22×C127—22no—
156C22×C127—42no—
157C22×C127—41no—
158C22×C127—41no—
159C22×C127—41no—
160C22×C127—41no—
161C22×C127—41no—
162C22×C127—81no—
163C22×C127—81no—
164C22×C127—81no—
165C22×C127—81no—
166C22×C127—81no—
167C22×C127—81no—
168C22×C127—81no—
169C22×C127—81no—
170C22×C127—81no—
171C22×C127—81no—
172C22×C127C2×#9911yescharacteristic
173C22×C127#41611yescharacteristic
174C22×C127C2×#10411yescharacteristic
175C4×C127—21no—
176C4×C127—21no—
177C4×C127—22no—
178C4×C127—41no—
179C4×C127—41no—
180C4×C127—41no—
181C4×C127—81no—
182C4×C127—81no—
183C4×C127—81no—
184#11737C12711yesmaximal, characteristic, direct product factor, Sylow
185C2×C127—21no—
186C2×C127—21no—
187C2×C127—42no—
188C2×C127—81no—
189C2×C127—161no—
190C2×C127#150111yescharacteristic
191C2×C127#212111yescharacteristic
192C2×C127#213411yescharacteristic
193#2635C2×C12711yescharacteristic
194C4×#100C2×C12711yescharacteristic, complemented
195#1459C2×C12711yescharacteristic, complemented
196#1353C2×C12712yescomplemented
197#1345C2×C12712yescomplemented
198C127#1173711yescharacteristic, direct product factor, Sylow
199C2×#121C4×C12711yescharacteristic
200C2×C4×D4C22×C12711yescharacteristic
201C2×#100—21no—
202C2×C22⋊C8—21no—
203C4×M16—21no—
204#400C22×C12711yescharacteristic
205#399C4×C12711yescharacteristic
206#394—21no—
207#394C22×C12711yescharacteristic
208#392—21no—
209#392C4×C12711yescharacteristic
210#388—21no—
211#386—21no—
212#381C4×C12711yescharacteristic
213#343C22×C12712yes—
214#324C22×C12712yes—
215#323—21no—
216C22×D4—21no—
217C22×D4—21no—
218C22×D4C2×C4×C12711yescharacteristic
219C22×D4D4×C12711yescharacteristic
220C23×C4C2×C4×C12711yescharacteristic
221C23×C4D4×C12711yescharacteristic
222C2×M16—22no—
223C22×C8—41no—
224#121—41no—
225#121—41no—
226C4×D4—41no—
227C4×D4—41no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4C2×C4×C12711yescharacteristic
230C2×C4⋊C4C23×C12711yescharacteristic
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C22⋊C4—21no—
234C2×C22⋊C4—21no—
235C2×C22⋊C4—21no—
236C2×C22⋊C4—21no—
237C2×C22⋊C4C2×C4×C12711yescharacteristic
238C2×C22⋊C4D4×C12711yescharacteristic
239C2×C42D4×C12711yescharacteristic
240#100—24no—
241C22⋊C8—22no—
242C22⋊C8—41no—
243#97—41no—
244C4×C8—41no—
245#95—21no—
246#95—21no—
247#95—21no—
248#95C2×C4×C12711yescharacteristic
249#95C2×C4×C12711yescharacteristic
250C24—21no—
251C24C22⋊C4×C12711yescharacteristic
252C24C22⋊C4×C12711yescharacteristic
253C2×D4—22no—
254C2×D4—22no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—42no—
258C2×D4—42no—
259C2×D4—81no—
260C2×D4—81no—
261C2×D4—81no—
262C2×D4—81no—
263C2×D4—81no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—21no—
271C22×C4—81no—
272C22×C4—81no—
273C22×C4C22⋊C4×C12711yescharacteristic
274C22×C4C22⋊C4×C12711yescharacteristic
275C22×C4C22×C4×C12711yescharacteristic
276C22×C4C2×D4×C12711yescharacteristic
277C22×C4C2×D4×C12711yescharacteristic
278M16—24no—
279M16—42no—
280C2×C8—42no—
281C2×C8—42no—
282C2×C8—82no—
283C4⋊C4—41no—
284C4⋊C4—41no—
285C4⋊C4—81no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—42no—
291C22⋊C4—81no—
292C22⋊C4—81no—
293C22⋊C4—81no—
294C22⋊C4—81no—
295C42—21no—
296C42—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23—21no—
302C23—41no—
303C23—41no—
304C23—41no—
305C23—41no—
306C23—41no—
307C23—41no—
308C23—41no—
309C23—41no—
310C23—41no—
311C23—41no—
312C23—41no—
313C23#104×C12712yes—
314C23C2×C22⋊C4×C12711yescharacteristic
315D4—44no—
316D4—82no—
317D4—84no—
318D4—84no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—41no—
325C2×C4—42no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4#99×C12711yescharacteristic
342C2×C4#99×C12711yescharacteristic
343C2×C4#135×C12712yes—
344C8—44no—
345C8—82no—
346C22—21no—
347C22—21no—
348C22—22no—
349C22—42no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22C2×#99×C12711yescharacteristic
366C22#416×C12711yescharacteristic
367C22C2×#104×C12711yescharacteristic
368C4—21no—
369C4—21no—
370C4—22no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—81no—
375C4—81no—
376C4—81no—
377C2—21no—
378C2—21no—
379C2—42no—
380C2—81no—
381C2—161no—
382C2C127×#150111yescharacteristic
383C2C127×#212111yescharacteristic
384C2C127×#213411yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC127×#2635C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C4×#100×C127C2semidirect
3. C127×#1459C2semidirect
4. C127×#1353C2semidirect
5. C127×#1345C2semidirect
184. #11737C127direct (N × H)
194. C4×#100C2×C127semidirect
195. #1459C2×C127semidirect
196. #1353C2×C127semidirect
197. #1345C2×C127semidirect
198. C127#11737direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#26352
C4×#100×C1272
C127×#14592
C127×#13532
C127×#13452
#11737127