Finite Group Databasebeta

← C127×#10502 #44574175

Subgroups — C127×#10502 #44574175

Order 32512.

412 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3227C211yesmaximal, characteristic
2C127×#1997C211yesmaximal, characteristic, complemented
3C127×#1987C211yesmaximal, characteristic, complemented
4C127×#1980C211yesmaximal, characteristic
5C127×#1565C211yesmaximal, characteristic, complemented
6C127×#1547C211yesmaximal, characteristic
7C127×#1303C211yesmaximal, characteristic, complemented
8#532×C127C2211yescharacteristic
9C2×C4⋊Q8×C127C2211yescharacteristic
10#498×C127—21no—
11#486×C127—21no—
12#481×C127—22no—
13#476×C127—21no—
14#476×C127—21no—
15#431×C127C2211yescharacteristic
16#423×C127C2211yescharacteristic
17C2×C4⋊C8×C127C2211yescharacteristic
18C2×#104×C127—21no—
19C2×#104×C127—21no—
20C4×M16×C127C2211yescharacteristic
21C4×C4⋊C4×C127C2211yescharacteristic
22#343×C127—21no—
23#343×C127—21no—
24#340×C127—22no—
25#335×C127—21no—
26#334×C127—21no—
27#332×C127—21no—
28#331×C127—21no—
29C2×#41×C127—21no—
30C22×Q8×C127—21no—
31C2×M16×C127—21no—
32C2×M16×C127D411yescharacteristic
33C2×M16×C127D411yescharacteristic
34C22×C8×C127—21no—
35C4⋊Q8×C127—21no—
36C4⋊Q8×C127—21no—
37C4⋊Q8×C127—21no—
38C4⋊Q8×C127—21no—
39C4⋊Q8×C127D411yescharacteristic
40#127×C127D411yescharacteristic
41#124×C127—21no—
42#121×C127—21no—
43#121×C127—21no—
44C4×D4×C127—21no—
45C4×D4×C127—21no—
46C2×C4⋊C4×C127—21no—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊C4×C127D412yes—
49C2×C42×C127—21no—
50C2×C42×C127C2311yescharacteristic
51#106×C127—22no—
52#106×C127—22no—
53C4⋊C8×C127—21no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57C4⋊C8×C127D411yescharacteristic
58C4⋊C8×C127D411yescharacteristic
59#104×C127—42no—
60#104×C127—42no—
61#102×C127—22no—
62#102×C127—22no—
63C22⋊C8×C127—21no—
64#97×C127—21no—
65C4×C8×C127—21no—
66C4×C8×C127—21no—
67#95×C127—21no—
68#41×C127—41no—
69#41×C127—41no—
70#41×C127—41no—
71#41×C127—41no—
72C2×Q8×C127—21no—
73C2×Q8×C127—41no—
74C2×Q8×C127—41no—
75C2×Q8×C127—82no—
76C2×D4×C127—21no—
77C2×D4×C127—21no—
78C2×D4×C127—21no—
79C2×D4×C127—41no—
80C22×C4×C127—22no—
81C22×C4×C127—41no—
82C22×C4×C127—41no—
83C22×C4×C127C2×D411yescharacteristic
84C22×C4×C127C2×D411yescharacteristic
85C22×C4×C127#4111yescharacteristic
86M16×C127—21no—
87M16×C127—21no—
88M16×C127—21no—
89M16×C127—41no—
90M16×C127—41no—
91M16×C127SD1612yes—
92C2×C8×C127—21no—
93C2×C8×C127—21no—
94C2×C8×C127—21no—
95C2×C8×C127—21no—
96C2×C8×C127—42no—
97C2×C8×C127—41no—
98C2×C8×C127—41no—
99C4⋊C4×C127—22no—
100C4⋊C4×C127—22no—
101C4⋊C4×C127—21no—
102C4⋊C4×C127—22no—
103C4⋊C4×C127—21no—
104C4⋊C4×C127—41no—
105C4⋊C4×C127—41no—
106C4⋊C4×C127—41no—
107C22⋊C4×C127—41no—
108C22⋊C4×C127—41no—
109C42×C127—41no—
110C42×C127—41no—
111C42×C127C2×D411yescharacteristic
112C42×C127C2×D411yescharacteristic
113C42×C127#4111yescharacteristic
114C42×C127#4111yescharacteristic
115C23×C127—41no—
116C23×C127#12111yescharacteristic
