Finite Group Databasebeta

← C127×#13337 #44577010

Subgroups — C127×#13337 #44577010

Order 32512.

554 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#509×C127C211yesmaximal, characteristic
2C22×SD32×C127C211yesmaximal, characteristic, complemented
3C127×#3156C211yesmaximal, characteristic, complemented
4C2×#362×C127C211yesmaximal, characteristic, complemented
5C2×#359×C127C211yesmaximal, characteristic, complemented
6C127×#1978C211yesmaximal, characteristic, complemented
7C127×#1379C211yesmaximal, characteristic, complemented
8C2×#137×C127—21no—
9C2×#135×C127C2211yescharacteristic
10C22×Q16×C127C2211yescharacteristic
11C22×D8×C127C2211yescharacteristic
12#536×C127—21no—
13#509×C127—22no—
14#509×C127—22no—
15C2×SD32×C127—22no—
16C2×SD32×C127—21no—
17C2×SD32×C127—22no—
18C2×SD32×C127—22no—
19C2×D16×C127—21no—
20C2×M32×C127C2211yescharacteristic
21C22×C16×C127C2211yescharacteristic
22#497×C127—22no—
23#495×C127—21no—
24#494×C127—21no—
25C2×#108×C127C2211yescharacteristic
26#418×C127—21no—
27C2×#100×C127—21no—
28#405×C127C2211yescharacteristic
29#362×C127—22no—
30#359×C127—22no—
31C2×#41×C127—21no—
32C22×Q8×C127—21no—
33C22×D4×C127—21no—
34#137×C127—42no—
35#137×C127—42no—
36#135×C127—21no—
37#135×C127—21no—
38#135×C127—21no—
39#135×C127—21no—
40C2×Q16×C127—22no—
41C2×Q16×C127—21no—
42C2×Q16×C127—21no—
43C2×Q16×C127—21no—
44C2×Q16×C127—21no—
45C2×Q16×C127—21no—
46C2×Q16×C127D412yes—
47C2×Q16×C127D411yescharacteristic
48C2×SD16×C127—22no—
49C2×SD16×C127—21no—
50C2×D8×C127—21no—
51C2×D8×C127—21no—
52C2×D8×C127—21no—
53C2×D8×C127—21no—
54C2×D8×C127—21no—
55C2×D8×C127D411yescharacteristic
56C2×D8×C127D412yes—
57C2×M16×C127—21no—
58C2×M16×C127D411yescharacteristic
59C22×C8×C127C2311yescharacteristic
60C4⋊Q8×C127—22no—
61#124×C127—22no—
62#123×C127—42no—
63C22⋊Q8×C127—42no—
64#117×C127D411yescharacteristic
65SD32×C127—28no—
66SD32×C127—24no—
67D16×C127—24no—
68M32×C127—21no—
69M32×C127D412yes—
70C2×C16×C127—21no—
71C2×C16×C127—21no—
72C2×C16×C127—21no—
73C2×C16×C127D412yes—
74#108×C127—21no—
75#108×C127—21no—
76#102×C127—42no—
77#100×C127—42no—
78#97×C127—21no—
79C4×C8×C127—21no—
80C24×C127—41no—
81#41×C127—41no—
82#41×C127—41no—
83#41×C127—41no—
84#41×C127—41no—
85C2×Q8×C127—22no—
86C2×Q8×C127—21no—
87C2×Q8×C127—41no—
88C2×Q8×C127—41no—
89C2×Q8×C127—41no—
90C2×Q8×C127—41no—
91C2×Q8×C127—41no—
92C2×D4×C127—21no—
93C2×D4×C127—22no—
94C2×D4×C127—41no—
95C2×D4×C127—41no—
96C2×D4×C127—41no—
97C2×D4×C127—41no—
98C2×D4×C127—41no—
99C2×D4×C127—41no—
100C22×C4×C127—41no—
101C22×C4×C127—41no—
102C22×C4×C127C2×D411yescharacteristic
103Q16×C127—22no—
104Q16×C127—21no—
105Q16×C127—22no—
106Q16×C127—21no—
107Q16×C127—44no—
108Q16×C127—41no—
109Q16×C127—41no—
110SD16×C127—44no—
111SD16×C127—41no—
112SD16×C127—41no—
113D8×C127—21no—
114D8×C127—22no—
115D8×C127—22no—
116D8×C127—21no—
117D8×C127—41no—
118D8×C127—41no—
119M16×C127—21no—
120M16×C127—41no—
121M16×C127—41no—
122M16×C127D812yes—
123C2×C8×C127—21no—
124C2×C8×C127—41no—
125C2×C8×C127C2×D411yescharacteristic
126C2×C8×C127C2×D411yescharacteristic
127C2×C8×C127C2×D411yescharacteristic
128C2×C8×C127C2×D411yescharacteristic
129C2×C8×C127C2×D411yescharacteristic
