Finite Group Databasebeta

← C127×#11906 #44575579

Subgroups — C127×#11906 #44575579

Order 32512.

440 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 114 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×#2564C211yesmaximal, characteristic
2C127×#1800C211yesmaximal, characteristic
3C127×#1459C211yesmaximal, characteristic
4C127×#1354C212yesmaximal, complemented
5C127×#1353C212yesmaximal, complemented
6C2×C22⋊Q8×C127C411yescharacteristic
7C2×C4×D4×C127C2211yescharacteristic
8#423×C127—21no—
9C2×#100×C127—21no—
10C2×C22⋊C8×C127—21no—
11#400×C127C2211yescharacteristic
12#399×C127C411yescharacteristic
13#395×C127C2211yescharacteristic
14#393×C127C411yescharacteristic
15#387×C127—21no—
16#386×C127—21no—
17#385×C127—21no—
18#380×C127—21no—
19C2×#95×C127C411yescharacteristic
20#343×C127C2212yes—
21#324×C127C2212yes—
22#323×C127—21no—
23C22×Q8×C127C2×C411yescharacteristic
24C22×D4×C127D411yescharacteristic
25C23×C4×C127—21no—
26C23×C4×C127C2×C411yescharacteristic
27C23×C4×C127D411yescharacteristic
28C2×M16×C127—22no—
29C22×C8×C127—41no—
30C22⋊Q8×C127—41no—
31C22⋊Q8×C127—41no—
32C4×D4×C127—41no—
33C4×D4×C127—41no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127C2×C411yescharacteristic
38C2×C4⋊C4×C127C2311yescharacteristic
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127C2×C411yescharacteristic
43C2×C22⋊C4×C127D411yescharacteristic
44C2×C42×C127D411yescharacteristic
45C4⋊C8×C127—41no—
46C4⋊C8×C127—41no—
47#100×C127—42no—
48C22⋊C8×C127—22no—
49C22⋊C8×C127—41no—
50#95×C127—21no—
51#95×C127—21no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127C2×C411yescharacteristic
56#95×C127C2×C411yescharacteristic
57C24×C127C22⋊C411yescharacteristic
58C24×C127C22⋊C411yescharacteristic
59C2×Q8×C127—41no—
60C2×Q8×C127—81no—
61C2×D4×C127—41no—
62C2×D4×C127—41no—
63C2×D4×C127SD1612yes—
64C2×D4×C127Q1612yes—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127—21no—
71C22×C4×C127—21no—
72C22×C4×C127—21no—
73C22×C4×C127—42no—
74C22×C4×C127—42no—
75C22×C4×C127—81no—
76C22×C4×C127—81no—
77C22×C4×C127—81no—
78C22×C4×C127C22⋊C411yescharacteristic
79C22×C4×C127C22⋊C411yescharacteristic
80C22×C4×C127C22×C411yescharacteristic
81C22×C4×C127C2×D411yescharacteristic
82C22×C4×C127C2×D411yescharacteristic
83M16×C127—42no—
84M16×C127—42no—
85C2×C8×C127—42no—
86C2×C8×C127—42no—
87C2×C8×C127—82no—
88C4⋊C4×C127—41no—
89C4⋊C4×C127—41no—
90C4⋊C4×C127—42no—
91C4⋊C4×C127—41no—
92C4⋊C4×C127—41no—
93C4⋊C4×C127—81no—
94C22⋊C4×C127—41no—
95C22⋊C4×C127—41no—
96C22⋊C4×C127—42no—
97C22⋊C4×C127—42no—
98C22⋊C4×C127—81no—
99C42×C127—21no—
100C42×C127—21no—
101C23×C127—21no—
102C23×C127—21no—
103C23×C127—21no—
104C23×C127—21no—
105C23×C127—41no—
106C23×C127—41no—
107C23×C127—41no—
108C23×C127—41no—
109C23×C127#10312yes—
110C23×C127#10312yes—
111C23×C127C2×C22⋊C411yescharacteristic
112Q8×C127—82no—
113D4×C127—42no—
114D4×C127—42no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—22no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—41no—
122C2×C4×C127—42no—
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—41no—
130C2×C4×C127—41no—
131C2×C4×C127—41no—
132C2×C4×C127—41no—
133C2×C4×C127—41no—
134C2×C4×C127—41no—
135C2×C4×C127—41no—
136C2×C4×C127—41no—
137C2×C4×C127—81no—
138C2×C4×C127—81no—
139C2×C4×C127—81no—
140C2×C4×C127—84no—
141C2×C4×C127#9911yescharacteristic
142C2×C4×C127#9911yescharacteristic
143C2×C4×C127C2×SD1611yescharacteristic
144C2×C4×C127C2×Q1611yescharacteristic
145C8×C127—82no—
146C8×C127—82no—
147C22×C127—21no—
148C22×C127—21no—
149C22×C127—22no—
150C22×C127—22no—
151C22×C127—42no—
152C22×C127—42no—
153C22×C127—42no—
154C22×C127—41no—
155C22×C127—41no—
156C22×C127—41no—
157C22×C127—41no—
158C22×C127—81no—
159C22×C127C2×#9911yescharacteristic
160C22×C127C2×#10311yescharacteristic
161C22×C127#42111yescharacteristic
162C4×C127—21no—
163C4×C127—21no—
164C4×C127—21no—
165C4×C127—21no—
166C4×C127—42no—
167C4×C127—41no—
168C4×C127—41no—
169C4×C127—41no—
170C4×C127—81no—
