Finite Group Databasebeta

← C127×#10496 #44574169

Subgroups — C127×#10496 #44574169

Order 32512.

402 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 90 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×#1967C211yesmaximal, characteristic, complemented
3C127×#1569C211yesmaximal, characteristic, complemented
4C127×#1557C211yesmaximal, characteristic, complemented
5C127×#1527C211yesmaximal, characteristic, complemented
6C127×#1525C211yesmaximal, characteristic, complemented
7C127×#1291C211yesmaximal, 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#423×C127C2211yescharacteristic
19C2×#101×C127—21no—
20C2×#100×C127—21no—
21C4×M16×C127C2211yescharacteristic
22C4×M16×C127C2211yescharacteristic
23#335×C127—21no—
24#334×C127—21no—
25#332×C127—21no—
26#331×C127—21no—
27#329×C127—21no—
28#329×C127—21no—
29#329×C127—21no—
30#329×C127—21no—
31C2×#41×C127—21no—
32C22×Q8×C127D411yescharacteristic
33C22×D4×C127D411yescharacteristic
34C2×SD16×C127—21no—
35C2×SD16×C127—21no—
36C2×D8×C127—21no—
37C2×D8×C127—21no—
38C2×M16×C127—21no—
39C2×M16×C127—21no—
40C2×M16×C127—21no—
41C4⋊Q8×C127D411yescharacteristic
42#127×C127D411yescharacteristic
43#124×C127—21no—
44#124×C127—21no—
45#124×C127—21no—
46#124×C127—21no—
47#124×C127—21no—
48#121×C127—21no—
49#121×C127—21no—
50C4×D4×C127—21no—
51C4×D4×C127—21no—
52C2×C22⋊C4×C127—21no—
53C2×C22⋊C4×C127—21no—
54C2×C42×C127C2311yescharacteristic
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57C4⋊C8×C127—21no—
58C4⋊C8×C127D411yescharacteristic
59C4⋊C8×C127D411yescharacteristic
60#103×C127—21no—
61#103×C127—21no—
62#102×C127—21no—
63#102×C127—21no—
64#101×C127—42no—
65#100×C127—42no—
66C22⋊C8×C127—21no—
67C22⋊C8×C127—21no—
68#97×C127—21no—
69#97×C127—21no—
70#97×C127—21no—
71#97×C127D411yescharacteristic
72#97×C127D411yescharacteristic
73C4×C8×C127—21no—
74C4×C8×C127—21no—
75C24×C127—21no—
76#41×C127—82no—
77C2×Q8×C127—21no—
78C2×Q8×C127—21no—
79C2×Q8×C127—21no—
80C2×Q8×C127—41no—
81C2×Q8×C127—41no—
82C2×D4×C127—21no—
83C2×D4×C127—21no—
84C2×D4×C127—21no—
85C2×D4×C127—21no—
86C2×D4×C127—21no—
87C2×D4×C127—41no—
88C2×D4×C127—41no—
89C2×D4×C127—41no—
90C22×C4×C127—21no—
91C22×C4×C127—41no—
92C22×C4×C127C2×D411yescharacteristic
93C22×C4×C127#4111yescharacteristic
94C22×C4×C127#4111yescharacteristic
95SD16×C127—81no—
96SD16×C127—81no—
97D8×C127—81no—
98D8×C127—81no—
99M16×C127—22no—
100M16×C127—42no—
101M16×C127—41no—
102M16×C127—41no—
103M16×C127—41no—
104C2×C8×C127—21no—
105C2×C8×C127—21no—
106C2×C8×C127—21no—
107C2×C8×C127—21no—
108C2×C8×C127—41no—
109C2×C8×C127—41no—
110C2×C8×C127—41no—
111C4⋊C4×C127—21no—
112C4⋊C4×C127—21no—
113C22⋊C4×C127—41no—
114C22⋊C4×C127—41no—
115C22⋊C4×C127—41no—
116C22⋊C4×C127—41no—
117C22⋊C4×C127—41no—
118C22⋊C4×C127—41no—
119C42×C127C2×D411yescharacteristic
120C42×C127C2×D411yescharacteristic
121C42×C127C2×D411yescharacteristic
122C42×C127#4111yescharacteristic
123C23×C127—42no—
124C23×C127—41no—
125C23×C127—41no—
126C23×C127—81no—
127C23×C127—81no—
128C23×C127#12311yescharacteristic
129Q8×C127—41no—
130Q8×C127—41no—
131Q8×C127—81no—
132Q8×C127—81no—
133D4×C127—41no—
134D4×C127—41no—
135D4×C127—41no—
136D4×C127—41no—
137D4×C127—81no—
138D4×C127—81no—
139D4×C127—81no—
140D4×C127—82no—
141C2×C4×C127—21no—
142C2×C4×C127—21no—
143C2×C4×C127—41no—
144C2×C4×C127—41no—
145C2×C4×C127—42no—
146C2×C4×C127—41no—
147C2×C4×C127—41no—
148C2×C4×C127—82no—
149C2×C4×C127#12011yescharacteristic
150C2×C4×C127#12111yescharacteristic
151C2×C4×C127#12111yescharacteristic
152C2×C4×C127#12111yescharacteristic
153C2×C4×C127#12311yescharacteristic
154C2×C4×C127#12411yescharacteristic
155C8×C127—22no—
156C8×C127—41no—
157C8×C127—42no—
158C8×C127—41no—
159C8×C127—41no—
160C8×C127—81no—
161C8×C127—81no—
162C22×C127—21no—
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—162no—
172C22×C127#39411yescharacteristic
173C4×C127—21no—
174C4×C127—21no—
175C4×C127—21no—
176C4×C127—21no—
177C4×C127—21no—
178C4×C127—81no—
179C4×C127—81no—
180C4×C127#45311yescharacteristic
181C4×C127#45511yescharacteristic
182#10496C12711yesmaximal, characteristic, direct product factor, Sylow
183C2×C127—41no—
184C2×C127—161no—
185C2×C127—161no—
186C2×C127#203711yescharacteristic
