Finite Group Databasebeta

← C127×#8574 #44572247

Subgroups — C127×#8574 #44572247

Order 32512.

614 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊Q8×C127C211yesmaximal, characteristic
2C127×#1797C211yesmaximal, characteristic
3C2×#328×C127C212yesmaximal
4C127×#1434C211yesmaximal, characteristic
5C127×#1294C212yesmaximal
6C2×C22⋊Q8×C127C2211yescharacteristic
7C2×C4×Q8×C127C411yescharacteristic, complemented
8C22×C42×C127C2211yescharacteristic
9C2×C4⋊C8×C127—21no—
10C2×C22⋊C8×C127C2212yes—
11#391×C127C411yescharacteristic, complemented
12#389×C127C411yescharacteristic, complemented
13#387×C127—21no—
14#385×C127—21no—
15#380×C127C2211yescharacteristic
16C4×C4⋊C4×C127—21no—
17C4×C4⋊C4×C127C411yescharacteristic, complemented
18C4×C22⋊C4×C127—21no—
19C2×#95×C127—21no—
20C2×#95×C127—21no—
21C2×#95×C127C2212yes—
22#336×C127—21no—
23#328×C127—24no—
24C22×Q8×C127C2×C411yescharacteristic
25C23×C4×C127—22no—
26C23×C4×C127D411yescharacteristic
27C23×C4×C127D411yescharacteristic
28C23×C4×C127C2311yescharacteristic
29C22×C8×C127—22no—
30C22⋊Q8×C127—21no—
31C22⋊Q8×C127—21no—
32C22⋊Q8×C127D412yes—
33C22⋊Q8×C127Q812yes—
34C4×Q8×C127—42no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127C2×C411yescharacteristic
39C2×C4⋊C4×C127C2×C411yescharacteristic
40C2×C4⋊C4×C127C2×C411yescharacteristic
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—21no—
43C2×C42×C127—21no—
44C2×C42×C127—21no—
45C2×C42×C127—42no—
46C2×C42×C127C2×C411yescharacteristic
47C2×C42×C127C2×C411yescharacteristic
48C2×C42×C127D411yescharacteristic
49C2×C42×C127D411yescharacteristic
50C4⋊C8×C127—42no—
51C22⋊C8×C127—22no—
52C22⋊C8×C127—22no—
53#95×C127—24no—
54#95×C127—21no—
55#95×C127—21no—
56#95×C127—21no—
57#95×C127—21no—
58#95×C127—21no—
59#95×C127—22no—
60#95×C127—22no—
61#95×C127—42no—
62C24×C127C2×D411yescharacteristic
63C2×Q8×C127—21no—
64C2×Q8×C127—41no—
65C2×Q8×C127—41no—
66C2×Q8×C127C4⋊C412yes—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—22no—
70C22×C4×C127—22no—
71C22×C4×C127—22no—
72C22×C4×C127—22no—
73C22×C4×C127—24no—
74C22×C4×C127—21no—
75C22×C4×C127—21no—
76C22×C4×C127—41no—
77C22×C4×C127—41no—
78C22×C4×C127—41no—
79C22×C4×C127—41no—
80C22×C4×C127—42no—
81C22×C4×C127—42no—
82C22×C4×C127—42no—
83C22×C4×C127—42no—
84C22×C4×C127—42no—
85C22×C4×C127—42no—
86C22×C4×C127C22⋊C411yescharacteristic
87C22×C4×C127C22⋊C411yescharacteristic
88C22×C4×C127C22⋊C411yescharacteristic
89C22×C4×C127C22⋊C411yescharacteristic
90C22×C4×C127C22×C411yescharacteristic
91C22×C4×C127C2×D411yescharacteristic
92C22×C4×C127C2×D411yescharacteristic
93C22×C4×C127C2×Q811yescharacteristic
94C22×C4×C127#4111yescharacteristic
95C22×C4×C127#4111yescharacteristic
96C2×C8×C127—42no—
97C2×C8×C127—42no—
98C2×C8×C127—42no—
99C4⋊C4×C127—21no—
100C4⋊C4×C127—22no—
101C4⋊C4×C127—22no—
102C4⋊C4×C127—41no—
103C4⋊C4×C127—41no—
104C4⋊C4×C127—42no—
105C4⋊C4×C127—42no—
106C4⋊C4×C127C4⋊C412yes—
107C22⋊C4×C127—22no—
108C22⋊C4×C127—22no—
109C22⋊C4×C127—42no—
110C42×C127—22no—
111C42×C127—22no—
112C42×C127—41no—
113C42×C127—41no—
114C42×C127—42no—
115C42×C127—42no—
116C23×C127—21no—
117C23×C127—21no—
118C23×C127—21no—
119C23×C127—21no—
120C23×C127C2×C22⋊C411yescharacteristic
121C23×C127#12111yescharacteristic
122C23×C127C22⋊Q811yescharacteristic
123C23×C127#13512yes—
124C23×C127#13712yes—
125Q8×C127—42no—
126Q8×C127—42no—
127C2×C4×C127—21no—
128C2×C4×C127—21no—
