Finite Group Databasebeta

← C127×#7836 #44571509

Subgroups — C127×#7836 #44571509

Order 32512.

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

normal subgroups only

This group has 378 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×#2806C211yesmaximal, characteristic
2C127×#2100C211yesmaximal, characteristic
3C127×#2095C211yesmaximal, characteristic
4C127×#2095C211yesmaximal, characteristic
5C127×#1272C211yesmaximal, characteristic
6C127×#1272C211yesmaximal, characteristic
7C127×#1271C211yesmaximal, characteristic
8C2×#107×C127—21no—
9C2×#107×C127—21no—
10C2×#103×C127—21no—
11C2×#103×C127—21no—
12#398×C127—21no—
13#398×C127—21no—
14#395×C127—21no—
15#391×C127—21no—
16#391×C127C2211yescharacteristic
17#391×C127C2211yescharacteristic
18#389×C127—21no—
19#389×C127C2211yescharacteristic
20#387×C127—21no—
21#384×C127C2211yescharacteristic
22#340×C127—21no—
23#340×C127—21no—
24#336×C127C2211yescharacteristic
25#336×C127C2211yescharacteristic
26#336×C127C2211yescharacteristic
27C22×Q8×C127D411yescharacteristic
28C22×Q8×C127D411yescharacteristic
29C22×C8×C127—21no—
30C22×C8×C127—21no—
31C22×C8×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×C127—21no—
39C2×C4⋊C4×C127—21no—
40C2×C4⋊C4×C127D411yescharacteristic
41C2×C4⋊C4×C127D411yescharacteristic
42C2×C4⋊C4×C127D411yescharacteristic
43C2×C4⋊C4×C127D411yescharacteristic
44C2×C42×C127—21no—
45C2×C42×C127C2311yescharacteristic
46#107×C127—42no—
47#107×C127—42no—
48#103×C127—42no—
49#103×C127—42no—
50#95×C127—21no—
51#95×C127—21no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127—21no—
56#95×C127—21no—
57#95×C127—21no—
58C2×Q8×C127—21no—
59C2×Q8×C127—21no—
60C2×Q8×C127—21no—
61C2×Q8×C127—41no—
62C2×Q8×C127—41no—
63C2×Q8×C127—41no—
64C2×Q8×C127—41no—
65C2×Q8×C127Q1612yes—
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—41no—
73C22×C4×C127C2×D411yescharacteristic
74C22×C4×C127C2×D411yescharacteristic
75C22×C4×C127C2×D411yescharacteristic
76C2×C8×C127—22no—
77C2×C8×C127—22no—
78C2×C8×C127—41no—
79C2×C8×C127—41no—
80C2×C8×C127—41no—
81C2×C8×C127—41no—
82C2×C8×C127—41no—
83C2×C8×C127—41no—
84C2×C8×C127—41no—
85C4⋊C4×C127—21no—
86C4⋊C4×C127—41no—
87C4⋊C4×C127—41no—
88C4⋊C4×C127—41no—
89C4⋊C4×C127—41no—
90C4⋊C4×C127—41no—
91C4⋊C4×C127—41no—
92C4⋊C4×C127—41no—
93C4⋊C4×C127—42no—
94C4⋊C4×C127—41no—
95C4⋊C4×C127—41no—
96C4⋊C4×C127—81no—
97C4⋊C4×C127—81no—
98C4⋊C4×C127—81no—
99C4⋊C4×C127—81no—
100C4⋊C4×C127Q1612yes—
101C42×C127—41no—
102C42×C127—81no—
103C23×C127#12011yescharacteristic
104Q8×C127—42no—
105Q8×C127—42no—
106Q8×C127—81no—
107Q8×C127—81no—
108C2×C4×C127—21no—
109C2×C4×C127—21no—
110C2×C4×C127—21no—
111C2×C4×C127—21no—
112C2×C4×C127—21no—
113C2×C4×C127—21no—
114C2×C4×C127—22no—
115C2×C4×C127—22no—
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—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—81no—
133C2×C4×C127—81no—
134C2×C4×C127—81no—
135C2×C4×C127C2×Q1611yescharacteristic
136C2×C4×C127C2×Q1611yescharacteristic
137C2×C4×C127#13511yescharacteristic
138C2×C4×C127#13711yescharacteristic
139C2×C4×C127#13711yescharacteristic
140C2×C4×C127#13711yescharacteristic
141C8×C127—42no—
142C8×C127—42no—
143C8×C127—81no—
144C22×C127#45111yescharacteristic
145C22×C127#45111yescharacteristic
146C22×C127#45211yescharacteristic
147C22×C127#45311yescharacteristic
148C22×C127#45311yescharacteristic
149C22×C127#45411yescharacteristic
150C22×C127#45811yescharacteristic
151C4×C127—21no—
152C4×C127—21no—
153C4×C127—21no—
154C4×C127—21no—
155C4×C127—21no—
156C4×C127—21no—
157C4×C127—42no—
158C4×C127—42no—
159C4×C127—81no—
160C4×C127—81no—
161C4×C127—81no—
162C4×C127—81no—
163C4×C127—161no—
164#7836C12711yesmaximal, characteristic, direct product factor, Sylow
