Finite Group Databasebeta

← C127×#8435 #44572108

Subgroups — C127×#8435 #44572108

Order 32512.

696 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3507C211yesmaximal, characteristic
2C127×#1805C211yesmaximal, characteristic, complemented
3C127×#1542C211yesmaximal, characteristic, complemented
4C127×#1518C211yesmaximal, characteristic, complemented
5C127×#1517C211yesmaximal, characteristic
6C127×#1480C211yesmaximal, characteristic
7C127×#1479C211yesmaximal, characteristic, complemented
8#559×C127C412yescomplemented
9#557×C127C412yescomplemented
10#556×C127—21no—
11#556×C127—22no—
12#554×C127—21no—
13#552×C127—22no—
14#539×C127—22no—
15#536×C127—21no—
16#533×C127C2211yescharacteristic
17#532×C127C2211yescharacteristic
18#529×C127—22no—
19#520×C127—21no—
20C2×C4×Q8×C127C2211yescharacteristic
21#431×C127C2211yescharacteristic
22#431×C127C2211yescharacteristic
23C2×C4⋊C8×C127C2211yescharacteristic
24C2×#103×C127—21no—
25#382×C127C2211yescharacteristic
26#340×C127—21no—
27#333×C127—21no—
28#332×C127—21no—
29#328×C127—22no—
30#327×C127—22no—
31Q8⋊C8×C127—22no—
32D4⋊C8×C127—22no—
33C2×#41×C127—21no—
34C22×Q8×C127D411yescharacteristic
35C22×C8×C127—21no—
36C4⋊Q8×C127—22no—
37C4⋊Q8×C127C2×C411yescharacteristic
38C4⋊Q8×C127D411yescharacteristic
39C4⋊Q8×C127D411yescharacteristic
40#127×C127C2×C411yescharacteristic
41#126×C127—24no—
42#126×C127—24no—
43#125×C127—22no—
44#125×C127—24no—
45#125×C127—21no—
46#124×C127—22no—
47#124×C127—22no—
48#124×C127—21no—
49#123×C127—24no—
50#123×C127—24no—
51C22⋊Q8×C127—22no—
52C22⋊Q8×C127—22no—
53C22⋊Q8×C127—24no—
54C22⋊Q8×C127—21no—
55C22⋊Q8×C127D412yes—
56#121×C127—21no—
57#121×C127D412yes—
58C4×Q8×C127—22no—
59C4×Q8×C127—22no—
60C4×Q8×C127—21no—
61C4×Q8×C127—21no—
62C4×Q8×C127—21no—
63C4×Q8×C127C2×C412yes—
64C4×Q8×C127C2×C412yes—
65C4×Q8×C127D412yes—
66C4×D4×C127—24no—
67C4×D4×C127—22no—
68C4×D4×C127—22no—
69C4×D4×C127—21no—
70C4×D4×C127D412yes—
71#117×C127—22no—
72#117×C127—24no—
73#117×C127—21no—
74C2×C4⋊C4×C127—22no—
75C2×C4⋊C4×C127—21no—
76C2×C4⋊C4×C127—21no—
77C2×C4⋊C4×C127D411yescharacteristic
78C2×C42×C127—21no—
79C2×C42×C127C2311yescharacteristic
80C4⋊C8×C127—21no—
81C4⋊C8×C127—21no—
82C4⋊C8×C127—21no—
83C4⋊C8×C127—21no—
84#103×C127—42no—
85C22⋊C8×C127—21no—
86C22⋊C8×C127—21no—
87C4×C8×C127—21no—
88C4×C8×C127—21no—
89#95×C127—21no—
90#95×C127—21no—
91#41×C127—41no—
92#41×C127—41no—
93#41×C127—41no—
94#41×C127—41no—
95C2×Q8×C127—21no—
96C2×Q8×C127—21no—
97C2×Q8×C127—21no—
98C2×Q8×C127—21no—
99C2×Q8×C127—21no—
100C2×Q8×C127—21no—
101C2×Q8×C127—21no—
102C2×Q8×C127C22⋊C412yes—
103C2×Q8×C127C22⋊C412yes—
104C2×D4×C127—22no—
105C2×D4×C127—21no—
106C2×D4×C127—21no—
