Finite Group Databasebeta

← C127×#13321 #44576994

Subgroups — C127×#13321 #44576994

Order 32512.

552 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×SD32×C127C211yesmaximal, characteristic, complemented
2C2×#473×C127C211yesmaximal, characteristic, complemented
3C127×#3058C211yesmaximal, characteristic
4C2×#361×C127C211yesmaximal, characteristic, complemented
5C127×#2141C211yesmaximal, characteristic, complemented
6C2×#350×C127C211yesmaximal, characteristic, complemented
7C127×#1382C211yesmaximal, characteristic, complemented
8C2×#137×C127—21no—
9C22×Q16×C127C2211yescharacteristic
10C22×D8×C127C2211yescharacteristic
11C2×#131×C127C2211yescharacteristic
12#535×C127—21no—
13C2×SD32×C127—22no—
14C2×SD32×C127—22no—
15C2×SD32×C127—22no—
16C2×M32×C127C2211yescharacteristic
17C22×C16×C127C2211yescharacteristic
18#473×C127—22no—
19#473×C127—22no—
20#469×C127—22no—
21#466×C127—22no—
22C2×#108×C127C2211yescharacteristic
23#427×C127C2211yescharacteristic
24#418×C127—21no—
25C2×#101×C127—21no—
26#361×C127—22no—
27#358×C127—22no—
28#350×C127—22no—
29C2×#41×C127D411yescharacteristic
30C22×Q8×C127—21no—
31C22×D4×C127—21no—
32#137×C127—24no—
33#137×C127—42no—
34C2×Q16×C127—21no—
35C2×Q16×C127—21no—
36C2×Q16×C127—21no—
37C2×Q16×C127—21no—
38C2×Q16×C127—21no—
39C2×Q16×C127—41no—
40C2×Q16×C127D412yescomplemented
41C2×SD16×C127—41no—
42C2×D8×C127—21no—
43C2×D8×C127—21no—
44C2×D8×C127—21no—
45C2×D8×C127—21no—
46C2×D8×C127—21no—
47C2×D8×C127D412yes—
48#131×C127—21no—
49#131×C127—21no—
50#131×C127—21no—
51#131×C127—21no—
52C2×M16×C127—21no—
53C2×M16×C127—21no—
54C2×M16×C127D411yescharacteristic
55C22×C8×C127—21no—
56C22×C8×C127C2311yescharacteristic
57#127×C127—41no—
58#124×C127—41no—
59#121×C127—24no—
60#120×C127—42no—
61#117×C127—21no—
62SD32×C127—28no—
63M32×C127—21no—
64M32×C127—21no—
65C2×C16×C127—21no—
66C2×C16×C127—21no—
67C2×C16×C127—21no—
68C2×C16×C127D412yescomplemented
69#108×C127—21no—
70#108×C127D412yescomplemented
71#107×C127D412yes—
72#106×C127—21no—
73#102×C127—24no—
74#101×C127—24no—
75C24×C127—41no—
76#41×C127—21no—
77#41×C127—21no—
78#41×C127—21no—
79#41×C127—21no—
80C2×Q8×C127—22no—
81C2×Q8×C127—41no—
82C2×Q8×C127—41no—
83C2×Q8×C127—41no—
84C2×Q8×C127—41no—
85C2×Q8×C127—41no—
86C2×Q8×C127D811yescharacteristic
87C2×D4×C127—21no—
88C2×D4×C127—22no—
89C2×D4×C127—44no—
90C2×D4×C127—41no—
91C2×D4×C127—41no—
92C2×D4×C127—41no—
93C2×D4×C127—41no—
94C2×D4×C127—41no—
95C2×D4×C127D811yescharacteristic
96C22×C4×C127—21no—
97C22×C4×C127—41no—
98C22×C4×C127C2×D411yescharacteristic
99Q16×C127—22no—
100Q16×C127—22no—
101Q16×C127—44no—
102Q16×C127—41no—
103Q16×C127—41no—
104SD16×C127—44no—
105D8×C127—22no—
106D8×C127—22no—
107D8×C127—41no—
108D8×C127—41no—
109M16×C127—21no—
110M16×C127—22no—
111M16×C127—21no—
112M16×C127—41no—
113M16×C127—41no—
114M16×C127—41no—
115C2×C8×C127—21no—
116C2×C8×C127—41no—
117C2×C8×C127—41no—
118C2×C8×C127—41no—
119C2×C8×C127C2×D411yescharacteristic
120C2×C8×C127C2×D411yescharacteristic
121C2×C8×C127C2×D411yescharacteristic
122C2×C8×C127C2×D411yescharacteristic
123C2×C8×C127C2×D411yescharacteristic
124C2×C8×C127#4111yescharacteristic
125C4⋊C4×C127—22no—
126C22⋊C4×C127—44no—
127C22⋊C4×C127—41no—
128C42×C127—41no—
