Finite Group Databasebeta

← C127×#10508 #44574181

Subgroups — C127×#10508 #44574181

Order 32512.

414 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 94 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×#3213C211yesmaximal, characteristic
2C127×#1983C211yesmaximal, characteristic, complemented
3C127×#1573C211yesmaximal, characteristic, complemented
4C127×#1551C211yesmaximal, characteristic, complemented
5C127×#1502C211yesmaximal, characteristic, complemented
6C127×#1469C211yesmaximal, characteristic, complemented
7C127×#1285C211yesmaximal, characteristic, complemented
8#532×C127C2211yescharacteristic
9C2×#124×C127C2211yescharacteristic
10#496×C127—21no—
11#489×C127—21no—
12#463×C127—21no—
13#463×C127—21no—
14#448×C127—21no—
15#447×C127—21no—
16#432×C127C2211yescharacteristic
17#432×C127C2211yescharacteristic
18#431×C127C2211yescharacteristic
19C2×C4⋊C8×C127C2211yescharacteristic
20C2×#103×C127—21no—
21C2×#102×C127—21no—
22C4×C4⋊C4×C127C2211yescharacteristic
23#335×C127—21no—
24#334×C127—21no—
25#333×C127—21no—
26#331×C127—21no—
27#327×C127—22no—
28#323×C127—22no—
29C2×#41×C127—21no—
30C22×Q8×C127D411yescharacteristic
31C22×D4×C127D411yescharacteristic
32C2×SD16×C127—21no—
33C2×SD16×C127—21no—
34C2×D8×C127—21no—
35C2×D8×C127—21no—
36C22×C8×C127—21no—
37C4⋊Q8×C127D411yescharacteristic
38#127×C127D411yescharacteristic
39#124×C127—21no—
40#124×C127—21no—
41#124×C127—21no—
42#124×C127—21no—
43#124×C127—21no—
44#121×C127—21no—
45#121×C127—21no—
46C4×D4×C127—21no—
47C4×D4×C127—21no—
48C2×C4⋊C4×C127—21no—
49C2×C22⋊C4×C127—21no—
50C2×C22⋊C4×C127—21no—
51C2×C42×C127—21no—
52C2×C42×C127C2311yescharacteristic
53C4⋊C8×C127—21no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57C4⋊C8×C127D411yescharacteristic
58C4⋊C8×C127D411yescharacteristic
59#103×C127—21no—
60#103×C127—21no—
61#103×C127—42no—
62#102×C127—21no—
63#102×C127—21no—
64#102×C127—42no—
65C22⋊C8×C127—21no—
66C22⋊C8×C127—21no—
67C22⋊C8×C127D412yes—
68#97×C127—21no—
69#97×C127—21no—
70C4×C8×C127—21no—
71#95×C127—21no—
72C24×C127—21no—
73#41×C127—81no—
74#41×C127—81no—
75C2×Q8×C127—21no—
76C2×Q8×C127—21no—
77C2×Q8×C127—21no—
78C2×Q8×C127—41no—
79C2×Q8×C127—41no—
80C2×D4×C127—21no—
81C2×D4×C127—21no—
82C2×D4×C127—21no—
83C2×D4×C127—21no—
84C2×D4×C127—21no—
85C2×D4×C127—41no—
86C2×D4×C127—41no—
87C2×D4×C127—41no—
88C22×C4×C127—21no—
89C22×C4×C127—41no—
90C22×C4×C127—41no—
91C22×C4×C127C2×D411yescharacteristic
92C22×C4×C127C2×D411yescharacteristic
93C22×C4×C127#4111yescharacteristic
94SD16×C127—81no—
95SD16×C127—81no—
96D8×C127—81no—
97D8×C127—81no—
98C2×C8×C127—21no—
99C2×C8×C127—21no—
100C2×C8×C127—22no—
101C2×C8×C127—41no—
102C2×C8×C127—41no—
103C2×C8×C127—41no—
104C2×C8×C127—41no—
105C4⋊C4×C127—22no—
106C4⋊C4×C127—21no—
107C4⋊C4×C127—21no—
108C4⋊C4×C127—41no—
109C22⋊C4×C127—41no—
110C22⋊C4×C127—41no—
111C22⋊C4×C127—41no—
112C22⋊C4×C127—41no—
113C22⋊C4×C127—41no—
114C22⋊C4×C127—41no—
115C42×C127—81no—
116C42×C127C2×D411yescharacteristic
