Finite Group Databasebeta

← C127×#11699 #44575372

Subgroups — C127×#11699 #44575372

Order 32512.

552 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 126 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×#2619C211yesmaximal, characteristic
2C127×#1742C211yesmaximal, characteristic, complemented
3C127×#1458C211yesmaximal, characteristic, complemented
4C127×#1345C214yesmaximal, complemented
5C22×M16×C127—21no—
6C2×#127×C127C411yescharacteristic
7C2×#121×C127—21no—
8C2×#117×C127C2211yescharacteristic
9#431×C127—21no—
10#394×C127—21no—
11#394×C127C2212yes—
12#392×C127—21no—
13#392×C127C412yes—
14#390×C127—21no—
15#382×C127C411yescharacteristic
16#343×C127—21no—
17#343×C127C2212yes—
18#324×C127C2212yes—
19#323×C127—21no—
20C22×D4×C127—22no—
21C22×D4×C127—21no—
22C22×D4×C127—21no—
23C22×D4×C127C2×C412yes—
24C23×C4×C127D411yescharacteristic
25C2×M16×C127—24no—
26C2×M16×C127—22no—
27C2×M16×C127—41no—
28C2×M16×C127—42no—
29C22×C8×C127—41no—
30#127×C127—41no—
31#127×C127—41no—
32#121×C127—42no—
33#121×C127—42no—
34#117×C127—41no—
35#117×C127—41no—
36C2×C4⋊C4×C127—21no—
37C2×C4⋊C4×C127D411yescharacteristic
38C2×C4⋊C4×C127C2311yescharacteristic
39C2×C22⋊C4×C127—22no—
40C2×C22⋊C4×C127—22no—
41C2×C22⋊C4×C127—22no—
42C2×C22⋊C4×C127C2×C411yescharacteristic
43C2×C22⋊C4×C127D411yescharacteristic
44C2×C42×C127C2×C411yescharacteristic
45C2×C42×C127D411yescharacteristic
46C4⋊C8×C127—41no—
47C22⋊C8×C127—22no—
48C4×C8×C127—41no—
49#95×C127—21no—
50#95×C127C2×C412yes—
51C24×C127—22no—
52C24×C127C22⋊C411yescharacteristic
53C2×D4×C127—42no—
54C2×D4×C127—42no—
55C2×D4×C127—44no—
56C2×D4×C127—41no—
57C2×D4×C127—41no—
58C2×D4×C127—42no—
59C2×D4×C127—42no—
60C2×D4×C127—82no—
61C2×D4×C127—82no—
62C2×D4×C127—82no—
63C2×D4×C127—82no—
64C22×C4×C127—21no—
65C22×C4×C127—21no—
66C22×C4×C127—22no—
67C22×C4×C127—22no—
68C22×C4×C127C22⋊C411yescharacteristic
69C22×C4×C127C22⋊C411yescharacteristic
70C22×C4×C127C22⋊C411yescharacteristic
71C22×C4×C127D812yes—
72C22×C4×C127SD1612yes—
73C22×C4×C127C22×C411yescharacteristic
74C22×C4×C127C2×D411yescharacteristic
75C22×C4×C127C2×D411yescharacteristic
76M16×C127—24no—
77M16×C127—44no—
78M16×C127—42no—
79C2×C8×C127—42no—
80C2×C8×C127—44no—
81C2×C8×C127—42no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—42no—
85C22⋊C4×C127—41no—
86C22⋊C4×C127—41no—
87C22⋊C4×C127—42no—
88C22⋊C4×C127—42no—
89C22⋊C4×C127—82no—
90C22⋊C4×C127—82no—
91C42×C127—21no—
92C42×C127—21no—
93C42×C127—21no—
94C42×C127—21no—
95C23×C127—21no—
96C23×C127—21no—
97C23×C127—41no—
98C23×C127—41no—
99C23×C127—42no—
100C23×C127—42no—
101C23×C127—42no—
102C23×C127—42no—
103C23×C127—42no—
104C23×C127—42no—
105C23×C127—42no—
106C23×C127#10212yes—
107C23×C127C2×C22⋊C411yescharacteristic
108D4×C127—84no—
109D4×C127—84no—
110D4×C127—88no—
111D4×C127—82no—
112D4×C127—82no—
113C2×C4×C127—21no—
114C2×C4×C127—21no—
115C2×C4×C127—22no—
116C2×C4×C127—22no—
117C2×C4×C127—22no—
118C2×C4×C127—22no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
125C2×C4×C127—41no—
126C2×C4×C127—41no—
127C2×C4×C127—42no—
128C2×C4×C127—42no—
129C2×C4×C127—42no—
130C2×C4×C127#9911yescharacteristic
131C2×C4×C127#9911yescharacteristic
132C2×C4×C127#10212yes—
133C2×C4×C127#10412yes—
134C2×C4×C127C2×D811yescharacteristic
135C2×C4×C127C2×SD1611yescharacteristic
136C8×C127—44no—
137C8×C127—82no—
138C22×C127—21no—
139C22×C127—21no—
140C22×C127—22no—
141C22×C127—42no—
142C22×C127—41no—
143C22×C127—41no—
144C22×C127—81no—
145C22×C127—82no—
146C22×C127—82no—
147C22×C127—82no—
148C22×C127—82no—
149C22×C127—82no—
150C22×C127—82no—
151C22×C127—82no—
152C22×C127C2×#9911yescharacteristic
153C22×C127C2×#10211yescharacteristic
154C22×C127C2×#10411yescharacteristic
155C4×C127—21no—
156C4×C127—21no—
157C4×C127—41no—
158C4×C127—41no—
159C4×C127—41no—
160C4×C127—41no—
161C4×C127—82no—
162C4×C127#32712yes—
163C4×C127#32712yes—
164#11699C12711yesmaximal, characteristic, direct product factor, Sylow
165C2×C127—21no—
166C2×C127—21no—
167C2×C127—42no—
168C2×C127—162no—
169C2×C127C2×#32711yescharacteristic
