Finite Group Databasebeta

← C127×#10335 #44574008

Subgroups — C127×#10335 #44574008

Order 32512.

574 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 106 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×#3195C211yesmaximal, characteristic
2C127×#2503C211yesmaximal, characteristic
3C127×#2502C211yesmaximal, characteristic
4C127×#1821C211yesmaximal, characteristic
5C127×#1508C211yesmaximal, characteristic
6C127×#1508C211yesmaximal, characteristic
7C127×#1297C211yesmaximal, characteristic
8C2×C22⋊Q8×C127C2211yescharacteristic
9C2×C22⋊Q8×C127C2211yescharacteristic
10C22×C4⋊C4×C127C2211yescharacteristic
11#483×C127—21no—
12#483×C127—21no—
13#470×C127—22no—
14#451×C127—21no—
15#451×C127—21no—
16#407×C127C2211yescharacteristic
17#407×C127C2211yescharacteristic
18#400×C127—22no—
19#398×C127—22no—
20#391×C127—21no—
21#391×C127—21no—
22#385×C127—22no—
23#384×C127—21no—
24#382×C127—21no—
25#381×C127—22no—
26C4×C22⋊C4×C127C2211yescharacteristic
27C4×C22⋊C4×C127C2211yescharacteristic
28#343×C127—22no—
29#328×C127—22no—
30#328×C127—22no—
31C22×Q8×C127D411yescharacteristic
32C22×Q8×C127D411yescharacteristic
33C23×C4×C127D412yes—
34C23×C4×C127C2311yescharacteristic
35C2×Q16×C127—22no—
36C2×M16×C127—21no—
37C2×M16×C127D412yes—
38C22⋊Q8×C127—21no—
39C22⋊Q8×C127—21no—
40C22⋊Q8×C127—21no—
41C22⋊Q8×C127—21no—
42C22⋊Q8×C127—21no—
43C22⋊Q8×C127—21no—
44C22⋊Q8×C127—21no—
45C22⋊Q8×C127—21no—
46C2×C4⋊C4×C127—21no—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊C4×C127—21no—
49C2×C4⋊C4×C127—21no—
50C2×C4⋊C4×C127—21no—
51C2×C4⋊C4×C127—21no—
52C2×C4⋊C4×C127—21no—
53C2×C4⋊C4×C127—21no—
54C2×C4⋊C4×C127—24no—
55C2×C4⋊C4×C127D411yescharacteristic
56C2×C4⋊C4×C127D411yescharacteristic
57C2×C22⋊C4×C127—21no—
58C2×C22⋊C4×C127—21no—
59C2×C22⋊C4×C127—21no—
60C2×C22⋊C4×C127—21no—
61C2×C42×C127—21no—
62C2×C42×C127—21no—
63#106×C127—22no—
64#103×C127—22no—
65#103×C127—22no—
66C22⋊C8×C127—21no—
67C22⋊C8×C127—21no—
68C22⋊C8×C127—21no—
69C22⋊C8×C127—21no—
70#95×C127—24no—
71#95×C127—24no—
72#95×C127—24no—
73#95×C127D412yes—
74#95×C127D412yes—
75C24×C127C2×D411yescharacteristic
76C2×Q8×C127—21no—
77C2×Q8×C127—21no—
78C2×Q8×C127—21no—
79C2×Q8×C127—21no—
80C2×Q8×C127—42no—
81C2×Q8×C127—42no—
82C22×C4×C127—22no—
83C22×C4×C127—22no—
84C22×C4×C127—21no—
85C22×C4×C127—21no—
86C22×C4×C127—21no—
87C22×C4×C127—22no—
88C22×C4×C127—22no—
89C22×C4×C127—21no—
90C22×C4×C127—22no—
91C22×C4×C127—42no—
92C22×C4×C127—44no—
93C22×C4×C127C2×D411yescharacteristic
94C22×C4×C127C2×D411yescharacteristic
95C22×C4×C127C2×D411yescharacteristic
96C22×C4×C127C2×D411yescharacteristic
97C22×C4×C127C2×D411yescharacteristic
98C22×C4×C127#4111yescharacteristic
99Q16×C127—82no—
100M16×C127—42no—
101M16×C127—42no—
102C2×C8×C127—22no—
103C2×C8×C127—41no—
104C4⋊C4×C127—21no—
105C4⋊C4×C127—21no—
106C4⋊C4×C127—21no—
107C4⋊C4×C127—21no—
108C4⋊C4×C127—41no—
109C4⋊C4×C127—41no—
110C4⋊C4×C127—41no—
111C4⋊C4×C127—41no—
112C4⋊C4×C127—41no—
