Finite Group Databasebeta

← C127×#8432 #44572105

Subgroups — C127×#8432 #44572105

Order 32512.

740 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3501C211yesmaximal, characteristic
2C127×#1804C211yesmaximal, characteristic
3C127×#1542C211yesmaximal, characteristic, complemented
4C127×#1518C211yesmaximal, characteristic, complemented
5C127×#1518C211yesmaximal, characteristic, complemented
6C127×#1481C211yesmaximal, characteristic, complemented
7C127×#1478C211yesmaximal, characteristic
8#554×C127—21no—
9#554×C127—22no—
10#554×C127—22no—
11#554×C127C412yescomplemented
12D4×Q8×C127—21no—
13D4×Q8×C127C412yescomplemented
14#544×C127—21no—
15#543×C127—22no—
16#533×C127C2211yescharacteristic
17#533×C127C2211yescharacteristic
18C2×C22⋊Q8×C127—22no—
19#518×C127—21no—
20C2×C4×D4×C127C2211yescharacteristic
21#431×C127C2211yescharacteristic
22#431×C127C2211yescharacteristic
23C2×C4⋊C8×C127C2211yescharacteristic
24C2×#102×C127—21no—
25#382×C127C2211yescharacteristic
26#340×C127—21no—
27#333×C127—21no—
28#332×C127—21no—
29#328×C127—22no—
30#328×C127—22no—
31Q8⋊C8×C127—22no—
32D4⋊C8×C127—22no—
33C22×Q8×C127—22no—
34C22×D4×C127D411yescharacteristic
35C23×C4×C127—21no—
36C22×C8×C127—21no—
37C4⋊Q8×C127—22no—
38C4⋊Q8×C127—22no—
39C4⋊Q8×C127C2×C411yescharacteristic
40C4⋊Q8×C127C2×C411yescharacteristic
41C4⋊Q8×C127D411yescharacteristic
42C4⋊Q8×C127D411yescharacteristic
43#125×C127—22no—
44#125×C127—22no—
45#125×C127—21no—
46#125×C127—21no—
47C22⋊Q8×C127—24no—
48C22⋊Q8×C127—24no—
49C22⋊Q8×C127—24no—
50C22⋊Q8×C127—24no—
51C22⋊Q8×C127—22no—
52C22⋊Q8×C127—24no—
53C22⋊Q8×C127—21no—
54C22⋊Q8×C127—21no—
55C22⋊Q8×C127—22no—
56C22⋊Q8×C127—24no—
57C22⋊Q8×C127D412yes—
58C22⋊Q8×C127D412yes—
59C4×Q8×C127—21no—
60C4×Q8×C127—21no—
61C4×Q8×C127C2×C412yes—
62C4×Q8×C127D412yes—
63C4×D4×C127—22no—
64C4×D4×C127—22no—
65C4×D4×C127—22no—
66C4×D4×C127—22no—
67C4×D4×C127—21no—
68C4×D4×C127—21no—
69C4×D4×C127C2×C412yes—
70C4×D4×C127D412yes—
71#117×C127—21no—
72#117×C127—21no—
73C2×C4⋊C4×C127—24no—
74C2×C4⋊C4×C127—22no—
75C2×C4⋊C4×C127—21no—
76C2×C4⋊C4×C127D411yescharacteristic
77C2×C22⋊C4×C127—24no—
78C2×C22⋊C4×C127—21no—
79C2×C42×C127C2311yescharacteristic
80C4⋊C8×C127—21no—
81C4⋊C8×C127—21no—
82C4⋊C8×C127—21no—
83C4⋊C8×C127—21no—
84#102×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—
91C24×C127—21no—
92C2×Q8×C127—24no—
93C2×Q8×C127—21no—
94C2×Q8×C127—21no—
95C2×Q8×C127—84no—
96C2×Q8×C127C22⋊C412yes—
97C2×Q8×C127C22⋊C412yes—
98C2×D4×C127—21no—
99C2×D4×C127—21no—
100C2×D4×C127—21no—
101C2×D4×C127C22⋊C412yes—
102C2×D4×C127SD1612yes—
103C2×D4×C127Q1612yes—
104C22×C4×C127—24no—
105C22×C4×C127—24no—
106C22×C4×C127—21no—
