Finite Group Databasebeta

← C127×#9346 #44573019

Subgroups — C127×#9346 #44573019

Order 32512.

444 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3095C211yesmaximal, characteristic
2C127×#2924C211yesmaximal, characteristic
3C127×#1825C211yesmaximal, characteristic
4C127×#1520C211yesmaximal, characteristic
5C127×#1472C211yesmaximal, characteristic
6C127×#1305C211yesmaximal, characteristic
7C127×#1298C211yesmaximal, characteristic
8C2×C22⋊Q8×C127C2211yescharacteristic
9C2×#117×C127C2211yescharacteristic
10#485×C127—21no—
11#485×C127—21no—
12#484×C127—21no—
13#483×C127—21no—
14#433×C127—22no—
15#432×C127—21no—
16#431×C127—21no—
17#428×C127C411yescharacteristic, complemented
18#428×C127C411yescharacteristic, complemented
19#424×C127—21no—
20#419×C127C411yescharacteristic, complemented
21#419×C127C411yescharacteristic, complemented
22#407×C127C2211yescharacteristic
23#407×C127C2211yescharacteristic
24C2×C22⋊C8×C127C2211yescharacteristic
25C2×C22⋊C8×C127C2211yescharacteristic
26#405×C127—21no—
27#380×C127C2211yescharacteristic
28#340×C127—21no—
29#340×C127—21no—
30#328×C127—21no—
31#328×C127—21no—
32#324×C127—22no—
33C22×Q8×C127C2×C411yescharacteristic
34C23×C4×C127C2311yescharacteristic
35C2×M16×C127—21no—
36C2×M16×C127C2×C411yescharacteristic
37C2×M16×C127C2×C411yescharacteristic
38C22×C8×C127—21no—
39C22×C8×C127—21no—
40C22⋊Q8×C127—21no—
41C22⋊Q8×C127—21no—
42C22⋊Q8×C127—21no—
43C22⋊Q8×C127—21no—
44#117×C127—21no—
45#117×C127—21no—
46#117×C127C2×C411yescharacteristic
47#117×C127C2×C411yescharacteristic
48#117×C127D411yescharacteristic
49#117×C127D411yescharacteristic
50C2×C4⋊C4×C127—21no—
51C2×C4⋊C4×C127—21no—
52C2×C4⋊C4×C127C2×C411yescharacteristic
53C2×C4⋊C4×C127D411yescharacteristic
54C2×C4⋊C4×C127D411yescharacteristic
55C2×C22⋊C4×C127—21no—
56C2×C22⋊C4×C127—21no—
57C2×C22⋊C4×C127—21no—
58C2×C42×C127—21no—
59#107×C127—21no—
60#107×C127—21no—
61#106×C127—21no—
62#106×C127—21no—
63C4⋊C8×C127—22no—
64C4⋊C8×C127—22no—
65#103×C127—21no—
66#103×C127—21no—
67#103×C127—21no—
68#103×C127—21no—
69C22⋊C8×C127—21no—
70C22⋊C8×C127—21no—
71C22⋊C8×C127—21no—
72C22⋊C8×C127—21no—
73C22⋊C8×C127—21no—
74C22⋊C8×C127—21no—
75C22⋊C8×C127D412yes—
76C22⋊C8×C127D411yescharacteristic
77C22⋊C8×C127D411yescharacteristic
78#97×C127—22no—
79C4×C8×C127—22no—
80#95×C127—21no—
81C24×C127#4111yescharacteristic
82C2×Q8×C127—21no—
83C2×Q8×C127—21no—
84C2×Q8×C127—41no—
85C2×Q8×C127—41no—
86C22×C4×C127—21no—
87C22×C4×C127—21no—
88C22×C4×C127—21no—
89C22×C4×C127—21no—
90C22×C4×C127—41no—
91C22×C4×C127—41no—
92C22×C4×C127—41no—
93C22×C4×C127C22×C411yescharacteristic
94C22×C4×C127C2×D411yescharacteristic
95C22×C4×C127C2×D411yescharacteristic
96C22×C4×C127C2×D411yescharacteristic
97C22×C4×C127C2×D411yescharacteristic
98C22×C4×C127#4111yescharacteristic
99M16×C127—41no—
100M16×C127—41no—
101M16×C127—41no—
102M16×C127—41no—
103C2×C8×C127—21no—
104C2×C8×C127—21no—
105C2×C8×C127—21no—
106C2×C8×C127—22no—
107C2×C8×C127—21no—
108C2×C8×C127—41no—
109C2×C8×C127—41no—
110C2×C8×C127—41no—
111C2×C8×C127—41no—
112C2×C8×C127—41no—
113C4⋊C4×C127—21no—
114C4⋊C4×C127—21no—
115C4⋊C4×C127—21no—
116C4⋊C4×C127—21no—
117C4⋊C4×C127—41no—
118C4⋊C4×C127—41no—
119C4⋊C4×C127—41no—
120C4⋊C4×C127—41no—
121C4⋊C4×C127C22⋊C411yescharacteristic
122C4⋊C4×C127C22⋊C411yescharacteristic
