Finite Group Databasebeta

← C127×#9340 #44573013

Subgroups — C127×#9340 #44573013

Order 32512.

480 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3217C211yesmaximal, characteristic
2C127×#2995C211yesmaximal, characteristic, complemented
3C127×#1965C211yesmaximal, characteristic, complemented
4C127×#1555C211yesmaximal, characteristic, complemented
5C127×#1529C211yesmaximal, characteristic, complemented
6C127×#1307C211yesmaximal, characteristic, complemented
7C127×#1291C211yesmaximal, characteristic, complemented
8C2×#127×C127C2211yescharacteristic
9#529×C127C2211yescharacteristic
10#496×C127—21no—
11#490×C127—21no—
12#460×C127—21no—
13#459×C127—21no—
14#450×C127C412yes—
15#447×C127C412yes—
16#446×C127—21no—
17#436×C127—21no—
18#435×C127—21no—
19#435×C127—21no—
20#433×C127—21no—
21#432×C127C2211yescharacteristic
22#432×C127C2211yescharacteristic
23#432×C127C2211yescharacteristic
24#424×C127—21no—
25#423×C127C2211yescharacteristic
26C2×#100×C127—21no—
27C2×#100×C127—21no—
28C4×M16×C127C2211yescharacteristic
29#331×C127—21no—
30#331×C127—21no—
31#330×C127—21no—
32#329×C127—21no—
33C22×D4×C127—21no—
34C22×D4×C127—21no—
35C22×D4×C127C2×C412yes—
36C2×SD16×C127—22no—
37C2×D8×C127—22no—
38C2×M16×C127—21no—
39C2×M16×C127—21no—
40C2×M16×C127D411yescharacteristic
41C2×M16×C127D411yescharacteristic
42C22×C8×C127—21no—
43#127×C127—21no—
44#127×C127—21no—
45#127×C127—21no—
46#127×C127—21no—
47#126×C127—21no—
48#125×C127D411yescharacteristic
49#124×C127D411yescharacteristic
50#123×C127—21no—
51C22⋊Q8×C127C2×C411yescharacteristic
52#121×C127C2×C411yescharacteristic
53C4×Q8×C127D411yescharacteristic
54C4×D4×C127—21no—
55C4×D4×C127D411yescharacteristic
56#117×C127—21no—
57C2×C42×C127C2311yescharacteristic
58C4⋊C8×C127—21no—
59C4⋊C8×C127—21no—
60C4⋊C8×C127—21no—
61C4⋊C8×C127—21no—
62C4⋊C8×C127—21no—
63C4⋊C8×C127—21no—
64C4⋊C8×C127D411yescharacteristic
65C4⋊C8×C127D411yescharacteristic
66#102×C127—22no—
67#102×C127—22no—
68#100×C127—42no—
69#100×C127—42no—
70C22⋊C8×C127—21no—
71C22⋊C8×C127—21no—
72C22⋊C8×C127—21no—
73C22⋊C8×C127—21no—
74C22⋊C8×C127C2×C412yes—
75#97×C127—21no—
76#97×C127—21no—
77#97×C127—21no—
78#97×C127—21no—
79#97×C127—21no—
80C4×C8×C127—21no—
81C4×C8×C127—21no—
82C24×C127—22no—
83C2×Q8×C127C22⋊C411yescharacteristic
84C2×D4×C127—21no—
85C2×D4×C127—22no—
86C2×D4×C127—22no—
87C2×D4×C127—41no—
88C2×D4×C127—41no—
89C2×D4×C127—41no—
90C2×D4×C127—41no—
91C2×D4×C127—41no—
92C2×D4×C127—41no—
93C2×D4×C127—41no—
94C2×D4×C127—41no—
95C2×D4×C127—82no—
96C2×D4×C127—82no—
97C2×D4×C127C22⋊C411yescharacteristic
98C22×C4×C127—21no—
99C22×C4×C127C22×C411yescharacteristic
100C22×C4×C127C2×D411yescharacteristic
101C22×C4×C127#4111yescharacteristic
102SD16×C127—82no—
103D8×C127—82no—
104M16×C127—22no—
105M16×C127—41no—
106M16×C127—41no—
107M16×C127—41no—
108M16×C127—81no—
109C2×C8×C127—22no—
110C2×C8×C127—21no—
111C2×C8×C127—21no—
112C2×C8×C127—21no—
113C2×C8×C127—21no—
114C2×C8×C127—41no—
115C2×C8×C127—41no—
116C2×C8×C127—81no—
117C4⋊C4×C127—21no—
118C4⋊C4×C127—21no—
119C4⋊C4×C127—21no—
120C4⋊C4×C127—21no—
121C4⋊C4×C127C22⋊C411yescharacteristic
122C4⋊C4×C127C22⋊C411yescharacteristic
123C22⋊C4×C127—21no—
124C22⋊C4×C127—21no—