107C2×D4×C127C22⋊C412yes—
108C22×C4×C127—21no—
109C22×C4×C127—24no—
110C22×C4×C127—21no—
111C22×C4×C127—22no—
112C22×C4×C127—41no—
113C22×C4×C127C2×D411yescharacteristic
114C22×C4×C127C2×D411yescharacteristic
115C22×C4×C127C2×D411yescharacteristic
116C2×C8×C127—41no—
117C2×C8×C127—41no—
118C2×C8×C127—41no—
119C2×C8×C127—41no—
120C2×C8×C127—41no—
121C4⋊C4×C127—24no—
122C4⋊C4×C127—24no—
123C4⋊C4×C127—24no—
124C4⋊C4×C127—22no—
125C4⋊C4×C127—21no—
126C4⋊C4×C127—22no—
127C4⋊C4×C127—21no—
128C4⋊C4×C127—21no—
129C4⋊C4×C127—22no—
130C4⋊C4×C127—21no—
131C4⋊C4×C127—22no—
132C4⋊C4×C127—21no—
133C4⋊C4×C127—41no—
134C4⋊C4×C127—41no—
135C4⋊C4×C127C22⋊C412yes—
136C4⋊C4×C127C22⋊C412yes—
137C4⋊C4×C127C22⋊C412yes—
138C22⋊C4×C127—24no—
139C22⋊C4×C127—24no—
140C22⋊C4×C127—24no—
141C22⋊C4×C127—22no—
142C22⋊C4×C127—22no—
143C22⋊C4×C127—22no—
144C42×C127—24no—
145C42×C127—22no—
146C42×C127—22no—
147C42×C127—22no—
148C42×C127C22×C411yescharacteristic
149C42×C127C2×D411yescharacteristic
150C42×C127C2×D411yescharacteristic
151C42×C127C2×D411yescharacteristic
152C23×C127—22no—
153C23×C127#12011yescharacteristic
154Q8×C127—22no—
155Q8×C127—22no—
156Q8×C127—42no—
157Q8×C127—41no—
158Q8×C127—41no—
159Q8×C127—41no—
160Q8×C127—41no—
161Q8×C127—81no—
162D4×C127—42no—
163D4×C127—42no—
164D4×C127—42no—
165D4×C127—42no—
166D4×C127—41no—
167D4×C127—41no—
168C2×C4×C127—22no—
169C2×C4×C127—22no—
170C2×C4×C127—22no—
171C2×C4×C127—22no—
172C2×C4×C127—22no—
173C2×C4×C127—41no—
174C2×C4×C127—41no—
175C2×C4×C127—41no—
176C2×C4×C127—41no—
177C2×C4×C127—42no—
178C2×C4×C127—42no—
179C2×C4×C127—81no—
180C2×C4×C127—84no—
181C2×C4×C127—81no—
182C2×C4×C127—81no—
183C2×C4×C127—81no—
184C2×C4×C127C2×C22⋊C411yescharacteristic
185C2×C4×C127C2×C22⋊C411yescharacteristic
186C2×C4×C127C2×C22⋊C411yescharacteristic
187C2×C4×C127#12011yescharacteristic
188C2×C4×C127#12011yescharacteristic
189C2×C4×C127#12011yescharacteristic
190C2×C4×C127#13511yescharacteristic
191C2×C4×C127#13511yescharacteristic
192C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
193C2×C4×C127#13711yescharacteristic
194C8×C127—81no—
195C8×C127—81no—
196C8×C127—81no—
197C22×C127—21no—
198C22×C127—21no—
199C22×C127—42no—
200C22×C127—42no—
201C22×C127—42no—
202C22×C127#37911yescharacteristic
203C22×C127#44911yescharacteristic
204C22×C127#45211yescharacteristic
205C4×C127—21no—
206C4×C127—21no—
207C4×C127—21no—
208C4×C127—21no—
209C4×C127—42no—
210C4×C127—42no—
211C4×C127—42no—
212C4×C127—42no—
213C4×C127—42no—
214C4×C127—161no—
215C4×C127#41611yescharacteristic
216C4×C127#41711yescharacteristic
217C4×C127#44911yescharacteristic
218C4×C127#45211yescharacteristic
