Finite Group Databasebeta

← C127×#13322 #44576995

Subgroups — C127×#13322 #44576995

Order 32512.

520 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q32×C127C211yesmaximal, characteristic, complemented
2C2×#473×C127C211yesmaximal, characteristic
3C127×#3059C211yesmaximal, characteristic
4C2×#362×C127C211yesmaximal, characteristic, complemented
5C127×#2141C211yesmaximal, characteristic, complemented
6C2×#350×C127C211yesmaximal, characteristic
7C127×#1382C211yesmaximal, characteristic, complemented
8C2×#137×C127—21no—
9C22×Q16×C127C2211yescharacteristic
10C22×Q16×C127C2211yescharacteristic
11C2×#131×C127C2211yescharacteristic
12#536×C127—21no—
13C2×Q32×C127—22no—
14C2×Q32×C127—22no—
15C2×Q32×C127—22no—
16C2×M32×C127C2211yescharacteristic
17C22×C16×C127C2211yescharacteristic
18#473×C127—22no—
19#473×C127—22no—
20#470×C127—22no—
21#467×C127—22no—
22C2×#108×C127C2211yescharacteristic
23#427×C127C2211yescharacteristic
24#419×C127—21no—
25C2×#101×C127—21no—
26#362×C127—22no—
27#358×C127—22no—
28#350×C127—22no—
29C2×#41×C127D411yescharacteristic
30C22×Q8×C127—21no—
31C22×Q8×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—21no—
40C2×Q16×C127—21no—
41C2×Q16×C127—21no—
42C2×Q16×C127—21no—
43C2×Q16×C127—21no—
44C2×Q16×C127—41no—
45C2×Q16×C127D412yes—
46C2×Q16×C127D412yes—
47C2×SD16×C127—41no—
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
57C4⋊Q8×C127—41no—
58#124×C127—41no—
59#123×C127—42no—
60C22⋊Q8×C127—24no—
61#117×C127—21no—
62Q32×C127—28no—
63M32×C127—21no—
64M32×C127—21no—
65C2×C16×C127—21no—
66C2×C16×C127—21no—
67C2×C16×C127—21no—
68C2×C16×C127D412yes—
69#108×C127—21no—
70#108×C127D412yes—
71#107×C127D412yes—
72#106×C127—21no—
73#103×C127—24no—
74#101×C127—24no—
75#41×C127—21no—
76#41×C127—21no—
77#41×C127—21no—
78#41×C127—21no—
79C2×Q8×C127—22no—
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×C127—41no—
87C2×Q8×C127—41no—
88C2×Q8×C127—41no—
89C2×Q8×C127—41no—
90C2×Q8×C127—41no—
91C2×Q8×C127D811yescharacteristic
92C2×D4×C127—21no—
93C2×D4×C127D811yescharacteristic
94C22×C4×C127—21no—
95C22×C4×C127—41no—
96C22×C4×C127—41no—
97C22×C4×C127C2×D411yescharacteristic
98Q16×C127—22no—
99Q16×C127—22no—
100Q16×C127—22no—
101Q16×C127—22no—
102Q16×C127—44no—
103Q16×C127—41no—
104Q16×C127—41no—
105Q16×C127—41no—
106Q16×C127—41no—
107SD16×C127—44no—
108M16×C127—21no—
109M16×C127—22no—
110M16×C127—21no—
111M16×C127—41no—
112M16×C127—41no—
113M16×C127—41no—
114C2×C8×C127—21no—
115C2×C8×C127—41no—
116C2×C8×C127—41no—
117C2×C8×C127—41no—
118C2×C8×C127C2×D411yescharacteristic
119C2×C8×C127C2×D411yescharacteristic
120C2×C8×C127C2×D411yescharacteristic
121C2×C8×C127C2×D411yescharacteristic
122C2×C8×C127C2×D411yescharacteristic
123C2×C8×C127#4111yescharacteristic
124C4⋊C4×C127—22no—
125C4⋊C4×C127—44no—
126C22⋊C4×C127—44no—
127C22⋊C4×C127—41no—
128C42×C127—41no—
129C16×C127—22no—