165C2×C127#161411yescharacteristic
166C2×C127#161711yescharacteristic
167C2×C127#161811yescharacteristic
168C2×C127#163211yescharacteristic
169C2×C127#163311yescharacteristic
170C2×C127#163611yescharacteristic
171C2×C127#165611yescharacteristic
172#2806C2×C12711yescharacteristic
173#2100C2×C12711yescharacteristic
174#2095C2×C12711yescharacteristic
175#2095C2×C12711yescharacteristic
176#1272C2×C12711yescharacteristic
177#1272C2×C12711yescharacteristic
178#1271C2×C12711yescharacteristic
179C127#783611yescharacteristic, direct product factor, Sylow
180C2×#107—21no—
181C2×#107—21no—
182C2×#103—21no—
183C2×#103—21no—
184#398—21no—
185#398—21no—
186#395—21no—
187#391—21no—
188#391C22×C12711yescharacteristic
189#391C22×C12711yescharacteristic
190#389—21no—
191#389C22×C12711yescharacteristic
192#387—21no—
193#384C22×C12711yescharacteristic
194#340—21no—
195#340—21no—
196#336C22×C12711yescharacteristic
197#336C22×C12711yescharacteristic
198#336C22×C12711yescharacteristic
199C22×Q8D4×C12711yescharacteristic
200C22×Q8D4×C12711yescharacteristic
201C22×C8—21no—
202C22×C8—21no—
203C22×C8—21no—
204C2×C4⋊C4—21no—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—21no—
207C2×C4⋊C4—21no—
208C2×C4⋊C4—21no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4D4×C12711yescharacteristic
213C2×C4⋊C4D4×C12711yescharacteristic
214C2×C4⋊C4D4×C12711yescharacteristic
215C2×C4⋊C4D4×C12711yescharacteristic
216C2×C42—21no—
217C2×C42C23×C12711yescharacteristic
218#107—42no—
219#107—42no—
220#103—42no—
221#103—42no—
222#95—21no—
223#95—21no—
224#95—21no—
225#95—21no—
226#95—21no—
227#95—21no—
228#95—21no—
229#95—21no—
230C2×Q8—21no—
231C2×Q8—21no—
232C2×Q8—21no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8Q16×C12712yes—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—41no—
245C22×C4C2×D4×C12711yescharacteristic
246C22×C4C2×D4×C12711yescharacteristic
247C22×C4C2×D4×C12711yescharacteristic
248C2×C8—22no—
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—41no—
256C2×C8—41no—
257C4⋊C4—21no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—41no—
262C4⋊C4—41no—
263C4⋊C4—41no—
264C4⋊C4—41no—
265C4⋊C4—42no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—81no—
269C4⋊C4—81no—
270C4⋊C4—81no—
271C4⋊C4—81no—
272C4⋊C4Q16×C12712yes—
273C42—41no—
274C42—81no—
275C23#120×C12711yescharacteristic
276Q8—42no—
277Q8—42no—
278Q8—81no—
279Q8—81no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
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—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4C2×Q16×C12711yescharacteristic
308C2×C4C2×Q16×C12711yescharacteristic
309C2×C4#135×C12711yescharacteristic
310C2×C4#137×C12711yescharacteristic
311C2×C4#137×C12711yescharacteristic
312C2×C4#137×C12711yescharacteristic
313C8—42no—
314C8—42no—
315C8—81no—
316C22#451×C12711yescharacteristic
317C22#451×C12711yescharacteristic
318C22#452×C12711yescharacteristic
319C22#453×C12711yescharacteristic
320C22#453×C12711yescharacteristic
321C22#454×C12711yescharacteristic
322C22#458×C12711yescharacteristic
323C4—21no—
324C4—21no—
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—42no—
330C4—42no—
331C4—81no—
332C4—81no—
333C4—81no—
334C4—81no—
335C4—161no—
336C2C127×#161411yescharacteristic
337C2C127×#161711yescharacteristic
338C2C127×#161811yescharacteristic
339C2C127×#163211yescharacteristic
340C2C127×#163311yescharacteristic
341C2C127×#163611yescharacteristic
342C2C127×#165611yescharacteristic
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
164. #7836C127direct (N × H)
179. C127#7836direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#28062
C127×#21002
C127×#20952
C127×#12722
C127×#12712
#7836127