Finite Group Databasebeta

← C127×#12195 #44575868

Subgroups — C127×#12195 #44575868

Order 32512.

458 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 70 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×#2572C211yesmaximal, characteristic, complemented
2C127×#2007C211yesmaximal, characteristic, complemented
3C127×#1616C211yesmaximal, characteristic, complemented
4C127×#1598C211yesmaximal, characteristic
5C127×#1353C211yesmaximal, characteristic, complemented
6C127×#1345C211yesmaximal, characteristic, complemented
7C127×#1319C211yesmaximal, characteristic, complemented
8C2×#137×C127—21no—
9#537×C127C2211yescharacteristic
10#481×C127—21no—
11#447×C127—21no—
12C2×#104×C127—21no—
13#400×C127C2211yescharacteristic
14#394×C127C2211yescharacteristic
15#393×C127—21no—
16#391×C127C2211yescharacteristic
17#388×C127—21no—
18#386×C127—21no—
19#383×C127—21no—
20#381×C127—21no—
21C4×C22⋊C4×C127—21no—
22#343×C127C2211yescharacteristic
23#327×C127—21no—
24#327×C127—21no—
25#324×C127C2211yescharacteristic
26#324×C127C2211yescharacteristic
27C2×#41×C127—21no—
28C22×Q8×C127D411yescharacteristic
29C22×D4×C127D411yescharacteristic
30C23×C4×C127—21no—
31#137×C127—42no—
32#137×C127—42no—
33C2×Q16×C127—41no—
34C2×SD16×C127—41no—
35C2×D8×C127—41no—
36C2×M16×C127—21no—
37C22⋊Q8×C127—41no—
38#121×C127—21no—
39#121×C127—21no—
40#121×C127—41no—
41C2×C4⋊C4×C127D411yescharacteristic
42C2×C4⋊C4×C127C2311yescharacteristic
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—21no—
45C2×C22⋊C4×C127—21no—
46C2×C22⋊C4×C127—21no—
47C2×C22⋊C4×C127—21no—
48C2×C42×C127—21no—
49C2×C42×C127D411yescharacteristic
50#106×C127—41no—
51#104×C127—42no—
52#102×C127—41no—
53#102×C127—41no—
54C22⋊C8×C127—21no—
55C22⋊C8×C127—21no—
56#95×C127—21no—
57#95×C127—21no—
58#95×C127—21no—
59#95×C127—21no—
60#95×C127—21no—
61#95×C127—21no—
62#95×C127—21no—
63#95×C127D411yescharacteristic
64#95×C127D411yescharacteristic
65C24×C127—21no—
66#41×C127—41no—
67#41×C127—41no—
68#41×C127—41no—
69#41×C127—41no—
70C2×Q8×C127—21no—
71C2×Q8×C127—21no—
72C2×Q8×C127—21no—
73C2×Q8×C127—41no—
74C2×Q8×C127—41no—
75C2×D4×C127—21no—
76C2×D4×C127—21no—
77C2×D4×C127—21no—
78C2×D4×C127—41no—
79C2×D4×C127—42no—
80C2×D4×C127—41no—
81C22×C4×C127—21no—
82C22×C4×C127—21no—
83C22×C4×C127—21no—
84C22×C4×C127—21no—
85C22×C4×C127—21no—
86C22×C4×C127—41no—
87C22×C4×C127—42no—
88C22×C4×C127—42no—
89C22×C4×C127—81no—
90C22×C4×C127C2×D411yescharacteristic
91C22×C4×C127C2×D411yescharacteristic
92C22×C4×C127C2×D411yescharacteristic
93Q16×C127—44no—
94SD16×C127—44no—
95D8×C127—82no—
96M16×C127—22no—
97M16×C127—41no—
98C2×C8×C127—41no—
99C2×C8×C127—41no—
100C2×C8×C127—41no—
101C4⋊C4×C127—21no—
102C4⋊C4×C127—21no—
103C4⋊C4×C127—41no—
104C4⋊C4×C127—41no—
105C22⋊C4×C127—42no—
106C22⋊C4×C127—41no—
107C22⋊C4×C127—41no—
108C22⋊C4×C127—42no—
109C22⋊C4×C127—41no—
110C22⋊C4×C127—41no—
111C22⋊C4×C127—81no—
112C22⋊C4×C127—81no—
113C42×C127—41no—
114C42×C127—42no—
115C23×C127—22no—
116C23×C127—41no—