129C2×C4×C127—21no—
130C2×C4×C127—21no—
131C2×C4×C127—21no—
132C2×C4×C127—21no—
133C2×C4×C127—21no—
134C2×C4×C127—21no—
135C2×C4×C127—22no—
136C2×C4×C127—22no—
137C2×C4×C127—21no—
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—21no—
143C2×C4×C127—41no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—44no—
148C2×C4×C127—44no—
149C2×C4×C127—41no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—41no—
153C2×C4×C127—44no—
154C2×C4×C127—44no—
155C2×C4×C127—44no—
156C2×C4×C127—41no—
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—82no—
164C2×C4×C127—82no—
165C2×C4×C127—82no—
166C2×C4×C127#9912yes—
167C2×C4×C127#10412yes—
168C2×C4×C127C2×C4⋊C411yescharacteristic
169C2×C4×C127#11711yescharacteristic
170C2×C4×C127#12111yescharacteristic
171C2×C4×C127C22⋊Q811yescharacteristic
172C8×C127—82no—
173C22×C127—21no—
174C22×C127—21no—
175C22×C127—21no—
176C22×C127—21no—
177C22×C127—22no—
178C22×C127—22no—
179C22×C127—22no—
180C22×C127—22no—
181C22×C127#38011yescharacteristic
182C22×C127C2×#9911yescharacteristic
183C22×C127#41011yescharacteristic
184C22×C127#41611yescharacteristic
185C22×C127#41911yescharacteristic
186C22×C127C2×#10411yescharacteristic
187C22×C127#42111yescharacteristic
188C22×C127#46412yes—
189C22×C127#47912yes—
190C4×C127—21no—
191C4×C127—21no—
192C4×C127—21no—
193C4×C127—21no—
194C4×C127—22no—
195C4×C127—22no—
196C4×C127—42no—
197C4×C127—42no—
198C4×C127—41no—
199C4×C127—41no—
200C4×C127—84no—
201C4×C127—81no—
202C4×C127—81no—
203#8574C12711yesmaximal, characteristic, direct product factor, Sylow
204C2×C127—22no—
205C2×C127—22no—
206C2×C127#150011yescharacteristic
207C2×C127#150811yescharacteristic
208C2×C127#151511yescharacteristic
209C2×C127#151611yescharacteristic
210C2×C127#179911yescharacteristic
211C2×C127#180511yescharacteristic
212C2×C127#180611yescharacteristic
213C4×C22⋊Q8C2×C12711yescharacteristic
214#1797C2×C12711yescharacteristic
215C2×#328C2×C12712yes—
216#1434C2×C12711yescharacteristic
217#1294C2×C12712yes—
218C127#857411yescharacteristic, direct product factor, Sylow
219C2×C22⋊Q8C22×C12711yescharacteristic
220C2×C4×Q8C4×C12711yescharacteristic, complemented
221C22×C42C22×C12711yescharacteristic
222C2×C4⋊C8—21no—
223C2×C22⋊C8C22×C12712yes—
224#391C4×C12711yescharacteristic, complemented
225#389C4×C12711yescharacteristic, complemented
226#387—21no—
227#385—21no—
228#380C22×C12711yescharacteristic
229C4×C4⋊C4—21no—
230C4×C4⋊C4C4×C12711yescharacteristic, complemented
231C4×C22⋊C4—21no—
232C2×#95—21no—
233C2×#95—21no—
234C2×#95C22×C12712yes—
235#336—21no—
236#328—24no—
237C22×Q8C2×C4×C12711yescharacteristic
238C23×C4—22no—
239C23×C4D4×C12711yescharacteristic
240C23×C4D4×C12711yescharacteristic
241C23×C4C23×C12711yescharacteristic
242C22×C8—22no—
243C22⋊Q8—21no—
244C22⋊Q8—21no—
245C22⋊Q8D4×C12712yes—
246C22⋊Q8Q8×C12712yes—
247C4×Q8—42no—
248C2×C4⋊C4—21no—
249C2×C4⋊C4—21no—
250C2×C4⋊C4—21no—
251C2×C4⋊C4C2×C4×C12711yescharacteristic
252C2×C4⋊C4C2×C4×C12711yescharacteristic
253C2×C4⋊C4C2×C4×C12711yescharacteristic
254C2×C22⋊C4—21no—
255C2×C22⋊C4—21no—
256C2×C42—21no—
257C2×C42—21no—
258C2×C42—42no—
259C2×C42C2×C4×C12711yescharacteristic
260C2×C42C2×C4×C12711yescharacteristic
261C2×C42D4×C12711yescharacteristic
262C2×C42D4×C12711yescharacteristic
263C4⋊C8—42no—
264C22⋊C8—22no—
265C22⋊C8—22no—
266#95—24no—
267#95—21no—
268#95—21no—
269#95—21no—
270#95—21no—
271#95—21no—
