Finite Group Databasebeta

← C127×#13324 #44576997

Subgroups — C127×#13324 #44576997

Order 32512.

514 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#510×C127C211yesmaximal, characteristic, complemented
2C127×#3067C211yesmaximal, characteristic
3C2×#473×C127C211yesmaximal, characteristic, complemented
4C2×#362×C127C211yesmaximal, characteristic, complemented
5C127×#2143C211yesmaximal, characteristic, complemented
6C127×#2115C211yesmaximal, characteristic, complemented
7C127×#1388C211yesmaximal, characteristic, complemented
8#575×C127—21no—
9C2×#137×C127—21no—
10C2×#135×C127C2211yescharacteristic
11C22×Q16×C127C2211yescharacteristic
12C2×#131×C127C2211yescharacteristic
13#510×C127—22no—
14#510×C127—22no—
15C2×Q32×C127—21no—
16C2×SD32×C127—21no—
17C2×M32×C127C2211yescharacteristic
18C2×M32×C127C2211yescharacteristic
19#473×C127—22no—
20#473×C127—21no—
21#473×C127—22no—
22#472×C127—21no—
23#471×C127—22no—
24C2×#108×C127C2211yescharacteristic
25C2×#108×C127C2211yescharacteristic
26#413×C127—21no—
27C2×#101×C127—21no—
28#362×C127—22no—
29#359×C127—22no—
30#349×C127—22no—
31C2×#41×C127—21no—
32C2×#41×C127D411yescharacteristic
33C22×Q8×C127—21no—
34#137×C127—24no—
35#137×C127—22no—
36#137×C127—42no—
37#137×C127—41no—
38AGL(1,ℤ/8)×C127—22no—
39AGL(1,ℤ/8)×C127—41no—
40#135×C127—21no—
41#135×C127—21no—
42#135×C127—21no—
43#135×C127—21no—
44#135×C127—42no—
45C2×Q16×C127—21no—
46C2×Q16×C127—21no—
47C2×Q16×C127—21no—
48C2×Q16×C127—21no—
49C2×Q16×C127—21no—
50C2×Q16×C127—41no—
51C2×Q16×C127D411yescharacteristic
52C2×Q16×C127D412yes—
53C2×SD16×C127—21no—
54C2×SD16×C127—41no—
55C2×D8×C127D411yescharacteristic
56#131×C127—21no—
57#131×C127—21no—
58#131×C127—21no—
59#131×C127—21no—
60C2×M16×C127—21no—
61C2×M16×C127—21no—
62C2×M16×C127—21no—
63C2×M16×C127D411yescharacteristic
64C22×C8×C127—21no—
65C22×C8×C127C2311yescharacteristic
66Q32×C127—24no—
67SD32×C127—24no—
68M32×C127—21no—
69M32×C127—21no—
70M32×C127—21no—
71M32×C127D412yes—
72C2×C16×C127—21no—
73C2×C16×C127—21no—
74#108×C127—21no—
75#108×C127—21no—
76#108×C127D412yes—
77#108×C127D412yes—
78#101×C127—24no—
79#101×C127—22no—
80#100×C127—22no—
81#41×C127—21no—
82#41×C127—21no—
83#41×C127—21no—
84#41×C127—21no—
85#41×C127—41no—
86#41×C127—41no—
87#41×C127—41no—
88#41×C127—41no—
89C2×Q8×C127—21no—
90C2×Q8×C127—22no—
91C2×Q8×C127—41no—
92C2×Q8×C127—41no—
93C2×Q8×C127—41no—
94C2×Q8×C127—41no—
95C2×Q8×C127—41no—
96C2×Q8×C127D811yescharacteristic
97C2×D4×C127—21no—
98C2×D4×C127—21no—
99C2×D4×C127—41no—
100C2×D4×C127D811yescharacteristic
101C22×C4×C127—21no—
102C22×C4×C127—41no—
103C22×C4×C127—41no—
104C22×C4×C127C2×D411yescharacteristic
105Q16×C127—22no—
106Q16×C127—21no—
107Q16×C127—22no—
108Q16×C127—21no—
109Q16×C127—44no—
110Q16×C127—42no—
111Q16×C127—41no—
112Q16×C127—41no—
113SD16×C127—44no—
114SD16×C127—42no—
115SD16×C127—42no—
116SD16×C127—41no—
117SD16×C127—41no—
118D8×C127—21no—
119D8×C127—21no—
120D8×C127—42no—
121M16×C127—21no—
122M16×C127—22no—
123M16×C127—21no—
124M16×C127—22no—
125M16×C127—41no—
126M16×C127—41no—
127M16×C127—41no—
128M16×C127—41no—
129C2×C8×C127—21no—
130C2×C8×C127—41no—
131C2×C8×C127—41no—
132C2×C8×C127—41no—
133C2×C8×C127—41no—
134C2×C8×C127C2×D411yescharacteristic
135C2×C8×C127C2×D411yescharacteristic
136C2×C8×C127C2×D411yescharacteristic