117Q8×C127—41no—
118Q8×C127—41no—
119Q8×C127—82no—
120Q8×C127—82no—
121D4×C127—41no—
122D4×C127—41no—
123D4×C127—41no—
124D4×C127—41no—
125D4×C127—81no—
126D4×C127—81no—
127D4×C127—81no—
128C2×C4×C127—21no—
129C2×C4×C127—21no—
130C2×C4×C127—41no—
131C2×C4×C127—42no—
132C2×C4×C127—41no—
133C2×C4×C127—42no—
134C2×C4×C127—81no—
135C2×C4×C127—81no—
136C2×C4×C127—81no—
137C2×C4×C127—81no—
138C2×C4×C127—82no—
139C2×C4×C127#12011yescharacteristic
140C2×C4×C127#12111yescharacteristic
141C2×C4×C127#12111yescharacteristic
142C2×C4×C127#12311yescharacteristic
143C2×C4×C127#12311yescharacteristic
144C2×C4×C127#12411yescharacteristic
145C2×C4×C127C2×SD1611yescharacteristic
146C2×C4×C127#13511yescharacteristic
147C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C127#13711yescharacteristic
149C8×C127—22no—
150C8×C127—41no—
151C8×C127—41no—
152C8×C127—41no—
153C8×C127—81no—
154C8×C127—81no—
155C22×C127—21no—
156C22×C127—21no—
157C22×C127—81no—
158C22×C127—81no—
159C22×C127—81no—
160C22×C127#39411yescharacteristic
161C22×C127#46011yescharacteristic
162C22×C127#46411yescharacteristic
163C4×C127—21no—
164C4×C127—21no—
165C4×C127—21no—
166C4×C127—82no—
167C4×C127—82no—
168C4×C127—81no—
169C4×C127#45411yescharacteristic
170C4×C127#45611yescharacteristic
171C4×C127#46111yescharacteristic
172C4×C127#46311yescharacteristic
173C4×C127#46511yescharacteristic
174C4×C127#46811yescharacteristic
175#10502C12711yesmaximal, characteristic, direct product factor, Sylow
176C2×C127—21no—
177C2×C127—21no—
178C2×C127—161no—
179C2×C127#203811yescharacteristic
180C2×C127#204811yescharacteristic
181C2×C127#205511yescharacteristic
182#3227C2×C12711yescharacteristic
183#1997C2×C12711yescharacteristic, complemented
184#1987C2×C12711yescharacteristic, complemented
185#1980C2×C12711yescharacteristic
186#1565C2×C12711yescharacteristic, complemented
187#1547C2×C12711yescharacteristic
188#1303C2×C12711yescharacteristic, complemented
189C127#1050211yescharacteristic, direct product factor, Sylow
190#532C22×C12711yescharacteristic
191C2×C4⋊Q8C22×C12711yescharacteristic
192#498—21no—
193#486—21no—
194#481—22no—
195#476—21no—
196#476—21no—
197#431C22×C12711yescharacteristic
198#423C22×C12711yescharacteristic
199C2×C4⋊C8C22×C12711yescharacteristic
200C2×#104—21no—
201C2×#104—21no—
202C4×M16C22×C12711yescharacteristic
203C4×C4⋊C4C22×C12711yescharacteristic
204#343—21no—
205#343—21no—
206#340—22no—
207#335—21no—
208#334—21no—
209#332—21no—
210#331—21no—
211C2×#41—21no—
212C22×Q8—21no—
213C2×M16—21no—
214C2×M16D4×C12711yescharacteristic
215C2×M16D4×C12711yescharacteristic
216C22×C8—21no—
217C4⋊Q8—21no—
218C4⋊Q8—21no—
219C4⋊Q8—21no—
220C4⋊Q8—21no—
221C4⋊Q8D4×C12711yescharacteristic
222#127D4×C12711yescharacteristic
223#124—21no—
224#121—21no—
225#121—21no—
226C4×D4—21no—
227C4×D4—21no—
228C2×C4⋊C4—21no—
229C2×C4⋊C4—21no—
230C2×C4⋊C4D4×C12712yes—
231C2×C42—21no—
232C2×C42C23×C12711yescharacteristic
233#106—22no—
