Finite Group Databasebeta

← C127×#19297 #44582970

Subgroups — C127×#19297 #44582970

Order 32512.

616 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#500×C127C211yesmaximal, characteristic, complemented
2C127×#3079C212yesmaximal
3C127×#2965C211yesmaximal, characteristic
4C127×#1696C214yesmaximal, complemented
5C127×#1695C214yesmaximal, complemented
6C127×#1566C211yesmaximal, characteristic, complemented
7C127×#1548C212yesmaximal, complemented
8C2×C4⋊Q8×C127C2212yes—
9C4×#41×C127C2211yescharacteristic
10#500×C127—21no—
11#500×C127—21no—
12#500×C127C2214yes—
13#477×C127C2214yes—
14#476×C127C2214yes—
15#475×C127—22no—
16#474×C127—22no—
17#446×C127C2212yes—
18#436×C127C2212yes—
19#435×C127—22no—
20#431×C127—21no—
21#431×C127C2211yescharacteristic
22#428×C127—22no—
23C2×#107×C127—22no—
24#423×C127C2212yes—
25#417×C127—22no—
26C4×M16×C127—21no—
27C2×C4×C8×C127C2211yescharacteristic
28#334×C127C2214yes—
29#333×C127C2218yes—
30C2×#41×C127D411yescharacteristic
31C22×Q8×C127—22no—
32C2×M16×C127—22no—
33C2×M16×C127—22no—
34C22×C8×C127D412yes—
35C4⋊Q8×C127—22no—
36C4⋊Q8×C127—22no—
37C4⋊Q8×C127—22no—
38C4⋊Q8×C127C2314yes—
39C4×Q8×C127D411yescharacteristic
40C4×Q8×C127C2311yescharacteristic
41C4×D4×C127—21no—
42C4×D4×C127—21no—
43C4×D4×C127D411yescharacteristic
44C4×D4×C127C2311yescharacteristic
45#117×C127—21no—
46#117×C127D411yescharacteristic
47C2×C4⋊C4×C127—22no—
48C2×C4⋊C4×C127—22no—
49C2×C42×C127—21no—
50C2×C42×C127C2311yescharacteristic
51#107×C127—24no—
52#107×C127—24no—
53#107×C127—24no—
54#106×C127—24no—
55C4⋊C8×C127—22no—
56C4⋊C8×C127—22no—
57C4⋊C8×C127C2312yes—
58C4⋊C8×C127C2314yes—
59#103×C127—24no—
60#102×C127—24no—
61C22⋊C8×C127—21no—
62C22⋊C8×C127—22no—
63#97×C127—22no—
64C4×C8×C127—21no—
65C4×C8×C127D411yescharacteristic
66C4×C8×C127D411yescharacteristic
67C4×C8×C127C2312yes—
68#41×C127—24no—
69C2×Q8×C127—24no—
70C2×Q8×C127—42no—
71C2×Q8×C127—84no—
72C2×Q8×C127C2×D411yescharacteristic
73C2×D4×C127—21no—
74C2×D4×C127C2×D411yescharacteristic
75C22×C4×C127—21no—
76C22×C4×C127—21no—
77C22×C4×C127—21no—
78C22×C4×C127—42no—
79C22×C4×C127C2×D411yescharacteristic
80C22×C4×C127C2×D411yescharacteristic
81C22×C4×C127#4111yescharacteristic
82M16×C127—44no—
83M16×C127—44no—
84C2×C8×C127—24no—
85C2×C8×C127—22no—
86C2×C8×C127—24no—
87C2×C8×C127C2×D412yes—
88C2×C8×C127C2×D412yes—
89C4⋊C4×C127—21no—
90C4⋊C4×C127—21no—
91C4⋊C4×C127—24no—
92C4⋊C4×C127—24no—
93C4⋊C4×C127—42no—
94C4⋊C4×C127—42no—
95C4⋊C4×C127C2×D411yescharacteristic
96C4⋊C4×C127C2×D411yescharacteristic
97C22⋊C4×C127—21no—
98C22⋊C4×C127—21no—
99C22⋊C4×C127—21no—
100C42×C127—21no—
101C42×C127—21no—
102C42×C127—21no—
103C42×C127C2×D411yescharacteristic