137C2×C8×C127C2×D411yescharacteristic
138C2×C8×C127C2×D411yescharacteristic
139C2×C8×C127#4111yescharacteristic
140C16×C127—22no—
141C16×C127—41no—
142C23×C127—21no—
143C23×C127—41no—
144C23×C127#13511yescharacteristic
145Q8×C127—21no—
146Q8×C127—21no—
147Q8×C127—41no—
148Q8×C127—42no—
149Q8×C127—42no—
150Q8×C127—41no—
151Q8×C127—81no—
152Q8×C127—81no—
153D4×C127—21no—
154D4×C127—21no—
155D4×C127—41no—
156D4×C127—41no—
157D4×C127—41no—
158D4×C127—41no—
159D4×C127—81no—
160D4×C127—81no—
161C2×C4×C127—21no—
162C2×C4×C127—41no—
163C2×C4×C127—41no—
164C2×C4×C127—41no—
165C2×C4×C127—42no—
166C2×C4×C127—81no—
167C2×C4×C127—81no—
168C2×C4×C127—81no—
169C2×C4×C127—81no—
170C2×C4×C127#12011yescharacteristic
171C2×C4×C127#12011yescharacteristic
172C2×C4×C127#12111yescharacteristic
173C2×C4×C127C2×D811yescharacteristic
174C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
175C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
176C8×C127—41no—
177C8×C127—42no—
178C8×C127—42no—
179C8×C127#12011yescharacteristic
180C8×C127#12111yescharacteristic
181C8×C127#12111yescharacteristic
182C8×C127#12711yescharacteristic
183C22×C127—41no—
184C22×C127—41no—
185C22×C127—81no—
186C22×C127—81no—
187C22×C127—161no—
188C22×C127#44911yescharacteristic
189C22×C127#44911yescharacteristic
190C22×C127#46611yescharacteristic
191C4×C127—41no—
192C4×C127—81no—
193C4×C127—82no—
194C4×C127#39211yescharacteristic
195C4×C127#44711yescharacteristic
196C4×C127#44711yescharacteristic
197C4×C127#46911yescharacteristic
198#13324C12711yesmaximal, characteristic, direct product factor, Sylow
199C2×C127—21no—
200C2×C127—21no—
201C2×C127—21no—
202C2×C127—81no—
203C2×C127—161no—
204C2×C127#199911yescharacteristic
205C2×#510C2×C12711yescharacteristic, complemented
206#3067C2×C12711yescharacteristic
207C2×#473C2×C12711yescharacteristic, complemented
208C2×#362C2×C12711yescharacteristic, complemented
209#2143C2×C12711yescharacteristic, complemented
210#2115C2×C12711yescharacteristic, complemented
211#1388C2×C12711yescharacteristic, complemented
212C127#1332411yescharacteristic, direct product factor, Sylow
213#575—21no—
214C2×#137—21no—
215C2×#135C22×C12711yescharacteristic
216C22×Q16C22×C12711yescharacteristic
217C2×#131C22×C12711yescharacteristic
218#510—22no—
219#510—22no—
220C2×Q32—21no—
221C2×SD32—21no—
222C2×M32C22×C12711yescharacteristic
223C2×M32C22×C12711yescharacteristic
224#473—22no—
225#473—21no—
226#473—22no—
227#472—21no—
228#471—22no—
229C2×#108C22×C12711yescharacteristic
230C2×#108C22×C12711yescharacteristic
231#413—21no—
232C2×#101—21no—
233#362—22no—
234#359—22no—
235#349—22no—
236C2×#41—21no—
237C2×#41D4×C12711yescharacteristic
238C22×Q8—21no—
239#137—24no—
240#137—22no—
241#137—42no—
242#137—41no—
243AGL(1,ℤ/8)—22no—
244AGL(1,ℤ/8)—41no—
245#135—21no—
246#135—21no—
247#135—21no—
248#135—21no—
249#135—42no—
250C2×Q16—21no—
251C2×Q16—21no—
252C2×Q16—21no—
253C2×Q16—21no—
254C2×Q16—21no—
255C2×Q16—41no—
256C2×Q16D4×C12712yes—
257C2×Q16D4×C12711yescharacteristic
258C2×SD16—21no—
259C2×SD16—41no—
260C2×D8D4×C12711yescharacteristic
261#131—21no—
262#131—21no—
263#131—21no—
264#131—21no—
265C2×M16—21no—
266C2×M16—21no—
267C2×M16—21no—
268C2×M16D4×C12711yescharacteristic
269C22×C8—21no—
270C22×C8C23×C12711yescharacteristic
271Q32—24no—
