Finite Group Databasebeta

← C127×#10462 #44574135

Subgroups — C127×#10462 #44574135

Order 32512.

374 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3078C211yesmaximal, characteristic
2C127×#1801C211yesmaximal, characteristic
3C127×#1566C211yesmaximal, characteristic
4C127×#1550C211yesmaximal, characteristic
5C127×#1493C211yesmaximal, characteristic
6C2×Q8⋊C8×C127C211yesmaximal, characteristic
7C127×#1292C211yesmaximal, characteristic
8#533×C127C2211yescharacteristic
9C2×C4×Q8×C127C2211yescharacteristic
10#479×C127—22no—
11#477×C127—21no—
12#475×C127—21no—
13#428×C127—21no—
14#423×C127C2211yescharacteristic
15#423×C127C2211yescharacteristic
16#423×C127C2211yescharacteristic
17C2×C4⋊C8×C127C2211yescharacteristic
18#419×C127—21no—
19C2×#101×C127—21no—
20C2×C4×C8×C127C2211yescharacteristic
21#343×C127—21no—
22#334×C127—22no—
23#333×C127—21no—
24#332×C127—21no—
25Q8⋊C8×C127—21no—
26Q8⋊C8×C127—21no—
27Q8⋊C8×C127—21no—
28Q8⋊C8×C127—21no—
29C22×Q8×C127D411yescharacteristic
30C2×M16×C127—21no—
31C2×M16×C127—21no—
32C2×M16×C127—21no—
33C22×C8×C127—21no—
34C22×C8×C127—21no—
35C4⋊Q8×C127D411yescharacteristic
36C4⋊Q8×C127D411yescharacteristic
37#125×C127—21no—
38C22⋊Q8×C127—21no—
39C22⋊Q8×C127—21no—
40C4×Q8×C127—21no—
41C4×Q8×C127—21no—
42C4×Q8×C127—21no—
43C4×Q8×C127—21no—
44C4×Q8×C127—21no—
45C4×Q8×C127—21no—
46#117×C127—21no—
47C2×C4⋊C4×C127—21no—
48C2×C4⋊C4×C127D411yescharacteristic
49C2×C42×C127—21no—
50C2×C42×C127C2311yescharacteristic
51#107×C127—22no—
52#106×C127—22no—
53C4⋊C8×C127—21no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57C4⋊C8×C127—21no—
58C4⋊C8×C127—21no—
59C4⋊C8×C127—21no—
60C4⋊C8×C127D412yes—
61#103×C127—22no—
62#103×C127—22no—
63#101×C127—42no—
64C4×C8×C127—21no—
65C4×C8×C127D411yescharacteristic
66C4×C8×C127D411yescharacteristic
67C2×Q8×C127—21no—
68C2×Q8×C127—21no—
69C2×Q8×C127—21no—
70C2×Q8×C127—21no—
71C2×Q8×C127—21no—
72C2×Q8×C127—21no—
73C2×Q8×C127—21no—
74C2×Q8×C127SD1612yes—
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127C2×D411yescharacteristic
78C22×C4×C127#4111yescharacteristic
79C22×C4×C127#4111yescharacteristic
80M16×C127—41no—
81M16×C127—41no—
82M16×C127—41no—
83M16×C127—41no—
84M16×C127—41no—
85M16×C127—41no—
86C2×C8×C127—21no—
87C2×C8×C127—22no—
88C2×C8×C127—21no—
89C2×C8×C127—42no—
90C2×C8×C127—41no—
91C2×C8×C127—41no—
92C2×C8×C127—41no—
93C2×C8×C127—81no—
94C4⋊C4×C127—21no—
95C4⋊C4×C127—21no—
96C4⋊C4×C127—21no—
97C4⋊C4×C127—21no—
98C4⋊C4×C127—21no—
99C4⋊C4×C127—21no—
100C4⋊C4×C127—41no—
101C4⋊C4×C127—41no—
102C4⋊C4×C127—41no—
103C4⋊C4×C127—41no—
104C22⋊C4×C127—41no—
105C42×C127—41no—
106C42×C127—41no—
107C42×C127—41no—
108C42×C127C2×D411yescharacteristic
109C42×C127C2×D411yescharacteristic
110C42×C127C2×D411yescharacteristic
111C42×C127#4111yescharacteristic
112C23×C127#12311yescharacteristic
113Q8×C127—22no—
114Q8×C127—22no—
115Q8×C127—41no—
116Q8×C127—41no—
117Q8×C127—41no—
118Q8×C127—41no—
119Q8×C127—81no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—22no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—41no—
129C2×C4×C127—81no—
130C2×C4×C127#12011yescharacteristic
131C2×C4×C127#12111yescharacteristic
132C2×C4×C127#12111yescharacteristic
133C2×C4×C127#12111yescharacteristic
134C2×C4×C127#12311yescharacteristic
135C2×C4×C127#12411yescharacteristic
136C2×C4×C127C2×SD1611yescharacteristic
137C2×C4×C127#13511yescharacteristic
138C2×C4×C127#13711yescharacteristic
139C2×C4×C127#13711yescharacteristic
140C8×C127—22no—
141C8×C127—41no—
142C8×C127—42no—
143C8×C127—81no—
144C8×C127—81no—
145C8×C127—81no—
146C22×C127—21no—
147C22×C127—21no—
148C22×C127#39411yescharacteristic
149C22×C127#48311yescharacteristic
150C22×C127#48511yescharacteristic
151C4×C127—21no—
152C4×C127—21no—
153C4×C127—21no—
154C4×C127—42no—
155C4×C127—81no—
156C4×C127—81no—
157C4×C127—81no—
158C4×C127#44811yescharacteristic
159C4×C127#45211yescharacteristic
160C4×C127#46511yescharacteristic
161C4×C127#47011yescharacteristic
162C4×C127#47111yescharacteristic
163C4×C127#47311yescharacteristic