117C23×C127—41no—
118C23×C127—41no—
119C23×C127—41no—
120C23×C127—41no—
121C23×C127—41no—
122C23×C127—41no—
123C23×C127#12011yescharacteristic
124Q8×C127—42no—
125Q8×C127—41no—
126Q8×C127—41no—
127Q8×C127—81no—
128D4×C127—41no—
129D4×C127—41no—
130D4×C127—42no—
131D4×C127—81no—
132D4×C127—81no—
133D4×C127—81no—
134D4×C127—81no—
135D4×C127—81no—
136C2×C4×C127—21no—
137C2×C4×C127—21no—
138C2×C4×C127—22no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—41no—
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—41no—
153C2×C4×C127—41no—
154C2×C4×C127—41no—
155C2×C4×C127—41no—
156C2×C4×C127—41no—
157C2×C4×C127—41no—
158C2×C4×C127—81no—
159C2×C4×C127—81no—
160C2×C4×C127—84no—
161C2×C4×C127#13511yescharacteristic
162C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
163C8×C127—42no—
164C8×C127—81no—
165C8×C127—81no—
166C22×C127—21no—
167C22×C127—21no—
168C22×C127—42no—
169C22×C127—42no—
170C22×C127—42no—
171C22×C127—81no—
172C22×C127—81no—
173C22×C127—81no—
174C22×C127—81no—
175C22×C127—81no—
176C22×C127—81no—
177C22×C127—81no—
178C22×C127#44911yescharacteristic
179C22×C127#45311yescharacteristic
180C22×C127B(4,𝔽2)11yescharacteristic
181C4×C127—21no—
182C4×C127—21no—
183C4×C127—42no—
184C4×C127—41no—
185C4×C127—41no—
186C4×C127—81no—
187C4×C127—81no—
188C4×C127—81no—
189C4×C127—81no—
190C4×C127—81no—
191#12195C12711yesmaximal, characteristic, direct product factor, Sylow
192C2×C127—21no—
193C2×C127—21no—
194C2×C127—82no—
195C2×C127—161no—
196C2×C127#160011yescharacteristic
197C2×C127#219711yescharacteristic
198C2×C127#220411yescharacteristic
199#2572C2×C12711yescharacteristic, complemented
200#2007C2×C12711yescharacteristic, complemented
201#1616C2×C12711yescharacteristic, complemented
202#1598C2×C12711yescharacteristic
203#1353C2×C12711yescharacteristic, complemented
204#1345C2×C12711yescharacteristic, complemented
205#1319C2×C12711yescharacteristic, complemented
206C127#1219511yescharacteristic, direct product factor, Sylow
207C2×#137—21no—
208#537C22×C12711yescharacteristic
209#481—21no—
210#447—21no—
211C2×#104—21no—
212#400C22×C12711yescharacteristic
213#394C22×C12711yescharacteristic
214#393—21no—
215#391C22×C12711yescharacteristic
216#388—21no—
217#386—21no—
218#383—21no—
219#381—21no—
220C4×C22⋊C4—21no—
221#343C22×C12711yescharacteristic
222#327—21no—
223#327—21no—
224#324C22×C12711yescharacteristic
225#324C22×C12711yescharacteristic
226C2×#41—21no—
227C22×Q8D4×C12711yescharacteristic
228C22×D4D4×C12711yescharacteristic
229C23×C4—21no—
230#137—42no—
231#137—42no—
232C2×Q16—41no—
233C2×SD16—41no—
234C2×D8—41no—
235C2×M16—21no—
236C22⋊Q8—41no—
237#121—21no—
238#121—21no—
239#121—41no—
240C2×C4⋊C4D4×C12711yescharacteristic
241C2×C4⋊C4C23×C12711yescharacteristic
242C2×C22⋊C4—21no—
243C2×C22⋊C4—21no—
244C2×C22⋊C4—21no—
245C2×C22⋊C4—21no—
246C2×C22⋊C4—21no—
247C2×C42—21no—
248C2×C42D4×C12711yescharacteristic
249#106—41no—
250#104—42no—
251#102—41no—
252#102—41no—
253C22⋊C8—21no—