107C22×C4×C127—22no—
108C22×C4×C127—22no—
109C22×C4×C127—41no—
110C22×C4×C127—82no—
111C22×C4×C127C2×D411yescharacteristic
112C22×C4×C127C2×D411yescharacteristic
113C22×C4×C127C2×D411yescharacteristic
114C2×C8×C127—41no—
115C2×C8×C127—41no—
116C2×C8×C127—41no—
117C2×C8×C127—41no—
118C2×C8×C127—41no—
119C4⋊C4×C127—24no—
120C4⋊C4×C127—24no—
121C4⋊C4×C127—24no—
122C4⋊C4×C127—21no—
123C4⋊C4×C127—21no—
124C4⋊C4×C127—21no—
125C4⋊C4×C127—22no—
126C4⋊C4×C127—22no—
127C4⋊C4×C127—22no—
128C4⋊C4×C127—21no—
129C4⋊C4×C127—21no—
130C4⋊C4×C127—21no—
131C4⋊C4×C127—21no—
132C4⋊C4×C127—22no—
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—22no—
141C22⋊C4×C127—22no—
142C22⋊C4×C127—22no—
143C22⋊C4×C127—22no—
144C42×C127—22no—
145C42×C127—22no—
146C42×C127C22×C411yescharacteristic
147C42×C127C2×D411yescharacteristic
148C42×C127C2×D411yescharacteristic
149C42×C127C2×D411yescharacteristic
150C23×C127—22no—
151C23×C127—22no—
152C23×C127—22no—
153C23×C127—81no—
154C23×C127—81no—
155C23×C127#12011yescharacteristic
156Q8×C127—42no—
157Q8×C127—42no—
158Q8×C127—42no—
159Q8×C127—81no—
160Q8×C127—84no—
161D4×C127—22no—
162D4×C127—22no—
163D4×C127—22no—
164D4×C127#10314yes—
165C2×C4×C127—22no—
166C2×C4×C127—22no—
167C2×C4×C127—22no—
168C2×C4×C127—22no—
169C2×C4×C127—22no—
170C2×C4×C127—41no—
171C2×C4×C127—41no—
172C2×C4×C127—44no—
173C2×C4×C127—82no—
174C2×C4×C127—81no—
175C2×C4×C127—84no—
176C2×C4×C127—84no—
177C2×C4×C127—81no—
178C2×C4×C127—81no—
179C2×C4×C127—81no—
180C2×C4×C127C2×C22⋊C411yescharacteristic
181C2×C4×C127C2×C22⋊C411yescharacteristic
182C2×C4×C127C2×C22⋊C411yescharacteristic
183C2×C4×C127#12011yescharacteristic
184C2×C4×C127#12011yescharacteristic
185C2×C4×C127#12011yescharacteristic
186C2×C4×C127C2×SD1611yescharacteristic
187C2×C4×C127C2×Q1611yescharacteristic
188C2×C4×C127#13711yescharacteristic
189C2×C4×C127#13711yescharacteristic
190C8×C127—81no—
191C8×C127—81no—
192C8×C127—81no—
193C22×C127—21no—
194C22×C127—21no—
195C22×C127—24no—
196C22×C127—42no—
197C22×C127—42no—
198C22×C127—82no—
199C22×C127—82no—
200C22×C127#37911yescharacteristic
201C22×C127#44811yescharacteristic
202C22×C127#45111yescharacteristic
203C4×C127—21no—
204C4×C127—21no—
205C4×C127—21no—
206C4×C127—21no—
207C4×C127—42no—
208C4×C127—42no—
209C4×C127—42no—
210C4×C127—42no—
211C4×C127—42no—
212C4×C127—161no—
213C4×C127C2×#10311yescharacteristic
214C4×C127#41911yescharacteristic
215C4×C127#44811yescharacteristic
216C4×C127#45111yescharacteristic
217#8432C12711yesmaximal, characteristic, direct product factor, Sylow
218C2×C127—21no—
219C2×C127—21no—
220C2×C127—44no—
221C2×C127#178711yescharacteristic
222C2×C127#179411yescharacteristic
