Finite Group Databasebeta

← C127×#13339 #44577012

Subgroups — C127×#13339 #44577012

Order 32512.

534 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#510×C127C211yesmaximal, characteristic
2C22×Q32×C127C211yesmaximal, characteristic, complemented
3C127×#3156C211yesmaximal, characteristic
4C2×#362×C127C211yesmaximal, characteristic, complemented
5C2×#359×C127C211yesmaximal, characteristic
6C127×#1979C211yesmaximal, characteristic, complemented
7C127×#1379C211yesmaximal, characteristic, complemented
8C2×#137×C127—21no—
9C2×#135×C127C2211yescharacteristic
10C22×Q16×C127C2211yescharacteristic
11C22×Q16×C127C2211yescharacteristic
12#536×C127—21no—
13#510×C127—22no—
14#510×C127—22no—
15C2×Q32×C127—22no—
16C2×Q32×C127—22no—
17C2×Q32×C127—21no—
18C2×Q32×C127—22no—
19C2×SD32×C127—21no—
20C2×M32×C127C2211yescharacteristic
21C22×C16×C127C2211yescharacteristic
22#497×C127—22no—
23#495×C127—21no—
24#494×C127—21no—
25C2×#108×C127C2211yescharacteristic
26#419×C127—21no—
27C2×#101×C127—21no—
28#405×C127C2211yescharacteristic
29#362×C127—22no—
30#359×C127—22no—
31C2×#41×C127—21no—
32C22×Q8×C127—21no—
33C22×Q8×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×C127—21no—
47C2×Q16×C127—21no—
48C2×Q16×C127—21no—
49C2×Q16×C127—21no—
50C2×Q16×C127—21no—
51C2×Q16×C127D412yes—
52C2×Q16×C127D412yes—
53C2×Q16×C127D411yescharacteristic
54C2×SD16×C127—22no—
55C2×SD16×C127—21no—
56C2×D8×C127D411yescharacteristic
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
65Q32×C127—28no—
66Q32×C127—24no—
67SD32×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#103×C127—42no—
77#101×C127—42no—
78#97×C127—21no—
79C4×C8×C127—21no—
80#41×C127—41no—
81#41×C127—41no—
82#41×C127—41no—
83#41×C127—41no—
84C2×Q8×C127—22no—
85C2×Q8×C127—21no—
86C2×Q8×C127—22no—
87C2×Q8×C127—41no—
88C2×Q8×C127—41no—
89C2×Q8×C127—41no—
90C2×Q8×C127—41no—
91C2×Q8×C127—41no—
92C2×Q8×C127—41no—
93C2×Q8×C127—41no—
94C2×Q8×C127—41no—
95C2×Q8×C127—41no—
96C2×Q8×C127—41no—
97C2×D4×C127—21no—
98C2×D4×C127—41no—
99C22×C4×C127—41no—
100C22×C4×C127—41no—
101C22×C4×C127—41no—
102C22×C4×C127C2×D411yescharacteristic
103Q16×C127—22no—
104Q16×C127—22no—
105Q16×C127—22no—
106Q16×C127—21no—
107Q16×C127—22no—
108Q16×C127—21no—
109Q16×C127—44no—
110Q16×C127—41no—
111Q16×C127—41no—
112Q16×C127—41no—
113Q16×C127—41no—
114SD16×C127—44no—
115SD16×C127—41no—
116SD16×C127—41no—
117D8×C127—21no—
118D8×C127—21no—
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×C127AGL(1,ℤ/8)11yescharacteristic
140Q8×C127—41no—
141Q8×C127—42no—
142Q8×C127—42no—
143Q8×C127—42no—
144Q8×C127—41no—
145Q8×C127—42no—
146Q8×C127—81no—
147Q8×C127—81no—
148Q8×C127—81no—
149Q8×C127—81no—
150D4×C127—41no—
151D4×C127—41no—
152D4×C127—81no—
153D4×C127—81no—
154C2×C4×C127—22no—
155C2×C4×C127—42no—