104C42×C127C2×D411yescharacteristic
105C42×C127#4111yescharacteristic
106C42×C127C2411yescharacteristic
107C23×C127—21no—
108C23×C127#12111yescharacteristic
109Q8×C127—22no—
110Q8×C127—84no—
111Q8×C127—84no—
112D4×C127—22no—
113D4×C127—42no—
114C2×C4×C127—22no—
115C2×C4×C127—22no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—42no—
120C2×C4×C127—42no—
121C2×C4×C127—42no—
122C2×C4×C127—44no—
123C2×C4×C127—84no—
124C2×C4×C127#12111yescharacteristic
125C2×C4×C127#12111yescharacteristic
126C2×C4×C127#12111yescharacteristic
127C2×C4×C127#13714yes—
128C2×C4×C127C22×D411yescharacteristic
129C2×C4×C127C22×D411yescharacteristic
130C2×C4×C127C2×#4111yescharacteristic
131C8×C127—22no—
132C8×C127—42no—
133C8×C127—44no—
134C8×C127#13714yes—
135C22×C127—21no—
136C22×C127—21no—
137C22×C127—41no—
138C22×C127—41no—
139C22×C127—41no—
140C22×C127#47012yes—
141C22×C127C2×#12111yescharacteristic
142C4×C127—21no—
143C4×C127—21no—
144C4×C127—41no—
145C4×C127—41no—
146C4×C127—41no—
147C4×C127—84no—
148C4×C127#47012yes—
149C4×C127#47212yes—
150C4×C127C2×#13712yes—
151C4×C127C2×#13712yes—
152#19297C12711yesmaximal, characteristic, direct product factor, Sylow
153C2×C127—22no—
154C2×C127—81no—
155C2×C127#303911yescharacteristic
156C2×C127C2×#47011yescharacteristic
157C2×C127C2×#47211yescharacteristic
158C2×#500C2×C12711yescharacteristic, complemented
159#3079C2×C12712yes—
160#2965C2×C12711yescharacteristic
161#1696C2×C12714yescomplemented
162#1695C2×C12714yescomplemented
163#1566C2×C12711yescharacteristic, complemented
164#1548C2×C12712yescomplemented
165C127#1929711yescharacteristic, direct product factor, Sylow
166C2×C4⋊Q8C22×C12712yes—
167C4×#41C22×C12711yescharacteristic
168#500—21no—
169#500—21no—
170#500C22×C12714yes—
171#477C22×C12714yes—
172#476C22×C12714yes—
173#475—22no—
174#474—22no—
175#446C22×C12712yes—
176#436C22×C12712yes—
177#435—22no—
178#431—21no—
179#431C22×C12711yescharacteristic
180#428—22no—
181C2×#107—22no—
182#423C22×C12712yes—
183#417—22no—
184C4×M16—21no—
185C2×C4×C8C22×C12711yescharacteristic
186#334C22×C12714yes—
187#333C22×C12718yes—
188C2×#41D4×C12711yescharacteristic
189C22×Q8—22no—
190C2×M16—22no—
191C2×M16—22no—
192C22×C8D4×C12712yes—
193C4⋊Q8—22no—
194C4⋊Q8—22no—
195C4⋊Q8—22no—
196C4⋊Q8C23×C12714yes—
197C4×Q8D4×C12711yescharacteristic
198C4×Q8C23×C12711yescharacteristic
199C4×D4—21no—
200C4×D4—21no—
201C4×D4D4×C12711yescharacteristic
202C4×D4C23×C12711yescharacteristic
203#117—21no—
204#117D4×C12711yescharacteristic
205C2×C4⋊C4—22no—
206C2×C4⋊C4—22no—
207C2×C42—21no—
208C2×C42C23×C12711yescharacteristic
209#107—24no—
210#107—24no—
211#107—24no—
212#106—24no—
213C4⋊C8—22no—
214C4⋊C8—22no—
