Finite Group Databasebeta

← C127×#9432 #44573105

Subgroups — C127×#9432 #44573105

Order 32512.

436 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3180C211yesmaximal, characteristic
2C127×#2968C211yesmaximal, characteristic, complemented
3C127×#1530C211yesmaximal, characteristic, complemented
4C127×#1517C211yesmaximal, characteristic, complemented
5C127×#1512C211yesmaximal, characteristic, complemented
6C127×#1302C211yesmaximal, characteristic, complemented
7C127×#1295C211yesmaximal, characteristic, complemented
8#532×C127C2211yescharacteristic
9#529×C127C2211yescharacteristic
10#501×C127C411yescharacteristic, complemented
11#496×C127C411yescharacteristic, complemented
12#490×C127C411yescharacteristic, complemented
13#489×C127C411yescharacteristic, complemented
14#466×C127—21no—
15#465×C127—21no—
16#446×C127—21no—
17#442×C127—21no—
18#440×C127—21no—
19#435×C127—21no—
20#435×C127—21no—
21C8×D4×C127—21no—
22#433×C127—21no—
23#432×C127C2211yescharacteristic
24#431×C127C2211yescharacteristic
25#405×C127—21no—
26C2×#97×C127C2211yescharacteristic
27C2×#97×C127C2211yescharacteristic
28#382×C127C2211yescharacteristic
29#329×C127—21no—
30#329×C127—21no—
31#328×C127—21no—
32#327×C127—21no—
33#327×C127—21no—
34#327×C127—21no—
35C2×#41×C127—21no—
36C2×SD16×C127—21no—
37C2×D8×C127—21no—
38C2×M16×C127—21no—
39C22×C8×C127—21no—
40C22×C8×C127—21no—
41C22×C8×C127—21no—
42C4⋊Q8×C127C2×C411yescharacteristic
43#127×C127C2×C411yescharacteristic
44#126×C127—21no—
45#125×C127C2×C411yescharacteristic
46#124×C127—21no—
47#124×C127C2×C411yescharacteristic
48#123×C127—21no—
49C22⋊Q8×C127D411yescharacteristic
50#121×C127—21no—
51#121×C127—21no—
52#121×C127D411yescharacteristic
53C4×Q8×C127D411yescharacteristic
54C4×D4×C127—21no—
55C4×D4×C127—21no—
56C4×D4×C127—21no—
57C4×D4×C127D411yescharacteristic
58#117×C127—21no—
59C2×C4⋊C4×C127—21no—
60C2×C42×C127C2311yescharacteristic
61#107×C127—21no—
62#106×C127—21no—
63C4⋊C8×C127—21no—
64C4⋊C8×C127—21no—
65C4⋊C8×C127—21no—
66C4⋊C8×C127—21no—
67#103×C127—21no—
68#102×C127—21no—
69#102×C127—21no—
70#102×C127—21no—
71C22⋊C8×C127—21no—
72C22⋊C8×C127—21no—
73C22⋊C8×C127—21no—
74C22⋊C8×C127D411yescharacteristic
75C22⋊C8×C127D411yescharacteristic
76#97×C127—21no—
77#97×C127—21no—
78#97×C127—21no—
79#97×C127—21no—
80#97×C127C2×C411yescharacteristic
81#97×C127C2×C411yescharacteristic
82#97×C127D411yescharacteristic
83#97×C127D411yescharacteristic
84C4×C8×C127—21no—
85C4×C8×C127—21no—
86#95×C127—21no—
87#95×C127—21no—
88#41×C127—81no—
89#41×C127—81no—
90C2×Q8×C127—21no—
91C2×Q8×C127C22⋊C411yescharacteristic
92C2×D4×C127—21no—
93C2×D4×C127—21no—
94C2×D4×C127—21no—
95C2×D4×C127—21no—
96C2×D4×C127—41no—
97C2×D4×C127C22⋊C411yescharacteristic
98C22×C4×C127—21no—
99C22×C4×C127—41no—
100C22×C4×C127—41no—
101C22×C4×C127C2×D411yescharacteristic
102C22×C4×C127C2×D411yescharacteristic
103C22×C4×C127#4111yescharacteristic
104SD16×C127—42no—
105D8×C127—42no—
106M16×C127—42no—
107C2×C8×C127—21no—
108C2×C8×C127—21no—
109C2×C8×C127—21no—
110C2×C8×C127—21no—
111C2×C8×C127—21no—
112C2×C8×C127—21no—
113C2×C8×C127—42no—
114C2×C8×C127—42no—
115C2×C8×C127—42no—
116C2×C8×C127—41no—
117C4⋊C4×C127—21no—
118C4⋊C4×C127—21no—
119C4⋊C4×C127—21no—
120C4⋊C4×C127—21no—
121C4⋊C4×C127—21no—
122C4⋊C4×C127—21no—
123C4⋊C4×C127—81no—
124C4⋊C4×C127C22⋊C411yescharacteristic
125C4⋊C4×C127C22⋊C411yescharacteristic
126C22⋊C4×C127—21no—
