Finite Group Databasebeta

← C127×#12119 #44575792

Subgroups — C127×#12119 #44575792

Order 32512.

404 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 70 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×#3204C211yesmaximal, characteristic, complemented
2C127×#2191C211yesmaximal, characteristic, complemented
3C127×#2190C211yesmaximal, characteristic, complemented
4C127×#2017C211yesmaximal, characteristic, complemented
5C127×#1342C211yesmaximal, characteristic, complemented
6C127×#1341C211yesmaximal, characteristic, complemented
7C127×#1321C211yesmaximal, characteristic, complemented
8#575×C127—21no—
9#575×C127C2211yescharacteristic
10#537×C127—21no—
11#510×C127—21no—
12#509×C127—21no—
13#483×C127—21no—
14#481×C127—21no—
15#470×C127C2211yescharacteristic
16#469×C127C2211yescharacteristic
17#465×C127—21no—
18#452×C127—21no—
19#449×C127—21no—
20#408×C127—21no—
21#408×C127C2211yescharacteristic
22#360×C127—21no—
23#360×C127—21no—
24#349×C127C2211yescharacteristic
25#349×C127C2211yescharacteristic
26#338×C127C2211yescharacteristic
27C2×#41×C127—21no—
28C2×#41×C127—21no—
29C2×#41×C127D411yescharacteristic
30#137×C127—41no—
31#137×C127—41no—
32#137×C127—41no—
33AGL(1,ℤ/8)×C127—41no—
34AGL(1,ℤ/8)×C127—41no—
35AGL(1,ℤ/8)×C127—41no—
36#135×C127—21no—
37#135×C127—21no—
38#135×C127—42no—
39C2×Q16×C127D411yescharacteristic
40C2×SD16×C127—21no—
41C2×D8×C127D411yescharacteristic
42C2×M16×C127—21no—
43C2×M16×C127C2311yescharacteristic
44C22×C8×C127D411yescharacteristic
45C22⋊Q8×C127—21no—
46C22⋊Q8×C127—21no—
47C22⋊Q8×C127—41no—
48#121×C127—21no—
49#121×C127—21no—
50#121×C127—41no—
51#121×C127—41no—
52#121×C127—41no—
53C2×C4⋊C4×C127—21no—
54Q32×C127—41no—
55SD32×C127—41no—
56SD32×C127—41no—
57D16×C127—41no—
58M32×C127—21no—
59M32×C127—21no—
60#106×C127—21no—
61#106×C127D411yescharacteristic
62#106×C127D411yescharacteristic
63#103×C127—21no—
64#103×C127—21no—
65#102×C127—21no—
66#102×C127—21no—
67C22⋊C8×C127—21no—
68C22⋊C8×C127—21no—
69C22⋊C8×C127—42no—
70#41×C127—41no—
71#41×C127—41no—
72#41×C127—41no—
73#41×C127—41no—
74#41×C127—41no—
75#41×C127—41no—
76#41×C127—81no—
77#41×C127—81no—
78C2×Q8×C127—21no—
79C2×Q8×C127—21no—
80C2×Q8×C127D811yescharacteristic
81C2×D4×C127—21no—
82C2×D4×C127—21no—
83C2×D4×C127—21no—
84C2×D4×C127—41no—
85C2×D4×C127—41no—
86C2×D4×C127—41no—
87C2×D4×C127—41no—
88C2×D4×C127D811yescharacteristic
89C22×C4×C127—21no—
90C22×C4×C127—41no—
91C22×C4×C127—41no—
92C22×C4×C127—41no—
93C22×C4×C127C2×D411yescharacteristic
94Q16×C127—21no—
95Q16×C127—21no—
96Q16×C127—41no—
97Q16×C127—42no—
98SD16×C127—41no—
99SD16×C127—41no—
100SD16×C127—42no—
101SD16×C127—42no—
102SD16×C127—81no—
103D8×C127—21no—
104D8×C127—21no—
105D8×C127—41no—
106D8×C127—42no—
107M16×C127—41no—
108M16×C127—41no—
109M16×C127—41no—
110C2×C8×C127—22no—
111C2×C8×C127—21no—
112C2×C8×C127—41no—
113C2×C8×C127C2×D411yescharacteristic
114C2×C8×C127C2×D411yescharacteristic
