Finite Group Databasebeta

← C127×#8471 #44572144

Subgroups — C127×#8471 #44572144

Order 32512.

924 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3499C211yesmaximal, characteristic
2C127×#1997C212yesmaximal, complemented
3C127×#1560C211yesmaximal, characteristic, complemented
4C127×#1525C211yesmaximal, characteristic, complemented
5C127×#1489C212yesmaximal, complemented
6C2×2−1+4×C127C412yes—
7D4×Q8×C127—22no—
8#547×C127—22no—
9#547×C127—24no—
10#536×C127—22no—
11#536×C127C412yes—
12#532×C127—21no—
13#532×C127C2211yescharacteristic
14C2×C4⋊Q8×C127—21no—
15C2×C4⋊Q8×C127C2211yescharacteristic
16C4×#41×C127C2211yescharacteristic
17#423×C127C2212yes—
18C4×M16×C127C2212yes—
19#343×C127—24no—
20#333×C127—21no—
21#331×C127—21no—
22#329×C127—22no—
23Q8⋊C8×C127—22no—
24D4⋊C8×C127—22no—
252−1+4×C127—44no—
262−1+4×C127—44no—
27C2×#41×C127—22no—
28C2×#41×C127—22no—
29C2×#41×C127—24no—
30C2×#41×C127C2×C411yescharacteristic
31C2×#41×C127C2×C412yes—
32C22×Q8×C127—22no—
33C22×Q8×C127—22no—
34C22×Q8×C127C2×C412yes—
35C2×M16×C127—22no—
36C2×M16×C127—22no—
37C4⋊Q8×C127—24no—
38C4⋊Q8×C127—22no—
39C4⋊Q8×C127—21no—
40C4⋊Q8×C127—21no—
41C4⋊Q8×C127—22no—
42C4⋊Q8×C127D411yescharacteristic
43#127×C127D411yescharacteristic
44#124×C127—22no—
45#124×C127D412yes—
46#123×C127—28no—
47#123×C127—24no—
48C22⋊Q8×C127—28no—
49C22⋊Q8×C127—24no—
50#121×C127—24no—
51#121×C127—22no—
52C4×Q8×C127D412yes—
53C4×D4×C127—24no—
54C4×D4×C127—22no—
55C4×D4×C127—22no—
56C4×D4×C127D412yes—
57#117×C127—21no—
58#117×C127C2×C411yescharacteristic
59C2×C4⋊C4×C127—24no—
60C2×C4⋊C4×C127D414yes—
61C2×C42×C127—21no—
62C2×C42×C127C2311yescharacteristic
63C4⋊C8×C127—22no—
64C4⋊C8×C127—22no—
65#97×C127—22no—
66C4×C8×C127—22no—
67#41×C127—22no—
68#41×C127—22no—
69#41×C127—48no—
70#41×C127—42no—
71#41×C127—42no—
72#41×C127—416no—
73#41×C127—44no—
74#41×C127—44no—
75C2×Q8×C127—24no—
76C2×Q8×C127—22no—
77C2×Q8×C127—22no—
78C2×Q8×C127—42no—
79C2×Q8×C127—42no—
80C2×Q8×C127—48no—
81C2×Q8×C127—44no—
82C2×Q8×C127—44no—
83C2×Q8×C127C22⋊C411yescharacteristic
84C2×Q8×C127C22⋊C412yes—
85C2×D4×C127—21no—
86C2×D4×C127—24no—
87C2×D4×C127—22no—
88C2×D4×C127—22no—
89C2×D4×C127C22⋊C411yescharacteristic
90C2×D4×C127C22⋊C412yes—
91C22×C4×C127—21no—
92C22×C4×C127—24no—
93C22×C4×C127—24no—
94C22×C4×C127—22no—
95C22×C4×C127—22no—
96C22×C4×C127C22⋊C414yes—
97C22×C4×C127C22×C411yescharacteristic
98C22×C4×C127C2×D412yes—
99M16×C127—24no—
100M16×C127—42no—
101M16×C127—44no—
102C2×C8×C127—42no—
103C2×C8×C127—42no—
104C4⋊C4×C127—28no—
105C4⋊C4×C127—22no—
106C4⋊C4×C127—24no—
107C4⋊C4×C127—24no—
108C4⋊C4×C127—22no—
109C4⋊C4×C127C22⋊C412yes—
110C22⋊C4×C127—28no—
111C22⋊C4×C127—21no—
112C22⋊C4×C127—22no—
113C22⋊C4×C127—24no—