219#8435C12711yesmaximal, characteristic, direct product factor, Sylow
220C2×C127—21no—
221C2×C127—21no—
222C2×C127—82no—
223C2×C127#178811yescharacteristic
224C2×C127#179411yescharacteristic
225C2×C127#179611yescharacteristic
226#3507C2×C12711yescharacteristic
227#1805C2×C12711yescharacteristic, complemented
228#1542C2×C12711yescharacteristic, complemented
229#1518C2×C12711yescharacteristic, complemented
230#1517C2×C12711yescharacteristic
231#1480C2×C12711yescharacteristic
232#1479C2×C12711yescharacteristic, complemented
233C127#843511yescharacteristic, direct product factor, Sylow
234#559C4×C12712yescomplemented
235#557C4×C12712yescomplemented
236#556—21no—
237#556—22no—
238#554—21no—
239#552—22no—
240#539—22no—
241#536—21no—
242#533C22×C12711yescharacteristic
243#532C22×C12711yescharacteristic
244#529—22no—
245#520—21no—
246C2×C4×Q8C22×C12711yescharacteristic
247#431C22×C12711yescharacteristic
248#431C22×C12711yescharacteristic
249C2×C4⋊C8C22×C12711yescharacteristic
250C2×#103—21no—
251#382C22×C12711yescharacteristic
252#340—21no—
253#333—21no—
254#332—21no—
255#328—22no—
256#327—22no—
257Q8⋊C8—22no—
258D4⋊C8—22no—
259C2×#41—21no—
260C22×Q8D4×C12711yescharacteristic
261C22×C8—21no—
262C4⋊Q8—22no—
263C4⋊Q8C2×C4×C12711yescharacteristic
264C4⋊Q8D4×C12711yescharacteristic
265C4⋊Q8D4×C12711yescharacteristic
266#127C2×C4×C12711yescharacteristic
267#126—24no—
268#126—24no—
269#125—22no—
270#125—24no—
271#125—21no—
272#124—22no—
273#124—22no—
274#124—21no—
275#123—24no—
276#123—24no—
277C22⋊Q8—22no—
278C22⋊Q8—22no—
279C22⋊Q8—24no—
280C22⋊Q8—21no—
281C22⋊Q8D4×C12712yes—
282#121—21no—
283#121D4×C12712yes—
284C4×Q8—22no—
285C4×Q8—22no—
286C4×Q8—21no—
287C4×Q8—21no—
288C4×Q8—21no—
289C4×Q8C2×C4×C12712yes—
290C4×Q8C2×C4×C12712yes—
291C4×Q8D4×C12712yes—
292C4×D4—24no—
293C4×D4—22no—
294C4×D4—22no—
295C4×D4—21no—
296C4×D4D4×C12712yes—
297#117—22no—
298#117—24no—
299#117—21no—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4D4×C12711yescharacteristic
304C2×C42—21no—
305C2×C42C23×C12711yescharacteristic
306C4⋊C8—21no—
307C4⋊C8—21no—
308C4⋊C8—21no—
309C4⋊C8—21no—
310#103—42no—
311C22⋊C8—21no—
312C22⋊C8—21no—
313C4×C8—21no—
314C4×C8—21no—
315#95—21no—
316#95—21no—
317#41—41no—
318#41—41no—
319#41—41no—
320#41—41no—
321C2×Q8—21no—
322C2×Q8—21no—
323C2×Q8—21no—
324C2×Q8—21no—
325C2×Q8—21no—
326C2×Q8—21no—
327C2×Q8—21no—
328C2×Q8C22⋊C4×C12712yes—
329C2×Q8C22⋊C4×C12712yes—
330C2×D4—22no—
331C2×D4—21no—
332C2×D4—21no—
333C2×D4C22⋊C4×C12712yes—
334C22×C4—21no—
335C22×C4—24no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—41no—
339C22×C4C2×D4×C12711yescharacteristic
340C22×C4C2×D4×C12711yescharacteristic
341C22×C4C2×D4×C12711yescharacteristic