123C4⋊C4×C127C22⋊C411yescharacteristic
124C4⋊C4×C127C22⋊C411yescharacteristic
125C22⋊C4×C127—21no—
126C22⋊C4×C127—21no—
127C22⋊C4×C127—21no—
128C22⋊C4×C127—21no—
129C22⋊C4×C127—41no—
130C22⋊C4×C127—41no—
131C22⋊C4×C127—81no—
132C42×C127—21no—
133C42×C127—21no—
134C42×C127—21no—
135C42×C127—21no—
136C23×C127—21no—
137C23×C127—21no—
138C23×C127—41no—
139C23×C127—41no—
140C23×C127C4×D411yescharacteristic
141C23×C127#12111yescharacteristic
142C23×C127#12311yescharacteristic
143Q8×C127—41no—
144Q8×C127—41no—
145Q8×C127—81no—
146C2×C4×C127—21no—
147C2×C4×C127—21no—
148C2×C4×C127—21no—
149C2×C4×C127—21no—
150C2×C4×C127—21no—
151C2×C4×C127—21no—
152C2×C4×C127—21no—
153C2×C4×C127—21no—
154C2×C4×C127—21no—
155C2×C4×C127—21no—
156C2×C4×C127—41no—
157C2×C4×C127—41no—
158C2×C4×C127—41no—
159C2×C4×C127—41no—
160C2×C4×C127—41no—
161C2×C4×C127—42no—
162C2×C4×C127—41no—
163C2×C4×C127—41no—
164C2×C4×C127—81no—
165C2×C4×C127—81no—
166C2×C4×C127—81no—
167C2×C4×C127—81no—
168C2×C4×C127—81no—
169C2×C4×C127C2×C22⋊C411yescharacteristic
170C2×C4×C127C4×D411yescharacteristic
171C2×C4×C127#12011yescharacteristic
172C2×C4×C127#12111yescharacteristic
173C8×C127—41no—
174C8×C127—41no—
175C8×C127—42no—
176C8×C127—41no—
177C8×C127—41no—
178C8×C127—81no—
179C22×C127—21no—
180C22×C127—21no—
181C22×C127—21no—
182C22×C127—21no—
183C22×C127—21no—
184C22×C127—21no—
185C22×C127—21no—
186C22×C127—21no—
187C22×C127—81no—
188C22×C127—81no—
189C22×C127#38611yescharacteristic
190C22×C127#47111yescharacteristic
191C22×C127#47311yescharacteristic
192C4×C127—21no—
193C4×C127—21no—
194C4×C127—21no—
195C4×C127—41no—
196C4×C127—41no—
197C4×C127—41no—
198C4×C127—41no—
199C4×C127—81no—
200C4×C127—81no—
201C4×C127—161no—
202C4×C127#41011yescharacteristic
203C4×C127#41011yescharacteristic
204#9346C12711yesmaximal, characteristic, direct product factor, Sylow
205C2×C127—21no—
206C2×C127—21no—
207C2×C127—41no—
208C2×C127—41no—
209C2×C127#188111yescharacteristic
210C2×C127#189911yescharacteristic
211C2×C127#190811yescharacteristic
212#3095C2×C12711yescharacteristic
213#2924C2×C12711yescharacteristic
214#1825C2×C12711yescharacteristic
215#1520C2×C12711yescharacteristic
216#1472C2×C12711yescharacteristic
217#1305C2×C12711yescharacteristic
218#1298C2×C12711yescharacteristic
219C127#934611yescharacteristic, direct product factor, Sylow
220C2×C22⋊Q8C22×C12711yescharacteristic
221C2×#117C22×C12711yescharacteristic
222#485—21no—
223#485—21no—
224#484—21no—
225#483—21no—
226#433—22no—
227#432—21no—
228#431—21no—
229#428C4×C12711yescharacteristic, complemented
230#428C4×C12711yescharacteristic, complemented
231#424—21no—
232#419C4×C12711yescharacteristic, complemented
233#419C4×C12711yescharacteristic, complemented
234#407C22×C12711yescharacteristic
235#407C22×C12711yescharacteristic
236C2×C22⋊C8C22×C12711yescharacteristic
237C2×C22⋊C8C22×C12711yescharacteristic
238#405—21no—
239#380C22×C12711yescharacteristic
240#340—21no—
241#340—21no—
242#328—21no—
243#328—21no—
244#324—22no—
245C22×Q8C2×C4×C12711yescharacteristic
246C23×C4C23×C12711yescharacteristic
247C2×M16—21no—
248C2×M16C2×C4×C12711yescharacteristic
249C2×M16C2×C4×C12711yescharacteristic
250C22×C8—21no—
251C22×C8—21no—
252C22⋊Q8—21no—
253C22⋊Q8—21no—
254C22⋊Q8—21no—
255C22⋊Q8—21no—
256#117—21no—
257#117—21no—
258#117C2×C4×C12711yescharacteristic