114C42×C127—21no—
115C42×C127—22no—
116C42×C127C2×D412yes—
117C42×C127C2×D411yescharacteristic
118C42×C127C2×D411yescharacteristic
119C23×C127—21no—
120C23×C127—22no—
121C23×C127C2×C22⋊C411yescharacteristic
122Q8×C127—21no—
123Q8×C127—42no—
124Q8×C127—44no—
125Q8×C127—48no—
126Q8×C127—42no—
127Q8×C127—42no—
128Q8×C127#10012yes—
129D4×C127—24no—
130D4×C127—21no—
131D4×C127—42no—
132D4×C127—44no—
133D4×C127—48no—
134D4×C127—42no—
135D4×C127—42no—
136D4×C127#10012yes—
137C2×C4×C127—24no—
138C2×C4×C127—21no—
139C2×C4×C127—21no—
140C2×C4×C127—21no—
141C2×C4×C127—22no—
142C2×C4×C127—22no—
143C2×C4×C127—22no—
144C2×C4×C127—22no—
145C2×C4×C127—24no—
146C2×C4×C127—48no—
147C2×C4×C127—48no—
148C2×C4×C127—42no—
149C2×C4×C127—42no—
150C2×C4×C127—42no—
151C2×C4×C127—42no—
152C2×C4×C127—44no—
153C2×C4×C127C2×C22⋊C411yescharacteristic
154C2×C4×C127C2×C22⋊C411yescharacteristic
155C2×C4×C127#12012yes—
156C2×C4×C127#12012yes—
157C8×C127—44no—
158C8×C127—82no—
159C22×C127—22no—
160C22×C127—21no—
161C22×C127—22no—
162C22×C127—42no—
163C22×C127—44no—
164C22×C127—42no—
165C22×C127#37911yescharacteristic
166C4×C127—22no—
167C4×C127—21no—
168C4×C127—22no—
169C4×C127—42no—
170C4×C127—42no—
171C4×C127—44no—
172C4×C127C2×#10011yescharacteristic
173C4×C127C2×#10011yescharacteristic
174C4×C127#45412yes—
175C4×C127#45612yes—
176#8471C12711yesmaximal, characteristic, direct product factor, Sylow
177C2×C127—41no—
178C2×C127—42no—
179C2×C127—82no—
180C2×C127#178311yescharacteristic
181C2×C127#179312yes—
182#3499C2×C12711yescharacteristic
183#1997C2×C12712yescomplemented
184#1560C2×C12711yescharacteristic, complemented
185#1525C2×C12711yescharacteristic, complemented
186#1489C2×C12712yescomplemented
187C127#847111yescharacteristic, direct product factor, Sylow
188C2×2−1+4C4×C12712yes—
189D4×Q8—22no—
190#547—22no—
191#547—24no—
192#536—22no—
193#536C4×C12712yes—
194#532—21no—
195#532C22×C12711yescharacteristic
196C2×C4⋊Q8—21no—
197C2×C4⋊Q8C22×C12711yescharacteristic
198C4×#41C22×C12711yescharacteristic
199#423C22×C12712yes—
200C4×M16C22×C12712yes—
201#343—24no—
202#333—21no—
203#331—21no—
204#329—22no—
205Q8⋊C8—22no—
206D4⋊C8—22no—
2072−1+4—44no—
2082−1+4—44no—
209C2×#41—22no—
210C2×#41—22no—
211C2×#41—24no—
212C2×#41C2×C4×C12711yescharacteristic
213C2×#41C2×C4×C12712yes—
214C22×Q8—22no—
215C22×Q8—22no—
216C22×Q8C2×C4×C12712yes—
217C2×M16—22no—
218C2×M16—22no—
219C4⋊Q8—24no—
220C4⋊Q8—22no—
221C4⋊Q8—21no—
222C4⋊Q8—21no—
223C4⋊Q8—22no—
224C4⋊Q8D4×C12711yescharacteristic
225#127D4×C12711yescharacteristic
226#124—22no—
227#124D4×C12712yes—
228#123—28no—
229#123—24no—
230C22⋊Q8—28no—
231C22⋊Q8—24no—
232#121—24no—
233#121—22no—
234C4×Q8D4×C12712yes—
235C4×D4—24no—