171C4×C127—81no—
172C4×C127—81no—
173#11906C12711yesmaximal, characteristic, direct product factor, Sylow
174C2×C127—21no—
175C2×C127—21no—
176C2×C127—42no—
177C2×C127—42no—
178C2×C127#152011yescharacteristic
179C2×C127#212111yescharacteristic
180C2×C127#213211yescharacteristic
181#2564C2×C12711yescharacteristic
182#1800C2×C12711yescharacteristic
183#1459C2×C12711yescharacteristic
184#1354C2×C12712yescomplemented
185#1353C2×C12712yescomplemented
186C127#1190611yescharacteristic, direct product factor, Sylow
187C2×C22⋊Q8C4×C12711yescharacteristic
188C2×C4×D4C22×C12711yescharacteristic
189#423—21no—
190C2×#100—21no—
191C2×C22⋊C8—21no—
192#400C22×C12711yescharacteristic
193#399C4×C12711yescharacteristic
194#395C22×C12711yescharacteristic
195#393C4×C12711yescharacteristic
196#387—21no—
197#386—21no—
198#385—21no—
199#380—21no—
200C2×#95C4×C12711yescharacteristic
201#343C22×C12712yes—
202#324C22×C12712yes—
203#323—21no—
204C22×Q8C2×C4×C12711yescharacteristic
205C22×D4D4×C12711yescharacteristic
206C23×C4—21no—
207C23×C4C2×C4×C12711yescharacteristic
208C23×C4D4×C12711yescharacteristic
209C2×M16—22no—
210C22×C8—41no—
211C22⋊Q8—41no—
212C22⋊Q8—41no—
213C4×D4—41no—
214C4×D4—41no—
215C2×C4⋊C4—21no—
216C2×C4⋊C4—21no—
217C2×C4⋊C4—21no—
218C2×C4⋊C4C2×C4×C12711yescharacteristic
219C2×C4⋊C4C23×C12711yescharacteristic
220C2×C22⋊C4—21no—
221C2×C22⋊C4—21no—
222C2×C22⋊C4—21no—
223C2×C22⋊C4C2×C4×C12711yescharacteristic
224C2×C22⋊C4D4×C12711yescharacteristic
225C2×C42D4×C12711yescharacteristic
226C4⋊C8—41no—
227C4⋊C8—41no—
228#100—42no—
229C22⋊C8—22no—
230C22⋊C8—41no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—21no—
235#95—21no—
236#95C2×C4×C12711yescharacteristic
237#95C2×C4×C12711yescharacteristic
238C24C22⋊C4×C12711yescharacteristic
239C24C22⋊C4×C12711yescharacteristic
240C2×Q8—41no—
241C2×Q8—81no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4SD16×C12712yes—
245C2×D4Q16×C12712yes—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4—81no—
259C22×C4C22⋊C4×C12711yescharacteristic
260C22×C4C22⋊C4×C12711yescharacteristic
261C22×C4C22×C4×C12711yescharacteristic
262C22×C4C2×D4×C12711yescharacteristic
263C22×C4C2×D4×C12711yescharacteristic
264M16—42no—
265M16—42no—
266C2×C8—42no—
267C2×C8—42no—
268C2×C8—82no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—42no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—81no—
275C22⋊C4—41no—
276C22⋊C4—41no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C22⋊C4—81no—
280C42—21no—
281C42—21no—
282C23—21no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23#103×C12712yes—
291C23#103×C12712yes—
292C23C2×C22⋊C4×C12711yescharacteristic
293Q8—82no—
294D4—42no—
295D4—42no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—41no—
303C2×C4—42no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—84no—
322C2×C4#99×C12711yescharacteristic
323C2×C4#99×C12711yescharacteristic
324C2×C4C2×SD16×C12711yescharacteristic
325C2×C4C2×Q16×C12711yescharacteristic
326C8—82no—
327C8—82no—
328C22—21no—
329C22—21no—
330C22—22no—
331C22—22no—
332C22—42no—
333C22—42no—
334C22—42no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—81no—
340C22C2×#99×C12711yescharacteristic
341C22C2×#103×C12711yescharacteristic
342C22#421×C12711yescharacteristic
343C4—21no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—42no—
348C4—41no—
349C4—41no—
350C4—41no—
351C4—81no—
352C4—81no—
353C4—81no—
354C2—21no—
355C2—21no—
356C2—42no—
357C2—42no—
358C2C127×#152011yescharacteristic
359C2C127×#212111yescharacteristic
360C2C127×#213211yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC22×D4×C127D4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×D4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1354C2semidirect
5. C127×#1353C2semidirect
173. #11906C127direct (N × H)
184. #1354C2×C127semidirect
185. #1353C2×C127semidirect
186. C127#11906direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#25642
C127×#18002
C127×#14592
C127×#13542
C127×#13532
#11906127