272SD32—24no—
273M32—21no—
274M32—21no—
275M32—21no—
276M32D4×C12712yes—
277C2×C16—21no—
278C2×C16—21no—
279#108—21no—
280#108—21no—
281#108D4×C12712yes—
282#108D4×C12712yes—
283#101—24no—
284#101—22no—
285#100—22no—
286#41—21no—
287#41—21no—
288#41—21no—
289#41—21no—
290#41—41no—
291#41—41no—
292#41—41no—
293#41—41no—
294C2×Q8—21no—
295C2×Q8—22no—
296C2×Q8—41no—
297C2×Q8—41no—
298C2×Q8—41no—
299C2×Q8—41no—
300C2×Q8—41no—
301C2×Q8D8×C12711yescharacteristic
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—41no—
305C2×D4D8×C12711yescharacteristic
306C22×C4—21no—
307C22×C4—41no—
308C22×C4—41no—
309C22×C4C2×D4×C12711yescharacteristic
310Q16—22no—
311Q16—21no—
312Q16—22no—
313Q16—21no—
314Q16—44no—
315Q16—42no—
316Q16—41no—
317Q16—41no—
318SD16—44no—
319SD16—42no—
320SD16—42no—
321SD16—41no—
322SD16—41no—
323D8—21no—
324D8—21no—
325D8—42no—
326M16—21no—
327M16—22no—
328M16—21no—
329M16—22no—
330M16—41no—
331M16—41no—
332M16—41no—
333M16—41no—
334C2×C8—21no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8C2×D4×C12711yescharacteristic
340C2×C8C2×D4×C12711yescharacteristic
341C2×C8C2×D4×C12711yescharacteristic
342C2×C8C2×D4×C12711yescharacteristic
343C2×C8C2×D4×C12711yescharacteristic
344C2×C8#41×C12711yescharacteristic
345C16—22no—
346C16—41no—
347C23—21no—
348C23—41no—
349C23#135×C12711yescharacteristic
350Q8—21no—
351Q8—21no—
352Q8—41no—
353Q8—42no—
354Q8—42no—
355Q8—41no—
356Q8—81no—
357Q8—81no—
358D4—21no—
359D4—21no—
360D4—41no—
361D4—41no—
362D4—41no—
363D4—41no—
364D4—81no—
365D4—81no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—42no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4#120×C12711yescharacteristic
376C2×C4#120×C12711yescharacteristic
377C2×C4#121×C12711yescharacteristic
378C2×C4C2×D8×C12711yescharacteristic
379C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
380C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
381C8—41no—
382C8—42no—
383C8—42no—
384C8#120×C12711yescharacteristic
385C8#121×C12711yescharacteristic
386C8#121×C12711yescharacteristic
387C8#127×C12711yescharacteristic
388C22—41no—
389C22—41no—
390C22—81no—
391C22—81no—
392C22—161no—
393C22#449×C12711yescharacteristic
394C22#449×C12711yescharacteristic
395C22#466×C12711yescharacteristic
396C4—41no—
397C4—81no—
398C4—82no—
399C4#392×C12711yescharacteristic
400C4#447×C12711yescharacteristic
401C4#447×C12711yescharacteristic
402C4#469×C12711yescharacteristic
403C2—21no—
404C2—21no—
405C2—21no—
406C2—81no—
407C2—161no—
408C2C127×#199911yescharacteristic
subgroupG/H
center, socleC2×C127#1999
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC127×#3067C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C127 ◁ C22×C4×C127 ◁ C2×#131×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#510×C127C2semidirect
3. C2×#473×C127C2semidirect
4. C2×#362×C127C2semidirect
5. C127×#2143C2semidirect
6. C127×#2115C2semidirect
7. C127×#1388C2semidirect
198. #13324C127direct (N × H)
205. C2×#510C2×C127semidirect
207. C2×#473C2×C127semidirect
208. C2×#362C2×C127semidirect
209. #2143C2×C127semidirect
210. #2115C2×C127semidirect
211. #1388C2×C127semidirect
212. C127#13324direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#510×C1272
C127×#30672
C2×#473×C1272
C2×#362×C1272
C127×#21432
C127×#21152
C127×#13882
#13324127