Finite Group Databasebeta

← C127×#7835 #44571508

Subgroups — C127×#7835 #44571508

Order 32512.

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

normal subgroups only

This group has 350 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×#2805C211yesmaximal, characteristic
2C127×#2100C211yesmaximal, characteristic
3C127×#2100C211yesmaximal, characteristic
4C127×#2095C211yesmaximal, characteristic
5C127×#1272C211yesmaximal, characteristic
6C127×#1271C211yesmaximal, characteristic
7C127×#1271C211yesmaximal, characteristic
8C2×#107×C127—21no—
9C2×#103×C127—21no—
10#400×C127—21no—
11#400×C127—21no—
12#395×C127—21no—
13#391×C127C2211yescharacteristic
14#389×C127—21no—
15#389×C127C2211yescharacteristic
16#389×C127C2211yescharacteristic
17#387×C127—21no—
18#387×C127—21no—
19#384×C127C2211yescharacteristic
20#340×C127—21no—
21#340×C127—21no—
22#340×C127—21no—
23#340×C127—21no—
24#336×C127C2211yescharacteristic
25#336×C127C2211yescharacteristic
26#336×C127C2211yescharacteristic
27C22×Q8×C127D411yescharacteristic
28C22×C8×C127—21no—
29C22×C8×C127—21no—
30C22×C8×C127—21no—
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—21no—
37C2×C4⋊C4×C127—21no—
38C2×C4⋊C4×C127D411yescharacteristic
39C2×C4⋊C4×C127D411yescharacteristic
40C2×C4⋊C4×C127D411yescharacteristic
41C2×C4⋊C4×C127D411yescharacteristic
42C2×C4⋊C4×C127D411yescharacteristic
43C2×C42×C127—21no—
44C2×C42×C127C2311yescharacteristic
45#107×C127—42no—
46#103×C127—42no—
47#95×C127—21no—
48#95×C127—21no—
49#95×C127—21no—
50#95×C127—21no—
51#95×C127—21no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127—21no—
56C2×Q8×C127—21no—
57C2×Q8×C127—21no—
58C2×Q8×C127—41no—
59C2×Q8×C127—41no—
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—41no—
67C22×C4×C127C2×D411yescharacteristic
68C22×C4×C127C2×D411yescharacteristic
69C22×C4×C127C2×D411yescharacteristic
70C2×C8×C127—22no—
71C2×C8×C127—41no—
72C2×C8×C127—41no—
73C2×C8×C127—41no—
74C2×C8×C127—41no—
75C2×C8×C127—41no—
76C2×C8×C127—41no—
77C2×C8×C127—41no—
78C2×C8×C127—41no—
79C4⋊C4×C127—21no—
80C4⋊C4×C127—21no—
81C4⋊C4×C127—21no—
82C4⋊C4×C127—41no—
83C4⋊C4×C127—41no—
84C4⋊C4×C127—41no—
85C4⋊C4×C127—41no—
86C4⋊C4×C127—41no—
87C4⋊C4×C127—42no—
88C4⋊C4×C127—42no—
89C4⋊C4×C127—41no—
90C4⋊C4×C127—41no—
91C4⋊C4×C127—41no—
92C4⋊C4×C127—41no—
93C4⋊C4×C127—81no—
94C4⋊C4×C127—81no—
95C4⋊C4×C127Q1612yes—
96C42×C127—41no—
97C42×C127—81no—
98C23×C127#12011yescharacteristic
99Q8×C127—42no—
100Q8×C127—81no—
101C2×C4×C127—21no—
102C2×C4×C127—21no—
103C2×C4×C127—21no—
104C2×C4×C127—21no—
105C2×C4×C127—21no—
106C2×C4×C127—21no—
107C2×C4×C127—22no—
108C2×C4×C127—41no—
109C2×C4×C127—41no—
110C2×C4×C127—41no—
111C2×C4×C127—41no—
112C2×C4×C127—41no—
113C2×C4×C127—41no—
114C2×C4×C127—41no—
115C2×C4×C127—41no—
116C2×C4×C127—41no—
117C2×C4×C127—41no—
118C2×C4×C127—41no—
119C2×C4×C127—41no—
120C2×C4×C127—41no—
121C2×C4×C127—41no—
122C2×C4×C127—41no—
123C2×C4×C127—41no—
124C2×C4×C127—41no—
125C2×C4×C127—81no—
126C2×C4×C127—81no—
127C2×C4×C127—81no—
128C2×C4×C127C2×Q1611yescharacteristic
129C2×C4×C127#13511yescharacteristic
130C2×C4×C127#13511yescharacteristic
131C2×C4×C127#13711yescharacteristic
132C2×C4×C127#13711yescharacteristic
133C2×C4×C127#13711yescharacteristic
134C8×C127—42no—
135C8×C127—81no—
136C8×C127—81no—
137C22×C127#45111yescharacteristic
138C22×C127#45211yescharacteristic
139C22×C127#45211yescharacteristic
140C22×C127#45311yescharacteristic
141C22×C127#45411yescharacteristic
142C22×C127#45411yescharacteristic
143C22×C127#45811yescharacteristic
144C4×C127—21no—
145C4×C127—21no—
146C4×C127—21no—
147C4×C127—21no—