127C22⋊C4×C127—21no—
128C22⋊C4×C127—21no—
129C22⋊C4×C127—21no—
130C22⋊C4×C127—21no—
131C22⋊C4×C127—41no—
132C22⋊C4×C127—41no—
133C42×C127—21no—
134C42×C127C22×C411yescharacteristic
135C42×C127C2×D411yescharacteristic
136C42×C127C2×D411yescharacteristic
137C42×C127#4111yescharacteristic
138C23×C127—21no—
139C23×C127—41no—
140C23×C127#12111yescharacteristic
141Q8×C127—41no—
142Q8×C127—81no—
143D4×C127—41no—
144D4×C127—41no—
145D4×C127—41no—
146D4×C127—41no—
147D4×C127—41no—
148D4×C127—81no—
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×C127—41no—
162C2×C4×C127—82no—
163C2×C4×C127—81no—
164C2×C4×C127—81no—
165C2×C4×C127—81no—
166C2×C4×C127C2×C22⋊C411yescharacteristic
167C2×C4×C127C4×D411yescharacteristic
168C2×C4×C127C4×D411yescharacteristic
169C2×C4×C127#12011yescharacteristic
170C2×C4×C127#12111yescharacteristic
171C2×C4×C127#12311yescharacteristic
172C8×C127—22no—
173C8×C127—22no—
174C8×C127—41no—
175C8×C127—41no—
176C8×C127—41no—
177C8×C127—41no—
178C8×C127—81no—
179C22×C127—21no—
180C22×C127—21no—
181C22×C127—41no—
182C22×C127—41no—
183C22×C127—41no—
184C22×C127—81no—
185C22×C127—81no—
186C22×C127—81no—
187C22×C127#38611yescharacteristic
188C22×C127#47111yescharacteristic
189C22×C127#47211yescharacteristic
190C4×C127—21no—
191C4×C127—21no—
192C4×C127—21no—
193C4×C127—21no—
194C4×C127—21no—
195C4×C127—21no—
196C4×C127—41no—
197C4×C127—41no—
198C4×C127—41no—
199C4×C127—81no—
200C4×C127—161no—
201#9432C12711yesmaximal, characteristic, direct product factor, Sylow
202C2×C127—21no—
203C2×C127—21no—
204C2×C127—81no—
205C2×C127—161no—
206C2×C127#188411yescharacteristic
207C2×C127#190611yescharacteristic
208C2×C127#190711yescharacteristic
209#3180C2×C12711yescharacteristic
210#2968C2×C12711yescharacteristic, complemented
211#1530C2×C12711yescharacteristic, complemented
212#1517C2×C12711yescharacteristic, complemented
213#1512C2×C12711yescharacteristic, complemented
214#1302C2×C12711yescharacteristic, complemented
215#1295C2×C12711yescharacteristic, complemented
216C127#943211yescharacteristic, direct product factor, Sylow
217#532C22×C12711yescharacteristic
218#529C22×C12711yescharacteristic
219#501C4×C12711yescharacteristic, complemented
220#496C4×C12711yescharacteristic, complemented
221#490C4×C12711yescharacteristic, complemented
222#489C4×C12711yescharacteristic, complemented
223#466—21no—
224#465—21no—
225#446—21no—
226#442—21no—
227#440—21no—
228#435—21no—
229#435—21no—
230C8×D4—21no—
231#433—21no—
232#432C22×C12711yescharacteristic
233#431C22×C12711yescharacteristic
234#405—21no—
235C2×#97C22×C12711yescharacteristic
236C2×#97C22×C12711yescharacteristic
237#382C22×C12711yescharacteristic
238#329—21no—
239#329—21no—
240#328—21no—
241#327—21no—
242#327—21no—
243#327—21no—
244C2×#41—21no—
245C2×SD16—21no—
246C2×D8—21no—
247C2×M16—21no—
248C22×C8—21no—
249C22×C8—21no—
250C22×C8—21no—
251C4⋊Q8C2×C4×C12711yescharacteristic
252#127C2×C4×C12711yescharacteristic
253#126—21no—
254#125C2×C4×C12711yescharacteristic
255#124—21no—
256#124C2×C4×C12711yescharacteristic
257#123—21no—
258C22⋊Q8D4×C12711yescharacteristic
259#121—21no—
260#121—21no—
261#121D4×C12711yescharacteristic
262C4×Q8D4×C12711yescharacteristic
263C4×D4—21no—
264C4×D4—21no—
265C4×D4—21no—
266C4×D4D4×C12711yescharacteristic
267#117—21no—
268C2×C4⋊C4—21no—
269C2×C42C23×C12711yescharacteristic
270#107—21no—
271#106—21no—
272C4⋊C8—21no—
273C4⋊C8—21no—
