Finite Group Databasebeta

← C127×#13679 #44577352

Subgroups — C127×#13679 #44577352

Order 32512.

386 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 58 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×#3288C211yesmaximal, characteristic
2C127×#2203C211yesmaximal, characteristic, complemented
3C127×#2201C211yesmaximal, characteristic, complemented
4C127×#1657C211yesmaximal, characteristic, complemented
5C127×#1406C211yesmaximal, characteristic, complemented
6C127×#1404C211yesmaximal, characteristic, complemented
7C127×#1403C211yesmaximal, characteristic, complemented
8#577×C127—21no—
9#576×C127—21no—
10#563×C127C2211yescharacteristic, complemented
11#496×C127C2211yescharacteristic
12#490×C127—21no—
13#472×C127—21no—
14#471×C127—21no—
15#458×C127—21no—
16#456×C127—21no—
17#455×C127C2211yescharacteristic
18#454×C127C2211yescharacteristic
19#453×C127—21no—
20#444×C127—21no—
21#356×C127—21no—
22#355×C127C2211yescharacteristic, complemented
23#354×C127C2211yescharacteristic, complemented
24#352×C127—21no—
25#330×C127—21no—
26#329×C127C2211yescharacteristic, complemented
272−1+4×C127D411yescharacteristic
28H(5,𝔽2)×C127—21no—
29H(5,𝔽2)×C127D411yescharacteristic
30#137×C127—21no—
31#137×C127—41no—
32#137×C127—41no—
33AGL(1,ℤ/8)×C127—21no—
34AGL(1,ℤ/8)×C127—21no—
35AGL(1,ℤ/8)×C127—21no—
36AGL(1,ℤ/8)×C127—41no—
37AGL(1,ℤ/8)×C127—41no—
38AGL(1,ℤ/8)×C127—41no—
39#135×C127—21no—
40#135×C127—41no—
41#135×C127—41no—
42C2×SD16×C127—21no—
43C2×SD16×C127—41no—
44C2×D8×C127—21no—
45C2×D8×C127—41no—
46#131×C127—21no—
47#131×C127—21no—
48C4⋊Q8×C127—21no—
49#127×C127D411yescharacteristic
50#126×C127—41no—
51#125×C127—21no—
52#124×C127C2311yescharacteristic
53#123×C127—21no—
54#123×C127—41no—
55C22⋊Q8×C127—41no—
56#108×C127—21no—
57#104×C127—21no—
58#104×C127—21no—
59#104×C127—41no—
60#102×C127—41no—
61#102×C127—41no—
62#101×C127—21no—
63#101×C127D411yescharacteristic
64#100×C127—21no—
65#100×C127D411yescharacteristic
66#99×C127—21no—
67#99×C127—41no—
68#97×C127—21no—
69#97×C127D411yescharacteristic
70#41×C127—21no—
71#41×C127—21no—
72#41×C127—41no—
73#41×C127—41no—
74#41×C127—41no—
75#41×C127—41no—
76#41×C127—41no—
77C2×Q8×C127—21no—
78C2×Q8×C127—41no—
79C2×Q8×C127C2×D411yescharacteristic
80C2×D4×C127—21no—
81C2×D4×C127—41no—
82C2×D4×C127—41no—
83C2×D4×C127—41no—
84C2×D4×C127—41no—
85C2×D4×C127—41no—
86C2×D4×C127—81no—
87C2×D4×C127C2×D411yescharacteristic
88C22×C4×C127—21no—
89Q16×C127—21no—
90Q16×C127—41no—
91Q16×C127—81no—
92SD16×C127—21no—
93SD16×C127—21no—
94SD16×C127—41no—
95SD16×C127—41no—
96SD16×C127—41no—
97SD16×C127—41no—
98SD16×C127—41no—
99SD16×C127—41no—
100SD16×C127—81no—
101D8×C127—21no—
102D8×C127—41no—
103D8×C127—41no—
104D8×C127—41no—
105D8×C127—41no—
106D8×C127—41no—
107M16×C127—21no—
108M16×C127—21no—
109M16×C127—41no—
110M16×C127—41no—
111M16×C127—41no—
112C2×C8×C127—21no—
113C2×C8×C127—41no—
114C2×C8×C127—41no—
115C2×C8×C127—41no—
116C4⋊C4×C127—21no—