113C4⋊C4×C127—41no—
114C4⋊C4×C127—41no—
115C4⋊C4×C127—41no—
116C4⋊C4×C127—84no—
117C22⋊C4×C127—24no—
118C22⋊C4×C127—42no—
119C22⋊C4×C127—41no—
120C22⋊C4×C127—41no—
121C22⋊C4×C127—41no—
122C22⋊C4×C127—41no—
123C42×C127—42no—
124C42×C127—42no—
125C23×C127—22no—
126C23×C127—22no—
127C23×C127—41no—
128C23×C127#12011yescharacteristic
129C23×C127#12011yescharacteristic
130C23×C127#12111yescharacteristic
131Q8×C127—42no—
132Q8×C127—42no—
133Q8×C127—81no—
134Q8×C127—81no—
135C2×C4×C127—22no—
136C2×C4×C127—22no—
137C2×C4×C127—22no—
138C2×C4×C127—24no—
139C2×C4×C127—41no—
140C2×C4×C127—41no—
141C2×C4×C127—41no—
142C2×C4×C127—42no—
143C2×C4×C127—42no—
144C2×C4×C127—42no—
145C2×C4×C127—42no—
146C2×C4×C127—44no—
147C2×C4×C127—42no—
148C2×C4×C127—42no—
149C2×C4×C127—41no—
150C2×C4×C127—41no—
151C2×C4×C127—41no—
152C2×C4×C127—41no—
153C2×C4×C127—42no—
154C2×C4×C127—42no—
155C2×C4×C127—44no—
156C2×C4×C127—42no—
157C2×C4×C127—42no—
158C2×C4×C127—82no—
159C2×C4×C127#12011yescharacteristic
160C2×C4×C127#12111yescharacteristic
161C2×C4×C127#12111yescharacteristic
162C2×C4×C127#12711yescharacteristic
163C8×C127—42no—
164C8×C127—81no—
165C22×C127—21no—
166C22×C127—21no—
167C22×C127—21no—
168C22×C127—21no—
169C22×C127—21no—
170C22×C127—21no—
171C22×C127—21no—
172C22×C127—44no—
173C22×C127#39211yescharacteristic
174C22×C127#45512yes—
175C22×C127#45612yes—
176C4×C127—21no—
177C4×C127—21no—
178C4×C127—21no—
179C4×C127—44no—
180C4×C127—82no—
181C4×C127—81no—
182C4×C127—82no—
183C4×C127—81no—
184C4×C127—81no—
185C4×C127—81no—
186C4×C127#45812yes—
187#10335C12711yesmaximal, characteristic, direct product factor, Sylow
188C2×C127—22no—
189C2×C127—22no—
190C2×C127—41no—
191C2×C127#200411yescharacteristic
192C2×C127#200511yescharacteristic
193C2×C127#202211yescharacteristic
194#3195C2×C12711yescharacteristic
195#2503C2×C12711yescharacteristic
196#2502C2×C12711yescharacteristic
197#1821C2×C12711yescharacteristic
198#1508C2×C12711yescharacteristic
199#1508C2×C12711yescharacteristic
200#1297C2×C12711yescharacteristic
201C127#1033511yescharacteristic, direct product factor, Sylow
202C2×C22⋊Q8C22×C12711yescharacteristic
203C2×C22⋊Q8C22×C12711yescharacteristic
204C22×C4⋊C4C22×C12711yescharacteristic
205#483—21no—
206#483—21no—
207#470—22no—
208#451—21no—
209#451—21no—
210#407C22×C12711yescharacteristic
211#407C22×C12711yescharacteristic
212#400—22no—
213#398—22no—
214#391—21no—
215#391—21no—
216#385—22no—
217#384—21no—
218#382—21no—
219#381—22no—
220C4×C22⋊C4C22×C12711yescharacteristic
221C4×C22⋊C4C22×C12711yescharacteristic
222#343—22no—
223#328—22no—
224#328—22no—
225C22×Q8D4×C12711yescharacteristic
226C22×Q8D4×C12711yescharacteristic
227C23×C4D4×C12712yes—
228C23×C4C23×C12711yescharacteristic
229C2×Q16—22no—
230C2×M16—21no—
231C2×M16D4×C12712yes—
232C22⋊Q8—21no—
233C22⋊Q8—21no—
234C22⋊Q8—21no—
235C22⋊Q8—21no—
236C22⋊Q8—21no—
237C22⋊Q8—21no—
238C22⋊Q8—21no—
239C22⋊Q8—21no—
240C2×C4⋊C4—21no—
241C2×C4⋊C4—21no—