274C4⋊C8—21no—
275C4⋊C8—21no—
276#103—21no—
277#102—21no—
278#102—21no—
279#102—21no—
280C22⋊C8—21no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8D4×C12711yescharacteristic
284C22⋊C8D4×C12711yescharacteristic
285#97—21no—
286#97—21no—
287#97—21no—
288#97—21no—
289#97C2×C4×C12711yescharacteristic
290#97C2×C4×C12711yescharacteristic
291#97D4×C12711yescharacteristic
292#97D4×C12711yescharacteristic
293C4×C8—21no—
294C4×C8—21no—
295#95—21no—
296#95—21no—
297#41—81no—
298#41—81no—
299C2×Q8—21no—
300C2×Q8C22⋊C4×C12711yescharacteristic
301C2×D4—21no—
302C2×D4—21no—
303C2×D4—21no—
304C2×D4—21no—
305C2×D4—41no—
306C2×D4C22⋊C4×C12711yescharacteristic
307C22×C4—21no—
308C22×C4—41no—
309C22×C4—41no—
310C22×C4C2×D4×C12711yescharacteristic
311C22×C4C2×D4×C12711yescharacteristic
312C22×C4#41×C12711yescharacteristic
313SD16—42no—
314D8—42no—
315M16—42no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—21no—
319C2×C8—21no—
320C2×C8—21no—
321C2×C8—21no—
322C2×C8—42no—
323C2×C8—42no—
324C2×C8—42no—
325C2×C8—41no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—21no—
330C4⋊C4—21no—
331C4⋊C4—21no—
332C4⋊C4—81no—
333C4⋊C4C22⋊C4×C12711yescharacteristic
334C4⋊C4C22⋊C4×C12711yescharacteristic
335C22⋊C4—21no—
336C22⋊C4—21no—
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C42—21no—
343C42C22×C4×C12711yescharacteristic
344C42C2×D4×C12711yescharacteristic
345C42C2×D4×C12711yescharacteristic
346C42#41×C12711yescharacteristic
347C23—21no—
348C23—41no—
349C23#121×C12711yescharacteristic
350Q8—41no—
351Q8—81no—
352D4—41no—
353D4—41no—
354D4—41no—
355D4—41no—
356D4—41no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—81no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—82no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4C2×C22⋊C4×C12711yescharacteristic
376C2×C4C4×D4×C12711yescharacteristic
377C2×C4C4×D4×C12711yescharacteristic
378C2×C4#120×C12711yescharacteristic
379C2×C4#121×C12711yescharacteristic
380C2×C4#123×C12711yescharacteristic
381C8—22no—
382C8—22no—
383C8—41no—
384C8—41no—
385C8—41no—
386C8—41no—
387C8—81no—
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—81no—
394C22—81no—
395C22—81no—
396C22#386×C12711yescharacteristic
397C22#471×C12711yescharacteristic
398C22#472×C12711yescharacteristic
399C4—21no—
400C4—21no—
401C4—21no—
402C4—21no—
403C4—21no—
404C4—21no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—81no—
409C4—161no—
410C2—21no—
411C2—21no—
412C2—81no—
413C2—161no—
414C2C127×#188411yescharacteristic
415C2C127×#190611yescharacteristic
416C2C127×#190711yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3180C2
LCSG ▷ C42 ▷ 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×#2968C2semidirect
3. C127×#1530C2semidirect
4. C127×#1517C2semidirect
5. C127×#1512C2semidirect
6. C127×#1302C2semidirect
7. C127×#1295C2semidirect
10. #501×C127C4semidirect
11. #496×C127C4semidirect
12. #490×C127C4semidirect
13. #489×C127C4semidirect
201. #9432C127direct (N × H)
210. #2968C2×C127semidirect
211. #1530C2×C127semidirect
212. #1517C2×C127semidirect
213. #1512C2×C127semidirect
214. #1302C2×C127semidirect
215. #1295C2×C127semidirect
216. C127#9432direct (N × H)
219. #501C4×C127semidirect
220. #496C4×C127semidirect
221. #490C4×C127semidirect
222. #489C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#31802
C127×#29682
C127×#15302
C127×#15172
C127×#15122
C127×#13022
C127×#12952
#9432127