259#117C2×C4×C12711yescharacteristic
260#117D4×C12711yescharacteristic
261#117D4×C12711yescharacteristic
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4C2×C4×C12711yescharacteristic
265C2×C4⋊C4D4×C12711yescharacteristic
266C2×C4⋊C4D4×C12711yescharacteristic
267C2×C22⋊C4—21no—
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C42—21no—
271#107—21no—
272#107—21no—
273#106—21no—
274#106—21no—
275C4⋊C8—22no—
276C4⋊C8—22no—
277#103—21no—
278#103—21no—
279#103—21no—
280#103—21no—
281C22⋊C8—21no—
282C22⋊C8—21no—
283C22⋊C8—21no—
284C22⋊C8—21no—
285C22⋊C8—21no—
286C22⋊C8—21no—
287C22⋊C8D4×C12712yes—
288C22⋊C8D4×C12711yescharacteristic
289C22⋊C8D4×C12711yescharacteristic
290#97—22no—
291C4×C8—22no—
292#95—21no—
293C24#41×C12711yescharacteristic
294C2×Q8—21no—
295C2×Q8—21no—
296C2×Q8—41no—
297C2×Q8—41no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—41no—
303C22×C4—41no—
304C22×C4—41no—
305C22×C4C22×C4×C12711yescharacteristic
306C22×C4C2×D4×C12711yescharacteristic
307C22×C4C2×D4×C12711yescharacteristic
308C22×C4C2×D4×C12711yescharacteristic
309C22×C4C2×D4×C12711yescharacteristic
310C22×C4#41×C12711yescharacteristic
311M16—41no—
312M16—41no—
313M16—41no—
314M16—41no—
315C2×C8—21no—
316C2×C8—21no—
317C2×C8—21no—
318C2×C8—22no—
319C2×C8—21no—
320C2×C8—41no—
321C2×C8—41no—
322C2×C8—41no—
323C2×C8—41no—
324C2×C8—41no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4C22⋊C4×C12711yescharacteristic
334C4⋊C4C22⋊C4×C12711yescharacteristic
335C4⋊C4C22⋊C4×C12711yescharacteristic
336C4⋊C4C22⋊C4×C12711yescharacteristic
337C22⋊C4—21no—
338C22⋊C4—21no—
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—81no—
344C42—21no—
345C42—21no—
346C42—21no—
347C42—21no—
348C23—21no—
349C23—21no—
350C23—41no—
351C23—41no—
352C23C4×D4×C12711yescharacteristic
353C23#121×C12711yescharacteristic
354C23#123×C12711yescharacteristic
355Q8—41no—
356Q8—41no—
357Q8—81no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—41no—
375C2×C4—41no—
376C2×C4—81no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4C2×C22⋊C4×C12711yescharacteristic
382C2×C4C4×D4×C12711yescharacteristic
383C2×C4#120×C12711yescharacteristic
384C2×C4#121×C12711yescharacteristic
385C8—41no—
386C8—41no—
387C8—42no—
388C8—41no—
389C8—41no—
390C8—81no—
391C22—21no—
392C22—21no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—21no—
398C22—21no—
399C22—81no—
400C22—81no—
401C22#386×C12711yescharacteristic
402C22#471×C12711yescharacteristic
403C22#473×C12711yescharacteristic
404C4—21no—
405C4—21no—
406C4—21no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—41no—
411C4—81no—
412C4—81no—
413C4—161no—
414C4#410×C12711yescharacteristic
415C4#410×C12711yescharacteristic
416C2—21no—
417C2—21no—
418C2—41no—
419C2—41no—
420C2C127×#188111yescharacteristic
421C2C127×#189911yescharacteristic
422C2C127×#190811yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127#41
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
17. #428×C127C4semidirect
18. #428×C127C4semidirect
20. #419×C127C4semidirect
21. #419×C127C4semidirect
204. #9346C127direct (N × H)
219. C127#9346direct (N × H)
229. #428C4×C127semidirect
230. #428C4×C127semidirect
232. #419C4×C127semidirect
233. #419C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#30952
C127×#29242
C127×#18252
C127×#15202
C127×#14722
C127×#13052
C127×#12982
#9346127