130C2×C8×C127#4111yescharacteristic
131C4⋊C4×C127—44no—
132C4⋊C4×C127D812yes—
133C22⋊C4×C127—21no—
134C22⋊C4×C127—44no—
135C42×C127—21no—
136C16×C127—22no—
137C16×C127—22no—
138C23×C127—41no—
139C23×C127—42no—
140C23×C127—81no—
141C23×C127—81no—
142C23×C127—162no—
143C23×C127AGL(1,ℤ/8)11yescharacteristic
144Q8×C127—41no—
145Q8×C127—42no—
146Q8×C127—42no—
147Q8×C127—41no—
148Q8×C127—81no—
149Q8×C127—81no—
150D4×C127—42no—
151D4×C127—41no—
152D4×C127—41no—
153D4×C127—42no—
154D4×C127—81no—
155D4×C127—81no—
156D4×C127—81no—
157D4×C127—81no—
158C2×C4×C127—22no—
159C2×C4×C127—42no—
160C2×C4×C127—41no—
161C2×C4×C127—81no—
162C2×C4×C127—81no—
163C2×C4×C127—81no—
164C2×C4×C127—81no—
165C2×C4×C127#12011yescharacteristic
166C2×C4×C127#12111yescharacteristic
167C2×C4×C127#12711yescharacteristic
168C2×C4×C127C2×D811yescharacteristic
169C2×C4×C127C2×D811yescharacteristic
170C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
171C8×C127—22no—
172C8×C127—81no—
173C8×C127#12011yescharacteristic
174C8×C127#12011yescharacteristic
175C8×C127#12111yescharacteristic
176C8×C127#12111yescharacteristic
177C22×C127—22no—
178C22×C127—82no—
179C22×C127—81no—
180C22×C127—82no—
181C22×C127—162no—
182C22×C127—162no—
183C22×C127—162no—
184C22×C127#44711yescharacteristic
185C22×C127#45911yescharacteristic
186C22×C127#49611yescharacteristic
187C4×C127—42no—
188C4×C127—81no—
189C4×C127—82no—
190C4×C127#39211yescharacteristic
191C4×C127#44711yescharacteristic
192C4×C127#45911yescharacteristic
193C4×C127#49311yescharacteristic
194#13337C12711yesmaximal, characteristic, direct product factor, Sylow
195C2×C127—21no—
196C2×C127—21no—
197C2×C127—161no—
198C2×C127—162no—
199C2×C127#201111yescharacteristic
200C2×C127#219312yes—
201C2×#509C2×C12711yescharacteristic
202C22×SD32C2×C12711yescharacteristic, complemented
203#3156C2×C12711yescharacteristic, complemented
204C2×#362C2×C12711yescharacteristic, complemented
205C2×#359C2×C12711yescharacteristic, complemented
206#1978C2×C12711yescharacteristic, complemented
207#1379C2×C12711yescharacteristic, complemented
208C127#1333711yescharacteristic, direct product factor, Sylow
209C2×#137—21no—
210C2×#135C22×C12711yescharacteristic
211C22×Q16C22×C12711yescharacteristic
212C22×D8C22×C12711yescharacteristic
213#536—21no—
214#509—22no—
215#509—22no—
216C2×SD32—22no—
217C2×SD32—21no—
218C2×SD32—22no—
219C2×SD32—22no—
220C2×D16—21no—
221C2×M32C22×C12711yescharacteristic
222C22×C16C22×C12711yescharacteristic
223#497—22no—
224#495—21no—
225#494—21no—
226C2×#108C22×C12711yescharacteristic
227#418—21no—
228C2×#100—21no—
229#405C22×C12711yescharacteristic
230#362—22no—
231#359—22no—
232C2×#41—21no—
233C22×Q8—21no—
234C22×D4—21no—
235#137—42no—
236#137—42no—
237#135—21no—
238#135—21no—
239#135—21no—
240#135—21no—
241C2×Q16—22no—
242C2×Q16—21no—
243C2×Q16—21no—
244C2×Q16—21no—
245C2×Q16—21no—
246C2×Q16—21no—
247C2×Q16D4×C12712yes—
248C2×Q16D4×C12711yescharacteristic
249C2×SD16—22no—
250C2×SD16—21no—
251C2×D8—21no—
252C2×D8—21no—
253C2×D8—21no—
254C2×D8—21no—
255C2×D8—21no—
256C2×D8D4×C12712yes—
257C2×D8D4×C12711yescharacteristic
258C2×M16—21no—
259C2×M16D4×C12711yescharacteristic
260C22×C8C23×C12711yescharacteristic