148C4×C127—21no—
149C4×C127—21no—
150C4×C127—42no—
151C4×C127—81no—
152C4×C127—81no—
153C4×C127—81no—
154C4×C127—81no—
155C4×C127—81no—
156C4×C127—161no—
157#7835C12711yesmaximal, characteristic, direct product factor, Sylow
158C2×C127#161511yescharacteristic
159C2×C127#161711yescharacteristic
160C2×C127#161811yescharacteristic
161C2×C127#163211yescharacteristic
162C2×C127#163611yescharacteristic
163C2×C127#163811yescharacteristic
164C2×C127#165711yescharacteristic
165#2805C2×C12711yescharacteristic
166#2100C2×C12711yescharacteristic
167#2100C2×C12711yescharacteristic
168#2095C2×C12711yescharacteristic
169#1272C2×C12711yescharacteristic
170#1271C2×C12711yescharacteristic
171#1271C2×C12711yescharacteristic
172C127#783511yescharacteristic, direct product factor, Sylow
173C2×#107—21no—
174C2×#103—21no—
175#400—21no—
176#400—21no—
177#395—21no—
178#391C22×C12711yescharacteristic
179#389—21no—
180#389C22×C12711yescharacteristic
181#389C22×C12711yescharacteristic
182#387—21no—
183#387—21no—
184#384C22×C12711yescharacteristic
185#340—21no—
186#340—21no—
187#340—21no—
188#340—21no—
189#336C22×C12711yescharacteristic
190#336C22×C12711yescharacteristic
191#336C22×C12711yescharacteristic
192C22×Q8D4×C12711yescharacteristic
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—21no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—21no—
203C2×C4⋊C4D4×C12711yescharacteristic
204C2×C4⋊C4D4×C12711yescharacteristic
205C2×C4⋊C4D4×C12711yescharacteristic
206C2×C4⋊C4D4×C12711yescharacteristic
207C2×C4⋊C4D4×C12711yescharacteristic
208C2×C42—21no—
209C2×C42C23×C12711yescharacteristic
210#107—42no—
211#103—42no—
212#95—21no—
213#95—21no—
214#95—21no—
215#95—21no—
216#95—21no—
217#95—21no—
218#95—21no—
219#95—21no—
220#95—21no—
221C2×Q8—21no—
222C2×Q8—21no—
223C2×Q8—41no—
224C2×Q8—41no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—41no—
232C22×C4C2×D4×C12711yescharacteristic
233C22×C4C2×D4×C12711yescharacteristic
234C22×C4C2×D4×C12711yescharacteristic
235C2×C8—22no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—41no—
248C4⋊C4—41no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—81no—
259C4⋊C4—81no—
260C4⋊C4Q16×C12712yes—
261C42—41no—
262C42—81no—
263C23#120×C12711yescharacteristic
264Q8—42no—
265Q8—81no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—81no—
293C2×C4C2×Q16×C12711yescharacteristic
294C2×C4#135×C12711yescharacteristic
295C2×C4#135×C12711yescharacteristic
296C2×C4#137×C12711yescharacteristic
297C2×C4#137×C12711yescharacteristic
298C2×C4#137×C12711yescharacteristic
299C8—42no—
300C8—81no—
301C8—81no—
302C22#451×C12711yescharacteristic
303C22#452×C12711yescharacteristic
304C22#452×C12711yescharacteristic
305C22#453×C12711yescharacteristic
306C22#454×C12711yescharacteristic
307C22#454×C12711yescharacteristic
308C22#458×C12711yescharacteristic
309C4—21no—
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—42no—
316C4—81no—
317C4—81no—
318C4—81no—
319C4—81no—
320C4—81no—
321C4—161no—
322C2C127×#161511yescharacteristic
323C2C127×#161711yescharacteristic
324C2C127×#161811yescharacteristic
325C2C127×#163211yescharacteristic
326C2C127×#163611yescharacteristic
327C2C127×#163811yescharacteristic
328C2C127×#165711yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C127#120
commutator, Frattini, cosocleC2×C42C23×C127
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ G

Complements

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

NH ≅ G/Ntype
157. #7835C127direct (N × H)
172. C127#7835direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#28052
C127×#21002
C127×#20952
C127×#12722
C127×#12712
#7835127