Finite Group Databasebeta

← C127×#8478 #44572151

Subgroups — C127×#8478 #44572151

Order 32512.

656 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 150 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×#3504C211yesmaximal, characteristic
2C127×#1544C211yesmaximal, characteristic, complemented
3C127×#1537C211yesmaximal, characteristic, complemented
4C127×#1488C212yesmaximal
5C127×#1470C212yesmaximal, complemented
6#557×C127—22no—
7#554×C127—22no—
8#554×C127—24no—
9#544×C127—22no—
10#544×C127C412yes—
11#533×C127—21no—
12#533×C127C2211yescharacteristic
13C2×#125×C127—21no—
14C2×#125×C127C2211yescharacteristic
15#520×C127C412yes—
16C4×#41×C127C2211yescharacteristic
17#432×C127C2212yes—
18#431×C127C2212yes—
19#332×C127—22no—
20#330×C127—21no—
21#330×C127—21no—
22Q8⋊C8×C127—22no—
23D4⋊C8×C127—22no—
24#324×C127—24no—
25C2×#41×C127C2×C411yescharacteristic
26C4⋊Q8×C127—24no—
27C4⋊Q8×C127—22no—
28C4⋊Q8×C127—22no—
29C4⋊Q8×C127D412yes—
30#125×C127—24no—
31#125×C127—24no—
32#125×C127—22no—
33#125×C127—22no—
34#125×C127—21no—
35#125×C127—21no—
36#125×C127—22no—
37#125×C127D411yescharacteristic
38#125×C127D411yescharacteristic
39C22⋊Q8×C127—24no—
40C22⋊Q8×C127—24no—
41C22⋊Q8×C127—24no—
42C22⋊Q8×C127—24no—
43C22⋊Q8×C127—22no—
44C4×Q8×C127—24no—
45C4×Q8×C127—22no—
46C4×Q8×C127—22no—
47C4×Q8×C127D412yes—
48C4×D4×C127—22no—
49C4×D4×C127—24no—
50C4×D4×C127—22no—
51C4×D4×C127D412yes—
52#117×C127—22no—
53#117×C127—21no—
54#117×C127C2×C411yescharacteristic
55#117×C127C2×C412yes—
56C2×C4⋊C4×C127—24no—
57C2×C4⋊C4×C127—22no—
58C2×C4⋊C4×C127C2×C412yes—
59C2×C4⋊C4×C127D414yes—
60C2×C42×C127—21no—
61C2×C42×C127C2311yescharacteristic
62C4⋊C8×C127—22no—
63C4⋊C8×C127—22no—
64C22⋊C8×C127—22no—
65C22⋊C8×C127—22no—
66#97×C127—22no—
67C4×C8×C127—22no—
68#41×C127—22no—
69#41×C127—22no—
70C2×Q8×C127—24no—
71C2×Q8×C127—22no—
72C2×Q8×C127C22⋊C411yescharacteristic
73C2×D4×C127—21no—
74C2×D4×C127C22⋊C411yescharacteristic
75C22×C4×C127—21no—
76C22×C4×C127—24no—
77C22×C4×C127—22no—
78C22×C4×C127C22⋊C414yes—
79C22×C4×C127C22×C411yescharacteristic
80C22×C4×C127C2×D412yes—
81C2×C8×C127—42no—
82C2×C8×C127—42no—
83C4⋊C4×C127—24no—
84C4⋊C4×C127—24no—
85C4⋊C4×C127—24no—
86C4⋊C4×C127—24no—
87C4⋊C4×C127—22no—
88C4⋊C4×C127—22no—
89C4⋊C4×C127—22no—
90C4⋊C4×C127—24no—
91C4⋊C4×C127—24no—
92C4⋊C4×C127—22no—
93C4⋊C4×C127—22no—
94C4⋊C4×C127—22no—
95C4⋊C4×C127C22⋊C412yes—
96C4⋊C4×C127C22⋊C412yes—
97C4⋊C4×C127C22⋊C412yes—
98C22⋊C4×C127—24no—
99C22⋊C4×C127—22no—
100C22⋊C4×C127—21no—
101C22⋊C4×C127—22no—
102C42×C127—24no—
103C42×C127—21no—
104C42×C127—22no—
105C42×C127—22no—
106C42×C127C2×D412yes—
107C42×C127C2×D411yescharacteristic
108C42×C127C2×D411yescharacteristic
109C23×C127—21no—
110C23×C127C2×C22⋊C411yescharacteristic
111Q8×C127—21no—
112Q8×C127—82no—
113Q8×C127—84no—
114Q8×C127#10112yes—
115D4×C127—24no—
116D4×C127—21no—
117D4×C127#10112yes—
118C2×C4×C127—24no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—22no—
123C2×C4×C127—22no—
124C2×C4×C127—24no—
125C2×C4×C127—22no—
126C2×C4×C127—42no—
127C2×C4×C127—44no—
128C2×C4×C127—82no—
129C2×C4×C127—84no—
130C2×C4×C127C2×C22⋊C411yescharacteristic
131C2×C4×C127C2×C22⋊C411yescharacteristic
132C2×C4×C127#12012yes—
133C2×C4×C127#12012yes—
134C8×C127—82no—
135C8×C127—82no—
136C22×C127—22no—
137C22×C127—21no—
138C22×C127—22no—
139C22×C127—42no—
140C22×C127#37911yescharacteristic
141C4×C127—22no—
142C4×C127—22no—
143C4×C127—21no—
144C4×C127—22no—
145C4×C127—44no—
146C4×C127—42no—
147C4×C127—42no—
148C4×C127—42no—
149C4×C127C2×#10111yescharacteristic
150C4×C127C2×#10111yescharacteristic
151#8478C12711yesmaximal, characteristic, direct product factor, Sylow