261C4⋊Q8—22no—
262#124—22no—
263#123—42no—
264C22⋊Q8—42no—
265#117D4×C12711yescharacteristic
266SD32—28no—
267SD32—24no—
268D16—24no—
269M32—21no—
270M32D4×C12712yes—
271C2×C16—21no—
272C2×C16—21no—
273C2×C16—21no—
274C2×C16D4×C12712yes—
275#108—21no—
276#108—21no—
277#102—42no—
278#100—42no—
279#97—21no—
280C4×C8—21no—
281C24—41no—
282#41—41no—
283#41—41no—
284#41—41no—
285#41—41no—
286C2×Q8—22no—
287C2×Q8—21no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×D4—21no—
294C2×D4—22no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4C2×D4×C12711yescharacteristic
304Q16—22no—
305Q16—21no—
306Q16—22no—
307Q16—21no—
308Q16—44no—
309Q16—41no—
310Q16—41no—
311SD16—44no—
312SD16—41no—
313SD16—41no—
314D8—21no—
315D8—22no—
316D8—22no—
317D8—21no—
318D8—41no—
319D8—41no—
320M16—21no—
321M16—41no—
322M16—41no—
323M16D8×C12712yes—
324C2×C8—21no—
325C2×C8—41no—
326C2×C8C2×D4×C12711yescharacteristic
327C2×C8C2×D4×C12711yescharacteristic
328C2×C8C2×D4×C12711yescharacteristic
329C2×C8C2×D4×C12711yescharacteristic
330C2×C8C2×D4×C12711yescharacteristic
331C2×C8#41×C12711yescharacteristic
332C4⋊C4—44no—
333C4⋊C4D8×C12712yes—
334C22⋊C4—21no—
335C22⋊C4—44no—
336C42—21no—
337C16—22no—
338C16—22no—
339C23—41no—
340C23—42no—
341C23—81no—
342C23—81no—
343C23—162no—
344C23AGL(1,ℤ/8)×C12711yescharacteristic
345Q8—41no—
346Q8—42no—
347Q8—42no—
348Q8—41no—
349Q8—81no—
350Q8—81no—
351D4—42no—
352D4—41no—
353D4—41no—
354D4—42no—
355D4—81no—
356D4—81no—
357D4—81no—
358D4—81no—
359C2×C4—22no—
360C2×C4—42no—
361C2×C4—41no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4#120×C12711yescharacteristic
367C2×C4#121×C12711yescharacteristic
368C2×C4#127×C12711yescharacteristic
369C2×C4C2×D8×C12711yescharacteristic
370C2×C4C2×D8×C12711yescharacteristic
371C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
372C8—22no—
373C8—81no—
374C8#120×C12711yescharacteristic
375C8#120×C12711yescharacteristic
376C8#121×C12711yescharacteristic
377C8#121×C12711yescharacteristic
378C22—22no—
379C22—82no—
380C22—81no—
381C22—82no—
382C22—162no—
383C22—162no—
384C22—162no—
385C22#447×C12711yescharacteristic
386C22#459×C12711yescharacteristic
387C22#496×C12711yescharacteristic
388C4—42no—
389C4—81no—
390C4—82no—
391C4#392×C12711yescharacteristic
392C4#447×C12711yescharacteristic
393C4#459×C12711yescharacteristic
394C4#493×C12711yescharacteristic
395C2—21no—
396C2—21no—
397C2—161no—
398C2—162no—
399C2C127×#201111yescharacteristic
400C2C127×#219312yes—
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC2×#509×C127C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ #405×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×SD32×C127C2semidirect
3. C127×#3156C2semidirect
4. C2×#362×C127C2semidirect
5. C2×#359×C127C2semidirect
6. C127×#1978C2semidirect
7. C127×#1379C2semidirect
194. #13337C127direct (N × H)
202. C22×SD32C2×C127semidirect
203. #3156C2×C127semidirect
204. C2×#362C2×C127semidirect
205. C2×#359C2×C127semidirect
206. #1978C2×C127semidirect
207. #1379C2×C127semidirect
208. C127#13337direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#509×C1272
C22×SD32×C1272
C127×#31562
C2×#362×C1272
C2×#359×C1272
C127×#19782
C127×#13792
#13337127