117C4⋊C4×C127—21no—
118C4⋊C4×C127—41no—
119C4⋊C4×C127—41no—
120C4⋊C4×C127—41no—
121C4⋊C4×C127—81no—
122C22⋊C4×C127—21no—
123C22⋊C4×C127—41no—
124C22⋊C4×C127—41no—
125C22⋊C4×C127—41no—
126C22⋊C4×C127—81no—
127C42×C127—21no—
128C42×C127C2×D411yescharacteristic
129C23×C127—21no—
130C23×C127—41no—
131C23×C127—41no—
132C23×C127—81no—
133Q8×C127—21no—
134Q8×C127—21no—
135Q8×C127—41no—
136Q8×C127—41no—
137Q8×C127—81no—
138D4×C127—21no—
139D4×C127—21no—
140D4×C127—41no—
141D4×C127—41no—
142D4×C127—41no—
143D4×C127—41no—
144D4×C127—41no—
145D4×C127—41no—
146D4×C127—81no—
147D4×C127—81no—
148D4×C127—81no—
149D4×C127—82no—
150C2×C4×C127—21no—
151C2×C4×C127—21no—
152C2×C4×C127—41no—
153C2×C4×C127—41no—
154C2×C4×C127—41no—
155C2×C4×C127—41no—
156C2×C4×C127—41no—
157C2×C4×C127—81no—
158C2×C4×C127—81no—
159C2×C4×C127—81no—
160C2×C4×C127—81no—
161C2×C4×C127#12011yescharacteristic
162C8×C127—21no—
163C8×C127—21no—
164C8×C127—41no—
165C8×C127—41no—
166C8×C127—81no—
167C8×C127—81no—
168C22×C127—41no—
169C22×C127—41no—
170C22×C127—41no—
171C22×C127—81no—
172C22×C127—81no—
173C22×C127—161no—
174C22×C127—161no—
175C22×C127—321no—
176C22×C127B(4,𝔽2)11yescharacteristic
177C4×C127—21no—
178C4×C127—41no—
179C4×C127—41no—
180C4×C127—41no—
181C4×C127—41no—
182C4×C127—81no—
183C4×C127—81no—
184C4×C127—161no—
185#13679C12711yesmaximal, characteristic, direct product factor, Sylow
186C2×C127—21no—
187C2×C127—81no—
188C2×C127—81no—
189C2×C127—81no—
190C2×C127—161no—
191C2×C127#219611yescharacteristic
192#3288C2×C12711yescharacteristic
193#2203C2×C12711yescharacteristic, complemented
194#2201C2×C12711yescharacteristic, complemented
195#1657C2×C12711yescharacteristic, complemented
196#1406C2×C12711yescharacteristic, complemented
197#1404C2×C12711yescharacteristic, complemented
198#1403C2×C12711yescharacteristic, complemented
199C127#1367911yescharacteristic, direct product factor, Sylow
200#577—21no—
201#576—21no—
202#563C22×C12711yescharacteristic, complemented
203#496C22×C12711yescharacteristic
204#490—21no—
205#472—21no—
206#471—21no—
207#458—21no—
208#456—21no—
209#455C22×C12711yescharacteristic
210#454C22×C12711yescharacteristic
211#453—21no—
212#444—21no—
213#356—21no—
214#355C22×C12711yescharacteristic, complemented
215#354C22×C12711yescharacteristic, complemented
216#352—21no—
217#330—21no—
218#329C22×C12711yescharacteristic, complemented
2192−1+4D4×C12711yescharacteristic
220H(5,𝔽2)—21no—
221H(5,𝔽2)D4×C12711yescharacteristic
222#137—21no—
223#137—41no—
224#137—41no—
225AGL(1,ℤ/8)—21no—
226AGL(1,ℤ/8)—21no—
227AGL(1,ℤ/8)—21no—
228AGL(1,ℤ/8)—41no—
229AGL(1,ℤ/8)—41no—
230AGL(1,ℤ/8)—41no—
231#135—21no—
232#135—41no—
233#135—41no—
234C2×SD16—21no—
235C2×SD16—41no—
236C2×D8—21no—
237C2×D8—41no—
238#131—21no—
239#131—21no—
240C4⋊Q8—21no—
241#127D4×C12711yescharacteristic
242#126—41no—
243#125—21no—
244#124C23×C12711yescharacteristic
245#123—21no—
246#123—41no—
247C22⋊Q8—41no—
248#108—21no—
249#104—21no—