152C2×C127—41no—
153C2×C127—42no—
154C2×C127#178411yescharacteristic
155C2×C127#179412yes—
156#3504C2×C12711yescharacteristic
157#1544C2×C12711yescharacteristic, complemented
158#1537C2×C12711yescharacteristic, complemented
159#1488C2×C12712yes—
160#1470C2×C12712yescomplemented
161C127#847811yescharacteristic, direct product factor, Sylow
162#557—22no—
163#554—22no—
164#554—24no—
165#544—22no—
166#544C4×C12712yes—
167#533—21no—
168#533C22×C12711yescharacteristic
169C2×#125—21no—
170C2×#125C22×C12711yescharacteristic
171#520C4×C12712yes—
172C4×#41C22×C12711yescharacteristic
173#432C22×C12712yes—
174#431C22×C12712yes—
175#332—22no—
176#330—21no—
177#330—21no—
178Q8⋊C8—22no—
179D4⋊C8—22no—
180#324—24no—
181C2×#41C2×C4×C12711yescharacteristic
182C4⋊Q8—24no—
183C4⋊Q8—22no—
184C4⋊Q8—22no—
185C4⋊Q8D4×C12712yes—
186#125—24no—
187#125—24no—
188#125—22no—
189#125—22no—
190#125—21no—
191#125—21no—
192#125—22no—
193#125D4×C12711yescharacteristic
194#125D4×C12711yescharacteristic
195C22⋊Q8—24no—
196C22⋊Q8—24no—
197C22⋊Q8—24no—
198C22⋊Q8—24no—
199C22⋊Q8—22no—
200C4×Q8—24no—
201C4×Q8—22no—
202C4×Q8—22no—
203C4×Q8D4×C12712yes—
204C4×D4—22no—
205C4×D4—24no—
206C4×D4—22no—
207C4×D4D4×C12712yes—
208#117—22no—
209#117—21no—
210#117C2×C4×C12711yescharacteristic
211#117C2×C4×C12712yes—
212C2×C4⋊C4—24no—
213C2×C4⋊C4—22no—
214C2×C4⋊C4C2×C4×C12712yes—
215C2×C4⋊C4D4×C12714yes—
216C2×C42—21no—
217C2×C42C23×C12711yescharacteristic
218C4⋊C8—22no—
219C4⋊C8—22no—
220C22⋊C8—22no—
221C22⋊C8—22no—
222#97—22no—
223C4×C8—22no—
224#41—22no—
225#41—22no—
226C2×Q8—24no—
227C2×Q8—22no—
228C2×Q8C22⋊C4×C12711yescharacteristic
229C2×D4—21no—
230C2×D4C22⋊C4×C12711yescharacteristic
231C22×C4—21no—
232C22×C4—24no—
233C22×C4—22no—
234C22×C4C22⋊C4×C12714yes—
235C22×C4C22×C4×C12711yescharacteristic
236C22×C4C2×D4×C12712yes—
237C2×C8—42no—
238C2×C8—42no—
239C4⋊C4—24no—
240C4⋊C4—24no—
241C4⋊C4—24no—
242C4⋊C4—24no—
243C4⋊C4—22no—
244C4⋊C4—22no—
245C4⋊C4—22no—
246C4⋊C4—24no—
247C4⋊C4—24no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—22no—
251C4⋊C4C22⋊C4×C12712yes—
252C4⋊C4C22⋊C4×C12712yes—
253C4⋊C4C22⋊C4×C12712yes—
254C22⋊C4—24no—
255C22⋊C4—22no—
256C22⋊C4—21no—
257C22⋊C4—22no—
258C42—24no—
259C42—21no—
260C42—22no—
261C42—22no—
262C42C2×D4×C12712yes—
263C42C2×D4×C12711yescharacteristic
264C42C2×D4×C12711yescharacteristic
265C23—21no—
266C23C2×C22⋊C4×C12711yescharacteristic
267Q8—21no—
268Q8—82no—
269Q8—84no—
270Q8#101×C12712yes—
271D4—24no—
272D4—21no—
273D4#101×C12712yes—
274C2×C4—24no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—24no—
281C2×C4—22no—
282C2×C4—42no—
283C2×C4—44no—
284C2×C4—82no—
285C2×C4—84no—
286C2×C4C2×C22⋊C4×C12711yescharacteristic
287C2×C4C2×C22⋊C4×C12711yescharacteristic
288C2×C4#120×C12712yes—
289C2×C4#120×C12712yes—
290C8—82no—
291C8—82no—
292C22—21no—
293C22—22no—
294C22—22no—
295C22—42no—
296C22#379×C12711yescharacteristic
297C4—21no—
298C4—22no—
299C4—22no—
300C4—22no—
301C4—44no—
302C4—42no—
303C4—42no—
304C4—42no—
305C4C2×#101×C12711yescharacteristic
306C4C2×#101×C12711yescharacteristic
307C2—41no—
308C2—42no—
309C2C127×#178411yescharacteristic
310C2C127×#179412yes—
subgroupG/H
center, socleC22×C127#379
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C42C23×C127
prime radicalC2×#41×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×#1544C2semidirect
3. C127×#1537C2semidirect
5. C127×#1470C2semidirect
151. #8478C127direct (N × H)
157. #1544C2×C127semidirect
158. #1537C2×C127semidirect
160. #1470C2×C127semidirect
161. C127#8478direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#35042
C127×#15442
C127×#15372
C127×#14882
C127×#14702
#8478127