156C2×C4×C127—41no—
157C2×C4×C127—42no—
158C2×C4×C127—81no—
159C2×C4×C127—81no—
160C2×C4×C127—81no—
161C2×C4×C127—81no—
162C2×C4×C127—81no—
163C2×C4×C127—81no—
164C2×C4×C127#12011yescharacteristic
165C2×C4×C127#12111yescharacteristic
166C2×C4×C127#12711yescharacteristic
167C2×C4×C127C2×D811yescharacteristic
168C2×C4×C127C2×D811yescharacteristic
169C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
170C8×C127—22no—
171C8×C127—81no—
172C8×C127#12011yescharacteristic
173C8×C127#12011yescharacteristic
174C8×C127#12111yescharacteristic
175C8×C127#12111yescharacteristic
176C22×C127—22no—
177C22×C127—82no—
178C22×C127—81no—
179C22×C127#44711yescharacteristic
180C22×C127#45911yescharacteristic
181C22×C127#49611yescharacteristic
182C4×C127—42no—
183C4×C127—81no—
184C4×C127—82no—
185C4×C127—82no—
186C4×C127#39211yescharacteristic
187C4×C127#44711yescharacteristic
188C4×C127#45911yescharacteristic
189C4×C127#49311yescharacteristic
190#13339C12711yesmaximal, characteristic, direct product factor, Sylow
191C2×C127—21no—
192C2×C127—21no—
193C2×C127—161no—
194C2×C127#201111yescharacteristic
195C2×C127#219512yes—
196C2×#510C2×C12711yescharacteristic
197C22×Q32C2×C12711yescharacteristic, complemented
198#3156C2×C12711yescharacteristic
199C2×#362C2×C12711yescharacteristic, complemented
200C2×#359C2×C12711yescharacteristic
201#1979C2×C12711yescharacteristic, complemented
202#1379C2×C12711yescharacteristic, complemented
203C127#1333911yescharacteristic, direct product factor, Sylow
204C2×#137—21no—
205C2×#135C22×C12711yescharacteristic
206C22×Q16C22×C12711yescharacteristic
207C22×Q16C22×C12711yescharacteristic
208#536—21no—
209#510—22no—
210#510—22no—
211C2×Q32—22no—
212C2×Q32—22no—
213C2×Q32—21no—
214C2×Q32—22no—
215C2×SD32—21no—
216C2×M32C22×C12711yescharacteristic
217C22×C16C22×C12711yescharacteristic
218#497—22no—
219#495—21no—
220#494—21no—
221C2×#108C22×C12711yescharacteristic
222#419—21no—
223C2×#101—21no—
224#405C22×C12711yescharacteristic
225#362—22no—
226#359—22no—
227C2×#41—21no—
228C22×Q8—21no—
229C22×Q8—21no—
230#137—42no—
231#137—42no—
232#135—21no—
233#135—21no—
234#135—21no—
235#135—21no—
236C2×Q16—22no—
237C2×Q16—21no—
238C2×Q16—21no—
239C2×Q16—21no—
240C2×Q16—21no—
241C2×Q16—21no—
242C2×Q16—21no—
243C2×Q16—21no—
244C2×Q16—21no—
245C2×Q16—21no—
246C2×Q16—21no—
247C2×Q16D4×C12712yes—
248C2×Q16D4×C12712yes—
249C2×Q16D4×C12711yescharacteristic
250C2×SD16—22no—
251C2×SD16—21no—
252C2×D8D4×C12711yescharacteristic
253C2×M16—21no—
254C2×M16D4×C12711yescharacteristic
255C22×C8C23×C12711yescharacteristic
256C4⋊Q8—22no—
257#124—22no—
258#123—42no—
259C22⋊Q8—42no—
260#117D4×C12711yescharacteristic
261Q32—28no—
262Q32—24no—
263SD32—24no—
264M32—21no—
265M32D4×C12712yes—
266C2×C16—21no—
267C2×C16—21no—
268C2×C16—21no—