187C2×C127#204811yescharacteristic
188C2×C127#205011yescharacteristic
189#3213C2×C12711yescharacteristic
190#1967C2×C12711yescharacteristic, complemented
191#1569C2×C12711yescharacteristic, complemented
192#1557C2×C12711yescharacteristic, complemented
193#1527C2×C12711yescharacteristic, complemented
194#1525C2×C12711yescharacteristic, complemented
195#1291C2×C12711yescharacteristic, complemented
196C127#1049611yescharacteristic, direct product factor, Sylow
197#532C22×C12711yescharacteristic
198C2×#124C22×C12711yescharacteristic
199#496—21no—
200#489—21no—
201#463—21no—
202#463—21no—
203#448—21no—
204#447—21no—
205#432C22×C12711yescharacteristic
206#432C22×C12711yescharacteristic
207#423C22×C12711yescharacteristic
208C2×#101—21no—
209C2×#100—21no—
210C4×M16C22×C12711yescharacteristic
211C4×M16C22×C12711yescharacteristic
212#335—21no—
213#334—21no—
214#332—21no—
215#331—21no—
216#329—21no—
217#329—21no—
218#329—21no—
219#329—21no—
220C2×#41—21no—
221C22×Q8D4×C12711yescharacteristic
222C22×D4D4×C12711yescharacteristic
223C2×SD16—21no—
224C2×SD16—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×M16—21no—
228C2×M16—21no—
229C2×M16—21no—
230C4⋊Q8D4×C12711yescharacteristic
231#127D4×C12711yescharacteristic
232#124—21no—
233#124—21no—
234#124—21no—
235#124—21no—
236#124—21no—
237#121—21no—
238#121—21no—
239C4×D4—21no—
240C4×D4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—21no—
243C2×C42C23×C12711yescharacteristic
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8D4×C12711yescharacteristic
248C4⋊C8D4×C12711yescharacteristic
249#103—21no—
250#103—21no—
251#102—21no—
252#102—21no—
253#101—42no—
254#100—42no—
255C22⋊C8—21no—
256C22⋊C8—21no—
257#97—21no—
258#97—21no—
259#97—21no—
260#97D4×C12711yescharacteristic
261#97D4×C12711yescharacteristic
262C4×C8—21no—
263C4×C8—21no—
264C24—21no—
265#41—82no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×Q8—21no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C22×C4—21no—
280C22×C4—41no—
281C22×C4C2×D4×C12711yescharacteristic
282C22×C4#41×C12711yescharacteristic
283C22×C4#41×C12711yescharacteristic
284SD16—81no—
285SD16—81no—
286D8—81no—
287D8—81no—
288M16—22no—
289M16—42no—
290M16—41no—
291M16—41no—
292M16—41no—
293C2×C8—21no—
294C2×C8—21no—
295C2×C8—21no—
296C2×C8—21no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C22⋊C4—41no—
303C22⋊C4—41no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—41no—
308C42C2×D4×C12711yescharacteristic
309C42C2×D4×C12711yescharacteristic
310C42C2×D4×C12711yescharacteristic
311C42#41×C12711yescharacteristic
312C23—42no—
313C23—41no—
314C23—41no—
315C23—81no—
316C23—81no—
317C23#123×C12711yescharacteristic
318Q8—41no—
319Q8—41no—
320Q8—81no—
321Q8—81no—
322D4—41no—
323D4—41no—
324D4—41no—
325D4—41no—
326D4—81no—
327D4—81no—
328D4—81no—
329D4—82no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—82no—
338C2×C4#120×C12711yescharacteristic
339C2×C4#121×C12711yescharacteristic
340C2×C4#121×C12711yescharacteristic
341C2×C4#121×C12711yescharacteristic
342C2×C4#123×C12711yescharacteristic
343C2×C4#124×C12711yescharacteristic
344C8—22no—
345C8—41no—
346C8—42no—
347C8—41no—
348C8—41no—
349C8—81no—
350C8—81no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—81no—
355C22—81no—
356C22—81no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—162no—
361C22#394×C12711yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—81no—
368C4—81no—
369C4#453×C12711yescharacteristic
370C4#455×C12711yescharacteristic
371C2—41no—
372C2—161no—
373C2—161no—
374C2C127×#203711yescharacteristic
375C2C127×#204811yescharacteristic
376C2C127×#205011yescharacteristic
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×#1967C2semidirect
3. C127×#1569C2semidirect
4. C127×#1557C2semidirect
5. C127×#1527C2semidirect
6. C127×#1525C2semidirect
7. C127×#1291C2semidirect
182. #10496C127direct (N × H)
190. #1967C2×C127semidirect
191. #1569C2×C127semidirect
192. #1557C2×C127semidirect
193. #1527C2×C127semidirect
194. #1525C2×C127semidirect
195. #1291C2×C127semidirect
196. C127#10496direct (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×#19672
C127×#15692
C127×#15572
C127×#15272
C127×#15252
C127×#12912
#10496127