Finite Group Databasebeta

← C127×#12176 #44575849

Subgroups — C127×#12176 #44575849

Order 32512.

486 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#2677C211yesmaximal, characteristic, complemented
2C127×#2044C211yesmaximal, characteristic
3C127×#1613C211yesmaximal, characteristic
4C127×#1601C211yesmaximal, characteristic
5C127×#1352C211yesmaximal, characteristic, complemented
6C127×#1351C211yesmaximal, characteristic, complemented
7C127×#1326C211yesmaximal, characteristic, complemented
8#534×C127C2211yescharacteristic
9C2×C4⋊Q8×C127—21no—
10C2×C22⋊Q8×C127—21no—
11#481×C127—21no—
12#448×C127—21no—
13C2×#99×C127—21no—
14#399×C127C2211yescharacteristic
15#398×C127—21no—
16#395×C127—21no—
17#393×C127C2211yescharacteristic
18#388×C127—21no—
19#387×C127—21no—
20#386×C127—21no—
21#385×C127C2211yescharacteristic
22#342×C127C2211yescharacteristic
23#327×C127—21no—
24#327×C127—21no—
25#323×C127C2211yescharacteristic
26#323×C127C2211yescharacteristic
27C22×Q8×C127—21no—
28C22×Q8×C127D411yescharacteristic
29C22×D4×C127—21no—
30C23×C4×C127D411yescharacteristic
31C2×SD16×C127—41no—
32C4⋊Q8×C127—44no—
33#123×C127—41no—
34C22⋊Q8×C127—44no—
35#121×C127—21no—
36#121×C127—21no—
37#120×C127—41no—
38C2×C4⋊C4×C127—21no—
39C2×C4⋊C4×C127—21no—
40C2×C4⋊C4×C127—21no—
41C2×C4⋊C4×C127—21no—
42C2×C4⋊C4×C127—21no—
43C2×C4⋊C4×C127—21no—
44C2×C4⋊C4×C127D411yescharacteristic
45C2×C22⋊C4×C127—21no—
46C2×C22⋊C4×C127—21no—
47C2×C22⋊C4×C127—21no—
48C2×C22⋊C4×C127—41no—
49C2×C22⋊C4×C127D411yescharacteristic
50C2×C22⋊C4×C127C2311yescharacteristic
51C2×C42×C127—21no—
52#106×C127—41no—
53#103×C127—41no—
54#102×C127—41no—
55#99×C127—42no—
56C22⋊C8×C127—21no—
57C22⋊C8×C127—21no—
58#95×C127—21no—
59#95×C127—21no—
60#95×C127—21no—
61#95×C127—21no—
62#95×C127—41no—
63#95×C127D411yescharacteristic
64#95×C127D411yescharacteristic
65C24×C127—21no—
66C24×C127C2×D411yescharacteristic
67C2×Q8×C127—42no—
68C2×Q8×C127—42no—
69C2×Q8×C127—42no—
70C2×Q8×C127—41no—
71C2×Q8×C127—81no—
72C2×D4×C127—21no—
73C2×D4×C127—21no—
74C2×D4×C127—41no—
75C2×D4×C127—41no—
76C2×D4×C127—41no—
77C2×D4×C127—41no—
78C2×D4×C127—41no—
79C2×D4×C127—41no—
80C22×C4×C127—21no—
81C22×C4×C127—21no—
82C22×C4×C127—21no—
83C22×C4×C127—21no—
84C22×C4×C127—21no—
85C22×C4×C127—21no—
86C22×C4×C127—21no—
87C22×C4×C127—42no—
88C22×C4×C127—41no—
89C22×C4×C127—41no—
90C22×C4×C127C2×D411yescharacteristic
91C22×C4×C127C2×D411yescharacteristic
92SD16×C127—82no—
93C2×C8×C127—41no—
94C2×C8×C127—41no—
95C4⋊C4×C127—24no—
96C4⋊C4×C127—21no—
97C4⋊C4×C127—21no—
98C4⋊C4×C127—41no—
99C4⋊C4×C127—42no—
100C4⋊C4×C127—42no—
101C4⋊C4×C127—42no—
102C4⋊C4×C127—42no—
103C4⋊C4×C127—42no—
104C22⋊C4×C127—21no—
105C22⋊C4×C127—41no—
106C22⋊C4×C127—42no—
107C22⋊C4×C127—42no—
108C22⋊C4×C127—41no—
109C22⋊C4×C127—41no—
110C22⋊C4×C127—41no—
111C22⋊C4×C127—41no—
112C22⋊C4×C127—82no—
113C22⋊C4×C127SD1612yescomplemented
114C42×C127—42no—
115C23×C127—21no—
116C23×C127—21no—
117C23×C127—41no—
118C23×C127—41no—
119C23×C127—41no—
120C23×C127—41no—
121C23×C127—41no—
122C23×C127—81no—
