Finite Group Databasebeta

← C127×#11854 #44575527

Subgroups — C127×#11854 #44575527

Order 32512.

412 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 102 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×#2583C211yesmaximal, characteristic
2C127×#1821C211yesmaximal, characteristic
3C2×#324×C127C211yesmaximal, characteristic
4C127×#1354C212yesmaximal, complemented
5C127×#1346C212yesmaximal, complemented
6C2×C22⋊Q8×C127C411yescharacteristic
7C22×C4⋊C4×C127C2211yescharacteristic
8#407×C127—21no—
9C2×C22⋊C8×C127—21no—
10#398×C127C411yescharacteristic
11#398×C127C2211yescharacteristic
12#395×C127C411yescharacteristic
13#395×C127C2211yescharacteristic
14#389×C127—21no—
15#389×C127—21no—
16#385×C127—21no—
17#385×C127—21no—
18C4×C22⋊C4×C127C411yescharacteristic
19#343×C127—21no—
20#343×C127C2212yes—
21#324×C127—21no—
22#324×C127C2212yes—
23C22×Q8×C127C2×C411yescharacteristic
24C23×C4×C127C2×C411yescharacteristic
25C23×C4×C127D411yescharacteristic
26C23×C4×C127D411yescharacteristic
27C2×M16×C127—22no—
28C22×C8×C127—41no—
29C22⋊Q8×C127—41no—
30C22⋊Q8×C127—41no—
31C2×C4⋊C4×C127—21no—
32C2×C4⋊C4×C127—21no—
33C2×C4⋊C4×C127—21no—
34C2×C4⋊C4×C127—21no—
35C2×C4⋊C4×C127—21no—
36C2×C4⋊C4×C127—41no—
37C2×C4⋊C4×C127—41no—
38C2×C4⋊C4×C127C2×C411yescharacteristic
39C2×C4⋊C4×C127C2×C411yescharacteristic
40C2×C4⋊C4×C127D411yescharacteristic
41C2×C4⋊C4×C127D411yescharacteristic
42C2×C4⋊C4×C127C2311yescharacteristic
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—21no—
45C2×C42×C127—21no—
46C22⋊C8×C127—22no—
47C22⋊C8×C127—41no—
48C22⋊C8×C127—41no—
49C22⋊C8×C127—41no—
50#95×C127—21no—
51#95×C127—21no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127C2×C411yescharacteristic
55#95×C127C2×C411yescharacteristic
56C24×C127C22⋊C411yescharacteristic
57C2×Q8×C127—41no—
58C2×Q8×C127—81no—
59C22×C4×C127—21no—
60C22×C4×C127—21no—
61C22×C4×C127—21no—
62C22×C4×C127—21no—
63C22×C4×C127—21no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—21no—
67C22×C4×C127—22no—
68C22×C4×C127—21no—
69C22×C4×C127—21no—
70C22×C4×C127—41no—
71C22×C4×C127—81no—
72C22×C4×C127—81no—
73C22×C4×C127C22⋊C411yescharacteristic
74C22×C4×C127C22⋊C411yescharacteristic
75C22×C4×C127C22⋊C411yescharacteristic
76C22×C4×C127C22×C411yescharacteristic
77C22×C4×C127C2×D411yescharacteristic
78C22×C4×C127C2×D411yescharacteristic
79M16×C127—42no—
80M16×C127—42no—
81C2×C8×C127—42no—
82C2×C8×C127—42no—
83C2×C8×C127—82no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C4⋊C4×C127—41no—
87C4⋊C4×C127—41no—
88C4⋊C4×C127—41no—
89C4⋊C4×C127—42no—
90C4⋊C4×C127—42no—
91C4⋊C4×C127—42no—
92C4⋊C4×C127—81no—
93C4⋊C4×C127—81no—
94C22⋊C4×C127—24no—
95C22⋊C4×C127—41no—
96C22⋊C4×C127—41no—
97C42×C127—81no—
98C23×C127—22no—
99C23×C127—21no—
100C23×C127—21no—
101C23×C127—41no—
102C23×C127#9911yescharacteristic
103C23×C127#9911yescharacteristic
104C23×C127C2×C22⋊C411yescharacteristic
105Q8×C127—82no—
106C2×C4×C127—21no—
107C2×C4×C127—21no—
108C2×C4×C127—22no—
109C2×C4×C127—22no—
110C2×C4×C127—21no—
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—42no—
118C2×C4×C127—42no—
119C2×C4×C127—41no—
120C2×C4×C127—41no—
121C2×C4×C127—42no—
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—81no—
135C2×C4×C127—81no—
136C2×C4×C127—81no—
137C2×C4×C127#13512yes—
138C8×C127—82no—
139C8×C127—82no—
140C22×C127—21no—
141C22×C127—21no—
142C22×C127—21no—
143C22×C127—21no—
144C22×C127—21no—
145C22×C127—21no—
146C22×C127—21no—
147C22×C127—42no—
148C22×C127—42no—
149C22×C127#35612yes—
150C22×C127C2×#9911yescharacteristic
151C22×C127#41611yescharacteristic
152C22×C127#42111yescharacteristic
153C4×C127—22no—
154C4×C127—42no—
155C4×C127—42no—
156C4×C127—41no—
157C4×C127—41no—
158C4×C127—41no—
159C4×C127—41no—
160C4×C127—41no—
161C4×C127—81no—