130C16×C127—41no—
131C23×C127—21no—
132C23×C127AGL(1,ℤ/8)11yescharacteristic
133Q8×C127—21no—
134Q8×C127—21no—
135Q8×C127—42no—
136Q8×C127—42no—
137Q8×C127—42no—
138Q8×C127—42no—
139Q8×C127—81no—
140Q8×C127—81no—
141Q8×C127—81no—
142Q8×C127—81no—
143D4×C127—21no—
144D4×C127—21no—
145D4×C127—41no—
146D4×C127—41no—
147C2×C4×C127—21no—
148C2×C4×C127—41no—
149C2×C4×C127—41no—
150C2×C4×C127—42no—
151C2×C4×C127—42no—
152C2×C4×C127—42no—
153C2×C4×C127—81no—
154C2×C4×C127—81no—
155C2×C4×C127—81no—
156C2×C4×C127—81no—
157C2×C4×C127#12011yescharacteristic
158C2×C4×C127#12011yescharacteristic
159C2×C4×C127#12111yescharacteristic
160C2×C4×C127C2×D811yescharacteristic
161C2×C4×C127#13511yescharacteristic
162C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
163C8×C127—41no—
164C8×C127—42no—
165C8×C127#12011yescharacteristic
166C8×C127#12111yescharacteristic
167C8×C127#12111yescharacteristic
168C8×C127#12711yescharacteristic
169C22×C127—22no—
170C22×C127—42no—
171C22×C127—41no—
172C22×C127#44711yescharacteristic
173C22×C127#44911yescharacteristic
174C22×C127#46911yescharacteristic
175C4×C127—41no—
176C4×C127—82no—
177C4×C127—82no—
178C4×C127—82no—
179C4×C127#39211yescharacteristic
180C4×C127#44711yescharacteristic
181C4×C127#44911yescharacteristic
182C4×C127#46611yescharacteristic
183#13322C12711yesmaximal, characteristic, direct product factor, Sylow
184C2×C127—21no—
185C2×C127—21no—
186C2×C127—81no—
187C2×C127#199911yescharacteristic
188C2×C127#219512yes—
189C22×Q32C2×C12711yescharacteristic, complemented
190C2×#473C2×C12711yescharacteristic
191#3059C2×C12711yescharacteristic
192C2×#362C2×C12711yescharacteristic, complemented
193#2141C2×C12711yescharacteristic, complemented
194C2×#350C2×C12711yescharacteristic
195#1382C2×C12711yescharacteristic, complemented
196C127#1332211yescharacteristic, direct product factor, Sylow
197C2×#137—21no—
198C22×Q16C22×C12711yescharacteristic
199C22×Q16C22×C12711yescharacteristic
200C2×#131C22×C12711yescharacteristic
201#536—21no—
202C2×Q32—22no—
203C2×Q32—22no—
204C2×Q32—22no—
205C2×M32C22×C12711yescharacteristic
206C22×C16C22×C12711yescharacteristic
207#473—22no—
208#473—22no—
209#470—22no—
210#467—22no—
211C2×#108C22×C12711yescharacteristic
212#427C22×C12711yescharacteristic
213#419—21no—
214C2×#101—21no—
215#362—22no—
216#358—22no—
217#350—22no—
218C2×#41D4×C12711yescharacteristic
219C22×Q8—21no—
220C22×Q8—21no—
221#137—24no—
222#137—42no—
223C2×Q16—21no—
224C2×Q16—21no—
225C2×Q16—21no—
226C2×Q16—21no—
227C2×Q16—21no—
228C2×Q16—21no—
229C2×Q16—21no—
230C2×Q16—21no—
231C2×Q16—21no—
232C2×Q16—21no—
233C2×Q16—41no—
234C2×Q16D4×C12712yes—
235C2×Q16D4×C12712yes—
236C2×SD16—41no—
237#131—21no—
238#131—21no—
239#131—21no—
240#131—21no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16D4×C12711yescharacteristic
244C22×C8—21no—