125C22⋊C4×C127—21no—
126C22⋊C4×C127—21no—
127C22⋊C4×C127—21no—
128C42×C127—21no—
129C42×C127C2×D411yescharacteristic
130C42×C127C2×D411yescharacteristic
131C42×C127C2×D411yescharacteristic
132C42×C127#4111yescharacteristic
133C23×C127—21no—
134C23×C127—42no—
135C23×C127—42no—
136C23×C127—42no—
137C23×C127—82no—
138C23×C127—82no—
139C23×C127C4×D411yescharacteristic
140Q8×C127—41no—
141D4×C127—41no—
142D4×C127—42no—
143D4×C127—42no—
144D4×C127—82no—
145D4×C127—81no—
146D4×C127—81no—
147D4×C127—82no—
148D4×C127—82no—
149D4×C127—81no—
150D4×C127—81no—
151D4×C127—81no—
152C2×C4×C127—21no—
153C2×C4×C127—21no—
154C2×C4×C127—21no—
155C2×C4×C127—21no—
156C2×C4×C127—21no—
157C2×C4×C127—41no—
158C2×C4×C127—41no—
159C2×C4×C127—41no—
160C2×C4×C127—41no—
161C2×C4×C127C2×C22⋊C411yescharacteristic
162C2×C4×C127C4×D411yescharacteristic
163C2×C4×C127#12011yescharacteristic
164C2×C4×C127#12111yescharacteristic
165C2×C4×C127#12111yescharacteristic
166C2×C4×C127#12311yescharacteristic
167C8×C127—42no—
168C8×C127—42no—
169C8×C127—41no—
170C8×C127—41no—
171C8×C127—41no—
172C8×C127—41no—
173C8×C127—81no—
174C22×C127—21no—
175C22×C127—21no—
176C22×C127—21no—
177C22×C127—41no—
178C22×C127—41no—
179C22×C127—41no—
180C22×C127—82no—
181C22×C127—82no—
182C22×C127—82no—
183C22×C127—162no—
184C22×C127—162no—
185C22×C127#38611yescharacteristic
186C4×C127—21no—
187C4×C127—21no—
188C4×C127—21no—
189C4×C127—21no—
190C4×C127—21no—
191C4×C127—41no—
192C4×C127—41no—
193C4×C127—41no—
194C4×C127#45311yescharacteristic
195C4×C127#45411yescharacteristic
196#9340C12711yesmaximal, characteristic, direct product factor, Sylow
197C2×C127—41no—
198C2×C127—81no—
199C2×C127—162no—
200C2×C127#188311yescharacteristic
201C2×C127#190311yescharacteristic
202C2×C127#191411yescharacteristic
203#3217C2×C12711yescharacteristic
204#2995C2×C12711yescharacteristic, complemented
205#1965C2×C12711yescharacteristic, complemented
206#1555C2×C12711yescharacteristic, complemented
207#1529C2×C12711yescharacteristic, complemented
208#1307C2×C12711yescharacteristic, complemented
209#1291C2×C12711yescharacteristic, complemented
210C127#934011yescharacteristic, direct product factor, Sylow
211C2×#127C22×C12711yescharacteristic
212#529C22×C12711yescharacteristic
213#496—21no—
214#490—21no—
215#460—21no—
216#459—21no—
217#450C4×C12712yes—
218#447C4×C12712yes—
219#446—21no—
220#436—21no—
221#435—21no—
222#435—21no—
223#433—21no—
224#432C22×C12711yescharacteristic
225#432C22×C12711yescharacteristic
226#432C22×C12711yescharacteristic
227#424—21no—
228#423C22×C12711yescharacteristic
229C2×#100—21no—
230C2×#100—21no—
231C4×M16C22×C12711yescharacteristic
232#331—21no—
233#331—21no—
234#330—21no—
235#329—21no—
236C22×D4—21no—
237C22×D4—21no—
238C22×D4C2×C4×C12712yes—
239C2×SD16—22no—
240C2×D8—22no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16D4×C12711yescharacteristic
244C2×M16D4×C12711yescharacteristic
245C22×C8—21no—
246#127—21no—
247#127—21no—
248#127—21no—
249#127—21no—
250#126—21no—
251#125D4×C12711yescharacteristic
252#124D4×C12711yescharacteristic
253#123—21no—
254C22⋊Q8C2×C4×C12711yescharacteristic
255#121C2×C4×C12711yescharacteristic
256C4×Q8D4×C12711yescharacteristic
257C4×D4—21no—