123C23×C127—81no—
124C23×C127#12011yescharacteristic
125C23×C127C2×SD1611yescharacteristic
126C23×C127#13711yescharacteristic
127Q8×C127—42no—
128Q8×C127—81no—
129Q8×C127—84no—
130D4×C127—81no—
131D4×C127—81no—
132D4×C127—81no—
133D4×C127—81no—
134D4×C127—81no—
135D4×C127—81no—
136C2×C4×C127—22no—
137C2×C4×C127—22no—
138C2×C4×C127—22no—
139C2×C4×C127—22no—
140C2×C4×C127—21no—
141C2×C4×C127—21no—
142C2×C4×C127—41no—
143C2×C4×C127—41no—
144C2×C4×C127—41no—
145C2×C4×C127—41no—
146C2×C4×C127—41no—
147C2×C4×C127—41no—
148C2×C4×C127—41no—
149C2×C4×C127—41no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—42no—
153C2×C4×C127—41no—
154C2×C4×C127—41no—
155C2×C4×C127—41no—
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—81no—
163C2×C4×C127—81no—
164C2×C4×C127—81no—
165C2×C4×C127—81no—
166C8×C127—81no—
167C8×C127—81no—
168C22×C127—21no—
169C22×C127—21no—
170C22×C127—21no—
171C22×C127—21no—
172C22×C127—41no—
173C22×C127—41no—
174C22×C127—41no—
175C22×C127—41no—
176C22×C127—81no—
177C22×C127—82no—
178C22×C127—81no—
179C22×C127—81no—
180C22×C127—81no—
181C22×C127—161no—
182C22×C127#44811yescharacteristic
183C22×C127#45411yescharacteristic
184C22×C127B(4,𝔽2)11yescharacteristic
185C4×C127—42no—
186C4×C127—42no—
187C4×C127—41no—
188C4×C127—42no—
189C4×C127—42no—
190C4×C127—41no—
191C4×C127—81no—
192C4×C127—81no—
193C4×C127—81no—
194C4×C127—161no—
195#12176C12711yesmaximal, characteristic, direct product factor, Sylow
196C2×C127—21no—
197C2×C127—21no—
198C2×C127—41no—
199C2×C127—41no—
200C2×C127—161no—
201C2×C127#159911yescharacteristic
202C2×C127#219611yescharacteristic
203C2×C127#220111yescharacteristic
204#2677C2×C12711yescharacteristic, complemented
205#2044C2×C12711yescharacteristic
206#1613C2×C12711yescharacteristic
207#1601C2×C12711yescharacteristic
208#1352C2×C12711yescharacteristic, complemented
209#1351C2×C12711yescharacteristic, complemented
210#1326C2×C12711yescharacteristic, complemented
211C127#1217611yescharacteristic, direct product factor, Sylow
212#534C22×C12711yescharacteristic
213C2×C4⋊Q8—21no—
214C2×C22⋊Q8—21no—
215#481—21no—
216#448—21no—
217C2×#99—21no—
218#399C22×C12711yescharacteristic
219#398—21no—
220#395—21no—
221#393C22×C12711yescharacteristic
222#388—21no—
223#387—21no—
224#386—21no—
225#385C22×C12711yescharacteristic
226#342C22×C12711yescharacteristic
227#327—21no—
228#327—21no—
229#323C22×C12711yescharacteristic
230#323C22×C12711yescharacteristic
231C22×Q8—21no—
232C22×Q8D4×C12711yescharacteristic
233C22×D4—21no—
234C23×C4D4×C12711yescharacteristic
235C2×SD16—41no—
236C4⋊Q8—44no—
237#123—41no—
238C22⋊Q8—44no—
239#121—21no—
240#121—21no—
241#120—41no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—21no—
245C2×C4⋊C4—21no—
246C2×C4⋊C4—21no—
247C2×C4⋊C4—21no—
248C2×C4⋊C4D4×C12711yescharacteristic
249C2×C22⋊C4—21no—
250C2×C22⋊C4—21no—
251C2×C22⋊C4—21no—
252C2×C22⋊C4—41no—
253C2×C22⋊C4D4×C12711yescharacteristic
254C2×C22⋊C4C23×C12711yescharacteristic
255C2×C42—21no—
256#106—41no—
257#103—41no—
258#102—41no—
259#99—42no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262#95—21no—