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⋊C4—24no—
249C2×C4⋊C4D4×C12711yescharacteristic
250C2×C4⋊C4D4×C12711yescharacteristic
251C2×C22⋊C4—21no—
252C2×C22⋊C4—21no—
253C2×C22⋊C4—21no—
254C2×C22⋊C4—21no—
255C2×C42—21no—
256C2×C42—21no—
257#106—22no—
258#103—22no—
259#103—22no—
260C22⋊C8—21no—
261C22⋊C8—21no—
262C22⋊C8—21no—
263C22⋊C8—21no—
264#95—24no—
265#95—24no—
266#95—24no—
267#95D4×C12712yes—
268#95D4×C12712yes—
269C24C2×D4×C12711yescharacteristic
270C2×Q8—21no—
271C2×Q8—21no—
272C2×Q8—21no—
273C2×Q8—21no—
274C2×Q8—42no—
275C2×Q8—42no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—21no—
279C22×C4—21no—
280C22×C4—21no—
281C22×C4—22no—
282C22×C4—22no—
283C22×C4—21no—
284C22×C4—22no—
285C22×C4—42no—
286C22×C4—44no—
287C22×C4C2×D4×C12711yescharacteristic
288C22×C4C2×D4×C12711yescharacteristic
289C22×C4C2×D4×C12711yescharacteristic
290C22×C4C2×D4×C12711yescharacteristic
291C22×C4C2×D4×C12711yescharacteristic
292C22×C4#41×C12711yescharacteristic
293Q16—82no—
294M16—42no—
295M16—42no—
296C2×C8—22no—
297C2×C8—41no—
298C4⋊C4—21no—
299C4⋊C4—21no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—41no—
305C4⋊C4—41no—
306C4⋊C4—41no—
307C4⋊C4—41no—
308C4⋊C4—41no—
309C4⋊C4—41no—
310C4⋊C4—84no—
311C22⋊C4—24no—
312C22⋊C4—42no—
313C22⋊C4—41no—
314C22⋊C4—41no—
315C22⋊C4—41no—
316C22⋊C4—41no—
317C42—42no—
318C42—42no—
319C23—22no—
320C23—22no—
321C23—41no—
322C23#120×C12711yescharacteristic
323C23#120×C12711yescharacteristic
324C23#121×C12711yescharacteristic
325Q8—42no—
326Q8—42no—
327Q8—81no—
328Q8—81no—
329C2×C4—22no—
330C2×C4—22no—
331C2×C4—22no—
332C2×C4—24no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—42no—
337C2×C4—42no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—44no—
341C2×C4—42no—
342C2×C4—42no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—41no—
346C2×C4—41no—
347C2×C4—42no—
348C2×C4—42no—
349C2×C4—44no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—82no—
353C2×C4#120×C12711yescharacteristic
354C2×C4#121×C12711yescharacteristic
355C2×C4#121×C12711yescharacteristic
356C2×C4#127×C12711yescharacteristic
357C8—42no—
358C8—81no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—44no—
367C22#392×C12711yescharacteristic
368C22#455×C12712yes—
369C22#456×C12712yes—
370C4—21no—
371C4—21no—
372C4—21no—
373C4—44no—
374C4—82no—
375C4—82no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4—81no—
380C4#458×C12712yes—
381C2—22no—
382C2—22no—
383C2—41no—
384C2C127×#200411yescharacteristic
385C2C127×#200511yescharacteristic
386C2C127×#202211yescharacteristic
subgroupG/H
center, socleC22×C127#392
commutator, Frattini, cosocleC23×C4C23×C127
prime radicalC24×C127C2×D4
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C23×C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
187. #10335C127direct (N × H)
201. C127#10335direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31952
C127×#25032
C127×#25022
C127×#18212
C127×#15082
C127×#12972
#10335127