258C4×D4D4×C12711yescharacteristic
259#117—21no—
260C2×C42C23×C12711yescharacteristic
261C4⋊C8—21no—
262C4⋊C8—21no—
263C4⋊C8—21no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—21no—
267C4⋊C8D4×C12711yescharacteristic
268C4⋊C8D4×C12711yescharacteristic
269#102—22no—
270#102—22no—
271#100—42no—
272#100—42no—
273C22⋊C8—21no—
274C22⋊C8—21no—
275C22⋊C8—21no—
276C22⋊C8—21no—
277C22⋊C8C2×C4×C12712yes—
278#97—21no—
279#97—21no—
280#97—21no—
281#97—21no—
282#97—21no—
283C4×C8—21no—
284C4×C8—21no—
285C24—22no—
286C2×Q8C22⋊C4×C12711yescharacteristic
287C2×D4—21no—
288C2×D4—22no—
289C2×D4—22no—
290C2×D4—41no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—41no—
296C2×D4—41no—
297C2×D4—41no—
298C2×D4—82no—
299C2×D4—82no—
300C2×D4C22⋊C4×C12711yescharacteristic
301C22×C4—21no—
302C22×C4C22×C4×C12711yescharacteristic
303C22×C4C2×D4×C12711yescharacteristic
304C22×C4#41×C12711yescharacteristic
305SD16—82no—
306D8—82no—
307M16—22no—
308M16—41no—
309M16—41no—
310M16—41no—
311M16—81no—
312C2×C8—22no—
313C2×C8—21no—
314C2×C8—21no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—41no—
318C2×C8—41no—
319C2×C8—81no—
320C4⋊C4—21no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4C22⋊C4×C12711yescharacteristic
325C4⋊C4C22⋊C4×C12711yescharacteristic
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C22⋊C4—21no—
331C42—21no—
332C42C2×D4×C12711yescharacteristic
333C42C2×D4×C12711yescharacteristic
334C42C2×D4×C12711yescharacteristic
335C42#41×C12711yescharacteristic
336C23—21no—
337C23—42no—
338C23—42no—
339C23—42no—
340C23—82no—
341C23—82no—
342C23C4×D4×C12711yescharacteristic
343Q8—41no—
344D4—41no—
345D4—42no—
346D4—42no—
347D4—82no—
348D4—81no—
349D4—81no—
350D4—82no—
351D4—82no—
352D4—81no—
353D4—81no—
354D4—81no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4C2×C22⋊C4×C12711yescharacteristic
365C2×C4C4×D4×C12711yescharacteristic
366C2×C4#120×C12711yescharacteristic
367C2×C4#121×C12711yescharacteristic
368C2×C4#121×C12711yescharacteristic
369C2×C4#123×C12711yescharacteristic
370C8—42no—
371C8—42no—
372C8—41no—
373C8—41no—
374C8—41no—
375C8—41no—
376C8—81no—
377C22—21no—
378C22—21no—
379C22—21no—
380C22—41no—
381C22—41no—
382C22—41no—
383C22—82no—
384C22—82no—
385C22—82no—
386C22—162no—
387C22—162no—
388C22#386×C12711yescharacteristic
389C4—21no—
390C4—21no—
391C4—21no—
392C4—21no—
393C4—21no—
394C4—41no—
395C4—41no—
396C4—41no—
397C4#453×C12711yescharacteristic
398C4#454×C12711yescharacteristic
399C2—41no—
400C2—81no—
401C2—162no—
402C2C127×#188311yescharacteristic
403C2C127×#190311yescharacteristic
404C2C127×#191411yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3217C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#2995C2semidirect
3. C127×#1965C2semidirect
4. C127×#1555C2semidirect
5. C127×#1529C2semidirect
6. C127×#1307C2semidirect
7. C127×#1291C2semidirect
196. #9340C127direct (N × H)
204. #2995C2×C127semidirect
205. #1965C2×C127semidirect
206. #1555C2×C127semidirect
207. #1529C2×C127semidirect
208. #1307C2×C127semidirect
209. #1291C2×C127semidirect
210. C127#9340direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#32172
C127×#29952
C127×#19652
C127×#15552
C127×#15292
C127×#13072
C127×#12912
#9340127