117C42×C127C2×D411yescharacteristic
118C42×C127#4111yescharacteristic
119C42×C127#4111yescharacteristic
120C23×C127—41no—
121C23×C127—41no—
122C23×C127—41no—
123C23×C127—41no—
124C23×C127—81no—
125C23×C127—81no—
126C23×C127#12111yescharacteristic
127Q8×C127—42no—
128Q8×C127—41no—
129Q8×C127—41no—
130Q8×C127—81no—
131D4×C127—42no—
132D4×C127—41no—
133D4×C127—41no—
134D4×C127—41no—
135D4×C127—41no—
136D4×C127—81no—
137D4×C127—81no—
138D4×C127—81no—
139D4×C127—81no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—21no—
143C2×C4×C127—21no—
144C2×C4×C127—41no—
145C2×C4×C127—42no—
146C2×C4×C127—41no—
147C2×C4×C127—41no—
148C2×C4×C127—82no—
149C2×C4×C127—81no—
150C2×C4×C127—81no—
151C2×C4×C127—81no—
152C2×C4×C127#12011yescharacteristic
153C2×C4×C127#12111yescharacteristic
154C2×C4×C127#12111yescharacteristic
155C2×C4×C127#12311yescharacteristic
156C2×C4×C127#12311yescharacteristic
157C2×C4×C127#12411yescharacteristic
158C8×C127—42no—
159C8×C127—41no—
160C8×C127—41no—
161C8×C127—81no—
162C8×C127—81no—
163C22×C127—21no—
164C22×C127—21no—
165C22×C127—81no—
166C22×C127—81no—
167C22×C127—81no—
168C22×C127—81no—
169C22×C127—81no—
170C22×C127—81no—
171C22×C127—161no—
172C22×C127—161no—
173C22×C127#39411yescharacteristic
174C22×C127#47111yescharacteristic
175C22×C127#47211yescharacteristic
176C4×C127—21no—
177C4×C127—21no—
178C4×C127—21no—
179C4×C127—21no—
180C4×C127—21no—
181C4×C127—82no—
182C4×C127—81no—
183C4×C127—81no—
184C4×C127#45311yescharacteristic
185C4×C127#45511yescharacteristic
186#10508C12711yesmaximal, characteristic, direct product factor, Sylow
187C2×C127—21no—
188C2×C127—21no—
189C2×C127—161no—
190C2×C127—161no—
191C2×C127#203711yescharacteristic
192C2×C127#205111yescharacteristic
193C2×C127#205311yescharacteristic
194#3213C2×C12711yescharacteristic
195#1983C2×C12711yescharacteristic, complemented
196#1573C2×C12711yescharacteristic, complemented
197#1551C2×C12711yescharacteristic, complemented
198#1502C2×C12711yescharacteristic, complemented
199#1469C2×C12711yescharacteristic, complemented
200#1285C2×C12711yescharacteristic, complemented
201C127#1050811yescharacteristic, direct product factor, Sylow
202#532C22×C12711yescharacteristic
203C2×#124C22×C12711yescharacteristic
204#496—21no—
205#489—21no—
206#463—21no—
207#463—21no—
208#448—21no—
209#447—21no—
210#432C22×C12711yescharacteristic
211#432C22×C12711yescharacteristic
212#431C22×C12711yescharacteristic
213C2×C4⋊C8C22×C12711yescharacteristic
214C2×#103—21no—
215C2×#102—21no—
216C4×C4⋊C4C22×C12711yescharacteristic
217#335—21no—
218#334—21no—
219#333—21no—
220#331—21no—
221#327—22no—
222#323—22no—
223C2×#41—21no—
224C22×Q8D4×C12711yescharacteristic
225C22×D4D4×C12711yescharacteristic
226C2×SD16—21no—
227C2×SD16—21no—
228C2×D8—21no—
229C2×D8—21no—
230C22×C8—21no—
231C4⋊Q8D4×C12711yescharacteristic
232#127D4×C12711yescharacteristic
233#124—21no—
234#124—21no—
235#124—21no—
236#124—21no—
237#124—21no—
238#121—21no—
239#121—21no—