272#95—22no—
273#95—22no—
274#95—42no—
275C24C2×D4×C12711yescharacteristic
276C2×Q8—21no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×Q8C4⋊C4×C12712yes—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—22no—
283C22×C4—22no—
284C22×C4—22no—
285C22×C4—22no—
286C22×C4—24no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—41no—
292C22×C4—41no—
293C22×C4—42no—
294C22×C4—42no—
295C22×C4—42no—
296C22×C4—42no—
297C22×C4—42no—
298C22×C4—42no—
299C22×C4C22⋊C4×C12711yescharacteristic
300C22×C4C22⋊C4×C12711yescharacteristic
301C22×C4C22⋊C4×C12711yescharacteristic
302C22×C4C22⋊C4×C12711yescharacteristic
303C22×C4C22×C4×C12711yescharacteristic
304C22×C4C2×D4×C12711yescharacteristic
305C22×C4C2×D4×C12711yescharacteristic
306C22×C4C2×Q8×C12711yescharacteristic
307C22×C4#41×C12711yescharacteristic
308C22×C4#41×C12711yescharacteristic
309C2×C8—42no—
310C2×C8—42no—
311C2×C8—42no—
312C4⋊C4—21no—
313C4⋊C4—22no—
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—42no—
318C4⋊C4—42no—
319C4⋊C4C4⋊C4×C12712yes—
320C22⋊C4—22no—
321C22⋊C4—22no—
322C22⋊C4—42no—
323C42—22no—
324C42—22no—
325C42—41no—
326C42—41no—
327C42—42no—
328C42—42no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23C2×C22⋊C4×C12711yescharacteristic
334C23#121×C12711yescharacteristic
335C23C22⋊Q8×C12711yescharacteristic
336C23#135×C12712yes—
337C23#137×C12712yes—
338Q8—42no—
339Q8—42no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—22no—
349C2×C4—22no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—44no—
361C2×C4—44no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—44no—
367C2×C4—44no—
368C2×C4—44no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—41no—
375C2×C4—82no—
376C2×C4—82no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4#99×C12712yes—
380C2×C4#104×C12712yes—
381C2×C4C2×C4⋊C4×C12711yescharacteristic
382C2×C4#117×C12711yescharacteristic
383C2×C4#121×C12711yescharacteristic
384C2×C4C22⋊Q8×C12711yescharacteristic
385C8—82no—
386C22—21no—
387C22—21no—
388C22—22no—
389C22—22no—
390C22—22no—
391C22—22no—
392C22—21no—
393C22—21no—
394C22#380×C12711yescharacteristic
395C22C2×#99×C12711yescharacteristic
396C22#410×C12711yescharacteristic
397C22#416×C12711yescharacteristic
398C22#419×C12711yescharacteristic
399C22C2×#104×C12711yescharacteristic
400C22#421×C12711yescharacteristic
401C22#464×C12712yes—
402C22#479×C12712yes—
403C4—22no—
404C4—22no—
405C4—21no—
406C4—21no—
407C4—21no—
408C4—21no—
409C4—42no—
410C4—41no—
411C4—41no—
412C4—42no—
413C4—84no—
414C4—81no—
415C4—81no—
416C2—22no—
417C2—22no—
418C2C127×#150011yescharacteristic
419C2C127×#150811yescharacteristic
420C2C127×#151511yescharacteristic
421C2C127×#151611yescharacteristic
422C2C127×#179911yescharacteristic
423C2C127×#180511yescharacteristic
424C2C127×#180611yescharacteristic
subgroupG/H
center, socleC23×C127C2×C22⋊C4
commutatorC22×C4C22×C4×C127
Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C127 ◁ C22×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
7. C2×C4×Q8×C127C4semidirect
11. #391×C127C4semidirect
12. #389×C127C4semidirect
17. C4×C4⋊C4×C127C4semidirect
203. #8574C127direct (N × H)
218. C127#8574direct (N × H)
220. C2×C4×Q8C4×C127semidirect
224. #391C4×C127semidirect
225. #389C4×C127semidirect
230. C4×C4⋊C4C4×C127semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊Q8×C1272
C127×#17972
C2×#328×C1272
C127×#14342
C127×#12942
#8574127