115C4⋊C4×C127—21no—
116C4⋊C4×C127—21no—
117C4⋊C4×C127—41no—
118C4⋊C4×C127—41no—
119C4⋊C4×C127—41no—
120C22⋊C4×C127—41no—
121C22⋊C4×C127—41no—
122C22⋊C4×C127—41no—
123C22⋊C4×C127—41no—
124C16×C127—41no—
125C16×C127—41no—
126C23×C127—21no—
127C23×C127—41no—
128C23×C127—41no—
129C23×C127AGL(1,ℤ/8)11yescharacteristic
130Q8×C127—41no—
131Q8×C127—41no—
132Q8×C127—41no—
133Q8×C127—41no—
134Q8×C127—41no—
135D4×C127—41no—
136D4×C127—41no—
137D4×C127—41no—
138D4×C127—41no—
139D4×C127—41no—
140D4×C127—81no—
141D4×C127—81no—
142D4×C127—82no—
143D4×C127—81no—
144D4×C127—161no—
145D4×C127—161no—
146C2×C4×C127—21no—
147C2×C4×C127—21no—
148C2×C4×C127—21no—
149C2×C4×C127—41no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—41no—
153C2×C4×C127—41no—
154C2×C4×C127—41no—
155C2×C4×C127—81no—
156C2×C4×C127—82no—
157C2×C4×C127—81no—
158C2×C4×C127—161no—
159C2×C4×C127#12011yescharacteristic
160C2×C4×C127C2×D811yescharacteristic
161C8×C127—21no—
162C8×C127—21no—
163C8×C127—42no—
164C8×C127—41no—
165C22×C127—21no—
166C22×C127—41no—
167C22×C127—41no—
168C22×C127—41no—
169C22×C127—41no—
170C22×C127—81no—
171C22×C127—81no—
172C22×C127—82no—
173C22×C127—81no—
174C22×C127—81no—
175C22×C127#44711yescharacteristic
176C4×C127—21no—
177C4×C127—41no—
178C4×C127—81no—
179C4×C127—81no—
180C4×C127—81no—
181C4×C127—81no—
182C4×C127#45311yescharacteristic
183C4×C127B(4,𝔽2)11yescharacteristic
184#12119C12711yesmaximal, characteristic, direct product factor, Sylow
185C2×C127—21no—
186C2×C127—41no—
187C2×C127—81no—
188C2×C127—161no—
189C2×C127—161no—
190C2×C127#159511yescharacteristic
191#3204C2×C12711yescharacteristic, complemented
192#2191C2×C12711yescharacteristic, complemented
193#2190C2×C12711yescharacteristic, complemented
194#2017C2×C12711yescharacteristic, complemented
195#1342C2×C12711yescharacteristic, complemented
196#1341C2×C12711yescharacteristic, complemented
197#1321C2×C12711yescharacteristic, complemented
198C127#1211911yescharacteristic, direct product factor, Sylow
199#575—21no—
200#575C22×C12711yescharacteristic
201#537—21no—
202#510—21no—
203#509—21no—
204#483—21no—
205#481—21no—
206#470C22×C12711yescharacteristic
207#469C22×C12711yescharacteristic
208#465—21no—
209#452—21no—
210#449—21no—
211#408—21no—
212#408C22×C12711yescharacteristic
213#360—21no—
214#360—21no—
215#349C22×C12711yescharacteristic
216#349C22×C12711yescharacteristic
217#338C22×C12711yescharacteristic
218C2×#41—21no—
219C2×#41—21no—
220C2×#41D4×C12711yescharacteristic
221#137—41no—
222#137—41no—
223#137—41no—
224AGL(1,ℤ/8)—41no—
225AGL(1,ℤ/8)—41no—
226AGL(1,ℤ/8)—41no—
227#135—21no—
228#135—21no—
229#135—42no—
230C2×Q16D4×C12711yescharacteristic
231C2×SD16—21no—
232C2×D8D4×C12711yescharacteristic
233C2×M16—21no—
234C2×M16C23×C12711yescharacteristic
235C22×C8D4×C12711yescharacteristic
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—41no—
239#121—21no—
240#121—21no—
241#121—41no—
