Finite Group Databasebeta

← C127×#9530 #44573203

Subgroups — C127×#9530 #44573203

Order 32512.

428 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C127×#3110C211yesmaximal, characteristic
2C127×#2985C211yesmaximal, characteristic, complemented
3C127×#1559C211yesmaximal, characteristic, complemented
4C127×#1486C211yesmaximal, characteristic
5C127×#1466C211yesmaximal, characteristic
6C127×#1307C211yesmaximal, characteristic, complemented
7C127×#1287C211yesmaximal, characteristic, complemented
8#533×C127C2211yescharacteristic
9C2×C4×D4×C127C2211yescharacteristic
10#484×C127C412yes—
11#474×C127—21no—
12#461×C127—21no—
13#450×C127C412yes—
14#446×C127—22no—
15#446×C127—21no—
16C8×Q8×C127—21no—
17#440×C127—22no—
18#433×C127—22no—
19#432×C127C2211yescharacteristic
20#432×C127C2211yescharacteristic
21#432×C127C2211yescharacteristic
22#431×C127C2211yescharacteristic
23#423×C127C2211yescharacteristic
24#333×C127—21no—
25#332×C127—21no—
26D4⋊C8×C127—21no—
27D4⋊C8×C127—21no—
28#323×C127—22no—
29C22×D4×C127C2×C411yescharacteristic
30C23×C4×C127—21no—
31C2×SD16×C127—22no—
32C2×M16×C127—21no—
33C4⋊Q8×C127D411yescharacteristic
34C4⋊Q8×C127D411yescharacteristic
35#125×C127—21no—
36C22⋊Q8×C127—21no—
37C22⋊Q8×C127C2×C412yes—
38C4×Q8×C127—21no—
39C4×Q8×C127D412yes—
40C4×D4×C127—21no—
41C4×D4×C127—21no—
42C4×D4×C127—21no—
43C4×D4×C127—21no—
44#117×C127—21no—
45C2×C4⋊C4×C127C2×C411yescharacteristic
46C2×C22⋊C4×C127—21no—
47C2×C42×C127C2311yescharacteristic
48#107×C127—22no—
49C4⋊C8×C127—22no—
50C4⋊C8×C127—22no—
51C4⋊C8×C127—21no—
52C4⋊C8×C127—21no—
53C4⋊C8×C127—21no—
54C4⋊C8×C127—21no—
55C4⋊C8×C127—21no—
56C4⋊C8×C127—21no—
57#103×C127—22no—
58#102×C127—22no—
59C22⋊C8×C127—21no—
60C22⋊C8×C127—21no—
61C22⋊C8×C127C2×C412yes—
62C22⋊C8×C127D412yes—
63#97×C127—22no—
64#97×C127—21no—
65#97×C127—21no—
66#97×C127—21no—
67C4×C8×C127—22no—
68C4×C8×C127D411yescharacteristic
69C4×C8×C127D411yescharacteristic
70C24×C127—21no—
71C2×Q8×C127—21no—
72C2×Q8×C127C22⋊C412yes—
73C2×D4×C127—21no—
74C2×D4×C127—21no—
75C2×D4×C127—42no—
76C22×C4×C127—21no—
77C22×C4×C127—41no—
78C22×C4×C127—41no—
79C22×C4×C127—81no—
80C22×C4×C127—81no—
81C22×C4×C127C22×C411yescharacteristic
82C22×C4×C127C2×D411yescharacteristic
83C22×C4×C127#4111yescharacteristic
84SD16×C127—44no—
85M16×C127—81no—
86C2×C8×C127—22no—
87C2×C8×C127—21no—
88C2×C8×C127—22no—
89C2×C8×C127—21no—
90C2×C8×C127—41no—
91C2×C8×C127—41no—
92C4⋊C4×C127—22no—
93C4⋊C4×C127—21no—
94C4⋊C4×C127—21no—
95C4⋊C4×C127—21no—
96C4⋊C4×C127—22no—
97C4⋊C4×C127—21no—
98C4⋊C4×C127—21no—
99C4⋊C4×C127C22⋊C412yes—
100C22⋊C4×C127—22no—
101C22⋊C4×C127—41no—
102C22⋊C4×C127—41no—
103C42×C127—22no—
104C42×C127C2×D411yescharacteristic
105C42×C127C2×D411yescharacteristic
106C42×C127C2×D411yescharacteristic
107C42×C127#4111yescharacteristic
108C23×C127—22no—
109C23×C127—41no—
110C23×C127—41no—
111C23×C127—81no—
112C23×C127—81no—
113C23×C127C4×D411yescharacteristic
114Q8×C127—42no—
115Q8×C127—41no—
116Q8×C127—41no—
117D4×C127—22no—
118D4×C127—22no—
119D4×C127—41no—
120D4×C127—41no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—22no—
124C2×C4×C127—22no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—41no—
128C2×C4×C127—82no—
129C2×C4×C127—81no—
130C2×C4×C127—81no—
131C2×C4×C127—81no—
132C2×C4×C127C2×C22⋊C411yescharacteristic
133C2×C4×C127C4×D411yescharacteristic
134C2×C4×C127#12011yescharacteristic
135C2×C4×C127#12111yescharacteristic
136C2×C4×C127#12111yescharacteristic
137C2×C4×C127#12311yescharacteristic
138C8×C127—41no—
139C8×C127—42no—
140C8×C127—41no—
141C8×C127—42no—
142C8×C127—81no—
143C8×C127—81no—
144C22×C127—21no—
145C22×C127—21no—
146C22×C127—21no—
147C22×C127—42no—
148C22×C127—82no—
149C22×C127—82no—
150C22×C127—81no—
151C22×C127—81no—
152C22×C127#38611yescharacteristic
153C4×C127—21no—
154C4×C127—21no—
155C4×C127—21no—
156C4×C127—21no—
157C4×C127—21no—
158C4×C127—42no—
159C4×C127—42no—
160C4×C127—81no—
161C4×C127#47111yescharacteristic
162C4×C127#47211yescharacteristic
163#9530C12711yesmaximal, characteristic, direct product factor, Sylow
164C2×C127—41no—
165C2×C127—82no—
166C2×C127#189111yescharacteristic