245C22×C8C23×C12711yescharacteristic
246C4⋊Q8—41no—
247#124—41no—
248#123—42no—
249C22⋊Q8—24no—
250#117—21no—
251Q32—28no—
252M32—21no—
253M32—21no—
254C2×C16—21no—
255C2×C16—21no—
256C2×C16—21no—
257C2×C16D4×C12712yes—
258#108—21no—
259#108D4×C12712yes—
260#107D4×C12712yes—
261#106—21no—
262#103—24no—
263#101—24no—
264#41—21no—
265#41—21no—
266#41—21no—
267#41—21no—
268C2×Q8—22no—
269C2×Q8—22no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8D8×C12711yescharacteristic
281C2×D4—21no—
282C2×D4D8×C12711yescharacteristic
283C22×C4—21no—
284C22×C4—41no—
285C22×C4—41no—
286C22×C4C2×D4×C12711yescharacteristic
287Q16—22no—
288Q16—22no—
289Q16—22no—
290Q16—22no—
291Q16—44no—
292Q16—41no—
293Q16—41no—
294Q16—41no—
295Q16—41no—
296SD16—44no—
297M16—21no—
298M16—22no—
299M16—21no—
300M16—41no—
301M16—41no—
302M16—41no—
303C2×C8—21no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8C2×D4×C12711yescharacteristic
308C2×C8C2×D4×C12711yescharacteristic
309C2×C8C2×D4×C12711yescharacteristic
310C2×C8C2×D4×C12711yescharacteristic
311C2×C8C2×D4×C12711yescharacteristic
312C2×C8#41×C12711yescharacteristic
313C4⋊C4—22no—
314C4⋊C4—44no—
315C22⋊C4—44no—
316C22⋊C4—41no—
317C42—41no—
318C16—22no—
319C16—41no—
320C23—21no—
321C23AGL(1,ℤ/8)×C12711yescharacteristic
322Q8—21no—
323Q8—21no—
324Q8—42no—
325Q8—42no—
326Q8—42no—
327Q8—42no—
328Q8—81no—
329Q8—81no—
330Q8—81no—
331Q8—81no—
332D4—21no—
333D4—21no—
334D4—41no—
335D4—41no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4#120×C12711yescharacteristic
347C2×C4#120×C12711yescharacteristic
348C2×C4#121×C12711yescharacteristic
349C2×C4C2×D8×C12711yescharacteristic
350C2×C4#135×C12711yescharacteristic
351C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
352C8—41no—
353C8—42no—
354C8#120×C12711yescharacteristic
355C8#121×C12711yescharacteristic
356C8#121×C12711yescharacteristic
357C8#127×C12711yescharacteristic
358C22—22no—
359C22—42no—
360C22—41no—
361C22#447×C12711yescharacteristic
362C22#449×C12711yescharacteristic
363C22#469×C12711yescharacteristic
364C4—41no—
365C4—82no—
366C4—82no—
367C4—82no—
368C4#392×C12711yescharacteristic
369C4#447×C12711yescharacteristic
370C4#449×C12711yescharacteristic
371C4#466×C12711yescharacteristic
372C2—21no—
373C2—21no—
374C2—81no—
375C2C127×#199911yescharacteristic
376C2C127×#219512yes—
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC2×#41×C127D4
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×Q32×C127C2semidirect
4. C2×#362×C127C2semidirect
5. C127×#2141C2semidirect
7. C127×#1382C2semidirect
183. #13322C127direct (N × H)
189. C22×Q32C2×C127semidirect
192. C2×#362C2×C127semidirect
193. #2141C2×C127semidirect
195. #1382C2×C127semidirect
196. C127#13322direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q32×C1272
C2×#473×C1272
C127×#30592
C2×#362×C1272
C127×#21412
C2×#350×C1272
C127×#13822
#13322127