Finite Group Databasebeta

← C127×#7834 #44571507

Subgroups — C127×#7834 #44571507

Order 32512.

396 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 94 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×#2808C211yesmaximal, characteristic
2C127×#2100C211yesmaximal, characteristic, complemented
3C127×#2095C211yesmaximal, characteristic, complemented
4C127×#2094C211yesmaximal, characteristic
5C127×#1272C211yesmaximal, characteristic, complemented
6C127×#1271C211yesmaximal, characteristic, complemented
7C127×#1270C211yesmaximal, characteristic
8C2×#107×C127—21no—
9C2×#106×C127—21no—
10C2×#103×C127—21no—
11C2×#102×C127—21no—
12#397×C127—21no—
13#394×C127—21no—
14#393×C127—21no—
15#391×C127C2211yescharacteristic
16#390×C127C2211yescharacteristic
17#389×C127C2211yescharacteristic
18#388×C127—21no—
19#388×C127—21no—
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×D4×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×C127D411yescharacteristic
37C2×C4⋊C4×C127D411yescharacteristic
38C2×C4⋊C4×C127D411yescharacteristic
39C2×C4⋊C4×C127D411yescharacteristic
40C2×C22⋊C4×C127—21no—
41C2×C22⋊C4×C127—21no—
42C2×C22⋊C4×C127—21no—
43C2×C22⋊C4×C127—21no—
44C2×C22⋊C4×C127—21no—
45C2×C22⋊C4×C127—21no—
46C2×C42×C127—21no—
47C2×C42×C127C2311yescharacteristic
48#107×C127—42no—
49#106×C127—42no—
50#103×C127—42no—
51#102×C127—42no—
52#95×C127—21no—
53#95×C127—21no—
54#95×C127—21no—
55#95×C127—21no—
56#95×C127—21no—
57#95×C127—21no—
58C24×C127—21no—
59C2×Q8×C127—21no—
60C2×Q8×C127—21no—
61C2×Q8×C127—41no—
62C2×Q8×C127—41no—
63C2×D4×C127—21no—
64C2×D4×C127—21no—
65C2×D4×C127—41no—
66C2×D4×C127—41no—
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—21no—
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—41no—
94C4⋊C4×C127—42no—
95C4⋊C4×C127—41no—
96C4⋊C4×C127—41no—
97C22⋊C4×C127—41no—
98C22⋊C4×C127—41no—
99C22⋊C4×C127—41no—
100C22⋊C4×C127—41no—
101C22⋊C4×C127—81no—
102C22⋊C4×C127—81no—
103C22⋊C4×C127—81no—
104C22⋊C4×C127—81no—
105C42×C127—41no—
106C42×C127—81no—
107C23×C127—41no—
108C23×C127—41no—
109C23×C127—41no—
110C23×C127—41no—
111C23×C127—41no—
112C23×C127—41no—
113C23×C127—41no—
114C23×C127#12011yescharacteristic
115Q8×C127—42no—
116Q8×C127—81no—
117D4×C127—42no—
118D4×C127—81no—
119C2×C4×C127—21no—
120C2×C4×C127—21no—
121C2×C4×C127—21no—
122C2×C4×C127—21no—
123C2×C4×C127—21no—
124C2×C4×C127—21no—
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—41no—
136C2×C4×C127—41no—
137C2×C4×C127—41no—
138C2×C4×C127—41no—
139C2×C4×C127—41no—
140C2×C4×C127—81no—
141C2×C4×C127—81no—
142C2×C4×C127—81no—
143C2×C4×C127#13511yescharacteristic
144C2×C4×C127#13511yescharacteristic
145C2×C4×C127#13511yescharacteristic
146C2×C4×C127#13711yescharacteristic
147C2×C4×C127#13711yescharacteristic
148C2×C4×C127#13711yescharacteristic
149C8×C127—42no—
150C8×C127—42no—
151C8×C127—81no—
152C22×C127—81no—
153C22×C127—81no—
154C22×C127—81no—
155C22×C127—81no—
156C22×C127—81no—
157C22×C127—81no—
158C22×C127—81no—
159C22×C127#45211yescharacteristic
160C22×C127#45211yescharacteristic
161C22×C127#45211yescharacteristic
162C22×C127#45311yescharacteristic
163C22×C127#45311yescharacteristic
164C22×C127#45411yescharacteristic
165C22×C127#45811yescharacteristic
166C4×C127—21no—
167C4×C127—21no—
168C4×C127—21no—
169C4×C127—21no—
170C4×C127—21no—
171C4×C127—21no—
172C4×C127—81no—
173C4×C127—81no—
174C4×C127—81no—
175C4×C127—81no—
176C4×C127—81no—
177C4×C127—161no—
178#7834C12711yesmaximal, characteristic, direct product factor, Sylow
179C2×C127—161no—
180C2×C127#161511yescharacteristic
181C2×C127#161811yescharacteristic
182C2×C127#161811yescharacteristic
183C2×C127#163011yescharacteristic
184C2×C127#163411yescharacteristic
185C2×C127#163811yescharacteristic
186C2×C127#165611yescharacteristic
187#2808C2×C12711yescharacteristic