254C22⋊C8—21no—
255#95—21no—
256#95—21no—
257#95—21no—
258#95—21no—
259#95—21no—
260#95—21no—
261#95—21no—
262#95D4×C12711yescharacteristic
263#95D4×C12711yescharacteristic
264C24—21no—
265#41—41no—
266#41—41no—
267#41—41no—
268#41—41no—
269C2×Q8—21no—
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×D4—21no—
275C2×D4—21no—
276C2×D4—21no—
277C2×D4—41no—
278C2×D4—42no—
279C2×D4—41no—
280C22×C4—21no—
281C22×C4—21no—
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—21no—
285C22×C4—41no—
286C22×C4—42no—
287C22×C4—42no—
288C22×C4—81no—
289C22×C4C2×D4×C12711yescharacteristic
290C22×C4C2×D4×C12711yescharacteristic
291C22×C4C2×D4×C12711yescharacteristic
292Q16—44no—
293SD16—44no—
294D8—82no—
295M16—22no—
296M16—41no—
297C2×C8—41no—
298C2×C8—41no—
299C2×C8—41no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C22⋊C4—42no—
305C22⋊C4—41no—
306C22⋊C4—41no—
307C22⋊C4—42no—
308C22⋊C4—41no—
309C22⋊C4—41no—
310C22⋊C4—81no—
311C22⋊C4—81no—
312C42—41no—
313C42—42no—
314C23—22no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23—41no—
319C23—41no—
320C23—41no—
321C23—41no—
322C23#120×C12711yescharacteristic
323Q8—42no—
324Q8—41no—
325Q8—41no—
326Q8—81no—
327D4—41no—
328D4—41no—
329D4—42no—
330D4—81no—
331D4—81no—
332D4—81no—
333D4—81no—
334D4—81no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—41no—
341C2×C4—41no—
342C2×C4—41no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
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—41no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—84no—
360C2×C4#135×C12711yescharacteristic
361C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
362C8—42no—
363C8—81no—
364C8—81no—
365C22—21no—
366C22—21no—
367C22—42no—
368C22—42no—
369C22—42no—
370C22—81no—
371C22—81no—
372C22—81no—
373C22—81no—
374C22—81no—
375C22—81no—
376C22—81no—
377C22#449×C12711yescharacteristic
378C22#453×C12711yescharacteristic
379C22B(4,𝔽2)×C12711yescharacteristic
380C4—21no—
381C4—21no—
382C4—42no—
383C4—41no—
384C4—41no—
385C4—81no—
386C4—81no—
387C4—81no—
388C4—81no—
389C4—81no—
390C2—21no—
391C2—21no—
392C2—82no—
393C2—161no—
394C2C127×#160011yescharacteristic
395C2C127×#219711yescharacteristic
396C2C127×#220411yescharacteristic
subgroupG/H
center, socleC22×C127B(4,𝔽2)
commutator, Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC127×#1598C2
LCSG ▷ C2×C4⋊C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C127 ◁ C2×C4⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C127×#2572C2semidirect
2. C127×#2007C2semidirect
3. C127×#1616C2semidirect
5. C127×#1353C2semidirect
6. C127×#1345C2semidirect
7. C127×#1319C2semidirect
191. #12195C127direct (N × H)
199. #2572C2×C127semidirect
200. #2007C2×C127semidirect
201. #1616C2×C127semidirect
203. #1353C2×C127semidirect
204. #1345C2×C127semidirect
205. #1319C2×C127semidirect
206. C127#12195direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#25722
C127×#20072
C127×#16162
C127×#15982
C127×#13532
C127×#13452
C127×#13192
#12195127