242#121—41no—
243#121—41no—
244C2×C4⋊C4—21no—
245Q32—41no—
246SD32—41no—
247SD32—41no—
248D16—41no—
249M32—21no—
250M32—21no—
251#106—21no—
252#106D4×C12711yescharacteristic
253#106D4×C12711yescharacteristic
254#103—21no—
255#103—21no—
256#102—21no—
257#102—21no—
258C22⋊C8—21no—
259C22⋊C8—21no—
260C22⋊C8—42no—
261#41—41no—
262#41—41no—
263#41—41no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—81no—
268#41—81no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8D8×C12711yescharacteristic
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—41no—
279C2×D4D8×C12711yescharacteristic
280C22×C4—21no—
281C22×C4—41no—
282C22×C4—41no—
283C22×C4—41no—
284C22×C4C2×D4×C12711yescharacteristic
285Q16—21no—
286Q16—21no—
287Q16—41no—
288Q16—42no—
289SD16—41no—
290SD16—41no—
291SD16—42no—
292SD16—42no—
293SD16—81no—
294D8—21no—
295D8—21no—
296D8—41no—
297D8—42no—
298M16—41no—
299M16—41no—
300M16—41no—
301C2×C8—22no—
302C2×C8—21no—
303C2×C8—41no—
304C2×C8C2×D4×C12711yescharacteristic
305C2×C8C2×D4×C12711yescharacteristic
306C4⋊C4—21no—
307C4⋊C4—21no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—41no—
311C22⋊C4—41no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C16—41no—
316C16—41no—
317C23—21no—
318C23—41no—
319C23—41no—
320C23AGL(1,ℤ/8)×C12711yescharacteristic
321Q8—41no—
322Q8—41no—
323Q8—41no—
324Q8—41no—
325Q8—41no—
326D4—41no—
327D4—41no—
328D4—41no—
329D4—41no—
330D4—41no—
331D4—81no—
332D4—81no—
333D4—82no—
334D4—81no—
335D4—161no—
336D4—161no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—81no—
347C2×C4—82no—
348C2×C4—81no—
349C2×C4—161no—
350C2×C4#120×C12711yescharacteristic
351C2×C4C2×D8×C12711yescharacteristic
352C8—21no—
353C8—21no—
354C8—42no—
355C8—41no—
356C22—21no—
357C22—41no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—81no—
362C22—81no—
363C22—82no—
364C22—81no—
365C22—81no—
366C22#447×C12711yescharacteristic
367C4—21no—
368C4—41no—
369C4—81no—
370C4—81no—
371C4—81no—
372C4—81no—
373C4#453×C12711yescharacteristic
374C4B(4,𝔽2)×C12711yescharacteristic
375C2—21no—
376C2—41no—
377C2—81no—
378C2—161no—
379C2—161no—
380C2C127×#159511yescharacteristic
subgroupG/H
center, socleC2×C127#1595
commutator, Frattini, cosocleC2×M16C23×C127
LCSG ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C2×C4×C127 ◁ C2×M16×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#3204C2semidirect
2. C127×#2191C2semidirect
3. C127×#2190C2semidirect
4. C127×#2017C2semidirect
5. C127×#1342C2semidirect
6. C127×#1341C2semidirect
7. C127×#1321C2semidirect
184. #12119C127direct (N × H)
191. #3204C2×C127semidirect
192. #2191C2×C127semidirect
193. #2190C2×C127semidirect
194. #2017C2×C127semidirect
195. #1342C2×C127semidirect
196. #1341C2×C127semidirect
197. #1321C2×C127semidirect
198. C127#12119direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32042
C127×#21912
C127×#21902
C127×#20172
C127×#13422
C127×#13412
C127×#13212
#12119127