170C2×C127#212211yescharacteristic
171C2×C127#213411yescharacteristic
172#2619C2×C12711yescharacteristic
173#1742C2×C12711yescharacteristic, complemented
174#1458C2×C12711yescharacteristic, complemented
175#1345C2×C12714yescomplemented
176C127#1169911yescharacteristic, direct product factor, Sylow
177C22×M16—21no—
178C2×#127C4×C12711yescharacteristic
179C2×#121—21no—
180C2×#117C22×C12711yescharacteristic
181#431—21no—
182#394—21no—
183#394C22×C12712yes—
184#392—21no—
185#392C4×C12712yes—
186#390—21no—
187#382C4×C12711yescharacteristic
188#343—21no—
189#343C22×C12712yes—
190#324C22×C12712yes—
191#323—21no—
192C22×D4—22no—
193C22×D4—21no—
194C22×D4—21no—
195C22×D4C2×C4×C12712yes—
196C23×C4D4×C12711yescharacteristic
197C2×M16—24no—
198C2×M16—22no—
199C2×M16—41no—
200C2×M16—42no—
201C22×C8—41no—
202#127—41no—
203#127—41no—
204#121—42no—
205#121—42no—
206#117—41no—
207#117—41no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4D4×C12711yescharacteristic
210C2×C4⋊C4C23×C12711yescharacteristic
211C2×C22⋊C4—22no—
212C2×C22⋊C4—22no—
213C2×C22⋊C4—22no—
214C2×C22⋊C4C2×C4×C12711yescharacteristic
215C2×C22⋊C4D4×C12711yescharacteristic
216C2×C42C2×C4×C12711yescharacteristic
217C2×C42D4×C12711yescharacteristic
218C4⋊C8—41no—
219C22⋊C8—22no—
220C4×C8—41no—
221#95—21no—
222#95C2×C4×C12712yes—
223C24—22no—
224C24C22⋊C4×C12711yescharacteristic
225C2×D4—42no—
226C2×D4—42no—
227C2×D4—44no—
228C2×D4—41no—
229C2×D4—41no—
230C2×D4—42no—
231C2×D4—42no—
232C2×D4—82no—
233C2×D4—82no—
234C2×D4—82no—
235C2×D4—82no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—22no—
239C22×C4—22no—
240C22×C4C22⋊C4×C12711yescharacteristic
241C22×C4C22⋊C4×C12711yescharacteristic
242C22×C4C22⋊C4×C12711yescharacteristic
243C22×C4D8×C12712yes—
244C22×C4SD16×C12712yes—
245C22×C4C22×C4×C12711yescharacteristic
246C22×C4C2×D4×C12711yescharacteristic
247C22×C4C2×D4×C12711yescharacteristic
248M16—24no—
249M16—44no—
250M16—42no—
251C2×C8—42no—
252C2×C8—44no—
253C2×C8—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—42no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—42no—
260C22⋊C4—42no—
261C22⋊C4—82no—
262C22⋊C4—82no—
263C42—21no—
264C42—21no—
265C42—21no—
266C42—21no—
267C23—21no—
268C23—21no—
269C23—41no—
270C23—41no—
271C23—42no—
272C23—42no—
273C23—42no—
274C23—42no—
275C23—42no—
276C23—42no—
277C23—42no—
278C23#102×C12712yes—
279C23C2×C22⋊C4×C12711yescharacteristic
280D4—84no—
281D4—84no—
282D4—88no—
283D4—82no—
284D4—82no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—22no—
290C2×C4—22no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—42no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4#99×C12711yescharacteristic
303C2×C4#99×C12711yescharacteristic
304C2×C4#102×C12712yes—
305C2×C4#104×C12712yes—
306C2×C4C2×D8×C12711yescharacteristic
307C2×C4C2×SD16×C12711yescharacteristic
308C8—44no—
309C8—82no—
310C22—21no—
311C22—21no—
312C22—22no—
313C22—42no—
314C22—41no—
315C22—41no—
316C22—81no—
317C22—82no—
318C22—82no—
319C22—82no—
320C22—82no—
321C22—82no—
322C22—82no—
323C22—82no—
324C22C2×#99×C12711yescharacteristic
325C22C2×#102×C12711yescharacteristic
326C22C2×#104×C12711yescharacteristic
327C4—21no—
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—82no—
334C4#327×C12712yes—
335C4#327×C12712yes—
336C2—21no—
337C2—21no—
338C2—42no—
339C2—162no—
340C2C2×#327×C12711yescharacteristic
341C2C127×#212211yescharacteristic
342C2C127×#213411yescharacteristic
subgroupG/H
center, socleC22×C127C2×#99
commutatorC22×C4C22×C4×C127
Frattini, cosocleC2×C4⋊C4C23×C127
prime radicalC127×#2619C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C127 ◁ C22×C4×C127 ◁ C2×#117×C127 ◁ G

Complements

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

NH ≅ G/Ntype
2. C127×#1742C2semidirect
3. C127×#1458C2semidirect
4. C127×#1345C2semidirect
164. #11699C127direct (N × H)
173. #1742C2×C127semidirect
174. #1458C2×C127semidirect
175. #1345C2×C127semidirect
176. C127#11699direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#26192
C127×#17422
C127×#14582
C127×#13452
#11699127