215C4⋊C8C23×C12712yes—
216C4⋊C8C23×C12714yes—
217#103—24no—
218#102—24no—
219C22⋊C8—21no—
220C22⋊C8—22no—
221#97—22no—
222C4×C8—21no—
223C4×C8D4×C12711yescharacteristic
224C4×C8D4×C12711yescharacteristic
225C4×C8C23×C12712yes—
226#41—24no—
227C2×Q8—24no—
228C2×Q8—42no—
229C2×Q8—84no—
230C2×Q8C2×D4×C12711yescharacteristic
231C2×D4—21no—
232C2×D4C2×D4×C12711yescharacteristic
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—42no—
237C22×C4C2×D4×C12711yescharacteristic
238C22×C4C2×D4×C12711yescharacteristic
239C22×C4#41×C12711yescharacteristic
240M16—44no—
241M16—44no—
242C2×C8—24no—
243C2×C8—22no—
244C2×C8—24no—
245C2×C8C2×D4×C12712yes—
246C2×C8C2×D4×C12712yes—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—24no—
250C4⋊C4—24no—
251C4⋊C4—42no—
252C4⋊C4—42no—
253C4⋊C4C2×D4×C12711yescharacteristic
254C4⋊C4C2×D4×C12711yescharacteristic
255C22⋊C4—21no—
256C22⋊C4—21no—
257C22⋊C4—21no—
258C42—21no—
259C42—21no—
260C42—21no—
261C42C2×D4×C12711yescharacteristic
262C42C2×D4×C12711yescharacteristic
263C42#41×C12711yescharacteristic
264C42C24×C12711yescharacteristic
265C23—21no—
266C23#121×C12711yescharacteristic
267Q8—22no—
268Q8—84no—
269Q8—84no—
270D4—22no—
271D4—42no—
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—42no—
278C2×C4—42no—
279C2×C4—42no—
280C2×C4—44no—
281C2×C4—84no—
282C2×C4#121×C12711yescharacteristic
283C2×C4#121×C12711yescharacteristic
284C2×C4#121×C12711yescharacteristic
285C2×C4#137×C12714yes—
286C2×C4C22×D4×C12711yescharacteristic
287C2×C4C22×D4×C12711yescharacteristic
288C2×C4C2×#41×C12711yescharacteristic
289C8—22no—
290C8—42no—
291C8—44no—
292C8#137×C12714yes—
293C22—21no—
294C22—21no—
295C22—41no—
296C22—41no—
297C22—41no—
298C22#470×C12712yes—
299C22C2×#121×C12711yescharacteristic
300C4—21no—
301C4—21no—
302C4—41no—
303C4—41no—
304C4—41no—
305C4—84no—
306C4#470×C12712yes—
307C4#472×C12712yes—
308C4C2×#137×C12712yes—
309C4C2×#137×C12712yes—
310C2—22no—
311C2—81no—
312C2C127×#303911yescharacteristic
313C2C2×#470×C12711yescharacteristic
314C2C2×#472×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#121
commutator, Frattini, cosocleC42C24×C127
prime radicalC2×#41×C127D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#500×C127C2semidirect
4. C127×#1696C2semidirect
5. C127×#1695C2semidirect
6. C127×#1566C2semidirect
7. C127×#1548C2semidirect
152. #19297C127direct (N × H)
158. C2×#500C2×C127semidirect
161. #1696C2×C127semidirect
162. #1695C2×C127semidirect
163. #1566C2×C127semidirect
164. #1548C2×C127semidirect
165. C127#19297direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#500×C1272
C127×#30792
C127×#29652
C127×#16962
C127×#16952
C127×#15662
C127×#15482
#19297127