164#10462C12711yesmaximal, characteristic, direct product factor, Sylow
165C2×C127—21no—
166C2×C127—21no—
167C2×C127#203511yescharacteristic
168C2×C127#205011yescharacteristic
169C2×C127#205211yescharacteristic
170#3078C2×C12711yescharacteristic
171#1801C2×C12711yescharacteristic
172#1566C2×C12711yescharacteristic
173#1550C2×C12711yescharacteristic
174#1493C2×C12711yescharacteristic
175C2×Q8⋊C8C2×C12711yescharacteristic
176#1292C2×C12711yescharacteristic
177C127#1046211yescharacteristic, direct product factor, Sylow
178#533C22×C12711yescharacteristic
179C2×C4×Q8C22×C12711yescharacteristic
180#479—22no—
181#477—21no—
182#475—21no—
183#428—21no—
184#423C22×C12711yescharacteristic
185#423C22×C12711yescharacteristic
186#423C22×C12711yescharacteristic
187C2×C4⋊C8C22×C12711yescharacteristic
188#419—21no—
189C2×#101—21no—
190C2×C4×C8C22×C12711yescharacteristic
191#343—21no—
192#334—22no—
193#333—21no—
194#332—21no—
195Q8⋊C8—21no—
196Q8⋊C8—21no—
197Q8⋊C8—21no—
198Q8⋊C8—21no—
199C22×Q8D4×C12711yescharacteristic
200C2×M16—21no—
201C2×M16—21no—
202C2×M16—21no—
203C22×C8—21no—
204C22×C8—21no—
205C4⋊Q8D4×C12711yescharacteristic
206C4⋊Q8D4×C12711yescharacteristic
207#125—21no—
208C22⋊Q8—21no—
209C22⋊Q8—21no—
210C4×Q8—21no—
211C4×Q8—21no—
212C4×Q8—21no—
213C4×Q8—21no—
214C4×Q8—21no—
215C4×Q8—21no—
216#117—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4D4×C12711yescharacteristic
219C2×C42—21no—
220C2×C42C23×C12711yescharacteristic
221#107—22no—
222#106—22no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—21no—
227C4⋊C8—21no—
228C4⋊C8—21no—
229C4⋊C8—21no—
230C4⋊C8D4×C12712yes—
231#103—22no—
232#103—22no—
233#101—42no—
234C4×C8—21no—
235C4×C8D4×C12711yescharacteristic
236C4×C8D4×C12711yescharacteristic
237C2×Q8—21no—
238C2×Q8—21no—
239C2×Q8—21no—
240C2×Q8—21no—
241C2×Q8—21no—
242C2×Q8—21no—
243C2×Q8—21no—
244C2×Q8SD16×C12712yes—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4C2×D4×C12711yescharacteristic
248C22×C4#41×C12711yescharacteristic
249C22×C4#41×C12711yescharacteristic
250M16—41no—
251M16—41no—
252M16—41no—
253M16—41no—
254M16—41no—
255M16—41no—
256C2×C8—21no—
257C2×C8—22no—
258C2×C8—21no—
259C2×C8—42no—
260C2×C8—41no—
261C2×C8—41no—
262C2×C8—41no—
263C2×C8—81no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C22⋊C4—41no—
275C42—41no—
276C42—41no—
277C42—41no—
278C42C2×D4×C12711yescharacteristic
279C42C2×D4×C12711yescharacteristic
280C42C2×D4×C12711yescharacteristic
281C42#41×C12711yescharacteristic
282C23#123×C12711yescharacteristic
283Q8—22no—
284Q8—22no—
285Q8—41no—
286Q8—41no—
287Q8—41no—
288Q8—41no—
289Q8—81no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—81no—
300C2×C4#120×C12711yescharacteristic
301C2×C4#121×C12711yescharacteristic
302C2×C4#121×C12711yescharacteristic
303C2×C4#121×C12711yescharacteristic
304C2×C4#123×C12711yescharacteristic
305C2×C4#124×C12711yescharacteristic
306C2×C4C2×SD16×C12711yescharacteristic
307C2×C4#135×C12711yescharacteristic
308C2×C4#137×C12711yescharacteristic
309C2×C4#137×C12711yescharacteristic
310C8—22no—
311C8—41no—
312C8—42no—
313C8—81no—
314C8—81no—
315C8—81no—
316C22—21no—
317C22—21no—
318C22#394×C12711yescharacteristic
319C22#483×C12711yescharacteristic
320C22#485×C12711yescharacteristic
321C4—21no—
322C4—21no—
323C4—21no—
324C4—42no—
325C4—81no—
326C4—81no—
327C4—81no—
328C4#448×C12711yescharacteristic
329C4#452×C12711yescharacteristic
330C4#465×C12711yescharacteristic
331C4#470×C12711yescharacteristic
332C4#471×C12711yescharacteristic
333C4#473×C12711yescharacteristic
334C2—21no—
335C2—21no—
336C2C127×#203511yescharacteristic
337C2C127×#205011yescharacteristic
338C2C127×#205211yescharacteristic
subgroupG/H
center, socleC22×C127#394
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC23×C127#123
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
164. #10462C127direct (N × H)
177. C127#10462direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#30782
C127×#18012
C127×#15662
C127×#15502
C127×#14932
C2×Q8⋊C8×C1272
C127×#12922
#10462127