269C2×C16D4×C12712yes—
270#108—21no—
271#108—21no—
272#103—42no—
273#101—42no—
274#97—21no—
275C4×C8—21no—
276#41—41no—
277#41—41no—
278#41—41no—
279#41—41no—
280C2×Q8—22no—
281C2×Q8—21no—
282C2×Q8—22no—
283C2×Q8—41no—
284C2×Q8—41no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×D4—21no—
294C2×D4—41no—
295C22×C4—41no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4C2×D4×C12711yescharacteristic
299Q16—22no—
300Q16—22no—
301Q16—22no—
302Q16—21no—
303Q16—22no—
304Q16—21no—
305Q16—44no—
306Q16—41no—
307Q16—41no—
308Q16—41no—
309Q16—41no—
310SD16—44no—
311SD16—41no—
312SD16—41no—
313D8—21no—
314D8—21no—
315M16—21no—
316M16—41no—
317M16—41no—
318M16D8×C12712yes—
319C2×C8—21no—
320C2×C8—41no—
321C2×C8C2×D4×C12711yescharacteristic
322C2×C8C2×D4×C12711yescharacteristic
323C2×C8C2×D4×C12711yescharacteristic
324C2×C8C2×D4×C12711yescharacteristic
325C2×C8C2×D4×C12711yescharacteristic
326C2×C8#41×C12711yescharacteristic
327C4⋊C4—44no—
328C4⋊C4D8×C12712yes—
329C22⋊C4—21no—
330C22⋊C4—44no—
331C42—21no—
332C16—22no—
333C16—22no—
334C23—41no—
335C23AGL(1,ℤ/8)×C12711yescharacteristic
336Q8—41no—
337Q8—42no—
338Q8—42no—
339Q8—42no—
340Q8—41no—
341Q8—42no—
342Q8—81no—
343Q8—81no—
344Q8—81no—
345Q8—81no—
346D4—41no—
347D4—41no—
348D4—81no—
349D4—81no—
350C2×C4—22no—
351C2×C4—42no—
352C2×C4—41no—
353C2×C4—42no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4#120×C12711yescharacteristic
361C2×C4#121×C12711yescharacteristic
362C2×C4#127×C12711yescharacteristic
363C2×C4C2×D8×C12711yescharacteristic
364C2×C4C2×D8×C12711yescharacteristic
365C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
366C8—22no—
367C8—81no—
368C8#120×C12711yescharacteristic
369C8#120×C12711yescharacteristic
370C8#121×C12711yescharacteristic
371C8#121×C12711yescharacteristic
372C22—22no—
373C22—82no—
374C22—81no—
375C22#447×C12711yescharacteristic
376C22#459×C12711yescharacteristic
377C22#496×C12711yescharacteristic
378C4—42no—
379C4—81no—
380C4—82no—
381C4—82no—
382C4#392×C12711yescharacteristic
383C4#447×C12711yescharacteristic
384C4#459×C12711yescharacteristic
385C4#493×C12711yescharacteristic
386C2—21no—
387C2—21no—
388C2—161no—
389C2C127×#201111yescharacteristic
390C2C127×#219512yes—
subgroupG/H
center, socleC22×C127#447
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC2×#135×C127C22
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×Q32×C127C2semidirect
4. C2×#362×C127C2semidirect
6. C127×#1979C2semidirect
7. C127×#1379C2semidirect
190. #13339C127direct (N × H)
197. C22×Q32C2×C127semidirect
199. C2×#362C2×C127semidirect
201. #1979C2×C127semidirect
202. #1379C2×C127semidirect
203. C127#13339direct (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
C22×Q32×C1272
C127×#31562
C2×#362×C1272
C2×#359×C1272
C127×#19792
C127×#13792
#13339127