250#104—21no—
251#104—41no—
252#102—41no—
253#102—41no—
254#101—21no—
255#101D4×C12711yescharacteristic
256#100—21no—
257#100D4×C12711yescharacteristic
258#99—21no—
259#99—41no—
260#97—21no—
261#97D4×C12711yescharacteristic
262#41—21no—
263#41—21no—
264#41—41no—
265#41—41no—
266#41—41no—
267#41—41no—
268#41—41no—
269C2×Q8—21no—
270C2×Q8—41no—
271C2×Q8C2×D4×C12711yescharacteristic
272C2×D4—21no—
273C2×D4—41no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—41no—
278C2×D4—81no—
279C2×D4C2×D4×C12711yescharacteristic
280C22×C4—21no—
281Q16—21no—
282Q16—41no—
283Q16—81no—
284SD16—21no—
285SD16—21no—
286SD16—41no—
287SD16—41no—
288SD16—41no—
289SD16—41no—
290SD16—41no—
291SD16—41no—
292SD16—81no—
293D8—21no—
294D8—41no—
295D8—41no—
296D8—41no—
297D8—41no—
298D8—41no—
299M16—21no—
300M16—21no—
301M16—41no—
302M16—41no—
303M16—41no—
304C2×C8—21no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—41no—
308C4⋊C4—21no—
309C4⋊C4—21no—
310C4⋊C4—41no—
311C4⋊C4—41no—
312C4⋊C4—41no—
313C4⋊C4—81no—
314C22⋊C4—21no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—81no—
319C42—21no—
320C42C2×D4×C12711yescharacteristic
321C23—21no—
322C23—41no—
323C23—41no—
324C23—81no—
325Q8—21no—
326Q8—21no—
327Q8—41no—
328Q8—41no—
329Q8—81no—
330D4—21no—
331D4—21no—
332D4—41no—
333D4—41no—
334D4—41no—
335D4—41no—
336D4—41no—
337D4—41no—
338D4—81no—
339D4—81no—
340D4—81no—
341D4—82no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—81no—
350C2×C4—81no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4#120×C12711yescharacteristic
354C8—21no—
355C8—21no—
356C8—41no—
357C8—41no—
358C8—81no—
359C8—81no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—81no—
364C22—81no—
365C22—161no—
366C22—161no—
367C22—321no—
368C22B(4,𝔽2)×C12711yescharacteristic
369C4—21no—
370C4—41no—
371C4—41no—
372C4—41no—
373C4—41no—
374C4—81no—
375C4—81no—
376C4—161no—
377C2—21no—
378C2—81no—
379C2—81no—
380C2—81no—
381C2—161no—
382C2C127×#219611yescharacteristic
subgroupG/H
center, socleC2×C127#2196
commutator, Frattini, cosocle#124C23×C127
prime radicalC127×#3288C2
LCSG ▷ #124 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C127 ◁ C2×C4×C127 ◁ #124×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2203C2semidirect
3. C127×#2201C2semidirect
4. C127×#1657C2semidirect
5. C127×#1406C2semidirect
6. C127×#1404C2semidirect
7. C127×#1403C2semidirect
10. #563×C127C22semidirect
22. #355×C127C22semidirect
23. #354×C127C22semidirect
26. #329×C127C22semidirect
185. #13679C127direct (N × H)
193. #2203C2×C127semidirect
194. #2201C2×C127semidirect
195. #1657C2×C127semidirect
196. #1406C2×C127semidirect
197. #1404C2×C127semidirect
198. #1403C2×C127semidirect
199. C127#13679direct (N × H)
202. #563C22×C127semidirect
214. #355C22×C127semidirect
215. #354C22×C127semidirect
218. #329C22×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#32882
C127×#22032
C127×#22012
C127×#16572
C127×#14062
C127×#14042
C127×#14032
#13679127