342C2×C8—41no—
343C2×C8—41no—
344C2×C8—41no—
345C2×C8—41no—
346C2×C8—41no—
347C4⋊C4—24no—
348C4⋊C4—24no—
349C4⋊C4—24no—
350C4⋊C4—22no—
351C4⋊C4—21no—
352C4⋊C4—22no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—22no—
356C4⋊C4—21no—
357C4⋊C4—22no—
358C4⋊C4—21no—
359C4⋊C4—41no—
360C4⋊C4—41no—
361C4⋊C4C22⋊C4×C12712yes—
362C4⋊C4C22⋊C4×C12712yes—
363C4⋊C4C22⋊C4×C12712yes—
364C22⋊C4—24no—
365C22⋊C4—24no—
366C22⋊C4—24no—
367C22⋊C4—22no—
368C22⋊C4—22no—
369C22⋊C4—22no—
370C42—24no—
371C42—22no—
372C42—22no—
373C42—22no—
374C42C22×C4×C12711yescharacteristic
375C42C2×D4×C12711yescharacteristic
376C42C2×D4×C12711yescharacteristic
377C42C2×D4×C12711yescharacteristic
378C23—22no—
379C23#120×C12711yescharacteristic
380Q8—22no—
381Q8—22no—
382Q8—42no—
383Q8—41no—
384Q8—41no—
385Q8—41no—
386Q8—41no—
387Q8—81no—
388D4—42no—
389D4—42no—
390D4—42no—
391D4—42no—
392D4—41no—
393D4—41no—
394C2×C4—22no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—81no—
406C2×C4—84no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—81no—
410C2×C4C2×C22⋊C4×C12711yescharacteristic
411C2×C4C2×C22⋊C4×C12711yescharacteristic
412C2×C4C2×C22⋊C4×C12711yescharacteristic
413C2×C4#120×C12711yescharacteristic
414C2×C4#120×C12711yescharacteristic
415C2×C4#120×C12711yescharacteristic
416C2×C4#135×C12711yescharacteristic
417C2×C4#135×C12711yescharacteristic
418C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
419C2×C4#137×C12711yescharacteristic
420C8—81no—
421C8—81no—
422C8—81no—
423C22—21no—
424C22—21no—
425C22—42no—
426C22—42no—
427C22—42no—
428C22#379×C12711yescharacteristic
429C22#449×C12711yescharacteristic
430C22#452×C12711yescharacteristic
431C4—21no—
432C4—21no—
433C4—21no—
434C4—21no—
435C4—42no—
436C4—42no—
437C4—42no—
438C4—42no—
439C4—42no—
440C4—161no—
441C4#416×C12711yescharacteristic
442C4#417×C12711yescharacteristic
443C4#449×C12711yescharacteristic
444C4#452×C12711yescharacteristic
445C2—21no—
446C2—21no—
447C2—82no—
448C2C127×#178811yescharacteristic
449C2C127×#179411yescharacteristic
450C2C127×#179611yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radical#532×C127C22
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×#1805C2semidirect
3. C127×#1542C2semidirect
4. C127×#1518C2semidirect
7. C127×#1479C2semidirect
8. #559×C127C4semidirect
9. #557×C127C4semidirect
219. #8435C127direct (N × H)
227. #1805C2×C127semidirect
228. #1542C2×C127semidirect
229. #1518C2×C127semidirect
232. #1479C2×C127semidirect
233. C127#8435direct (N × H)
234. #559C4×C127semidirect
235. #557C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35072
C127×#18052
C127×#15422
C127×#15182
C127×#15172
C127×#14802
C127×#14792
#8435127