129C16×C127—22no—
130C16×C127—41no—
131C23×C127—21no—
132C23×C127—42no—
133C23×C127—81no—
134C23×C127—81no—
135C23×C127—162no—
136C23×C127AGL(1,ℤ/8)11yescharacteristic
137Q8×C127—21no—
138Q8×C127—21no—
139Q8×C127—42no—
140Q8×C127—42no—
141Q8×C127—81no—
142Q8×C127—81no—
143D4×C127—21no—
144D4×C127—21no—
145D4×C127—41no—
146D4×C127—41no—
147D4×C127—42no—
148D4×C127—42no—
149D4×C127—81no—
150D4×C127—81no—
151D4×C127—164no—
152C2×C4×C127—21no—
153C2×C4×C127—41no—
154C2×C4×C127—41no—
155C2×C4×C127—42no—
156C2×C4×C127—42no—
157C2×C4×C127—81no—
158C2×C4×C127—81no—
159C2×C4×C127#12011yescharacteristic
160C2×C4×C127#12011yescharacteristic
161C2×C4×C127#12111yescharacteristic
162C2×C4×C127C2×D811yescharacteristic
163C2×C4×C127#13511yescharacteristic
164C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
165C8×C127—41no—
166C8×C127—42no—
167C8×C127#12011yescharacteristic
168C8×C127#12111yescharacteristic
169C8×C127#12111yescharacteristic
170C8×C127#12711yescharacteristic
171C22×C127—22no—
172C22×C127—42no—
173C22×C127—41no—
174C22×C127—84no—
175C22×C127—82no—
176C22×C127—162no—
177C22×C127—162no—
178C22×C127#44711yescharacteristic
179C22×C127#44911yescharacteristic
180C22×C127#46911yescharacteristic
181C4×C127—41no—
182C4×C127—82no—
183C4×C127—82no—
184C4×C127#39211yescharacteristic
185C4×C127#44711yescharacteristic
186C4×C127#44911yescharacteristic
187C4×C127#46611yescharacteristic
188#13321C12711yesmaximal, characteristic, direct product factor, Sylow
189C2×C127—21no—
190C2×C127—21no—
191C2×C127—81no—
192C2×C127—162no—
193C2×C127#199911yescharacteristic
194C2×C127#219412yes—
195C22×SD32C2×C12711yescharacteristic, complemented
196C2×#473C2×C12711yescharacteristic, complemented
197#3058C2×C12711yescharacteristic
198C2×#361C2×C12711yescharacteristic, complemented
199#2141C2×C12711yescharacteristic, complemented
200C2×#350C2×C12711yescharacteristic, complemented
201#1382C2×C12711yescharacteristic, complemented
202C127#1332111yescharacteristic, direct product factor, Sylow
203C2×#137—21no—
204C22×Q16C22×C12711yescharacteristic
205C22×D8C22×C12711yescharacteristic
206C2×#131C22×C12711yescharacteristic
207#535—21no—
208C2×SD32—22no—
209C2×SD32—22no—
210C2×SD32—22no—
211C2×M32C22×C12711yescharacteristic
212C22×C16C22×C12711yescharacteristic
213#473—22no—
214#473—22no—
215#469—22no—
216#466—22no—
217C2×#108C22×C12711yescharacteristic
218#427C22×C12711yescharacteristic
219#418—21no—
220C2×#101—21no—
221#361—22no—
222#358—22no—
223#350—22no—
224C2×#41D4×C12711yescharacteristic
225C22×Q8—21no—
226C22×D4—21no—
227#137—24no—
228#137—42no—
229C2×Q16—21no—
230C2×Q16—21no—
231C2×Q16—21no—
232C2×Q16—21no—
233C2×Q16—21no—
234C2×Q16—41no—
235C2×Q16D4×C12712yescomplemented
236C2×SD16—41no—
237C2×D8—21no—
238C2×D8—21no—
239C2×D8—21no—
240C2×D8—21no—
241C2×D8—21no—
242C2×D8D4×C12712yes—
243#131—21no—
244#131—21no—
245#131—21no—
246#131—21no—
247C2×M16—21no—
248C2×M16—21no—
249C2×M16D4×C12711yescharacteristic
250C22×C8—21no—
251C22×C8C23×C12711yescharacteristic
252#127—41no—
253#124—41no—
254#121—24no—
255#120—42no—
256#117—21no—
257SD32—28no—
258M32—21no—
259M32—21no—
260C2×C16—21no—
261C2×C16—21no—
262C2×C16—21no—
263C2×C16D4×C12712yescomplemented
264#108—21no—