240C4×D4—21no—
241C4×D4—21no—
242C2×C4⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C42—21no—
246C2×C42C23×C12711yescharacteristic
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8D4×C12711yescharacteristic
252C4⋊C8D4×C12711yescharacteristic
253#103—21no—
254#103—21no—
255#103—42no—
256#102—21no—
257#102—21no—
258#102—42no—
259C22⋊C8—21no—
260C22⋊C8—21no—
261C22⋊C8D4×C12712yes—
262#97—21no—
263#97—21no—
264C4×C8—21no—
265#95—21no—
266C24—21no—
267#41—81no—
268#41—81no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—21no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C22×C4—21no—
283C22×C4—41no—
284C22×C4—41no—
285C22×C4C2×D4×C12711yescharacteristic
286C22×C4C2×D4×C12711yescharacteristic
287C22×C4#41×C12711yescharacteristic
288SD16—81no—
289SD16—81no—
290D8—81no—
291D8—81no—
292C2×C8—21no—
293C2×C8—21no—
294C2×C8—22no—
295C2×C8—41no—
296C2×C8—41no—
297C2×C8—41no—
298C2×C8—41no—
299C4⋊C4—22no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C22⋊C4—41no—
309C42—81no—
310C42C2×D4×C12711yescharacteristic
311C42C2×D4×C12711yescharacteristic
312C42#41×C12711yescharacteristic
313C42#41×C12711yescharacteristic
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—81no—
319C23—81no—
320C23#121×C12711yescharacteristic
321Q8—42no—
322Q8—41no—
323Q8—41no—
324Q8—81no—
325D4—42no—
326D4—41no—
327D4—41no—
328D4—41no—
329D4—41no—
330D4—81no—
331D4—81no—
332D4—81no—
333D4—81no—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—82no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4#120×C12711yescharacteristic
347C2×C4#121×C12711yescharacteristic
348C2×C4#121×C12711yescharacteristic
349C2×C4#123×C12711yescharacteristic
350C2×C4#123×C12711yescharacteristic
351C2×C4#124×C12711yescharacteristic
352C8—42no—
353C8—41no—
354C8—41no—
355C8—81no—
356C8—81no—
357C22—21no—
358C22—21no—
359C22—81no—
360C22—81no—
361C22—81no—
362C22—81no—
363C22—81no—
364C22—81no—
365C22—161no—
366C22—161no—
367C22#394×C12711yescharacteristic
368C22#471×C12711yescharacteristic
369C22#472×C12711yescharacteristic
370C4—21no—
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—82no—
376C4—81no—
377C4—81no—
378C4#453×C12711yescharacteristic
379C4#455×C12711yescharacteristic
380C2—21no—
381C2—21no—
382C2—161no—
383C2—161no—
384C2C127×#203711yescharacteristic
385C2C127×#205111yescharacteristic
386C2C127×#205311yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3213C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1983C2semidirect
3. C127×#1573C2semidirect
4. C127×#1551C2semidirect
5. C127×#1502C2semidirect
6. C127×#1469C2semidirect
7. C127×#1285C2semidirect
186. #10508C127direct (N × H)
195. #1983C2×C127semidirect
196. #1573C2×C127semidirect
197. #1551C2×C127semidirect
198. #1502C2×C127semidirect
199. #1469C2×C127semidirect
200. #1285C2×C127semidirect
201. C127#10508direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32132
C127×#19832
C127×#15732
C127×#15512
C127×#15022
C127×#14692
C127×#12852
#10508127