223C2×C127#179511yescharacteristic
224#3501C2×C12711yescharacteristic
225#1804C2×C12711yescharacteristic
226#1542C2×C12711yescharacteristic, complemented
227#1518C2×C12711yescharacteristic, complemented
228#1518C2×C12711yescharacteristic, complemented
229#1481C2×C12711yescharacteristic, complemented
230#1478C2×C12711yescharacteristic
231C127#843211yescharacteristic, direct product factor, Sylow
232#554—21no—
233#554—22no—
234#554—22no—
235#554C4×C12712yescomplemented
236D4×Q8—21no—
237D4×Q8C4×C12712yescomplemented
238#544—21no—
239#543—22no—
240#533C22×C12711yescharacteristic
241#533C22×C12711yescharacteristic
242C2×C22⋊Q8—22no—
243#518—21no—
244C2×C4×D4C22×C12711yescharacteristic
245#431C22×C12711yescharacteristic
246#431C22×C12711yescharacteristic
247C2×C4⋊C8C22×C12711yescharacteristic
248C2×#102—21no—
249#382C22×C12711yescharacteristic
250#340—21no—
251#333—21no—
252#332—21no—
253#328—22no—
254#328—22no—
255Q8⋊C8—22no—
256D4⋊C8—22no—
257C22×Q8—22no—
258C22×D4D4×C12711yescharacteristic
259C23×C4—21no—
260C22×C8—21no—
261C4⋊Q8—22no—
262C4⋊Q8—22no—
263C4⋊Q8C2×C4×C12711yescharacteristic
264C4⋊Q8C2×C4×C12711yescharacteristic
265C4⋊Q8D4×C12711yescharacteristic
266C4⋊Q8D4×C12711yescharacteristic
267#125—22no—
268#125—22no—
269#125—21no—
270#125—21no—
271C22⋊Q8—24no—
272C22⋊Q8—24no—
273C22⋊Q8—24no—
274C22⋊Q8—24no—
275C22⋊Q8—22no—
276C22⋊Q8—24no—
277C22⋊Q8—21no—
278C22⋊Q8—21no—
279C22⋊Q8—22no—
280C22⋊Q8—24no—
281C22⋊Q8D4×C12712yes—
282C22⋊Q8D4×C12712yes—
283C4×Q8—21no—
284C4×Q8—21no—
285C4×Q8C2×C4×C12712yes—
286C4×Q8D4×C12712yes—
287C4×D4—22no—
288C4×D4—22no—
289C4×D4—22no—
290C4×D4—22no—
291C4×D4—21no—
292C4×D4—21no—
293C4×D4C2×C4×C12712yes—
294C4×D4D4×C12712yes—
295#117—21no—
296#117—21no—
297C2×C4⋊C4—24no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4D4×C12711yescharacteristic
301C2×C22⋊C4—24no—
302C2×C22⋊C4—21no—
303C2×C42C23×C12711yescharacteristic
304C4⋊C8—21no—
305C4⋊C8—21no—
306C4⋊C8—21no—
307C4⋊C8—21no—
308#102—42no—
309C22⋊C8—21no—
310C22⋊C8—21no—
311C4×C8—21no—
312C4×C8—21no—
313#95—21no—
314#95—21no—
315C24—21no—
316C2×Q8—24no—
317C2×Q8—21no—
318C2×Q8—21no—
319C2×Q8—84no—
320C2×Q8C22⋊C4×C12712yes—
321C2×Q8C22⋊C4×C12712yes—
322C2×D4—21no—
323C2×D4—21no—
324C2×D4—21no—
325C2×D4C22⋊C4×C12712yes—
326C2×D4SD16×C12712yes—
327C2×D4Q16×C12712yes—
328C22×C4—24no—
329C22×C4—24no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—22no—
333C22×C4—41no—
334C22×C4—82no—
335C22×C4C2×D4×C12711yescharacteristic
336C22×C4C2×D4×C12711yescharacteristic
337C22×C4C2×D4×C12711yescharacteristic
338C2×C8—41no—
339C2×C8—41no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—41no—
343C4⋊C4—24no—
344C4⋊C4—24no—