265#108D4×C12712yescomplemented
266#107D4×C12712yes—
267#106—21no—
268#102—24no—
269#101—24no—
270C24—41no—
271#41—21no—
272#41—21no—
273#41—21no—
274#41—21no—
275C2×Q8—22no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8D8×C12711yescharacteristic
282C2×D4—21no—
283C2×D4—22no—
284C2×D4—44no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4D8×C12711yescharacteristic
291C22×C4—21no—
292C22×C4—41no—
293C22×C4C2×D4×C12711yescharacteristic
294Q16—22no—
295Q16—22no—
296Q16—44no—
297Q16—41no—
298Q16—41no—
299SD16—44no—
300D8—22no—
301D8—22no—
302D8—41no—
303D8—41no—
304M16—21no—
305M16—22no—
306M16—21no—
307M16—41no—
308M16—41no—
309M16—41no—
310C2×C8—21no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8C2×D4×C12711yescharacteristic
315C2×C8C2×D4×C12711yescharacteristic
316C2×C8C2×D4×C12711yescharacteristic
317C2×C8C2×D4×C12711yescharacteristic
318C2×C8C2×D4×C12711yescharacteristic
319C2×C8#41×C12711yescharacteristic
320C4⋊C4—22no—
321C22⋊C4—44no—
322C22⋊C4—41no—
323C42—41no—
324C16—22no—
325C16—41no—
326C23—21no—
327C23—42no—
328C23—81no—
329C23—81no—
330C23—162no—
331C23AGL(1,ℤ/8)×C12711yescharacteristic
332Q8—21no—
333Q8—21no—
334Q8—42no—
335Q8—42no—
336Q8—81no—
337Q8—81no—
338D4—21no—
339D4—21no—
340D4—41no—
341D4—41no—
342D4—42no—
343D4—42no—
344D4—81no—
345D4—81no—
346D4—164no—
347C2×C4—21no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—81no—
353C2×C4—81no—
354C2×C4#120×C12711yescharacteristic
355C2×C4#120×C12711yescharacteristic
356C2×C4#121×C12711yescharacteristic
357C2×C4C2×D8×C12711yescharacteristic
358C2×C4#135×C12711yescharacteristic
359C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
360C8—41no—
361C8—42no—
362C8#120×C12711yescharacteristic
363C8#121×C12711yescharacteristic
364C8#121×C12711yescharacteristic
365C8#127×C12711yescharacteristic
366C22—22no—
367C22—42no—
368C22—41no—
369C22—84no—
370C22—82no—
371C22—162no—
372C22—162no—
373C22#447×C12711yescharacteristic
374C22#449×C12711yescharacteristic
375C22#469×C12711yescharacteristic
376C4—41no—
377C4—82no—
378C4—82no—
379C4#392×C12711yescharacteristic
380C4#447×C12711yescharacteristic
381C4#449×C12711yescharacteristic
382C4#466×C12711yescharacteristic
383C2—21no—
384C2—21no—
385C2—81no—
386C2—162no—
387C2C127×#199911yescharacteristic
388C2C127×#219412yes—
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC127×#3058C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×#131×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×SD32×C127C2semidirect
2. C2×#473×C127C2semidirect
4. C2×#361×C127C2semidirect
5. C127×#2141C2semidirect
6. C2×#350×C127C2semidirect
7. C127×#1382C2semidirect
40. C2×Q16×C127D4semidirect
68. C2×C16×C127D4semidirect
70. #108×C127D4semidirect
188. #13321C127direct (N × H)
195. C22×SD32C2×C127semidirect
196. C2×#473C2×C127semidirect
198. C2×#361C2×C127semidirect
199. #2141C2×C127semidirect
200. C2×#350C2×C127semidirect
201. #1382C2×C127semidirect
202. C127#13321direct (N × H)
235. C2×Q16D4×C127semidirect
263. C2×C16D4×C127semidirect
265. #108D4×C127semidirect

Maximal subgroups

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

subgroupindex
C22×SD32×C1272
C2×#473×C1272
C127×#30582
C2×#361×C1272
C127×#21412
C2×#350×C1272
C127×#13822
#13321127