Finite Group Databasebeta

← C127×#11833 #44575506

Subgroups — C127×#11833 #44575506

Order 32512.

382 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 98 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×#2632C211yesmaximal, characteristic
2C127×#1801C211yesmaximal, characteristic, complemented
3C127×#1467C211yesmaximal, characteristic, complemented
4C127×#1354C212yesmaximal, complemented
5C127×#1345C212yesmaximal
6C2×#124×C127C411yescharacteristic
7C2×C4×Q8×C127C2211yescharacteristic
8#432×C127—21no—
9#423×C127—21no—
10C2×#101×C127—21no—
11#399×C127—21no—
12#395×C127C411yescharacteristic
13#395×C127C2211yescharacteristic
14#394×C127C411yescharacteristic
15#394×C127C2211yescharacteristic
16#393×C127—21no—
17#388×C127—21no—
18#388×C127—21no—
19#383×C127C411yescharacteristic
20#343×C127C2212yes—
21#324×C127—21no—
22#324×C127C2212yes—
23C22×Q8×C127C2×C411yescharacteristic
24C22×Q8×C127D411yescharacteristic
25C22×D4×C127C2×C411yescharacteristic
26C2×M16×C127—22no—
27#124×C127—41no—
28#124×C127—41no—
29C4×Q8×C127—41no—
30C4×Q8×C127—41no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127C2×C411yescharacteristic
34C2×C4⋊C4×C127D411yescharacteristic
35C2×C4⋊C4×C127C2311yescharacteristic
36C2×C22⋊C4×C127—21no—
37C2×C22⋊C4×C127—21no—
38C2×C22⋊C4×C127—21no—
39C2×C22⋊C4×C127—21no—
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C42×C127C2×C411yescharacteristic
43C2×C42×C127D411yescharacteristic
44C2×C42×C127D411yescharacteristic
45C4⋊C8×C127—41no—
46C4⋊C8×C127—41no—
47C4⋊C8×C127—41no—
48#101×C127—42no—
49C22⋊C8×C127—22no—
50#97×C127—41no—
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×C127—21no—
58C2×Q8×C127—21no—
59C2×Q8×C127—21no—
60C2×Q8×C127—41no—
61C2×Q8×C127—41no—
62C2×Q8×C127—41no—
63C2×Q8×C127—81no—
64C2×D4×C127—41no—
65C2×D4×C127—81no—
66C22×C4×C127—21no—
67C22×C4×C127—21no—
68C22×C4×C127—21no—
69C22×C4×C127C22⋊C411yescharacteristic
70C22×C4×C127C22⋊C411yescharacteristic
71C22×C4×C127C22⋊C411yescharacteristic
72C22×C4×C127C22⋊C411yescharacteristic
73C22×C4×C127C22×C411yescharacteristic
74C22×C4×C127C2×D411yescharacteristic
75C22×C4×C127C2×D411yescharacteristic
76M16×C127—42no—
77M16×C127—42no—
78C2×C8×C127—42no—
79C2×C8×C127—42no—
80C4⋊C4×C127—41no—
81C4⋊C4×C127—41no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—81no—
84C4⋊C4×C127—81no—
85C22⋊C4×C127—42no—
86C22⋊C4×C127—42no—
87C22⋊C4×C127—41no—
88C22⋊C4×C127—41no—
89C22⋊C4×C127—41no—
90C22⋊C4×C127—41no—
91C22⋊C4×C127—81no—
92C22⋊C4×C127—81no—
93C42×C127—21no—
94C42×C127—21no—
95C42×C127—21no—
96C42×C127—21no—
97C42×C127—21no—
98C42×C127—21no—
99C23×C127—41no—
100C23×C127—41no—
101C23×C127—41no—
102C23×C127—41no—
103C23×C127—41no—
104C23×C127—41no—
105C23×C127—41no—
106C23×C127C2×C22⋊C411yescharacteristic
107Q8×C127—42no—
108Q8×C127—42no—
109Q8×C127—82no—
110D4×C127—82no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—21no—
116C2×C4×C127—21no—
117C2×C4×C127—21no—
118C2×C4×C127—21no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—41no—
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#9911yescharacteristic
136C2×C4×C127#9911yescharacteristic
137C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C127#13711yescharacteristic
139C8×C127—82no—
140C8×C127—82no—
141C22×C127—21no—
142C22×C127—21no—
143C22×C127—81no—
144C22×C127—81no—
145C22×C127—81no—
146C22×C127—81no—
147C22×C127—81no—
148C22×C127—81no—
149C22×C127—81no—
150C22×C127C2×#9911yescharacteristic
151C22×C127#41711yescharacteristic
152C22×C127#42111yescharacteristic
153C4×C127—21no—
154C4×C127—21no—
155C4×C127—21no—
156C4×C127—21no—
157C4×C127—41no—
158C4×C127—41no—
159C4×C127—41no—
160C4×C127—41no—
161C4×C127—41no—
162C4×C127—81no—
163C4×C127—81no—
164C4×C127—81no—
165#11833C12711yesmaximal, characteristic, direct product factor, Sylow