167C2×C127#190511yescharacteristic
168C2×C127#190711yescharacteristic
169#3110C2×C12711yescharacteristic
170#2985C2×C12711yescharacteristic, complemented
171#1559C2×C12711yescharacteristic, complemented
172#1486C2×C12711yescharacteristic
173#1466C2×C12711yescharacteristic
174#1307C2×C12711yescharacteristic, complemented
175#1287C2×C12711yescharacteristic, complemented
176C127#953011yescharacteristic, direct product factor, Sylow
177#533C22×C12711yescharacteristic
178C2×C4×D4C22×C12711yescharacteristic
179#484C4×C12712yes—
180#474—21no—
181#461—21no—
182#450C4×C12712yes—
183#446—22no—
184#446—21no—
185C8×Q8—21no—
186#440—22no—
187#433—22no—
188#432C22×C12711yescharacteristic
189#432C22×C12711yescharacteristic
190#432C22×C12711yescharacteristic
191#431C22×C12711yescharacteristic
192#423C22×C12711yescharacteristic
193#333—21no—
194#332—21no—
195D4⋊C8—21no—
196D4⋊C8—21no—
197#323—22no—
198C22×D4C2×C4×C12711yescharacteristic
199C23×C4—21no—
200C2×SD16—22no—
201C2×M16—21no—
202C4⋊Q8D4×C12711yescharacteristic
203C4⋊Q8D4×C12711yescharacteristic
204#125—21no—
205C22⋊Q8—21no—
206C22⋊Q8C2×C4×C12712yes—
207C4×Q8—21no—
208C4×Q8D4×C12712yes—
209C4×D4—21no—
210C4×D4—21no—
211C4×D4—21no—
212C4×D4—21no—
213#117—21no—
214C2×C4⋊C4C2×C4×C12711yescharacteristic
215C2×C22⋊C4—21no—
216C2×C42C23×C12711yescharacteristic
217#107—22no—
218C4⋊C8—22no—
219C4⋊C8—22no—
220C4⋊C8—21no—
221C4⋊C8—21no—
222C4⋊C8—21no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226#103—22no—
227#102—22no—
228C22⋊C8—21no—
229C22⋊C8—21no—
230C22⋊C8C2×C4×C12712yes—
231C22⋊C8D4×C12712yes—
232#97—22no—
233#97—21no—
234#97—21no—
235#97—21no—
236C4×C8—22no—
237C4×C8D4×C12711yescharacteristic
238C4×C8D4×C12711yescharacteristic
239C24—21no—
240C2×Q8—21no—
241C2×Q8C22⋊C4×C12712yes—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—42no—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—81no—
249C22×C4—81no—
250C22×C4C22×C4×C12711yescharacteristic
251C22×C4C2×D4×C12711yescharacteristic
252C22×C4#41×C12711yescharacteristic
253SD16—44no—
254M16—81no—
255C2×C8—22no—
256C2×C8—21no—
257C2×C8—22no—
258C2×C8—21no—
259C2×C8—41no—
260C2×C8—41no—
261C4⋊C4—22no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—22no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4C22⋊C4×C12712yes—
269C22⋊C4—22no—
270C22⋊C4—41no—
271C22⋊C4—41no—
272C42—22no—
273C42C2×D4×C12711yescharacteristic
274C42C2×D4×C12711yescharacteristic
275C42C2×D4×C12711yescharacteristic
276C42#41×C12711yescharacteristic
277C23—22no—
278C23—41no—
279C23—41no—
280C23—81no—
281C23—81no—
282C23C4×D4×C12711yescharacteristic
283Q8—42no—
284Q8—41no—
285Q8—41no—
286D4—22no—
287D4—22no—
288D4—41no—
289D4—41no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—22no—
293C2×C4—22no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—82no—
298C2×C4—81no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4C2×C22⋊C4×C12711yescharacteristic
302C2×C4C4×D4×C12711yescharacteristic
303C2×C4#120×C12711yescharacteristic
304C2×C4#121×C12711yescharacteristic
305C2×C4#121×C12711yescharacteristic
306C2×C4#123×C12711yescharacteristic
307C8—42no—
308C8—41no—
309C8—42no—
310C8—41no—
311C8—81no—
312C8—81no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—42no—
317C22—82no—
318C22—82no—
319C22—81no—
320C22—81no—
321C22#386×C12711yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—42no—
328C4—42no—
329C4—81no—
330C4#471×C12711yescharacteristic
331C4#472×C12711yescharacteristic
332C2—41no—
333C2—82no—
334C2C127×#189111yescharacteristic
335C2C127×#190511yescharacteristic
336C2C127×#190711yescharacteristic
subgroupG/H
center, socleC22×C127#386
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC22×D4×C127C2×C4
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×#2985C2semidirect
3. C127×#1559C2semidirect
6. C127×#1307C2semidirect
7. C127×#1287C2semidirect
163. #9530C127direct (N × H)
170. #2985C2×C127semidirect
171. #1559C2×C127semidirect
174. #1307C2×C127semidirect
175. #1287C2×C127semidirect
176. C127#9530direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#31102
C127×#29852
C127×#15592
C127×#14862
C127×#14662
C127×#13072
C127×#12872
#9530127