162C4×C127—81no—
163#11854C12711yesmaximal, characteristic, direct product factor, Sylow
164C2×C127—21no—
165C2×C127—21no—
166C2×C127—22no—
167C2×C127—41no—
168C2×C127#151611yescharacteristic
169C2×C127#212111yescharacteristic
170C2×C127C2×#35611yescharacteristic
171#2583C2×C12711yescharacteristic
172#1821C2×C12711yescharacteristic
173C2×#324C2×C12711yescharacteristic
174#1354C2×C12712yescomplemented
175#1346C2×C12712yescomplemented
176C127#1185411yescharacteristic, direct product factor, Sylow
177C2×C22⋊Q8C4×C12711yescharacteristic
178C22×C4⋊C4C22×C12711yescharacteristic
179#407—21no—
180C2×C22⋊C8—21no—
181#398C4×C12711yescharacteristic
182#398C22×C12711yescharacteristic
183#395C4×C12711yescharacteristic
184#395C22×C12711yescharacteristic
185#389—21no—
186#389—21no—
187#385—21no—
188#385—21no—
189C4×C22⋊C4C4×C12711yescharacteristic
190#343—21no—
191#343C22×C12712yes—
192#324—21no—
193#324C22×C12712yes—
194C22×Q8C2×C4×C12711yescharacteristic
195C23×C4C2×C4×C12711yescharacteristic
196C23×C4D4×C12711yescharacteristic
197C23×C4D4×C12711yescharacteristic
198C2×M16—22no—
199C22×C8—41no—
200C22⋊Q8—41no—
201C22⋊Q8—41no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—41no—
208C2×C4⋊C4—41no—
209C2×C4⋊C4C2×C4×C12711yescharacteristic
210C2×C4⋊C4C2×C4×C12711yescharacteristic
211C2×C4⋊C4D4×C12711yescharacteristic
212C2×C4⋊C4D4×C12711yescharacteristic
213C2×C4⋊C4C23×C12711yescharacteristic
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C42—21no—
217C22⋊C8—22no—
218C22⋊C8—41no—
219C22⋊C8—41no—
220C22⋊C8—41no—
221#95—21no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95C2×C4×C12711yescharacteristic
226#95C2×C4×C12711yescharacteristic
227C24C22⋊C4×C12711yescharacteristic
228C2×Q8—41no—
229C2×Q8—81no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—41no—
242C22×C4—81no—
243C22×C4—81no—
244C22×C4C22⋊C4×C12711yescharacteristic
245C22×C4C22⋊C4×C12711yescharacteristic
246C22×C4C22⋊C4×C12711yescharacteristic
247C22×C4C22×C4×C12711yescharacteristic
248C22×C4C2×D4×C12711yescharacteristic
249C22×C4C2×D4×C12711yescharacteristic
250M16—42no—
251M16—42no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—82no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—42no—
261C4⋊C4—42no—
262C4⋊C4—42no—
263C4⋊C4—81no—
264C4⋊C4—81no—
265C22⋊C4—24no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C42—81no—
269C23—22no—
270C23—21no—
271C23—21no—
272C23—41no—
273C23#99×C12711yescharacteristic
274C23#99×C12711yescharacteristic
275C23C2×C22⋊C4×C12711yescharacteristic
276Q8—82no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—42no—
293C2×C4—41no—
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—81no—
306C2×C4—81no—
307C2×C4—81no—
308C2×C4#135×C12712yes—
309C8—82no—
310C8—82no—
311C22—21no—
312C22—21no—
313C22—21no—
314C22—21no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—42no—
319C22—42no—
320C22#356×C12712yes—
321C22C2×#99×C12711yescharacteristic
322C22#416×C12711yescharacteristic
323C22#421×C12711yescharacteristic
324C4—22no—
325C4—42no—
326C4—42no—
327C4—41no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—81no—
333C4—81no—
334C2—21no—
335C2—21no—
336C2—22no—
337C2—41no—
338C2C127×#151611yescharacteristic
339C2C127×#212111yescharacteristic
340C2C2×#356×C12711yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC24×C127C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C24×C127 ◁ C22×C4⋊C4×C127 ◁ G

Complements

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

NH ≅ G/Ntype
4. C127×#1354C2semidirect
5. C127×#1346C2semidirect
163. #11854C127direct (N × H)
174. #1354C2×C127semidirect
175. #1346C2×C127semidirect
176. C127#11854direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#25832
C127×#18212
C2×#324×C1272
C127×#13542
C127×#13462
#11854127