234#106—22no—
235C4⋊C8—21no—
236C4⋊C8—21no—
237C4⋊C8—21no—
238C4⋊C8—21no—
239C4⋊C8D4×C12711yescharacteristic
240C4⋊C8D4×C12711yescharacteristic
241#104—42no—
242#104—42no—
243#102—22no—
244#102—22no—
245C22⋊C8—21no—
246#97—21no—
247C4×C8—21no—
248C4×C8—21no—
249#95—21no—
250#41—41no—
251#41—41no—
252#41—41no—
253#41—41no—
254C2×Q8—21no—
255C2×Q8—41no—
256C2×Q8—41no—
257C2×Q8—82no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—41no—
262C22×C4—22no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4C2×D4×C12711yescharacteristic
266C22×C4C2×D4×C12711yescharacteristic
267C22×C4#41×C12711yescharacteristic
268M16—21no—
269M16—21no—
270M16—21no—
271M16—41no—
272M16—41no—
273M16SD16×C12712yes—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—42no—
279C2×C8—41no—
280C2×C8—41no—
281C4⋊C4—22no—
282C4⋊C4—22no—
283C4⋊C4—21no—
284C4⋊C4—22no—
285C4⋊C4—21no—
286C4⋊C4—41no—
287C4⋊C4—41no—
288C4⋊C4—41no—
289C22⋊C4—41no—
290C22⋊C4—41no—
291C42—41no—
292C42—41no—
293C42C2×D4×C12711yescharacteristic
294C42C2×D4×C12711yescharacteristic
295C42#41×C12711yescharacteristic
296C42#41×C12711yescharacteristic
297C23—41no—
298C23#121×C12711yescharacteristic
299Q8—41no—
300Q8—41no—
301Q8—82no—
302Q8—82no—
303D4—41no—
304D4—41no—
305D4—41no—
306D4—41no—
307D4—81no—
308D4—81no—
309D4—81no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—82no—
321C2×C4#120×C12711yescharacteristic
322C2×C4#121×C12711yescharacteristic
323C2×C4#121×C12711yescharacteristic
324C2×C4#123×C12711yescharacteristic
325C2×C4#123×C12711yescharacteristic
326C2×C4#124×C12711yescharacteristic
327C2×C4C2×SD16×C12711yescharacteristic
328C2×C4#135×C12711yescharacteristic
329C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
330C2×C4#137×C12711yescharacteristic
331C8—22no—
332C8—41no—
333C8—41no—
334C8—41no—
335C8—81no—
336C8—81no—
337C22—21no—
338C22—21no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22#394×C12711yescharacteristic
343C22#460×C12711yescharacteristic
344C22#464×C12711yescharacteristic
345C4—21no—
346C4—21no—
347C4—21no—
348C4—82no—
349C4—82no—
350C4—81no—
351C4#454×C12711yescharacteristic
352C4#456×C12711yescharacteristic
353C4#461×C12711yescharacteristic
354C4#463×C12711yescharacteristic
355C4#465×C12711yescharacteristic
356C4#468×C12711yescharacteristic
357C2—21no—
358C2—21no—
359C2—161no—
360C2C127×#203811yescharacteristic
361C2C127×#204811yescharacteristic
362C2C127×#205511yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radical#532×C127C22
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×#1997C2semidirect
3. C127×#1987C2semidirect
5. C127×#1565C2semidirect
7. C127×#1303C2semidirect
175. #10502C127direct (N × H)
183. #1997C2×C127semidirect
184. #1987C2×C127semidirect
186. #1565C2×C127semidirect
188. #1303C2×C127semidirect
189. C127#10502direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32272
C127×#19972
C127×#19872
C127×#19802
C127×#15652
C127×#15472
C127×#13032
#10502127