345C4⋊C4—24no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—22no—
350C4⋊C4—22no—
351C4⋊C4—22no—
352C4⋊C4—21no—
353C4⋊C4—21no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—22no—
357C4⋊C4—41no—
358C4⋊C4—41no—
359C4⋊C4C22⋊C4×C12712yes—
360C4⋊C4C22⋊C4×C12712yes—
361C4⋊C4C22⋊C4×C12712yes—
362C22⋊C4—24no—
363C22⋊C4—24no—
364C22⋊C4—22no—
365C22⋊C4—22no—
366C22⋊C4—22no—
367C22⋊C4—22no—
368C42—22no—
369C42—22no—
370C42C22×C4×C12711yescharacteristic
371C42C2×D4×C12711yescharacteristic
372C42C2×D4×C12711yescharacteristic
373C42C2×D4×C12711yescharacteristic
374C23—22no—
375C23—22no—
376C23—22no—
377C23—81no—
378C23—81no—
379C23#120×C12711yescharacteristic
380Q8—42no—
381Q8—42no—
382Q8—42no—
383Q8—81no—
384Q8—84no—
385D4—22no—
386D4—22no—
387D4—22no—
388D4#103×C12714yes—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—41no—
396C2×C4—44no—
397C2×C4—82no—
398C2×C4—81no—
399C2×C4—84no—
400C2×C4—84no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4C2×C22⋊C4×C12711yescharacteristic
405C2×C4C2×C22⋊C4×C12711yescharacteristic
406C2×C4C2×C22⋊C4×C12711yescharacteristic
407C2×C4#120×C12711yescharacteristic
408C2×C4#120×C12711yescharacteristic
409C2×C4#120×C12711yescharacteristic
410C2×C4C2×SD16×C12711yescharacteristic
411C2×C4C2×Q16×C12711yescharacteristic
412C2×C4#137×C12711yescharacteristic
413C2×C4#137×C12711yescharacteristic
414C8—81no—
415C8—81no—
416C8—81no—
417C22—21no—
418C22—21no—
419C22—24no—
420C22—42no—
421C22—42no—
422C22—82no—
423C22—82no—
424C22#379×C12711yescharacteristic
425C22#448×C12711yescharacteristic
426C22#451×C12711yescharacteristic
427C4—21no—
428C4—21no—
429C4—21no—
430C4—21no—
431C4—42no—
432C4—42no—
433C4—42no—
434C4—42no—
435C4—42no—
436C4—161no—
437C4C2×#103×C12711yescharacteristic
438C4#419×C12711yescharacteristic
439C4#448×C12711yescharacteristic
440C4#451×C12711yescharacteristic
441C2—21no—
442C2—21no—
443C2—44no—
444C2C127×#178711yescharacteristic
445C2C127×#179411yescharacteristic
446C2C127×#179511yescharacteristic
subgroupG/H
center, socleC22×C127#379
commutatorC42C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC22×D4×C127D4
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
3. C127×#1542C2semidirect
4. C127×#1518C2semidirect
5. C127×#1518C2semidirect
6. C127×#1481C2semidirect
11. #554×C127C4semidirect
13. D4×Q8×C127C4semidirect
217. #8432C127direct (N × H)
226. #1542C2×C127semidirect
227. #1518C2×C127semidirect
228. #1518C2×C127semidirect
229. #1481C2×C127semidirect
231. C127#8432direct (N × H)
235. #554C4×C127semidirect
237. D4×Q8C4×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#35012
C127×#18042
C127×#15422
C127×#15182
C127×#14812
C127×#14782
#8432127