188#2100C2×C12711yescharacteristic, complemented
189#2095C2×C12711yescharacteristic, complemented
190#2094C2×C12711yescharacteristic
191#1272C2×C12711yescharacteristic, complemented
192#1271C2×C12711yescharacteristic, complemented
193#1270C2×C12711yescharacteristic
194C127#783411yescharacteristic, direct product factor, Sylow
195C2×#107—21no—
196C2×#106—21no—
197C2×#103—21no—
198C2×#102—21no—
199#397—21no—
200#394—21no—
201#393—21no—
202#391C22×C12711yescharacteristic
203#390C22×C12711yescharacteristic
204#389C22×C12711yescharacteristic
205#388—21no—
206#388—21no—
207#387—21no—
208#384C22×C12711yescharacteristic
209#340—21no—
210#340—21no—
211#336C22×C12711yescharacteristic
212#336C22×C12711yescharacteristic
213#336C22×C12711yescharacteristic
214C22×Q8D4×C12711yescharacteristic
215C22×D4D4×C12711yescharacteristic
216C22×C8—21no—
217C22×C8—21no—
218C22×C8—21no—
219C2×C4⋊C4—21no—
220C2×C4⋊C4—21no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4D4×C12711yescharacteristic
224C2×C4⋊C4D4×C12711yescharacteristic
225C2×C4⋊C4D4×C12711yescharacteristic
226C2×C4⋊C4D4×C12711yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C22⋊C4—21no—
230C2×C22⋊C4—21no—
231C2×C22⋊C4—21no—
232C2×C22⋊C4—21no—
233C2×C42—21no—
234C2×C42C23×C12711yescharacteristic
235#107—42no—
236#106—42no—
237#103—42no—
238#102—42no—
239#95—21no—
240#95—21no—
241#95—21no—
242#95—21no—
243#95—21no—
244#95—21no—
245C24—21no—
246C2×Q8—21no—
247C2×Q8—21no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—41no—
253C2×D4—41no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4C2×D4×C12711yescharacteristic
261C22×C4C2×D4×C12711yescharacteristic
262C22×C4C2×D4×C12711yescharacteristic
263C2×C8—22no—
264C2×C8—22no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—41no—
272C4⋊C4—21no—
273C4⋊C4—21no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—42no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C22⋊C4—41no—
288C22⋊C4—81no—
289C22⋊C4—81no—
290C22⋊C4—81no—
291C22⋊C4—81no—
292C42—41no—
293C42—81no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23#120×C12711yescharacteristic
302Q8—42no—
303Q8—81no—
304D4—42no—
305D4—81no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—81no—
330C2×C4#135×C12711yescharacteristic
331C2×C4#135×C12711yescharacteristic
332C2×C4#135×C12711yescharacteristic
333C2×C4#137×C12711yescharacteristic
334C2×C4#137×C12711yescharacteristic
335C2×C4#137×C12711yescharacteristic
336C8—42no—
337C8—42no—
338C8—81no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22—81no—
344C22—81no—
345C22—81no—
346C22#452×C12711yescharacteristic
347C22#452×C12711yescharacteristic
348C22#452×C12711yescharacteristic
349C22#453×C12711yescharacteristic
350C22#453×C12711yescharacteristic
351C22#454×C12711yescharacteristic
352C22#458×C12711yescharacteristic
353C4—21no—
354C4—21no—
355C4—21no—
356C4—21no—
357C4—21no—
358C4—21no—
359C4—81no—
360C4—81no—
361C4—81no—
362C4—81no—
363C4—81no—
364C4—161no—
365C2—161no—
366C2C127×#161511yescharacteristic
367C2C127×#161811yescharacteristic
368C2C127×#161811yescharacteristic
369C2C127×#163011yescharacteristic
370C2C127×#163411yescharacteristic
371C2C127×#163811yescharacteristic
372C2C127×#165611yescharacteristic
subgroupG/H
center, socleC23×C127#120
commutator, Frattini, cosocleC2×C42C23×C127
prime radicalC22×D4×C127D4
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
2. C127×#2100C2semidirect
3. C127×#2095C2semidirect
5. C127×#1272C2semidirect
6. C127×#1271C2semidirect
178. #7834C127direct (N × H)
188. #2100C2×C127semidirect
189. #2095C2×C127semidirect
191. #1272C2×C127semidirect
192. #1271C2×C127semidirect
194. C127#7834direct (N × H)

Maximal subgroups

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

subgroupindex
C127×#28082
C127×#21002
C127×#20952
C127×#20942
C127×#12722
C127×#12712
C127×#12702
#7834127