236C4×D4—22no—
237C4×D4—22no—
238C4×D4D4×C12712yes—
239#117—21no—
240#117C2×C4×C12711yescharacteristic
241C2×C4⋊C4—24no—
242C2×C4⋊C4D4×C12714yes—
243C2×C42—21no—
244C2×C42C23×C12711yescharacteristic
245C4⋊C8—22no—
246C4⋊C8—22no—
247#97—22no—
248C4×C8—22no—
249#41—22no—
250#41—22no—
251#41—48no—
252#41—42no—
253#41—42no—
254#41—416no—
255#41—44no—
256#41—44no—
257C2×Q8—24no—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—42no—
261C2×Q8—42no—
262C2×Q8—48no—
263C2×Q8—44no—
264C2×Q8—44no—
265C2×Q8C22⋊C4×C12711yescharacteristic
266C2×Q8C22⋊C4×C12712yes—
267C2×D4—21no—
268C2×D4—24no—
269C2×D4—22no—
270C2×D4—22no—
271C2×D4C22⋊C4×C12711yescharacteristic
272C2×D4C22⋊C4×C12712yes—
273C22×C4—21no—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—22no—
277C22×C4—22no—
278C22×C4C22⋊C4×C12714yes—
279C22×C4C22×C4×C12711yescharacteristic
280C22×C4C2×D4×C12712yes—
281M16—24no—
282M16—42no—
283M16—44no—
284C2×C8—42no—
285C2×C8—42no—
286C4⋊C4—28no—
287C4⋊C4—22no—
288C4⋊C4—24no—
289C4⋊C4—24no—
290C4⋊C4—22no—
291C4⋊C4C22⋊C4×C12712yes—
292C22⋊C4—28no—
293C22⋊C4—21no—
294C22⋊C4—22no—
295C22⋊C4—24no—
296C42—21no—
297C42—22no—
298C42C2×D4×C12712yes—
299C42C2×D4×C12711yescharacteristic
300C42C2×D4×C12711yescharacteristic
301C23—21no—
302C23—22no—
303C23C2×C22⋊C4×C12711yescharacteristic
304Q8—21no—
305Q8—42no—
306Q8—44no—
307Q8—48no—
308Q8—42no—
309Q8—42no—
310Q8#100×C12712yes—
311D4—24no—
312D4—21no—
313D4—42no—
314D4—44no—
315D4—48no—
316D4—42no—
317D4—42no—
318D4#100×C12712yes—
319C2×C4—24no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—24no—
328C2×C4—48no—
329C2×C4—48no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—44no—
335C2×C4C2×C22⋊C4×C12711yescharacteristic
336C2×C4C2×C22⋊C4×C12711yescharacteristic
337C2×C4#120×C12712yes—
338C2×C4#120×C12712yes—
339C8—44no—
340C8—82no—
341C22—21no—
342C22—22no—
343C22—22no—
344C22—42no—
345C22—42no—
346C22—44no—
347C22#379×C12711yescharacteristic
348C4—21no—
349C4—22no—
350C4—22no—
351C4—42no—
352C4—44no—
353C4—42no—
354C4C2×#100×C12711yescharacteristic
355C4C2×#100×C12711yescharacteristic
356C4#454×C12712yes—
357C4#456×C12712yes—
358C2—41no—
359C2—42no—
360C2—82no—
361C2C127×#178311yescharacteristic
362C2C127×#179312yes—
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC127×#3499C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1997C2semidirect
3. C127×#1560C2semidirect
4. C127×#1525C2semidirect
5. C127×#1489C2semidirect
176. #8471C127direct (N × H)
183. #1997C2×C127semidirect
184. #1560C2×C127semidirect
185. #1525C2×C127semidirect
186. #1489C2×C127semidirect
187. C127#8471direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#34992
C127×#19972
C127×#15602
C127×#15252
C127×#14892
#8471127