263#95—21no—
264#95—21no—
265#95—21no—
266#95—41no—
267#95D4×C12711yescharacteristic
268#95D4×C12711yescharacteristic
269C24—21no—
270C24C2×D4×C12711yescharacteristic
271C2×Q8—42no—
272C2×Q8—42no—
273C2×Q8—42no—
274C2×Q8—41no—
275C2×Q8—81no—
276C2×D4—21no—
277C2×D4—21no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C22×C4—21no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—21no—
288C22×C4—21no—
289C22×C4—21no—
290C22×C4—21no—
291C22×C4—42no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4C2×D4×C12711yescharacteristic
295C22×C4C2×D4×C12711yescharacteristic
296SD16—82no—
297C2×C8—41no—
298C2×C8—41no—
299C4⋊C4—24no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—42no—
304C4⋊C4—42no—
305C4⋊C4—42no—
306C4⋊C4—42no—
307C4⋊C4—42no—
308C22⋊C4—21no—
309C22⋊C4—41no—
310C22⋊C4—42no—
311C22⋊C4—42no—
312C22⋊C4—41no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—82no—
317C22⋊C4SD16×C12712yescomplemented
318C42—42no—
319C23—21no—
320C23—21no—
321C23—41no—
322C23—41no—
323C23—41no—
324C23—41no—
325C23—41no—
326C23—81no—
327C23—81no—
328C23#120×C12711yescharacteristic
329C23C2×SD16×C12711yescharacteristic
330C23#137×C12711yescharacteristic
331Q8—42no—
332Q8—81no—
333Q8—84no—
334D4—81no—
335D4—81no—
336D4—81no—
337D4—81no—
338D4—81no—
339D4—81no—
340C2×C4—22no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—22no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—41no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—41no—
350C2×C4—41no—
351C2×C4—41no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—42no—
357C2×C4—41no—
358C2×C4—41no—
359C2×C4—41no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C8—81no—
371C8—81no—
372C22—21no—
373C22—21no—
374C22—21no—
375C22—21no—
376C22—41no—
377C22—41no—
378C22—41no—
379C22—41no—
380C22—81no—
381C22—82no—
382C22—81no—
383C22—81no—
384C22—81no—
385C22—161no—
386C22#448×C12711yescharacteristic
387C22#454×C12711yescharacteristic
388C22B(4,𝔽2)×C12711yescharacteristic
389C4—42no—
390C4—42no—
391C4—41no—
392C4—42no—
393C4—42no—
394C4—41no—
395C4—81no—
396C4—81no—
397C4—81no—
398C4—161no—
399C2—21no—
400C2—21no—
401C2—41no—
402C2—41no—
403C2—161no—
404C2C127×#159911yescharacteristic
405C2C127×#219611yescharacteristic
406C2C127×#220111yescharacteristic
subgroupG/H
center, socleC22×C127B(4,𝔽2)
commutator, Frattini, cosocleC2×C22⋊C4C23×C127
prime radical#534×C127C22
LCSG ▷ C2×C22⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C2×C22⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2677C2semidirect
5. C127×#1352C2semidirect
6. C127×#1351C2semidirect
7. C127×#1326C2semidirect
113. C22⋊C4×C127SD16semidirect
195. #12176C127direct (N × H)
204. #2677C2×C127semidirect
208. #1352C2×C127semidirect
209. #1351C2×C127semidirect
210. #1326C2×C127semidirect
211. C127#12176direct (N × H)
317. C22⋊C4SD16×C127semidirect

Maximal subgroups

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

subgroupindex
C127×#26772
C127×#20442
C127×#16132
C127×#16012
C127×#13522
C127×#13512
C127×#13262
#12176127