166C2×C127—21no—
167C2×C127—21no—
168C2×C127—161no—
169C2×C127#151311yescharacteristic
170C2×C127#212211yescharacteristic
171C2×C127#213311yescharacteristic
172#2632C2×C12711yescharacteristic
173#1801C2×C12711yescharacteristic, complemented
174#1467C2×C12711yescharacteristic, complemented
175#1354C2×C12712yescomplemented
176#1345C2×C12712yes—
177C127#1183311yescharacteristic, direct product factor, Sylow
178C2×#124C4×C12711yescharacteristic
179C2×C4×Q8C22×C12711yescharacteristic
180#432—21no—
181#423—21no—
182C2×#101—21no—
183#399—21no—
184#395C4×C12711yescharacteristic
185#395C22×C12711yescharacteristic
186#394C4×C12711yescharacteristic
187#394C22×C12711yescharacteristic
188#393—21no—
189#388—21no—
190#388—21no—
191#383C4×C12711yescharacteristic
192#343C22×C12712yes—
193#324—21no—
194#324C22×C12712yes—
195C22×Q8C2×C4×C12711yescharacteristic
196C22×Q8D4×C12711yescharacteristic
197C22×D4C2×C4×C12711yescharacteristic
198C2×M16—22no—
199#124—41no—
200#124—41no—
201C4×Q8—41no—
202C4×Q8—41no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4C2×C4×C12711yescharacteristic
206C2×C4⋊C4D4×C12711yescharacteristic
207C2×C4⋊C4C23×C12711yescharacteristic
208C2×C22⋊C4—21no—
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C22⋊C4—21no—
212C2×C22⋊C4—21no—
213C2×C22⋊C4—21no—
214C2×C42C2×C4×C12711yescharacteristic
215C2×C42D4×C12711yescharacteristic
216C2×C42D4×C12711yescharacteristic
217C4⋊C8—41no—
218C4⋊C8—41no—
219C4⋊C8—41no—
220#101—42no—
221C22⋊C8—22no—
222#97—41no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95C2×C4×C12711yescharacteristic
228#95C2×C4×C12711yescharacteristic
229C24—21no—
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—81no—
236C2×D4—41no—
237C2×D4—81no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4C22⋊C4×C12711yescharacteristic
242C22×C4C22⋊C4×C12711yescharacteristic
243C22×C4C22⋊C4×C12711yescharacteristic
244C22×C4C22⋊C4×C12711yescharacteristic
245C22×C4C22×C4×C12711yescharacteristic
246C22×C4C2×D4×C12711yescharacteristic
247C22×C4C2×D4×C12711yescharacteristic
248M16—42no—
249M16—42no—
250C2×C8—42no—
251C2×C8—42no—
252C4⋊C4—41no—
253C4⋊C4—41no—
254C4⋊C4—41no—
255C4⋊C4—81no—
256C4⋊C4—81no—
257C22⋊C4—42no—
258C22⋊C4—42no—
259C22⋊C4—41no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—81no—
264C22⋊C4—81no—
265C42—21no—
266C42—21no—
267C42—21no—
268C42—21no—
269C42—21no—
270C42—21no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23—41no—
276C23—41no—
277C23—41no—
278C23C2×C22⋊C4×C12711yescharacteristic
279Q8—42no—
280Q8—42no—
281Q8—82no—
282D4—82no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4#99×C12711yescharacteristic
308C2×C4#99×C12711yescharacteristic
309C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
310C2×C4#137×C12711yescharacteristic
311C8—82no—
312C8—82no—
313C22—21no—
314C22—21no—
315C22—81no—
316C22—81no—
317C22—81no—
318C22—81no—
319C22—81no—
320C22—81no—
321C22—81no—
322C22C2×#99×C12711yescharacteristic
323C22#417×C12711yescharacteristic
324C22#421×C12711yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—41no—
334C4—81no—
335C4—81no—
336C4—81no—
337C2—21no—
338C2—21no—
339C2—161no—
340C2C127×#151311yescharacteristic
341C2C127×#212211yescharacteristic
342C2C127×#213311yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC22×D4×C127C2×C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×C4×Q8×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1801C2semidirect
3. C127×#1467C2semidirect
4. C127×#1354C2semidirect
165. #11833C127direct (N × H)
173. #1801C2×C127semidirect
174. #1467C2×C127semidirect
175. #1354C2×C127semidirect
177. C127#11833direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#26322
C127×#18012
C127×#14672
C127×#13542
C127×#13452
#11833127